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Facilitated transport membranes (FTMs) constitute an emerging class of polymer materials with promising properties for carbon capture applications. The key feature of these membranes is the presence of chemical groups which, in the presence of water, engage in a reaction with dissolved carbon dioxide, thus enhancing the permeability and selectivity of the membrane. Currently, little is known about the organization of these membranes on a molecular level, reaction mechanisms and detailed chemical balance, transport of water, ion species and dissolved gas molecules. The nature of the actual facilitation mechanism and the factors responsible for this effect remain unclear. Here, we use a case of polyvinylamine (PVAm), one of the most studied fixed carrier material for FTMs, to propose molecular models of the hydrated polymers. We aim to understand how transport of water is governed by structural properties of the membrane, such as the free volume, pore limiting diameter, and degree of protonation. We observe that even at the highest experimentally used hydration level, the mobility of water in PVAm matrices is significantly lower than that in bulk water; unlike in bulk systems, chloride ions exhibit much slower diffusion in confined water; this, in turn, affects the diffusion of water, which also diminishes in the presence of chloride ions.