Size and roughness dependent temperature effects on surface charge of silica nanoparticles

Silica nanoparticles (SNP) with different sizes and surface areas are used in numerous micro/nanofluidic applications, while their surface charge properties play a major role in their function. In many of these applications, SNPs also undergo temperature variation. We present that an increase in temperature yields a substantial increase in SNP surface charge depending on nanoparticle size and surface roughness, which cannot be estimated by existing theory. As a continuation of our earlier work characterizing the deviation of SNP surface charging from theoretical predictions due to curvature and EDL overlap effects, this study presents the differentiation from the theory in temperature dependence under various conditions. As we calculate surface chemistry as a function of local ionic conditions (Charge Regulation), temperature variation changed the equilibrium constants of protonation/deprotonation reactions of the SNP surface, in addition to changes occurring in relative permittivity and ionic mobilities. Results show that variation of SNP surface charge by temperature decreases by decreasing particle size and/or increasing roughness size, compare to theoretical flat plate calculations considering similar temperature-dependent properties and charge regulation on the surface. We characterized these deviations by obtaining an "electrokinetic similarity" between different systems of various size and roughness at various ionic conditions based on the non-dimensional groups of lambda/DP and lambda/DR. Based on these, we devised a phenomenological model as an extension to the flat plate theory to successfully predict the surface charge of SNPs as a function of the particle size, roughness size, and temperature. The current findings are important for the characterization of SNPs through temperature variations and can also be used to adjust the surface charge of SNPs by tuning the temperature.