Home

Ideal Polymers near Attractive and Repulsive Surfaces


  Yacov Kantor [1]  ,  Mehran Kardar [2]  
 [1] Tel Aviv University
[2] Massachusetts Institute of Technology

Interactions between polymers and attractive or repulsive surfaces depend on the balance between the energy of the interactions and large entropic contribution of the polymer. In the presence of scale-free (SF) surfaces (such as cones, wedges, planes, lines, etc.) many equilibrium features retain some properties of the free space and frequently can be described by universal exponents independent of system details. This is valid both for repulsive surfaces and for attractive surfaces at adsorption transition critical point (ATCP) [1]. Some critical exponents characterizing the system depend on the SF surface type. Ideal, self-avoiding and Θ polymers have their own sets of critical surface-related exponents [1].

If a polymer is attached to a SF surface at a distance h from another SF surface, and the surfaces are either repulsive or at ATCP, then for h smaller than the polymer size, the polymer mediated force will be given by F=AkBT/h, where T is the temperature of the system. The coefficient A can be related to the critical exponents and can be positive (repulsion) or negative (attraction). The case of purely repulsive surfaces has been studied before [2,3]. By proper choice of surfaces one may have "index matched" situation of A=0, when the surfaces effectively do not interact.

For ideal polymers the partition function Z can be found by solving diffusion equation, with repulsive or ATCP boundaries of statistical mechanics represented by absorbing or reflecting [4] boundary conditions, respectively, of the diffuser. Purely repulsive cases were considered in detail [3]. When all surfaces are at ATCP the force constant A=0, but for mixtures of repulsive and attractive surfaces we found some non-trivial results.

[1] E. J. Janse van Rensburg, The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles, Oxford U. Press (2015).

[2] M. F. Maghrebi, Y. Kantor and M. Kardar, Europhys. Lett. 96, 66002 (2011).

[3] Y. Hammer and Y. Kantor, Phys. Rev. E 89, 022601 (2014).

[4] R. J. Rubin, AIP Conf. Proc. 109, 73 (1984).