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In polymer chemistry, the Flory–Fox equation is a simple empirical formula that relates molecular weight to the glass transition temperature of a polymer system. The equation was first proposed in 1950 by Paul J. Flory and Thomas G. Fox while at Cornell University.〔 〕 Their work on the subject overturned the previously held theory that the glass transition temperature was the temperature at which viscosity reached a maximum. Instead, they demonstrated that the glass transition temperature is the temperature at which the free space available for molecular motions achieved a minimum value. While its accuracy is usually limited to samples of narrow range molecular weight distributions, it serves as a good starting point for more complex structure-property relationships. ==Overview== The Flory–Fox equation relates the number-average molecular weight, ''M''n, to the glass transition temperature, ''T''g, as shown below: : where ''T''g,∞ is the maximum glass transition temperature that can achieved at a theoretical infinite molecular weight and ''K'' is an empirical parameter that is related to the free volume present in the polymer sample. It is this concept of “free volume” that is observed by the Flory–Fox equation. Free volume can be most easily understood as a polymer chain's “elbow room” in relation to the other polymer chains surrounding it. The more elbow room a chain has, the easier it is for the chain to move and achieve different physical conformations. Free volume decreases upon cooling from the rubbery state until the glass transition temperature at which point it reaches some critical minimum value and molecular rearrangement is effectively “frozen” out, so the polymer chains lack sufficient free volume to achieve different physical conformations. This ability to achieve different physical conformations is called segmental mobility. Free volume not only depends on temperature, but also on the number of polymer chain ends present in the system. End chain units exhibit greater free volume than units within the chain because the covalent bonds that make up the polymer are shorter than the intermolecular nearest neighbor distances found at the end of the chain. In other words, end chain units are less dense than the covalently bonded interchain units. This means that a polymer sample with long chain lengths (high molecular weights) will have fewer chain ends per total units and less free volume than a polymer sample consisting of short chains. In short, chain ends can be viewed as an “impurity” when considering the packing of chains, and more impurity results in a lower ''T''g. Thus, glass transition temperature is dependent on free volume, which in turn is dependent on the average molecular weight of the polymer sample. This relationship is described by the Flory–Fox equation. Low molecular weight values result in lower glass transition temperatures whereas increasing values of molecular weight result in an asymptotic approach of the glass transition temperature to ''T''g,∞ . The figure to the left clearly displays this relationship – as molecular weight increases, the glass transition temperature increases asymptotically to ''T''g,∞ (in this arbitrary case shown in the image, ''T''g,∞ = 365 K). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Flory–Fox equation」の詳細全文を読む スポンサード リンク
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