Molar volume group contributions

For polymers the solubility coefficient is calculated for the polymer repeat unit. Where no molar volume data exists (e.g. for polymers) then a molar volume group contribution estimation method must be used (Van Krevelen, 1990). 

Table I. Group Molar Attraction Constant, Fj, and Molar Volume Group Contributions V, of Rubbery Amorphous...

Table II. Group Contributions to the Cohesive Energy, Ui and and Molar Volume Group Contributions, Vi, at 25°C...

Taking into account the molar volume group contributions for glassy polymers 18) and the group molar attraction constants at 25°C, the calculated values of 5ptba... 

Suface Tension. The relationship between surface tension and Hquid molar volume (220), and the group contribution methods for Hquid molar volume can be utilized to estimate surface tension. 

Tyn-Calus This correlation requires data in the form of molar volumes and parachors = ViCp (a property which, over moderate temperature ranges, is nearly constant), measured at the same temperature (not necessarily the temperature of interest). The parachors for the components may also be evaluated at different temperatures from each other. Quale has compiled values of fj for many chemicals. Group contribution methods are available for estimation purposes (Reid et al.). The following suggestions were made by Reid et al. The correlation is constrained to cases in which fig < 30 cP. If the solute is water or if the solute is an organic acid and the solvent is not water or a short-chain alcohol, dimerization of the solute A should be assumed for purposes of estimating its volume and parachor. For example, the appropriate values for water as solute at 25°C are = 37.4 cmVmol and yn = 105.2 cm g Vs mol. Finally, if the solute is nonpolar, the solvent volume and parachor should be multiplied by 8 Ig. 

Constantinou, L., R. Gani, and J. P. O Connell, "Estimation of the acentric factor and the liquid molar volume at 298K through a new group contribution method". Fluid Phase Equilibria 103, 11, (1995). 

In the above table, Mj, Vi, Yj and Hj are the contributions for group i for estimating the molecular weight, the molar volume, the glass-transition temperature, and the water absorption, respectively. The model equations for each of these properties are as follows ... 

Values of molar volumes can be calculated from densities measured for the liquid salt, or can be calculated as for hypothetical subcooled liquid at 298.15 K using the group contribution method [47]. As expected, the molar volumes of 1,3-dialkylimidazolium salts and quaternary ammonium salts increase progressively as the length of alkyl chain of the substituent increases. Some molar volumes values at 298.15 K are listed in Table 1.3. 

LSER Model of Leahy In the LSER model of Leahy [22], the cavity term is substituted by the molar volume, Vm, at 25°C in g cm-3 or by the intrinsic molecular volume, V), in mLmoL1. The dipolar term and the hydrogen-bonding terms are represented by the dipole moment, n, and the HBA basicity, (3, respectively. Group contribution schemes have been developed to calculate the solvatochromic parameters from molecular structure input [23]. Leahy [22] gives the following equation derived with a diverse set of monofunctional liquids ... 

The molar attraction constants of dispersiS, dipole-dipole interactionsFpi hydrogen bonding,Ehi and the molar volume/ forthe drug and the hydrophobic block may be determined from group contribution tables provided by Hoftyzer-Van Krevelen and Fedor (Krevelen, 1990). 

All current activity coefficient estimation models are by necessity semi-empirical in nature, because too little is known about solution theory for outright estimation. Chemical modeling is not readily available and is not far enough developed to make this type of calculation. The constants required by these models must be estimated using either experimental data (e.g. an infinite dilution activity coefficient or a molar volume) or group contributions derived from experimental data (e.g. interaction constants, molecular volumes and surface areas). 

It will be shown that the molar volumetric properties can be calculated with a remarkable accuracy from additive group contributions. Furthermore there exist interesting correlations with the Van der Waals volume. 

The molar volume at room temperature is one of the first physical quantities, for which group contribution methods have been proposed. Atomic contribution methods were derived by Traube (1895) and by Le Bas (1915). A characteristic difference between the two approaches was that Traube added to the sum of atomic contributions for a given compound an additional value called "residual volume" (Q), so that... 

TABLE 4.4 Group contribution of CH2 to molar volume of liquids... 

The best confirmations of the additivity of molar volume were obtained from the studies of homologous series. Studies of several series of compounds with increasing numbers of CH2 groups have led to rather accurate values for the contribution of this group to the molar volume. Values found by several investigators are summarised in Table 4.4. The mean value is 16.45 cm3/mol with a standard deviation of 0.2 cm3/mol. 

The rubbery amorphous state of polymers has the greatest correspondence with the liquid state of organic compounds. So it may be expected that the molar volume per structural unit of polymers in this state can be predicted by using the averaged values of the group contributions mentioned in Table 4.5 (Van Krevelen and Hoftyzer, 1969). 

TABLE 4.5 Group contributions to the molar volume of organic liquids at room temperature (cmVmol) ... 

At room temperature, those amorphous polymers are in the rubbery state of which the glass transition temperature is lower than 25 °C. The available literature data on the densities for this class of polymers are mentioned in Table 4.6. For each polymer, the molar volume Vr has been calculated from the density. These values of Vr have been compared with Eq. (4.3), using group contributions mentioned in Table 4.4. Although there was an... 

Table 4.10 gives our recommended values for the group contributions (increments) to the various molar volumes at 298 K. 

The molar volume V = 123.8 cm3/mol. Addition of the group contributions gives... 

Due to the fact that the extrapolation of surface tensions of melts to room temperature leads to reliable values for the solid polymer, the surface tension of solid polymers may be calculated from the parachor per structural unit by applying Eq. (8.5). The molar volume of the amorphous state has to be used, since semi-crystalline polymers usually have amorphous surfaces when prepared by cooling from the melt. We have found that the original group contributions given by Sugden show the best correspondence with experimental values for polymers. 

From Table 8.1 (Sugden s values) we obtain the following group contributions to the parachor and the molar volume ... 

Recommended values for group contributions to standard molar volume, 87 Recoverable shear, 531,551 Recoverable shear strain, 551 Recrystallisation, 703 Rectilinear flow, 527 Redox doping, 341 Reduced... 

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