Elasticity and fluctuations of unidirectionally tethered and rippled (Pβ′) membranes

Abstract

Unidirectionally tethered ("smectic") membranes are shown to display anomalous elasticity, with both the in-plane smectic layer bend modulus K1 and the elastic modulus κz for the bend of the membrane itself transverse to the tethering direction diverging at long wavelengths, according to K1(q)=qz-25f1(azqz53) and κz(q)=qz-87fz(azqz75), where f1 and fz are universal scaling functions, az and are microscopic lengths, and the exponents are exact. These results apply to otherwise fluid membranes with adhered oriented polymers, and to the "rippled" Pβ′ phase of membranes. © 1995 The American Physical Society.