Hence, plotting as in Fig. 6b the left side expression as a function of (c+ + c−) yields the exchange rate kf from the value of the intercept. Since factor K is also extracted from the slope, the other parameters can be derived as [12]: equation(13a) kb=(Rav+-Rav-)2-K24kf equation(13b) Rf=Rav++Rav-+K2-kf equation(13c) Rb=Rav++Rav–K2-kbwhere index “av” indicates the average value of the fitted R+ and R− parameters. The different

parameters extracted from the find more fits performed in Fig. 6 are represented in Table 1. The intercept in Fig. 6b is precisely defined (note the relative scale on the vertical axis). However, one should keep in mind that the model is based on a number of assumptions (among others, a single exchange event with a unique exchange rate) and therefore precision does not necessarily imply the validity of the model. Hence, the longitudinal relaxation rate of the agarose obtained via Eq. (13c) is selleck chemicals negative which is unphysical and is a clear indicator of the incompleteness of the simple two-phase model. As we shall discuss below, this has important implications concerning experimental strategies. From the data, an average exchange time Tex can be calculated on the conventional

manner as equation(14) Tex=kf+kbkfkb We obtained Tex = 8.1 ms which was in the same order as previous measurements for water in aspen wood (16 ms) [48], in poly [2-hydroxyethyl-methacrylaye] (21.1 ms) [12], in polyelectrolyte multilayers (24.6 ms) [37] and in filter paper (44 ms) [4]. Since the water transverse relaxation time T2 in this system was short (<1 ms), water diffusion experiments in the agarose-water gel require stimulated-echo experiments where the diffusion time Δ used can be up to the much longer longitudinal relaxation time T1 (∼400 ms). Fig. 7a presents the results of diffusion measurements with Δ varying from 5 ms to 50 ms and fitted using Eq. (1). As shown in Fig. 7b (red square), the fitted apparent diffusion coefficients using Eq. (1)

decrease with increasing diffusion time, a feature that could easily be misinterpreted SPTLC1 as a sign of restricted or obstructed diffusion. Fitting the data to Eq. (7a) with exchange rates set to the values in Table 1 (purple square in Fig. 7b) is supposed to correct for the exchange [4], [6], [7], [8], [9] and [12] effects in the diffusional decay. Indeed, this provides higher apparent diffusion coefficients which is as expected, since magnetization exchange with immobile agarose decreases average displacement compared to that with magnetization residing exclusively in mobile water molecules. Under our experimental conditions, the approximation Δ ≈ τ2 may have been invalid for our shortest diffusion times; for those cases, it was therefore important to use a signal expression [6] which did not rely this approximation equation(15) E(q)=e-AΔ-δ3eAτ22coshBτ22-A+CBsinhBτ22coshB0τ22-CB0sinhB0τ22with constants A, B, B0 and C defined in Appendix A.