E5 Glass Transition (Tg): Dependence on Molecular Weight and Mixture

Topic

The molecular weight of this polymer—the same value established by another model in this set based on the polymer's chain-length distribution—determines its glass transition temperature according to the Fox-Flory relationship: each molecular chain end contributes an excess of free volume in its immediate vicinity that is not provided by a segment located within the chain itself; consequently, the lower the molecular weight, the greater the number of chain ends per unit mass, and the greater the total excess free volume. Conversely, a higher molecular weight means fewer chain ends contributing this excess free volume per unit mass, causing the glass transition temperature to approach an upper limiting value in accordance with the Fox-Flory relationship.

When this polymer is mixed with a second component rather than constituting the entire sample, the glass transition temperature of the mixture is determined by the proportions of the two components, in accordance with the Fox rule: this rule combines the glass transition temperatures of the polymer and the second component (in their pure states), weighting each according to the mass fraction of that component within the mixture. A higher mass fraction of the polymer in the mixture causes the mixture's glass transition temperature to shift closer to that of the pure polymer, in accordance with the Fox rule. Consequently, given this model—characterized by the glass transition temperature and its dependence on molecular weight and mixture composition—the presence of a plasticizer dissolved between the polymer's molecular chains causes a depression in the glass transition temperature, in accordance with the Gordon-Taylor relationship. Each plasticizer molecule—being much smaller and more mobile than the polymer chains—intercalates between them, thereby contributing additional free volume; this contribution mirrors the free volume associated with each molecular chain end in the kinetic free-volume mechanism—a mechanism that also describes the glass transition in other glassy materials within different modeling frameworks—and this added free volume consequently lowers the glass transition temperature. Thus, a higher concentration of the plasticizer within the polymer results in a greater depression of the glass transition temperature, consistent with the Gordon-Taylor relationship.

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