Diffusion coefficient INDEX

Tables 2,3, and 4 outline many of the physical and thermodynamic properties ofpara- and normal hydrogen in the sohd, hquid, and gaseous states, respectively. Extensive tabulations of all the thermodynamic and transport properties hsted in these tables from the triple point to 3000 K and at 0.01—100 MPa (1—14,500 psi) are available (5,39). Additional properties, including accommodation coefficients, thermal diffusivity, virial coefficients, index of refraction, Joule-Thorns on coefficients, Prandti numbers, vapor pressures, infrared absorption, and heat transfer and thermal transpiration parameters are also available (5,40). Thermodynamic properties for hydrogen at 300—20,000 K and 10 Pa to 10.4 MPa (lO " -103 atm) (41) and transport properties at 1,000—30,000 K and 0.1—3.0 MPa (1—30 atm) (42) have been compiled. Enthalpy—entropy tabulations for hydrogen over the range 3—100,000 K and 0.001—101.3 MPa (0.01—1000 atm) have been made (43). Many physical properties for the other isotopes of hydrogen (deuterium and tritium) have also been compiled (44).

Here the index 0 at Z) refers to the diffusion coefficient in a system at rest (no bias), and Vq denotes the zero approximation i.e., this relation is applicable for slow drift in dilute medium only. 

Fig. 2.14 The scheme of the cylindrical lens method for diffusion coefficient measurement (1) the source with the horizontal slit (2) the condenser supplying a handle of parallel beams (3) the cuvette with a refraction index gradient where the beams are deflected (4) the objective lens focusing the parallel beams to a single point (5) the optical member with an oblique slit and a cylindrical lens (6) the photosensitive material...

The transition between crystalline and amorphous polymers is characterized by the so-called glass transition temperature, Tg. This important quantity is defined as the temperature above which the polymer chains have acquired sufficient thermal energy for rotational or torsional oscillations to occur about the majority of bonds in the chain. Below 7"g, the polymer chain has a more or less fixed conformation. On heating through the temperature Tg, there is an abrupt change of the coefficient of thermal expansion (or), compressibility, specific heat, diffusion coefficient, solubility of gases, refractive index, and many other properties including the chemical reactivity. 

As noted earlier, there are refractive index and viscosity issues to be dealt with. Figure 7 shows the change of the diffusion coefficient... 

The physical properties of solvents greatly influence the choice of solvent for a particular application. The solvent should be liquid under the temperature and pressure conditions at which it is employed. Its thermodynamic properties, such as the density and vapor pressure, temperature and pressure coefficients, as well as the heat capacity and surface tension, and transport properties, such as viscosity, diffusion coefficient, and thermal conductivity, also need to be considered. Electrical, optical, and magnetic properties, such as the dipole moment, dielectric constant, refractive index, magnetic susceptibility, and electrical conductance are relevant, too. Furthermore, molecular... 

Fig. la-f. The mutual diffusion coefficient (D22)v of dextran as a function of dextran concentration for a dextran T10 (Mw 1(f), b dextran T20 (M 2 x 1(f), c dextran T70 (Mw 7 x 10 ), d dextran FDR7783 (Mw 1.5 x 105), e dextran T500 (Mw 5 x10s), and f dextran T2000 (Mw 2x 106) 0,valuesofD22obtainedbymeasurementofthebyconcentrationgradientrelaxation as monitored by refractive index methods ( ), values of D22 obtained by photon correlation spectroscopy. Data obtained from ref. and unpublished work. For earlier studies of dextran mutual... 

The coefficient Ex is called the turbulent (or eddy) diffusion coefficient it has the same dimension as the molecular diffusion coefficient [L2 1]. The index x indicates the coordinate axis along which the transport occurs. Note that the turbulentjliffusion coefficient can be interpreted as the product of a mean transport distance Lx times a mean velocity v = (Aa At) l Egex, as found in the random walk model, Eq. 18-7. 

Consistency of the model with optical data showing index of refraction as a function of growth temperature (85), data on 02 solubility and diffusion coefficient in Si02, and isotopic tracer data (86). 

In Equation (9.6), x is the direction of flux, nt [mol m-3 s 1 ] is the total molar density, X [1] is the mole fraction, Nd [mol m-2 s 1] is the mole flux due to molecular diffusion, D k [m2 s 1] is the effective Knudsen diffusion coefficient, D [m2 s 1] is the effective bimolecular diffusion coefficient (D = Aye/r), e is the porosity of the electrode, r is the tortuosity of the electrode, and J is the total number of gas species. Here, a subscript denotes the index value to a specific specie. The first term on the right of Equation (9.6) accounts for Knudsen diffusion, and the following term accounts for multicomponent bulk molecular diffusion. Further, to account for the porous media, along with induced convection, the Dusty Gas Model is required (Mason and Malinauskas, 1983 Warren, 1969). This model modifies Equation (9.6) as ... 

All sample specific quantities are found within the last term, rj is the solution viscosity, D the diffusion coefficient, Ks the thermal conductivity, ST the Soret coefficient, and (dn / <)c)rp the concentration derivative of the refractive index at constant temperature and pressure. 

Since the interferometer used for (dn / dT)c>p measurement is heated completely, and not just the cuvette, it has been made out of Zerodur (Schott, Mainz), which has a negligible thermal expansion coefficient. Precise values of the refractive index increments are crucial for the determination of the thermal diffusion coefficient and the Soret coefficient. The accuracy achieved for (dn / dc)ftP is usually better than 1 %, and the accuracy of (dn / dT)rp better than 0.1 %. 

The ratio of 6.8 for the two peak areas from stochastic TDFRS is close to the value of 5.9 as expected from the concentration ratio and the refractive index increments of the two PS, which depends on molar mass due to end-group effects. The thermal diffusion coefficient DT= 1.12 x 10 7 cm2 (sK) l is in excellent agreement with the value found previously in our laboratory [36]. 

K represents the following constant parameters n is the index of refraction of the liquid, X is the laser wavelength in air, and 0 is the angle at which the scattering intensity is measured. For polydisperse samples, the autocorrelation function plot is the sum of exponentials for each size range. Once the average translational diffusion coefficient of the sample is determined, the equivalent spherical diameter can be determined by using the Stokes-Einstein... 

In this study, we employed PCS to measure the decay rate of the order-parameter fluctuations in dilute supercritical solutions of heptane, benzene, and decane in CC - The refractive index increment with concentration is much larger than the refractive index increment with temperature in these systems. Therefore the order-parameter fluctuations detected by light scattering are mainly concentration fluctuations and their decay rate T is proportional to the binary diffusion coefficient, D = V/q. The... 

We are still dealing with two species as in the uncoupled case and the same boundary conditions apply they are reformulated in the present matrix-vector form here. As noted above, there is a common condition for all experiments, the flux condition (6.30), generalised to include the normalised diffusion coefficients, to the gradient condition (6.32), and we now write out its discrete form fully, pairing the two species terms for each spatial index ... 

In all expressions the Einstein repeated index summation convention is used. Xi, x2 and x3 will be taken to be synonymous with x, y and z so that o-n = axx etc. The parameter B will be temperature-dependent through an activation energy expression and can be related to microstructural parameters such as grain size, diffusion coefficients, etc., on a case-by-case basis depending on the mechanism of creep involved.1 In addition, the index will depend on the mechanism which is active. In the linear case, n = 1 and B is equal to 1/3t/ where 17 is the linear shear viscosity of the material. Stresses, strains, and material parameters for the fibers will be denoted with a subscript or superscript/, and those for the matrix with a subscript or superscript m. 

Figure 3 Diffusion coefficient versus the polymerisation index of the labelled chains, N, in the case N P (filled circles, fixed matrix) and N=P (open squares) at T = 23°C. When the matrix is frozen, the power law D N 2 pO. typical of the reptation process, is observed down to very low values of N, leading to an evaluation of the minimum number of monomers to create an entanglement for PDMS Ng = 100. For comparison, data from reference 51, with P = N and T = 60°C, are reported as open circles.

Figure 4 Self diffusion coefficient of the small probe, CH3-CH2-CH2-NBD, versus the PDMS polymerization index (now only unlabelled PDMS is used). Given the low accuracy of the experiment at such high values of the diffusion coefficient (relative uncertainty larger than 10%, contrary to the data on figure 3, which are all slower by more than one decade and thus far easier to measure accurately), it seems that there is no significant change of the friction...

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