Applications of the octanol–air partitioning ratio: a critical review

Abstract

The octanol–air partition ratio (K_OA), also referred to as the octanol–air partition coefficient, has a wide range of applications in environmental chemistry. In this review, we explore the historical context of using octanol as a surrogate for various types of organic matter. We examine in detail the single-parameter linear free energy relationships (spLFERs) that rely on the K_OA to describe partitioning equilibria between the gas phase and vegetation, soil, particles, dust, surfaces, materials, and animal tissues. We further use poly-parameter linear free energy relationships (ppLFERs) to estimate how well octanol approximates the partitioning properties of these divergent phases. While the availability of ppLFERs for many environmentally and biologically relevant phases has rendered some of the spLFERs based on the K_OA largely obsolete, the K_OA still serves a useful purpose as a single parameter describing the tendency of a neutral organic chemical to partition from the gas phase into a wide variety of organic phases. As such, it is a well-defined, easy-to-comprehend and experimentally accessible descriptor of compound volatility from organic phases.

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Environmental significance

There is a long tradition of using the solvent octan-1-ol as a surrogate for a large variety of organic matter when seeking to predict the phase distribution of organic compounds. While not as ubiquitous and common as the octanol–water partitioning ratio K_OW, the octanol–air partitioning ratio K_OA is widely used when studying the partitioning of organic compounds between organic matter and the gas phase. With the increasing availability and acceptance of methods for predicting the partitioning of organic vapours from air into soil organic matter, atmospheric particles, biological tissues, and polymers, that do not depend on a surrogate organic solvent phase, it is valid to explore whether there is still a role to play for simple linear regressions involving the logarithm of the K_OA. This review concludes that there is continued need for a single parameter quantifying organic compound volatility from organic phases and the K_OA is well suited to fulfill this role.

1 Introduction

Phase equilibrium processes involving the gas phase have been studied for over two centuries, beginning with an effort to understand gas solubilities (e.g., Bunsen,¹ Henry,² and Ostwald³), improving drug and anesthetic delivery based on the permeability of these compounds into cells and lipids (e.g., Meyer⁴ and Overton⁵), for use in chemical separation processes and partition chromatography (e.g., Pierotti et al.⁶ and Porter et al.⁷) and understanding the behaviour and fate of chemicals in the environment.^8,9 The study of chemical partitioning between gaseous, aqueous, and organic phases has since become a fundamental aspect of environmental and physical chemistry, as well as medicinal and pharmaceutical sciences.

Chemical equilibrium partition ratios, K₁₂, hereafter simply referred to as partition ratios, describe the relative chemical concentrations in two adjacent phases at equilibrium and are dependent on environmental conditions such as temperature. In many instances, partition ratios are referred to as partition coefficients; however, because this property is influenced by external conditions (i.e., temperature), IUPAC guidelines recommend the use of the term partition ratios.¹⁰ Because partition ratios of chemicals can span many orders of magnitude, they are often expressed on a base 10 logarithmic scale (i.e., log₁₀ K₁₂).

In this review we examine the role of the octanol–air partition ratio (K_OA) and its relevance to our understanding of environmental chemical fate processes. In previous work we explored the different methods used to measure and estimate the K_OA of an organic chemical.¹¹ Here, we summarize all of the different phase equilibria that have been described with the help of the K_OA including partitioning between the gas phase and vegetation, soil, particles, dust, surfaces, materials (e.g., polyurethane), and animal tissue. We further evaluate how good a surrogate octan-1-ol is for these phases and highlight the limitations of simple regressions between equilibrium partitioning ratios and the K_OA. We also explore the use of the K_OA in bioaccumulation and chemical risk assessments and as a coordinate in chemical space plots. Considering the availability of tools for estimating environmentally relevant phase equilibria involving the gas phase that do not rely on the K_OA, we further address the question of why the K_OA still serves a useful purpose.

1.1 What is the K_OA?

Partitioning between octanol and air has been described directly and indirectly with different physical–chemical properties. It is directly quantified using the octanol–air partition ratio (K_OA), Ostwald coefficient in octanol (L_oct; e.g., Boyer and Bircher¹²), the Gibbs energy for octanol–air phase transfer (; e.g., Berti et al.¹³), and Henry's law constant in octanol (k^oct_H, Pa m³ mol⁻¹; Roberts¹⁴). It has also been indirectly quantified by combining either a chemical's vapour pressure with the activity coefficients at infinite dilution in octanol (e.g., Hussam and Carr¹⁵) or the octanol–water (K_OW) and the air–water partition ratios (K_AW; e.g., Finizio et al.¹⁶).

K _OA is the concentration of a chemical in octanol divided by the concentration of a chemical in air at equilibrium (eqn (1)).

The K_OA of a chemical can be derived from any one of the variables mentioned above. Details regarding these calculations are described in more detail by Baskaran et al.¹¹

1.2 A brief history of partition ratios

Interest in partitioning properties and in particular the K_OA grew and waned throughout the years in various sub-disciplines including physical, analytical, medicinal, pharmaceutical, and environmental chemistry. Exploration of partition ratios began with investigations into the solubility of gases in water and later other solvents. Henry's law constant,² Bunsen absorption coefficient,¹ and Ostwald coefficient³ were gas-solvent partition properties dependent on different external conditions.^17,18 Partitioning into organic phases and specifically lipids became of interest after the discovery of anesthesia in 1846.¹⁹ At the turn of the 20th century, Meyer⁴ and Overton⁵ independently proposed that narcotics were being dissolved in lipids to cause narcosis rather than cholesterols and lipids dissolving into the narcotics.⁵ In their experiments to identify chemicals partitioning to lipids, both Meyer and Overton found it challenging to use biological lipids because of their tendency to develop emulsions. They suggested the use of a partition ratio (P) between water and another organic phase instead. Overton initially used olive oil as the reference phase as it was cheaper and easier to obtain than long chain alcohols, which were known to have solvation properties closely related to those of biological lipids. Overton also noted that the high melting points of these alcohols implies that measurements would need to be made at physiologically unrealistic temperatures. In the following decades, there were few significant advances in the study of partition ratios; physical and biological chemists focused on the solubilities of different chemicals in various solvents²⁰ and developed manometric devices for measuring the solubilities of gases in blood.²¹ In 1935, Meyer and Hemmi²² returned to the idea of partition ratios and proposed the use of oleyl alcohol over olive oil, as oleyl alcohol would act as a better surrogate for body lipids when describing the partitioning of more polar compounds.

It was only in the early 1950s however that the use of solvent-water partition ratios was re-popularized by the work of Collander.^23–25 In 1947, Collandar published his work “On Lipoid Solubility” where he compared the solvent-water partition ratios for a number of different solvents including octan-1-ol, referred to as octanol henceforth, olive oil and oleic acid.²³ In particular, he noted that research has yet to identify a solvent that can dissolve a variety of solutes and represent the lipid phase well.²³ Collander found that the partition ratios in one alcohol/water system can be used to calculate the partition ratios in another alcohol/water system.²⁴ Octanol was favoured as it was, unlike ethyl ether, not very soluble in water and while hydrophilic substances and bases were more soluble in octanol, hydrophobic solutes were equally soluble in ethyl ether and octanol.²⁴ Over the next two decades, different solvents, including various alcohols, were considered for the organic reference phase.²⁶ In some of their earliest work, Hansch and colleagues found partition ratios had additive–constituent properties — which allows for fragment-based estimation techniques.^27–29 Hansch et al. commonly used octanol as the reference organic phase in these works.^27,28 Hansch later noted that multiple works showed good correlation between the octanol–water partition ratio and various organic bio-polymers.³⁰ They reported on these developments and the applicability of the octanol–water phase ratio in drug design in some of the very first volumes of the Annual Reports in Medicinal Chemistry.^30,31 The use of partition ratios, particularly the K_OW, in drug design took off after the publication of various works by Hansch and their colleagues, including one of the earliest review papers on partitioning, by Leo et al. in 1971.²⁹

It is important to note that initial measurements for partition ratios would have been extremely challenging in the absence of modern analytical instruments; early methods included the use of manometers¹² and coulometry.²⁷ The development of partition chromatography, including gas chromatography in the 1940s and 1950s,³² led to more measurements and increased interest in gas–liquid partition ratios. In 1959, in an effort to improve understanding of separation processes, Pierotti et al.^33,34 measured the infinite dilution activity coefficient of various solutes in multiple solvents using gas–liquid chromatography.

The first directly reported K_OA value, albeit referred to as an Ostwald coefficient, appears to be by Boyer and Bircher in 1960, while investigating the solubility of various gases in different alcohols using a modified Van Slyke-Neill blood gas apparatus.^12,21 Another set of K_OA data was published 13 years later in an effort to understand characteristics of solvents used in gas chromatography.³⁵ The next reported measurement of K_OA was published in 1978.³⁶ This work built on work by Battino and co-workers exploring gas–liquid partitioning of gaseous compounds, driven in part by the desire to find a solvent that could act as a model for partitioning of compounds (including anesthetics) between the gas phase and cell membranes.^37,38

By the 1980s, environmental chemists had adopted the use of K_OW from the pharmaceutical industry for use in predicting the environmental fate and behaviour of chemicals (e.g., Smith et al.⁸). Paterson et al.³⁹ were perhaps the first to identify the K_OA as a useful descriptor for plant–air partitioning and noted the dearth of experimental K_OA values. At the same time, octanol–air partitioning became increasingly of interest to the physical chemistry community in the mid 1980s as Pollack et al.,⁴⁰ Carr (e.g., Hussam and Carr¹⁵), and Cabani (e.g., Berti et al.¹³) and colleagues explored the thermodynamics of gas–liquid equilibria, reporting Gibbs energies of solutions and infinite dilution activity coefficients for solutes in octanol.

Exploration of the K_OA and other gas–liquid partition ratios to characterize the behaviour of inhaled anesthetics was renewed in the early 1990s (e.g., Taheri et al.^41,42 and Liu et al.⁴³). In the same decade, Harner and Carr began independently reporting K_OA values for various solutes. Harner's focus was on the use of K_OA to understand the environmental partitioning behaviour of chemicals between air and various types of organic matter.⁴⁴ Dallas and Carr⁴⁵ were interested in understanding the effect that the mutual solubility of octanol and water has on the K_OW. A head space sampling system developed by Carr and colleagues made measuring vapour–liquid equilibria easier.^15,45 In the following two decades interest in the K_OA has not waned and many more measurements of the K_OA have been reported.¹¹

2 Single-parameter linear free energy relationships involving the K_OA

2.1 Phase concentration ratios involving air

In many investigations involving organic chemicals, concentrations in a phase in contact with air are measured, e.g., concentration in phase X C_X in units of mol m⁻³. It is then quite common to calculate ratios between those concentrations and the concentration in the air, e.g., C_A in mol m⁻³:We use the variable Q to designate this concentration ratio, because we want to reserve K for equilibrium partition ratios and it is generally not established whether chemical equilibrium between phase X and the air exists. Whereas Q_XA is dimensionless (or rather has units of m³ air m⁻³ phase X), other units for such concentration ratios are quite common because the concentration in phase X can be expressed in different units, e.g., per mass of phase X rather than per volume of phase X. For example, the concentration ratio between atmospheric particles and the gas phase is often expressed in units of m³ air µg⁻¹ particles. The dimensionless Q_PA value can be obtained as:where TSP is the concentration of total suspended particulates in the air (µg m⁻³; Finizio et al.¹⁶).

If phase X is a biological phase, e.g., the foliage of a plant, the concentration ratio is sometimes referred to as a bioconcentration factor (BCF).

Generally, the C_A in eqn (1) refers to the concentration in the gas phase. However, in some cases, the total concentration in air C_TA, i.e., concentration in both the gas and particle phase (C_P) has been measured and is used for the ratio calculation:

2.2 The types of single parameter linear energy relationships involving K_OA

Many studies seek to relate the concentration ratios Q_XA obtained for different chemicals against the K_OA of those chemicals. This typically takes the form:

Q_XA = aK_OA^m (5)

or, in logarithmic form:

log₁₀ Q_XA = m log₁₀ K_OA + log₁₀ a (6)

These types of equations are called single parameter linear free energy relationships (spLFERs). The implicit assumption underlying these relationships is that phase X, or a constituent of phase X, has solvation properties that resemble those of octanol. An example, where the entirety of phase X is assumed to have octanol-resembling solvation properties, are organic surface films. More commonly, phase X has different constituents that may contribute to the uptake of chemicals. In this case, the concentration ratio may be expressed as the sum of the concentration ratios in the bulk phase constituents weighted by the constituents' abundance in the bulk phase, e.g.:

Q_XA = f_AX + f_WXK_WA + af_ORXK_OA^m + f_YXK_YA + a_Surface/XK_Surface/A (7)

where f_AX, f_WX, f_ORX, and f_YX are the volume fraction of air, water, octanol-resembling phase and any other phase Y in bulk phase X and a_Surface/X is the surface area to volume ratio of surface in phase X. K_YA is the equilibrium partition ratio between phase Y and air and K_Surface/A is an equilibrium surface adsorption constant onto surface from air (with units of m).

In many cases, the assumption is then made, explicitly or implicitly, that the term af_ORXK^m_OA is larger than all of the other terms in eqn (7), in which case we obtain:

Q_XA = af_ORXK^m_OA (8)

or, in logarithmic form:

log₁₀ Q_XA = m log₁₀ K_OA + log₁₀ f_ORX + log₁₀ a (9)

Examples of such composite bulk phases are soil, atmospheric particles and biological materials.

In earlier papers, when the K_OA had not been well established as a concept and when few experimental K_OA values were available, K_OW/K_AW instead of K_OA was used in relationships of type 5, 6, 8, and 9, i.e., the K_OA was estimated as the ratio of the K_OW and the equilibrium air water partition ratio K_AW. It is believed that K_OW/K_AW in general has far higher uncertainty than K_OA values, especially if predicted properties are being used. This has been observed in some correlations between empirical K_OA and K_OW/K_AW values with Q_XA.^46,47

2.3 A thermodynamic look at spLFERs involving K_OA

According to Goss and Schwarzenbach:⁴⁸where R, T, v_O, M_O, ρ_O, and γ_O are the ideal gas constant, absolute temperature, the molar volume, molar mass, and density of octanol at infinite dilution, and the activity coefficient of the chemical in octanol at infinite dilution, respectively. P_L is the vapour pressure of the subcooled liquid at saturation. Analogously, the equilibrium partition ratio between phase X containing the octanol-resembling constituent and air is:where v_OR, M_OR, ρ_OR, and γ_OR are the molar volume, molar mass, and density of, and the activity coefficient of the chemical in, the octanol-resembling constituent of phase X at infinite dilution. Combining eqn (10) and (11) we get:In other words, if the concentration ratio Q_XA reflects equilibrium partitioning, parameter a in eqn (8) is the ratio of the solubility of the solute in the octanol-resembling constituent of phase X [i.e., 1/(v_ORγ_OR)] divided by the solubility of the solute in octanol [i.e., 1/(v_Oγ_O)]. Also, we would expect exponent m to be 1.

Incidentally, eqn (11) corresponds to a single parameter linear free energy relationship between K_XA and P_L. In other words, Q_XA can be, and often has been, related to P_L in equations of the type:

Q_XA = aP_L^−m (13)

or, in logarithmic form:

log₁₀ Q_XA = −m log₁₀ P_L + log₁₀ a (14)

Equations involving K_OA are believed to be preferable over those involving P_L, because the ratio γ_O/γ_OR is less variable for different compounds than is γ_OR.⁴⁹ Finizio et al.¹⁶ also noted that because the P_L cannot be measured directly it can incur large errors for chemicals with high melting points that are solids at environmentally relevant temperatures. However, whether spLFERs involving P_L or K_OA are preferable may also depend on which of these two parameters can be obtained with higher reliability.⁵⁰

Eqn (10) and (11) also illustrate a potential issue with spLFERs involving the K_OA (or the P_L). Both K_OA and K_XA are inversely proportional to P_L. The P_L varies over many orders of magnitude between different chemicals, whereas γ_O and γ_OR vary only over a small range. K_XA and K_OA (and also K_XA and P_L) are therefore bound to be highly correlated if the dataset includes chemicals of divergent volatility. This auto-correlation issue has been discussed by Paterson and Mackay⁵¹ and will be discussed further below.

2.4 Reasons why exponent/slope m in spLFERs involving K_OA is not 1

There are several reasons why the exponent/slope m in equations of type 5, 6, 8, and 9 can deviate from 1.

The first is that Q_XA does not reflect equilibrium conditions. If a chemical's K_XA is large, it can take a long time to reach equilibrium. If the chemical originates in the gas phase, the measured C_X is lower than it should be at equilibrium and the Q_XA for such high K_XA compounds accordingly is lower than K_XA. This leads to slopes m that are lower than 1. If, however, the chemical originates in phase X, non-achievement of equilibrium leads to a measured C_A that is lower than it should be at equilibrium. Q_XA for high K_XA compounds then is higher than K_XA and slopes m are more likely to exceed 1. An example of the latter would be a dust particle that includes polymer fragments containing the chemical of interest as an additive.

The K_OA threshold for non-achievement of equilibrium depends on a number of factors, such as the size, viscosity, composition and homogeneity of the octanol-resembling constituent in phase X, the mass transfer kinetics between air and that phase and the time available for equilibration. However, often several studies indicate similar threshold values. For example, vegetation is likely to reach equilibrium with gas phase chemicals with a log₁₀ K_OA below 8.^52,53 On the other hand, compounds with a log₁₀ K_OA in excess of 13 are unlikely to achieve equilibrium with atmospheric particles within the atmospheric lifetime of most particles.⁵⁴

Disequilibrium may also be a result of temperature differences between air and the condensed phase X. Partitioning between gas and condensed phases are generally highly temperature dependent and the low heat capacity of air means that temperature can fluctuate far more quickly in air than in phase X. This, however, tends not to be an issue in laboratory experiments, where thermal equilibrium can typically be ensured. Some chemicals may also form non-exchangeable residues in the condensed phase, e.g., in soil organic matter, and thus are not available for partitioning but can be chemically extracted during analysis.

Another reason for slopes m being lower than 1 could be the use of total air concentrations C_TA instead of gas phase concentrations C_A (eqn (4)versuseqn (2)). In that case, Q_XA is too small (relative to K_XA) for low volatility chemicals that partition to atmospheric particles.

The final reason for deviations of slopes m from 1 are differences in the solvation properties of octanol and the octanol-resembling phase. Goss and Schwarzenbach⁴⁸ show that a slope of 1 is obtained if γ_O/γ_OR is constant. For substances within a compound class, slopes deviating from 1 can be obtained if γ_O/γ_OR varies proportionally with K_OA.

2.5 Phase equilibria that have been described with spLFERs involving the K_OA

2.5.1 Vegetation–air partitioning. The uptake of many organic chemicals into plants from the air is driven largely by partitioning between air and the plant foliage. However, a mechanistic understanding of that process is often elusive due to complex composition of plant foliage and poorly defined solvation properties of the foliage constituents. For example, cellulose has a very minor capacity to sorb organic molecules and the solvation properties of cuticular waxes depend on the extent of their crystallinity. Nevertheless, repeated attempts have been made at relating empirically the measured partitioning into plants to a chemical's K_OA.³⁹ Bacci et al.⁵⁵ proposed a simple spLFER relating the plant bioconcentration factors (BCF), defined as the ratio of the concentration in vegetation divided by the concentration in air, to the K_OA, i.e., eqn (8) with a and m being equal to 1. At the same time, Riederer⁵⁶ proposed to estimate BCFs in plants using an equation of type 7 based on the K_OA (calculated from K_OW and K_AW) and a measured cuticle–air partition ratio K_Cuticle/A, again with a and m assumed to be 1. Note that Riederer⁵⁶ considered here the plant lipids to be the octanol-resembling part of the plant, whereas the cuticle was a separate compartment. A later, simplified approach dropped the term containing K_Cuticle/A^57,58 to estimate the vegetation–air partition ratios (K_VA):

K_VA = f_A + f_WK_WA + f_LK_OA (15)

which implies that the cuticle is now subsumed in the octanol-resembling phase. If the first two terms are considered negligible (Steyaert et al.;⁵⁸ see Section 2.2), an equation similar to that by Bacci et al.⁵⁵ is obtained. Muir et al.⁵⁹ also observed a correlation between BCFs measured in lichen and K_OA. Applying these concepts, a multi-compartment model for plants was developed which did not use K_OA directly, but used K_OW and K_AW to estimate air-leaf partitioning and bioconcentration in leaves.⁶⁰ Muller et al.⁶⁰ defined a different compartment for proteins, lipids, and carbohydrates, each with independent values for a and m.

Subsequently, the K_OA has been applied repeatedly to estimate chemical uptake in different plant species (e.g., Tremolda et al.,⁶¹ Dowdy and McKone,⁶² Keymeulen et al.⁶³). Tolls and McLachlan⁶⁴ reported a correlation of equation type 5 between log₁₀ K_VA measured for welsh ray grass and log₁₀ K_OA with R² values of 0.89 to 0.90. K_OA values that were consistently lower than the K_VA were attributed to differences in the temperature at which the two variables had been measured.⁶⁴ Brown et al.⁶⁵ also found linear correlations between the log₁₀ of the whole pine needle–air partition ratio (log₁₀ K_Pine/A, R² = 0.96) and the pine needle wax–air partition ratio (log₁₀ K_Wax/A, R² = 0.70) and the log₁₀ K_OA. The regression coefficients a and m in eqn (6) are thus specific to the plant species (e.g., Tolls and McLachlan,⁶⁴ Kömp and McLachlan,⁶⁶ McLachlan,⁵³ Nizzetto et al.⁶⁷). The intercept should further be dependent on whether the concentration in vegetation is expressed on a fresh or dry weight basis. Most spLFER equations are for 25 °C but exploration of the interspecies variability of K_VA in relation to the K_OA showed that K_VA is more temperature dependent than the K_OA.⁶⁶ In a modelling effort, Taylor et al.⁶⁸ used eqn (6) with m equal to 0.7 and log₁₀ a equal to 0.15 for clover–air partitioning as a general model for plant–air partitioning whenever no plant specific model is available. We stress that most of these studies were limited to non-polar organic contaminants.

The K_OA (or K_OW and K_AW combined) has also been related to the partitioning between specific parts of a plant and air, including leaf–air,^55,65 bark–air,^69,70 tree core–air⁷¹ and cuticle–air.⁶³ The capacity to quantify these individual partition ratios in plants has advanced passive-sampling techniques in both indoor and outdoor environments for organic pollutants. For example, in indoor air, olive trees have been used to measure polycyclic aromatic hydrocarbons⁷² and in outdoor environments, bark, leaf, litter, and pine needles have been used as passive samplers for PBDEs,⁷³ chlorobenzenes,⁷⁴ and various volatile organic compounds.⁷⁵

In addition to partitioning between air and individual plants and plant parts, the K_OA can be used to describe bulk phase partitioning between the gas phase and entire forest canopies. Horstmann and McLachlan⁷⁶ measured deposition of chemicals onto deciduous and coniferous canopies in Germany and found that the distribution of chemicals with log₁₀ K_OA < 10 approached equilibrium. Accordingly, they derived equations in the form of eqn (5) to relate pseudo canopy–air partition ratios K_Canopy/A with the K_OA, both for a deciduous canopy (m = 0.76, log₁₀ a = 1.15) and a coniferous canopy (m = 0.69, log₁₀ a = 1.58). Su et al.⁷⁷ conducted a similar study in a deciduous forest in Canada and derived a similar correlation (m = 0.67, log₁₀ a = 2.04). Many of these equations were derived from datasets comprising only a small subset of structurally related chemicals (e.g., PCBs) and thus these models likely work best when applied to chemicals of similar size and structure.

The relationships above assume that chemical equilibrium is established between the vegetation and the atmospheric gas phase. However, as mentioned in Section 2.4, this is generally only a defensible assumption for relatively volatile chemicals, whereas for less volatile chemicals the kinetics of uptake and plant growth play a more important role in controlling plant bioaccumulation and bioconcentration.⁷⁸ McLachlan⁵³ presented a conceptual framework, which illustrates how measurements of plant uptake can be used to delineate the K_OA ranges within which different processes, including wet and dry deposition, are dominant. Volatile chemicals with low log₁₀ K_OA (<8.5) reach equilibrium and the K_VA is directly correlated with the log₁₀ K_OA. For involatile chemicals with high log₁₀ K_OA (>11), particle bound deposition is important which is apparent in another correlation of the log₁₀ of the particle–air partition ratio log₁₀ K_PA with log₁₀ K_OA.⁵³ For chemicals with intermediate log₁₀ K_OA (8.5–11) uptake into plants from air is not a function of K_OA, but rather a function of the kinetics of the transport from air to the plant storage compartment and the time of exposure. Later modelling work⁵² confirmed that non-volatile chemicals (log₁₀ K_OA > 8) do not approach equilibrium between plants and air and so the application of the K_OA for estimating plant BCFs and K_VA is more applicable to volatile chemicals. More volatile chemicals (log₁₀ K_OA < 5) also have the potential to volatilize from a plant's stem, trunk, and leaves.⁷⁹

2.5.2 Soil–air partitioning. The potential for the K_OA to describe soil–air partitioning processes was first identified by Harner and Mackay.⁴⁴ Given the lack of measured K_OA values, many early studies relied on the K_OW/K_AW ratio to estimate partitioning ratios between soil (organic matter) and air K_SA (e.g., Hippelein and McLachlan⁸⁰ and Borisover and Graber⁸¹). Earlier, Karickhoff had shown that for a relatively small and largely non-polar group of compounds the logarithm of the organic carbon–water partition ratios (log₁₀ K_OC) is highly correlated with the log₁₀ K_OW, with a slope of ∼1.⁸²K_OW/K_AW and the organic carbon–air partition ratio K_OC/A were found to be similarly related.⁸¹ Accordingly, Hippelein and McLachlan⁸⁰ extended the Karickhoff equation to soil–air partitioning:where f_OC is the fraction of organic carbon in the soil and ρ_OC is the density of the soil organic carbon. A regression of experimental K_SA values for chlorobenzenes, PAHs, and PCBs, with experimental values of both K_OA and K_OW/K_AW produced near identical results and the slope of these regression approached unity, suggesting that interactions between such non-polar chemicals and soil organic matter are similar to those with octanol.⁸⁰ An m of 1 in these relationships indicates that octanol may be a better surrogate for soil organic carbon than for plant tissues.

As more directly measured K_OA became available, its role in soil–air partitioning became evident and the K_OA was used directly to describe soil–air partitioning.^80,83 For example, volatilization fluxes of pesticides from sludge-amended soil were found to correlate with K_OA and the pesticide concentration in the sludge.^84,85 He et al.⁸⁶ found that when using directly measured K_OA values, the predicted K_SA value was ∼2.7 times greater than the experimental K_SA, while K_SA values predicted using experimental K_OW/K_AW values were in better agreement with experimental K_SA values. This prompted He et al.⁸⁶ to develop a modified Karickhoff equation:

with a second correction to be applied when estimating K_SA below 0 °C:The use of experimental K_OA values in these correlation equations is preferable over using two empirical values for K_OW and K_AW.^80,86 We suspect that there are some inconsistencies in the property data used by He et al. to develop these correlations as some K_OA, K_AW, and K_OW values are from a curated review of property data for PCBs by Li et al.⁸⁷ which include final adjusted values. Therefore, the three partitioning values should be internally consistent and both K_OA and K_OW/K_AW should predict the same K_SA value.

Contrary to expectations, Hippelein and McLachlan⁸⁸ observed that the absorption of organic chemicals in organic matter showed dependence on relative humidity and proposed a semi-empirical equation for predicting K_SA:

where A is a normalization constant quantifying the similarity of octanol to organic carbon, B is the slope of the regression between K_SA and RH, and is the internal energy of soil–air phase change, which also varies with RH.⁸⁸ Hippelein and McLachlan recommend an A value of 2 and a value of 0.0437 for B as they found B to be relatively constant across penta- and hexachlorobenzene and various PCBs.⁸⁰ As both B and are chemical specific, or at least homologue specific, using this semi-empirical equation for predicting K_SA to describe general soil–air partitioning poses some challenges with data availability.⁸⁹ Instead, Davie-Martin et al.⁸⁹ suggest that compound group specific multiple linear regressions using K_OA, RH, and temperature be used for estimating K_SA because this approach requires fewer chemical specific properties (i.e., B and ) and performed much better than the general equation. However, there are limitations to this approach, as the f_OC term is not included in the regression and K_SA is assumed to be linearly correlated with RH.

While the relationships above all assume that partitioning of chemicals to soils from the air is solely governed by absorption on soil organic matter, this assumption is often not valid, especially in air-dry soil and soil with a low organic matter content. Under such circumstances, adsorption to mineral surfaces can become dominant.^90,91 In particular, relative humidity plays a critical role in determining the relative importance of adsorption to the mineral–air interface. If only absorption processes (i.e., sorption into soil organic matter) is considered, estimates of the K_SA are likely to be underestimated.⁹¹ In other words, whenever adsorption plays a role in soil–air partitioning, using octanol as a surrogate for soil will be insufficient.^91,92

2.5.3 Particle–air partitioning in the atmosphere. Before the K_OA was introduced in environmental and atmospheric chemistry, the Junge–Pankow model based on the subcooled liquid vapour pressure P_L was generally used to predict the fraction of a chemical adsorbed onto particles (eqn (11); Junge⁹³ and Pankow⁹⁴). This relationship would generally take the form of eqn (14), a linear regression between the log₁₀ particle–air partitioning ratio and log₁₀ P_L.⁹⁵

Whereas in its original formulation, the Junge–Pankow relationship was based on the assumption that chemicals adsorb onto the surface of the particles, Pankow⁹⁶ showed that the use of P_L is also compatible with an absorption model of particle–air partitioning, which took the form of eqn (11) and related P_L to . If chemicals are absorbed into a particle's organic matter (OM) fraction, the K_OA can serve as an alternative measure for estimating (see Section 2.3 and Finizio et al.¹⁶ for details). Assuming an octanol density (ρ_O) of 820 kg m⁻³,¹⁶ a ratio M_Oγ_O/M_OMγ_OM equal to 1 and that all OM present in the aerosol is available for partitioning,⁹⁵ simplifies eqn (11) to an equation of type 6, where log₁₀ a equals −11.91 and m is 1.

A strong relationship between and K_OA would suggest that interactions of neutral organic chemicals with the OM in the particles is similar to that in octanol, i.e., via absorption, rather than surface adsorption.¹⁶ Indeed, K_OA and values have been found to be correlated for a number of compound classes including PAHs, PCBs, organochlorine pesticides, and PCNs^16,95 and the K_OA is often considered to be a better predictor than P_L for particle–air partitioning,^95,97,98i.e., the K_OA-based model performs better than the Junge–Pankow model.^95,97,99 The K_OA based model is believed to act as a more universal model for , as structurally similar compounds tended to group together when regressing against the K_OA, but this did not occur when was regressed against P_L.^95,97,98

While the regressions between K_OA and can be quite strong (R² 0.60 to 0.99), slopes of the regression are often less than 1 (e.g., Falconer and Harner,⁹⁷ Finizio et al.,¹⁶ Harner and Bidleman,⁹⁵ Radonic et al.¹⁰⁰). Two explanations have been proposed to explain this: octanol and OM have different solvation properties or equilibrium has not been reached (see Section 2.4). It is likely that both explanations hold true. For example, the polarity of secondary aerosol particles can differ from octanol, such that the activity ratio of a chemical in octanol and organic matter deviates from 1, thus the slope of a K_OA and regression will also differ from 1.¹⁰¹ Yeo et al.¹⁰² suggested that the activity ratio assumption of 1 held true for multi-ortho PCBs but not for non/mono-ortho PCBs based on regressions of K_OA and P_L from Harner and Bidleman.⁹⁵ Götz et al.¹⁰³ noted that the K_OA based model tended to overestimate the and recommended using an M_O/M_OM value of 0.26 in eqn (11).

The presence of soot or elemental carbon can also alter the particle–air partitioning of chemicals because then adsorption to such sorbents can occur in addition to bulk phase absorption.¹⁰⁴ In these instances a model based solely on K_OA has a tendency to underestimate the ,^104–106 and a second term to describe the adsorption to soot is needed:¹⁰⁴

where f_EC and α_EC is the fraction and specific surface area of elemental carbon in the aerosol, α_AC is the surface area of activated carbon, and is the soot–air partitioning ratio in units of L kg⁻¹.¹⁰⁴ The 10¹² included in the denominator is for unit conversion. However, Helm and Bidleman¹⁰⁷ found the opposite to be true, where the model overpredicts the whereas using K_OA alone better agreed with field measurements. The differing conclusions from the various studies do not reject the suitability of K_OA as parameter for predicting , rather suggests that better characterization of the particle phase (e.g., the polarity) is needed to better understand chemical interactions between particle and gas phase.

2.5.4 Dust–air partitioning. Descriptions of indoor dust–air partitioning are largely based on particle–air partitioning systems. Weschler and Nazaroff,¹⁰⁸ like many others, found it more convenient to use K_OA instead of P_L to describe the partitioning; assuming chemicals partition into dust OM as they would in octanol, Q_Dust/A (dimensionless) can be estimated using a form of eqn (8), where f_ORX is the fraction of OM in dust.¹⁰⁸

Dust–air partitioning can also be defined by which has units of m³ mg⁻¹ and is often used in place of Q_Dust/A (Weschler and Nazaroff;¹⁰⁹ see Section 2.1). Whether the equilibrium partitioning of a chemical with dust is kinetically limited depends on both the K_OA and size and viscosity of the particle, whereby chemicals with higher log₁₀ K_OA values take longer to equilibrate as do larger particles.¹⁰⁸ Weschler and Nazaroff¹⁰⁹ found a correlation between measured and K_OA values—however they note that for some points in the regression the values are calculated using K_OA. For chemicals with high log₁₀K_OA values, the or Q_Dust/A value is less than what would be expected which is attributed to non-equilibrium conditions (Weschler and Nazaroff,¹⁰⁹ Zhang et al.;¹¹⁰ see Section 2.4).

Similarly, Shoeib et al.^111,112 found that the K_OA model for Q_Dust/A tended to under-predict the concentration in the dust phase, which could be attributed to differences in how some compounds (e.g., MeFOSE and EtFOSE) interact with octanol and organic matter or non-equilibrium conditions.¹¹² It is possible that the dust particles contain varying levels of contaminants, depending on whether they originate from the physical degradation of polymers containing the chemical as additive or whether the chemical is being taken up in the particles from the gas phase.¹¹² Indeed, this was observed in house dust samples, where the bromine concentration for BDE 209 contaminated samples varied highly.¹¹³

Using Weschler and Nazaroff's¹⁰⁹ equations for (i.e., eqn (3) and (8)) and assuming values for f_OM,Dust and ρ_Dust, Li et al.¹¹⁴ present an equation for in the form of eqn (6), where m equals 1 and log₁₀ a is −13.0.

Chemicals with log₁₀ K_OA values between 8 and 11, had measured values similar to predicted values.¹¹⁴ Chemicals with log₁₀ K_OA values less than 8 had predicted values that were higher than the measured value, likely because air concentration levels were underestimated.¹¹⁴ Predicted values lower than measured values for chemicals with log₁₀K_OA values greater than 11 were again attributed to disequilibrium conditions.¹¹⁴

Recently, Wei et al.¹¹⁵ combined eqn (4) and (6) parameterized for both K_PA and K_Dust as functions of K_OA, to estimate a dust–total air partition ratio K_Dust/TA:

log₁₀ Q_Dust/A = (m₁ − m₂)log₁₀ K_OA + log₁₀ a₁ − log₁₀ a₂ − log₁₀ TSP (21)

where m₁ and m₂ are slopes of log₁₀ Q_Dust/A and log₁₀ Q_PA against log₁₀ K_OA, respectively, and log₁₀ a₁ and log₁₀ a₂ are the intercepts of these regressions. If TSP × Q_PA is much less than 1, particle–air partitioning is negligible and the use of eqn (21) is redundant.¹¹⁵ Wei et al.¹¹⁵ observed good agreement between K_OA and Q_Dust/TA for phthalates, which were estimated to have TSP × Q_PA values less than one. Whereas PAHs which have a wider range in TSP × Q_PA values, showed a poorer correlation between K_OA and Q_Dust/TA.¹¹⁵

2.5.5 Surface–air partitioning. Surface–air partitioning describes the process of adsorption of a gas-phase chemical onto the surface or interface of another medium.⁹⁰ Similar to soil–air partitioning, it is influenced by relative humidity; water molecules are present in higher concentrations and have the capacity to form strong hydrogen bonds, and are thus more likely to sorb onto surfaces than organic compounds.⁹⁰ Thus, any relationship between surface–air partition ratios and K_OA is likely to be somewhat specific to the surface, the type of compounds and relative humidity.⁹²

However, the organic film present on many surfaces is often treated as a bulk-phase, and therefore an absorption model using K_OA has been applied to estimate film–air partition ratios Q_Film/A (e.g., Harner and Bidleman,⁹⁵ Weschler and Nazaroff¹⁰⁸). Implicit in these approaches is either the assumption that surface adsorption is negligible or that adsorption to the film surface and absorption in the bulk film can be collectively described with one partitioning constant. The latter can be problematic, as the time scales for equilibration are often widely different for surface and bulk phase uptake. Also, adsorption scales with surface area and absorption with mass. In some instances, the term film–air partitioning has been used to describe partitioning between thin polymer films and air (e.g., ethylene vinyl acetate¹¹⁶); these instances are described in Section 2.5.6.

Q _Film/A values for both indoor^117,118 and outdoor¹¹⁹ films were found to be correlated with, or similar to, K_OA values. Subsequently, studies have used organic films as passive environmental samplers relating K_OA and Q_Film/A using eqn (8), where m and log₁₀ a are both 1.^120,121 While the measured Q_Film/A correlated well with K_OA, Wu et al.¹²² observed very shallow regression slopes particularly for films obtained from rural environments.

Bi et al.¹²³ reported on the of mirrors, plates, and windows in units of m and, assuming that organic films are present on all impervious surfaces, converted these values to dimensionless Q_Film/A, by estimating a film thickness and percentage of organic material in the film. These Q_Film/A values were in good agreement with K_OA.

Li et al.¹¹⁴ presented a simplified relationship between K_OA and a window film–air partition ratio. As with , estimated values for chemicals with log₁₀ K_OA values between 8 and 11 agreed well with experimental values, chemicals with log₁₀ K_OA < 8 were over-predicted, and those with log₁₀ K_OA values > 11 were under-predicted.¹¹⁴

The time needed for a chemical to reach equilibrium with a surface film is dependent on both the K_OA, the thickness of the film (X; m), and the mass transfer coefficient from bulk air onto the film (MTC_S in units of m h⁻¹):¹⁰⁸

As discussed in Section 2.4, it can take several months for surface–air partitioning of chemicals with very high log₁₀ K_OA values to reach equilibrium. For chemicals with log₁₀ K_OA > 12, this can be upwards of 1 year.¹²⁴

While modelling film growth by SVOCs deposition, Weschler and Nazaroff¹²⁵ noted that the majority of chemicals in organic film have log₁₀ K_OA values between 10 and 13. Because chemicals with low K_OA values equilibrate quickly between organic films and air, films can become enriched in chemicals with higher log₁₀ K_OA over time.¹²⁵

The K_OA has also been used to estimate a time-dependent uptake coefficient (k_a) for gaseous compounds by liquid organic films:

where α is the surface accommodation coefficient, t is the time, c is the average thermal velocity, and D_l is the liquid diffusion coefficient.¹²⁶ While predicted uptake of PAHs into organic films was underestimated, there was some correlation between the K_OA and k_a.¹²⁶

2.5.6 Material–air partitioning. The partitioning of chemicals between various materials, such as polymers, physical surfaces, and clothing has often been correlated with K_OA. Many of these materials are used as passive-air sampling sorbents for various organic compounds. The issues associated with combining surface adsorption and bulk absorption in a single partitioning constant mentioned in the preceding section often apply also for uptake in materials.

Ockenden and colleagues¹²⁷ found that the K_OA was linearly correlated with the sampling rate of PCBs into triolein containing semi-permeable membrane devices (SPMD) used as passive air samplers (PASs), thus the K_OA could be used to estimate the amount of time required by non-polar substances to equilibrate with the PAS.

Multiple studies have shown correlations between K_OA and the partitioning between air and polymer material used in other PASs, including polyurethane foam,¹²⁸ low density polyethylene,¹²⁹ ethylene vinyl acetate,¹³⁰ and activated carbon and florisil.¹³¹ De Coensel¹³² noted that given the strong correlation between the K_OA and K_PDMS/A (polydimethyl siloxane–air partition ratio) for p-dichlorobenzene and naphthalene, K_PDMS/A could even be used to estimate K_OA. However such an approximation is likely to be limited to non-polar substances as the interactions of polar substances with PDMS and octanol is not the same.

The K_OA has also been correlated with partitioning between various textile materials such as cotton and air, generally showing fairly strong correlations.¹³³ Yu et al.¹³⁴ observed that the correlation between the cotton–air partition ratio Q_Cotton/A and K_OA is specific to different homologous compound groups. However, Saini et al.¹³⁵ found a low correlation between K_OA and measured Q_Cotton/A which was attributed to the irregularity and variance in the material itself, as polyester–air partition ratios K_Polyester/A were more strongly correlated with K_OA.

Won et al.¹³⁶ also observed linear relationships between K_OA and partition ratios between carpet, vinyl, and drywall material and air under different conditions. Partitioning between latex paint and air was also found to be correlated with K_OA.¹³⁷

Reppas-Chrysovitsinos et al.¹³⁸ compiled published material–air partition ratios (K_MA) and presented a general single parameter equation based on eqn (6), where m is equal to 1 and log₁₀ a equal to −1.22. They also present K_OA-based equations to estimate specific material–air partitioning ratios for polyethylene, polyurethane, PDMS, carbohydrates, polyoxymethylene (POM), and nylons.¹³⁸

Arguably, adsorption is the most relevant sorption process to describe partitioning to non-porous and non-organic material and octanol is unlikely to be a relevant surrogate for surfaces and materials whenever adsorption is the dominant uptake process.

2.5.7 Animal tissue–air partitioning. Poulin and Krishnan initially recommended against using octanol to describe tissue–air and blood–air partitioning because the solubility of hydrophobic organics is greater in octanol than in actual lipids¹³⁹ and instead used solubility in vegetable oil.^139,140 In 1996, they later presented equations for estimating K_Tissue/A and K_Blood/A using K_OA as it is easily predicted from the K_OW and K_AW.¹⁴¹ Their equations were similar to what Steyaert et al.⁵⁸ used for plant–air partitioning and eqn (7):

K_XA = K_OA(f_{neutral lipids} + 0.3f_phosolipids) + K_AW(f_water + 0.7f_{phospholipids}) (24)

where K_XA describes the partitioning between either blood or tissue and air and f_i is the fraction of neutral lipids, phospholipids, and water in either blood or tissue. This equation is different from the general equation presented in Section 2.2 because it assumes that chemical interactions between air and phospholipids more closely resemble those between air and water. Current approaches in bioaccumulation modelling group lipids into a single phase and add a non-lipid organic matter phase to describe proteins (e.g., Li et al.¹⁴²) or individually consider partitioning into each biological phase (e.g., Endo et al.¹⁴³).

Hau and Connell correlated odour thresholds¹⁴⁴ and nasal pungency thresholds¹⁴⁵ of chemicals with K_OW and K_AW but not with K_OA. This is likely because methods for measuring and estimating K_OW and K_AW were well-established and there were few measurements of K_OA at the time. Later, Hau et al.¹⁴⁶ showed biophase–air partitioning ratios to be related to K_OA and as a result the minimum alveolar concentration (MAC), which describes the potency of anaesthetics, is also related to K_OA. Slightly different correlations between K_OA and MAC were observed for alkanes and alcohols, however if the MAC of chemicals with very high K_OW values is corrected with the blood/brain partition ratio, then the regressions converge, and a single equation can describe the relationship between MAC and K_OA:¹⁴⁶

log₁₀ MAC_corr = −1.10 log₁₀ K_OA + 2.41 (25)

Nielsen et al.¹⁴⁷ found the K_OA to be a good proxy for sensory irritant receptor–air partitioning such that it can be used to estimate RD₅₀, the concentration at which a chemical causes a 50% decrease in respiratory frequency in an air-breathing organism:

log₁₀ RD₅₀ = 0.8361 log₁₀ K_OA − 6.0879 (26)

Raines et al.¹⁴⁸ similarly found a correlation between K_OA and the concentration of aromatic inhaled drugs needed to inhibit the N-methyl-D-aspartate receptor by 50%.

More recently, the K_OA has also been utilized in food science to estimate release behaviour of flavour compounds from an octanol–water emulsion.^149,150 Measured blood–air and milk–air partition ratios¹⁵¹ and feces–air partition ratios¹⁵² were also shown to correlate with the K_OA. K_OA has also been used as a surrogate for lipid–air partitioning to predict respiratory elimination rates¹⁵³ and human skin uptake¹⁰⁸ in environmental chemical fate models. Kelly and Gobas¹⁵⁴ noted that the estimated biomagnification factor of persistent neutral organic chemicals for wolves was correlated with K_OA.

Bioaccumulation assessments based solely on octanol–water partition ratios (K_OW) fail to take into account the role of respiratory elimination in air-breathing organisms.¹⁵³ In fact, chemicals with log₁₀ K_OW values less than 5, and thus not considered bioaccumulative by various regulatory agencies (e.g., the Government of Canada¹⁵⁵), can have the potential to biomagnify in air-breathing organisms. Modelling results from Gobas et al.¹⁵³ indicate that persistent chemicals with log₁₀ K_OA greater than 5 and log₁₀ K_OW greater than 2 have the potential to bioaccumulate in terrestrial food chains. This was further supported by modelling work by Czub and McLachlan⁵² who found that in humans chemicals with log₁₀ K_OA between 6 and 10 and log₁₀ K_OW value between 2 and 9 had high environmental bioaccumulation potentials and Kelly et al.¹⁵⁶ who noted that chemicals with log₁₀ K_OA values greater than 6 and log₁₀ K_OW values greater than 2 can biomagnify in air-breathing organisms. Of the chemicals listed on Canada's 2003 Domestic Substances List, 57% have an estimated log₁₀ K_OW value between 2 and 5 and an estimated K_OA, value greater 5—and thus are potentially bioaccumulative.¹⁵³ Providing evidence beyond modelling studies, Moses et al.¹⁵⁷ found lipid-normalized concentrations of dieldrin, heptachlor epoxide and β-hexachlorocyclohexane to be 5–14 times higher in seals than in fish. These chemicals have log₁₀ K_OW values around 5 or lower and log₁₀ K_OA values greater than 8.

More recent modelling studies on compounds released indoors have also shown that inhalation exposure is the primary exposure route of persistent volatile organic compounds with log₁₀ K_OA values less than 6,¹⁵⁸ while for chemicals with log₁₀ K_OA greater than 6, non-dietary ingestion (i.e., hand-to-mouth) is the primary exposure pathway, particularly in children.^158,159

3 How good a surrogate is n-octanol for various types of phases?

While many studies reviewed in Section 2 reported strong linear relationships between log₁₀ Q_XA (where X is an organic phase) and log₁₀ K_OA, it is not really possible to compare these relationships with each other, for example to assess whether the solvation properties of a particular phase more closely resemble those of octanol than those of another. This is because of divergent datasets used in those studies that include different types and numbers of chemicals and because of the unknown and variable uncertainty of the K_OA and Q_XA values used in these relationships. Also, as mentioned before, it is not always assured that the Q_XA data refer to equilibrium conditions.

However, we can test how good a surrogate K_OA is for other partitioning equilibria between an organic phase X and air by comparing K_XA values that have either been obtained with a K_OA-based spLFER prediction or by a poly-parameter linear free energy relationship (ppLFER) that has been calibrated directly for phase X. In some cases (i.e., plant cuticles, storage lipid, membrane lipid), we can directly compare the K_OA with a ppLFER-predicted K_XA. Furthermore, we sometimes have to rely on thermodynamic triangles to estimate a K_XA from ppLFER-predicted K_XW and K_AW values (natural organic matter NOM, storage lipids, membrane lipids, tissue, POM). To avoid the uncertainty in K_OA influencing the comparison, we can also predict the K_OA at the appropriate temperature with ppLFERs.^160,161 This approach is thus similar to the one used by Endo et al.,¹⁴³ when probing the extent to which n-octanol is a good surrogate for various biomaterials. Table 1 details the partition ratios that are being compared. We used 1316 organic chemicals with complete sets of experimental solute descriptors, as supplied by the UFZ-LSER database.¹⁶² We note that this set of chemicals is limited to generally small and primarily non-polar substances. More complex multifunctional chemicals or chemicals with unusual substitutions, such as the polyflourinated alkyl substances, are not well-represented.

Table 1 List of ppLFERs and K_OA-based predictions compared in Fig. 1. The K_OA and K_AW are always predicted with ppLFERs by Baskaran et al.¹⁶⁰ and Abraham et al.¹⁶⁶ NOM: natural organic matter; OC: organic carbon; POM: polyoxymethylene; PDMS: polydimethyl siloxane; PUF: polyurethane foam

Phase X	ppLFER predicted KXA	log10 KOA spLFER based prediction
NOM	Average log10 KNOM/A for 10 different organic matter systems including humic acids, fulvic acids, and natural organic matter, predicted with ppLFER by Niederer et al.^167	log10 KOC/A predicted with spLFER by Borisover and Graber^81 using KOA at 15 °C
OC	log10 KOC/A calculated as log10 KWA + log10 KOC, where KOC is predicted with ppLFER by Nguyen et al.^168	log10 KOC/A predicted with spLFER by Borisover and Graber^81 using KOA at 25 °C
Plant cuticles	log10 KPlant/A predicted with ppLFER by Platts and Abraham^163	log10 KOA at 25 °C
Storage lipid	log10 KStorage-lipid/A calculated as log10 KWA + log10 KStorage-lipid/W where KStorage-lipid/W is predicted with ppLFER by Geisler et al.^164	log10 KOA at 37 °C
Membrane lipid	log10 KMembrane-lipid/A calculated as log10 KWA + log10 KMembrane-lipid/W where KMembrane-lipid/W is predicted with ppLFER by Endo et al.^165	log10 KOA at 37 °C
Tissue	log10 KTissue/A calculated as log10 KTissue/W + log10 KWA where KTissue/W is predicted with a composition model by Endo et al.^143 using ppLFERs for KStorage-lipid/W by Geisler et al.,^164KMembrane-lipid/W by Endo et al.,^165KAlbumin/W by Endo and Goss,^169KProtein/W by Endo et al.^170	log10 KTissue/A predicted using a fractional composition model with KOA to 37 °C; KTissue/A = (fStorage-lipid + fMembrane-lipid)KOA + fWKWA
Aerosols	Average of log10 KPA for aerosol sampled in Dübendorf fall & winter, Aspvretn, and Roost, predicted using ppLFERs by Arp et al.^171	log10 KPA predicted with spLFER by Harner and Bidleman^95 using KOA at 15 °C
POM	log10 KPOM/A calculated as log10 KPOM/W + log10 KWA where KPOM/W is predicted with ppLFER by Endo et al.^172	log10 KPOM/A predicted with spLFER by Reppas-Chrysovitsinos et al.^138 using KOA at 25 °C
PDMS	log10 KPDMS/A predicted with ppLFER by Sprunger et al.^173	log10 KPDMS/A predicted with spLFER by Reppas-Chrysovitsinos et al.^138 using KOA at 25 °C

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In general, there are very strong correlations (R² > 0.89) between the K_OA based spLFER and ppLFER estimated values of log₁₀ K_XA (Fig. 1). Such good correlations can at least in part be attributed to a statistical issue discussed by Paterson and Mackay,⁵¹ who assert that apparently significant correlations can be obtained by inadvertently correlating a quantity with itself. In the current case, log₁₀ K_XA and log₁₀ K_OA are almost inevitably correlated, because of the presence of the “solubility in air” in their denominator (eqn (10) and (11)). The vapour pressure, or “solubility in air”, of substances ranges over many orders of magnitude, whereas the solubilities of substances in organic phases vary little and thus contribute little to the variation in partition ratios between chemicals. For similar reasons the K_OA is very highly correlated with the liquid saturation vapour pressure.⁵⁰ In order to eliminate this auto-correlation, we also plot the difference between ppLFER and spLFER estimates of K_XA against the log₁₀ K_OA used to generate the spLFER estimate (Fig. 2).

Fig. 1 Correlation between log₁₀ K_XA predicted using system specific ppLFERs plotted against log₁₀ K_XA predicted using spLFERs using log₁₀ K_OA. The red solid lines show the line of best fit, blue dashed lines indicate a 1 : 1 relationship, and blue dotted lines have slopes of 1 and intercepts of ±1 log₁₀ unit. NOM: natural organic matter; OC: organic carbon; POM: polyoxymethylene; PDMS: polydimethyl siloxane; PUF: polyurethane foam.

Fig. 2 The difference between ppLFER and spLFER estimates for log₁₀ K_XA plotted against the log₁₀ K_OA used to derive the spLFER estimate.

Thus, if the K_OA is a good surrogate for a partitioning equilibrium, we expect to see a regression with a slope m of near unity in Fig. 1 (ref. 47) and a horizontal regression line in Fig. 2. By normalizing ppLFER estimated values of K_XA by spLFER estimates of K_XA we can better visualize the variation in K_XA with K_OA that is not easily observed in Fig. 1. For example, a negative slope in Fig. 2 indicates that as the K_OA of a chemical increases, the K_OA based estimate (i.e., the spLFER estimate) is greater than the ppLFER estimate. This suggests that when the slope is negative (<0), the activity ratio (γ_O/γ_X) is greater than 1 whereas a positive slope suggests that the activity ratio is less than 1. In Table 2 we present the slopes and intercepts of the regressions and coefficients of determination (R²) of both plots and the root mean squared error (RMSE) between the spLFER and ppLFER-based estimates.

Table 2 Statistics on the regressions presented in Fig. 1 and 2. The slopes and intercepts reported here are not the same as the spLFERs used to calculate the respective K_XA values

Phase X	Fig. 1			Fig. 2			RMSE
	Slope	Intercept	R ^2	Slope	Intercept	R ^2
NOM	0.78	−0.04	0.98	−0.24	0.14	0.79	0.42
OC	0.83	−0.22	0.89	−0.18	−0.08	0.25	1.02
Plant cuticle	1.07	−0.19	0.99	0.07	−0.19	0.28	0.39
Storage lipids	0.96	−0.31	0.97	−0.04	−0.31	0.06	0.50
Membrane lipids	0.99	−0.41	0.97	−0.01	−0.41	0.00	0.53
Tissue	1.12	0.97	0.99	0.12	0.52	0.95	0.26
POM	0.93	−0.47	0.92	−0.07	−0.42	0.07	0.87
PDMS	0.84	0.58	0.97	−0.16	0.72	0.57	0.45
Aerosols	0.93	−0.50	0.99	−0.07	0.37	0.31	0.33

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Slopes near 1 in Fig. 1 and near 0 in Fig. 2 and RMSE values of 0.50 and 0.53 respectively, indicate that the K_OA value is a good surrogate for the partitioning between storage and membrane lipids and the gas phase and a very good predictor for partitioning into tissue. The results for PDMS are similar to those of storage and membrane lipids. The K_OA also appears to be a reasonable surrogate for the partitioning between aerosols⁹⁵ and plant cuticles¹⁶³ and the gas phase, with RMSE values of 0.33 and 0.39 respectively. In the case of partitioning to soil organic matter from the gas phase, the spLFERs based on the K_OA have the highest RMSE and tend to give predictions that are biased low for compounds with high K_OA values, indicated by the slopes in the plots in Fig. 2 being negative and the large scatter below the regression line. To a smaller extent that is also the case for the K_OA-based spLFERs for POM and PDMS¹³⁸ and the storage¹⁶⁴ and membrane lipids.¹⁶⁵ The opposite is the case for the K_OA and K_AW-based fractional composition model for K_Tissue/A where a positive slope in Fig. 2 suggest that relying on K_OA to estimate partitioning into tissues leads to an overestimation for low volatility compounds.

4 Is the K_OA obsolete?

4.1 Alternative means for predicting environmental phase equilibria involving the gas phase

A major motivation for introducing the K_OA as an equilibrium partitioning property was to use it in the prediction of other equilibria between environmental phases and the gas phase. Accordingly, the literature is replete with linear free energy relationships that regress an environmentally relevant partitioning ratio involving the gas phase against K_OA (see also Section 2). Those predictive equations suffer from the same shortcomings as other single-parameter linear free energy relationships, namely they have no universal applicability, but require different regression coefficients for different compound groups capable of undergoing a variety of intermolecular interactions.⁹² The longevity and popularity of those equations can be explained in part by their robustness for largely non-polar substances and the prevalence of such substances among the contaminants of historical concern.

Major progress in predicting environmental phase equilibria has been made in the decades since the K_OA has first been introduced. In particular, poly-parameter linear free energy relationships (ppLFERs) have become a viable method for predicting partition ratios involving environmental phases, mostly, because (i) calibrations have been performed to determine system constants (the regression constants of the ppLFER equations) for most environmentally relevant phase equilibria or can be estimated,^162,174 (ii) solute descriptors for numerous contaminants have been experimentally determined.¹⁷⁵ When carefully calibrated system constants and experimental solute descriptors are combined, ppLFERs can achieve prediction accuracy on the order of 0.3 log₁₀ units.¹⁷⁶ Even for substances, for which no experimental solute descriptors exist, those descriptors can now be predicted with the help of QSPRs^162,177 and still result in a prediction accuracy for environmental phase equilibria better than one order of magnitude.¹⁷⁶K_OA-based spLFERs would be hard pressed to match such accuracy, even if they were only applied to substances appropriate for a particular regression, i.e., similar to the substances used in the calibration of that spLFER. In other words, there is no longer the need for a parameter such as K_OA to predict contaminant partitioning from the gas phase into organism lipids,¹⁶⁴ soil organic matter,¹⁶⁷ atmospheric particles,¹⁷¹ or sampling sorbents.¹⁷⁸

The merit of ppLFER extends beyond the provision of estimates that tend to be more precise than estimates from K_OA-based spLFERs. By describing the different intermolecular interactions involved in partitioning, ppLFERs also provide a mechanistic understanding of organic chemical solvation in various phases.¹⁷⁹

The question therefore arises whether there is still a need for the K_OA. The answer is two-fold. First there are still some partitioning equilibria between air and organic phases, which need to be predicted with the help of K_OA-based spLFERs. Second, the utility of the K_OA is not limited to the prediction of specific environmentally relevant phase equilibria.

4.2 Continued need for K_OA-based predictions of environmental phase equilibria

Currently, there are no robust ppLFERs that would be able to predict partitioning into plants. The ppLFER for plant cuticles by Platts and Abraham¹⁶³ suffers from (i) a limited suitability of isolated tomato cuticles to represent plant foliage more generally and (ii) a calibration that had not a sufficiently diverse set of substances to be widely applicable with confidence. Therefore, K_OA-based prediction methods are still required for the very plant–air phase equilibria, for which the K_OA was first introduced.³⁹ Important examples include the empirical K_OA-based equations for predicting partitioning in forest canopies (eqn (9) and (10) in Horstmann and McLachlan,⁷⁶eqn (11) in Su et al.⁷⁷).

While many environmentally relevant phase equilibria can now be predicted directly, the availability of tools to predict partition ratios at a variety of temperatures is much more limited. For example, while ppLFERs for predicting gas particle partitioning at 15 °C exist,¹⁷¹ atmospheric temperatures range over more than 60 K. The K_OA for many contaminants has been determined as a function of temperature or can be predicted using a ppLFER for the internal energy of phase transfer from octanol to gas phase .^161,180 It is thus possible to estimate an environmentally relevant equilibrium partition ratio at any temperature by either (i) applying K_OA-based spLFERs by inserting (empirical or predicted) K_OA values at the relevant temperatures or by (ii) adjusting the environmentally relevant partition ratio to the desired temperature using van't Hoff's equation and the (empirical or predicted) . Implicit in either approach is that the temperature dependence of the partitioning between the environmentally relevant phase and the gas phase is well described by the temperature dependence of octanol–air partitioning. Admittedly, one can obviously also adjust an equilibrium partitioning ratio derived from a ppLFER using such a . Note, since the K_OA and many other environmentally relevant phase equilibrium ratios are commonly defined using molar volumetric concentration in the gas phase (rather than a partial pressure), the needs to be used in the van't Hoff equation. can be obtained from the enthalpy of phase transfer by deducting the product of the ideal gas constant and absolute temperature.

There is need to further explore the extent of agreement between the internal energy of phase transfer between various environmentally relevant phases X and the gas phase and . This is currently limited by the availability of measurements for K_XA at different temperatures, but there are indications that can deviate from .⁶⁶

4.3 The need for a single parameter describing partitioning from the gas phase into a wide variety of environmentally relevant organic phases

However, even if well-calibrated ppLFER equations existed for all relevant partitioning equilibria between air and organic phases at all desired temperatures, it would still be useful to have a single parameter that can serve to describe the tendency of a neutral organic chemical to partition from the gas phase into a wide variety of organic phases of environmental relevance. For such a parameter to be most useful, it needs to be (i) well-defined, (ii) directly accessible to measurement, and (iii) a reasonable surrogate for a wide variety of organic phases. The K_OA is better suited to this role than other parameters:

• An equilibrium partition ratio involving a real environmental organic phase is not a good choice because environmental phases are of variable composition and therefore not sufficiently well-defined.

• While the saturation vapour pressure is the traditional parameter for expressing compound volatility, the solid state vapour pressure is not an appropriate parameter to describe the volatility of a substance from any organic phase other than its own pure solid phase, because of the strong influence of the lattice energy.

• Although this can be in principle corrected by using the saturation vapour pressure of the sub-cooled liquid, it has the drawback that this parameter cannot be determined directly by experiment. It also implies that the organic reference phase is a different one for every substance.

• While other organic solvents or polymers may be equally good (and possibly even better) surrogates of environmental organic phases relative to octanol, the knowledge of how good a surrogate octanol is, is much better than for any other organic solvent (see Section 3).

As such, the K_OA can still play an important role as a measure of volatility from organic phases. It is an easy to comprehend, single chemical characteristic that can be used to judge a chemical's propensity to undergo a very wide range of environmental processes. Just by knowing a compound's K_OA, it is possible to infer a tremendous amount of information on its environmental behaviour. This is illustrated in Fig. 3. For example, instead of requiring separate parameters to assess a chemical's equilibrium phase distribution in atmosphere and soils, its susceptibility to evaporate or be exhaled, and the importance of processes controlling its deposition to plants, this can all be deduced from the compound's K_OA. At the same time, it can inform you about the suitability of a sampling sorbent for the compound and which human exposure pathways are likely to be relevant.

Fig. 3 Relationship between K_OA range and the environmental fate of common contaminants. Vertical lines are indicative of the log₁₀ K_OA, blue and brown bars indicate the relative dominant phase a chemical will be present in,^{52,53,181–183} red bars indicate the bioaccumulation potential of chemicals within a K_OA range,^{52,158,181,184–186} and green bars indicate the K_OA range of various compound groups. PCBs: polychorinated biphenyls; PAHs: polycyclic aromatic hydrocarbons; PBDEs: polybrominated diphenyl ethers; OCPs: organochlorine pesticides; cVMS: cyclic volatile methylsiloxanes; nPFAS: per- and poly-fluoroalkyl substances.

Another example for the utility of such a parameter is that it can serve as a volatility threshold for classification, prioritization and possibly even regulation of chemicals (Section 2.5.7). For example, K_OA is being used as a threshold for the potential to bioaccumulate in air-breathing species.¹⁸⁷

Another advantage of K_OA is the possibility to use it in analyses that require the display of model results as a function of the chemical partitioning space. By taking advantage of octan-1-ol being able to represent a wide variety of organic phases reasonably well, the K_OA facilitates the display of model-derived contaminant behaviour in a chemical partitioning space defined by coordinates of hydrophobicity and volatility. For example, when Czub et al.¹⁸⁸ plotted the model calculated combined Arctic Contamination and BioAccumulation Potential (AC-BAP) of organic chemicals as a function of K_OA and K_AW, octan-1-ol simultaneously serves to approximate the solvation properties of soil and sedimentary organic matter, forest canopies, organic aerosol particles and lipids in a variety of organisms (plants, food animals, humans). Similarly, in Li et al.'s¹⁵⁸ analysis of human exposure pathway, the K_OA is used simultaneously to estimate partition equilibria between a very large variety of phases and the gas phase. This includes soil and sediment organic matter, atmospheric particles, house dust, various indoor surfaces, plant and animal lipids and human skin. While it would be possible to perform the type of model calculations performed by Czub et al.¹⁸⁸ and Li et al.¹⁵⁸ using partitioning ratios that are not estimated from K_OA, it would be much more difficult to perform the systematic investigation of how the model results depend on the partitioning characteristics of an organic chemical without relying on partitioning ratios involving octan-1-ol. It would clearly be impossible to display them in a two-dimensional partitioning space.

5 Conclusion

This review examines the role of the K_OA in environmental chemistry. We examined the historical context of partition ratios and the various ways the K_OA is used to predict and describe gas partitioning properties in the real environment. The K_OA is shown to be a reasonable surrogate for multiple environmental phases and has applications in environmental, atmospheric, physical chemical, medical, and food sciences. It is more advantageous to use the K_OA to describe these partitioning processes instead of vapour pressure, because it is well defined, has broader applicability, and can be reliably estimated and measured.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was funded by the European Chemical Industry Council (CEFIC) through project ECO 41 of the Long-range Research Initiative (LRI).

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Footnote

† Current affiliation and address: Department of Environmental Engineering, Norwegian Geotechnical Institute, Sandakerveien 140, 0484, Oslo, Norway.

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