Hildebrand parameter

Vandenburg et al. [37,489] have described the use of Hildebrand solubility parameters in a simple and fast solvent selection procedure for PFE of a variety of polymers. Hildebrand parameters for several common solvents and polymers are presented in Tables 3.2 and 3.34, respectively. When the proper solvent mixture for the polymer was determined, PFE resulted in essentially the same recoveries as the traditional extraction methods, but used much less time and solvent. PFE can be used to give very fast extractions and appears to offer the greatest flexibility of solvents and solvent mixtures. The method is ideal for a laboratory which analyses a large number of different polymers. 

Table 3.3. Calculated global properties and experimentally derived Hildebrand parameters (8) for a group of organic molecules.

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). 

Hildebrand parameter and high polarity advantageously influence organic chemical reactions (such as hydroformylation), has sufficiently high polarity and density differences compared to organic (reaction) products to enable separation of the phases after the homogeneously catalyzed reaction is completed [17]. 

The Hildebrand parameter as the unit of solubility of non-electrolytes in organic solvents/ reaction products is high... 

Many solvent properties are related to density and vary with pressure in a SCF. These include the dielectric constant (er), the Hildebrand parameter (S) and n [5], The amount a parameter varies with pressure is different for each substance. So, for example, for scC02, which is very nonpolar, there is very little variation in the dielectric constant with pressure. However, the dielectric constants of both water and fluoroform vary considerably with pressure (Figure 6.3). This variation leads to the concept of tunable solvent parameters. If a property shows a strong pressure dependence, then it is possible to tune the parameter to that required for a particular process simply by altering the pressure [6], This may be useful in selectively extracting natural products or even in varying the chemical potential of reactants and catalysts in a reaction to alter the rate or product distributions of the reaction. 

RESONANCE RAMAN SPECTROSCOPY HILDEBRAND PARAMETER HILL COEFFICIENT... 

One of the approaches to calculating the solubility of compounds was developed by Hildebrand. In his approach, a regular solution involves no entropy change when a small amount of one of its components is transferred to it from an ideal solution of the same composition when the total volume remains the same. In other words, a regular solution can have a non-ideal enthalpy of formation but must have an ideal entropy of formation. In this theory, a quantity called the Hildebrand parameter is defined as ... 

Where 5 = Hildebrand parameter AU = molar energy of vaporization of i Vi = molar volume of i. 

Because the entropy of formation in Hildebrand theory is ideal, this approach should be restricted to those systems in which there are no structure effects due to solute-solvent and solvent-solvent interactions. The implication of this is that the solute should be non-ionic and not have functional groups which can interact with the solvent. According to Equation (4.8), the maximum solubility occurs when the Hildebrand parameter of the solvent is equal to the Hildebrand parameter of the solute. That is, when plotting the solubility versus the Hildebrand parameter, the solubility exhibits a maximum when the solubility parameter of the solvent is equal to the solubility parameter of the solute. 

The Hildebrand parameter for the solvent in Equation (4.8), 61, needs to be replaced by the value for the mixture determined by multiplying the pure solvent values by their volume fractions as given below for a two-solvent system. 

Even though Hildebrand theory should not apply to solvent systems having considerable solvent-solvent or solute-solvent interactions, the solubility of compounds in co-solvent systems have been found to correlate with the Hildebrand parameter and dielectric constant of the solvent mixture. Often the solubility exhibits a maximum when plotting the solubility versus either the mixed solvent Hildebrand parameter or the solvent dielectric constant. When comparing different solvent systems of similar solvents, such as a series of alcohols and water, the maximum solubility occurs at approximately the same dielectric constant or Hildebrand parameter. This does not mean that the solubilities exhibit the same maximum solubility. 

Hildebrand parameter A parameter measuring the cohesion of a solvent (energy required to create a cavity in the solvent). 

The solubility parameter has found previous use in membrane science. Casting solution components and composition have been selected using the Hansen solubility parameters (68-71). The total Hansen solubility parameter, which is equivalent to the Hildebrand parameter (.72), has been used to explain permeation and separation in reverse osmosis (23). Hansen s partial parameters have also been used to explain permeation and separation in pervaporatlon (61). The findings of these studies (61,73) plus those reported elsewhere in this volume (74) do lend credence to the use of 6, 6, and 6, for membrane material selection. 

Of direct importance for the aqueous biphase processes are the physiological (entries 2,4 of Table 2), economic (1,3,6), ecological/safety-related (2,4), process engineering (1, 6, 7, 9, 11, 12, 13), and chemical and physical properties (1,5,6,8,10,12,14) of water. The different properties interact and complement each other. Thus water, whose high Hildebrand parameter [31, 32] and high polarity advantageously influence organic chemical reactions (such as hydro-... 

High Hildebrand parameter as unit of solubility of nonelectrolytes in organic solvents... 

Figure 1.1-3 The density and the solvent power (as expressed by the Hildebrand parameter) of SCCO2 as a function of temperature and pressure [IS, 16].

In an attempt to improve on the Hildebrand parameter and take into account the range of intermolecular interactions present in the majority of real fluids, there have been a number of multi-contribution derivations of the Hildebrand parameter (4). Probably the best known of these are the Hansen parameters where the Hildebrand parameter is broken down into three intermolecular contributions - dispersion forces, polar forces and hydrogen bonding forces ... 

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