Search

Abstract: The density of chain atoms in the volume element dV centered on atom i has been obtained for short and long freely jointed (FJ) chains. The Gaussian distribution function is used for long chains, and Treloar''s corrections to this distribution are imposed for short chains. For long FJ chains, the density of chain atoms is a maximum when atom i is located midway along the contour of the chain, and it is a minimum when atom i is any of the three atoms at either end of the chain. The ratio of these densities is 2. Short FJ chains can exhibit qualitatively different behavior, with the site of the maximum density shifting from the middle to the end of the chain when the number of bonds decreases from 8 to 7. This shift is imposed by the strong deviations from the Gaussian distribution when n is small. [Copyright &y& Elsevier]

Abstract: By poly(A-B) we denote a chain with repeating sequence –A-B–, such as polyoxymethylene. Here A and B stand for a single atom, e.g., –O–, or a group of atoms, e.g., –CH2–. All n bond vectors are of the same length, l, as are all bond dipole moment vectors, m. The manner in which the characteristic ratio of the dipole moment, D n ≡〈μ 2〉0/nm 2 approaches its asymptotic limit is related quantitatively to the behavior of subchains of various sizes in poly(A-B). Illustrative numerical calculations with rotational isomeric state (RIS) models for several polymers are consistent with the predictions. The approach of D n to its asymptotic limit is sensitive to longer subchains than is the approach of the characteristic ratio of the end-to-end distance, C n ≡〈r 2〉0/nl 2, to its asymptotic limit, due to the differences in the connectivity of the bond vectors (head-to-tail) and the bond dipole moment vectors (head-to-head, tail-to-tail). [Copyright &y& Elsevier]

Abstract: End effects in unperturbed chains with a specified number of bonds, n, have previously been characterized using the conformations at individual bonds and the mean square unperturbed dimensions of subchains situated at various positions along the chain. Both criteria have found that the end effects are extremely weak in typical flexible chains, such as unperturbed polyethylene. Of course, these criteria detect no end effect at all in a freely jointed chain. This conclusion requires modification if the end effects are defined differently, using the mean square radius of gyration of the n+1 chain atoms about chain atom i, denoted . The values of depend on i in all chains, including the freely jointed chain. The range for the volume specified by suggests that the average density of chain segments about a terminal atom is roughly 1/3 of the average density of chain segments about the atom midway along the contour of any long unperturbed chain. The severity of these end effects in finite chains depends on the detailed local structure, becoming more severe for more extended chains. The end effect detected by in regular freely jointed star-branched polymers becomes more severe as the number of branches increases. [Copyright &y& Elsevier]

Dense melts of coarse-grained representations of poly(silylenemethylene) (PSM) and poly(dimethylsilylenemethylene) (PDMSM) have been simulated at 373 K. The PSM melt has very little structure, and the individual chains have conformations in good agreement with the prediction from the rotational isomeric state (RIS) model for the single chain. For PDMSM, however, the melt is much more strongly structured, and the individual chains have mean square dimensions 40% higher than the ones predicted by the RIS model for the single chain. Intermolecular packing interactions in the structured PDMSM melt are accompanied by expansion of individual chains. [Copyright &y& Elsevier]

A rotational isomeric state model has been developed for the poly(silylenemethylenes) with repeating sequence [Si(CH3)R–CH2]x, R=–O(CH2)NOC6H4C6H5. The model incorporates all first- and second-order interactions, as well as higher order interactions that are mandatory in some of the conformations. Chains with all possible stereochemical sequences prefer a local conformation that is a run of trans states at the C–Si bonds in the backbone. This preference arises from an attractive second-order interaction of the first methylene group in the side-chain bonded to chain atom i with the silicon atoms indexed i±2. Unperturbed chains have larger dimensions than the simpler chain in which R is merely a methyl group. The temperature coefficients of the unperturbed dimensions are large and negative. The preference of unperturbed atactic, isotactic, and syndiotactic chains for the same local conformation may contribute to the facile formation of smectic phases by the presumably atactic chain, as reported by Park et al. [Macromolecules 35 (2002) 2776]. [Copyright &y& Elsevier]

The initial development of inhomogeneity upon stepwise cooling from the melt has been investigated in an elastomeric polypropylene (elPP), with isotactic and atactic blocks in the same chain. The simulation employs coarse-grained chains, with one bead for each repeating unit, on a high coordination lattice. Short-range intramolecular interactions are described by a rotational isomeric state model. Intermolecular interactions are derived from the behavior of pairs of molecules of propane in the gas phase. Analysis of the rates of equilibration of the simulations shows that there is sufficient time for local conformational relaxation at all temperatures studied from 298 to 473 K. However, at the lower temperatures there is insufficient time for the more extensive rearrangement of the chains required for development of the intermolecular interactions that would stabilize crystals of the isotactic blocks. Therefore the simulation is appropriate for the investigation of any heterogeneity that might develop before the onset of significant crystallization of the isotactic blocks. The fraction of C–C bonds in different rotational isomeric states changes very little over the temperature range covered. Intermolecular pair correlation functions have similar shapes when calculated for all beads, or for just those beads that appear in isotactic blocks. Nevertheless, there is greater heterogeneity in the elPP at 298 K than in isotactic polypropylene at the same temperature and thermal history. The heterogeneity of elPP can be detected by an analysis of the orientations of pairs of coarse-grained bonds and also from an analysis of the dynamics of individual beads. This heterogeneity of elPP, which appears before the onset of significant crystallization of the isotactic blocks, has contributions from individual 31 helices in the isotactic blocks and from strongly extended chain segments in those portions of the atactic blocks that are rich in racemo diads. [Copyright &y& Elsevier]

Abstract: A new generation of on-lattice MC simulations for dense melts of coarse-grained POE chains has been developed so that the MC simulations include nanoscale filler particles. In this novel approach, filler particles and polymer chains are built from the same chemical structural building unit. Early simulations pointed an ambiguous behavior for the response of the matrix chains to the introduction of the nanoparticles. When the size of nanoparticles is comparable to that of matrix chains, or even smaller, a significant amount of chain expansion (for matrix chains) is always the case, which challenges the current theoretical considerations in this field. Our recent simulations show that the chain expansion behavior is not triggered by an artificially created “extra volume” effect. Furthermore, the relation between chain expansion behavior and a potential enhancement in the free volume is found to be irrelevant based on our analysis on the pair correlation and scattering functions. [Copyright &y& Elsevier]

Abstract: Simulations of dense one-component melts of coarse-grained polyethylene (PE) and polyoxyethylene (POE) chains have been modified so that some of the parent chains are collapsed intramolecularly to become filler particles. All intermolecular pairs of beads (filler–filler, filler–matrix, matrix–matrix) interact via exactly the same Lennard–Jones (LJ) potential. Filler particles are obtained by an increase in the strength of the minimum in their intramolecular LJ potential. The response of the mean square radius of gyration, 〈s 2〉matrix, of the free matrix chains to disordered arrangements of the filler particles is evaluated for differences in the compactness and mobility of the filler particles, and for various relationships between the mass of matrix chains and filler particles. Even with this simple model, where distinctive surface—matrix interactions are completely suppressed, the response of 〈s 2〉matrix to the filler particles is complex. It depends on the completeness of the collapse of the chains that represent the filler particles, the mobility of these particles, their concentration, and the relationship between the number of beads in the matrix chains and filler particles. Expansion of the matrix chains is seen when the particles and matrix are both represented by a small number of beads, but contraction of matrix chains can be observed when both species contain a large number of beads. The mobility of the filler particles is likely to be an important issue when they are small, i.e. nanoparticles, and the matrix is not glassy. [Copyright &y& Elsevier]

Abstract: Simulations of dense melts of coarse-grained chains have been modified so that they contain filler particles. Since the filler particles and matrix chains are constructed from the same repeat unit, all of the intermolecular energetic interactions in the system (filler–filler, filler–matrix, matrix–matrix) are identical. The collapse of individual chains to form filler particles is achieved by a simple modification in the strength of the minimum in the Lennard–Jones potential governing pair-wise intramolecular interactions within a filler particle. Even when completely collapsed, the filler particles retain mobility in their internal degrees of freedom. Their centers of mass are also mobile. The filler particles can be collapsed completely to dense, impenetrable objects, but they can also be collapsed incompletely to produce permeable filler particles. There is no evidence for spontaneous aggregation of impermeable filler particles, but sufficiently permeable filler particles can aggregate. The parameters used in the simulations insure that the aggregation cannot be energetically driven. Matrix chains that fill space within a permeable filler particle have severe restrictions placed on their available conformations. The reduction in the conformational entropy of the matrix chains can be alleviated if the permeable filler particles interpenetrate, or aggregate. Then fewer matrix chains must enter the permeable filler particles in order to maintain the density of the system. The simulation detects no aggregation of impermeable filler particles because it is not necessary for matrix chains to enter completely collapsed particles. [Copyright &y& Elsevier]