## A kinetic model of the formation of organic monolayers on hydrogen-terminated silicon by hydrosilation of alkenes

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### Abstract

We have analyzed a kinetic model for the formation of organic monolayers based on a previously suggested free radical chain mechanism for the reaction of unsaturated molecules with hydrogen-terminated silicon surfaces (Linford, M. R.; Fenter, P. M.; Chidsey, C. E. D. J. Am. Chem. Soc 1995, 117, 3145). A direct consequence of this mechanism is the nonexponential growth of the monolayer, and this has been observed spectroscopically. In the model, the initiation of silyl radicals on the surface is pseudo first order with rate constant, ki, and the rate of propagation is determined by the concentration of radicals and unreacted Si-H nearest neighbor sites with a rate constant, kp. This propagation step determines the rate at which the monolayer forms by addition of alkene molecules to form a track of molecules that constitute a self-avoiding random walk on the surface. The initiation step describes how frequently new random walks commence. A termination step by which the radicals are destroyed is also included. The solution of the kinetic equations yields the fraction of alkylated surface sites and the mean length of the random walks as a function of time. In meanfield approximation we show that (1) the average length of the random walk is proportional to (k p/ki)1/2, (2) the monolayer surface coverage grows exponentially only after an induction period, (3) the effective first-order rate constant describing the growth of the monolayer and the induction period (kt) is k = (2kikp)1/2, (4) at long times the effective first-order rate constant drops to ki, and (5) the overall activation energy for the growth kinetics is the mean of the activation energies for the initiation and propagation steps. Monte Carlo simulations of the mechanism produce qualitatively similar kinetic plots, but the mean random walk length (and effective rate constant) is overestimated by the mean field approximation and when kp ≫ ki, we find k ∼ ki0.7kp0.3 and E a = (0.7Ei, + 0.3Ep). However the most striking prediction of the Monte Carlo simulations is that at long times, t ≫ l/k, the effective first-order rate constant decreases to ki even in the absence of a chemical termination step. Experimental kinetic data for the reaction of undec-1-ene with hydrogen-terminated porous silicon under thermal reflux in toluene and ethylbenzene gave a value of k = 0.06 min -1 and an activation energy of 107 kJ mol-1. The activation energy is in reasonable agreement with density functional calculations of the transition state energies for the initiation and propagation steps. © 2005 American Chemical Society.

### Publication metadata

**Author(s): **Woods M, Carlsson S, Hong Q, Patole SN, Lie LH, Houlton A, Horrocks BR

**Publication type: **Article

**Publication status:** Published

**Journal: **Journal of Physical Chemistry B

**Year: **2005

**Volume: **109

**Issue: **50

**Pages: **24035-24045

**Print publication date: **22/12/2005

**ISSN (print): **1520-6106

**ISSN (electronic): **1520-5207

**Publisher: **American Chemical Society

**URL: **http://dx.doi.org/10.1021/jp052542e

**DOI: **10.1021/jp052542e

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