{'fraction_non_alphanumeric': 0.027210884353741496, 'fraction_numerical': 0.016439909297052153, 'mean_word_length': 5.044520547945205, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Physical basis for the formation and stability of silica nanoparticles in basic solutions of monovalent cations.

The colloidal stability, phase behavior, and solubility of silica nanoparticles (3-10 nm) that are formed in basic solutions of monovalent cations (primarily tetrapropylammonium) are investigated using a combination of chemical equilibria and electrostatic models. The free-energy gain associated with the formation of an electric double layer surrounding the nanoparticle was obtained by solving the Poisson-Boltzmann equation. This free energy is an important contribution to the total free energy of the particle and is second only to the formation of Si-O-Si bonds. The free energy of formation of the nanoparticles becomes increasingly negative with an increase in particle size and density, which explains the lower solubility of nanoparticles compared to that of amorphous silica. There is a minimum in the free energy of condensation as a function of size that qualitatively explains why the formation of small particles with a uniform size (<5 nm) is energetically favorable. The electrostatic models provide an estimate for the nanoparticle surface potential, which is significantly higher (-120 to -170 mV) than that of zeolite silicalite-1 (-60 to -80 mV) prepared in similar solutions. This result explains the stability of such small particles in solution. It is also shown that a condensation model that is based on silica solubility can describe the phase diagram for nanoparticle formation reported by Fedeyko et al. (J. Phys. Chem. B 2004, 108, 12271) over a wide range of pH and, in conjunction with a complexation model, provides an approximate equilibrium constant (pKa = 8.4) for the dissociation of nanoparticle silanol groups.