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This research article will describe the design and use of polyelectrolyte hydrogel particles as internal curing agents in concrete and present new results on relevant hydrogel-ion interactions. When incorporated into concrete, hydrogel particles release their stored water to fuel the curing reaction, resulting in reduced volumetric shrinkage and cracking and thus increasing concrete service life. The hydrogel's swelling performance and mechanical properties are strongly sensitive to multivalent cations that are naturally present in concrete mixtures, including calcium and aluminum. Model poly(acrylic acid(AA)-acrylamide(AM))-based hydrogel particles with different chemical compositions (AA:AM monomer ratio) were synthesized and immersed in sodium, calcium, and aluminum salt solutions. The presence of multivalent cations resulted in decreased swelling capacity and altered swelling kinetics to the point where some hydrogel compositions displayed rapid deswelling behavior and the formation of a mechanically stiff shell. Interestingly, when incorporated into mortar, hydrogel particles reduced mixture shrinkage while encouraging the formation of specific inorganic phases (calcium hydroxide and calcium silicate hydrate) within the void space previously occupied by the swollen particle.

We obtain an expression for the second derivative of the line in a PT diagram denoting a first-order phase transition for a pure hydrostatic system. Our result goes beyond the classical Clausius–Clapeyron equation, which provides only the first derivative of the pressure with respect to the temperature along the transition line. We present two pedagogical derivations suitable for an undergraduate thermodynamics class; the first one uses derivatives of the entropy while the second one uses derivatives of the enthalpy. The final expression for the second derivative involves only standard thermodynamic quantities such as the specific heats, the isothermal compressibilities, and the coefficients of thermal expansion of the two phases at the transition line. As an illustration, we compute the second derivatives of the freezing and vaporization lines of water at atmospheric pressure, and show that at this pressure the freezing line is concave down (negative second derivative) while the vaporization line is concave up (positive second derivative).