Cohesive energy density parameters

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. 

Several researchers such as Small, Hoy and McClellan (6-8) examined the chanical structure and chemical groiqj contributions to the Cohesive Energy Density parameters. Through their efforts... 

In the DDT example, when it is combined in a formulation with xylene at a 30% weight-by-weight ratio, we have an estimated 18% volume-by-volume ratio of DDT to xylene. As this example demonstrates, we derive reasonable parameters for the Cohesive Energy Density parameters and molar volume using this technique. 

In this expression, he divides the number of calories generated on the lipophile side of the surfactant by the number of calories generated by the hydrophile side of the surfactant. The amount of calories reflects or implies a proportional amount of swelling of the hydrophile and the lipophile, i.e., the greater number of calories on the lipophile side, the more tendency there is to form an oil in water type of emulsion. This definition of the C.E.R. (or Cohesive Energy Ratio) parameter leads to a direct expression which ties HLB to the Cohesive Energy Density parameter directly. The expression is ... 

This was acconplished by considering the Beerbower expression for the determination of the surface tension, using Cohesive Energy Density parameters and average molar volumes... 

Thus, by considering the apparent solubilities of water with various types of inorganic salts, and the surface tensions of these solutions, we were able to make determinations concerning the apparent associated Cohesive Energy Density parameters. 

In Figure 1 a conparison is made between the volume fraction of inorganic salt in the water solution and the surface tension divided by the Beerbower correction factor, divided by the cube root of the molar volume. Using this data, in addition to the data found in Table I, we are able to make reasonable approximations for the Cohesive Energy Density parameters associated with various concentrations of inorganic salt solutions. 

To this point, we have considered the interaction of nonionic surfactants within the framework of the mathanatical model. The activity and character of anionics in emulsification is complicated by the ionization steps which an anionic surfactant may take when exposed to salt solutions. For instance, in a dialkyl metallic salt, there are three compounds which may exist in various concentrations, depending ipon the ionic strength of the salt solution which, in turn, would exhibit, at least, three different HLB nuiiibers. To address the problem of generating Cohesive Energy Density parameters for the anionic hydrophiles, certain standardized assunptions... 

In the pursuit of a mathematical model to determine an optimized surfactant system, all the criteria mentioned to this point are critical. However, secondary mechanisms must be considered, such as the entropy of mixing associated with the interaction of the molar volume of the lipophile and the molar volume of the oil. This energy should be minimized as much as possible to ensure adhesion of the lipophile to the oil phase. Beerbower analyzed this entropy of mixing, using molar volumes and Cohesive Energy Density parameters. The equations associated with his mathematical approach are given below (11)... 

Tfaeie have been a number of attempts to develop solvent parameter scales that could be used to correlate ttiermodynamic and kinetic results in terms of these patametois. Gutmann s Donor Numbers, discussed previously, are sometimes used as a solvent property scale. Kamlet and Taft and co-workers developed the solvatochromic parameters, Uj, B, and n that are related to the hydrogen bonding acidity, basicity and polarity, respectively, of the solvent. Correlations with these parameters also use the square of tte Hildebrand solubility parameter, (5, that gives the solvent cohesive energy density. Parameters for some common solvents are collected in Table 3.6. 

The solubility parameter is not calculated directly. It is calculated as the square root of the cohesive energy density. There are a number of group additivity techniques for computing cohesive energy. None of these techniques is best for all polymers. 

Table 8.2 Values of the Cohesive Energy Density (CED) for Some Common Solvents and the Solubility Parameter 6 for These Solvents and Some Common Polymers...

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... 

Thermodynamic Properties The variation in solvent strength of a supercritical fluid From gaslike to hquidlike values may oe described qualitatively in terms of the density, p, or the solubihty parameter, 6 (square root of the cohesive energy density). It is shown For gaseous, hquid, and SCF CO9 as a function of pressure in Fig. 22-17 according to the rigorous thermodynamic definition ... 

The polymer has a low cohesive energy density (the solubility parameter 5 is about 16.1 MPa ) and would be expected to be resistant to solvents of solubility parameter greater than 18.5 MPa. Because it is a crystalline material and does... 

Because of the high cohesive energy density and their crystalline state the polymers are soluble only in a few liquids of similar high solubility parameter and which are capable of specific interaction with the polymers. 

Hansen [137-139], and later van Krevelen [114] proposed the generalization of the solubility parameter concept to attempt to include the effects of strong dipole interactions and hydrogen bonding interactions. It was proposed that the cohesive energy density be written as the sum of three terms, viz. 

We encountered the quantity AE ap/V in Eq. (8-35) it is the cohesive energy density. The square root of this quantity plays an important role in regular solution theory, and Hildebrand named it the solubility parameter, 8. 

This expression is known as the cohesive energy density and in S.I. is expressed in units of megapascals. The square root of this expression is more commonly encountered in quantitative studies and is known as the solubility parameter and given the symbol 6, i.e. ... 

Cohesive energy density is the energy of isothermal vaporization per unit volume to the ideal-gas state. It is the square of the Hildebrand solubility parameter. 

Cohesive energy (or free energy) density parameter (Chaps. XII and XIII). 

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). 

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