Transport Properties in Ionic Media
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3 Experimental example of porous charged medium: Na on membrane The Na on 117 membrane [8,9] is a porous and charged medium composed by a linear polymer of uorocarbon with an anionic ending : a sulfonate group. These anionic groups build inverted micelles and thus form, in the hydrophobic polymer matrix, hydrophilic cavities in which aqueous solutions can penetrate. The diameter of these cavities is about 40 A. They are connected by small pores whose size has been estimated at 10 A length and 10 A diameter. Another interesting characteristic of the Na on membranes is the anionic site concentration in the hydrophilic domains : it is about 4 mol:l;1 . In this experimental section, we deal with the determination of the self-diusion coecient of the tetramethyl ammonium ion N(CH3 )+4 by dierent experimental techniques. These measurements at dierent times scales allow to get a complete picture of the ionic transport processes in the membrane. The times range extends from the picosecond with Neutron Quasi-Elastic Scattering experiments to millisecond with NMR experiments and to minute with radiotracers experiments.
3.1 Experimental results 3.1.1
NQES
The NQES experiments were performed with the time-of- ight spectrometer mibemol at Laboratoire Leon Brillouin (CEA Saclay, France). The studied samples were : Na on membranes equilibrated with solutions of N(CH3 )+4 in D2 O at 0.5 and 2 mol/kg ; N(CH3 )4 Cl in D2 O solutions at 1, 3.5, 4.5 and 8 mol/kg. The elastic and quasi-elastic peaks were extracted from the scattered intensity using the " tmib" program (LLB). For a simple diusion the incoherent scattering function Sinc(q; !) can be written in the following manner [10] : 1 y (q ) Sinc (q; !) = 2 (1) ! + (y(q))2
with ~! the energy transfer and y(q) the half width at half maximum of Sinc (q). In the limit of small q, y(q) becomes : lim y(q) = Dq2
q!0
(2)
where D is the self-diusion coecient. The self-diusion coecients of N(CH3 )+4 ions are thus obtained from a linear regression on a plot of y(q) as a function of q2 . The resolution 20 eV corresponds approximately to an observation time of 9 10;11 s and, with a self-diusion coecient about 10;5 cm2 :s;1 , to a displacement of 3 A. This length is quite small as compared with Na on cavity size, thus allowing one to use the same model for determining the self-diusion coecient of N(CH3 )+4 ions in solutions and in Na on membrane from NQES spectra. In order to compare the selfdiusion in solution and within a Na on membrane, the values of D are plotted as a function of the molality of N(CH3 )+4 on Figure 3. One can notice that the self-diusion coecients in Na on membrane are placed on the curve formed by the values of the self-diusion coecient in solution. It appears therefore that the self-diusion process is similar, within this time and space scales, to that in non-con ned solution. T9.5.3
Figure 4: Variation of the apparent selfdiusion coecient of N(CH3 )+4 in Na on membrane () versus the square root of the diusion interval in NMR se
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