Neutron scattering study of depletion interactions in a colloid-polymer mixture

Influence of solvent quality on depletion potentials in colloid-polymer mixtures

As first explained by the classic Asakura-Oosawa (AO) model, effective attractive forces between colloidal particles induced by depletion of nonadsorbing polymers can drive demixing of colloid-polymer mixtures into colloid-rich and colloid-poor phases, with practical relevance for purification of water, stability of foods and pharmaceuticals, and macromolecular crowding in biological cells. By idealizing polymer coils as effective penetrable spheres, the AO model qualitatively captures the influence of polymer depletion on thermodynamic phase behavior of colloidal suspensions. In previous work, we extended the AO model to incorporate aspherical polymer conformations and showed that fluctuating shapes of random-walk coils can significantly modify depletion potentials [W. K. Lim and A. R. Denton, Soft Matter 12, 2247 (2016); J. Chem. Phys. 144, 024904 (2016)]. We further demonstrated that the shapes of polymers in crowded environments sensitively depend on solvent quality [W. J. Davis and A. R. Denton, J. Chem. Phys. 149, 124901 (2018)]. Here, we apply Monte Carlo simulation to analyze the influence of solvent quality on depletion potentials in mixtures of hard-sphere colloids and nonadsorbing polymer coils, modeled as ellipsoids whose principal radii fluctuate according to random-walk statistics. We consider both self-avoiding and non-self-avoiding random walks, corresponding to polymers in good and theta solvents, respectively. Our simulation results demonstrate that depletion of polymers of equal molecular weight induces much stronger attraction between colloids in good solvents than in theta solvents and confirm that depletion interactions are significantly influenced by aspherical polymer conformations.

Polymer-mediated interaction between nanoparticles during hydration and dehydration: a small-angle X-ray scattering study

Polymer-mediated interactions such as DNA-protein binding, protein aggregation, and filler reinforcement in polymers play crucial roles in many important biological and industrial processes. In this work, we report a detailed investigation of interactions between nanoparticles in the presence of high volume fractions of an adsorbing polymer. Small-angle X-ray scattering (SAXS) revealed the existence of a stable gel-like structure in the polymer-nanoparticle dispersion, whereby anchored polymer molecules on nanoparticles acted as bridging centres, while basic interactions between nanoparticles remained repulsive. Time-resolved SAXS measurements showed that the local volume fraction of nanoparticles increased during the drying of the dispersion owing to the shrinkage of the gel-like structure. Further, nanoparticle clusters in the dehydrated composite films showed percolated networks of nanoparticles, except for 5% loading that showed a phase-separated morphology as the volume fraction of nanoparticles remained lower than the percolation threshold. A significant restructuring of nanoparticle clusters occurred upon the hydration of nanocomposite films caused by the expansion of polymer networks induced by hydration forces. Temporal evolution of the volume fraction of nanoparticles during dehydration unveiled three distinct stages similar to the logistic growth function and this was attributed to the evaporation of free, intermediate, and bound water in the different stages. A plausible mechanism was elucidated based on the spring action analogy between anchored polymer chains and nanoparticles during hydration and dehydration processes.

Phase stability of dispersions of hollow silica nanocubes mediated by non-adsorbing polymers

Although there are theoretical predictions (Eur. Phys. J. E 41, 110 (2018)) for the rich-phase behaviour of colloidal cubes mixed with non-adsorbing polymers, a thorough verification of this phase behaviour is still underway; experimental studies on mixtures of cubes and non-adsorbing polymers in bulk are scarce. In this paper, mixtures of hollow silica nanocubes and linear polystyrene in N,-N-dimethylformamide are used to measure the structure factor of the colloidal cubes as a function of non-adsorbing polymer concentration. Together with visual observations these structure factors enabled us to assess the depletion-mediated phase stability of cube-polymer mixtures. The theoretical and experimental phase boundaries for cube-depletant mixtures are in remarkable agreement, despite the simplifications underlying the theory employed.

Stratification of Colloidal Particles on a Surface: Study by a Colloidal Probe Atomic Force Microscopy Combined with a Transform Theory

Colloidal probe atomic force microscopy (CP-AFM) can be used for measuring force curves between the colloidal probe and the substrate in a colloidal suspension. In the experiment, an oscillatory force curve reflecting the layer structure of the colloidal particles on the substrate is usually obtained. However, the force curve is not equivalent to the interfacial structure of the colloidal particles. In this paper, the force curve is transformed into the number density distribution of the colloidal particles as a function of the distance from the substrate surface using our newly developed transform theory. It is found by the transform theory that the interfacial stratification is enhanced by an increase in an absolute value of the surface potential of the colloidal particle, despite a simultaneous increase in a repulsive electrostatic interaction between the substrate and the colloidal particle. To elucidate the mechanism of the stratification, an integral equation theory is employed. It is found that crowding of the colloidal particles in the bulk due to the increase in the absolute value of the surface potential of the colloidal particle leads to pushing out some colloidal particles to the wall. The combined method of CP-AFM and the transform theory (the experimental-theoretical study of the interfacial stratification) is related to colloidal crystallization, glass transition, and aggregation on a surface. Thus, the combined method is important for developments of colloidal nanotechnologies.

Influence of polymer shape on depletion potentials and crowding in colloid-polymer mixtures

Depletion-induced interactions between colloids in colloid-polymer mixtures depend in range and strength on size, shape, and concentration of depletants. Crowding by colloids in turn affects shapes of polymer coils, such as biopolymers in biological cells. By simulating hard-sphere colloids and random-walk polymers, modeled as fluctuating ellipsoids, we compute depletion-induced potentials and polymer shape distributions. Comparing results with exact density-functional theory calculations, molecular simulations, and experiments, we show that polymer shape fluctuations play an important role in depletion and crowding phenomena.

Depletion stabilization in nanoparticle-polymer suspensions: multi-length-scale analysis of microstructure

We study the mechanism of depletion stabilization and the resultant microstructure of aqueous suspensions of nanosized silica and poly(vinyl alcohol) (PVA). Rheology, small-angle light scattering (SALS), and small-angle X-ray scattering (SAXS) techniques enable us to analyze the microstructure at broad length scale from single particle size to the size of a cluster of aggregated particles. As PVA concentration increases, the microstructure evolves from bridging flocculation, steric stabilization, depletion flocculation to depletion stabilization. To our surprise, when depletion stabilization occurs, the suspension shows the stabilization at the cluster length scale, while maintaining fractal aggregates at the particle length scale. This sharply contrasts previously reported studies on the depletion stabilization of microsized particle and polymer suspensions, which exhibits the stabilization at the particle length scale. On the basis of the evaluation of depletion interaction, we propose that the depletion energy barrier exists between clusters rather than particles due to the comparable size of silica particle and the radius gyration of PVA.

Structure and interaction in the polymer-dependent reentrant phase behavior of a charged nanoparticle solution

Small-angle neutron scattering (SANS) studies have been carried out to examine the evolution of interaction and structure in a nanoparticle (silica)-polymer (polyethylene glycol) system. The nanoparticle-polymer solution interestingly shows a reentrant phase behavior where the one-phase charged stabilized nanoparticles go through a two-phase system (nanoparticle aggregation) and back to one-phase as a function of polymer concentration. Such phase behavior arises because of the nonadsorption of polymer on nanoparticles and is governed by the interplay of polymer-induced attractive depletion with repulsive nanoparticle-nanoparticle electrostatic and polymer-polymer interactions in different polymer concentration regimes. At low polymer concentrations, the electrostatic repulsion dominates over the depletion attraction. However, the increase in polymer concentration enhances the depletion attraction to give rise to the nanoparticle aggregation in the two-phase system. Further, the polymer-polymer repulsion at high polymer concentrations is believed to be responsible for the reentrance to one-phase behavior. The SANS data in polymer contrast-matched conditions have been modeled by a two-Yukawa potential accounting for both repulsive and attractive parts of total interaction potential between nanoparticles. Both of these interactions (repulsive and attractive) are found to be long range. The magnitude and the range of the depletion interaction increase with the polymer concentration leading to nanoparticle clustering. At higher polymer concentrations, the increased polymer-polymer repulsion reduces the depletion interaction leading to reentrant phase behavior. The nanoparticle clusters in the two-phase system are characterized by the surface fractal with simple cubic packing of nanoparticles within the clusters. The effect of varying ionic strength and polymer size in tuning the interaction has also been examined.

Small-angle neutron scattering study of structure and interaction of nanoparticle, protein, and surfactant complexes

Small-angle neutron scattering (SANS) measurements have been carried out from the multicomponent system composed of Ludox HS40 silica nanoparticle, bovine serum albumin (BSA) protein, and sodium dodecyl sulfate (SDS) surfactant in an aqueous system under the solution condition that all the components are negatively charged. Although the components are similarly charged, strong structural evolutions among them have been observed. The complexes of different components in pairs (nanoparticle-protein, nanoparticle-surfactant, and protein-surfactant) have been examined to correlate the role of each component in the three-component nanoparticle-protein-surfactant system. The nanoparticle-protein system shows depletion interaction induced aggregation of nanoparticles in the presence of protein. Both nanoparticle and surfactant coexist individually in a nanoparticle-surfactant system. In the case of a protein-surfactant system, the cooperative binding of surfactant with protein leads to micelle-like clusters of surfactant formed along the unfolded protein chain. The structure of the three-component (nanoparticle-protein-surfactant) system is found to be governed by the synergetic effect of nanoparticle-protein and protein-surfactant interactions. The nanoparticle aggregates coexist with the structures of protein-surfactant complex in the three-component system. The nanoparticle aggregation as well as unfolding of protein is enhanced in this system as compared to the corresponding two-component systems.

Drying of a charge-stabilized colloidal suspension in situ monitored by vertical small-angle X-ray scattering

We report a first application of vertical small-angle X-ray scattering to investigate the drying process of a colloidal suspension by overcoming gravity related restrictions. From the observation of the drying behavior of charge-stabilized colloidal silica in situ, we find the solidification of the colloidal particles exhibits an initial ordering, followed by a sudden aggregation when they overcome an electrostatic energy barrier. The aggregation can be driven not only by capillary pressure but also by thermal motion of the particles. The dominating contribution is determined by the magnitude of the energy barrier at the transition, which significantly decreases during drying due to an increased ionic strength.

Block-copolymer-induced long-range depletion interaction and clustering of silica nanoparticles in aqueous solution

Small-angle neutron scattering (SANS) has been carried out to examine the block-copolymer-induced depletion interaction of charged silica nanoparticles in aqueous solution. The measurements have been performed on fixed concentrations (1 and 10 wt. %) of anionic Ludox silica nanoparticles having sizes of 8 and 16 nm in the presence of 0.1M NaCl and varying concentration of polyethylene oxide-polypropylene oxide-polyethylene oxide P85 [(EO)(26)(PO)(39)(EO)(26)] block copolymer. The presence of the block copolymer induces an attractive depletion interaction between charge-stabilized nanoparticles. The effective interaction of silica nanoparticles is modeled by a combination of two Yukawa potentials accounting for attractive depletion and repulsive electrostatic forces. The depletion interaction is found to be a long-range attraction whose magnitude and range increase with block-copolymer concentration. The depletion interaction is further enhanced by tuning the self-assembly of the block copolymer through the variation of temperature. The increase of the depletion interaction ultimately leads to clustering of nanoparticles and is confirmed by the presence of a Bragg peak in the SANS data. The positioning of the Bragg peak suggests simple-cubic-type packing of particles within the clusters. The scattering from the clusters in the low-Q region is governed by the Porod scattering, indicating that clusters are quite large (order of microns). The depletion interaction is also found to be strongly dependent on the size of the nanoparticles.

Homopolymer induced aggregation of poly(ethylene oxide)n-b-poly(butylene oxide)m polymersomes

We have studied the addition of poly(ethylene oxide) homopolymer (PEO) to a range of polymersome dispersions composed of amphiphilic di- and triblock copolymers. A number of E(n)B(m) E(n)B(m)E(n) and B(m)E(n)B(m) (E = poly(ethylene oxide) B = poly(butylene oxide)) block copolymers of varying molecular weights that spontaneously form polymersomes in water were investigated. This resulted in the aggregation of the dispersed polymersomes by two mechanisms, PEO adsorption or depletion interactions, and is shown to be dependent on PEO concentration. The aggregation kinetics and the resultant structures were analyzed by dynamic light scattering (DLS), small-angle X-ray scattering (SAXS) and scanning electron microscopy (SEM). There is a critical relationship between the polymersome corona thickness t and the PEO radius of gyration R(g), where R(g) must equal t to induce aggregation. This phenomenon has been reported with small self-assembling surfactants such as sodium dodecyl sulfate, but here we show an insight into how this transposes into much larger block copolymer systems which show great promise as biomimetic delivery vectors for controlled release.

A structural comparison of models of colloid-polymer mixtures

We study the structure of colloidal fluids with reference to colloid-polymer mixtures. We compare the one-component description of the Asakura-Oosawa (AO) idealization of colloid-polymer mixtures with the full two-component model. We also consider the Morse potential, a variable range interaction, for which the ground state clusters are known. Mapping the state points between these systems, we find that the pair structure of the full AO model is equally well described by the Morse potential and the one-component AO approach. We employ a recently developed method to identify in the bulk fluid the ground state clusters relevant to the Morse potential. Surprisingly, when we measure the cluster populations, we find that the Morse fluid is significantly closer the full AO fluid than the one-component AO description.

Low energy methods of phase separation in colloidal dispersions and microemulsions

The majority of work on phase separation of colloidal systems has been concerned with the energy intensive approaches such as ultracentrifugation, solvent evaporation, changes of temperature and pressure etc. However, in modern nanotechnology it is desirable to minimize environmental impact in order to achieve separation and recovery of colloidal products. In this review recent research on phase separation methods, requiring relatively lower energy consumption are summarized. These include polymer-, solvent- and photo-induced approaches to phase separation.

Testing the scaling behavior of microemulsion-polymer mixtures

The phase behavior and structural properties of "protein limit" mixtures of small (radius 20-30 A) water-in-oil microemulsion droplets (colloids) and large (radius 130-580 A) nonadsorbing polymer chains have been investigated. Accepted theoretical scaling relations for describing correlations have been applied and do not account fully for the observations; solvency effects may account for the deviations. The polymer/colloid size ratio has been varied from around 4 to 19 by using three different molecular weights of polyisoprene. Small-angle neutron scattering (SANS) has been used to determine partial structure factors (PSF) through contrast variation. The structure factors describing colloid-colloid interactions for the three polymers at fixed polymer concentration are shown to exhibit the same scaling behavior as the phase boundaries, provided that samples are sufficiently far from the demixing phase transition. The structure factors show a dramatic increase at low wavevectors on approaching the phase boundary, and behavior in this region does not obey expected scaling relations. By calculating effective polymer Flory-Huggins parameters, the effect of apparent solvent properties on adding microemulsion are shown to be less dramatic for the higher molecular weight polymers. This study extends previous work carried out on microemulsion-polymer mixtures.

Time-resolved in situ small-angle X-ray scattering study of silica particle formation in nonionic water-in-oil microemulsions

The formation of silica particles by the ammonia-catalyzed hydrolysis of tetraethyl orthosilicate (TEOS) in the polyoxyethylene (5) nonylphenyl ether (NP-5)/cyclohexane/water microemulsion system was investigated by time-resolved small-angle X-ray scattering (SAXS). The SAXS data could be modeled as a combination of two species where one describes the silica-particle containing microemulsion droplets and the other the reverse droplets. The analysis allowed the determination of the evolution of the system of particles of silica and reverse droplets. A model of nucleation and growth of the silica particles is confirmed and the volume fraction versus time data for the silica particles is in agreement with first order kinetics with respect to TEOS concentration. Moreover to describe the long time evolution of the system, a correlation among the silica particles has been taken into account by introducing a structure factor with a local silica volume fraction eta = 0.1. This high local density is 2 orders of magnitude larger than the global silica fraction and can be explained in terms of depleting interaction.

Gold nanoparticles decorated with oligo(ethylene glycol) thiols: protein resistance and colloidal stability

The interactions between proteins and gold colloids functionalized with protein-resistant oligo(ethylene glycol) (OEG) thiol, HS(CH2)11(OCH2CH2)6OMe (EG6OMe), in aqueous solution have been studied by small-angle X-ray scattering (SAXS) and UV-vis spectroscopy. The mean size, 2R, and the size distribution of the decorated gold colloids have been characterized by SAXS. The monolayer-protected gold colloids have no correlations due to the low volume fraction in solution and are stable in a wide range of temperatures (5-70 degrees C), pH (1.3-12.4), and ionic strength (0-1.0 M). In contrast, protein (bovine serum albumin) solutions with concentrations in the range of 60-200 mg/mL (4.6-14.5 vol %) show a pronounced correlation peak in SAXS, which results from the repulsive electrostatic interaction between charged proteins. These protein interactions show significant dependence on ionic strength, as would be expected for an electrostatic interaction (Zhang et al. J. Phys. Chem. B 2007, 111, 251). For a mixture of proteins and gold colloids, the protein-protein interaction changes little upon mixing with OEG-decorated gold colloids. In contrast, the colloid-colloid interaction is found to be strongly dependent on the protein concentration and the size of the colloid itself. Adding protein to a colloidal solution results in an attractive depletion interaction between functionalized gold colloids, and above a critical protein concentration, c*, the colloids form aggregates and flocculate. Adding salt to such mixtures enhances the depletion effect and decreases the critical protein concentration. The aggregation is a reversible process (i.e., diluting the solution leads to dissolution of aggregates). The results also indicate that the charge of the OEG self-assembled monolayer at a curved interface has a rather limited effect on the colloidal stabilization and the repulsive interaction with proteins.

Depletion interactions: a new control parameter for the self-assembly of diblock copolymer micelles

Small angle neutron scattering was performed on disordered mixtures of nonadsorbing homopolymer (A) chains and diblock (A-B) copolymer micelles in an A selective solvent. Increasing the molecular weight or concentration of A led to an increase in the aggregation number, and a decrease in the effective hard-sphere diameter of the micelles. Furthermore an intermicellar attractive force developed, which was successfully modeled by the Asakura-Oosawa depletion potential. Via an alternative model we also extracted information about mesoscopic clusters of micelles formed due to this attractive force.

Measuring colloidal interactions with confocal microscopy

We use confocal laser scanning microscopy to measure interactions in colloidal suspensions. By inverting the radial distribution function, determined by tracking the particle coordinates, we obtain the effective interaction between the colloidal particles. Although this method can be applied to arbitrary colloidal interactions, here we demonstrate its efficacy with two well-known systems for which accurate theories are available: a colloid-polymer mixture and binary hard spheres. The high sensitivity of this method allows for the precise determination of complex interactions, as exemplified, for example, by the accurate resolution of the oscillatory effective potential of the binary hard sphere system. We argue that the method is particularly well suited for the determination of attractive forces.

Colloid-polymer mixtures in the protein limit

This review discusses the structure and phase behaviour of mixtures of colloidal particles and non-adsorbing polymers in the protein limit of large polymers and small colloids. The vast majority of work on colloid-polymer mixtures has been concerned with the colloid limit of large colloidal particles and small polymer chains. In this regime, the diameter of the colloidal particles, , is larger than the characteristic size of the polymer-taken as twice their radius of gyration, . The opposite limit, of size ratios , is called the protein limit due to the common practice of adding polymer to protein solutions in order to aid protein crystallisation. Theoretical predictions for systems in the protein limit are considered briefly and then the main focus is on recent experimental studies of mixtures in the protein limit.

How does solvent molecular size affect the microscopic structure in polymer solutions?

Monte Carlo simulation has been used to investigate the effects of linear solvent molecular size on polymer chain conformation in solutions. Increasing the solvent molecular size leads to shrinkage of the polymer chains and increase of the critical overlap concentrations. The root-mean-square radius of gyration of polymer chains (R(g)) is less sensitive to the variation of polymer concentration in solutions of larger solvent molecules. In addition, the dependency of R(g) on polymer concentration under normal solvent conditions and solvent molecular size is in good agreement with scaling laws. When the solvent molecular size approaches the ideal end-to-end distance of the polymer chain, an extra aggregation of polymer chains occurs, and the solvent becomes the so-called medium-sized solvent. When the size of solvent molecules is smaller than the medium size, the polymer chains are swollen or partially swollen. However, when the size of solvent molecules is larger than the medium size, the polymer coils shrink and segregate, enwrapped by the large solvent molecules.

Small angle neutron scattering study of sodium dodecyl sulfate micellar growth driven by addition of a hydrotropic salt

The structures of aggregates formed in aqueous solutions of an anionic surfactant, sodium dodecyl sulfate (SDS), with the addition of a cationic hydrotropic salt, p-toluidine hydrochloride (PTHC), have been investigated by small angle neutron scattering (SANS). The SANS spectra exhibit a pronounced peak at low salt concentration, indicating the presence of repulsive intermicellar interactions. Model-independent real space information about the structure is obtained from a generalized indirect Fourier transformation (GIFT) technique in combination with a suitable model for the interparticle structure factor. The interparticle interaction is captured using the rescaled mean spherical approximation (RMSA) closure relation and a Yukawa form of the interaction potential. Further quantification of the geometrical parameters of the micelles was achieved by a complete fit of the SANS data using a prolate ellipsoidal form factor and the RMSA structure factor. The present study shows that PTHC induces a decrease in the fractional charge of the micelles due to adsorption at the micellar surface and consequent growth of the SDS micelles from nearly globular to rodlike as the concentration of PTHC increases.

Depletion-induced phase separation in colloid-polymer mixtures

Phase separation can be induced in a colloidal dispersion by adding non-adsorbing polymers. Depletion of polymer around the colloidal particles induces an effective attraction, leading to demixing at sufficient polymer concentration. This communication reviews theoretical and experimental work carried out on the polymer-mediated attraction between spherical colloids and the resulting phase separation of the polymer-colloid mixture. Theoretical studies have mainly focused on the limits where polymers are small or large as compared to the colloidal size. Recently, however, theories are being developed that cover a wider colloid-polymer size ratio range. In practical systems, size polydispersity and polyelectrolytes (instead of neutral polymers) and/or charges on the colloidal surfaces play a role in polymer-colloid mixtures. The limited amount of theoretical work performed on this is also discussed. Finally, an overview is given on experimental investigations with respect to phase behavior and results obtained with techniques enabling measurement of the depletion-induced interaction potential, the structure factor, the depletion layer thickness and the interfacial tension between the demixed phases of a colloid-polymer mixture.

Macromolecular theory of solvation and structure in mixtures of colloids and polymers

The structural and thermodynamic properties of mixtures of colloidal spheres and nonadsorbing polymer chains are studied within a general two-component macromolecular liquid state approach applicable for all size asymmetry ratios. The dilute limits, when one of the components is at infinite dilution but the other concentrated, are presented and compared to field theory and to models that replace polymer coils with spheres. Whereas the derived analytical results compare well, qualitatively and quantitatively, with mean-field scaling laws where available, important differences from "effective sphere" approaches are found for large polymer sizes or semidilute concentrations.

Structure and dynamics of concentrated dispersions of polystyrene latex spheres in glycerol: static and dynamic x-ray scattering

X-ray photon correlation spectroscopy and small-angle x-ray scattering measurements are applied to characterize the dynamics and structure of concentrated suspensions of charge-stabilized polystyrene latex spheres dispersed in glycerol, for volume fractions between 2.7% and 52%. The static structures of the suspensions show essentially hard-sphere behavior. The short-time dynamics shows good agreement with predictions for the wave-vector-dependent collective diffusion coefficient, which are based on a hard-sphere model [C. W. J. Beenakker and P. Mazur, Physica A 126, 349 (1984)]. However, the intermediate scattering function is found to violate a scaling behavior found previously for a sterically stabilized hard-sphere suspension [P. N. Segre and P. N. Pusey, Phys. Rev. Lett. 77, 771 (1996)]. Our measurements are parametrized in terms of a viscoelastic model for the intermediate scattering function [W. Hess and R. Klein, Adv. Phys. 32, 173 (1983)]. Within this framework, two relaxation modes are predicted to contribute to the decay of the dynamic structure factor, with mode amplitudes depending on both wave vector and volume fraction. Our measurements indicate that, for particle volume fractions smaller than about 0.30, the intermediate scattering function is well described in terms of single-exponential decays, whereas a double-mode structure becomes apparent for more concentrated systems.

Depletion interaction of casein micelles and an exocellular polysaccharide

Casein micelles become mutually attractive when an exocellular polysaccharide produced by Lactococcus lactis subsp. cremoris NIZO B40 (hereafter called EPS) is added to skim milk. The attraction can be explained as a depletion interaction between the casein micelles induced by the nonadsorbing EPS. We used three scattering techniques (small-angle neutron scattering, turbidity measurements, and dynamic light scattering) to measure the attraction. In order to connect the theory of depletion interaction with experiment, we calculated structure factors of hard spheres interacting by a depletion pair potential. Theoretical predictions and all the experiments showed that casein micelles became more attractive upon increasing the EPS concentration.

Analysis of Attractive Interactions between Latex Particles in the Presence of Nonadsorbing Polymers by Turbidimetry

The analysis of attractive forces between latex particles by scattering measurements is reconsidered. The change effected on the structure factor S(q) (q = (4pin0/lambda0)sin(θ/2), where θ is the scattering angle, n0 is the refractive index of the medium, and lambda0 is the wavelength in vacuo) of a suspension of latex particles by weak attractions is considered in terms of the HMSA-integral equation theory as presented recently by Bergenholtz et al. (1996, Mol. Phys. 87, 331). Model calculations using this approach show that turbidimetry is highly suitable to obtain quantitative information on attractive forces between the latex particles. The method of analysis developed here is applied to previous turbidimetric data obtained from mixtures of a polystyrene latex and a nonadsorbing polymer, hydroxyethylcellulose (HEC) (1997, Langmuir 13, 551). Here the addition of HEC leads to attractive depletion forces between the PS particles by the nonbalanced osmotic pressure of the polymeric HEC molecules. The turbidimetric data which are not afflicted by multiple scattering can be analyzed quantitatively in terms of an Asakura-Oosawa interaction potential between the latex particles. The osmotic pressure derived from this analysis is much smaller than the actual osmotic pressure exerted by the dissolved HEC. Possible reasons for this discrepancy are discussed. Copyright 1999 Academic Press.

Polymer shape anisotropy and the depletion interaction

We calculate the second and third virial coefficients of the effective sphere-sphere interaction due to polymer-induced depletion forces. By utilizing the anisotropy of a typical polymer conformation, we can consider polymers that are roughly the same size as the spheres. We argue that recent experiments are laboratory evidence for polymer shape anisotropy.