Faculty of Chemistry

Adam Mickiewicz University, Poznań

Modelling of solvent effect on the conformation of a chain grafted to the Modelling of solvent effect on the conformation of a chain grafted to the planar surfaceplanar surface

Grażyna Nowicka, Waldemar Nowicki

The conformation of an isolated linear polymer molecule near an inert impenetrable planar surface has been studied. Linear polymer chains consisting of up to 200 segments were modelled as self-avoiding walks (SAWs) on the primitive cubic lattice having a lattice constant equal to a. The positions of successive segments in a chain were chosen by the (112) algorithm. A lattice coordination number for the algorithm chosen is equal to 24. The chain was assumed to be terminally attached to the surface. The chain generating algorithm has been modified in such a way that the chain avoids the visited sites, i.e. only previously unvisited sites can be selected for successive steps. No configurational bias improvement has been applied. Instead, some variants of the self-repelling self-avoiding walk (SRSAW) algorithms have been employed. The SRSAW algorithms have been obtained by additional modifications of the SAW method. The modifications consisted in blocking some lattice sites adjacent to sites already occupied by chain segments.

The method applied allows a simulation of the chain conformation in a wide solvent quality range. The parameter v, determined from the dependence of the chain gyration radius, RG, and average end-to-end

distance, RH, on the number of segments in the chain, N, is used to characterize the solvent. It has been calculated for free chains (i.e. chains unperturbed by the presence of surface) from the following equation:

Faculty of Chemistry, UAM, Grunwaldzka 6, 60-780 Poznań, PolandEmail: gnow@amu.edu.pl

where b is the segment length equal to 61/2a for (112) algorithm.The conformational entropies of unperturbed chains and chains terminally attached to the surface have been calculated by means of the statistical counting method (SCM) [1].The difference in entropies of free and tethered chains has been assumed as the entropy of chain adsorption, S. In the range of the chain length examined, S scales with the number of segments in the chain, N, as [2]:

For the solution (v=1/2) the exponent is found to be of 1/2. The effect of solution properties on the conformation of chain anchored to the planar surface is discussed in terms of the relationship between both universal scaling exponents, v and .  References1. D. Zhao, Y. Huang, Z. He, R. Qian, J. Chem. Phys. 104 (1996) 16722. Ł. Spisak, W. Nowicki, Proceedings of International Scientific Conference “Surfactants and Dispersed System In Theory and Practice SURUZ”, Ed. K.A. Wilk, PALMAPress, Wrocław, 2007, p. 231

NS ~

vNb

R6G

Linear dimensions of the free polymer chain The difference between entropy of free and anchored chain

Dependencies between scaling exponents in Eqs (1, 2) and (3)

Statistical counting method

effective coordination number

number of conformations

conformational entropy

Statistical counting method

effective coordination number

number of conformations

conformational entropy

i

ii

1

1

1N

N

ii

1

1

N lnN

ii

BkS

SRSAW algorithms

SRSAW algorithms

(1, 2)

(3)

A

B

B

A

B

B

vbNR H