Critical conditions for formation of infinite networks in branched‐chain polymers

The conditions necessary for infinite network formation due to the bifunctional inter‐unit junction were reinvestigated, and the difference in theories between Flory and Case or Kahn was mentioned. The theory is extended to a more general case than those of Flory and of Case or Kahn. It also deals with the critical point in the condensation reaction between mixtures of two types of functional groups containing one or more functionalities. It is shown that at the critical point, {article}{empty}{document}PA PB ( 1 - ρ ₁ )( 1 - σ ₁ )∑_ⁿ ρ i ( fi - 1 ) ∑_ⁿ σ i ( gi - 1 ) = 1{document} and/or {article}{empty}{document}$ [ {{1 {/ { {1 {( {1 + r} )}}} . -} {( {1 + r} )}}} ][ {rP_A ∑_{}^n {σ i ( {gi - 1} ) + P_B ∑_{}^n {ρ i ( {fi - 1} )} } } ] = 1${document} where PA and PB are the respective probabilities that an A or B group has reacted, fi and gi are the functionalities of Ai and Bi monomers, r is the ratio of A groups to B groups at the initial state, and ρi, σi, are the molar fractions of Ai and Bi, respectively.