Partition Coefficients and Their Uses

Chemical Reviews 525 Volume 71, Number 6 December 1971 PARTITION COEFFICIENTS AND THEIR USES ALBERT LEO,* CORWIN HANSCH, AND DAVID ELKINS Department of Chemistry, Pomona College, Claremont, California 91 711 Received March 31, 1971 Contents impossible since Chemical Abstracts has not indexed the majority of the work of the last few decades under the subject I. Introduction 525 A. Purpose 525 of partitioning. While reference may be made under the name B. Historical 526 of a compound, this is of very little help in organizing a list 11. Theoretical 527 of known values. Actually, in recent years relatively few par- A. Henry’s Law 527 tition coefficients have been determined in studies simply de- B. Nonideal Behavior of Solutes 521 voted to an understanding of the nature of the partition co- C. Thermodynamics of Partitioning Systems 531 efficient. The vast majority have been measured for some D. Energy Requirements for Phase Transfer 532 secondary reason such as the correlation of relative lipophilic 111. Experimental Methods 531 character with biological properties of a set of congeners. IV. Linear Free-Energy Relationships In the course of structure-activity studies undertaken by among Systems 538 this laboratory over the past decade, many values for partition V. Additive-Constitutive Properties 542 VI. Uses of Partition Measurements 548 coefficients of drugs have been found in the biochemical and A. Countercurrent Distribution 548 pharmaceutical literature. From references in these papers, B. Measurement of Equilibria 548 many other values have come to light. As these values have C. Relationship to HLB and Emulsion been uncovered, they have been fed into a computer-based Systems 548 “keyed-retrieval” compilation which, while admittedly not D. Measurement of Dissolution and complete, is still far more comprehensive than any yet pub- Partitioning Rate of Drugs 549 lished. E. Liquid Ion-Exchange Media and This compilation is not the primary reason for the present Ion-Selective Electrodes 550 review. Work8 on the correlation of hydrophobic bonding in F. Measurement of Hydrophobic Bonding biochemical systems with partition coefficients has been Ability. Structure-Activity Parameters 550 VII. The Use of Table XVII 551 greatly hindered because of the lack of any survey of the VIII. Glossary of Terms 554 field. This review is written in the hope that the organization of the scattered works on this subject will be of help to others. However, the more dynamic part of the subject is the use of 1. Introduction the partition coefficient in the study of intermolecular forces of organic compounds. This subject, while still in.the em- A. PURPOSE bryonic stage, holds promise for the better understanding of In spite of the scientific community’s continuing interest over the interaction of small organic molecules with biomacro- the past 90 years in partitioning measurements, no compre- molecules. Equation 1 is one of many known examples9 of a hensive review of the subject has ever been published. In fact, nr S 1 no extensive list of partition coefficients has appeared in the log - = 0.75 log P f 2.30 42 0.960 0.159 (1) literature. The largest compilation is that of Seidell;’ smaller C compilations have been made by Collander, ~-5von Metzsch,G linear free energy relationship relating two “partitioning-like” and Landolt.’ The task of making a complete listing is nearly processes. In eq 1, C is the molar concentration of organic compound necessary to produce a 1 : 1 complex with bovine (1) A. Seidell, “Solubility of Organic Compounds,” Vol. 11, 3rd ed, serum albumin via equilibrium dialysis. This partitioning Van Nostrand, Princeton, N. J., 1941. process is related linearly to log P which is the partition CO- (2) R.Collander, Physiol. Plant., 7, 420 (1954). efficient of the compound between octanol and water. The (3) R.Collander, Acta Chem. Scand., 3, 717 (1949). (4) R. Collander, ibid., 4, 1085 (1950). number of molecules studied is represented by n, r is the cor- (5) R.Collander, ibid., 5, 774 (1951). (6) F. von Metzsch, Angew. Chem., 65,586 (1953). (7) Landolt-Bornstein “Zahlenwerte and Functionen,” Vol. 2, Springer- (8) C. Hansch, Accounts Chem. Res., 2,232 (1969). Verlag, Berlin, 1964, p’698. (9) F. Helmer, K.Kiehs, and C. Hansch, Biochemistry, 7,2858 (1968). 526 Chemical Reviews, 1971, Vol. 71, No. 6 A. Leo, C Hansch, and D. Elkins relation coefficient, and s is the standard deviation from re- coefficient for the benzoic acid monomer and the dimerization gression. Many such linear relationships between solutes constant for the acid in benzene.la Since benzoic acid exists partitioned in different solvent systems have been uncovered largely as the dimer in benzene at the concentration em- (section IV). A summary of this work should provide a better ployed, the monomer concentration in benzene is propor- understanding of the octanol-water model system and further tional to the square root of its total concentration in that the application of such linear free energy relationships to solvent. Of coulse, Nernst was also aware that, at low con- “partitioning-like’’ processes in more complex biological centrations, the concentration of benzoic acid in the aqueous systems. phase would have to be corrected for ionization. Another aspect of this review is to summarize the present This association and dissociation of solutes in different understanding of the recently discoveredlo additive-constitu- phases remains the most vexing problem in studying partition tive character of the partition coefficient. This property prom- coefficients. For a true partition coefficient, one must con- ises to be of value in studying the conformation of molecules sider the same species in each phase. A precise definition of in solution. this in the strictest sense is impossible. Since water molecules and solvent molecules will form bonds of varying degrees of B. HISTORICAL firmness with different solutes, any system more complex than rare gases in hydrocarbons and water becomes impossible The distribution of a solute between two phases in which it is to define sharply at the molecular level. Very little attention soluble has been an important subject for experimentation has been given to the fact that solutes other than carboxylic and study for many years. In one form or another this tech- acids may carry one or more water molecules bound to them nique has been used since earliest times to isolate natural into the nonaqueous phase. This is quite possible in solvents products such as the essences of flowers. such as sec-butyl alcohol which on a molar basis contains The first systematic study of distribution between two more molecules of water in the butanol phase than butanol! immiscible liquids which led to a theory with predictive During the early years of the twentieth century a great capabilities was carried out by Berthelot and Jungfleisch. l1 number of careful partition experiments were reported in the These investigators accurately measured the amounts present literature, most of which were carried out with the objective of at equilibrium of both IZ and Brz when distributed between determining the ionization constant in an aqueous medium CSZand water. They also measured the amounts of various of moderately ionized acids and bases. As a point of historical organic acids, HzS04,HC1, and NH3when distributed between fact, the method did not live up to its early promise, partly ethyl ether and water. From these early investigations came because of unexpected association in the organic solvents the first appreciation of the basic fact that the ratio of the chosen and partly because of solvent changes which will be concentrations of solute distributed between two immiscible discussed in detail in a following section. solvents was a constant and did not depend on the relative After reliable ionization constants became available through volumes of solutions used. other means, partitioning measurements were used to cal- It was concluded from these early observations that there culate the association constants of organic acids in the non- was a small variation in partition coefficient with temperature, aqueous phase as a function of the temperature. This yielded with the more volatile solvent being favored by a temperature values of AH, AS, and AG for the association reaction.14-18 decrease. It was also evident that some systems, notably However, any calculation of self-association constants from succinic acid partitioned between ether and water, did not obey partition data alone can be misleading when hydrate formation their simple “rule” even in dilute solution, but they intuitively occurs. 19,20 felt the rule would be justified nonetheless. Asearly as 1909, Herzzlpublished formulas which related the In 1891, Nernst made the next significant contribution to partition coefficient (P)to the number of extractions necessary the subject. l2 He stressed the fact that the partition coefficient to remove a given weight of solute from solution. His for- would be constant only if a single molecular species were mula, with symbols changed to conform to present usage, is being considered as partitioned between the two phases. as follows. Considered in this light, partitioning could be treated by If W ml of solution contains xo g of solute, repeat- classical thermodynamics as an equilibrium process where the edly extracted with L ml of a solvent, and XI g of solute re- tendency of any single molecular species of solute to leave mains after the first extraction, then (xo - xt)/L = concentra- one solvent and enter another would be a measure of its tion of solute in extracting phase and xl/W = concentration activity in that solvent and would be related in the usual remaining in original solution. fashion to the other commonly measured activity functions such as partial pressure, osmotic pressure, and chemical po- (13) Occasionally, K values obtained in this fashion have been re- tential.

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