Info

Figure 4: A plot of the scaled surface tension, y/y*, as a function of the scaled temperature T/T* for polyethylene oligomers and some low molecular weight liquids. y* and T* are defined in figure 1.

the difference between them reflecting the entropic contribution to the surface tension due to the loss of configurations available to chain-like molecules at the liquid/vapor interface. To emphasize this fact, we calculated the scaled surface tensions of a number of small molecule liquids below their boiling points and this data is included in figure 4 where we have fitted curves to the high and low molecular weight data. As expected the PE oligomers lie between the curves unless the molecular weight is high enough so that the entropic contribution is complete. The upper curve can now be used as our reference curve for polymer surface tension data.

Using the polymer master curve we can now use it to compute the functions ni for different polymers for which we have PVT and surface tension data. The functions ni define the mapping between the polymer master curves shown in figures 2, which where constructed using the information set (y, vsp, a, P,T, P), and the master curve shown in figure 4 which was constructed using the information set (y, Vsp, a, CED,T, P). The assumption that there is an exact scaleing of the surface tension with the information set (y, vsp, a, CED,T, P) is not proved and can only be verified by repeating the analysis described above for PE using other polymer oligomers. The better we describe this master curve the more accurate the predictions will be for the functions ni and hence the better our predictions of the true CED's of the various polymer liquids will be.

Temperature (C)

Figure 5: A plot of the CED for a number of different polymers as a function of the temperature. The polymer types are indicated in the legend where the abreviations have the following meaning. PE, polyethylene; PEG, poly(ethylene oxide); aPP, atatic polypropylene; PMMA, poly(methyl methacrylate); PDMS, poly(dimethyl siloxane); PTMeO, poly(tetra-methylene oxide); PPG, poly(propylene oxide); PHFP, poly(hexafluoro propylene); PHFPO, poly(hexafluoro propylene oxide); 3GT, poly( propylene terephthalate); PCPT, polycaprolactone; PS, polystyrene; PEKK, poly(ether ketone ketone); P2VP, polyvinylpyrrolidone).

Temperature (C)

Figure 5: A plot of the CED for a number of different polymers as a function of the temperature. The polymer types are indicated in the legend where the abreviations have the following meaning. PE, polyethylene; PEG, poly(ethylene oxide); aPP, atatic polypropylene; PMMA, poly(methyl methacrylate); PDMS, poly(dimethyl siloxane); PTMeO, poly(tetra-methylene oxide); PPG, poly(propylene oxide); PHFP, poly(hexafluoro propylene); PHFPO, poly(hexafluoro propylene oxide); 3GT, poly( propylene terephthalate); PCPT, polycaprolactone; PS, polystyrene; PEKK, poly(ether ketone ketone); P2VP, polyvinylpyrrolidone).

We computed the values of ni for a number of polymers with different chemical structures. As observed by Hildebrand and others, we observe that fluoropolymers with weak dispersive interactions have large values of n, and more polar molecules with stronger interactions have values close to 1. Polymers with weaker interactions, fluoropolymers for example, increase with temperature, and polymers with strong polar interaction exhibit weak temperature dependence. Clearly these data pose many interesting questions concerning the relationship between this function n and the chemical structure of the molecules. This is a subject of ongoing research. Figure 5 shows the CED's for these same polymers computed using the above analysis. While the accuracy of the predicted values is still in question, we feel that this approach offers the best route to realistic values of the CED for polymer systems. The values of the CED can be used for phase studies and other calculations where one needs the CED. We can construct thermodynamic tables for enthalpies and entropies for the polymer liquid state relative to an ideal gas state. In cases where we compute enthalpies of mixing, we can hope that we are computing the main contribution to the enthalpy of mixing correctly, and we can hope to dispense with some of the adjustable parameters used in the application of these theories.

References

(1) D.W. vanKrevelen "Properties of Polymers,TheirEstimationandCorrelationwithChemical

Structure,"Elsevier,Amsterdam,(1976).

(2) J. H. Hildebrand, R. L. Scott; " The Solubility ofNonelectrolytes, " 3rd Edition, Reinhold Publishing

Corporation, (1950).

(3) J. H. Hildebrand, J. M. Prausnitz, and R. L. Scott; " RegularandRelatedSolutions, " Van Nostrand

Reinhold Company, NewYork (1970).

(4) G. T. Dee, andB. B. Sauer,Advances inPhysics, Vol. 47, No. 2, 161-205, (1998).

(5) P. Zoller. In H. Mark, N. Bikales, C. Overberger, and G. Menges, eds., "Encyclopedia of Polymer

Science andEngineering, " Vol. 5, Wiley, New York, 2nd Edition., p. 69, (1986).

(6)B. B. Sauer,N.V. DiPaolo, J. ColloidlnterfaceSci., 144:527 (1991).

(7) G. I. Allen, G. Gee, and G. J. Wilson, Polymer, 1 (4), 456 (1960).

(8) P. J. Flory, R. A. Orwoll, and A. J. Vrij,,4m. Chem. Soc, 86:3507(1964).

(9) I.C. Sanchez and R.H. Lacombe, J.Phys. Chem., 80:2352(1976).

(10) ) G. T. Dee and B. B. Sauer, J. Colloid Interface Sci. , 152:85 (1992).

(11) G.T. Dee and D.J.Walsh,Macromolecules, 21: 811 (1988).

(12) D. Patterson and A.K. Rastogi, J. Phys. Chem., 74:1067 (1970).

(13) G. T. Dee and B. B. Sauer, POLYMER, Vol. 36, No.8, 1673, (1995).

(14) T.G. Fox and P.J. Flory, J. Polym. Sci., 14:315 (1954).

(15) K. M. Hong and J. Noolandi, Macromolecules, 14:1223 (1981).

(16) K. M. Hong and J. Noolandi, Macromolecules, 14:1229 (1981).

0 0

Post a comment