Partly quenched systems

Sec. 4 is concerned with the development of the theory of inhomogeneous partly quenched systems. The theory involves the inhomogeneous, or second-order, replica OZ equations and the Born-Green-Yvon equation for the density profile of adsorbed fluid in disordered media. Some computer simulation results are also given. 

Concluding remarks include a summarizing discussion and an outline of possible future studies of partly quenched systems that are, in our opinion, of interest. 

By definition, an observable property of a partly quenched system,/pg, in the grand canonical ensemble is obtained as... 

To define the correlation functions of partly quenched systems requires one to consider fluctuations. There are two types of fluctuations thermal fluctuations for a given configuration of matrix species, and fluctuations induced by disorder. We characterize the average over disorder of thermal fluctuations by the variance... 

Finally, in this part of the work we would like to discuss to some extent practical tools to obtain thermodynamic properties of adsorbed fluids. We have mentioned above that the compressibility equation is the only simple recipe, for the moment, to obtain the thermodynamics of partly quenched simple fluids. The reason is that the virial equation is difficult to implement it has not been tested for partly quenched systems. Nevertheless, for the sake of completeness, we present the virial equation in the form [22,25]... 

However, we also need to discuss how the attractive interactions between species can be included in the theory of partly quenched systems. These interactions comprise an intrinsic feature of realistic models for partially quenched fluid systems. In particular, the model for adsorption of methane in xerosilica gel of Kaminsky and Monson [41] is characterized by very strong attraction between matrix obstacles and fluid species. Besides, the fluid particles attract each other via the Lennard-Lones potential. Both types of attraction (the fluid-matrix and fluid-fluid) must be included to gain profound insight into the phase transitions in partly quenched media. The approach of Ford and Glandt to obtain the chemical potential utilizing... 

HOMOGENEOUS, PARTLY QUENCHED SYSTEMS WITH SHORT-RANGE INTERACTIONS... 

The correlation functions of the partly quenched system satisfy a set of replica Ornstein-Zernike equations (21)-(23). Each of them is a 2 x 2 matrix equation for the model in question. As in previous studies of ionic systems (see, e.g.. Refs. 69, 70), we denote the long-range terms of the pair correlation functions in ROZ equations by qij. Here we apply a linearized theory and assume that the long-range terms of the direct correlation functions are equal to the Coulomb potentials which are given by Eqs. (53)-(55). This assumption represents the mean spherical approximation for the model in question. Most importantly, (r) = 0 as mentioned before, the particles from different replicas do not interact. However, q]f r) 7 0 these functions describe screening effects of the ion-ion interactions between ions from different replicas mediated by the presence of charged obstacles, i.e., via the matrix. The functions q j (r) need to be obtained to apply them for proper renormalization of the ROZ equations for systems made of nonpoint ions. 

Nevertheless, previous developments and some of our results prove that the structural properties of several systems with short-range repulsive forces are straightforwardly and sufficiently accurately given by ROZ integral equations. Thermodynamic properties are much more difficult to describe. Reliable tools exist to obtain thermodynamics at high temperatures or for states far from phase transitions. Of particular importance, and far from being solved, are the issues related to phase transitions in partly quenched systems, even for simple models with attractive interactions. It seems that the results obtained by Kierlik et al. [27], may serve as a helpful reference in this direction. 

The theory of quenched-annealed fluids is a rapidly developing area. In this chapter we have attempted to present some of the issues already solved and to discuss only some of the problems that need further study. Undoubtedly there remains much room for theoretical developments. On the other hand, accumulation of the theoretical and simulation results is required for further progress. Of particular importance are the data for thermodynamics and phase transitions in partly quenched, even quite simple systems. The studies of the models with more sophisticated interactions and model complex fluids, closer to the systems of experimental focus and of practical interest, are of much interest and seem likely to be developed in future. 

The more or less isoelectronic systems CaW04 and CaMo04 show broadband emission with maxima at 410 nm and 530 nm, respectively. Whereas CaW04 is very efficient at room temperature, CaMo04 is partly quenched (96). 

When the annealed alloy is investigated a different state of affairs is observed. At small concentrations of aluminium the distribution of these atoms is still statistical, but beyond about 18 atomic per cent the aluminium atoms show a marked tendency to favour the b positions and to forsake the positions a> c and d. This is represented in % 13-036, from which it will be seen that at the composition Fe3Al almost every b site is occupied by aluminium while all the other positions contain iron atoms. With this arrangement, fig. 13.02 now represents only one unit cell. Beyond 25 atomic per cent the b sites remain almost fully occupied by aluminium and the new aluminium atoms enter the d positions, and from about 30 per cent onwards the concentration in these sites grows rapidly, in part at the expense of the b positions, in the way shown by the curve d in fig. 13.03 b. Beyond about 38 per cent the b and d sites are equally occupied by aluminium and the state of the annealed alloy is then the same as that of the quenched system. 

The forward reaction of Equation 3.4 is diffusion controlled and consequently its rate will vary inversely with the viscosity of the medium. The ratio /e/f m is commonly used as a measure of the ease of excimer formation, and /m being the excimer and monomer emission, respectively. Excimer formation in micellar systems requires at least two probe molecules per micelle for the reaction of Equation 3.4 to occur within the micelles. The ratio /e//m is thus dependent on the distribution of probe molecules among the micelles which is assumed to follow a Poisson distribution. At the commonly used probe/surfactant molar ratio of 0.01, Zachariasse [13] calculates from Poisson statistics that 27% of sodium dodecyl sulphate (NaDS) micelles are more than singly occupied. There is difficulty in the interpretation of the fluorescence data since excimer emission occurs alongside the partly quenched monomer fluorescence in doubly or higher occupied micelles, whereas singly occupied micelles show only unquenched monomer fluorescence. This situation leads to uncertainty in the calculated microviscosity and may explain the anomalous value of 150 cP proposed by Pownall and Smith [11] for the micro viscosity of the micellar core of hexadecyltrimethylammonium bromide. 

Elame Arrester A flame arrester is a device permeable to gas flow but impermeable to any flame. It quenches the flame and cools the products sufficiently to prevent reignition at arrester outlet. Arresters are used to prevent a flame propagating into the system from outside (such as via a tank vent) or one part of the system to another (such as through connected piping). 

A porphinatoaluminum alkoxide is reported to be a superior initiator of c-caprolactone polymerization (44,45). A living polymer with a narrow molecular weight distribution (M /Mjj = 1.08) is ob-tmned under conditions of high conversion, in part because steric hindrance at the catalyst site reduces intra- and intermolecular transesterification. Treatment with alcohols does not quench the catalytic activity although methanol serves as a coinitiator in the presence of the aluminum species. The immortal nature of the system has been demonstrated by preparation of an AB block copolymer with ethylene oxide. The order of reactivity is e-lactone > p-lactone. 

---