Statistical Mechanics and Reaction Kinetics of AB_g Hyperbranched Polymer Reaction

Hong Xiaozhong et al.: The statistical mechanics and reaction kinetics of hyperbranched polymer reactions of the human-horse type. This article aims to link the average macromolecular physical quantity with the thermodynamic quantity and study the connection between dynamic methods and statistical mechanics methods. The relationship between the degree of reaction at equilibrium and the thermodynamic quantities of the reaction system. For a reaction system where the temperature is T and the pressure is P, the change of the Gibbs free energy of the polymerization is AG. For AB type polycondensation reaction system, if K is the reaction equilibrium constant, when the reaction reaches equilibrium, according to the reaction kinetics Theoretically, the formula is represented by the concentration of the functional group A and the B functional group, and the molecular term portion represents the concentration of the functional group that has undergone the polymerization reaction and the concentration of the generated small molecule.

The statistical interpretation gives the probability of bonding between two kinds of free functional groups, and also gives the analytical expression between the degree of reaction after complete equilibrium and the thermodynamic quantity of the reaction system, that is, the above formula determines the equilibrium system of the reaction system. The analytical expression of the degree of reaction and the thermodynamic quantities of the reaction system. Thus, under certain external conditions, the thermodynamic quantities of the reaction system actually determine the maximum degree of reaction of the reaction system, and therefore other thermodynamic quantities of the reaction system are also determined.

2 Kinetic Theory of Polycondensation Reaction For the polycondensation reaction, according to the Tobolsky and Eisenberg models, the kinetic equation describing the equilibrium polymerization of the system can be expressed as the kinetic equation representing 1 (m-1) aggregate and one monomer generation. The process of 1 m-mer. The symbol Mm denotes an m-mer and X denotes a small molecule formed during the polycondensation reaction.

Assuming that the equilibrium constant corresponding to this step is fc - 1. The concentration of m-polymer in the reaction system is expressed by e, and the concentration of small molecules is expressed, and the recurrence relation is used repeatedly to obtain the m-polymer in the reaction system. The concentration e is calculated by further calculating the total concentration of the polymer in the obtainable system = g, and then physical quantities such as number average polymerization degree, number average, and weight average molecular weight distribution can be calculated.

For the polycondensation reaction shown in Equation (6), if the rate constants for positive and negative reactions are k+ and k-, respectively, then for the AR-type polycondensation reaction system, the following equation can be obtained: because of the equilibrium constant K and positive and negative reaction rate of the reaction system The relationship between the constants, ie k+ direct calculations, shows that this result is completely consistent with the previous equation (5) obtained by statistical mechanics. In addition, since the monomer concentration does not change with time when the reaction system reaches equilibrium, Equation (4) derived from statistical theory can be obtained again from Equation (11).

3 Thermodynamic characterization of macromolecule quantities This section gives analytical expressions of the degree of reaction and the thermodynamic quantities of the reaction system. At the same time, the thermodynamic quantities of the reaction system and the average of the reaction system are investigated using the quantitative distribution function of the reaction system and the secondary slewing radius as an example. The effect of polymer physical quantity. Then discuss the relationship between dynamic theory and statistical mechanics theory.

For the AR type polycondensation reaction, using equation (4), the number distribution function Pm in equation (2) can be expressed as Pm=NCm(1,g)−. If you use dynamics assumption (9), how many dynamic equilibrium constants can be expected to be multiplied, then the number of bonds in the polymer corresponds to this. Therefore, statistical mechanics and reaction kinetic theory are consistent with each other. It is noteworthy that the application of kinetic theory can simplify the characterization of the average polymer physical quantity of the system. Here, the secondary gyration radius of the reaction system is taken as an example to illustrate.

The expression of the secondary radius of gyration <R2>2 of the reaction system is that where bo denotes the average bond length and D is the combined form (4), the secondary radius of gyration <R2>2 of the AB type polycondensation reaction can be represented again. This expression is obviously simpler.

The statistical mechanics and reaction kinetics theory of AB-type hyperbranched polymer reactions are discussed above. The analytical expressions between the reaction degree and time and other thermodynamic quantities of the reaction system are given, and statistical mechanics methods and reaction kinetics are proved. The method describes the equivalence of the AB hyperbranched polymer reaction. It can be seen that the equal activity hypothesis retained in statistical mechanics studies corresponds to the equilibrium constant in dynamics. In the dynamic method, the relationship between the degree of response and time can be strictly solved, and the relationship between the inverse and thermodynamic quantities is not generally considered in statistical mechanics. Both provide insights into the process of studying the polymer reaction.

Hong Xiaozhong et al.: Statistical Mechanics and Reaction Kinetics of Human-selective Hyperbranched Polymer Reactions