6.
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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