Volume, dependent cohesion parameter

Fig. 8. Volume-dependent cohesion parameter (8 ) versus Hansen hydrogen-bonding parameter for polylactide and ethers. Values indicated for solvents with A8<5MPa (FUR, furan EPH, epichlorohydrin THD, tetrahydrofuran 14D, 1,4-dioxane MEL, methylal (dimethoxymethane) BCE, bis(2-chloroethyl) ether ANI, anisole (methoxyben-zene) DME, di-(2-methoxyethyl) ether DBE, dibenzyl ether PXP, bis-(m-phenoxyphenol) ether).

Fig. 9. Volume-dependent cohesion parameter (S ) versus Hansen hydrogen-bonding parameter for polylactide and alcohol. Values indicated for solvents with AS <5 MPa (3CP, 3-chloropropanol BEA, benzyl alcohol CHL, cyclohexanol IPL, 1-pentanol 2EB, 2-ethyl-1-butanol DAL, diacetone alcohol DBU, 1,3-dimethyl-l-butanol ELA, ethyl lactate BLA, n-butyl lactate EME, ethylene glycol monoethyl ether DGM, diethylene glycol monoethyl ethermethyl DGE, diethylene glycol monoethyl ether EGB, ethylene glycol mono-n-butyl ether 2EH, 2-ethyl-1-hexanol lOL, 1-octanol 20L, 2-octanol DGN, diethylene glycol mono n-butyl ether IDE, 1-decanol TDA, l-tridecanol NON, nonyl OA9, oleyl alcohol).

Bagley and co-workers [14,15,80,81] and Scigliano [82] utilized the chemical-bond-discriminating property of cohesive and internal pressures to subdivide the Hildebrand parameter in another way. One part corresponding to the physical or nonchemical effects is the volume-dependent Hildebrand parameter, defined by... 

In this approach, connectivity indices were used as the principle descriptor of the topology of the repeat unit of a polymer. The connectivity indices of various polymers were first correlated directly with the experimental data for six different physical properties. The six properties were Van der Waals volume (Vw), molar volume (V), heat capacity (Cp), solubility parameter (5), glass transition temperature Tfj, and cohesive energies ( coh) for the 45 different polymers. Available data were used to establish the dependence of these properties on the topological indices. All the experimental data for these properties were trained simultaneously in the proposed neural network model in order to develop an overall cause-effect relationship for all six properties. 

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. 

Using PCA, Cramer found that more than 95% of the variances in six physical properties (activity coefficient, partition coefficient, boiling point, molar refractivity, molar volume, and molar vaporization enthalpy) of 114 pure liquids can be explained in terms of only two parameters which are characteristic of the solvent molecule (Cramer 111, 1980). These two factors are correlated to the molecular bulk and cohesiveness of the individual solvent molecules, the interaction of which depends mainly upon nonspecific, weak intermolecular forces. 

The Rq equation combines both the HLB and cohesive energy densities, and provides a more quantitative estimate of emulsifier selection, while R considers HLB, molar volume and chemical match. The success of this approach depends on the availability of data relating to the solubility parameters of the various surfactant portions some values are provided in the book by Barton [24]. 

The cavity term is a measure of the endoergic cavity-forming process, that is, the free energy necessary to separate the solvent molecules, overcoming solvent-solvent cohesive interactions, and provide a suitably size cavity for the solute. The magnitude of the cavity term depends on the —> Hildebrand solubility parameter 5na.nd volume descriptors ofthe solute. The solute volume... 

Values of solubility parameters and cohesive energy of some polymers are given in Table 3.7. The value of E,oi, is also dependent on the molar volume. For polymers the appropriate volume is that occupied by each repeat unit in the solid state. Thus E qj, represents the cohesive energy per repeat unit volume, Vr. These simple relations as stated before, however, are not exact stronger interactions change the validity of Equation 3.11. However, significant practical predictions can be made from the values in Table 3.7, such as what solvents will dissolve a given polymer. 

Askadskii has shown that Fedors assumption that the contributions of atoms or groups of atoms are additive is not quite correct because the same atom in different groups occupies different volume. In addition, atoms can interact with each other in a different way depending on their arrangement within the molecular stracture. These influences were taken into account to increase the precision of the computation of the cohesion energy in a new calculation method for solubility parameters. This takes into a consideration the enviromnent of each atom in a molecule and the type of intermolecular interaction. 

The diffusivity D is a kinetic parameter related to polymer mobility, while the solubility coefficient is a thermodynamic parameter which is dependent upon the strength of the interactions in the polymer-penetrant mixture. Chemical modifications of polymers affect the coefficients of diffusion and of solubility. Changes in material structure have a greater effect on diffusion coefficient, whereas the solubility coefficient depends mainly on the character of the low-molecular-mass compound. Permeability is determined by factors such as the magnitude of the free volume, and crosslinking which reduces the segmental mobility and the free volume and diminishes the permeability coefficient. A reduction of interchain cohesion and of crystallinity increases the permeability coefficient. The transition from the amorphous to the crystaUine state usually decreases the permeability. A decrease in crystallinity may increase the permeability. The permeability of polymers is determined primarily by the amount of the amorphous phase [62,300, 301]. 

The remaining interactions in molecules that have permanent dipole moments, that is, the dipole-dipole and dipole-induced-dipole interactions, have the same dependence on intermolecular separation as the London potential, varying as and are of lesser magnitude at ordinary temperatures (Atkins, 1998). These two interactions and the previously mentioned dispersion interaction are collectively known as van der Waals interactions. They are related to such measurable properties as surface tension and energy of vaporization, and to concepts such as the internal pressure, the cohesive energy density (energy of vaporization per unit volume, A UIV), and the solubility parameter, 6, which is the square root of the cohesive energy density (Hildebrand and Scott, 1962). 

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