Free energy and thermal fluctuations of neutral lipid bilayers

A new method is proposed to calculate the free energy of lamellar liquid crystals lipid bilayers/water. The root-mean-square fluctuation of the distance between two neighboring bilayers is calculated for a number of distributions by minimizing the total free energy. Analytical solutions for the free energy are derived for a Gaussian distribution of distances, which are compared with numerical solutions obtained for more realistic distributions, which account for the correlation between the fluctuations of neighboring bilayers. Calculations are performed for typical values of the interaction parameters, and the comparison with experiment provides a more than qualitative agreement. The calculations also show that at infinite separation distance there is a minimum of zero free energy and that a local minimum can occur at a finite distance, which can be stable or unstable. The two minima are separated by a potential barrier. An unbinding transition occurs when the free energies of the two minima are equal to zero.