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Mechanics-based model for non-affine swelling in perfluorosulfonic acid (PFSA) membranes

“…structural reorganization). As 3 a result, both the total volume and the total number of SO 3 groups in the RVE increase during swelling, which is in agreement with the observations from various experiments [11,18,19,21,22,35] and the degree of cluster coalescence is therefore attributed to the nonaffine swelling ratio k. The derivation of Eq. (9) is purely geomet rical, and based on the observed phenomenon of non-affine swelling deformation during sorption.…”

“…The non-affine swelling behavior is assumed to be independent of temperature. (iii) Non-affine deformation is here associated with the structural reorganization at the nanoscale [11,[18][19][20][21]34,35]. Alternatively, this type of deformation could also be attributed to the lamellar dilution of rod-like particles [33] or to randomness in the nanostructure at different scales.…”

“…It is well established that the swelling of PFSA membranes is non-affine. For example, the microscopic swelling strain (defined as the inter-cluster distance) is much larger than the macroscopic swelling strain (which is related to the water content of the membrane) [11,[18][19][20][21]29,[33][34][35]. In this study, since we assume that the volume is nearly filled by close-packed RVEs of the same size, the inter-cluster distance is the outer diameter of the RVEs, 2b.…”

“…These water-filled hydrophilic domains are separated from the hydrophobic polymer matrix resulting in a two-phase nanostructure as observed through a vast number of scattering experiments [9,[20][21][22][23][24][25][34][35][36][37]. Upon water uptake, 3 water molecules initially ionize the SO 3 groups and remain bound to them.…”

“…Consequently, the magnitude of the strain of the individual water-filled nano-domains is higher than that of the overall macroscopic swelling strain of the material. This relationship is referred to as non-affine deformation and has been shown to occur for PFSA membranes by a number of studies in literature [11,[18][19][20][21][22]29,[33][34][35]. Despite the growing body of literature on the sorption behavior [7,8,10,24,34,35,38,40,[44][45][46][47][48][49][50] and nano-structural modeling and characterization [11,13,[17][18][19][20][21][22]28,29,31,[33][34][35][36]39,49,51,52] of PFSA ionomers, the relationship between the water uptake and nanostructure, temperature, mechanical properties and membrane pretreatment is not well established.…”