Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model

The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate the location of phase transitions: the collapse transition in the bulk and the adsorption transition in the presence of a surface. The bulk and surface cross-over exponents, ϕ and ϕ S , are estimated from the scaling behavior of the leading partition function zeros.

KEMAMPUAN ADSORPSI KITOSAN UNTUK ION LOGAM TIMBAL (Pb2+) DAN KADMIUM (Cd2+)

ABSTRACT Chitosan is natural polymer that has been known to posses the capacity to adsorb various transition metals. This capacity of adsorption is resulted from the ability of chitosan to form complex compound with metal, especially Pb and Cd. The formation of chitosan-metal complex is enabled by the presence of active hydroxil group in chitosan molecule. The results of this study on adsorption of Pb2+ and Cd2+ revealed the existence of linear relationship between the amount of the metal adsorbed with concentration of the metal tested. It was found that for Pb2+, the maximum adsorption was 10.32 mg/g which was achieved for the metal concentration of 50 mg/L, and 24.998 mg/g for Cd2+ at metal concentration of 100 mg/L. The optimum contact time for adsorption was found to be 24 hours for both metals. The adsorption was found to take place with the adsorption energy of 29.82 kJ/mol for Pb2+ and 17.23 kJ/mol for Cd2+. Keywords: chitin, chitosan, adsorption, transition metal, and toxic metal

Conformation and adsorption transition on an attractive surface of a ring polymer in solution

Ring polymers have the same critical adsorption point and crossover exponent as linear chains.