Self-diffusion viscosity

The transport properties of liquid water also have a strongly anomalous behavior, in particular at low temperature [1,2]. Properties such as self-diffusion, viscosity, and different relaxation times show a strong non-Arrhenius temperature dependence, the characteristic activation energy increasing with decreasing tern-... 

The program is then simply to start at a high temperature, where p T) — Peq( ) lower the temperature at a fixed q<0. The result forp T) can then be used in (8.2) to (8.4) for to obtain results that can be compared directly with experiment. The only quantity that we must specify in addition to those in the equilibrium theory is the relaxation time r T). Since t(T ) is to describe the relaxation by diffusion of structural modes represented by the variation of p, it should have the same temperature dependence as the shear viscosity rj. That is, we suppose that the same microscopic movement processes underlie self-diffusion, viscosity, and structural relaxation. This supposition is consistent with existing theories and with a number of experimental results indicating that the activation enthalpy A A for volume or enthalpy relaxation is generally the same as the activation enthalpy for the viscosity tj. We therefore assume that r(T) can be expressed by the Doolittle equation. 

I. Self-Diffusion, Viscosity and Density of Nearly Spherical and Disk Like Molecules in the Pure Liquid Phase... 

COMPUTING SELF-DIFFUSIVITIES, VISCOSITIES, ELECTRICAL CONDUCTmTIES, AND THERMAL CONDUCTIVITIES FOR IONIC LIQUIDS... 

There have been several studies undertaken to compute macroscopic transport properties of ionic liquids, despite the difficulties mentioned above. These properties include the self-diffusivity, viscosity, electrical conductivity, and thermal conductivity. In this section we review some of these works, but first some background is given on how these transport properties are computed. 

In the case of the alkan-l-ols, experimental measurements of self-diffusion, viscosity and thermal conductivity for methanol to decan-l-ol (Assael et al. 1994b) were used to calculate the values for Vq and the Rx factors. However, in this case, parameters R, and Ro were found to be weak functions of temperature, especially for the first few alkanols of the series, while only parameter Rx was found to be still a constant for a liquid. Thus, these parameters had to be optimized together with the characteristic molar volumes. 

To conclude the application of the scheme to single liquids, and in addition to the groups of liquids considered above, some simple molecular fluids were examined by Assael et al. (1992b). These are CS2, CeHja, CCI4, CH3CN and CH3CI, for which self-diffusion, viscosity and thermal conductivity measurements were all available to provide a more critical test of the correlation. As before, the data are used to calculate the temperature dependence of the characteristic molar volumes, Fb(/10 m mol ), as... 

Dense fluid transport property data are successfully correlated by a scheme which is based on a consideration of smooth hard-sphere transport theory. For monatomic fluids, only one adjustable parameter, the close-packed volume, is required for a simultaneous fit of isothermal self-diffusion, viscosity and thermal conductivity data. This parameter decreases in value smoothly as the temperature is raised, as expected for real fluids. Diffusion and viscosity data for methane, a typical pseudo-spherical molecular fluid, are satisfactorily reproduced with one additional temperamre-independent parameter, the translational-rotational coupling factor, for each property. On the assumption that transport properties for dense nonspherical molecular fluids are also directly proportional to smooth hard-sphere values, self-diffusion, viscosity and thermal conductivity data for unbranched alkanes, aromatic hydrocarbons, alkan-l-ols, certain refrigerants and other simple fluids are very satisfactorily fitted. From the temperature and carbon number dependency of the characteristic volume and the carbon number dependency of the proportionality (roughness) factors, transport properties can be accurately predicted for other members of these homologous series, and for other conditions of temperature and density. Furthermore, by incorporating the modified Tait equation for density into... 

The shear viscosity is a tensor quantity, with components T] y, t],cz, T)yx> Vyz> Vzx> Vzy If property of the whole sample rather than of individual atoms and so cannot be calculat< with the same accuracy as the self-diffusion coefficient. For a homogeneous fluid the cor ponents of the shear viscosity should all be equal and so the statistical error can be reducf by averaging over the six components. An estimate of the precision of the calculation c then be determined by evaluating the standard deviation of these components from tl average. Unfortunately, Equation (7.89) cannot be directly used in periodic systems, evi if the positions have been unfolded, because the unfolded distance between two particl may not correspond to the distance of the minimum image that is used to calculate the fore For this reason alternative approaches are required. 

Another advance in the concepts of hquid-phase diffusion was provided by Hildebrand, who adapted a theory of viscosity to self-diffusivity. He postulated that = B(V — where is the... 

Transport Properties Although the densities of supercritical fluids approach those of conventional hquids, their transport properties are closer to those of gases, as shown for a typical SCF such as CO9 in Table 22-12. For example, the viscosity is several orders of magnitude lower than at liquidlike conditions. The self-diffusion coefficient ranges between 10" and 10" em /s, and binaiy-diffusiou coefficients are similar [Liong, Wells, and Foster, J. Supercritical Fluids 4, 91 (1991) Catchpole and King, Ind. Eng. Chem. Research, 33,... 

Following the general trend of looldng for a molecular description of the properties of matter, self-diffusion in liquids has become a key quantity for interpretation and modeling of transport in liquids [5]. Self-diffusion coefficients can be combined with other data, such as viscosities, electrical conductivities, densities, etc., in order to evaluate and improve solvodynamic models such as the Stokes-Einstein type [6-9]. From temperature-dependent measurements, activation energies can be calculated by the Arrhenius or the Vogel-Tamman-Fulcher equation (VTF), in order to evaluate models that treat the diffusion process similarly to diffusion in the solid state with jump or hole models [1, 2, 7]. 

Some 30 years ago, transport properties of molten salts were reviewed by Janz and Reeves, who described classical experimental techniques for measuring density, electrical conductance, viscosity, transport number, and self-diffusion coefficient. 

To summarize, there is a sizable and self-consistent body of data indicating that rotational and translational mobility of molecules inside swollen gel-type CFPs are interrelated and controlled mainly by viscosity. Accordingly, T, self-diffusion and diffusion coefficients bear the same information (at least for comparative purposes) concerning diffusion rates within swollen gel phases. However, the measurement of r is by far the most simple (it requires only the collection of a single spectrum). For this reason, only r values have been used so far in the interpretation of diffusion phenomena in swollen heterogeneous metal catalysts supported on CFPs [81,82]. 

X 10 cm by measuring molecularly dispersed water in toluene and by correcting for local viscosity differences between toluene and these microemulsions [36]. Values for Dfnic were taken as the observed self-diffusion coefficient for AOT. The apparent mole fraction of water in the continuous toluene pseudophases was then calculated from Eq. (1) and the observed water proton self-diffusion data of Fig. 9. These apparent mole fractions are illustrated in Fig. 10 (top) as a function of... 

Figures 8 and 9 show the dependence of the self-diffusion constant and the viscosity of polyethylene melts on molecular weight [47,48]. For small molecular weights the diffusion constant is inversely proportional to the chain length - the number of frictional monomers grows linearly with the molecular weight. This behavior changes into a 1/M2 law with increasing M. The diffusion...

Another static quantity, the entropy, is also thought to be intimately related to various dynamic properties of liquids such as the viscosity p and the self-diffusivity D. In the next section, we discuss some of the main ways in which computer simulations have been used to probe this connection in recent years. 

The prediction for the diffusion constant at Eq. (4) is in very good agreement with measurements of the self-diffusion constants of polymer melts [14] while results on the viscosity have consistently given a stronger dependence of the characteristic times and viscosities on molecular weight of approximately The investigation of these discrepancies in the context of linear polymers has de-... 

The impedance factor is strictly empirical, accounting primarily for the geometry of the soil pore network bnt also for ion exclusion by negative adsorption from narrow pores, and for the increased viscosity of water near charged surfaces. It is similar for all simple ions and molecules. It can be measured by following the self diffusion of a nonadsorbed ion, such as Cl , for which C = 0lCl and hence D =... 

The diffusion coefficient D is one-third of the time integral over the velocity autocorrelation function CvJJ). The second identity is the so-called Einstein relation, which relates the self-diffusion coefficient to the particle mean square displacement (i.e., the ensemble-averaged square of the distance between the particle position at time r and at time r + f). Similar relationships exist between conductivity and the current autocorrelation function, and between viscosity and the autocorrelation function of elements of the pressure tensor. 

---