Glass transition temperatures of molecular weight fractions of polystyrene were plotted as a function of molecular weight. The function increases with increasing molecular weight. At low molecular weights, the increase is substantial, but at higher molecular weight there is less of an increase, and the function appears to be approaching an assymptote.
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T. G. Fox, P. J. Flory, J. Appl. Phys., 21, 581 (1950)
This general function above generates the graph shown below.
This is of interest for discussions intending to define a polymer. The Fox Flory Glass Transition Temperature deals specifically with glass transition, but a general version of this equation is shown, along with the graph, to illustrate the idea of general mechanical property vs. molecular weight. A chain of monomers is considered a polymer when the molecular weight is sufficient for the value of the mechanical property to be close to the maximum value.
An Excel document, Mechanical Property, is the source for the above graph. It allows changing the maximum property value, the constant, and the size of the "step" for changes to molecular weight.
