Relaxation dynamics in glycerol-water mixtures: I. Glycerol-rich mixtures

We discuss the relaxation dynamics of glycerol-water mixtures, as studied by dielectric spectroscopy in the frequency range from 1 Hz to 250 MHz and at temperatures between 173 and 323 K. The experimental results obtained for the glycerol-rich mixtures suggest that the main dielectric relaxation process, as well as the so-called high-frequency "excess wing" (EW) and dc conductivity, follow the same temperature dependence. This result indicates that all of these processes are induced by the same molecular origin. A new phenomenological function is proposed to describe the whole dielectric spectrum in the covered frequency range, and some possible mechanisms of dielectric behaviors through the dc conductivity, the main relaxation process, and the EW are discussed.     

Dynamic mechanism of photochemical induction of turing superlattices in the chlorine dioxide-iodine-malonic acid reaction-diffusion system

We study the mechanism of development of superlattice Turing structures from photochemically generated hexagonal patterns of spots with wavelengths several times larger than the characteristic wavelength of the Turing patterns that spontaneously develop in the nonilluminated system. Comparison of the experiment with numerical simulations shows that interaction of the photochemical periodic forcing with the Turing instability results in generation of multiple resonant triplets of wave vectors, which are harmonics of the external forcing. Some of these harmonics are situated within the Turing instability band and are therefore able to maintain their amplitude as the system evolves and after illumination ceases, while photochemically generated harmonics outside the Turing band tend to decay.     

Superlattice Turing structures in a photosensitive reaction-diffusion system

Families of complex superlattice structures, consisting of combinations of basic hexagonal or square patterns, are found in a photosensitive reaction-diffusion system. The structures are induced by simple illumination patterns whose wavelengths are appropriately related to that of the system's intrinsic Turing pattern. Computer simulations agree with the structures and their stability. The technique offers a general approach to generating superlattices for use in information storage and other applications.     

Improved lower bounds on the total variation distance for the Poisson approximation

New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen–Stein method. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is addressed.     

Anomalies in supercooled NaCl aqueous solutions: a microscopic perspective

In this work we studied the effect of NaCl on the thermodynamic and dynamic properties of supercooled water, for salt concentrations between 0.19 and 1.33 mol?kg(-1), using molecular dynamic simulations for TIP5P∕E water model and ion parameters specially designed to be used in combination with this potential. We studied the isobaric heat capacity (C(p)) temperature dependence and observed a maximum in C(p), occurring at T(m), that moves to lower temperature values with increasing salt concentration. Many characteristic changes were observed at scaled temperature T∕T(m) ～ 0.96, namely a minimum in the density of the system, a reduction of the slope of the number of hydrogen bonds vs. temperature, and a crossover from Vogel-Tamman-Fulcher to Arrhenius dynamics. Finally, at low temperatures we observed that water dynamics become heterogeneous with an apparently common relationship between the fraction of immobile molecules and T/T(m) for all studied systems.     

Some Useful Integral Representations for Information-Theoretic Analyses

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for quantities that involve expectations of the logarithm of a positive random variable. Here, in the same spirit, we derive an exact integral representation (in one or two dimensions) of the moment of a nonnegative random variable, or the sum of such independent random variables, where the moment order is a general positive non-integer real (also known as fractional moments). The proposed formula is applied to a variety of examples with an information-theoretic motivation, and it is shown how it facilitates their numerical evaluations. In particular, when applied to the calculation of a moment of the sum of a large number, n, of nonnegative random variables, it is clear that integration over one or two dimensions, as suggested by our proposed integral representation, is significantly easier than the alternative of integrating over n dimensions, as needed in the direct calculation of the desired moment.     

Redox and acid-base coupling in ultrathin polyelectrolyte films

A single layer of poly(allylamine) with a covalently attached osmium pyridine-bipyridine complex adsorbed onto a Au surface modified by mercaptopropanesulfonate has been studied theoretically with a molecular approach and experimentally by cyclic voltammetry. These investigations have been carried out at different pHs and ionic strengths of the electrolyte solution in contact with the redox polyelectrolyte modified electrode. The theory predicts strong coupling between the acid-base and redox equilibria, particularly for low ionic strength, pH close to the pKa, and high concentration of redox sites. The coupling leads to a decrease in the peak potential at pH values above the apparent pKa of the weak polyelectrolyte, in good agreement with the experimental pH dependence at 4 mM NaNO3. Theoretical calculations suggest that the inflection point in the peak position versus pH curves can be used to estimate the apparent pKa of the amino groups in the polymer. Comparison of the apparent pKa for PAH-Os in the film with that of poly(allylamine) reported in the literature shows that the underlying charged thiol strongly influences charge regulation in the film. A systematic study of the film thickness and the degree of protonation in sulfonate and amino groups for solutions of different pH and ionic strength shows the coupling between the different interactions. It is found that the variation of the film properties has a non-monotonic dependence on bulk pH and salt concentration. For example, the film thickness shows a maximum with electrolyte ionic strength, whose origin is attributed to the balance between electrostatic amino-amino repulsions and amino-sulfonate attractions.     

Monte Carlo simulation and molecular theory of tethered polyelectrolytes

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.