Externally governed hydrogel swelling is a highly convenient yet inherently challenging process, as it requires both responsive materials and appropriately tuned external stimuli. In this work, for the first time, the influence of simultaneous action of external physical fields—ultrasound (US) and microwave heating (MW), combined with cooling—on the isothermal swelling kinetics of poly(methacrylic acid) (PMAA) hydrogel was investigated and compared with swelling under conventional thermal heating (TH) under isothermal conditions. Swelling kinetics were monitored over a temperature range of 248–318 K, under simultaneous cooling with either US, MW, or TH. The well-established Peppas model was used to determine swelling kinetics parameters, revealing a significant acceleration in the swelling process under MW (up to 48.8 times at 313 K), as well as different water penetrating mechanisms (non-Fickian diffusion) compared to TH and US (Super-case II). Additionally, it was demonstrated that the swelling conversion curves could be mathematically described using a “shrinking boundary surfaces” model. Isothermal swelling constants and the corresponding kinetic parameters (activation energy E_a and pre-exponential factor ln A) were calculated. The results confirmed that external physical fields significantly influence the thermal activation and swelling behavior of PMAA xerogels, offering insight into field-responsive transport processes in hydrogel networks.

The kinetics of gas reaction $HOCl\underset{{k_r }}{\overset{{k_f }}{\longleftrightarrow}}H(^2 S) + OCl(X^2 \Pi _i )$ was analyzed by the MP4 method. In the temperature range of 100–373 K the rate constants k _f and k _r and equilibrium constant K were changed from 1.10 × 10⁻²²⁰ to 1.17 × 10⁻⁵² s⁻¹, from 2.89 × 10⁻¹⁶ to 1.68 × 10⁻⁵s⁻¹ and from 3.80 × 10⁻²⁰⁵ to 6.96 × 10⁻⁴⁸ respectively. In the above temperature range, the activation energy of the forward reaction (E _f) is 105.05 kcal/mol. In the same temperature interval there are two kinetic domains for the reverse reaction with activation energies (E _r1 = 5.53 kcal/mol when T is 100–273 K and E _r2 = 14.50 kcal/mol when T is 273–373 K, respectively.