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Molecular modeling techniques were applied to predicting binding energies for nanocomposites comprising exfoliated clay layers treated with ammonium salts (usually quaternary) and dispersed in nylon 6,6 resin. For each of 12 selected ammonium ions (quats), a molecular dynamics simulation was performed at 600 K for 100–300 ps with a time step of 0.001 ps on a computer model built from 20 repeating units of nylon 6,6 polymer, six quat molecules and a montmorillonite platelet. Several conformations were selected from the equilibrated time region, energy minimization carried out and binding energies calculated between nylon 6,6 and the clay platelet, between nylon 6,6 and the quat, and between the quat and the platelet. It was found that the binding energy between nylon 6,6 and the clay platelet decreases almost linearly with the volume of adsorbed quat. Consequently, pristine clay yields the highest binding strength to the nylon. Clays partially substituted by long quats were found to be equivalent to those fully substituted with short quats.

Monte Carlo simulations have been performed on a self-avoiding simple cubic lattice chain with the nearest-neighbor interactions for a range of chain lengths N from 40 to 1000 segments to investigate equilibrium properties of polymer chains from an athermal to a collapsed state. Both the fraction of segments in the clusters and the number of contacts exhibit the three stage process for the chain collapse, consistent with our previous molecular dynamics simulations of a fully atomistic chain. In the collapse region corresponding to the nearest-neighbor interaction parameter larger than 0.5 for a segment-solvent pair, polymer chains are quite spherical and both ends lie nearly randomized within the sphere. The peak height of the specific heat is proportional to N(lnN) 3/11 ', as predicted by the renormalization group theory.

In order to study the collapse of polymer chains, atomistic simulations of atactic poly(vinyl chloride) (PVC) were performed. An isolated PVC chain with a degree of polymerization (DP) larger than 40 quickly folds from an all-trans zigzag form into a nearly spherical compact state, whose density is close to the bulk one. PVC chains with DP < 30 remain unperturbed. The radius of gyration (S) and the monomer clustering exhibit two-stage and three-stage processes for the chain collapse, respectively. In the first stage, nearest monomers stick together and both the end-to-end distance and S sharply decrease. The shape of the chain changes from a thin wire to a sausage. The second stage corresponds to the transition from a sharp to gradual decrease in S. During this stage, distant monomers along the contour start coming within an interaction radius of each other. The third stage is characterized by an appearance of self-entanglements. In the collapsed chain, no new torsion states develop but the distribution becomes richer in gauche ± states than in the unperturbed chain.

A correlation function formalism for the intrinsic viscosity of polymers is studied. For this purpose, a Fokker‐Planck equation and the momentum flux equation in the full phase space of the polymer are derived by an application of the projection operator method to the whole system consisting of the polymer and solvent molecules. These relations are further reduced to Kirkwood's Fokker‐Planck equation and the corresponding flux in the polymer coordinate space. These steps give a molecular‐theoretical basis to the Kirkwood equation, and the reduced flux obtained is essentially equivalent to that suggested previously by Stockmayer and co‐workers. Some comments are made on related studies, particularly that of Doi and Okano, which is considered to be erroneous.

In order to test the two‐parameter theory of dilute polymer solutions, light‐scattering and intrinsic‐viscosity measurements were carried out on fractions of poly‐p‐methylstyrene in toluene, dichloroethane, cyclohexane, and methyl ethyl ketone at 30°C, and in diethyl succinate at temperatures ranging from 16 to 60°C. The theta temperature for this polymer in diethyl succinate was found to be 16.4°C. With the data for the statistical‐radius expansion factor αS and the interpenetration function Ψ appearing in the second virial coefficient, validity of a theory of these quantities was examined using the two criteria introduced previously: (1) consistency in the values of the excluded‐volume parameter z determined from αS and Ψ, and (2) linearity between z and the square root of the molecular weight. It was found that the Yamakawa–Tanaka theory of αS and the Kurata–Yamakawa theory of Ψ were a self‐consistent pair of intramolecular and intermolecular theories of interaction which satisfied both of the two crit...

Further Test of the Two-Parameter Theory of Dilute Polymer Solutions: Poly( p -bromostyrene)

Light‐scattering and intrinsic‐viscosity measurements were carried out on fractions of poly‐p‐chlorostyrene and poly‐p‐bromostyrene in toluene at 30°C. Unperturbed dimensions were estimated from the Berry plots of second virial coefficients and also from the Stockmayer–Fixman plots of intrinsic viscosities. Values of the binary‐cluster integral β per monomeric unit were determined by the two methods proposed in the previous paper; one is based on the use of the Yamakawa–Tanaka equation for the statistical‐radius expansion factor, and the other the modified Stockmayer–Fixman plot. The results by the two methods were in excellent agreement with each other. The differences in β between poly‐p‐chlorostyrene and poly‐p‐methylstyrene, and between poly‐p‐bromostyrene and poly‐p‐methylstyrene in toluene, were analyzed using the theory of dilute solutions of polar polymers developed by Yamakawa and Rice on the basis of the cavity field and reaction field arguments. The agreement between theory and experiment was found to be satisfactory. The difference in β between polystyrene and poly‐p‐methylstyrene in toluene is also discussed. It is suggested that a complete theoretical calculation of the whole β should be based on the theory of simple liquids.

The intrinsic viscosity of flexible ring polymers with small excluded volume is calculated on the basis of the theory presented previously by Yamakawa and Tanaka for linear chains. The cubed viscosity-radius expansion factor is obtained as αη,r3=1+1.21z+···, so that αη,r3/αη,13=1+0.15z+···, where the subscripts r and 1 refer to ring and linear forms, respectively, and z is the well-known excluded-volume parameter. This result supports the prediction derived by Fukatsu and Kurata by an approximate perturbation method. Some comments on the Bloomfield–Zimm theory and the Yu–Fujita theory are also given.