Percepciones

The polarisability correction term^ Ô, used in equation (11-12), is an empirical factor limited to one of three values, 0.5 for halogenated aliphatics, 1.0 for aromatics or 0.0 for all other compounds. The alternative for Ô selected by Abraham 1^^, was the excess molar refiraction.

Molar refi*action, MRx, is often used as a measure of polarisability and can be defined as:

MRx = 10[(n^-l)/(n^ + 2)]V (01-3)

Where

• n is the refiractive index of a solute that is liquid at 20®C (for solids, the refractive index of the hypothetical liquid at 20°C can be calculated)

• V is the McGowan characteristic volume in (cm^moT^)/100.

Because of the volume term in molar refiraction, the latter always increase with increasing size. The refractive index function itself is rather better indication of the

presence of polaiisable electrons in a molecule; thus values of the refractive index are always larger for aromatic or halogenated aliphatic compounds than for other aliphatics. The excess molar refraction, E, (lO'^cm^moT^) is:

E — MRx(observed) ” MRx(for alVane wifli same V ) (1 1 1 " 4 )

By substracting the molar refraction for an alkane of the same characteristic volume, the dispersive component of molar refraction (already accounted in V and L in the solvation equation) is removed. E provides a quantitative measure of the ability of a solute to interact with the solvent through n and n electrons.

For liquids:

E can be obtained from the experimental refractive index, n, (20°C sodium D lamp) for solutes that are liquid at 20®c using a modified Lorentz-Lorentz equation:

E = M R x - (MRx)alkane (III-5 )

where MRx = 10[(n^-1 )/(n^ + 2)]V

and (MRx)aikanc = 2 .8 3 1 9 5 .V - 0.52553 (m-6)

For solids:

The refractive index of the hypothetical liquid at 20°C can be calculated or, as molar refraction is an additive property, it is assumed that E is too. Thus, E can be obtained by the summation of known E values of molecular fiagments or substructures o f the compound

ni-2.2 S, the polarisability/dipolarity descriptor

In equation (U-2), n*i was used instead of the solute dipolarity/polarisability term, ti*. Several problems arise from these ti terms:

• Til* is experimentally accessible only for compounds that are liquid at 298 K. Therefore, values of t i * had to be estimated for associated compounds such as acids, phenols, alcohols and amides as well as gaseous and solid solutes.

• T ti* is suggested to be identical to Tt* for non-associated liquids, but this may not always be the case.

It therefore seemed necessary to develop a method that would allow the determination o f a dipolarity / polarisability scale, S (previously called 712^), that would be free energy related and include all types of solute molecule. Abraham and co-workers constructed the new dipolar / polarisability parameter, S, from the extensive sets of retention gas liquid chromatographic (GLC) data and hundreds of solutes S values were thereby obtained

ni-2.3 A and B, the hydrogen bond acidity and basicity

In equation (11-12), a new descriptor, am, had to be developed in order to represent the solute hydrogen bond acidity and pi W2is used as a surrogate for p. Abraham et al developed an acidity and a basicity scale using 1:1 complexation constants, log K, of a series of monomeric acids against given reference bases in tetrachloromethane at 298K:

A H + ;B - — ^ A H . .. B

Abraham showed that log K values for bases against 34 reference acids in tetrachloromethane could be assembled as a set of 34 linear equations of the following form:

Log K = LA.logK^B + Da (HI-7)

Where:

• Log K^b defines a solute hydrogen bond basicity scale over a range of reference

acids

• La and Da characterise the particular acid

It was found that the equations intersected at log K^b = -1.1 and a natural origin or zero

point could be established. The origin was shifted to zero. The final scale was defined as:

p" 2 = (log K"b +1 .1)/4.636 (m-8)

A similar approach was used to develop a hydrogen bond acidity scale, log Kb , using

1:1 hydrogen bond complexation equilibrium constants in tetrachloromethane against given reference acids was developed. The origin of the scale was again (-1,1) and was shifted to zero. The final scale was defined as:

The relation between 2 and was found via the correlation of 1312 equilibrium constants in tetrachloromethane^^^l

Log K = 7.354 a^2 P^2 - 1.094 * (IH-l0)

n = 1312, = 0.9912, sd = 0.09

a^2 and p^2 values define the influence of solute structure on 1:1 complexation, but when the solute is surrounded by solvent molecules, it will undergo multiple hydrogen bonding. The ‘summation’ or ‘overall’ hydrogen bonding is then designated by Za^2 and Ep^2 that represents the ability of a solute to interact with a large excess of solvent molecules.

N.B.(1): The new notations for Ea^2 and zp^2 are A and B

N.B.(2): The H bond basicity of certain solutes in water-solvent partitions seems to vary with the particular water-solvent system. For a large number of solutes, ZP2^ is constant and can be used in equations that describe any gas to condensed phase process and any water-solvent partition process. However, EP2” has to be modified for certain water- solvent partition processes.

It has been observed that the hydrogen bond basicity of certain compounds was different for transfer between water and wet or dry solvents that contain a rather high proportion of water when saturated (e.g. octanol, ethyl acetate, diethyl ether etc). Zp2^ is replaced by Zp2^ for these solutes whose basicity is found to change substantially between wet and diy solvents:

• aniline and alkylanilines • pyridine and alkylpyridines

• sulphoxides (but not sulphones or sulphonamides)^^^^

ni-2.4 V, the Me Gowan characteristic volume

V (previously called Vx) is the McGowan characteristic volume (in cm^mol'VlOO)^^^"^^^ and represents the three-dimensional space occupied by a solute. It can be easily calculated by simple summation of bonds and atoms in the molecule. All bonds, whether single double or triple, count as ‘one bond’.

Abraham’s calculation of the Me Gowan volume:

B = N - 1 + R g (m-11)

Where B = number of bonds,

with all bonds (single, double, triple) counting as one N = total number of atoms

Rg = total number of ring structures V can then be calculated as follow:

V = (Eatom contribution - (6.56x B))/100 (m-12)

Table 1 : Atom contribution, in cm ^ mol"^

C = 16.35 N = 14.39 0 = 1 2 . 43 F = 10.48 H = 8.71 Si = 26.83 P = 24.78 8 = 22.91 01 = 20.95 B = 18.32 Ge = 31.02 As = 29.42 Se = 27.81 Br = 26.21

Sn = 39.35 Sb = 37.74 Te = 36.14 1 = 34.35

IÏI-2.5 L, the gas-hexadecane partition coefficient

If we consider the first step in the cavity theory of solvation, the larger the solute, the larger will be the cavity. But from step 3, the larger the solute, the larger will be its tendency to take part in solute-solvent interactions of the general London dispersion type. To combine the two effects, L (previously called log or Ostwald solubility coefficient was defined as solute gas-hexadecane partition coefficient at

L = Iconcentration of solute in hexadecanel (111-13) [concentration of solute in gas phase]

Abraham chose hexadecane as a reference solvent for solute descriptor as it is a readily available non-polar liquid of well-defined structure. In addition, L can be readily obtained from GLC measurements.

For volatile compounds:

L can be obtained by direct GLC measurements using packed columns coated with hexadecane at 298K and a number of n-alkanes are measured as standards. L of the test solute can then be determined jfrom its retention time.

For non-volatile compounds:

A similar approach can be used with non-polar stationary phases at more elevated temperatures. In this case, the non-polar stationary phase is calibrated using the solvation equation with only E and L.

Log ( Ir) = c + e.E + l.L (III-1 4 )

So that knowing, log ( Ir) and E for the solute of interest, and the coefficients, c, e and 1,

L can be readily obtained.

The first four descriptors, E, S, A and B, can be regarded as measures of the tendency of a solute to undergo various solute / solvent interactions, all of which are energetically favourable, i.e. exoergic. On the other hand, L and V are both measure of the size of a solute, so will be a measure of the cavity term. Furthermore, since the size of the solute is related to general dispersion interactions, both L and V describe solute / solvent dispersion interactions