Michal Borkovec

Molecular dynamics study of an isomerizing diatomic in a Lennard‐Jones fluid

The behavior of the reaction rate of an isomerizing diatomic molecule solvated in a Lennard‐Jones fluid is studied by molecular dynamics simulations. A comprehensive study of solvation effects on the rate constant, using the reactive flux absorbing boundary approximation of Straub and Berne, is presented. We provide simulation data over three orders of magnitude in solvent density for four systems differing in the mass of the solvent atoms and frequencies of the internal potential. Rate constants are also calculated for the model system using both Langevin Dynamics with exponential memory and impulsive collision dynamics of the BGK model. A simple method for calculating the average energy transfer and collision frequency is used to determine the collision efficiency for systems in which the mass of the solvent atoms is lighter than, equal to, or heavier than that of the atoms composing the isomerizing diatomic. We find that for solvents of equal and heavy mass compared to the solute the impulsive collisio...

Non‐Markovian activated rate processes: Comparison of current theories with numerical simulation data

We calculate the barrier crossing rate constants for a Brownian particle in a double well potential experiencing a non‐Markovian friction kernel using a full stochastic simulation. We compare the simulation results with recently proposed interpolation formulas which are based on the Grote–Hynes theory and the energy diffusion mechanism. We find that such formulas can fail by orders of magnitude in a physically interesting regime. Slow activation in an effective dynamic double well potential is probably responsible for the deviations observed.

Acid-base properties of poly(propylene imine)dendrimers

Abstract Potentiometric titration experiments of poly(propylene imine) dendrimers (up to the fifth generation) were carriedout at salt concentrations of 0.1, 0.5 and 1.0 M KCl and NaCl. The experiments were performed at two different locations on different instruments and were converted to titration curves using two different methods, resulting in a consistent experimental data set for the dendrimers measured. The titration curves feature two distinct steps around p H 6 and 10 with an intermediate plateau at 2/3 of the total ionizable groups. This protonation pattern reflects short-ranged repulsive interactions between ionizables sites and can be modeled using an Ising model with nearest-neighbour pair interactions. The intermediate plateau results from the stability of an onion-like structure where all odd shells of the dendrimer are protonated, while the even ones remain deprotonated. The Ising model permits a quantitative analysis of the titration curves. For larger dendrimers, this Ising approach is shown to be superior to the classical analysis in terms of successive protonation equilibria.

Reaction dynamics in the low pressure regime: The Kramers model and collisional models of molecules with many degrees of freedom

The escape rate constant out of a metastable well for an impulsive collisional (BGK) model and the Fokker–Planck frictional (Kramers) model is evaluated analytically for arbitrary potentials and any number of degrees of freedom in the low collision or low friction limit. Completely statistical behavior of the collisionless dynamical system is assumed. The rate constants increase dramatically with the number of degrees of freedom. The result of the weak collision Kramers model allows us to evaluate the collision efficiency βc without adjustable parameters. It is argued that some reactions could be described by a non‐Markovian Kramers model with an appropriate number of degrees of freedom.

Release and transport of colloidal particles in natural porous media: 2. Experimental results and effects of ligands

We present an extensive experimental data set of particle release from natural porous media saturated with monovalent cations. The generation process of mobile colloidal particles is studied by means of leaching of saturated laboratory columns packed with a noncalcareous soil material with various monovalent electrolytes and by analyzing the colloids in the effluent over typically 1000 pore volumes. The concentration of released particles cannot be modeled with simple first-order kinetics but can be rationalized in terms of a distribution of release rate coefficients k. The experimentally observed effluent concentration often decays with time as a power law c ∝ t−(α+l) for long times, suggesting a distribution of release rate coefficients p(k) ∝ kα−1 for small k. The observed values of exponent α range between 0.01 and 0.8. The composition of the pore water is found to have a profound influence on the particle release characteristics. With decreasing salt concentration the rate for particle release increases. Anionic organic and inorganic ligands have a major effect on the release process. For the ligands studied, the amount of released particles decreases in the sequence malonate, chloride, phtalate, and azide.

From micelles to microemulsion droplets: size distributions, shape fluctuations, and interfacial tensions

We present a theoretical description of the aggregation equilibrium of nonswollen and water‐swollen micelles in oil (or vice versa). While we specialize on spherical, noninteracting aggregates, we treat the competition between phase separation, dissolution in monomers and formation of micelles with variable extent of swelling. The present model is based on an interfacial free energy of the surfactant monolayer which includes stretching and bending contributions. This free energy allows one to desribe both, the macroscopic interface in a two‐phase system and the internal interface surrounding the aggregates on equal footing. The extent of swelling of the micelles at the CMC is determined by the bending energy of the saturated surfactant monolayer. Increasing the splay modulus or decreasing the spontaneous curvature favors swollen micelles (microemulsion droplets) and ultralow interfacial tensions. We present explicit results for the size distributions of the aggregates and interfacial tensions. Considering...

Measurement of Sorption Isotherms with Flow-Through Reactors

A simple flow-through reactor technique is described for measurements of sorption isotherms on solid environmental materials such as soils, crushed rocks, aquifer materials, or peat. The applicability of the method was established by determining copper sorption isotherms at effectively constant pH for two different soil samples. The experimental results compare favorably with independent batch and column studies. Potential advantages of the flow-through technique are exemplified by studying the sorption behavior of one soil sample that shows in batch experiments a pronounced dependence on the solid concentration (particle concentration effect). Comparison of these results with the flow-through reactor technique and independent column experiments confirms unequivocally that in this case the influence of the solid concentration is an artifact due to insufficient pre-washing of the soil with the background electrolyte solution and has nothing to do with the shaking process in batch experiments. The present results indicate that incomplete removal of preadsorbed ions may often represent a major source of error in sorption studies and may be difficult to recognize in batch experiments.

Shortcomings of current theories of non‐Markovian activated rate processes

We calculate the barrier crossing rate constants for a Brownian particle in a double well potential experiencing a non‐Markovian friction kernel using full stochastic simulation. We compare the simulation results with recently proposed interpolation formulas which are based on the Grote–Hynes relation and energy diffusion mechanism. We find that such formulas fail in the intermediate regime by orders of magnitude. Therefore we question interpretations of dependence of isomerization rate data on the viscosity based on such ideas.

Structure of adsorbed polyelectrolyte monolayers investigated by combining optical reflectometry and piezoelectric techniques.

Polyelectrolyte monolayers on solid substrates are studied with optical reflectivity and the quartz crystal microbalance (QCM). In particular, we investigate the adsorption of anionic poly(styrene sulfonate) (PSS) on amino-functionalized silica as well as cationic poly(allylamine hydrochloride) (PAH) and poly-L-lysine (PLL) on bare silica. By comparing the dry and wet masses measured on identical substrates with these two techniques, we obtain information on the layer thickness and water content of these layers. Monolayers typically feature an adsorbed dry mass of about 0.1-2 mg/m(2), a layer thickness of 0.5-2 nm, and a water content of 20-50%. One finds that the layer thickness increases with increasing concentrations of monovalent salts and polyelectrolytes.

Measurements of dispersion forces between colloidal latex particles with the atomic force microscope and comparison with Lifshitz theory

Interaction forces between carboxylate colloidal latex particles of about 2 μm in diameter immersed in aqueous solutions of monovalent salts were measured with the colloidal probe technique, which is based on the atomic force microscope. We have systematically varied the ionic strength, the type of salt, and also the surface charge densities of the particles through changes in the solution pH. Based on these measurements, we have accurately measured the dispersion forces acting between the particles and estimated the apparent Hamaker constant to be (2.0 ± 0.5) × 10(-21) J at a separation distance of about 10 nm. This value is basically independent of the salt concentration and the type of salt. Good agreement with Lifshitz theory is found when roughness effects are taken into account. The combination of retardation and roughness effects reduces the value of the apparent Hamaker constant and its ionic strength dependence with respect to the case of ideally smooth surfaces.