RESUMEN
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.
RESUMEN
The structure and the percolation behavior of the composite of carbon nanotubes (CNTs), CNT molecular junctions and polymers are studied using Monte Carlo (MC) simulations. We model a CNT as a rigid rod composed of hard spheres. "X" and "Y" molecular junctions of CNTs are constructed by joining four and three segments of CNTs, respectively. The model system consists of CNTs mixed with either "X" or "Y" molecular junctions. The system is equilibrated using Monte Carlo simulations and the equilibrated configurations are used to locate the clusters of connected molecules via a recursive algorithm. The fraction (P(perc)) of configurations with a percolating cluster is then estimated for a given total volume fraction (phi(t)) of molecules. When P(perc) reaches 0.5, phi(t) of the system is considered a percolation threshold concentration (phi(c)). The percolation behavior is found to be sensitive to the aspect ratio of CNTs and the concentration and the shape of molecular junctions. phi(c) is decreased with an increase in the aspect ratio of CNTs. As the mole fraction of molecular junctions is increased, phi(c) is decreased significantly, which suggests that molecular junctions could enhance the electric conductivity of CNT-polymer composites. X junctions are found to construct a percolating network more effectively than Y junctions. More interestingly, even though molecular junctions change the percolation behavior significantly, the site-site pair correlation functions of CNTs hardly show any difference as the mole fraction of molecular junctions is increased. This implies that the percolation of CNTs is determined by the subtle many-body correlation of CNTs that is not captured by the site-site pair correlation functions.
RESUMEN
We investigate the dynamics and the mechanism of flame retardants in polycarbonate matrixes to explore for a way of designing efficient and environment-friendly flame retardants. The high phosphorus content of organic phosphates has been considered as a requirement for efficient flame retardants. We show, however, that one can enhance the efficiency of flame retardants even with a relatively low phosphorus content by tuning the dynamics and the intermolecular interactions of flame retardants. This would enable one to design bulkier flame retardants that should be less volatile and less harmful in indoor environments. UL94 flammability tests indicate that even though the phosphorus content of 2,4-di-tert-butylphenyl diphenyl phosphate (DDP) is much smaller with two bulky tertiary butyl groups than that of triphenyl phosphate (TPP), DDP should be as efficient of a flame retardant as 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 with a greater phosphorus content than DDP, is less efficient as a flame retardant than both DDP and TPP. Dynamic secondary ion mass spectrometry and molecular dynamics simulations reveal that the diffusion of DDP is slower by an order of magnitude at low temperature than that of TPP but becomes comparable to that of TPP at the ignition temperature. This implies that DDP should be much less volatile than TPP at low temperature, which is confirmed by thermogravimetric analysis. We also find from Fourier transform infrared spectroscopy that Fries rearrangement and char formation are suppressed more by DDP than by TPP. The low volatility and the suppressed char formation of DDP suggest that the enhanced flame retardancy of DDP should be attributed to its slow diffusivity at room temperature and yet sufficiently high diffusivity at high temperature.