Cohesive energy density correlation

The polarity of the polymer is important only ia mixtures having specific polar aprotic solvents. Many solvents of this general class solvate PVDC strongly enough to depress the melting temperature by more than 100°C. SolubiUty is normally correlated with cohesive energy densities or solubiUty parameters. For PVDC, a value of 20 0.6 (J/cm (10 0.3 (cal/cm ) has been estimated from solubiUty studies ia nonpolar solvents. The value... 

Figure 3.4 shows a fair correlation between vo-2ot and the Hildebrand solubility parameter 8 (linear correlation coefficient = 0.930) which makes intuitive sense. The Hildebrand parameter, which is often used to characterize liquids, is defined as the square root of the cohesive energy density (Barton 1991), while vcr2o( can be viewed as reflecting how strongly a molecule interacts with others of the same kind (Murray et al. 1994). 

Volumes of activation can be unambiguously determined only from the pressure dependence of the rate constants. Attempts to obtain volumes of activation from the correlation of rate constants with the solubility parameter 22 or the cohesive energy density parameter (ced)23, which are related to the internal pressure of solvents, have not led to clear-cut results. 

Thus taking into account the cohesion energy density allows essentially to improve upon results of correlation analysis on influence of medium properties on kinetics of oxidation of propanethiole by chlorine dioxide. At the same time a significance of this factor is indirect proof of radical stages in the process. 

Whereas the polarity effect is ascribed to the dielectric constant, the hydrophobic effect is a consequence of the high cohesive energy density (c.e.d.) of water, resulting from a unique hydrogen-bonding network (Lubineau et al., 1994). Given table 6.5, which compares the cohesive energy density and the dielectric constant of selection of common solvents at 25°C, there is no correlation between the structuralization and the polarity of the solvents. 

Porter has shown for several solvents a correlation between the cohesive energy density (CED) and the Onsager reaction field parameter... 

Dielectric constant and cohesive energy density are determined by the same type of electrical force. Based on that observation van Krevelen reported that values of e at room Icrnpcralure (RT) correlate with the solubility parameter 8 ... 

BIO, Bristow, G. M., and W. F. Watson Viscosity-equilibrium swelling correlations for natural rubber cohesive energy densities of polymers. Part 2. Cohesive energy densities from viscosity measurements. Trans. Faraday Soc. 54, 1567, 1742 (1958). 

Since the unrelaxed bulk modulus, Ku e.g., determined by ultrasonic propagation velocity measurements, is a good measure of the cohesive energy density, CED (Ku 11 CED Chapter 10), and CED gives a good indication of the overall material s polarity, one can expect a correlation between Ku and W. This is shown in Fig. 14.3 for the amine-epoxy and styrene-vinyl ester networks. The following relationship is found ... 

A considerable solvent dependence has been reported by Debye and coworkers32 33 in their already mentioned study of a-monoglycerides in benzene, chlorobenzene, and chloroform. The authors found a correlation between the cohesive energy densities of the solvents and the clustering tendency of the nonionic surfactants with decreasing cohesive energy the aggregation increased. In chloroform no micelles were found. 

The modulus of elasticity in the glassy state depends on intermolecular forces 1 (. Therefore, Tobolsky 28) proposed the following equation correlating the bulk modulus of elasticity (B) at 0 K and cohesive energy density (82) ... 

The square root of cohesive energy density is called solubility parameter. It is widely used for correlating polymer solvent interactions. As a refinement, three solubility parameter components can be distinguished, representing dispersion, polar, and hydrogen bond interactions. 

Since the surface tension is a manifestation of intermolecular forces, it may be expected to be related to other properties derived from intermolecular forces, such as internal pressure, compressibility and cohesion energy density. This is found to be so indeed. In the first place there exists a relationship between compressibility and surface tension. According to McGowan (1967) the correlation is ... 

The Rao function has the same form as the Sugden function or Molar Parachor (Ps = My1/4/p), derived by Sugden in 1924, which correlates the surface tension with the chemical structure. Also the Small function or Molar Attraction Function, which correlates the cohesion energy density, ecoh, and the solubility parameter, 8, with the chemical structure, has this form ... 

The value of kd was obtained from the determination of triplet lifetimes by measuring the decay of phosphorescence and found to be insensitive to changes in solvent polarity. The k2 values derived from Eqs. 10 and 11 were correlated with solvent parameters using the linear solvation energy relationship described by Abraham, Kamlet and Taft and co-workers [18] (Eq. 12), which relates rate constants (k) to four different solvation parameters (1) or the square of the Hildebrand solubility parameter (solvent cohesive energy density), (2) n or solvent dipolarity or polarizability, (3) a, or solvent hydrogen bond donor acidity (solvent electrophilic assistance), and (4) or solvent hydrogen bond acceptor basicity (solvent nucleophilic assistance). 

Estimate pressure—volume—temperature (PVT) relations, cohesive energy densities, pair correlation functions, X-ray scattering curves, elastic constants, and other properties. 

Graessley et al, (1994,1995) have proposed an alternative scheme that correlates the x values for polyolefin blends with differences in inferred values of the solubility parameters of the pure components [see Eq. (2-31)]. For the series of polyolefins they studied, values of for the pure components can be assigned in such a way that the x parameters of the mixtures computed from Eq. (2-31) are in reasonable qualitative agreement with measured values. Direct estimates of the (5 s can be obtained from the following formula derived from the van der Waals cohesive energy density (Hildebrand and Scott 1950 Krishnamoorti et al. 1996) ... 

Enthalpy of mixing, AH, can be correlated to cohesive energy density, i.e., solubility parameter (5) as... 

There are many theories [1] and empirical correlations [1,3,5] to calculate y. The intermolecular interactions which play a role in determining y and the cohesive energy density ecoh arc Quite similar. The surface tension at room temperature (where ecoh has been best quantified) can therefore be estimated by Equation 7.1 [3] ... 

The same types of electrical forces which determine the values of the molar polarization and the dielectric constant also determine the cohesive energy density [2], An approximate correlation, given by Equation 9.4, has thus been found [3] between at room temperature and the solubility parameter 8 for polymers. This equation can be used to provide a rough estimate of the value of the dielectric constant at room temperature. 

Kambour [41,42] showed graphically the existence of correlations for the minimum strain and stress required for the inception of crazing, in terms of the cohesive energy density, the difference between Tg and the testing temperature, and E (or oy). Since failure with crazing... 

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