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.     

计算平均力势的理论方法

A universal theoretical framework is proposed for calculating potential of mean force (PMF) between two solute particles immersed in a solvent bath, the present method overcomes all of drawbacks of previous methods. The only input required to implement the recipe is solvent density distribution profile around a single solute particle. The universal framework is applied to calculate the PMF between two large spherical particles immersed in small hard sphere solvent bath. Comparison between the present predictions and existing simulation data shows reliability of the present recipe. Effects of solvent-solute interaction detail, solvent bulk density, and solute size on the excess PMF are investigated. The resultant conclusion is that depletion of solvent component by the solute particle induces attractive excess PMF, while gathering of solvent component by the solute particle induces repulsive excess PMF, high solvent bulk density and large solute size can strengthen the tendency of attraction or repulsion. Relevance of transition from depletion attraction to gathering repulsion with the biomolecular interaction, i.e. hydrophobic attraction and hydration repulsion, is discussed.     

Brownian dynamics simulation of a model simple electrolyte in solvents of low dielectric constant

Brownian dynamics simulations are performed to investigate the ionic transport of model simple electrolytes, in which ions are interacting with each other through the repulsive core and Coulombic interactions. The equivalent conductivity and self-diffusion coefficient show minima as the function of the number density of ions when the dielectric constant of the solvent is low. Although the minimum of the former is in harmony with various experiments, no experiment has ever been reported on that of the latter. The analysis of time-dependent transport coefficients reveals that the presence of the minima is ascribed to the slow dynamics, rather than to static association models. The inclusion of a model function that resembles the short-range part of the potential of mean force induced by solvent affects the transport coefficients qualitatively, which suggests the importance of solvent-induced potential of mean force in the conduction mechanism of electrolytes in solvents of low dielectric constant.     

Pair interaction potentials of colloids by extrapolation of confocal microscopy measurements of collective suspension structure

A method for measuring the pair interaction potential between colloidal particles by extrapolation measurement of collective structure to infinite dilution is presented and explored using simulation and experiment. The method is particularly well suited to systems in which the colloid is fluorescent and refractive index matched with the solvent. The method involves characterizing the potential of mean force between colloidal particles in suspension by measurement of the radial distribution function using 3D direct visualization. The potentials of mean force are extrapolated to infinite dilution to yield an estimate of the pair interaction potential, U(r). We use Monte Carlo simulation to test and establish our methodology as well as to explore the effects of polydispersity on the accuracy. We use poly-12-hydroxystearic acid-stabilized poly(methyl methacrylate) particles dispersed in the solvent dioctyl phthalate to test the method and assess its accuracy for three different repulsive systems for which the range has been manipulated by addition of electrolyte.     

Steric stabilization of spherical colloidal particles: Implicit and explicit solvent

We present the results of Monte Carlo simulations and density functional theory treatment of interactions between spherical colloidal brushes both in implicit (good) solvent and in an explicit polymeric solution. Overall, theory is seen to be in good agreement with simulations. We find that interactions between hard-sphere particles grafted with hard-sphere chains are always repulsive in implicit solvent. The range and steepness of the repulsive interaction is sensitive to the grafting density and the length of the grafted chains. When the brushes are immersed in an explicit solvent of hard-sphere chains, a weak mid-range attraction arises, provided the length of the free chains exceeds that of the grafted chains.     

Solvent mediated interactions close to fluid-fluid phase separation: microscopic treatment of bridging in a soft-core fluid

Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation, and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed "wetting" film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a "bridging" transition as the wetting films join to form a fluid bridge. The effective (solvent mediated) potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a nonzero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein-Zernike equations.     

温度对二甲基亚砜水溶液的结构和热力学性质的影响

应用参考作用格位模型理论计算了二甲基亚砜(DMSO)摩尔分数为0.002时不同温度下溶液的微观结构和热力学性质. 计算结果表明, DMSO加入到水中能够增强溶液的分子网络结构. 温度升高, 配位数减小, 溶液中分子排布趋向无序. 平均力势的波动增大表明分子间的诱导力表现为斥力. 计算得到的各种热力学性质显示: 温度升高, 溶液的熵和溶剂化自由能增加, 相互作用能和过剩化学位也增加, 即高温下溶液越来越偏离理想溶液; 空位形成能降低表明溶液分子结构在高温下更容易重组.     

Phase behavior and structure formation in linear multiblock copolymer solutions by Monte Carlo simulation

The solution phase behavior of short, strictly alternating multiblock copolymers of type (A(n)B(n))(m) was studied using lattice Monte Carlo simulations. The polymer molecules were modeled as flexible chains in a monomeric solvent selective for block type A. The degree of block polymerization n and the number of diblock units per chain m were treated as variables. We show that within the regime of parameters accessible to our study, the thermodynamic phase transition type is dependent on the ratio of m / n. The simulations show microscopic phase separation into roughly spherical aggregates for m / n ratios less than a critical value and first-order macroscopic precipitation otherwise. In general, increasing m at fixed n, or n at fixed m, promotes the tendency toward macroscopic phase precipitation. The enthalpic driving force of phase change is found to universally scale with chain length for all multiblock systems considered and is independent of the existence of a true phase transition. For aggregate forming systems at low amphiphile concentrations, multiblock chains are shown to self-assemble into intramolecular, multichain clusters. Predictions for microstructural dimensions, including critical micelle concentration, equilibrium size, shape, aggregation parameters, and density distributions, are provided. At increasing amphiphile density, interaggregate bridging is shown to result in the formation of networked structures, leading to an eventual solution-gel transition. The gel is swollen and consists of highly interconnected aggregates of approximately spherical morphology. Qualitative agreement is found between experimentally observed physical property changes and phase transitions predicted by simulations. Thus, a potential application of the simulations is the design of multiblock copolymer systems which can be optimized with regard to solution phase behavior and ultimately physical and mechanical properties.     

Ordered packing of soft discoidal system

A novel mesoscopic simulation method is adopted to study the ordered packing of the anisotropic disklike particles with a soft repulsive interaction, which possesses a modified anisotropic conservative force type used in dissipative particle dynamics. We examine the influence of the shape of the particles, the angular width of the repulsion, and the strength of the repulsion on the packing structures. Specifically, an ordered hexagonal columnar structure is obtained in our simulations. Our study demonstrates that an anisotropic repulsive potential between soft discoidal particles is sufficient to produce a relatively ordered hexagonal columnar structure.     

Effect of bidispersity in grafted chain length on grafted chain conformations and potential of mean force between polymer grafted nanoparticles in a homopolymer matrix

In efforts to produce polymeric materials with tailored physical properties, significant interest has grown around the ability to control the spatial organization of nanoparticles in polymer nanocomposites. One way to achieve controlled particle arrangement is by grafting the nanoparticle surface with polymers that are compatible with the matrix, thus manipulating the interfacial interactions between the nanoparticles and the polymer matrix. Previous work has shown that the molecular weight of the grafted polymer, both at high grafting density and low grafting density, plays a key role in dictating the effective inter-particle interactions in a polymer matrix. At high grafting density nanoparticles disperse (aggregate) if the graft molecular weight is higher (lower) than the matrix molecular weight. At low grafting density the longer grafts can better shield the nanoparticle surface from direct particle-particle contacts than the shorter grafts and lead to the dispersion of the grafted particles in the matrix. Despite the importance of graft molecular weight, and evidence of non-trivial effects of polydispersity of chains grafted on flat surfaces, most theoretical work on polymer grafted nanoparticles has only focused on monodisperse grafted chains. In this paper, we focus on how bidispersity in grafted chain lengths affects the grafted chain conformations and inter-particle interactions in an implicit solvent and in a dense homopolymer polymer matrix. We first present the effects of bidispersity on grafted chain conformations in a single polymer grafted particle using purely Monte Carlo (MC) simulations. This is followed by calculations of the potential of mean force (PMF) between two grafted particles in a polymer matrix using a self-consistent Polymer Reference Interaction Site Model theory-Monte Carlo simulation approach. Monte Carlo simulations of a single polymer grafted particle in an implicit solvent show that in the bidisperse polymer grafted particles with an equal number of short and long grafts at low to medium grafting density, the short grafts are in a more coiled up conformation (lower radius of gyration) than their monodisperse counterparts to provide a larger free volume to the longer grafts so they can gain conformational entropy. The longer grafts do not show much difference in conformation from their monodisperse counterparts at low grafting density, but at medium grafting density the longer grafts exhibit less stretched conformations (lower radius of gyration) as compared to their monodisperse counterparts. In the presence of an explicit homopolymer matrix, the longer grafts are more compressed by the matrix homopolymer chains than the short grafts. We observe that the potential of mean force between bidisperse grafted particles has features of the PMF of monodisperse grafted particles with short grafts and monodisperse grafted particles with long grafts. The value of the PMF at contact is governed by the short grafts and values at large inter-particle distances are governed by the longer grafts. Further comparison of the PMF for bidisperse and monodisperse polymer grafted particles in a homopolymer matrix at varying parameters shows that the effects of matrix chain length, matrix packing fraction, grafting density, and particle curvature on the PMF between bidisperse polymer grafted particles are similar to those seen between monodisperse polymer grafted particles.     

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.     

Pressure dependence of the vapor-liquid-liquid phase behavior in ternary mixtures consisting of n-alkanes, n-perfluoroalkanes, and carbon dioxide

Expansion of an organic solvent by an inert gas can be used to tune the solvent's liquid density, solubility strength, and transport properties. In particular, gas expansion can be used to induce miscibility at low temperatures for solvent combinations that are biphasic at standard pressure. Configurational-bias Monte Carlo simulations in the Gibbs ensemble were carried out to investigate the vapor-liquid-liquid equilibria and microscopic structures for two ternary systems: n-decane/n-perfluorohexane/CO2 and n-hexane/n-perfluorodecane/CO2. These simulations employed the united-atom version of the transferable potential for phase equilibria (TraPPE-UA) force field. Initial simulations for binary mixtures of n-alkanes and n-perfluoroalkanes showed that special mixing parameters are required for the unlike interactions of CHx and CFy pseudoatoms to yield satisfactory results. The calculated upper critical solution pressures for the ternary mixtures at a temperature of 298 K are in excellent agreement with the available experimental data and predictions using the SAFT-VR (statistical associating fluid theory of variable range) equation of state. The simulations yield asymmetric compositions for the coexisting liquid phases and different degrees of microheterogeneity as measured by local mole fraction enhancements.     

Molecular simulation of interaction between passivated gold nanoparticles in supercritical CO2

Molecular dynamics simulations have been performed to study the potential of mean force (PMF) between passivated gold nanoparticles (NPs) in supercritical CO(2) (scCO(2)). The nanoparticle model consists of a 140 atom gold nanocore and a surface self-assembled monolayer, in which two kinds of fluorinated alkanethiols were considered. The molecular origin of the thermodynamics interaction and the solvation effect has been comprehensively studied. The simulation results demonstrate that increasing the solvent density and ligand length can enhance the repulsive feature of the free energy between the passivated Au nanoparticles in scCO(2), which is in good agreement with previous experimental results. The interaction forces between the two passivated NPs have been decomposed to reveal various contributions to the free energy. It was revealed that the interaction between capping ligands and the interaction between the capping ligands and scCO(2) solvent molecules cooperatively determine the total PMF. A thermodynamic entropy-energy analysis for each PMF contribution was used to explain the density dependence of PMF in scCO(2) fluid. Our simulation study is expected to provide a novel microscopic understanding of the effect of scCO(2) solvent on the interaction between passivated Au nanoparticles, which is helpful to the dispersion and preparation of functional metal nanoparticles in supercritical fluids.     

Effect of discrete macroion charge distributions in solutions of like-charged macroions

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on structural properties of aqueous solutions of like-charged macroions has been investigated by Monte Carlo simulations. Two discrete charge distributions have been considered: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both discrete charge distributions have been examined with fixed and mobile macroion charges. Different boundary conditions have been applied to examine various properties. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion and the effect increases with counterion valence. As a consequence, with mono- and divalent counterions the potential of mean force between two macroions becomes less repulsive and with trivalent counterions more attractive. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the potential of mean force between two macroions becomes more repulsive/less attractive.     

Nonlinear effects on solvation dynamics in simple mixtures

The authors applied the time dependent density functional method (TDDFM) and a linear model to solvation dynamics in simple binary solvents. Changing the solute-solvent interactions at t=0, the authors calculated the time evolution of density fields for solvent particles after the change (t>0) by the TDDFM and linear model. First, the authors changed the interaction of only one component of solvents. In this case, the TDDFM showed that the solvation time decreased monotonically with a mole fraction of the solvent strongly interacting with the solute. The monotonical decreases agreed with experimental results, while the linear model did not reproduce these results. The authors also calculated the solvation time by changing the interaction of both components. The calculation showed that the mole fraction dependence had the peak. The TDDFM presented a much higher peak than the linear model. The difference between the TDDFM and the linear model was caused by a nonlinear effect on an exchange process of solvent particles.     

Cylindrical inclusions in a copolymer membrane

The membrane-mediated interaction between two parallel, cylindrical inclusions is investigated by using the self-consistent field theory (SCFT). The rodlike inclusions are located within the interior of the bilayer and are enveloped by two monolayers. They may exhibit one of the two basic types of behaviors involving pinching two monolayers together and swelling them outward. For different parameters, we calculate the density profile of the deformation membrane, the associated interaction free energy, as well as the conformational entropy of polymer chains. The similarity of the two types of interaction potentials is the qualitative characteristics. An energy barrier separates an attractive from a repulsive region; the repulsive region is preceded by a weak attraction at a large distance. The difference between them, which is due to the different contact environments around the rods, lies in the appearance of a small barrier at a short distance in the pinching structure. Particular emphasis is put on the closely energetic and entropic analyses of the interaction potential. We show that the chemical potential energy has provided a qualitative trend and roughly dominated the basic shape of the interaction potential; the amphiphile entropy in the swelling structure and the solvent entropy in the pinching structure, combined with the corresponding chemical potential energy, are responsible for the repulsive barrier at an intermediate distance and for the weak attraction at a large distance, respectively. The influence of inclusion hydrophobicity on the interaction potential is taken into account. In particular, the pinching and swelling structures can appear and can transform into each other in a system at intermediate hydrophobicity.     

The interaction of patterned solutes in binary solvent mixtures

Mean solute-solute forces and solute-induced solvent structure are investigated for pairs of chemically patterned (patched) solutes in binary mixtures near demixing coexistence. The isotropic and anisotropic hypernetted-chain integral equation theories as well as a superposition approximation are solved and compared. The patched solutes consist of one end that favors the majority species in the mixture while the other end favors the minority species. A wide range of patch sizes is considered. The isotropic and anisotropic theories are found to be in good agreement for most orientations, including the most attractive and most repulsive configurations. However, some differences arise for asymmetrical orientations where unlike ends of the solute particles face each other. In contrast, superposition often gives a rather poor approximation to the mean force, even though the results obtained for the solvent densities agree qualitatively with the anisotropic theory. The mean force is sensitive to small differences in the densities particularly near demixing. For patched solutes the influence of demixing-like behavior is evident both in the orientational dependence and in the range of the mean force acting between solutes.     

Understanding the stabilization of liquid-phase-exfoliated graphene in polar solvents: molecular dynamics simulations and kinetic theory of colloid aggregation

Understanding the solution-phase dispersion of pristine, unfunctionalized graphene is important for the production of conducting inks and top-down approaches to electronics. This process can also be used as a higher-quality alternative to chemical vapor deposition. We have developed a theoretical framework that utilizes molecular dynamics simulations and the kinetic theory of colloid aggregation to elucidate the mechanism of stabilization of liquid-phase-exfoliated graphene sheets in N-methylpyrrolidone (NMP), N,N'-dimethylformamide (DMF), dimethyl sulfoxide (DMSO), γ-butyrolactone (GBL), and water. By calculating the potential of mean force between two solvated graphene sheets using molecular dynamics (MD) simulations, we have found that the dominant barrier hindering the aggregation of graphene is the last layer of confined solvent molecules between the graphene sheets, which results from the strong affinity of the solvent molecules for graphene. The origin of the energy barrier responsible for repelling the sheets is the steric repulsions between solvent molecules and graphene before the desorption of the confined single layer of solvent. We have formulated a kinetic theory of colloid aggregation to model the aggregation of graphene sheets in the liquid phase in order to predict the stability using the potential of mean force. With only one adjustable parameter, the average collision area, which can be estimated from experimental data, our theory can describe the experimentally observed degradation of the single-layer graphene fraction in NMP. We have used these results to rank the potential solvents according to their ability to disperse pristine, unfunctionalized graphene as follows: NMP ≈ DMSO > DMF > GBL > H(2)O. This is consistent with the widespread use of the first three solvents for this purpose.     

A simple theory of the interaction between polymer brushes immersed in a supercritical fluid

We use a simple two-order parameter model to describe the interaction between the brushes of polymers terminally attached to flat surfaces immersed in a supercritical solvent. Our approach makes it possible to take into account the high compressibility of the supercritical solvent, which proves to give a significant contribution to the disjoining force acting between polymer brushes. Our theory explains why the interaction between brushes can change from repulsive to attractive with decreasing solvent density. This theoretical finding is verified by making a comparison with recent computer simulations. A reasonably good agreement between the results of the present theory and the simulations is found.