Entropic Elasticity of Lamellar Tethered Membrane Phases
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ENTROPIC ELASTICITY OF LAMELLAR TETHERED MEMBRANE PHASES LEONARDO GOLUBOVICO AND T.C. LUBENSKY` 'Chemical Engineering 210-41, Caltech, "=Physics Dept., Univ. of Pennsylvania,
Pasadena, CA 91125 Philadelphia, PA 19104
ABSTRACT Entropic elastic constants of lamellar tethered membrane phases are considered both in the vicinity of and at temperatures well below the membrane crumpling transition critical point. We calculate entropic forces acting on boundaries of physics these systems. Various predictions of the statistical of tethered membranes, such as the breakdown of the classical membrane elasticity theory at low temperatures or the existence of the crumpling transition, can be tested experimentally by using our results. INTRODUCTION In recent years there has been a considerable interest in the statistical physics of tethered, crystalline membranes which are two-dimensional generalizations of linear polymers.(I]-[71 One of the most striking theoretical findings in this field is the breakdown of the classical elasticity theory yielding, at low temperatures, a power law divergence of the membrane's effective bending rigidity constant at long length-scales x with an exponent i1>0: K(x) - xFL.[21-[4] This divergence stabilizes the long range orientational order of 2d tethered membranes at A related issue is the existence of a low temperatures. crumpling transition separating a high-temperature crumpled phase from the low-temperature asymptotically flat phase.[41,[6],[7] These theoretical results can be tested, in principle, by studying mechanical properties of lamellar tethered membrane phases which can be synthesized by polymerizing fluid membranes in their lamellar phases.[8] Then, an important theoretical physics of a problem arises. One has to link the statistical free membrane with that of an ensemble of membranes forming a stack [ Fig. 1] While the bare interaction between membranes is usually a short range repulsion, thermal fluctuations may conspire to produce long range entropic interactions [See Refs.9 and 10] known to play important role in lamellar [11] and other phases of fluid membranes.[121
Fig.l: A stack of tethered membranes Mat. Res. Soc. Symp. Proc. Vol. 248. ©1992 Materials Research Society
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In this talk we outline results of our recent study of these entropic interactions in lamellar tethered membrane phases [131 and discuss their possible experimental consequences in more detail. Some aspects of this problem were recently addressed, by a different approach, also by Toner [14] who considered situations well below the crumpling phase transition temperature Tc. Our approach enables to consider elastic properties of the stack also in the vicinity of and well above Tc. In particular, we were able to consider the entropic pressure of the stack on its basal boundary, PD, as well as that on the lateral boundary,PL [ For free lateral boundaries, as in Fig. 1, obviously PL=O.I METHOD We use the approach previously applied to lamellar fluid membrane phases in Ref.10. It is based on the fact that a me
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