Monte Carlo simulation of structure and nanoscale interactions in polymer nanocomposites

Off-lattice Monte Carlo simulations in the canonical ensemble are used to study polymer-particle interactions in nanocomposite materials. Specifically, nanoscale interactions between long polymer chains (N=550) and strongly adsorbing colloidal particles of comparable size to the polymer coils are quantified and their influence on nanocomposite structure and dynamics investigated. In this work, polymer-particle interactions are computed from the integrated force-distance curve on a pair of particles approaching each other in an isotropic polymer medium. Two distinct contributions to the polymer-particle interaction potential are identified: a damped oscillatory component that is due to chain density fluctuations and a steric repulsive component that arises from polymer confinement between the surfaces of approaching particles. Significantly, in systems where particles are in a dense polymer melt, the latter effect is found to be much stronger than the attractive polymer bridging effect. The polymer-particle interaction potential and the van der Waals potential between particles determine the equilibrium particle structure. Under thermodynamic equilibrium, particle aggregation is observed and there exists a fully developed polymer-particle network at a particle volume fraction of 11.3%. Near-surface polymer chain configurations deduced from our simulations are in good agreement with results from previous simulation studies.     

Monte Carlo simulation of phase separation kinetics in a concentrated polymer solution

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Nanoparticles in solutions of adsorbing polymers: pair interactions, percolation, and phase behavior

We study the polymer adsorption characteristics, pair-interaction potentials, and phase and percolation behavior in nanoparticle-polymer mixtures. We propose a "saturable" adsorption model to capture the effect of the finite surface saturation capacity for adsorption, and use polymer self-consistent field theory in combination with a McMillan-Mayer framework [McMillan, W. G., Jr.; Mayer, J. E. J. Chem. Phys. 1945, 13, 276] to compute the pair-interaction potentials. Our results demonstrate novel size effects that distinguish the adsorption characteristics of nanoparticles from that of larger particles. Specifically, we predict that the nanoparticle regime is characterized by a significant adsorbance of polymers, albeit distributed predominantly in the form of tails. We also demonstrate that an interplay between the surface saturation, polymer-to-particle size ratios, and the polymer concentrations governs the overall effective interactions between nanoparticles in the presence of an adsorbing polymer. We use simple, mean-field models to relate these characteristics to the phase and percolation behavior in such systems. Our results show that the percolation thresholds for smaller particles are significantly smaller (and, overall, correspond only to a few volume percent) compared to that of the larger particles. Further, with a decrease in the size of the particles, we also predict a considerable increase in the miscibility of the polymer-particle mixtures. Our results are qualitatively in accord with many experimental observations in the nanoparticle regime.     

自由基引发的凝胶化反应的Monte Carlo模拟

基于自由基凝胶化反应的基本原理,在一个具有周期性边界条件的二维网络上,利用动态ＭｏｎｔｅＣａｒｌｏ 方法模拟了聚合物凝胶的自由基凝胶化反应,得到了凝胶的具体结构,研究了总单体浓度（ 单体浓度和交联剂浓度之和） 对凝胶的分形结构和孔径分布的影响．模拟中首次考虑了聚合后单体的运动对凝胶结构的影响．结果表明：考虑聚合后单体的运动,可使所得凝胶网络的分形维数和凝胶化所需的最低浓度均显著小于动力学凝胶化模型和ＤＬＡ 模型的相应值．用移动气泡法得到了凝胶网络的孔径分布,发现凝胶网络中大孔所占百分率明显多于随机纤维网络模型．     

Interpretation of the experimental data on the reduction reaction of NO by CO on rhodium by Monte Carlo simulations and by solving the kinetic equations of the reaction mechanism

Some mechanisms of the reduction reaction of NO by CO on rhodium are analyzed and discussed, solving the kinetics equations and using Monte Carlo simulations, in terms of its ability to interpret the recent experiments of Zaera et al., who used a molecular beam method to study experimentally the kinetics of the reaction. Critical use is also made of the information on rate constants available for this system in the literature. Uniform catalytic surfaces and the statistical incipient percolation cluster (IPC) fractal are considered in the simulations.     

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.     

Swelling and fractal heterogeneities in networks

In this paper we revisit old swelling data on polymer networks that have not been interpreted theoretically on a closed molecular basis. If the osmotic pressure of the swollen network is compared to the osmotic pressure of the corresponding uncrosslinked solution unsolved problems appear, when the relative osmotic pressure is plotted against the degree of swelling, i.e. the deformation due to swelling. A significant maximum appears which cannot be explained by any of the recently derived elastic models, such as junction constraint or other entanglement models. It is suggested in this paper that the maximum is a consequence of structural heterogeneities of fractal nature. If such fractal heterogeneities are assumed a strong maximum in the relative osmotic pressure can be reproduced. The physical reason is the different thermodynamic behavior of uncrosslinked linear chains and crosslinked self-similar (non-linear) polymers. The conclusion is supported by numerical (Monte Carlo) simulations.     

Mechanical behavior and wrinkling patterns of phase-separated binary polymer blend film

The wrinkling of phase-separated binary polymer blend film was studied through combining the Monte Carlo (MC) simulation for morphologies with the lattice spring model (LSM) for mechanical properties. The information of morphology and structure obtained by use of MC simulation is input to the LSM composed of a three-dimensional network of springs, which allows us to determine the wrinkling and the mechanical properties of polymer blend film, such as strain, stress, and Young’s modulus. The simulated results show that the wrinkling of phase-separated binary polymer blend film is related not only to the structure of morphology, but also to the disparity in elastic moduli between polymers of blend. Our simulation results provide fundamental insight into the relationship between morphology, wrinkling, and mechanical properties for phase-separated polymer blend films and can yield guidelines for formulating blends with the desired mechanical behavior. The wrinkling results also reveal that the stretching of the phase-separated film can form the micro-template, which has a wide application prospect.     

Rheological study of the sol-gel transition in silica alkoxides

The sol-gel transition of the system tetramethylorthosilicate-water-methanol under basic conditions has been studied by rheological measurements. The gelation time t(g) has been determined from the measurements of the elastic G' and viscous G' moduli as a function of time at different frequencies according to Winter's criterion. At gelation time the frequency dependence of both moduli follows a power law with an exponent related to the fractal dimension of the network structure. Different initial monomer concentrations, hydrolysis molar ratios, and temperatures are studied. The decrease of the gelation time with an increase of initial monomer concentration or hydrolysis molar ratio is well-described by a power law. An apparent activation energy is deduced from the temperature dependence of gelation time.     

Mesoscale modeling of electrical percolation in fiber-filled systems

The research described in this paper primarily involves mesoscale simulations: dissipative particle dynamics (DPD) of packed assemblies of oriented fibers suspended in a viscous medium. Computer simulations have been performed in order to explore how the aspect ratio and degree of fiber alignment affect the critical volume fraction (percolation threshold) required to achieve electrical conductivity. The fiber network impedance was assessed using Monte Carlo simulations after establishing the structural arrangement with DPD. The predictions are compared with the predictions of classical percolation theory and found to be in close agreement. The approach is thus validated and can be extended to systems that cannot be tackled analytically; in particular, the work is motivated by long-standing interest in materials which display a complex percolation behavior.     

水溶性高分子弱凝胶体系凝胶化过程的Monte Carlo模拟

为研究弱凝胶的形成过程,并把高分子弱凝胶用于三次采油,采用三维Monte Carlo模拟了高分子溶液凝胶化过程. 模拟预测了凝胶化开始的时间,得到了凝胶化过程中分子量分布的演化规律和胶团生长的三维图像. 发现生成溶胶与凝胶团的歧化过程,初始聚合物的浓度对能否形成凝胶至关重要,低于临界浓度不能形成凝胶. 模拟了凝胶化速度和聚合物浓度以及交联剂浓度的关系,并与粘度随凝胶化时间变化的实验结果进行比较, 结果表明, 聚合物浓度较高时,浓度对交联反应的影响减弱,这一趋势与实验结果相一致.     

Stability of thin polymer films: influence of solvents

The interface and surface properties and the wetting behavior of polymer-solvent mixtures are investigated using Monte Carlo simulations and self-consistent field calculations. We carry out Monte Carlo simulations in the framework of a coarse-grained bead-spring model using short chains (oligomers) of N(P)=5 beads and a monomeric solvent, N(S)=1. The self-consistent field calculations are based on a simple phenomenological equation of state for compressible binary mixtures and we employ Gaussian chain model. The bulk behavior of the polymer-solvent mixture belongs to type III in the classification of van Konynenburg and Scott [Phil. Trans. R. Soc. London, Ser. A 298, 495 (1980)]. It is characterized by a triple line on which the polymer-liquid coexists with solvent-vapor and a solvent-rich liquid. The solvent is not homogeneously distributed across the dense polymer film but tends to accumulate at the surface and the polymer-vapor interface. This solvent enrichment at the interface and surface becomes more pronounced upon increasing the vapor pressure and alters the surface and interface tensions. This effect gives rise to a nonmonotonic dependence of the contact angle on the vapor pressure and one might observe reentrant wetting. The results of the Monte Carlo simulations and the self-consistent field calculations qualitatively agree. The profiles of drops are investigated by Monte Carlo simulations and a pronounced solvent enrichment is observed at the wedge formed by the substrate and the liquid-vapor interface at the three-phase contact line.     

Thermodynamics and partitioning of homopolymers into a slit-A grand canonical Monte Carlo simulation study

Grand canonical ensemble Monte Carlo simulation (GCMC) combined with the histogram reweighting technique was used to study the thermodynamic equilibrium of a homopolymer solution between a bulk and a slit pore. GCMC gives the partition coefficients that agree with those from canonical ensemble Monte Carlo simulations in a twin box, and it also gives results that are not accessible through the regular canonical ensemble simulation such as the osmotic pressure of the solution. In a bulk polymer solution, the calculated osmotic pressure agrees very well with the scaling theory predictions both for the athermal polymer solution and the theta solution. However, one cannot obtain the osmotic pressure of the confined solution in the same way since the osmotic pressure of the confined solution is anisotropic. The chemical potentials in GCMC simulations were found to differ by a translational term from the chemical potentials obtained from canonical ensemble Monte Carlo simulations with the chain insertion method. This confirms the equilibrium condition of a polymer solution partition between the bulk and a slit pore: the chemical potentials of the polymer chain including the translational term are equal at equilibrium. The histogram reweighting method enables us to obtain the partition coefficients in the whole range of concentrations based on a limited set of simulations. Those predicted bulk-pore partition coefficient data enable us to perform further theoretical analysis. Scaling predictions of the partition coefficient at different regimes were given and were confirmed by the simulation data.     

Simulation of interaction forces between nanoparticles in the presence of Lennard-Jones polymers: freely adsorbing homopolymer modifiers

The force between two nanoscale colloidal particles dispersed in a solution of freely adsorbing Lennard-Jones homopolymer modifiers is calculated using the expanded grand canonical Monte Carlo simulation method. We investigate the effect of polymer chain length (N), nanoparticle diameter (sigma(c)), and colloid-polymer interaction energy (epsilon(cp)) on polymer adsorption (Gamma) and polymer-induced forces (F(P)(r)) between nanoparticles in the full thermodynamic equilibrium condition. There is a strong correlation between polymer adsorption and the polymer-mediated nanoparticle forces. When the polymer adsorption is weak, as in the case of smaller diameters and short polymer chain lengths (sigma(c) = 5, N = 10), the polymers do not have any significant effect on the bare nanoparticle interactions. The adsorbed amount increases with increasing particle diameter, polymer chain length, and colloid-polymer interaction energy. In general, for strong polymer-particle adsorption the polymer-governed force profiles between nanoparticles show short-range repulsion and long-ranged attraction, suggesting that homopolymers would not be ideal for achieving stabilization in nanoparticle dispersions. The attraction is likely due to bridging, as well as polymer segment-segment interactions. The location and magnitude of attractive minimum in the force profile can be controlled by varying N and epsilon(cp). The results show partial agreement and some marked differences with previous theoretical and experimental studies of forces in the limit of flat walls in an adsorbing polymer solution. The difference could be attributed to incorporation of long-ranged colloid-polymer potential in our simulations and the influence of the curvature of the nanoparticles.     

Stability boundaries, percolation threshold, and two-phase coexistence for polydisperse fluids of adhesive colloidal particles

We study the polydisperse Baxter model of sticky hard spheres (SHS) in the modified mean spherical approximation (mMSA). This closure is known to be the zero-order approximation C0 of the Percus-Yevick closure in a density expansion. The simplicity of the closure allows a full analytical study of the model. In particular we study stability boundaries, the percolation threshold, and the gas-liquid coexistence curves. Various possible subcases of the model are treated in details. Although the detailed behavior depends upon the particularly chosen case, we find that, in general, polydispersity inhibits instabilities, increases the extent of the nonpercolating phase, and diminishes the size of the gas-liquid coexistence region. We also consider the first-order improvement of the mMSA (C0) closure (C1) and compare the percolation and gas-liquid boundaries for the one-component system with recent Monte Carlo simulations. Our results provide a qualitative understanding of the effect of polydispersity on SHS models and are expected to shed new light on the applicability of SHS models for colloidal mixtures.     

Phase separation of a model binary polymer solution in an external field

The phase separation of a simple binary mixture of incompatible linear polymers in solution is investigated using an extension of the sedimentation equilibrium method, whereby the osmotic pressure of the mixture is extracted from the density profiles of the inhomogeneous mixture in a gravitational field. In Monte Carlo simulations the field can be tuned to induce significant inhomogeneity, while keeping the density profiles sufficiently smooth for the macroscopic condition of hydrostatic equilibrium to remain applicable. The method is applied here for a simplified model of ideal but mutually avoiding polymers, which readily phase separate at relatively low densities. The Monte Carlo data are interpreted with the help of an approximate bulk phase diagram calculated from a simple, second-order virial coefficient theory. By derivation of effective potentials between polymer centers of mass, the binary mixture of polymers is coarse-grained to a "soft colloid" picture reminiscent of the Widom-Rowlinson model for incompatible atomic mixtures. This approach significantly speeds up the simulations and accurately reproduces the behavior of the full monomer resolved model.     

Electric double layers with electrolyte mixtures: integral equations theories and simulations

A study of a planar electric double layer (EDL) in the presence of mixtures of electrolyte is presented. In particular, results from the Hyper-Netted-Chain/Mean-Spherical-Approximation (HNC/MSA) theory are compared with Monte Carlo (MC) simulations. In this way, the charge inversion induced by mixtures of multivalent and monovalent counterions is probed. Since overcharging phenomena in nature emerge under such conditions, the role of ion-ion correlations in the EDL appears as a crucial point in this kind of study. Unlike previous related works, a realistic hydrated ion size is used in the HNC/MSA calculations and simulations. In this way, a qualitative agreement between the results obtained from the theory and MC simulations is found. However, some discrepancies arise when the charge inversion is expected to be more noticeable, namely at high surface charges and/or elevated concentrations of multivalent electrolytes. Such differences are explained in terms of an overestimation of the charge inversion by the integral equation (IE) formalism.     

Topological effect in ring polymers investigated with Monte Carlo simulation

We studied equilibrium conformations of ring polymers in the melt over the wide range of segment number up to 1000 by the Monte Carlo simulations and the bond fluctuation model, and estimated Flory's scaling exponent nu. The radial distribution function of segments for the ring polymers in the melt is obtained. We have found that nu for ring polymers is decreased with increasing segment number N, and nu goes down to 0.365 when N reaches 1000, whose value is apparently smaller than the theoretically predicted one, i.e., 25. Those values are in contrast to the well established nu value of 0.5 for linear polymers in the melt. This is because ring polymer chains in the melt are squeezed both by their own topological effect and the compression effect by the neighboring ring polymer coils which are also squeezed at bulk state. The difference in our result and the theory may be due to the fact that the estimation of topological entropy loss was ignored in the theoretical prediction, while it has been taken into consideration in the present study. If polymer coils repel each other in melt at N --> infinity, we have the limiting nu value of 13, so we conclude that nu is in the range of 13 < or = nu < 0.365 when the molecular weight of a ring polymer is high enough.     

Structures and adsorption of binary hard-core Yukawa mixtures in a slitlike pore: grand canonical Monte Carlo simulation and density-functional study

The grand canonical ensemble Monte Carlo simulation and density-functional theory are applied to calculate the structures, local mole fractions, and adsorption isotherms of binary hard-core Yukawa mixtures in a slitlike pore as well as the radial distribution functions of bulk mixtures. The excess Helmholtz energy functional is a combination of the modified fundamental measure theory of Yu and Wu [J. Chem. Phys. 117, 10156 (2002)] for the hard-core contribution and a corrected mean-field theory for the attractive contribution. A comparison of the theoretical results with the results from the Monte Carlo simulations shows that the corrected theory improves the density profiles of binary hard-core Yukawa mixtures in the vicinity of contact over the original mean-field theory. Both the present corrected theory and the simulations suggest that depletion and desorption occur at low temperature, and the local segregation can be observed in most cases. For binary mixtures in the hard slitlike pore, the present corrected theory predicts more accurate surface excesses than the original one does, while in the case of the attractive pore, no improvement is found in the prediction of a surface excess of the smaller molecule.     

Gelation in aqueous solutions of carboxylated polyacrylamide in the presence of chromium(III) acetate,studied by oscillation rheometry

The time dependences of the elastic moduli and loss moduli of aqueous solutions of Alcoflood-254S carboxylated polyacrylamide, containing chromium(III) acetate as a cross-linking agent, were studied by oscillation rheometry in the temperature interval 50–80°?. The gel time increases with a decrease in the temperature, as well as in the concentration of the polymer and cross-linking agent. The elastic properties of hydrogels at the moment of the onset of their formation, characterizing the concentration of cross-links between the macromolecules, are due to the polymer concentration in the solution and are independent of the chromium(III) acetate concentration and temperature. Presumably, equal degree of conversion in the reaction between carboxylate groups of the polymer and chromium(III) ion, leading to cross-linking of macromolecules of carboxylated polyacrylamide, allows determination of the kinetic parameters of the gelation from data obtained by oscillation rheometry under nonisothermal conditions.