J. Phys. Chem. B 2001, 105, 2351-2355
2351
Tracer-Desorption 1H NMR Measurement of Diffusion Coefficients in Polyphosphazene Ion-Exchange Membranes Roy Carter,†, Ronald F. Evilia,‡ and Peter N. Pintauro*,† Department of Chemical Engineering, Tulane UniVersity, New Orleans, Louisiana 70118, and Department of Chemistry, UniVersity of New Orleans, New Orleans, Louisiana 70148 ReceiVed: August 21, 2000; In Final Form: December 5, 2000
The growth of an NMR signal due to diffusion of solute out of a thin membrane has been investigated for the measurement of diffusion rates under conditions that are not suitable for accurate application of pulsed field gradient methods. Such conditions include those where the internal solute signal is either too small or too broad to be utilized or where the diffusion rate is too slow to yield observable attenuation of the NMR signal with commonly available gradient strengths or possible gradient application times. The method was used to measure the mutual diffusion coefficient of methanol in a series of polyphosphazene-based cation-exchange membranes, which are currently being examined for possible use in direct liquid methanol fuel cells. Diffusion coefficients at 25 °C were in the range of 8.0 × 10-8 to 4.0 × 10-7 cm2/s for methanol concentrations of 1.0-5.0 M and were significantly smaller than those reported for a Nafion perfluorosulfonic acid membrane. Successful application of the tracer-desorption NMR approach requires that the external solute signal be observable in a single pulse and that the membrane desorption rate not be too fast (the diffusion coefficient should be 100 Hz) located at ∼3.3 ppm and for H2O at ∼5.2 ppm (trace amounts of H2O were present in the D2O solvent and were detected in the membrane by 1H NMR). The width of the internal CH3OD peak and the overlap of the CH3OD peak with the polymer’s background signal were undesirable for the application of the PFGNMR method. Nevertheless, a PFGNMR experiment was carried out, but no reliable and reproducible attenuation could be measured, even at the instrument’s maximum gradient strength of 100 G/cm. Turning our attention to the tracer-desorption technique, we first checked 1H NMR spectra of pure CH3OD and a solution of CH3OD in D2O, to identify the location of the CH3OD peak in free solution. Sharp, well-defined peaks for CH3 (at 3.3 ppm) and H in trace H2O (at 4.8 ppm), which are typical for 1H NMR were observed. These same peaks were observed during a methanol desorption experiment, as shown in Figure 3, where the external methanol and water spectra at three different desorption times are shown for a cross-linked polyphosphazene membrane (which was originally equilibrated in 5.0 M CH3OD). There was a significant difference in peak height between internal and external CH3OD signals due to differences in the local chemical environment seen by methanol inside and outside the membrane. Additionally, the external CH3OD peak height increased continuously with time during the desorption process and thus could be analyzed using eq 1. A typical methanol desorption curve is shown in Figure 4, where the relative peak height for methanol in the external solution is plotted as a function of the square root of time. Data are shown for two (repeated) desorption experiments with a 1.4 mmol/g IEC sulfonated polyphosphazene membrane that was UV-cross-linked with 15 mol % benzophenone and equilibrated in 3.0 M CH3OD. The solid line in this figure is the best fit of eq 1 to the data, using 9.5 × 10-8 cm2/s as the mutual diffusion coefficient for methanol. Although no NMR data could be collected during the early stages of CH3OD desorption (i.e., at times less than ca. 60 s), there was a sufficient number of data
Figure 4. CH3OD desorption curve for a cross-linked 1.4 mmol/g IEC polyphosphazene membrane equilibrated in 3.0 M CH3OD/D2O at 25 °C and Nafion 117 (Nafion data from ref 19): (b, 2) experimental data from repeated experiments; (s) best fit of eq 1 to the data with D ) 9.5 × 10-8 cm2/s; (---) eq 1 with D ) 9.5 × 10-8 cm2/s + 20%; (- - -) eq 1 with D ) 9.5 × 10-8 cm2/s - 20%; (- - -) theoretical desorption curve for Nafion 117.
points and sufficient reproducibility in the measurements for 0.3 < Mt/M∞ < 0.9 that D could be determined accurately. The error in the methanol diffusion coefficient was estimated by generating theoretical desorption curves with values of D that deviated from the “best-fit” diffusion coefficient by (20%. As can be seen by the dashed curves in Figure 4, the analysis is clearly sensitive to the choice of D in eq 1, and the error in the final value of the methanol diffusion coefficient is
