Measuring the thermal conductivity of hydrogels with a bidirectional 3ω method

Hydrogels are soft, water-absorbing polymer materials with diverse applications in biomedicine and agriculture. Recently, hydrogels have been proposed to encapsulate water-soluble phase change materials that store energy in their latent heat of solidification. In these applications, the thermal conductivity of these materials affects their performance. Few methods exist for measuring the thermal conductivity of small quantities of hydrogels. Here, we describe an implementation of the bidirectional 3ω technique to measure the thermal conductivity of hydrogels with particular attention to their moisture content. Our implementation of the technique can probe sample volumes as little as ∼20 μl and yields the thermal conductivity without requiring fitting of additional thermal parameters. We numerically simulate 3ω sensor designs with frequency-domain 3-D models to quantify and reduce errors introduced by the choice of substrate and insulation layer thickness. Frequencies in the ∼1-20 Hz range yield less error for the materials considered here. We verify our setup with measurements on water and report values for polyacrylamide and poly(2-acrylamido-2-methylpropane sulfonic acid) (PAMPS) hydrogels. Our swollen hydrogels exhibited thermal conductivities nearly equivalent to water, 0.6 W m-1 K-1, and we estimate thermal conductivities of 0.43 and 0.42 W m-1 K-1 for neat polyacrylamide and PAMPS, respectively. Finally, we estimate an error of ±7%, consistent with other 3ω methods, with the largest error coming from the sensor calibration. We find that our implementation of the bidirectional 3ω method gives reasonable results and can be employed for prototyping soft materials relevant to thermal storage.