Polymer parachors

It appears that for these cyclic polymers the values of the specific refraction and the specific parachor are almost constant, though the refractive index, the density and the surface tension vary notably. The specific refraction and the specific parachor are independent of the degree of polymerization. 

The specific surface energy of a polymer can be estimated by means of an additive quantity, the Parachor. Alternatively, it maybe calculated from the molar cohesive density (which is also additive). Rules are given for the estimation of the interfacial tension and the contact angle of a liquid on a solid. 

Estimation of surface tensions of solid polymers from the parachor... 

Due to the fact that the extrapolation of surface tensions of melts to room temperature leads to reliable values for the solid polymer, the surface tension of solid polymers may be calculated from the parachor per structural unit by applying Eq. (8.5). The molar volume of the amorphous state has to be used, since semi-crystalline polymers usually have amorphous surfaces when prepared by cooling from the melt. We have found that the original group contributions given by Sugden show the best correspondence with experimental values for polymers. 

Table 8.2 compares the experimental values of the surface tension of polymers (obtained by different methods) and the calculated values, the latter being obtained by means of the parachor. The discrepancies between the different experimental values are reasonably small. The calculated values are, with a few exceptions, in reasonable agreement with the experimental values. 

Sole K (Ed), "Polymer Compatibility and Incompatibility Principles and Practice", Vol 2, MMI Symp Series, New York, 1982. Sugden S, "The Parachor and Valency , Routledge, London, 1930. 

The purpose of this paper is to use data already aquired on critical surface tension for a correlation with solubility parameters and parachors of polymers. The theoretical background of these parameters is briefly mentioned. The evaluation of the calculated values is then discussed. Because of the complexity of the polymer conformation on the surface, we do not imply that a straight-forward relationship between the surface and the bulk properties is available, even in the case of a liquid-like amorphous polymer. Another purpose of this paper is, therefore, to point out the complicating factors and the difficulties in predicting the surface wettability on the basis of bulk properties. 

In 1965, Roe (27), Marwedel (20), and Lee and co-workers (13) independently suggested that parachor could be used to calculate the surface tension of a polymer. We, therefore, use the following equation for the calculation ... 

It is important to note that the correlation coefficient is slightly increased in the case of the solubility parameter but decreased in the case of the parachor after the three hydrogen-bonded polymers were removed from the Tables. 

Critical surface tensions of functional polymers were experimentally determined. This set of data and the data on elastomers obtained previously were used to elucidate the proposed solubility parameter-surface tension relationship and the proposed parachor-surface tension relationship. The results show that the former has a higher correlation coefficient than the latter. The correlation coefficients, including three highly hydrogen-bonded polymers, are 0.731 for the former and 0.299 for the latter. Otherwise, they are 0.762 for the former and 0.178 for the latter. For the size of samples examined, we can conclude that the proposed solubility parameter-relationship is more effective than the proposed parachor-relationship in calculating critical surface tension of a polymer. 

The surface tension, interfacial tension and adhesion phenomena will be discussed, and a new correlation for the molar parachor will be presented, in Chapter 7. The calculation of the interfacial tension from the surface tensions of the components will also be discussed, and shown to be in need for significant improvements. In this context, an introduction will also be provided to advanced numerical simulation methods that are becoming increasingly useful in modeling the interfacial phenomena and phasic behavior of polymer-containing systems. 

Figure 7.3. The results of a fit using the van der Waals volume Vw and a correction index NPS, to the molar parachor P calculated by the group contributions of van Krevelen supplemented by the atomic and structural contributions of Sugden, for a set of 115 polymers.

It has been shown that the parachor concept is applicable to polymers [Roe, 1965, 1968, 1969 Wu, 1970]. The surface tension is given by... 

Surface tension of TLCPs can also be predicted using group contribution. Van Krevelen [60] has studied and summarized the hypotheses to estimate surface tension of a solid polymer by means of additive quantities, the parachor and the cohesive energy density. The parachor (Ps), which was first introduced by Sugden [61], has the following additive quantity and is independent of temperature ... 

Various paths have been used to circumvent the difficulty. The simplest is to obtain Yg extrapolation of the surface tensions of the polymer melt as a function of temperaturell (for data on surface and interfacial tensions of polymer melts see reference 12).Calcula-tions based on the parachors have also been undertakenl3, Other methods have been used to estimate the surface energy of polymers from various molecular properties (e.g., reference 14). 

Three other methods have been widely used to estimate polymer melt surface tensions. The oldest of these methods is based on the parachor method first proposed for small molecules by Sugden. ... 

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