Beyond the Young-Laplace model for cluster growth during dewetting of thin films: effective coarsening exponents and the role of long range dewetting interactions.

Long range dewetting forces acting across thin films, such as the fundamental van der Waals interactions, may drive the formation of large clusters (tall multilayer islands) and pits, observed in thin films of diverse materials such as polymers, liquid crystals, and metals. In this study we further develop the methodology of the nonequilibrium statistical mechanics of thin films coarsening within continuum interface dynamics model incorporating long range dewetting interactions. The theoretical test bench model considered here is a generalization of the classical Mullins model for the dynamics of solid film surfaces. By analytic arguments and simulations of the model, we study the coarsening growth laws of clusters formed in thin films due to the dewetting interactions. The ultimate cluster growth scaling laws at long times are strongly universal: Short and long range dewetting interactions yield the same coarsening exponents. However, long range dewetting interactions, such as the van der Waals forces, introduce a distinct long lasting early time scaling behavior characterized by a slow growth of the cluster height/lateral size aspect ratio (i.e., a time-dependent Young angle) and by effective coarsening exponents that depend on cluster size. In this study, we develop a theory capable of analytically calculating these effective size-dependent coarsening exponents characterizing the cluster growth in the early time regime. Such a pronounced early time scaling behavior has been indeed seen in experiments; however, its physical origin has remained elusive to this date. Our theory attributes these observed phenomena to ubiquitous long range dewetting interactions acting across thin solid and liquid films. Our results are also applicable to cluster growth in initially very thin fluid films, formed by depositing a few monolayers or by a submonolayer deposition. Under this condition, the dominant coarsening mechanism is diffusive intercluster mass transport while the cluster coalescence plays a minor role, both in solid and in fluid films.

Effects of antimicrobial peptide revealed by simulations: translocation, pore formation, membrane corrugation and euler buckling.

We explore the effects of the peripheral and transmembrane antimicrobial peptides on the lipid bilayer membrane by using the coarse grained Dissipative Particle Dynamics simulations. We study peptide/lipid membrane complexes by considering peptides with various structure, hydrophobicity and peptide/lipid interaction strength. The role of lipid/water interaction is also discussed. We discuss a rich variety of membrane morphological changes induced by peptides, such as pore formation, membrane corrugation and Euler buckling.

Dislocation dynamics and surface coarsening of rippled states in the epitaxial growth and erosion on (110) crystal surfaces.

Rippled one-dimensionally periodic structures are commonly seen in the experimental studies of the epitaxial growth and erosion on low symmetry rectangular (110) crystal surfaces. Rippled states period (wavelength) and amplitude grow via a coarsening process that involves motion and annihilations of the dislocations disordering perfect periodicity of these structures. Unlike the ordinary dislocations in equilibrium systems, the dislocations of the growing rippled states are genuinely traveling objects, never at rest. Here, we theoretically elucidate the structure and dynamics of these far-from-equilibrium topological defects. We derive fundamental dislocation dynamics laws that relate the dislocation velocity to the rippled state period. Next, we use our dislocations velocity laws to derive the coarsening laws for the temporal evolution of the rippled state period lambda and the ripple amplitude w (surface roughness). For the simple rippled states on (110) surfaces, we obtain the coarsening law lambda approximately w approximately t{2/7} . Under some circumstances however, we find that these states may exhibit a faster coarsening with lambda approximately w approximately t{1/3} . We also discuss the dislocations in the rectangular rippled surface states for which we derive the coarsening law with lambda approximately w approximately t{1/4} . The coarsening laws that occur at the transition from the rippled to the rhomboidal pyramid state are also discussed, as well as the crossover effects that occur in rippled states in the proximity of this transition on (110) crystal surfaces.

Vertical asymmetry and the ripple-rotation transition in epitaxial growth and erosion on (110) crystal surfaces.

Vertical (up-down) asymmetry is ubiquitous feature of the nonequilibrium statistical mechanics of realistic growing interfaces. Yet, the actual role of vertical asymmetry (VA) in epitaxial growth on crystal surfaces is still elusive. Is vertical asymmetry a primary or secondary factor in epitaxial growth and erosion? Can vertical asymmetry alone produce major qualitative effects on long length scale interface morphologies? To address these questions in depth, we theoretically discuss the effects of vertical growth asymmetry on far-from-equilibrium interfacial morphologies occurring in the epitaxial growth and erosion of (110) crystal surfaces. We theoretically elucidate the so-called ripple rotation transition on the Ag(110) crystal surface [F. B. de Mongeot; Phys. Rev. Lett. 84, 2445 (2000), G. Constantini, J. Phys.: Condens. Matter 13, 5875 (2001)], as the transition between the rectangular rippled states (checker-board structures of alternating rectangular pyramids and pits). We show that the experimental surface diffraction data seen in this transition can be understood only by invoking vertical growth asymmetry. In the proximity of the transition point, we find that vertical asymmetry itself produces an interface morphology yielding a four-lobe near in-phase diffraction pattern having four peaks along the principal axes of the (110) surface, in accord with the experiments on Ag(110). Moreover, on the two sides of the ripple rotation transition, we find two exotic interface states induced by vertical asymmetry, which correspond well /to the interface morphologies seen on Ag(110). We document our results by numerical simulations and by analytic arguments. Our theoretical findings, in combination with experiments, provide the first rigorous evidence that VA plays a significant role in epitaxial growth and erosion on crystal surfaces.

DNA molecules on periodically microstructured lipid membranes: localization and coil stretching.

We explore large scale conformations of DNA molecules adsorbed on curved surfaces. For that purpose, we investigate the behavior of DNA adsorbed on periodically shaped cationic lipid membranes. These unique membrane morphologies are supported on grooved, one-dimensionally periodic microstructured surfaces. Strikingly, we find that these periodically structured membranes are capable to stretch DNA coils. We elucidate this phenomenon in terms of surface curvature dependent potential energy attained by the adsorbed DNA molecules. Due to it, DNA molecules undergo a localization transition causing them to stretch by binding to highly curved sections (edges) of the supported membranes. This effect provides a new venue for controlling conformations of semiflexible polymers such as DNA by employing their interactions with specially designed biocompatible surfaces. We report the first experimental observation of semiflexible polymers unbinding transition in which DNA molecules unbind from one-dimensional manifolds (edges) while remaining bound to two-dimensional manifolds (cationic membranes).

DNA localization and stretching on periodically microstructured lipid membranes.

We study the conformational behavior of DNA molecules adsorbed on cationic-lipid membranes that are supported on grooved, one-dimensionally periodic microstructured surfaces. We reveal a striking ability of these periodically structured membranes to stretch DNA coils. We elucidate this DNA stretching phenomenon in terms of surface curvature dependent potential energy attained by the adsorbed DNA molecules. Because of it, DNA molecules undergo a localization transition causing them to stretch by binding to highly curved sections of the supported membranes.

Interfacial states and far-from-equilibrium transitions in the epitaxial growth and erosion on (110) crystal surfaces.

We discuss the far-from-equilibrium interfacial phenomena occurring in the multilayer homoepitaxial growth and erosion on (110) crystal surfaces. Experimentally, these rectangular symmetry surfaces exhibit a multitude of interesting nonequilibrium interfacial structures, such as the rippled one-dimensional periodic states that are not present in the homoepitaxial growth and erosion on the high symmetry (100) and (111) crystal surfaces. Within a unified phenomenological model, we reveal and elucidate this multitude of states on (110) surfaces as well as the transitions between them. By analytic arguments and numerical simulations, we address experimentally observed transitions between two types of rippled states on (110) surfaces. We discuss several intermediary interface states intervening, via consecutive transitions, between the two rippled states. One of them is the rhomboidal pyramid state, theoretically predicted by Golubovic [Phys. Rev. Lett. 89, 266104 (2002)] and subsequently seen, by de Mongeot and co-workers, in the epitaxial erosion of Cu(110) and Rh(110) surfaces [A. Molle, Phys. Rev. Lett. 93, 256103 (2004), and A. Molle, Phys. Rev. B 73, 155418 (2006)]. In addition, we find a number of interesting intermediary states having structural properties somewhere between those of rippled and pyramidal states. Prominent among them are the rectangular rippled states of long rooflike objects (huts) recently seen on Ag(110) surface. We also predict the existence of a striking interfacial structure that carries nonzero, persistent surface currents. Periodic surface currents vortex lattice formed in this so-called buckled rippled interface state is a far-from-equilibrium relative of the self-organized convective flow patterns in hydrodynamic systems. We discuss the coarsening growth of the multitude of the interfacial states on (110) crystal surfaces.

Finite-size thermomechanical effects in smectic liquid crystals: The vapor pressure paradox as an anharmonic phenomenon.

We pursue a systematic statistical mechanics study of finite smectic stacks of semiflexible manifolds bounded by interfaces under tension. We address, by analytic calculations and Monte Carlo simulations, the effects of the surface tension on smectic interlayer distances. We use our theoretical results to elucidate the so called vapor pressure paradox (VPP) in multilamellar membrane phases and explain the experiments of Katsaras [Biophys. J. 73, 2924 (1997); 75, 2157 (1998)]. We show that the effects of the interfacial tension are substantially weaker than suggested by the previous theoretical discussion of the VPP effects [R. Podgornik and V. A. Parsegian, Biophys. J. 72, 942 (1997)]. By consistently taking into account the discrete, layered character of smectic liquid crystals, and anharmonic phonon effects, we show that the essence of VPP effects is in spatially nonuniform thermal expansion of smectic interlayer separations. We find that the average period of the whole finite stack can be both smaller (ordinary VPP effect at high enough interfacial tensions) or bigger (a reverse VPP effect at low interfacial tensions, overlooked in previous studies), relative to the average period of the corresponding infinite smectic stack. Looking at stacks from outside, these two effects show up as if there is an attractive (for the ordinary VPP effect), or repulsive (for the reverse VPP effect) pseudo-Casimir force acting between the two stack interfaces. We show however that the physics of VPP effects is obscured by schematically invoking Casimir-like forces. Rather, the ordinary and the reverse VPP effects are to be both characterized as thermomechanical anharmonic effects caused by a spatially nonuniform thermal expansion of smectic interlayer distances. Interlayer distances close to stack surfaces expand less (more) for the ordinary (reverse) VPP effect than those deep in the stack. The reverse VPP prevails at low interfacial tensions, simply because the membrane at the top of the stack is more free to fluctuate than membranes in the bulk. By increasing interfacial tension above a threshold value, fluctuations of the membrane at the stack top become suppressed, and the ordinary VPP effect prevails. In this study, we demonstrate that finite-size VPP effects in a strongly entropic system, such as the sterically stabilized lamellar phases, can be described quantitatively well by a simple analytic approach.

Interfaces of semi-infinite smectic liquid crystals and equations of state of infinite smectic stacks of semiflexible manifolds.

In this paper, we first elucidate the classical problem of the elastic free energy of a semi-infinite smectic-A liquid crystals, that fills the semispace above an interface (a boundary smectic layer) of a given shape. For the free energy of this interface, we obtain an effective interface Hamiltonian that takes into account the system discreteness introduced by the layered character of smectic-A liquid crystals. It is thus applicable to both short and long wavelength fluctuations of the interface shape. Next, we use our interface Hamiltonian to develop an efficient approach to the statistical mechanics of stacks of N semiflexible manifolds, such as two-dimensional smectic phases of long semiflexible polymers and three-dimensional lamellar fluid membrane phases. Within our approach, doing the practically interesting thermodynamic limit N--> infinity is reduced to considering a small stack, with just a few interacting manifolds, representing a subsystem of an infinite smectic. This dramatic reduction in the number of degrees of freedom is achieved by treating the first (the last) manifold of the small stack as an interface with the semi-infinite smectic medium below (above) the small stack. We illustrate our approach by considering in detail two-dimensional sterically stabilized smectic liquid crystals of long semiflexible polymers with hard-core repulsion. Smectic bulk (N= infinity ) equation of state and the universal constant characterizing entropic repulsion in these phases are obtained with a high accuracy from numerical simulations of small subsystems with just a few semiflexible polymers.

Epitaxial growth and erosion on (110) crystal surfaces: structure and dynamics of interfacial States.

We study nonequilibrium interfacial states in multilayer epitaxial growth and erosion on rectangular symmetry crystal surfaces. We elucidate a recently observed transition between two kinds of rippled states on (110) surfaces. We predict several novel interface states intervening, via consecutive transitions, between the two rippled states. We predict coarsening laws of the dynamics of the rippled and the intervening states on (110) crystal surfaces.

Smectic phases of semiflexible manifolds: constant-pressure ensemble.

We pursue the constant-pressure ensemble approach to elucidate the statistical mechanics of the smectic phases of semiflexible manifolds, such as two-dimensional smectic phases of long semiflexible polymers and three-dimensional lamellar fluid membrane phases. We use this approach to consider in detail sterically stabilized phases of semiflexible polymers in two-dimensional (2D) smectic systems. For these 2D systems, we obtain the universal constants characterizing the entropic repulsion between semiflexible polymers, such as those in the osmotic pressure P=alpha(k(B)T)(4/3)/kappa(1/3)(a-a(min))(5/3) with alpha found here to be congruent with 0.432 (here, a is the smectic phase period, and a(min) and kappa are the polymer cross-sectional diameter and bending rigidity constant, respectively). We address, by numerical simulations and analytic arguments, finite stacks of N semiflexible manifolds, and discuss in detail the practically interesting thermodynamic limit N--> infinity. We show that the thermodynamic limit is quickly approached within the constant-pressure ensemble: Already from numerical simulations involving just few semiflexible polymers under constant isotropic pressure, one can obtain the infinite 2D smectic equation of state within a few percent accuracy. We use our results to discuss the competition of electrostatic and entropic effects in quasi-2D smectic phases of DNA-cationic-lipid complexes. We use our quantitative results to discuss in detail the elasticity, topological defects, anomalous elasticity, and the effects of externally applied tension in sterically stabilized 2D smectic phases of long semiflexible polymers.