13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- active agents [15-21]. The solvolysis of silicon dioxide with water and fatty alcohols has been studied broadly. In our wear tests, however, the driving frequency is high enough and it is believe that there is not sufficient time to form fully native oxide on tribo-surfaces. Hence the reaction substrate is determined to be silicon instead of silicon dioxide. To compare the solvolysis reactivity of different compounds, the activation energy Eb of reaction 1 2 1 2 2 1 1 2 - OR -OR | | Si Si H OR R OH | | Si Si + → ≡ − + ≡ − − (4) is calculated in the framework of the density functional theory where Si(111) cluster model Si7H16 is used (Fig. 6). The calculation is carried out with the Dmol3 software packaged in Material Studio v5.5, employing the BP functional and the DND basis set. Similar model is also used to calculate the hydrolysis barriers for SiO2(111) and (HO)3Si-O-Si(OH)3, which gives the same transient structures and reaction energies given by Gaussian [22]. The virtual reaction 3 16 6 3 15 6 O Si H | OH Si Si H H Si Si OH HO H Si − − ≡ = − ≡ → + ≡ − (5) is used to estimate the upper limit of Eb (149.7kJ/mol) for ROH compounds, where the H-H-H plane in HO-Si≡H3 is parallel to the Si(111) surface. Figure 6. The Si7H16 cluster model used in DFT calculation. H atoms are fully restricted. Besides the thermal-solvolysis there can be another way to graft carbon chains onto silicon atoms, which depends on the dangling bonds formed in the rubbing process. The friction force in dry nitrogen environment is only several times larger than that in above vapor conditions. Since almost all the driving work in dry nitrogen condition is consumed on the formation of silicon dangling bonds, it is supposed that dangling bonds still forms in vapor conditions. In this paper we ignore the dynamic details in the formation of dangling bonds and use the reaction Si OR Si H Si Si ROH 2 1 2 1 ≡ − + ≡ → ≡ − + • • + ≡ (6) to judge the reactivity of dangling bonds with different small molecules and define this reaction in terms of tribo-solvolysis. Two unsaturated Si atoms are used in this reaction to avoid odd number of electrons in DFT calculation. The distance from one Si atom to the other is set to be two times of equilibrium distance to contain the adsorbed small molecules. The energy of Si··Si is 351kJ/mol higher than Si-Si of equilibrium state and the energy change ΔE in Reaction (6) is used as the reactivity of tribo-solvolysis. Figure 7 shows the DFT calculation results of Eb and ΔE. Eb and ΔE at the reference point are 149.7kJ/mol and -351kJ/mol, respectively. The distance Δ from each compound to the reference
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