The relationship of C∞ to the lateral surface free energy σ: estimation of C∞ for the melt from rate of crystallization data

The expression σ = constant × C∞−1 is proposed for the lateral surface free energy that appears in polymer crystallization theory; C∞ is the characteristic ratio of the polymer molecules in the melt and the constant consists of known parameters. Given C∞, the theory predicts an accurate value of σ for polyethylene. It is shown that C∞ for polyethylene in the melt state can be obtained directly from the nucleation rate constant Kg and the fold surface free energy σe (C∞(theor.) = 6.53 for melt, C∞(expt) = 6.7 from chain dimensions in dilute θ solvents). The corresponding results for i-polystyrene are C∞(theor.) = 10.45 for the melt and C∞(expt) = 10.5 from chain dimensions. The treatment clarifies the meaning of the empirical α parameter and shows prospects for being applicable to other polymers.