Partition coefficient

In the

Despite formal recommendation to the contrary, the term partition coefficient remains the predominantly used term in the scientific literature.[8]^{[additional citation(s) needed]}

In contrast, the

The partition coefficient, abbreviated P, is defined as a particular ratio of the

To a first approximation, the non-polar phase in such experiments is usually dominated by the un-ionized form of the solute, which is electrically neutral, though this may not be true for the aqueous phase. To measure the partition coefficient of ionizable solutes, the pH of the aqueous phase is adjusted such that the predominant form of the compound in solution is the un-ionized, or its measurement at another pH of interest requires consideration of all species, un-ionized and ionized (see following).

A corresponding partition coefficient for ionizable compounds, abbreviated log P ^I, is derived for cases where there are dominant ionized forms of the molecule, such that one must consider partition of all forms, ionized and un-ionized, between the two phases (as well as the interaction of the two equilibria, partition and ionization).^{[11]: 57ff, 69f [12]} M is used to indicate the number of ionized forms; for the I-th form (I = 1, 2, ... , M) the logarithm of the corresponding partition coefficient, ${\displaystyle \log P_{\text{oct/wat}}^{I}}$, is defined in the same manner as for the un-ionized form. For instance, for an octanol–water partition, it is

${\displaystyle \log \ P_{\text{oct/wat}}^{\mathrm {I} }=\log _{10}\left({\frac {{\big [}{\text{solute}}{\big ]}_{\text{octanol}}^{I}}{{\big [}{\text{solute}}{\big ]}_{\text{water}}^{I}}}\right).}$

To distinguish between this and the standard, un-ionized, partition coefficient, the un-ionized is often assigned the symbol log P⁰, such that the indexed ${\displaystyle \log P_{\text{oct/wat}}^{I}}$ expression for ionized solutes becomes simply an extension of this, into the range of values I > 0.^{[citation needed]}

Distribution coefficient and log D

The distribution coefficient, log D, is the ratio of the sum of the concentrations of all forms of the compound (ionized plus un-ionized) in each of the two phases, one essentially always aqueous; as such, it depends on the pH of the aqueous phase, and log D = log P for non-ionizable compounds at any pH.^[13][14] For measurements of distribution coefficients, the pH of the aqueous phase is buffered to a specific value such that the pH is not significantly perturbed by the introduction of the compound. The value of each log D is then determined as the logarithm of a ratio—of the sum of the experimentally measured concentrations of the solute's various forms in one solvent, to the sum of such concentrations of its forms in the other solvent; it can be expressed as^{[10]: 275–8}

${\displaystyle \log D_{\text{oct/wat}}=\log _{10}\left({\frac {{\big [}{\text{solute}}{\big ]}_{\text{octanol}}^{\text{ionized}}+{\big [}{\text{solute}}{\big ]}_{\text{octanol}}^{\text{un-ionized}}}{{\big [}{\text{solute}}{\big ]}_{\text{water}}^{\text{ionized}}+{\big [}{\text{solute}}{\big ]}_{\text{water}}^{\text{un-ionized}}}}\right).}$

In the above formula, the superscripts "ionized" each indicate the sum of concentrations of all ionized species in their respective phases. In addition, since log D is pH-dependent, the pH at which the log D was measured must be specified. In areas such as drug discovery—areas involving partition phenomena in biological systems such as the human body—the log D at the physiologic pH = 7.4 is of particular interest.^{[citation needed]}

It is often convenient to express the log D in terms of P^I, defined above (which includes P⁰ as state I = 0), thus covering both un-ionized and ionized species.^[12] For example, in octanol–water:

${\displaystyle \log D_{\text{oct/wat}}=\log _{10}\left(\sum _{I=0}^{M}f^{I}P_{\text{oct/wat}}^{I}\right),}$

which sums the individual partition coefficients (not their logarithms), and where ${\displaystyle f^{I}}$ indicates the pH-dependent mole fraction of the I-th form (of the solute) in the aqueous phase, and other variables are defined as previously.^{[12][verification needed]}

Example partition coefficient data

The values for the octanol-water system in the following table are from the

Values for other compounds may be found in a variety of available reviews and monographs.[2]^{: 551ff [21][page needed][22]: 1121ff [23][page needed][24]} Critical discussions of the challenges of measurement of log P and related computation of its estimated values (see below) appear in several reviews.^[11][24]

Applications

Pharmacology

A drug's distribution coefficient strongly affects how easily the drug can reach its intended target in the body, how strong an effect it will have once it reaches its target, and how long it will remain in the body in an active form.^[25] Hence, the log P of a molecule is one criterion used in decision-making by medicinal chemists in pre-clinical drug discovery, for example, in the assessment of druglikeness of drug candidates.^[26] Likewise, it is used to calculate lipophilic efficiency in evaluating the quality of research compounds, where the efficiency for a compound is defined as its potency, via measured values of pIC₅₀ or pEC₅₀, minus its value of log P.^[27]

Pharmacokinetics

In the context of

Hydrophobic insecticides and herbicides tend to be more active. Hydrophobic agrochemicals in general have longer half-lives and therefore display increased risk of adverse environmental impact.[36]

Metallurgy

In metallurgy, the partition coefficient is an important factor in determining how different impurities are distributed between molten and solidified metal. It is a critical parameter for purification using zone melting, and determines how effectively an impurity can be removed using directional solidification, described by the Scheil equation.^[6]

Consumer product development

Many other industries take into account distribution coefficients, for example in the formulation of make-up, topical ointments, dyes, hair colors and many other consumer products.^[37]

Measurement

A number of methods of measuring distribution coefficients have been developed, including the shake-flask, separating funnel method, reverse-phase HPLC, and pH-metric techniques.^[10]: 280

Separating-funnel method

In this method the solid particles present into the two immiscible liquids can be easily separated by suspending those solid particles directly into these immiscible or somewhat miscible liquids.

Shake flask-type

The classical and most reliable method of log P determination is the shake-flask method, which consists of dissolving some of the solute in question in a volume of octanol and water, then measuring the concentration of the solute in each solvent.

An advantage of this method is that it is fast (5–20 minutes per sample). However, since the value of log P is determined by linear regression, several compounds with similar structures must have known log P values, and extrapolation from one chemical class to another—applying a regression equation derived from one chemical class to a second one—may not be reliable, since each chemical classes will have its characteristic regression parameters.^{[citation needed]}

pH-metric

The pH-metric set of techniques determine lipophilicity pH profiles directly from a single acid-base titration in a two-phase water–organic-solvent system.^{[10]: 280–4} Hence, a single experiment can be used to measure the logarithms of the partition coefficient (log P) giving the distribution of molecules that are primarily neutral in charge, as well as the distribution coefficient (log D) of all forms of the molecule over a pH range, e.g., between 2 and 12. The method does, however, require the separate determination of the pK_a value(s) of the substance.

Electrochemical

Polarized liquid interfaces have been used to examine the thermodynamics and kinetics of the transfer of charged species from one phase to another. Two main methods exist. The first is ITIES, "interfaces between two immiscible electrolyte solutions".^[41] The second is droplet experiments.^[42] Here a reaction at a triple interface between a conductive solid, droplets of a redox active liquid phase and an electrolyte solution have been used to determine the energy required to transfer a charged species across the interface.^[43]

Single-cell approach

There are attempts to provide partition coefficients for drugs at a single-cell level.^[44][45] This strategy requires methods for the determination of concentrations in individual cells, i.e., with Fluorescence correlation spectroscopy or quantitative Image analysis. Partition coefficient at a single-cell level provides information on cellular uptake mechanism.^[45]

Prediction

There are many situations where prediction of partition coefficients prior to experimental measurement is useful. For example, tens of thousands of industrially manufactured chemicals are in common use, but only a small fraction have undergone rigorous

For cases where the molecule is un-ionized:[13]^[14]

${\displaystyle \log D\cong \log P.}$

For other cases, estimation of log D at a given pH, from log P and the known mole fraction of the un-ionized form, ${\displaystyle f^{0}}$, in the case where partition of ionized forms into non-polar phase can be neglected, can be formulated as^[13][14]

${\displaystyle \log D\cong \log P+\log \left(f^{0}\right).}$

The following approximate expressions are valid only for monoprotic acids and bases:^[13][14]

${\displaystyle {\begin{aligned}\log D_{\text{acids}}&\cong \log P+\log \left[{\frac {1}{1+10^{\mathrm {p} H-\mathrm {p} K_{a}}}}\right],\\\log D_{\text{bases}}&\cong \log P+\log \left[{\frac {1}{1+10^{\mathrm {p} K_{a}-\mathrm {pH} }}}\right].\end{aligned}}}$

Further approximations for when the compound is largely ionized:^[13][14]

• for acids with ${\displaystyle \mathrm {pH} -\mathrm {p} K_{a}>1}$, ${\displaystyle \log D_{\text{acids}}\cong \log P+\mathrm {p} K_{a}-\mathrm {pH} }$,
• for bases with ${\displaystyle \mathrm {p} K_{a}-\mathrm {pH} >1}$, ${\displaystyle \log D_{\text{bases}}\cong \log P-\mathrm {p} K_{a}+\mathrm {pH} }$.

For prediction of pK_a, which in turn can be used to estimate log D, Hammett type equations have frequently been applied.^[57][58]

Log P from log S

If the solubility, S, of an organic compound is known or predicted in both water and 1-octanol, then log P can be estimated as^[46][59]

${\displaystyle \log P=\log S_{\text{o}}-\log S_{\text{w}}.}$

There are a variety of approaches to predict solubilities, and so log S.^[60][61]

Octanol-water partition coefficient

The partition coefficient between n-Octanol and water is known as the n-octanol-water partition coefficient, or K_ow.^[62] It is also frequently referred to by the symbol P, especially in the English literature. It is also known as n-octanol-water partition ratio.^[63][64][65]

K_ow, being a type of partition coefficient, serves as a measure of the relationship between lipophilicity (fat solubility) and hydrophilicity (water solubility) of a substance. The value is greater than one if a substance is more soluble in fat-like solvents such as n-octanol, and less than one if it is more soluble in water.^{[citation needed]}

Example values

Values for log K_ow typically range between -3 (very hydrophilic) and +10 (extremely lipophilic/hydrophobic).^[66]

The values listed here^[67] are sorted by the partition coefficient. Acetamide is hydrophilic, and 2,2′,4,4′,5-Pentachlorobiphenyl is lipophilic.

See also

References