Electrostatic Maxwell stress model of the shapes of condensed phase domains in monolayers at the air-water interface

The formation mechanism of the shapes of condensed phase domains in monolayers at the air-water interface was investigated taking into account the surface pressure, line tension, and electrostatic energy due to the spontaneous polarization generated in normal and in-plane direction. By deriving the shape equation of monolayer domains as the mechanical balance at the domain boundary, we found that the electrostatic energy contributes to the shape equation as electrostatic Maxwell stress. Development of a cusp from condensed phase domains of fatty acid monolayers, which has been experimentally observed, was analyzed by the shape equation. It was found that the development of a cusp originated from the strong Maxwell stress, which was induced by the non-uniform orientational distribution in the fatty acid domain, and that cusped shapes gave a minimum of the free energy of the domain. It demonstrates that the shape equation with Maxwell stress, which is derived in the present study, is useful to study the formation mechanism of the shapes of condensed phase domains in monolayers.     

Geometry-dependent stripe rearrangement processes induced by strain on preordered microwrinkle patterns

A preordered microwrinkle pattern on a metal-capped surface of a soft elastomer is employed to elucidate the elementary buckling phenomenon during strain-induced stripe rearrangement processes. The preordered one-dimensional stripe tends to align perpendicular to the direction of strain reversibly when lateral compressive strain is applied on the substrate at some angle phi with respect to the stripe orientation. For any value of strain, the film surface can be decomposed in domains containing stripes with two different orientations, namely the original and applied strain orientations. As strain is increased, the domains of the second type of stripes progressively grow and invade the whole surface. Interestingly, the domain shapes during growth are composed of parallelogram units that simply depend on phi and stripe wavelength. Moreover, domain growth proceeds in characteristic directions depending on the shape of the domain unit.     

Quantifying growth of symmetric and asymmetric lipid bilayer domains

Here, we examine by atomic force microscopy (AFM) the kinetics and morphology of lipid domain growth during lipid phase separation by rapid thermal cooling of fully mixed two-component supported lipid bilayers. At the undercooled temperatures chosen, symmetric 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC)-rich domains favored slower reaction-limited growth whereas asymmetric galactosylceramide (GalCer)-rich domains favored faster diffusion-limited growth, indicated by shape factors and kinetic exponents. Because kinetically limited conditions could be accessed, we were able to estimate the activation energy barrier (approximately 16kT) and lateral diffusion coefficient (approximately 0.20 microm2/s) of lipid molecular addition to a growing domain. We discuss these results with respect to transition states, obstructed diffusion, and the necessity for coordinating growth in both leaflets in a symmetric lipid domain.     

Role of dipolar interaction in the mesoscopic domains of phospholipid monolayers: dipalmitoylphosphatidylcholine and dipalmitoylphosphatidylethanolamine

The role of dipolar interactions in determining the lipid domain shapes at the air-water interface with a change in the chemical structure of the head groups of lipids is theoretically studied. The phospholipids considered are dipalmitoylphosphatidylcholine (D,L-DPPC) and dipalmitoylphosphatidylethanolamine (DPPE). Despite closely similar chemical structures, the domains of the two lipids are strikingly different. The DPPC domains exhibit elongated arms, while the DPPE domains are nearly round-shaped. To compare the dipolar repulsions in the domains of the two phospholipids, different energy-minimized conformers of DPPC and DPPE are studied using the semiempirical quantum chemical method (PM3). It is found that the dipole moment of DPPC is significantly larger than that of DPPE. The in-plane and out-of-plane components of the dipole moments are calculated using grazing incidence X-ray diffraction data at different surface pressure values, as used in the experiment. The result indicates that the magnitude of the dipolar interaction is significantly larger in DPPC than that in DPPE over the surface pressure range considered. The enhanced dipolar repulsion corroborates well with the difference in the domain shapes in the two phospholipid monolayers. The larger dipolar repulsion in DPPC leads to development of elongated domain arms, while relatively less dipolar repulsion allows a closed shape of the condensed-phase DPPE domains.     

Endothermic decompositions of inorganic monocrystalline thin plates. I. Shape of polycrystalline product domains versus constraints and time

Copper sulfate pentahydrate dehydration into trihydrate was investigated using monocrystalline platelets with varying crystallographic orientations. The morphological and kinetic features of the trihydrate domains were examined. Different shapes were observed: polygons (parallelograms, hexagons) and ellipses; their conditions of occurrence are reported in the (P, T) diagram. At first (for about 2 min), the ratio of the long to the short axes of elliptical domains changes with time; these subsequently develop homothetically and the rate ratio is then only pressure dependent. Temperature influence is inferred from that of pressure. Polygonal shapes are time dependent and result in ellipses. So far, no model can be put forward. Yet, qualitatively, the polygonal shape of a domain may be explained by the prevalence of the crystal arrangement and the elliptical shape by that of the solid tensorial properties. The influence of those factors might be modulated versus pressure, temperature, interface extent, and, thus, time.     

Crystalline protein domains and lipid bilayer vesicle shape transformations

Cellular membranes can take on a variety of shapes to assist biological processes including endocytosis. Membrane-associated protein domains provide a possible mechanism for determining membrane curvature. We study the effect of tethered streptavidin protein crystals on the curvature of giant unilamellar vesicles (GUVs) using confocal, fluorescence, and differential interference contrast microscopy. Above a critical protein concentration, streptavidin domains align and percolate as they form, deforming GUVs into prolate spheroidal shapes in a size-dependent fashion. We propose a mechanism for this shape transformation based on domain growth and jamming. Osmotic deflation of streptavidin-coated GUVs reveals that the relatively rigid streptavidin protein domains resist membrane bending. Moreover, in contrast to highly curved protein domains that facilitate membrane budding, the relatively flat streptavidin domains prevent membrane budding under high osmotic stress. Thus, crystalline streptavidin domains are shown to have a stabilizing effect on lipid membranes. Our study gives insight into the mechanism for protein-mediated stabilization of cellular membranes.     

Shape group theory of van der Waals surfaces

In this article we present a method for the study of shapes of general, asymmetric van der Waals surfaces. The procedure is simple to apply and it consists of two steps. First, the surface is decomposed into spherical domains, according to the interpenetration of the van der Waals atomic spheres. Each domain defines a topological object that is either a 2-manifold or some truncated 2-manifold. Second, we compute the homology groups for all the objects into which the surface is divided. These groups are topological and homotopical invariants of the domains, hence they remain invariant to conformational changes that preserve the essential features of these domains of decomposition. In particular, these homology groups do not depend explicitly on the molecular symmetry. Major rearrangements of the nuclear configurations, however, do alter the decomposition into spherical domains, and the corresponding variation of the homology groups can be followed easily under conformational rearrangements. We discuss a partitioning of the metric internal configuration spaceM into shape regions of van der Waals surfaces, which allows one to identify those rearrangements which introduce an essential change in shape and to distinguish them from those which do not alter the fundamental shape of the molecular surface. The dependence of the shape group partitioning ofM on the symmetry under permutation of nuclear changes is discussed briefly, considering a simple illustrative example.     

Fluorescence blinking, exciton dynamics, and energy transfer domains in single conjugated polymer chains

In order to understand exciton migration and fluorescence intensity fluctuation mechanisms in conjugated polymer single molecules, we studied fluorescence decay dynamics at "on" and "off" fluorescence intensity levels with 20 ps time resolution using MEH-PPV [poly(2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylenevinylene] dispersed in PMMA. Two types of intensity fluctuations were distinguished for single chains of conjugated polymers. Abrupt intensity fluctuations (blinking) were found to be always accompanied by corresponding changes in fluorescence lifetime. On the contrary, during "smooth" intensity fluctuations no lifetime change was observed. Time-resolved data in combination with data on fluorescence emission and excitation anisotropy lead to a picture where a single polymer molecule is seen as consisting of several energy transfer domains. Exciton migration is efficient within a domain and not efficient between domains. Each domain can have several emitting low-energy sites over which the exciton continuously migrates until it decays. Emission of individual domains is often highly polarized. Fluorescence from a domain can be strongly quenched by Forster energy transfer to a quencher (hole polaron) if the domain overlaps with the quenching sphere.     

Twin-like domains in chiral smectic C liquid crystals

In the chiral smectic C phase of liquid crystals with the phase transition N*-SmC*, texture development depending on the sample thickness is reported. In very thin samples, domains of rectangular-like shape are observed. As two possible tilts of smectic layers are possible for one anchoring direction, smectic layers inside a domain, called twin-like domains, are tilted with respect to layers in outer regions, similarly to crystalline planes in solid crystalline twins. An elastic model of such a twin domain is proposed and its energy determined.     

Twin‐like domains in chiral smectic C liquid crystals

In the chiral smectic C phase of liquid crystals with the phase transition N*–SmC*, texture development depending on the sample thickness is reported. In very thin samples, domains of rectangular‐like shape are observed. As two possible tilts of smectic layers are possible for one anchoring direction, smectic layers inside a domain, called twin‐like domains, are tilted with respect to layers in outer regions, similarly to crystalline planes in solid crystalline twins. An elastic model of such a twin domain is proposed and its energy determined.     

Representation of square-cell configurations in the complex plane: Tools for the characterization of molecular monolayers and cross sections of molecular surfaces

Two numerical codes, a complex face vector F and a real face vector D are developed for the characterization of square-cell configurations (lattice animals), used for representing the shapes of molecular monolayers and cross sections of molecular surfaces. The real face vector D represents all the intrinsic properties, size, and shape of the lattice animal. The complex face vector F contains complete information about the size, the shape, and also the placement of the particular lattice animal with respect to the lattice. Based on the properties of the face vectors, a method is developed for the classification of similar animals into equivalence classes. The face vector method is proposed for an algorithmic, nonvisual computer analysis of similarity of shapes of molecular monolayers and planar domains of cross sections of molecular surfaces, approximated by lattice animals.     

Domain Size and Fluctuations at Domain Interfaces in Lipid Mixtures

Biomembranes consist of a complex mixture of a large number of lipids and proteins. In such mixtures, microscopic domains and macroscopically separated phases may exist. Here, we discuss phase behavior and domains formation of binary lipid mixtures. We show that the domain formation is accompanied by large fluctuations at the domain boundaries, resulting in altered physical properties at the boundaries, for instance in a pronounced increase of the elastic constants. Therefore, we argue that the physics of the membrane depends on the overall length scale of its domains interfaces. We present here confocal microscopy images, calorimetric melting profiles and Monte-Carlo simulations to understand the factors that determine domain formation, their sizes and the role of the domain interfaces.     

Logical Models of Molecular Shapes and Their Families

A new discrete mathematical model of molecular shape is proposed, making use of the partition property of a representation of molecular shape. According to its geometrical and topological structure, a molecular surface can be partitioned into unbounded two-dimensional subsets (domains) and some common subsets of closures of two or more domains. The sets of these domains as a base of a finite topology, containing the Boolean n-cube as a lower Boolean sub-lattice of this topology, defines the domain of the proposed logical model. A logical function can be obtained that reflects the properties of the topological domains as well as the interrelations on the set of domains. Based on classical or quantum-chemical representations of molecular shape, these models allow one the implementation of methods of logical diagnostics in chemistry, and the definition of a metric on the set of molecular shape equivalence classes. The families of molecular shapes can be considered as sets of logical models. The proposed model is unified in the sense that the structures of differentiable and non-differentiable surfaces can be represented in the same mathematical framework. These logical models will also work for interpenetrations of the above types of surfaces.     

Appearance and disappearance of dendritic and chiral patterns in domains of Langmuir monolayers observed with Brewster angle microscopy

Investigations on the aggregation behavior and morphology of Langmuir films of enantiomeric (L) and racemic (DL) N-acyl amino acids on pure aqueous as well as metal cation containing subphases were carried out at the mesoscale level with the help of Brewster angle microscopy (BAM). In the case of N-hexadecanoyl alanine on a pure aqueous subphase at 298 K the L-enantiomer forms crystal platelets, while the irregular fractal-like shape of the domains of the racemic mixture can be explained by a diffusion limited aggregation (DLA) growth mechanism. At 303 K the L-enantiomer shows a dendritic growth pattern, which leads to explicitly chiral domain shapes that correspond with the chirality of the film-forming molecules and for which hydrogen bridges as directed attractive forces are assumed to be responsible. The compression of the L-enantiomer on a zinc ion containing subphase is accompanied by a remarkable metamorphosis of the condensed structure. Starting from torus-like domains they were at first converted into strongly wound S-shaped domains, finally turning into a seahorse-like appearance. The origin of these chiral shapes can be explained on the basis of an electrostatic growth model. The enantiomer of N-hexadecanoyl alanine methyl ester shows three different asymmetric dendritic growth patterns. The domains of the racemic mixture are dendritic too, but in contrast they are symmetric and have a notably low branching density. On a pure aqueous subphase the L-enantiomer of N-octadecanoyl valine exhibits dendritic growth as well, but the overall outer shape of the domains is not explicitly chiral.     

Predicting the shape and structure of face-centered cubic gold nanocrystals smaller than 3 nm.

Although a number of computational studies have examined the relative stability of icosahedral and decahedral gold clusters from 1 to 3 nm in size, few studies have focussed on the variety of face-centered cubic (fcc) nanoparticles in this size regime. In most cases small fcc gold particles are assumed to adopt the truncated octahedral shape, but in light of the fact that the shape and structure of gold nanoparticles is known to vary, the relative stability of fcc polyhedra may change with size. Presented here are results of first-principles calculations investigating the preferred shape of gold particles less than 3 nm in size. Our results indicate that the equilibrium shape of fcc gold nanoparticles less than 1 nm is the cuboctahedron, but this shape rapidly becomes energetically unstable with respect to the truncated octahedron, octahedron and truncated cube shapes as the size increases.     

Polymorphic domains in monolayers of isomeric triple-chain phospholipids

Monolayers of two isomeric branched chain phosphatidyl cholines at the air/water interface have been studied by means of fluorescence microscopy. The lipids differ in the position of the branched chain at the glycerol backbone and carry three chains per headgroup of almost equal length. Most qualitative features of the compression isotherms are similar except a difference of 4 Ų/molecule in the minimum molecular area at high lateral pressures. This indicates a more condensed solid phase of compound C2 and is also reflected in the shapes of domains observed in the LE/LC phase coexistence range: domains with sharp edges and a mostly hexagonal shape are formed. On the other hand, the compound C1 with a larger limiting molecular area exhibits a smooth domain boundary and a shape instability as theoretically predicted.     

A Multidirectional Superelastic Organic Crystal by Versatile Ferroelastical Manipulation

Mechanical twinning changes atomic, molecular, and crystal orientations along with directions of the anisotropic properties of the crystalline materials while maintaining single crystallinity in each domain. However, such deformability has been less studied in brittle organic crystals despite their remarkable anisotropic functions. Herein we demonstrate a direction‐dependent mechanical twinning that shows superelasticity in one direction and ferroelasticity in two other directions in a single crystal of 1,3‐bis(4‐methoxyphenyl)urea. The crystal can undergo stepwise twinning and ferroelastically forms various shapes with multiple domains oriented in different directions, thereby affording a crystal that shows superelasticity in multiple directions. This adaptability and shape recoverability in a ferroelastic and superelastic single crystal under ambient conditions are of great importance in future applications of organic crystals as mechanical materials, such as in soft robotics.     

Mesoscale simulation of morphology in hydrated perfluorosulfonic acid membranes

Current fuel cell proton exchange membranes rely on a random network of conducting hydrophilic domains to transport protons across the membrane. Despite extensive investigation, details of the structure of the hydrophilic domains in these membranes remain unresolved. In this study a dynamic self-consistent mean field theory has been applied to obtain the morphologies of hydrated perfluorosulfonic acid membranes (equivalent weight of 1100) as a model system for Nafion at several water contents. A coarse-grained mesoscale model was developed by dividing the system into three components: backbone, side chain, and water. The interaction parameters for this model were generated using classical molecular dynamics. The simulated morphology shows phase separated micelles filled with water, surrounded by side chains containing sulfonic groups, and embedded in the fluorocarbon matrix. The size distribution and connectivity of the hydrophilic domains were analyzed and the small angle neutron scattering (SANS) pattern was calculated. At low water content (lambda<6, where lambda is the number of water molecules per sulfonic group) the isolated domains obtained from simulation are nearly spherical with a domain size smaller than that fitted to experimental SANS data. At higher water content (lambda>8), the domains deform into elliptical and barbell shapes as they merge. The simulated morphology, hydrophilic domain size and shape are generally consistent with some experimental observations.     

Metric Properties of Factor Space of Molecular Shapes

Molecular shape equivalence classes defined with respect to equivalence of geometrical and topological properties are represented by logical models. Consequently, the factor space of molecular shapes is provided by a metric useful in shape comparisons.     

Temperature and compression rate independent domain shape in Langmuir monolayers of di-n-dodecyl hydrogen phosphate at the air-water interface

Thermodynamic and morphological properties of Langmuir monolayers of di-n-dodecyl hydrogen phosphate (DDP) have been studied by film balance and Brewster angle microscopy (BAM) over a wide range of temperature between 5 and 40 degrees C. From pi-A isotherms, a generalized phase diagram consisting of gas (G), liquid expanded (LE) and liquid condensed (LC) phases is constructed for the DDP monolayers. The BAM images show the formation of gas bubble in the bright background of LE phase during G-LE phase transitions and fingering LC domains during LE-LC phase transitions. The shapes of these domains are independent of temperature, showing a sharp contrast to the temperature-dependent monolayer morphologies of amphiphilic systems where the shape of the LC domains changes either from compact circular to fingering or from irregular or spiral to compact patterns with increasing temperature. In addition, the domains do not show any change in their shapes with decreasing the compression rate. Since the two-alkyl chains are directly attached by covalent bonds to the phosphate group, the rearrangement of the molecules needs to move the whole molecules including the hydration sphere. The difficulty related to such a movement of the molecules causes the fingering domains, which are independent of external variables. Although the domains are formed in a fingering shape, the equilibrium shape can be attained by about 120 min at 15 degrees C indicating a rather slow relaxation rate.