Dynamics of Fractional Brownian Walks

We investigate the dynamics of polymers whose solution configurations are represented by fractional Brownian walks. The calculation of the two dynamical quantities considered here, the longest relaxation time tau(r) and the intrinsic viscosity [eta], is formulated in terms of Langevin equations and is carried out within the continuum approach developed in an earlier paper. Our results for tau(r) and [eta] reproduce known scaling relations and provide reasonable numerical estimates of scaling amplitudes. The possible relevance of the work to the study of globular proteins and other compact polymeric phases is discussed.

Molecular-dynamics studies of systems of confined dumbbell molecules

We present the results of molecular-dynamics simulations of systems of dumbbell molecules confined by parallel molecular walls. We have carried out systematic studies of three cases: freezing, steady flows, and stick-slip friction. We find that the molecular orientational degrees of freedom cause the surface layers to deviate from a planar configuration. Nevertheless, steady flows, in a channel as narrow as 15 molecular sizes, display continuum behavior. A range of mechanisms in the dynamics of the freezing of a confined fluid is found, as a function of the wall-fluid interactions and the bond length of the dumbbell molecules. The simple order-disorder transition associated with stick-slip motion in the presence of a layer of monoatomic lubricant molecules is supplanted by more complex behavior due to rotational degrees of freedom of the diatomic molecules.

Ultrafast solvation dynamics in water: Isotope effects and comparison with experimental results

A detailed theoretical study of solvation dynamics in water is presented. The motivation of the present study comes from the recent experimental observation that the dynamics of solvation of an ion in water is ultrafast and the solvation time correlation function decays with a time constant of about 55 fs. The slower decay in the long time can be described by a sum of two exponentials with time constants equal to 126 and 880 fs. The molecular theory (developed earlier) predicts a time constant equal to 52 fs for the initial Gaussian decay and time constants equal to 134 and 886 fs for the two exponential components at the long time. This nearly perfect agreement is obtained by using the most detailed dynamical information available in the literature. The present study emphasizes the importance of the intermolecular vibrational band originating from the O...O stretching mode of the O�H...O units in the initial dynamics and raises several interesting questions regarding the nature of the decay of this mode. We have also studied the effects of isotope substitution on solvation dynamics. It is predicted that a significant isotope effect may be observed in the long time. The experimental results have also been compared with the prediction of the dynamic mean spherical approximation (DMSA); the agreement is not satisfactory at the long time. It is further found that the molecular theory and the DMSA lead to virtually identical results if the translational modes of the solvent molecules are neglected in the former. DMSA has also been used to investigate the dynamics of solvation of a dipolar solute in water. It is found that the dynamics of dipolar solvation exhibit features rather different from those of ion solvation. © 1995 American Institute of Physics.

Ultrafast Solvation Dynamics Of An Ion In A Restricted Environment

The solvation dynamics of an excited coumarin dye molecule (C-480) enclosed within a restricted space have been studied using molecular hydrodynamic theory (MHT) and compared with the recent experimental findings. The solvation dynamics of the dye molecule within the cavity of a toroidal gamma-cyclodextrin molecule have been shown to be explained only in terms of the freezing of the solvent translational modes using MHT. The results of the theoretical calculation are in good agreement with the experimental results. The inertial components of the solvation time correlation function remain the same in both the restricted environment and in the free space. These results are interesting in the light of the simulation studies of Maroncelli and Fleming [J chem Phys, 89 (1988) 5044] which concludes that the participation of the different solvation shells in controlling the dynamics are much different. The earlier studies have been reviewed and the recent findings are discussed.

Monte Carlo and molecular dynamics simulation of argon clusters andn-alkanes in the confined regions of zeolites

Geometry and energy of argon clusters confined in zeolite NaCaA are compared with those of free clusters. Results indicate the possible existence of magic numbers among the confined clusters. Spectra obtained from instantaneous normal mode analysis of free and confined clusters give a larger percentage of imaginary frequencies for the latter indicating that the confined cluster atoms populate the saddle points of the potential energy surface significantly. The variation of the percentage of imaginary frequencies with temperature during melting is akin to the variation of other properties. It is shown that confined clusters might exhibit inverse surface melting, unlike medium-to-large-sized free clusters that exhibit surface melting. Configurational-bias Monte Carte (CBMC) simulations of n-alkanes in zeolites Y and A are reported. CBMC method gives reliable estimates of the properties relating to the conformation of molecules. Changes in the conformational properties of n-butane and other longer n-alkanes such as n-hexane and n-heptane when they are confined in different zeolites are presented. The changes in the conformational properties of n-butane and n-hexane with temperature and concentration is discussed. In general, in zeolite Y as well as A, there is significant enhancement of the gauche population as compared to the pure unconfined fluid.

A molecular dynamics study and molecular level explanation of pressure dependence of ionic conductivity of potassium chloride in water

Experimental ionic conductivity of different alkali ions in water shows markedly different dependences on pressure. Existing theories such as that of Hubbard-Onsager are unable to explain these dependences on pressure of the ionic conductivity for all ions. We report molecular dynamics investigation of potassium chloride solution at low dilution in water at several pressures between 1 bar and 2 kbar. Two different potential models have been employed. One of the models successfully reproduces the experimentally observed trend in ionic conductivity of K+ ions in water over the 0.001-2 kbar range. We also propose a theoretical explanation, albeit at a qualitative level, to account for the dependence of ionic conductivity on pressure in terms of the previously studied Levitation Effect. It also provides a microscopic picture in terms of the pore network in liquid water.

Solvation dynamics in monohydroxy alcohols: Agreement between theory and different experiments

Recently three different experimental studies on ultrafast solvation dynamics in monohydroxy straight-chain alcohols (C-1-C-4) have been carried out, with an aim to quantify the time constant (and the amplitude) of the ultrafast component. The results reported are, however, rather different from different experiments. In order to understand the reason for these differences, we have carried out a detailed theoretical study to investigate the time dependent progress of solvation of both an ionic and a dipolar solute probe in these alcohols. For methanol, the agreement between the theoretical predictions and the experimental results [Bingemann and Ernsting J. Chem. Phys. 1995, 102, 2691 and Horng et al. J: Phys, Chern, 1995, 99, 17311] is excellent. For ethanol, propanol, and butanol, we find no ultrafast component of the time constant of 70 fs or so. For these three liquids, the theoretical results are in almost complete agreement with the experimental results of Horng et al. For ethanol and propanol, the theoretical prediction for ionic solvation is not significantly different from that of dipolar solvation. Thus, the theory suggests that the experiments of Bingemann and Ernsting and those of Horng et al. studied essentially the polar solvation dynamics. The theoretical studies also suggest that the experimental investigations of Joo et al. which report a much faster and larger ultrafast component in the same series of solvents (J. Chem. Phys. 1996, 104, 6089) might have been more sensitive to the nonpolar part of solvation dynamics than the polar part. In addition, a discussion on the validity of the present theoretical approach is presented. In this theory the ultrafast component arises from almost frictionless inertial motion of the individual solvent molecules in the force field of its neighbors.

Solvation dynamics of a charge bubble in water

A microscopic theory is used to calculate the solvation-time correlation function, (S(t)), of a light, non-stationary charge bubble in water. The calculated correlation function is found to be similar to the energy-time correlation function of a solvated electron. The ionic mobility of a charge bubble of the size of the hydrated electron is also calculated. It is found that the mobility of the charge plays a very important role in its own solvation.

Strong shock approximation in the new theory of shock dynamics

This paper investigates the propagation of a strong shock into an inhomogeneous medium using the new theory of shock dynamics. The equations are simple to solve and involve no trial-and-error method commonly used in this case. The results compare favourably with earlier results obtained in the case of self-similar flows, which arise as a special case of this theory.

Structure and silver ion transport in AgI-Ag2MoO4 glasses: A molecular dynamics study

The structure and dynamics of silver ion conducting AgI-Ag2MoO4 glasses have been simulated by molecular dynamics simulation over a wide range of compositions. Formation of silver iodide like aggregates have been identified only in the AgI rich glasses. Increase in silver ion conductivity with an increase in AgI content in the glass is seen as in experiments. The dynamics of ion transport suggests that Ag+ ion transport occurs largely through paths connected by silver ion sites of mixed iodide-oxide coordination. The Van Hove correlation functions indicate that Ag+ ions prefer migration along the pathways formed with connected sites of similar coordination.

Isomerization dynamics in viscous liquids: Microscopic investigation of the coupling and decoupling of the rate to and from solvent viscosity and dependence on the intermolecular potential

A detailed investigation of viscosity dependence of the isomerization rate is carried out for continuous potentials by using a fully microscopic, self-consistent mode-coupling theory calculation of both the friction on the reactant and the viscosity of the medium. In this calculation we avoid approximating the short time response by the Enskog limit, which overestimates the friction at high frequencies. The isomerization rate is obtained by using the Grote-Hynes formula. The viscosity dependence of the rate has been investigated for a large number of thermodynamic state points. Since the activated barrier crossing dynamics probes the high-frequency frictional response of the liquid, the barrier crossing rate is found to be sensitive to the nature of the reactant-solvent interaction potential. When the solute-solvent interaction is modeled by a 6-12 Lennard-Jones potential, we find that over a large variation of viscosity (eta), the rate (k) can indeed be fitted very well to a fractional viscosity dependence: (k similar to eta(-alpha)), with the exponent alpha in the range 1 greater than or equal to alpha >0. The calculated values of the exponent appear to be in very good agreement with many experimental results. In particular, the theory, for the first time, explains the experimentally observed high value of alpha even at the barrier frequency, omega(b). similar or equal to 9 X 10(12) s(-1) for the isomerization reaction of 2-(2'-propenyl)anthracene in liquid eta-alkanes. The present study can also explain the reason for the very low value of vb observed in another study for the isomerization reaction of trans-stilbene in liquid n-alkanes. For omega(b) greater than or equal to 2.0 X 10(13) s(-1), we obtain alpha similar or equal to 0, which implies that the barrier crossing rate becomes identical to the transition-state theory predictions. A careful analysis of isomerization reaction dynamics involving large amplitude motion suggests that the barrier crossing dynamics itself may become irrelevant in highly viscous liquids and the rate might again be coupled directly to the viscosity. This crossover is predicted to be strongly temperature dependent and could be studied by changing the solvent viscosity by the application of pressure. (C) 1999 American Institute of Physics. [S0021-9606(9950514-X].

Structural characterization and chain dynamics of poly(alpha-methylstyrene peroxide) by NMR spectroscopy

Poly(alpha-methylstyrene peroxide) has been synthesized and characterized spectroscopically. The H-1 and C-13 NMR spectra are shown to reveal the stereochemical features and the endgroups in the peroxide chain. The preliminary studies on the chain dynamics of the polyperoxide chain has been done by measuring the spin-lattice relaxation times (T-1) of the main chain as well as the side chain carbons. It has been shown from the dependence of the spin-lattice relaxation times that the polyperoxide chain is more flexible compared to the corresponding hydrocarbon-backbone analog.

Nonlinear dynamics and chaotic motions in feedback-controlled two- and three-degree-of-freedom robots

The dynamics of a feedback-controlled rigid robot is most commonly described by a set of nonlinear ordinary differential equations. In this paper we analyze these equations, representing the feedback-controlled motion of two- and three-degrees-of-freedom rigid robots with revolute (R) and prismatic (P) joints in the absence of compliance, friction, and potential energy, for the possibility of chaotic motions. We first study the unforced or inertial motions of the robots, and show that when the Gaussian or Riemannian curvature of the configuration space of a robot is negative, the robot equations can exhibit chaos. If the curvature is zero or positive, then the robot equations cannot exhibit chaos. We show that among the two-degrees-of-freedom robots, the PP and the PR robot have zero Gaussian curvature while the RP and RR robots have negative Gaussian curvatures. For the three-degrees-of-freedom robots, we analyze the two well-known RRP and RRR configurations of the Stanford arm and the PUMA manipulator respectively, and derive the conditions for negative curvature and possible chaotic motions. The criteria of negative curvature cannot be used for the forced or feedback-controlled motions. For the forced motion, we resort to the well-known numerical techniques and compute chaos maps, Poincare maps, and bifurcation diagrams. Numerical results are presented for the two-degrees-of-freedom RP and RR robots, and we show that these robot equations can exhibit chaos for low controller gains and for large underestimated models. From the bifurcation diagrams, the route to chaos appears to be through period doubling.

Polar and nonpolar solvation dynamics, ion diffusion, and vibrational relaxation: Role of biphasic solvent response in chemical dynamics

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Solvation dynamics in nonassociated polar solvents

Ultrafast solvation dynamics in three nonassociated polar solvents, namely, acetonitrile, dimethyl sulfoxide, and acetone, have been studied by using the molecular hydrodynamic theory. For solvation in acetonitrile, the solvent memory function required for this study has been obtained from recent dielectric relaxation measurements of Venabales and Schuttenmaer; earlier theoretical studies used only the Kerr relaxation data. As the latter provides only an indirect information regarding the polar dynamical response of the dipolar liquid, it fails to provide a fully quantitative description of the solvation time correlation function, S(t). The present study with full dielectric data, on the other hand, gives excellent agreement with the experimental results. The theory shows that the ultrafast part of the solvation dynamics originates almost entirely from the high-frequency component of dielectric relaxation (with time constant 0.177 ps), although the latter represents only a small part of the latter. For DMSO and acetone, however, the present theory predicts a decay slower than the experimental observation. It is proposed that for these two solvents specific chromophore-solvent interactions might be responsible for the-large discrepancy. On the basis of the theory, two experimental studies have also been proposed.