The effects of adsorbate lateral interactions on the kinetics of surface diffusion and desorption are studied by means of kinetic and thermodynamic Monte Carlo simulations. This study is motivated by recent diffusion and desorption experiments on the NH3/Re(001) system, which show that the activation energies of these processes decrease (in different fashions) with increasing surface coverage, the interactions between the adsorbates are thus assumed to be repulsive. A long range dipole-dipole-like potential is used to simulate both the diffusion and desorption processes. Most calculations are carried out with the interaction range extending up to fourth-order neighbors. Longer ranges are found to barely affect the kinetic behavior. On the other hand, shorter ranges of interaction result in qualitatively and quantitatively different structural (thermodynamic phase) behaviors and, consequently, in very different kinetics of diffusion and desorption. The model used to calculate diffusion kinetics assumes that the activation barrier to particle diffusion depends, simultaneously, on the local environments of both the initial and the final sites involved in the elementary event of particle jumps. The chemical diffusion coefficient is evaluated based on thermodynamic and kinetic Monte Carlo simulations. It is found to increase with surface coverage, reflecting the repulsive nature of the interactions. Yet, unlike the experimental results, the increase is nonmonotonic but rather, somewhat oscillatory-reflecting the structural phase transitions of the adsorbed layer. The activation energy of desorption is found to decrease by about 15 kcal/mole as the coverage increases from 0 to 1, showing steeper slopes around the coverages corresponding to a perfectly ordered adlayer phase. These results are in satisfactory qualitative and quantitative agreement with experiment. Finally, it is shown that the coverage dependence of the activation barrier to diffusion can be reasonably well evaluated from equilibrium thermodynamic desorption data. (C) 1996 American Institute of Physics.

A detailed treatment is provided of the various free-energy terms that contribute to the transfer of a polyalanine ct-helix from the aqueous phase into lipid bilayers. In agreement with previous work, the hydrophobic effect is found to provide the major driving force for helix insertion, However, an opposing effect of comparable magnitude is also identified and is attributed to the large free-energy penalty associated with the desolvation of peptide hydrogen bonds on transfer to the low dielectric environment of the bilayer. Lipid perturbation effects as well as the entropy loss associated with helix immobilization in the bilayer are also evaluated. Two configurations of a membrane-bound 25mer polyalanine helix were found to be lower in free energy than the isolated helix in the aqueous phase, The first corresponds to the case of vertical insertion, in which a helix terminus protrudes from each side of the bilayer. The second minimum is for the case of horizontal insertion, for which the helix is adsorbed upon the surface of the bilayer. The calculated free-energy minima are found to be in good agreement with recent measurements of related systems, Large free-energy barriers resulting from desolvation of unsatisfied hydrogen-bonding groups al the helix termini are obtained for both insertion processes. The barriers for insertion are significantly reduced if the helix termini are assumed to be ‘’capped’’ through the formation of hydrogen bonds with polar sidechains, For uncapped helices, our results support recently proposed models in which helices are inserted by first adsorbing on the membrane surface and then having one terminus ‘’swing around’’ so as to penetrate the bilayer,

We present an overview of the modern study of complex fluids which, because of the overwhelming breadth and richness of this field, unavoidably neglects many interesting systems and research developments. In proposing a definition of the field. we discuss first the special role played by phenomenological theory and the limitations of molecular-level description. The remainder of the article is organized into sections which treat model colloids, micellized surfactant solutions, interfacial films and microemulsions, bilayers and membranes, and new materials. In each instance we try to provide a physical basis for the special nature of interactions and long-range ordering transitions in these novel colloidal and thin layer systems. At the heart of understanding these highly varied phenomena lie the curvature dependence of surface energies and the coupling between self-assembly on small length scales and phase changes at large ones..

A statistical thermodynamic approach is used to analyze the various contributions to the free energy change associated with the insertion of proteins and protein fragments into lipid bilayers. The partition coefficient that determines the equilibrium distribution of proteins between the membrane and the solution is expressed as the ratio between the partition functions of the protein in the two phases. It is shown that when all of the relevant degrees of freedom (i.e., those that change their character upon insertion into the membrane) can be treated classically, the partition coefficient is fully determined by the ratio of the configurational integrals and thus does not involve any mass-dependent factors, a conclusion that is also valid for related processes such as protein adsorption on a membrane surface or substrate binding to proteins. The partition coefficient, and hence the transfer free energy, depend only on the potential energy of the protein in the membrane. Expressing this potential as a sum of a ‘’static’’ term, corresponding to the equilibrium (minimal free energy) configuration of the protein in the membrane, and a ‘’dynamical’’ term representing fluctuations around the equilibrium configuration, we show that the static term contains the ‘’solvation’’ and ‘’lipid perturbation’’ contributions to the transfer free energy. The dynamical term is responsible for the ‘’immobilization’’ Free energy, reflecting the loss of translational and rotational entropy of the protein upon incorporation into the membrane. Based on a recent molecular theory of lipid-protein interactions, the lipid perturbation and immobilization contributions are then expressed in terms of the elastic deformation free energy resulting from the perturbation of the lipid environment by the foreign (protein) inclusion; The model is formulated for cylindrically shaped proteins, and numerical estimates are given for the insertion of an a-helical peptide into a lipid bilayer. The immobilization free energy is shown to be considerably smaller than in previous estimates of this quantity, and the origin of the difference is discussed in detail.

We consider the possibility of smectic and columnar phases in fluids and colloidal suspensions of aligned rods and disks interacting through excluded-volume forces. After briefly reviewing previous work, and applying known cell model techniques to compare the phase behaviors of disks and rods, we present and discuss the results from new Monte Carlo simulations of perfectly oriented rods (spherocylinders) and disks (torocylinders). We conclude tentatively that columnar phases are stable only in the case of disks.

Pore formation in unilamellar lipid vesicles is believed to occur when the concentration of membrane-bound drug molecules exceeds a certain value. We treat this phenomenon in analogy with that of the micellization of surfactant in bulk aqueous solutions, thereby relating the threshold concentration of drug molecules to the free energy associated with transferring a molecule to a pore from its uniformly-dispersed state in the membrane. Incorporating the effect of lateral tension induced by osmotic pressure, we calculate the lowering of the pore-formation threshold with increasing tension. These predictions are tested by direct measurements on liposomal dispersions involving the antifungal drug amphotericin B.

The angular intensity distribution of He beams scattered from compact clusters and from diffusion limited aggregates, epitaxially grown on metal surfaces, is investigated theoretically. The purpose is two-fold: to distinguish compact cluster structures from diffusion limited aggregates, and to find observable signatures that can characterize the compact clusters at the atomic level of detail. To simplify the collision dynamics, the study is carried out in the framework of the sudden approximation, which assumes that momentum changes perpendicular to the surface are targe compared with momentum transfer due to surface corrugation. The diffusion limited aggregates on which the scattering calculations were done, were generated by kinetic Monte Carlo simulations, It is demonstrated, by focusing on the example of compact Pt heptamers, that signatures of structure of compact clusters may indeed be extracted from the scattering distribution. These signatures enable both an experimental distinction between diffusion limited aggregates and compact clusters, and a determination of the cluster structure, The characteristics comprising the signatures are, to varying degrees, the rainbow, Fraunhofer, specular and constructive interference peaks, all seen in the intensity distribution, It is also shown, how the distribution of adsorbate heights above the metal surface can be obtained by an analysis of the specuIar peak attenuation. The results contribute to establishing He scattering as a powerful tool in the investigation of surface disorder and epitaxial growth on surfaces, alongside with STM.

This article describes briefly several applications of a molecular theory of lipid organization in membranes to systems of biophysical interest. After introducing the basic concepts of this mean field theory we outline three of its recent applications. i) Calculations of lipid chain conformational statistics in membrane bilayers, and comparison of the results (e.g. bond orientational order parameters) to experiment and molecular dynamics simulations. Good agreement is found. ii) A molecular model for lipid-protein interactions, which explicitly considers the effects of a rigid hydrophobic protein on the elastic (conformational) properties of the lipid bilayer. We also analyze the role of the ‘hydrophobic mismatch’ between the protein and lipid bilayer thickness. iii) A molecular level calculation of the vesicle to micelle transition, attendant upon the addition of (’curvature loving’) surfactant to a lipid bilayer vesicle. Future applications, e.g. to the calculation of the free energy barriers involved in membrane fusion are briefly mentioned.

A two-dimensional lattice model, originally introduced by Granek et al. [J. Chem. Phys. 101, 4331 (l994)], is used to demonstrate the intricate coupling between the intramicellar interactions that determine the optimal aggregation geometry of surfactant molecules in dilute solution, and the intermicellar interactions that govern the phase behavior at higher concentrations. Three very different scenarios of self-assembly and phase evolution are analyzed in detail, based on Monte Carlo studies and theoretical interpretations involving mean-field, Landau-Ginzburg, Bethe-Peierls, and virial expansion schemes. The basic particles in the model are ‘’unit micelles’’ which, due to spontaneous self-assembly or because of excluded area interactions, can fuse td form larger aggregates; These aggregates are envisaged as hat micelles composed of a bilayerlike body surrounded: by a curved semitoroidal rim. The system’s Hamiltonian involves one- through four-body potentials between the unit micelles, which account for their tendency to form aggregates of different shapes, e.g., elongated vs disklike micelles. Equivalently the configurational energy of the system is a sum of micellar self-energies involving the packing free energies of the constituent molecules in the bilayer body and in rim segments of different local curvature. The rim energy is a sum of a line tension term and a 1D curvature energy which depends on the rim spontaneous curvature and bending rigidity. Different combinations of these molecular parameters imply different optimal packing geometries and hence different self-assembly and phase behaviors. The emphasis in this paper Is on systems of ‘’curvature loving’’ amphiphiles which, in our model, are characterized by negative line tension. The three systems studied are: (i) A dilute solution of stable disklike micelles which, upon increasing the concentration, undergoes a first-order phase transition to a continuous bilayer with isolated hole defects. An intermediate modulated ‘’checkerboard’’ phase appears under certain conditions at low temperatures. (ii) A system of unit micelles which in dilute solution tend to associate into Linear micelles. These micelles are rodlike gt low temperatures, becoming increasingly more flexible as the temperature increases.-Upon increasing the concentration the micelles grow and undergo (in 2D) a continuous transition into nematic and ‘’stripe’’ phases of long rods. At still higher concentrations the micellar stripes fuse into continuous sheets with line defects. (iii) A system in which, already in dilute solution, the micelles favor the formation of branched aggregates, analogous to the branched cylindrical micelles recently observed in certain surfactant solutions, As the concentration increases the micelles associate into networks (’’gels’’) composed of a mesh of linear micelles linked by ‘’T-like’’ intermicellar junctions. The network may span the entire system or phase separate and coexist with a dilute micellar phase, depending on the details of the molecular packing parameters. (C) 1995 American Institute of Physics.

The elastic behavior of mixed bilayers composed of two amphiphilic components with different chain length (and identical head groups) is studied using two molecular level models. In both, the bilayer free energy is expressed as a sum of chain, head group and interfacial contributions as well as a mixing entropy term. The head group and interfacial terms are modeled using simple phenomenological but general expressions. The models differ in their treatment of the chain conformational free energy. In one it is calculated using a detailed mean-field molecular theory. The other is based on a simple ‘’compression’’ model. Both models lead to similar conclusions. Expressing the bilayer free energy as a sum of its two monolayer contributions, a thermodynamic stability analysis is performed to examine the possibility of spontaneous vesicle formation. To this end, we expand the bilayer free energy as a power series (up to second order) in terms of the monolayer curvatures, their amphiphilic compositions and the average cross sectional areas per molecule; all variables are coupled, with the molecular composition and areas treated as degrees of freedom which are allowed to relax during bending. Using reasonable molecular interaction parameters we find that a second order transition from a planar to a curved (vesicle) geometry in a randomly mixed bilayer is unlikely. Most of our analysis is devoted to calculating the spontaneous curvature and the bending rigidity of the bilayer as a function of its amphiphile chain composition. We find that adding short chain amphiphiles to a layer of long chain molecules reduces considerably its bending rigidity, as already known from calculations involving only the chain contributions. However, we find that inclusion of head group and interfacial interactions moderates the effect of the added short chains. We also find that the bending rigidity Of pure monolayers is approximately linear in chain length, as compared to the nearly cubic dependence implied by the chain free energy alone (at constant head group area). Our main result involves the calculation of the spontaneous curvature as a function of composition. We find, for different chain mixtures, that upon adding short chains to long chain monolayers, the spontaneous curvature first increases nearly Linearly with composition and then (beyond mole fraction of about 0.5) begins to saturate towards the spontaneous curvature of a pure short chain layer. Qualitative arguments are provided to explain this behavior. (C) 1995 American Institute of physics.

A molecular model is used to calculate the free energy of mixed vesicles and cylindrical micelles, composed of lipid molecules and short chain surfactants. The free energy of both aggregates (modeled as an infinite planar bilayer and an infinite cylindrical aggregate) is represented as a sum of internal free energy and mixing entropy contributions. The internal free energy is treated as a sum of chain (conformational), head group, and surface tension terms. Calculating the free energy of each aggregation geometry as a function of lipid/surfactant composition and using common tangent construction we obtain the compositions of the bilayer and the micelle at the phase transition. By varying certain molecular parameters (such as the ‘’hard core’’ area of the surfactant head group or the length of the surfactant tail) we study the role of molecular packing characteristics in determining the compositions at phase coexistence. We find, as expected, that upon increasing the preference of the surfactant for the micellar geometry (larger spontaneous curvature) the bilayer is solubilized at lower surfactant/lipid concentration ratios. For some typical values of the parameters used, reasonable agreement with experimental results for mixtures of egg phosphatidylcholine and octylglucoside is obtained.

We study the two-dimensional (2-D) structural and thermodynamic changes in smectic-A/lamellar phases of self-assembling surfactant systems, in which the rim associated with a bilayer edge has a preferred curvature. This property was not considered in previous studies of 2-D aggregation, where an infinite bilayer emerges already at very low concentrations. A lattice Hamiltonian is used to describe the bending energy of the rim: An occupied lattice site corresponds to a minimum, disklike, micelle, and a bending energy penalty is associated with corners and straight edges depending on the value of the spontaneous curvature. When the spontaneous radius of curvature of the rim is small and the bending modulus is large, we find that the ‘’condensation’’ transition-i.e., the ‘’collapse’’ of the finite aggregates into a continuous bilayer-is postponed to high concentrations. At low concentrations the bending energy leads to an effective repulsive interaction between the aggregates, which in turn can result in ordered (modulated) structures for not too large ratios of thermal energy to bending energy (which is the expected situation in most systems of interest). Our model should be applicable to the systems of decylammonium chloride and cesium perflourooctanoate studied by Boden and co-workers (NMR and conductivity measurements) and Zasadzinski and co-workers (freeze fracture), where monodisperse micellar disks are observed to layer in stacked planes. In the latter system a 2-D order of disk-shaped aggregates appears within the smectic-A layers, which is also consistent with our theory. Experimental studies of the structural evolution under further condensation of the system are not yet available.

A molecular, mean-field theory of chain packing statistics in aggregates of amphiphilic molecules is applied to calculate the conformational properties of the lipid chains comprising the hydrophobic cores of dipalmitoyl-phosphatidylcholine (DPPC), dioleoyl-phosphatidylcholine (DOPC), and palmitoyl-oleoyl-phosphatidylcholine (POPC) bilayers in their fluid state. The central quantity in this theory, the probability distribution of chain conformations, is evaluated by minimizing the free energy of the bilayer assuming only that the segment density within the hydrophobic region is uniform (liquidlike). Using this distribution we calculate chain conformational properties such as bond orientational order parameters and spatial distributions of the various chain segments. The lipid chains, both the saturated palmitoyl (-(CH2)(1)4-CH3) and the unsaturated oleoyl (-(CH2)(7)-CH=CH-(CH2)(7)-CH3) chains are modeled using rotational isomeric state schemes. All possible chain conformations are enumerated and their statistical weights are determined by the self-consistency equations expressing the condition of uniform density. The hydrophobic core of the DPPC bilayer is treated as composed of single (palmitoyl) chain amphiphiles, i.e., the interactions between chains originating from the same lipid headgroup are assumed to be the same as those between chains belonging to different molecules. Similarly, the DOPC system is treated as a bilayer of oleoyl chains. The POPC bilayer is modeled as an equimolar mixture of palmitoyl and oleoyl chains. Bond orientational order parameter profiles, and segment spatial distributions are calculated for the three systems above, for several values of the bilayer thickness (or, equivalently, average area/headgroup) chosen, where possible, so as to allow for comparisons with available experimental data and/or molecular dynamics simulations. In most cases the agreement between the mean-field calculations, which are relatively easy to perform, and the experimental and simulation data is very good, supporting their use as an efficient tool for analyzing a variety of systems subject to varying conditions (e.g., bilayers of different compositions or thicknesses at different temperatures).

The interaction free energy between a hydrophobic, transmembrane, protein and the surrounding lipid environment is calculated based on a microscopic model for lipid organization. The protein is treated as a rigid hydrophobic solute of thickness d(P), embedded in a lipid bilayer of unperturbed thickness d(L)o. The lipid chains in the immediate vicinity of the protein are assumed to adjust their length to that of the protein (e.g., they are stretched when d(P) > d(L)o) in order to bridge over the lipid-protein hydrophobic mismatch (d(P) - d(L)o). The bilayer’s hydrophobic thickness is assumed to decay exponentially to its asymptotic, unperturbed, value. The lipid deformation free energy is represented,as a sum of chain (hydrophobic core) and interfacial (head-group region) contributions. The chain contribution is calculated using a detailed molecular theory of chain packing statistics, which allows the calculation of conformational properties and thermodynamic functions (in a mean-field approximation) of the lipid tails. The tails are treated as single chain amphiphiles, modeled using the rotational isomeric state scheme. The interfacial free energy is represented by a phenomenological expression, accounting for the opposing effects of head-group repulsions and hydrocarbon-water surface tension. The lipid deformation free energy DELTAF is calculated as a function of d(P) - d(L)o. Most calculations are for C-14 amphiphiles which, in the absence of a protein, pack at an average area per head-group a0 congruent-to 32 angstrom2 (d(L)o congruent-to 24.5 angstrom), corresponding to the fluid state of the membrane. When d(P) = d(L)o, DELTAF > 0 and is due entirely to the loss of conformational entropy experienced by the chains around the protein. When d(P) > d(L)o, the interaction free energy is further increased due to the enhanced stretching of the tails. When d(P) < d(L)o, chain flexibility (entropy) increases, but this contribution to DELTAF is overcounted by the increase in the interfacial free energy. Thus, DELTAF obtains a minimum at d(P) - d(L)o congruent-to 0. These qualitative interpretations are supported by detailed numerical calculations of the various contributions to the interaction free energy, and of chain conformational properties. The range of the perturbation of lipid order extends typically over few molecular diameters. A rather detailed comparison of our approach to other models is provided in the Discussion.

The two successive fluid-fluid phase transitions in surfactant Langmuir monolayers are described using a highly simplified molecular model: a ‘reactive’ mixture of inter-converting squares of two different sizes. The model is solved by a mean-field lattice approach and by Monte Carlo simulations. The mean-field scheme involves a re-division of the original lattice into ‘cells’ which can contain either one large square representing the (projection on the lattice of) an amphiphilic molecule in a conformationally disordered (’expanded’) state, or clusters consisting of 1-4 small squares, each representing an ordered (’stretched’) molecule. This procedure circumvents some of the difficulties associated with the size disparity of the adsorbed particles. In spite of its simplicity, the model can explain some major, as well as some subtle, characteristics of experimental monolayer phase diagrams. These include the conditions under which the monolayer exhibits one phase transition, two or none; the decrease of the triple point temperature with increasing chain length, and the gradual decrease with temperature of the liquid-condensed phase density.