Surface shear rheology of monolayers at the surface of water.

CIS-01345; No of Pages 10 Advances in Colloid and Interface Science xxx (2013) xxx–xxx

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Historical perspective

Surface shear rheology of monolayers at the surface of water D. Langevin ⁎ Laboratoire de Physique des Solides, Université Paris Sud 11, Bâtiment 510, 91405 Orsay, France

a r t i c l e

i n f o

Available online xxxx Keywords: Surface shear rheology Monolayers Surface of water

a b s t r a c t The knowledge of surface shear rheology is important to understand and model flow in systems where interfaces are present: multiphase flow, wetting, foaming and others. The topic has been investigated for more than 100 years, but the knowledge accumulated is still partial. The experimental devices used for the measurement of the viscoelastic parameters are delicate to operate and the response of the monolayers is complex, usually non-linear and time dependent. Furthermore, it is difficult to decouple from the response of the bulk liquid. Important discrepancies between microscopic and macroscopic methods were reported and remain to be clarified. The knowledge of shear properties does not suffice in general to achieve proper descriptions of the flow behavior and measurements of compression properties are needed as well. This paper presents examples taken from the literature and discusses the current level of understanding. © 2013 Elsevier B.V. All rights reserved.

Contents 1. 2. 3. 4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . Definition of surface shear rheological parameters . . . . . . Instruments for the measurement of the surface shear rheology Experiments . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Soluble monolayers . . . . . . . . . . . . . . . . . 4.2. Insoluble monolayers of fatty substances . . . . . . . 4.3. Polymer monolayers . . . . . . . . . . . . . . . . . 4.3.1. Insoluble polymer monolayers . . . . . . . . 4.3.2. Polyelectrolyte–surfactant mixed monolayers . 4.4. Protein monolayers . . . . . . . . . . . . . . . . . 4.5. Particles monolayers . . . . . . . . . . . . . . . . 5. Discussion and conclusion . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction Monolayers adsorbed at the surface of water are able not only to change the surface tension, but also to create a mechanical resistance to surface stresses. Although this had been remarked very early (in the ancient times, the sailors used oil to calm the waves on the sea), it was only about a century ago when Lord Rayleigh demonstrated that oily substances could form monolayers at the surface of water [1]. When these substances are partially soluble in water, it becomes difficult to evaluate the amount of the substance left at the surface. The issue was addressed by Gibbs who proposed a thermodynamic theory

⁎ Corresponding author.

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0 0 0 0 0 0 0 0 0 0 0 0 0

allowing to relate surface and bulk concentrations [2]. Langmuir used this description to compare soluble and insoluble layers of fatty acids and fatty alcohols. He introduced a method called the Langmuir balance in order to compress insoluble monolayers and to study the variation of surface pressure (decrease of surface tension produced by the monolayer) versus surface area [3]. He identified various types of twodimensional phases separated by phase transitions. These monolayers appeared therefore as interesting model systems for 2D phase transitions and many studies of insoluble monolayers followed. The resistance of a liquid surface to deformation was first discussed by Plateau who wanted to explain the resistance of soap films to rupture. He measured the difference in damping rates of a compass needle rotating in the surface and in the bulk liquid and proposed to interpret the results by introducing a surface viscosity [4]. In these experiments

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Please cite this article as: Langevin D, Surface shear rheology of monolayers at the surface of water, Adv Colloid Interface Sci (2013), http:// dx.doi.org/10.1016/j.cis.2013.10.030

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D. Langevin / Advances in Colloid and Interface Science xxx (2013) xxx–xxx

however, the deformations were mixed compression and shear deformations. Later on, Boussinesq proposed a theoretical framework distinguishing between compression and shear surface viscosities. His aim was to explain why fluid droplets settled slowly under gravity, behaving as hard spheres, while they were expected to settle much faster, due to fluid recirculation in their interior [5]. The existence of a surface viscosity in experiments performed with water was attributed to the adsorption of surface-active contaminants. These results stimulated much of the early experimental work on surface shear viscosity [6]. Later on, Levich [7] showed that the velocity reduction was rather due to surface tension gradients, i.e. a Marangoni effect arising from surface concentration gradients in the monolayer created by the flow. Levich was also able to solve the long standing issue of the anomalous damping of surface waves on water (sailors' problem) using the same ideas. He introduced a surface compression modulus E in order to quantify these effects. It was observed early that monolayers could be solid-like, so a surface shear viscosity was not sufficient to describe their response to stresses. Mouquin and Rideal introduced a surface shear elastic modulus G to interpret experiments done on fatty acids [8]. Many other studies followed, but the values measured were rather small, of the order of a few mN/m or less [9], incompatible with theories for two-dimensional solids [10]: G N 16πkBTm / Σ, where kB is the Boltzmann constant, Tm the melting temperature and Σ the area per molecule in the solid phase; with Tm = 300 K and Σ = 0.2 nm2/molecule, one gets G N 1 N/m. The invention of imaging techniques such as fluorescence microscopy [11] and Brewster-angle microscopy [12,13] allowed one to visualize the domains of the different phases in equilibrium and it was then realized that the solid phases were in general made of small solid domains surrounded by a residual fluid phase, so that the mechanical response to stresses was much less than expected. Experiments performed on single domains showed that the shear modulus was indeed compatible with the theory [14]. Many different types of solid structures were evidenced in insoluble monolayers of fatty substances both with imaging and X-ray scattering methods [15]. Although the structures of monolayers became well understood after the introduction of these imaging methods, their mechanical properties remain less explored, in particular the shear properties. In the case of soluble monolayers, the response to compression dominates over the response to shear: these monolayers are fluid-like, so the shear modulus is zero and the shear viscosity is much smaller than the compression viscosity, which includes the dissipation resulting from molecular exchanges between surface and bulk [7]. Furthermore, the surface shear viscosities are frequently smaller than the accuracy of most available instruments. Insoluble monolayers can have larger shear viscosities and were investigated more intensively. They include irreversibly adsorbed monolayers, made of polymers, proteins or particles. Commercial instruments became available in the recent years and the topic is now more active. Monolayers play important roles in many practical applications where the control of surface properties is requested: wetting, twophase flow including microfluidics, coating including Langmuir– Blodgett layers, foams, emulsions and others. The knowledge of surface rheology is then necessary to achieve the control desired. However, relating surface rheology and the phenomena observed is a difficult challenge, especially since responses to compression and shear are generally mixed up. To date, the behavior of soluble monolayers in several phenomena such as foam drainage [16] and coating with surfactant solutions [17] was clarified, but many others remain less well understood [18]. The role of surface shear rheology in phenomena involving insoluble layers is also poorly understood. In this review, we will first define the surface shear viscoelastic parameters and describe the instruments developed for their measurement. We will then present examples of measurements done with different types of monolayers at the surface of water. Some instruments can be used to investigate surface rheology at liquid–liquid interfaces, a conceptually identical topic. The study of oil/water interfaces, of interest

for the understanding of emulsions is quite active presently. It will not be addressed in this review excepted in the final discussion, when commenting the possible relevance of surface shear rheology in phenomena involving surface motion. 2. Definition of surface shear rheological parameters Strictly speaking, it is not possible to define a surface viscosity: viscosity is an integral of a velocity correlation function that diverges in two dimensions. However, although the variation of the physical properties across a surface between two fluids is sharp, it is not discontinuous, the width of the surface region being of order 1 nm. Gibbs proposed accordingly to define surface properties as excess properties [2]. The formalism of excess properties was applied later by Goodrich to define surface rheological parameters [19]. Let us consider for instance a monolayer at the surface of a liquid of viscosity η0 and submitted to a shear stress. If we chose z as the vertical direction, a velocity v along the x direction varying along y, the shear rate γ˙ is ∂v/∂y and the bulk shear stress is σ = η∂v/∂y, in the small shear rate limit, i.e. in the linear regime. Close to the surface the local viscosity varies and the shear stress can be described using a viscosity η(z) equal to η0 far from the surface and increasing close to the surface due to the presence of the monolayer (Fig. 1). The surface viscosity ηS can be obtained from the equation: Z0 ηS ¼

þ Z∞

½ηðzÞ−η0 dz− −∞

ηðzÞdz 0

where the position of the surface is the plane z = 0. This position is arbitrary, and is usually chosen so that the excess surface concentration of the liquid is zero. Typical values of surface viscosities of fluid monolayers (measured with the macroscopic methods described in Section 3) are of the order of 1 μN.s/m (1 μPa.m.s). This is equivalent to a local viscosity ηS/d, d being the thickness of the monolayer, hence to an equivalent local bulk viscosity of 103 Pa.s, i.e. 106 times larger than the water viscosity. Even fluid monolayers are therefore extremely viscous media. The elastic modulus G can be defined in the same way, using a shear deformation u along Ox, instead of a shear velocity v. The strain γ is then

Fig. 1. Schematic variation of the shear viscosity near the surface; the area between the curve and the lines η(z b 0) = η0 and η(z N 0) = 0 is the surface viscosity ηS.



∂u/∂y and the stress is σ = G ∂u/∂y, in the small strain limit, i.e. in the linear regime. When the timescale of the measurement is comparable to a relaxation time in the monolayer, both G and ηS are non-zero and time dependent, the monolayer is viscoelastic. A convenient description, valid in the linear regime, makes use of a frequency dependent complex modulus: G⁎(ω) = G′(ω) + iG″(ω) where G′ and G″ are the storage and loss modulus, respectively and ω is the frequency. These moduli are easily accessible in experiments where sinusoidal deformations are exerted. With the former notations: G* = G + iωηS. Viscoelastic systems generally behave as elastic solids at small strains, but flow at larger strains. When there is only one relaxation time τ0, G′ and G″ usually follow the Maxwell model: ′

G ðωÞ∝

ðωτ0 Þ2 1 þ ðωτ0 Þ2

and

″

G ðωÞ∝

ωτ0 : 1 þ ðωτ0 Þ2

ð1Þ

In the case of soft solids, the relaxation time usually decreases when the shear rate increases as •ν 1 1 ¼ þ Kγ0 ; τ τ0

ð2Þ

•

with γ 0 ¼ γ0 ω being the strain rate amplitude, K a phenomenological constant and ν a phenomenological positive exponent usually close to 1. The proposed scaling behavior (Eq. (2)) was investigated by Weitz and colleagues in soft bulk systems (gels, emulsions, foams). They showed that investigating shear rate variations in addition to frequency variations is a useful method to extend the range of frequencies probed, provided Eq. (2) holds. They called the method strain-rate frequency superposition (SRFS) [20]. The method has some drawbacks, as was discussed recently, and should be only used when the deviations to linear behavior are small [21]. 3. Instruments for the measurement of the surface shear rheology There are numerous methods allowing the measurement of surface shear viscoelastic parameters; details can be found in earlier reviews [6,22,23]. In the following, we will briefly describe the main types of devices. After the pioneering experiments of Plateau, many devices based on the motion of a float under a known stress were proposed. Magnetic floats, needles or disks are popular because they are easy to control using magnetic fields. A commercial instrument using a magnetic needle, in which small deformations can be detected (strains down to 10−7) is presently commercialized [24]. It allows determining both modulus and viscosity and visualizing eventual textural changes induced by the deformation. Another early method is the so called channel viscometer, applicable only to insoluble monolayers [25,26]. The method makes use of Langmuir troughs equipped with a fixed barrier pierced with a

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channel and a mobile barrier forcing the layer to flow through the channel towards an adjacent compartment (Fig. 2). The device is a 2D analog of a capillary viscometer: the surface viscosity is calculated from the time variation of the difference in surface pressures between the two compartments. Fig. 2 shows a velocity profile measured across the channel: while the dotted line represents the expected Poiseuille profile; the experiments are in agreement with a flatter profile, calculated taking into account the motion of the subphase. This illustrates one of the difficulties in surface viscosity measurements: the monolayer does not move independently of the liquid subphase, which motion needs to be accounted for. In the above example, the contribution of the monolayer was negligible, and the surface viscosity could not be measured. A convenient criterion makes use of the Boussinesq number B = ηS / (ηL), η being the bulk viscosity and L the characteristic size in the instrument used: the surface viscosity becomes measurable when B N 1. With η = 1 mPa.s and L = 1 mm, the measurable ηS are above 1 μN.s/m. Another early method is based in the measurement of the damping of a torsion pendulum oscillating in the surface. Oscillating disks, rings, bobs or needles have been used [28,29]. Devices such as bicones or du Nouy rings can now be mounted on commercial bulk rheometers [30] and allow exploring a larger range of frequencies and strains. Recently such a setup was modified to allow subphase exchange without disrupting the interface [31]. A double wall ring geometry was proposed, providing an improved accuracy [32]. An early and still employed simple method consists in looking at the motion of talc particles on the surface under the action of air currents [33]. This allows to qualitatively distinguish between fluid, viscous and viscoelastic monolayers. Following the idea, particle tracking techniques were recently developed. These methods have a much better sensitivity, because they involve large Boussinesq numbers. However, there are still very large unexplained discrepancies between the measurements made with these methods and the mechanical ones [34]. Let us finally mention a method introduced by Petkov et al. [35] and making use of the anisotropy of the elastic compression modulus when a solid monolayer is compressed uniaxially. The compression moduli in the directions respectively parallel and perpendicular to the compression, E// and E⊥ are such that: E== ¼ E þ G E⊥ ¼ E−G:

ð3Þ

E being the isotropic compression modulus. The method is only applicable if the relaxation times are longer than the time of the measurement. 4. Experiments Many determinations of surface shear viscoelastic parameters can be found in the literature. Large discrepancies appeared early, in particular for the surface viscosities. It was soon realized that in some of the early

Fig. 2. Left: scheme of a channel surface viscosimeter; right: velocity profile across the channel. Data from [27].



techniques, the deformations produced were not purely shear and were not free of compression deformation. The situation progressively clarified when better instruments became available and when corrections for bulk entrainment were properly made. It became also evident that the rheological parameters were frequently frequency dependent, because of relaxation processes in these dense media, and that the responses were frequently non-linear, i.e. the parameters depend upon the amplitude of the deformation. It is therefore only when measurements are made in the same conditions (frequency, amplitude) that results can be compared. In the following, we will present a selection of results obtained with different types of monolayers.

100

G', G'' (mPa m)

4

10

G' G'' G'Max G''Max

1

4.1. Soluble monolayers 0,1

Soluble monolayers adsorbed at the surface of water are obtained using fatty substances with short alkyl chains, such as decanoic acid, or classical surfactants, such as sodium dodecyl sulfate (SDS). A number of studies showed that the viscosity values were close to the limit of accuracy of the instruments, so that precise values of the surface shear viscosities were difficult to obtain. SDS monolayers were among the most studied: the measured values of the surface shear viscosity above the critical micellar concentration (cmc) where the monolayer density changes little) range from 2.3 μN.s/m (measured with a rotating wall knife edge) [36], 1.45 μN.s/m (drag of a small spherical float) [37] 0.6 μN.s/m (magnetic disk oscillating in a soap film) [38], 0.1 μN.s/m (deep channel viscometer) [39], 0.08 μN.s/m (transition in foam drainage regime) [16] and 0.036 μN.s/m (velocity profiles in the Plateau borders of draining foams) [40]. These values span an interval of two orders of magnitude and it is not easy to identify the source of discrepancies. One possibility would be to investigate if theses viscosities are frequency and shear rate dependent. The surface viscosities can be increased by adding an insoluble substance, for instance dodecanol with SDS. Above the cmc, the surface layers contain about one molecule of dodecanol par molecule of SDS, provided the amount of dodecanol is not too low (at least 2 wt.% with respect to SDS) [41]. In this case, again scattered values were measured, 100 μN.s/m [39], 5 μN.s/m [36] and 1.8 μN.s/m [16], without correlations with the amount of dodecanol (resp 0.4 wt.%, 0.1 wt.% and 1 wt.%). Other surfactant mixtures were reported recently to have high surface shear viscosities: mixtures of 0.33 wt.% sodium lauryl-dioxyethylene sulfate (SLES), 0.17 wt.% cocoamidopropyl betaine (CAPB), with or without 0.02 wt.% myristic acid, which viscosities decrease when the shear rate increases. The monolayers exhibit therefore shear thinning behavior [42]. The zero shear limits of the surface viscosity are 2.3 mN.s/m and 6.9 mN.s/m, without and with myristic acid, respectively. If surfactants of opposite charges are mixed, compact gel like layers can be obtained with non-zero shear moduli. An example is shown in Fig. 3 with mixed monolayers of myristic acid and cetyltrimethylammonium chloride (CTAC), studied using an Anton Paar rheometer equipped with a bicone [43]. One sees in Fig. 3 that at low frequencies the behavior of the monolayer is qualitatively similar to a Maxwell behavior, with a single relaxation time (Eq. (1)). The SFRS treatment of the data showed that Eq. (2) was fulfilled, with a relaxation time at rest τ0 ~ 6 s. The gel like monolayers become fluid above T ~ 53 °C (G′ ~ G″) and both G′ and G″ become very small above 65 °C. The temperature behavior is similar to that of the bilayers of the vesicles formed in the mixed bulk solution, which melt at temperatures around 55 °C. The melting temperature can therefore be identified with the melting temperature of the hydrocarbon chains of the surfactant molecules [44]. 4.2. Insoluble monolayers of fatty substances Insoluble layers of fatty substances behave as 2D systems and exhibit a variety of phases: gas, liquid, gel or solid. The liquid phases are generally called liquid expanded (LE) whereas the gel phase is called liquid

0,1

1

10

ω(s-1) Fig. 3. Oscillatory measurements of the surface shear storage G′ and loss moduli G″ for a mixed myristic acid-CTAC layer adsorbed at the water surface as a function of frequency at constant strain amplitude, γ0 = 0.01%. The experimental data has been fitted to a Maxwell model (lines). Adapted from Ref. [43].

condensed (LC). Note that the number of different phases can be quite large (15 for docosanoic acid) [15]. The monolayers have surface viscosities which are very low except in the denser phases. Little effort has been devoted to the topic until the theory of 2D melting was proposed by Kosterlitz and Thouless [10], after which experiments such as those of Abraham et al. [9] were undertaken. As explained in the introduction, the measured shear moduli were well below the theoretical prediction. The explanation came only when imaging methods became available and that the polycrystalline textures were revealed. Liquid condensed phases are gel-like, and more frequently homogeneous, hence reliable measurements can be made. In solid and LC phases, the hydrocarbon chains are ordered, whereas they are disordered (molten) in LE phases [15]. When the monolayers are made of fatty substances with hydrocarbon chains, the viscosity values measured in the LC phases are typically above 10 μN.s/m, whereas in the LE phases they are of the order of 0.1 μN.s/m or less. The viscosities of monolayers made of fluorinated substances were found between 100 and 1000 times larger than those of their hydrocarbon homologs [45]. In order to access the low viscosities of the LE phases, methods such as particle tracking methods [46] or monitoring the shape relaxation of domains in coexisting surface phases [47] have been used. Non-linear effects are more frequently observed in the denser phases as could be expected [48]. Lipids are a special class of fatty substances that were extensively studied in view of their potential interest in Biophysics. However, their response to shear stresses is weak, so existing measurements are still scarce. The surface rheology of dipalmitoyl phosphatidyl choline (DPPC) monolayers was measured with a torsion shear rheometer as a function of surface pressure and shown to be smaller than the instrument's accuracy excepted in the dense phases formed above a surface pressure of 20 mN/m [49]. More recently, Squires and coworkers improved the instrumental accuracy using magnetic nanodisks. They showed that just above the LE–LC transition, the LC phase possesses a small elastic modulus, of order 1 μN/m, attributed to the distorsion of the LC domains, as suggested by the fluorescence images of the monolayer [50]. Around a surface pressure of 10 mN/m, the yield strain is of the order of 10% and G″ N G′; ηS varies exponentially with surface pressure, reaching values of the order of 1 μN.s/m around a pressure of 12 mN/m. Above this pressure, the monolayer elastic modulus increases, signaling a possible transition towards a more condensed phase. Experiments done with a bicone by Espinosa et al. at the typical surface pressure in biological membranes (30 mN/m) are in qualitative agreement, although the measured values for G′ and G″ are about 100



times larger [51]. We will find later similar discrepancies between macroscopic and microscopic methods. The behavior of other lipids at the pressure of 30 mN/m was also investigated by Espinosa and coworkers. While many lipids form fluidlike monolayers (surface viscosities of the order of 10 μN.s/m), palmitoyl oleyl glycerol phosphatidyl choline (POPC) layers are more viscous (ηS ~ 1 N.s/m), DPPC layers are slightly viscoelastic, as seen before, and ceramides even form solid-like phases with high shear moduli (G′ ~ 50 mN/m). The 2-dimensional solids obtained with ceramides have a small Poisson ratio typical of solids (ν b 1) but they are softer than rigid crystals (for which ν = 0). Their yield strain is quite small, around 10−3, above which the monolayers undergo plastic deformations. When a uniaxial compression is performed, the compression elastic modulus is anisotropic, and depends on the orientation in which the surface pressure is measured compared to the direction of the compression [52]. Using the method of Petkov and coworkers, G values were obtained and found in agreement with those measured with the bicone. 4.3. Polymer monolayers Most polymers soluble in water being polyelectrolytes, the majority of existing studies on adsorbed layers were made with aqueous solutions of these polymers. A few studies deal with polyethylene oxide (PEO) and with small molecular weight species such as pluronics, which are generally considered as large surfactant molecules (and used as such), rather than as macromolecules. Because polyelectrolytes have charged monomers, these polymers are not in general surfaceactive and they do not adsorb at surfaces. In order to promote adsorption, surfactants of opposite charge can be added. Polyelectrolytes with hydrophobic backbones or hydrophobically modified polymers can however adsorb at the surface of water, even in the absence of added surfactant. Polymers insoluble in water can be deposited at the surface using a volatile solvent as for the insoluble monolayers made of small molecules described in Section 4.2. Most of the studies dealing with this class of monolayers were devoted to the understanding of polymer dynamics in two dimensions. Overall, the shear rheological studies of polymer monolayers are still scarce. 4.3.1. Insoluble polymer monolayers A classification of polymer monolayers into expanded or condensed monolayers was proposed by Crisp [53,54], and is similar to that of the fatty substances. Polymers with polar groups adopt extended conformations at the surface and the monolayers are of the expanded type. More hydrophobic polymers are in near collapsed conformations at the surface and the monolayers are of the condensed type. Later, de Gennes used scaling theories to predict that the chain radius of gyration should scale with the number of monomers in the chain N as RF ~ Nν, ν being the Flory exponent [55]. LE monolayers correspond to good solvent conditions and ν ~ 3/4. In this case, the chains are able to interpenetrate above the concentration Γ* at which the chains become in contact (Γ* = 1 / (πRF2)). Above Γ* (semidilute region) the chains form a gellike network with mesh size ξ. LC monolayers correspond to poor solvent conditions, for which ν ~ 0.5. In this case, the chains do not interpenetrate and behave more as individual disk-like particles. Above Γ*, these monolayers become glassy. For a recent review, see [56]. Using homemade shear rheometers, Sacchetti et al. [57] and more recently Barentin et al. [58] measured the shear viscosity of polymer monolayers in good-solvent conditions (such as PEO and polyvinyl acetate (PVAc)). They found that the shear viscoelastic coefficients are much smaller than the compression ones. The key idea for the understanding of this difference is that a large entropy is lost by the chains during compression, whereas no conformational change is caused by shear. As a consequence, the viscous relaxation is much faster in the case of a shear deformation. Shear rheology was used to investigate if reptation-like motion could be present in semi-dilute polymer monolayers. The concentration

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and molecular weight dependencies of the shear viscosity have been measured for PVAc [59] and polytertbutylacrylate (PtBA) [60]. The resistance to shear increases strongly with polymer concentration, as expected from a highly entangled system (G′ ~ Γ3 and G″ ~ Γ6). Other signatures for reptation are the absence of molecular weight dependence of G′, and the N3-dependence of the shear viscosity in PtBA layers above N = Ne, the minimum number of monomers allowing the chains to entangle (Fig. 4). In the PtBA case, Ne ~ 100, remarkably similar to the value found for bulk solutions. Fig. 4 shows that series of measurements done by particle tracking and mechanical methods follow the same scaling, despite order of magnitude differences in viscosity values [61]. Above Γ*, polymer monolayers in poor solvent conditions such as polymethylmethacrylate (PMMA) have a shear modulus that depends on the number of monomers N [62]. Linear N dependencies of the shear viscosities were reported for PMMA and other hydrophobic polymers [63,64]. Above Γ*, these monolayers are in a glassy state at room temperature, as evidenced by the finite shear modulus. When heated above a temperature Tg, the modulus G′ starts to decrease and the transition has been identified as a glass transition. Significant Tg variations were detected for different polymers, depending on their chemical nature [65]. The glass transition temperature Tg of these layers was also found to be much lower than the bulk value (Fig. 5). Whereas large changes in Tg are expected to occur with extremely thin films, of thicknesses of a few nm, when segmental motions are affected by the presence of limiting bulk phases, most existing experimental data correspond to thicker layers. The above results could therefore contribute to a better understanding of the glass transition.

4.3.2. Polyelectrolyte–surfactant mixed monolayers When surfactants and polymers are mixed in aqueous solutions, aggregates may form in bulk above a surfactant concentration called critical aggregation concentration (cac) [66]. The equilibrium surface tension of the mixed solutions exhibits a plateau after the cac, which origin is similar to that of the plateau observed after the critical micelle concentration (cmc) of pure surfactant solutions. Surface shear properties of a variety of these monolayers were qualitatively probed by Regismond et al. [67] using the motion of talc particles on the surface under the action of air currents. This allowed them to qualitatively distinguish between fluid, viscous and visco-elastic monolayers.

Fig. 4. Surface shear viscosity for monolayers of PtBA as a function of the chain length in a dense state (surface pressure: 16 mN/m). Open squares correspond to data obtained using particle tracking while the open circles were obtained from conventional oscillatory rheometers. Solid lines in both sets of data represent the scaling behavior of the shear viscosity with the molecular weight. Ne marks the critical chain length when entanglements between the polymer chains begin. After [61].


6


Fig. 5. Ratio of film-Tg to bulk-Tg versus layer thickness for the different polymers, open symbols. Closed symbols: thicker layers deposited on gold (h ≥ Rg). The lines represent the best fits to the empirical Keddie–Jones relationship. Adapted from [65].

One of the most complete studies concerns the mixed layers of dodecyl trimethyl ammonium bromide (DTAB) and sodium polystyrene sulfonate (PSS) for which the compression moduli were also measured [68]. The experiments were performed using magnetic needles. G′ and G″ were found to be non-zero only close to the concentration C0 where the amount of positive surfactant charges compensates the negative charges of the polymer in bulk, their maximum values being close to 1 mN/m. The surfactant–polymer bulk aggregates are then close to neutral and partly hydrophobic because of the polymer styrene groups and the surfactant chains: their bulk solubility is therefore limited, and surface adsorption is favored. G′ and G″ had very close values over the entire range of surfactant concentrations investigated, and G′ was higher than G″, which is characteristic of an elastic gel-like layer. Close to their maxima, G′ and G″ varied as G′ ~ ωn′ and G″ ~ ωn″, n′ and n″ being nearly equal and ranging between 0.3 and 0.6. In general, the lower the exponent n, the more solid-like the material is. Other series of experiments were done with polyacrylamide sulfonate (PAMPS), carboxymethylcellulose (CMC) and DNA in mixed solutions with DTAB. In these experiments, a rheometer equipped with a

bicone was used, allowing proving a wider range of strains, including the non-linear response. The study evidenced extremely large differences in shear behavior between mixed surface layers containing polyelectrolytes of different stiffness [31]. The layers containing DNA, which is the most rigid, are solid like and can even exhibit a brittle behavior in the region where the layers are thick (Fig. 6) [69]. The SFRS treatment showed that the scaling ω–γ˙ was obeyed and that the relaxation time varied with shear rate following Eq. (2). G′ is maximum close to the cac, also close to C0, after which precipitation started in the bulk solutions. The maximum value of G′ was found more than 10 times higher than G″ and about 100 times higher than for the PSS–DTAB system (80 mN/m instead of 1 mN/m). More flexible polyelectrolytes such as CMC lead to more viscoelastic layers (G′ ~ 0.3 mN/m, only 3 times higher than G″), and very flexible ones such as PAMPS to purely viscous layers. The monolayer shear response is therefore extremely sensitive to polymer stiffness. However, the viscosities are similar for all the layers, including the PSS system: ηS ~ 10 μN.s/m and a similar relaxation time of the order of tens of seconds was found in all the systems (excepted PAMPS–DTAB layers, which were too fluid). It should be stressed that these polyelectrolyte–surfactant mixed layers are metastable systems: once adsorbed, they behave as insoluble layers, and their structure may depend on the adsorption history. Marked hysteresis and non-linear behavior are frequent. Upon large applied strains, the layers thicken locally or fracture, depending on the type of polymer used. 4.4. Protein monolayers Protein monolayers were among the first for which surface viscosities were measured. Indeed, they frequently form very stiff layers able to immobilize small particles at the surface, an effect easily observable with the eye. In his review published in 1972, Joly quotes “Practically all the fundamental results on the mechanical properties of protein monolayers were obtained before 1955” [6]. Although these layers had been among the most studied at that time, many other studies followed however after the 70s, when new experimental tools became available [71]. Flexible proteins, such as β-casein, also called “soft” proteins, change conformation more easily than globular proteins, such as βlactoglobulin. They adsorb in slightly larger amounts at the surface

Fig. 6. Left: Interfacial stress as a function of strain for the DTAB–DNA surface layers; the frequency used is 1 Hz. The line has a slope 1 and indicates a linear regime. The horizontal arrows mark the onset of deviation to linearity, and correspond to the yield stress (after ref. [69]). Right: Brewster angle microscopy (BAM) picture of a sheared and fractured layer (after ref. [70]).



Fig. 7 shows the typical variation of G′ and G″ with γ0 obtained with a monolayer of silica nanoparticles at the air–water interface, which looks quite similar to the variation reported for three-dimensional soft solids (hard sphere suspensions, hydrogels, emulsions, foams) [20]. The frequency dependence of the moduli recorded at constant strain amplitude is also similar for these different systems: G″ is larger than G′ at low frequencies and lower at high frequencies with G″ being maximum at the crossover point. The SFRS method applies to these particle monolayers and Eq. (2) leads to a relaxation time τ0 of a few thousand seconds. The yield strain amplitude γY is quite high, 10%, much higher than for other nanoparticles (gold) adsorbed at an oil–water interface [86]. As for three-dimensional systems, the yield stress (σY) varies • with shear rate as: σY = σY0 + Aγ ν0 . When melting cycles are performed, it is only when the layer is allowed to heal during long times (comparable to τ0, a few thousands of seconds) that the initial modulus is recovered. The strain amplitude ′ dependence of the moduli after melting is also similar: G′ ~ γ0 −v and −v″ G″ ~ γ0 , with v′ ~ 2 v″ and depends on the particle hydrophobicity. This overall behavior is similar to that of three-dimensional soft solids.

5. Discussion and conclusion As can be seen from the results described above, the measurement of the shear response of monolayers at liquid surfaces evidences still today a number of contradictory results. For low molecular weight species, the response is weak, and can only be studied with very sensitive devices such as particle tracking methods (active and passive) introduced recently. However, huge discrepancies between the shear parameters measured with these devices and the more conventional surface rheometer are systematically found. The origin of these discrepancies needs to be clarified. It was proposed in a recent paper that the particle tracking experiments should be performed with tracers located below the surface: in this case, the coupling with the surface layer is weaker, but the results are compatible with those obtained using macroscopic techniques [87]. Apart from fundamental questions relative to specificities of twodimensional systems, such as 2D melting, the knowledge of the shear properties is needed to model the phenomena occurring when liquid surfaces are submitted to flow. The problem includes two-phase flow, wetting, spreading, coating, microfluidics, emulsification, foaming and others. In practice, situations where the surfaces are submitted to pure shear flows are not frequent. The surface deformation may also include compression, sometimes extension. Whereas surface compression

G' and G'' (Pa.m)

(typically 2–3 mg/m 2 instead of 1–2 mg/m 2 for the globular proteins). Flexible proteins also produce slightly larger surface pressures, and can potentially displace globular proteins from the surface: for instance β-casein can displace β-lactoglobulin. However, because of the quasi-irreversibility of the adsorption, the adsorbed layer is dominated in practice by the protein that presents itself first at the surface [72,73]. Proteins can also be displaced from the surface by surfactants, when the latter produce larger surface pressures. In the case of pure proteins, and in the absence of convective motion, the adsorption kinetics is much slower than predicted by diffusion mechanisms. After an initial diffusive step, a second long reorganization process takes place in the protein monolayer. The second process is in general longer for globular proteins such as β-lactoglobulin, because their partial unfolding at the surface requires greater energies. For concentrations of the order of 0.1 g/l, the process takes 1–2 h. It is faster for flexible proteins such as βcasein, which possesses little secondary structure even in solution. The degree of crowding in the surface layer has also a considerable influence on the degree of conformational change [72,73]. The lower the adsorbed amount, the more space the protein has to spread out at the surface, and hence the greater the opportunity for unfolding. Early adsorbing proteins tend to exhibit a large loss of activity and are poorly exchangeable with the bulk phase after adsorption. At still longer times, a third process takes place: surface gelification is observed, especially with the globular proteins. It is believed that upon partial unfolding, proteins develop attractive interactions and cross-links. Late adsorbing proteins tend to retain more activity, and can also participate in loosely held multilayers. The formation of multilayers gives rise to a very unusual mechanical behavior of drops: rigid skins form around the drops [74]. At the end of the whole adsorption process, the surface tension values are very similar for most proteins. The difference in shear parameters is much larger. The surface shear viscosity is of the order of 1 mN.s/m for flexible proteins, and 1 N.s/m for globular proteins [75]. This is much larger than surface viscosities of surfactant solutions (less than 1 μN.s/m). In the case of globular proteins, the shear parameters are very small during the first adsorption stages and reach large values (a few tens of mN/m) only after many hours, probably because they are associated to the third adsorption stage of surface gelification. A special class of proteins, hydrophobins, forms still more rigid layers, with elastic moduli around 200 mN/m and viscosities above 10 N.s/m, which decrease about linearly with frequency [76]. Microrheological techniques were applied recently to the study of protein layer aging. For comparable ages, the measured moduli and viscosities were orders of magnitude smaller than those obtained using conventional mechanical methods. Active and passive rheology also gave different results and this was attributed to non-linear response with the magnetic nanowire used [77]. The viscoelasticity of protein monolayers has been shown to deviate significantly from linearity, displaying a clear dependence on the magnitude of strain and strain rates [78,79]. Rigid protein layers can be even brittle and rupture even for moderate shear rate [78–81]. When surfactants are added and are able to replace the proteins at the surface, the shear viscoelasticity drops to much smaller values, although remaining larger than that of surfactant solutions, when the protein is still present at the surface. The effect on the compression parameters is similar, although much less spectacular [75].

7

G' G''

0.1

4.5. Particles monolayers 0.01

Particle monolayers at liquid interfaces are actively studied as model two-dimensional systems [82,83]. They exhibit solid-like phases that behave as soft solids [84–86]. For bulk soft solids and at low strain amplitude γ0, G′ is much larger than G″. Above a critical strain amplitude called yield strain amplitude γY, the solid melts, G″ exhibits a maximum and remains larger than G′ afterwards. Both moduli then follow power ′ ″ laws: G′ ~ γ0 −v and G″ ~ γ0 −v with v′ ~ 2 v″.

0.01

0.1

γ0 (%)

1

10

Fig. 7. Variation of viscoelastic moduli versus strain amplitude for a silica nanoparticle monolayer at the air–water surface. The particles are partially hydrophobic with radius ~ 10 nm. Γ = 50 mg/m2 and a frequency of 2 Hz, bicone device. After ref. [84].


8


Fig. 8. Streamlines of (a) arachidyl alcohol and (b) polyoctadecylmethacrylate (PODMA) through a 4:1 contraction. Arachidyl alcohol exhibits no measurable vortices, while PODMA shows large vortices in the salient corners. After ref. [89].

It has been postulated that coalescence of emulsions could be favored by the fracture of the protein layers at the drop surfaces [93]. The same phenomenon might occur for the solid DTAB–DNA mixed layers, which cannot stabilize foam films (films break after a few seconds), whereas the more viscoelastic PAMPS–DTAB layers give rise to very stable films [94]. It has been also reported that when viscoelastic skins are formed around drops when shrunken, coalescence appears inhibited [95]. It is rather easy to include both surface viscosities, compression and shear, to model flow in the presence of interfaces, since they frequently appear as a sum [88]. Including surface elasticity together with surface viscosity is a complex task from the numerical point of view. Further progresses are however desirable. In summary, despite more than 100 years of efforts, the field of surface shear rheology is still little explored. Progresses will be made when a better knowledge of the artifacts of the techniques will become available, especially when the discrepancies between microscopic and macroscopic methods will be clarified. The knowledge of shear properties will not suffice in general to achieve proper descriptions of the flow behavior and measurements of compression properties will be needed. Special care of frequency and amplitude dependencies will be necessary, as monolayers are frequently viscoelastic and present non-linear

6000

80

G' - BSA

BSA G' BSA G'' BSA + SDS G' BSA + SDS G''

60

5000

G', G'' (Pa)

Interfacial G', G'' (mN.m-1)

rheology has been extensively studied, little is known yet about surface extensional rheology [88]. An example is shown in Fig. 8, with a flow configuration including a contraction. A clear difference is seen between a Newtonian fatty alcohol monolayer and a non-Newtonian polymer monolayer [89]. In the case of soluble surfactant systems, the response to compression is usually much larger than the response to shear, especially in situations of confinement (when the surfactant available in bulk is less than the amount adsorbed at the surfaces and no bulk-surface exchanges can occur). The response to shear only dominates at high concentrations when bulk-surface exchanges are fast. These situations are found for instance in foam drainage [16], coating of plates with very soluble surfactants [17] or lifetime of antibubbles [42]. In the case of insoluble systems, the shear and compression viscoelastic parameters may have comparable values and it is very difficult to identify the role of the shear parameters in a general type of flow. Among the few existing hints of their important role, we can mention the rheological behavior of emulsions stabilized by proteins which follows closely the interfacial behavior (Fig. 9) [90,91] and the coalescence of bubbles covered by proteins [92]. Note that in the last case, bubble disproportionation was found rather correlated to the compression elasticity.

40 20

G' - BSA + SDS G'' - BSA

4000

G'' - BSA + SDS

3000 2000 1000

0

0

1

2

3

Shear stress

4

5

(mN.m-1)

6

7

0

1

10 100 Shear Stress (Pa)

1000

Fig. 9. Interfacial and bulk shear parameters, G′ and G″, measured for water–octane interfaces and emulsions made from bovine serum albumin (BSA), with and without SDS added. Data from [90].



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Surface dilational moduli of polymer and blended polymer monolayers spread at air-water interfaces.

Influence of Surface Morphology on the Shear-Induced Wear of Alkylsilane Monolayers: Molecular Dynamics Study.

Adsorption of water at the SrO surface of ruthenates.

Effect of surface elasticity on the rheology of nanometric liquids.

Spontaneous formation of lecithin bilayers at the air-water surface.

water interface.

Observation of pH-Induced Protein Reorientation at the Water Surface.

Surface organic monolayers control the hygroscopic growth of submicrometer particles at high relative humidity.

Surface freezing of water.

Surface Science. Stability at the surface.

Dilational surface elasticity of spread monolayers of polystyrene microparticles.

rutile TiO₂(110) interface.

Soft electrostatic repulsion in particle monolayers at liquid interfaces: surface pressure and effect of aggregation.

Surface shear-transformation zones in amorphous solids.

The Dynamic Surface Tension of Water.

Gray solitons on the surface of water.

pH and the surface tension of water.

Chemoresponsive Colloidosomes via Ag⁺ Soldering of Surface-Assembled Nanoparticle Monolayers.

Surface functionalization of organic semiconductor films by segregated monolayers.

water interface.

Self-assembled monolayers on a ferromagnetic permalloy surface.

Effect of dentin surface roughness on shear bond strength.

Recognition at the leaf surface.

water interface.