Viscous solvent colloidal system for direct visualization of suspension structure, dynamics and rheology

We introduce a model colloid system comprised of particles dispersed in a viscous solvent that can be applied to 3D direct visualization studies of suspension structure, dynamics and rheology. The colloids are poly(methyl methacrylate) (PMMA) spheres sterically stabilized by a copolymer of poly(diphenyl-dimethyl) (DPDM) siloxane that matches the refractive index of PMMA. The monodisperse particles, synthesized with mean diameter varying from 0.7 to 1.1 microm, are stably dispersed in a DPDM siloxane solvent, with viscosity varying from 2.2 to 4.3 Pa s at 20 degrees C. As opposed to other classes of PMMA colloids dispersed in organic solvents, this system displays minimal charge interactions. At room temperature, pair potential interactions (measured by extrapolation of pair correlation functions to infinite dilution) are well modeled by a generalized Lennard-Jones alpha-2alpha potential (alpha=10) with dimensionless interaction energy, epsilon/k(B)T=0.6. We use the DPDM-PMMA colloidal system in conjunction with confocal microscopy studies to measure: (i) the radial distribution function in 3D at dilute concentrations and (ii) the colloid self-diffusivity in 3D at dilute concentrations. Both measurements, neither previously reported in uncharged systems, are facilitated by the slow, viscous dynamics of the system. We also show that the viscosity and particle size of the system are such that the high-volume fraction shear thickening transition can be accessed at shear rates amenable to direct visualization.     

Thermodiffusion of interacting colloids. I. A statistical thermodynamics approach

The thermal diffusion coefficient of colloids consists of two additive contributions, one related to specific interactions between the surfaces of colloidal particles with solvent molecules, and a contribution due to interactions between the colloidal particles. In the present paper, the effect of intercolloidal particle interactions on their thermodiffusive behavior is discussed within a statistical thermodynamics framework. Transport coefficients are expressed in terms of the interaction potential between the colloidal spheres. A special feature of macromolecular systems is that this interaction potential is a potential of mean force, which is temperature dependent. It is shown that under certain conditions this implicit temperature dependence gives rise to negative Soret coefficients, that is, to diffusion of macromolecules to hot regions.     

Computer simulation of colloidal dispersions

This paper discusses recent applications of statistical mechanics to dispersions with particular emphasis on the computer simulation of the dynamic properties.Fundamental to any computation on a colloidal dispersion is the knowledge of the potential of mean force for at least a pair of suspended particles. At low-to-moderate particle concentrations for stable dispersions, statistical mechanical calculations based on the normal DLVO pair potential produce reasonable agreement with experiment for a number of equilibrium properties of simple latex dispersions. This phenomenon indicates that under these conditions the DLVO pair potential is a reasonable effective pair potential. However, recent Monte Carlo simulations and experimental measurements with liquids of spherical molecules suggest that the force between a pair of dispersed particles at very small separation may differ significantly from that predicted by DLVO theory.The computation of dynamic properties of dispersions involves problems not encountered in the above equilibrium calculations. In particular, one must include the effects of indirect hydrodynamic as well as direct interactions among the particles. This computation may be easily accomplished at moderately low particle concentrations and the results of such calculations are able to give a very detailed analysis of the results of Photon Correlation Spectroscopy measurements on ion exchanged polystyrene latex suspensions at low concentration. These computations also, once again, emphasize the usefulness of DLVO pair potentials as effective pair potentials for systems of strongly interacting particles.     

Thermodynamic and structural properties of confined discrete-potential fluids

The thermodynamic and structural behaviors of confined discrete-potential fluids are analyzed by computer simulations, studying in a systematic way the effects observed by varying the density, temperature, and parameters of the potentials that characterize the molecule-molecule interactions. The Gibbs ensemble simulation technique for confined fluids [A. Z. Panagiotopoulos, Mol. Phys. 62, 701 (1987)] is applied to a fluid confined between two parallel hard walls. Two different systems have been considered, both formed by spherical particles that differ by the interparticle pair potential: a square well plus square shoulder or a square shoulder plus square well interaction. These model interactions can describe in an effective way pair potentials of real molecular and colloidal systems. Results are compared with the simpler reference systems of square-shoulder and square-well fluids, both under confinement. From the adsorption characterization through the use of density profiles, it is possible to obtain specific values of the interparticle potential parameters that result in a positive to negative adsorption transition.     

低密度溶液中溶剂的重组织性质

分析了溶液的微观结构,结果表明,单个溶质粒子影响其周围的溶剂的结构,溶质粒子间的相互作用也将影响溶剂的结构,溶质对溶剂结构的影响称作溶剂的重组织.提出了二阶重组织能及二阶重组织熵等概念,可以描述在两个溶质粒子发生碰撞时对其周围溶剂结构的影响.利用二元系的集团展开理论,给出了溶剂的一阶、二阶重组织能和重组织熵的表达式.统计热力学分析给出了溶剂-溶剂径向分布函数与溶质和溶剂化学势之间的关系,给出了无限稀溶液模型是否成立的宏观判据.提出的理论可用于低密度的二元溶液.     

Self-diffusion in submonolayer colloidal fluids near a wall

Theoretical expressions are developed to describe self-diffusion in submonolayer colloidal fluids that require only equilibrium structural information as input. Submonolayer colloidal fluids are defined for the purpose of this work to occur when gravity confines colloids near a planar wall surface so that they behave thermodynamically as two dimensional fluids. Expressions for self-diffusion are generalized to consider different colloid and surface interaction potentials and interfacial concentrations from infinite dilution to near fluid-solid coexistence. The accuracy of these expressions is demonstrated by comparing self-diffusion coefficients predicted from Monte Carlo simulated equilibrium particle configurations with standard measures of self-diffusion evaluated from Stokesian Dynamics simulated particle trajectories. It is shown that diffusivities predicted for simulated equilibrium fluid structures via multibody hydrodynamic resistance tensors and particle distribution functions display excellent agreement with values computed from mean squared displacements and autocorrelation functions of simulated tracer particles. Results are obtained for short and long time self-diffusion both parallel and normal to underlying planar wall surfaces in fluids composed of particles having either repulsive electrostatic or attractive van der Waals interactions. The demonstrated accuracy of these expressions for self-diffusion should allow their direct application to experiments involving submonolayer colloidal fluids having a range of interaction potentials and interfacial concentrations.     

Test of athermal terms of activity coefficient models by Monte Carlo simulation with hard-core models

The infinite dilution activity coefficients of exactly athermal fluids were calculated by Monte Carlo simulation with hard-core models. The hard-core models used in this work were hard-sphere and hard-spherocylinder models. The Widom test particle method was adopted to calculate the residual chemical potentials of solutes in pure solvent and in pure solute solutions. The infinite dilution activity coefficients of solutes were obtained from the residual chemical potentials of solutes. The infinite dilution activity coefficients calculated by Monte Carlo simulation were compared with those of athermal terms in activity coefficient equations. Staverman–Guggenheim equation overestimates the activity coefficients. The deviations of activity coefficients increase with increasing the hard-core volume of solute. Flory–Huggins equation based on molar volume gives good results for the hard-spherocylinder systems. Elbro-FV equation gives good results for both the hard-sphere and hard-spherocylinder systems.     

Interactions between polymer brush-coated spherical nanoparticles: the good solvent case

The interaction between two spherical polymer brushes is studied by molecular dynamics simulation varying both the radius of the spherical particles and their distance, as well as the grafting density and the chain length of the end-grafted flexible polymer chains. A coarse-grained bead-spring model is used to describe the macromolecules, and purely repulsive monomer-monomer interactions are taken throughout, restricting the study to the good solvent limit. Both the potential of mean force between the particles as a function of their distance is computed, for various choices of the parameters mentioned above, and the structural characteristics are discussed (density profiles, average end-to-end distance of the grafted chains, etc.). When the nanoparticles approach very closely, some chains need to be squeezed out into the tangent plane in between the particles, causing a very steep rise of the repulsive interaction energy between the particles. We consider as a complementary method the density functional theory approach. We find that the quantitative accuracy of the density functional theory is limited to large nanoparticle separation and short chain length. A brief comparison to Flory theory and related work on other models also is presented.     

Analytical coarse-grained description for polymer melts

Starting from the Ornstein-Zernike equation the authors derive an analytical theory, at the level of pair correlation functions, which coarse grains polymer melts into liquids of interacting soft colloidal particles. Since it is analytical, the presented coarse-graining approach will be useful in developing multiscale modeling procedures to simulate complex fluids of macromolecules. The accuracy of the theory is tested by its capacity to reproduce the liquid structure, as given by the center-of-mass intermolecular total pair correlation function. The theory is found to agree well with the structure predicted by molecular dynamics simulations of the liquid described at the united atom level as well as by molecular dynamics simulations of the liquid of interacting colloidal particles. The authors perform simulations of the liquid of interacting colloidal particles having as input the potential obtained from their analytical total pair correlation function by enforcing the hypernetted-chain closure approximation. Tests systems are polyethylene melts of chains with increasing degrees of polymerization and polymer melts of chains with different chemical architectures. They also discuss the effect of adopting different conventional approximations for intra- and intermolecular monomer structure factors on the accuracy of the coarse-graining procedure, as well as the relevance of higher-order corrections to their expression.     

Interactions between colloidal particles in amphiphilic mixtures: a density functional theory study

We present a density functional theory study of interactions between spherical colloidal particles in amphiphile solutions. Theory is found to be in good agreement with previously published molecular dynamics simulations. It is used to analyze the effect of the amphiphile solution bulk density, the chain length, and the solvent mole fraction on the potential of mean force between the particles. The general features of the potential of mean force are rationalized in terms of formation of layers and bilayers of amphiphilic molecules in the intercolloidal gap. Theory yields the same general trends as observed in simulations and in experiments. In particular, the computed mean force changes its character from repulsive to attractive and back to repulsive as the solvent mole fraction is gradually increased.     

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.     

How to impose stick boundary conditions in coarse-grained hydrodynamics of Brownian colloids and semi-flexible fiber rheology

Long-range hydrodynamics between colloidal particles or fibers is modelled by the fluid particle model. Two methods are considered to impose the fluid boundary conditions at colloidal surfaces. In the first method radial and transverse friction forces between particle and solvent are applied such that the correct friction and torque follows for moving or rotating particles. The force coefficients are calculated analytically and checked by numerical simulation. In the second method a collision rule is used between colloidal particle and solvent particle that imposes the stick boundary conditions exactly. The collision rule comprises a generalisation of the Lowe-Anderson thermostat to radial and transverse velocity differences.     

The inclusion of electrostatic and dispersion interactions into potentials of mean torque for solutes dissolved in uniaxial liquid crystal solvents

A potential of mean torque is derived for a solute at infinite dilution in a uniaxial liquid crystal solvent, which contains terms originating from the dispersion interaction, and the electrostatic interaction between quadrupole moments on both molecules. It is shown that the electrostatic term is non-zero only if the solute-solvent vectors are distributed with lower than spherical symmetry. If this distribution has cylindrical symmetry then both the electrostatic and dispersion terms in the potential of mean torque are shown to depend on order parameters for the orientational distribution of the solute-solvent vectors, as well as on the order parameters of the solvent molecules.     

(2n,n) potential and sticky-sphere fluids

The authors investigate the behavior of a model fluid for which the interaction energy between molecules at a separation r is of the form 4epsilon[(sigma/r)2n-(sigma/r)n], where epsilon and sigma are constants and n is a large integer. The particular properties they study are the pressure p, the mean square force F2, the elastic shear modulus at infinite frequency Ginfinity, the bulk modulus at infinite frequency Kinfinity, and the potential energy per molecule u. They show that if n is sufficiently large it is possible to derive the properties of the system in terms of two parameters, the values of the cavity function and of its derivative at the position r=sigma. As an example they examine in detail the cases with n=144 and n=72 for three different temperatures and they test the theory by comparison with a computer simulation of the system. They use the simulated pressure and the average mean square force to determine the two parameters and use these values to evaluate other properties; it is found that the theory produces results which agree with computer simulation to within approximately 3%. It is also shown that the model, when the parameter n is large, is equivalent to Baxter's sticky-sphere model with the strength of the adhesion determined by the value of n and the temperature. They use Baxter's solution of the Percus-Yevick equations for the sticky-sphere model to determine the cavity function and from that the values of the same properties. In this second approach there are no free parameters to determine from simulation; all properties are completely determined by the theory. The results obtained agree with computer simulation only to within approximately 6%. This suggests that for this model one needs a better approximation to the cavity function than that provided by the Percus-Yevick solution. Nevertheless, the model looks promising for the study of (typically small) colloidal liquids where the range of attraction is short but finite when compared to its diameter, in contrast to Baxter's sticky-sphere limit where the attractive interaction range is taken to be infinitely narrow. The continuous function approach developed here enables important physical properties such as the infinite shear modulus to be computed, which are finite in experimental systems but are undefined in the sticky-sphere model.     

Diffusion, sedimentation, and rheology of concentrated suspensions of core-shell particles

Short-time dynamic properties of concentrated suspensions of colloidal core-shell particles are studied using a precise force multipole method which accounts for many-particle hydrodynamic interactions. A core-shell particle is composed of a rigid, spherical dry core of radius a surrounded by a uniformly permeable shell of outer radius b and hydrodynamic penetration depth κ(-1). The solvent flow inside the permeable shell is described by the Brinkman-Debye-Bueche equation, and outside the particles by the Stokes equation. The particles are assumed to interact non-hydrodynamically by a hard-sphere no-overlap potential of radius b. Numerical results are presented for the high-frequency shear viscosity, η(∞), sedimentation coefficient, K, and the short-time translational and rotational self-diffusion coefficients, D(t) and D(r). The simulation results cover the full three-parametric fluid-phase space of the composite particle model, with the volume fraction extending up to 0.45, and the whole range of values for κb, and a/b. Many-particle hydrodynamic interaction effects on the transport properties are explored, and the hydrodynamic influence of the core in concentrated systems is discussed. Our simulation results show that for thin or hardly permeable shells, the core-shell systems can be approximated neither by no-shell nor by no-core models. However, one of our findings is that for κ(b - a) ? 5, the core is practically not sensed any more by the weakly penetrating fluid. This result is explained using an asymptotic analysis of the scattering coefficients entering into the multipole method of solving the Stokes equations. We show that in most cases, the influence of the core grows only weakly with increasing concentration.     

Pair structure of the hard-sphere Yukawa fluid: an improved analytic method versus simulations, Rogers-Young scheme, and experiment

We present a comprehensive study of the equilibrium pair structure in fluids of nonoverlapping spheres interacting by a repulsive Yukawa-like pair potential, with special focus on suspensions of charged colloidal particles. The accuracy of several integral equation schemes for the static structure factor, S(q), and radial distribution function, g(r), is investigated in comparison to computer simulation results and static light scattering data on charge-stabilized silica spheres. In particular, we show that an improved version of the so-called penetrating-background corrected rescaled mean spherical approximation (PB-RMSA) by Snook and Hayter [Langmuir 8, 2880 (1992)], referred to as the modified PB-RMSA (MPB-RMSA), gives pair structure functions which are in general in very good agreement with Monte Carlo simulations and results from the accurate but nonanalytical and therefore computationally more expensive Rogers-Young integral equation scheme. The MPB-RMSA preserves the analytic simplicity of the standard rescaled mean spherical (RMSA) solution. The combination of high accuracy and fast evaluation makes the MPB-RMSA ideally suited for extensive parameter scans and experimental data evaluation, and for providing the static input to dynamic theories. We discuss the results of extensive parameter scans probing the concentration scaling of the pair structure of strongly correlated Yukawa particles, and we determine the liquid-solid coexistence line using the Hansen-Verlet freezing rule.     

On the mechanism of hydrophobic association of nanoscopic solutes

The hydration behavior of two planar nanoscopic hydrophobic solutes in liquid water at normal temperature and pressure is investigated by calculating the potential of mean force between them at constant pressure as a function of the solute-solvent interaction potential. The importance of the effect of weak attractive interactions between the solute atoms and the solvent on the hydration behavior is clearly demonstrated. We focus on the underlying mechanism behind the contrasting results obtained in various recent experimental and computational studies on water near hydrophobic solutes. The length scale where crossover from a solvent separated state to the contact pair state occurs is shown to depend on the solute sizes as well as on details of the solute-solvent interaction. We find the mechanism for attractive mean forces between the plates is very different depending on the nature of the solute-solvent interaction which has implications for the mechanism of the hydrophobic effect for biomolecules.     

Engineering DNA-mediated colloidal crystallization

DNA is a powerful and versatile tool for nanoscale self-assembly. Several researchers have assembled nanoparticles and colloids into a variety of structures using the sequence-specific binding properties of DNA. Until recently, however, all of the reported structures were disordered, even in systems where ordered colloidal crystals might be expected. We detail the experimental approach and surface preparation that we used to form the first DNA-mediated colloidal crystals, using 1 mum diameter polystyrene particles. Control experiments based on the depletion interaction clearly indicate that two standard methods for grafting biomolecules to colloidal particles (biotin/avidin and water-soluble carbodiimide) do not lead to ordered structures, even when blockers are employed that yield nominally stable, reversibly aggregating dispersions. In contrast, a swelling/deswelling-based method with poly(ethylene glycol) spacers resulted in particles that readily formed ordered crystals. The sequence specificity of the interaction is demonstrated by the crystal excluding particles bearing a noninteracting sequence. The temperature dependence of gelation and crystallization agree well with a simple thermodynamic model and a more detailed model of the effective colloidal pair interaction potential. We hypothesize that the surfaces yielded by the first two chemistries somehow hinder the particle-particle rolling required for annealing ordered structures, while at the same time not inducing a significant mean-force interaction that would alter the self-assembly phase diagram. Finally, we observe that particle crystallization kinetics become faster as the grafted-DNA density is increased, consistent with the particle-particle binding process being reaction, rather than diffusion limited.     

Recent advances in the electric double layer in colloid science

The interaction between charged colloidal particles is mediated by their electric double layers. Given that pairs of like-charged particles experience a repulsion, why do some dilute colloidal dispersions become unstable and condense at low ionic strengths? This puzzling paradox appears to have been largely resolved over the past year by a careful analysis of all the contributions to the thermodynamic potential of the dispersion. Condensation can be predicted using the traditional pair repulsion of the Poisson–Boltzmann theory without invoking any long-range attractions in the pair potential. However, it has emerged that one has to go beyond the Poisson–Boltzmann theory to account for the instability that occurs in confined colloidal dispersions. Other recent advances in the ubiquitous Poisson–Boltzmann theory have included effective surface charge approaches in calculating the electrokinetic zeta potential, and the modelling of charge regulation in colloidal systems.     

Depletion force between anisometric colloidal particles

A simple mathematical model for the depletion force between two arbitrarily shaped large convex colloidal particles immersed in a suspension of small spherical particles is proposed. Using differential geometry, the interaction potential is expressed in terms of the mean and Gaussian curvature of the particle surfaces. The accuracy of theoretical results is tested by Monte Carlo simulations for parallel and nonparallel circular cylinders. The agreement between theoretical results and simulated data is very good if the density of the depletion agent is not too high.