CRITICAL-BEHAVIOR OF AN INTERACTING POLYMER-CHAIN IN A POROUS MODEL SYSTEM - EXACT RESULTS FOR TRUNCATED SIMPLEX LATTICES

We present an exact and a Flory-type study of thermal and geometrical properties of interacting chain polymers situated on a class of porous model systems represented by the truncated simplex lattices. Within the exact approach, we have developed a systematic use of recursion relations for both the partition functions and their various derivatives. We have thereby been able to obtain a proper solution of the polymer problem, demonstrating that the studied model has a finite critical temperature (THETA not-equal 0 K, with well-defined critical exponents), in the cases of the truncated 4-simplex and 6-simplex lattices. However, we show that in the 5-simplex case there is no finite THETA temperature. This finding is in contrast with the generally accepted qualitative argument that leads to the conclusion that the more ramified lattices are more likely to allow of existence of the THETA point. The same finding shows that the problem of existence of a collapse transition on regular fractals is more intricate than one could expect, and hence one can infer that for stochastic fractals (such as the critical percolation clusters) the same problem should be approached rather cautiously. Besides, our results for the 4-simplex case demonstrate that the model under study is in the same class of universality as a model, studied previously, with a restricted set of interactions, which should be relevant to the problem of the possible difference between the THETA and THETA' point.