Water sorption and swelling

Considering the final product (e.g., paper), the moisture content in the surrounded air in fibers, thus, has significant infiuence on the strength properties of the product (Fig. 2.8). As a result, all tests of paper strength properties must be carried out under standard, constant air conditions (i.e., temperature 23°C, RH 50%). 

Changes of tensile index of different paper grades vs. relative air humidity. 0%—initial tensile index value measured under standard conditions [51], 

Another characteristic feature of cellulose-water interactions is the fact, that, depending on the moisture level, the properties of water associated with the cellulose can differ from those known under normal conditions. This phenomenon has a great technological meaning (e.g., pressing and drying efficiency). For this purpose, water in cellulose fibers is classified according to its properties and usually three main types of water are discerned (Fig. 2.9)  

Free water is located inside the lumen, large pores and between fibers in papermaking pulps. This water is kept by surface tension forces. This water can be removed using pressing operation, vacuum suction, or centrifugation. Freezing bound water is located in 

Total amount of water in fibrous materials can be easily measured by use of gravimetric methods. There are also several methods that allow the measurement of the amount of total bound water, such as water retention value (WRV], fiber saturation point (FSC], and differential scanning calorimetry (DSC]. 

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Although there is no bulk liquid with which adsorbed cations can be exchanged in the experiments made in atmospheres of controlled relative humidity, successive experiments can be made with different adsorbed cation populations, and it is found that the succession of dehydration steps varies with size and hydration energy of the cation (Posner and Quirk, 1964). There is also a dependence upon the type and extent of substitution in the aluminosilicate framework White (1958), for example, observed that two montmorillonites with the same cation-exchange capacity, loaded with the same cation, may have different water sorption and swelling properties. 

To build a model of water sorption and swelling in PEMs, three microscopic equilibrium conditions of water must be accounted for in the PEM and the adjacent medium. The global equilibrium state corresponds to the minimum of the appropriate thermodynamic free energy, in this case the Gibbs energy. 

The insensitivity of water sorption and swelling to P should not be seen as an argument for neglecting pressure driven flux mechanisms in models of PEM... 

The theory of bundle formation in the section Aggregation Prenomena in Solutions of Charged Polymers provides sizes, as well as electrostatic and elastic properties of ionomer bundles. The theory of water sorption and swelling, described in this section, gives a statistical distribution of pore size and local stress in pores. The merging point of both theories is a theory of fracture formation in charged polymer... 

In general, pores swell nonuniformly, as seen in the section Water Sorption and Swelling of PEMs. As a simplification, the random network was assumed to consist of two types of pores. Nonswollen or dry pores (referred to as red pores) permit only a small residual conductance resulting from tightly bound surface water. Swollen or wet pores (referred to as blue pores) contain extra water with high bulklike conductance. Water uptake corresponds to the swelling of wet pores and to the increase of their relative fraction. In this model, proton transport in the PEM is mapped as a percolation problem, wherein randomly distributed sites represent pores of variable size and conductance. The distinction of red and blue pores accounts for variations of proton transport properties due to different water environments at the microscopic scale, as discussed in the section Water in PEMs Classification Schemes. ... 

Water Sorption and Swelling in Response to External Conditions... 

Membrane structure and external conditions determine water sorption and swelling. The resulting water distribution determines transport properties and operation. Water sorption and swelling are central in rationalizing physical properties and electrochemical performance of the PEM. The key variable that determines the thermodynamic state of the membrane is the water content k. The equilibrium water content depends on the balance of capillary, osmotic, and electrostatic forces. Relevant external conditions include the temperature, relative humidity, and pressure in adjacent reservoirs of liquid water or vapor. The theoretical challenge is to establish the equation of state of the PEM that relates these conditions to A.. A consistent treatment of water sorption phenomena, presented in the section A Model of Water Sorption, revokes many of the contentious issues in understanding PEM structure and function. 

The water content is the state variable of PEMs. Water uptake from a vapor or liquid water reservoir results in a characteristic vapor sorption isotherm. This isotherm can be described theoretically under a premise that the mechanism of water uptake is sufficiently understood. The main assumption is a distinction between surface water and bulk water. The former is chemisorbed at pore walls and it strongly interacts with sulfonate anions. Weakly bound bulk-like water equilibrates with the nanoporous PEM through the interplay of capillary, osmotic, and elastic forces, as discussed in the section Water Sorption and Swelling of PEMs in Chapter 2. Given the amounts and random distribution of water, effective transport properties of the PEM can be calculated. Applicable approaches in theory and simulation are rooted in the theory of random heterogeneous media. They involve, for instance, effective medium theory, percolation theory, or random network simulations. 

Eikerling, M. and Berg, P. 2011. Poroelectroelastic theory of water sorption and swelling in polymer electrolyte membranes. 7(13), 5976-5990. 

In membrane research, Michael has developed a poroelectroelastic theory of water sorption and swelling together with Peter Berg (NTNU Trondheim). It rationalizes the impact of external conditions, statistical distribution of anionic head groups, and microscopic elastic properties of the polymer on water sorption and swelling. This work has opened up an intriguing research area the study of internal mechanical stresses in charged elastic media, induced by water sorption. 

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