Theory of Charged Gels: Swelling, Elasticity, and Dynamics

The fundamental attributes of charged hydrogels containing predominantly water and controllable amounts of low molar mass electrolytes are of tremendous significance in biological context and applications in healthcare. However, a rigorous theoretical formulation of gel behavior continues to be a challenge due to the presence of multiple length and time scales in the system which operate simultaneously. Furthermore, chain connectivity, the electrostatic interaction, and the hydrodynamic interaction all lead to long-range interactions. In spite of these complications, considerable progress has been achieved over the past several decades in generating theories of variable complexity. The present review presents an analytically tractable theory by accounting for correlations emerging from topological, electrostatic, and hydrodynamic interactions. Closed-form formulas are derived for charged hydrogels to describe their swelling equilibrium, elastic moduli, and the relationship between microscopic properties such as gel diffusion and macroscopic properties such as elasticity. In addition, electrostatic coupling between charged moieties and their ion clouds, which significantly modifies the elastic diffusion coefficient of gels, and various scaling laws are presented. The theoretical formulas summarized here are useful to adequately capture the essentials of the physics of charged gels and to design new hydrogels with specified elastic and dynamical properties.

Experimental Verification of the Balance between Elastic Pressure and Ionic Osmotic Pressure of Highly Swollen Charged Gels

The equilibrium swelling degree of a highly swollen charged gel has been thought to be determined by the balance between its elastic pressure and ionic osmotic pressure. However, the full experimental verification of this balance has not previously been conducted. In this study, we verified the balance between the elastic pressure and ionic osmotic pressure of charged gels using purely experimental methods. We used tetra-PEG gels created using the molecular stent method (St-tetra-PEG gels) as the highly swollen charged gels to precisely and separately control their network structure and charge density. The elastic pressure of the gels was measured through the indentation test, whereas the ionic osmotic pressure was determined by electric potential measurement without any strong assumptions or fittings. We confirmed that the two experimentally determined pressures of the St-tetra-PEG gels were well balanced at their swelling equilibrium, suggesting the validity of the aforementioned relationship. Furthermore, from single-strand level analysis, we investigated the structural requirements of the highly swollen charged gels in which the elasticity and ionic osmosis are balanced at their swelling equilibrium.

Effect of Nonlinear Elasticity on the Swelling Behaviors of Highly Swollen Polyelectrolyte Gels

Polyelectrolyte gels exhibit swelling behaviors that are dependent on the external environment. The swelling behaviors of highly charged polyelectrolyte gels can be well explained using the Flory–Rehner model combined with the Gibbs–Donnan effect and Manning’s counterion condensation effect (the FRGDM model). This study investigated the swelling properties of a series of model polyelectrolyte gels, namely tetra-polyacrylic acid-polyethylene glycol gels (Tetra-PAA-PEG gels), and determined the applicability of the FRGDM model. The swelling ratio (Vs/V0) was well reproduced by the FRGDM model in the moderate swelling regime (Vs/V0 < 10). However, in the high swelling regime (Vs/V0 > 10), the FRGDM model is approx. 1.6 times larger than the experimental results. When we introduced the finite extensibility to the elastic free energy in the FRGDM model, the swelling behavior was successfully reproduced even in the high swelling regime. Our results reveal that finite extensibility is one of the factors determining the swelling equilibrium of highly charged polyelectrolyte gels. The modified FRGDM model reproduces well the swelling behavior of a wide range of polyelectrolyte gels.

Investigation of the Effects of Different Hydrophilic and Hydrophobic Comonomers on the Volume Phase Transition Temperatures and Thermal Properties of N-Isopropylacrylamide-Based Hydrogels

In this work, a series of thermally responsive terpolymers of N-isopropylacrylamide (NIPA) with three different comonomer contents was synthesized, and their swelling behaviour was studied as a function of composition and temperature. Temperature-sensitive, random cross-linked terpolymers of NIPA were prepared from methyl methacrylate (MMA), N-tert-butylacrylamide (NTBA), and acrylic acid (AA) using a free radical polymerization method. In the synthesis of terpolymer hydrogels, N,N-methylene bisacrylamide (BIS) was used as cross-linkers and ammonium persulfate (APS) as initiator. The NIPA content of the monomer feed varied from 80 to 50 mol %, and other comonomer feed varied from 40 to 5 mol %. The swelling equilibrium of these hydrogels was studied as a function of temperature and hydrophobic and hydrophilic comonomer contents. The swelling properties of the polymers were investigated in pure water at temperatures from 10 to 80°C. All of the synthesized gels were found to be sensitive to temperature. Glass transition temperature analyses and thermal analyses of the synthesized hydrogels were studied. The volume phase transition temperature and the swelling equilibrium (r) values of NIPA-based hydrogels synthesized in different feed ratios and in varying monomer contents were found in the range of 17–52°C and 14–51 g H2O/g polymer, respectively. The glass temperature (Tg) of the NIPA/AA/(MMA or NTBA) hydrogels synthesized with feed ratios of 50/40/10 was found to be 133 or 142°C, respectively. The initial and the end degradation that were determined for hydrogels at high temperatures indicated the quite good thermal stability of hydrogels. When the mass loss of the synthesized hydrogels was 50%, the temperatures were measured between 247 and 258°C.

The evaluation of temperature and pH influences on equilibrium swelling of poly(n-isopropylacrylamide-co-acrylic acid) hydrogels

Hydrogels are synthesized by the method of radical polymerization of monomers: N-isopropylacrylamide (NIPAM) and acrylic acid (AA). Characterization of poly(N-isopropylacrylamide- co-acrylic acid) hydrogels, p(NIPAM/AA), has been performed by Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD) and by determination of the swelling behaviour in aqueous solutions at different temperatures (25, 31 and 37?C) and pH values (2.2, 4.5, 6 and 6.8). After lyophilisation in the solution at pH 6 and temperature of 25?C, p(NIPAM/AA) hydrogels have rapidly reached equilibrium degree of swelling, ?e, in comparison to non-lyophilized samples. The mechanism of solvent transport within matrix in lyophilized samples corresponds to less Fickian diffusion, whereas Super case II diffusion is characteristic for non-lyophilized samples. p(NIPAM/AA) hydrogel with 1.5 mol% of ethylene glycol dimethacrylate (EGDM) at the temperature of 25?C and pH 6.8, has reached the highest swelling equilibrium degree, ?e = 259.8. The results of swelling studies have shown that p(NIPAM/AA) hydrogels can be classified as superabsorbent polymers (SAPs). For the evaluation of pH and temperature influences on synthesized hydrogels swelling, a full three-level experimental design has been used. Two-factor interaction model (2FI) is the most optimal model of a full three-level experimental design for representing the swelling equilibrium degree of p(NIPAM/AA) hydrogels as a function of investigated parameters, i.e., temperature and pH.

Influence of process parameters on property of PP/EPDM blends prepared by a novel vane extruder

In this study, thermoplastic elastomers based on polypropylene (PP) and ethylene-propylene-diene terpolymer (EPDM) were prepared via direct melt blending in a novel vane extruder. The influence of processing temperature and rotor speed on the degree of cross-linking of the EPDM phase, the tensile properties, the melting behavior and the crystallization morphology of PP/EPDM blends was investigated. It was observed that the volume fraction (Vr) of the vulcanizate arriving swelling equilibrium reached the maximum value when the processing temperature was 190°C. The tensile properties showed better performance at 195°C, at which the PP/EPDM blend obtained good dispersive mixing performance. Moreover, the Vr of the vulcanizate arriving swelling equilibrium reached the maximum value when the rotor speed was 60 rpm, at which the dispersive mixing performance and tensile properties of the PP/EPDM blend were better.