Long polymers near wedges and cones

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Yosi Hammer, Yacov Kantor

Abstract

We perform a Monte Carlo study of N-step self-avoiding walks, attached to the corner of an impenetrable wedge in two dimensions (d=2), or the tip of an impenetrable cone in d=3, of sizes ranging up to N=10^{6} steps. We find that the critical exponent γ_{α}, which determines the dependence of the number of available conformations on N for a cone or wedge with opening angle α, is in good agreement with the theory for d=2. We study the end-point distribution of the walks in the allowed space and find similarities to the known behavior of random walks (ideal polymers) in the same geometry. For example, the ratio between the mean square end-to-end distances of a polymer near the cone or wedge and a polymer in free space depends linearly on γ_{α}, as is known for ideal polymers. We show that the end-point distribution of polymers attached to a wedge does not separate into a product of angular and radial functions, as it does for ideal polymers in the same geometry. The angular dependence of the end position of polymers near the wedge differs from theoretical predictions.

References

Jul 23, 2004·The Journal of Chemical Physics·Hsiao-Ping Hsu, Peter Grassberger
Feb 2, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Mohammad F MaghrebiMehran Kardar
Oct 30, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yosi Hammer, Yacov Kantor
May 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Nir Alfasi, Yacov Kantor

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Citations

Jul 11, 2016·The Journal of Chemical Physics·Yosi Hammer, Yacov Kantor
Sep 28, 2017·Physical Review. E·Raz Halifa Levi, Yacov Kantor
Sep 28, 2017·Physical Review. E·Yacov Kantor, Mehran Kardar

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