Effects of memory on the coherent scattering function for the rouse–zimm model of dilute polymer solutions

We study the effect of the memory function on the coherent scattering function of a dilute polymer solution, taking into account hydrodynamic interactions among the polymer segments. The line shape, given by a sum of two exponentials, is very accurate numerically for ka ? 3 (with a the length of a polymer segment) and for times such that ω₀(k)t ? 1.5 [with ω₀(k) the initial slope]. However, this approximation to the scattering function is not nearly so accurate at the smaller values of ka encountered in light scattering experiments. The amplitudes and relaxation times associated with the two exponentials are found to be markedly dependent on the strength of the hydrodynamic interactions.     

Hydrodynamic correlation functions for molten salts

Abstract

The linearized hydrodynamic equations for a binary ionic fluid, with specific reference to a dissociated molten salt, are used to evaluate correlation functions of local fluctuation variables and the corresponding response functions. Previous results for the instantaneous correlation functions are extended and connected with thermodynamic fluctuation theory. Different dynamical behaviours, depending on the relative magnitude of the relaxation frequency for charge fluctuations and the sound wave frequency, are demonstrated. When 4πσ/? > ck, charge fluctuations are uncoupled from mass fluctuations, the latter being isomorphous to those of a one-component neutral fluid. Kubo relations for the transport coefficients are derived in this regime. When 4πσ/? < ck, the behaviour of the ionic fluid becomes isomorphous to that of a neutral mixture, with electrical conduction playing a role analogous to interdiffusion and contributing, in particular, to the damping of sound waves. An interpolation formula between these two limiting behaviours of the relaxation frequencies is also derived. The consequences of these results for the light scattering spectrum of an ionic fluid are briefly discussed     

A master equation for S(q,ω) leading to the hydrodynamic regime for simple fluids

A master equation relating the coherent and incoherent dynamical structure factors S(q, ω) and S_S(q, ω) is introduced on the basis of physical arguments suggested by previous theories. It is shown that, once S_S(q, ω) and the first six moments of S(q, ω) are known, the resulting expression for S(q, ω) contains the correct hydrodynamic regime as well as the free particle behaviour. The relationships thus introduced between the transport coefficients and the molecular quantities are compared to the experimental data for liquid argon. Molecular dynamics data are also well reproduced.     

Comparative sensitivity analysis of transport properties and reaction rate coefficients

Transport properties of chemical species are required for many combustion models. A sensitivity analysis is conducted to assess the significance of transport properties and their underlying molecular parameterizations for atmospheric pressure premixed laminar flames for three different fuels and two different approaches to transport property calculations. The analysis is performed at both the macroscopic level of Arrhenius A-factors and transport coefficients as well as at the molecular scale. First- and second-order sensitivities of reactant, intermediate, and product species concentrations, temperature, and flame velocity were calculated with respect to various parameters, all within the mixture approximation using ADIFOR 2.0, a software package that supports exact differentiation. Parameters considered were the binary diffusion coefficients, pure species thermal conductivity coefficients, and thermal diffusion ratios. The more fundamental molecular parameters: collision diameters, well depths, dipole moments, polarizabilities, and the rotational relaxation collision numbers were also considered. Influential transport properties are found to be as important in flame modeling as influential reaction rates, and both should be taken into account when building chemical mechanisms. Transport parameter importance was found to vary according to the independent variable being considered and the flame type. Magnitudes of sensitivities appear to be more influenced by the underlying molecular parameters than the approach used to compute the transport properties. The number of significant sensitivities to transport parameters increases for the progression: flame temperature, flame velocity, reactant species, product species, and intermediate radical species. Many dependent variables have significant sensitivities to the pure species thermal conductivities of N₂, O₂, and the fuel. At the molecular level, large sensitivities to the collision diameters of several species are also observed, but significant sensitivity to well depths, although observed is less and more rare. Large sensitivities are not observed to the rotational relaxation collision number, the dipole moment, or to the molecular polarizability. Second-order sensitivities are significant for a number of dependent variables. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 538–553, 2005     

The transport of adsorbate mixtures in porous materials: Basic equations for pores with simple geometry

The basic equations governing the transport of single and binary adsorbate mixtures through single pores are considered. An irreversible thermodynamic formulation is adopted and both viscous and diffusive terms are incorporated following the earlier work of Mason and co-workers. The links between phenomenological coefficients and molecular properties are demonstrated. For single components, the gas phase and high density limits are considered. By using simple hydrodynamic models it is shown that the phenomenological coefficients in the mixture equations can all be expressed as functions of the coefficients for the individual components in the same pore, and the properties of the component adsorption isotherms. Whilst it is appreciated that the hydrodynamic approach will be of limited value in very small pores, it is argued that useful insights can be gained into the feasibility of membrane separation processes from this method. The general equations can be used in future development of network models for porous materials.     

Excess thermodynamic properties of ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate and N-octyl-2-pyrrolidone from T = (298.15 to 323.15) K at atmospheric pressure

Density (ρ), refractive index (n_D) and speed of sound (u) values are measured for the binary mixture of 1-butyl-3-methylimidazolium tetrafluoroborate and N-octyl-2-pyrrolidone over the entire range of mole fraction at temperatures from T = (298.15 to 323.15) K under atmospheric pressure. Using the basic experimental data, various acoustic and excess thermodynamic parameters are calculated and are discussed in terms of molecular interactions between the present investigated binary system. The excess values are fitted to Redlich–Kister polynomial equation to estimate the binary coefficients and standard deviation between the experimental and calculated values. Further, the molecular interactions in the binary mixture system are analysed using the experimental FT-IR spectrum recorded at room temperature.     

The electrical properties of heterogeneous mixtures containing an oriented spheroidal dispersed phase

Theoretical equations for the permittivity and conductivity of a heterogeneous mixture containing an oriented dispersed phase of spheroidal shape are limited to low volume fractions of dispersed phase. Two new sets of equations have been derived here for such systems using approaches which have been shown previously to be applicable to higher concentrations. One set has generalised forms of equations given by Bruggeman and Hanai and includes simplifications applicable to oil in water (O/W) and water in oil (W/O) systems. The other set has generalised forms of an equation given by Looyenga. Tabulated mixture permittivityε and dielectric incrementΔε values are presented and, with the exception ofO 〈W systems containing prolate spheroids, the two types of equation show significant differences in bothε andΔε. For both typesΔε is strongly dependent on the ratio of the conductivities of the two media of aW/O system. The relevance of the mixture equations to the electrical behaviour of micellar, microemulsion and liquid crystalline systems is considered.     

Testing the accuracy of correlations for multicomponent mass transport of adsorbed gases in metal-organic frameworks: diffusion of H2/CH4 mixtures in CuBTC

Mass transport of chemical mixtures in nanoporous materials is important in applications such as membrane separations, but measuring diffusion of mixtures experimentally is challenging. Methods that can predict multicomponent diffusion coefficients from single-component data can be extremely useful if these methods are known to be accurate. We present the first test of a method of this kind for molecules adsorbed in a metal-organic framework (MOF). Specifically, we examine the method proposed by Skoulidas, Sholl, and Krishna (SSK) ( Langmuir, 2003, 19, 7977) by comparing predictions made with this method to molecular simulations of mixture transport of H 2/CH 4 mixtures in CuBTC. These calculations provide the first direct information on mixture transport of any species in a MOF. The predictions of the SSK approach are in good agreement with our direct simulations of binary diffusion, suggesting that this approach may be a powerful one for examining multicomponent diffusion in MOFs. We also use our molecular simulation data to test the ideal adsorbed solution theory method for predicting binary adsorption isotherms and a method for predicting mixture self-diffusion coefficients.     

Hydrodynamic Correlation Functions for Binary Mixtures

Abstract

Correlation functions of various local thermodynamic variables of binary mixtures are obtained from the linearized hydrodynamic equations following the method of Mountain and Deutch. “Non-Lorentzian” parts of the time Fourier transformed correlation functions which have not been included by these authors are obtained here and their effect on the light scattering spectrum considered. An extension of the treatment by Fox and Uhlenbeck of Landau and Lifshitz hydrodynamical fluctuation theory to binary mixtures has been accomplished and correlation functions of the "fluctuating forces" are obtained for this case.     

Competitive facilitated transport through liquid membranes

A mathematical model is presented which solves the dimensionless, transient, non-linear partial differential equations governing the competitive facilitated transport of two gases through a liquid membrane. The model incorporates the mass transfer coefficients in the boundary conditions for the free gas concentrations. Several studies were carried out. A comparison of this model with a steady-state “equilibrium core” model was excellent. Through varying the dimensionless parameters, it was found that gas I would have a higher steady-state facilitation factor than gas 2 if k₁ >k₂ and k_-1k_-2. The boundary conditions and mass transfer coefficients were also varied to see their effects on the facilitation factors. The idea of pumping one of the gases against its concentration gradient was shown to be theoretically possible.     

Frequency spectra of disordered metals: especially liquid Rb

The phonon frequency spectrum g(ω) of a crystal, such as body centred cubic (bcc) Rb, is known to be characterized by the Van Hove singularities at ω?≠?0. However, for a liquid metal like Rb, g(ω) has a single, hydrodynamic-like singularity, namely a cusp ∝ ω ^(1/2), at ω?=?0. Here, we note first that computer simulation on liquid Rb near freezing has revealed a rather well-defined Debye frequency ω_D. Therefore, we propose here a zeroth-order model g ₀ (ω ) of g(ω) for Rb, which combines the Debye model with the ‘hydrodynamic’ ω ^(1/2) cusp. The corresponding velocity autocorrelation function 〈 v (t)·v (0)〉 has correctly a long-time tail ∝ t ^-(3/2). The terms from g ₀ (ω ) involving ω_D are then damped by weak exponential factors exp (-α _i t), and the resulting first-order approximation, g ₁ (ω ) say, to the frequency spectrum is found to have features in common with the molecular dynamics (MD) simulation form. Thus ω_D is fixed, as well as transport coefficients for the known thermodynamic state. The article concludes with a more qualitative discussion on supercooled liquids, and on metallic glasses such as Fe, for which MD simulations exist.     

Non-Fickian interdiffusion of dynamically asymmetric species: a molecular-dynamics study

We use molecular dynamics combined with dissipative particle dynamics to construct a model of a binary mixture where the two species differ only in their dynamic properties (friction coefficients). For an asymmetric mixture of slow and fast particles we study the interdiffusion process. The relaxation of the composition profile is investigated in terms of its Fourier coefficients. While for weak asymmetry we observe Fickian behavior, a strongly asymmetric system exhibits clear indications of anomalous diffusion, which occurs in a crossover region between cases I (Fickian) and II (sharp front moving with constant velocity), and is close to the case II limit.     

Bulk properties of a liquid phase mixture {ethylene glycol+<Emphasis Type="Italic">tert</Emphasis>-butanol} in the temperature range 278.15–348.15 K and pressures of 0.1-100 MPa. I. Experimental results,excess and partial molar volumes

The densities ρ and coefficients of compressibility k = ΔV/V ₀ of a binary mixture {ethylene glycol (1) + tert-butanol (2)} in the temperature range of 278.15–323.15 K and pressures of 0.1–100 MPa over the entire range of compositions of liquid phase state are measured. Found that the coefficients of compressibility k of the mixture increase both with an increase in the concentration of tert-butanol and with a rise in temperature and pressure. The excess molar volumes of the mixture, apparent, partial molar volumes, and limiting partial molar volumes of the components are calculated. It is showed that the excess molar volumes of the mixture are negative and decrease when the pressure increases. The excess molar volumes are described by the Redlich-Kister equation. The partial molar volumes of ethylene glycol sharply decrease in the range of high concentrations of tert-butanol. The dependences of partial molar volumes of ethylene glycol are characterized by the presence of a region of temperature inversion. The “negative compressibility” of the limiting partial volumes of ethylene glycol is revealed.     

Self-motion response and incoherent scattering function in classical liquids

Abstract

The self-motion response function and incoherent scattering function S_s(k, ω) for simple classical liquids is studied using an exact representation presented in a previous paper. The latter can be termed a generalized mean field representation to distinguish it from the generalized hydrodynamic representation introduced elsewhere. It is shown that the present formalism offers a natural and convenient way of relating the experimentally determined S_s(k, ω) to some basic quantities involving only the interaction. Using a small part of the recent experimental data on incoherent neutron scattering in liquid argon, we are able to calculate S_s(k, ω) and other quantities of interest and to compare with the rest of the data     

Fluctuation-dissipation relations for polymer systems. I. The molecular weight dependence of the viscosity

Generalised Langevin equations are used to describe the motion of interacting polymer molecules. In these equations the many-body aspects of the problem are incorporated into generalised friction functions and random forces. The so-called second fluctuation-dissipation relation gives a general relation between these two quantities and enables us to relate the spatial correlations present in the environment to a normal mode dependent friction coefficient and force constant. We then show how the various regimes of molecular weight dependence of the viscosity can be understood in a fairly general and non-specific way in terms of the spatial correlations of the random forces representing the rest of the system of polymer and solvent molecules. In particular a molecular weight dependence of M³ is shown to be a general feature of a spatially corelated environment.     

Dielectric relaxation study of binary mixture of sulfolane and N,N-dimethylformamide in benzene solution using microwave absorption data

The dielectric constant (???) and dielectric loss (???) for dilute solutions of the binary mixture of different molar concentrations of sulfolane and DMF in benzene solution has been measured at 9.885 GHz and different temperatures (25, 30, 35, 40°C) by using standard microwave techniques. Following the single frequency concentration variational method, the dielectric relaxation time (??) and dipole moment (??) have been calculated. It is found that dielectric relaxation process can be treated as the rate process, just like the viscous flow. The presence of solute-solute molecular associations in benzene solution has been proposed. Energy parameters (??H _?, ??F _?, ??S _?) for dielectric relaxation process of binary mixture at 50% mole fraction in benzene at 25, 30, 35, and 40°C have been calculated and compared with the corresponding energy parameters (??H _??, ??F _??, ??S _??) for the viscous flow.     

On the molecular theory of relaxation processes and the viscoelastic properties of magnetic liquids

The kinetic equations for one-and two-particle distribution functions including the contributions of spatial correlation of density and correlation of velocities were used to obtain equations of generalized hydrodynamics of magnetic liquids, whose transfer coefficients microscopically depended on the spatial and time scales. (The relaxing flows in these equations comprise kinetic and potential parts, which ensures the inclusion of translational and structural relaxation processes.) The system of generalized hydrodynamics equations obtained can be used to study transfer phenomena in magnetic liquids. Smoluchowski equations for binary density n ₂(q ₁, q ₂, t) and binary flow of particles I ₂(q ₁, q ₂, t) were obtained and their general solutions found to construct a closure of the initial kinetic equation for the one-particle distribution function. The asymptotic behavior of these solutions at low frequencies (ω → 0) was analyzed and found to coincide with the long-time asymptotes of autocorrelation functions. The viscoelastic properties of magnetic liquids were studied over a wide range of frequencies in the presence of an external magnetic field H. Microscopic equations for viscosity coefficients and elastic moduli were found and their asymptotic behavior in slow and fast processes considered.     

Stochastic theory of direct simulation Monte Carlo method

A treatment of direct simulation Monte Carlo method as a Markov process with a master equation is given and the corresponding master equation is derived. A hierarchy of equations for the reduced probability distributions is derived from the master equation. An equation similar to the Boltzmann equation for single particle probability distribution is derived using assumption of molecular chaos. It is shown that starting from an uncorrelated state, the system remains uncorrelated always in the limit N→∞, where N is the number of particles. Simple applications of the formalism to direct simulation money games are given as examples to the formalism. The formalism is applied to the direct simulation of homogenous gases. It is shown that appropriately normalized single particle probability distribution satisfies the Boltzmann equation for simple gases and Wang Chang–Uhlenbeck equation for a mixture of molecular gases. As a consequence of this development we derive Birds no time counter algorithm. We extend the analysis to the inhomogeneous gases and define a new direct simulation algorithm for this case. We show that single particle probability distribution satisfies the Boltzmann equation in our algorithm in the limit N→∞, V _k →0, Δt→0 where V _k is the volume of kth cell. We also show that our algorithm and Bird’s algorithm approach each other in the limit N _k →∞ where N _k is the number of particles in the volume V _k .     

Investigations of Molecular Interactions in Binary Mixtures of the Ionic Liquid [Emim][BF<Subscript>4</Subscript>] and <Emphasis Type="Italic">N</Emphasis>-Methylaniline at Temperatures from 293.15 to 323.15 K

Density (ρ) and speed of sound (u) values were measured for the binary mixture of 1-ethyl-3-methylimidazolium tetrafluoroborate ([Emim][BF₄]) and N-methylaniline over the entire range of mole fractions at temperatures from 293.15 to 323.15 K under atmospheric pressure. Using the basic experimental data, various acoustic and thermodynamic parameters were calculated and are discussed with regard to the molecular interactions in the binary systems. The partial molar volumes and partial molar isentropic compressibilities at infinite dilution have also been calculated. The excess values were fitted to Redlich–Kister polynomial equation to estimate the binary coefficients and standard deviation between the experimental and calculated values. Further, the molecular interactions in the binary mixture system are analyzed using the experimental FT-IR spectra recorded at room temperature.