On the generalized continuum model of dipolar solvation dynamics

The continuum model of dipolar solvation dynamics is reviewed. The effects of non-spherical molecular shapes, of non-Debye dielectric relaxation of the polar solvent and of dielectric inhomogeneity of the solvent around the solute dipole are investigated. Several new theoretical results are presented. It is found that our generalized continuum model, which takes into account the dielectric inhomogeneity of the surrounding solvent, provides a description of solvation dynamics consistent with recent experimental results.

Internal noise-driven generalized Langevin equation from a nonlocal continuum model

Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree of freedom, is derived. The GLE features a memory-dependent multiplicative or internal noise, which appears upon recognizing that the microrotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the present GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum, a phenomenon that is ubiquitous across a broad class of response regimes in solids and fluids. This renders the proposed GLE a potentially useful model in such cases.

Molecular expression for dielectric friction on a rotating dipole: Reduction to the continuum theory

Recently we presented a microscopic expression for dielectric friction on a rotating dipole. This expression has a rather curious structure, involving the contributions of the transverse polarization modes of the solvent and also of the molecular length scale processes. It is shown here that under proper limiting conditions, this expression reduces exactly to the classical continuum model expression of Nee and Zwanzig [J. Chem. Phys. 52, 6353 (1970)]. The derivation requires the use of the asymptotic form of the orientation‐dependent total pair correlation function, the neglect of the contributions of translational modes of the solvent, and also the use of the limit that the size of the solvent molecules goes to zero. Thus, the derivation can be important in understanding the validity of the continuum model and can also help in explaining the results of a recent computer simulation study of dielectric relaxation in a Brownian dipolar lattice.

A model for heat transfer in a honey bee swarm

A swarm is a temporary structure formed when several thousand honey bees leave their hive and settle on some object such as the branch of a tree. They remain in this position until a suitable site for a new home is located by the scout bees. A continuum model based on heat conduction and heat generation is used to predict temperature profiles in swarms. Since internal convection is neglected, the model is applicable only at low values of the ambient temperature T-a. Guided by the experimental observations of Heinrich (1981a-c, J. Exp. Biol. 91, 25-55; Science 212, 565-566; Sci. Am. 244, 147-160), the analysis is carried out mainly for non-spherical swarms. The effective thermal conductivity is estimated using the data of Heinrich (1981a, J. Exp. Biol. 91, 25-55) for dead bees. For T-a = 5 and 9 degrees C, results based on a modified version of the heat generation function due to Southwick (1991, The Behaviour and Physiology of Bees, PP 28-47. C.A.B. International, London) are in reasonable agreement with measurements. Results obtained with the heat generation function of Myerscough (1993, J. Theor. Biol. 162, 381-393) are qualitatively similar to those obtained with Southwick's function, but the error is more in the former case. The results suggest that the bees near the periphery generate more heat than those near the core, in accord with the conjecture of Heinrich (1981c, Sci. Am. 244, 147-160). On the other hand, for T-a = 5 degrees C, the heat generation function of Omholt and Lonvik (1986, J. Theor. Biol. 120, 447-456) leads to a trivial steady state where the entire swarm is at the ambient temperature. Therefore an acceptable heat generation function must result in a steady state which is both non-trivial and stable with respect to small perturbations. Omholt and Lonvik's function satisfies the first requirement, but not the second. For T-a = 15 degrees C, there is a considerable difference between predicted and measured values, probably due to the neglect of internal convection in the model.

Elasto-plastic analysis of jointed rocks using discrete continuum and equivalent continuum approaches

Results from elasto-plastic numerical simulations of jointed rocks using both the equivalent continuum and discrete continuum approaches are presented, and are compared with experimental measurements. Initially triaxial compression tests on different types of rocks with wide variation in the uniaxial compressive strength are simulated using both the approaches and the results are compared. The applicability and relative merits and limitations of both the approaches for the simulation of jointed rocks are discussed. It is observed that both the approaches are reasonably good in predicting the real response. However, the equivalent continuum approach has predicted somewhat higher stiffness values at low strains. Considering the modelling effort involved in case of discrete continuum approach, for problems with complex geometry, it is suggested that a proper equivalent continuum model can be used, without compromising much on the accuracy of the results. Then the numerical analysis of a tunnel in Japan is taken up using the continuum approach. The deformations predicted are compared well against the field measurements and the predictions from discontinuum analysis. (C) 2012 Elsevier Ltd. All rights reserved.

A micropolar cohesive damage model for delamination of composites

A micropolar cohesive damage model for delamination of composites is proposed. The main idea is to embed micropolarity, which brings an additional layer of kinematics through the micro-rotation degrees of freedom within a continuum model to account for the micro-structural effects during delamination. The resulting cohesive model, describing the modified traction separation law, includes micro-rotational jumps in addition to displacement jumps across the interface. The incorporation of micro-rotation requires the model to be supplemented with physically relevant material length scale parameters, whose effects during delamination of modes I and II are brought forth using numerical simulations appropriately supported by experimental evidences. (C) 2015 Elsevier Ltd. All rights reserved.

Ultrafast Solvation Dynamics of an Ion in the gamma-Cyclodextrin Cavity: The Role of Restricted Environment

A detailed study of the solvation dynamics of a charged coumarin dye molecule in gamma-cyclodextrin/water has been carried out by using two different theoretical approaches. The first approach is based on a multishell continuum model (MSCM). This model predicts the time scales of the dynamics rather well, provided an accurate description of the frequency-dependent dielectric function is supplied. The reason for this rather surprising agreement is 2-fold. First, there is a cancellation of errors, second, the two-zone model mimics the heterogeneous microenvironment surrounding the ion rather well. The second approach is based on the molecular hydrodynamics theory (MI-IT). In this molecular approach, the solvation dynamics has been studied by restricting the translational motion of the solvent molecules enclosed within the cavity. The results from the molecular theory are also in good agreement with the experimental results. Our study indicates that, in the present case, the restricted environment affects only the long time decay of the solvation time correlation function. The short time dynamics is still governed by the librational (and/or vibrational) modes present in bulk water.

Ruthenium(II)-CO complexes of N-[(2-pyridyl)methyliden]-alpha(or beta)-aminonaphthalene: Synthesis, spectral studies, crystal structure, redox properties and DFT calculation

The characterization and properties of trans-(X)-[RuX2(CO)(2)(alpha/beta-NaiPy)] (1, 2) (alpha-NaiPy (a), beta-NaiPy (b); X = Cl (1), I (2)) are described in this work. The structures are confirmed by single crystal X-ray diffraction studies. Reaction of these compounds with Me3NO in MeCN has isolated monocarbonyl trans-(X)-RuX2(CO)(MeCN)(alpha/beta-NaiPy)] (3, 4). The complexes show intense emission properties. Quantum yields of 1 and 2 (phi= 0.02-0.08) are higher than 3 and 4 (phi = 0.006-0.015). Voltammogram shows higher Ru(III)/Ru(II) (1.3-1.5 V) potential of 1 and 2 than that of 3 and 4 (0.8-0.9 V) that may be due to coordination of two pi-acidic CO groups in former. The electronic spectra and redox properties of the complexes are compared with the results obtained by density functional theory (DFT) and time-dependent density functional theory (TD-DFT) using polarizable continuum model (CPCM).

Time Domain Characteristics of Electrical Measures for a Piezoelectric Thin Film to Identify Defects in the Substrate

A reduced 3D continuum model of dynamic piezoelectricity in a thin-film surface-bonded to the substrate/host is presented in this article. While employing large area flexible thin piezoelectric films for novel applications in device/diagnostics, the feasibility of the proposed model in sensing the surface and/or sub-surface defects is demonstrated through simulations - which involve metallic beams with cracks and composite beam with delaminations of various sizes. We have introduced a set of electrical measures to capture the severity of the damage in the existing structures. Characteristics of these electrical measures in terms of the potential difference and its spatial gradients are illustrated in the time domain. Sensitivity studies of the proposed measures in terms of the defected areas and their region of occurence relative to the sensing film are reported. The simulations' results for electrical measures for damaged hosts/substrates are compared with those due to undamaged hosts/substrates, which show monotonicity with high degree of sensitivity to variations in the damage parameters.

Ultrasonic wave characteristics of nanorods via nonlocal strain gradient models

This paper studies an ultrasonic wave dispersion characteristics of a nanorod. Nonlocal strain gradient models (both second and fourth order) are introduced to analyze the ultrasonic wave behavior in nanorod. Explicit expressions are derived for wave numbers and the wave speeds of the nanorod. The analysis shows that the fourth order strain gradient model gives approximate results over the second order strain gradient model for dynamic analysis. The second order strain gradient model gives a critical wave number at certain wave frequency, where the wave speeds are zero. A relation among the number of waves along the nanorod, the nonlocal scaling parameter (e(0)a), and the length of the nanorod is obtained from the nonlocal second order strain gradient model. The ultrasonic wave characteristics of the nanorod obtained from the nonlocal strain gradient models are compared with the classical continuum model. The dynamic response behavior of nanorods is explained from both the strain gradient models. The effect of e(0)a on the ultrasonic wave behavior of the nanorods is also observed. (C) 2010 American Institute of Physics.

Molecular theory of solvation and solvation dynamics of a classical ion in a dipolar liquid

A microscopic theory of equilibrium solvation and solvation dynamics of a classical, polar, solute molecule in dipolar solvent is presented. Density functional theory is used to explicitly calculate the polarization structure around a solvated ion. The calculated solvent polarization structure is different from the continuum model prediction in several respects. The value of the polarization at the surface of the ion is less than the continuum value. The solvent polarization also exhibits small oscillations in space near the ion. We show that, under certain approximations, our linear equilibrium theory reduces to the nonlocal electrostatic theory, with the dielectric function (c(k)) of the liquid now wave vector (k) dependent. It is further shown that the nonlocal electrostatic estimate of solvation energy, with a microscopic c(k), is close to the estimate of linearized equilibrium theories of polar liquids. The study of solvation dynamics is based on a generalized Smoluchowski equation with a mean-field force term to take into account the effects of intermolecular interactions. This study incorporates the local distortion of the solvent structure near the ion and also the effects of the translational modes of the solvent molecules.The latter contribution, if significant, can considerably accelerate the relaxation of solvent polarization and can even give rise to a long time decay that agrees with the continuum model prediction. The significance of these results is discussed.

Polarization relaxation, dielectric dispersion, and solvation dynamics in dense dipolar liquid

A unified treatment of polarization relaxation, dielectric dispersion and solvation dynamics in a dense, dipolar liquid is presented. It is shown that the information of solvent polarization relaxation that is obtained by macroscopic dielectric dispersion experiments is not sufficient to understand dynamics of solvation of a newly created ion or dipole. In solvation, a significant contribution comes from intermediate wave vector processes which depend critically on the short range (nearest‐neighbor) spatial and orientational order that are present in a dense, dipolar liquid. An analytic expression is obtained for the time dependent solvation energy that depends, in addition to the translational and rotational diffusion coefficients of the liquid, on the ratio of solute–solvent molecular sizes and on the microscopic structure of the polar liquid. Mean spherical approximation (MSA) theory is used to obtain numerical results for polarization relaxation, for wave vector and frequency dependent dielectric function and for time dependent solvation energy. We find that in the absence of translational contribution, the solvation of an ion is, in general, nonexponential. In this case, the short time decay is dominated by the longitudinal relaxation time but the long time decay is dominated by much slower large wave vector processes involving nearest‐neighbor molecules. The presence of a significant translational contribution drastically alters the decay behavior. Now, the long‐time behavior is given by the longitudinal relaxation time constant and the short time dynamics is controlled by the large wave vector processes. Thus, although the continuum model itself is conceptually wrong, a continuum model like result is recovered in the presence of a sizeable translational contribution. The continuum model result is also recovered in the limit of large solute to solvent size ratio. In the opposite limit of small solute size, the decay is markedly nonexponential (if the translational contribution is not very large) and a complete breakdown of the continuum model takes place. The significance of these results is discussed.

Steady compressible flow of granular materials through a wedge-shaped hopper: The smooth wall, radial gravity problem

A continuum model based on the critical state theory of soil mechanics is used to generate stress and density profiles, and to compute discharge velocities for the plane flow of cohesionless materials. Two types of yield loci are employed, namely, a yield locus with a corner, and a smooth yield locus. The yield locus with a corner leads to computational difficulties. For the smooth yield locus, results are found to be relatively insensitive to the shape of the yield locus, the location of the upper traction-free surface and the density specified on this surface. This insensitivity arises from the existence of asymptotic stress and density fields, to which the solution tends to converge on moving down the hopper. Numerical and approximate analytical solutions are obtained for these fields and the latter is used to derive an expression for the discharge velocity. This relation predicts discharge velocities to within 13% of the exact (numerical) values. While the assumption of incompressibility has been frequently used in the literature, it is shown here that in some cases, this leads to discharge velocities which are significantly higher than those obtained by the incorporation of density variation.

Microscopic expression for frequency and wave vector dependent dielectric constant of a dipolar liquid

A microscopic expression for the frequency and wave vector dependent dielectric constant of a dense dipolar liquid is derived starting from the linear response theory. The new expression properly takes into account the effects of the translational modes in the polarization relaxation. The longitudinal and the transverse components of the dielectric constant show vastly different behavior at the intermediate values of the wave vector k. We find that the microscopic structure of the dense liquid plays an important role at intermediate wave vectors. The continuum model description of the dielectric constant, although appropriate at very small values of wave vector, breaks down completely at the intermediate values of k. Numerical results for the longitudinal and the transverse dielectric constants are obtained by using the direct correlation function from the mean‐spherical approximation for dipolar hard spheres. We show that our results are consistent with all the limiting expressions known for the dielectric function of matter.