Statistical Mechanics of Confined Biological Materials

In this work, we propose a model to study the Statistical Mechanics of a confined bilayer-membrane that fluctuates between two interactive flat substrates. From the scaling laws point of view, the bilayer-membranes and strings are very similar. Therefore, it is sufficient to consider only the problem of a string. We assume that the bilayer-membrane (or string) interact with the substrate via a Double Morse potential that reproduces well the characteristics of the real interaction. We show that the Statistical Mechanic of the string can be adequately described by the Schrdinger equation approach that we solve exactly using the Bethe method. Finally, from the exact value of the energy of the ground state, we extract the expression of the free energy density as well as the specific heat.