Integral equation theory for two-dimensional polymer melts

The polymer reference interaction site model theory is investigated for two-dimensional polymer melts composed of freely-jointed hard disk chains and tangent-disk rods. Exact results for the intramolecular pair correlation functions are input into the theory, and predictions of the theory for the intermolecular pair correlation functions are tested via comparison with simulation. The theory is not as accurate for this system as it is for three-dimensional polymer melts, and the quantitative predictions are not good except at the highest area fractions. Possible reasons for the deficiency in the theory are discussed.     

Miscibility of isotactic polypropylene with atactic polystyrene

The miscibility of isotactic polypropylene-atactic polystyrene blends using dilatometric, TOA, DAT and stress-strain methods were studied. It appears that the blends are heterogeneous, having two glass transition temperatures. However, some interactions between components are evident to change theTgs of their amorphous phases and theTm of isotactic polypropylene crystals. The results are discussed on the basis of the blends' thermal and tensile properties.     

Phase separation in polyisoprene/polystyrene blends by a systematically coarse-grained model

The authors have successfully developed a structurally coarse-grained 1,4-cis-polyisoprene-atactic polystyrene blend model by systematic mapping between a detailed atomistic model and a mesoscale model. This is to their best knowledge the first time that a chemically specific polymer blend model has been used to study the phase separation morphology and kinetics in a blend. A structurally optimized force-field model has many advantages over simple bead-spring models in terms of representing the chain microstructure. It keeps the identity of the polymers, particularly the structure through radial distribution functions. Starting from randomly mixed initial configurations, the blends show a clear phase separation for chain lengths around 10 monomers and this separation becomes more pronounced with the increase of chain length. The ensuing morphology is lamellar at equiweight concentrations and cylindrical or spherical at unbalanced concentrations. Morphologies are validated to be stable under increasing system sizes and further characterized quantitatively by density profiles.     

Integral equation theory for symmetric nonadditive hard sphere mixtures

An integral equation theory is presented for the pair correlation functions and phase behavior of symmetric nonadditive hard sphere mixtures with hard sphere diameters given by sigma(A)(A)() = sigma(BB) = lambdad and sigma(AB) = d. This mixture exhibits a fluid-fluid phase separation into an A-rich phase and a B-rich phase at high densities. The theory incorporates, into the closure approximation, all terms that can be calculated exactly in the density expansion of the direct correlation functions. We find that the closure approximation developed in this work is accurate for the structure and phase behavior over the entire range of lambda, when compared to computer simulations, and is significantly more accurate than the previous theories.     

Integral equation theory for athermal solutions of linear polymers

An integral equation model is developed for athermal solutions of flexible linear polymers with particular reference to good solvent conditions. Results from scaling theory are used in formulating form factors for describing the single chain structure, and the impact of solvent quality on the chain fractal dimension is accounted for. Calculations are performed within the stringlike implementation of the polymer reference interaction site model with blobs (as opposed to complete chains) treated as the constituent structural units for semidilute solutions. Results are presented for the second virial coefficient between polymer coils and the osmotic compressibility as functions of the chain length and polymer volume fraction, respectively. Findings from this model agree with results from scaling theory and experimental measurements, as well as with an earlier investigation in which self-avoiding chains were described using Gaussian form factors with a chain length and concentration-dependent effective statistical segment length. The volume fractions at the threshold for connectedness percolation are evaluated within a coarse-grained closure relation for the connectedness Ornstein-Zernike equation. Results from these calculations are consistent with the usual interpretation of the semidilute crossover concentration for model solutions of both ideal and swollen polymer coils.     

Crystallization kinetics of isotactic polypropylene blended with atactic polystyrene

Crystallization kinetic parameters, such as spherulitic growth rates, nucleation densities, and Avrami-exponents, have been determined by optical microscopy for isotactic polypropylene blended with atactic polystyrene. It is found that the crystallization of iPP is strongly influenced by the presence of polystyrene. With increasing PS concentration in the blend, the nucleation densities decrease, while the spherulitic growth rates as well as the positions of thermal peaks, measured by DSC, remain independent of sample composition. Due to the formation of interfaces as a consequence of increasing dispersion of polystyrene the nucleation changes from preferentially thermal to athermal.     

Integral equation theory for correcting truncation errors in molecular simulations

Various strategies for correcting structural and energetic artefacts of molecular simulations with truncated potentials based on integral equation theory are described and applied to liquid water. The performance of the methods is examined for a range of cutoff distances and different shifted-force potentials. With the recently enhanced damped Coulomb potential (D. Zahn, B. Schilling, S.M. Kast, J. Phys. Chem. B, 106 (2002) 10725), parameterised and corrected by integral equation theory, radial distribution functions and excess internal energy very close to the Ewald simulation limit are obtained from a simulation with a cutoff distance of only 6 Å.     

Hydrophobic interactions with coarse-grained model for water

Integral equation theory is applied to a coarse-grained model of water to study potential of mean force between hydrophobic solutes. Theory is shown to be in good agreement with the available simulation data for methane-methane and fullerene-fullerene potential of mean force in water; the potential of mean force is also decomposed into its entropic and enthalpic contributions. Mode coupling theory is employed to compute self-diffusion coefficient of water as well as diffusion coefficient of a dilute hydrophobic solute; good agreement with molecular dynamics simulation results is found.     

Martini coarse-grained model for polyethylenimine

As a polycation with diverse applications in biomedical and environmental engineering, polyethylenimine (PEI) can be synthesized with varying degrees of branching, polymerization, and can exist in different protonation states. There have been some interests in molecular modeling of PEI at all-atom or coarse-grained (CG) levels, but present CG models are limited to linear PEIs. Here we present the methodology to systematically categorize bond lengths, bond angles and dihedral angles, which allows us to model branched PEIs. The CG model was developed under the Martini scheme based on eight ~600 Da PEIs, with four different degree of branching at two different protonation states. Comparison of the CG model with all-atom simulations shows good agreement for both local (distributions for bonded interactions) and global (end-to-end distance, radius of gyration) properties, with and without salt. Compatibility of the PEI model with other CG bio-molecules developed under the Martini scheme will allow for large-scale simulations of many PEI-enabled processes. © 2018 Wiley Periodicals, Inc.     

Integral equation theory for hard spheres confined on a cylindrical surface: anisotropic packing entropically driven

The structure of two-dimensional (2D) hard-sphere fluids on a cylindrical surface is investigated by means of the Ornstein-Zernike integral equation with the Percus-Yevick and the hypernetted-chain approximation. The 2D cylindrical coordinate breaks the spherical symmetry. Hence, the pair-correlation function is reformulated as a two-variable function to account for the packing along and around the cylinder. Detailed pair-correlation function calculations based on the two integral equation theories are compared with Monte Carlo simulations. In general, the Percus-Yevick theory is more accurate than the hypernetted-chain theory, but exceptions are observed for smaller cylinders. Moreover, analysis of the angular-dependent contact values shows that particles are preferentially packed anisotropically. The origin of such an anisotropic packing is driven by the entropic effect because the energy of all the possible system configurations of a dense hard-sphere fluid is the same. In addition, the anisotropic packing observed in our model studies serves as a basis for linking the close packing with the morphology of an ordered structure for particles adsorbed onto a cylindrical nanotube.     

Mesoscale model of polymer melt structure: self-consistent mapping of molecular correlations to coarse-grained potentials

Development and application of coarse-graining methods to condensed phases of macromolecules is an active area of research. Multiscale modeling of polymeric systems using coarse-graining methods presents unique challenges. Here we apply a coarse-graining method that self-consistently maps structural correlations from detailed molecular dynamics (MD) simulations of alkane oligomers onto coarse-grained potentials using a combination of MD and inverse Monte Carlo methods. Once derived, the coarse-grained potentials allow computationally efficient sampling of ensemble of conformations of significantly longer polyethylene chains. Conformational properties derived from coarse-grained simulations are in excellent agreement with experiments. The level of coarse graining provides a control over the balance of computational efficiency and retention of chemical identity of the underlying polymeric system. Challenges to extension and application of this and similar structure-based coarse-graining methods to model dynamics and phase behavior in polymeric systems are briefly discussed.     

A new cell model for equation of state of polyethylene melt and n-alkane

The connectivity of successive carbon atoms in polymer decreases the degrees of freedom, and hence, the external degrees of freedom should correspond only to translational motion. We therefore, introduce a coarse-grained particle of a few successive monomers. A cell model (or the hard core model with attractive potential) for the particles can accordingly be used for the derivation of the equation of state of polymers. Modifying the classical cell model by Lennard-Jones and Devonshire, we construct a new equation of state for polyethylene melt and for liquid n-alkane; the free volume term is modified by using the Sutherland potential instead of the Lennard-Jones potential. The characteristic quantities P*, V*0, and T* in the equation of state are almost independent of temperature; the principle of corresponding state holds well. Since our equation of state contains the external degrees of freedom explicitly, we can evaluate the external degrees of freedom, c, for CH2. The value of c for the coarse-grained particle is equal to 1, and hence the particle is composed of 1/c repeating units. The linear length of the particle evaluated, 4.09 A at 0 K, is consistent with that obtained by neutron and x-ray scatterings.     

Parameterization of a coarse-grained model of cholesterol with point-dipole electrostatics

We present a new coarse-grained (CG) model of cholesterol (CHOL) for the electrostatic-based ELBA force field. A distinguishing feature of our CHOL model is that the electrostatics is modeled by an explicit point dipole which interacts through an ideal vacuum permittivity. The CHOL model parameters were optimized in a systematic fashion, reproducing the electrostatic and nonpolar partitioning free energies of CHOL in lipid/water mixtures predicted by full-detailed atomistic molecular dynamics simulations. The CHOL model has been validated by comparison to structural, dynamic and thermodynamic properties with experimental and atomistic simulation reference data. The simulation of binary DPPC/cholesterol mixtures covering the relevant biological content of CHOL in mammalian membranes is shown to correctly predict the main lipid behavior as observed experimentally.     

A coarse-grained model for polyethylene glycol polymer

A coarse-grained (CG) model of polyethylene glycol (PEG) was developed and implemented in CG molecular dynamics (MD) simulations of PEG chains with degree of polymerization (DP) 20 and 40. In the model, two repeat units of PEG are grouped as one CG bead. Atomistic MD simulation of PEG chains with DP = 20 was first conducted to obtain the bonded structural probability distribution functions (PDFs) and nonbonded pair correlation function (PCF) of the CG beads. The bonded CG potentials are obtained by simple inversion of the corresponding PDFs. The CG nonbonded potential is parameterized to the PCF using both an inversion procedure based on the Ornstein-Zernike equation with the Percus-Yevick approximation (OZPY(-1)) and a combination of OZPY(-1) with the iterative Boltzmann inversion (IBI) method (OZPY(-1)+IBI). As a simple one step method, the OZPY(-1) method possesses an advantage in computational efficiency. Using the potential from OZPY(-1) as an initial guess, the IBI method shows fast convergence. The coarse-grained molecular dynamics (CGMD) simulations of PEG chains with DP = 20 using potentials from both methods satisfactorily reproduce the structural properties from atomistic MD simulation of the same systems. The OZPY(-1)+IBI method yields better agreement than the OZPY(-1) method alone. The new CG model and CG potentials from OZPY(-1)+IBI method was further tested through CGMD simulation of PEG with DP = 40 system. No significant changes are observed in the comparison of PCFs from CGMD simulations of PEG with DP = 20 and 40 systems indicating that the potential is independent of chain length.     

Solvent-free coarse-grained lipid model for large-scale simulations

A coarse-grained molecular model, which consists of a spherical particle and an orientation vector, is proposed to simulate lipid membrane on a large length scale. The solvent is implicitly represented by an effective attractive interaction between particles. A bilayer structure is formed by orientation-dependent (tilt and bending) potentials. In this model, the membrane properties (bending rigidity, line tension of membrane edge, area compression modulus, lateral diffusion coefficient, and flip-flop rate) can be varied over broad ranges. The stability of the bilayer membrane is investigated via droplet-vesicle transition. The rupture of the bilayer and worm-like micelle formation can be induced by an increase in the spontaneous curvature of the monolayer membrane.     

A transferable coarse-grained model for hydrogen-bonding liquids

We present here a recent development of a generalized coarse-grained model for use in molecular simulations. In this model, interactions between coarse-grained particles consist of both van der Waals and explicit electrostatic components. As a result, the coarse-grained model offers the transferability that is lacked by most current effective-potential based approaches. The previous center-of-mass framework (P. A. Golubkov and P. Ren, J. Chem. Phys., 2006, 125, 64103) is generalized here to include arbitrary off-center interaction sites for both Gay-Berne and multipoles. The new model has been applied to molecular dynamic simulations of neat methanol liquid. By placing a single point multipole at the oxygen atom rather than at the center of mass of methanol, there is a significant improvement in the ability to capture hydrogen-bonding. The critical issue of transferability of the coarse-grained model is verified on methanol-water mixtures, using parameters derived from neat liquids without any modification. The mixture density and internal energy from coarse-grained molecular dynamics simulations show good agreement with experimental measurements, on a par with what has been obtained from more detailed atomic models. By mapping the dynamics trajectory from the coarse-grained simulation into the all-atom counterpart, we are able to investigate atomic-level structure and interaction. Atomic radial distribution functions of neat methanol, neat water and mixtures compare favorably to experimental measurements. Furthermore, hydrogen-bonded 6- and 7-molecule chains of water and methanol observed in the mixture are in agreement with previous atomic simulations.