Self-diffusion in solutions

Krauss CJ, Spinks JWT. Temperature coefficients for self-diffusion in solution. Canadian Journal of Chemistry 1954, 32, 71-78. 

Grinberg, F. A., Skirda, V. A., Maklakov, V. A., Ragovina, L. Z., and Niki-forova, G. G. (1987). Self-diffusion in solutions of polyblock polysulfone-polybutadiene copolymer. Vysokomol. Soedin. Ser. A 29, 2029-2034 (in Russian). 

The following papers had experimental foci different from those examined above. Several provide very interesting information on polymer self-diffusion in solution. Others are not amenable to the above analysis. 

E.D. von Meerwall, E.J.Amis and J.D. Ferry, "Self-Diffusion in Solutions of Polystyrene in Tetrahydrofuran Comparison of... 

E. D. von Meerwall, E. J. Amis, and J. D. Ferry. Self-diffusion in solutions of polystyrene in tetrahydrofuran Comparison of concentration dependences of the diffusion coefficient of polymer, solvent, and a ternary probe component. Macromolecules, 18(1985), 260-266. 

B. P. Chekal and J. M. Torkelson. Relationship between chain length and the concentration dependence of polymer and oligomer self-diffusion in solution. Macromolecules, 35 (2002), 8126-8138. 

Maklakov AI, Skirde VD, Fatkullin NF (1987) Self-diffusion in polymer solutions and melts (in Russian). University Publ, Kazan... 

The beauty of the reptation model is that it is able to make predictions about molecular flow both in solution and at fracture by assuming that the molecules undergo the same kind of motions in each case. For both self-diffusion in concentrated solutions and at fracture, the force to overcome in pulling the polymer molecule through the tube is assumed to be frictional. 

Hadden, DA, Master of Science Thesis, Florida State University, Tallahassee, FL, 1999. Hadden, D Rill, RL McFadden, L Locke, BR, Oligonucleotide and Water Self-Diffusion in Pluronic Triblock Copolymer Gels and Solutions by Pulsed Field Gradient Nuclear Magnetic Resonance, Macromolecules 33, 4235, 2000. 

Malmsten, M Lindman, B, Water Self-Diffusion in Aqueous Block Copolymer Solutions, Macromolecules 25, 5446, 1992. 

Rymden, R. Stilbs, P. (1985a). Counterion self-diffusion in aqueous solutions of poly(acrylic acid) and poly(methacrylic acid). Journal of Physical Chemistry, 89, 2425-8. 

Diffusion in solution is the process whereby ionic or molecular constituents move under the influence of their kinetic activity in the direction of their concentration gradient. The process of diffusion is often known as self-diffusion, molecular diffusion, or ionic diffusion. The mass of diffusing substance passing through a given cross section per unit time is proportional to the concentration gradient (Fick s first law). 

Finally, two articles review recent experimental and theoretical developments with respect to self-diffusion in polymer solutions, either concentrated A5), or dilute and semidilute A6) with emphasis on scaling concepts. Both include references to the recent PGSE literature. 

Figure 3.2 Diffusion couple for measuring solute self-diffusion in a binary system.

Four different types of diffusivities are summarized in Table 3.1. These include the self-diffusivity in a pure material, D the self-diffusivity of solute i in a binary system, Df, the intrinsic diffusivity of component i in a chemically inhomogeneous system, Dand the interdiffusivity, D, in a chemically inhomogeneous system. These diffusivities are applicable only in certain reference frames which are also listed in Table 3.1. In the remainder of this book, the type of diffusivity under discussion will be identified by these symbols when this information is relevant. When a diffusivity is identified in this manner, it may be assumed that the diffusion under consideration is being described in the proper corresponding frame. 

Exercise 9.1 yielded an expression, Eq. 9.18, for the enhancement of the effective bulk self-diffusivity due to fast self-diffusion along dislocations present in the material at the density, p. Find a corresponding expression for the enhancement of the effective bulk self-diffusivity of solute atoms due to fast solute self-diffusion along dislocations. Assume that the solute atoms segregate to the dislocations according to simple McLean-type segregation where c2 c2L = k — constant, where cf5 is the solute concentration in the dislocation cores and cXL is the solute concentration in the crystal. 

The formal potential, E0/, contains useful information about the ease of oxidation of the redox centers within the supramolecular assembly. For example, a shift in E0/ towards more positive potentials upon surface confinement indicates that oxidation is thermodynamically more difficult, thus suggesting a lower electron density on the redox center. Typically, for redox centers located close to the film/solution interface, e.g. on the external surface of a monolayer, the E0 is within 100 mV of that found for the same molecule in solution. This observation is consistent with the local solvation and dielectric constant being similar to that found for the reactant freely diffusing in solution. The formal potential can shift markedly as the redox center is incorporated within a thicker layer. For example, E0/ shifts in a positive potential direction when buried within the hydrocarbon domain of a alkane thiol self-assembled monolayer (SAM). The direction of the shift is consistent with destabilization of the more highly charged oxidation state. 

Diffusion is a physical process that involves the random motion of molecules as they collide with other molecules (Brownian motion) and, on a macroscopic scale, move from one part of a system to another. The average distance that molecules move per unit time is described by a physical constant called the diffusion coefficient, D (in units of mm2/s). In pure water, molecules diffuse at a rate of approximately 3xl0"3 mm2 s 1 at 37°C. The factors influencing diffusion in a solution (or self-diffusion in a pure liquid) are molecular weight, intermolecular... 

Anderko and Lencka find. Eng. Chem. Res. 37, 2878 (1998)] These authors present an analysis of self-diffusion in multicomponent aqueous electrolyte systems. Their model includes contributions of long-range (Coulombic) and short-range (hard-sphere) interactions. Their mixing rule was based on equations of nonequilibrium thermodynamics. The model accurately predicts self-diffusivities of ions and gases in aqueous solutions from dilute to about 30 mol/kg water. It makes it possible to take single-solute data and extend them to multicomponent mixtures. 

R. Mills and V.M.M. Lobo, Self-diffusion in electrolyte solutions, Elsevier, Amsterdam, 1989. 

D. Girlich, H.-D. Fudemann, C. Buttersack and K. Buchholz, c,T-dependence of the self diffusion in concentrated aqueous sucrose solutions, Z. Naturforsch., 1994, 49c, 258-264. 

In an excellent review article, Tirrell [2] summarized and discussed most theoretical and experimental contributions made up to 1984 to polymer self-diffusion in concentrated solutions and melts. Although his conclusion seemed to lean toward the reptation theory, the data then available were apparently not sufficient to support it with sheer certainty. Over the past few years further data on self-diffusion and tracer diffusion coefficients (see Section 1.3 for the latter) have become available and various ideas for interpreting them have been set out. Nonetheless, there is yet no established agreement as to the long timescale Brownian motion of polymer chains in concentrated systems. Some prefer reptation and others advocate essentially isotropic motion. Unfortunately, we are unable to see the chain motion directly. In what follows, we review current challenges to this controversial problem by referring to the experimental data which the author believes are of basic importance. 

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