Molar friction

Diffusion coefficient, cm /sec Molecular frictional factor Molar frictional factor... 

Bueche et al. (33) determined chain dimensions indirectly, through measurements of the diffusion coefficient of C1 Magged polymers in concentrated solutions and melts.The self-diffusion coefficient is related to the molar frictional coefficient JVa 0 through the Einstein equation ... 

The polysaccharide corresponding to the first, immobile fraction was examined by the Svedberg ultracentrifuge technique. The sedimentation constant, S20, was equal to 1.6 X 10 c.g.s. units, and was independent of change of concentration. A 1 % solution of the polysaccharide was calculated from data obtained in this investigation to have a polysaccharide content of 0.91% the polysaccharide thus contained 9% of extraneous matter. The diffusion constant, D20, was found to be 11 X 10 and the partial specific volume, 0.619. A molar frictional ratio of 1.5 was obtained. This indicated that the particles were elongated ellipsoids (see p. 320). A molecular weight of 9,000 was calculated as compared with the value 7,300 obtained by Tennet and Watson. The polysaccharide reacted with immune serum in a dilution of 1 6,000,-... 

In its applicability to self diffusion and to gaseous systems, the tendency of the resistivities to be constant was first observed by Ljunggren. In condensed systems in general, the conditions are more complicated, as shown for example by the usefulness of Stokes law for molar frictions. 

Classical thermod5mamics and theories of state equilibrium show an admirable flexibility with regard to the choice of components primarily only the number of these is essential. This advantage has been taken over by the diffusion theory with the thermodynamic factor as an intermediate link. As a consequence, it must be admitted that the molar frictions contained in the theory ( /c<) do not necessarily correspond to the frictional coefficients of the special molecular species contained in the mixture. So that the latter shall be the case, a component must consist of only one kind of molecule, and (in calculating the molar properties contained in the theory) the molecular weight of the component must be chosen according to the actual molecular species. 

Articles by the present writer > > and by Ljunggren are concerned with the thermod5mamics and frictional properties of components consisting of a nximber of molecular species in rapid equilibrium with one another. One result is a simple law which is vahd for the molar friction of a binary system, e.g. O of component 2, expressed in terms of the frictions of the different molecular species of this component. Assume that the molecular weight of the component is chosen to be Af, corresponding to simple molecules with the chemical symbol A. Other molecules in equihbrium with A are A (n = 2,. . . ) with frictions O. In the actual solution, the fraction of the component which exists as A is written It is easily shown that the inverse of the component friction O is given by... 

The diffusion constant is independently evaluated by observing the changes in concentration of a solution in a stationary tube as the solute diffuses into pure solvent with which the solution forms a hquid boundary. From this can be calculated the molar frictional coefficient (/). 

Frictional coefficients Generally, these are introduced in hydrodynamics in order to ascribe a Newtonian friction to particles or molecules. A molar frictional coefficient... 

Frictional Ratios The molar frictional coefficient, /sp, of an unsolvated spherical molecule may be computed by the formula based on Stokes law ... 

In few cases, only the molar frictional coefficient /q, rather than/o//sp, was quoted in the literature. These values are inserted in the same column as the values for the frictional ratio. 

Molar frictional coefficient at zero concentration Concaitration Eq. (A2)... 

The sedimentation coefficient s°, or its normalized form 5 0 w function of the conformation and flexibility of a macromolecule (via its translational frictional property) and its mass. So if we are going to obtain conformation and flexibility information we need to know the molecular weight (molar mass)... 

We have carried out a wide range of studies concerned with the dextran concentration dependence of the transport of the linear flexible polymers and have varied both molecular mass and chemical composition of this component. Moreover, we have studied the effect of the variation of the molar mass of the dextran on the transport of the flexible polymers 51). In general, the transport of these polymers in dextran solutions may be described on common ground. At low dextran concentrations the transport coefficients of the polymers are close to their values in the absence of the dextran and may even exhibit a lower value. This concentration range has been discussed in terms of normal time-independent diffusional processes in which frictional interactions predominate. We have been able to identify critical dextran concentrations associated with the onset of rapid transport of the flexible polymers. These critical concentrations, defined as C, are summarized in Table 1. They are... 

As the results of Schwander and Cerf (188) and of Leray (180,181), which were obtained on samples of DNA from calf thymus, have been reproduced already in several review articles (1,3), the present discussion can be kept rather short. When the viscosity of the solvent (1.0 molar aquous solution of sodium chloride) is increased by replacing part of the water by glycerol, the behaviour of the initial slope of the extinction angle curve follows the qualitative pattern, as given by Fig. 5.10. At low solvent viscosities the molecules seem to behave like frozen molecules, at high solvent viscosities they seem to become flexible coils exhibiting internal friction. These results have been considered to prove the correctness of Cerf s theoretical model. 

The dependence of the friction coefficient of the poly(acrylamide) gel on the total concentration of polymers of the gel, including both the main constituent and cross-linker, has been studied under the experimental conditions of a constant molar concentration of the cross-linker at 1 mol%. The total concentration was changed from 400 mM to 2.8 M which corresponds to a concentration from about 3 to 20 wt.%. The temperature was fixed at 20 0.1 °C. 

Starting with ketones and hydrogen peroxide in the presence of a catalytic amount of acid, mixtures of up to eight components have been identified, i.e.. (1, X = OH. R3 = H), (1, X = OOH, R3 = H), (2, X = Y = OH). (2, X = Y = OOH), (2, Y = OH, Y = OOH), (3). (4), and (5). The ketone structure and reaction conditions, i.e., acid strength, reactant molar ratios, temperature, and time, determine which compounds form and predominate. Mixtures of several peroxide structures usually are present. Individual peroxides have been isolated from several ketones under different conditions (Table 5). The pure peroxides should be handled with extreme caution since most, especially those derived from the low moleculai weight ketones, ate shock- and friction-sensitive and can explode violently. Methyl ethyl ketone peroxide (MEKP) mixtures are produced commercially only as solutions containing <40 wt% MEKPs in solvents, commonly dialkyl phthalates. 

Single-stage simulations reveal that intermolecular friction forces do not lead to reverse diffusion effects, and thus the molar fluxes calculated with the effective diffusion approach differ only slightly from those obtained via the Maxwell-Stefan equations without the consideration of generalized driving forces. This result is as expected for dilute solutions and allows one to reduce model complexity for the process studied (143). 

The Svedberg equation relates 5 to the molar mass of the particles, M2, their translational diffusion coefficient, D (related to the frictional force exerted on the particle), and to (dp/dc2)kl ... 

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