Cohesive energy density parameter determinations

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. 

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 ... 

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 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)... 

Table 10.5 Hildebrand s solubility parameter and cohesive energy density determined from this cohesive energy density from bulk modulus Hydroxyl concentration for some networks, (a) Molar ratio dimethacrylate/ methacrylate = 5 x 10 4 (500 ppm) (b) aromatic poly(bismaleimide) from BASF. 

As early as 1916 Hildebrand pointed out that the order of solubility of a given solute in a series of solvents is determined by the internal pressures of the solvents. Later Scatchard (1931) introduced the concept of "cohesive energy density" into Hildebrand s theories, identifying this quantity with the cohesive energy per unit volume. Finally Hildebrand (1936) gave a comprehensive treatment of this concept and proposed the square root of the cohesive energy density as a parameter identifying the behaviour of specific solvents. In 1949 he proposed the term solubility parameter and the symbol S. 

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). 

There are many common features, as well as differences, between the main physical factors determining the cohesive energy density (or the solubility parameter), and those determining other important properties such as the surface tension (Chapter 7), dielectric constant and effective dipole moment (Chapter 9). See references [18], [21] and [22] for examples of the use... 

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. 

The energy of vaporization is not accessible for polymers, but cohesive energy density of polymers can be determined from PVT-data. However, common ways for determining polymer solubility parameters use thermodynamic properties of polymer solutions and their relations to excess enthalpy or excess Gibbs energy per unit volume. These excess quantities are related to the (square) difference between the solubility parameters of solvents and polymers, i.e. (d -... 

An important criterion for determining the chemical compatibility between an adherend and an adhesive in a solvent is the solubility parameter, 6. The solubility parameter is the square root of the cohesive energy density, CED ... 

The concept of the solubility parameter 6, which is frequently used in studies of polymer compatibility, is not always applicable. The solubility parameter is equal to the square root of the substance s cohesion energy density (6 = VDEC) and reflects only intermolecular interaction without accounting for the entropy factor. This parameter is an integral characteristic of only intermolecular interaction, and the components miscibility is determined by the presence of functional groups capable of specific interactions in the polymer molecules. This is why... 

The need to measure interactions in polymer systems was recognized early in the evolution of the polymer field. One widely practised approach is through the determination of "solubility" or "cohesion" parameters,6. The parameter is, in effect, a cohesive energy density, as defined by Hildebrand in... 

A computational model based on molecular dynamics was developed to predict the miscibility of indomethacin in the carriers polyethylene oxide (PEO), glucose, and sucrose (Gupta et al. 2011). The cohesive energy density and the solubility parameters were determined by simulations using the condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field. The simulations predicted miscibility for indomethacin with PEO (A5 < 2), borderline miscibility with sucrose (A5 < 7), and immiscibility with glucose (A5 > 10 Table 2.2). 

The polymer solubility parameter 5 value can be determined by its cohesion energy density W as follows [10] ... 

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