Arun Yethiraj

Monte Carlo density functional theory of nonuniform polymer melts

A theory for nonuniform polymer melts is presented, which combines density functional theory with Monte Carlo methods. The theory treats the ideal gas functional exactly via a single chain simulation and uses the weighted density approximation for the excess free energy functional. The bulk fluid properties required in the theory are obtained from a generalized Flory equation of state. The predictions of the theory are compared to Monte Carlo simulations for the density profiles of semiflexible polymer melts confined between flat plates. Good agreement between theory and simulation is found for 3mers and 20mers and for several densities and molecular stiffnesses.

A New Coarse-Grained Model for Water: The Importance of Electrostatic Interactions

A new coarse-grained (CG) model is developed for water. Each CG unit consists of three charged sites, and there is an additional nonelectrostatic soft interaction between central sites on different units. The interactions are chosen to mimic the properties of 4-water clusters in atomistic simulations: the nonelectrostatic component is modeled using a modified Born-Mayer-Huggins potential, and the charges are chosen to reproduce the dipole moment and quadrupole moment tensor of 4-water clusters from atomistic simulations. The parameters are optimized to reproduce experimental data for the compressibility, density, and permittivity of bulk water and the surface tension and interface potential for the air-water interface. This big multipole water (BMW) model represents a qualitative improvement over existing CG water models; for example, it reproduces the dipole potential in membrane-water interface when compared to experiment, with modest additional computational cost as compared to the popular MARTINI CG model.

Polymer reference interaction site model theory: New molecular closures for phase separating fluids and alloys

The polymer reference interaction site model integral equation theory when combined with known atomic‐like closure approximations is shown to be qualitatively inconsistent with classical mean field predictions for both long wavelength concentration fluctuations and the molecular weight dependence of the critical temperature of binary polymer blends. The fundamental error is shown to arise from the failure of atomic‐like closures to explicitly account for strong correlations between the segments on two interpenetrating polymer coils which are close in space but widely separated in chemical sequence. A family of new ‘‘molecular’’ closures are formulated which explicitly account for chemical‐bonding mediated correlations. These new closures are all qualitatively consistent with mean field scaling of the critical temperature with chain length. A detailed analytical derivation of the predictions of the new closures for thread‐like symmetric blends is carried out, and the influence of density and concentration ...

Site–site correlations in short chain fluids

Intramolecular and intermolecular site–site correlations in short chain fluids are obtained via Monte Carlo simulation for volume fractions ranging between 0.05 and 0.35. The chains are modeled as pearl necklaces of freely jointed hard spheres; chains composed of 4 and 8 beads are studied. The intramolecular distribution between a pair of beads separated by a fixed number of segments along the chain is found to be remarkably independent of the position of the pair along the chain. At low densities the intermolecular site–site pair distribution function at contact is found to be much less than one due to the ‘‘correlation hole’’ effect. The contact value increases as the density is increased, and decreases as the chain length is increased. We use the intramolecular correlations measured to obtain polymer reference interaction site model predictions for the intermolecular site–site distribution function. We find that the theory accurately reproduces the local structure of the fluid, but significantly overestimates the contact value of the distribution function, especially at low densities. A comparison of freely jointed chain results with simulations of chains with fixed bond angles and torsional rotations treated in the rotational isomeric state approximation shows that the correlation hole is more pronounced in freely jointed chains. We test a superposition approximation used to evaluate the three body term in the pressure equation for chain molecules. We find that the three‐body term is sizeable, and that the superposition approximation significantly underestimates the three‐body contribution.

Short chains at surfaces and interfaces: A quantitative comparison between density-functional theories and Monte Carlo simulations

The surface and interfacial properties of a molecular liquid composed of short linear chains are investigated using molecular density-functional theories. The molecules are modeled as spherical sites connected by springs, and each site interacts with other sites and the surfaces with a modified Lennard-Jones interaction. In the density-functional theories, the ideal gas free energy functional is treated exactly (using a partial enumeration scheme) and the excess (over ideal gas) free energy functional is treated using a weighted density approximation (WDA). The latter requires the thermodynamic properties of the homogeneous fluid and a prescription for the weighting function. The thermodynamics of the homogeneous system is described via Wertheim’s perturbation theory, and various approximations for the weighting function in the WDA are tested. We find that for the theory to be accurate, it is important to decompose the excess free energy function into a repulsive and an attractive part, with different approximations for the two parts. Results from several approximations are in good agreement with Monte Carlo simulations for the chain conformations, density oscillations (packing) in the vicinity of surfaces, and the surface tension, for both liquid–vapor interfaces and attractive surfaces.

Density functional theory of polymers: A Curtin-Ashcroft type weighted density approximation

A density functional theory is presented that combines an exact expression for the ideal gas free energy functional with a weighted density approximation for the excess free energy functional. The weighting function required in the theory is obtained from the Curtin-Ashcroft recipe, with a bulk fluid direct correlation function from the polymer reference interaction site model integral equation theory. The theory is in quantitative agreement with computer simulations for the density profiles of freely jointed tangent sphere hard chains at a hard wall, about as accurate as the Curtin-Ashcroft theory is for hard spheres at a hard wall. For a more realistic fused-sphere chain model with fixed bond angles and bond lengths, the theory is in excellent agreement with simulations at low and intermediate densities but overestimates the magnitude of layering at high densities for short chains. The theory becomes more accurate as the chain length is increased.

Monte Carlo simulations and integral equation theory for microscopic correlations in polymeric fluids

Monte Carlo simulations are performed for polymer chains modeled as pearl necklaces of freely jointed tangent hard spheres; chains composed of 20, 50, and 100 beads are studied at volume fractions ranging from 0.1 to 0.35. The mean‐square end‐to‐end distance, the radius of gyration, and the intramolecular and intermolecular site–site distribution functions are monitored in the simulations. Various approximations for the intramolecular structure factor, w(k), are tested. It is found that the w(k) from the semi‐flexible chain model is the most accurate. The polymer ‘‘reference interaction site model’’ (PRISM) theory of Curro and Schweizer is tested using both approximate and exact expressions for w(k). It is found that, at the densities examined here, the theory is accurate for the local structure except near contact where it tends to overestimate the value of the intermolecular site–site distribution function, g(r). The polymer‐RISM theory is also solved with the generalized mean spherical approximation...

Monte Carlo simulation of hard chain–hard sphere mixtures in slitlike pores

The structure of mixtures of hard chains (modeled as a pearl necklace of freely jointed hard spheres) and hard spheres in slitlike pores is studied using a canonical ensemble Monte Carlo method. Simulation results for the density profiles in pores with wall separations varying from two to ten hard sphere diameters are presented at overall volume fractions of 0.12 and 0.34, and the effect of pore size, chain concentration, and chain length on the structure of the chains is investigated. It is found that the chains are depleted at the wall at the lower density, but enhanced at the wall (relative to the center of the pore) at the higher density; this depletion increases as the chain length is increased. It is found that the enhancement of monomers and depletion/enhancement of chains at the wall becomes more marked as the pore size is increased. As all the pores we study are integer multiples of the bead diameter, we do not observe the oscillatory variation of the wall density with wall separation which is ex...

Generalized Flory equations of state for square‐well chains

The hard chain Dickman–Hall generalized Flory (GF) and Honnell–Hall generalized Flory‐dimer (GF‐D) equations of state are extended to square‐well chain fluids. The molecules are modeled as a pearl necklace of freely jointed spheres that interact via site–site square‐well intermolecular potentials. Equations of state for square‐well monomers and square‐well dimers (required in the GF‐D theory) are obtained from integral equations with a mean spherical approximation (MSA) closure. The theories are compared to Monte Carlo simulation data for the pressure of square‐well 4‐mers, 8‐mers, and 16‐mers. The GF‐D theory is in excellent agreement with the simulation data; the GF theory overestimates the pressure in all cases. A closed‐form equation of state for square‐well chains is obtained by employing equations of state for square‐well monomers and for square‐well dimers using second order perturbation theory. The resulting equation is very accurate when compared to simulations, but not as accurate as when the mo...

PHASE BEHAVIOR OF SEMIFLEXIBLE TANGENT HARD SPHERE CHAINS

The isotropic–nematic phase transition in semiflexible hard chain fluids is investigated via an Onsager type density functional theory. The angle-dependent excluded volume of two chains required in the theory is obtained via Monte Carlo simulations. The theory predicts an isotropic to nematic phase transition at lower densities than those predicted by previous theories. These results compare favorably with available simulation data.