cyclic anhydrides have also recently been shown to provide a wide array of functionalized polyesters, both saturated and unsaturated. Ring-opening polymerization of lactones and lactides is also applied on the industrial scale. Other methods Numerous other reactions have been reported for the synthesis of selected polyesters, but are limited to laboratory-scale syntheses using specific conditions, for example using dicarboxylic acid salts and dialkyl halides or reactions between bisketenes and diols. Instead of acyl chlorides, so-called activating agents can be used, such as 1,1'-carbonyldiimidazole, dicyclohexylcarbodiimide, or trifluoroacetic anhydride. The polycondensation proceeds via the in situ conversion of the carboxylic acid into a more reactive intermediate while the activating agents are consumed. The reaction proceeds, for example, via an intermediate N-acylimidazole which reacts with catalytically acting sodium alkoxide: The use of activating agents for the production of high-melting aromatic polyesters and polyamides under mild conditions has been subject of intensive academic research since the 1980s, but the reactions have not gained commercial acceptance as similar results can be achieved with cheaper reactants. Thermodynamics of polycondensation reactions Polyesterifications are grouped by some authors into two main categories: a) equilibrium polyesterifications (mainly alcohol-acid reaction, alcohol–ester and acid–ester interchange reactions, carried out in bulk at high temperatures), and b) non-equilibrium polyesterifications, using highly reactive monomers (for example acid chlorides or activated carboxylic acids, mostly carried out at lower temperatures in solution). The acid-alcohol based polyesterification is one example of an equilibrium reaction. The ratio between the polymer-forming ester group (-C(O)O-) and the condensation product water (H2O) against the acid-based (-C(O)OH) and alcohol-based (-OH) monomers is described by the equilibrium constant KC. The equilibrium constant of the acid-alcohol based polyesterification is typically KC ≤ 10, what is not high enough to obtain high-molecular weight polymers (DPn ≥ 100), as the number average degree of polymerization (DPn) can be calculated from the equilibrium constant KC. In equilibrium reactions, it is therefore necessary to remove the condensation product continuously and efficiently from the reaction medium in order to drive the equilibrium towards polymer. The condensation product is therefore removed at reduced pressure and high temperatures (150–320 °C, depending on the monomers) to prevent the back reaction. With the progress of the reaction, the concentration of active chain ends is decreasing and the viscosity of the melt or solution increasing. For an increase of the reaction rate, the reaction is carried out at high end group concentration (preferably in