Antecedentes de la Nueva Geografía Económica

Effective partition coefficients of water in membrane active layers (𝐾_𝐴𝐿) were obtained from the water uptake measurements in liquid water as given by

𝐾_𝐴𝐿 = 𝑚𝑙

𝑀𝑊_𝐻2𝑂𝐶_𝐻2𝑂𝛿𝐴𝐿. (4.9)

In Equation 4.9, it is assumed that the membrane does not swell by a significant amount when immersed in liquid water. While active layer swelling was not measured in this study, other studies in the literature have reported 13±6% swelling observed for SWC4+ membrane, 7±2% swelling for ESPA and 4.8±4.4% for ESPA1 membrane, and 35±2% for XLE

membrane.15,27 _{Therefore, while active layer swelling was not characterized in this study, errors} in the water partition coefficients estimated with Equation 4.9 are expected to be at most 35%. The values of 𝐾𝐴𝐿 for the five membranes studied were in the range of 0.33(±0.04) – 0.72(±0.11) and are listed in Table 4.2.

Water partition coefficients in the active layers polymer (𝐾_𝑃) were obtained from the water uptake measurements in humidified nitrogen gas as given by

𝐾𝑃 = _𝑀𝑊 𝑚𝑣

𝐻2𝑂𝐶𝐻2𝑂𝛿𝑃 . (4.10)

The polymer thickness was used in the calculation instead of the active layer thickness , because water uptake by the voids under humidified nitrogen gas was negligible and only the polymer was responsible for the mass increase (𝑚_𝑣) caused by water uptake, according to the findings in Chapter 3. The values of 𝐾𝑃 for the five membranes studied were in the range of 0.19(±0.03) – 0.26(±0.13) and are listed in Table 4.2. A comparison of the values of 𝐾_𝐴𝐿 and 𝐾_𝑃 indicates that the existence of voids within membrane active layer increased the partition

coefficient of the active layer by a factor of 1.7-3.4 (𝐾_𝐴𝐿/𝐾_𝑃). The increased partition coefficient of the active layer caused by the voids can be explained by the fact that the water partition

coefficient of active layer polymer (𝐾_𝑃) is smaller than 1 while the water partition coefficient of voids is 1 (as the voids are filled with water when the membrane is in contact with liquid water). Therefore, the effective water partition coefficient of the active layer (𝐾𝐴𝐿), which is a function of the partitioning into polymer and voids, is higher than the water partition coefficient of the polymer (𝐾_𝑃).

As discussed in Section 4.1, Zhang et al. obtained water uptake values by active layers of FT30 and LF10 membranes under humidified nitrogen gas and Lee et al. obtained water uptake value by active layer of SW30 membrane also under humidified helium gas.17,18 Zhang et al. also calculated the concentration of water in the membrane active layers (𝐶𝑚, mol·m-3), but did not take into account in the calculations the void fractions of the active layers because of a lack of awareness of the existence of the voids. Similarly, the value of 𝐶_𝑚 for the SW30 membrane active layer can also be calculated for the study of Lee et al. based on the water uptake value

they reported, though they did not report the value of 𝐶_𝑚 in their study. Because of the unawareness of the existence of the voids, the 𝐶𝑚 values they obtained and the corresponding values of 𝐾 that can be calculated from their study are neither effective active layer properties (as the water uptake tests were conducted under humidified nitrogen gas instead of liquid water) nor polymer properties of membrane active layers (as the existence of voids was not accounted for). The values of 𝐶_𝑚 obtained by Zhang et al. were 7.7×103 mol·m-3 and 8.7×103 mol·m-3 for the FT30 and LF10 RO membranes,17 respectively, so the corresponding partition coefficients calculated as 𝐾 = 𝐶_𝑚/𝐶_𝐻2𝑂 are 0.14 and 0.16 for the FT30 and LF10 RO membranes,

respectively. The values of 𝐶_𝑚 calculated based on the study of Lee et al. is 15.4×103 mol·m-3 for the SW30 membrane and the corresponding value of K is 0.28.

While Zhang et al. used similar water uptake tests under humidified nitrogen gas as the tests used in this study to obtain the 𝐾_𝑃 values, the water partition coefficients obtained from their study are smaller than the values of 𝐾_𝑃 obtained for the four RO membranes in this study (average 𝐾_𝑃 of 0.22±0.03 for the four RO membranes) because they did not take into account the existence of voids within membrane active layers. In fact, if the existence of voids were ignored in the present study (i.e., 𝑓_{𝑝𝑜𝑟𝑒} = 0), the water partition coefficients of active layer polymer (𝐾_𝑃′) would have been calculated to be 0.16±0.02 for NF90, 0.13±0.02 for XLE, 0.19±0.01 for ESPA3, 0.16±0.05 for SWC4+ and 0.15±0.01 for SW30HR as shown in Table 4.2, with an average of 0.16±0.02 for the four RO membranes (XLE, ESPA3, SWC4+ and SW30HR membranes). This average value is not statistically different from the partition coefficients obtained by Zhang et al. While Lee et al. used a different water uptake measurement technique and obtained a 2 times higher water uptake by the SW30 membrane active layer compared to this

calculated from the Lee et al. study is only 1.3 times higher than the value of 𝐾_𝑃 for the

SW30HR membrane. Therefore, not taking into account the existence of voids could lead to an underestimation of the partition coefficient of the active layer polymer by a factor of 1.2-1.4 (𝐾_𝑃′/𝐾_𝑃) in membrane characterization.