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

The collapse transition of a single polymer chain in two and three dimensions was studied using the bond-fluctuation model. The obtained exponents v of the scaling law [S-N(2)]similar to N-2v agree with values proposed in the literature as well as above, at and below the Theta-temperature T-Theta. Transition curves and scaling analysis plots are presented. The scaling function alpha(S)(3) tau N-1/2 vs tau N-1/2 has a pronounced maximum before leveling off in the fully collapsed regime in accordance with the theory [alpha(S)(2)=[S-N(2)]/[S-N(2)](Theta), tau=\(T-T-Theta)/T-Theta\]. An analyzing of the subchain distances leads to disagreements with the blob model. The subchains are locally swollen for T>T-Theta and shrunken for T<T-Theta. The probability distribution function of internal distances for T greater than or equal to T-Theta can be described by scaling functions of the form f(s)(x) similar to x(Ks) exp( - D(s)x(delta s)) for large x, x being the scaled distance. In contrast for T<T-Theta none of these functions describe the data. The dynamic properties above T-Theta are in agreement with the Rouse model, but below T-Theta differences occur; the center of mass diffusion becomes anomalous and the relaxation times rise with a power law in N of the form tau(i)(N)similar to N-2+3/d (d being the dimension of space). (C) 1996 American Institute of Physics.