Effect of attractions on the structure of polymer solutions confined between surfaces: a density functional approach

A density functional theory is presented to study the effect of attractions on the structure of polymer solutions confined between surfaces. The polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres, both having Yukawa-type attractions and the mixture being confined between attractive Yukawa-type surfaces. The present theory treats the ideal gas free energy functional exactly and uses weighted density approximation for the hard chain and hard sphere contributions to the excess free energy functional. The attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions on the density profiles of the polymer and the solvent molecules are found to agree quite well with the Monte Carlo simulation results for varying densities, chain lengths, wall separations, and different sets of interaction potentials.     

Effect of attractive interactions on the structure of polymer melts confined between surfaces: a density-functional approach

A density-functional theory is presented to study the structure of polymers, having attractive interactions, confined between attractive surfaces. The theory treats the ideal-gas free-energy functional exactly and uses weighted density approximation for the hard-chain contribution to the excess free-energy functional. The bulk interactions of freely jointed hard spheres are obtained from generalized Flory equation of state and the attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions are found to be in quite good agreement with the Monte Carlo simulation results for varying densities, chain lengths, and different interaction potentials. The results confirm important implications of using different approximations for the hard-sphere and attractive interactions.     

Structure of inhomogeneous polymer solutions: a density functional approach

The structure of polymer solutions confined between surfaces is studied using a density functional theory where the polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres. The present theory uses the concept of universality of the free energy density functional to obtain the first-order direct correlation function of the nonuniform system from that of the corresponding uniform system, calculated through the Verlet-modified type bridge function. The uniform bulk fluid direct correlation function required as input has been calculated from the reference interaction site model integral equation theory using the Percus-Yevick closure relation. The calculated results on the density profiles of the polymer as well as the solvent are shown to compare well with computer simulation results.     

Effect of Interaction upon Translocation of Confined Polymer Chain Through Nanopore

The effect of the interaction between nanopore and chain monomer on the translocation of a single polymer chain confined in a finite size square through an interacting nanopore to a large space has been studied by two-dimensional bond fluctuation model with Monte Carlo simulation. Results indicate that the free energy barrier before the successful translocation of the chain depends linearly on the chain length as well as the nanopore length for different pore-polymer interaction, and the attractive interaction reduces the free energy barrier, leading to the reduction of the average trapping time.     

Density functional theory of realistic models of polyethylene liquids in slit pores: comparison with monte carlo simulations

Density functional theory is applied to study properties of fully detailed, realistic models of polyethylene liquids near surfaces and compared to results from Monte Carlo simulations. When the direct correlation functions from polymer reference interaction site model (PRISM) theory are used as input, the theory somewhat underpredicts the density oscillations near the surface. However, good agreement with simulation is obtained with empirical scaling of the PRISM-predicted direct correlation functions. Effects of attractive interactions are treated using the random-phase approximation. The results of theoretical predictions for the attractive system are also in reasonable agreement with simulation results. In general, the theory performs best when the wall-polymer interaction strength is comparable to polymer-polymer interactions.     

Adsorption of chain molecules into a thin film structure and solvation interaction versus molecular flexibility

The influence of molecular flexibility on the properties of thin fluid films formed by linear chain molecules is studied by means of a singlet level of inhomogeneous integral equation theory. The considered m-mer chain molecules are formed through the polymerization of m hard-sphere beads with two sticky bonds randomly placed inside each bead core. Different molecular flexibility, from totally flexible up to almost completely rigid is reached by varying the interbead bonding length. The homogeneous properties of the same model that is necessary input to the singlet approach are extracted from the Wertheim’s theory of polymerization. The adsorption, local density distribution, disjoining pressure and solvation force of the chain molecule films confined by attractive and repulsive surfaces are analyzed. The obtained results indicate significant influence of the molecular flexibility on the film layering that is the origin of oscillations of solvation interaction arising between film surfaces. The oscillations of solvation pressure and force become more pronounced with restriction of molecular flexibility and with increase of bulk volume fraction of chain molecules. The decay of the oscillations across the film depends on the chain length and on the physical nature of the film surfaces, i.e. whether they are lyophilic or lyophobic. The partitioning of chain molecules from the bulk into the film strongly depends on the chain flexibility and this effect is more pronounced for the lyophilic surfaces.     

Density functional theory of homopolymer mixtures confined in a slit

A density functional theory (DFT) is developed for polymer mixtures with shorted-ranged attractive interparticle interactions confined in a slit. Different weighting functions are used separately for the repulsive part and the attractive part of the excess free energy functional by applying the weighted density approximation. The predicted results by DFT are in good agreement with the corresponding simulation data indicating the reliability of the theory. Furthermore, the center-of-mass profiles and the end-to-end distance distributions are obtained by the single chain simulation; the predictions also agree well with simulation data. The results reveal that both the attraction of the slit wall and the temperature has stronger effect on longer chains than on shorter ones because the intrasegment correlation of chains increases with increasing chain length.     

Hybrid density functional theory for homopolymer mixtures confined in a selective nanoslit

By integrating polymer density function theory (DFT) and single-chain molecular simulation, a hybrid DFT is developed for homopolymer mixtures confined in a selective nanoslit. Two weighting functions are adopted separately in the polymer DFT for repulsive and attractive contributions to the excess free energy functional. The theoretical results agree well with simulation data for the density profiles, configurations (tail, loop and train), adsorption amounts, layer thicknesses, and partition coefficients. The polymer-slit interaction is found to have a large effect on the density profiles and partition coefficients but is found to have a small effect on the average sizes and percentages of the configurations. Nearly half of the polymer segments form tails, and the other half form trains. In addition, bridges are observed to form for sufficiently long polymer chains. As the length difference between two polymers increases, the effect of chain connectivity becomes increasingly important.     

Transitions of tethered polymer chains: a simulation study with the bond fluctuation lattice model

A polymer chain tethered to a surface may be compact or extended, adsorbed or desorbed, depending on interactions with the surface and the surrounding solvent. This leads to a rich phase diagram with a variety of transitions. To investigate these transitions we have performed Monte Carlo simulations of a bond fluctuation model with Wang-Landau and umbrella sampling algorithms in a two-dimensional state space. The simulations' density-of-states results have been evaluated for interaction parameters spanning the range from good- to poor-solvent conditions and from repulsive to strongly attractive surfaces. In this work, we describe the simulation method and present results for the overall phase behavior and for some of the transitions. For adsorption in good solvent, we compare with Metropolis Monte Carlo data for the same model and find good agreement between the results. For the collapse transition, which occurs when the solvent quality changes from good to poor, we consider two situations corresponding to three-dimensional (hard surface) and two-dimensional (very attractive surface) chain conformations, respectively. For the hard surface, we compare tethered chains with free chains and find very similar behavior for both types of chains. For the very attractive surface, we find the two-dimensional chain collapse to be a two-step transition with the same sequence of transitions that is observed for three-dimensional chains: a coil-globule transition that changes the overall chain size is followed by a local rearrangement of chain segments.     

Simulation Study on Translocation of Confined Chain Through Interacting Nanopore

The translocation of a confined polymer chain through an interacting nanopore has been studied using two-dimensional bond fluctuation model with Monte Carlo dynamics. For different pore-polymer interaction, the average escaping time〈Τesc〉of the polymer chain through the nanopore, increases roughly linearly with the chain length and the nanopore length, respectively. However, the large repulsive and attractive pore-polymer interaction adds the difficulty of the monomers of the chain entering and leaving the nanopore, respec-tively, leading to the nonmonotonical dependence of〈Τesc〉on the pore-polymer interaction. The detailed translocation dynamics of the chain through the interacting nanopore is inves-tigated too.     

单链DNA在受限环境中伸展的Monte Carlo模拟

Stretching and relaxation of a single DNA molecule tethered in a specially designed thin slit were studied using Monte Carlo simulation combined with bond fluctuation method. It was found that the extension and relaxation of the single DNA molecule are greatly affected by the confined environment. If the extent of the confined environment is increased by decreasing the distance between the two planar surfaces of the slit, the extension of the single DNA molecule increases, due to the screening of the hydrodynamic interaction of DNA segments by the planar surfaces of the slit. The relaxation of the single DNA molecule in different confined environments verifies this assumption completely. The correlation between the end-to-end separation and flow velocity obtained by Monte Carlo simulation is in good agreement with either the experimental results or theoretical consideration reported previously.     

Density profiles and solvation forces for a Yukawa fluid in a slit pore

The effect of varying wall-particle and particle-particle interactions on the density profiles near a single wall and the solvation forces between two walls immersed in a fluid of particles is investigated by grand canonical Monte Carlo simulations. Attractive and repulsive particle-particle and particle-wall interactions are modeled by a versatile hard-core Yukawa form. These simulation results are compared to theoretical calculations using the hypernetted chain integral equation technique, as well as with fundamental measure density functional theory (DFT), where particle-particle interactions are either treated as a first order perturbation using the radial distribution function or else with a DFT based on the direct-correlation function. All three theoretical approaches reproduce the main trends fairly well, but exhibit inconsistent accuracy, particularly for attractive particle-particle interactions. We show that the wall-particle and particle-particle attractions can couple together to induce a nonlinear enhancement of the adsorption and a related "repulsion through attraction" effect for the effective wall-wall forces. We also investigate the phenomenon of bridging, where an attractive wall-particle interaction induces strongly attractive solvation forces.     

Solvation forces in ionic and neutral liquids: A density functional approach

The solvation forces between two planar charged surfaces in ionic solutions, corresponding to charged and neutral hard spheres representing the ions and the solvent, respectively, are studied here using a weighted density functional theory for inhomogeneous Coulomb systems developed by us recently. The hard sphere contributions to the one-particle correlation function are evaluated nonperturbatively using a position-dependent effective density, while the electrical contributions are obtained through a perturbative expansion around this weighted density. The calculated results on the solvation forces between two charged hard walls compare well with available simulation results for ionic systems. For a neutral system, the present results show good agreement with the experimentally observed oscillating forces for two mica surfaces in octamethylcyclotetrasiloxane. The present approach thus provides a direct route to the calculation of interaction energies between colloidal particles.     

Microstructure and self-assembly of inhomogeneous rigid rodlike chains between two neutral surfaces: A hybrid density functional approach

We use a hybrid density functional approach to investigate the microstructure and self-assembly of inhomogeneous rigid rodlike chains between two neutral surfaces, i.e., two hard walls. In the calculation, the rodlike molecule is modeled as a rigid rod linearly connected by the tangent sphere beads. The hybrid method combines a single-chain Monte Carlo (MC) simulation for the ideal-gas part of Helmholtz energy and a DFT approach for the excess Helmholtz energy. The DFT approach includes a modified fundamental measure theory for the excluded-volume effect, the first order thermodynamics perturbation theory for chain connectivity, and the mean field approximation for the van der Waals attraction. We investigate the effect of the chain length (i.e., aspect ratio) of the rodlike molecule and the separation between two surfaces on the microstructure and self-assembly of inhomogeneous rigid rodlike chains. For the athermal systems, the rodlike chain fluids present a smaller partitioning coefficient compared to the flexible chain fluids. For the thermal systems, lamellar thin films formed by the rigid rodlike molecules perpendicular to the neutral surface are observed. The effects of the head-head interaction and the separation on the self-assembly of the rodlike chain fluids in the slit are investigated.     

Confinement induced critical micelle concentration shift

In this work, extensive lattice Monte Carlo simulations were performed to investigate the influence of confinement on critical micelle concentration (CMC). It is found that the CMC of surfactants in a confined space is shifted from its bulk value, and the shift is affected by the presence of the confining boundaries, which induces both the finite size effect and the wall-surfactant interaction. In general, for strongly confined system (the system with narrow pore size), the finite size effect dominates the CMC shift because the confined space cannot accommodate fully developed micelles, and the rapid increase of the entropic loss due to the decrease of the pore size results in the rapid increase of CMC. In contrast, for a weakly confined space, the CMC shift depends on the interaction between the walls and surfactants. For the systems with two weakly hydrophilic surfaces, the local density depletion of the surfactants near the walls results in lower CMCs than the bulk value, and the CMC shifts to a higher value as the pore size increases. For the systems with moderately hydrophilic surfaces, the shifts of CMCs show a similar behavior as those for weakly hydrophilic surfaces, but the CMCs are near their bulk values in the range of weak confinement. For the systems with strongly attractive wall-surfactant interactions, the strong adsorption also results in lower CMCs than their bulk value, but the CMCs decrease with the increase of pore size.     

Adsorption and disjoining pressure isotherms of confined polymers using dissipative particle dynamics

The adsorption and disjoining pressure isotherms of polymers confined by planar walls are obtained using Monte Carlo (MC) simulations in the Grand Canonical (GC) ensemble in combination with the mesoscopic technique known as dissipative particle dynamics (DPD). Two models of effective potentials for the confining surfaces are used: one with both an attractive and a repulsive term and one with a purely repulsive term. As for the polymer, seven-bead linear model of polyethylene glycol (PEG) dissolved in water is used. The results indicate remarkably good agreement between the trends shown by our adsorption isotherms and those obtained from experiments of PEG on oxide surfaces. Additionally, the disjoining pressure isotherm of water shows oscillations, while those of PEG display the same trend for both wall models. Moreover, it is found that the disjoining pressure isotherms are in qualitative agreement with those from experiments on confined linear polymers.     

Simulating equilibrium surface forces in polymer solutions using a canonical grid method

A new simulation method for nonuniform polymer solutions between planar surfaces at full chemical equilibrium is described. The technique uses a grid of points in a two-dimensional thermodynamic space, labeled by surface area and surface separations. Free energy differences between these points are determined via Bennett's optimized rates method in the canonical ensemble. Subsequently, loci of constant chemical potential are determined within the grid via simple numerical interpolation. In this way, a series of free energy versus separation curves are determined for a number of different chemical potentials. The method is applied to the case of hard sphere polymers between attractive surfaces, and its veracity is confirmed via comparisons with established alternative simulation techniques, namely, the grand canonical ensemble and isotension ensemble methods. The former method is shown to fail when the degree of polymerization is too large. An interesting interplay between repulsive steric interactions and attractive bridging forces occurs as the surface attraction and bulk monomer density are varied. This behavior is further explored using polymer density functional theory, which is shown to be in good agreement with the simulations. Our results are also discussed in light of recent self-consistent field calculations which correct the original deGennes results for infinitely long polymers. In particular, we look at the role of chain ends by investigating the behavior of ring polymers.     

Properties of branched confined polymers

A model of star-branched polymer chains confined in a slit formed by two parallel surfaces was studied. The chains were embedded to a simple cubic lattice and consisted of f=3 branches of equal length. The macromolecules had the excluded volume and the confining surfaces were impenetrable for polymer segments. No attractive interactions between polymer segments and then between polymer segments and the surfaces were assumed and therefore the system was a thermal. Monte Carlo simulations were carried out employing the sampling algorithm based on chain's local changes of conformation. Lateral diffusion of star-branched chains was studied. Dynamic properties of star-branched chains between the walls with impenetrable rod-like obstacles were also studied and compared to the previous case. The density profiles of polymer segments on the slit were determined. The analysis of contacts between the polymer chain and the surfaces was also carried out.     

Prediction of the orientations of adsorbed protein using an empirical energy function with implicit solvation

When simulating protein adsorption behavior, decisions must first be made regarding how the protein should be oriented on the surface. To address this problem, we have developed a molecular simulation program that combines an empirical adsorption free energy function with an efficient configurational search method to calculate orientation-dependent adsorption free energies between proteins and functionalized surfaces. The configuration space is searched systematically using a quaternion rotation technique, and the adsorption free energy is evaluated using an empirical energy function with an efficient grid-based calculational method. In this paper, the developed method is applied to analyze the preferred orientations of a model protein, lysozyme, on various functionalized alkanethiol self-assembled monolayer (SAM) surfaces by the generation of contour graphs that relate adsorption free energy to adsorbed orientation, and the results are compared with experimental observations. As anticipated, the adsorbed orientation of lysozyme is predicted to be dependent on the discrete organization of the functional groups presented by the surface. Lysozyme, which is a positively charged protein, is predicted to adsorb on its 'side' on both hydrophobic and negatively charged surfaces. On surfaces with discrete positively charged sites, attractive interaction energies can also be obtained due to the presence of discrete local negative charges present on the lysozyme surface. In this case, 'end-on' orientations are preferred. Additionally, SAM surface models with mixed functionality suggest that the interactions between lysozyme and surfaces could be greatly enhanced if individual surface functional groups are able to access the catalytic cleft region of lysozyme, similar to ligand-receptor interactions. The contour graphs generated by this method can be used to identify low-energy orientations that can then be used as starting points for further simulations to investigate conformational changes induced in protein structure following initial adsorption.     

Effect of surface grafted polymers on the adsorption of different model proteins

Adsorption of a model protein to a surface with end-grafted polymers was studied by Monte Carlo simulations. In the model the effect on protein adsorption in the presence of end-grafted polymers was evaluated by calculating the change in free energy between an end-grafted surface and a surface without polymers. The change in free energy was calculated using statistical mechanical perturbation theory. Apart from ordinary athermal polymer-polymer and protein-polymer interactions we also study a broad selection of systems by varying the interaction between proteins and polymers and effective polymer-solvent interactions. The interactions between the molecules span an interval from -0.5 to +0.5 kT. Consequently, general features of protein adsorption to end-grafted surfaces is investigated by systematically changing properties like hydrophilicity/hydrophobicity of the polymer, protein and surface as well as grafting density, degree of polymerization and protein size. Increasing grafting density as well as degree of polymerization decreases the adsorption of protein except in systems with attractive polymer-protein interactions, where adsorption increases with increasing chain length and higher grafting density. At a critical polymer-protein interaction neither chain length nor grafting density affects the free energy of adsorption. Hydrophilic polymers were found to prevent adsorption better than hydrophobic polymers. Very small particles with radii comparable to the size of a polymer segment were, however, better excluded from the surface when using hydrophobic than hydrophilic polymers. For systems with attractive polymer-protein interaction not only the volume of the protein was shown to be of importance but also the size of the exposed surface.