Diffusion, coefficients table

For a range of diffusion coefficients Table II shows values that may be expected for heterogeneous standard rate constants and apparent molecular weights. These numbers are presented as an illustration of their relative magnitudes and the manner in which they interrelate. It must be observed that the apparent molecular weight is a reaction parameter and does not, necessarily, express the molecular size. 

Based on properties in solution such as intrinsic viscosity and sedimentation and diffusion rates, conclusions can be drawn concerning the polymer configuration. Like most of the synthetic polymers, such as polystyrene, cellulose in solution belongs to a group of linear, randomly coiling polymers. This means that the molecules have no preferred structure in solution in contrast to amylose and some protein molecules which can adopt helical conformations. Cellulose differs distinctly from synthetic polymers and from lignin in some of its polymer properties. Typical of its solutions are the comparatively high viscosities and low sedimentation and diffusion coefficients (Tables 3-2 and 3-3). 

The observed conductivity is always found to be less than that calculated from the sum of the diffusion coefficients (Table 5.27), i.e., from the Nemst-Einstein relation [Eq. (5.61)]. Conductive transport depends only on the charged species because it is only charged particles that respond to an external field. If therefore two species of opposite charge unite, either permanently or temporarily, to give an uncharged entity, they will not contribute to the conduction flux (Fig. 5.34). They will, however, contribute to the diffusion flux. There will therefore be a certain amount of currentless diffusion, and the conductivity calculated from the sum of the diffusion coefficients will exceed the observed value. Currentless diffusion will lead to a deviationfrom the Nernst-Einstein relation. 

For instantaneous equilibration, the simulation predicts that is as predicted by theory, Equation 10, and tg is given by equation 13. Thus tR should be slightly less than F due to the gaseous diffusion coefficient. Table I shows the experimental values of tR and FM at several flow rates. 

The characteristic time for diffusion within cells or cell compartments of various sizes can be estimated from the diffusion coefficient (Table 4.8). Diffusion is an efficient method for distributing molecules throughout a small cell ( 1 /xm) even when the diffusion coefficient is low, diffusion times are less than 10 s. For larger cell compartments, diffusion is very slow, so that large cells ( 100 q,m) cannot rely on diffusion to distribute substrates or newly produced proteins. 

StiU, to have an orientation in the elution order of different ions under the SEC conditions, information on the relative sizes of the ions is essential. Therefore, while fidly recognizing the argumentativeness of the absolute values of ion radii and noting that substantially different values can be found in the Hterature, we present here one of the most complete and self-consistent Hst of crystal radii and the effective radii of hydrated ions from the work of Nightingale [158] the hydrated radii have been calculated from the Umiting ionic equivalent conductance and limiting ionic diffusion coefficients (Table 12.5). 

Despite of these limitations, which make no possible to know a estimated values with accuracy, it is possible to have an idea of their possible range of values, considered all of these methods reasonable compromises. Consequently, for each electrolyte, either the use of a given a value from one specific method of estimation, or the use of an average value from all of the methods is legitimate (Table 4.1). In our case, we have used the average values of that parameter in the estimation of diffusion coefficients (Table 4.2), because almost all values obtained from different a values, are close each other (deviations, in general, < 2%). 

The properties of ions in solution depend, of course, on the solvent in which they are dissolved. Many properties of ions in water are described in Chapters 2 and 4, including thermodynamic, transport, and some other properties. The thermodynamic properties are mainly for 25°C and include the standard partial molar heat capacities and entropies (Table 2.8) and standard molar volumes, electrostriction volumes, expansibilities, and compressibilities (Table 2.9), the standard molar enthalpies and Gibbs energies of formation (Table 2.8) and of hydration (Table 4.1), the standard molar entropies of hydration (Table 4.1), and the molar surface tension inaements (Table 2.11). The transport properties of aqueous ions include the limiting molar conductivities and diffusion coefficients (Table 2.10) as well as the B-coefficients obtained from viscosities and NMR data (Table 2.10). Some other properties of... 

Diffusion coefficients (Table 2.3) decrease approximately linearly with crosslink density or the reciprocal of the molecular weight between crosslinks at low to moderate degrees of crosslinking. At higher densities the decrease is nonlinear. 

Table 4. Diffusion Coefficients for Dilute Solutions of Gases in Liquids at 20°C ...

Table 5. Values of the Diffusion Coefficient and of M-c/T Apc Various Gases in Air at 0°C and at Atmospheric Pressure ...

Information on ionization energies, solubiUties, diffusion coefficients, and soHd—Hquid distribution coefficients is available for many impurities from nearly all columns of the Periodic Table (86). Extrinsic Ge and Si have been used almost exclusively for infrared detector appHcations. Of the impurities,... 

The diffusion of metal ions in vitreous siUca has not been studied as extensively as that of the gaseous species. The alkaU metals have received the most attention because their behavior is important in electrical appHcations. The diffusion coefficients for various metal ions are Hsted in Table 5. The general trend is for the diffusion coefficient to increase with larger ionic sizes and higher valences. 

The effect of copolymer composition on gas permeability is shown in Table 9. The inherent barrier in VDC copolymers can best be exploited by using films containing Htde or no plasticizers and as much VDC as possible. However, the permeabiUty of even completely amorphous copolymers, for example, 60% VDC—40% AN or 50% VDC—50% VC, is low compared to that of other polymers. The primary reason is that diffusion coefficients of molecules in VDC copolymers are very low. This factor, together with the low solubiUty of many gases in VDC copolymers and the high crystallinity, results in very low permeabiUty. PermeabiUty is affected by the kind and amounts of comonomer as well as crystallinity. A change from PVDC to 50 wt °/ VC or 40 wt % AN increases permeabiUty 10-fold, but has Httle effect on the solubiUty coefficient. 

Table 11. Diffusion Coefficients and Solubility Coefficients of Selected Penetrants in Polymers at 25°C ...

Humidity does not affect the permeabihty, diffusion coefficient, or solubihty coefficient of flavor/aroma compounds in vinyhdene chloride copolymer films. Studies based on /n j -2-hexenal and D-limonene from 0 to 100% rh showed no difference in these transport properties (97,98). The permeabihties and diffusion coefficients of /n j -2-hexenal in two barrier polymers are compared in Table 12. Humidity does not affect the vinyhdene chloride copolymer. In contrast, transport in an EVOH film is strongly plasticized by humidity. 

Table 10 contains some selected permeabiUty data including diffusion and solubiUty coefficients for flavors in polymers used in food packaging. Generally, vinyUdene chloride copolymers and glassy polymers such as polyamides and EVOH are good barriers to flavor and aroma permeation whereas the polyolefins are poor barriers. Comparison to Table 5 shows that the large molecule diffusion coefficients are 1000 or more times lower than the small molecule coefficients. The solubiUty coefficients are as much as one million times higher. Equation 7 shows how to estimate the time to reach steady-state permeation t if the diffusion coefficient and thickness of a film are known. 

Values for many properties can be determined using reference substances, including density, surface tension, viscosity, partition coefficient, solubihty, diffusion coefficient, vapor pressure, latent heat, critical properties, entropies of vaporization, heats of solution, coUigative properties, and activity coefficients. Table 1 Hsts the equations needed for determining these properties. 

Fuller-Schettler-Giddings The parameters and constants for this correlation were determined by regression analysis of 340 experimental diffusion coefficient values of 153 binary systems. Values of X Vj used in this equation are in Table 5-16. 

TABLE 16-8 Self Diffusion Coefficients in Polystyrene-divinylbenzene Ion Exchangers... 

Example 8 Estimation of Rate Coejficient Estimate the rate coefficient for flow of a 0.01-M water solution of NaCl through a bed of cation exchange particles in hydrogen form with e = 0.4. The superficial velocity is 0.2 cm/s and the temperature is 25 C. The particles are 600 im in diameter, and the diffusion coefficient of sodium ion is 1.2 X 10 cmVs in solution and 9.4 X 10 cmVs inside the particles (of. Table 16-8). The bulk density is 0.7 g dry resin/cnd of bed, and the capacity of the resin is 4.9 mequiv/g dry resin. The mass action eqiiihbrium constant is 1.5. 

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,... 

Table 6.2 Data for diffusion coefficients in pure metals...

Quite extraordinary diffusion coefficients of impurities from odier parts of die Periodic Table are found, and especially in die important case of lidiium or copper diffusion, where die eidiancement over self-diffusion is by six to eight orders of magnitude. This indicates diat diese atoms do not form part of die sp network in die sUmcture, but more closely resemble separate atoms in die sp iiiaUix. 

Table 10.1 Self diffusion coefficients of some liquid metals expressed by an Arrhenius equation...

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