Ions, absolute mobility diffusion

Millet determined self-diffusion coefficients for Na and Cs+ ions in hydrated 1200 EW membranes using conductivity measurements and the Einstein equation, D+ = u+kT, where u+ is the absolute mobility of the given cation. u+ can be derived from the equivalent conductivity according to A = 0+IC+ = Fu+, where 0+ is the specific conductivity, C+ is the cation concentration (calculated on the basis of the dry membrane density, EW, and the water content), and F is the Faraday constant. The values of D+ determined via these conductivity measurements... 

Discussing the situation in which the influence of the concentration gradient of ions is balanced by the electric field acting in the opposite direction of the gradient, Einstein found that the diffusion coefficient is proportional to the absolute mobility of the ion ... 

Table 2.3 gives the self-diffusion coefficients of some important ions in submerged soils and Figure 2.2 shows the values for the elemental ions plotted against ionic potential ( z /r where z is the absolute ionic charge and r the crystal ionic radius). As the ionic potential increases the hydration layer of water molecules around the ion increases, and therefore the mobility tends to decrease. Also, at the same ionic potential, cations diffuse faster than anions. The mobilities... 

The absolute magnitude of the calculated value of Qa depends on the way in which the relation between diffusion coefficient and mobility for ion states differs from the classical Einstein form. If we introduce parameters 0+ and 6 and write... 

The ion mobility is a function of the ionic charge and the operating temperature, pressure, and ionic concentration and ion size. Despite the form of Eq. (5.11), the mobUity typically increases with temperature due to a decrease in the viscosity of the electrolyte, which increases diffusivity. The ionic mobilities of various ions in solution are highly varied and available in various literature, but generally on the order of 10 -10 " (cm A s) at 25°C. The absolute value is necessary in Eq. (5.11) due to the charge on the ionic species J since mobility is always a positive quantity. Using ionic mobility, Eq. (5.10) can be written as... 

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