Monte Carlo simulation studies of the size and shape of linear and star-branched polymers embedded in the tetrahedral lattice

Abstract

SUMMARY: In recent years the author investigated the size and shape of linear and star-branched model chains as a function of functionality (number of arms) F and chain length (total number of beads) N for several lattice and off-lattice random walk models as well as for self-avoiding random walks (embedded in the tetrahedral lattice) subjected to various thermodynamic conditions. Not only mean values -characteristic quantities averaged over a large number of configurations of given length, functionality and thermodynamic conditions -have been computed, but also distributions of shape parameters, and the correlation operative between size and shape has been explored. The present feature article in principle summarizes these results, however, the data given in part are recomputed for still larger sample sizes and chain-lengths as in the underlying papers. In addition to stars with F = 4, 8 and 12 arms, so far unpublished investigations on stars with F = 3, F = 6 and F = 10 arms are presented and discussed.

Star Polymers in Good Solvents From Dilute to Concentrated Regimes: Crossover Approach

“…There is no theoretical expression for asphericity of stars with EV interaction, but MC simulations [30,37,49,54,125] indicate that, similar to ideal star polymers, the asphericity of stars with EV also vanishes with increasing of f .…”

“…The RG calculations of Miyake and Freed [129] (d = 3 and ǫ = 1 in equation (4.4) in [129]) yield qualitatively better predictions for the swelling parameter α 2 and ratio g(f ), which predicts that at constant N, α 2 ∝ g(f ) ∝ f at f ≫ 1, while at constant molecular weight, the ratio g(f ) ∝ const + const · f −1 at f 2, in a qualitative agreement with MC simulations [37,55,125].…”

“…The range of the topics of these researches is extremely wide. It includes the conformation properties of isolated star polymers [18,27,37,42,49,50,[52][53][54] and dilute star polymers solutions in good solvents [19,24,30,41,[43][44][45][46]48,55,56,[64][65][66], the second virial coefficient [45,46,48,55,56,67,68], equation of state and thermodynamic properties of star polymers in semidilute and concentrated regimes [14,22,25,28,62,63], freezing of star polymers [33,[58][59][60], adsorption [20,21,23], and star polymers grafted to a wall [29,31,46]. A special place in these studies occupy star polymers at theta conditions …”

Conformations and Dynamics of Stars and Dendrimers: The Gaussian Self-Consistent Approach

“…In linear and star polymers, its molar mass dependence is given by the power law [12][13][14][15][16][17] R 2 S ∝ N 2ν , (1.2) where ν is the Flory exponent. For either topology, ν = 0.5 for the RW model and in the Θ state, and ν ∼ = 0.6 in a good solvent (apart from f -dependent prefactors).…”

“…The hydrodynamic interaction is embodied in matrix H with elements [27,30,31]: 17) where ζ r = ζ/6πη 0 l is the reduced friction coefficient (set equal to 0.25 [32]), η 0 is the solvent viscosity and, in the Gaussian approximation, r…”