Shape transformation transitions in a model of fixed-connectivity surfaces supported by skeletons

A compartmentalized surface model of Nambu and Goto is studied on triangulated spherical surfaces by using the canonical Monte Carlo simulation technique. One-dimensional bending energy is defined on the skeletons and at the junctions, and the mechanical strength of the surface is supplied by the one-dimensional bending energy defined on the skeletons and junctions. The compartment size is characterized by the total number L^′ of bonds between the two-neighboring junctions and is assumed to have values in the range from L^′ = 2 to L^′ = 8 in the simulations, while that of the previously reported model is characterized by L^′ = 1, where all vertices of the triangulated surface are the junctions. Therefore, the model in this paper is considered to be an extension of the previous model in the sense that the previous model is obtained from the model in this paper in the limit of L^′↦1. The model in this paper is identical to the Nambu-Goto surface model without curvature energies in the limit of L^′↦∞ and hence is expected to be ill-defined at sufficiently large L^′. One remarkable result obtained in this paper is that the model has a well-defined smooth phase even at relatively large L^′ just as the previous model of L^′↦ 1. It is also remarkable that the fluctuations of surface in the smooth phase are crucially dependent on L^′; we can see no surface fluctuation when L^′≤ 2, while relatively large fluctuations are seen when L^′≥ 3.     

Phase transition of compartmentalized surface models

Two types of surface models have been investigated by Monte Carlo simulations on triangulated spheres with compartmentalized domains. Both models are found to undergo a first-order collapsing transition and a first-order surface fluctuation transition. The first model is a fluid surface one. The vertices can freely diffuse only inside the compartments, and they are prohibited from the free diffusion over the surface due to the domain boundaries. The second is a skeleton model. The surface shape of the skeleton model is maintained only by the domain boundaries, which are linear chains with rigid junctions. Therefore, we can conclude that the first-order transitions occur independent of whether the shape of surface is mechanically maintained by the skeleton (=the domain boundary) or by the surface itself.     

Phase structure of intrinsic curvature models on dynamically triangulated disk with fixed boundary length

A first-order phase transition is found in two types of intrinsic curvature models defined on dynamically triangulated surfaces of disk topology. The intrinsic curvature energy is included in the Hamiltonian. The smooth phase is separated from a non-smooth phase by the transition. The crumpled phase, which is different from the non-smooth phase, also appears at sufficiently small curvature coefficient α. The phase structure of the model on the disk is identical to that of the spherical surface model, which was investigated by us and reported previously. Thus, we found that the phase structure of the fluid surface model with intrinsic curvature is independent of whether the surface is closed or open.     

Phase transitions in a fluid surface model with a deficit angle term

Nambu-Goto model is investigated by using the canonical Monte Carlo simulation technique on dynamically triangulated surfaces of spherical topology. We find that the model has four distinct phases; crumpled, branched-polymer, linear, and tubular. The linear phase and the tubular phase appear to be separated by a first-order transition. It is also found that there is no long-range two-dimensional order in the model. In fact, no smooth surface can be seen in the whole region of the curvature modulus α, which is the coefficient of the deficit angle term in the Hamiltonian. The bending energy, which is not included in the Hamiltonian, remains large even at sufficiently large α in the tubular phase. On the other hand, the surface is spontaneously compactified into a one-dimensional smooth curve in the linear phase; one of the two degrees of freedom shrinks, and the other degree of freedom remains along the curve. Moreover, we find that the rotational symmetry of the model is spontaneously broken in the tubular phase just as in the same model on the fixed connectivity surfaces.     

Shape transformation transitions of a tethered surface model

A surface model of Nambu and Goto is studied statistical mechanically by using the canonical Monte Carlo simulation technique on a spherical meshwork. The model is defined by the area energy term and a one-dimensional bending energy term in the Hamiltonian. We find that the model has a large variety of phases; the spherical phase, the planar phase, the long linear phase, the short linear phase, the wormlike phase, and the collapsed phase. Almost all two neighboring phases are separated by discontinuous transitions. It is also remarkable that no surface fluctuation can be seen in the surfaces both in the spherical phase and in the planar phase.     

Phase structure of a surface model with many fine holes

We study the phase structure of a surface model by using the canonical Monte Carlo simulation technique on triangulated, fixed connectivity, and spherical surfaces with many fine holes. The size of a hole is assumed to be of the order of lattice spacing (or bond length) and hence can be negligible compared to the surface size in the thermodynamic limit. We observe in the numerical data that the model undergoes a first-order collapsing transition between the smooth phase and the collapsed phase. Moreover the Hasudorff dimension H remains in the physical bound, i.e., H < 3 not only in the smooth phase but also in the collapsed phase at the transition point. The second observation is that the collapsing transition is accompanied by a continuous transition of surface fluctuations. This second result distinguishes the model in this paper and the previous one with many holes, whose size is of the order of the surface size, because the previous surface model with large-sized holes has only the collapsing transition and no transition of surface fluctuations.     

Nucleation-and-growth problem in model lipid membranes undergoing subgel phase transitions is a problem of time scale

In this Rapid Note, we show that the problem of growth of molecular superlattice in a fully hydrated dipalmitoylphosphatidylcholine (DPPC) membrane during the gel-to-subgel phase transformation process is a problem of time scale. There are, in fact, two time scales. The first is an “integrated” or, in some sense, stagnant time scale, that reflects the well-known isotropic growth effect in the d-dimensional space, but assigns the problem to be still in a category of Debye relaxation kinetics. The fraction of old (parent) phase does not suit the Paley-Wiener criterion for relaxation functions, and the time behavior is exclusively due to the geometrical characteristics of the kinetic process. The second (multi-instantaneous) time scale, in turn, is recognised to be a “broken” (fractional time derivative) or memory-feeling (dynamic) scale, which carries some very essential physics of the phenomenon under study, and classifies the problem to be of non-Debye (viz., stretched exponential) nature. It may, in principle, contain all the important effects, like small scale coexistence, presence of collisions between domains, with possible annihilation and creation of domain boundaries, and/or a headgroup packing, hydration against lipid mobility behavior, and finally, a multitude of quasi-crystalline states. It turns out, that within the range of validity of the dynamic scale approximation proposed, the criterion for relaxation functions is very well fulfilled. Received 30 November 1998     

Adhesion of binary giant vesicles containing negative spontaneous curvature lipids induced by phase separation

We report the adhesion of binary giant vesicles composed of two types of phospholipids, one has negative spontaneous curvature which tends to bend toward the head group and the other has zero spontaneous curvature. In a homogeneous one-phase region, the giant vesicles do not adhere to each other, whereas in a coexisting two-phase region, the giant vesicles show adhesion. A fluorescence microscope observation reveals that the adhesion takes place through the domains rich in phospholipids having negative spontaneous curvature. We propose a phase separation induced hemifusion model where two apposed monolayers of adjacent vesicles are hemifused in order to reduce the bending energy of monolayers with negative spontaneous curvature and the boundary energy between the domains and matrix. We provide a strong evidence for the hemifusion model by lipid transfer experiments.     

Critical dynamics of lateral and transversal phase separations in bilayer biomembranes and surfactants

We consider bilayer biomembranes or surfactants made of two chemically incompatible amphiphile molecules, which may laterally or transversely phase separate into macrodomains, upon variation of some suitable parameter (temperature, lateral pressure, etc.). The purpose is an extensive study of the dynamics of both lateral and transverse phase separations, when the bilayer is suddenly cooled down from a high initial temperature towards a final one very close to the spinodal point. The critical dynamics are investigated through the partial dynamic structure factors of different species. Using a two-order parameter field theory, where the two fields are the composition fluctuations of one component in the leaflets of the bilayer, combined with an extended van Hove approach that is based on two coupled Langevin equations (with noise), we exactly compute these dynamic structure factors. We first find that the dynamics is governed by two time scales. The longest one, , can be related to the thermal correlation length, | T - T _c|^-1/2 , by , with the dynamic critical exponent z = 4 , where is an atomic length scale, T the absolute temperature, and T_c its critical value. The characteristic time can be interpreted as the time required for the formation of the final macrophase domains. The second time scale is rather shorter, and can be viewed as the short time during which the unlike phospholipids execute local motion. Second, we demonstrate that the dynamic structure factors obey exact scaling laws, and depend on three lengths, namely the wavelength q^-1 (q is the wave vector modulus), the correlation length , and a length scale R(t) t ^1/z (z = 4representing the size of macrophase domains at time t . Of course, the two lengths and R(t) coincide at the final time at which the bilayer reaches its final equilibrium state. Finally, the present work must be considered as a natural extension of our previously published one dealing with the study of lateral and transverse phase separations from a static point of view.     

Effect of physical ageing in thin glassy polymer films

We have studied the effect of physical ageing in thin supported glassy polystyrene films by using ellipsometry to detect overshooting in the expansivity-temperature curve upon heating of aged samples. Films with thickness 10-200 nm have been aged at 70^° C and 80^° C (below the bulk glass transition temperature). We observe clear relaxation peaks in the expansivity-temperature curve for films thicker than 18 nm but not for the 10 nm film. The intensity of the relaxation peak is inversely proportional to the film thickness, while the temperatures characteristic to the relaxation peak are almost independent of the film thickness. These observations are successfully interpreted by the idea that the surface layer of the order of 10 nm has liquid-like thermal properties. Received 28 October 2002 / Published online: 1 April 2003 RID="a" ID="a"Present address: Yokohama Research Center, Mitsubishi Chemical Corporation, 1000 Kamoshida-chou, Aoba-ku, Yokohama 227-8502, Japan; e-mail: kawana@rc.m-kagaku.co.jp     

Effect of atmosphere on reductions in the glass transition of thin polystyrene films

We have used nulling ellipsometry to measure the glass transition temperature, T _g , of thin films of polystyrene in ambient, dry nitrogen, and vacuum environments. For all environments, the measured T _g values decrease with decreasing film thickness in a way that is quantitatively similar to previously reported studies in ambient conditions. These results provide strong reinforcement of previous conclusions that such reduced T _g values are an intrinsic property of the confined material. Furthermore, the results are in contrast to recent reports which suggest that the T _g reductions measured by many researchers are the results of artifacts (i.e. degradation of the polymer due to annealing in ambient conditions, or moisture content).     

Diffusion in supported lipid bilayers: Influence of substrate and preparation technique on the internal dynamics

The diffusion law of DMPC and DPPC in Supported Lipid Bilayers (SLB), on different substrates, has been investigated in details by Fluorescence Recovery After Patterned Photobleaching (FRAPP). Over micrometer length scales, we demonstrate the validity of a purely Brownian diffusive law both in the gel and the fluid phases of the lipids. Measuring the diffusion coefficient as a function of temperature, we characterize the gel-to-liquid phase transition of DMPC and DPPC. It is shown that, depending on the type of substrate and the method used for bilayer preparation, completely different behaviours can be observed. On glass substrates, using the Langmuir-Blodgett deposition technique, both leaflets of the bilayer have the same dynamics. On mica, the dynamics of the proximal leaflet is slower than the dynamics of the distal leaflet, although the transition temperature is the same for both layers. Preparing bilayers from vesicle fusion in same conditions leads to more random behaviours and shifted transition temperatures.     

Shape optimization in lipid nanotube networks

Starting from a high surface free-energy state, lipid nanotube networks are capable to self-organize into tree-like structures with particular geometrical features. In this work we analyze the process of self-organization in such networks, and report a strong similarity to the Euclidian Steiner Tree Problem (ESTP). ESTP is a well-known NP-hard optimization problem of finding a network connecting a given set of terminal points on a plane, allowing addition of auxiliary points, with the overall objective to minimize the total network length. The present study shows that aggregate lipid structures self-organize into geometries that correspond to locally optimal solutions to such problems.     

Molecular dynamics of hyperbranched polyesters in the confinement of thin films

Broadband Dielectric Spectroscopy is employed to investigate the molecular dynamics in thin films of hyperbranched polyesters (type AB₁B₂, with -OH and -OCOCH₃ as terminal groups). Three relaxation processes are detected: alpha, beta and gamma. While the latter two are not influenced by the confinement, a pronounced effect is observed on the alpha relaxation: with decreasing film thickness the slower relaxation modes of the dynamic glass transition are gradually suppressed, resulting in an increase of the average relaxation rate and in a linear decrease of the dielectric strength. This is attributed to an immobilization in confinement of the polymeric segments located at the periphery of the hyperbranched macromolecular structures.     

Morphological instabilities of polymer crystals

We present experimental observations at comparatively low supercooling of morphology transitions from dendritic to faceted structures in polymer crystals growing in thin films of a poly-2-vinylpyridineblock-polyethyleneoxid copolymer. Our results are compared with theoretical concepts describing morphological instabilities of single crystals. Although these concepts originally were not developed for polymers, they allow to describe and interpret our experimental results quite well. In particular, the measured temperature dependence of the width W and frequency of dendritic side branches and the radius of curvature ρ of the growth tips of the crystals follow these concepts. We present preliminary evidence for the influence of polymer attachment kinetics and reorganisation processes behind the growth front. Polymer thin films provide valuable model systems for studying general concepts of crystallisation and allow to distinguish at which point the connectivity of the crystallising units within chain-like molecules starts to play a measurable role.     

Spontaneous-search method and short-time dynamics: applications to the Domany-Kinzel cellular automaton

The one-dimensional Domany-Kinzel cellular automaton is investigated by two numerical approaches: (i) the spontaneous-search method, which is a method appropriated for a search of criticality; (ii) short-time dynamics. Both critical frontiers of the system are investigated, namely, the one separating the frozen and active phases, as well as the critical line determined by damage spreading between two cellular automata, that splits the active phase into the nonchaotic and chaotic phases. The efficiency of the spontaneous-search method is established herein through a precise estimate of both critical frontiers, and in addition to that, it is shown that this method may also be used in the determination of the critical exponent ν_⊥. Using the critical frontiers obtained, other exponents are estimated through short-time dynamics. It is verified that the critical exponents of both critical frontiers fall in the universality class of directed percolation.     

Nano-meter-sized domain formation in lipid membranes observed by small angle neutron scattering

Using a contrast matching technique of small angle neutron scattering (SANS), we have investigated a phase separation to liquid-disordered and liquid-ordered phases on ternary small unilamellar vesicles (SUVs) composed of deuterated-saturated, hydrogenated-unsaturated phosphatidylcholine lipids and cholesterol, where the equilibrium size of these domains is constrained to less than 10nm by the system size. Below a miscibility temperature, we observed characteristic scattering profiles with a maximum, indicating the formation of nano-meter-sized domains on the SUVs. The observed profiles can be described by a multi-domain model rather than a mono-domain model. The nano-meter-sized domain is agitated by thermal fluctuations and eventually ruptured, which may result in the multi-domain state. The kinetically trapped nano-meter-sized domains grow to a mono-domain state by decreasing temperature. Furthermore, between the miscibility and disorder-order transition temperature of saturated lipid, the integrated SANS intensity increased slightly, indicating the formation of nano-meter-sized heterogeneity prior to the domain nucleation.     

Molecular dynamics in thin films of isotactic poly(methyl methacrylate)

The molecular dynamics in thin films (18 nm-137 nm) of isotactic poly(methyl methacrylate) (i-PMMA) of two molecular weights embedded between aluminium electrodes are measured by means of dielectric spectroscopy in the frequency range from 50 mHz to 10 MHz at temperatures between 273 K and 392 K. The observed dynamics is characterized by two relaxation processes: the dynamic glass transition (α-relaxation) and a (local) secondary β-relaxation. While the latter does not depend on the dimensions of the sample, the dynamic glass transition becomes faster (≤2 decades) with decreasing film thickness. This results in a shift of the glass transition temperature T _g to lower values compared to the bulk. With decreasing film thickness a broadening of the relaxation time distribution and a decrease of the dielectric strength is observed for the α-relaxation. This enables to deduce a model based on immobilized boundary layers and on a region displaying a dynamics faster than in the bulk. Additionally, T _g was determined by temperature-dependent ellipsometric measurements of the thickness of films prepared on silica. These measurements yield a gradual increase of T _g with decreasing film thickness. The findings concerning the different thickness dependences of T _g are explained by changes of the interaction between the polymer and the substrates. A quantitative analysis of the T _g shifts incorporates recently developed models to describe the glass transition in thin polymer films. Received 12 August 2001 and Received in final form 16 November 2001