Why usually to obtain a sol using titanium isopropoxide ratio of alkoxide to water take 1/1? Indeed, in this case, only one alkoxide group is hydrolyzed
Some quick googling gave me a link to DOI 10.1007/s10971-009-2121-0, which tells that "in the case of titania, titanium clusters (polyoxoalcoxides) have been suggested to serve as the primary building blocks for particles and gels. In particularly Ti11O13(OC3H7)18 has been proposed as a building block in titanium isopropoxide (TTIP) based sol–gel processes based on results from 17O NMR spectroscopy. A stable solution of these clusters can be obtained by hydrolysis of TTIP under low hydrolysis ratios (h1.5 hydrolysis of TTIP does not result in a stable solution of polyalkoxides but results in precipitation of titanium dioxide particles." Probably, this article and references therein can be a good starting point to answer this question.
Convey my greetings to the solid state chemistry department;)
About this "sol" I would like to say it is not visible by laser diffraction, there is no opalescence. It is rather the oligomer ideal solution. However all called it "sol"
Like Missyul answered lower amount of water reduces the rate of hydrolysis and there by condensation preventing precipitation, but protocols using very high water ratios with a chelating agent yields highly stable particulate sols. One of the recipes we have used extensively, you can find it here Chem. Mater., 2002, 14 (7), pp 2876–2881, use 1:100 precursor to water.