Critical Behavior of Two Interacting Linear Polymer Chains in a Good Solvent

Details Critical Behavior of Two Interacting Linear Polymer Chains in a Good Solvent Critical Behavior of Two Interacting Linear Polymer Chains in a Good Solvent

Dec 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997jsp....89..981k&link_type=abstract

Journal of Statistical Physics, Volume 89, Issue 5-6, pp. 981-995

Physics

6

Segregation, Entanglement, Tricritical Line, Contact Exponent, Finite-Size Scaling, Fractals

Scientific paper

A model of two interacting (chemically different) linear polymer chains is solved exactly using the real-space renormalization group transformation on a family of Sierpinski gasket type fractals and on a truncated 4-simplex lattice. The members of the family of the Sierpinski gasket-type fractals are characterized by an integer scale factor b which runs from 2 to ∞. The Hausdorff dimension d F of these fractals tends to 2 from below as b → ∞. We calculate the contact exponent y for the transition from the State of segregation to a State in which the two chains are entangled for b = 2-5. Using arguments based on the finite-size scaling theory, we show that for b→∞, y = 2 - v(b) d F, where v is the end-toend distance exponent of a chain. For a truncated 4-simplex lattice it is shown that the system of two chains either remains in a State in which these chains are intermingled in such a way that they cannot be told apart, in the sense that the chemical difference between the polymer chains completely drop out of the thermodynamics of the system, or in a State in which they are either zipped or entangled. We show the region of existence of these different phases separated by tricritical lines. The value of the contact exponent y is calculated at the tricritical points.

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