Thermally activated escape rate for the Brownian motion of a fixed axis rotator in an asymmetrical double-well potential for all values of the dissipation

The Kramers theory of the escape rate of a Brownian particle from a potential well as extended by Mel'nikov and Meshkov is used to evaluate the relaxation times and the dynamic susceptibility for the rotational Brownian motion of fixed axis rotators in an asymmetric double-well potential. An expression for the escape rate valid for all values of the dissipation including the very low damping (VLD), very high damping (VHD), and crossover regimes is derived. It is shown that this expression provides a good asymptotic estimate of the inverse of the smallest nonvanishing eigenvalue lambda(1) of the underlying Fokker-Planck operator calculated by using the matrix-continued fraction method. For low barriers, where the Mel'nikov and Meshkov approach is not applicable, analytic equations for the correlation time tau( parallel) of the longitudinal dipole correlation function in the VLD and VHD limits are derived and a simple extrapolating equation valid for all values of the damping is proposed.     

Thermally activated escape rate for a Brownian particle in a double-well potential for all values of the dissipation

The translational Brownian motion in a (2-4) double-well potential is considered. The escape rate, the position correlation function and correlation time, and the generalized susceptibility are evaluated from the solution of the underlying Langevin equation by using the matrix-continued fraction method. The escape rate and the correlation time are compared with the Kramers theory of the escape rate of a Brownian particle from a potential well as extended by Mel'nikov and Meshkov [J. Chem. Phys. 85, 1018 (1986)]. It is shown that in the low-temperature limit, the universal Mel'nikov and Meshkov expression for the escape rate provides a good estimate of both escape rate and inverse position correlation time for all values of the dissipation including the very low damping (VLD), very high damping (VHD), and turnover regimes. Moreover, for low barriers, where the Mel'nikov and Meshkov method is not applicable, analytic equations for the correlation time in the VLD and VHD limits are derived.     

Inertial and bias effects in the rotational brownian motion of rodlike molecules in a uniaxial potential

Inertial effects in the rotational brownian motion in space of a rigid dipolar rotator (needle) in a uniaxial potential biased by an external field giving rise to asymmetry are treated via the infinite hierarchy of differential-recurrence relations for the statistical moments (orientational correlation functions) obtained by averaging the Euler-Langevin equation over its realizations in phase space. The solutions of this infinite hierarchy for the dipole correlation function and its characteristic times are obtained using matrix continued fractions showing that the model simultaneously predicts both slow overbarrier (or interwell) relaxation at low frequencies accompanied by intermediate frequency Debye relaxation due to fast near-degenerate motion in the wells of the potential (intrawell relaxation) as well as the high frequency resonance (Poley) absorption due to librations of the dipole moments. It is further shown that the escape rate of a brownian particle from a potential well as extended to the Kramers turnover problem via the depopulation factor yields a close approximation to the longest (overbarrier) relaxation time of the system. For zero and small values of the bias field parameter h, both the dipole moment correlation time and the longest relaxation time have Arrhenius behavior (exponential increase with increasing barrier height). While at values of h in excess of a critical value however far less than that required to achieve nucleation, the Arrhenius behavior of the correlation time disappears.     

Thermally activated escape rate for the Brownian motion of a fixed axis rotator in a double well potential for all values of the dissipation

The extension of the Kramers theory of the escape rate of a Brownian particle from a potential well to the entire range of damping proposed by Mel'nikov and Meshkov [J. Chem, Phys. 85, 1018 (1986)] is applied to the rotational Brownian motion of fixed axis rotators in a double well cosine potential. The procedure yields an expression for the Kramers escape rate valid for all values of the dissipation including the very low damping (VLD), very high damping (VHD), and crossover regimes. This equation provides a good asymptotic estimate of the correlation time tau per pendicular of the longitudinal dipole moment correlation function calculated by solving the underlying Langevin equation using the matrix-continued fraction method. Moreover, for low barriers, where the Mel'nikov and Meshkov approach is not applicable, analytic equations for tau in the VLD and VHD limits are derived and a simple extrapolating equation that is valid for all values of the damping is proposed.     

High field 207Pb spin-lattice relaxation in solid lead nitrate and lead molybdate

Spin-lattice relaxation rates of lead have been measured at 17.6 T (156.9 MHz) as a function of temperature in polycrystalline lead nitrate and lead molybdate. Comparing the results with relaxation rates measured at lower fields, it is found that at high fields and low temperature, chemical shift anisotropy (CSA) makes small but observable contributions to lead relaxation in both materials. At 17.6 T and 200 K, CSA accounts for about 15% of the observed relaxation rate. Above 300 K, the dominant relaxation mechanism even at 17.6 T is an indirect Raman process involving modulation of the (207)Pb spin-rotation tensor, as first proposed by Grutzner et al. [J. Am. Chem. Soc. 123, 7094 (2001)] and later treated theoretically in more detail by Vega et al. [Phys. Rev. B 74, 214420 (2006)]. The improved signal to noise ratio at high fields makes it possible to quantify relaxation time anisotropy by analyzing saturation-recovery functions for individual frequencies on the powder pattern line shape. No orientation dependence is found for the spin-lattice relaxation rate of either material. It is argued from examination of the appropriate theoretical expressions, derived here for the first time, that the lack of observable relaxation time anisotropy is probably a general feature of this indirect Raman mechanism.     

Nonlinear viscoelastic behavior of styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer

Studies on the nonlinear viscoelastic behavior of styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer (SEEPS) were carried out. The nonlinear viscoelastic region was determined through dynamic strain sweep test, and the critical shear strain (γ_c) of transition from linear viscoelastic region to nonlinear viscoealstic region was obtained. The relaxation time and modulus corresponding to the characteristic relaxation modes were also acquired through simulating the linear relaxation modulus curves using Maxwell model, and the damping functions were evaluated. Meanwhile, it is found that the nonlinear relaxation modulus obtained at relatively low shear strains follows the strain–time separation principle, and the damping function of SEEPS can be fit to Laun double exponential model well. Moreover, the successive start‐up of shear behavior, the steady shear behavior, and the relaxation behavior after steady shear were investigated, respectively. The results showed that Wagner model, derived from the K‐BKZ (Kearsley‐Bernstein, Kearsley, Zapas) constitutive equation, could simulate the experiment data well, and in addition, experiment data under the lower shear rates are almost identical with the fitting data, but there exists some deviation for data under considerable high shear rates. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1309–1319, 2006     

Damped torsional oscillator model for polymer molecules

At present the widely used model for explaining viscoelastic and dielectric properties of polymer solutions is that of Rouse and Bueche. Here the polymer molecule is considered as an array of Gaussian subunits, each of which acts as an entropy spring. The motion of these segments is damped by the viscous drag of the surrounding solvent (RB model). An alternative model is presented, in which the segments are torsional oscillators consisting of two or three backbone links, and the damping is due to hindered internal rotation (DTO model). The mathematical treatment of these two models is essentially identical, but the physical interpretation of the constants used is very different. The DTO model has previously been applied by one of us to the interpretation of viscoelastic data. It is here applied to the interpretation of dielectric loss data. It is shown that dielectric measurements in dilute solution should very readily discriminate between the two approaches. Finally it is shown that the relaxation time computed from the DTO model is in closer agreement with published NMR data on poly(propylene oxide) 2025, than is the RB relaxation time. The postulates of the DTO model appear to be confirmed for this low molecular weight polymer. An even more sensitive distinction should be available by studies of the relaxation time as a function of polymer concentration.     

Interaction of NH(X 3Sigma-) with He: potential energy surface, bound states, and collisional Zeeman relaxation

A detailed analysis of the He-NH((3)Sigma(-)) van der Waals complex is presented. We discuss ab initio calculations of the potential energy surface and fitting procedures with relevance to cold collisions, and we present accurate calculations of bound energy levels of the triatomic complex as well as collisional properties of NH molecules in a buffer gas of (3)He. The influence of the external magnetic field used to trap the NH molecules and the effect of the atom-molecule interaction potential on the collisionally induced Zeeman relaxation are explored. It is shown that minute variations of the interaction potential due to different fitting procedures may alter the Zeeman relaxation rate at ultralow temperatures by as much as 50%.     

Brownian motion description of activation energies from NMR-relaxation times for rotating molecular-groups

A general formula is derived (containing eigenvalues and eigenfunctions of some diffusion equation) for activation energies from NMR-relaxation times for rotating molecular groups. Numerical calculations for a trigonometric three well potential in the strong damping (Smoluchowski) limit show that there may be a considerable difference between activation energy and barrier height. In the low damping limit there is fairly good agreement.     

Dynamic strength of molecularly bonded surfaces

This study reports a theoretical analysis of the forced separation of two adhesive surfaces linked via a large number of parallel noncovalent bonds. To describe the bond kinetics, we implement a three-state reaction model with kinetic rates obtained from a simple integral expression of the mean first passage time for diffusive barrier crossing in a pulled-distance-dependent potential. We then compute the rupture force for the separation of adhesive surfaces at a constant rate. The results correspond well with a Brownian dynamics simulation of the same system. The separation rate relative to the intrinsic relaxation time of the bonds defines three loading regimes and the general dependence of the adhesion on kinetic or thermodynamic parameters of the bonds. In the equilibrium regime, the rupture force asymptotically approaches the equilibrium rupture force, which increases linearly with the equilibrium bond energy. In the near-equilibrium regime, the rupture force increases with the separation rate and increasingly correlates with the bond rupture barrier. In the far-from-equilibrium regime where rebinding is irrelevant, the rupture force varies linearly with the rupture barrier.     

Linear viscoelastic properties of transient networks formed by associating polymers with multiple stickers

We have developed a single-chain theory that describes dynamics of associating polymer chains carrying multiple associative groups (or stickers) in the transient network formed by themselves and studied linear viscoelastic properties of this network. It is shown that if the average number N of stickers associated with the network junction per chain is large, the terminal relaxation time τ(A) that is proportional to τ(X)N(2) appears. The time τ(X) is the interval during which an associated sticker goes back to its equilibrium position by one or more dissociation steps. In this lower frequency regime ω<1/τ(X), the moduli are well described in terms of the Rouse model with the longest relaxation time τ(A). The large value of N is realized for chains carrying many stickers whose rate of association with the network junction is much larger than the dissociation rate. This associative Rouse behavior stems from the association/dissociation processes of stickers and is different from the ordinary Rouse behavior in the higher frequency regime, which is originated from the thermal segmental motion between stickers. If N is not large, the dynamic shear moduli are well described in terms of the Maxwell model characterized by a single relaxation time τ(X) in the moderate and lower frequency regimes. Thus, the transition occurs in the viscoelastic relaxation behavior from the Maxwell-type to the Rouse-type in ω<1/τ(X) as N increases. All these results are obtained under the affine deformation assumption for junction points. We also studied the effect of the junction fluctuations from the affine motion on the plateau modulus by introducing the virtual spring for bound stickers. It is shown that the plateau modulus is not affected by the junction fluctuations.     

Dynamics of interatomic Coulombic decay in quantum dots

In this work we demonstrate that the interatomic Coulombic decay (ICD), an ultrafast electron relaxation process known for atoms and molecules, is possible in general binding potentials. We used the multiconfiguration time-dependent Hartree method for fermions to study ICD in real time in a two-electron model system of two potential wells. Two decay channels were identified and analyzed by using the box stabilization analysis as well as by evaluating the autocorrelation function and measuring the outgoing electron flux during time-propagations. The total and partial ICD widths of an excited state localized in one potential well as a function of the distance between the two potentials was obtained. Finally, we discuss the results with a view to a possible application of ICD in quantum dot technology.     

Effects of counterion valency on the damping of phonons propagating along the axial direction of liquid-crystalline DNA

The phonon propagation and damping along the axial direction of films of aligned 40 wt % calf-thymus DNA rods are studied by inelastic x-ray scattering (IXS). The IXS spectra are analyzed with the generalized three effective eigenmode theory, from which we extract the dynamic structure factor S(Q,E) as a function of transferred energy E=variant Planck's over 2piomega, and the magnitude of the transferred wave vector Q. S(Q,E) of a DNA sample typically consists of three peaks, one central Rayleigh scattering peak, and two symmetric Stokes and anti-Stokes Brillouin side peaks. By analyzing the Brillouin peaks, the phonon excitation energy and damping can be extracted at different Q values from about 4 to 30 nm(-1). A high-frequency sound speed is obtained from the initial slope of the linear portion of the dispersion relation below Q=4 nm(-1). The high-frequency sound speed obtained in this Q range is 3100 ms, which is about twice faster than the ultrasound speed of 1800 ms, measured by Brillouin light scattering at Q approximately 0.01 nm(-1) at the similar hydration level. Our observations provide further evidence of the strong coupling between the internal dynamics of a DNA molecule and the dynamics of the solvent. The effect on damping and propagation of phonons along the axial direction of DNA rods due to divalent and trivalent counterions has been studied. It is found that the added multivalent counterions introduce stronger phonon damping. The phonons at the range between approximately 12.5 and approximately 22.5 nm(-1) are overdamped by the added counterions according to our model analyses. The intermediate scattering function is extracted and it shows a clear two-step relaxation with the fast relaxation time ranging from 0.1 to 4 ps.     

On the calculation of time correlation functions by potential scaling

We present and analyze a general method to calculate time correlation functions from molecular dynamics on scaled potentials for complex systems for which simulation is affected by broken ergodicity. Depending on the value of the scaling factor, correlations can be calculated for times that can be orders of magnitude longer than those accessible to direct simulations. We show that the exact value of the time correlation functions of the original system (i.e., with unscaled potential) can be obtained, in principle, using an action-reweighting scheme based on a stochastic path-integral formalism. Two tests (involving a bistable potential model and a dipeptide bond-vector orientational relaxation) are exemplified to showcase the strengths, as well as the limitations of the approach, and a procedure for the estimation of the time-dependent standard deviation error is outlined.     

Medium effect in the electroreduction of nitromesitylene

One-electron reduction of nitromesitylene to the corresponding radical anion has been studied at a hanging mercury drop electrode in various perchlorate salt solutions in five organic solvents: dimethylsulfoxide, dimethylacetamide, propylene carbonate, hexamethylphosphoramide and N-methylformamide. Standard redox potentials, diffusion coefficients, standard rate constants and transfer coefficients have been evaluated from cyclic voltammetry measurements. The results obtained are compared with the literature data for dimethylformamide and acetonitrile solutions.The standard rate constants were found to depend on the cation of the supporting electrolyte as well as on the solvent. It is shown that the rate constants corrected for both ion-pair formation and the double layer effect cannot be described by classical theories of heterogeneous electron transfer. It is shown that the dynamic dielectric properties of the solvent, described by the dielectric relaxation time, influence the rate of the heterogeneous charge transfer. The greater the dielectric relaxation time of the solvent, the smaller is the reaction rate.     

Survival paths for reaction dynamics in fluctuating environments

We study rate processes in general Gaussian fluctuating environments using a path integral formalism. We derive a variational equation for the dominant survival path when the fluctuations relax exponentially or according to a stretched exponential law. In the case of a slowly varying barrier, the equilibrium regression approximation which is used by Frauenfelder and coworkers emerges. In this approximation, the survival path follows the ordinary law of relaxation to equilibrium. If the rate coefficients vary rapidly with environmental variables, however, the dominant survival paths exhibit more complex behaviour. Many phenomena analogous to geometrical optics occur. These include reflection off of rapid variations in rate constant, as well as refraction, giving paths very different from the equilibrium relaxation properties. A model with a piece-wise linear rate exhibits the basic phenomena, and the survival path equation is exactly solved for the general stretched exponential relaxing environment.     

Diffusion-reaction approach to electronic relaxation in solution. Exact solution for delta function sink models

We give a general method for finding the exact solution for the problem of electronic relaxation in solution, modelled by a particle undergoing diffusive motion in a potential in presence of a delta function sink. The diffusive motion is described by the Smoluchowski equation and the sink could be a delta function of arbitrary position and strength. The solution requires the knowledge of the Laplace transform of the Green’s function for the motion in the absence of the sink. We use the method to find the solution of the problem in the case where the diffusive motion is on a parabolic potential. This has been an unsolved problem for some time and is of considerable importance as a model for non-radiative electronic relaxation of a molecule in solution. The solution is analyzed to obtain the viscosity and temperature dependences of the rate constants.     

Time-dependent quantum theory III. Model for vibrational relaxation in crystals

A one-dimensional model consisting of a “diatomic” spring attached on one side to a rigid wall and on the other side to a linear array of mass-springs is proposed as a model for the vibrational relaxation of small solute molecules in host lattices. A modification allowing a change in the equilibrium internuclear extension of the diatomic spring is also incorporated. The Hamiltonian divides naturally into pure diatomic, pure linear crystal, and the two mixed perturbation terms, one giving rise to stepwise vibrational cascade damping accompanied by phonon emission, and the other process, lattice relaxation, giving rise to phonon emission without any change of the quantum number of the diatomic spring. The cascade damping rate for a diatomic spring with a frequency less than the the maximum frequency of the linear crystal is calculated to second-order, and it is shown that the perturbation series converges in this range. An upper bound to the cascade damping rate for a diatomic spring with a frequency greater (i.e., 4.5 ×) than the cut-off frequency of the linear crystal is determined to be very small, λ ≦ 10⁴ sec ^?;1. The rate for the lattice relaxation process corresponds to a line-width λ = 6 cm ^?1 at ⁰K. An explanation for the thermal quenching of the low-temperature luminescence of SO₂ is based upon induced cascade-phonon emission.     

Dielectric relaxation spectroscopy of aqueous micellar electrolyte solutions: A novel application to infer Dukhin number and zeta potential of a micelle

The complex permittivities of aqueous SDS solutions, with and without the addition of sodium chloride (NaCl), are measured in the frequency range from 200 MHz to 14 GHz. The SDS concentrations are chosen such that the SDS molecules aggregate to micelles. In this frequency range, the measured spectra allow for the identification of two different relaxation processes. That is, the relaxation of the water molecules at frequencies above 1 GHz and the micellar relaxation at frequencies lower than 1 GHz. It is found that the addition of NaCl to the system mostly affects the micellar relaxation process. In detail, the time constant as well as the amplitude of the relaxation decrease by adding NaCl. These effects are attributed to the change in the solution conductivity that changes the properties of the micelle's electrical double layer. We also extract the Dukhin number of the micelles as a function of surfactant and electrolyte content from the measurements. The Dukhin number is a dimensionless group that describes the influence of the surface conductivity on a phenomena. A regression between Dukhin numbers and free sodium ions is found so that all data collapses on a single curve independent of the surfactant concentration. The surface conductivity is a manifestation of the electrical double layer and we use the Bikerman equation to infer the zeta potential of the micelles. Comparison to literature data shows very good agreement and proves that dielectric relaxation spectroscopy can be engaged to infer the zeta potential of micelles. Abbreviations: CMC critical micelle concentration, DRS dielectric relaxation spectroscopy, EDL electrical double layer     

Electrorheological Kelvin-Helmholtz instability of a fluid sheet

The present work deals with the gravitational stability of an electrified Maxwellian fluid sheet shearing under the influence of a vertical periodic electric field. The field produces surface charges on the interfaces of the fluid sheet. Due to the rather complicated nature of the problem a mathematical simplification is considered where the weak effects of viscoelastic fluids are taken into account. The solutions of the linearized equations of motion and boundary conditions lead to two simultaneous Mathieu equations with damping terms and having complex coefficients. Stability criteria are discussed through the assumption of symmetric and anti-symmetric deformations. The disappearance of surface charges from the interfaces obeys a certain relation derived in the marginal state. Furthermore, the case dealing with general deformation is discussed through marginal state analysis. The stability behavior in resonant and nonresonant cases are studied. In addition, the stability picture in the case of absence of the field frequency is studied. The numerical examination for stability showed that the relaxation time ratio plays a destabilizing influence in the case of anti-symmetric deformation or in the general deformation. The stabilizing effect for the relaxation time ratio is saved in the case of general deformation in the presence of the field frequency. In the later case the viscosity, the velocity, and the thickness parameter play a stabilizing influence. A dual role is readied for these parameters in the absence of the field frequency or in the anti-symmetric deformation. The field frequency still plays a destabilizing role in both cases.