Scale-Free Power-Law Distribution of Emulsion-Polymerized Branched Polymers: Power Exponent of the Molecular Weight Distribution

Abstract

Summary: The molecular weight distribution (MWD), formed in emulsion polymerization that involves the polymer transfer reaction during Interval II, may approach the power-law distribution as polymerization proceeds. The power exponent, α, of the weight fraction distribution W(M) = M−α conforms to the relationship, α = 1/Pb, where Pb is the probability that the chain end is connected to a backbone chain. The MWD of emulsion-polymerized polyethylene reported in literature agrees reasonably well with the relationship, W(M) = M−α with α = 1/Pb. This simple relationship could be used to estimate the Pb value from the MWD data, possibly leading to determining the polymer transfer constant under well-designed experimental conditions. Because α > 1, the number-average MW always approaches a finite value, but the weight- and higher order-averages of MWD may continue to increase as the particle grows without limit depending on the magnitude of Pb. The power-law distributions are self-similar, possessing the nature of fractals and lacking a characteristic scale. The i-th moment of the MWD for the present reaction system continues to increase without limit during Interval II for Pb ≥ 1/i. Molecular weight distribution of the emulsion-polymerized polyethylene.