Applicability of law of mass action to distribution of manganese between slag melts and liquid iron

According to the law of mass action and the coexistence theory of slag structure, the distribution of manganese between MnO FeO SiO 2 and MgO MnO FeO SiO 2 slag melts as well as liquid iron was analyzed. It is shown that K ′ Mn and K MnO are only dependent on temperature and don’t change with basicities and compositions of slag melts. So the distribution of manganese between the above mentioned slag melts and molten iron obeys the law of mass action. But analysis of experimental results from other sources shows that K ′ Mn and K MnO really change with basicities of slag, which is probably arisen from not approaching equilibrium under low basicity slag melts.

Statistical and thermodynamic properties of binary self-condensing vinyl polymerization

The thermodynamic properties of a binary self-condensing vinyl polymerization system consisting of monomers and inimers are investigated by the principle of statistical mechanics.In detail,in terms of two types of canonical partition functions constructed from different viewpoints,the equilibrium free energy,the law of mass action and the size distribution of hyperbranched polymers are obtained.As an application,the specific heat,equation of state and isothermal compressibility concerning the polymerization are given as well.To study the dimension of hyperbranched polymers in the system,a recursion formula satisfied by the(k+1)-th and k-th mean square radius of gyration is derived,and then the first,second and third radius of gyration under different solvent conditions are presented.The influences of the fraction of inimers,the conversion of vinyl groups and the solvent effect on the average dimension of hyperbranched polymers are discussed.

Statistical thermodynamic properties of a new self-condensing vinyl polymerization system

A new self-condensing vinyl polymerization system consisting of *ABf-type inimers is studied by the principle of statistical mechanics. To obtain the relevant average properties of the system, a differential equation satisfied by the polymeric moment of interest is given, and as a result the zeroth, first, second, and third polymeric moments together with the size distribution function of hyperbranched polymers(HBPs) are explicitly presented. As an application of the method of statistical mechanics, several thermodynamic quantities such as the equilibrium free energy, law of mass action, isothermal compressibility, internal energy, and the specific heat associated with the polymerization are all derived. Furthermore, the scaling behavior of asymptotic size distribution function is discussed, by which a reasonable interpretation of the polydispersity index near the end of polymerization can be made. Also, the expressions of some structural parameters such as the numbers of inimers, terminal units, chain units, branched units, and the degree of branching(DB) are calculated. It is found that a high functionality is helpful to improve the DB of the resultant HBPs. These results show that the functionality f has a significant effect on the thermodynamic quantities and structural properties of HBPs.