The influence of the polymer chain stiffness on tracer diffusion in polymeric matrices

The diffusion of penetrants in polymers is of technological importance in many areas including chromatography and fuel cell membranes. In this work, the effect of chain conformations on tracer diffusion is studied using molecular simulations and a percolation theory. The polymeric matrix is composed of tangent hard sphere chains that are fixed in space; conformations are changed by tuning the stiffness of the chains. The tracer diffusion coefficient is relatively insensitive to the chain stiffness when polymer chains are frozen as in polymer glasses with the local chain dynamics switched off. An analysis of the matrix using percolation theory shows that the polymer volume fraction at the free volume percolation threshold is also relatively insensitive to the chain stiffness, consistent with the diffusion results. This is surprising because the site‐site intermolecular pair correlation functions in the matrix are quite sensitive to the chain stiffness. In contrast, the tracer diffusion coefficient in a melt of mobile chains decreases significantly as the chain stiffness is increased. We conclude that tracer diffusion is only weakly correlated with the chain conformations and local chain dynamics plays an important role. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Permeation of a hard sphere fluid into a quenched matrix

The permeation of a hard sphere fluid through a model membrane, composed of quenched (in space) hard spheres, is studied using molecular dynamics simulations. The fluid is initially placed outside the porous matrix and their initial intake is investigated and found to be non-Fickian. This non-Fickian behavior can be attributed to the high concentration difference between the fluid in the bulk and in the membrane. Once the system is equilibrated, the authors mark fluid particles that are outside the membrane and investigate their diffusion (color diffusion). Color diffusion is Fickian, and the mass intake and density profiles are well described by a continuum composite medium model with no adjustable parameters, i.e., with self-diffusion coefficients obtained from simulations. The matrix becomes impermeable when there are no percolating paths for the fluid.     

Self-diffusion of rodlike and spherical particles in a matrix of charged colloidal spheres: a comparison between fluorescence recovery after photobleaching and fluorescence correlation spectroscopy

The fluorescence recovery after photobleaching (FRAP) method and the fluorescence correlation spectroscopy (FCS) have been applied on suspensions of highly charged colloidal spheres with a small content of rod-shaped tobacco mosaic virus (TMV) particles. Since these methods only determine the self-diffusion coefficient of the fluorescently labeled species, D(S) of the rods and the spheres could independently be measured. The ionic strength of the dispersion medium has been varied to measure self-diffusion of rods and spheres in dependence on the degree of order of the matrix spheres. In contrast to FRAP, which allows the determination of the long-time self-diffusion coefficient D(S) (L), FCS measures self-diffusion on a shorter time scale. Thus a comparison of the results that were obtained by FCS and FRAP, in combination with Brownian Dynamics simulations, gives insight into the time dependence of the self-diffusion coefficient of an interacting colloidal system. As the mean interparticle distance of the matrix is of the same order of magnitude as the length of a TMV rod, the rotational motion is influenced by the assembly of spheres around a TMV particle. Since FCS is sensitive both to translational and rotational motion, whereas FRAP, which probes the diffusion at much larger length scales, is only sensitive to the translational motion of TMV, the comparison of diffusion coefficients measured employing FRAP and FCS can give some insights in the rotational diffusion: the experimental data indicate a slowing down of the rotational motion of a TMV rod with increasing structural order of the matrix spheres.     

Monte Carlo simulation and self-consistent integral equation theory for polymers in quenched random media

The conformational properties and static structure of freely jointed hard-sphere chains in matrices composed of stationary hard spheres are studied using Monte Carlo simulations and integral equation theory. The simulations show that the chain size is a nonmonotonic function of the matrix density when the matrix spheres are the same size as the monomers. When the matrix spheres are of the order of the chain size the chain size decreases monotonically with increasing matrix volume fraction. The simulations are used to test the replica-symmetric polymer reference interaction site model (RSP) integral equation theory. When the simulation results for the intramolecular correlation functions are input into the theory, the agreement between theoretical predictions and simulation results for the pair-correlation functions is quantitative only at the highest fluid volume fractions and for small matrix sphere sizes. The RSP theory is also implemented in a self-consistent fashion, i.e., the intramolecular and intermolecular correlation functions are calculated self-consistently by combining a field theory with the integral equations. The theory captures qualitative trends observed in the simulations, such as the nonmonotonic dependence of the chain size on media fraction.     

Effect of excluded volume interactions on the interfacial properties of colloid-polymer mixtures

We report a numerical study of equilibrium phase diagrams and interfacial properties of bulk and confined colloid-polymer mixtures using grand canonical Monte Carlo simulations. Colloidal particles are treated as hard spheres, while the polymer chains are described as soft repulsive spheres. The polymer-polymer, colloid-polymer, and wall-polymer interactions are described by density-dependent potentials derived by Bolhuis and Louis [Macromolecules 35, 1860 (2002)]. We compared our results with those of the Asakura-Oosawa-Vrij model [J. Chem. Phys. 22, 1255 (1954); J. Polym Sci 33, 183 (1958); Pure Appl. Chem. 48, 471 (1976)] that treats the polymers as ideal particles. We find that the number of polymers needed to drive the demixing transition is larger for the interacting polymers, and that the gas-liquid interfacial tension is smaller. When the system is confined between two parallel hard plates, we find capillary condensation. Compared with the Asakura-Oosawa-Vrij model, we find that the excluded volume interactions between the polymers suppress the capillary condensation. In order to induce capillary condensation, smaller undersaturations and smaller plate separations are needed in comparison with ideal polymers.     

Adsorption of comb copolymers on weakly attractive solid surfaces

In this work continuum and lattice Monte Carlo simulation methods are used to study the adsorption of linear and comb polymers on flat surfaces. Selected polymer segments, located at the tips of the side chains in comb polymers or equally spaced along the linear polymers, are attracted to each other and to the surface via square-well potentials. The rest of the polymer segments are modeled as tangent hard spheres in the continuum model and as self-avoiding random walks in the lattice model. Results are presented in terms of segment-density profiles, distribution functions, and radii of gyration of the adsorbed polymers. At infinite dilution the presence of short side chains promotes the adsorption of polymers favoring both a decrease in the depletion-layer thickness and a spreading of the polymer molecule on the surface. The presence of long side chains favors the adsorption of polymers on the surface, but does not permit the spreading of the polymers. At finite concentration linear polymers and comb polymers with long side chains readily adsorb on the solid surface, while comb polymers with short side chains are unlikely to adsorb. The simple models of comb copolymers with short side chains used here show properties similar to those of associating polymers and of globular proteins in aqueous solutions, and can be used as a first approximation to investigate the mechanism of adsorption of proteins onto hydrophobic surfaces.     

Structures and dynamics of thermosensitive microgel suspensions studied with three-dimensional cross-correlated light scattering

The structure factors, short- and long-time diffusion coefficients, and hydrodynamic interactions of concentrated poly(N-isopropylacryamide) microgel suspensions were measured with simultaneous static and dynamic three-dimensional cross-correlated light scattering. The data are interpreted through comparison to hard sphere theory. The structure factors are known to be described well by the hard sphere approximation. When the structure factor is fit to an effective hard sphere volume fraction and radius, the diffusion and hydrodynamic interactions are also well described by the hard sphere model. We demonstrate that one single hard sphere volume fraction is sufficient to describe the microgel structures, hydrodynamic interactions, and long- and short-time collective diffusion coefficients. This result is surprising because the particle form of the microgels at these temperatures is not rigid, but rather "fuzzy" spheres with dangling polymer chains.     

The effect of rotational and translational energy exchange on tracer diffusion in rough hard sphere fluids

A study is presented of tracer diffusion in a rough hard sphere fluid. Unlike smooth hard spheres, collisions between rough hard spheres can exchange rotational and translational energy and momentum. It is expected that as tracer particles become larger, their diffusion constants will tend toward the Stokes-Einstein hydrodynamic result. It has already been shown that in this limit, smooth hard spheres adopt "slip" boundary conditions. The current results show that rough hard spheres adopt boundary conditions proportional to the degree of translational-rotational energy exchange. Spheres for which this exchange is the largest adopt "stick" boundary conditions while those with more intermediate exchange adopt values between the "slip" and "stick" limits. This dependence is found to be almost linear. As well, changes in the diffusion constants as a function of this exchange are examined and it is found that the dependence is stronger than that suggested by the low-density, Boltzmann result. Compared with smooth hard spheres, real molecules undergo inelastic collisions and have attractive wells. Rough hard spheres model the effect of inelasticity and show that even without the presence of attractive forces, the boundary conditions for large particles can deviate from "slip" and approach "stick."     

Coupled ion and network dynamics in polymer electrolytes: Monte Carlo study of a lattice model

Monte Carlo simulations are used to study ion and polymer chain dynamic properties in a simplified lattice model with only one species of mobile ions. The ions interact attractively with specific beads in the host chains, while polymer beads repel each other. Cross linking of chains by the ions reduces chain mobilities which in turn suppresses ionic diffusion. Diffusion constants for ions and chains as a function of temperature follow the Vogel-Tammann-Fulcher (VTF) law with a common VTF temperature at low ion concentration, but both decouple at higher concentrations, in agreement with experimental observations. Our model allows us to introduce pressure as an independent variable through calculations of the equation of state using the quasichemical approximation, and to detect an exponential pressure dependence of the ionic diffusion.     

Diffusive solvent dynamics in a polymer gel electrolyte studied by quasielastic neutron scattering

A quasielastic neutron scattering study has been performed on a polymer gel electrolyte consisting of lithium perchlorate dissolved in ethylene carbonate/propylene carbonate and stabilized with poly(methyl methacrylate). The dynamics of the solvent, which is crucial for the ion conduction in this system, was probed using the hydrogen/deuterium contrast variation method with nondeuterated solvent and a deuterated polymer matrix. Two relaxation processes of the solvent were studied in the 10-400 microeV range at different temperatures. From analysis of the momentum transfer dependence of the processes we conclude that the faster process ( approximately 100 microeV) is related to rotational diffusion of the solvent and the slower process ( approximately 10 microeV) to translational diffusion of the solvent. The translational diffusion is found to be similar to the diffusion in the corresponding liquid electrolyte at short distances, but geometrically constrained by the polymer matrix at distances beyond approximately 5 A. The study indicates that the hindered diffusion of the solvent on a length scale of the polymer network interchain distance ( approximately 5-20 A) is sufficient to explain the reduced macroscopic diffusivity and ion conductivity of the gel electrolyte compared to the liquid electrolyte.     

Conformation and diffusion behavior of ring polymers in solution: a comparison between molecular dynamics, multiparticle collision dynamics, and lattice Boltzmann simulations

We have studied the effect of chain topology on the structural properties and diffusion of polymers in a dilute solution in a good solvent. Specifically, we have used three different simulation techniques to compare the chain size and diffusion coefficient of linear and ring polymers in solution. The polymer chain is modeled using a bead-spring representation. The solvent is modeled using three different techniques: molecular dynamics (MD) simulations with a particulate solvent in which hydrodynamic interactions are accounted through the intermolecular interactions, multiparticle collision dynamics (MPCD) with a point particle solvent which has stochastic interactions with the polymer, and the lattice Boltzmann method in which the polymer chains are coupled to the lattice fluid through friction. Our results show that the three methods give quantitatively similar results for the effect of chain topology on the conformation and diffusion behavior of the polymer chain in a good solvent. The ratio of diffusivities of ring and linear polymers is observed to be close to that predicted by perturbation calculations based on the Kirkwood hydrodynamic theory.     

Effect of grafting on nanoparticle segregation in polymer/nanoparticle blends near a substrate

Nanoparticles in polymer films have shown the tendency to migrate to the substrate due to an entropic-based attractive depletion interaction between the particles and the substrate. It is also known that polymer-grafted nanoparticles show better dispersion in a polymer matrix. Here, molecular dynamics simulations are employed to study the effect of grafting on the nanoparticle segregation to the substrate. The nanoparticles were modeled as spheres and the polymers as bead-spring chains. The polymers of the grafts and the matrix are identical in nature. For a purely repulsive system, the nanoparticle density near the surface was found to decrease as the length of grafted chains and the number of grafts increased and in the bulk, the nanoparticles are well-dispersed. Whereas, in case of attractive systems with interparticle interactions on the order of thermal energy, the nanoparticles segregated to the substrate even more strongly, essentially forming clusters on the wall and in the bulk. However, due to the presence of grafted chains on the nanoparticles, the clusters formed in the bulk are structurally anisotropic. The effect of grafts on nanoparticle segregation to the surface was found to be qualitatively similar to the purely repulsive case.     

Structure and internal dynamics of a side chain liquid crystalline polymer in various phases by molecular dynamics simulations: a step towards coarse graining

Side chain liquid crystalline polymer with relatively long spacer was modeled on a semiatomistic level and studied in different liquid crystalline phases with the aid of molecular dynamics simulations. Well equilibrated isotropic, polydomain smectic and monodomain smectic phases were studied for their structural and dynamic properties. Particular emphasis was given to the analysis on a coarse-grained level, where backbones, side chains, and mesogens were considered in terms of their equivalent ellipsoids. The authors found that the liquid crystalline phase had a minor influence on the metrics of these objects but affected essentially their translational and orientational order. In the monodomain smectic phase, mesogens, backbones, and side chains are confined spatially. Their diffusion and shape dynamics are frozen along the mesogen director (the one-dimensional solidification) and the reorientation times increase by one to one-and-half orders of magnitude. In this phase, besides obvious orientational order of mesogens and side chains, a stable detectable order of the backbones was also observed. The backbone director is confined in the plane perpendicular to the mesogen director and constantly changes its orientation within this plane. The backbone diffusion in these planes is of the same range as in the polydomain smectic phase at the same temperature. A detailed analysis of the process of field-induced growth of the smectic phase was performed. The study revealed properties of liquid crystalline polymers that may enable their future fully coarse-grained modeling.     

A different diffusion mechanism for drug molecules in amorphous polymers

Polymer materials are widely used in controlled drug release, and the diffusion property of drug molecules in these materials is of great importance. In this work, the diffusion behavior of a model drug (aspirin) in different ratios of poly(lactic acid-co-ethylene glycol) (PLA-PEG) was investigated by molecular dynamics simulations. Two major factors, which influence the diffusion of aspirin in polymer matrix: the wriggling of the polymer chain and the free volume of the polymer matrix, are discussed. The wriggling of the polymer chain mainly controls the diffusion of aspirin molecules. Free volume becomes the secondary effect. For two different polymers having a similar degree of wriggling, the free volume controls the diffusion of the aspirin molecules. Comparing with the diffusion behavior of small gas molecules in polymer matrix, a different mechanism was proposed for the drug molecules. The drug molecules can only diffuse along with the wriggling of the polymer matrix.     

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.     

Dynamics of poly(p‐phenylene) ladder polymers in solution

Photon correlation spectroscopy in both polarized and depolarized geometry was employed to investigate the dynamics of a ribbon‐type polymer exhibiting good solubility. In dilute solution, the translational diffusion for all examined molecular weights has confirmed the picture of wormlike chains with rather short (∼ 7 nm) persistence length (Macromolecules 1997, 30, 273). In the semidilute regime, the total concentration fluctuations display, besides the fast dominant cooperative diffusion, a second slower diffusive process that exhibits weak concentration dependence and is not related to the self‐diffusion measured by pulse‐field‐gradient NMR. The concentration dependence of the cooperative and the self‐diffusion coefficient as well as of the zero‐shear viscosity cannot be consistently described by neither flexible nor stiff chain models. Presence of aggregates was revealed at high concentrations. Owing to the short persistence length, the rotational diffusion is too fast to be adequately investigated. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2211–2220, 1999     

Demixing in athermal mixtures of colloids and excluded-volume polymers from density functional theory

We study the structure and interfacial properties of model athermal mixtures of colloids and excluded volume polymers. The colloid particles are modeled as hard spheres whereas the polymer coils are modeled as chains formed from tangentially bonded hard spheres. Within the framework of the nonlocal density functional theory we study the influence of the chain length on the surface tension and the interfacial width. We find that the interfacial tension of the colloid-interacting polymer mixtures increases with the chain length and is significantly smaller than that of the ideal polymers. For certain parameters we find oscillations on the colloid-rich parts of the density profiles of both colloids and polymers with the oscillation period of the order of the colloid diameter. The interfacial width is few colloid diameters wide and also increases with the chain length. We find the interfacial width for the end segments to be larger than that for the middle segments and this effect is more pronounced for longer chains.     

Motion of star‐branched chains in polymer networks: a Monte Carlo study

A simple model of branched polymers in confined space is developed. Star‐branched polymer molecules are built on a simple cubic lattice with excluded volume and no attractive interactions (good solvent conditions). A single star molecule is trapped in a network of linear polymer chains of restricted mobility. The simulations are carried out using the classical Metropolis algorithm. Static and dynamic properties of the star‐branched polymer are determined using various networks. The dependence of the longest relaxation time and the self‐diffusion coefficient on chain length and network properties are discussed and the proper scaling laws formulated. The possible mechanism of motion is discussed. The differences between the motion of star‐branched polymers in such a network are compared with the cases of a dense matrix of linear chains and regular rod‐like obstacles.     

Structure and dynamics in a monolayer of dipolar spheres

The structure and dynamics in a monolayer of dipolar soft spheres have been investigated using molecular dynamics simulations. This is a basic model of colloidal ferrofluid monolayers, and other magnetic liquids in planar geometries, which can exhibit self-assembled chainlike aggregates due to strong dipole-dipole interactions. The effects of such chaining on the structure, single-particle translational and rotational motions, and the collective rotational motions are examined. The signatures of aggregation in the various structural and dynamical functions considered in this study could prove useful in experimental investigations of strongly dipolar materials.