We have argued that for chain molecular models incorporating nonvanishing long-range interactions the trivariate distribution function W(XX, YY, ZZ)—XX, YY and ZZ being the three principal axes of the equivalent elipsoid—would provide a more adequate basis for assessing the chain flexibility. The magnitude of the second moment of the distribution would be a direct indicator of flexibility. This led to the determination of the flexibility behaviour of n-alkane molecules as function of temperature. For the molecules of up to 25 segments, initially flexibility increases rapidly with temperature, but at higher temperatures it declines. The flexibility of the longer molecules is found to be always an increasing function of temperature. The observed flexibility behaviour is interpreted in terms of the temperature-dependent configurational behaviour of the molecules.

'Monte Carlo' computer simulation of chain molecules. I

The Monte Carlo simulation technique (the bond fluctuation model) has been used for the study of the equilibrium conformations of comb-branched polymers consisting of a long flexible main chain and side chains grafted at a regular separation onto the main chain. The solvent has been supposed to be good (athermal) for the main and side chains. The global conformation and the gyration radius of the polymer, as well as the local conformational structure of the comb, have been analyzed as functions of the length of the side chains and spacers. The effect of induced rigidity of the comb due to the interaction between side chains has been observed. We have found the results of the simulation to be in reasonable agreement with the predictions of the scaling theory of comb-branched polymers.

Comb-Branched Polymers: Monte Carlo Simulation and Scaling

A three dimensional continuous space Monte Carlo computer simulation study is presented to discuss the extension of flexible, linear polymer chains due to the presence of equally flexible side chains. We consider the enhancement of the persistence length of bottle-brush structures in an athermal solution due to steric interactions between the side chains, The largest structure studied consists of a backbone of 100 beads with 50 side chains of 20 beads each, The persistence length lambda is evaluated in two different ways using the radius of gyration of the backbone and the bond angle correlation function, respectively. A correct description of the backbone conformations is shown to require at least two characteristic lengths. At a small length scale the backbone behaves flexible; the extension occurs at a larger length scale. There is a strong indication that the ratio between the persistence length and the diameter, which is the determining factor for lyotropic behavior of conventional semiflexible chains, levels off as a function of the side chain length. The value of this ratio is, moreover, too small to induce lyotropic behavior along this line. Recent experimental observations of lyotropic behavior of polymacromonomers are discussed in terms of these findings. (C) 1997 American Institute of Physics.

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On lyotropic behavior of molecular bottle-brushes: A Monte Carlo computer simulation study

Single-chain Monte Carlo simulations were carried out, in continuous space, of polymers with various topologies (branched and linear) in the good solvent. Using an inherently flexible bead-and-spring model, the backbone of linear polymers with either linear or dendritic side-groups attached was found to be elongated, indicative of an induced stiffness. This “topological stiffness” was compared to the “intrinsic stiffness” of semiflexible linear polymers in terms of various observables. Semiflexible comb polymers, which contained both types of stiffness, were also considered.

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Intrinsic and +topological stiffness in branched polymers

The angular dependence of scattered light, P(X), from randomly branched homopolycondensates was calculated by using moment-generating functions. Analytical expressions could be derived both for Gaussian sub-chains and for sub-chains obeying random flight statistics. For small X values (region of scattered visible light), P(X) can be well approximated by Zimm's formula: 






which holds for linear (f = 2) and branched polycondensates as well. At large X values (X-ray small angle scattering), however, strong deviations from the linear Zimm formula appear. The effect of excluded volume alters the mean-square radius of gyration but has no detectable influence on the shape of the particle scattering factor.

Angular distribution of rayleigh scattering from randomly branched polycondensates

A Monte Carlo procedure was used to simulate flexible branched macromolecules on a high‐speed digital computer. The molecules studied were of the regular‐comb type. Configurational and statistical thermodynamic properties were evaluated according to prescriptions used for linear flexible chains. The effects of branching on these properties are discussed.

Lawrence V. Gallacher

Papers

Monte Carlo Study of Flexible Branched Macromolecules