Cohesive pressure

The long-range van der Waals interaction provides a cohesive pressure for a thin film that is equal to the mutual attractive force per square centimeter of two slabs of the same material as the film and separated by a thickness equal to that of the film. Consider a long column of the material of unit cross section. Let it be cut in the middle and the two halves separated by d, the film thickness. Then, from one outside end of one of each half, slice off a layer of thickness d insert one of these into the gap. The system now differs from the starting point by the presence of an isolated thin layer. Show by suitable analysis of this sequence that the opening statement is correct. Note About the only assumptions needed are that interactions are superimposable and that they are finite in range. 

Cohesive Pressure, Internal Pressure, and Solubility Parameter... 

The cohesive pressure (c) of a solvent, otherwise known as cohesive energy density (CED), is a measure of the attractive forces acting in a liquid, including dispersive, dipolar and H-bonding contributions, and is related to the energy of vaporization and the molar volume (Equation 1.1) ... 

Table 1.5 Cohesive pressures (c), Hildebrand s solubility parameter (5), and internal pressures (n) for a range of representative solvents [1, 2]...

As already mentioned, the cavity term corresponds to the endoeigic process of separating the solvent molecules to provide a suitably sized and shaped enclosure for the solute, and measures the work required for such a purpose. This term is related to the tightness or structuredness of solvents as caused by intermolecular solvent/solvent interactions. The association of solvent molecules in the liquid state in order to accommodate the solute molecules can be quantified by means of the surface area and texture of the solute that are related with the m coefficient and by the cohesive pressure of the solvent given by fl. 

As a cavity has to he opened in a solvent in order to introduce a solute, the strength of the solvent-solvent bonding will be a factor in determining solubility. The cohesive pressure, c, is defined by eqn. 3.1. 

The cohesive pressure c is a measure of the total molecular cohesion per unit volume, given by eqn. 3.11... 

The square root of the cohesive pressure c as defined in eqn. 3.11 has been termed the solubility parameter 5 by Hildebrand and Scott (1962) because of its value in correlating and predicting the solvency of solvents for nonelectrolyte solutes. Solvency is defined as the ability of solvents to dissolve a compound. A selection of 5-values is given in table 3.10. 

Cohesion Pressure. A term in Van der Waal s equation introduced to take care of the effect of molecular attraction. It is usually expressed as a/Vwhere at is a constant and V is the volume of the gas. 

The solubility parameter is defined as the square root of the cohesive energy density. The most common presentation of the solubility parameter is in units of cal1/2cm 3/2. Here, the cohesive energy is expressed per unit volume. A more modem format that is found in some of the literature after 1990 utilizes SI units derived from cohesive pressures. It is possible to convert between the two scales with the following equations ... 

Thus, as a rough guide, the solubility parameters expressed in the SI system of cohesive pressures are numerically approximately double the values expressed in the older system. 

Dipole moment Cohesive pressure Dielectric constant Refractive index Melting point and boiling point Donor numbers Acceptor numbers E, a, and 7t ... 

The square route of the cohesive pressure is termed Hildebrand s solubility parameter (5). Hildebrand observed that two liquids are miscible if the difference in 5 is less than 3.4 units, and this is a useful rule of thumb. However, it is worth mentioning that the inverse of this statement is not always correct, and that some solvents with differences larger than 3.4 are miscible. For example, water and ethanol have values for 5 of 47.9 and 26.0 MPa°-, respectively, but are miscible in all proportions. The values in the table are measured at 25 °C. In general, liquids become more miscible with one another as temperature increases, because the intermolecular forces are disrupted by vibrational motion, reducing the strength of the solvent-solvent interactions. Some solvents that are immiscible at room temperature may become miscible at higher temperature, a phenomenon used advantageously in multiphasic reactions. 

In this connection, two other physical solvent properties are important the cohesive pressure c (also called cohesive energy density) and the internal pressure r of a solvent [98-100, 175]. 

Table 3-2. Cohesive pressures, c, internal pressures, k, and their ratio n = njc for thirty organic solvents, arranged in order of decreasing n, that is, in order of increasing structuredness , at 20 °C [99, 154, 175].

The final limitation of the pure electrostatic theory is its inability to predict solvent effects for reactions involving isopolar transition states. Since no creation, destruction, or distribution of charge occurs on passing from the reactants to the activated complex of these reactions, their rates are expected to be solvent-independent. However, the observed rate constants usually vary with solvent, although the variations rarely exceed one order of magnitude [cf. Section 5.3.3). These solvent effects may be explained in terms of cohesive forces of a solvent acting on a solute, usually measured by the cohesive pressure of the solvent [cf. Section 5.4.2). 

In any solution reaction, cavities in the solvent must be created to accommodate reactants, activated complex, and products. Thus, the ease with which solvent molecules can be separated from each other to form these cavities is an important factor in solute solubility cf. Section 2.1). Furthermore, because solubility and reactivity are often related phenomena, the intermolecular forces between solvent molecules must also influence rates of reaction. The overall attractive forces between solvent molecules gives the solvent as a whole a cohesion which must be overcome before a cavity is created. The degree of cohesion may be estimated using the surface tension, but a more reliable estimate is obtained by considering the energy necessary to separate the solvent molecules. This is known as the cohesive pressure c (also called cohesive energy density) [228-... 

Values of c are calculated from experimentally determined enthalpies (heats) of vapourization of the solvent to a gas of zero pressure, AH, at a temperature T, as well as from the molecular mass M, the density of the solvent g, and the gas constant, R. The cohesive pressure characterizes the amount of energy needed to separate molecules of a Hquid and is therefore a measure of the attractive forces between solvent molecules. The cohesive pressure c is related to the internal pressure n, because cohesion is related to the pressure within a liquid cf. Eq. (3-6) in Section 3.2 for the precise definition of n. ... 

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