Publications

Chromosomal sites in rod-like bacteria move sub-diffusely, driven by the out-of-equilibrium nature of the viscoelastic, crowded intracellular environment. Furthermore, it has been shown that there is a pronounced dynamical asymmetry between longitudinal (long-axis) and transverse (radial) motions, manifested in different exponents in the mean-square displacements MSDt~tα, αl and αr respectively. Here, using polymer simulations and experimental observations of a locus in Bacillus subtilis, we substantiate the notion that asymmetric dynamics are a result of the asymmetric structure of the bacterial chromosome modeled as a bottlebrush polymer in a poor solvent. Our simulations recapitulate the observed asymmetry as well as the range of the observed exponent values that are related to scaling models of polymer dynamics, lending support to the notion that asymmetric dynamics is a consequence of the bottlebrush structure of the bacterial chromosome.

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.

The three-dimensional organization of chromatin contributes to transcriptional control, but information about native chromatin distribution is limited. Imaging chromatin in live Drosophila larvae, with preserved nuclear volume, revealed that active and repressed chromatin separates from the nuclear interior and forms a peripheral layer underneath the nuclear lamina. This is in contrast to the current view that chromatin distributes throughout the nucleus. Furthermore, peripheral chromatin organization was observed in distinct Drosophila tissues, as well as in live human effector T lymphocytes and neutrophils. Lamin A/C up-regulation resulted in chromatin collapse toward the nuclear center and correlated with a significant reduction in the levels of active chromatin. Physical modeling suggests that binding of lamina-associated domains combined with chromatin self-attractive interactions recapitulate the experimental chromatin distribution profiles. Together, our findings reveal a novel mode of mesoscale organization of peripheral chromatin sensitive to lamina composition, which is evolutionary conserved.

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.

This article describes the redesign of a project-based course on soft and biological materials to include computational modeling. Including the construction of computational models in the course is described as a shift from constructivism - a theory that characterizes the development of formal reasoning, to constructionism - a theory that focuses on learning while constructing artifacts. This shift ameliorated two drawbacks in the original course: the limited conceptualization of entropy resulting from an unproductive use of the disorder metaphor, and the dependence of most students on the teacher for writing theoretical explanations for their final papers. In the redesigned curriculum, computer simulations provide concrete dynamic representations that students can draw upon for developing nuanced, formal reasoning on entropy and the 2nd law of thermodynamics. In addition, core computational models act as a flexible web that can be extended and modified, and allow a significant proportion of the students to build theoretical models on their own. We conclude that while the new design reflects a shift towards constructionism, we did not adopt a fully constructionist approach, rather a blend of constructivist and constructionist approaches.

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.

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.

An introduction to the physical properties of living active matter at the mesoscopic scale (tens of nanometers to micrometers) and their unique features compared with dead, nonactive matter is presented. This field of research is increasingly denoted as biological physics where physics includes chemical physics, soft matter physics, hydrodynamics, mechanics, and the related engineering sciences. The focus is on the emergent properties of these systems and their collective behavior, which results in active self-organization and how they relate to cellular-level biological function. These include locomotion (cell motility and migration) forces that give rise to cell division, the growth and form of cellular assemblies in development, the beating of heart cells, and the effects of mechanical perturbations such as shear flow (in the bloodstream) or adhesion to other cells or tissues. An introduction to the fundamental concepts and theory with selected experimental examples related to the authors' own research is presented, including red-blood-cell membrane fluctuations, motion of the nucleus within an egg cell, self-contracting acto-myosin gels, and structure and beating of heart cells (cardiomyocytes), including how they can be driven by an oscillating, mechanical probe.

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 the nonlinear elastic responses of polydisperse biopolymer gels to uniaxial compression. We analyze the competition between compressive stiffening due to polymer densification by out-going solvent flow and compressive softening due to continuous polymer buckling. We point out that the polydispersity in polymer lengths can result in an intrinsic, equilibrium mode of nonaffine compression: nonuniform strain but with uniform force distribution, which is found to be more energetically preferable than affine deformation. In this case, the gel softens significantly after the onset of polymer buckling at small compression, but as compression increases, densification-induced stiffening becomes important and a modulus plateau should be observed for a large range of strain. We also relate our results to recent compression experiments on collagen gels and fibrin gels.

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.

Cells probe their mechanical environment and can change the organization of their cytoskeletons when the elastic and viscous properties of their environment are modified. We use a model in which the forces exerted by small, contractile acto-myosin filaments (e.g., nascent stress fibers in stem cells) on the extracellular matrix are modeled as local force dipoles. In some cases, the strain field caused by these force dipoles propagates quickly enough so that only static elastic interactions need be considered. On the other hand, in the case of significant energy dissipation, strain propagation is slower and may be eliminated completely by the relaxation of the cellular cytoskeleton (e.g., by cross-link dissociation). Here, we consider several dissipative mechanisms that affect the propagation of the strain field in adhered cells and consider these effects on the interaction between force dipoles and their resulting mutual orientations. This is a first step in understanding the development of orientational (nematic) or layering (smectic) order in the cytoskeleton. We use the theory to estimate the propagation time of the strain fields over a cellular distance for different mechanisms and find that in some cases it can be of the order of seconds, thus competing with the cytoskeletal relaxation time. Furthermore, for a simple system of two force dipoles, we predict that in some cases the orientation of force dipoles might change significantly with time, e.g., for short times the dipoles exhibit parallel alignment while for later times they align perpendicularly.

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.

Adherent cells exert active forces and elastically deform their substrate. We consider a simple model geometry of a spread cell adhered to a thick substrate layer. We show how anisotropic cell shapes and active cell contractility induce cytoskeletal shear within the cell in a substrate-stiffness dependent manner. This cytoskeletal shear represents a possible mechanical guidance cue for cell force polarization, and could, for example, trigger initial nematic alignment of nascent stress fibers at early stages of cytoskeletal organization. Cell induced substrate strains propagate a depth into the substrate that is comparable to the linear dimension of the spread cell. As a consequence, cellular strains depend on the lateral dimensions of the spread cell. We employ Fourier techniques and a mean-field coupling approximation, which allows both for analytical progress and qualitative insight.

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.

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.

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.

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.

Several cell types, among them red blood cells, have a cortical, two-dimensional (2D) network of filaments sparsely attached to their lipid bilayer. In many mammalian cells, this 2D polymer network is connected to an underlying 3D, more rigid cytoskeleton. In this paper, we consider the pressure exerted by the thermally fluctuating, cortical network of filaments on the bilayer and predict the bilayer deformations that are induced by this pressure. We treat the filaments as flexible polymers and calculate the pressure that a network of such linear chains exerts on the bilayer; we then minimize the bilayer shape in order to predict the resulting local deformations. We compare our predictions with membrane deformations observed in electron micrographs of red blood cells. The polymer pressure along with the resulting membrane deformation can lead to compartmentalization, regulate in-plane diffusion and may influence protein sorting as well as transmit signals to the polymerization of the underlying 3D cytoskeleton.

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.

We predict the nature (attractive or repulsive) and range (exponentially screened or long-range power law) of the electrostatic interactions of oppositely charged, planar plates as a function of the salt concentration and surface charge densities (whose absolute magnitudes are not necessarily equal). An analytical expression for the crossover between attractive and repulsive pressure is obtained as a function of the salt concentration. This condition reduces to the high-salt limit of Parsegian and Gingell where the interaction is exponentially screened and to the zero salt limit of Lau and Pincus in which the important length scales are the inter-plate separation and the Gouy-Chapman length. In the regime of low salt and high surface charges we predict - for any ratio of the charges on the surfaces - that the attractive pressure is long-ranged as a function of the spacing. The attractive pressure is related to the decrease in counter-ion concentration as the inter-plate distance is decreased. Our theory predicts several scaling regimes with different scaling expressions for the pressure as a function of salinity and surface charge densities. The pressure predictions can be related to surface force experiments of oppositely charged surfaces that are prepared by coating one of the mica surfaces with an oppositely charged polyelectrolyte.

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.

Cell/matrix adhesions are modulated by cytoskeletal or external stresses and adapt to the mechanical properties of the extracellular matrix. We propose that this mechanosensitivity arises from the activation of a mechanosensor located within the adhesion itself. We show that this mechanism accounts for the observed directional growth of focal adhesions and the reduction or even cessation of their growth when cells adhere to a soft extracellular matrix. We predict quantitatively that both the elasticity and the thickness of the matrix play a key role in the dynamics of focal adhesions. Two different types of dynamics are expected depending on whether the thickness of the matrix is of order of or much larger than the adhesion size. In the latter situation, we predict that the adhesion region reaches a saturation size that can be tuned by the mechanical properties of the matrix.

Motivated by recent attempts to confine biochemical processes inside water-in-oil microemulsions, we studied the composition and stability of mixed-amphiphile water-swollen micelles in oil from a theoretical point of view. A novel adsorption model demonstrates how the micellar contents (DNA, proteins, etc.) can dramatically affect the composition of the amphiphilic film and the resulting distribution of micelles. Special attention is given to the effect of electrostatic interactions within the micelles as well as between different ones. Since in a low dielectric medium charge fluctuations can lead to long-range intermicellar attractions, we suggest that the presence of amphiphilic polymers in the surfactant film may be needed to stabilize such microemulsions.

Experimental measurements of the shape, fluctuations and adhesion properties of biological cells were analyzed. Particular emphasis was placed on the role of the cytoskeletal and cell elasticity and the shape and adhesion of elastic cells was contrasted with fluid-filled vesicles. The shapes of cells that adhere to a substrate were strongly determined by the cytoskeletal elasticity that can be varied experimentally by drugs that depolymerize the cytoskeleton. It was shown that cell adhesion strongly depends on the forces exerted on the adhesion sites by the tension of the cytoskeleton.

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 predict theoretically the thermodynamics and relaxation kinetics of solutions of cylindrical branched micelles. Using a recently developed theory in combination with the experimental data, we explain the unusual, inverted temperature dependence of the phase separation observed in wormlike micelles and dilute microemulsions. We extend the model to treat the temperature dependence of the relaxation kinetics and explain the observations.

We calculate the hydrodynamic interaction [Formula presented] (Oseen interaction kernel) and relaxation frequency [Formula presented] for the fluctuations of a membrane that is harmonically bounded to a permeable or impermeable wall. We show that due to the confining wall there is an increase in the effective viscosity of the fluid surrounding the membrane. This has been observed in experiments on confined membranes, such as lamellar phases and the red-blood cell membrane. Our results allow a quantitative analysis of these experiments, in terms of the strength of the membrane confining potential and dislocations.

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.

One approach to the understanding of fusion in cells and model membranes involves stalk formation and expansion of the hemifusion diaphragm. We predict theoretically the initiation of hemifusion by stalk expansion and the dynamics of mesoscopic hemifusion diaphragm expansion in the light of recent experiments and theory that suggested that hemifusion is driven by intramembrane tension far from the fusion zone. Our predictions include a square-root scaling of the hemifusion zone size on time as well as an estimate of the minimal tension for initiation of hemifusion. Whereas a minimal amount of pressure is evidently needed for stalk formation, it is not necessarily required for stalk expansion. The energy required for tension-induced fusion is much smaller than that required for pressure-driven fusion.

Mechanical force is known to play an important role in the regulation of cellular behaviour, including adhesion, motility, differentiation and proliferation. For stationary, mechanically active cells like fibroblasts, adhesion to flat substrates occurs mainly at sites of focal adhesions, which are micron-sized protein aggregates at the plasma membrane, which on the cytoplasmic side connect to the actin cytoskeleton. In recent years, evidence has been growing that focal adhesions act as mechanosensors which convert mechanical force into biochemical signalling. We have investigated the relationship between force and aggregation at focal adhesions by a new method which combines elastic micro-patterned substrates (to record substrate deformation), fluorescence labelling of focal adhesion proteins (to monitor aggregation) and numerical solution of the inverse problem of linear elasticity theory (to calculate forces at focal adhesions). We have found that force correlates linearly with lateral size of aggregation, with a stress constant of 5.5 nN/μm². This finding indicates that mechanosensing involves regulation of aggregation.

Self-assembly in soft-matter systems often results in the formation of locally cylindrical or chain-like structures. We review the theory of these systems whose large-scale structure and properties depend on whether the chains are finite, with end-caps or join to form junctions that result in networks. Physical examples discussed here include physical gels, wormlike micelles, dipolar fluids and microemulsions. In all these cases, the competition between end-caps and junctions results in an entropic phase separation into junction-rich and junction-poor phases, as recently observed by electron microscopy and seen in computer simulations. A simple model that accounts for these phenomena is reviewed. Extensions of these ideas can be applied to treat network formation and phase separation in a system of telechelic (hydrophobically tipped, hydrophilic) polymers and oil-in-water microemulsions, as observed in recent experiments.

We predict theoretically that long-wavelength surface charge modulations universally reduce the pressure between the charged surfaces with counterions compared with the case of uniformly charged surfaces with the same average surface charge density. The physical origin of this effect is the fact that surface charge modulations always lead to enhanced counterion localization near the surfaces, and hence, fewer charges at the midplane. We confirm the last prediction with Monte Carlo simulations.

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.

Recent experimental results demonstrate that it is possible to grow a variety of different multiphase, nested nanotube structures. This paper predicts the structure and energetics of such multiphase nanotubes. There are several distinct contributions to the energetics: the internal and external surface energies, the energy of the interface between the different phases, the long-range (van der Waals) interactions between interfaces, and the elastic bending energy. We perform energy minimizations to compare the energies of two- and three-layer films and nanotubes. We present physical guidelines, quantitative theory, and structure maps that show how materials and geometric parameters influence the stability of competing structures.

We predict a condensation phenomenon in an overall neutral system, consisting of a single charged plate and its oppositely charged counterions. Based on the \u201ctwo-fluid\u201d model, in which the counterions are divided into a \u201cfree\u201d and a \u201ccondensed\u201d 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.

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.

Mechanical forces play a major role in the regulation of cell adhesion and cytoskeletal organization. In order to explore the molecular mechanism underlying this regulation, we have investigated the relationship between local force applied by the cell to the substrate and the assembly of focal adhesions. A novel approach was developed for real-time, high-resolution measurements of forces applied by cells at single adhesion sites. This method combines micropatterning of elastomer substrates and fluorescence imaging of focal adhesions in live cells expressing GFP-tagged vinculin. Local forces are correlated with the orientation, total fluorescence intensity and area of the focal adhesions, indicating a constant stress of 5.5 ± 2 nNμm-2. The dynamics of the force-dependent modulation of focal adhesions were characterized by blocking actomyosin contractility and were found to be on a time scale of seconds. The results put clear constraints on the possible molecular mechanisms for the mechanosensory response of focal adhesions to applied force.

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.

Effective pair potentials for hollow nanoparticles such as those made from carbon (fullerenes) or metal dichalcogenides (inorganic fullerenes) consist of a hard core repulsion and a deep, but short-ranged, van der Waals attraction. We investigate them for single-walled and multiwalled nanoparticles and show that in both cases, in the limit of large radii the interaction range scales inversely with the radius R, while the well depth scales linearly with R. We predict the values of the radius R and the wall thickness h at which the gas-liquid coexistence disappears from the phase diagram. We also discuss unusual material properties of the solid, which include a large heat of sublimation and a small surface energy.

We predict theoretically the gradual formation of fluctuating, connected microemulsion networks from disconnected cylinders as the spontaneous curvature and the radius are varied, in agreement with recent direct measurements of these topological transitions. We discuss the role of the topological defects, the network junction and the end-cap of the disconnected cylinders, in the connectivity transition. The optimal shapes and curvature energies of the junctions and end-caps are calculated numerically and compared with analytic approximations.

Direct evidence by cryogenic temperature transmission electron microscopy shows the existence of networks in microemulsions near the two-phase closed loops. Networks formed by interconnected oil-swollen cylinders were observed in the water-rich regions of the phase diagram of the C₁₂E₅ /water/n-octane system. The coexisting phases within the loops were shown to be concentrated and dilute networks. Similar micellar networks were also found in the binary system. These observations substantiate the suggested theoretical link between the structural bicontinuity and the unique phase separation and criticality of microemulsions: All these regimes are governed by the entropic attraction between network junctions.

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.

Recent experiments that probe the effect of confinement on the dynamical properties of thin liquid films have shown that these films undergo an abrupt transition to a solid below a critical thickness To model this behavior, we present a mean-field theory for confinement-induced first-order phase transitions based on a Ginzburg-Landau type expression for the free-energy. We show how the equilibrium melting temperature increases as the film thickness is decreased; for thick films, the melting temperature approaches its bulk value. The predicted phase diagram includes three phases: an ordinary liquid (where both the surface layer and the bulk of the film are liquid), a crystalline solid phase (where both the surface layer and the bulk are ordered) and a quasi-liquid phase in which the bulk of the film is liquid-like but the surfaces are ordered. Transitions between the phases are always first order.

We developed an experimental technique which probes the dynamics of a single colloidal particle over many decades in time, with spatial resolution of a few nanometers. By scattering a focused laser beam from a particle observed in an optical microscope, we measure its fluctuations via the temporal autocorrelation function of the scattered intensity g\(t\). This technique is demonstrated by applying it to a single Brownian particle in an optical trap of force constant k. The decay times of g\(t\), which are related to the particle position autocorrelation function, scale as k⁻¹, as expected from theory.

We review the theory of curvature elasticity of thin, fluid films starting with a phenomenological formalism motivated by microscopic, physical examples. The effects of t?inite compressibility of the layer, exchange of molecules between the film and the soluiicn, and the intrinsic bending stiffness of the film are taker, into account; these degrees of freedom account for all the important molecular modes of the system. The effects of fluctuations of the number of molecules in the film (which is in equilibrium with surfactant molecules or micelles in solution) and in the area per molecule about its equilibrium value is shown to soften the curvature elastic moduli. The relationship of the bending moduli to the pressure distribution in the film is discussed and it is demonstrated that isotropic liquid films have no bending modulus, in the continuum limit. The bending moduli for charged membranes and for block copolymers are estimated. Finally, some recent experimental measure of curvature elasticity are discussed and compared with the theory.

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 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 investigate the effect of mixing two diblock copolymers of identical chemical structure but different molecular weight on self-assembled bilayers, using theoretical concepts of curvature elastic energy. Entropy and chain-chain interactions are found to favour ideal mixing in the two monolayers composing the bilayer, while curvature energy favours an inhomogeneous distribution of chains among the layers and, therefore, vesicle formation. The vesicle phase boundaries are determined as a function of mixture composition and molecular weight. We find that adding a small fraction of shorter chains to a copolymer bilayer is much more effective in destabilizing lamellar bilayers than the addition of a small fraction of longer chains.

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.

Surfactant monolayers at water-oil interfaces and amphiphilic bilayers in either water or oil exhibit large-scale, isotropic structures in the neighborhood of ordered, lamellar phases. A model for the structure, based upon a treatment of bicontinuous microemulsions, is used to compare the phase stability of the lamellar and bicontinuous L3 phases.

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.

The curvature free energy of an interfacial membrane is used to predict the relative stability of cylindrical, lamellar and ordered, bicontinuous, saddle-shaped structures. Because they are surfaces of constant mean curvature, the saddle-shaped structures have a finite range of stability as a function of concentration even when the saddle-splay elastic constant bar K

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 a model for dynamic percolation relevant to the electrical conductivity of water in oil microemulsions. The charge carriers reside on percolation cluster sites and can propagate by hopping between nearest-neighbor sites. The cluster sites also undergo diffusion, so that the clusters continuously rearrange themselves. The conductivity below the percolation threshold pc is finite and, as p→pc, increases as pc-p∥−s˜where s̃ differs from the static exponent s. In the neighborhood of pc, the conductivity depends as a power law on the rate of cluster rearrangement.

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.

The primary focus of instability discussed in this paper is beading, which is the process by which an initially uniform film which has been deposited on a substrate, breaks up into an array of beads or islands. The author examine the thermodynamics of the beading process and the effects of small perturbations on an initially uniform, flat film. They find that small perturbations do not lead to beading and that perturbations with amplitudes sufficient to bring the film surface into contact with the substrate are required. The physical origin of these types of pertubations are elucidated, and it is shown that these perturbations may be associated with microstructural defects. The dynamical aspects of beading are also discussed.

We have used small-angle neutron scattering to study surfactant interactions in an inverted micellar and a related microemulsion system. The structure-factor fits imply an attractive interaction between micelles with a short-ranged potential due to the overlapping of the surfactant hydrocarbon tails. The linear increase in this interaction with size accounts for the critical transition observed in the microemulsion. This analysis is confirmed by Monte Carlo simulations.

The domain growth kinetics of magnetically ordering systems with p-fold degenerate ground states is analyzed. We present Monte Carlo results for the approach to equilibrium of systems with multigenerate ground states which have been rapidly quenched from T å Tc to T « Tc. We show that pinning center are effective in slowing the dynamics of domain growth in systems with p ⩾ 3.

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.

A model, self-consistent band structure is calculated for a thin film of n graphite layers bounded by two, partially ionized intercalant layers for stages n=2-8. The quantum mechanics of the electrons in the graphite layers is modeled using a variant of the three-dimensional linear combination of atomic orbitals Hamiltonian whose parameters have been determined for pure graphite. The effects of the nonhomogeneous distribution of electrons in the n layers (screening) are taken into account by adding a self-consistently determined layer-potential term to the tight-binding Hamiltonian. The layer charge densities, potentials, and total energies are presented for n=2-8 along with representative band structures for charge transfer per intercalant (f) of f=1 and 14 (referred to C12nX). The stage dependence of the total energy in this model is related to the stage dependence of the chemical potential (intercalant vapor pressure) in an intercalation reaction. Comparison of theory and experiment indicates the significance of the electronic energy in stabilizing the high-stage structures.

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.