Partition coefficient

A partition coefficient or distribution coefficient is a measure of differential solubility of a compound in two solvents. For non-ionizable solutes, the logarithm of the ratio of the concentrations of the solute in the solvents is called log P (sometimes LogP). For ionizable solutes, it is more complicated since the solute may exist in multiple forms (both ionized and non-ionized) in each phase. The ratio of the sum of concentrations of the solute's various forms in one solvent, to the sum of the concentrations of its forms in the other solvent is called the "distribution coefficient" (D), and is generally given as the logarithm, LogD. The best known solvent system for partition coefficients is the one based on octanol and water. The octanol-water partition coefficient ^[1] is a measure of the hydrophobicity and hydrophilicity of a substance. In the context of drug-like substances, hydrophobicity is related to absorption, bioavailability, hydrophobic drug-receptor interactions, metabolism and toxicity. In the field of hydrogeology, the octanol water partition coefficient, or K_ow, is used to predict and model the migration of dissolved hydrophobic organic compounds in soil and groundwater.

Application

Shake flask (or tube) method

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. The most common method of measuring the distribution of the solute is by UV/VIS spectroscopy. There are a number of pros and cons to this method:

Pros:

Most accurate method
Accurate for broadest range of solutes (neutral and charged compounds applicable)
Chemical structure does not have to be known beforehand.

Cons:

Time consuming (>30 minutes per sample)
Octanol and water must be premixed and equilibrated (takes at least 24 hours to equilibrate)
Complete solubility must be attained, and it can be difficult to detect small amounts of undissolved material.
The concentration vs. UV-Vis response must be linear over the solute's concentration range. (See Beer-Lambert law)
If the compound is extremely lipophilic or hydrophilic, the concentration in one of the phases will be exceedingly small, and thus difficult to quantify.
Relative to chromatographic methods, large amounts of material are required.

As an alternative to UV/VIS spectroscopy other methods can be used to measure the distribution, one of the best is to use a carrier free radiotracer. In this method (which is well suited for the study of the extraction of metals) a known amount of a radioactive material is added to one of the phases. The two phases are then brought into contact and mixed until equilibrium has been reached. Then the two phases are separated before the radioactivity in each phase is measured. If an energy dispersive detector can be used (such as a high purity germanium detector) then it is possible to use several different radioactive metals at once, with the more simple gamma ray detectors it is only possible to use one radioactive element in the sample.

If the volume of both of the phases are the same then the math is very simple.

For a hypothetical solute (S)

D or P = radioactivity of the organic phase / radioactivity of the aqueous phase

D or P = [S_organic]/[S_aqueous]

In such an experiment using a carrier free radioisotope the solvent loading is very small, hence the results are different from those which are obtained when the concentration of the solute is very high. A disadvantage of the carrier free radioisotope experiment is that the solute can absorb on the surfaces of the glass (or plastic) equipment or at the interface between the two phases. To guard against this the mass balance should be calculated.

It should be the case that

radioactivity of the organic phase + radioactivity of the aqueous phase = initial radioactivity of the phase bearing the radiotracer

For nonradioactive metals, it is possible in some cases to use ICP-MS or ICP-AES. Sadly ICP methods often suffer from many interferences which do not apply to gamma spectrscopy so hence the use of radiotracers (counted by gamma ray spectroscopy) is often more straightforward.

HPLC determination

A faster method of log P determination makes use of high-performance liquid chromatography. The log P of a solute can be determined by correlating its retention time with similar compounds with known log P values.

Pros:

Fast method of determination (5-20 minutes per sample)

Cons:

The solute's chemical structure must be known beforehand.
Since the value of log P is determined by linear regression, several compounds with similar structures must have known log P values.
Different chemical classes will have different correlation coefficients, between-class comparisons are not significant.

Electrochemical methods

In the recent past some experiments using polarised 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.

ITIES, Interfaces between two immiscible electrolyte solutions which for example has been used at Ecole Polytechnique Fédérale de Lausanne. [1]
Droplet experiments which have been used by Alan Bond, Frank Marken[2] and also by the team at the Ecole Polytechnique Fédérale de Lausanne. 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.

Prediction

QSAR algorithms calculate a log P in several different ways:

Fragment based prediction (group contribution)

It has been shown that the log P of a compound can be determined by the sum of its fragments. Fragmentary log P values have been determined statistically. This method gives mixed results and is generally not trusted to have accuracy of more than ±0.1 units.

Data mining prediction

A typical data mining based prediction uses e.g. support vector machines, decision trees, neural networks are usually very successful for calculating log P values when trained with compounds that have similar chemical structures and known log P values.

Molecule mining prediction

Molecule mining approaches apply a similarity matrix based prediction or an automatic fragmentation scheme into molecular substructures. Furthermore there exist also approaches using maximum common subgraph searches or molecule kernels.

Example data

The given values^[2] are sorted by the partition coefficient. Acetamide is hydrophilic and 2,2',4,4',5-Pentachlorobiphenyl is lipophilic.

Component	log P_OW	T	Literature
Acetamide	-1,155	25 °C	^[3]
Methanol	-0,824	19 °C	^[4]
Formic acid	-0,413	25 °C	^[5]
Diethyl ether	0,833	20 °C	^[4]
p-Dichlorobenzene	3,370	25 °C	^[6]
Hexamethylbenzene	4,610	25 °C	^[6]
2,2',4,4',5-Pentachlorobiphenyl	6,410	Ambient	^[7]

Limitations

LogP is not an accurate determinant of solubility for ionizable compounds because it only correctly describes the partition coefficient of neutral (uncharged) molecules. Taking the example of drug discovery we see how the limitations of logP can effect research. Since the majority of drugs (approximately 80%) are ionizable, logP is not an appropriate predictor of a compound's behaviour in the changing pH environments of the body. The distribution coefficient (LogD) is the correct descriptor for ionizable systems.

References

^ J. Sangster, Octanol-Water Partition Coefficients: Fundamentals and Physical Chemistry, Vol. 2 of Wiley Series in Solution Chemistry, John Wiley & Sons, Chichester, 1997.
^ Dortmund Data Bank
^ Wolfenden R., Biochem.J., 17(1), S.201-204, 1978
^ ^a ^b Collander R., Acta Chem.Scand., 5, S.774-780, 1951
^ Whitehead K.E., Geankoplis Ch.J., Ind.Eng.Chem., 47(10), S.2114-2122, 1955
^ ^a ^b Wasik S.P., Tewari Y.B., Miller M.M., Martire D.E., NBS Techn.Rep., Rep.No. NBSIR 81-2406, S.1-56, 1981 Cite error: The named reference "Wasik" was defined multiple times with different content (see the help page).
^ Brodsky J., Ballschmiter K., Fresenius Z.Anal.Chem., 331, S.295-301, 1988

[Sangster-1] J. Sangster, Octanol-Water Partition Coefficients: Fundamentals and Physical Chemistry, Vol. 2 of Wiley Series in Solution Chemistry, John Wiley & Sons, Chichester, 1997.

[2] Dortmund Data Bank

[3] Wolfenden R., Biochem.J., 17(1), S.201-204, 1978

[Collander-4] Collander R., Acta Chem.Scand., 5, S.774-780, 1951

[5] Whitehead K.E., Geankoplis Ch.J., Ind.Eng.Chem., 47(10), S.2114-2122, 1955

[Wasik-6] Wasik S.P., Tewari Y.B., Miller M.M., Martire D.E., NBS Techn.Rep., Rep.No. NBSIR 81-2406, S.1-56, 1981 Cite error: The named reference "Wasik" was defined multiple times with different content (see the help page).

[7] Brodsky J., Ballschmiter K., Fresenius Z.Anal.Chem., 331, S.295-301, 1988

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v t e Chemical solutions
Solution	Ideal solution Aqueous solution Solid solution Buffer solution Flory–Huggins Mixture Suspension Colloid Phase diagram Phase separation Eutectic point Alloy Saturation Supersaturation Serial dilution Dilution (equation) Apparent molar property Miscibility gap
Concentration and related quantities	Molar concentration Mass concentration Number concentration Volume concentration Normality Molality Mole fraction Mass fraction Isotopic abundance Mixing ratio Ternary plot
Solubility	Solubility equilibrium Total dissolved solids Solvation Solvation shell Enthalpy of solution Lattice energy Raoult's law Henry's law Solubility table (data) Solubility chart Miscibility
Solvent	(Category) Acid dissociation constant Protic solvent Polar aprotic solvent Inorganic nonaqueous solvent Solvation List of boiling and freezing information of solvents Partition coefficient Polarity Hydrophobe Hydrophile Lipophilic Amphiphile Lyonium ion Lyate ion