Publications

Abstract: Liquidliquid phase separation (LLPS) in binary or multi-component solutions is a well-studied subject in soft matter with extensive applications in biological systems. In recent years, several experimental studies focused on LLPS of solutes in hydrated gels, where the formation of coexisting domains induces elastic deformations within the gel. While the experimental studies report unique physical characteristics of these systems, such as sensitivity to mechanical forces and stabilization of multiple, periodic phase-separated domains, the theoretical understanding of such systems and the role of long-range interactions have not emphasized the nonlinear nature of the equilibrium binodal for strong segregation of the solute. In this paper, we formulate a generic, mean-field theory of a hydrated gel in the presence of an additional solute which changes the elastic properties of the gel. We derive equations for the equilibrium binodal of the phase separation of the solvent and solute and show that the deformations induced by the solute can result in effective long-range interactions between phase-separating solutes that can either enhance or, in the case of externally applied pressure, suppress phase separation of the solute relative to the case where there is no gel. This causes the coexisting concentrations at the binodal to depend on the system-wide average concentration, in contrast to the situation for phase separation in the absence of the gel. Graphical abstract: (Figure presented.)

We present a scaling view of underscreening observed in salt solutions in the range of concentrations greater than about 1 M, in which the screening length increases with concentration. The system consists of hydrated clusters of positive and negative ions with a single unpaired ion as suggested by recent simulations. The environment of this ion is more hydrated than average which leads to a self-similar situation in which the size of this environment scales with the screening length. The prefactor involves the local dielectric constant and the cluster density. The scaling arguments as well as the cluster model lead to scaling of the screening length with the ion concentration, in agreement with observations.

Chromosomes are arranged in distinct territories within the nucleus of animal cells. Recent experiments have shown that these territories overlap at their edges, suggesting partial mixing during interphase. Experiments that knock-down of condensin II proteins during interphase indicate increased chromosome mixing, which demonstrates control of the mixing. In this study, we use a generic polymer simulation to quantify the dynamics of chromosome mixing over time. We introduce the chromosome mixing index, which quantifies the mixing of distinct chromosomes in the nucleus. We find that the chromosome mixing index in a small confinement volume (as a model of the nucleus), increases as a power-law of the time, with the scaling exponent varying non-monotonically with self-interaction and volume fraction. By comparing the chromosome mixing index with both monomer subdiffusion due to (non-topological) intermingling of chromosomes as well as even slower reptation, we show that for relatively large volume fractions, the scaling exponent of the chromosome mixing index is related to Rouse dynamics for relatively weak chromosome attractions and to reptation for strong attractions. In addition, we extend our model to more realistically account for the situation of the Drosophila chromosome by including the heterogeneity of the polymers and their lengths to account for microphase separation of euchromatin and heterochromatin and their interactions with the nuclear lamina. We find that the interaction with the lamina further impedes chromosome mixing.

Maintaining homeostasis is a fundamental characteristic of living systems. In cells, this is contributed to by the assembly of biochemically distinct organelles, many of which are not membrane bound but form by the physical process of liquid-liquid phase separation (LLPS). By analogy with LLPS in binary solutions, cellular LLPS was hypothesized to contribute to homeostasis by facilitating "concentration buffering," which renders the local protein concentration within the organelle robust to global variations in the average cellular concentration (e.g., due to expression noise). Interestingly, concentration buffering was experimentally measured in vivo in a simple organelle with a single solute, while it was observed not to be obeyed in one with several solutes. Here, we formulate theoretically and solve analytically a physical model of LLPS in a ternary solution of two solutes (φ and ψ ) that interact both homotypically (φ-φ attractions) and heterotypically (φ- ψ attractions). Our physical theory predicts how the coexisting concentrations in LLPS are related to expression noise and thus, generalizes the concept of concentration buffering to multicomponent systems. This allows us to reconcile the seemingly contradictory experimental observations. Furthermore, we predict that incremental changes of the homotypic and heterotypic interactions among the molecules that undergo LLPS, such as those that are caused by mutations in the genes encoding the proteins, may increase the efficiency of concentration buffering of a given system. Thus, we hypothesize that evolution may optimize concentration buffering as an efficient mechanism to maintain LLPS homeostasis and suggest experimental approaches to test this in different systems.

We analytically predict the concentration profile of a long polymer chain in a poor solvent, confined between two walls where some of its monomers can form strong bonds with the walls. In contrast to adsorption boundary conditions, these concentration profiles can vary nonmonotonically. Boundary conditions that lead to a decrease in the monomer concentration at the walls (at fixed, total monomer concentration) show a transition between concentration profiles in which the polymer concentration is organized peripherally (near the walls) and profiles in which the polymer concentration is the highest in the center (away from the walls). We conclude by discussing the relevance of our findings to experimental observations and simulation studies of chromatin organization in the nucleus of living cells.

Spontaneous contractions of cardiomyocytes are driven by calcium oscillations due to the activity of ionic calcium channels and pumps. The beating phase is related to the time-dependent deviation of the oscillations from their average frequency, due to noise and the resulting cellular response. Here, we demonstrate experimentally that, in addition to the short-time (1-2 Hz), beat-to-beat variability, there are long-time correlations (tens of minutes) in the beating phase dynamics of isolated cardiomyocytes. Our theoretical model relates these long-time correlations to cellular regulation that restores the frequency to its average, homeostatic value in response to stochastic perturbations.

Multivalent molecules can bind a limited number of multiple neighbors via specific interactions. In this paper, we investigate theoretically the self-assembly and phase separation of such molecules in dilute solution. We show that the equilibrium size (n) distributions of linear or branched assemblies qualitatively differ; the former decays exponentially with the relative size n/N (N = 〈n〉), while the latter decays as a power law, with an exponential cutoff only for n ≳ N2 ≫ N. In some cases, finite, branched assemblies are unstable and show a sol-gel transition at a critical concentration. In dilute solutions, non-specific interactions result in phase separation, whose critical point is described by an effective Flory Huggins theory that is sensitive to the nature of these distributions. This journal is

The classical Debye-Hückel (DH) theory clearly accounts for the origin of screening in electrolyte solutions and works rather well for dilute electrolyte solutions. While the Debye screening length decreases with the ion concentration and is independent of ion size, recent surface-force measurements imply that for concentrated solutions, the screening length exhibits an opposite trend; it increases with ion concentration and depends on the ionic size. The screening length is usually defined by the response of the electrolyte solution to a test charge but can equivalently be derived from the charge-charge correlation function. By going beyond DH theory, we predict the effects of ion size on the charge-charge correlation function. A simple modification of the Coulomb interaction kernel to account for the excluded volume of neighboring ions yields a nonmonotonic dependence of the screening length (correlation length) on the ionic concentration, as well as damped charge oscillations for high concentrations.

During a first-order phase transition, an interfacial layer is formed between the coexisting phases and kinetically limits homogeneous nucleation of the new phase in the original phase. This inhibition is commonly alleviated by the presence of impurities, often of unknown origin, that serve as heterogeneous nucleation sites for the transition. Living systems present a theoretical opportunity: the regulated structure of living systems allows modelling of the impurities, enabling quantitative analysis and comparison between homogeneous and heterogeneous nucleation mechanisms, usually a difficult task. Here, we formulate an analytical model of heterogeneous nucleation of holes in the nuclear lamina, a phenomenon with implications in cancer metastasis, ageing and other diseases. We then present measurements of hole nucleation in the lamina of nuclei migrating through controlled constrictions and fit the experimental data to our heterogeneous nucleation model as well as a homogeneous model. Surprisingly, we find that different mechanisms dominate depending on the density of filaments that comprise the nuclear lamina.

Meso-porous electrodes (pore width « 1µm) are a central component in electrochemical energy storage devices and related technologies, based on the capacitive nature of electric double-layers at their surfaces. This requires that such charging, limited by ion transport within the pores, is attained over the device operation time. Here we measure directly electric double layer charging within individual nano-slits, formed between gold and mica surfaces in a surface force balance, by monitoring transient surface forces in response to an applied electric potential. We find that the nano-slit charging time is of order 1s (far slower than the time of order 3×10−2s characteristic of charging an unconfined surface in our configuration), increasing at smaller slit thickness, and decreasing with solution ion concentration. The results enable us to examine critically the nanopore charging dynamics, and indicate how to probe such charging in different conditions and aqueous environments.

Myosin II filaments form ordered superstructures in both cross-striated muscle and non-muscle cells. In cross-striated muscle, myosin II (thick) filaments, actin (thin) filaments and elastic titin filaments comprise the stereotypical contractile units of muscles called sarcomeres. Linear chains of sarcomeres, called myofibrils, are aligned laterally in registry to form cross-striated muscle cells. The experimentally observed dependence of the registered organization of myofibrils on extracellular matrix elasticity has been proposed to arise from the interactions of sarcomeric contractile elements (considered as force dipoles) through the matrix. Non-muscle cells form small bipolar filaments built of less than 30 myosin II molecules. These filaments are associated in registry forming superstructures (stacks) orthogonal to actin filament bundles. Formation of myosin II filament stacks requires the myosin II ATPase activity and function of the actin filament crosslinking, polymerizing and depolymerizing proteins. We propose that the myosin II filaments embedded into elastic, intervening actin network (IVN) function as force dipoles that interact attractively through the IVN. This is in analogy with the theoretical picture developed for myofibrils where the elastic medium is now the actin cytoskeleton itself. Myosin stack formation in non-muscle cells provides a novel mechanism for the self-organization of the actin cytoskeleton at the level of the entire cell.This article is part of the theme issue Self-organization in cell biology.

We theoretically predict and compare with experiments, transitions from spontaneous beating to dynamical entrainment of cardiomyocytes induced by an oscillating, external mechanical probe. In accord with recent experiments, we predict the dynamical behavior as a function of the probe amplitude and frequency. The theory is based on a phenomenological model for a non-linear oscillator, motivated by acto-myosin contractility. The generic behavior is independent of the detailed, molecular origins of the dynamics and, consistent with experiment, we find three regimes: spontaneous beating with the natural frequency of the cell, entrained beating with the frequency of the probe, and a "bursting" regime where the two frequencies alternate in time. We quantitatively predict the properties of the "bursting" regime as a function of the amplitude and frequency of the probe. Furthermore, we examine the pacing process in the presence of weak noise and explain how this might relate to cardiomyocyte physiology.

Many of the most important molecules of life are polymers. In animals, the most abundant of the proteinaceous polymers are the collagens, which constitute the fibrous matrix outside cells and which can also self-assemble into gels. The physically measurable stiffness of gels, as well as tissues, increases with the amount of collagen, and cells seem to sense this stiffness. An understanding of this mechanosensing process in complex tissues, including fibrotic disease states with high collagen, is now utilizing ' omics data sets and is revealing polymer physics-type, nonlinear scaling relationships between concentrations of seemingly unrelated biopolymers. The nuclear structure protein lamin A provides one example, with protein and transcript levels increasing with collagen 1 and tissue stiffness, and with mechanisms rooted in protein stabilization induced by cytoskeletal stress. Physics-based models of fibrous matrix, cytoskeletal force dipoles, and the lamin A gene circuit illustrate the wide range of testable predictions emerging for tissues, cell cultures, and even stem cell-based tissue regeneration. Beyond the epigenetics of mechanosensing, the scaling in cancer of chromosome copy number variations and other mutations with tissue stiffness suggests that genomic changes are occurring by mechanogenomic processes that now require elucidation.

In the version of this Letter originally published, the numbering of Supplementary Video files and the references to those files in the text did not match. All online versions of the Letter have been corrected so that the Supplementary Videos are numbered sequentially from 117.

Mechanobiological studies of cell assemblies have generally focused on cells that are, in principle, identical. Here we predict theoretically the effect on cells in culture of locally introduced biochemical signals that diffuse and locally induce cytoskeletal contractility which is initially small. In steady-state, both the concentration profile of the signaling molecule as well as the contractility profile of the cell assembly are inhomogeneous, with a characteristic length that can be of the order of the system size. The long-range nature of this state originates in the elastic interactions of contractile cells (similar to long-range "macroscopic modes" in non-living elastic inclusions) and the non-linear diffusion of the signaling molecules, here termed mechanogens. We suggest model experiments on cell assemblies on substrates that can test the theory as a prelude to its applicability in embryo development where spatial gradients of morphogens initiate cellular development.

We present a model of biopolymer gels that includes two types of elastic nonlinearities, stiffening under extension and softening (due to buckling) under compression, to predict the elastic anisotropy induced by both external as well as internal (e.g., due to cell contractility) stresses in biopolymer gels. We show how the stretch-induced anisotropy and the strain-stiffening nonlinearity increase both the amplitude and power-law range of transmission of internal, contractile, cellular forces, and relate this to recent experiments.

We present a generic and unified theory to explain how cells respond to perturbations of their mechanical environment such as the presence of neighboring cells, slowly applied stretch, or gradients of matrix rigidity. Motivated by experiments, we calculate the local balance of forces that give rise to a tendency for the cell to locally move or reorient, with a focus on the contribution of feedback and homeostasis to cell contractility (manifested by a fixed displacement, strain or stress) that acts on the adhesions at the cell boundary. These forces can be either reinforced or diminished by elastic stresses due to mechanical perturbations of the matrix. Our model predicts these changes and how their balance with local protrusive forces that act on the cell's leading edge either increase or decrease the tendency of the cell to locally move (toward neighboring cells or rigidity gradients) or reorient (in the direction of slowly applied stretch or rigidity gradients).

We review recent theoretical efforts that predict how line-active molecules can promote lateral heterogeneities (or domains) in model membranes. This fundamental understanding may be relevant to membrane composition in living cells, where it is thought that small domains, called lipid rafts, are necessary for the cells to be functional. The theoretical work reviewed here ranges in scale from coarse grained continuum models to nearly atomistic models. The effect of line active molecules on domain sizes and shapes in the phase separated regime or on fluctuation length scales and lifetimes in the single phase, mixed regime, of the membrane is discussed. Recent experimental studies on model membranes that include line active molecules are also presented together with some comparisons with the theoretical predictions.

A recently proposed ternary mixture model is used to predict fluctuation domain lifetimes in the one phase region. The membrane is made of saturated, unsaturated, and hybrid lipids that have one saturated and one unsaturated hydrocarbon chain. The hybrid lipid is a natural linactant which can reduce the packing incompatibility between saturated and unsaturated lipids. The fluctuation lifetimes are predicted as a function of the hybrid lipid fraction and the fluctuation domain size. These lifetimes can be increased by up to three orders of magnitude compared to the case of no hybrids. With hybrid, small length scale fluctuations have sizable amplitudes even close to the critical temperature and, hence, benefit from enhanced critical slowing down. The increase in lifetime is particularly important for nanometer scale fluctuation domains where the hybrid orientation and the other lipids composition are highly coupled.

A ternary mixture model is proposed to describe composition fluctuations in mixed membranes composed of saturated, unsaturated, and hybrid lipids (with one saturated and one unsaturated hydrocarbon chain). The hybrids are line-active and can reduce the packing incompatibility between the saturated and unsaturated lipids. We introduce a lattice model that extends previous studies by taking into account the dependence of the interactions of the hybrid lipids on their orientations in a simple way. A methodology to recast the free energy of the lattice model in terms of a continuous, isotropic field theory is proposed and used to analyze composition fluctuations in the one-phase region (above the critical temperature). The effect of hybrid lipids on fluctuation domains rich in saturated/unsaturated lipids is predicted. The correlation length of such fluctuations decreases significantly with increasing amounts of hybrids; this implies that nanoscale fluctuation domains are more probable compared to the case with no hybrids. Smaller correlated fluctuation domains arise even when the temperature is close to a critical point, where very large correlation lengths are normally expected. This decrease in the correlation length is largest as the hybrid composition tends toward a crossover value above which stripelike fluctuations are predicted. This crossover value defines the Lifshitz line. The characteristic wavelength of the stripelike fluctuations is large close to the Lifshitz point but decreases toward a molecular size in a membrane that contains only hybrids. Micrometer size, stripelike domains have recently been observed experimentally in giant unilamelar vesicles (GUVs) made of saturated, unsaturated, and hybrid lipids. These results suggest that the line activity of hybrid lipids in such mixtures may be significant only at large hybrid fractions; in that regime, the interface between domains can be diffuse and several hybrid molecules with correlated orientations can separate saturated and unsaturated lipid regions.

We present design guidelines for using Adapted Primary Literature (APL) as part of current interdisciplinary topics to introductory physics students. APL is a text genre that allows students to comprehend a scientific article, while maintaining the core features of the communication among scientists, thus representing an authentic scientific discourse. We describe the adaptation of a research paper by Nobel Laureate Paul Flory on phase equilibrium in polymer-solvent mixtures that was presented to high school students in a project-based unit on soft matter. The adaptation followed two design strategies: a) Making explicit the interplay between the theory and experiment. b) Re-structuring the text to map the theory onto the students' prior knowledge. Specifically, we map the theory of polymer-solvent systems onto a model for binary mixtures of small molecules of equal size that was already studied in class.

A dynamical model of a soft, thermally fluctuating two-dimensional tube is used to study the effect of thermal fluctuations of a confining environment on diffusive transport. The tube fluctuations in both space and time are driven by Brownian motion and suppressed by surface tension and the rigidity of the surrounding environment. The dynamical fluctuations modify the concentration profile boundary condition at the tube surface. They decrease the diffusive transport rate through the tube for two important cases: uniform tube fluctuations (wave vector, q = 0 mode) for finite tube lengths and fluctuations of any wave vector for infinitely long tubes.

Contractile function of striated muscle cells depends crucially on the almost crystalline order of actin and myosin filaments in myofibrils, but the physical mechanisms that lead to myofibril assembly remains ill-defined. Passive diffusive sorting of actin filaments into sarcomeric order is kinetically impossible, suggesting a pivotal role of active processes in sarcomeric pattern formation. Using a one-dimensional computational model of an initially unstriated actin bundle, we show that actin filament treadmilling in the presence of processive plus-end crosslinking provides a simple and robust mechanism for the polarity sorting of actin filaments as well as for the correct localization of myosin filaments. We propose that the coalescence of crosslinked actin clusters could be key for sarcomeric pattern formation. In our simulations, sarcomere spacing is set by filament length prompting tight length control already at early stages of pattern formation. The proposed mechanism could be generic and apply both to premyofibrils and nascent myofibrils in developing muscle cells as well as possibly to striated stress-fibers in non-muscle cells.

We show how strain stiffening affects the elastic response to internal forces, caused either by material defects and inhomogeneities or by active forces that molecular motors generate in living cells. For a spherical force dipole in a material with a strongly nonlinear strain energy density, strains change sign with distance, indicating that, even around a contractile inclusion or molecular motor, there is radial compression; it is only at a long distance that one recovers the linear response in which the medium is radially stretched. Scaling laws with irrational exponents relate the far-field renormalized strain to the near-field strain applied by the inclusion or active force.

We describe an elective course on soft matter at the level of introductory physics. Soft matter physics serves as a context that motivates the presentation of basic ideas in statistical thermodynamics and their applications. It also is an example of a contemporary field that is interdisciplinary and touches on chemistry, biology, and physics. We outline a curriculum that uses the lattice gas model as a quantitative and visual tool, initially to introduce entropy, and later to facilitate the calculation of interactions. We demonstrate how free energy minimization can be used to teach students to understand the properties of soft matter systems such as the phases of fluid mixtures, wetting of interfaces, self-assembly of surfactants, and polymers. We discuss several suggested activities in the form of inquiry projects which allow students to apply the concepts they have learned to experimental systems.

Hybrid lipids (with one saturated tail and one unsaturated tail) have been proposed as agents that can reduce the line tension between domains. We use a liquid crystal model to predict the effect of the degree of unsaturation in the unsaturated tails of hybrid lipids on the miscibility phase diagram and line tension between domains in membranes comprising saturated lipids (with two saturated tails), hybrid lipids, and cholesterol (SHC membranes). In contrast to SHC membranes containing hybrid lipids with a single (or small) degree of unsaturation, for which the phase diagram shows two distinct two-phase regions, SHC membranes containing hybrid lipids with degrees of unsaturation larger than a threshold value exhibit a single two-phase region. This enables hybrid lipids with larger degrees of unsaturation to steadily increase their chain order with decreasing temperature and enhances the reduction of the line tension. This theory predicts that the line tension between domains in SHC membranes is sensitive to the degrees of unsaturation of hybrid lipids.

We have quantitatively and systemically measured the morphologies and dynamics of fluctuations in human RBC membranes using a full-field laser interferometry technique that accurately measures dynamic membrane fluctuations. We present conclusive evidence that the presence of adenosine 5'-triphosphate (ATP) facilitates nonequilibrium dynamic fluctuations in the RBC membrane and that these fluctuations are highly correlated with specific regions in the biconcave shape of RBCs. Spatial analysis reveals that these nonequilibrium membrane fluctuations are enhanced at the scale of the spectrin mesh size. Our results indicate the presence of dynamic remodeling in the RBC membrane cortex powered by ATP, which results in nonequilibrium membrane fluctuations. (This conference proceeding paper is primary based on our recent publication - please refer to YK Park et al., Proc. Nat. Acad. Sci., 107, 1289 (2010) for details.)

We use a liquid-crystal model to predict that hybrid lipids (lipids that have one saturated and one unsaturated tail) can stabilize line interfaces between domains in mixed membranes of saturated lipids, hybrid lipids, and cholesterol (SHC membranes). The model predicts the phase separation of SHC membranes with both parabolic and loop binodals depending on the cholesterol concentration, modeled via an effective pressure. In some cases, the hybrid lipids can reduce the line tension to zero in SHC membranes at temperatures that approach the critical temperature as the pressure is increased. The differences in the hybrid saturated tail conformational order in bulk and at the interface are responsible for the reduction of the line tension.

A simple model of the line activity of a hybrid lipid (e.g., POPC) with one fully saturated chain and one partially unsaturated chain demonstrates that these lipids preferentially pack at curved interfaces between phase-separated saturated and unsaturated domains. We predict that the domain sizes typically range from tens to hundreds of nm, depending on molecular interactions and parameters such as molecular volume and area per headgroup in the bulk fluid phase. The role of cholesterol is taken into account by an effective change in the headgroup areas and the domain sizes are predicted to increase with cholesterol concentration.

The remarkable deformability of the human red blood cell (RBC) results from the coupled dynamic response of the phospholipid bilayer and the spectrin molecular network. Here we present quantitative connections between spectrin morphology and membrane fluctuations of human RBCs by using dynamic full-field laser interferometry techniques. We present conclusive evidence that the presence of adenosine 5-triphosphate (ATP) facilitates non-equilibrium dynamic fluctuations in the RBC membrane that are highly correlated with the biconcave shape of RBCs. Spatial analysis of the fluctuations reveals that these non-equilibrium membrane vibrations are enhanced at the scale of spectrin mesh size. Our results indicate that the dynamic remodeling of the coupled membranes powered by ATP results in non-equilibrium membrane fluctuations manifesting from both metabolic and thermal energies and also maintains the biconcave shape of RBCs.

We present a theoretical treatment of the orientational response to external stress of active, contractile cells embedded in a gel-like elastic medium. The theory includes random forces as well as forces that arise from the deformation of the matrix and those due to the internal regulation of the stress fibers and focal adhesions of the cell. We calculate both the static and high frequency limits of the orientational response in terms of the cellular polarizability. For systems in which the forces due to regulation and activity dominate the mechanical forces, we show that there is a non-linear dynamical response which, in the high frequency limit, causes the cell to orient nearly perpendicular to the direction of the applied stress.

Cell membranes contain small domains (on the order of nanometers in size, sometimes called rafts) of lipids whose hydrocarbon chains are more ordered than those of the surrounding bulk-phase lipids. Whether these domains are fluctuations, metastable, or thermodynamically stable, is still unclear. Here, we show theoretically how a lipid with one saturated hydrocarbon chain that prefers the ordered environment and one partially unsaturated chain that prefers the less ordered phase, can act as a line-active component. We present a unified model that treats the lipids in both the bulk and at the interface and show how they lower the line tension between domains, eventually driving it to zero at sufficiently large interaction strengths or at suffi-ciently low temperatures. In this limit, finite-sized domains stabilized by the packing of these hybrid lipids can form as equilibrium structures.

This special issue of the Journal of Physical Chemistry contains research articles on the properties of soft matterpolymers, colloids, liquid crystals, surfactant self-assembly, wetting, and biologically inspired materials. As mentioned in the biography of de Gennes, our understanding of these systems was, in many cases, formed and, in all cases, vastly informed by the concepts and analogies that he introduced. Some of the papers published here are directly related to de Gennes particular contributions, and we mention a few representative examples of such papers.

We present a comprehensive, theoretical treatment of the orientational response to external stress of active, contractile cells embedded in a gel-like elastic medium. The theory includes both the forces that arise from the deformation of the matrix as well as forces due to the internal regulation of the stress fibers and focal adhesions of the cell. We calculate the time-dependent response of both the magnitude and the direction of the elastic dipole that characterizes the active forces exerted by the cell, for various situations. For static or quasistatic external stress, cells orient parallel to the stress while for high frequency dynamic external stress, cells orient nearly perpendicular. Both numerical and analytical calculations of these effects are presented. In addition we predict the relaxation time for the cellular response for both slowly and rapidly varying external stresses; several characteristic scaling regimes for the relaxation time as a function of applied frequency are predicted. We also treat the case of cells for which the regulation of the stress fibers and focal adhesions is controlled by strain (instead of stress) and show that the predicted dependence of the cellular orientation on the Poisson ratio of the matrix can differentiate strain vs stress regulation of cellular response.

The fluctuation spectra and the intermembrane interaction of two membranes at a fixed average distance are investigated. Each membrane can either be a fluid or a solid membrane, and in isolation, its fluctuations are described by a bare or a wave-vector-dependent bending modulus, respectively. The membranes interact via their excluded-volume interaction; the average distance is maintained by an external, homogeneous pressure. For strong coupling, the fluctuations can be described by a single, effective membrane that combines the elastic properties. For weak coupling, the fluctuations of the individual, noninteracting membranes are recovered. The case of a composite membrane consisting of one fluid and one solid membrane can serve as a microscopic model for the plasma membrane and cytoskeleton of the red blood cell. We find that, despite the complex microstructure of bilayers and cytoskeletons in a real cell, the fluctuations with wavelengths λ 400 nm are well described by the fluctuations of a single, polymerized membrane (provided that there are no inhomogeneities of the microstructure). The model is applied to the fluctuation data of discocytes ("normal" red blood cells), a stomatocyte, and an echinocyte. The elastic parameters of the membrane and an effective temperature that quantifies active, metabolically driven fluctuations are extracted from the experiments.

Many physiological processes depend on the response of biological cells to mechanical forces generated by the contractile activity of the cell or by external stresses. Using a simple theoretical model that includes the forces due to both the mechanosensitivity of cells and the elasticity of the matrix, we predict the dynamics and orientation of cells in both the absence and presence of applied stresses. The model predicts many features observed in measurements of cellular forces and orientation including the increase with time of the cellular forces in the absence of applied stress and the consequent decrease of the force in the presence of quasi-static stresses. We also explain the puzzling observation of parallel alignment of cells for static and quasi-static stresses and of nearly perpendicular alignment for dynamically varying stresses. In addition, we predict the response of the cellular orientation to a sinusoidally varying applied stress as a function of frequency.

Mechanical forces generated by contractile cells allow the cells to sense their environment and to interact with other cells. By locally pulling on their environment, cells can sense and respond to mechanical features such as the local stress (or strain), the shape of a cellular domain, and the surrounding rigidity; at the same time, they also modify the mechanical state of the system. This creates a mechanical feedback loop that can result in self-polarization of cells. In this paper, we present a quantitative mechanical model that predicts the self-polarization of cells in spheroidally shaped domains, comprising contractile cells and an elastic matrix, that are embedded in a three-dimensional, cell-free gel. The theory is based on a generalization of the known results for passive inclusions in solids to include the effects of cell activity. We use the active cellular susceptibility tensor presented by Zemel [Phys. Rev. Lett. 97, 128103 (2006)] to calculate the polarization response and hence the elastic stress field developed by the cells in the cellular domain. The cell polarization is analyzed as a function of the shape and the elastic moduli of the cellular domain compared with the cell-free surrounding material. Consistent with experiment, our theory predicts the development of a stronger contractile force for cells in a gel that is surrounded by a large, cell-free material whose elastic modulus is stiffer than that of the gel that contains the cells. This provides a quantitative explanation of the differences in the development of cellular forces as observed in free and fixed gels. In the case of an asymmetrically shaped (spheroidal) domain of cells, we show that the anisotropic elastic field within the domain leads to a spontaneous self-polarization of the cells along the long axis of the domain.

Focal adhesions are micrometer-sized protein aggregates that connect actin stress fibers to the extracellular matrix, a network of macromolecules surrounding tissue cells. The actin fibers are under tension due to actin-myosin contractility. Recent measurements have shown that as the actin force is increased, these adhesions grow in size and in the direction of the force. This is in contrast to the growth of condensed domains of surface-adsorbed molecules in which the dynamics are isotropic. We predict these force-sensitive, anisotropic dynamics of focal adhesions from a model for the adsorption of proteins from the cytoplasm to the adhesion site. Our theory couples the mechanical forces and elasticity to the adsorption dynamics via force-induced conformational changes of molecular-sized mechanosensors located in the focal adhesion. We predict the velocity of both the front and back of the adhesion as a function of the applied force. In addition, our results show that the relative motion of the front and back of the adhesion is asymmetric and in different ranges of forces, the adhesion can either shrink or grow in the direction of the force.

The concept of network immunity, i.e., the robustness of the network connectivity after a random deletion of edges or vertices, has been investigated in biological or communication networks. We apply this concept to a self-assembling, physical network of microemulsion droplets connected by telechelic polymers, where more than one polymer can connect a pair of droplets. The gel phase of this system has higher immunity if it is more likely to survive (i.e., maintain a macroscopic, connected component) when some of the polymers are randomly degraded. We consider the distribution p(σ) of the number of polymers between a pair of droplets, and show that gel immunity decreases as the variance of p(σ) increases. Repulsive interactions between the polymers decrease the variance, while attractive interactions increase the variance, and may result in a bimodal p(σ).

We show theoretically how adenosine 5-triphosphate (ATP)-induced dynamic dissociations of spectrin filaments (from each other and from the membrane) in the cytoskeleton network of red blood cells (RBC) can explain in a unified manner both the measured fluctuation amplitude as well as the observed shape transformations as a function of intracellular ATP concentration. Static defects can be induced by external stresses such as those present when RBCs pass through small capillaries. We suggest that the partially freed actin at these defect sites may explain the activation of the CFTR membrane-bound protein and the subsequent release of ATP by RBCs subjected to deformations. Our theoretical predictions can be tested by experiments that measure the correlation between variations in the binding of actin to spectrin, the activity of CFTR, and the amount of ATP released.

Cellular adhesions are modulated by cytoskeletal forces or external stresses and adapt to the mechanical properties of the extracellular matrix. We propose that this mechanosensitivity can be driven at least in part by the elastic, cell-contractility-induced deformations of protein molecules that form the adhesion. The model accounts for observations of anisotropic growth and shrinkage of focal adhesions in the direction of the force and predicts that focal adhesions only grow within a range of force that is determined by the composition and matrix properties. This prediction is consistent with the observations of a force threshold for the appearance of elongated focal adhesions and the disruption of adhesions into fibrils on a mobile extracellular matrix. The growth dynamics is calculated and the predicted sliding of focal adhesions is consistent with several experiments.

We calculate the elastic response of thin films grafted to a solid substrate whose upper surface is subject to a stress. This issue is addressed in the context of biological cell adhesion where adhesive junctions consist of a thin layer of proteins grafted to the extracellular matrix and sheared by the cell contractility apparatus. We show that the finite thickness of the layer limits stress-induced deformations to short ranges proportional to the thickness of the film. In addition, we show that the attachment boundary condition creates an effective shear response to surface stresses that couples all the directions, even for fluidlike layers. We predict that perturbations with wavelengths of order of the film thickness induce resonancelike responses for isotropic rubberlike materials or anisotropic media with high shear moduli. We use these results to predict the elastic deformations of a layer of proteins under shear stress and propose that the resulting, polarized elastic response to local surface forces can explain the observed, anisotropic growth of cell-substrate junctions when subject to external stresses.

Elastic interactions of active cells with soft materials was discussed and it was compared to the case of physical force dipoles. It was found that the physical and cellular force dipoles interact in opposite ways with each other. It was also found that in general, free and clamped boundaries have opposite effects. The elastic equations for anisotrophic force contraction dipoles in different geometries and with different boundary conditions were also solved and the results were used to predict optimal position and orientation of mechanosensing cells in soft materials.

This reply discusses the problem of the interpretation of neutron spin-echo experiments on micromulsion droplets. It is explained how shape fluctuations and polydispersity are coupled in these systems in which the total surface area is a fixed quantity. Other interpretations by Lisy and coworkers do not agree with ours on this particular point. This is problably the reason why they obtain unrealistic values of the bending elastic contants, whereas the description that we use leads to excellent agreements with independent determinations of these elastic constants.

We predict the thermodynamic and structural behavior of solutions of self-assembling chains, cross-links and end-cap molecules. We find that at the mean-field level, the entropy of self-assembled junctions induces an effective attraction that can result in equilibrium between a sol phase and a connected network. A connected network can also be formed in a non-thermodynamic transition upon increase of the monomer or cross-link density, or with decreasing temperature. For rigid rods, at low temperatures, we predict a transition from an isotropic network to anisotropic bundles of rods linked by cross-links, that is triggered by the interplay between the configurational entropy of the cross-link distribution, and the rotational and translational entropy of the rods.

Fluids that respond to magnetic fields are predicted to display complex behavior and morphologies. New experiments with colloidal dispersions provide direct evidence for self-assembled chains and networks in such systems. Computer simulation of a dilute network phase of magnetic colloidal particles showed that this phase coexists with a high-density network phase in some regions of the phase diagram.

We propose an explanation for the recently measured slow fluctuations and \u201cblinking\u201d in the surface-enhanced Raman scattering spectrum of single molecules adsorbed on a silver colloidal particle. We suggest that these fluctuations may be related to the dynamic relaxation of the surface roughness on the nanometer scale and show that there are two classes of roughness with qualitatively different dynamics. The predictions agree with the measurements of surface roughness relaxation. Using a theoretical model for the kinetics of surface roughness relaxation in the presence of charges and optical electrical fields, we predict that the high-frequency electromagnetic field increases both the effective surface tension and the surface diffusion constant and thus accelerates the surface smoothing kinetics and time scale of the Raman fluctuations in a manner that is linear with the laser power intensity, while the addition of salt retards the surface relaxation kinetics and increases the time scale of the fluctuations. These predictions are in qualitative agreement with the Raman experiments.

We study a generic model of self-assembling chains that can branch and form networks with branching points (junctions) of arbitrary functionality. The physical realizations include physical gels, wormlike micelles, dipolar fluids, and microemulsions. The model maps the partition function of a solution of branched, self-assembling, mutually avoiding clusters onto that of a Heisenberg magnet in the mathematical limit of zero spin components. As for the calculation of thermodynamic properties as well as the scattering structure factor, the mapping rigorously accounts for all possible cluster configurations, except for closed rings. The model is solved in the mean-field approximation. It is found that despite the absence of any specific interaction between the chains, the presence of the junctions induces an effective attraction between the monomers, which in the case of threefold junctions leads to a first-order reentrant phase separation between a dilute phase consisting mainly of single chains, and a dense network, or two network phases. The model is then modified to predict the structural properties at the mean-field level. Independent of the phase separation, we predict a percolation (connectivity) transition at which an infinite network is formed. The percolation transition partially overlaps with the first-order transition, and is a continuous, nonthermodynamic transition that describes a change in the topology of the system. Our treatment that predicts both the thermodynamic phase equilibria as well as the spatial correlations in the system allows us to treat both the phase separation and the percolation threshold within the same framework. The density-density correlation has the usual Ornstein-Zernicke form at low monomer densities. At higher densities, a peak emerges in the structure factor, signifying the onset of medium-range order in the system. Implications of the results for different physical systems are discussed.

We predict a condensation phenomenon in an overall neutral system, consisting of a single charged plate and its oppositely charged counterions. Based on the "two-fluid" model, in which the counterions are divided into a "free" and a "condensed" fraction, we argue that for high surface charge, fluctuations can lead to a phase transition in which a large fraction of counterions is condensed. Furthermore, we show that depending on the valence, the condensation is either a first-order or a smooth transition.

We review the continuum, statistical thermodynamics of surfaces and interfaces in soft matter where both the energy and entropy of the surface are comparable. These systems include complex fluids that are dominated by either surface tension or the interfacial curvature, such as: fluid and solid interfaces, colloidal dispersions, macromolecular solutions, membranes, and other self-assembling aggregates such as micelles, vesicles, and microemulsions. The primary focus is on the theoretical concepts, their universality, and the role of fluctuations and inhomogeneities with connections to relevant experimental systems.

Using both small-amplitude and singular-perturbation theories we predict theoretically that the presence of surface charge modulations gives rise to an enhancement of the counterion density near the surface above and beyond that of a uniform, charged surface. We confirm these predictions with Monte Carlo simulations. Our study focuses on the weak-to moderate-coupling regime which is complementary to a similar investigation performed by Moreira and Netz (Europhys. Lett., 57 (2002) 911) in the strong-coupling case.

We calculate the static properties of macroion density fluctuations in both bull; and in confined, strongly interacting, macroion suspensions (macroions interact via the Derjaguin-Landau-Verwey-Overbeek potential) in terms of a simple density-functional ansatz. We show how to map a strongly interacting suspension to a weakly interacting one and obtain the renormalized charge, diameter and scattering structure factors analytically. The model is extrapolated to predict crystalline order in terms of a Hansen-Verlet-type of criterion as well as an effective hard-sphere crystallization condition, and good agreement with simulations is found. The increase in correlations observed in recent experiments in two, confined layers is demonstrated.

Experiments have shown that the depletion of polymer in the region between two apposed (contacting or nearly contacting) bilayer membranes leads to fusion. In this paper we show theoretically that the addition of nonadsorbing polymer in solution can promote lateral contraction and phase separation of the lipids in the outer monolayers of the membranes exposed to the polymer solution, i.e., outside the contact zone. This initial phase coexistence of higher- and lower-density lipid domains in the outer monolayer results in surface tension gradients in the outer monolayer. Initially, the inner layer lipids are not exposed to the polymer solution and remain in their original "unstressed" state. The differential stresses on the bilayers give rise to a Marangoni flow of lipid from the outer monolayers in the "contact zone" (where there is little polymer and hence a uniform phase) to the outer monolayers in the "reservoir" (where initially the surface tension gradients are large due to the polymer-induced phase separation). As a result, the low-density domains of the outer monolayers in the contact zone expose their hydrophobic chains, and those of the inner monolayers, to the solvent and to each other across the narrow water gap, allowing fusion to occur via a hydrophobic interaction. More generally, this type of mechanism suggests that fusion and other intermembrane interactions may be triggered by Marangoni flows induced by surface tension gradients that provide "action at a distance" far from the fusion or interaction zone.

Multi-walled hollow nanoparticles made from tungsten disulphide (WS²) show exceptional tribological performance as additives to liquid lubricants due to effective transfer of low shear strength material onto the sliding surfaces. Using a scaling approach based on continuum elasticity theory for shells and pairwise summation of van der Waals interactions, we show that van der Waals interactions cause strong adhesion to the substrate which favors release of delaminated layers onto the surfaces. For large and thin nanoparticles, van der Waals adhesion can cause considerable deformation and subsequent delamimation. For the thick WS² nanoparticles, deformation due to van der Waals interactions remains small and the main mechanism for delamimation is pressure which in fact leads to collapse beyond a critical value. We also discuss the effect of shear flow on deformation and rolling on the substrate.

We predict theoretically the gradual formation of fluctuating, connected microemulsion networks from disconnected globules as the spontaneous curvature is varied, in agreement with recent direct measurements of these topological transitions. The connectivity induced instability together with emulsification failure of the network relate the ultralow tensions and wetting transition to the changing microstructure.

The effect of rigid inclusions on the phase behavior of a film containing a mixture of lipid molecules is investigated. In the proposed model, the inclusion-induced deformation of the film, and the resulting energy cost are strongly dependent upon the spontaneous curvature of the mixed film. The spontaneous curvature is in turn strongly influenced by the composition of film. This coupling between the film composition and the energy per inclusion leads to a lateral modulation of the composition, which follows the local curvature of the membrane. In particular, it is shown that inclusions may induce a global phase separation in a film which would otherwise be homogeneously mixed. The mixed film is then composed of patches of different average composition, separated by the inclusions. This process may be of relevance to explain some aspects of lipid-protein association in biological membranes.

Gradual disruption of the actin cytoskeleton induces a series of structural shape changes in cells leading to a transformation of cylindrical cell extensions into a periodic chain of 'pearls.' Quantitative measurements of the pearling instability give a square-root behavior for the wavelength as a function of drug concentration. We present a theory that explains these observations in terms of the interplay between rigidity of the submembranous actin shell and tension that is induced by boundary conditions set by adhesion points. The theory allows estimation of the rigidity and thickness of this supporting shell. The same theoretical considerations explain the shape of nonadherent edges in the general case of untreated cells.

A tutorial review of the theory of curvature elasticity of thin films is presented with an emphasis on the physical origins of the bending energy. We begin with a discussion of surface curvature and focus on the role of special surfaces of curvature to show how such surfaces can be defined to eliminate either the coupling of the compressibility and bending terms (neutral surface) or the saddle-splay (Gaussian curvature) modulus. Next, we consider phenomenological models for curvature elasticity and discuss the coupling of the curvature degrees of freedom with other properties of the system such as the packing area and the number of molecules at the interface. The pressure distribution in the film is related to the bending moduli. We then connect the elastic moduli to the physical properties of both solid and liquid thin films with a detailed discussion of the role of solid elasticity (including defects), electrostatic interactions (applicable to polar head groups and chain packing (using a block copolymer model of amphiphilic molecules). Finally, we demonstrate the effects of fluctuations and inhomogeneities in these systems in a discussion of the role of thermal undulations in renormalizing the bending moduli and of mixtures of amphiphiles of different chain lengths in fluid films. The article is concluded with a brief review of experimental characterizations of curvature elasticity in self-assembling systems.

We discuss the properties of fluid membranes, whose fluctuations are restricted due to lack of area. The additional free-energy cost of the difference between the actual and optimum areas of the membrane is derived, and two ways in which the membrane can lower this free-energy cost are discussed. Firstly, it is shown that the area dependence of the surface tension can surprisingly lead to a stable hole of finite size in the membrane. We then discuss the surface-tension-driven exchange between two membranes, and conclude that this process is likely to be observed between a tense and a fluctuating membrane. The relevance of these results for recent observations on systems of vesicles is briefly discussed.

We propose that phase separation in a mixed, two-component, substrate in the presence of adsorbing molecules can be incomplete, with an equilibrium finite domain size. The free energy of the system is shown to decrease near interfaces between the two substrate components, as a result of mismatch between the natural spacing of the adsorbate molecules and the periodic potential of the substrate lattice. These systems are of current experimental interest in the context of surface induced freezing, where ice nucleation of varying efficiency is achieved by mixed monolayers of two types of amphiphiles above supercooled water.

We consider the fluctuations of charges in membranes and their effect on the interactions between two fluid membranes a distance h apart. For the case where the counterions are highly localized in the membrane planes we find that the attraction scales as 1/h³ at large distances and as 1/h when the membranes are closer than a typical screening length. When the counterions are delocalized between the membranes a simple ideal-gas approximation indicates that a primary contribution to the membrane attraction are the fluctuations of this gas; in some cases, these attractions can exceed the repulsive interactions found for uniform charge distributions (the Poisson-Boltzmann or mean-field repulsions). These results may be relevant to understanding the role of charge fluctuations in membrane attraction and adhesion.

Bound membranes respond to pinning sites by locally unbinding and overshooting their equilibrium spacing. This nonlinear response can lead to long-ranged interactions between these sites. We introduce a theory which incorporates bending elasticity, fluctuations, and intermembrane interactions to calculate the profiles of bound membranes subject to local pinning. This theory predicts several scaling regimes where the overshoot scales both with the pinning strength and site size. We also calculate the effective, membrane induced interaction between the sites, and predict aggregation properties. Aggregation and reversibility of pinning sites leads to interesting collective phenomena.

We present a simple model of surface modified first-order phase transitions, based on the density-functional theory of freezing. Motivated by recent experiments of surface induced freezing, we show how supercooling may in fact be inhibited below a certain temperature which depends on the lattice mismatch between the monolayer and the nucleated crystal, as well as on the macroscopic strength of the surface treatment. We also apply the model to systems which tend to surface-freeze above the melting point, and correlate their surface-freezing and supercooling temperatures.

We introduce a continuum model which shows that dislocations and/or grain boundaries are intrinsic features of nested fullerenes whose thickness exceeds a critical value to relieve the large inherent strains in these structures. The ratio of the thickness to the radius of the nested fullerenes is determined by the ratio of the surface to curvature and dislocation (or grain boundary) energies. Confirming experimental evidence is presented for nested fullerenes with small thicknesses and with spherosymmetric shapes.

The solubility of proteins in membranes depends both on the protein properties and membrane characteristics. In this paper, we calculate the concentration of membrane inclusions as a function of their concentration in solution and the physical properties of the membrane. We find that the membrane deformation plays a key role in determining the adsorption. When there is no thickness mismatch between the inclusions and the membrane, the effective adsorption energy decreases with the lipid spontaneous curvature and hence strongly favors protein adsorption into the membrane.

A self-consistent field model is used to study the effect of mixing on self-assembled diblock copolymer monolayers and bilayers, in the strong segregation limit. The mixtures contain chains of identical chemistry but different molecular weights or asymmetries. The interactions between such chains are shown to be attractive, so that segregation is unfavorable. The equilibrium curvature and surface density of the monolayer vary nonlinearly with mixture composition, due to interactions between the components. In bilayers, the spontaneous curvature energy promotes demixing, i.e., nonuniform distribution of the components between the two monolayers composing the bilayer. While a homogeneously mixed system adopts a lamellar configuration, in the demixed bilayer equilibrium vesicles are favorable. The stability boundaries of the lamellar, vesicular, and saddle-shaped phases are calculated as a function of chain characteristics and mixture composition.

Recent experiments that probe the effect of alcohol monolayers on the freezing of water are an example of well-characterized surface nucleation, where one has control over the instability by systematic surface modification. We present a simple theory of surface-modified, first-order phase transitions and show how supercooling may in fact be inhibited below a minimal supercooling temperature which is dependent on the macroscopic strength and spatial extent of the surface treatment. The results show that the temperature range where supercooling is possible can indeed vanish for strong enough surface treatments, in qualitative agreement with the experiments.

The Gaussian model of random interfaces is related to the statistical mechanics of microemulsions by a variational approximation to the free energy. This allows the prediction of the structure factor as a function of surfactant and water/oil concentrations and the bending modulus. Different scaling regimes for the behaviour of the structure factor (and the real-space structure) are identified and we predict how the structure changes from one with a well-defined length scale to one with no well-defined domain size as the surfactant concentration or the bending energy are decreased. Upon a further decrease in these quantities, the correlation length of the exponential decay diverges, signifying an instability of this system.

The surfaces of thin, liquid films can be unstable due to thinning van der Waals interactions, leading to the formation of holes in the initially uniform film. These instabilities can be greatly retarded in viscoelastic materials (and completely inhibited in elastic materials) even when the finite frequency shear modulus, E, is small compared to the infinite frequency modulus, G. This occurs when E/G much greater than (a/h0)5 much less than 1 where a is a molecular size and h0 is the film thickness. We relate the growth rate of the instability to the dynamic viscosity, eta (omega), with examples for the cases of a polymer brush, an elastic fluid (gel), and a transient polymer network, described by reptation dynamics.

We apply the continuum theory of van der Waals interactions to a four-component, layered system, composed of a bulk vapor phase, a thin hydrocarbon film, and a water film which is in equilibrium with bulk ice, at the triple point. We find that for thin hydrocarbon films, these interactions result in a finite film of water at the ice surface with a thickness which increases with the hydrocarbon film thickness, d, reaching a value of about 1000 Å for d ≈ 300 Å. This corresponds to incomplete surface melting of ice but with a relatively thick wetting layer. However, for larger d, we predict a discontinuous wetting transition as the water film thickness jumps to infinity, indicating complete surface melting of ice.

We calculate the structure factor for microemulsions with finite spontaneous curvature by using a statistical mechanics model of the interface ensemble. The morphological transition between hard spheres and the random bicontinuous phase is treated in a unified fashion, and the implications for experiment are discussed.

We study the curvature elastic properties of monolayers of diblock copolymers adsorbed at the interface of two incompatible solvents which are also selective solvents for the two blocks. At saturation, the interfacial free energy is minimized with respect to contributions from the chain conformation free energy, the interfacial tension, and the two-dimensional translational entropy of the chains. For a curved interface, this minimization leads naturally to curvature elasticity. The three elastic coefficients, the spontaneous radius of curvature, the bending modulus, and the Gaussian bending modulus, as functions of the molecular weights, the interfacial tension, the interaction parameters, etc., are obtained for a number of cases. Our study employs the theory for grafted chains recently developed by Milner et al. to obtain the chain conformation free energy which takes into account the nonuniformity of the chain-end distribution. This improvement not only affects the overall prefactor of the free energy but it changes the relative values of the three elastic coefficients as well. We consider the cases of both a swollen monolayer and a monolayer consisting of a melt of copolymer chains, as well as an interesting case where one of the blocks is in the swollen condition and the other block is in the melt condition. Because the chains in the melt and the swollen conditions have distinctively different scaling behaviors, the mixed case displays some features that are different from either the swollen and the melt cases.

Neutron spin-echo and small-angle neutron-scattering techniques were employed to study both the size and the shape fluctuations of the di-2-ethylhexyl sulfosuccinate water-in-oil microemulsion system. We observe a softening of the bending rigidity of the interface with the addition of butanol as cosurfactant. Comparison of both techniques with the theory implies that for the simultaneous description of the shape and size fluctuations both the splay and saddle-splay bending moduli are the key parameters, and the spontaneous curvature has little influence.

The wetting behavior of two-phase systems confined inside cylindrical pores is studied theoretically. The confined geometry gives rise to wetting configurations, or microstructures, which have no analog in the well-studied planar case. Many features observed in experiments on binary liquid mixtures in porous media, previously interpreted in terms of random fields, are shown to be consistent with wetting in a confined geometry with no randomness.

We show that the Marangoni effect drives the fingering instability observed at the edge of an aqueous surfactant drop spreading on a thin film of water. A calculation of the unperturbed flow profile demonstrates that the spreading of the drop is controlled by the dynamics of a thin layer which develops in front of the drop. The surface-tension gradient in this region leads to the fingering instability via a mechanism mathematically similar to that in Hele-Shaw flow despite the very different underlying physics.

The curvature elastic energy of bilayer vesicles formed by a mixture of two surfactants, which individually form either micelles or lamellar bilayer phases is described theoretically. In the limit of large bending elastic modulus K being much greater than the temperature T, the free energy is minimized by vesicles with different concentrations of the two surfactants in each monolayer of the bilayer. Vesicles are more stable than lameliar structures only when interactions or complexing of the two surfactants is taken into account.

We consider the electrostatics of charged, cylindrical micelles with spherical end-caps. In the semidilute regime (volume fraction Φ 0 depends on the renormalized coulomb charge of an end cap. These results may help explain anomalies, seen at low added salt, in recent experiments on the dynamics of worm-like micelles.

We report on a new hydrodynamic instability which occurs at the spreading edge of a thin wetting film. A drop of aqueous surfactant solution placed on a glass surface moistened with a thin layer of water spreads by propagating fingers, whose velocity and shape depend on the thickness of the ambient water layer and on the surfactant concentration. The two fluids are miscible and show negligible viscosity difference, ruling out a Saffman-Taylor instability. We propose that the Marangoni effect, which is fluid flow induced by gradients in surface tension, drives the instability.

We study the micellization of associating polymers (hydrocarbon chains with dipolar head groups in hydrophobic solvents) for the case where the polar heads form a linear array. The head interaction is assumed to be short ranged and the chain conformation (free) energy is assumed to follow spherical scaling in the small aggregation number limit and to have cylindrical scaling in the large aggregation number limit. In the small aggregation number limit, the aggregation number is only weakly dependent on the chain length. Numerical solutions as well as analytical studies show that the size distribution displays features of both the spherical and cylindrical aggregates: namely the absence of a sharp CMC transition and a rather sharp distribution function with a width that increases slowly with the mean aggregation number. In the large aggregation limit, the aggregation number can be a strong function of the chain molecular weight. We discuss the importance of the end cap effect in determining the mean size as a function of the chain lengths.

We present a simple model for the anomalous (flow-birefringent) isotropic phase, known as L3, that is seen in certain surfactant solutions at volume fractions of a few percent. The proposed structure consists of locally sheetlike sections of semi-flexible surfactant bilayer, connected up at larger distances into a multiply connected random surface, having a preferred structural length scale of order the persistence length of the bilayer. A first-order transition between this isotropic sheetlike phase and the nearby swollen lamellar phase is described.

The hydrodynamic fluctuations of nearly spherical vesicles and microemulsion droplets are considered. The incompressibility of the enclosed fluid and surfactant or lipid layer imposes a constraint of constant droplet volume and area on the fluctuations. These overdamped modes, driven by bending energy and damped by viscosity of the surrounding fluids, change the shape of the surface and may scatter neutrons or light. A dynamical structure factor S(q,t) is computed and a first frequency moment at fixed wave number ω char (q) obtained. In the limit of a stiff droplet at fixed excess area, a new mode is obtained an overdamped oscillation among ellipsoidal shapes about the minimum-energy (usually prolate) shape. Prospects for observing this fluctuation are discussed.

A universal mechanism which results in shortrange attractive interactions between globules in micellar, vessicular, or microemulsion systems is described. The perturbation of the surfactant concentration profile by the globules is the physical origin of this attraction.

A stability theory is presented which describes the conditions under which thin films rupture. It is found that holes in the film will either grow or shrink, depending on whether their initial radius is larger or smaller than a critical value. If the holes grow large enough, they impinge to form islands; the size of which are determined by the surface energies. The formation of grooves where the grain boundary meets the free surface is a potential source of holes which can lead to film rupture. Equilibrium grain boundary groove depths are calculated for finite grain sizes. Comparison of groove depth and film thickness yields microstructural conditions for film rupture. In addition, pits which form at grain boundary vertices, where three grains meet, are another source of film instability.

A simple model is used to calculate the phase behavior of microemulsions. The surfactant film at the oil-water interface is treated as an incompressible layer whose bending constant is renormalized by thermal fluctuations. Two- and three-phase equilibria involving upper-, lower-, and middle-phase microemulsions are found. The structure of the middle phase is characterized by the persistence length of the film, beyond which the bending constant is renormalized to smaller values.

We study the extent to which excluded volume determines the percolation threshold for permeable elements in the continuum. An expansion due to Coniglio, De Angelis, Forlani, and Lauro exploits a similarity between the statistical mechanics of hard particles and statistics of percolation of permeable objects. This expansion shows that the expectation value of the excluded volume completely determines the threshold at lowest order in element density. Permeable rods in the continuum may be analyzed with the help of Onsagers treatment of virial coefficients for hard rods. Systems of rods provide cases in which higher-order terms will alter the proportionality of threshold to the inverse of the expected excluded volume and cases in which this proportionality remains exact.

A Monte Carlo study of spherical particles shows that increased interaction strength may either raise or lower the volume fraction required for percolation. The sense of the change depends on the distance at which two particles are considered connected, the dimensionality, and the proximity to the critical temperature. An on-lattice simulation supports the continuum result.

We determine the aspect-ratio dependence of the critical percolation threshold for various systems of rods. An exact expansion, due to Coniglio et al., tests the conjecture that the threshold is proportional to the inverse of the expected excluded volume. We confirm the conjecture, and show that the proportionality becomes equality, for isotropic rods in three dimensions, in the slender-rod limit. In this limit, the critical region in which nonclassical exponents are valid vanishes.

Monte Carlo simulations have been carried out to study the effect of temperature on the growth kinetics of a circular grain in two dimensions (20) and a spherical grain in three dimensions (3~) for the Ising model. The domain radius shrinks as R 2(t) = R ~ - at, where Ro and R (t) are the initial and instantaneous radii, respectively. The slope a is strongly temperature dependent for T> 0.6Tc in 20 and for T> 0.2Tc in 3D, in contrast to earlier theories which neglect fluctuations. An analytical theory for d = 2 which considers the thermal fluctuations which give rise to roughening of the domain walls agrees with the T dependence of the Monte Carlo data in this regime.

Monte Carlo simulations have been carried out to study the effect of temperature on the growth kinetics of a circular grain. As predicted by d=3 theories of domain kinetics, the circular domain shrinks linearly with time as A(t)=A0−αt, where A0 and A(t) are the initial and instantaneous areas, respectively. However, in contrast to d=3, the slope α is strongly temperature dependent for T>~0.6Tc. An analytical theory which considers the thermal fluctuations agrees with the T dependence of the Monte Carlo data in this regime.

The approach to equilibrium of ordered superlattice structures on surfaces is analyzed. Both Monte Carlo methods as well as analytic models of interacting domain walls are used to study the kinetics of quenched, two-dimensional systems with Q degenerate equilibrium states. In particular, the growth of long-range order in the magnetic analogs (Q-component Potts models) of the commensurate superlattice structures found on surfaces is analyzed in a study of the kinetics of typical domain geometries that are found when systems are quenched from high (disordered state) to low temperatures. Calculations and simulations of the time and temperature dependence of the domain sizes for the model system of isolated domains indicate that for two dimensions roughening fluctuations of the domain walls strongly influence the grain growth kinetics. Strip-shaped domains approach equilibrium almost entirely through these fluctuations, while circular domains shrink due to deterministic curvature, but with a rate that is strongly temperature dependent even for temperatures outside the critical region. Pinning effects in systems with Q≥3 lead to extremely slow kinetics for particular domain geometries. Low-temperature quenches on a triangular lattice indicate that these pinned geometries are rarely nucleated, while quenches on a square lattice equilibrate much more slowly due to pinning. The application of the theory to superlattice grain growth on surfaces is discussed in the following paper which presents results for the kinetics of quenched systems in terms of the simple domain geometries examined here.

The domain-coarsening kinetics of ordering systems with p-folddegenerate equilibrium states, quenched from high temperatures, is analyzed. For long times (t) and low temperatures, the domain sizes equilibrate as a power law in
t for p~d+1, where d is the spatial dimensionality of the system. The relation of these slowly equilibrating, kinetically disordered systems to glasses and suggestions for simulations and experiments are discussed.

The nonlinear Thomas-Fermi equations which describe the screening of intercalant layers in graphite intercalation compounds are solved analytically in the approximation that the graphite c-axis band dispersion is neglected. The total energy of the system of charged intercalant layers and the self-consistent charge distribution are calculated analytically for general configurations of the intercalant layers. Because of electrostatic screening, pure stage configurations minimize the total (electrostatic plus band) energy for fixed chemical potential. Estimates of the stage dependence of both the electrostatic and elastic interactions between intercalant layers are presented. Experimental tests of these mechanisms for staging are suggested.

We examine an elastic mechanism for staging based on the domain model for graphite intercalation compounds first proposed by Daumas and Hérold. The attractive elastic interactions between intercalant atoms are shown to result in the formation of two-dimensional intercalant islands. The interaction energies of these islands are calculated as a function of island size and separation in a simplified strip geometry and related to the domain model. Because of these long range (range ∼ island size) coherency strains, the free energy of mixed or randomly staged crystals is greater than that of a pure stage intercalation compound. The implications of both the elastic and electronic interactions on the thermodynamics of intercalation (stage dependence of the equilibrium vapor pressure) are discussed. Experiments are suggested where the kinetics of the staging process are related to the microscopic interactions involved.

The orbital magnetic susceptibility (χorc) of graphite intercalation compounds is calculated for H→c→ using a tight-binding model for the π-electron energy bands and the compact expression for χorc derived by Fukuyama, which includes both intraband and interband terms. The results are presented as an approximate analytic expression for χorc as a function of Fermi level μ (0

First- and second-order Raman scattering are described for EuSe near TN = 4.6 K. The second-order spectral features are interpreted using previous mode assignments for EuSe. Spin fluctuation effects are described for T ≳ TN and related to the phonon dispersion relations.

The ordering and fluctuations of the spins in the magnetic semiconductors EuSe and EuTe are correlated with the selection rules and intensities of inelastic light scattering from one phonon-one spin excitations in these materials. Calculations of the Raman line shape in EuSe are presented for T > >Tc and T ≈ Tc.