Concentration dependence of diffusion coefficient

Diffusion and molecular weight are related in three ways  

Empirical Relation For homologous polymers, we have an equation relating D and M analogous to the Mark-Houwink equation for intrinsic viscosity  

The translational diffusion coefficient is considered to be a constant only for particles in dilute solution. In general, if the solution is not dilute, D is dependent on 

The parameter Do is the diffusion coefficient at infinite dilution. The term ko is the hydrodynamic and thermodynamic combined factor and can be expressed in either of two different ways  

In Eqs. (10.24) and (10.25) f is the first-order frictional coefficient, V is the polymer molecular volume, y is the activity coefficient of the polymer in solution, v is the partial specific volume of the solvent, and p is the density of the solution. Equation (10.24) fits the description for the behavior of synthetic polymers, while Eq. (10.25) fits that for biological polymers, particularly proteins. Substituting Eq. (10.24) into Eq. (10.23), we obtain 

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Concentration dependence of diffusion coefficient in good solvent. Filled ... 

The reptation prediction of the concentration dependence of diffusion coefficient in athermal solvent is slightly weaker than in 0-solvent, since... 

Y. P. Tang Diffusion of Carbon Dioxide in Liquids—Concentration Dependence of Diffusion Coefficient and Diffusion in Mixed Solvents, Ph.D. Dissertation, University of Texas, 1963. 

C. E. Rogers and D. Machin, "The Concentration Dependence of Diffusion Coefficients in Polymer-Penetrant Systems", CRC Critical Rev, in Macromol. Sci., April 1972, pp. 245-313. 

Figure 6.1.3. Kinetic curves of plane layer swelling at different values of concentration dependence of diffusion coefficient (e=0.1,d = 2/9) a - power law mode (l-s = 0 2-s=l 3-s = 1.5 4-s = 2.5) b - exponential (5 - s = 5) and blow-up mode (6 - s = 5.5). [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol. soed., X42,74 (2000)].

Figure 15a. Concentration dependence of diffusion coefficients for SDS micelles in media of different ionic strength at 25 °C. b. Relaxation dme distributions using DLT for SDS micelles at Cerent concentrations in 10 mM NaQ at 25 °C.

Based on the assumption of complete dissociation, the concentration dependence of diffusion coefficient D is described e.g., by (2)... 

Scaling laws predict that the exponent of p for M should vary from 2.25 in good solvents to 3 in theta solvent conditions for the concentration dependence of diffusion coefficients the same exponents are 0.75 and 1 respectively. At 308 K an exponent of 1.17 was observed, which within the experimental error agreed with predictions. However, at 333 K, the exponent was 0.46, much lower than theory predicts. This observation and the high exponent observed for M were attributed to the presence of dangling chains in the network, since the correlation functions were observed to become more non-exponential as the temperature... 

Fig. 4. Polymer concentration dependence of diffusion coefficient. (Reproduced from Reference [4].) Sample, Na-PSS. Mol. Wt. Mw = 4.9 x 10, Mn = 3.2 x lO. ...

In general, the diffusion coefficient of an electrolyte is a function of concentration. One of the reasons for the concentration dependence of diffusion coefficient is the electrolyte effect of ionic atmosphere around each ion. A similar effect of ionic atmosphere should be observed for diffusion and sedimentation coefficients of a poly electrolyte. Moreover, the effect of ionic atmosphere should remain even at the limit of infinite dilution of polyelectrolyte if the concentration of added neutral salt is kept constant, since the ionic atmosphere does not disappear. 

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