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Dissociative adsorption onto a surface introduces dynamic correlations between neighboring sites not found in non-dissociative absorption. We study surface coverage dynamics where reversible dissociative adsorption of dimers occurs on a finite linear lattice. We derive analytic expressions for the equilibrium surface coverage as a function of the number of reactive sites, N, and the ratio of the adsorption and desorption rates. Using these results, we characterize the finite size effect on the equilibrium surface coverage. For comparable N's, the finite size effect is significantly larger when N is even than when N is odd. Moreover, as N increases, the size effect decays more slowly in the even case than in the odd case. The finite-size effect becomes significant when adsorption and desorption rates are considerably different. These finite-size effects are related to the number of accessible configurations in a finite system where the odd-even dependence arises from the limited number of accessible configurations in the even case. We confirm our analytical results with kinetic Monte Carlo simulations. We also analyze the surface-diffusion case where adsorbed atoms can hop into neighboring sites. As expected, the odd-even dependence disappears because more configurations are accessible in the even case due to surface diffusion.

We investigate the dynamics and themechanism of flame retardantsin polycarbonate matrixes to explore for a way of designing efficientand environment-friendly flame retardants. The high phosphorus contentof organic phosphates has been considered as a requirement for efficientflame retardants. We show, however, that one can enhance the efficiencyof flame retardants even with a relatively low phosphorus contentby tuning the dynamics and the intermolecular interactions of flameretardants. This would enable one to design bulkier flame retardantsthat should be less volatile and less harmful in indoor environments.UL94 flammability tests indicate that even though the phosphorus contentof 2,4-di-tert-butylphenyl diphenyl phosphate (DDP)is much smaller with two bulky tertiary butyl groups than that oftriphenyl phosphate (TPP), DDP should be as efficient of a flame retardantas TPP, which is a widely used flame retardant. On the other hand,the 2-tert-butylphenyl diphenyl phosphate (2-tBuDP), with a lower phosphorus content than TPP but witha greater phosphorus content than DDP, is less efficient as a flameretardant than both DDP and TPP. Dynamic secondary ion mass spectrometryand molecular dynamics simulations reveal that the diffusion of DDPis slower by an order of magnitude at low temperature than that ofTPP but becomes comparable to that of TPP at the ignition temperature.This implies that DDP should be much less volatile than TPP at lowtemperature, which is confirmed by thermogravimetric analysis. Wealso find from Fourier transform infrared spectroscopy that Friesrearrangement and char formation are suppressed more by DDP than byTPP. The low volatility and the suppressed char formation of DDP suggestthat the enhanced flame retardancy of DDP should be attributed toits slow diffusivity at room temperature and yet sufficiently highdiffusivity at high temperature. [ABSTRACT FROM AUTHOR]