Diffusion second virial coefficient

Here D is the translational diffusion coefficient of the solute molecule at C —> 0 with C the mass concentration of the solute, kd the diffusion second virial coefficient, f a dimensionless parameter depending on polymer chain structure and solvent, and the mean square radius of gyration of the polymer chain. Hence, for C and q small enough, Eq. (2.3) may be approximated by... 

Spectroscopic data do not seem to exist in the literature for He-X complexes where X = Ne, Kr, Ar, Xe. Inter atomic ground state potentials for these speeies have been derived from or compared with beam scattering (differential cross sections, DCS), diffusion, second virial coefficients and similar sourees (see, for example, [03Gie, 930gi, 91Kei]). 

The viscosity, themial conductivity and diffusion coefficient of a monatomic gas at low pressure depend only on the pair potential but through a more involved sequence of integrations than the second virial coefficient. The transport properties can be expressed in temis of collision integrals defined [111] by... 

Miscellaneous Generalized Correlations. Generalized charts and corresponding states equations have been pubhshed for many other properties in addition to those presented. Most produce accurate results over a wide range of conditions. Some of these properties include (/) transport properties (64,91) (2) second virial coefficients (80,92) (J) third virial coefficients (72) (4) Hquid mixture activity coefficients (93) (5) Henry s constant (94) and 6) diffusivity (95). 

The unconventional applications of SEC usually produce estimated values of various characteristics, which are valuable for further analyses. These embrace assessment of theta conditions for given polymer (mixed solvent-eluent composition and temperature Section 16.2.2), second virial coefficients A2 [109], coefficients of preferential solvation of macromolecules in mixed solvents (eluents) [40], as well as estimation of pore size distribution within porous bodies (inverse SEC) [136-140] and rates of diffusion of macromolecules within porous bodies. Some semiquantitative information on polymer samples can be obtained from the SEC results indirectly, for example, the assessment of the polymer stereoregularity from the stability of macromolecular aggregates (PVC [140]), of the segment lengths in polymer crystallites after their controlled partial degradation [141], and of the enthalpic interactions between unlike polymers in solution (in eluent) [142], as well as between polymer and column packing [123,143]. 

The essence of this model for the second virial coefficient is that an excluded volume is defined by surface contact between solute molecules. As such, the model is more appropriate for molecules with a rigid structure than for those with more diffuse structures. For example, protein molecules are held in compact forms by disulfide bridges and intramolecular hydrogen bonds by contrast, a randomly coiled molecule has a constantly changing outline and imbibes solvent into the domain of the coil to give it a very soft surface. The present model, therefore, is much more appropriate for the globular protein than for the latter. Example 3.3 applies the excluded-volume interpretation of B to an aqueous protein solution. 

The diffuse part of the double layer is of little concern to us at this point. Chapters 11 and 12 explore in detail various models and phenomena associated with the ion atmosphere. At present it is sufficient for us to note that the extension in space of the ion atmosphere may be considerable, decreasing as the electrolyte content of the solution increases. As micelles approach one another in solution, the diffuse parts of their respective double layers make the first contact. This is the origin of part of the nonideality of the micellar dispersion and is reflected in the second virial coefficient B as measured by osmometry or light scattering. It is through this connection that z can be evaluated from experimental B values. 

Kobayashi, H. Molecular weight dependence of intrinsic viscosity, diffusion constant, and second virial coefficient of polyacrylonitrile. J. Polymer Sci. 39, 369-388 (1959). 

How efficient is the described representation of the ArCC>2 potential To answer this question the above PES along with a few empirical potentials have been used to derive a number of properties, such as the ground vibrational state and dissociation energy of the complex, ground state rotational constants, the mean square torque, the interaction second virial coefficients, diffusion coefficients, mixture viscosities, thermal conductivities, the NMR relaxation cross sections, and many others [47]. Overall, the ab initio surface provided very good simulations of the empirical estimates of all studied properties. The only parameters that were not accurately reproduced were the interaction second virial coefficients. It is important that its performance proved comparable to the best empirical surface 3A of Bohac, Marshall and Miller [48], This fact must be greeted with satisfaction since no empirical adjustments were performed for the ab initio surface. 

After the pioneering quantum mechanical work not much new ground was broken until computers and software had matured enough to try fresh attacks. In the meantime the study of intermolecular forces was mainly pursued by thermodynamicists who fitted model potentials, often of the Lennard-Jones form [10] 4e[(cr/R) — (cr// ) ], to quantities like second virial coefficients, viscosity and diffusion coefficients, etc. Much of this work is described in the authoritative monograph of Hirschfelder et al. [11] who, incidentally, also gave a good account of the relationship of Drude s classical work to that of London. 

A study of the unlike interactions in rare-gas mixtures has also been performed by Kestin and co-workers. - Their work, which is based on empirical corresponding states functions, leads to significantly different values of for many of the mixtures. In particular, they find s larger than unity for Ar + Kr, Ar + Xe, and Kr -t- Xe. The parameters they obtained for like interactions have been chosen to optimize the fit to measured second virial coefficients, diffusion constants, and viscosities, but most of the unlike parameters have been based on diffusion data alone. This may be the reason for the disparity between their results and those of Lin and Robinson. 

Fluid phase interactions - Second virial coefficients Solution interactions - Partial molar volumes - Solubilities Surface interactions - Adsorption isotherms Diffusion coefficients Mass transfer coefficients Molecular masses... 

Hellmann et al. [23, 177,178] have proposed ab initio force fields for several small molecules, such as helium, neon, or methane, based on the Tang and Toennies potential (9) and coulombic terms (14). With these force fields, gas phase properties like second virial coefficient, shear viscosity, thermal conductivity, or self-diffusion coefficient can be predicted extremely accurately. Typically, the generated data are within the experimental uncertainty. 

A, is the second virial coefficient, D is the translational diffusion coefficients, is the hydrodynamic radius, and iXy/iT)- is the width of the line width distribution... 

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