Volume-temperature relationships polyethylene

Zoller, P. Bolli, P., "Pressure-Volume-Temperature Relationships of Solid and Molten Polyethylene terephthalate)," J. Macromol. Sci., Phys., B18, 555 (1980). 

Universal Calibration In the conventional calibration (described above), there is a problem when a sample that is chemically different from the standards used to calibrate the column is analyzed. However, this is a common situation for instance, a polyethylene sample is run by GPC while the calibration curve is constructed with polystyrene standards. In this case, the MW obtained with the conventional calibration is a MW related to polystyrene, not to polyethylene. On the other hand, it is very expensive to constmct calibration curves of every polymer that is analyzed by GPC. In order to solve this problem, a universal calibration technique, based on the concept of hydrodynamic volume, is used. As mentioned before, the basic principle behind GPC/SEC is that macromolecules are separated on the basis of their hydrodynamic radius or volume. Therefore, in the universal calibration a relationship is made between the hydrodynamic volume and the retention (or, more properly, elution volume) volume, instead of the relationship between MW and elution volume used in the conventional calibration. The universal calibration theory assumes that two different macromolecules will have the same elution volume if they have the same hydrodynamic volume when they are in the same solvent and at the same temperature. Using this principle and the constants K and a from the Mark-Houwink-Sakurada equation (Eq. 17.18), it is possible to obtain the absolute MW of an unknown polymer. The universal calibration principle works well with linear polymers however, it is not applicable to branched polymers. 

Fig. 3.10 Relationship of specific volume to temperature for mixtures of polyethylene (M = 50000) with a-chloronaphthalene for the indicated weight (lui) and volume (ui) fractions. Dashed lines represent calculations according to Eq. (3.16), assuming equilibrium between the crystalline and liquid phases. (From Chiang and Flory (28))...

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