Condensation in Solution: Polycations and Polyanions

Condensation of metal complexes in solution forms entities in which the cations are linked by hydroxo (HO−) or oxo (O2−) bridges. The reaction is initiated by the addition of a base to an aquocomplex: . . . 2[Cr(OH2)6]3++ 2HO- → [Cr2(OH)2(OH2)8]4+ + 2 H2O . . . or by the addition of an acid to an anionic complex: . . . 2 [CrO4]2- + 2H+ → [Cr2O7]2- + H2O . . . Thus, purely aquo- and purely oxocomplexes are stable in solution, and the condensation of cations is initiated by hydroxylation. With regard to electrically charged hydroxylated complexes, the reaction forms discrete and soluble entities—polycations and polyanions with a molecular complexity which depends on acidity conditions. This chapter presents a detailed study of their formation and structure. With regard to noncharged hydroxylated complexes, the condensation reaction is no longer limited and leads to the formation of a solid (a subject that is examined in the following chapters). The hydroxylation reaction is the key stage to initiate the condensation of cations in solution. It is thus important to precise the mechanism of the successive steps of the process, in order to understand why the behavior of a cation is closely related to its oxidation state, and why the reaction product may be a discrete molecular species or a solid. As a cation generally exhibits its maximum coordination number in the initial monomeric complex and in condensed species, the condensation reaction is a substitution that proceeds according to one of three basic mechanisms: dissocia­tion, association, and interchange or direct displacement [1, 2]. Dissociative substitution is a two-step process involving the formation of a reduced-coordination intermediate: In the first step, a labile ligand, the leaving group, breaks its bond in the starting complex before a nucleophilic entering group completes, in the second step, the cation coordination (Fig. 3.1 a). Associative substitution is also a two-step process in which the intermediate temporarily has increased coordination. The bond with the nucleophilic entering group (first step) occurs prior to the release of the leaving group (second step) (Fig. 3.1 b).

The Equation of a State of Porous Mixture of Condensed Substances With Specific Heat the Dependence on the Temperature

The work is devoted to a problem of the description of behavior of multispecies mixtures of various powders under shock-wave loading. At the description of a mixture the model of interacting and interpenetrating continua, the principles of which construction are stated in the monographies of R. I. Nigmatulin, is used. The equilibrium condition is satisfied by conditions of equality of pressure, temperatures and mass velocity of species. The presence of gas inside pores is taken into account. The porous mixture of the several condensed substances in thermodynamic equilibrium is represented as single-phase continuous medium with the equation of a state in the Mie-Grüneisen form, which parameters expressed in terms of the corresponding parameters of the species. The numerical calculations of shock adiabats for porous substances and porous mixtures of the condensed species are performed with use of various models of the equation of a state of a mixture taking into account: a) only elastic pressure and elastic energy; b) both elastic, and thermal terms with constant specific heat of substance and Grüneisen oefficient; c) elastic and thermal terms with specific heat of substance the dependence on the temperature and variable Grüneisen coefficient. The results of computations are compared with experimental data.