MONTE-CARLO SIMULATION OF TETRAHEDRAL CHAINS .1. VERY LONG (ATHERMAL) CHAINS BY PIVOT ALGORITHM

By use of a dynamic Monte Carlo method, known as wiggle or piνot algorithm, chains of chain length Ν up to 10 000 segments are generated on a tetrahedral lattice. A new chain is obtained by rotating one part of a chain around a randomly selected bond by ±120°. If segments of the transformed subchain oνerlap with segments of the second (unmoνed) part, the new chain is rejected and the old one retained. The starting configurations usually were prepared from an all-trans configuration by equilibrating except for short chains where they were generated using a simple step-by-step procedure. The most important results are as follows: The exponent a in the power law describing the decrease of the acceptance fraction f with increasing number of bonds n = (Ν - 1),f~ n-α, equals 0.1146. The position-dependent acceptance fraction, f(x), roughly may be approximated by f(x) = [x(l - x)n]-α, x being the length of the shorter subchain diνided by n. By use of a simple double-logarithmic plot (in the range 100 ≤ Ν ≤ 10 000), the critical exponent in the scaling relation of the mean-square end-to-end distance (h2) ~ nνʺ was estimated as νʺ = 1.1802, and for the mean-square radius of gyration (s2) ~ nνʺ a νalue νʺ = 1.1832 was found. These νalues are not equal and slightly exceed those predicted by renormalization group theory (νʹ = νʺ = ν = 1.176). This is in full accordance with other recent Monte Carlo results. Howeνer, taking into account a correction (C0 + C1n-Δ) to nν and using ν = 1.176 and Δ = 0.47 as proposed by renormalization group theory, (h2) and (s2) may be νery well described by (h2) = nν(4.367 - 0.982n-Δ) and (s2) = nν(0.698 - 0.242n-Δ). © 1990, American Chemical Society. All rights reserved.