Transport properties of borosilicate glass membranes in molten salts

Quantitative AFM analysis of phase separated borosilicate glass surfaces

“…( 3)) we can give a rough estimate of the activation energy E in = 135 ± 45kJ.mol −1 . This value seems to be consistent with typical results from literature: by electrical resistivity measurements in ion exchanged Corning 7740 borosilicate glasses, Garfinkel [27] obtained activation energies in the range 80 − 120kJ.mol −1 ; activation energies measured for the diffusion of sodium in silicate networks are also in the same range [28].…”

Alkali ion mobility and exchange equilibriums in silica glass

“…The variance is given in all cases except for the data from Figure 2. Since the exact dimensions of the membrane were not known, the conductance rather than the specific conductivity was determined, so that the preexponential A term of eq 9 and the similar grouping of constants of eq 8 are not included in the table. The heat of activation values ( *) were consistently larger by about 2 kcal mol-1 than the corresponding Ee values.…”

“…In an earlier paper by Garfinkel,9 just the opposite temperature dependence was reported. However, ref 9 contains an error in eq 2 which renders eq 4, 7, and 8 of ref 9 unusable, so that the mobility ratios shown in Figure 2 of ref 9 are not correct. From the present study, the ion mobility results given in ref 8 have the expected temperature dependence.…”

“…In a defect mechanism the diffusion coefficient may be expressed in the form10•11 D = Nv exp(AS*/72) exp(-AH*/RT) (7) where AS and AH * are the entropy and heat of activation for conduction, N is the defect concentration, and v is the vibrational frequency of the diffusing ion. Equations 6 and 7 may then be combined to yield z2F2c = exp(AS*/72) exp(-AH*/RT) (8) It is assumed that AS , N, v, and c are approximately temperature independent. The enthalpy of activation for conduction is then obtained from the slope of the log vs. 1/T relationship.12…”

“…The conductance-temperature data may also be fitted to an empirical Arrhenius-type equation of the form13 = A exp(-EB/RT) (9) where A is a constant. No particular relationship between ion conduction and diffusion is implied by this equation.…”