Bundles of Interacting Strings in two Dimensions

1993

Phys. Rev. Lett.

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...

Section: U« C (N) = E£(oo) -[U?(oo) -U?(l)]/n>contrasting

confidence: 99%

Unbinding of symmetric and asymmetric stacks of membranes

Netz

1993

Phys. Rev. Lett.

“…At this fixed point, the decay of the one-point function (<$o(r)) M ~ JJ, X° and the two-point function ($ 0 (0)<&O(0)A* ~ M X°M~X°[ 1 + O(|/ir| x 2~xo)] is faster than for a free interface; this could be observed in finite-size studies of the two-dimensional Ising model with a line of stronger bonds. The results of the € expansion are also in good agreement with exact transfer matrix calculations [9].…”

Section: Critical Roughening Of Interfaces: a New Class Of Renormalizsupporting

confidence: 76%

Critical roughening of interfaces: A new class of renormalizable field theories

Lässig

1993

Phys. Rev. Lett.

A renormalizable field theory is developed for (multi)critical roughening of interacting interfaces in systems of dimension d < 3. There is an infinite hierarchy of universality classes that mirrors the series of multicritical points in Ising systems. The relevant operator algebra of these theories is built up by local scaling fields that are singular distributions of the basic field variable. Critical indices, e.g., the exponent a s of the specific heat, are obtained analytically in an e expansion. The extension of our results to d = 3 is discussed.PACS numbers: 64.60. Pr, 05.70.Jk, ll.10.Gh In recent years, much effort has been devoted to the study of low-dimensional manifolds such as domain boundaries, interfaces, polymers, or membranes. New experimental tools have been developed that make it possible to probe these objects in much detail. The structure of surfaces and interfaces can be studied on a microscopic scale using surface x-ray and neutron scattering, and even one-dimensional domain boundaries or surface steps can now be observed directly by atomic force microscopy.The statistical mechanics of these systems is governed by the interplay between intermolecular forces and fluctuations due to thermal excitation or quenched disorder. If these fluctuations are strong enough, a single manifold is in a scale-invariant rough state. Ising domain walls in two dimensions or in three dimensions above the roughening temperature are an example.In real systems, however, the position of a manifold may still be constrained by walls or defect planes, or by the presence of other manifolds, if they lead to an effective potential that is attractive over a microscopic range a and tends to zero at larger distances. For example, in the standard Ising model with a plane of weaker bonds, a domain wall is subject to an effective potential well; if the spin-spin interactions or the structure of the defect plane are more complex, the potential may have both attractive and repulsive parts within the range a. The discussion in the sequel includes such more general potentials.At low temperature or weak quenched disorder, the manifold is then localized to the position of lowest energy up to fluctuations of order a and is hence smooth on larger scales, while at high temperature or strong disorder, it is in a delocalized state with shape fluctuations on all scales up to the size of the system. The roughening, wetting, or unbinding transition separating these two regimes [1] may be of first or second order. In the latter case, the size of typical fluctuations diverges as the critical point is approached from below. Close to criticality, as they become large compared to a, the fluctuations wipe out microscopic details of the interactions, i.e., they renormalize the binding potential. Universal scaling behavior emerges, at least for sufficiently short-ranged potentials.So far, this type of transition has been studied by transfer matrix calculations for interfaces in twodimensional systems and by functional renormalization group methods ...

“…This has to be compared with the behavior of thermally excited strings [19][20][21] and of strings in a random potential [22][23][24][25][26] for which one finds two and six different universality classes, respectively.…”

Section: Universality Classes For the Strong Fluctuation Regimementioning

confidence: 99%

Semi-flexible polymers with attractive interactions

Bundschuh

Lässig

The European Physical Journal E

2000

The delocalization and unbinding transitions of two semi-flexible polymers which experience attractive interactions are studied by a variety of theoretical methods. In two-dimensional systems, one has to distinguish four different universality classes for the interaction potentials. In particular, the delocalization transitions from a potential well and the unbinding transitions from such a well in the presence of a hard wall exhibit distinct critical behavior governed by different critical exponents. In three-dimensional systems, we predict first-order transitions with a jump in the energy density but with critical or self-similar fluctuations leading to distribution functions with power law tails. The predicted critical behavior is confirmed numerically by transfer matrix calculations in two dimensions and by Monte Carlo simulations in three dimensions. This behavior should be accessible to experiments on biopolymers such as actin filaments or microtubuli.