Effect of polymer size and chain length on depletion interactions between two colloids

A density functional theory based on the weighted density has been developed to investigate the depletion interactions between two colloids immersed in a bath of the binary polymer mixtures, where the colloids are modeled as hard spheres and the polymers as freely jointed tangent hard-sphere chain mixtures. The theoretical calculations for the depletion forces between two colloids induced by the polymer are in good agreement with the computer simulations. The effects of polymer packing fraction, degree of polymerization, polymer/polymer size ratio, colloid/polymer size ratio on the depletion interactions, and colloid-colloid second virial coefficient B2 due to polymer-mediated interactions have been studied. With increasing the polymer packing fraction, the depletion interaction becomes more long ranged and the attractive interaction near the colloid becomes deeper. The effect of degree polymerization shows that the long chain gives a more stable dispersion for colloids rather than the short chain. The strong effective colloid-colloid attraction appears for the large colloid/polymer and polymer/polymer size ratio. The location of maximum repulsion Rmax is found to appear Rmax approximately sigmac+Rg2 for the low polymer packing fraction and this is shifted to smaller separation Rmax approximately sigmac+sigmap2 with increasing the polymer packing fraction, where sigmap2 and Rg2 are the small-particle diameter and the radius of gyration of the polymer with the small-particle diameter, respectively.     

Charged colloid-polymer mixtures: a study on electrostatic depletion attraction

In this work, light scattering methods have been used to study the effect of adding charged polymer chains on the structural and dynamic properties of a charged colloidal system. The experimental measurements of the static structure factor S(cc)(q) show that as the polymer concentration increases, the main peak moves to higher q-values, which is interpreted in terms of the electrostatically enhanced depletion attraction induced by the polymer. Moreover, we found that the shift of the peak depends on the interplay between two relevant length scales, the polymer radius of gyration, R(g), and the Debye length, κ(-1). To reach these conclusions, the polymer reference interaction site model has been employed to explain the experimental results and to study how the effective depletion attraction depends on the polymer concentration, R(g) and κ(-1). Additionally, the measurements of the dynamic structure factor f(q, τ) indicate that the colloidal diffusion increases with the polymer concentration. Both static and dynamic analysis point out that the repulsion between colloids becomes weaker as the charged polymer is added.     

Interaction forces between colloidal particles in a solution of like-charged, adsorbing nanoparticles

We have measured the force between a weakly charged micron-sized colloidal particle and flat substrate in the presence of highly charged nanoparticles of the same sign under solution conditions such that the nanoparticles physically adsorb to the colloidal particle and substrate. The objective was to investigate the net effect on the force profile between the microparticle and flat substrate arising from both nanoparticle adsorption and nanoparticles in solution. The experiments used colloidal probe atomic force microscopy (CP-AFM) to measure the force profile between a relatively large (5 μm) colloidal probe glass particle and a planar glass substrate in aqueous solutions at varying concentrations of spherical nanoparticles. At very low nanoparticle concentrations, the primary effect was an increase in the electrostatic repulsion between the surfaces due to adsorption of the more highly charged nanoparticles. As the nanoparticle concentration is increased, a depletion attraction formed, followed by longer-range structural forces at the highest nanoparticle concentrations studied. These results suggest that, depending on their concentration, such nanoparticles can either stabilize a dispersion of weakly-charged colloidal particles or induce flocculation. This behavior is qualitatively different from that in nonadsorbing systems, where the initial effect is the development of an attractive depletion force.     

Polymer-particle mixtures: depletion and packing effects

The structure of polymers in the vicinity of spherical colloids is investigated by Monte Carlo simulations and integral equation theory. Polymers are represented by a simple bead-spring model; only repulsive Lennard-Jones interactions are taken into account. Using advanced trial moves that alter chain connectivity, depletion and packing effects are analyzed as a function of chain length and density, both at the bond and the chain level. Chain ends segregate to the colloidal surface and polymer bonds orient parallel to it. In the dilute regime, the polymer chain length governs the range of depletion and has a negligible influence on monomer packing in dense polymer melts. Polymers adopt an ellipsoidal shape, with the larger axis parallel to the surface of the particle, as they approach larger colloids. The dimensions are perturbed within the range of the depletion layer.     

Interactions between colloidal particles in polymer solutions: A density functional theory study

We present a density functional theory study of colloidal interactions in a concentrated polymer solution. The colloids are modeled as hard spheres and polymers are modeled as freely jointed tangent hard sphere chains. Our theoretical results for the polymer-mediated mean force between two dilute colloids are compared with recent simulation data for this model. Theory is shown to be in good agreement with simulation. We compute the colloid-colloid potential of mean force and the second virial coefficient, and analyze the behavior of these quantities as a function of the polymer solution density, the polymer chain length, and the colloid/polymer bead size ratio.     

Evidence of hydration forces between proteins

Proteins are fundamental molecules in biology that are also involved in a wide range of industrial and biotechnological processes. Consequently, many works in the literature have been devoted to the study of protein–protein and protein–surface interactions in aqueous solutions. The results have been usually interpreted within the frame of the classical Derjaguin–Landau–Verwey–Overbeek (DLVO) theory for colloidal systems. However, against the DLVO predictions, striking evidence of repulsive forces between proteins at high salt concentrations has been observed in different works based on the analysis of the second virial coefficient or on the direct measurement of protein interaction with an atomic force microscope. Hydration forces due to the adsorption of hydrated cations onto the negatively charged protein surfaces have been invoked to rationalize this anomalous repulsion. The hydration forces between proteins provide protein-covered particles with a non-DLVO colloidal stability at high salt concentrations, as different studies in the literature has proven. This review summarizes the most relevant results published so far on the presence of hydration forces between proteins and protein-coated colloidal particles.     

Sedimentation of aggregating colloids

We investigate the combined effects of gravity, attractive interactions, and brownian motion in suspensions of colloidal particles and nonadsorbing polymer. Depending on the effective strength of gravitational forces, resulting from a density mismatch between the colloids and the solvent, and the magnitude and range of the depletion interactions induced by the polymer, sedimentation in these suspensions can result in an equilibrium structure or a kinetically arrested state. We employ large-scale molecular dynamics simulations to systematically classify the different regimes that arise as a function of attraction strength and gravitational stress. Whereas strong attractions lead to cluster aggregation and low-density arrested states, moderate attractions can enhance crystallization of the colloidal particles in the sediment. We make direct comparisons to experimental results to infer general conclusions about the mechanisms leading to mechanically stable sediments.     

Structure, surface excess and effective interactions in polymer nanocomposite melts and concentrated solutions

The Polymer Reference Interaction Site Model (PRISM) theory is employed to investigate structure, effective forces, and thermodynamics in dense polymer-particle mixtures in the one and two particle limit. The influence of particle size, degree of polymerization, and polymer reduced density is established. In the athermal limit, the surface excess is negative implying an entropic dewetting interface. Polymer induced depletion interactions are quantified via the particle-particle pair correlation function and potential of mean force. A transition from (nearly) monotonic decaying, attractive depletion interactions to much stronger repulsive-attractive oscillatory depletion forces occurs at roughly the semidilute-concentrated solution boundary. Under melt conditions, the depletion force is extremely large and attractive at contact, but is proceeded by a high repulsive barrier. For particle diameters larger than roughly five monomer diameters, division of the force by the particle radius results in a nearly universal collapse of the depletion force for all interparticle separations. Molecular dynamics simulations have been employed to determine the depletion force for nanoparticles of a diameter five times the monomer size over a wide range of polymer densities spanning the semidilute, concentrated, and melt regimes. PRISM calculations based on the spatially nonlocal hypernetted chain closure for particle-particle direct correlations capture all the rich features found in the simulations, with quantitative errors for the amplitude of the depletion forces at the level of a factor of 2 or less. The consequences of monomer-particle attractions are briefly explored. Modification of the polymer-particle pair correlations is relatively small, but much larger effects are found for the surface excess including an energetic driven transition to a wetting polymer-particle interface. The particle-particle potential of mean force exhibits multiple qualitatively different behaviors (contact aggregation, steric stabilization, local bridging attraction) depending on the strength and spatial range of the polymer-particle attraction.     

Forces between nanorods with end-adsorbed chains in a homopolymer melt

Adsorbed or grafted polymers are often used to provide steric stabilization of colloidal particles. When the particle size approaches the nanoscale, the curvature of the particles becomes relevant. To investigate this effect for the case of cylindrical symmetry, I use a classical fluids density functional theory applied to a coarse-grained model to study the polymer-mediated interactions between two nanorods. The rods are coated with end-adsorbing chains and immersed in a polymer melt of chemically identical, nonadsorbing chains. The force between the nanorods is found to be nonmonotonic, with an attractive well when the two brushes come into contact with each other, followed by a steep repulsion at shorter distances. The attraction is due to the entropic phenomenon of autophobic dewetting, in which there is a surface tension between the brush and the matrix chains. These results are similar to previous results for planar and spherical polymer brushes in melts of the same polymer. The depth of the attractive well increases with matrix chain molecular weight and with the surface coverage. The attraction is very weak when the matrix chain molecular weight is similar to or smaller than the brush molecular weight, but for longer matrix chains the magnitude of the attraction can become large enough to cause aggregation of the nanorods.     

Surface forces between telechelic brushes revisited: the origin of a weak attraction

Telechelic polymers are useful for surface protection and stabilization of colloidal dispersions by the formation of polymer brushes. A number of theoretical investigations have been reported on a weak attraction between two telechelic brushes when they are at the classical contact, i.e., when the surface separation is approximately equal to the summation of the brush thicknesses. While recent experiments have confirmed the weak attraction between telechelic brushes, its origin remains elusive because of conflicting approximations used in the previous theoretical calculations. In this paper, we have investigated the telechelic polymer-mediated surface forces by using a polymer density functional theory (PDFT) that accounts for both the surface-adhesive energy and segment-level interactions specifically. Within a single theoretical framework, the PDFT is able to capture both the depletion-induced attraction in the presence of weakly adhesive polymers and the steric repulsion between compressed polymer brushes. In comparison of the solvation forces between telechelic brushes with those between brushes formed by surfactant-like polymers and with those between two asymmetric surfaces mediated by telechelic polymers, we conclude that the weak attraction between telechelic brushes is primarily caused by the bridging effect. Although both the surfactant-like and telechelic polymers exhibit a similar scaling behavior for the brush thickness, a significant difference has been observed in terms of the brush microstructures, in particular, the segment densities near the edges of the polymer brushes.     

环状高分子对胶体稳定性影响的理论研究

将改进的基本度量理论与热力学微扰理论相结合,提出了胶体/高分子系统排空相互作用的IRDFT理论。该理论解释了在实际胶体系统中起重要作用的排斥体积效应和高分子链内相关性的竞争机制。应用该IRDFT,分别以线性链状和环状结构的高分子及其单体为排空元,计算了不同排空元条件下的胶体间排空相互作用。研究表明:对于絮凝破坏,自由环状高分子具有更大的优势。     

Integral equation theory study on the structure and effective interactions in star polymer nanocomposite melts

The polymer reference interaction site model theory is used to investigate the radial distribution function, potential of mean force, depletion force, and second virial coefficient in star polymer nanocomposite melts. The contact aggregation of nanoparticles for relatively weak nanoparticle-monomer attraction and the bridging aggregation of nanoparticles for very large nanoparticle-monomer attraction are observed. The star architecture can well suppress the organization states of direct contact and bridging structure for the moderate nanoparticle-monomer attraction, and promote the bridging-type organization for relatively large nanoparticle-monomer attraction. At constant particle volume fraction, the arm length quantitatively affects the organization states of star polymer nanocomposite melt, and larger repulsive barriers are existent to prevent the contact aggregation of larger nanoparticles. These observations provide useful information for the development of new nanocomposite materials.     

Charging and aggregation of positively charged latex particles in the presence of anionic polyelectrolytes

Charging behavior and colloidal stability of amidine latex particles are studied in the presence of poly(sodium styrene sulfonate) (PSS) and KCl. Detailed measurements of electrophoretic mobility, adsorbed layer thickness, and aggregation (or coagulation) rate constant on varying the polymer dose, molecular mass of the polymer, and ionic strength are reported. Polyelectrolyte adsorption leads to the characteristic charge reversal (or overcharging) of the colloidal particles at the isoelectric point (IEP). In accordance with classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, uncharged particles tend to aggregate because of van der Waals attraction, whereas charged particles are stabilized by electrical double layer repulsion. Attractive patch-charge interactions originating from the laterally inhomogeneous structure of the adsorbed polymer substantially decrease the suspension stability or even accelerate the aggregation rate beyond diffusion control. These electrostatic non-DLVO forces become progressively important with increasing molecular mass of the polymer and the ionic strength of the solution. At higher polymer dose of typically 10 times the IEP, one observes the formation of a saturated layer of the adsorbed polymer with a thickness of several nanometers. Its thickness increases with increasing molecular mass, whereby the layer becomes increasingly porous. This layer does not seem to be involved in the suspension stabilization, since at such high polymer doses the double layer repulsion has attained sufficient strength to stabilize the suspension.     

Influence of second virial coefficient and persistence length on dilute solution polymer conformation

The effect of different types of short- and long-range intrachain interactions along the polymeric backbone on the persistence length of a polymer, as well as on other properties such as solvation (characterized by the second virial coefficient), dilute solution conformation, specific refractive index increment, and intrinsic viscosity, were studied using multi-detector size-exclusion chromatography and off-line techniques. The polymers in this study, namely, polystyrene (PS), poly(vinyl chloride) (PVC), and poly(p-vinylbenzyl chloride) (PpVBC), were chosen based on intrachain interactions specific to each, intrachain repulsion in PVC, attraction in PS, and hindered attraction in PpVBC, and also based on a coincidence in molar mass averages and distributions between the polymers. The latter allowed polymeric properties of the three polymers to be compared to each other at the same molar mass and/or degree of polymerization. From the comparisons emerged the effects of intrachain repulsion between consecutive monomers and of the second virial coefficient on chain stiffness and solvation. The increase in the second virial coefficient corresponded to an increase in both polymer solvation and rigidity, while increased intrachain repulsion between consecutive monomers increased polymer solvation while decreasing chain rigidity.

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.     

Density-functional study of interfacial properties of colloid-polymer mixtures

Interfacial properties of colloid-polymer mixtures are examined within an effective one-component representation, where the polymer degrees of freedom are traced out, leaving a fluid of colloidal particles interacting via polymer-induced depletion forces. Restriction is made to zero-, one-, and two-body effective potentials, and a free energy functional is used that treats colloid excluded volume correlations within Rosenfeld's fundamental measure theory, and depletion-induced attraction within first-order perturbation theory. This functional allows a consistent treatment of both ideal and interacting polymers. The theory is applied to surface properties near a hard wall, to the depletion interaction between two walls, and to the fluid-fluid interface of demixed colloid-polymer mixtures. The results of the present theory compare well with predictions of a fully two-component representation of mixtures of colloids and ideal polymers (the Asakura-Oosawa model) and allow a systematic investigation of the effects of polymer-polymer interactions on interfacial properties. In particular, the wall surface tension is found to be significantly larger for interacting than for ideal polymers, whereas the opposite trend is predicted for the fluid-fluid interfacial tension.     

Influence of confinement on the electrostatic interaction between charged colloids: a (N,V,T) Monte Carlo study within hyperspherical geometry

Monte Carlo simulations within closed hyperspherical geometry are used to analyze the ionic distribution around two confined charged colloids to determine the origin of the net attraction recently reported in the literature. A scaling procedure is used to compare our numerical results obtained with small ideal colloids with the conclusion of the measurements performed with large silica colloids. Although no electrostatic attraction is detected under confinement, our simulations exhibit a significant reduction of the electrostatic repulsion between charged colloids confined between two weakly charged walls. After rescaling to reproduce the electrostatic repulsion between large confined colloids, our numerical results are qualitatively consistent with the reported attraction because we reasonably expect a reduction of the electrostatic force between such confined colloids below the order of magnitude of their van der Waals attraction.     

Multiple dynamic regimes in colloid‐polymer dispersions: New insight using X‐ray photon correlation spectroscopy

We present an X‐ray photon correlation spectroscopy (XPCS) study of dynamic transitions in an anisotropic colloid‐polymer dispersion with multiple arrested states. The results provide insight into the mechanism for formation of repulsive glasses, attractive glasses, and networked gels of colloids with weakly adsorbing polymer chains. In the presence of adsorbing polymer chains, we observe three distinct regimes: a state with slow dynamics consisting of finite particles and clusters, for which interparticle interactions are predominantly repulsive; a second dynamic regime occurring above the saturation concentration of added polymer, in which small clusters of nanoparticles form via a short‐range depletion attraction; and a third regime above the overlap concentration in which dynamics of clusters are independent of polymer chain length. The observed complex dynamic state diagram is primarily governed by the structural reorganization of a nanoparticle cluster and polymer chains at the nanoparticle‐polymer surface and in the concentrated medium, which in turn controls the dynamics of the dispersion. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 752–760     

Effect of temperature on the reentrant condensation in polyelectrolyte-liposome complexation

Interactions of oppositely charged macroions in aqueous solution give rise to intriguing aggregation phenomena, resulting in finite-size, long-lived clusters, characterized by a quite narrow size distribution. Particularly, the adsorption of highly charged linear polyelectrolytes on oppositely charged colloidal particles is strongly correlated and some short-range order arises from competing electrostatic interactions between like-charged polymer chains (repulsion) and between polymer chains and particle surface (attraction). In these systems, in an interval of concentrations around the isoelectric point, relatively large clusters of polyelectrolyte-decorated particles form. However, the mechanisms that drive the aggregation and stabilize, at the different polymer/particle ratios, a well-defined size of the aggregates are not completely understood. Nor is clear the role that the correlated polyion adsorption plays in the aggregation, although the importance of "patchy interactions" has been stressed as the possible source of attractive interaction term between colloidal particles. Different models have been proposed to explain the formation of the observed cluster phase. However, a central question still remains unanswered, i.e., whether the clusters are true equilibrium or metastable aggregates. To elucidate this point, in this work, we have investigated the effect of the temperature on the cluster formation. We employed liposomes built up by DOTAP lipids interacting with a simple anionic polyion, polyacrylate sodium salt, over an extended concentration range below and above the isoelectric condition. Our results show that the aggregation process can be described by a thermally activated mechanism.     

Depletion interaction mediated by a polydisperse polymer studied with total internal reflection microscopy

Total internal reflection microscopy (TIRM) was applied to measure depletion forces between a charged colloidal sphere and a charged solid wall induced by dextran, a nonionic nonadsorbing polydisperse polysaccharide. The polymer size polydispersity is shown to greatly influence the depletion potential. Using the theory for the depletion interaction due to ideal polydisperse polymer chains, we could accurately describe the experimental data with a single adjustable parameter.