Monte Carlo Simulation Studies of the Size and Shape of Linear and Star‐Branched Copolymers Embedded in a Tetrahedral Lattice

Abstract

Characteristic properties of linear (F = 2) and star‐branched copolymers with F = 3 to 12 arms in common good, common theta and in selective solvents are summarized. Based on ensembles of chains or stars with chain lengths up to ≈50 000 segments, exponents of scaling laws of mean square dimensions of the whole star and of individual blocks and arms may be reduced to five cases. Several ratios which compare stars to linear chains (so‐called g factors) and shape‐parameters in the limit of infinite chain lengths are deduced from the prefactors of scaling laws and by proper extrapolation, respectively. Shape parameters give evidence for some orientation effects which in addition are directly demonstrated.

Entropic sampling of star-shaped polymers with different number of arms: temperature dependencies of structural properties

“…Lattice models have been widely used for a long time in the study of polymers [9]. These models are still useful now [10][11][12][13][14], since such an approach allows one to obtain reasonable results with minimal computational requirements.…”

“…All three components have different values, so we can state that the simulated stars have an average form of the three-axis ellipsoid. Knowledge of these components makes it possible to calculate the asphericity parameter of the star [11]:…”

“…We have also considered the parameter that allows us to distinguish between the oblate and the elongated forms [11] This parameter ranges over the interval [-0.25, 2], so it can be both negative (oblate form) and positive (elongated form). The temperature dependency of S * is presented in Fig.…”

Equilibrium properties of 3-arm star-shaped polyions: an entropic sampling Monte Carlo study

“…Though lattice models were introduced some time ago, they still have not lost their relevance [31][32][33][34][35]. On the one hand, simple models allow us to run simulations quickly and efficiently, on the other hand absence of chemical details gives possibility to get insight into underlying physical background of the studied phenomena.…”

“…Parameter S * varies in the range [−0.25, 2], and can be both negative (oblate shape) and positive (prolate shape) [32]. At T ≈ 1.2 the star is in a swollen state, its shape is close to spherical (S * ≈ 0, Fig.…”