A general route is shown to calculate the entropy production sigma as function of time t in a closed system during reversible polymerization. We treat the polymer molecules to behave nonideal and apply exemplarily the classical Flory-Huggins theory to get explicit expressions for the activity coefficient. At the beginning of the polymerization the system is in a nonequilibrium state where chemical reactions take place that irreversibly drive the system towards equilibrium with sigma approaching zero in the limit t-->infinity. The time-dependent course of the entropy production is explicitly calculated for two cases where the reaction starts (i) from monomer molecules polymerizing to a defined number average chain length xn,eq and (ii) from monodisperse polymer molecules reacting with each other under the constrain that xn is the same at the beginning and the end of the reaction. In both cases we find that the nature of the activity coefficient has an important effect on the curvature of sigma which may considerably differ from that of an ideal behavior.
Based on the theory of irreversible thermodynamics explicit expressions are derived for the entropy production during reversible polymerization of bifunctional linear polymers whose initial molecular weight distribution can be chosen arbitrarily. The time-dependent course of the entropy production is explicitly calculated for two cases where the reaction starts (a) from monomer and (b) from monodisperse polymer molecules. In both cases we treat the system to be ideal and the time dependant change of the number of molecules is described by a kinetic approach using two kinetic constants for the forward and backward reactions, respectively. During reversible polymerization the entropy production σred is a monotonously decreasing function approaching zero when the system reaches the equilibrium molecular weight distribution with σred being positive in accordance with the second law of thermodynamics. In case of starting reaction from monodisperse polymer molecules under constraint that the number average chain length remains constant during reaction we calculate the entropy of mixing and discuss it with results obtained from statistical considerations.
ABSTRACT:The kinetics of transesterification of dimethyl 2,6-naphthalenedicarboxylate (2,6-DMN) with 1,3-propanediol has been studied in the presence of various catalysts. The reaction was followed by measurement of the amount of methanol released, and the formation of oligomers with time. The oligomers obtained were quantitatively determined by high-pressure liquid chromatography (HPLC). Interpretation of the experimental data showed that the transesterification followed SchulzFlory statistics. Therefore, one kinetic constant was sufficient to describe the kinetics of transesterification of 2,6-DMN with 1,3-propanediol. The kinetic constants observed, when different catalysts were employed, revealed the following activity sequence for the transesterification: Co(II) Ͻ Ti(IV) Ͻ Mn(II) Ͻ Zn(II).
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