We investigate the dynamics of the classical Euler buckling of compressed solid membranes. We relate the membrane buckling dynamics to phase ordering phenomena. Membrane develops a wavelike pattern whose wavelength grows, via coarsening, as a power of time. Evolving membrane is similar to rough growing surfaces (“growing interfaces”) whose roughness grows as a power of time. Membrane buckling dynamics is characterized by a distinct scaling behavior not found in other coarsening phenomena

In integrated circuit manufacturing, the gaps between metal lines are a critical parameter, and polymer films are being evaluated as low k dielectric materials for VLSI. Desire to maximize the number of elements within a given area to increase clock speed and decrease power consumption have forced the gaps to become increasingly smaller. Currently, 0.25–0.18 micron line widths are the subject of much commercial interest. A line width of 0.25 microns is within a factor of 5 of the molecular dimension of most commercial polymers. Experiments have suggested polymer films slightly smaller than these dimensions may not have the expected bulk mechanical properties. This deviation from the expected behavior (i.e., Change in the glass transition temperature) would present significant technical challenges to the manufacturing and reliability of integrated circuits. These effects are extremely difficult to determine experimentally with requisite precision. Recently, an experimental technique, based on a highly modified quartz crystal microbalance, has been developed to study the mechanical properties of these ultra-thin polymer films with high precision. The experimental details and preliminary results from this recently developed state-of-the-art experimental technique will be presented.

The frictional response of two opposing polymer brushes subjected to steady shear was studied as a function of solvent condition and degree of compression using the Surface Forces Apparatus (SFA). The brushes were made by preferential adsorption of polyvinylpryridinepolystyrene (PVP-PS) block copolymers adsorbed onto atomically smooth surfaces from a dilute solution of toluene. Extremely parallel lateral motion was imparted to one surface and the response was detected at the opposing brush-covered surface. When the brushes were bathed in a good solvent, it was necessary to strongly compress the layers in order to observe frictional forces transmitted between the surfaces. However, when the solvent was changed to a near-theta solvent, large frictional forces were measured at weaker compressions. The onset of these frictional forces occurred at distances comparable to the distance at which the opposing layers contact one another and rapidly increase as the brushes are compressed. Arguments are advanced that this behavior is attributable to frictional interactions between the polymer chains and the solvent.

The wetting behavior of perfluorinated ionomers has been investigated as a function of polymer-surface interaction, the nature of the counter-ion and the structure of the polymer in the solvent from which it has been cast onto the surface. Two different ion-containing polymers, with a per-fluoro-carbon backbone were studied. They differ in the chemical composition and the polarity of their side chains. AFM results together with neutron reflectivity, light scattering and surface tension measurements had shown that the structure of the polymer in the parent solution has a profound effect on the wetting properties as well as the surface structure of the polymers.

Thermodynamic and kinetic properties of model dendrimers are investigated. We show that for ideal dendrimers, with a superimposed energy funnel descending from the periphery to the center, one should be able to control the preferred location of the excitation by monitoring the temperature relative to the energy funnel. This opens the possibility for a controlled drive of photochemical processes in these supermolecules. The mean first passage time (MFPT) of excitations to reach the center of a dendrimer is calculated. A minimum in the MFPT as a function of temperature is predicted.

We have used Grazing Incidence X-ray Scattering to study the depth dependence of the interfacial structure of smectic liquid crystal (8CB) hybrid films. These films are bounded by a grated glass substrate and air, and have been studied as a function of both temperature and thickness. Our measurements indicate the presence of both a chevron structure and a structure similar to the helical twist-grain-boundary (TGB) phase. Our measurements constitute the first to show that this structure can also be observed in hybrid smectic liquid crystal films. The twisted structure is the result of anchoring at two dissimilar competing confining surfaces.

The flow of a fluid confined between two solid plates (Hele-Shaw cell) is of considerable interest in a variety of applications. Further interest in two phase flow in this geometry stems from the close analogy between the dynamics of fluid-fluid interface and the propagation of the solidification front. While the flow of Newtonian fluids is rather well understood, it is much more complicated to compute flows of non-Newtonian fluids. We find that the dense-branching morphology of Newtonian liquids may be replaced by dendritic fingers with stable tips and sidebranches, and discuss resulting length scales.

The flow of a thin layer of fluid on a solid surface is of considerable technological importance; many industrial applications, ranging from spin coating of microchips to the design of photographic film, are susceptible to often undesirable instabilities. We use a recently developed numerical scheme to analyze the problem of flow down an inclined plane, and concentrate on the case of completely wetting fluid characterized by a small precursor film height, b. In particular, we explore the role of imperfections of the solid surface, exploring the influence of the length scale of the surface roughness on the film stability and eventual pattern formation (fingers and rivulets). It is found that perturbations characterized by very short length scale do not influence considerably the film stability, in contrast to the perturbations specified by longer length scales. Further, we find that the role of imperfections becomes more pronounced at smaller precursor film thicknesses, b. We also analyze the effect of a time dependent body force on the film stability.

Wetting properties and surface structure of polyaniline (PANI) thin films were studied as a function of the polymer thickness, using AFM and neutron reflectivity. Increasing the oxidation state as well as polymer thickness was found to increase the tendency of the polymer to form polycrystalline films. Three main regions with characteristic behavior were observed: ultra thin films of the order of several molecular layers, an intermediate thickness film of several molecular layers to ∼150nm, and films thicker than 150nm. In the ultra thin region the polymer formed nano-scale spherical domains. In the intermediate one, the films tend to be continuous and amorphous. In the thick films, crystallinity was observed.

A simple and direct method has been developed of determining absolute values of adsorbance, i.e. mass per unit area, of polymers adsorbed from solution on to mica surfaces. A commercially available Mettler UMT2 ultramicrobalance is used to measure the weight of mica sheets before and after the immersion of the mica sheets into polymer solution for a given period of time. The increase in weight of mica sheets is divided by the total area of mica surfaces to derive the adsorbance. Practically measurable change in adsorbance was evaluated to be 0.1 mg m2. As an example of the practical application of the present method, an experimental result is presented of the adsorption kinetics of polystyrene (M=66,000) adsorbed from cyclohexane on to mica surfaces at the 0 -temperature.

The diffusion of electrons in two dimensions is investigated when the model space has one or more sinks. A random walk approach is used to follow each electron until it is trapped at a sink. The times to capture are combined to form the survival time distribution. This is found to decay exponentially with time for the cases considered here. The characteristic time for the decay depends directly on the model space area and inversely on the number of traps or sinks and the trap radius. Power laws with non-integers are found for all three parameter dependences.

The crossover time from the early-time regime to the asymptotic regime for the A+B⃗+C reaction-diffusion system with initially separated reactants has been derived analytically by matching the rate expressions for the two regimes. The crossover time expression thus obtained shows an explicit dependence on the rate constant (k) and the initial reactant concentrations (ao, bo). For the A+2B⃗C system we performed computer simulations using two different methods. Crossover behaviors for the global reaction rate and reaction front width have been observed for both methods. The crossover time depends on the mechanism of the reaction.

We report on an adsorption study on two shale samples that have previously been investigated by small-angle neutron scattering (SANS). The scattering data indicate that these samples can be characterized as surface fractals in length from 5 Å to 500 Å, with the fractal dimension D between 2.83 and 2.75. Using the existing models for adsorption on fractal surfaces, the values of D deduced from the adsorption data appear to be consistently lower than the SANS results. We discuss these findings.

The behavior of two reaction fronts created in a system of two competing reactions has been investigated using the reaction between xylenol orange (XO) and chromium(III) ion in aqueous solution. Two reaction fronts have been shown to move in opposite directions, which is explained in terms of relative concentrations among three reactant species. This explanation was verified by the observation of only one reaction front for selected different relative concentrations, where both reaction fronts move in unison. As predicted by theory and confirmed by computer simulation, the position (xf) of each reaction front scales as t½, irrespective of the direction of motion.

We demonstrate here the implementation of an experimental system suitable for the study of the diffusion-limited A+B→0, non-classical reaction behavior. Using a combination of a fluorescent calcium indicator and a calcium ion which is initially “caged”, a pulse of near-UV light initiates the reaction which is followed as product formation vs. time. Sensitive dependence on the initial reactant distribution is observed through patterns in the uncaging UV light profile. The reaction progress passes through two non-classical time regimes, one due to roughness originating from laser speckles, followed by one exhibiting the three-dimensional Zeldovich rate of (1/ρA − 1/ρA0) ˜ t3/4, with features matching Monte Carlo simulations on this initial distribution.

A surface adsorption-diffusion-reaction model is proposed and tested by Monte Carlo simulations. The solvent shell effect is considered as a geometric constraint and the Langmuir adsorption mechanism is also incorporated. An anomalous power law of t1/2 is obtained for the amount of material removed from the surface vs. time. The result agrees well with etching experiments of SAM on a silica surface. We conclude that the unusual power law results from an interplay of vacancy growth and fusion at the surface.

Theoretical models and experimental data taken primarily from the literature provide predictive capabilities of the sound speed in porous materials and hence their acoustic impedance can be determined. Applying the acoustic approximation (weak discontinuity) at the interfaces of the porous material along with an attenuation model describing conditions within the porous system good fits to shock tube data on an elastomeric foam and on layers of kevlar were obtained.

We report a light-induced, surface-assisted structural phase transition from a common orthorhombic phase of crystalline gallium (α-gallium) to a highly reflective, metastable phase of more ‘metallic’ nature. The transition has been observed at the interface of gallium with fused silica at temperatures just below the metal's bulk melting point and affects only several tens of gallium atomic layers. The transition is fully reversible and occurs on a nanosecond/microsecond time scale. The transition appears to show some characteristic features of a second order structural phase transition, including an increase of the transition relaxation times at the critical temperature (of approximately 30°C). The transition has no apparent optical intensity threshold, and is induced by radiation of very low intensity of only 10−4 − 10−5 W/μm2. The two gallium phases involved in the phase transition have significantly different dielectric properties which gives rise to a gigantic cubic optical nonlinearity, χ(3) ∼ 1 esu. The transition can be stimulated by light at any wavelength in the visible and the infrared ranges out to at least 1.55μm. The effect is therefore of great interest for applications requiring light by light control at milliwatt power levels.

We study different boundary value problems for fractional diffusion equations which describe a non-Brownian particle. Absorbing and reflecting walls of a box, and the escape problem through a fluctuating bottleneck with coloured noise are considered.

This new architectural class of macromolecules has received substantial attention during the past decade. Three dendritic subclasses, which include (a) random hyperbranched (i.e., one-pot ABx, polymerizations), (b) dendritic grafted (i.e., Combburst® polymers) and (c) regular dendrons/dendrimers (e.g., Starburst® dendrimers) have been synthesized and characterized at a well-defined level in our laboratory. It is clear that their precisely controlled, nanoscale dimensions and architecture play critical roles in influencing physical properties and performance characteristics. Furthermore, these parameters have also distinguished dendrimers as fundamental modules for many nanotechnology applications, as well as for the construction of a new class of larger nanoscale entities which we have termed core-shell tecto(dendrimers). This account will overview these activities and focus on certain unique de Gennes dense packing (or congestion phenomena) and nanoscale container properties that have emerged from this novel architecture.