Abstract
The purpose is an exact study of the unbinding transition from two interacting manifolds (strings or bilayer membranes). These systems have similar scaling behavior, and then it is sufficient to consider only the strings’ problem. We assume that the manifolds interact via a realistic potential of Morse type. To this end, the use is made of the transfer matrix method, based on the resolution of a Schrödinger equation. We first determine the associated bound states and energy spectrum. Second, the exact ground state energy gives the free energy density, from which we extract the expression of the unbinding temperature. Third, we determine the contact probability between manifolds, from which we compute the (diverging) average separation and roughness of the manifolds. It is found that their critical behavior is close to that obtained using Field-Theoretical Renormalization-Group. The conclusion is that these analytical studies reveal that the Morse potential is a good candidate for the study of the unbinding phenomenon within manifolds. Finally, the discussion is extended to generalized Morse potential.
Highlights
Unbinding is a phenomenon that occurs in soft elastic manifolds, including strings and bilayer membranes [1,2,3]
The bilayer membrane remains stable at the minimum of the potential, provided that the potential depth is comparable to the thermal energy
We present an exact study of the unbinding transition with Morse potential (MP) using transfer matrix method (TMM)
Summary
Unbinding is a phenomenon that occurs in soft elastic manifolds, including strings and bilayer membranes [1,2,3]. The major result is that renormalization-group (RG) calculations predicted that fluid membranes possess similar scaling properties as strings in the vicinity of the critical potential depth [7] Such a property will be the key for the investigation of the unbinding transition in bilayer membranes. The unbinding transition from strings and bilayer membranes is often driven by steric-shape fluctuations [8] whose amplitude increases with temperature. These undulation forces act between lipid bilayers in the Lα-phase and prevent vesicles from coagulation and stabilize emulsions [9, 10].
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