Finite- N effects for ideal polymer chains near a flat impenetrable wall

• Published in: The European physical journal. E, Soft matter and biological physics Vol. 29; no. 1; pp. 107 - 115
• Main Authors: Matsen, M. W., Kim, J. U., Likhtman, A. E.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-05-2009; EDP Sciences
• Subjects: Applied sciences; Biological and Medical Physics; Biophysics; Complex Fluids and Microfluidics; Complex Systems; Exact sciences and technology; Nanotechnology; Organic polymers; Physicochemistry of polymers; Physics; Physics and Astronomy; Polymer Sciences; Properties and characterization; Regular Article; Soft and Granular Matter; Solution and gel properties; Surfaces and Interfaces; Thin Films; 61.25.he Polymer solutions; 82.35.Gh Polymers on surfaces; adhesion; 05.70.Np Interface and surface thermodynamics; Chemical solution; Liquid solid adsorption; Theoretical study; Polymer; Statistical mechanics; Modeling; Conformation
• ISSN: 1292-8941; 1292-895X
• DOI: 10.1140/epje/i2009-10454-2

This paper addresses the statistical mechanics of ideal polymer chains next to a hard wall. The principal quantity of interest, from which all monomer densities can be calculated, is the partition function,
G
N
(
z
) , for a chain of
N
discrete monomers with one end fixed a distance
z
from the wall. It is well accepted that in the limit of infinite
N
,
G
N
(
z
) satisfies the diffusion equation with the Dirichlet boundary condition,
G
N
(0) = 0 , unless the wall possesses a sufficient attraction, in which case the Robin boundary condition,
G
N
(0) = -
G
N
′
(0) , applies with a positive coefficient,
. Here we investigate the leading
N
-1/2
correction,
G
N
(
z
) . Prior to the adsorption threshold,
G
N
(
z
) is found to involve two distinct parts: a Gaussian correction (for
z
aN
1/2
with a model-dependent amplitude,
A
, and a proximal-layer correction (for
z
a
described by a model-dependent function,
B
(
z
) .