Aggregation kinetics and colloidal stability of functionalized nanoparticles Filippo Gambinossi, Steven E. Mylon, James K. Ferri PII: DOI: Reference:

S0001-8686(14)00242-5 doi: 10.1016/j.cis.2014.07.015 CIS 1469

To appear in:

Advances in Colloid and Interface Science

Received date: Revised date: Accepted date:

28 May 2014 30 July 2014 31 July 2014

Please cite this article as: Gambinossi Filippo, Mylon Steven E., Ferri James K., Aggregation kinetics and colloidal stability of functionalized nanoparticles, Advances in Colloid and Interface Science (2014), doi: 10.1016/j.cis.2014.07.015

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Aggregation kinetics and colloidal stability of

RI

PT

functionalized nanoparticles

Lafayette College, Department of Chemical and Biomolecular Engineering, Easton, Pennsylvania

NU

a

SC

Filippo Gambinossia, Steven E. Mylonb, and James K. Ferria*

(USA) 18042. E-mail: [email protected]; [email protected] Lafayette College, Department of Chemistry, Easton, Pennsylvania (USA) 18042. E-mail:

MA

b

AC CE P

TE

D

[email protected]

*To whom correspondence should be addressed: Prof. James K. Ferri James T. Marcus '50 Professor and Department Head Department of Chemical and Biomolecular Engineering Lafayette College Easton, Pennsylvania 18042 tel +1(610) 330-5820 fax +1(610) 330-5059 E-mail: [email protected]

1

ACCEPTED MANUSCRIPT ABSTRACT

MA

NU

SC

RI

PT

The functionalization of nanoparticles has primarily been used as a means to impart stability in nanoparticle suspensions. In most cases even the most advanced nanomaterials lose their function should suspensions aggregate and settle, but with the capping agents designed for specific solution chemistries, functionalized nanomaterials generally remain monodisperse in order to maintain their function. The importance of this cannot be underestimated in light of the growing use of functionalized nanomaterials for wide range of applications. Advanced functionalization schemes seek to exert fine control over suspension stability with small adjustments to a single, controllable variable. This review is specific to functionalized nanoparticles and highlights the synthesis and attachment of novel functionalization schemes whose design is meant to affect controllable aggregation. Some examples of these materials include stimulus responsive polymers for functionalization which rely on a bulk solution physicochemical threshold (temperature or pH) to transition from a stable (monodisperse) to aggregated state. Also discussed herein are the primary methods for measuring the kinetics of particle aggregation and theoretical descriptions of conventional and novel models which have demonstrated the most promise for the appropriate reduction of experimental data. Also highlighted are the additional factors that control nanoparticle stability such as the core composition, surface chemistry and solution condition. For completeness, a case study of gold nanoparticles functionalized using homologous block copolymers is discussed to demonstrate fine control over the aggregation state of this type of material. KEYWORDS:

AC CE P

TE

D

Aggregation kinetics, core-shell nanoparticles, colloidal stability, dynamic light scattering, functional polymers, nanoparticle functionalization

2

ACCEPTED MANUSCRIPT CONTENTS

AC CE P

TE

D

MA

NU

SC

RI

PT

1. Introduction 2. Synthetic approaches to nanoparticle functionalization 2.1. Overview 2.2. Direct vs. step-wise functionalization 2.3. Macromolecular encapsulation 2.3.1 Macromolecular encapsulation: ‘grafting-from’ strategy 2.3.2 Macromolecular encapsulation: ‘grafting-to’ strategy 2.3.3 Macromolecular encapsulation: ‘in-situ’ strategy 3. Aggregation kinetics and colloidal stability: experimental methods 3.1. Overview 3.2. Spectral turbidimetry (and other optical methods) 3.3. Time resolved dynamic light scattering (TR-DLS) 3.4. Fluorescence correlation spectroscopy (FCS) 4. Theoretical models: a brief overview 4.1. Favorable (fast) and unfavorable (slow) aggregation rate 4.2. Theoretical instability ratio 4.3. DLVO interaction potentials: core-shell approach 5. Core-shell composition and solution conditions: implication for colloidal stability 5.1. Effect of nanoparticle core 5.2. Effect of surface chemistry 5.3. Effect of solution condition 6. Case study. Programmable aggregation kinetics of Au@MeO2MAx-co-OEGMAy NPs: effect of surface chemistry, ionic strength and temperature 6.1. Overview 6.2 Aggregation kinetics for Au@(MeO2MAx-co-OEGMAy) NPs 6.3 Colloidal stability ratio and interparticle potential for Au@(MeO2MAx-co-OEGMAy) NPs 6.4 Summary 7. Closure 8. Acknowledgements 9. References

3

ACCEPTED MANUSCRIPT 1. INTRODUCTION Functionalized core-shell nanoparticles represent a growing class of materials which have a significant importance in diverse areas of science and technology, including water-oil separation, food

PT

processing, pharmaceutical formulation, biomedicine, energy storage, as well as for developing complex hierarchical systems [1-3]. The complexation between polymers and nanoparticles offers a good

RI

platform for engineering versatile hybrid structures with novel functionalities. One of the major

SC

challenges pertaining to all applications is the design of smart nanomaterials, whose colloidal stability

NU

can be easily controlled by an external trigger, such as pH, temperature or ionic strength. Depending on the particular application, dispersion stability or the kinetics of destabilization can be either a desired

MA

(material sensing, food processing) or an unwanted (waste-water treatment, water-oil separation, blood/brain barrier) effect.

D

This introduction highlights the impact of surface chemistry on the colloidal stability of core-shell

TE

nanoparticles for specific applications including emulsion and foam stabilization, drug-delivery, sensing

AC CE P

and actuation, and other technologies.

Emulsion and foam stabilizers. In general, amphiphilic polymers grafted on particle cores enhance fluid-fluid stability by increasing the interfacial energy and forming a mechanical barrier that prevents the coalescence of the dispersed phase. The potential to stabilize oil-water and air-water dispersions is of particular interest in applications such as oil recovery, cosmetics, pharmaceutical, agrochemicals and food processing [1, 4-8]. Polymer-coated nanoparticles can be used to control the release of encapsulated ingredients from an emulsified product or to manage the capture and release of water from crude oil. Recently, Calcagnile [1] and Nikje [9] presented flexible composite materials based on polyurethane foam functionalized with magnetic iron oxide nanoparticles, which can efficiently separate oil from water. These nanomaterials can recruit floating oil from polluted regions thereby purifying the aqueous phase.

4

ACCEPTED MANUSCRIPT Smart delivery systems. Hybrid core-shell nanoparticles can be utilized as nanocarriers for drugs, catalysts, and enzymes, because the polymer scaffold can be used to immobilize smaller particles or macromolecules [10-12]. In this respect, the use of living radical polymerization techniques (either in

PT

the ‘grafting from’ technique and for the synthesis of functionalized polymers) can be beneficial by helping to design polymer systems that can change dispersion characteristics to facilitate the reversible

RI

transport and release of drug molecules from aqueous to hydrophobic environments in response to a

SC

stimulus. Partially hydrophobic nanomaterials are of particular interest as smart delivery systems for

NU

biological membranes, catalysis, tissue engineering, and agrochemicals [13]. For example Guo et al. [14] grafted iron oxide nanoparticles with pH-responsive Poly(methyl methacrylate), PMMA, shell to

MA

selectively load anticancer drugs and deliver it to targeted cells. The PMMA in the polymer shell was used to provide the appropriate environment for loading of the drug at neutral pH. At pH i, j, and kiz is the dissociation rate constant of aggregates of size z. For short times, the aggregation kinetics can be approximated by the rate of doublet formation, which dominated over other higher order aggregate formation: dC1  k11C12  k12C1C2 dt dC 2 1  k11C12  k12C1C2 dt 2

(eq. 2)

Here C1 and C2 are respectively the number concentrations of monomer and doublet particles and k11 

and k12 are the forward and reverse rate constants. In case of irreversible association (i.e. no dissociation events), the increase in concentration of dimers is proportional to the product of the initial rate constant of aggregation, k11, and the square of the initial concentration of nanoparticle monomer, C0, simplifying equation (2):

10

ACCEPTED MANUSCRIPT dC2 1 dC1 1   k11C02 dt 2 dt 2

(eq. 3)

From equation (3) the instability ratio, W-1, under different solution conditions can be calculated by



the ratio of the rate constant for slow coagulation (unfavorable aggregation), (k11)slow to fast

11

slow

11

fast

RI

k  k 

(eq. 4)

SC

W 1 

PT

(nonrepulsive) aggregation, (k11)fast:

The resulting values for the instability ratio (0≤W-1≤1) represents the probability of association resulting from the collision of two colloidal particles.

NU



MA

The rate of aggregation, k11, of functionalized nanoparticles can be monitored using several experimental approaches. The most widely employed are optical methods such as turbidimetry, light

D

scattering (DLS, SLS), and fluorescence correlation spectroscopy (FCS). Each technique has its own

TE

advantages and disadvantages – no single technique is appropriate for all samples, especially under the

AC CE P

conditions of low concentration, high polydispersity, or sample complexity. Principles of operation as well as the benefits and drawbacks of the above mentioned techniques are discussed in the following sections. 3.2

Spectral turbidimetry

For diluted solutions (volume fraction < 10-4) spectral turbidimetry can be used to determine the particle size distribution (PSD) of suspensions composed of submicronic and micronic particles. [66] Turbidity has been used in the past to study the aggregation state of metal nanoparticles [67-69], and nanoemulsions [70]. In general the turbidity of a colloidal suspension can be defined as: [71, 72] 



   Cz t  z z1

(eq. 5)

where Cz is the number of aggregates of z particles per unit volume, and z is their total light scattering



cross section, which is dependent on the wavelength and on the ratio of the particle refractive index to

11

ACCEPTED MANUSCRIPT the surrounding medium refractive index. In the small time limit (t0) the time evolution of a suspension due to aggregation can be achieved by differentiating equation (5): d  dC dC    1 1   2 2 dt dt dt t0

(eq. 6)

(5) and (6), the aggregation rate can be deduced:

RI



PT

Here 1 and 2 are the optical cross sections of a single particle and a doublet. Combining equation (2),

SC

d  1       2  1k11C 20 dt t0 2 

(eq. 7)

and fast aggregation regimes:

W 1 

MA



NU

Then the instability ratio, W-1, can be obtained from the initial slope of the curve  vs. time under slow

d dt  d dt 

slow

D

fast

(eq. 8)

than measurement of the intensity of light scattered at a particular angle. [73]

AC CE P



TE

Benefits. Turbidity measurements using the spectrophotometer are less sensitive to multiple scattering

Drawbacks. In order to interpret the experimental results, turbidity measurements require calculation of the optical properties (cross-section) of the aggregates involved in the process. Not suitable for very diluted suspensions. Both the aggregation process and aggregate-like interaction are dependent on the aggregates’ morphology. 3.3

Time resolved dynamic light scattering (TR-DLS)

Time resolved dynamic light scattering (TR-DLS) is the most common method to determine the aggregation kinetics of colloidal particles. [65] It has been used to study the aggregation behavior of a wide range of engineered nanomaterials including quantum dots [74], metal nanoparticles [75-79], carbon nanotubes [80, 81], and solid lipid nanoparticles [82]. In this technique, the temporal evolution of the intensity fluctuations due to the Brownian motion of colloidal particles is used to measure the translational diffusion coefficient of the particles in suspensions. The effective aggregate size is calculated from the diffusion coefficient, D, using the Stokes-Einstein equation.[83] The measured 12

ACCEPTED MANUSCRIPT hydrodynamic radius of a coagulation suspension is an average of the hydrodynamic radii of the individual aggregates, weighted by their scattered light intensities. According to the Rayleigh-GansDebey (RGD) approximation, which is valid for particles that are relatively small compared to the

PT

wavelength of the laser light,[65] the temporal evolution of the average hydrodynamic radius, (dRH/dt), of the system is given by:

  1 R   R

RI

   H,2  H,1

(eq. 9)

SC

 I q 1 dRH  2   k11C02 1  2I1 q RH,0  dt  



NU

where I1(q) and I2(q) are the water vector q-dependent intensities of radiation scattered by monomers and dimers, respectively, RH,1 = f(RH,0) and RH,2 = 1.4f(RH,0) are the hydrodynamic radii of monomer and

MA

dimer, respectively, and RH,0 is the intitial monomeric nanoparticle radius. If dissociation events occur during the time of observation, however, k11 in equation (9) is replaced by

TE

16k113C02

    R

 2k21  4k11C0  k21 I 2 q I1 q 

H,1

RH ,2

2  



(eq. 10)

AC CE P

K eff 

D

the effective association constant, Keff: [84]

which is usually lower than the rate for an irreversible aggregation. By taking k12=0 limit of no



dissociation equation (10) correctly recovers the well-known result for the irreversible aggregation kinetics, i.e. Keff=k11.

From equation (9) the instability ratio, W-1, at different solution conditions is then calculated by dividing the slope obtained under slow coagulation over the slope obtained under fast (nonrepulsive) aggregation:

W 1 

dR dR

H H

 dt 

dt

slow

(eq. 11)

fast

Benefits. The determination of k11 by TR-DLS has been validated numerous times in the literature [65,



78, 80, 85-90]. Using conventional instrumentation, for moderate sized particles (RH > 30nm), this method is suitable for dilute suspensions; i.e. substantially less than that required for turbidity

13

ACCEPTED MANUSCRIPT measurements. When the most sensitive detectors are employed, this method can be applied to extremely dilute suspensions of even smaller particles. Drawbacks. DLS measurements are greatly biased by the presence of large aggregates or polydisperse

PT

solutions that can only be partially corrected by the algorithms of the DLS software. Both the aggregation process and aggregate-like interaction are dependent on aggregate morphology. At high

RI

electrolyte concentrations (high rate – fast regime) multiple scattering may occur which leads to a

SC

diffuse halo around the primary laser beam inside the cell and a reduced intercept of the autocorrelation

3.4

NU

function. Fluorescence correlation spectroscopy (FCS)

MA

In this approach, the particle/aggregate diffusion coefficient, D, is determined for fluorescently labeled particles passing through a laser-illuminated confocal volume (~1m3). Similar to DLS

D

technique, temporal fluctuations in the measured fluorescence intensity are used to derive an

TE

autocorrelation curve, which is related to the translational diffusion of the fluorophore through the

AC CE P

confocal volume. [91, 92] FCS has been used to determine the diffusion coefficients and aggregation behavior of QDs, nTiO2, and nZnO. [93-96] Benefits. This is a single or near single particle detection technique that determines a weight-averaged D under the conditions of the experiment. This gives FCS an important advantage over several other techniques for determining particle size, because it is generally not necessary to increase particle concentration in order to improve the analytical signal.[97] Bias is much less important than in DLS and the technique is much better suited to small particles and very diluted suspensions. Drawbacks. Diffusion coefficients are determined by calibrating the size and shape of the confocal volume with a standard dye. Additionally, nanoparticles need to be fluorescently labeled. The single particle detection of colloidal particles is limited by their photophysical properties, such as fluorescence intermittency and blinking. Blinking is manifested as finite episodes of laser induced fluorescence followed abruptly by long periods where no light is emitted. The effect appears not only to slow diffusion but to increase the probability of the particle entering the probe volume. [98, 99] 14

ACCEPTED MANUSCRIPT 4. Theoretical models: a brief overview 4.1 Favorable (fast) and unfavorable (slow) aggregation rate Fast aggregation rate. Under the approximation of von Smoluchowski [100], i.e. steady-state

PT

diffusion of the colloidal particles in the absence of interparticle interaction, the rate constant for the dimer formation in the fast or ‘diffusion-limited’ aggregation is given by:

fast



8kBT 3

(eq. 12)

SC

11

RI

k 

where kB is the Boltzman constant, T the absolute temperature, and  is the viscosity of the medium. Reversible aggregration has been proposed by Zaccone [84] and others [87, 101-105] to account for

NU



MA

experimental observations of fast aggregation rates, lower than Smoluchowski. Slow aggregation rate. Fuchs [106] provided a general expression for the slow or reaction-limited

D

aggregation, considering (k11)slow as the flux of colloids in a force field around a central particle under

8kBT 3 f h





 0





AC CE P

kslow  2RH

TE

the influence of their mutual interactions:

h 2RH

 T h



2

e

k BT

dh

 h 2  h  6  13  2 RH  RH  f h   h 2  h  6   4  RH  RH 



(eq. 13)

(eq. 14)

Here the interaction potential, (h), and the hydrodynamic retardation term [107], f(h), account for



the surface and viscous forces manifested between two spheres during mutual approach. Both terms are functions of the intersphere separation distance, h, and the particle size, RH.

15

ACCEPTED MANUSCRIPT 4.2 Theoretical instability ratio In using equation (13) for the instability ratio, however, the theoretical curve for W-1 as a function of

PT

the interaction energy is always lower than unity at low potentials, since the rapid rate of coagulation assumes that no attraction forces are in operation until the particles are in contact.

RI

To account for the attractive contribution to the interaction potential in rapid coagulation, and to

expression for the distance-dependent instability ratio: k BT

e

h 2R  f h e  h 2R   2

0

dh

H



 T h

k BT

2

0

MA

W 1 

 A h

NU





f h



SC

enable comparison between theory and experiments, McGown and Parfitt [108] derived the following

dh

D

H

(eq. 15)

particles. So defined, the instability ratio approaches to unity when the repulsion is entirely absent and is

AC CE P



TE

where (h) is the attraction potential energy, which depends on the geometry of the colloidal

expected to be more in accord with experimental reality. Details on the calculation of the contributions to the total interaction potential are shown in Section 4.3. Approximations for the calculation of the theoretical stability ratio. The theoretical instability ratio defined in equation (15) can be rewritten in the form:

1

W 1  2 0 e 

 T s 

k BT

(eq. 16)

ds

s  2

2

where s is the non-dimensional surface-to-surface distance defined by s=[(h/RH)-2], and (s) is the total



interparticle interaction energy. This relationship can be used to understand the behavior of the stability ratio with respect to the barrier against coagulation and to evaluate the physico-chemical properties of the dispersion. Because of the complexity of the interparticle interaction energy, the above task requires

16

ACCEPTED MANUSCRIPT numerical integration of equation (16). However, when the repulsion barrier is large, the expression for W-1 using asymptotic techniques can be expressed: 1  2k T 2 " B  s  T m

1

(eq. 17)

 T s m 

 k BT  e 2   s m  2 2

  



PT

W 1 

 



RI

Here sm is the value of s corresponding to the maximum in  and T" sm  T s 2 evaluated at s=sm. Other models: Maxwell-Boltzmann approach.

SC



Recently, an approach based on the Maxwell-

NU

Boltzmann distribution coupled with DLVO theory has  been developed to calculate the instability ratio of colloidal nanomaterials, including metal nanoparticles, polystyrene, carbon nanotubes, and graphite

MA

sheets.[109-111] Here we briefly summarize the main features of the model highlighting the main advantages with respect to the other approaches.

TE

D

This model considers the role of the binding energy, Eb=Emax-Emin, in aggregation kinetics and estimates the instability ratio W-1 as the ratio of the number of particles with kinetic energy exceeding

AC CE P

Eb, N, to the total number of particles with kinetic energy ranging from zero to infinity, N: 3

W

1



NE b  N0 







v

 m  2 mv 2 4   e 2kbT 

2k b T

   v dv



Eb

3

 m  2 mv 2  4   0 2k T  e  b 

v 2dv

2k b T

2

 0

e E E1 2dE E

12

e E dE

(eq. 18)

Here, m is the molecular mass, kb is the Boltzmann constant, T is the absolute temperature, v is the



velocity of random motion, and E is the random kinetic energy of nanoparticles. Since the denominator is constant, equation 19 symplifies to:

W 1  

 N    E e E E1 2dE b N

(eq. 19)

where  accounts for the drag effect on the kinetic energy distribution of nanoparticles and other



discrepancies of the DLVO prediction. To apply the Maxwell-Boltzmann distribution, the dispersed NPs are assumed to be Brownian particles with an average kinetic energy of 3kbT/2 in dilute systems.

17

ACCEPTED MANUSCRIPT With respect to equation (15) the modified instability ratio calculated with this model better accounts for the nanoscale transport of nanoparticles, which is governed by both interaction energy and random Brownian diffusion.

PT

4.3 DLVO interaction potentials: core-shell systems The total potential energy of interaction, (h), is according to classic Derjaguin-Landau-Verwey-

Here we also include other contributions to the interaction

SC

electrostatic (electrostatic) interactions.

RI

Overbeek (DLVO) theory [112, 113] is the sum of the attractive Van der Waals (vdW) and repulsive







NU

potential, such as hydration (hydration) and osmotic (osmotic) forces:





 h  vdW h  electrostatic h  hydration h  osmotic h

(eq. 20)



MA

A schematic of the DLVO interactions between two core-shell nanoparticles is shown in Scheme 3. Van der Waals potential. According to Vold and Vincent [114, 115] the van der Waals attraction

TE

D

potential for two identical nanoparticles of radius rcore coated with a homogenous polymer shell of thickness  can be calculated as the sum of the contributions from the shell – shell interaction, shell –



AC CE P

core interaction, and core – core interaction:







 vdW h   shellshell h  corecore h  coreshell h    2  2   h h 2   AW  AS H  ;1 AS  AC H ;1 2r  2  2r      1  core core           12 h  rcore   h  rcore  AW  AS   AS  AC  H ;  H ;      2r     core rcore  2rcore  2 2rcore  2   

 

 





(eq. 21)



where Ac, Aw, and As are the Hamaker constant for the particle core, water, and the particle shell and



H(x, y) is the unretarded geometrical function:

 

H x, y 

 x 2  xy  x  x y  2    2ln x 2  xy  x x 2  xy  x  y x  xy  x  y 

(eq. 22)

In the case that the separation distance, h, is small compared to the particle radius, rcore, i.e. x