Energies cohesive

The cohesive energy Ecoh of a substance in a condensed state is defined as the increase in internal energy U per mole of substance if all the intermolecular forces are eliminated The cohesive energy = Ecoh = Alt (dimension J/mol). 

For liquids of low molar weight, the cohesive energy is closely related to the molar heat of evaporation AHvap (at a given temperature)  

Therefore, for low-molar-mass substances Ecoh can easily be calculated from the heat of evaporation or from the course of the vapour pressure as a function of temperature. As polymers cannot be evaporated, indirect methods have to be used for the determination of their cohesive energy, e.g. comparative swelling or dissolving experiments in liquids of known cohesive energy density. The method is illustrated in Fig. 7.1. 

1 Equilibrium swelling as a function of the solubility parameter of the solvent for linear and cross-linked polymer. The cross-link density of 2 is larger than that of 1. 

Prediction of the cohesive energy by means of additive functions 

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Figure Cl. 1.6. Minimum energy stmctures for neutral Si clusters ( = 12-20) calculated using density functional theory witli tire local density approximation. Cohesive energies per atom are indicated. Note tire two nearly degenerate stmctures of Si g. Ho K M, Shvartsburg A A, Pan B, Lu Z Y, Wang C Z, Wacher J G, Fye J L and Jarrold M F 1998 Nature 392 582, figure 2.

Material properties can be further classified into fundamental properties and derived properties. Fundamental properties are a direct consequence of the molecular structure, such as van der Waals volume, cohesive energy, and heat capacity. Derived properties are not readily identified with a certain aspect of molecular structure. Glass transition temperature, density, solubility, and bulk modulus would be considered derived properties. The way in which fundamental properties are obtained from a simulation is often readily apparent. The way in which derived properties are computed is often an empirically determined combination of fundamental properties. Such empirical methods can give more erratic results, reliable for one class of compounds but not for another. 

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. 

We shall devote a considerable portion of this chapter to discussing the thermodynamics of mixing according to the Flory-Huggins theory. Other important concepts we discuss in less detail include the cohesive energy density, the Flory-Krigbaum theory, and a brief look at charged polymers. 

The quantity AU JV° is the internal energy of vaporization per unit volume and is called the cohesive energy density (CED) of component i. The square root of the CED is generally given the symbol 6j for component i. 

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...

For benzene at 25°C this becomes AU = 33,900 - 8.314 (298) = 31,400 J mol". The molar volume of a compound is given by V° = (molecular weight)/ (density). For benzene at 25°C, this becomes V° = 78.0/0.879 = 88.7 cm mol". Tlie cohesive energy density is simply the ratio AUy/V°, but in evaluating this numerically, the question of units arises. By convention, these are usually expressed in calories per cubic centimeter, so we write... 

A linear relationship exists between the cohesive energy density of an abrasive (10) and the WoodeU wear resistance values occurring between comndum H = 9) and diamond H = 42.5). The cohesive energy density is a measure of the lattice energy per unit volume. 

Therefore, monolayers may consist of two different chemisorption modes ordered in different domains, simultaneously coexisting homogeneous clusters, each characterized by a different conformer in their unit cell. This may explain the observation of 2D Hquid in butane- and hexanethiolate monolayers on gold (278), where VDW interactions do not provide enough cohesive energy to allow for small domains to coexist as a 2D soHd. 

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... 

A more polar comonomer, eg, an AN comonomer, increases the water-vapor transmission more than VC when other factors are constant. For the same reason, AN copolymers are more resistant to penetrants of low cohesive energy density. AH VDC copolymers, however, are very impermeable to ahphatic hydrocarbons. Comonomers that lower T and increase the free volume in the amorphous phase increase permeability more than the polar comonomers higher acrylates are an example. Plasticizers increase permeabiUty for similar reasons. 

The permachor method is an empirical method for predicting the permeabiUties of oxygen, nitrogen, and carbon dioxide in polymers (29). In this method a numerical value is assigned to each constituent part of the polymer. An average number is derived for the polymer, and a simple equation converts the value into a permeabiUty. This method has been shown to be related to the cohesive energy density and the free volume of the polymer (2). The model has been modified to liquid permeation with some success. 

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 ... 

Figure 8.1. The cold compression-tension behavior of condensed matter. The volume dependence of energy and pressure or tension are illustrated. The cohesive energy and maximum tension (theoretical spall strength) are properties of the material.

In (8.1), is the specific cohesive energy, v = 1/p is the specific volume and the reciprocal of the density p. Vq is the specific volume at zero pressure as shown in Fig. 8.1. The final parameter a is constrained by the relation for the bulk modulus... 

Note that the theoretical spall strength now depends upon the cohesive energy as well as the bulk modulus. Representative values for selected metals are shown in Table 8.1. These can be compared with experimental spall strengths in later sections. 

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