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

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/ P b , where P b 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/ P b . This simple relationship could be used to estimate the P b 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 P b . 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 P b  ≥ 1/ i .Molecular weight distribution of the emulsion‐polymerized polyethylene.