Microcapsule mechanics: From stability to function Martin P. Neubauer, Melanie Poehlmann, Andreas Fery PII: DOI: Reference:
S0001-8686(13)00169-3 doi: 10.1016/j.cis.2013.11.016 CIS 1361
To appear in:
Advances in Colloid and Interface Science
Please cite this article as: Neubauer Martin P., Poehlmann Melanie, Fery Andreas, Microcapsule mechanics: From stability to function, Advances in Colloid and Interface Science (2013), doi: 10.1016/j.cis.2013.11.016
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ACCEPTED MANUSCRIPT Microcapsule mechanics: From stability to function Martin P. Neubauera, Melanie Poehlmanna, Andreas Ferya,* University of Bayreuth, Department of Physical Chemistry II, Universitätsstraße 30, 95440 Bayreuth, Germany
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*Corresponding author. E-Mail address: [email protected] Tel.: +49 921 55 2753; Fax: +49 921 55 2059
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Keywords: Microcapsules; Mechanical Characterization; Shell Theory; Layer-by-Layer; Drug Delivery
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Abstract
Microcapsules are reviewed with special emphasis on the relevance of controlled mechanical properties
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for functional aspects. At first, assembly strategies are presented that allow control over the decisive
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geometrical parameters, diameter and wall thickness, which both influence the capsule’s mechanical performance. As one of the most powerful approaches the layer-by-layer technique is identified.
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Subsequently, ensemble and, in particular, single-capsule deformation techniques are discussed. The latter generally provide more in-depth information and cover the complete range of applicable forces from smaller than pN to N. In a theory chapter, we illustrate the physics of capsule deformation. The main focus is on thin shell theory, which provides a useful approximation for many deformation scenarios. Finally, we give an overview of applications and future perspectives where the specific design of mechanical properties turns microcapsules into (multi-)functional devices, enriching especially life sciences and material sciences.
I) Introduction Microcapsule-research is a classical example of a field, which has been driven and fueled by many disciplines ranging from biophysics, via fundamental colloid- and interface research in physical chemistry and synthesis – both organic and inorganic – up to applied sciences and engineering. Microcapsules have been an object of research in these areas for many decades. First studies date back as early as to the 1930s, when Bungenberg de Jong and co-workers investigated coacervates which can be seen as the first artificial, man-made microcapsules.[1, 2] At the same time Cole performed the first compression
ACCEPTED MANUSCRIPT experiments on single microcapsules, i.e. on arbacia eggs with a diameter around 75 µm.[3] Especially the development of novel synthesis strategies, e.g., layer-by-layer assembly, and techniques to characterize capsules on a single-capsule level has stimulated scientific research in this area within the
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past twenty years. At the same time, microcapsules have been increasingly used in industry. The first large-scale production of microcapsules was established for carbonless copy paper already in the
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1950s.[4] Today, microcapsules are designed for and employed in many different fields of application,
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such as pharmacy [5-11], food industry [12-22], agriculture [23-26], cosmetics [27-29], textile industry [30-32], printing [33], biosensor engineering [34-36], active coatings [37, 38] and construction [39-41]. For instance, in food technology active ingredients are protected from decomposition through
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environmental impacts or flavors are prevented from premature volatilization.[21] Textiles have been modified with microcapsules for long-term fragrance release, to introduce fire retardants and even to
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combat counterfeiting.[30] The interest in and the demand for intelligent, custom-made capsule systems is continuously rising. And scientific research plays a key role as the understanding of the fundamental
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properties of microcapsules is breaking ground for innovation.
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II) Microcapsules: Definition and Assembly Strategies In view of the broad range of capsule systems and the different context in which they have been investigated, it is no surprise that there are various, sometimes at least partially diverging definitions of the term microcapsules and microencapsulation.[42-46] Therefore, let us first clarify the semantics for the purpose of this review: Generally, microencapsulation is understood as the process by which one material of microscopic dimensions is entirely coated by another. Hence, a core-shell-composite or microcapsule is created where the core can take all aggregate states but the shell is solid. This fundamental definition already points out the two main components of microcapsules, core/interior/inner phase and shell/wall/membrane/outer phase, which can be tuned with respect to materials, permeability, size, shape etc. Out of this large variety of possible microcapsules it is indispensable to introduce some further constraints. In the context of this review article we examine mechanical properties of microcapsules. These are particularly interesting when dominated by the shell. Therefore, we limit ourselves to microcapsules being composed of a fluid core wrapped by a solid shell. In contrast, capsules consisting of a solid core will be referred to as core/shell particles and will not be in the center of interest. In terms of the mechanical properties of the shell, we limit ourselves to non-fluid shells. The broad class of vesicles formed from lipids or in general low-molecular weight species will thus
ACCEPTED MANUSCRIPT not be covered. The microcapsules considered in this review will always be spherical, if not stated differently, and their size will range from several hundreds of nanometers to some tens (in few cases to some hundreds) of micrometers, with the restriction that the shell thickness is small as compared to the
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diameter.
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The focus will finally be on artificial microcapsules, which naturally lets us start from reviewing the various approaches for the formation of microcapsules meeting the aforesaid definitions. As stated
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above, microcapsules find already various usages in industry. The industrially relevant encapsulation techniques are typically based on physicochemical processes that allow for large scale production. These
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include spray drying [47], co-extrusion, spinning disk, multiple-nozzle spraying, fluidized-bed coating and vacuum encapsulation.[42, 46] Among the advantages of these methods are the easy handling,
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upscalability and low costs. On the other hand, the obtained microcapsules are often polydisperse in diameter and shell thickness. In other words, current approaches allow for comparatively little control over the particles morphology and the possibilities of capsule design are rather restricted.
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A far better control over capsule core and shell dimensions and a selective introduction of functionality is
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provided by template-assisted and/or self-assembly approaches. Both soft and hard template-assisted methods offer fine-tuning of the core size and can be combined with a self-assembly process which
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allows excellent control over shell thickness, down to molecular level. Soft template-assisted methods are mostly emulsion-based, such as microfluidic processes [48-54], polymerosomes [6, 55-60] (which are typically nm-sized), colloidosomes [61-63], interfacial polymerization [64-67], interfacial assembly [68], inkjet printing [69, 70] or phase separation processes [71, 72]. A special case is the soft colloid templated multilayer assembly which offers control over all geometric parameters.[73, 74] The underlying principle was first exploited using hard templates, namely the layer-by-layer deposition technique.[75-80] Combining templates and self-assembly permits precise adjustment of geometry, diameter [81], shell thickness and shell material [82]. Furthermore, such methods allow for introduction of multifunctionality.[83] That means, in addition to enclosing their content until desired delivery, microcapsules are designed which, for example in medical applications, can be tracked within the human body, directed to a specific site and, finally, specifically triggered to release their cargo. A schematic overview of microcapsule designs obtained from template-assisted and self-assembly methods is given in Fig. 2.1. It becomes clear that the synthesis process strongly determines the choice of core and shell material, and the design possibilities.
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III) Mechanical Characterization of Microcapsules
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Fig. 2.1: Template-assisted and self-assembly methods for a controlled capsule design. The scheme shows typical wall materials (particles, multilayers, homogeneous film) and the crucial geometric parameters, diameter D and wall thickness h.
Mechanical properties of microcapsules become accessible through a variety of experimental
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techniques. These can be divided into two general categories: ensemble methods and methods on a
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single-capsule level. Ensemble methods measure a batch of capsules simultaneously, yielding average values. These measurements can often be performed in an automated, high-throughput fashion and a
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large number of capsules are captured. In contrast, single capsule measurements provide generally more detailed information on deformation properties, but require a sequential measurement of capsules. One possibility of determining mechanical properties of microcapsule ensembles is to make use of shear forces. A slurry or suspension of capsules can be measured, for instance, in a turbine reactor.[84] Here, rather high forces are acting provoking breakage of capsules. Therefore, such a method is mainly relevant for studying large deformation behavior and release under high stresses. A more sensitive approach is given by rheological investigations. Drochon et al. measured the viscosity of a diluted suspension of red blood cells and calculated the shear elastic modulus of the cell membrane.[85, 86] The underlying model has been derived by the same authors and other groups.[87-90] Suspensions of microcapsules under shear have been further studied experimentally by Bredimas et al. [91] and theoretically by the groups of Misbah [92-96] and Kalluri [97, 98]. Another means to obtain information about mechanical parameters of a multitude of capsules is to perform osmotic pressure experiments. With the upcoming of polyelectrolyte multilayer capsules (PEMCs) Gao and co-workers used this method to extract mechanical data.[99, 100] Upon increase of osmotic pressure the capsules started to deform and assumed a buckled shape. The onset of this
ACCEPTED MANUSCRIPT buckling was associated with a critical osmotic pressure which was shown to depend on capsule wall thickness and elastic modulus as well as on the size of the capsule. The established theoretical model allows for the calculation of the shells’ elastic modulus from the measured critical pressure. In a later
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study Datta et al. examined the buckling behavior of Pickering emulsion droplets by continuously reducing their volume.[101] The results show that these kinds of capsules undergo similar buckling
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transitions as known for typical polymer based thin shell systems.
Fig. 3.1: Schematic representation of single-capsule measurement techniques, each with typically available force range. Arrows indicate the directions in which forces are acting.
In the following, single capsule measurement techniques will be presented, ordered according to increasing force sensitivity. Fig. 3.1 gives a schematic overview. First, we focus on parallel plate compression where the capsule is deformed between two approaching plates with a typical force range between µN and N. Such studies date back to the early 1930s when Cole examined surface forces of the arbacia egg with a flat gold wire.[3] Starting from the late 1990s well defined compression of micron scale capsules was introduced. Zhang et al. developed a micromanipulation technique to measure burst forces of melamine formaldehyde (MF) microcapsules in a controlled fashion.[102] Fig. 3.2 shows
ACCEPTED MANUSCRIPT pictures from a similar deformation experiment. The immobilized microcapsule is deformed by the flat end of a cylindrical probe connected to a force transducer. The optical microscope allows for alignment and observation of the deformation in situ. As a result of approaching and retracting the probe a force
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versus deformation characteristic is obtained. Bursting of the capsule is associated with a sharp drop in the recorded force. Similar plate compression experiments on MF microcapsules were conducted by Hu
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et al.[103], Keller and Sottos investigated poly(urea-formaldehyde) microcapsules.[104] Theoretical
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treatment and simulations can be found in [105-107].
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Fig. 3.2: Sequence of images of an alginate capsule under parallel plate compression with a micromanipulator. Image adapted from [108]. Copyright 2003 Wiley. Used with permission from Carin et
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al., Compression of biocompatible liquid-filled HSA-alginate capsules: Determination of the membrane mechanical properties, Biotechnology & Bioengineering, John Wiley and Sons.
A technique closely related to plate compression testing is atomic force microscopy (AFM). Similar to the situation in a micromanipulator uniaxial deformations are effected, however, the accessible force range is shifted to smaller values (pN to µN) accompanied with higher resolution.[109] Therefore, it is a suitable tool for capsule systems to study shell mechanical properties in the small deformation regime on the order of the shell thickness. Often, the colloidal probe setup is used, where a particle of colloidal dimensions is attached to a tip-less cantilever to achieve well defined sphere-sphere deformation geometry. In analogy to plate compression AFM can be combined with optics and measurements in air and in liquid are feasible. With the help of reflection interference contact microscopy (RICM) the simultaneous observation of the capsule’s contact area with the substrate while performing a deformation experiment becomes possible. Fig. 3.3 depicts a typical force vs. deformation characteristic from a colloidal probe AFM measurement including the corresponding RICM images. First studies with the colloidal probe technique to characterize PEMCs were reported independently from Vinogradova
ACCEPTED MANUSCRIPT and co-workers [110-112] and from Fery and co-workers [113-115]. The elastic modulus of PSS/PAH multilayer capsule shells was determined to be in the low GPa range. It was shown that the shell thickness has a drastic influence on the mechanical properties. Further, by using an optical microscope in
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RICM mode it was possible to reconstruct the actual capsule shape both in undeformed state and during measurement. Other groups have employed the colloidal probe technique to study mechanical
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properties of vesicles [116], MF capsules [117] and biopolymer capsules [118] or the salt softening of
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PEMCs [119]. Shell mechanical properties of capsule systems can equally be investigated by AFM when using a cantilever with a sharp tip at its apex. However, measurements have to be performed carefully avoiding penetration of the shell. Consequently, the applicable force range is typically lower than with a
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colloidal probe. A variety of systems has been tested with this method, such as vesicles [120, 121], polymeric capsules [122], capsules with a silica shell [123], viral shells [124, 125] and polymersomes
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[126]. A third option for capsule deformation with AFM is to employ a tip-less cantilever. Here, the major constraint arises from the fact that commercially available cantilever holders are tilted by several degrees; a typical inclination angle is 10°. Therefore, compression will always be accompanied by some
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shearing or sliding, which can lead to pushing away the capsule in extreme cases. Yet, for moderate loads
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and small capsules (with respect to cantilever dimensions) these effects should be acceptably low. With
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this method a range of microcapsules and –bubbles have been investigated.[127-131]
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Fig. 3.3: Force-deformation characteristic of a polyelectrolyte multilayer microcapsule, 10 µm in radius. Insets show corresponding RICM micrographs. A clear correlation can be observed between applied loads and apparent contact area.[113] Buckling of the shell is evidenced by discontinuities in the curve and, correspondingly, abrupt changes in contact geometry. With kind permission from Springer Science and Business Media: Springer, the European Physical Journal E, 12 (2), 2003, p.215, Elastic properties of polyelectrolyte capsules studied by atomic force microscopy and RICM, F. Dubreuil, Figure 4.
A conceptually completely different approach is to apply shear stresses. The typical range of these stresses is from mPa to kPa, i.e. for capsules with a typical radius of 5 µm the applied forces can be estimated to be in between 0.1 pN to 0.1 µN. Several studies have been performed in Couette flow, i.e. the microcapsules are exposed to shear flow created by two concentric cylinders rotating in opposite direction.[132-136] The outer cylinder of the rheoscope is optically transparent, thus enabling observation of capsule shape and orientation with a microscope. An example is given in Fig. 3.4, where the shear rate has been increased until capsule break. A similar setup is used for spinning drop experiments.[137-142] Here, the microcapsule is placed within a liquid filled rotating tube and shape changes are again followed via microscope. In both methods, the shear modulus is determined, based on
ACCEPTED MANUSCRIPT the change in capsule shape as a function of applied shear forces. Theoretical models for different shear and flow conditions have been developed.[143-149] A related method is based on microfluidics. The microcapsules mechanical properties are studied by guiding them through narrow channels and
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following the change in shape. Such an approach has been reported both for biological cells [150] and
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artificial capsules [151-154]. Corresponding theoretical descriptions have been worked out.[155-162]
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Fig. 3.4: Series of images of an initially spherical polysiloxane microcapsule in shear flow at different shear rates ˙ until break. Reproduced from [136] with permission of The Royal Society of Chemistry (RSC).
A more sensitive technique is micropipette aspiration. It has originally been developed by Mitchison and Swann to examine elastic properties of living cells and the setup was therefore termed “cell elastimeter”.[163] A glass micropipette is connected to a movable reservoir which effects slight suction when lowered. In this way a single cell can be aspirated, held and depending on the position of the reservoir suction pressure can be systematically varied and capsules can be released after the experiments. Normally, applied pressures range between 1 Pa and 1 kPa. This means, with typical inner diameters of the capillary of 1-5 µm, forces in between pN to nN are exerted. Shape changes of the capsule are followed with an optical microscope (see Fig. 3.5). The observed bulging of the cell membrane is used to extract information about mechanical properties such as stiffness, Young’s modulus or internal pressure. Since these first pioneering contributions the technique has been improved further and applied to study both biological samples [164-169] and artificial capsules [170-
ACCEPTED MANUSCRIPT 173]. Theoretical models have been developed to accurately describe and evaluate micropipette
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aspiration experiments.[167, 174-180]
Fig. 3.5: Micropipette suction experiment with a polymersome. After aspiration (a) and collapse (b) a positive pressure is applied (c), finally leading to full recovery of the capsule (d). Scale bar is 5 µm. Reproduced from [173] with permission of The Royal Society of Chemistry (RSC).
Finally, a class of methods is discussed which enables the exertion of very low forces (several tens of fN to some hundreds of pN): optical and magnetic tweezers. Though mainly used to study biological samples (e.g., cells) we still add this paragraph to round out the picture concerning single-capsule deformation techniques. Generally, optical tweezers exploit the forces arising from a light source such that a dielectric particle can be trapped and manipulated. Detailed information about this technique and theoretical background can be found in [181-185]. In a classical experiment two beads which are attached to opposite sides of a cell are trapped with optical tweezers and then pulled apart to investigate the cells mechanical properties and determine elastic parameters such as the shear modulus of the cell membrane.[186-188] An example is given in Fig. 3.6, where the experimental observations are
ACCEPTED MANUSCRIPT accompanied by numerical simulations. Non-symmetric systems with only one traceable particle attached to a cell have been studied by Titushkin et al. [189] and by Frases and co-workers [190]. Calibration of optical tweezers has been treated in the group of Nussenzveig.[191, 192] A special case of
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optical tweezers is given in the optical stretcher where microcapsules can be directly trapped and deformed without additional particles. This method was introduced by Guck et al. [193], theoretical
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considerations can be found in [194-196]. The working principle of magnetic tweezers is similar to optical
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tweezers. Magnetic beads attached to a cell wall are trapped in a magnetic field and then moved to
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perform a microrheology experiment.[197-199]
Fig. 3.6: Cell deformation experiments with optical tweezers at increasing loads. Left, optical micrographs, right, corresponding simulations revealing strain distributions and 3D-shape changes. [200]
ACCEPTED MANUSCRIPT Reprinted from Acta Materialia, 52, C.T. Lim et al., Large deformation of living cells using laser traps,
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Copyright (2004) with permission from Elsevier.
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IV) Modeling – Physics of capsule deformation
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As it was shown in the previous part a wide range of techniques has been established to characterize mechanical properties of capsule systems. There are static, quasi-static and dynamic methods which all
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need to be evaluated with a suitable physical model to extract meaningful quantities out of the obtained data. As compared to the deformation of massive particles made from an elastically homogenous medium, modeling capsule deformation is intrinsically more challenging and qualitatively new features
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arise, which are often linked to nonlinear effects. In addition, several qualitatively different deformation regimes are found. Deformations can be on the same range or small as compared to the capsules' typical
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length scales such as wall thickness or radius, and capsules can be permeable or not, to mention only the
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most important aspects. In the following we first focus on the (more general) modeling of capsule deformation within the framework of shell theory before comparing to membrane approach and
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discussing more complex deformation scenarios. Shell structures are widely and successfully used in nature, architecture and technology, covering all length scales in-between biological cells and dome constructions.[201] However, the underlying physical concepts to describe their mechanical properties and to predict response to applied loads are the same. One of the major advantages of shells is that, despite often being very thin and thereby saving material, extreme stability and protection of the interior is nevertheless guaranteed. This brings us to a first important (and for many systems valid) simplification concerning theoretical treatment: the restriction to thin shells, i.e. structures with a shell thickness h to radius R ratio of less than 1/20.[202] Here, R corresponds to the radius of curvature of the middle surface between the inward and outward faces of the shell. In the course of this section shells will always be considered as thin. Further assumptions in thin shell theory are linear elasticity of the shell material (which is supposed to be homogeneous and isotropic), small deformation with respect to the shell thickness, and the Kirchhoff hypotheses (constant shell thickness, neglect of transverse normal stress and in-plane shear), together known as the KirchhoffLove assumptions. Additionally, the 3D-shell-problem is reduced to a 2D-problem by focusing on the middle surface of the shell.[202] One of the first scientists to present such a first-order approximation was Reissner.[203-207] His analysis revealed a linear scaling of applied force F and resulting deformation d.
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(1)
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Further variables in equation 1 are the radius of curvature R, shell thickness h and the material elastic constants, Young’s modulus E and Poisson’s ratio . Originally developed for point loads, Reissner’s
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theory has been experimentally proved to be valid also for less concentrated loading situations, e.g.,
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deformations with a colloidal probe.[109] In the context of microcapsules this simple result is particularly interesting as the shells’ elasticity modulus becomes directly accessible from small deformation experiments, e.g., parallel plate compression or AFM force spectroscopy. An overview over further first-
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and higher-order approximations is provided in [202].
A constraint to the simple description of small deformations can arise from membrane pre-tensions
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which become important for very thin shells. In a pioneering work, Ferri and co-workers tried to separate the contributions of surface tension and mechanical membrane tension to the overall deformation behavior of Pickering emulsion droplets.[208] A model was developed accounting for both tension
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contributions and including the shape changes of the capsule during compression. Based on
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experimental data, stress-strain relations are calculated and compared to the predictions of continuum mechanical shell models. Significant differences are found which are attributed to strong influence of
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surface tension effects originating from the oil-particle-water interface. Tan et al. built up on this work and investigated mechanical properties of droplets stabilized by clay particles.[209] Predictions from Ferri’s work are in good agreement with their experiments. As the determined surface Young’s modulus depends on the applied strain, it is clear that the shells’ elasticity cannot be described by a pure Hook law. This non-Hookean behavior is, again, suggested to result from interfacial tensions. Pre-inflation as it can arise from swelling has been identified as another source of pre-tension. It has been shown that the shape of capsules in axisymmetric flow is largely influenced by such additional mechanic tension.[162] A corresponding trend was found for capsules in shear flow. Here, the deformation characteristic is significantly altered and, for high pre-stresses, the validity of small deformation theory is passed.[148] Remaining under thin shell assumptions we now focus on larger deformations. For the simplest case, a capsule with infinite permeability, Pogorelov proposed the following relationship for a Hookean material under point load.[210]
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ACCEPTED MANUSCRIPT In this scenario, a dimple is forming and, in contrast to Reissner’s formula, the force no longer scales linearly but with the square root of deformation. Theoretical solutions of the large deformation problem under assumption of non-Hookean models, such as Neo-Hookean or Mooney-Rivlin, are presented in
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[211, 212]. These hyperelastic material models are used to describe the nonlinear stress-strain relation beyond Hookean elasticity. Here, effects such as yielding and thinning of the shell become important.
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Rachik et al. compare 3D (Neo-Hook, Mooney-Rivlin, Yeoh) with 2D constitutive models (STZC, Evans-
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Skalak).[105] Generally, they find that all investigated models (except for the Neo-Hookean) fit the experimental data well. However, a concluding recommendation which model to choose could not be given. One crucial parameter to consider will be the shell material’s properties, e.g. whether strain-
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hardening or -softening occurs at large deformations.[213, 214]
Several studies have used the onset of buckling, as described by Pogorelov, as a means for estimating
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elastic properties of shells.[215-219] Experimentally, this can be addressed by using osmotic pressure effects. For instance, Gao and co-workers made use of the osmotic pressure to calculate the elastic modulus of PSS/PAH polyelectrolyte capsules (see also Figure 4.1).[99] Following earlier argumentations
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the shell.
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[220, 221] a model is presented where the critical osmotic pressure is related to the elastic modulus of
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Here, pc is the critical pressure when buckling of the shell starts. This pressure scales directly with the shell thickness squared and indirectly with the square of radius, or, in other words, pc scales indirectly with the Föppl-von Kármán number .
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The experimental data clearly confirmed this relation and the determined modulus is in good agreement with independent measurements.[113] Vliegenthart and Gompper analyzed the problem of capsule buckling under external pressure by means of simulations.[222] They found that the shape of the capsules in the deformed state is determined by three variables, deformation rate, reduced volume and, again, the Föppl-von Kármán number . The simulations reveal two energy regimes. The first, for small indentations with circular dimple, follows the classic prediction after Landau and Lifshitz with the energy scaling like E 1/4.[223] When the shell is
ACCEPTED MANUSCRIPT deformed to a larger extend leading to polygonal shape of the dimple, the scaling exponent changes to
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less than 1/6.
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Fig. 4.1: Buckling of polyelectrolyte multilayer capsules induced by osmotic pressure.[99] With kind permission from Springer Science and Business Media: Springer, the European Physical Journal E, 5 (1),
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2001, p.21, Elasticity of hollow polyelectrolyte capsules prepared by the layer-by-layer technique, C. Dubreuil, Figure 2b.
Generally, the formation of a dimple or invagination upon large deformation of capsules has received much attention in the literature. Buckling instabilities have been observed and described in both experimental and theoretical studies.[224-242] A special case are pressurized shells which show wrinkling under point load conditions.[243] The same group has also studied the mechanical properties of pressurized shells under point loads.[244] In addition to the initial linear regime as predicted by Reissner for small deformations a second linear regime was found for large indentations. It is obvious that for a range of systems, particularly for large deformations, permeability is not negligible and, therefore, needs to be considered. For small deformations of a capsule, irrespective of permeability, the force F scales linearly with relative deformation (deformation divided by capsule radius R).[245]
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ACCEPTED MANUSCRIPT This is the basis for Reissner's reasoning. In the case of an impermeable membrane an additional term has to be considered. This term accounts for the stretching of the shell while being deformed. Here, the
(6)
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force scales cubically with deformation.[111]
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Hence, the complete description of the deformation of an impermeable capsule is given by the sum of equations 2 and 3. Plotting both scaling laws in a common graph (fig. 4.2) shows clearly that, as long as we restrict ourselves to small deformations on the order of the shell thickness, permeability issues are
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negligible. In contrast, for large deformations volume-constraint contributions become increasingly
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dominant. Therefore, capsule wall permeability has to be considered in modeling of large deformations.
Fig. 4.2: Linear elastic (continuous line) and volume-constraint (dotted line) contributions to forces F upon capsule deformation (relative deformation ), calculated for a capsule 10 µm in diameter, shell thickness of 20 nm and Young’s modulus of 1 GPa.
In this case, additional contributions arise particularly from edge bending at the sites of high curvature around the dimple and stretching caused by the rising fluid pressure.[246] Comparing both experimental data and theoretical calculations for the deformation of an empty and a water-filled racquetball Taber found that deformations below 20% are dominated by bending. Only for larger compression the loaddeflection curve of filled shells deviated from the square root like scaling and compared to the empty shells a stiffening was observed.[246]
ACCEPTED MANUSCRIPT Finally, at very high loads capsule burst can occur. Experimentally, Zhang et al. found for melamine formaldehyde (MF) microcapsules a clear correlation with both bursting force and displacement at burst increasing in a linear fashion with capsule diameter.[102] Additionally, it was discovered that burst
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typically occurs at a critical relative deformation of 70%, irrespective of capsule size.[247] MercadéPrieto et al. carried out finite element modeling (FEM) to elucidate the failure behavior of MF
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microcapsules.[106] The compression behavior between two parallel plates is simulated up to bursting
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by applying an elastic-perfectly plastic model with strain hardening and comparison with experimental data shows very good agreement. Strain at rupture for this system was found to be approximately 0.48 and a failure stress of around 350 MPa was obtained.
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After going through thin shell theory it is worth considering a special type of thin shell, which has often been treated in the literature: the membrane. Generally, shell structures support externally applied
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loads in two ways: in-plane (stretching and shear) and out-of-plane (bending and twisting).[109, 202] Thus, we can imagine two extreme cases. For very stiff, solid shells the out-of-plane mode can be largely neglected. The stability of these shells originates from their high resistance to bending - just imagine the
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huge dome constructions in architecture or the stiffness of an egg shell.[202] Accordingly, these thin
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shells carry axial loads almost exclusively by in-plane action. In contrast, stretching or shear can be neglected either in the small deformation limit of compliant shells as has been outlined above or, in
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general, for a special shell design. The particular architecture of fluid membranes allows for translational displacements of the constituting layers at vanishing energy cost. At the same time, bending and twisting moments are small, i.e. the main mechanical characteristic of a fluid membrane is its flexibility. It supports external loads only by its tension and deforms in pure bending.[202, 248] Such conditions are often fulfilled in biological systems. Surely, the prototypes of fluid membranes are cellular membranes or lipid bilayers. The bending resistance of such membranes has been treated in a range of publications.[248-254] The key variable to describe mechanical properties of membranes is the bending rigidity kbend. It is related to the area elastic modulus KA by a simple expression [250, 255]:
(7) Here, is a constant and h is again the membrane thickness. The bending rigidity is typically given in multiples of kBT in order to compare the stability of the extremely compliant membrane to the thermal energy, which may be sufficient to induce fluctuations. However, there is also a class of membrane-like systems with finite shear modulus, i.e. in-plane elastic energy has to be considered. In the literature, these are commonly referred to as tethered or polymerized membranes.[248, 249, 252] Here, the shell
ACCEPTED MANUSCRIPT consists of a (partly) interconnected network instead of a loose assembly of individual molecules in two distinct layers. Several studies described such membrane-like systems including both bending and shear contributions.[253, 254, 256] That means we are back in an intermediate regime where both in-plane
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and out-of-plane contributions have to be accounted for in physical modeling. Hence, when a fluid membrane is “properly” modified (cross-linked, strengthened), a transition is observed towards the
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universal shell-like behavior. In other words, the shell material sets the boundary conditions for the
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correct interpretation of mechanical data. In order to better capture transitory states or limiting cases Simmonds et al. suggest in their theoretical analysis to describe a spherical shell under load by the sum of a membrane-like, a shell-like and a slab-like solution.[257] This way, simplifications of the Kirchhoff-
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Love thin shell theory and errors resulting thereof should be overcome. Another theoretical treatment of a capsule’s wall mechanical properties in-between the state of fluid membranes and solid shells is
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presented by Tu and co-workers.[258]
While mainly axial deformation has been considered so far we now turn to a more complex scenario, namely capsules in (shear) flow. A recent overview of this topic can found in [146]. In the simplest case, a
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homogeneous thin elastic shell is modeled following Hooke’s law for small deformations. It is
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characterized by its surface shear modulus GS and area dilation modulus KS, with KS = GS(1+)/(1-) and being the Poisson’s ratio. The principle tensions T1,2 and extension ratios 1,2 are correlated to give the
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subsequent equations:
(8) (9)
More details on freely suspended microcapsules in simple shear flow can be found in a range of publications [87-89, 143] covering also tumbling [145, 147, 259], large deformations [90] or the effect of pre-stresses [148]. A closely related topic is the motion of capsules in channels, e.g., blood cells or delivery vehicles in arteries. Several groups have addressed this issue.[155-162] When a capsule flows through a constriction it assumes a certain shape depending on its mechanical properties, flow rate, channel size [155] and geometry [157, 158]. To conclude this section we would like to draw the readers’ attention to some examples of non-spherical capsules. Delorme and co-workers studied the mechanical properties of polyhedrons.[260] Both the elastic modulus (Reissner approximation for thin shells) and bending modulus (membrane theory) were determined and found to be in a reasonable range compared to independent measurements.
ACCEPTED MANUSCRIPT Additionally, a distinct difference in stiffness between facets and vertexes could be shown. The mechanical properties of ellipsoidal shells are studied in [261] and [262]. It is clearly shown how geometry, namely the curvature, influences the stiffness of a given shell, e.g., that a hen’s egg supports
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higher loads at its poles than around the equator. Additionally, the stiffening effect of internal pressure is
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examined (see fig. 4.3).
Fig. 4.3: a) Ellipsoidal shells with different aspect ratios b/a. b) Effect of aspect ratio on forcedeformation characteristic for axial loads on non-pressurized shells. c) Effect of internal pressure for a given aspect ratio (1.5). Pressure ranges from 0-10 kPa.[261] Copyright (2012) by the American Physical Society.
Another class of non-spherical microcontainers, capsids, is investigated in [263]. The authors present a corresponding elasticity theory and reveal the interrelation between energy and shape. This finally leads to a shape phase diagram, where the transitions from spherical to spherocylindrical to icosahedral geometries are given as a function of the spontaneous curvature and the Föppl-von Kármán number.
ACCEPTED MANUSCRIPT Mechanical properties of hollow tubes have been characterized and evaluated by Mueller et al. [81, 264], based on a model developed earlier for microtubules [265]. The scaling of the tube wall materials’ stiffness with wall thickness and radius is similar to the Reissner relation for spherical shells, yet with
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slightly higher exponents. Anisotropic microcapsules assuming cubic or pyramidal shapes were constructed via a layer-by-layer approach by Shchepelina and co-workers.[266] With the help of
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computer simulations it is demonstrated that these geometries provide enhanced mechanical properties
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compared to spherical capsules. Simulating osmotic pressure, the edges and corners, i.e. the regions of high curvature, act as a kind of intrinsic frame which stabilizes the whole structure, whereas the hollow spheres show the typical buckling instabilities. In a later work, hollow cubic capsules are investigated
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with regard to pH-induced shape changes.[267] While (PMAA)20 capsules show a shape transition to spherical structures, the (PMAA-PVPON)5 capsules retain their morphology. This difference is attributed
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to a change in materials’ stiffness. The more rigid composite better withstands the stresses due to pH triggered swelling, whereas the softer single-component capsule is subject to bending of its side faces. Generally, numerical methods such as finite element modeling (FEM) can help to understand
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experimental observations and to predict system response, particularly when more complex
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morphologies are investigated (e.g., the anisotropic capsules discussed before) and when deformation regimes beyond linear elasticity are probed (e.g., capsule burst). In these cases analytical treatment is
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often not possible. In FEM simulations the shell is modeled as consisting of a finite number of discrete elements.[268-270] With this approach several capsule systems have been studied, e.g., artificial spherical capsules [105-107, 271-274] and icosahedral viral capsids [275-278]. An alternative way to reduce complexity is to model the shell structures as spring networks. Here, the continuous shell is replaced by a grid with a set mesh size where the links between the nodes represent springs obeying a predefined elasticity law. This model has been shown to apply well to both icosahedral [237, 279-281] and spherical shells [222]. A related approach is coarse-grained simulation techniques [282-285] and meso-scale modeling [286, 287]. Instead of considering every single atom or molecule as in classical molecular dynamics simulations (which is far too time-consuming for micron-sized systems) several molecules or polymer segments are grouped and represented by one bead. Neighboring beads are connected by a bond to which a certain potential is attributed. Several groups employed this technique to examine mechanical properties of microcapsules [286, 288-290] and viral capsids [278, 291-293].
ACCEPTED MANUSCRIPT V) Functionality and Application Perspectives
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As has been outlined in the introductory section microencapsulation is already today an important processing method in industry and bears great potential for a wide range of applications. Mechanics of
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microcapsules plays a critical role for the ultimate purpose of most encapsulation applications: controlling release of the encapsulated material. Depending on the specific application, desired release
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scenarios range from prolonged release by diffusion through the capsule wall to quick burst release. For the first scenario, mechanical failure of microcapsules will result in premature release and has to be
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avoided by designing microcapsules in a way that they withstand the wear and tear associated to storage, transport and administration. For the second scenario, mechanical failure can become a
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powerful release mechanism, if mechanical properties can be designed such, that instabilities occur under the desired conditions. Thus it is no surprise, that recent patent literature puts strong emphasis on mechanical properties.[294, 295]
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In the light of the previous chapters, it is evident that especially controlling mechanical instabilities
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requires excellent control over relevant geometrical parameters of the microcapsules. For spherical systems these are radius and wall thickness. Therefore, template assisted methods like LBL greatly
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extend the possibilities, since the radius can be well adjusted using monodisperse templates and wall thicknesses can be controlled on the molecular scale. In the following we will illustrate this using some examples from recent literature focusing on PEMCs without claiming complete coverage of the broad field of microcapsules.
While mechanical experiments on PEMCs have first focused on estimating the Young’s modulus and its responsiveness towards external parameters like temperature [296, 297], pH [298, 299] and saltconcentration [119, 299, 300], so far the correlation between mechanical properties and release of encapsulated material has received little attention in this field. Fernandes et al. studied the release of a fluorescent dye from microcapsules as a function of deformation by colloidal probe AFM (Figure 5.1).[301] The change of fluorescence intensity within the microcapsule was followed and a clear correlation between deformation and fluorescence intensity of encapsulated dye was observed. Interestingly, a sharp drop in intensity occurred at a relative deformation around 20 %, which could be attributed to a transition from an elastic to a plastic deformation regime indicating mechanical failure at this point.
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Fig. 5.1: Fluorescence intensity as a function of relative deformation of a microcapsule (filled symbols) and control experiment (open symbols) with a microcapsule not subjected to deformation. Insets show
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corresponding images of a microcapsule at different degrees of deformation as indicated by arrows. Scale bar is 5 µm. Reproduced from [301] with permission of The Royal Society of Chemistry.
Similar studies were carried out by Palankar et al. who investigated the release of biodegradable polymer microcapsules upon mechanical deformation ex situ and their uptake by HeLa cells in vivo.[118] The technique opens the possibility to quantify forces for mechanical failure in a force regime several orders of magnitude below conventional indentation tests. An example for the relevance of this force regime can be found in recent studies of cellular uptake of microcapsules.[302], [303] The uptake process is accompanied by forces that are exerted on the microcapsule. If these forces are high enough to induce mechanical instability, encapsulated material will be released prematurely and not enter the intracellular area. The authors showed, using a series of microcapsules with varying deformability, that there is a clear correlation between microcapsule mechanics and the probability of release during the uptake process (see Figure 5.2). Apart from the relevance for intra-cellular delivery it was possible to estimate the forces that the cell wall exerts during incorporation. Thus mechanically well-defined microcapsules could serve as probes.
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Fig. 5.2: Release from microcapsules with different mechanical strength depending on annealing
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temperature. (a) Soft capsules release the fluorescently labeled encapsulate prematurely, i.e. outside the cell. The more rigid capsule is entirely uptaken without rupturing. b) Release as a function of applied
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force and deformation from single capsule measurements.[304] Copyright (2010) Wiley. Used with permission from Delcea et al., Mechanobiology: Correlation Between Mechanical Stability of Microcapsules Studied by AFM and Impact of Cell-Induced Stresses, Small, John Wiley and Sons.
However, the relevance of deformation properties for cellular uptake goes beyond these stability considerations. Several studies showed that mechanical properties as well influence the uptake probability significantly; yet, these studies investigated full instead of hollow spheres. Beningo et al. found that bone-marrow-derived macrophages from mice preferred harder particles to softer ones.[305] Here, the stiffness of polyacrylamide beads was tuned by changing the amount of crosslinker resulting in a more than threefold difference in modulus (absolute values were not given). In contrast, Liu et al. found that HepG2 cells internalized softer particles faster and to a greater extent than the stiffer ones.[306] Here, particles consisted of poly(2-hydroxyethyl methacrylate) (HEMA) and, again, the modulus was tuned by varying crosslinker content (compressive modulus from 15-156 kPa). Banquy et al. discovered that the stiffness of particles from the same material and similar modulus range had an influence on the pathway how they are taken up by murine macrophage cells.[307] In a theoretical study
ACCEPTED MANUSCRIPT Yi et al. show the wrapping of a vesicle by a cell membrane.[308] It is stated that due to energetical reasons, uptake of stiffer particles is preferred. While the different findings suggest that there is no simple design criterion for all cell types, the significance of deformability is central. Generally, the
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possibility to now prepare microcapsules with well-defined mechanics, study their properties on single particle level and correlate them with cellular uptake should provide the basis for gaining understanding
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of this behavior and for examining mechanical responsiveness for the uptake.
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While in the above examples, mechanical instability was due to an external force, PEMCs have as well been used to show burst release due to internal forces: Since their shells are semi-permeable, osmotic pressure provides a means for causing tension and eventually collapse or bursting of microcapsules.[100]
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This has been taken advantage of for programming the mechanical instability of microcapsules: De Geest and coworkers deposited a LbL shell onto hydrolyzable hydrogel-cores.[309, 310] The system is designed
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such, that the shell is impermeable for degradation products of the dextran-based gels. Thus increasing osmotic pressure can build up in the course of gel hydrolysis and trigger capsule-burst.[311] Mechanical stability and resistance toward osmotic pressure can be tuned by adjusting the composition and
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thickness of the capsule wall. Thus tailored release can be achieved covering timescales between
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seconds and days (see example of fast response in Figure 5.3).[312]
ACCEPTED MANUSCRIPT Fig. 5.3: Confocal microscopy images of LbL-coated microgels at different times. At 0 s sodium hydroxide is added leading to capsule burst and release of fluorescent dye after 10 s. Scale bar unit is µm.[312] Reprinted with permission from the Journal of the American Chemical Society, 130, 14480, De Geest
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et.al, Microcapsules ejecting nanosized species into the environment. Copyright (2008) American
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Chemical Society.
This is particularly useful for pharmaceutical applications like vaccination, where a sustained delivery of vaccines is desired. This can now be realized by a single vaccination with a cocktail of microcapsules
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displaying different, temporally tuned release profiles.[313] An interesting aspect of the burst release that is visible in Figure 5.3 is its directionality. Membrane failure occurs usually at a single point only, and
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the expulsion of the encapsulate is driven by the flows induced by the relaxation of the pressure difference. Therefore, release is not a diffusion controlled process in this case. Knowing the weak points of the membrane where mechanical instability occurs, the location of release can be predetermined;
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experimentally, defects or destabilizing elements can be included and addressed externally.[314]
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Deformation experiments have been carried out to elucidate the mechanical properties and their relevance for release for this class of microcapsules.[315] In this context, using non-spherical
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microcapsules offers interesting perspectives. As shown by Tsukruk et al., cubic or tetrahedral microcapsules exhibit “non-trivial rupture spots” at the edges/corners where strains are localized.[266] This opens the way towards directed release applications. While in the previous examples mechanical stability was investigated in a quasi-static deformation regime at low frequencies, high frequency mechanics of microcapsules have also caught much attention recently: Especially Ultrasound (US) is of broad interest, since ultrasound is widely used in medical diagnostics and therapies. Thus, microcapsules carrying therapeutic gases could – depending on US intensity – do both enhance contrast and systematically release of therapeutically active gases. The applied US intensities strongly determine the microcapsules response. For gas-filled microcapsules the acoustic response can typically be divided in three regimes: 1) linear oscillations for low-ultrasound intensities 2) non-linear oscillations also called harmonics for increased US intensities and 3) the fragmentation of microcapsules when a certain pressure threshold is reached.[316] Theoretical descriptions of the dynamic linear and non-linear deformation observed in experiments are discussed with regard to shell properties and the microcapsule length scales, radius and shell thickness for example in [317] and [318]. Recently, we showed for polymeric gas-filled microcapsules the change of low and high frequency mechanics upon integration of nanoparticles in the shell.[319] Theranostic concepts such
ACCEPTED MANUSCRIPT as US diagnosis combined with the release of therapeutic NO gases by high-intensity ultrasound or alternating magnetic fields were recently reported by different authors.[320, 321] However, oscillation of microcapsules during ultrasound exposure is restricted to gas-filled microcapsules with thin soft shells.
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For other designs of microcapsules, effects such as cavitation, the formation of small bubbles in the liquid medium, and thermal effects can be used to release therapeutics stored in liquid-filled
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microcapsules.[322]
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Shchukin and co-workers were among the first to investigate US-triggered release from PEMCs.[323] It could be shown that embedding of nanoparticles into the shell increases the sensitivity towards US. This
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effect could be attributed to both nanoparticle induced shell stiffening [324] raising the brittleness of the material and a higher density gradient which locally enhances US action. In later studies the correlation
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between shell thickness, amount of embedded nanoparticles and resistance against ultrasonic treatment was elucidated to more detail for PEMCs and polymer-shelled microcapsules.[325-327] Interestingly, while theory suggests and earlier studies on PEMCs found an increase of capsule stiffness with shell
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thickness [113, 325], Kolesnikova et al. observed a decrease in stiffness and elastic modulus with
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increasing shell thickness and amount of included nanoparticles.[325] Obviously, in this system the introduction of NPs makes the shell fragile, which is reflected by an increased sensitivity towards US.
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The mechanical instability of microcapsules can also be used to induce shape changes / break the spherical symmetry of capsules. As has been shown in the previous chapter capsule deformations are often accompanied by buckling, particularly for large compressions. Control over this process offers an elegant and simple way for the production of anisotropic particles with a multiplicity of available geometries. This is of great interest especially in the field of materials science, e.g., with regard to plasmonics or meta-materials, when tailored morphology is combined with directed assembly. Quilliet and co-workers present experimental and theoretical studies on non-trivial buckling.[240] They show that buckling can be easily induced by the removal of solvent from the capsules’ interior in order to give a variety of anisotropic shapes. These geometries depend mainly on the shell properties, in particular the Föppl-von Kármán number. A similar approach was adopted by Datta et al. for particle coated droplets.[101] The same group illustrated the drastic influence of inhomogeneities on the buckling process which could provide another means for tuning shapes.[231] Combining both buckling and assembly of sub-micron sized polymeric capsules was described by Yang and co-workers.[328] First, hexagonally packed 2D-arrays were created by convective self-assembly and then shape changes were induced via solvent evaporation. A similar approach has been reported recently by Zhang et al. for coreshell particles.[329] An interesting advancement for the application of non-spherical capsules has been
ACCEPTED MANUSCRIPT published recently by Wilson and co-workers.[330] Bowl-shaped micro-containers were produced by the controlled buckling of polymer vesicles to serve as moveable “artificial stomatocytes”. Softer anisotropic capsules were formed using osmotic pressure induced buckling, and their cavity was filled with
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catalytically active platinum nanoparticles turning hydrogen peroxide (which is present in the medium around the capsules) into oxygen and water. The oxygen produced inside the cavity escapes through the
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opening of the stomatocyte and, thereby, creates a pressure that is sufficient to propel the capsule in the
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opposite direction (Figure 5.4).
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Fig. 5.4: The anisotropic shape of polymer vesicles after a buckling transition is exploited for forming “artificial stomatocytes” and facilitating active motion on the colloidal scale: Catalytic platinum
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nanoparticles are introduced into the cavity and oxygen generated by decomposition of hydrogen peroxide results in propulsion. Reprinted by permission from Macmillian Publishers Ltd: Nature Chemistry, [330], copyright (2012).
Finally, adhesion is a crucial parameter for many applications of capsule systems. In the biological or medical domain it is important to know, understand, and eventually, modify or trigger adhesive interactions. For example, the adhesion between a capsular delivery container and target cells supposed to take up the cargo should be promoted specifically. On the other hand, adhesion may also not be desired, for instance, when capsules are intended to circulate for a longer period of time in blood vessels (e.g., for purposes of imaging or sustained release). Elsner et al. investigated the influence of shell thickness on adhesion.[331] It turned out that with increasing number of PE layers (which also means an increase in mechanical stability) adhesion of the capsules to the substrate decreased as monitored by the contact radius. Two deformation scenarios were distinguished based on which the scaling of contact radius along with shell thickness and radius could be predicted. Hence, tuning of shell thickness offers one convenient way of adjusting adhesion properties. A more general theory on the adhesion of vesicles
ACCEPTED MANUSCRIPT is presented by Seifert and co-workers.[332] They mainly focused on shape/shape changes and transitions from free to bound state. In a later publication shape equations were solved numerically.[333] An expression for a critical adhesion energy is derived and theoretical results are
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compared to the experimental data obtained from Elsner et al. showing good agreement. Wan and Liu worked out a model for adhesive contact mechanics of a thin-walled capsule to a flat substrate within
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linear elastic theory.[334] It is demonstrated that an increase of osmotic pressure can reduce contact
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area and even provoke detachment of the capsule from the substrate. Nolte and Fery introduced a method to align polyelectrolyte capsules on patterned substrates making use of electrostatic interactions.[335] This approach has been developed further to covalently bind the assembled capsules
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to the substrate.[336] By computational modeling, Alexeev et al. examined the fluid driven motion of a capsule on a substrate.[286, 289, 337] They found that besides stiffness and pattern of the substrate the
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mechanical properties of the microcapsules play an important role for the tuning of mutual adhesion. Based on these results concepts are introduced to selectively trap and burst the capsules[338] as well as to sort and guide them in a predetermined manner[339-341]. This opens an application perspective for,
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e.g., analytical devices for quality control regarding capsule mechanics or for a fractionation device
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allowing the extraction of capsules with desired mechanical properties from a given batch. Lastly, for an
VI) Conclusions
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in-depth study of shell adhesion, an exhaustive treatment of the topic can be found in [342].
Microcapsule mechanics is a fascinating topic, which has attracted attention from various scientific communities for many decades. Still, we are currently witnessing the dawn of a new era: Modern synthetic approaches like the layer-by-layer technique or other template-assisted self-assembly methods allow unprecedented control over geometrical parameters of capsules as well as on the composition of wall and interior. Consequently, mechanical properties like capsule stiffness in the small deformation range, buckling forces/pressures or burst forces / fracture strength can be adjusted accurately. This allows not only tailoring mechanical properties such that sufficient stability to withstand wear and tear in applications is ensured - rather mechanical properties and instabilities can be taken advantage of for introducing functionality. The present review focuses on novel possibilities and illustrates them by some selected examples from literature, without aiming for completeness of this highly dynamic field. Gaining control and further understanding of microcapsule mechanics requires a truly interdisciplinary approach. Therefore, the foundations in terms of suitable synthesis / assembly are introduced together with theoretical basics of microcapsules mechanics as well as an overview of experimental characterization
ACCEPTED MANUSCRIPT techniques with special emphasis on single microcapsule measurements. Thus, we hope to provide an
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entry point for interested researchers into this interdisciplinary field.
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References:
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Graphical abstract
ACCEPTED MANUSCRIPT Highlights: - This review focuses on the mechanical properties of microcapsules.
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- Ensemble and single-capsule measurement techniques are presented and compared. - Physical concepts are discussed describing and modeling shell deformation.
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- Application perspectives are outlined with capsule mechanics as key parameter.
S0001-8686(13)00169-3 doi: 10.1016/j.cis.2013.11.016 CIS 1361
To appear in:
Advances in Colloid and Interface Science
Please cite this article as: Neubauer Martin P., Poehlmann Melanie, Fery Andreas, Microcapsule mechanics: From stability to function, Advances in Colloid and Interface Science (2013), doi: 10.1016/j.cis.2013.11.016
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ACCEPTED MANUSCRIPT Microcapsule mechanics: From stability to function Martin P. Neubauera, Melanie Poehlmanna, Andreas Ferya,* University of Bayreuth, Department of Physical Chemistry II, Universitätsstraße 30, 95440 Bayreuth, Germany
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*Corresponding author. E-Mail address: [email protected] Tel.: +49 921 55 2753; Fax: +49 921 55 2059
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Keywords: Microcapsules; Mechanical Characterization; Shell Theory; Layer-by-Layer; Drug Delivery
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Abstract
Microcapsules are reviewed with special emphasis on the relevance of controlled mechanical properties
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for functional aspects. At first, assembly strategies are presented that allow control over the decisive
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geometrical parameters, diameter and wall thickness, which both influence the capsule’s mechanical performance. As one of the most powerful approaches the layer-by-layer technique is identified.
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Subsequently, ensemble and, in particular, single-capsule deformation techniques are discussed. The latter generally provide more in-depth information and cover the complete range of applicable forces from smaller than pN to N. In a theory chapter, we illustrate the physics of capsule deformation. The main focus is on thin shell theory, which provides a useful approximation for many deformation scenarios. Finally, we give an overview of applications and future perspectives where the specific design of mechanical properties turns microcapsules into (multi-)functional devices, enriching especially life sciences and material sciences.
I) Introduction Microcapsule-research is a classical example of a field, which has been driven and fueled by many disciplines ranging from biophysics, via fundamental colloid- and interface research in physical chemistry and synthesis – both organic and inorganic – up to applied sciences and engineering. Microcapsules have been an object of research in these areas for many decades. First studies date back as early as to the 1930s, when Bungenberg de Jong and co-workers investigated coacervates which can be seen as the first artificial, man-made microcapsules.[1, 2] At the same time Cole performed the first compression
ACCEPTED MANUSCRIPT experiments on single microcapsules, i.e. on arbacia eggs with a diameter around 75 µm.[3] Especially the development of novel synthesis strategies, e.g., layer-by-layer assembly, and techniques to characterize capsules on a single-capsule level has stimulated scientific research in this area within the
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past twenty years. At the same time, microcapsules have been increasingly used in industry. The first large-scale production of microcapsules was established for carbonless copy paper already in the
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1950s.[4] Today, microcapsules are designed for and employed in many different fields of application,
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such as pharmacy [5-11], food industry [12-22], agriculture [23-26], cosmetics [27-29], textile industry [30-32], printing [33], biosensor engineering [34-36], active coatings [37, 38] and construction [39-41]. For instance, in food technology active ingredients are protected from decomposition through
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environmental impacts or flavors are prevented from premature volatilization.[21] Textiles have been modified with microcapsules for long-term fragrance release, to introduce fire retardants and even to
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combat counterfeiting.[30] The interest in and the demand for intelligent, custom-made capsule systems is continuously rising. And scientific research plays a key role as the understanding of the fundamental
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properties of microcapsules is breaking ground for innovation.
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II) Microcapsules: Definition and Assembly Strategies In view of the broad range of capsule systems and the different context in which they have been investigated, it is no surprise that there are various, sometimes at least partially diverging definitions of the term microcapsules and microencapsulation.[42-46] Therefore, let us first clarify the semantics for the purpose of this review: Generally, microencapsulation is understood as the process by which one material of microscopic dimensions is entirely coated by another. Hence, a core-shell-composite or microcapsule is created where the core can take all aggregate states but the shell is solid. This fundamental definition already points out the two main components of microcapsules, core/interior/inner phase and shell/wall/membrane/outer phase, which can be tuned with respect to materials, permeability, size, shape etc. Out of this large variety of possible microcapsules it is indispensable to introduce some further constraints. In the context of this review article we examine mechanical properties of microcapsules. These are particularly interesting when dominated by the shell. Therefore, we limit ourselves to microcapsules being composed of a fluid core wrapped by a solid shell. In contrast, capsules consisting of a solid core will be referred to as core/shell particles and will not be in the center of interest. In terms of the mechanical properties of the shell, we limit ourselves to non-fluid shells. The broad class of vesicles formed from lipids or in general low-molecular weight species will thus
ACCEPTED MANUSCRIPT not be covered. The microcapsules considered in this review will always be spherical, if not stated differently, and their size will range from several hundreds of nanometers to some tens (in few cases to some hundreds) of micrometers, with the restriction that the shell thickness is small as compared to the
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diameter.
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The focus will finally be on artificial microcapsules, which naturally lets us start from reviewing the various approaches for the formation of microcapsules meeting the aforesaid definitions. As stated
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above, microcapsules find already various usages in industry. The industrially relevant encapsulation techniques are typically based on physicochemical processes that allow for large scale production. These
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include spray drying [47], co-extrusion, spinning disk, multiple-nozzle spraying, fluidized-bed coating and vacuum encapsulation.[42, 46] Among the advantages of these methods are the easy handling,
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upscalability and low costs. On the other hand, the obtained microcapsules are often polydisperse in diameter and shell thickness. In other words, current approaches allow for comparatively little control over the particles morphology and the possibilities of capsule design are rather restricted.
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A far better control over capsule core and shell dimensions and a selective introduction of functionality is
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provided by template-assisted and/or self-assembly approaches. Both soft and hard template-assisted methods offer fine-tuning of the core size and can be combined with a self-assembly process which
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allows excellent control over shell thickness, down to molecular level. Soft template-assisted methods are mostly emulsion-based, such as microfluidic processes [48-54], polymerosomes [6, 55-60] (which are typically nm-sized), colloidosomes [61-63], interfacial polymerization [64-67], interfacial assembly [68], inkjet printing [69, 70] or phase separation processes [71, 72]. A special case is the soft colloid templated multilayer assembly which offers control over all geometric parameters.[73, 74] The underlying principle was first exploited using hard templates, namely the layer-by-layer deposition technique.[75-80] Combining templates and self-assembly permits precise adjustment of geometry, diameter [81], shell thickness and shell material [82]. Furthermore, such methods allow for introduction of multifunctionality.[83] That means, in addition to enclosing their content until desired delivery, microcapsules are designed which, for example in medical applications, can be tracked within the human body, directed to a specific site and, finally, specifically triggered to release their cargo. A schematic overview of microcapsule designs obtained from template-assisted and self-assembly methods is given in Fig. 2.1. It becomes clear that the synthesis process strongly determines the choice of core and shell material, and the design possibilities.
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III) Mechanical Characterization of Microcapsules
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Fig. 2.1: Template-assisted and self-assembly methods for a controlled capsule design. The scheme shows typical wall materials (particles, multilayers, homogeneous film) and the crucial geometric parameters, diameter D and wall thickness h.
Mechanical properties of microcapsules become accessible through a variety of experimental
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techniques. These can be divided into two general categories: ensemble methods and methods on a
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single-capsule level. Ensemble methods measure a batch of capsules simultaneously, yielding average values. These measurements can often be performed in an automated, high-throughput fashion and a
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large number of capsules are captured. In contrast, single capsule measurements provide generally more detailed information on deformation properties, but require a sequential measurement of capsules. One possibility of determining mechanical properties of microcapsule ensembles is to make use of shear forces. A slurry or suspension of capsules can be measured, for instance, in a turbine reactor.[84] Here, rather high forces are acting provoking breakage of capsules. Therefore, such a method is mainly relevant for studying large deformation behavior and release under high stresses. A more sensitive approach is given by rheological investigations. Drochon et al. measured the viscosity of a diluted suspension of red blood cells and calculated the shear elastic modulus of the cell membrane.[85, 86] The underlying model has been derived by the same authors and other groups.[87-90] Suspensions of microcapsules under shear have been further studied experimentally by Bredimas et al. [91] and theoretically by the groups of Misbah [92-96] and Kalluri [97, 98]. Another means to obtain information about mechanical parameters of a multitude of capsules is to perform osmotic pressure experiments. With the upcoming of polyelectrolyte multilayer capsules (PEMCs) Gao and co-workers used this method to extract mechanical data.[99, 100] Upon increase of osmotic pressure the capsules started to deform and assumed a buckled shape. The onset of this
ACCEPTED MANUSCRIPT buckling was associated with a critical osmotic pressure which was shown to depend on capsule wall thickness and elastic modulus as well as on the size of the capsule. The established theoretical model allows for the calculation of the shells’ elastic modulus from the measured critical pressure. In a later
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study Datta et al. examined the buckling behavior of Pickering emulsion droplets by continuously reducing their volume.[101] The results show that these kinds of capsules undergo similar buckling
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transitions as known for typical polymer based thin shell systems.
Fig. 3.1: Schematic representation of single-capsule measurement techniques, each with typically available force range. Arrows indicate the directions in which forces are acting.
In the following, single capsule measurement techniques will be presented, ordered according to increasing force sensitivity. Fig. 3.1 gives a schematic overview. First, we focus on parallel plate compression where the capsule is deformed between two approaching plates with a typical force range between µN and N. Such studies date back to the early 1930s when Cole examined surface forces of the arbacia egg with a flat gold wire.[3] Starting from the late 1990s well defined compression of micron scale capsules was introduced. Zhang et al. developed a micromanipulation technique to measure burst forces of melamine formaldehyde (MF) microcapsules in a controlled fashion.[102] Fig. 3.2 shows
ACCEPTED MANUSCRIPT pictures from a similar deformation experiment. The immobilized microcapsule is deformed by the flat end of a cylindrical probe connected to a force transducer. The optical microscope allows for alignment and observation of the deformation in situ. As a result of approaching and retracting the probe a force
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versus deformation characteristic is obtained. Bursting of the capsule is associated with a sharp drop in the recorded force. Similar plate compression experiments on MF microcapsules were conducted by Hu
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et al.[103], Keller and Sottos investigated poly(urea-formaldehyde) microcapsules.[104] Theoretical
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treatment and simulations can be found in [105-107].
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Fig. 3.2: Sequence of images of an alginate capsule under parallel plate compression with a micromanipulator. Image adapted from [108]. Copyright 2003 Wiley. Used with permission from Carin et
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al., Compression of biocompatible liquid-filled HSA-alginate capsules: Determination of the membrane mechanical properties, Biotechnology & Bioengineering, John Wiley and Sons.
A technique closely related to plate compression testing is atomic force microscopy (AFM). Similar to the situation in a micromanipulator uniaxial deformations are effected, however, the accessible force range is shifted to smaller values (pN to µN) accompanied with higher resolution.[109] Therefore, it is a suitable tool for capsule systems to study shell mechanical properties in the small deformation regime on the order of the shell thickness. Often, the colloidal probe setup is used, where a particle of colloidal dimensions is attached to a tip-less cantilever to achieve well defined sphere-sphere deformation geometry. In analogy to plate compression AFM can be combined with optics and measurements in air and in liquid are feasible. With the help of reflection interference contact microscopy (RICM) the simultaneous observation of the capsule’s contact area with the substrate while performing a deformation experiment becomes possible. Fig. 3.3 depicts a typical force vs. deformation characteristic from a colloidal probe AFM measurement including the corresponding RICM images. First studies with the colloidal probe technique to characterize PEMCs were reported independently from Vinogradova
ACCEPTED MANUSCRIPT and co-workers [110-112] and from Fery and co-workers [113-115]. The elastic modulus of PSS/PAH multilayer capsule shells was determined to be in the low GPa range. It was shown that the shell thickness has a drastic influence on the mechanical properties. Further, by using an optical microscope in
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RICM mode it was possible to reconstruct the actual capsule shape both in undeformed state and during measurement. Other groups have employed the colloidal probe technique to study mechanical
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properties of vesicles [116], MF capsules [117] and biopolymer capsules [118] or the salt softening of
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PEMCs [119]. Shell mechanical properties of capsule systems can equally be investigated by AFM when using a cantilever with a sharp tip at its apex. However, measurements have to be performed carefully avoiding penetration of the shell. Consequently, the applicable force range is typically lower than with a
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colloidal probe. A variety of systems has been tested with this method, such as vesicles [120, 121], polymeric capsules [122], capsules with a silica shell [123], viral shells [124, 125] and polymersomes
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[126]. A third option for capsule deformation with AFM is to employ a tip-less cantilever. Here, the major constraint arises from the fact that commercially available cantilever holders are tilted by several degrees; a typical inclination angle is 10°. Therefore, compression will always be accompanied by some
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shearing or sliding, which can lead to pushing away the capsule in extreme cases. Yet, for moderate loads
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and small capsules (with respect to cantilever dimensions) these effects should be acceptably low. With
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this method a range of microcapsules and –bubbles have been investigated.[127-131]
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Fig. 3.3: Force-deformation characteristic of a polyelectrolyte multilayer microcapsule, 10 µm in radius. Insets show corresponding RICM micrographs. A clear correlation can be observed between applied loads and apparent contact area.[113] Buckling of the shell is evidenced by discontinuities in the curve and, correspondingly, abrupt changes in contact geometry. With kind permission from Springer Science and Business Media: Springer, the European Physical Journal E, 12 (2), 2003, p.215, Elastic properties of polyelectrolyte capsules studied by atomic force microscopy and RICM, F. Dubreuil, Figure 4.
A conceptually completely different approach is to apply shear stresses. The typical range of these stresses is from mPa to kPa, i.e. for capsules with a typical radius of 5 µm the applied forces can be estimated to be in between 0.1 pN to 0.1 µN. Several studies have been performed in Couette flow, i.e. the microcapsules are exposed to shear flow created by two concentric cylinders rotating in opposite direction.[132-136] The outer cylinder of the rheoscope is optically transparent, thus enabling observation of capsule shape and orientation with a microscope. An example is given in Fig. 3.4, where the shear rate has been increased until capsule break. A similar setup is used for spinning drop experiments.[137-142] Here, the microcapsule is placed within a liquid filled rotating tube and shape changes are again followed via microscope. In both methods, the shear modulus is determined, based on
ACCEPTED MANUSCRIPT the change in capsule shape as a function of applied shear forces. Theoretical models for different shear and flow conditions have been developed.[143-149] A related method is based on microfluidics. The microcapsules mechanical properties are studied by guiding them through narrow channels and
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following the change in shape. Such an approach has been reported both for biological cells [150] and
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artificial capsules [151-154]. Corresponding theoretical descriptions have been worked out.[155-162]
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Fig. 3.4: Series of images of an initially spherical polysiloxane microcapsule in shear flow at different shear rates ˙ until break. Reproduced from [136] with permission of The Royal Society of Chemistry (RSC).
A more sensitive technique is micropipette aspiration. It has originally been developed by Mitchison and Swann to examine elastic properties of living cells and the setup was therefore termed “cell elastimeter”.[163] A glass micropipette is connected to a movable reservoir which effects slight suction when lowered. In this way a single cell can be aspirated, held and depending on the position of the reservoir suction pressure can be systematically varied and capsules can be released after the experiments. Normally, applied pressures range between 1 Pa and 1 kPa. This means, with typical inner diameters of the capillary of 1-5 µm, forces in between pN to nN are exerted. Shape changes of the capsule are followed with an optical microscope (see Fig. 3.5). The observed bulging of the cell membrane is used to extract information about mechanical properties such as stiffness, Young’s modulus or internal pressure. Since these first pioneering contributions the technique has been improved further and applied to study both biological samples [164-169] and artificial capsules [170-
ACCEPTED MANUSCRIPT 173]. Theoretical models have been developed to accurately describe and evaluate micropipette
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aspiration experiments.[167, 174-180]
Fig. 3.5: Micropipette suction experiment with a polymersome. After aspiration (a) and collapse (b) a positive pressure is applied (c), finally leading to full recovery of the capsule (d). Scale bar is 5 µm. Reproduced from [173] with permission of The Royal Society of Chemistry (RSC).
Finally, a class of methods is discussed which enables the exertion of very low forces (several tens of fN to some hundreds of pN): optical and magnetic tweezers. Though mainly used to study biological samples (e.g., cells) we still add this paragraph to round out the picture concerning single-capsule deformation techniques. Generally, optical tweezers exploit the forces arising from a light source such that a dielectric particle can be trapped and manipulated. Detailed information about this technique and theoretical background can be found in [181-185]. In a classical experiment two beads which are attached to opposite sides of a cell are trapped with optical tweezers and then pulled apart to investigate the cells mechanical properties and determine elastic parameters such as the shear modulus of the cell membrane.[186-188] An example is given in Fig. 3.6, where the experimental observations are
ACCEPTED MANUSCRIPT accompanied by numerical simulations. Non-symmetric systems with only one traceable particle attached to a cell have been studied by Titushkin et al. [189] and by Frases and co-workers [190]. Calibration of optical tweezers has been treated in the group of Nussenzveig.[191, 192] A special case of
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optical tweezers is given in the optical stretcher where microcapsules can be directly trapped and deformed without additional particles. This method was introduced by Guck et al. [193], theoretical
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considerations can be found in [194-196]. The working principle of magnetic tweezers is similar to optical
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tweezers. Magnetic beads attached to a cell wall are trapped in a magnetic field and then moved to
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perform a microrheology experiment.[197-199]
Fig. 3.6: Cell deformation experiments with optical tweezers at increasing loads. Left, optical micrographs, right, corresponding simulations revealing strain distributions and 3D-shape changes. [200]
ACCEPTED MANUSCRIPT Reprinted from Acta Materialia, 52, C.T. Lim et al., Large deformation of living cells using laser traps,
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Copyright (2004) with permission from Elsevier.
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IV) Modeling – Physics of capsule deformation
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As it was shown in the previous part a wide range of techniques has been established to characterize mechanical properties of capsule systems. There are static, quasi-static and dynamic methods which all
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need to be evaluated with a suitable physical model to extract meaningful quantities out of the obtained data. As compared to the deformation of massive particles made from an elastically homogenous medium, modeling capsule deformation is intrinsically more challenging and qualitatively new features
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arise, which are often linked to nonlinear effects. In addition, several qualitatively different deformation regimes are found. Deformations can be on the same range or small as compared to the capsules' typical
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length scales such as wall thickness or radius, and capsules can be permeable or not, to mention only the
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most important aspects. In the following we first focus on the (more general) modeling of capsule deformation within the framework of shell theory before comparing to membrane approach and
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discussing more complex deformation scenarios. Shell structures are widely and successfully used in nature, architecture and technology, covering all length scales in-between biological cells and dome constructions.[201] However, the underlying physical concepts to describe their mechanical properties and to predict response to applied loads are the same. One of the major advantages of shells is that, despite often being very thin and thereby saving material, extreme stability and protection of the interior is nevertheless guaranteed. This brings us to a first important (and for many systems valid) simplification concerning theoretical treatment: the restriction to thin shells, i.e. structures with a shell thickness h to radius R ratio of less than 1/20.[202] Here, R corresponds to the radius of curvature of the middle surface between the inward and outward faces of the shell. In the course of this section shells will always be considered as thin. Further assumptions in thin shell theory are linear elasticity of the shell material (which is supposed to be homogeneous and isotropic), small deformation with respect to the shell thickness, and the Kirchhoff hypotheses (constant shell thickness, neglect of transverse normal stress and in-plane shear), together known as the KirchhoffLove assumptions. Additionally, the 3D-shell-problem is reduced to a 2D-problem by focusing on the middle surface of the shell.[202] One of the first scientists to present such a first-order approximation was Reissner.[203-207] His analysis revealed a linear scaling of applied force F and resulting deformation d.
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(1)
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Further variables in equation 1 are the radius of curvature R, shell thickness h and the material elastic constants, Young’s modulus E and Poisson’s ratio . Originally developed for point loads, Reissner’s
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theory has been experimentally proved to be valid also for less concentrated loading situations, e.g.,
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deformations with a colloidal probe.[109] In the context of microcapsules this simple result is particularly interesting as the shells’ elasticity modulus becomes directly accessible from small deformation experiments, e.g., parallel plate compression or AFM force spectroscopy. An overview over further first-
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and higher-order approximations is provided in [202].
A constraint to the simple description of small deformations can arise from membrane pre-tensions
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which become important for very thin shells. In a pioneering work, Ferri and co-workers tried to separate the contributions of surface tension and mechanical membrane tension to the overall deformation behavior of Pickering emulsion droplets.[208] A model was developed accounting for both tension
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contributions and including the shape changes of the capsule during compression. Based on
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experimental data, stress-strain relations are calculated and compared to the predictions of continuum mechanical shell models. Significant differences are found which are attributed to strong influence of
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surface tension effects originating from the oil-particle-water interface. Tan et al. built up on this work and investigated mechanical properties of droplets stabilized by clay particles.[209] Predictions from Ferri’s work are in good agreement with their experiments. As the determined surface Young’s modulus depends on the applied strain, it is clear that the shells’ elasticity cannot be described by a pure Hook law. This non-Hookean behavior is, again, suggested to result from interfacial tensions. Pre-inflation as it can arise from swelling has been identified as another source of pre-tension. It has been shown that the shape of capsules in axisymmetric flow is largely influenced by such additional mechanic tension.[162] A corresponding trend was found for capsules in shear flow. Here, the deformation characteristic is significantly altered and, for high pre-stresses, the validity of small deformation theory is passed.[148] Remaining under thin shell assumptions we now focus on larger deformations. For the simplest case, a capsule with infinite permeability, Pogorelov proposed the following relationship for a Hookean material under point load.[210]
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ACCEPTED MANUSCRIPT In this scenario, a dimple is forming and, in contrast to Reissner’s formula, the force no longer scales linearly but with the square root of deformation. Theoretical solutions of the large deformation problem under assumption of non-Hookean models, such as Neo-Hookean or Mooney-Rivlin, are presented in
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[211, 212]. These hyperelastic material models are used to describe the nonlinear stress-strain relation beyond Hookean elasticity. Here, effects such as yielding and thinning of the shell become important.
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Rachik et al. compare 3D (Neo-Hook, Mooney-Rivlin, Yeoh) with 2D constitutive models (STZC, Evans-
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Skalak).[105] Generally, they find that all investigated models (except for the Neo-Hookean) fit the experimental data well. However, a concluding recommendation which model to choose could not be given. One crucial parameter to consider will be the shell material’s properties, e.g. whether strain-
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hardening or -softening occurs at large deformations.[213, 214]
Several studies have used the onset of buckling, as described by Pogorelov, as a means for estimating
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elastic properties of shells.[215-219] Experimentally, this can be addressed by using osmotic pressure effects. For instance, Gao and co-workers made use of the osmotic pressure to calculate the elastic modulus of PSS/PAH polyelectrolyte capsules (see also Figure 4.1).[99] Following earlier argumentations
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the shell.
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[220, 221] a model is presented where the critical osmotic pressure is related to the elastic modulus of
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Here, pc is the critical pressure when buckling of the shell starts. This pressure scales directly with the shell thickness squared and indirectly with the square of radius, or, in other words, pc scales indirectly with the Föppl-von Kármán number .
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The experimental data clearly confirmed this relation and the determined modulus is in good agreement with independent measurements.[113] Vliegenthart and Gompper analyzed the problem of capsule buckling under external pressure by means of simulations.[222] They found that the shape of the capsules in the deformed state is determined by three variables, deformation rate, reduced volume and, again, the Föppl-von Kármán number . The simulations reveal two energy regimes. The first, for small indentations with circular dimple, follows the classic prediction after Landau and Lifshitz with the energy scaling like E 1/4.[223] When the shell is
ACCEPTED MANUSCRIPT deformed to a larger extend leading to polygonal shape of the dimple, the scaling exponent changes to
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less than 1/6.
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Fig. 4.1: Buckling of polyelectrolyte multilayer capsules induced by osmotic pressure.[99] With kind permission from Springer Science and Business Media: Springer, the European Physical Journal E, 5 (1),
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2001, p.21, Elasticity of hollow polyelectrolyte capsules prepared by the layer-by-layer technique, C. Dubreuil, Figure 2b.
Generally, the formation of a dimple or invagination upon large deformation of capsules has received much attention in the literature. Buckling instabilities have been observed and described in both experimental and theoretical studies.[224-242] A special case are pressurized shells which show wrinkling under point load conditions.[243] The same group has also studied the mechanical properties of pressurized shells under point loads.[244] In addition to the initial linear regime as predicted by Reissner for small deformations a second linear regime was found for large indentations. It is obvious that for a range of systems, particularly for large deformations, permeability is not negligible and, therefore, needs to be considered. For small deformations of a capsule, irrespective of permeability, the force F scales linearly with relative deformation (deformation divided by capsule radius R).[245]
(5)
ACCEPTED MANUSCRIPT This is the basis for Reissner's reasoning. In the case of an impermeable membrane an additional term has to be considered. This term accounts for the stretching of the shell while being deformed. Here, the
(6)
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force scales cubically with deformation.[111]
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Hence, the complete description of the deformation of an impermeable capsule is given by the sum of equations 2 and 3. Plotting both scaling laws in a common graph (fig. 4.2) shows clearly that, as long as we restrict ourselves to small deformations on the order of the shell thickness, permeability issues are
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negligible. In contrast, for large deformations volume-constraint contributions become increasingly
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dominant. Therefore, capsule wall permeability has to be considered in modeling of large deformations.
Fig. 4.2: Linear elastic (continuous line) and volume-constraint (dotted line) contributions to forces F upon capsule deformation (relative deformation ), calculated for a capsule 10 µm in diameter, shell thickness of 20 nm and Young’s modulus of 1 GPa.
In this case, additional contributions arise particularly from edge bending at the sites of high curvature around the dimple and stretching caused by the rising fluid pressure.[246] Comparing both experimental data and theoretical calculations for the deformation of an empty and a water-filled racquetball Taber found that deformations below 20% are dominated by bending. Only for larger compression the loaddeflection curve of filled shells deviated from the square root like scaling and compared to the empty shells a stiffening was observed.[246]
ACCEPTED MANUSCRIPT Finally, at very high loads capsule burst can occur. Experimentally, Zhang et al. found for melamine formaldehyde (MF) microcapsules a clear correlation with both bursting force and displacement at burst increasing in a linear fashion with capsule diameter.[102] Additionally, it was discovered that burst
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typically occurs at a critical relative deformation of 70%, irrespective of capsule size.[247] MercadéPrieto et al. carried out finite element modeling (FEM) to elucidate the failure behavior of MF
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microcapsules.[106] The compression behavior between two parallel plates is simulated up to bursting
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by applying an elastic-perfectly plastic model with strain hardening and comparison with experimental data shows very good agreement. Strain at rupture for this system was found to be approximately 0.48 and a failure stress of around 350 MPa was obtained.
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After going through thin shell theory it is worth considering a special type of thin shell, which has often been treated in the literature: the membrane. Generally, shell structures support externally applied
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loads in two ways: in-plane (stretching and shear) and out-of-plane (bending and twisting).[109, 202] Thus, we can imagine two extreme cases. For very stiff, solid shells the out-of-plane mode can be largely neglected. The stability of these shells originates from their high resistance to bending - just imagine the
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huge dome constructions in architecture or the stiffness of an egg shell.[202] Accordingly, these thin
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shells carry axial loads almost exclusively by in-plane action. In contrast, stretching or shear can be neglected either in the small deformation limit of compliant shells as has been outlined above or, in
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general, for a special shell design. The particular architecture of fluid membranes allows for translational displacements of the constituting layers at vanishing energy cost. At the same time, bending and twisting moments are small, i.e. the main mechanical characteristic of a fluid membrane is its flexibility. It supports external loads only by its tension and deforms in pure bending.[202, 248] Such conditions are often fulfilled in biological systems. Surely, the prototypes of fluid membranes are cellular membranes or lipid bilayers. The bending resistance of such membranes has been treated in a range of publications.[248-254] The key variable to describe mechanical properties of membranes is the bending rigidity kbend. It is related to the area elastic modulus KA by a simple expression [250, 255]:
(7) Here, is a constant and h is again the membrane thickness. The bending rigidity is typically given in multiples of kBT in order to compare the stability of the extremely compliant membrane to the thermal energy, which may be sufficient to induce fluctuations. However, there is also a class of membrane-like systems with finite shear modulus, i.e. in-plane elastic energy has to be considered. In the literature, these are commonly referred to as tethered or polymerized membranes.[248, 249, 252] Here, the shell
ACCEPTED MANUSCRIPT consists of a (partly) interconnected network instead of a loose assembly of individual molecules in two distinct layers. Several studies described such membrane-like systems including both bending and shear contributions.[253, 254, 256] That means we are back in an intermediate regime where both in-plane
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and out-of-plane contributions have to be accounted for in physical modeling. Hence, when a fluid membrane is “properly” modified (cross-linked, strengthened), a transition is observed towards the
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universal shell-like behavior. In other words, the shell material sets the boundary conditions for the
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correct interpretation of mechanical data. In order to better capture transitory states or limiting cases Simmonds et al. suggest in their theoretical analysis to describe a spherical shell under load by the sum of a membrane-like, a shell-like and a slab-like solution.[257] This way, simplifications of the Kirchhoff-
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Love thin shell theory and errors resulting thereof should be overcome. Another theoretical treatment of a capsule’s wall mechanical properties in-between the state of fluid membranes and solid shells is
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presented by Tu and co-workers.[258]
While mainly axial deformation has been considered so far we now turn to a more complex scenario, namely capsules in (shear) flow. A recent overview of this topic can found in [146]. In the simplest case, a
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homogeneous thin elastic shell is modeled following Hooke’s law for small deformations. It is
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characterized by its surface shear modulus GS and area dilation modulus KS, with KS = GS(1+)/(1-) and being the Poisson’s ratio. The principle tensions T1,2 and extension ratios 1,2 are correlated to give the
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subsequent equations:
(8) (9)
More details on freely suspended microcapsules in simple shear flow can be found in a range of publications [87-89, 143] covering also tumbling [145, 147, 259], large deformations [90] or the effect of pre-stresses [148]. A closely related topic is the motion of capsules in channels, e.g., blood cells or delivery vehicles in arteries. Several groups have addressed this issue.[155-162] When a capsule flows through a constriction it assumes a certain shape depending on its mechanical properties, flow rate, channel size [155] and geometry [157, 158]. To conclude this section we would like to draw the readers’ attention to some examples of non-spherical capsules. Delorme and co-workers studied the mechanical properties of polyhedrons.[260] Both the elastic modulus (Reissner approximation for thin shells) and bending modulus (membrane theory) were determined and found to be in a reasonable range compared to independent measurements.
ACCEPTED MANUSCRIPT Additionally, a distinct difference in stiffness between facets and vertexes could be shown. The mechanical properties of ellipsoidal shells are studied in [261] and [262]. It is clearly shown how geometry, namely the curvature, influences the stiffness of a given shell, e.g., that a hen’s egg supports
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higher loads at its poles than around the equator. Additionally, the stiffening effect of internal pressure is
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examined (see fig. 4.3).
Fig. 4.3: a) Ellipsoidal shells with different aspect ratios b/a. b) Effect of aspect ratio on forcedeformation characteristic for axial loads on non-pressurized shells. c) Effect of internal pressure for a given aspect ratio (1.5). Pressure ranges from 0-10 kPa.[261] Copyright (2012) by the American Physical Society.
Another class of non-spherical microcontainers, capsids, is investigated in [263]. The authors present a corresponding elasticity theory and reveal the interrelation between energy and shape. This finally leads to a shape phase diagram, where the transitions from spherical to spherocylindrical to icosahedral geometries are given as a function of the spontaneous curvature and the Föppl-von Kármán number.
ACCEPTED MANUSCRIPT Mechanical properties of hollow tubes have been characterized and evaluated by Mueller et al. [81, 264], based on a model developed earlier for microtubules [265]. The scaling of the tube wall materials’ stiffness with wall thickness and radius is similar to the Reissner relation for spherical shells, yet with
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slightly higher exponents. Anisotropic microcapsules assuming cubic or pyramidal shapes were constructed via a layer-by-layer approach by Shchepelina and co-workers.[266] With the help of
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computer simulations it is demonstrated that these geometries provide enhanced mechanical properties
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compared to spherical capsules. Simulating osmotic pressure, the edges and corners, i.e. the regions of high curvature, act as a kind of intrinsic frame which stabilizes the whole structure, whereas the hollow spheres show the typical buckling instabilities. In a later work, hollow cubic capsules are investigated
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with regard to pH-induced shape changes.[267] While (PMAA)20 capsules show a shape transition to spherical structures, the (PMAA-PVPON)5 capsules retain their morphology. This difference is attributed
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to a change in materials’ stiffness. The more rigid composite better withstands the stresses due to pH triggered swelling, whereas the softer single-component capsule is subject to bending of its side faces. Generally, numerical methods such as finite element modeling (FEM) can help to understand
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experimental observations and to predict system response, particularly when more complex
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morphologies are investigated (e.g., the anisotropic capsules discussed before) and when deformation regimes beyond linear elasticity are probed (e.g., capsule burst). In these cases analytical treatment is
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often not possible. In FEM simulations the shell is modeled as consisting of a finite number of discrete elements.[268-270] With this approach several capsule systems have been studied, e.g., artificial spherical capsules [105-107, 271-274] and icosahedral viral capsids [275-278]. An alternative way to reduce complexity is to model the shell structures as spring networks. Here, the continuous shell is replaced by a grid with a set mesh size where the links between the nodes represent springs obeying a predefined elasticity law. This model has been shown to apply well to both icosahedral [237, 279-281] and spherical shells [222]. A related approach is coarse-grained simulation techniques [282-285] and meso-scale modeling [286, 287]. Instead of considering every single atom or molecule as in classical molecular dynamics simulations (which is far too time-consuming for micron-sized systems) several molecules or polymer segments are grouped and represented by one bead. Neighboring beads are connected by a bond to which a certain potential is attributed. Several groups employed this technique to examine mechanical properties of microcapsules [286, 288-290] and viral capsids [278, 291-293].
ACCEPTED MANUSCRIPT V) Functionality and Application Perspectives
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As has been outlined in the introductory section microencapsulation is already today an important processing method in industry and bears great potential for a wide range of applications. Mechanics of
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microcapsules plays a critical role for the ultimate purpose of most encapsulation applications: controlling release of the encapsulated material. Depending on the specific application, desired release
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scenarios range from prolonged release by diffusion through the capsule wall to quick burst release. For the first scenario, mechanical failure of microcapsules will result in premature release and has to be
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avoided by designing microcapsules in a way that they withstand the wear and tear associated to storage, transport and administration. For the second scenario, mechanical failure can become a
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powerful release mechanism, if mechanical properties can be designed such, that instabilities occur under the desired conditions. Thus it is no surprise, that recent patent literature puts strong emphasis on mechanical properties.[294, 295]
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In the light of the previous chapters, it is evident that especially controlling mechanical instabilities
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requires excellent control over relevant geometrical parameters of the microcapsules. For spherical systems these are radius and wall thickness. Therefore, template assisted methods like LBL greatly
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extend the possibilities, since the radius can be well adjusted using monodisperse templates and wall thicknesses can be controlled on the molecular scale. In the following we will illustrate this using some examples from recent literature focusing on PEMCs without claiming complete coverage of the broad field of microcapsules.
While mechanical experiments on PEMCs have first focused on estimating the Young’s modulus and its responsiveness towards external parameters like temperature [296, 297], pH [298, 299] and saltconcentration [119, 299, 300], so far the correlation between mechanical properties and release of encapsulated material has received little attention in this field. Fernandes et al. studied the release of a fluorescent dye from microcapsules as a function of deformation by colloidal probe AFM (Figure 5.1).[301] The change of fluorescence intensity within the microcapsule was followed and a clear correlation between deformation and fluorescence intensity of encapsulated dye was observed. Interestingly, a sharp drop in intensity occurred at a relative deformation around 20 %, which could be attributed to a transition from an elastic to a plastic deformation regime indicating mechanical failure at this point.
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Fig. 5.1: Fluorescence intensity as a function of relative deformation of a microcapsule (filled symbols) and control experiment (open symbols) with a microcapsule not subjected to deformation. Insets show
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corresponding images of a microcapsule at different degrees of deformation as indicated by arrows. Scale bar is 5 µm. Reproduced from [301] with permission of The Royal Society of Chemistry.
Similar studies were carried out by Palankar et al. who investigated the release of biodegradable polymer microcapsules upon mechanical deformation ex situ and their uptake by HeLa cells in vivo.[118] The technique opens the possibility to quantify forces for mechanical failure in a force regime several orders of magnitude below conventional indentation tests. An example for the relevance of this force regime can be found in recent studies of cellular uptake of microcapsules.[302], [303] The uptake process is accompanied by forces that are exerted on the microcapsule. If these forces are high enough to induce mechanical instability, encapsulated material will be released prematurely and not enter the intracellular area. The authors showed, using a series of microcapsules with varying deformability, that there is a clear correlation between microcapsule mechanics and the probability of release during the uptake process (see Figure 5.2). Apart from the relevance for intra-cellular delivery it was possible to estimate the forces that the cell wall exerts during incorporation. Thus mechanically well-defined microcapsules could serve as probes.
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Fig. 5.2: Release from microcapsules with different mechanical strength depending on annealing
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temperature. (a) Soft capsules release the fluorescently labeled encapsulate prematurely, i.e. outside the cell. The more rigid capsule is entirely uptaken without rupturing. b) Release as a function of applied
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force and deformation from single capsule measurements.[304] Copyright (2010) Wiley. Used with permission from Delcea et al., Mechanobiology: Correlation Between Mechanical Stability of Microcapsules Studied by AFM and Impact of Cell-Induced Stresses, Small, John Wiley and Sons.
However, the relevance of deformation properties for cellular uptake goes beyond these stability considerations. Several studies showed that mechanical properties as well influence the uptake probability significantly; yet, these studies investigated full instead of hollow spheres. Beningo et al. found that bone-marrow-derived macrophages from mice preferred harder particles to softer ones.[305] Here, the stiffness of polyacrylamide beads was tuned by changing the amount of crosslinker resulting in a more than threefold difference in modulus (absolute values were not given). In contrast, Liu et al. found that HepG2 cells internalized softer particles faster and to a greater extent than the stiffer ones.[306] Here, particles consisted of poly(2-hydroxyethyl methacrylate) (HEMA) and, again, the modulus was tuned by varying crosslinker content (compressive modulus from 15-156 kPa). Banquy et al. discovered that the stiffness of particles from the same material and similar modulus range had an influence on the pathway how they are taken up by murine macrophage cells.[307] In a theoretical study
ACCEPTED MANUSCRIPT Yi et al. show the wrapping of a vesicle by a cell membrane.[308] It is stated that due to energetical reasons, uptake of stiffer particles is preferred. While the different findings suggest that there is no simple design criterion for all cell types, the significance of deformability is central. Generally, the
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possibility to now prepare microcapsules with well-defined mechanics, study their properties on single particle level and correlate them with cellular uptake should provide the basis for gaining understanding
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of this behavior and for examining mechanical responsiveness for the uptake.
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While in the above examples, mechanical instability was due to an external force, PEMCs have as well been used to show burst release due to internal forces: Since their shells are semi-permeable, osmotic pressure provides a means for causing tension and eventually collapse or bursting of microcapsules.[100]
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This has been taken advantage of for programming the mechanical instability of microcapsules: De Geest and coworkers deposited a LbL shell onto hydrolyzable hydrogel-cores.[309, 310] The system is designed
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such, that the shell is impermeable for degradation products of the dextran-based gels. Thus increasing osmotic pressure can build up in the course of gel hydrolysis and trigger capsule-burst.[311] Mechanical stability and resistance toward osmotic pressure can be tuned by adjusting the composition and
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thickness of the capsule wall. Thus tailored release can be achieved covering timescales between
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seconds and days (see example of fast response in Figure 5.3).[312]
ACCEPTED MANUSCRIPT Fig. 5.3: Confocal microscopy images of LbL-coated microgels at different times. At 0 s sodium hydroxide is added leading to capsule burst and release of fluorescent dye after 10 s. Scale bar unit is µm.[312] Reprinted with permission from the Journal of the American Chemical Society, 130, 14480, De Geest
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et.al, Microcapsules ejecting nanosized species into the environment. Copyright (2008) American
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Chemical Society.
This is particularly useful for pharmaceutical applications like vaccination, where a sustained delivery of vaccines is desired. This can now be realized by a single vaccination with a cocktail of microcapsules
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displaying different, temporally tuned release profiles.[313] An interesting aspect of the burst release that is visible in Figure 5.3 is its directionality. Membrane failure occurs usually at a single point only, and
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the expulsion of the encapsulate is driven by the flows induced by the relaxation of the pressure difference. Therefore, release is not a diffusion controlled process in this case. Knowing the weak points of the membrane where mechanical instability occurs, the location of release can be predetermined;
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experimentally, defects or destabilizing elements can be included and addressed externally.[314]
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Deformation experiments have been carried out to elucidate the mechanical properties and their relevance for release for this class of microcapsules.[315] In this context, using non-spherical
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microcapsules offers interesting perspectives. As shown by Tsukruk et al., cubic or tetrahedral microcapsules exhibit “non-trivial rupture spots” at the edges/corners where strains are localized.[266] This opens the way towards directed release applications. While in the previous examples mechanical stability was investigated in a quasi-static deformation regime at low frequencies, high frequency mechanics of microcapsules have also caught much attention recently: Especially Ultrasound (US) is of broad interest, since ultrasound is widely used in medical diagnostics and therapies. Thus, microcapsules carrying therapeutic gases could – depending on US intensity – do both enhance contrast and systematically release of therapeutically active gases. The applied US intensities strongly determine the microcapsules response. For gas-filled microcapsules the acoustic response can typically be divided in three regimes: 1) linear oscillations for low-ultrasound intensities 2) non-linear oscillations also called harmonics for increased US intensities and 3) the fragmentation of microcapsules when a certain pressure threshold is reached.[316] Theoretical descriptions of the dynamic linear and non-linear deformation observed in experiments are discussed with regard to shell properties and the microcapsule length scales, radius and shell thickness for example in [317] and [318]. Recently, we showed for polymeric gas-filled microcapsules the change of low and high frequency mechanics upon integration of nanoparticles in the shell.[319] Theranostic concepts such
ACCEPTED MANUSCRIPT as US diagnosis combined with the release of therapeutic NO gases by high-intensity ultrasound or alternating magnetic fields were recently reported by different authors.[320, 321] However, oscillation of microcapsules during ultrasound exposure is restricted to gas-filled microcapsules with thin soft shells.
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For other designs of microcapsules, effects such as cavitation, the formation of small bubbles in the liquid medium, and thermal effects can be used to release therapeutics stored in liquid-filled
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microcapsules.[322]
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Shchukin and co-workers were among the first to investigate US-triggered release from PEMCs.[323] It could be shown that embedding of nanoparticles into the shell increases the sensitivity towards US. This
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effect could be attributed to both nanoparticle induced shell stiffening [324] raising the brittleness of the material and a higher density gradient which locally enhances US action. In later studies the correlation
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between shell thickness, amount of embedded nanoparticles and resistance against ultrasonic treatment was elucidated to more detail for PEMCs and polymer-shelled microcapsules.[325-327] Interestingly, while theory suggests and earlier studies on PEMCs found an increase of capsule stiffness with shell
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thickness [113, 325], Kolesnikova et al. observed a decrease in stiffness and elastic modulus with
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increasing shell thickness and amount of included nanoparticles.[325] Obviously, in this system the introduction of NPs makes the shell fragile, which is reflected by an increased sensitivity towards US.
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The mechanical instability of microcapsules can also be used to induce shape changes / break the spherical symmetry of capsules. As has been shown in the previous chapter capsule deformations are often accompanied by buckling, particularly for large compressions. Control over this process offers an elegant and simple way for the production of anisotropic particles with a multiplicity of available geometries. This is of great interest especially in the field of materials science, e.g., with regard to plasmonics or meta-materials, when tailored morphology is combined with directed assembly. Quilliet and co-workers present experimental and theoretical studies on non-trivial buckling.[240] They show that buckling can be easily induced by the removal of solvent from the capsules’ interior in order to give a variety of anisotropic shapes. These geometries depend mainly on the shell properties, in particular the Föppl-von Kármán number. A similar approach was adopted by Datta et al. for particle coated droplets.[101] The same group illustrated the drastic influence of inhomogeneities on the buckling process which could provide another means for tuning shapes.[231] Combining both buckling and assembly of sub-micron sized polymeric capsules was described by Yang and co-workers.[328] First, hexagonally packed 2D-arrays were created by convective self-assembly and then shape changes were induced via solvent evaporation. A similar approach has been reported recently by Zhang et al. for coreshell particles.[329] An interesting advancement for the application of non-spherical capsules has been
ACCEPTED MANUSCRIPT published recently by Wilson and co-workers.[330] Bowl-shaped micro-containers were produced by the controlled buckling of polymer vesicles to serve as moveable “artificial stomatocytes”. Softer anisotropic capsules were formed using osmotic pressure induced buckling, and their cavity was filled with
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catalytically active platinum nanoparticles turning hydrogen peroxide (which is present in the medium around the capsules) into oxygen and water. The oxygen produced inside the cavity escapes through the
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opening of the stomatocyte and, thereby, creates a pressure that is sufficient to propel the capsule in the
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opposite direction (Figure 5.4).
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Fig. 5.4: The anisotropic shape of polymer vesicles after a buckling transition is exploited for forming “artificial stomatocytes” and facilitating active motion on the colloidal scale: Catalytic platinum
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nanoparticles are introduced into the cavity and oxygen generated by decomposition of hydrogen peroxide results in propulsion. Reprinted by permission from Macmillian Publishers Ltd: Nature Chemistry, [330], copyright (2012).
Finally, adhesion is a crucial parameter for many applications of capsule systems. In the biological or medical domain it is important to know, understand, and eventually, modify or trigger adhesive interactions. For example, the adhesion between a capsular delivery container and target cells supposed to take up the cargo should be promoted specifically. On the other hand, adhesion may also not be desired, for instance, when capsules are intended to circulate for a longer period of time in blood vessels (e.g., for purposes of imaging or sustained release). Elsner et al. investigated the influence of shell thickness on adhesion.[331] It turned out that with increasing number of PE layers (which also means an increase in mechanical stability) adhesion of the capsules to the substrate decreased as monitored by the contact radius. Two deformation scenarios were distinguished based on which the scaling of contact radius along with shell thickness and radius could be predicted. Hence, tuning of shell thickness offers one convenient way of adjusting adhesion properties. A more general theory on the adhesion of vesicles
ACCEPTED MANUSCRIPT is presented by Seifert and co-workers.[332] They mainly focused on shape/shape changes and transitions from free to bound state. In a later publication shape equations were solved numerically.[333] An expression for a critical adhesion energy is derived and theoretical results are
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compared to the experimental data obtained from Elsner et al. showing good agreement. Wan and Liu worked out a model for adhesive contact mechanics of a thin-walled capsule to a flat substrate within
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linear elastic theory.[334] It is demonstrated that an increase of osmotic pressure can reduce contact
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area and even provoke detachment of the capsule from the substrate. Nolte and Fery introduced a method to align polyelectrolyte capsules on patterned substrates making use of electrostatic interactions.[335] This approach has been developed further to covalently bind the assembled capsules
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to the substrate.[336] By computational modeling, Alexeev et al. examined the fluid driven motion of a capsule on a substrate.[286, 289, 337] They found that besides stiffness and pattern of the substrate the
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mechanical properties of the microcapsules play an important role for the tuning of mutual adhesion. Based on these results concepts are introduced to selectively trap and burst the capsules[338] as well as to sort and guide them in a predetermined manner[339-341]. This opens an application perspective for,
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e.g., analytical devices for quality control regarding capsule mechanics or for a fractionation device
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allowing the extraction of capsules with desired mechanical properties from a given batch. Lastly, for an
VI) Conclusions
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in-depth study of shell adhesion, an exhaustive treatment of the topic can be found in [342].
Microcapsule mechanics is a fascinating topic, which has attracted attention from various scientific communities for many decades. Still, we are currently witnessing the dawn of a new era: Modern synthetic approaches like the layer-by-layer technique or other template-assisted self-assembly methods allow unprecedented control over geometrical parameters of capsules as well as on the composition of wall and interior. Consequently, mechanical properties like capsule stiffness in the small deformation range, buckling forces/pressures or burst forces / fracture strength can be adjusted accurately. This allows not only tailoring mechanical properties such that sufficient stability to withstand wear and tear in applications is ensured - rather mechanical properties and instabilities can be taken advantage of for introducing functionality. The present review focuses on novel possibilities and illustrates them by some selected examples from literature, without aiming for completeness of this highly dynamic field. Gaining control and further understanding of microcapsule mechanics requires a truly interdisciplinary approach. Therefore, the foundations in terms of suitable synthesis / assembly are introduced together with theoretical basics of microcapsules mechanics as well as an overview of experimental characterization
ACCEPTED MANUSCRIPT techniques with special emphasis on single microcapsule measurements. Thus, we hope to provide an
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entry point for interested researchers into this interdisciplinary field.
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References:
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Graphical abstract
ACCEPTED MANUSCRIPT Highlights: - This review focuses on the mechanical properties of microcapsules.
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- Ensemble and single-capsule measurement techniques are presented and compared. - Physical concepts are discussed describing and modeling shell deformation.
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- Application perspectives are outlined with capsule mechanics as key parameter.
