Self diffusion constants dilute solutions

This equation is valid both in dilute and semidilute solutions. Unlike with dilute solutions, the scaling argument does not predict molecular weight dependence explicitly. (This must be so since one can derive the same formula for the self-diffusion constant Dq. Further information is needed to distinguish the functional form of D pp from that of Dc-) If one assumes that is independent of the molecular weight, then one has... 

In the semi-dilute regime, two kinds of dynamical processes should be distinguished collective processes involving cooperative motions of the solution and single chain processes involving the individual motion of a labeled chain. For instance, two independent diffusion constants can be defined, a cooperative diffusion constant, characterizing the relaxation of concentration fluctuations, and a self-diffusion constant for the motion of a labeled chain. 

Much less is known about micellar charge and counterion binding in the case of bile salts. Based on the result of ionic self-diffusion measurements [20,163,173], conductance studies [17,18,187], Na, and Ca activity coefficients [16,19,144,188,189] and NMR studies with Na, Rb and Cs [190], a number of generalities can be made. Below the operational CMC, all bile salts behave as fully dissociated 1 1 electrolytes, yet interionic effects between cations and bile salt anions decrease the equivalent conductance of very dilute solutions [17,18,187]. With the onset of micelle formation, counterions become bound to a small degree values at this concentration are about < 0.07-0.13 and are not greatly influenced by the species of monovalent alkali cations [163,190]. At concentrations above the CMC, values remain relatively constant to 100 mM in the case of C and this... 

In a quiescent dilute solution the motion of polymers is a random walk the mean squared distance (rc ) covered is the diffusion constant C, times the elapsed time t, as noted in Sect. 8.5. The various chains are far apart and thus do their random motions independently. As the concentration approaches 0, this ceases to be true. The random currents moving one polymer are also felt by its neighbors, so that nearby chains have similar motions. To characterize the motion we must specify two diffusion coefficients the self-diffusion coefficient and the cooperative diffusion coefficient. The self-diffusion coefficient Cs is defined by the motion of an individual chain as introduced above. 

Here, T is the temperature, k the Boltzmann constant, rj the viscosity of the solvent, and a is the diameter of a hydrodynamicaUy equivalent sphere. For an ideal dilute solution of non-interacting particles D corresponds to the self-diffusion coefficient [45]. 

For liquid electrolytes, ionic conductivity, self-diffusivity, and viscosity are three key properties. Though originally based on dilute aqueous electrolyte solutions, the Walden rule [52] has been proposed as a tool to provide insight to the proton transfer and ion association. The rule suggests that the molar cmiductivity of an electrolyte, A, is proportional to the fluidity, which can be expressed as the inverse of the shear viscosity i/. In other words, the product of the molar conductivity and viscosity of an electrolyte is a constant, as shown in (3.10). 

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