Free Energy of a Fluctuating Vesicle

Bivas, Isak, Free Energy of a Fluctuating Vesicle. Influence of the Fluctuations on the Laplace Law, 6, 93 see also Mechanical Properties of Lipid Bilayers Containing Grafted Lipids, 6, 207. 

Free Energy of a Fluctuating Vesicle. Influence of the Fluctuations on the Laplace Law... 

It is known that if bending moments act on a deformed membrane, the Laplace law is modified [1]. The problem is even more complicated in the case of a fluctuating membrane. The membrane s out-of-plane fluctuations change its effective elasticity [2,3] and renormalize the tension of the membrane [4], The aim of the present work is to find the relationship between the difference of the hydrostatic pressure Ap inside and outside a fluctuating giant vesicle, its tension a, and its elastic constants. For this purpose, the free energy of the vesicle is calculated. 

Since R [ 1), unless (ps is exponentially small. For stiff membranes, where 1, this implies that the vesicles can only exist as a dilute solution for surfactant volume fractions, volume fractions, the lowest free energy state is probably lamellar. Including the effects of the renormalization of the bending modulus to lower values due to long-wavelength fluctuations (see Chapter 6), changes the distribution of Eq. (8.21) from a simple exponential to the product of a power law in N and an exponential. ... 

The numerical examples presented in Fig. 3.12 demonstrate that in the macroscopic case the Wp distribution is practically Gaussian. Meantime, for the microscopic system there may be an essential deviation of the distribution from the Gaussian one. The physical reason for such a deviation is, of course, the effect of fluctuations. The knowledge of the distribution function Wp is important, since it allows the calculation of average values of the different characteristics of the whole system, for example, such as the proba-bility of finding a vesicle with a positive AF value, average free energy (AF), and so on. 

Two different bending elastic moduli exist A f, when the exchange of lipid molecules between the monolayers of the bilayer is free, and when it is blocked. When the exchange is forbidden, the number of the molecules in each monolayer of the bilayer is constant. At free flip-flop, the bending elasticity energy is lower because it has been minimized with respect to the difference between the number of molecules in each monolayer and, consequently, k < kf. For all phenomena related to the out-of-plane fluctuations of membranes, the relevant quantity is k [6-8]. These phenomena include the thermal fluctuations of quasispherical vesicles [9,10], as well as vesicle suction in micropipettes at very low suction pressures [1]. 

---