## Ah55222

If we use the internal pressures of the two components to compute this term we obtain the following expression:

Equation 3 shows that we do not have a good measure of the enthalpy of mixing, nor is the difference simply offset by a multiplicative constant. The problem is further compounded by the fact that the ratios ni may be functions of the thermodynamic variables of the system i.e. ni = ni (T,..). If the values of ni are similar and have values close to one then the enthalpy of mixing can be approximated. A second possibility is the case where the liquids have similar values of ni but ni is different from unity. In this case the enthalpy of mixing will be in error by a multiplicative constant and can be corrected by a fudge factor, as is the common practice in this field.

### The Internal Pressure and Surface Tension.

The surface tension of liquids, y, is a direct manifestation of the cohesive forces that hold the liquid state together. We have been working in the area of the surface tension of polymer liquids. We have acquired a substantial amount of data for high molecular weight liquids.10 PVT properties were also obtained for these same polymer samples.11 By scaling the surface tension data with an appropriate measure of the CED of the liquid, we should be able to collapse the data for many different polymers onto a single master curve. Implicit in this assumption is the fact that the CED and the density of the liquid are the dominant factors contributing to the surface tension. We can scale the surface tension using n computed from the PVT data and the measured density. Patterson and Rastogi12 were the first to do this for polymer liquids. Clearly, any quantity derived from this information set (y, vsp, a, P,T, P) can be used to scale the data, where vsp is the specific volume, a is the thermal expansivity, p is the isothermal compressibility, T is the temperature , and P is the pressure. In particular we can use the equation of state parameters obtained from fitting an equation of state to the PVT data.13 The master curve will be different but the information content will be the same. Figure 1 shows this exercise for a number of polyethylenes ranging from low molecular weight alkanes to rather large molecules. The striking feature about the PE data set is the complete collapse of the data to within a 2% scatter. The measured surface tensions for these liquids vary by over 200 % in this molecular weight range.10 Since the chemical structure of these liquids is similar at the local molecular level, we expect that the values of n for these molecules will be close in value and the complete collapse of the data onto a single curve reflects the dominant role played by the CED in the determination of the surface tension.

We repeated this exercise for polymer molecules of varying molecular weights but with different chemical 13structure. Figure 1 shows the result of the scaling for poly(ethylene oxide) (PEO), Poly(dimethyl siloxane) (PDMS), polystyrene (PS), and polyethylene (PE). For molecules with the same chemical structure but different molecular weights we observe a similar collapse of the data for each polymer type. However, we now observe that we have a different master curves for each polymer type. The obvious explanation is again to observe that we are not scaling with the true CED of these liquids and that in each case there is a shift factor coming from the function ni for each chemical structure. It is tempting to assume that if we knew the values of ni for each of these different polymer families, we could achieve a complete collapse of the data set onto a single master curve. The central idea of this paper is to turn this last idea around and propose that such a master curve exists. If we can determine this curve for one

Figure 1: A plot of the scaled surface tension, y/y* as a function of the scaled temperature T/T*.

y* = p*ib T*m (ck)1/3 where P* and T* are temperature dependant FOV equation of state fitting parameters, k is Boltzmann's constant and c is a constant.

Figure 1: A plot of the scaled surface tension, y/y* as a function of the scaled temperature T/T*.

y* = p*ib T*m (ck)1/3 where P* and T* are temperature dependant FOV equation of state fitting parameters, k is Boltzmann's constant and c is a constant.

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