This work reexamines equilibrium and kinetic features of polymer brushes end-adsorbed onto solid substrates from solution, providing a new interpretation of previously-published experimental results and insight into the comparison between experiments and existing kinetic models. The study centers on an end-modified polyethylene oxide (PEO) which may adsorb to form a polymer brush on a hydrophobic polystyrene latex, and whose main backbone also exhibits an attraction for the surface. In a previous work, Gao and Ou-Yang claim a sharp pancake-to-brush transition with increasing surface coverage of the samples with the strongest end group attraction to the substrate, and only a delicate increase in the hydrodynamic thickness of layers whose chain ends are weakly attracted to the surface. Our reevaluation of this data, however, collapses all molecular architectures to a single curve describing the hydrodynamic thickness at different surface loadings, and which shows a relatively sharp transition for all samples. Gao and Ou-Yang have also performed kinetic exchange experiments where low molecular weight species replace preadsorbed high molecular species (with the same endgroup-surface adsorption energy), and observed stretched exponential behavior in the evolution of the hydrodynamic thickness of the adsorbed layer. We employed Milner's treatment for brush exchange kinetics, to extract equivalent phenomenological parameters for more direct comparison between fundamental parameters and experiment.

The anomalous rate laws of diffusion limited elementary reactions in low dimensions have garnered attention over the past decade as researchers have become aware that the mean field approximation utilized in traditional kinetic rate equations is not valid in low and fractal dimensions. We use Monte Carlo simulations to study a diffusion limited system simultaneously undergoing A+B-->0 and A+A--> 0 reactions, a common situation in photochemistry. We are studying how this coupled system affects the attenuation of local fluctuations and thus the rate laws of the system in low dimensions and how these results compare to the mean field rate laws. Our results give useful guidelines for studying this type of reaction system experimentally.

The presence of a reaction front is a characteristic feature of a variety of physical, chemical and biological processes. A chemical reaction exhibits a front (spatially localized region where concentration of product is non zero), provided the diffusing reactants are separated in space. We study the reaction front dynamics of a termolecular A+2B--->C reaction with initially separated components in a capillary. The reaction tetra+2Ni2+--->1:2 complex is used, where ‘tetra’ is disodium ethyl bis(5-tetrazolylazo) acetate trihydrate. We measure and compare with theory the dynamic quantities that characterize the kinetic behavior of the system: the global reaction rate R(t), the location of the reaction center xf(t), the front's width w(t), and the local production rate R(xf,t). The non-classical nature of this dynamical system is confirmed.

Non-classical results due to reactant correlation effects have been observed in the study of Monte Carlo simulations of the A2 + B2 → 2AB reaction. These simulation results, interpreted by the Pair Density Analysis method and the experimental kinetic studies, may provide an explanation of the early time anomalous kinetic behavior of the catalytic hydrogen isotope exchange reaction exhibited for surface-diffusion limited conditions on alumina supported platinum islands.

Molecular motion in a series of cavities dominated by time dependent bottlenecks is studied as a model for molecular pathways in biomolecules. The problem is formulated by coupled rate and Langevin equations and is shown to be equivalent to n-dimensional reaction-diffusion equation where n is the number of cavities visited by the molecules. Results are presented for two cavities and a comparison is made between steady state and non steady state results.

Multiply charged metal clusters undergo fission at a certain size. This critical size can be predicted by the liquid drop model when some modifications are taken into consideration. In this work we revise the asymmetric liquid drop model (ALD) and modify it for the alkali metals. This modification addresses those fragmentation channels in which a parent cluster with charge Ze fissions into two fragments. One of the fragments is small and singly charged whereas the second fragment is large and carries the rest of the charge. A different energetic balance equation is presented in which the ionization energy of a single atom and the energy of formation of a small cluster are included. Results and comparison to experiments is provided for Na and Cs clusters. Prediction of the critical size of Na and Cs clusters with Ze>7 is part of the discussion.

Results of reducibility tests of reduction conducted on iron ore pellets by carbon are presented in this work. Work done is centered on reduction kinetics by carbon with conventional heat supply (heat transfer process) compared with reduction kinetics where heat is supplied by microwaves to whole volume. Ore used in this work is called “Alzada” which has reducibility characteristics well known, and is often used as standard for comparison. Importance of using actual pellet instead of dust is pointed. This work is part of a project related with microwaves for reduction of metallic oxides.

The escape rate is calculated for an electron in a one-dimensional potential well. First-order time-dependent perturbation theory is used with solutions of Schrödinger's equation and a set of coupled rate equations is numerically solved. The time evolution of an ensemble of one-electron systems is followed and the fraction of systems that remain in a bound state is found to decay exponentially as time passes. The characteristic time constant for the decay grows exponentially with an increase in the well depth. This is analogous to Kramers' result for the classical escape problem.

This paper presents a new method for preparing composites of phosphogypsum, a chemical industry waste, and synthetic (polyester, epoxide and vinyl ester) resins. These composites, after thermal improvement of the phosphogypsum, are called CLM (ceramic-like materials). They are characterized by highly desirable physical, chemical, mechanical and strength-related properties which enable there usage as anti-corrosive coatings for storage tanks and as durable floor coatings in many branches of industry.

Reaction kinetics in micellar solutions are studied theoretically with an emphasis on diffusioncontrolled luminescence quenching. Different spatial arrangements of reactants within individual micelles are analyzed and a general method for treating diffusion-controlled reactions in a finite volume employing an effective potential approximation is developed. Several models are considered for the exchange of reactants between micelles including migration mediated by the bulk phase and successive multiparticle hopping through transient channels connecting micelles during their sticky collisions. These results are combined in a general stochastic theory of reaction kinetics in micellar solutions with exchange. The theory is further extended to reactions in clusters of micelles using a continuous time random walk approach. Once the principal features of micellar kinetics are understood, one can extract important structural and dynamic information on the aggregates and their guest molecules by analyzing suitably designed experiments.

We formulate an approach to the A + A → products reaction based on a reaction-diffusion model. We construct the first equations in a moment hierarchy whose first two members are the global density of A particles and the pair correlation function. We terminate the hierarchy by relating the three-particle correlation function to two-particle correlation functions and thereby obtain a set of coupled equations that turns out to be linear and hence analytically tractable.

This approach leads naturally to the proportionality of the rate of the reaction to the pair correlation function evaluated at r=a, where a is the diameter of the reacting particles. It also confirms the relation between anomalous kinetics and the deviation of the pair correlation function from that associated with a random distribution of particles.

Numerical simulations in one and two dimensions that support our theory are presented in a companion paper in this session.

We study a reaction-diffusion system within the confines of a thin capillary tube. Xylenol orange and Cr 3+ are introduced into a capillary tube from opposite ends and meet in the middle forming a reaction front. Unequal initial concentrations of the reactants causes the center of the reaction front to move in time. Characteristics of the front such as the width of the reaction zone, w, the position of the center of the front, xf, the global reaction rate, R, and the local reaction rate, r(xf,t) are determined by continuously monitoring the product concentration in space vs. time. We observe crossover of the global rate from classical to non-classical behavior and a splitting of the reaction front.

The well-known model reactions A+A⇢0 and A+B⇢0 are examined in terms of the microscopic geometric arrangements of the reactants that may possibly lead to reaction. The reaction takes place only upon physical short-ranged collision of the reactants. Different dimensionalities are examined, and for each one of these arrangements all possible arrangements of the reactants are enumarated. Then, the frequency (probability) is taken into account, and an overall rate is formed. This rate is monitored in the course of the reaction in the simulation calculation and compared to the overall rate derived the traditional way from the densities. These two rates agree very well. Finally, the pair correlation functions are calculated as a function of time from the simulation data, and they are also in good agreement with previous studies.

A study of the dynamics of the reaction front that appears in diffusion-reaction systems of the form A + B → C with initially separated reactants in the presence of quenched disorder is presented. The scaling of the width of the front w is analyzed as a function of the “disorder strength” and the dimensionality of the system. It is shown that disorder strongly affects the width exponent α, ω tα even for d ≥ 2, where the mean field approximation is known to be valid. The scaling of the nearest neighbor distance, midpoint fluctuations and concentration profiles near the center of the front, are also studied.

Experimental data for the exchange of protons between proteins and the aqueous solvent is re-examined using a fractal model. The fraction of protons unexchanged from the protein, f is seen to follow a stretched exponential, at long times. For the protein, lysozyme, data over a range of temperatures were considered and accurate fits were obtained with a single, unadjusted scaling exponent, α. The time constant, τ, followed an Arrhenius law and gave an activation energy comparable to that obtained for free peptide exchange. A model is proposed where proton exchange occurs as a result of solvent reacting at the fractal surface of the protein. The protein itself is not treated as static but has units that diffuse to the surface. The diffusion of these units in the long time domain is assumed to be classical. In this model the scaling exponent, α, is related to the spectral dimension of the system. Treating the problem as a reaction of the type A+B→C in a confined region, the exponent is given by: α = (3 − ds)/4 where dS/4 is the fractal surface dimension of the protein. Using the value of 2.17 previously established for the surface dimension of lysozyme, data at 6 different temperatures could be fit with the corresponding α of 0.21. These results show that the fractal structure of a protein can influence difflusional processes of small molecules associating with the protein.

This work employed total internal reflectance fluorescence (TIRF) to examine the adsorption kinetics of polyethylene oxide (PEO) on silica from aqueous solution in controlled shearing flow. Studies with PEO, fluorescently labeled such that TIRF tracked the chain number on the surface, exhibited an overshoot in the early stages of adsorption. This overshoot was not seen with other polymers such as polyvinyl alcohol, and hydroxyethyl cellulose, possibly because these other polymers were labeled such that TIRF measured the interfacial mass. Indeed, reflectometry studies of PEO adsorption, sensitive to interfacial mass, showed no overshoot. This suggests that the overshoot results from the selectivity of the surface for high molecular weight populations within a polydisperse sample. Initially short chains adsorb because they diffuse to the surface quickly. At longer times, higher molecular weight chains reach the surface and replace the short chains. This evolution occurs as the mass coverage increases (according to reflectivity) but the number of adsorbed chains, and hence the TIRF signal decrease at long times. A study of the impact of the molecular weight distribution confirmed this hypothesis.

Several complications to the molecular weight selectivity hypothesis, however, arose: First, the same PEO samples which overshot during adsorption on silica showed no overshoot on a polystyrene substrate. This suggested that the ability to overshoot was governed by the substratesegment interactions, even though the molecular weight distribution within the sample determined the overshoot shape. Further, the effect of transport conditions (wall shear rate, bulk polymer concentration) were not completely consistent with the molecular weight competition hypothesis, which was based on surface-solution equilibrium, taking into account transport-limited rates of adsorption. Finally certain runs, where the adsorption process was interrupted by solvent flow and later allowed to proceed, never reached the full coverage seen for uninterrupted runs. Hence, the surface coverage and possibly the chain configurations can depend on the history of the adsorption process, a feature which points to surface relaxations and non-equilibrium structures.

The effects induced on the structure and dynamics of dilute microemulsion droplets by the confinement of polymer chains inside the droplets and by the adsorption of polymer on the surfactant shells from the outer continous phase were studied. The local structure changes were observed by small angle neutron scattering (SANS). The curvature fluctuations and the size distribution of the droplets increase for both chains inside and outside by different possible mechanisms, an induced size polydispersity minimizing osmotic stresses in the first case, a lowering of the film rigidity in the second one. Neutron spin echo techniques (NSE) were also used to probe the shape fluctuations of the same droplets with and without polymer. A sharp characteristic peak due to the contribution of the 1=2 mode is exhibited by the spectrum of relaxation times as a function of wavevector q. The height of this peak is decreased with the addition of polymer. i.e. the fluctuation of the 1=2 modes are dampened with the addition of polymer. The effect on the elastic coefficient K of the surfactant layer will be discussed below.

A population balance analysis of the statistical distribution of substrates over reversed micelles indicates the importance of accounting for concentration fluctuations within the micelles in interpreting observed enhancements in enzymatically-catalysed reactions in reversed micellar media. When the reactions are slow relative to the rates of solubilizate exchange via micellar coalescence and redispersion processes, analytical solutions to the detailed population balance equations are obtained, and the connection between Michaelis-Menten kinetics in reversed micellar media and bulk aqueous solution is made. It is shown that the finite occupancy number of the micelles at low water content leads to a statistical distribution of substrates over the micelle population, and that this can give rise to changes in the apparent reaction kinetics, even in the absence of changes in the intrinsic reaction parameters themselves. The model predictions are in good qualitative agreement with reported experimental results.

We performed dielectric spectroscopy measurements to study dynamics of collective modes of ferroelectric (FLC) and molecular motion of nematic (NLC) liquid crystals with polar molecules confined in silica macroporous and microporous glasses with average pore sizes of 1000 Å (volume fraction of pores 40%) and 100 Å (27%) respectively. For FLC the Goldstone and the soft modes are found in macropores. The rotational viscosity associated with the soft mode is about 10 times higher in pores than in the bulk. These modes are not detected in micropores although low frequency relaxation is present. The last one probably is not connected with the nature of liquid crystal but is associated with surface polarization effects typical for two component heterogeneous media. The difference between the dynamics of orientational motion of the polar molecules of NLC in confined geometries and in the bulk is qualitatively determined by the total energy Fs of the interaction between molecules and the surface of the pore wall, which is found Fs ≈ 102erg/cm2.

Characteristics of the A + B → C reaction-diffusion system with initially separated components are studied theoretically and experimentally. When the reaction is slow, the two species will mix before reacting. This leads to a series of crossovers from a rich initial behavior to an asymptotic time behavior. The crossovers depend on the system parameters, such as the diffusion coefficients and initial densities of the two species. In this paper we review our recent studies on this system. We elaborate on a theoretical study of momentum effects, and then focus on theoretical explanations of two experimental phenomena: 1) Non-universal and non-monotonic motion of the reaction front center. The latter occurs when one of the reactants has larger diffusion coefficient but smaller initial density. 2) Existence of more than one front. This occurs when two different transformations of the same reactant (on one of the sides of the system), react with the reactant on the other side with a different reaction constant - the majority slowly, but the minority much faster.