The collapse transition of a single polymer chain in two and three dimensions: A Monte Carlo study

Abstract

The collapse transition of a single polymer chain in two and three dimensions was studied using the bond‐fluctuation model. The obtained exponents ν of the scaling law 〈S 2 N 〉∼N 2ν agree with values proposed in the literature as well as above, at and below the Θ‐temperature T Θ. Transition curves and scaling analysis plots are presented. The scaling function α3 S τN 1/2 vs τN 1/2 has a pronounced maximum before leveling off in the fully collapsed regime in accordance with the theory [α2 S =〈S 2 N 〉/〈S 2 N 〉Θ, τ=‖(T−T Θ)/T Θ‖]. An analyzing of the subchain distances leads to disagreements with the blob model. The subchains are locally swollen for T≳T Θ and shrunken for T<T Θ. The probability distribution function of internal distances for T≥T Θ can be described by scaling functions of the form f s (x)∼x κ s exp(−D sx δ s ) for large x, x being the scaled distance. In contrast for T<T Θ none of these functions describe the data. The dynamic properties above T Θ are in agreement with the Rouse model, but below T Θ differences occur; the center of mass diffusion becomes anomalous and the relaxation times rise with a power law in N of the form τ i (N)∼N 2+3/d (d being the dimension of space).