A single polymer grafted to a porous membraneHsiao-Ping Hsu1, 2 and Peter Grassberger1
1 John-von-Neumann Institute for Computing, Forschungszentrum Jülich - D-52425 Jülich, Germany
2 Institute of Physics, Johannes Gutenberg University of Mainz - Staudinger Weg 7, D-55099 Mainz, Germany
received 22 August 2006; accepted in final form 9 November 2006; published January 2007
published online 3 January 2007
We study a single flexible chain molecule grafted to a membrane which has pores of size slightly larger than the monomer size. On both sides of the membrane there is the same solvent. When this solvent is good, i.e. when the polymer is described by a self-avoiding walk, it can fairly easily penetrate the membrane, so that the average number of membrane crossings tends, for chain length , to a positive constant. The average numbers of monomers on either side of the membrane diverges in this limit, although their ratio becomes infinite. For a poor solvent, in contrast, the entire polymer is located, for large N, on one side of the membrane. For good and for theta solvents (ideal polymers) we find scaling laws, whose exponents can in the latter case be easily understood from the behaviour of random walks.
82.35.Lr - Physical properties of polymers .
87.16.Dg - Membranes, bilayers, and vesicles .
44.05.+e - Analytical and numerical techniques .
© Europhysics Letters Association 2007