Daniel Kandel

Pearling Instabilities of Membrane Tubes with Anchored Polymers

We have studied the pearling instability induced on hollow tubular lipid vesicles by hydrophilic polymers with hydrophobic side groups along the backbone. The results show that the polymer concentration is coupled to local membrane curvature. The relaxation of a pearled tube is characterized by two different well-separated time scales, indicating two physical mechanisms. We present a model, which explains the observed phenomena and predicts polymer segregation according to local membrane curvature at late stages.

INITIAL STAGES OF THIN FILM GROWTH IN THE PRESENCE OF ISLAND-EDGE BARRIERS

A model of submonolayer thin film growth is studied, where the attachment of atoms to island edges is hindered by an energy barrier. A novel behavior of the density of islands, N_s, is predicted as a function of flux F and temperature T. For example, N_s scales as F^X with X=2i^*/(i^*+3), where i^* is the critical island size, in contrast with the standard result X=i^*/(i^*+2). The theory is applicable to surfactant mediated growth and chemical vapor deposition. It explains recent experiments, which are inconsistent with the standard theory.

Coiling of Cylindrical Membrane Stacks with Anchored Polymers

(Received 22 April 1999) We study experimentally a coiling instability of cylindrical multilamellar stacks of phospholipid membranes, induced by polymers with hydrophobic anchors grafted along their hydrophilic backbone. We interpret our experimental results in terms of a model in which local membrane curvature and polymer concentration are coupled. The model predicts the occurrence of maximally tight coils above a threshold polymer concentration. Indeed, only maximally tight coils are observed experimentally. Our system is unique in that coils form in the absence of twist and adhesion. The coil motif is ubiquitous in a wide range of natural contexts. One-dimensional filaments of mutant bacteria [1], supercoiled DNA molecules [2], and tendrils of climbing plants [3] all exhibit a writhing instability as a result of forcing or interaction with an external agent. Such systems are dominated by elastic properties, and the appearance of coils is a result of the relief of twist. In this paper we show that coiling can also be effected in cylindrical multilamellar tubes of phospholipid bilayers, by anchoring hydrophilic polymers with hydrophobic side groups grafted along the backbone. This system is unique in that, in contrast with the above examples, fluid membranes cannot support any twist. Yet coils are

The Surfactant Effect in Semiconductor Thin-Film Growth

This chapter discusses the effect of overlayers, commonly referred to as “surfactants,” on the epitaxial growth of semiconductors. Such overlayers make it possible to lower substantially the temperature required for growth of perfect epitaxial films. As device dimensions decrease, processing temperatures must be lowered to minimize diffusional broadening of interfaces and dopant profiles. Surfactants have been used to modify the growth mode of several systems, including metal layers in homoepitaxy and heteroepitaxy. The chapter also presents several theoretical models that explain the surfactant effect in semiconductor growth. These models may be divided into three categories. The first category comprises of models that concentrate on the microscopic aspects, attempting to understand the atomic-scale features and processes involved in this phenomenon. The second category comprises of models that are more concerned with the macroscopic aspects of the surfactant effect, such as island morphologies, distributions, and the effects of strain, without attempting to explain the details of the atomistic processes. The third category comprises of the models that attempt to combine both aspects (microscopic aspects and macroscopic aspects)—that is, they try to use realistic descriptions of the atomistic processes as the basis for macroscopic models.

Profile of a decaying crystalline cone

The decay of a crystalline cone below the roughening transition is studied. We consider local mass transport through surface diffusion, focusing on the two cases of diffusion limited and attachment-detachment limited step kinetics. In both cases, we describe the decay kinetics in terms of step flow models. Numerical simulations of the models indicate that in the attachment-detachment limited case the system undergoes a step bunching instability if the repulsive interactions between steps are weak. Such an instability does not occur in the diffusion limited case. In stable cases the height profile, h(r,t), is flat at radii r<R(t)\sim t^{1/4}. Outside this flat region the height profile obeys the scaling scenario \partial h/\partial r = {\cal F}(r t^{-1/4}). A scaling ansatz for the time-dependent profile of the cone yields analytical values for the scaling exponents and a differential equation for the scaling function. In the long time limit this equation provides an exact description of the discrete step dynamics. It admits a family of solutions and the mechanism responsible for the selection of a unique scaling function is discussed in detail. Finally we generalize the model and consider permeable steps by allowing direct adatom hops between neighboring terraces. We argue that step permeability does not change the scaling behavior of the system, and its only effect is a renormalization of some of the parameters.

Profile Scaling in Decay of Nanostructures

The flattening of a crystal cone below its roughening transition is studied by means of a step flow model. Numerical and analytical analyses show that the height profile, h(r,t), obeys the scaling scenario dh/dr = F(r t^{-1/4}). The scaling function is flat at radii r<R(t) \sim t^{1/4}. We find a one parameter family of solutions for the scaling function, and propose a selection criterion for the unique solution the system reaches.

Coiling instability of multilamellar membrane tubes with anchored polymers.

We study experimentally a coiling instability of cylindrical multilamellar stacks of phospholipid membranes, induced by polymers with hydrophobic anchors grafted along their hydrophilic backbone. Our system is unique in that coils form in the absence of both twist and adhesion. We interpret our experimental results in terms of a model in which local membrane curvature and polymer concentration are coupled. The model predicts the occurrence of maximally tight coils above a threshold polymer occupancy. A proper comparison between the model and experiment involved imaging of projections from simulated coiled tubes with maximal curvature and complicated torsions.

Defects, Interface Profile and Phase Transitions in Growth Models

The effect of a localized defect on the profile of a one-dimensional growing surface is studied. It is found that the width of the average profile scales with the distance R from the defect as Rγ. A phase transition is observed as the velocity of propagation at the defect site is increased. For small velocities γ < 1, while above a critical value the profile becomes linear (γ = 1). This system provides a very interesting example of a phase transition in a one-dimensional probabilistic dynamical system.

SELECTION OF THE SCALING SOLUTION IN A CLUSTER COALESCENCE MODEL

The scaling properties of the cluster size distribution of a system of diffusing clusters is studied in terms of a simple kinetic mean field model. It is shown that a one parameter family of mathematically valid scaling solutions exists. Despite this, the kinetics reaches a unique scaling solution independent of initial conditions. This selected scaling solution is marginally physical; i.e., it is the borderline solution between the unphysical and physical branches of the family of solutions.

Critical Acceleration of Lattice Gauge Simulations

We present a stochastic cluster algorithm that drastically reduces critical slowing down forZ2 lattice gauge theory in three dimensions. The dynamical exponentz is reduced fromz>2 (standard Metropolis algorithm) toz≈O.73. The Monte Carlo pseudodynamics acts on the gauge-invariant flux tubes that are known to be the relevant large-scale low-energy excitations. A comparison of our results with known results for the 3D Ising model andφ4 model supports the conjecture of universality classes for stochastic cluster algorithms.