Kinetics of ordering

Additional isothermal treatments at neighbouring temperatures small step annealing) yield plateau values of resistivity corresponding to equilibrium values at certain temperatures which reflect the order parameter in thermal equilibrium as a function of temperature ( equilibrium curve , curve 4 in Figure 1). This study can be used for an analysis of the kinetics of order-order relaxations (see Figure 3 below). 

R. Kozubski and W. Pfeiler, Atomistic image of the kinetics of order-order reactions in Ni3Al+B,... 

Comparison of the segregated-flow and maximum-mixedness models, with identical RTD functions, shows that the former gives better performance. This is consistent with the observations of Zwietering (1959), who showed that for power-law kinetics of order n > 1, the segregated-flow model produces the highest conversion. 

Show that the tabulated observations conform to kinetics of order 1.5,... 

F. Lancon and J. Viliam, in Kinetics of Ordering and Growth at Surfaces, M. J. Legally... 

In the literature on intracrystalline reactions, another formulation, which is more general than that shown in Table 2-1, has been advanced to treat the kinetics of order-disorder reactions (Mueller, 1969 Ganguly, 1982). The method is outlined below to help readers follow the literature. Those who are not interested in such details may jump to Section 2.1.5. 

Ganguly s treatment of the kinetics of order-disorder reactions... 

The kinetics of ordering in block copolymer melts have been studied using cell dynamics simulations of the TDGL equation (Bahiana and Oono 1990 Chakrabarti et al. 1991 Puri and Oono 1988 Qi and Wang 1996, 1997 Shiwa et al. 1996). Here, the time evolution of the order parameter ip is followed ... 

It is useful to begin with an extremely simple example. Suppose one has a mixture with only two reactants, Aj and A2, both of which react irreversibly with first-order kinetics. A semilog plot of c, (/ = 1,2) versus time (see Fig. 1) would be linear for both reactants. However, suppose that for some reason one is able to measure only the overall concentration Cj + C2 this is also plotted in Fig. 1. the curve is nonlinear, and it seems to indicate an overall kinetics of order larger than unit. This shows that the overall behavior of the mixture is qualitatively different... 

Pigs. 18 and 21). As in the case of Ni0(200°), the initial total order is close to zero when NiO(250°) is used as a catalyst and the reaction rate on the fresh sample decreases with time according to the kinetics of order one (74). Kinetics of order one are not followed, however, on regenerated catalysts. Reaction orders were determined in this case by the differential method and were found to vary from 1 (fresh catalyst) to 0.77 (constant activity). Since the initial total order is, in all cases, zero, it was concluded that, as in the case of the same reaction on NiO(200°), the reaction order with respect to time is apparent and results from the inhibition of the catalyst by carbon dioxide, the reaction product. Modification of the apparent order with the runs indicates that regenerated samples of Ni0(250°) are less inhibited than the fresh catalyst. 

Fig. 3. Computer simulation results using a time-dependent Ginzburg-Landau approach, showing the microstructural evolution after a temperature jump from the lamellar phase to the hexagonal cylinder phase for a moderately asymmetric diblock copolymer. The time units are arbitrary. (Reprinted with permission from Polymer 39, S. Y. Qi and Z.-G. Zheng, Weakly segregated block copolymers Anisotropic fluctuations and kinetics of order-order and order-disorder transitions, 4639-4648, copyright 1998, with permission of Excerpta Medica Inc.)...

The theoretical methods to investigate the evolution kinetics of ordered microdomain structures are those in the atomic-scale including molecular dynamics simulations, Monte Carlo simulations, dynamic SCFT, dynamic density functional theory (DDFT), and those in the meso-scale including dissipative particle dynamics (DPD) simulations, etc. More details of these approaches can be found in the literatures. 

The kinetics of ordering in solid solutions and even more so rate processes during phase transformations are both expermentally and theoretically very difficult subjects. Furthermore, in light of the previous discussion it is highly questionable whether order-disorder processes as they occur in simple glass forming (i.e., metal alloys) substances also take place in polymers. Nevertheless, attempts are being made to improve... 

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