THE COLLAPSE TRANSITION OF A SINGLE POLYMER-CHAIN IN 2 AND 3 DIMENSIONS - A MONTE-CARLO STUDY

The collapse transition of a single polymer chain in two and three dim ensions was studied using the bond-fluctuation model. The obtained exp onents 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-te mperature T-Theta. Transition curves and scaling analysis plots are pr esented. 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), t au=\(T-T-Theta)/T-Theta\]. An analyzing of the subchain distances lead s to disagreements with the blob model. The subchains are locally swol len for T>T-Theta and shrunken for T<T-Theta. The probability distribu tion function of internal distances for T greater than or equal to T-T heta 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 dista nce. In contrast for T<T-Theta none of these functions describe the da ta. The dynamic properties above T-Theta are in agreement with the Rou se model, but below T-Theta differences occur; the center of mass diff usion 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 o f space). (C) 1996 American Institute of Physics.