water partition coefficients Kow: A critical examination of the value of the methylene group contribution to log Kow for homologous series of organic compounds

Fluid Phase Equilibria 368 (2014) 120–141

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Octanol/water partition coefficients Kow : A critical examination of the value of the methylene group contribution to log Kow for homologous series of organic compounds Philip Molyneux ∗ Macrophile Associates, 33 Shaftesbury Avenue, Radcliffe-on-Trent, Nottingham NG12 2NH, UK

a r t i c l e

i n f o

Article history: Received 25 September 2013 Received in revised form 8 January 2014 Accepted 13 January 2014 Available online 23 January 2014 Keywords: Collander equation Graphical methods Linear free energy relationships Methylene group contribution Octanol–water partition coefficient, KOW

a b s t r a c t The literature data for the values of the octanol/water partition coefficient KOW are examined critically, specifically in relation to the methylene group increment in log KOW – here called the lipicity L – for homologous series. With simply substituted alkanes, the plots of L versus the methylene group number m are linear, following the form: L = ˛ + ˇm (Collander equation). The slope parameter ˇ represents the methylene group increment, which widely is expected to be constant on the simplest theoretical grounds, and assumed to be so in most practical applications. The Collander equation behaviour for some 84 homologous series and subseries, ranging in complexity from the alkanes up to the alkyladenines and alkyl galactosides, is presented graphically. Compounds with ␣,␻-disubstituted alkyl chains give nonlinear Collander plots. The remaining series give linear Collander plots, but the methylene group increment ˇ is not constant, the variation being statistically significant, with the distribution essentially normal ¯ = 0.52 and standard deviation (ˇ) = 0.06. The literature data (Gaussian) and with the mean value ˇ from other solvent/water systems – ethoxyethane (diethyl ether), and the two alkanes heptane and hexadecane – show similar behaviour. Most significantly, the fact that the methylene group increment ˇ is not constant casts doubts on the applicability of the linear free energy approach, and of the “fragmental methods” that are widely used in interpreting and predicting partition coefficients. More generally, the graphical approach used is essential in a proper treatment of correlations of this kind; the graphs form an atlas that shows at a glance the partition coefficient behaviour for these series, revealing anomalies in the literature data that need to be rectified, and gaps that need to be filled. © 2014 Elsevier B.V. All rights reserved.

1. Introduction1 1.1. Scope of the paper The partition coefficient values for organic substances, particularly with the system octanol–water, have acquired a great importance over recent years for a variety of scientific and technical reasons. The literature is correspondingly extensive, with many ramifications regarding the balance between hydrophobic/lipophilic and hydrophilic character, and the estimation of partition coefficients for complex compounds of interest, particularly drug substances and other compounds of pharmaceutical importance [1–7].

∗ Tel.: +44 0115 933 4813; fax: +44 0115 933 4813. E-mail address: [email protected] 1 The symbols and abbreviations used in this paper are listed in the Nomenclature section at the end. For numerical values, a set of data for a variable x with (for example) mean value x¯ = 1.23 and standard deviation (x) = 0.04 is summarised in the standard form x¯ = 1.23(4). 0378-3812/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2014.01.014

In particular, the octanol/water partition coefficient KOW is now widely used in prediction and interpretation of the biological activities of compounds, particularly the pharmaceutical and clinical activities (whether actual or potential) of drug substances, where the octanol phase is viewed as a partial model of hydrophobic regions in the active or receptor site in the biological system. By extension, it has also been applied by national regulatory agencies in evaluating the impact of materials discarded or escaping into the environment. The present paper is concerned specifically with one basic but significant matter, that is, the contribution made by the methylene group (CH2 ) in alkyl chains to the value of log KOW . Because of the consequent frequent reference to the methylene group, it is convenient to represent this group throughout as M; likewise, the methylene number m is the sum of these groups on the individual chains in the different parts of the molecule (n1 , n2 , . . .). 1.2. Partition coefficient KOW and its logarithm (Fig. 1) Focusing on the octanol–water partition coefficient for a substance A, this quantity relates to the equilibrium between the

P. Molyneux / Fluid Phase Equilibria 368 (2014) 120–141

121

Fig. 1. Schematics of the partition of butanol, HM4 OH (M = methylene group), as a typical alkyl-chain solute, between water (aq) and octanol (oc): (A) partition equilibrium; (B) “fragmental” transfer of the solute from water to octanol.

substance in the mutually saturated media, which for simplicity may be designated as “oc”, and “aq” A(aq)  A(oc)

(1)

and the equilibrium constant is given by KOW =

A(oc) A(aq)

(2)

where the square brackets represent equilibrium concentrations; it is presumed that the solute is at a sufficiently low concentration (“infinite dilution”) in each phase that solute-solute interactions are minimal, while with acids or bases the ionization is supressed (which may mean that it is necessary to use buffers so that the effects of the electrolytes may affect the equilibrium). This equilibrium is illustrated schematically in Fig. 1A for butanol, represented as HM4 OH in the present symbolism. The mutual saturation of the solvent pair means that, at 25 ◦ C, the “water phase” has a mole fraction octanol content of 7.5 × 10−5 ; by contrast, the “octanol phase” has a mole fraction water content of 0.275, equivalent to a water concentration of 1.7 M, indicating that this should be better referred to as “wet octanol” [8]. At the same time, it should be borne in mind that the chemical activity of the other component is essentially the same as that for the pure solvent, which is important in considering the state of solvation of any solute in that phase. The form of Eq. (2) suggests that KOW is dimensionless, and it is generally taken to be so. However, it is evident on closer examination that it is dimensionally sensitive, since as has been noted specifically [9] the numerical value will be different if the units of concentration are amount (moles)/volume (m3 ), when the units become (volume octanol)/volume water), contrasted with the use of mole fraction units for concentrations (in thermodynamic studies involving Raoult’s Law and the like) when the units become (moles octanol)/(moles water). In fact, the conventional approach is the first of these, and indeed the “volume” result is most appropriate when considering the limiting values of L with lessening molecular size (Section 1.3), and the relation of L to chromatographic parameters. The main focus of the partition studies is on the (decadic) logarithm of the partition coefficient, log KOW , since this provides entry to the thermodynamics of the transfer processes involved and the free energies of the solute in each of the two media [10] through the value standard free energy of transfer from water to octanol, G◦ (aq → oc) from the relationship G◦ (aq → oc) ≡ −2.303RT log KOW

(3)

In view of the centrality of quantity log KOW , both here and in the literature generally, it is convenient to shorten this simply to L in the rest of the paper: L ≡ log KOW

(4)

Likewise, the symbol suggests that this quantity L be named (octanol/water) lipicity, a term which will be used through the rest of the paper since it avoids becoming entangled in other common but conflicting terms such as “hydrophobic”, “hydrophilic”, “lipophobic”, or “lipophilic”. Where other organic media are involved, the organic medium may be indicated specifically, for example LEW for ethoxyethane/water (see Section 6.2) and LAW for alkanes/water (Section 6.3). If, on the simplest picture, this involves a linear free energy relationship (LFER) so that since by Eq. (3), L is also a free energy quantity, it may be expected to be the sum of independent, additive contributions, f, from the component “fragments” (atoms or groups) X of the molecule: L = ˙f (X)

(5)

However, this “additivity”, and hence “independence”, are features that have to be proved in specific cases. For example, in Fig. 1B for the transfer of the butanol molecule, if transfer processes for the chosen component groups are labelled alphabetically then the total value of L could be represented as the sum of contributions L(HM4 OH) = f (a) + f (b) + f (c) + f (d) + f (e) + f (f) + f (g)

(6)

and when the fragmental values f for any fragment is independent of location or surroundings, this would become L(HM4 OH) = 2f (H) + 4f (M) + f (O)

(7)

In practice, these two linked simplifying features of additivity and independence do not always apply, and various “corrections” may have to be applied because of the different partition behaviour of, say, the alkyl and hydroxyl hydrogens in butanol, as above. Also, in the present context, the methylene group is considered as an entity in itself, that is, as a “divalent united atom”, rather than being split into its constituent atoms. Historically speaking, the first important advance in this area was the formulation in 1964 by Hansch and co-workers [11] of a hydrophobic parameter ␲(X) describing the effect of the substitution of the group X for a hydrogen atom on a molecule Z-H (principally, aromatic compounds); in the present notation: ␲(X) ≡ L(Z-X)–L(Z-H)

(8)

This Hansch ␲-parameter is often used as part of quantitative structure-activity relationship (QSAR) approach, often as only one

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Table 1 Octanol/water partition coefficients for homologous and related series: Collander parameters for the least squares fit according to Eq. (9). The column “Fig.” indicates the figure where the data are plotted and “Sec.” the section where they are discussed. #

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73

Series

Alkanes Alkenes Alkynes Cycloalkanes Alkylcycloalkanes Fluoroalkanes Chloroalkanes Bromoalkanes Iodoalkanes Alkanols Alkanediols Alkoxyalkanes Oxacycloalkanes Cycloalkanols Alkanones Alkan-2-ones Alkanals Alkenones Beta-diketones Cycloalkanones Alkylamines Alkylene diamines Alkanoic acids Aminoalkanoic acids Alkyl alkanoates Methyl alkanoates Alkyl ethanoates Alkandioic acids Dialkyl alkandioates Alkanonitriles Alkanodinitriles Nitroalkanes Dinitroxyalkanes Alkanoamides Alkanoic hydrazides Alkyl carbamates Alkyl methylcarbamates Alkylureas Alkylbenzenes Methylbenzenes Bisphenylalkanes 2-Alkylphenols (O) 2-Alkylphenols (I) 3-Alkylphenols (O) 3-Alkylphenols (I) 4-Alkylphenols (O) 4-Alkylphenols (I) A-Alkylphenols (O) A-Alkylphenols (I) 3-Alkyl-1,2-benzenediols (O) 3-Alkyl-1,2-benzenediols (I) 4-Alkyl-1,2-benzenediols (O) 4-Alkyl-1,2-benzenediols (I) 4-Alkyl-1,3-benzenediols (O) 4-Alkyl-1,3-benzenediols (I) 5-Alkyl-1,3-benzenediols (O) 5-Alkyl-1,3-benzenediols (K) Alkyl-1,4-benzenediols Phenylalkanols Phenoxyalkanes 1-Phenyl-1-alkanones Phenyl-2-alkanones Phenylalkanoic acids Alkyl benzoates Dialkyl benzene-1,2-dicarboxylates Alkyl 4-hydroxybenzoates Alkyl 2,3,4-trihydroxybenzoates Alkyl 4-aminobenzoates 1-O-Alkyl galactosides 1-S-Alkyl thiogalactosides N-Alkylpyrrolidones Lactams 4-Alkylpyridines

Fig.

2 2 2 2 2 3 3 3 3 4 4 4 4 4 5 5 5 5 5 5 6 6 7 7 7 7 7 7 7 8 8 8 8 9 9 9 9 9 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 13 13 14 14 15 15 15 16 16 16 17 17 18 18 18

Sec.

4.2 4.2 4.2 4.2 4.2 4.3 4.3 4.3 4.3 4.4 4.4 4.4 4.4 4.4 4.5 4.5 4.5 4.5 4.5 4.5 4.6 4.6 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.8 4.8 4.8 4.8 4.9 4.9 4.9 4.9 4.9 4.10 4.10 4.10 4.11 4.11 4.11 4.11 4.11 4.11 4.11 4.11 4.11 4.11 4.11 4.11 4.11 4.11 4.11 4.11 4.11 4.12 4.12 4.13 4.13 4.14 4.14 4.14 4.15 4.15 4.15 4.16 4.16 4.17 4.17 4.17

Intercept, ˛

m-Range

Slope, ˇ

(LS)

Min

Max

Ave

sd

Ave

sd

0 0 0 0 0 1 1 1 1 0 4 0 2 5 2 2 0 5 5 6 0 2 1 1 1 1 1 3 3 1 0 2 2 1 0 1 2 0 0 0 1 0 7 0 5 0 7 0 5 0 7 0 5 0 7 0 15 0 1 1 1 2 1 1 0 0 1 1 2 2 3 3 0

10 7 7 8 10 5 8 10 7 16 6 8 5 7 10 10 5 6 11 12 8 3 19 7 22 22 6 7 20 8 8 6 10 4 6 8 6 4 14 5 2 3 15 2 15 5 13 5 15 0 15 4 15 12 15 0 19 1 6 3 3 4 7 4 16 6 6 8 8 8 5 7 9

0.46 1.17 0.33 0.00 0.00 0.22 0.22 0.48 1.03 −1.27 −2.53 −1.28 −1.16 −1.46 −1.38 −1.40 nd −1.98 −2.14 −1.85 −1.22 −3.26 −1.27 nd −0.67 −0.53 −0.75 −1.89 −1.66 −0.99 nd −1.05 nd −1.64 −2.07 −1.15 −1.13 −1.90 2.11 2.14 3.64 1.48 −0.54 1.48 −0.58 1.47 −0.58 1.46 −0.61 nd −1.48 0.94 −0.40 0.81 −1.92 0.80 −5.71 nd 0.60 1.59 1.11 0.19 1.00 1.61 0.72 1.46 0.41 0.90 −3.51 −2.92 −1.88 −1.88 0.67

0.06 0.05 0.02 nd nd 0.52 0.08 0.06 0.05 0.02 0.07 0.11 0.22 0.17 0.06 0.05 nd nd 0.12 0.10 0.05 nd 0.03 nd 0.04 0.05 0.03 0.08 0.10 0.05 nd 0.03 nd 0.05 0.03 0.00 0.08 0.13 0.02 0.02 0.10 0.01 0.10 0.01 0.34 0.01 0.45 0.01 0.17 nd 0.15 0.04 0.23 0.03 0.16 0.05 0.25 nd 0.03 0.03 0.03 0.33 0.03 0.03 0.06 0.02 0.08 0.03 0.04 0.14 0.21 0.09 0.01

0.608 0.583 0.596 0.578 0.576 0.439 0.564 0.568 0.520 0.542 0.418 0.556 0.388 0.549 0.562 0.567 nd 0.500 0.634 0.541 0.547 0.610 0.526 nd 0.496 0.494 0.481 0.496 0.482 0.520 nd 0.624 nd 0.465 0.503 0.500 0.514 0.567 0.547 0.509 0.555 0.483 0.705 0.478 0.709 0.518 0.694 0.508 0.706 nd 0.713 0.491 0.678 0.387 0.676 nd 0.875 nd 0.450 0.518 0.528 0.558 0.443 0.537 0.463 0.487 0.465 0.504 0.614 0.631 0.357 0.355 0.608

0.010 0.004 0.005 0.009 0.008 0.128 0.017 0.010 0.012 0.003 0.015 0.022 0.054 0.030 0.010 0.009 nd nd 0.015 0.013 0.011 nd 0.004 nd 0.004 0.005 0.010 0.018 0.013 0.013 nd 0.009 nd 0.022 0.009 0.001 0.021 0.049 0.004 0.009 0.059 0.012 0.008 0.017 0.030 0.009 0.043 0.009 0.015 nd 0.013 0.028 0.021 0.007 0.014 nd 0.014 nd 0.013 0.024 0.016 0.117 0.008 0.013 0.009 0.008 0.019 0.009 0.007 0.025 0.055 0.019 0.004

0.15 0.13 0.03 0.16 0.10 0.42 0.12 0.11 0.07 0.13 0.03 0.15 0.14 0.05 0.14 0.13 nd nd 0.07 0.06 0.12 nd 0.13 nd 0.17 0.15 0.08 0.06 0.06 0.10 nd 0.04 nd 0.09 0.05 0.01 0.06 0.18 0.13 0.13 0.08 0.09 0.05 0.08 0.23 0.09 0.20 0.11 0.17 nd 0.08 0.11 0.16 0.10 0.09 nd 0.04 nd 0.11 0.05 0.07 0.19 0.08 0.07 0.26 0.11 0.08 0.09 0.04 0.13 0.09 0.07 0.06

P. Molyneux / Fluid Phase Equilibria 368 (2014) 120–141

123

Table 1 (Continued) #

Series

Fig.

74 75 76 77 78 79 80 81 82 83 84

Alkyl pyridine-3-carboxylates 1-Alkylthymines 5,5-Dialkyl barbiturates 9-Alkyladenines Alkylxanthines: no 7-alkyl Alkylxanthines: with 7-methyl Alkanethiols Alkylthiaalkanes Alkylsilanes Trialkyl phosphates Alkylplumbanes

18 19 19 20 20 20 21 21 21 21 21

Sec.

Min 4.17 4.18 4.18 4.19 4.19 4.19 4.20 4.20 4.20 4.20 4.20

Intercept, ˛

m-Range

1 2 0 3 0 1 1 2 5 3 4

of several parameters relating to other physical properties of the compound. Subsequently, and by contrast, Rekker and co-workers [12,13] have considered the complete division of the solute molecule into components atoms or groups, that is, “fragments”, f(X) for a component group X in a molecule; summing up these f-values is then intended to give the value of L for that molecule. These two approaches have been expanded and developed extensively, in a manner that need not be summarised in the present paper. In the present paper, the focus is on one aspect of these correlations: the contribution that the methylene group makes to L, that is the quantity ␲(CH3 ) on the Hansch approach according to Eq (6), or the parameter f(CH2 ) on the Rekker approach. The two approaches summarised above generally depend on assuming this M-group contribution to be a constant; the present paper examines this assumption in a detailed way. 1.3. The zero of the scale of L, and the “zeronium” concept In the use of any scale of values, particularly those that may take positive or negative values, it is useful to consider the criteria where the value takes the value zero; this is the case with the present logarithmic partition coefficient parameter L, where the zero value relates to the situation where KOW = 1, that is the solute is evenly distributed between the two phases. The application of this concept to partition coefficients is that is provides a means of fixing the zero point for the L-scale. It is evident that at least in the early developments of this area, there was some controversy about this zero point [14]. However, it turns out this zero value for L should apply with vanishingly small solutes. To make this situation more concrete, it is useful to refer to the hypothetical element zeronium (symbol) Ze as the limiting condition for relative atomic mass AR → 0, that is, of zero mass point particles behaving classically; this concept has previously been applied specifically to fluid phase equilibria for the critical constants of the noble gases Ne–Rn [15]. Considering then the partition behaviour of the element Ze, it follows directly from thermodynamic considerations that the value of L(Ze) should be zero. For firstly, from the enthalpy viewpoint, such particles would by definition not interact with either medium, so that the enthalpy of transfer should be zero. Likewise, with the entropy factor, since we are normally working on a volume/volume basis (Section 1.2), then there should be similar entropic freedom for the particles in each phase so that the entropy of transfer should be zero. This means that the free energy of transfer should also be zero, giving by Eq. (3), L(Ze) = 0. In the present context this limit applies most specifically to the cyclic compounds, particularly those of the same repeat unit, such as the cycloalkanes with the methylene group M as the repeat unit, in the limit of zero ring size. In the wider context, it also applies to other cyclic compounds such as ethers of the polyethoxy type

Slope, ˇ

(LS)

Max

Ave

sd

Ave

sd

8 8 8 5 5 2 4 6 7 12 8

0.30 −1.22 −1.45 −3.47 −0.88 nd 0.15 0.09 nd −2.15 nd

0.04 0.00 0.02 0.08 0.07 nd 0.06 0.05 nd 0.21 nd

0.545 0.532 0.526 0.525 0.430 nd 0.543 0.475 nd 0.498 nd

0.010 0.000 0.006 0.009 0.022 nd 0.024 0.012 nd 0.021 nd

0.09 0.00 0.04 0.01 0.14 nd 0.05 0.04 nd 0.26 nd

(repeat unit M2 O, which includes the crown ethers), as well as the cyclic polyhomopeptides and the cyclic polysiloxanes. This rationalises the observation made by Leo and co-workers [16] that, when correlating values of L with molecular volume (from CPK models), the linear correlation observed did extrapolate essentially to zero (i.e., the zeronium condition) for their “Class II” substances comprising the noble gases and a diversity of halocarbons and aromatic solutes up to anthracene, although it apparently did not apply with their “Class I” compounds comprising the simple alkanes and cycloalkanes. Similar observations have been made by Moriguchi et al. [17].

1.4. Choice of compounds for the homologous series In the choice of the compounds in the homologous series, the primary requirement is for partition data being available for a sufficient range of chain lengths, preferably at least three or four members. For simplicity of interpretation, linear alkyl chains are chosen, unless otherwise indicated. The chosen substituted compounds are end-substituted, that is, on the 1-position for monosubstitution, and on the 1,n- (␣,␻-) positions for compounds with two substituents, unless otherwise indicated. In the case of functional groups such as the ethers, ketones and esters, the alkyl chains are split by the functional group, and the methylene group number is then the sum of the individual chain lengths. As well as compounds with true alkyl chains, there are also some with multiple alkyl group substitution, particularly by methyl groups, so that for example the term “methylbenzenes” represents all the compounds from C6 H6 to C6 Me6 inclusive. Because of the present focus on the methylene group, the structural formulae are shown here with the M groups highlighted, so that alkyl chains are given as -Mn -H; cyclic structures, where not represented directly as such (benzene rings, etc.), are shown in curly brackets enclosing the ring members {-. . .-}, so that for example {-M6 -} represents cyclohexane. 2. Data sources and selection of values In the present paper, the literature values of L have been taken predominantly from the Sangster KOW database (SKD) [7], since this is an extensive compilation, which seems to be comprehensive although apparently subject to revisions and additions; it should be noted that in the present case, all the data tabulated for a particular compound in the SKD are taken into consideration, not just the “Recommended value” which has been understandably selected in most cases. Additional data not included in the SKD (which comprises only strictly organic compounds) are those for four inorganic compounds that are important as the nominal first members (m = 0) of various organic series (as exampled): hydrogen [18,19] (alkanes); water [20] (alkanols and the alkoxyalkanes); ammonia

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P. Molyneux / Fluid Phase Equilibria 368 (2014) 120–141

[21] (alkylamines); and hydrogen sulfide [22] (alkanethiols and the thioethers). It has to be said that numerous of the entries in the SKD [7] turn out to be what is effectively “unpublished work”, or work not otherwise in the public domain. This applies notably to data quoted as from the Pomona Database [23], which does not seem to be accessible directly. Likewise, many entries taken from a paper by Abraham and co-workers [24] are characterised in the SKD [7] as from an “unknown source”. One further point in the consideration of these literature data is the effect of temperature. The review of the thermodynamics of partitioning by Sangster [10] indicates that the effect is quite small, amounting maximally to a change (positive or negative) of 0.01 units in L for one degree; this is fortunate, since although some data are reported specifically for the standard physico-chemical temperature of 25 ◦ C and others for the physiological temperature of 37 ◦ C, most refer only to “room temperature” or “ambient temperature”. Some of the scatter and deviations seen in the correlation plots may result from lack of control of this variable. In using the Sangster database, it became clear that there needed to be criteria for acceptance or rejection of the literature data tabulated, because of the presence of evidently “deviant” values. In this preliminary vetting or validation of data, the steps involved the following. Firstly omitted were those values that were specifically queried as “(?)” in the database itself, or were evidently suspect because they are “round numbers” such as 1.00 or 0.00 – except where these values did seem to be correct in relation to the other data. Secondly, any values were omitted for a single compound that are more than three standard deviations (3) from the mean value, L¯ , for the group of data that compound. Finally, for homologous series as discussed further below, any datum is rejected that has deviation more than 3(LS), where (LS) is the overall standard deviation value for the least squares linear fit to the data for that series. An additional factor to be considered is the method used for the determination of the value of L. Three methods have attained “official” status through their use for example in OECD Guidelines: the well-established “shake-flask” method [25]; the “slow stirring method” (which seeks to avoid the emulsions created in the former method) [26]; and the high-pressure liquid chromatographic (HPLC) method [27]. This last method, although potentially more rapid, needs to be carried out that more carefully since it is an indirect one; this applies particularly to the choice of the calibration standards, to ensuring that these and the “unknowns” have L-values within the same range. Other methods mentioned that have been used are: activity coefficients (by the UNIFAC method or otherwise); solubilities in the separate solvents (that is, pure water, and pure octanol); electrometric titration; and microemulsion chromatography. Inasmuch as these and other methods have been accepted as valid for the Sangster database [7], then they have also been accepted here. In all this work, goodness of fit to a given correlation equation is considered best in terms of the standard deviation value for the least squares lines fit to the series, (LS), rather than the correlation coefficient R2 , which may give a falsely optimistic view of the fit; for example, an R2 value of 0.97 is frequently taken to represent a good correlation, but in practice plotting the data often shows that this results from an overall excellent correlation but with one deviant point. In all of this, as emphasised throughout the present paper, the use of graphs is essential. Simply substituting the raw data into a computer program gives no idea of the fit, even if the residuals are also calculated, whereas the graph shows straightaway the extent of any correlation, and the presence of any deviant data, from which the computer may be used to refine the derived data.

3. Homologous series: determination of the correlation parameters 3.1. Listing of series: the Collander relation Table 1 lists homologous series for which partition data are available from the sources noted above. The homologous series are listed in table firstly in the conventional order of structure type for CHNO compounds – aliphatic, aromatic, heterocyclic – and finally structures containing other elements such S, P, Pb, or Si. This includes both strictly homologous series of the type XMn -Z, and methyl- (that is, multimethyl-) compounds such as the methylbenzenes (C6 H6 to C6 Me6 ). Within the homologous series, some subsets are included to see whether better correlations are obtained by defining the end groups more narrowly; for example, with the alkyl alkanoates, the subsets of the methyl alkanoates and of the alkyl methanoates (acetates) are listed separately. As the figures and the data in Table 1 indicate, in the simplest cases the plots of L versus m are linear, but in more complex cases (particularly with two end groups) they may be curved or even comprise two lines. It is more convenient to use plots against the carbon number c, with the slope still corresponding to the methylene group increment. Where the correlation is linear L =∝ +ˇm

(9)

it can be characterised by the two parameters ∝ (intercept parameter) and ˇ (slope parameter). The focus on here is then on the parameter ˇ, since it represents the methylene group contribution for the series in question. It is convenient to call Eq. (9) the Collander relation, after the Finnish scientist Runar Collander who pioneered much of the work in this area and noted the applicability of this same equation to numerous homologous series; the data from Collander’s work [28] for octanol/water has now been absorbed into current databases – see for example, references 39–42 in the Leo and Hansch 1979 database [2]. Likewise, plots of L versus the methylene group number m, or equivalently the carbon number c, can be referred to as Collander plots, and the parameters ˛ and ˇ as the Collander parameters. Series that conform to Eq. (9) may be referred to as Collander series, although this may require ignoring deviations commonly seen with the first members (m = 0). The goodness of fit of the literature data to Eq. (9) for any particular homologous series may then be quantified as the (LS), the standard deviation of the least squares fit to these data. Likewise, the scatter of individual values about the least squares line may expressed as the deviation L, defined by L = L(exp) − L(cal)

(10)

where L(exp) is the experimental (average) value of L (e.g., from the SKD) and L(cal) is that expected from this linear correlation. Of specific interest is L(0), the deviation for the first member of the series, whose value is often essentially zero, that is, comparable to the (LS) value for the whole set of data. For reference, and in advance of the discussion of specific homologous series, the value of (LS) averages about 0.10 for the “good” linear Collander plots with the octanol/water system. In the present case, the data are plotted as graphs of L versus the carbon number c for all these, since these show the reliability of the data, and the way they spread around the main line; this method – plotting against c rather than against m to follow Eq. (9) – also spreads the graphs so as to differentiate between, for example, the aliphatic and the aromatic compounds. For orientation, all the graphs are plotted with the L = 0 line (horizontal chain dotted line), where this is within the range of the literature values involved. They also show a fine dotted line with slope ˇ = 0.50, which is rounded average previously accepted in the

P. Molyneux / Fluid Phase Equilibria 368 (2014) 120–141

literature for the methylene group (as discussed below in Section 5.2), and which provides a comparison for the slopes of the lines fitting the literature data. The linear sections of the plots are fitted as appropriate by least squares to Eq. (9) to give the values of the parameters ˛ (intercept) and ˇ (slope) that are tabulated in Table 1; the following sections give notes on special features of the individual plots, particularly on any deviant points, and how the first member (m = 0) fits to the main line.

125

9

4. Notes on individual series 4.1. Preview

6

E

Lipicity L

These section give some notes on the plots shown in Figs. 2–21 and the corresponding entries in Table 1, particularly as regards the linearity or otherwise of the plots, the scatter of the points. As already noted these are plots of L versus the carbon number, c, rather than the methylene number m, since the end-group value for L will evidently depend on the complexity of the end group, which is more closely related to the c-value.

D

C B

3

A

4.2. Alkanes, alkenes and alkynes (Fig. 2)

H2 0  Ze 0

 (Ze) 5

10

15

Carbon number, c Fig. 2. Lipicity L versus carbon number c:  linear alkanes; 䊉 branched alkanes – A = methylpropane (isobutene), B = dimethylpropane (neopentane), C = 2,2- and 2,3dimethylbutane, D = 3,3-dimethylpentane, E = 2,2,4-trimethylpentane (isooctane);  alkenes; alkynes; cycloalkanes;  alkylcycloalkanes (the values of c for these last two and for the corresponding zeronium are increased by 5 units); zeronium, Ze (Section 1.3). The fine dotted sloping line in this and later figures is a reference line for the methylene group increment ˇ (value 0.5 unless otherwise labelled).

7

6

5

Lipicity L

The plots of these three types of hydrocarbons are shown in the figure. The data for the alkanes show an essentially linear dependence up to m = 10 (L = 6.7) but become increasingly scattered beyond that point, representing the increasing difficulty in measuring these higher L values. It will be noted that the line passes through the nominal first member of the series, H2 ; this is surprising since the hydrogen molecule shows deviations from “normal” behaviour such as with its critical constants [15] through quantum mechanical effects from its low relative molecular mass. The data available for seven branched alkanes are scattered around the linear alkanes line, below it for m ≤ 7 (L = −0.33) and above it for m = 8 and 9 (L = 0.33), but the data are too sparse to make any firm conclusions; later series that are discussed therefore involve only linear alkyl chains. The alkenes form another linear plot that extrapolates to the origin, i.e. zeronium Ze (Section 1.3), suggesting that the CH2 CH unit acts as two methylene groups, which could provide a simplification in considering other unsaturated solutes. The alkynes plot is are essentially linear, again passing though the nominal first member, ethyne (acetylene: CH CH). The data for the cycloalkanes and alkylcycloalkanes are plotted in Fig. 2 displaced to the right by five units; they are somewhat scattered, but are consistent with a line passing through the origin, that is, zeronium (as discussed in Section 1.3), also additionally plotted displaced by the same amount. The line is close to that for the alkenes, such if (say) ethane is plotted in the same way it would lie on it. It would be useful to also have data for the cycloalkanes with m = 4, and for m > 8, but nevertheless it seems that any strain (small rings) or flexing (large rings) does not greatly affect the L-value.

4

3

4.3. Haloalkanes (Fig. 3)

2 In these series, the data for the fluoroalkanes are too sparse and too scattered to give a meaningful correlation, and this series evidently requires more detailed examination. The other three haloalkanes give linear plots up to the limit studied (m = 8 or 10), with a fairly regular increase in L with halogen atomic number (Cl, Br, I). The intercepts correspond to the unionised hydrogen halide. 4.4. Alkanols, alkoxyalkanes and related compounds (Fig. 4) Here, the alkanols give an essentially linear correlation up to the highest chain length studied, m = 16, and extending down to

1

0 0

2

4

6

8

10

12

Carbon number, c Fig. 3. Lipicity L versus carbon number c:  fluoroalkanes;  chloroalkanes; bromoalkanes; iodoalkanes.

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8

Lipicity L

6

4

2

0

H2 O -2 0

5

10

15

20

Carbon number, c Fig. 4. Lipicity L versus carbon number c:  alkanols; 䊉 alkoxyalkanes;  alkanediols; cycloalkanols; + oxacycloalkanes.

H2 O as m = 0. The alkoxyalkanes (i.e., alkyl ethers) scatter about this same line. This concordance for the three structural types: H O H, R O H and R O R , indicates that the L-value is insensitive to the hydrogen donating character of the substance. This is illustrated by the fact that two linear isomers of C4 H10 O have similar L-values: butanol, 0.86(6); ethoxyethane (diethyl ether) 0.82(6). The alkanediols however give a curved plot, although this may also be interpreted as two straight lines; the nominal first member would be H2 O2 , but its L value with octanol/water does not seem to have been determined [2]. The cycloalkanols and the isomeric cyclooxaalkanes give linear plots, although with some deviations at the lower and upper end respectively. From the behaviour of the linear forms just discussed, these might be expected to form a single series, but there is no overlap between the present data from the two. 4.5. Aliphatic keto-compounds (Fig. 5) In this group, the simple alkanones give a rather scattered linear plot for m = 3, . . ., 11; the subset of the 2-alkanones (methyl alkyl ketones) follows essentially the same line. However, the corresponding alkanals (aldehydes) gives a curved plot lying above the alkanones line, but approaching it at the higher m-values; such anomalies in the values of L for aldehydes have been reported for example by Abraham et al. [24], who commented that the values deviated “wildly” from their standard correlation equation. Two effects may contribute to this anomalous behaviour. Firstly, the alkanals in aqueous solution (and also presumably in wet octanol) would be hydrated, almost completely for the lower members, to the gemdiol: R-CO-H(aq) + H2 O(l)  R-CH(OH)2 (aq)

(11)

This process has been suggested by Abraham et al. [24] as the main reason for the deviations seen. However, this would give the molecule a more hydrophilic character (compare the behaviour of

Fig. 5. Lipicity L versus carbon number c:  alkanones; × alkan-2-ones (methyl alkyl ketones);  alkenones; alkanals;  beta-diketones; 䊉 cycloalkanones.

alkanediols with that of the alkanols in Fig. 4) and hence expectedly a lower value of L. An alternative possibility, apparently not suggested before, is that since octanol is present in the system at its almost full chemical potential, it may react with the aldehyde in the aqueous phase to form some of the hemiacetal: R-CO-H(aq) + R OH(aq)  R-CH(OH)(OR )(aq)

(12)

R

here is the octyl group; even a small extent of this reacwhere tion would evidently greatly increase the L value, as is observed (Fig. 5). This is also in line with the facts that the aromatic aldehydes seem to show similar deviations, as discussed below in Section 4.15. Moreover, as discussed below in Section 6.2 (ethoxyethane/water) and 6.3 (alkanes/water), the behaviour of aldehydes in these other water/solvent systems (that is, in the absence of octanol) seems to be normal and in line with that of the ketones. The beta-diketones in Fig. 5 also form a linear series up to m = 9, albeit with scattering at the lower end; the interpretation of the partition data for this type of compounds is complicated by the formation of the enol isomer, to different extents in the two solvents. There are also sparse data for the cycloalkanones, and for the alkenones, but not sufficient to define correlation lines in either case. 4.6. Alkylamines and alkylene diamines (Fig. 6) The (primary) alkylamines here give an essentially linear plot for m = 0, . . ., 9, The L-value for NH3 (m = 0) of −1.14 is not too different from that of −1.38 for H2 O, although unfortunately both of these are single-point, uncorroborated values. Nevertheless, as shown in Fig. 6, the alkylamine and alkanol lines do run close and parallel to one another, with a small but consistent difference between these two series.

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127

4

12 2

8 0

Lipicity L

Lipicity L

10

NH3 H2O -2

6 4 2 0

-4 0

2

4

6

8

10

12

-2

Carbon number, c Fig. 6. Lipicity L versus carbon number c:  alkylamines; × alkanols;  alkylenediamines – neutral form;  alkylenediamines – salt form.

-4 5

0

10

15

20

25

Carbon number, c For the alkylene diamines, there are only two close points (m = 2 and 3) for the neutral (high pH) form, although the line they define is of “normal” slope; the line would be expected to extrapolate to the value at m = 0 for hydrazine (N2 H4 ) but its L-value does not seem to have been measured at least for the present system (octanol/water) [2]. The salt form (neutral pH) shows lower (more negative) values of L that are almost independent of chain length.

Fig. 7. Lipicity L versus carbon number c:  alkanoic acids; × alkyl alkanoates;  alkandioic acids; + dialkyl alkandioates; aminoalkanoic acids – zwitterion (neutral) form.

4.7. Alkanoic acids and related compounds (Fig. 7)

6 5 4 3

Lipicity L

The alkanoic acids shown in Fig. 7 form a linear correlation for m = 1, . . ., 19, but with m = 0 (formic acid) slightly deviant (+0.21). The derived alkyl alkanoates give a more scattered plot, with (LS) = 0.17. The plot for the alkandioic acids is curved upwards at the lower end for m = 0, . . ., 2, but essentially linear above for m = 3, . . ., 7; their dialkyl esters converge from above onto this line without defining a straight line in the measured range of m = 3, . . ., 8. The aminoalkanoic acids in their neutral (zwitterion) form have an essentially constant value of L = −3.0(3) for m = 1, . . ., 7, thus corresponding to ˇ ≈ 0. This unexpected behaviour is significant in the wider context, because of the biochemical activity of several of these compounds, notably those with m = 1 (glycine), 3 (GABA) and 5 (EACA) [29].

2 1 0

4.8. Alkanonitriles and nitro compounds (Fig. 8)

-1

The simple alkanonitriles (alkyl cyanides) give an essentially linear Collander plot in Fig. 8 for m = 1, . . ., 8, but with m = 0 (hydrogen cyanide; HCN) deviant high. The corresponding alkanodinitriles (alkylene dicyanides) show more complex behaviour: the L values decrease for m-values from 0 (cyanogen; C2 N2 ) to 2, rising as a curve for 2, . . ., 5, then finally essentially linear for 5, . . ., 8. In this same figure, the nitroalkanes show a linear correlation for m = 2, . . ., 6, with four literature values for m = 1 that are scattered

-2 0

2

4 6 8 Carbon number, c

10

12

Fig. 8. Lipicity L versus carbon number c:  alkanonitriles;  alkanodinitriles;  nitroalkanes; dinitroxyalkanes – Fischer [30];  dinitroxyalkanes – Pomona 1987 database [23].

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but deviant high on the average. There seem to be no literature data available for the simple nitroxyalkanes (alkyl nitrates); for the dinitroxyalkanes (alkylene dinitrates) the Collander plot is anomalous, being curved upwards throughout the span (m = 2, . . ., 10) but with the L-values higher than those of the nitroalkanes, even although the former having two nominally more hydrophilic end groups (that is, O NO2 versus NO2 ). The main data for the dinitroxyalkanes are from a single source [30], using an indirect experimental method (HPLC), but their L-value for m = 2 is supported by a similar value from the 1987 Pomona database [23] that was presumably obtained by the standard shake-flask method. 4.9. Alkanoamides and related compounds (Fig. 9) Within this group as shown on Fig. 9, the alkanoamides give a linear correlation for m = 2, . . ., 4, with the reported values for the m = 0 (formamide) scattered but deviant high on the average, with L = +0.36(26). The alkanoic hydrazides, obtained formally from the alkanoamides by inserting an extra NH group, are correspondingly more hydrophilic. Considering firstly the data for m = 0, . . ., 6, these give an essentially linear plot, lower than that for the alkanoamides by about 0.4 units; in this case the value for the parent compound (formic hydrazide) lies essentially on the line, while with m = 6 the reported value of 1.00 exactly is seemingly correct since it lies on the correlation line. However, the data for the higher members, m = 7, . . ., 12, are suspect, having reported values of “1.00”, “0.00” (four times) and “−1.00” as plotted; although these have been taken literally in drawing the figure, they have been ignored in obtaining the linear correlation parameters. These anomalous values for the

Fig. 9. Lipicity L versus carbon number c:  alkanoamides; alkyl carbamates; × alkyl N-methylcarbamates;  alkanoic hydrazides; alkylureas (values of c increased by four units as arrowed).

higher members may be due to some type of association of these longer chain amphiphilic compounds in the experimental studies. However, with the alkyl carbamates, obtained formally by inserting an expectedly hydrophilic oxygen atom into the alkanoamide molecule, the L-values are now raised (rather than lowered) by about 0.5 units. The alkyl methylcarbamates that have the same total methylene group number have closely similar Lvalues. The values for the alkylureas overlap those for the isomeric alkanoic hydrazides - for example, L(urea) = −2.00(65) and L(formic hydrazide) = −2.05 – so the alkylureas data are shifted four units to the right in Fig. 9 to avoid overlap. With these compounds, the L-values seem to be insensitive to different forms of alkyl substitution – the values for the highest members with m = 4 (butylurea and tetramethylurea) are closely similar as shown. 4.10. Alkylbenzenes and bisphenylalkanes (Fig. 10) Moving on to the carbocyclic aromatic compounds, the figure shows that for the alkylbenzenes there is a linear correlation extending essentially over the full reported span of m = 0, . . ., 14; the contrast here with the simple alkanes (Fig. 2) presumably reflects at least in part the easier detection and estimation of the alkylbenzenes by spectroscopy. In the case of the methylbenzenes (C6 H6 to C6 Me6 ,), where the plot in Fig. 10 is shifted up by two units to avoid confusion, there is a linear correlation up to m = 5, although the m = 6 compound then shows a downward deviation with some scattering. In this correlation, the data that Ritter et al. [31] assigned to heptyl-, octyl-, nonyl- and decylbenzene seem to represent in actual fact those for octyl-, nonyl, decyl-, and undecylbenzene respectively, and have been plotted accordingly.

Fig. 10. Lipicity L versus carbon number c:  alkylbenzenes;  methylbenzenes (value of L increased by two units as arrowed); bisphenylalkanes.

P. Molyneux / Fluid Phase Equilibria 368 (2014) 120–141

Fig. 11. Lipicity L versus carbon number c: alkylphenols (pooled data for 2-, 3- and 4-isomers): 䊉 Itokawa et al. [32],  other workers [7];  3-alkyl-1,2-benzenediols – Itokawa et al. [32];  3-alkyl-1,2-benzenediol – other data (only available for m = 0) [7]; 4-alkyl-1,2-benzenediols – Itokawa et al. [32];  4-alkyl-1,2-benzenediols – other workers [7].

There are a few scattered data for the bisphenylalkanes, with m = 2 and 3 showing a line of “normal” slope but with m = 0 high (evidently representing the loss of the electronic interaction between the two benzene rings), while m = 3 has a lower, widely deviant value. 4.11. Alkylphenols and alkylbenzenediols (Figs. 11 and 12)2 The literature for these groups of compounds have some markedly deviant data, notably those reported by Itokawa et al. [32], and by Kozubek [33], when compared with those from other workers listed in the Sangster Database [7]; in the latter case, for simplicity the individual values are not differentiated because of their mutual concordance, and have here been characterised simply as “other workers” (O). Taking the case of the alkylphenols, although the results from the 2-, 3- and 4-isomers have been differentiated in Table 1, they are sufficiently similar that they have been pooled for the plots in Fig. 11. It will be seen that the “O” (“other workers”) data for m = 1, . . ., 5 are concordant, and pass through the phenol group (m = 0) with a slope of the value expected; however the data of Itokawa et al. [32], although concordant amongst themselves, have a much higher slope to the correlation line and the extrapolated value for m = 0 (phenol) is two units lower than the “O” value.

2 In clarification of the nomenclature of these benzenediols, the following older (non-IUPAC) names are still encountered in the literature as synonyms for these and their derivatives: 1,2-benzenediol = (pyro)catechol; 1,3-benzenediol = resorcinol; 1,4-benzenediol = hydroquinone/quinol.

129

Fig. 12. Lipicity L versus carbon number c: 䊉 4-alkyl-1,3-benzenediols - Itokawa et al. [32];  4-alkyl-1,3-benzenediols - other workers [7];  5-alkyl-1,3benzenediols – Kozubek [33];  1,3-benzenediol – other workers [7]; alkyl-1,4-benzenediols (data available only for m = 0 and 1).

The same applies to the alkyl-1,2-benzenediols in Fig. 11 and the alkyl-1,3-benzenediols in Fig. 12; for the former, the deviant data for the longer chain compounds are those of Kozubek [33]. These anomalies with the data of Itokawa et al. [32] and Kozubek [33] seem to be the result of their use of the HPLC method incorrectly; this is an indirect method that requires a calibration of the HPLC results by correlation of the retention time data against those for compounds with known L-value, which in best practice should lie within the range for the studied compounds of interest [27]. With the work of Kozubek [33], the calibration compounds had L values from 2.8 to 5.1, whereas the derived (extrapolated) values for the alkyl-1,3-benzenediols had much higher values, from 6.9 to 10.4, well out of the calibration range. In the case of Itokawa et al. [32], the calibration compounds for their L-values were not specified, but the calibration line seems to be a poor fit, with a standard deviation of 0.47 units in L. With the last group of isomers, the alkyl-1,4-benzenediols, Fig. 12 shows that data are only available for the parent diol and the methyl derivative, and the three separate values here are widely deviant, so that no correlation data can be obtained. 4.12. Phenoxyalkanes and phenylalkanols (Fig. 13) The data for these two series of isomeric compounds are shown in Fig. 13. With the phenoxyalkanes, the data for m = 1, . . ., 3 give a rather scattered correlation line which passes somewhat above the phenol data (m = 0) although the spread in the literature values for this parent compound makes this uncertain. With the phenylalkanols, the data for m = 2, . . ., 6 give a linear correlation, but that for m = 1 deviate above these line and the phenol data (m = 0) more so, evidently reflecting the loss of electronic interaction between the ring and the hydroxyl group which is not complete even with

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Fig. 13. Lipicity L versus carbon number c:  phenol;  phenylalkanols; noxyalkanes.

phe-

one methylene group interposing; the last data point at m = 7 also deviates markedly, and has also been disregarded in fitting the line.

Fig. 14. Lipicity L versus carbon number c:  1-phenyl-1-alkanones; 䊉 benzaldehyde;  phenylalkan-2-ones;  phenylacetaldehyde.

4.13. Phenylalkanones and phenylalkanals (Fig. 14) With the data shown in Fig. 14 for these two series of isomeric carbonyl compounds, one can differentiate between the vicinal phenylalkanones, that is the 1-phenyl-1-alkanones, and the nonvicinal phenylalkan-2-ones, with at least one methylene group between the phenyl group and the carbonyl group. Of these two series, the 1-phenyl-1-alkanones gives an essentially linear plot for m = 2, . . ., 6 with some scatter for m = 7, but the first member (m = 1) is deviant and the extrapolated line is also lower (L = −1.1) than that for m = 0 (phenol); this evidently represent the loss of electronic interaction between the ring and the alkoxy group, which is not complete until m = 2. However, in the case of the phenoxyalkanes the correlation line (m = 2, . . ., 4) passes only 0.1 units above the average phenol point; here there is evidently only a minor effect of the alkylation on this electronic interaction. The two corresponding aldehydes, benzaldehyde and phenylacetaldehyde, are deviant high, in a similar fashion to the alkanals as compared with the alkanones (Fig. 5), and presumably for similar reasons as discussed in Section 4.5. 4.14. Phenylalkanoic acids, alkyl benzoates and dialkyl benzene-1,2-dicarboxylates (Fig. 15) The partition data for these related aromatic alkanoic acids and their alkyl esters are plotted in this figure. The phenylalkanoic acids give a linear plot for m = 1, . . ., 7, but with the parent compound, benzoic acid (m = 0) deviant high (L ≈ 0.9), reflecting the loss of resonance between the aromatic ring and the carboxyl group. The alkyl benzoates also give a linear plot for m = 1, . . ., 4, with the same parent compound now deviant high to a lesser extent (L ≈ 0.3). The dialkyl benzene-1,2-dicarboxylates (dialkyl phthalates) give a

rather scattered linear plot from m = 0, . . ., 16, that is, from the parent acid (here, on the correlation line) up the dioctyl ester. This plot for the linear-chain esters may be a guide to the partition behaviour of the branched alkyl esters likewise widely used as plasticizers. 4.15. Alkyl esters of other substituted benzoic acids (Fig. 16) This figure shows the partition data for the alkyl esters of three substituted benzoic acids. The esters of 4-hydroxybenzoic acid (alkyl parabens) give a linear plot from m = 0, . . ., 6, although the pentyl ester is deviant and has been ignored in fitting the plot. The alkyl esters of 2,3,4-trihydroxybenzoic acid (alkyl gallates) also give a linear plot for m = 1, . . ., 6, with the parent acid deviant upwards and also that for the octyl ester deviant downwards. The esters of 4-aminobenzoic acid also give a linear plot for m = 1, . . ., 8, with the parent acid deviant upwards. The deviant points in these two cases have again been disregarded in fitting the plots. Note that these two last parent acids have essentially the same value of L, so that their plotted points overlap in Fig. 16. There seems to be a correlation here between the levels of the Collander plots for these three series and the hydrogen-donating power of the molecules (1:2:3). The partition behaviour of these three groups of alkyl esters is important in the wider context because of their diverse applications – the parabens are used as antimicrobial preservatives, the gallates as antioxidants, while ethyl 4-aminobenzoate is a local anaesthetic (Benzocaine) [29]. 4.16. Alkyl glycosides (Fig. 17) Turning now to the heterocyclic compounds, the figure shows the partition data for various glycosides. The most extensive data here are for the 1-O-alkyl ethers of galactose, which give a linear

P. Molyneux / Fluid Phase Equilibria 368 (2014) 120–141

131

Fig. 15. Lipicity L versus carbon number c:  benzoic acid;  alkyl benzoates; phenylalkanoic acids; dialkyl benzene-1,2-dicarboxylates (dialkyl phthalates).

Fig. 17. Lipicity L versus carbon number c:  1-O-alkyl galactosides;  1-S-alkyl thiogalactosides; glucose; 3-O-methylglucose.

plot for m = 2, . . ., 8. Comparable data for glucose are only available for m = 0, which is deviant up from the galactoside plot, and for m = 1 with the 3-O-methyl derivative, which lies essentially on the galactoside plot; this last suggests that other glucose ethers may also lie on the same correlation line and regardless of the site of alkylation – as shown, these two sugars differ only in the orientation of the OH group at the 3-position. Anticipating the discussion of thiocompounds in Section 4.20, the data for the 1-thioalkylgalactosides are also seen to give a linear correlation m = 2, . . ., 8, displaced upwards from the O-compounds by about 0.7 units. 4.17. Cycloalkanoamides, N-alkylpyrrolidones, 4-alkylpyridines and alkyl pyridine-3-carboxylates (Fig. 18)

Fig. 16. Lipicity L versus carbon number c:  alkyl 4-hydroxybenzoates alkyl 4(alkyl parabens);  alkyl 2,3,4-trihydroxybenzoates (alkyl gallates); aminobenzoates – the data points for the parent acids for these last two series overlap.

The data these four series of N-containing heterocycles are plotted in Fig. 18. For the two isomeric aliphatic series, the cycloalkanoamides (lactams) and the N-alkylpyrrolidones, the figure show that for the range m = 3, . . ., 7, the their data lie essentially on a common line; the data for m = 3 are of course for the same compound, pyrrolidone. In listing these m-values, those in the ring and those substituting on the nitrogen have been combined. However, the data for the two longer chain N-alkylpyrrolidones, with m = 9 and 15, are deviant high from the extrapolation of this common line (L = 1.26 and 0.72), and have been disregarded in fitting the correlation line; this may be the result of some association with these longer-chain amphiphilic compounds in the experimental techniques. Looking at the aromatic heterocycles, Fig. 18 shows that the situation with the 4-alkylpyridines is rather complex. The most

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Fig. 18. Lipicity L versus carbon number c:  lactams (cycloalkanoamides);  Nalkylpyrrolidones; × 4-alkylpyridines – Yeh and Higuchi (aqueous phase 1 M NaCl) [34]; 4-alkylpyridines – other workers [7]; + alkyl pyridine-3-carboxylates.

extensive data are those for m = 0, . . ., 9 from Yeh and Higuchi [34], which give a good linear Collander plot, with (LS = 0.03), passing through m = 0; however, these data were obtained using 1 M NaCl rather than pure water as the aqueous phase. The multiple values from other workers in the SKB [7] for m = 1 and m = 2 average 0.1 units below those from Yeh and Higuchi [34], while the corresponding single values for m = 3 and 4 are below the correlation line (possibly due to incomplete ion-correction), although that for m = 4 is on the correlation line. In view of the likelihood that the 1 M NaCl used by Yeh and Higuchi [34] would have a saltingout effect, possibly mitigated by some dehydration of the (wet) octanol phase, and in view of the scattering of the other data, it is not possible to report reliable values for the parameters for this homologous series. The parallel data reported by Yeh and Higuchi [34] for these 4-alkylpyridines in hexadecane/water (1 M NaCl) are discussed below in Section 6.3. The data for the alkyl pyridine-4-carboxylates are also linear for m = 1, . . ., 8, but the parent acid (scattered values) is deviant down (L ≈ −0.7). 4.18. 1-Alkylthymines and 5,5-dialkylbarbiturates (Fig. 19) Turning to heterocycles with some biochemical importance, Fig. 19 shows that the partition data for the similarly-structured 1-alkylthymines and 5,5-dialkylbarbiturates give similar Collander plots. The plot for the 1-alkylthymines is essentially linear for m = 2, . . ., 8, but the parent compound is deviant (L = 0.62), evidently linked to the loss of hydration of the 1-NH group on alkylation; note that thymine itself is 5-methyluracil, although this methyl group is not included in the present methylene group count. This

Fig. 19. Lipicity L versus carbon number c:  1-alkylthymines;  5,5dialkylbarbiturates.

correlation provides a reference point for the partition behaviour of the pyrimidine nucleobases and their derivatives, although there does not seem to be any partition data for the alkyl derivatives of the other important pyrimidine nucleobase, cytosine. The plot for the 5,5-dialkylbarbiturates is linear for m = 0, . . ., 8, thus including in the present case the parent compound, barbituric acid; here it is C-alkylation that is involved in its derivatives. This plot gives an entry to the partition behaviour of the barbiturates with branched alkyl chains, also with pharmaceutical and clinical applications [29].

4.19. 9-Alkyladenines and alkylxanthines (Fig. 20) This figure shows partition data for two further series of bicyclic heteroaromatics of biochemical importance, but now with more complex behaviour in their Collander plots. For the 9alkyladenines, the plot is linear for m = 3, . . ., 5, but the data for m = 0 and 1 are deviant upwards (0.79 and 0.29); here evidently it requires at least two methylene groups to negate the hydration of the 9-NH group. This correlation provides a reference point for the partition behaviour of the purine nucleobases and their derivatives, although there do not seem to be any comparable data for alkyl derivatives of the other important purine nucleobase, guanine. For the 1,3-alkylxanthines, but with no 7-alkylation, the plot is rather scattered ((LS) = 0.14) but essentially linear from m = 0, . . ., 5. For the compounds with 7-methylation, the correlation is poorer, and a linear dependence cannot be established. This group of alkylxanthines includes three biochemically important members as labelled in the figure: A = theophylline (1,3-dimethylxanthine); B = theobromine (3,7-dimethylxanthine); C = caffeine (1,3,7-trimethylxanthine) [29].

P. Molyneux / Fluid Phase Equilibria 368 (2014) 120–141

Fig. 20. Lipicity L versus carbon number c:  9-alkyladenines;  1-alkyl, 3-alkylthymines (A = theophylline); 1-alkyl, 3-alkyl, 7-methylthymines (B = theobromine, C = caffeine).

4.20. Other heteroatomic series: compounds containing S, P, Si or Pb (Fig. 21) This figures shows partition behaviour for four series containing these heteroatoms. The data for hydrogen sulfide, alkylthiols (mercaptans) and alkylthialkanes (dialkyl sulfides) shown in Fig. 21 provide an entry into the partition behaviour of sulfur-containing compounds in general, notably the amino acids cysteine, cystine and methionine. The figure shows that, unlike parallel case of the oxa-compounds, where the data for H2 O and the two isomeric series ROH and ROR’ lie essentially on a common line (Section 4.4 and Fig. 4), there is a distinction between the three groups: H2 S, RSH, and RSR . In particular, although the RSH and RSR series both give essentially linear plots, these have different slopes and extrapolate to “H2 S” values of 0.15 and 0.09, which are lower but than that of 0.45 for H2 S itself. This discussion is made uncertain by the data being in many cases single unsupported values – that for H2 S is from the IUCLID database [22] and that for C2 H5 SH from an API database [35] with the others again from the Sangster database [7]; however, the linear correlations seen in Fig. 21 for data from multiple sources provide some support for their internal validity. The data for the alkylsilanes (with a diversity of chain lengths as indicated by Mx ) are mainly from the 1987 Pomona database [23], along with a single extra value for the tetramethyl derivative from a 1995 Hansch publication [36], which is 0.6 units lower from the earlier one, although it is presumably from essentially the same source. The data for the alkylplumbanes are mainly from Wang et al. [37], with an extra value for the tetramethyl compounds from the 1987 Pomona database [23] that is lower (L = −0.7). Also shown is the data point for dimethylpropane (neopentane) that is the carbon analogue of the former two groups, and which lies close to its silicon and lead analogues. There are indications here that the partition

133

Fig. 21. Lipicity L versus carbon number c: hydrogen sulfide; + alkanethiols; × alkylthialkanes;  alkylsilanes – 1987 Pomona database [23]; 䊉 alkylsilanes – 1995 Hansch publication [36];  trialkyl phosphates;  monobutyl phosphate; alkylplumbanes – Wang et al. [35]; alkylplumbanes – Pomona 1987 database [23];  dimethylbutane (neopentane).

behaviour is insensitive to the nature of the central atom (C, Si or Pb) and also insensitive to the chain lengths of the attached alkyl groups. However, these data are in general too scattered to draw any firm conclusions or correlations. The phosphate esters give lower L-values from their more hydrophilic structure, with an essentially linear if rather scattered correlation – (LS) = 0.26 – of normal slope (ˇ = 0.50(2)) for data from a diversity of sources; the data point for the monobutyl derivative also lies close to the correlation line. 5. Overview of the results for the homologous series 5.1. Preview It is evident, from the graphs shown, that for the monosubstituted compounds, and where data are available over a wide range of chain lengths, in many cases the plots of L versus carbon number are essentially linear, in conformity with the Collander relation Eq. (9). The main deviations from linearity seen with the mono-substituted compounds are for the first members (m = 0); however, even this effect is not universal, since does not seem to apply to the alkanes or to the alkanols, where the data for H2 and H2 O lie on their linear correlations. With the disubstituted compounds, deviations from the Collander equation (9) are much more common, as noted in the individual sections. Here the “end-group” effect seems to extend well beyond that seen with the monosubstituted compounds. As well as providing data for the slope parameter ˇ as discussed in the next section, the graphs shown provide a direct visual picture of the reliability of the literature data. For whereas the reliability of a single value is difficult to decide on its own, if it lies on or

134

P. Molyneux / Fluid Phase Equilibria 368 (2014) 120–141

Table 2 Literature values (average and standard deviation) for f(M), the fragmental contribution of the methylene group M to the lipicity L of homologous series. #

Year

Ref.

f(M)

Notes

Ave

sd

1

1964

[11]

0.51

0.04

2

1967

[38]

0.50

nd

3

1971

[1]

0.50

0.02

4

1972

[39]

0.50

nd

5

1974

[40]

0.52

nd

6

1979

[2]

0.56

nd

7 8

1979 1979

[2] [2]

0.66 0.54

nd nd

9 10

1979 1984

[2] [41]

0.66 0.456

nd 0.009

11

1986

[43]

0.4173

nd

12 13

1995 1997

[44] [45]

0.4911 0.576

nd nd

14

1997

[45]

0.450

nd

15

2000

[46]

0.531

nd

16

2000

[46]

0.564

nd

17

2006

[47]

0.50

nd

18

2014

–

0.52

0.06

2- and 3-CH3 - for 8 aromatic series (p. 5177) Value used for dialkylbarbiturates (p. 717) Comments on “exceptions” (Table XVI) “Preferred [literature] value” (Table 4) “Preferred [literature] value” (Table 21) Value used in calculations (pp. 15–16) f(CH3) – f(H) (p. 19) C3 –C8 alkanes, alkanols, alkylamines (p. 21) f(C) + 2f(H) (p. 333) Contribution for “-C-” (see Ref. [42]) f(C) + 2f(H) – entries 2 and 46 in Table I (p. 82) Table 1 (p. 85) CH2 in CH3 R – Table 1 (p. 617) – see next CH2 in CH2 R2 – Table 1 (p. 617) – see previous CH2 in chain – Table 3 (p. 104) – see next CH2 in ring – Table 3 (p. 104) – see previous From early (1964–1967) papers by Hansch et al. This work – 58 systems

close to the linear plot for that series then its reliability is enormously enhanced, while at the same time enhancing the reliability of the other members of the data-set. Nevertheless, care needs to be taken in such conclusions with data-set from just a single source using a single experimental method (especially an indirect one such as HPLC), as seen with the various alkylphenols; but where several sources using different methods are involved in the linear plot, the reliability both of the data and of the methods used are both enhanced. However, the linearity of these plots over such a wide range of chain lengths is from the theoretical viewpoint somewhat unexpected. For as the chain length is increased, the added methylene groups would be expected to start within the influence from the solvation shell of the end-group, but then move progressively out of the influence of this shell, so that the methylene group increment would be expected to similarly change progressively, leading to curvature in the plot. Viewing the equilibria for the homologous series in terms of the degree of coiling or extension of the alkyl chain, we would expect that the chain would be largely extended approximately as the random chain in the octanol phase, but much more contracted in the aqueous phase. Inasmuch as the value of the slope parameter ˇ relates to the transfer of the M unit from one environment to the other (Fig. 1B), and this environment is apparently much the same in octanol for whatever length of chain, with the latter having for small values of m got outside the influence of the end group, we must conclude that by contrast for the aqueous phase, the chain always remains within this influence of this end group, simply coiling around but with the thermal (microbrownian) motion continually exchanging the positions of the chain units within this volume.

5.2. Literature data for the methylene group increment For comparison with the present results, Table 2 lists some literature data for the methylene group increment to L, which is expressed in the original references either as the corresponding Hansch parameter ␲(CH3 ) or as the parallel methylene group fragmental contribution f(CH2 ); in the present case these will be given in the present notation as f(M). The entries in the table, which are in chronological order, indicate a disparity in the values, ranging overall from 0.42 to 0.66 – despite the fact that the individual references each consider this parameter as a constant quantity; even the apparently authoritative 1979 Hansch review [2] gives three different values – 0.54, 0.56, and 0.66 (twice) – as listed. Some references quote the contribution f(M) to three decimal places [41,45,46] or even four decimal places [43,44], although the high values of the standard deviations reported for the fit to the workers chosen data sets clearly do not justify such claimed precision. Finally, a recent standard pharmaceutical text [47] quotes the value in the “rounded” form of 0.50 as derived from the early (1964–1967) references cited. This is of course the “reference” value that has been used in the present figures as a convenient comparison with the observed correlation lines. 5.3. The slope parameter ˇ – well-established values (Fig. 22) As discussed earlier, the main focus in this paper is on the slope parameter ˇ for the Collander plots of L against methylene group number or carbon number, since this indicates the methylene group contribution to the thermodynamic of the partition process. Choosing from Table 1 the data that give well-established linear plots, that is, omitting those that have high values for the standard deviation in the ˇ-value or in the least-squares fit (LS) to the experimental data, as well as those not producing a linear plot of sufficient span to be trustworthy, gives a total of 58 series. The ˇ-values from these selected data are then plotted in Fig. 22 firstly (top) as a cumulative plot, and then (bottom) as a logit plot, that is, the ˇ-value versus the logit function p defined by p(N∗) ≡ log10

N N ∗ −N

(13)

where N is the cumulative number of the systems up to that value, and N* is the effective maximum value of N. The logit plot here is essentially linear with the best fit obtained for N* = 60 systems, with ¯ = 0.52 and standard deviation (ˇ) = 0.06, and with a mean value ˇ an overall span from 0.43 from 0.63 except for a stray group of four items beyond the lower end. The linearity of the logit plot indicates that the distribution of ˇ-values is essentially normal (Gaussian) [48]. From the mathematical viewpoint, the fact that this distribution is normal indicates that the variable ˇ is influenced by many small and unrelated random effects [49]. However, the interpretation from the physical and chemical viewpoints would require examining the behaviour of the alkyl chains in both the aqueous and the (wet) octanol phases, which is beyond the scope of the present paper. 6. Other solvent/water partition systems 6.1. Preview Although the main effort in partition coefficients currently goes into the octanol/water system, there is also a less extensive literature for other organic solvents. In the present context, data from these can provide comparisons for the methylene group increment, and also reveal any special features of the octanol data. The thermodynamics of the methylene group contribution particularly in drug molecules were reviewed specifically in 1972 by Davis et al.

P. Molyneux / Fluid Phase Equilibria 368 (2014) 120–141

135

Fig. 23. Ethoxyethane/water lipicity LEW versus carbon number [2]: 䊉 alkanols – Collanders’s data; ethoxyethane – other workers’ data;  alkanediols;  alkylamines;  alkanediamines.

Fig. 22. Distribution of the values of the Collander slope parameter ˇ (methylene group increment) for the homologous series in octanol/water – data from Table 1. Top: cumulative distribution plotted versus N(ˇ), the number of series with slope parameter less than this value. Bottom: logit plot of the distribution of the slope parameter ˇ; the abscissa variable p(60) is the logit value as given by Eq. (13), assigning the total number of series N* = 60.

[39] and then by the same group in 1974 as one of a number of such groups [40], but does seem to have been reviewed in any detail since then, except as citations of these earlier papers. In this section the literature on two other solvent systems: ethoxyethane/water and alkanes/water, is reviewed. 6.2. Ethoxyethane (diethyl ether) (Figs. 23 and 24) Partition data in the system ethoxyethane/water, as plots of as the corresponding lipicity LEW , versus carbon number c for homologous series as before, are shown in Figs. 23 and 24. The data for this system is taken primarily from the 1979 Pomona listing [2], which itself draws on an earlier paper by Collander [28a]; internet searching suggests that this has not been further extended except for minor additions, such as a confirmatory value for urea [50]. The Collander parameters obtained from these plots are listed in Table 3, with notes and discussion on specific series given below. There is a lack of partition data for simple hydrocarbons (alkanes, alkenes, etc.) in this system from these main references.

Fig. 24. Ethoxyethane/water lipicity LEW versus carbon number c [2]: alkanals;  propanone;  alkanoic acids;  alkanedioic acids; alkanoamides; alkylureas.

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Table 3 Collander parameters ˛EW and ˇEW for the partition coefficients of homologous series in ethoxyethane/water: the entries in the #1 column are those for the same series in octanol from Table 1. See Section 6.2 for notes and discussions on these systems. #

01 02 03 04 05 06 07 08

#1

10 11 17 21 23 28 34 38

Series

Alkanols Alkanediols Alkanals Alkylamines Alkanoic acids Alkanedioic acids Alkanoamides Alkylureas

Fig.

23 23 23 23 24 24 24 24

Intercept, ˛EW

m-Range

Slope, ˇEW

 (LS)

Min

Max

Ave

sd

Ave

sd

0 2 0 0 1 2 1 0

6 6 2 8 5 10 4 2

−1.82 −3.01 −1.01 −2.12 −0.90 nd −3.19 −3.44

0.03 0.09 0.11 0.11 0.03 nd 0.07 0.05

0.60 0.34 0.63 0.52 0.55 nd 0.62 0.48

0.01 0.02 0.09 0.02 0.01 nd 0.03 0.04

However, an estimate for the partition coefficient methane may be obtained as gas solubility ratio from the literature data for methane solubility in water and in ethoxyethane [51]; these data give LEW (CH4 ) = 1.49, which may be compared with the experimental values of 1.02(7) for octanol/water (Section 4.2), and 1.14 for alkanes/water (Section 6.3). This estimate for the pure solvents should be higher than those for the mutually saturated solvents as actually considered here, since the mutual saturation should bring the solvent properties of the two media closer to one another. The data for the alkanols in Fig. 23 is supplemented by the data for water, not otherwise listed [2], obtained from the solubility of water in ethoxyethane, 1.468% [52], which gives LEW (H2 O) = −1.83. The plot in this case is a good line except for the data obtained by Collander himself [28a], which are consistently about 0.2 units above the line through the other two sources [2] and this water value, and they have been disregarded in fitting the line. The only data for the alkoxyalkanes in this system is for ethoxyethane itself, where the value for its solubility in water of 6.05% [53] gives LEW = 1.07; as shown in Fig. 23, this is 0.4 units above the value for its isomer, butanol, on the correlation line for the alkanols and water. For the alkanediols, in contrast to the curved plot seen with octanol/water (Fig. 4), the plot in Fig. 23 is essentially linear for m = 2, . . ., 6, but with deviant (high) points for m = 0 (H2 O2 ) and m = 10. The data for the (primary) alkylamines shown in Fig. 23 give a rather scattered plot for m = 0, . . ., 8; as with the alkanols, this includes the parent compound, NH3 . The data for the alkanediamines gives an essentially linear plot for m = 2, . . ., 5, but with m = 0 (hydrazine: N2 H4 ) deviant high as with the alkanediols. Considering the data for the carbonyl-containing compounds in Fig. 24, the alkanoic acids give a linear plot for m = 1, . . ., 5, with formic acid (m = 0) being deviant high at L = 0.46(5) as seen with octanol (Fig. 7). However, the plot for the alkanedioic acids is curved over its full observed range from m = 2, . . ., 10, in contrast to the straight line behaviour seen with octanol (Fig. 7), although this latter is over a narrower range of chain lengths. The same plot also shows the behaviour of alkanals [2], where the three points for m = 0, . . ., 2 straddle the alkanoic acids plot; however, the data show no sign of the marked curvature shown by the corresponding alkanals in octanol/water in Fig. 5. This supports the idea, discussed in Section 4.5, that the octanol/water effects are related to some interaction of the alkanal in the aqueous phase with the dissolved octanol. The single point for ketones, that for propanone (acetone), lies about 0.4 units below the joint alkanols and alkanal data at m = 2. Also in Fig. 24, the alkanoamides give a linear plots for m = 1, . . ., 4, although in the latter case the first member, formamide (m = 0) is deviant high. Likewise with the alkylureas for m = 0, . . ., 8 (urea to tetraethylurea), although here the point for m = 4 is deviant low.

0.05 0.06 0.12 0.22 0.06 nd 0.07 0.09

Two features stand out in this brief survey of the ethoxyethane/water system. Firstly is the fact that the Collander plots are linear for both the mono- and disubstituted solutes, with the exception here of the alkandioic acids; however, the range of systems is evidently narrower than for octanol/water. Also, for the hydrogen bonding solutes, the alkanols and the alkylamines, pass essentially through the data points for the parent compounds, H2 O and NH3 . Secondly, the summarised parameters in Table 3 for this system gives an average value for the seven homologous series of the methylene group increment parameter ˇEW = 0.50, with a standard deviation of 0.21 units which represents a spread in the values even greater than that seen with octanol/water. 6.3. Alkanes/water (Figs. 25–28) The literature data obtained for homologous series with these two alkanes: heptane (hp) and heptadecane (hd) – as the organic solvent are shown in Figs. 25–28; in view of the higher methylene

Fig. 25. Alkanes/water lipicity LAW versus carbon number c (hp = heptane, alkanoic acids/hp – Goodman [54];  alkanoic acids/hp – hd = hexadecane): Smith and Tanford [55]; alkanoic acids/hp – Mukerjee [56];  alkanoic acids/hd – Abraham et al. [24,57]; × 4-alkylpyridines/hd – Abraham et al. [24,57]; + 4alkylpyridines/hd – Yeh and Higuchi (1 M NaCl) [34].

P. Molyneux / Fluid Phase Equilibria 368 (2014) 120–141

Fig. 26. Alkanes/water lipicity LAW versus carbon number c (all hexadecane) [24,57]:  alkanes;  alkenes; alkynes; cycloalkanes; × alkanols; + alkoxyalkanes;  alkylamines; 䊉 cycloalkanols;

zeronium (see Section 1.3).

group increments seen in this case, as discussed below, the reference line in the latter two figures is set at ˇ = 0.6. The Collander parameters obtained from these plots are listed in Table 4, with notes and discussion on specific series given below. Anticipating

Fig. 27. Alkanes/water lipicity LAW versus carbon number c (all hexadecane) [24,57]: alkanals; alkanones; - - - alkanoic acids – trendline from Fig. 25;  alkyl alkanoates (except methanoates);

alkyl methanoates;

zeronium (see Section 1.3).

137

Fig. 28. Alkanes/water lipicity LAW versus carbon number c (all hexadecane) [24,57]:  chloroalkanes;  bromoalkanes; iodoalkanes; + nitroalkanes; × alkanonitriles; alkylbenzenes; - - - 4-alkylpyridines – trendline from Fig. 25.

the similarity in the results obtained from these two alkanes, the log partition coefficients may be referred to collectively as LAW , and the Collander slope parameter (methylene group increment) as ˇAW . The Collander plots in Fig. 25 look at two specific features of the partition behaviour for the alkanes/water system: (a) with the alkanoic acids, any sensitivity of the partition data to the chain length of the alkane cosolvent; (b) with the 4-alkylpyridines, any sensitivity of the data to the nature of the aqueous phase, and to the experimental method used. With alkanoic acids in heptane/water, the overlapping ranges of data from Goodman [54] and Smith and Tanford [55] give a single line from m = 7, . . ., 21; the data of Mukerjee [56] are deviant, which Smith and Tanford [55] ascribe to an incorrect allowance for noncovalent association (hydrophobic interaction) in the aqueous phase. The data for the alkanoic acids in hexadecane/water for m = 1, . . ., 6 in Fig. 25 are those reported in two publications from the Abraham group [24,57]. There are two points to note in connection with these data. Firstly, the partition coefficients were obtained from the vaporphase solubilities in the two separate solvents; this is justifiable since there is such a small mutual solubility for the two, but it means that there is no possibility of solvent transfer along with the solute between the two phases. It is also stated [57] that this method obviates any gemdiol formation normally seen with the alkanals, as formulated here in Eq. (11) (Section 4.5). Secondly, although the data from the later paper [24] are stated to have been taken from the earlier paper [57], there are unexplained differences between some (but not all) of the two sets; the data have therefore been pooled, being treated at two sets rather than being averaged.

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P. Molyneux / Fluid Phase Equilibria 368 (2014) 120–141

Table 4 Collander parameters ˛AW and ˇAW (Eq. (9)) for homologous series with alkanes/water (alkane = heptane or hexadecane): column #1 are the corresponding entries for octanol/water in Table 1. See Section 6.3 for notes and discussions on these systems. #

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

#1

73 23 01 02 03 04 10 12 14 21 15 17 25 25 06 08 09 30 32 39

Series

4-Alkylpyridines Alkanoic acids Alkanes Alkenes Alkynes Cycloalkanes Alkanols Alkoxyalkanes Cycloalkanols Alkylamines Alkanones Alkanals Alkyl methanoates Alkyl alkanoates Chloroalkanes Bromoalkanes Iodoalkanes Alkanonitriles Nitroalkanes Alkylbenzenes

Fig.

25 25 26 26 26 26 26 26 26 26 27 27 27 27 28 28 28 28 28 28

Intercept, ˛AW

m-range

Slope, ˇAW

 (LS)

Min

Max

Ave

sd

Ave

sd

0 1 0 0 0 0 1 2 2 2 2 2 1 2 1 1 1 2 1 0

10 21 10 7 7 6 10 8 7 8 10 8 3 7 8 8 7 4 5 6

−0.55 −3.72 0.52 1.32 0.20 0.00 −3.43 −1.56 −3.64 −2.81 −2.35 −2.06 −1.30 −1.59 0.26 0.32 0.79 −2.02 −1.76 2.16

0.02 0.03 0.02 0.06 0.04 nd 0.01 0.04 0.26 0.03 0.03 0.03 0.07 0.04 0.07 0.05 0.03 0.03 0.03 0.02

0.638 0.620 0.658 0.593 0.612 0.651 0.636 0.612 0.568 0.586 0.650 0.674 0.635 0.612 0.571 0.646 0.649 0.630 0.718 0.630

0.003 0.002 0.004 0.013 0.010 0.009 0.002 0.007 0.044 0.006 0.005 0.005 0.034 0.009 0.011 0.010 0.005 0.010 0.010 0.010

There is then a common line in Fig. 25 for the alkanoic aids in these two alkanes, extending from m = 1, . . ., 21; the methylene group increment ˇAW is clearly higher here than that in octanol or ethoxyethane. The fact that the common line is obtained for the two distinct alkanes shows that the partition is insensitive to the chain length of the alkane used [24], and hence insensitive to the local environment being either a methyl or a methylene group. The fact that the alkanes/water line is lower than the ethoxyethane/water line (Fig. 24) is clearly due to the hydrophilic character of the carboxylic end group. This range corresponds to a remarkable linearity for the Collander plot for an increment of 20 methylene groups and of 12.5 units in the lipicity LAW . Secondly, Fig. 25 shows the data for 4-alkylpyridines with hexadecane from three sources–two sets from Abraham et al. [24,57] as already discussed, and from Yeh and Higuchi [34] where the aqueous medium is now 1 M NaCl (as previously shown in Fig. 18 and discussed in Section 4.17 for octanol/water). The full set gives a good common line ((LS) = 0.03) but with the data for the parent compound pyridine (m = 0) deviant upward L = 0.16(7). The fact that a common line is obtained for the two sets of data indicates that in this case, the partition coefficients are insensitive to the different experimental methods - shake-flask for Yeh and Higuchi [34] versus vapor solubility in the separate solvents for Abraham et al. [24,57] - and also insensitive to the use of 1 M NaCl as the aqueous phase for the data from Yeh and Higuchi [34] Turning to the partition data for the homologous series of hydrocarbons in hexadecane/water [24,57] shown in Fig. 26, the alkanes plot linear for the experimental range m = 0, . . ., 10. The fact that the line passes through m = 0 (H2 ), as with octanol/water (Fig. 2), is again surprising since hydrogen generally shows deviations from “normal” behaviour, such as seen with its critical constants [15], through quantum mechanical effects from its low relative molecular mass. The data for the alkenes (m = 0, . . ., 7) and for the cycloalkanes (m = 3, 5 and 6) overlap and give a line that passes within experimental uncertainty though the origin, that is, zeronium (Ze) (Section 3.1), as was the case with octanol (Fig. 2); in the case of the alkenes, this suggests that this equivalence of the alkene end-group CH CH2 to two methylene groups is a general phenomenon. The alkynes line is again lower down, linear for m = 0, . . ., 6. Considering the Collander plots for the remaining, more hydrophilic, series in Fig. 26, the plot for the alkoxyalkanes (ROR ) is

0.03 0.05 0.04 0.12 0.09 0.10 0.03 0.04 0.07 0.04 0.06 0.05 0.07 0.07 0.09 0.09 0.02 0.02 0.04 0.02

at a higher level than that for the alkanols (ROH), with their respective intercepts (m = 0) of −1.56(4) and −3.43(1) forming a regular series with the H2 O point at −4.38, reflecting the hydrogen-bond donating powers of the three types of solute (0:1:2). This contrasts with the situation with octanol where the three sets lie essentially on the same straight line (Fig. 4). The cycloalkanols, with only three points at m = 5, 6 and 7, gives an intercept of −3.6(3) that may be taken as an estimate of the oxygen fragmental contribution for the alkanes/water system. Finally, for Fig. 26, the alkylamines give a linear plot but with some scatter at the lower end for m = 0 (NH3 ) and m = 1. The plots in Fig. 27 relate to solutes with carbonyl or carboxyl groups. With the carbonyl compounds, the plots are linear both for the alkanones for m = 2, . . ., 10, and for the alkanals for m = 1, . . ., 8, with the alkanones plot lower by 0.4(1) units, and with only the point for formaldehyde (m = 0) deviant high for the alkanals. The linearity of the plot for the alkanals in this system contrasts with their behaviour with octanol/water (Fig. 5), where the correlation line is highly curved. Inasmuch as the behaviour for the alkanals with ethoxyethane/water was also normal (Fig. 24), this again suggests that the deviations seen with octanol are related to some interaction between these alkanals and the dissolved octanol in the water phase (Section 4.5). With the carboxyl compounds in Fig. 27, the data for the alkyl methanoates (formates) lie about 0.4 units above those for the other alkyl alkanoates, and these two sets have therefore been plotted separately. The figure also shows the trend line for the alkanoic acids, repeated from Fig. 25, lying 1.5(1) units below the esters line. Finally, Fig. 28 shows the Collander plots for the remaining more diverse series. The haloalkanes form a set of lines at levels in the order of increasing atomic number (size) of the halo-atom: chloro< bromo- < idodoalkanes. The plot for the nitroalkanes (m = 1, . . ., 5) is linear while that for the alkanonitriles (m = 1, . . ., 4) is also linear except for the first member (acetonitrile), which is high (+0.2). The alkylbenzenes (m = 0, . . ., 6) also give a linear plot that is higher than that for the 4-alkylpyridines by 2.5(1) for this same range, as shown by the trend line for the latter repeated from Fig. 25, representing the difference in lipicity of the =CH- and =N- groups in these aromatic rings. The overall picture here is that the Collander plots for the alkanes/water system are linear, albeit with deviations for the first member in some cases. However, the range of series is more

P. Molyneux / Fluid Phase Equilibria 368 (2014) 120–141

restricted than with octanol/water – in particular, there are none of the disubstituted series that showed nonlinear or otherwise anomalous Collander plots with octanol/water. The data for the 20 homologous series summarised in Table 4 give the average methylene group increment ˇAW = 0.63 with standard deviation 0.04, again indicating the marked spread of the values of this parameter for the alkanes/water system as seen with the octanol/water and ethoxyethane/water systems already considered. 6.4. Correlation of different solvent/water systems It would be useful to be able convert the partition coefficients for one solvent/water system to those involving another solvent. This problem was examined in the early work by Collander [28b], who suggested that relations exist of the form L2 = a12 + b12 L1

(14)

where L1 and L2 are the lipicities for organic solvents 1 and 2 respectively with water. This relation has been recently called the Collander equation [58], which suggests that this needs to be examined in the light of the present assignment of this term to Eq. (9). It has to be said that even in the original presentation of this form of relation, the fit to diverse series of compounds was not all that good; for example, if we examine Fig. 2 in Collander’s original paper [28b] correlating the partition data for ethoxyethane/water with those for iso-butanol/water for a diverse group of some 124 compounds, the data points scatter around the correlation line with an estimated standard deviation of about 0.3 units on either side; it is only when individual homologous series are considered, in Fig. 3 of that paper, that satisfactory correlations are to be seen. A similar conclusion is arrived at in the present case if corresponding plots for octanol and hexadecane are examined. This restriction to homologous series for both solvents is understandable, since Eq. (14) may be derived from the present Collander relation of Eq. (9) for a particular series in the two solvents to both of which this equation applies: L1 = ˛1 + ˇ1 m

(15)

L2 = ˛2 + ˇ2 m

(16)

whence by eliminating the methylene group number m the form of Eq. (14) is obtained. Thus this form of Eq. (14) is only a special case of this Collander relation of Eq. (9) considered in Section 3.1, and indeed will only apply if the Collander relation applies to both solvent/water systems. Under these circumstances, it is preferable to restrict the term “Collander relation” to single solvent/water partition systems, and to view Eq. (14) as a special case that applies under the restricted circumstances specified. 7. General discussion 7.1. Preview Although there has already been point-by-point discussion of specific systems and cases, it is useful to mention here some general points arising from these specific cases. 7.2. Use of graphs It is notable that although in the earlier work in this area, such as the pioneering work of Collander [28], there was routine use of the plots named here after that researcher, the use of these seems now to have lapsed. This may be because of the focus on computer programs and derived idea such a neural networks as a more compact and “automatic” way of treating these correlations. However, it is

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surprising if those who studied homologous series did not at some stage plot out their data in the manner here, as Collander plots of lipicity L versus carbon number c or methylene group number m. For such plotting as here used evidently reveals not only correlations between the plotted parameters, but also deviant data that need to be further investigated. The extensive use of graphs in the present paper is therefore intended not just to illustrate the values in published databases, but also to provide a critical display of their self-consistency. Indeed, these graphs collectively form an atlas of partition behaviour; for the charts (using the literal term used in spreadsheet nomenclature) reveal unexplored territory, and regions where the map data are deviant for some reason. 7.3. Coiling of the alkyl chains A underlying but unstated theme throughout this paper is the role played by the coiling or folding of the alkyl chains in the various media, as influenced by intramolecular noncovalent forces such as hydrophobic interactions in aqueous media, and as well as in the present context in non-aqueous media (octanol, ethoxyethane, alkanes, . . .) involved in partition equilibria. For each of the types of equilibrium will depend in part of the extents of such coiling in the each of two states involved. Examination of the literature for the viscosity and diffusivity behaviour of these alkyl chain solutes in aqueous solution suggests that, at least for the short chain compounds for which such data are available, the conformation is that of a somewhat expanded random coil [59], but this topic requires further examination which is beyond the scope of the present paper. 7.4. The methylene group increment ˇ The present paper is focussed on the parameter ˇ, methylene group increment to the value of the lipicity, L. The fact that, even when the Collander plot from Eq. 9 is linear for a given series, the values for different such series differ markedly, remains an enigma. It is possible, for example, that these differences relate to the intramolecular folding of the alkyl chains of the solute molecule in the aqueous phase, to different extents with different types of attached functional groups; the “micromicelle” so-formed that may solubilise the organic medium to different extents, again depending on the attached functional groups, and forming a molecular species that will have different partition behaviour to the original molecule of solute. There is scope here, also, for the comparison of this increment with that for related processes, such as vapor/solution equilibrium, micellisation, and the hydrophobic interaction. However, in the more general context, the fact that a single such value cannot be assigned to the methylene group “fragment”, indicates that the present widespread application of methods assigning fixed values to this and other fragments to interpret and predict partition coefficients, following the LFER approach, needs urgent re-examination. 8. Conclusions • The present paper has focused on the literature data for the octanol/water partition coefficient KOW , and specifically on the data for homologous series to investigate the constancy or otherwise of the methylene group increment to log KOW . • In the present context, it has been found useful to make a number of abbreviations - M = methylene group, log KOW ≡ lipicity L – to simplify the discussion. • Emphasis is placed on the use of graphs, notably plots of L versus the carbon number c or the equivalently the methylene group number m – here termed “Collander plots” – to demonstrate the

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P. Molyneux / Fluid Phase Equilibria 368 (2014) 120–141

consistency or otherwise of the literature values of L that may have been obtained from a diversity of sources and derived by a variety of experimental methods. These plots then provide an atlas of the literature values. It is striking to what extent the Collander plots are linear over a wide range of chain lengths, in several cases extending to the nominal parent or core compound with m = 0, for example, H2 with the alkanes, H2 O with the alkanols. This wide-span linearity suggests that the additional methylene groups remain in the same hydration sphere, that is, that the alkyl chains are coiled up near the end-group from the outset. However, the methylene group increments for those various homologous series that do give linear Collander plots, as represented by the Collander slope parameter ˇ, are not constant but has a normal (gaussian) distribution extending essentially from 0.43 to 0.63. Literature partition data are also examined from other solvent/water systems–ethoxyethane, and the two alkanes heptane and hexadecane (which seem to behave similarly). These show similar linear Collander plots, but with again a dispersion of the ˇ-parameters for the methylene group increment. The evidence from the literature on the conformation of alkyl chains in aqueous solution, from viscosity and from diffusivity, suggests that they adopt a compact conformation, consistent with the linearity of the Collander plots. This disparity between the ˇ-values for even these most favourable cases of linear Collander plots, and the fact that may series (especially those with groups at either end of the chain) show nonlinear plots, shows that it is not acceptable to use a sin¯ gle value of ˇ-value for even the methylene group; this in turn casts doubts on the widely-accepted and widely used concept of fixed values for the “fragments” of compounds.

List of symbols

aq ave c C ee, E f(X) hd hp I K KAW KEW KOW L (LOW ) L(exp) L(cal) LAW LEW m M M n N N* nd O oc

aqueous (phase) average value for specified variable carbon number solute concentration [M] ethoxyethane (diethyl ether) phase contribution of “fragment” X to lipicity L hexadecane (phase) heptane (phase) partition data of Izokawa et al. [32] (Section 4.11) partition data of Kozubek [33] (Section 4.11) alkanes/water partition coefficient ethoxyethane/water partition coefficient octanol/water partition coefficient log KOW – (octanol/water) lipicity (mean) experimental value of L calculated value of L, for example from linear fit to Eq. (9) log KAW – alkanes/water lipicity log KEW – ethoxyethane/water lipicity methylene group number for molecule (n1 + n2 + · · ·) methylene group molar concentration [mol dm−3 ] alkyl chain length (n1 , n2 , . . ., for multiple chains) number of values in the distribution of the homologous series (effective) maximum value of N no data/not determined partition data from workers other than I and K (Section 4.11) octanol (phase)

p(N*)

logit function for distribution with (effective) maximum value N* – Eq. (13) sd standard deviation for specified variable Sangster KOW database – Ref. [7] SKD Ze hypothetical element zeronium (Ar = 0) – Section 1.3 {-A. . .Z-} cyclo-A. . .Z mean value of parameter x x¯ y. . .z range of (literature) values of stated parameter (notably, m) from y to z ˛ Collander intercept parameter for octanol/water – Eq. (9) ˇ (ˇOW ) Collander slope parameter (methylene group increment) for octanol/water – Eq. (9) ˇAW ˇ-value for alkanes/water ˇ-value for ethoxyethane/water ˇEW L L(exp) − L(cal) ␲(X) Hansch hydrophobic parameter for group X – Eq. (8) (x) standard deviation for set of data for variable x

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