Flexible polymer with excluded volume at an interacting penetrable surface of variable dimension: a multiple-.epsilon. perturbation theory

1989 ◽  
Vol 22 (5) ◽  
pp. 2412-2419 ◽  
Author(s):  
Jack F. Douglas ◽  
Marios K. Kosmas
Keyword(s):  
Perturbation Theory ◽  
Excluded Volume ◽  
Variable Dimension ◽  
Flexible Polymer

A Variational Principle Governing the Generating Function for Conformations of Flexible Molecules

2006 ◽  
Vol 74 (3) ◽  
pp. 421-426 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Differential Equation ◽  
Variational Principle ◽  
Generating Function ◽  
Potential Field ◽  
Separation Distance ◽  
Excluded Volume ◽  
Central Feature ◽  
Local Form ◽  
Flexible Polymer ◽  
End To End

The generation of a random walk path under the action of an external potential field has been of interest for decades. The motivation derives largely from the prospect of incorporating the nonlocal excluded volume effect through such a potential in characterizing the statistical behavior of a long flexible polymer molecule. In working toward a continuum mean-field model, a central feature is a partial differential equation incorporating the influence of the potential and governing the generating function for the dependence of end to end separation distance of the molecule on its pathlength. The purpose here is to describe an approach in which the differential equation is recast as a global minimization of a functional. The variational approach is illustrated by an application to familiar configurations, the first of which is a molecule attached at one end to a noninteracting plane barrier in the presence of a uniform potential field. As a second illustration, the generating function is sought for a free molecule for the case in which conformations must be consistent with the excluded volume condition. This is accomplished by adapting a local form of the Flory approach to the phenomenon and extracting estimates of the expected end to end separation distance, the entropy and other statistical features of behavior. By means of the variational principle, the problem is recast into a form that admits a direct, noniterative analysis of conformations within the context of the self-consistent field theory.

Perturbation theory for a polymer chain with excluded volume interaction

1984 ◽  
Vol 80 (11) ◽  
pp. 5839-5850 ◽  
Author(s):  
M. Muthukumar ◽  
Bernie G. Nickel
Keyword(s):  
Perturbation Theory ◽  
Polymer Chain ◽  
Excluded Volume

scholarly journals ORIENTATION CORRELATION IN SIMPLIFIED MODELS OF POLYMER MELTS

1999 ◽  
Vol 10 (02n03) ◽  
pp. 355-360 ◽  
Author(s):  
ROLAND FALLER ◽  
MATHIAS PÜTZ ◽  
FLORIAN MÜLLER-PLATHE
Keyword(s):  
Chain Length ◽  
Polymer Melts ◽  
Excluded Volume ◽  
Spring Model ◽  
Simplified Models ◽  
Flexible Polymer ◽  
Local Ordering ◽  
Ordering Effects ◽  
Chain Order

We investigate mutual local chain order in systems of fully flexible polymer melts in a simple generic bead-spring model. The excluded-volume interaction together with the connectivity leads to local ordering effects which are independent of chain length between 25 and 700 monomers, i.e. in the Rouse as well as in the reptation regime. These ordering phenomena extend to a distance of about 3 to 4 monomer sizes and decay to zero afterwards.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

A Field Theory for Polymeric Networks with Excluded Volume

1995 ◽  
Vol 5 (10) ◽  
pp. 1241-1246 ◽  
Author(s):  
Thomas A. Vilgis ◽  
Michael P. Solf
Keyword(s):  
Field Theory ◽  
Excluded Volume ◽  
Polymeric Networks
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