Unbinding of symmetric and asymmetric stacks of membranes

Abstract

The unbinding of N membranes interacting with attractive potentials is considered theoretically for zero pressure. In the symmetric case, for which the membranes have the same bending rigidity, all N membranes unbind simultaneously at the ^-independent temperature T* but with iV-dependent effective critical exponents. In the asymmetric case, for which the lowest membrane acts as a rigid wall, they exhibit a sequence of unbinding transitions with universal exponents; the transition temperature of the uppermost membrane for a semi-infinite stack (N = oo) is again given by T*.PACS numbers: 82.70.-y, 64.60.-i Lipid bilayers in aqueous solutions often form multilayer systems consisting of well-aligned membrane stacks. Bulk samples of such multilayer systems have been experimentally studied for a long time, primarily by x-ray diffraction [1]. It is also possible, however, to observe stacks consisting of a relatively small number of bilayers. This can be done by optical microscopy for freely suspended stacks [2] or by surface reflectivity measurements for bilayers which have been immobilized onto an interface [3].The adhesion of the bilayers within the stack is governed by attractive van der Waals forces. These forces are renormalized by thermally excited shape fluctuations which act to reduce the adhesion energy [4]. This renormalization can be understood in a qualitative way if one considers the competition between the van der Waals attraction and the loss of entropy arising from the confinement of the membranes [5]. A more systematic treatment of this competition led to the theoretical prediction of a critical unbinding transition between bound and unbound membrane states [6] which has been observed experimentally for stacks of six to eight sugar-lipid membranes [7]. All membranes of these stacks appeared to be quite flexible and to have the same bending rigidity. The experimentally observed transitions were reversible and showed no hysteresis. In addition, the dependence of the unbinding temperature on the number of the membranes was found to be very weak.In this Letter, we theoretically study the adhesion and unbinding of N > 2 fluid membranes. We distinguish two different types of stacks which we call "symmetric" and "asymmetric." First, consider the symmetric case, for which all N membranes have the same bending rigidity and interact via identical potentials, which should apply to the stacks of sugar-lipid membranes as studied experimentally by Helfrich and co-workers [2,7]. In this case, we find that all N membranes unbind simultaneously at the N-independent temperature T°(N)=T°.However, we also find that the effective critical exponents for the unbinding transition depend on N and thus are nonuniversal over the accessible range of length scales. This is in marked contrast to other theoretical work, as will be discussed below. Next, consider an asymmetric stack, for which N -1 identical membranes are bound towards a rigid wall (labeled by n = 0). This corresponds, e.g., to a stack of bilayers which has been immo...

Statistical Mechanics and Dynamics of Two Supported Stacked Lipid Bilayers

“…[15,21] where only the case Ξ 1 = Ξ 2 was explored, we also find sequential thermal unbinding transitions: for Ξ 1 = Ξ 2 = 30 the upper bilayer unbinds at T u (2)/θ = 2.6 and the remaining bilayer then unbinds at T u (1)/θ = 3.3 (see 6 and 4). Moreover, membrane fluctuations increase when moving away from the substrate, η 2 − d 2 > η 1 − d 1 .…”

“…(15). Minimization of the variational free energy with respect to the four variational parameters A i and η i , yields the generalization of Eqs.…”

“…Double supported membranes belong to the latter category. The physics of asymmetric stacks studied by Monte-Carlo simulations [15,21], or by analytical tools for onedimensional strings [22], turned out to be very rich, showing for instance, over a certain range of the parameters, a peeling process where successive unbinding temperatures appear, the upper membrane unbinding first. This has to be compared to the case of symmetric stacks where T u is independent of the number of stacked membranes.…”

“…Lipowsky describes, in a very nice review [14], the various situations where unbinding occurs, among which are the cases of only steric repulsive interactions with applied external pressure, or attractive interactions between membranes, depending on experimental conditions. These theoretical studies essentially focus on the order of the transition and the values of the critical exponents, mostly using Monte-Carlo numerical simulations [15,16], or group renormalization techniques [17][18][19]. Interestingly, an analytical solution can be obtained when considering the unbinding of fluctuating strings (one dimensional objects) in two dimensions [20].…”

Coexistences of lamellar phases in ternary surfactant solutions

“…Note that ℓ−δ in the denominator corresponds to the inter-membrane distance in which membranes can undergo out-of-plane fluctuations. The numerical prefactor b was calculated to be b = 3π 2 /128 ≈ 0.23 in the original work by Helfrich [20], but its value is debatable in the literatures [27][28][29]. For example, Monte Carlo simulations in Ref.…”