Integral equation theory for atactic polystyrene melt with a coarse-grained model

Density Functional Theory of Polymer Structure and Conformations

We present a density functional approach to quantitatively evaluate the microscopic conformations of polymer chains with consideration of the effects of chain stiffness, polymer concentration, and short chain molecules. For polystyrene (PS), poly(ethylene oxide) (PEO), and poly(methyl methacrylate) (PMMA) melts with low-polymerization degree, as chain length increases, they display different stretching ratios and show non-universal scaling exponents due to their different chain stiffnesses. In good solvent, increase of PS concentration induces the decline of gyration radius. For PS blends containing short (m1=1−100) and long (m=100) chains, the expansion of long chains becomes unobvious once m1 is larger than 40, which is also different to the scaling properties of ideal chain blends.

Integral equation theory for atactic polystyrene nanocomposite melts with a multi-site model

In this work, a multi-site chain model was incorporated into the polymer reference interaction site model to investigate the structure and properties of atactic polystyrene (aPS) melt and the structural correlations of dilute spherical nanoparticles dissolved in aPS melt. The theoretically calculated X-ray scattering intensities, solubility parameters and intermolecular correlation functions of aPS and its nanocomposites are found to be in agreement with the corresponding molecular simulation and experimental data. The theory was further employed to investigate the distribution functions of different size effects of aPS-nanoparticle system with consideration of the potential of mean force and depletion force. The aggregation of large nanoparticles increases with the increase of the nanoparticle-site size ratio in the infinitely dilute limit. The results show that the present theory can be used to investigate the structure of aPS melt and its nanocomposite, and give a further understanding of the filler dispersion and aggregation. All the observations indicate molecular-level details of the underlying mechanisms, providing useful information for the future design control of new aPS-nanocomposite materials with tailored properties.

Systematic coarse-graining of the dynamics of entangled polymer melts: the road from chemistry to rheology

For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, thus automatically preventing bond crossing. This also implies an upper limit on the number of atoms that can be lumped together (up to five backbone carbon atoms) and therefore on the longest chain lengths that can be studied. To reach a higher degree of coarse-graining, in CGSD many more atoms are lumped together (more than ten backbone carbon atoms), leading to relatively soft beads. In that case friction and stochastic forces dominate the interactions, and action must be undertaken to prevent bond crossing. We also review alternative methods that make use of the tube model of polymer dynamics, by obtaining the entanglement characteristics through a primitive path analysis and by simulation of a primitive chain network. We finally review super-coarse-grained methods in which an entire polymer is represented by a single particle, and comment on ways to include memory effects and transient forces.

Use of the Ornstein-Zernike Percus-Yevick equation to extract interaction potentials from pair correlation functions

In this work, we test the ability of the Ornstein-Zernike equation in the Percus-Yevick approximation (OZPY) to generate interaction potentials from pair correlation functions (PCFs) of monatomic and diatomic Lennard-Jones fluids. The PCFs are generated by solving OZPY equation (monatomic fluid) and molecular-dynamics (MD) simulations (diatomic fluid). Since the interaction potentials are inputs in the OZPY method and the MD simulation, the extraction of the potential from the PCFs using OZPY is a test of self-consistency. This test is necessary if the procedure is to be used to generate coarse-grained (CG) potentials from PCFs. We find that the procedure is completely self-consistent for the monatomic fluid in the whole range of densities studied (reduced density up to 0.55, under reduced temperature of 2.0). In the diatomic case, we find that the procedure is generally self-consistent under both low and high densities, although there is a systematic deviation at high densities. The method is able to reproduce the two parameters (ε and σ) of the input Lennard-Jones potential model to within about 1%. This CG potential generating procedure can be straightforwardly extended to more complicated molecules.

Integral equation theory study on the structure and effective interactions in star polymer nanocomposite melts

The polymer reference interaction site model theory is used to investigate the radial distribution function, potential of mean force, depletion force, and second virial coefficient in star polymer nanocomposite melts. The contact aggregation of nanoparticles for relatively weak nanoparticle-monomer attraction and the bridging aggregation of nanoparticles for very large nanoparticle-monomer attraction are observed. The star architecture can well suppress the organization states of direct contact and bridging structure for the moderate nanoparticle-monomer attraction, and promote the bridging-type organization for relatively large nanoparticle-monomer attraction. At constant particle volume fraction, the arm length quantitatively affects the organization states of star polymer nanocomposite melt, and larger repulsive barriers are existent to prevent the contact aggregation of larger nanoparticles. These observations provide useful information for the development of new nanocomposite materials.