A coherent state field theory for gelation of f-arm star polymers

We present a coherent state field theory (CST) for reversible gelation of end-functional f-arm star polymers in an implicit solvent. At the mean-field level, the CST recovers all the essential results of the Flory-Stockmayer (FS) theory. Two necessary mean-field conditions are identified, one corresponding to the law of mass action, and another to the FS equation of gel fraction. Beyond the mean-field level, the Gaussian fluctuation theory is fully developed, which contains in particular the free energy of associative star polymers with variable crosslinking patterns. The expressions for densities of loop number, bond number, and cluster number are provided. Three systems, phantom stars, dilute solutions, and dense melts are examined in the pre-gel regime to elucidate the effects of loop formation and excluded volume interaction.