Membrane Rheology

Abstract

Surfactant monolayers and lipid bilayers are intrinsically two-dimensional structures with viscoelastic mechanical properties. Monolayers display a plethora of complex broken symmetry phases, each with its own rheological signature, while bilayers are of fundamental biological importance in forming the cell membrane and the principal internal partitions of the cell. Understanding the low-energy excitations and mechanical response of these materials is thus an important probe of novel two-dimensional phases and essential to biomechanics at the cellular level, cell recognition, and transport across membranes; as such, a number of macroscopic and microscopic techniques have been developed to explore the rheological properties of monolayers and membranes. In this chapter we review the fundamental physics and rheology of molecularly thin membranes, paying particular attention to the fact that these systems are necessarily bounded on one or both sides by an aqueous fluid. We develop the basic theory of both the in-and out-of-plane viscoelastic response of membranes and monolayers and apply this theory to the study of particle transport at the surface. Such transport measurements form the basis of typical rheological experiments. We also report on more recent investigations regarding the role of nontrivial membrane geometry on particle transport and examine a novel approach to monolayer and membrane microrheology using the thermal fluctuations of particles submerged beneath the membrane. We conclude with a discussion of open questions in the field and some speculations on future research directions. Overview of Membranes and Langmuir MonolayersThere is a class of molecules that, when introduced to water, spontaneously assemble at the air/water interface into a layer only one molecule thick. This nanoscale film is termed a Langmuir monolayer and its dynamics or rheology is the focus of the present chapter. While the ability to self-assemble into nanometerthick monolayers sounds like a dispatch from the frontiers of modern nanoscience, these systems are ubiquitous in nature and their study ancient in origin. In fact, such quotidian materials as olive oil and soap form these remarkable nanoscale structures. The historical record is rife with observations providing hints about these systems. Pliny the Elder remarked on the effect of oil on a body of water in the first century of the common era [1]:... all sea water is made smooth by oil, and so divers sprinkle oil on their face because it calms the rough element and carries light down with them.He was noting what was a common practice among divers in the Mediterranean who, by releasing a small quantity of oil that goes to the surface of the water above them and forms a thin film, flattened the waves and allowed for the better penetration of light into the depths. The spreading of oil on water was noted repeatedly over the next 2,000 years by others including Ben Franklin, who observed it from shipboard on a trip to England to complain about taxes (on behalf of the...

Advances in the microrheology of complex fluids

“…The Levine group explored the Faxén law corrections to the hydrodynamics of a bead optically trapped near a solid wall i.e. a liquid/solid interface [392,393]. They then extended the theory to provide corrections for the different boundary conditions that occur at a liquid/air interface and used their model to study the microrheology of a Langmuir monolayer of the surfactant DPCC, with reasonable agreement with the experiments [394].…”

Geometric localization of thermal fluctuations in red blood cells

“…Furthermore, because we assume uniform curvature in the shallow shell limit, to leading order in the geometry the fluid stress from the medium may be projected against a flat reference plane. This implies that we may write the effects of the hydrodynamic function exactly as $\xi (\text{𝒒})=2\mu q$ (12, 47, 48). We use this result in the following calculation of the dynamic correlation function.…”