Viscosity and Self-diffusion Coefficient

SIMULATIONS OF LIQUID HMX 3.1. Viscosity and self-diffusion coefficient 

Methodology. Equilibrium MD simulations were carried out at six different temperatures (550-800 K, at 50 K intervals) and atmospheric pressure. 

Calculation and results. For each temperature we calculated the HMX molecular center-of-mass self-diffusion coefficient determined as  

With the exception of 550 K, each trajectory was at least 45 times longer than the largest molecular relaxation time at a given temperature. The system at 550 K would have required upwards of 70 ns by these criteria, which is beyond the practical limits imposed by our computational resources. Therefore we stopped the simulations at this temperature after 20 ns, which was sufficient to 

Relaxation times and transport coefficients of liquid HMX obtained from MD simulations. 

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From the experimental data we were able to determine both the intramolecular and intermolecular relaxation rates as a function of pressure and temperature. The availability of shear viscosities and self-diffusion coefficients of EHB, which were measured earlier in our laboratory, provided the opportunity to test the dependence of the experimental cross-relaxation rates on viscosity and/or diffusion of EHB. The reorientational correlation time Tc describing overall molecular motion is coupled to the rj/T term through the Debye equation, which in a modified form is ... 

As a result of these complexities, although more than 100 different potential functions have been employed, no fully satisfactory model has yet been developed. But many of these models have been able to explain many of the experimental observables, such as density maximum, values of viscosity and self-diffusion coefficient, specific heat and compressibility, and dynamics of electron transfer reactions. 

Fig. 2.8. Reciprocal of the apparent value of as determined from viscosity (—) and self-diffusion coefficients (- -) using hard-sphere transport theory (Table 2.2). Transport coefficient data from H. H. Landolt and R. Bomstein, Zahlenwerte and Funktionen, 6th ed. (Berlin Springer, 1969), Vol. Ill, Part 5a, pp. 3, 516.

The thermal conductivity, viscosity, and self-diffusion coefficient of argon gas are listed for one or more temperatures in Tables A.16, A.18, and A.19 of the appendix. 

Figure 9.17 Solutions of bovine serum albumin, showing their viscosity ( ) and self-diffusion coefficient (0) (from Refs. (29,30)), and Dp of 322 ( ) and 655 (O) nm polystyrene spheres, with corresponding stretched exponentials in protein c, from data of Ullmann, et al.(28).

Table 1 Theoretical expressions for the kinematic shear viscosity v, the thermal diffusivity, Dr, and the self-diffusion coeflScient, D, in both two d = 2) and three (d = 3) dimensions. M is the average number of particles per ceU, a is the coUision angle, 1 b is Boltzmann s constant, T is the temperature, At is the time step, m is the particle mass, and a is the cell size. Except for selfdiffusion constant, for which there is no coUisional contribution, both the kinetic and collisional contributions are listed. The expressions for shear viscosity and self-diffusion coefficient include the effect of fluctuations in the number of particles per cell however, for brevity, the relations for thermal diffusivity are correct only up to 0(1/M) and 0(1/M ) for the kinetic and collisional contributions, respectively. For the complete expressions, see [28,53,54]...

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. 

In order to understand the influence of alcohol on the zeolitization process, it is useful to summarize the structural aspects of alcohol-water mixtures. Considerable work has been done in this area. It is well-recognized that at low alcohol concentrations the viscosity, reciprocal self-diffusion coefficient, the dielectric relaxation time and NMR relaxation times of the water molecules are all greater than that of pure water.(21-241 These observations indicate that addition of alcohol to water at low levels leads to an increased structure of water.(25) This concept is also supported by X-ray diffraction studies(26) and is commonly referred to as hydrophobic hydration.(27) On a molecular level, this effect... 

The temperature dependencies of the viscosity (Figure 5.6) and the summation of the self-diffusion coefficient (Dcation + Oanion) (Figure 5.4) interestingly show the contrasted profiles with the indication of inverse relationship between viscosity and self-diffiision coefficient. This can be explained in terms of the Stokes-Einstein equation, which correlates the self-diffusion coefficient (Dcation Danion) with viscosity (q) by the following relationship ... 

As stated in the earlier section on Generalized Equations of Motion, we would ultimately like to find a set of equations of motion in the form of Eq. [91] to compute transport coefficients such as the shear viscosity and self diffusion... 

Physical Mechanisms. The simplest interpretation of these results is that the transport coefficients, other than the thermal conductivity, of the water are decreased by the hydration interaction. The changes in these transport properties are correlated the microemulsion with compositional phase volume 0.4 (i.e. 60% water) exhibits a mean dielectric relaxation frequency one-half that of the pure liquid water, and ionic conductivity and water selfdiffusion coefficient one half that of the bulk liquid. In bulk solutions, the dielectric relaxation frequency, ionic conductivity, and self-diffusion coefficient are all inversely proportional to the viscosity there is no such relation for the thermal conductivity. The transport properties of the microemulsions thus vary as expected from simple changes in "viscosity" of the aqueous phase. (This is quite different from the bulk viscosity of the microemulsion.)... 

Of course, eventually, particles will reappear, through the equation = Po + RTln the existence of R depends on the existence of particles. But a theory of stress-driven deformation of a continuum does not require particles, even with stress-driven self-diffusion coefficients for viscosity and self-diffusion are the only things required. 

In fact, the latter have been obtained for most ions from the conductivities rather than from isotope labeling. Ion mobilities (hence molar conductivities and self-diffusion coefficients) increase with increasing temperatures. A flve-fold increase in Ae between 273 and 373 K has been noted. This is mainly because the viscosity of the solvent diminishes in this direction (Table 1.1 and see below). The transference numbers r+ and r are temperature-sensitive too, though only mildly. 

The coefficients of viscosity and self-diffusion of a simple gas, to a first approximation, can be expressed as functions of temperature by [12]... 

Figure 3. Density p [22], viscosity 77 [26], and self-diffusion coefficient D [27] of pure carbon dioxide as a function of pressure p at 313 K (for Du at 323 K).

Seki, S., Hayamizu, K, Tsuzaki, S., Fujii, K, Umebayashi, Y., Mitsugi, T., Kobayashi, T., Ohno, Y., Kobayashi, Y., Mita, Y., Miyashiro, H., Ishiguro, S. (2009) Relationship between Center Atom Sp>ecies (N, P) and Ionic Conductivity, Viscosity, Density, Self-diffusion Coefficient of Quaternary Cation Room-Temperature Ionic Liquids, Phys. Chem. Chem. Phys. VoL 11 3509-3514. 

The calculated viscosity, thermal conductivity and self-diffusion coefficients (the latter at 0.10 MPa) of nonionized monatomic lithium, sodium, potassium, rubidium and cesium vapors can be consulted for temperatures between 700 and 2000 K in Tables VIII to XII of the work of Fialho et al. (1993). 

Thus, we can see that it is important to examine the validity of a model by comparing several results produced by that model. Additionally, a good model of the stmcture of liquids must also satisfy the interpretation of properties other than the mere thermod5mamic values that are of interest to us here, e.g. surface tension, viscosity and self-diffusion. The major advantage of Eyring s cellular and vacancy model with a degeneration coefficient is that it also takes account of the dynamic properties of liquids. 

Seki S, Hayamizu K, Tsuzuki S, Fujii K, Umebayashi Y, Mitsugi T, Kobayashi T, Ohno Y, KobayasM Y, Mita Y, Miyashiro H, Ishiguro S (2009) Relationships between center atom species (N, P) and ionic conductivity, viscosity, density, self-diffusion coefficient of quaternary cation room-temperature ionic liquids. Phys Chem Chem Phys 11 3509-3514... 

Thermal diffusivity and self-diffusion coefficient As with the viscosity, there are both kinetic and collisional contributions to the thermal diffusivity, Dt. A detailed analysis of both contributions is given in [28], and the results are summarized in Table 1. The self-diffusion coefficient, D, of particle i is defined by... 

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. 

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]. 

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... 

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