19,306 research outputs found
On the chain length dependence of local correlations in polymer melts and a perturbation theory of symmetric polymer blends
The self-consistent field (SCF) theory of dense polymer liquids assumes that
short-range correlations are almost independent of how monomers are connected
into polymers. Some limits of this idea are explored in the context of a
perturbation theory for mixtures of structurally identical polymer species, A
and B, in which the AB pair interaction differs slightly from the AA and BB
interaction, and the difference is controlled by a parameter alpha Expanding
the free energy to O(\alpha) yields an excess free energy of the form alpha
, in both lattice and continuum models, where z(N) is a
measure of the number of inter-molecular near neighbors of each monomer in a
one-component liquid. This quantity decreases slightly with increasing N
because the self-concentration of monomers from the same chain is slightly
higher for longer chains, creating a deeper correlation hole for longer chains.
We analyze the resulting -dependence, and predict that , where is an invariant degree of
polymerization, and . This and other predictions are
confirmed by comparison to simulations. We also propose a way to estimate the
effective interaction parameter appropriate for comparisons of simulation data
to SCF theory and to coarse-grained theories of corrections to SCF theory,
which is based on an extrapolation of coefficients in this perturbation theory
to the limit . We show that a renormalized one-loop theory
contains a quantitatively correct description of the -dependence of local
structure studied here.Comment: submitted to J. Chem. Phy
Universality of subleading corrections for self-avoiding walks in presence of one dimensional defects
We study three-dimensional self-avoiding walks in presence of a
one-dimensional excluded region. We show the appearance of a universal
sub-leading exponent which is independent of the particular shape and
symmetries of the excluded region. A classical argument provides the estimate:
. The numerical simulation gives .Comment: 29 pages, latex2
An improved perturbation approach to the 2D Edwards polymer -- corrections to scaling
We present the results of a new perturbation calculation in polymer
statistics which starts from a ground state that already correctly predicts the
long chain length behaviour of the mean square end--to--end distance , namely the solution to the 2~dimensional~(2D) Edwards model.
The thus calculated is shown to be convergent in ,
the number of steps in the chain, in contrast to previous methods which start
from the free random walk solution. This allows us to calculate a new value for
the leading correction--to--scaling exponent~. Writing , where in 2D,
our result shows that . This value is also supported by an
analysis of 2D self--avoiding walks on the {\em continuum}.Comment: 17 Pages of Revtex. No figures. Submitted to J. Phys.
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