The Importance of the Mixing Energy in Ionized Superabsorbent Polymer Swelling Models

Abstract

The Flory-Rehner theoretical description of the free energy in a hydrogel swelling model can be broken into two swelling components: the mixing energy and the ionic energy. Conventionally for ionized gels, the ionic energy is characterized as the main contributor to swelling and, therefore, the mixing energy is assumed negligible. However, this assumption is made at the equilibrium state and ignores the dynamics of gel swelling. Here, the influence of the mixing energy on swelling ionized gels is quantified through numerical simulations on sodium polyacrylate using a Mixed Hybrid Finite Element Method. For univalent and divalent solutions, at initial porosities greater than 0.90, the contribution of the mixing energy is negligible. However, at initial porosities less than 0.90, the total swelling pressure is significantly influenced by the mixing energy. Therefore, both ionic and mixing energies are required for the modeling of sodium polyacrylate ionized gel swelling. The numerical model results are in good agreement with the analytical solution as well as experimental swelling tests.

Effect of the Cross-Linking Density on the Swelling and Rheological Behavior of Ester-Bridged β-Cyclodextrin Nanosponges

“…The equilibrium is reached when the opposing entropies are balanced, as extensively studied in the literature [67,[70][71][72]. According to the Flory-Rehner theory, the attraction of the water molecules by the hydrophilic polymer chains is described by the mixing energy, specifically the first three terms of Equation ( 10) ln(1−υ 2,m ), υ 2,m and χυ 2 2,m [73]. Meanwhile, the last term…”

Synthesis, classification and properties of hydrogels: their applications in drug delivery and agriculture

“…, in the completely swollen state), the Poisson's ratio relies on the deformation of the gel state, and the polymer network of the hydrogel becomes completely compressible, while in the dry state, the hydrogel network becomes incompressible. 46,47 So, depending on the amount of water and the polymer fraction, it is useful to identify its swelling capacity and mechanical properties. The second aspect is the average molecular weight between the crosslinks which is used to define the density of crosslinking, and the third aspect is the measure of the distance between the crosslinks which provides the mesh size in the hydrogel.…”

Expansion Microscopy: Super-Resolution Imaging with Hydrogels

“…Mixing swelling pressure (π mixing ) can be summarized as the free energy inherent in mixing polymer chains with molecules dissolved within the gel network, which can exert osmotic pressure . The mixing swelling pressure (π mixing ) also describes the attraction of hydrophilic polymer chains exerted on the H 2 O molecules in solution, causing influx into the polymer matrixand thereby swelling . A gel formed from a higher concentration of monomers, i.e., a denser gel, is thus generally expected to exert a higher mixing swelling pressure (π mixing ). , However, denser gels may be less elastic, which could counterbalance the effect by changing the elastic swelling pressure (π elastic ; see below).…”