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Scale‐Free Power‐Law Distribution of Emulsion‐Polymerized Branched Polymers: Power Exponent of the Molecular Weight Distribution
Author(s) -
Tobita Hidetaka
Publication year - 2005
Publication title -
macromolecular materials and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 96
eISSN - 1439-2054
pISSN - 1438-7492
DOI - 10.1002/mame.200400245
Subject(s) - emulsion polymerization , molar mass distribution , exponent , polymerization , power law , polymer , materials science , polyethylene , polymer chemistry , thermodynamics , emulsion , degree of polymerization , chemistry , physics , mathematics , organic chemistry , statistics , composite material , linguistics , philosophy
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/ 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.