I found an article that might be helpful. The article is titled "Synthesis and Characterizations of Silica Nanoparticles by a New Sol-Gel Method" by Reza Fazaeli et al. (Synthesis and Characterizations of Silica Nanoparticles by a New Sol .... can be found in researchgate or on sciencedirect) . The article describes the synthesis of silica nanoparticles by chemical methods from tetraethylorthosilicate (TEOS), polyethylene glycol 5% and hydrochloric acid 0.001 N. The sol-gel process was applied for the preparation of nano silica gel. This method is hydrolysis and condensation reactions of TEOS as precursor of silica.
The article doesn't mention the exact diameter of the nanoparticles synthesized but it does mention that the size distribution was narrow.
I hope this helps!
Source:
(1) Synthesis and Characterizations of Silica Nanoparticles by a New Sol .... https://www.researchgate.net/profile/Reza-Fazaeli-2/publication/234026406_Synthesis_and_Characterizations_of_Silica_Nanoparticles_by_aNew_Sol-Gel_Method/links/02bfe50e5cd48e890f000000/Synthesis-and-Characterizations-of-Silica-Nanoparticles-by-a-New-Sol-Gel-Method.pdf.
(2) A novel method for synthesis of silica nanoparticles. https://www.sciencedirect.com/science/article/pii/S0021979705001566.
(3) Synthesis and Characterizations of Silica Nanoparticles by a New Sol .... https://www.researchgate.net/publication/234026406_Synthesis_and_Characterizations_of_Silica_Nanoparticles_by_aNew_Sol-Gel_Method.
(4) Synthesis and Characterization of SiO2 Nanoparticles via Sol-gel Method .... https://www.sciencedirect.com/science/article/pii/S2214785315003430.
(5) Full article: A facile approach to synthesis of silica nanoparticles .... https://www.tandfonline.com/doi/full/10.1080/21870764.2021.1911057.