Structure-molar volume relationship

STRUCTURE-DENSITY AND STRUCTURE-MOLAR VOLUME RELATIONSHIPS 41... 

STRUCTURE-DENSIT YAND STRUCTURE-MOLAR VOLUME RELATIONSHIPS 43... 

The octanol-water partition coefficient, Kow, is the most widely used descriptor of hydrophobicity in quantitative structure activity relationships (QSAR), which are used to describe sorption to organic matter, soil, and sediments [15], bioaccumulation [104], and toxicity [105 107J. Octanol is an amphiphilic bulk solvent with a molar volume of 0.12 dm3 mol when saturated with water. In the octanol-water system, octanol contains 2.3 mol dm 3 of water (one molecule of water per four molecules of octanol) and water is saturated with 4.5 x 10-3 mol dm 3 octanol. Octanol is more suitable than any other solvent system (for) mimicking biological membranes and organic matter properties, because it contains an aliphatic alkyl chain for pure van der Waals interactions plus the alcohol group, which can act as a hydrogen donor and acceptor. 

Provided, therefore, the additive contributions for different structural components can be quantified, the partition coefficient can be readily computed, A long established and convenient means for such quantification is already available in the form of the parachor, which is equivalent to the molar volume of a substance when its surface tension is unity. Parachor is primarily an additive property and there are extensive tabulations of parachor equivalents for various structural elements, such as that by Quayle (30). Parachor (H) can be related to partition coefficient (P) using the relationship of McGowan (3I) -... 

The correlation between aqueous solubility and molar volume discussed by McAuliffe [5] for hydrocarbons, and the importance of the cavity term in the solvatochromic approach, indicates a significant solubility dependence on the molecular size and shape of solutes. Molecular size and shape parameters frequently used in quantitative structure-water solubility relationships (QSWSRs) are molecular volume and molecular connectivity indices. Moriguchi et al. [33] evaluated the following relationship to estimate Cw of apolar compounds and a variety of derivatives with hydrophilic groups ... 

In the first approach the activity of 3-alkyl and 3-alkylthio 1,1,l-trifluoro-propan-2-ones was considered for their structure-activity relationship (SAR) with MR. MR was used in the present study to model the enzyme-inhibitor attraction forces since MR is related to London dispersion forces (21,62,63) and has been also proposed to be really a corrected form of the molar volume (21). Figure 6 shows a clear parabolic relation between the molar I50... 

In their study of the fluoride ion affinities of various fluoroacids Mallouk et al. (Mallouk, T. E. Rosenthal, G. L. Muller, G. Brusasco, R. Bartlett, N. Inorg. Chem. 1984, 23, 3167-3173) employed the linear dependence of lattice energy upon the inverse of the cube root of the formula unit volume to determine the lattice energies of salts of unknown structure. From that empirical relationship which is (kcal mol" ) = 556.3 (molar volume in A )- / + 26.3, l/UCfiFfiAsPs) =115 kcal mol" and C/L(C,oFgAsF6) 108 kcal mol". ... 

Hayes Method. A relationship between polymer structure, glass transition temperature and molar cohesive energy (cohesive energy density multiplied by the molar volume) was found by Hayes (9) ... 

Correlations of Solubility with Molecular Parameters. The aqueous solubility of aromatic hydrocarbons has been shown by Klevens (25) to be related to carbon number, molar volume, and molecular length. These parameters along with the molar solubilities (expressed as — In S) of the compounds studied are presented in Table XIII. Figures 5 through 7 demonstrate the relationship between each of these parameters and solubility. These figures show that there are several compounds whose anomalous behavior makes accurate extrapolations of solubility from these relationships impossible. For example, anthracene and phenanthrene are structural isomers. They, therefore, have identical carbon numbers and very similar molar volumes. However, their aqueous solubilities differ by more than a factor of 20. Phenanthrene, fluoranthene, pyrene, and triphenylene all have very similar molecular lengths but their respective aqueous molar solubilities at 25°C are 5.6 X 10 6, 1.0 X 10"6, 6.8 X 10"7, and 2.8 X 10 8. 

The quantity of a substance that can be solubilized in surfactant micelles will depend on many factors, some of which have already been discussed. From the standpoint of the additive itself, such factors as molecular size and shape, polarity, branching, and the electronegativity of constituent atoms have all been found to be of some significance, depending on the exact system. One extensively explored factor relating the chemical structure of the additive to its solubilization is the relationship between the molar volume of the additive and the maximum amount of material that can be incorporated in a given surfactant solution. In general, one finds an inverse relationship between the molecular volume of the additive and the amount of material solubilized. 

Equation 2.10, which is a simplified form of the Wilke-Chang equation [11], shows the relationship between temperature and diffusion. In this equation. S is a constant that depends bothonthe solvent and the analyte molecule. For those who are interested in the quantitative relationship, the diffusion coefficient is inversely proportional the molar volume to the power ofO.6, so approximately to the square route of molecular mass (depending on detailed molecular structure, in particular for macromolecules). In this example, neither the solvent nor analyte is altered, and thus it can be directly concluded how the temperature influences the diffusion 2.10. It shows the linear increase of with increasing temperature, but at the same time we have to consider the decrease in viscosity, which is also a function of temperature, thus increasing the diffusion coefficient even more. 

The simplest structural descriptors are just the number of carbon atoms, or molecular weight, that is linearly related to the increase in gas chromatographic retention among a homologous series of compounds. This simple relationship led to the development of the Kovits retention index scale. A linear relationship between Kovits retention index and carbon number for homo-logues has been shown to hold for a number of chemical groups. Molar volume, molar refractivity, and molecular polarizability are other simple descriptors of molecular bulk that have been used in QSRR studies. 

The principal refractive indices and and the birefringence A = - of 40 ne-matogenic compounds (A=589 nm) for a temperature T n-i -7 =10K, are listed in Table 1. It follows from Eq. (8) that at a constant reduced temperature the magnitude of the birefringence is mainly determined by the molecular polarizability anisotropy a,-0[, but also by the molar volume V=M/p. On the other hand, a, - (Zt depends strongly on the structural features of the molecules. As can be seen from Table 1 some general relationships between molecular structure and birefringence can be derived ... 

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