Temperature-Dependent Protonic Exchange Affects Blue Energy Generation in Soft Nanochannels

Nanofluidic blue energy harvesting, based on salinity gradients, is strongly governed by ion selectivity and electrochemical coupling at the nanoscale. In this study, a comprehensive numerical framework is developed to investigate electrical energy generation, driven by coupled salinity and temperature gradients in a pH-sensitive polyelectrolyte layer (PEL) grafted nanochannel. The model incorporates temperature-dependent PEL ionization constants, ion partitioning effect arising from permittivity contrast, coupled electrothermal-ionic transport, and Soret-type thermo-diffusion effects. The modeling framework consisting of Poisson-Nernst-Planck (PNP) and energy equations has been solved using a finite-element approach and validated against established theoretical and experimental results. The numerical model is also validated against steady-state PNP solutions based on the classical nanochannel model. Results reveal that temperature-dependent PEL ionization critically regulates the space charge density and local pH distribution within the nanochannel. It is seen that increasing the right reservoir temperature (T_right) reduces the effective ionization strength of PEL functional groups. Besides, increasing local temperature shifts the neutral pH, at which the space charge density is zero, toward more acidic local conditions. It is shown that the ion partitioning effect induces a basic PEL region and an acidic core due to proton migration driven by Born energy differences. These coupled effects enhance cationic transport while suppressing anionic current at higher right reservoir pH (pH_R), resulting in strong cation selectivity with transference numbers exceeding 0.5. The diffusion potential follows the trend in the transference number and is strongly dependent on pH_R while it is mildly influenced by T_right. The enhanced ionic current consequently leads to a significant increase in the maximum pore power and power density with increasing pH_R and T_right. Notably, the power density exceeds 5 W m^-2 and the energy conversion efficiency, relative to the Gibbs free energy of mixing, surpasses 30% at alkaline pH_R, highlighting the potential of PEL-modified nanochannels for efficient blue energy harvesting.