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■Bio-mathematics, Statistics and Nano-Technologies: Mosquito Control Strategies

Figure 14.1: Schematic representation of acid (a) and base (b) catalyzed hydrolysis of

silane precursors.

pentacoordinated transition state in both acid and basic catalyzed systems (Scheme 14.1.a

and 14.1.b , respectively) (Danks et al. 2016, Gonzalez et al. 2019).

Depending on the conditions and the Si/H2O ratio, more than one alkoxyl group can

be hydrolyzed. The speed of each hydrolysis phase relies on the stability of the transition

state, which in turn depends on the relative electron withdrawal or donation power of the

-OH versus -OR groups. The result is that subsequent hydrolysis phases become progres-

sively slower under acidic conditions and faster under alkaline conditions. The condensa-

tion depends on the degree of hydrolysis that has already occurred because a silanol group

is required on at least one silicon center and is also catalyzed by acids or bases (Scheme

14.2.a and 14.2.b, respectively) with the formation of siloxane/methaloxanic bonds.

If the hydrolysis is complete before the first condensation phase occurs, the result-

ing product (OH)3Si-O-Si(OH)3 has 6 sites for the subsequent condensation phases in an

alkaline environment. Multiple condensation phases give rise to small, highly branched ag-

glomerates in the sol step, which eventually cross-link to form a colloidal gel. Under acidic

conditions, where the first hydrolysis phase is typically the fastest, condensation begins be-

fore the hydrolysis is complete. Condensation often occurs on terminal silanols, resulting

in chain-like structures in the sol and mesh gel. The consequences for the gel morphology

are represented in Figure 14.1 (Danks et al. 2016).

Figure 14.2: Schematic representation of acid (a) and base (b) catalyzed condensation re-

actions of hydrolyzed silane precursors.