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Evidence for Self-Association of Nonionic and Other Organic Solutes in Liquid Phases Comprising 1-Octanol and Water Keith B. Lodge*,† and Ebenezer J. Egyepong‡ Departments of Chemical Engineering and Chemistry, The UniVersity of Minnesota Duluth, 1303 Ordean Court, Duluth, Minnesota 55812-3025 ReceiVed: August 11, 2009; ReVised Manuscript ReceiVed: February 28, 2010
We use a monomer-single-multimer model to judge whether there is significant self-association of an organic solute distributed between 1-octanol and water. Self-association leads to octanol-water partition coefficients, Kow, that depend upon the concentration of solute and this affects their application, significantly so for lipophilic compounds. Our measurements, done over as wide a range of concentration as possible, suggest that: (1) For toluene, there is dimerization in the water and tetramerization in 1-octanol. (2) For p-xylene, there is significant self-association of unknown degree in 1-octanol. (3) Biphenyl exhibits no self-association in either phase. The model confirms the conclusion that there is self-association of nicotimamide only in the aqueous phase, a conclusion reached in original measurements and interpretation (Charman, W. N.; Lai, C. S. C.; Finnin, B. C.; Reed, B. L. Pharm. Res. 1991, 8, 1144-1150). Our analysis of published measurements on the four isomers of hexachlorocyclohexanes (Paschke, A.; Shu¨u¨rmann, G. Chem. Eng. Technol. 2000, 23, 666-670) leads to the conclusion that there is significant self-association of unknown degree in the aqueous phase. There is a discernible region of concentration-independent behavior as infinite dilution is approached in the aqueous phase, except notably for the hexachlorocyclohexanes. We suggest this is due to self-association incorporating the solvent to form multimer-solvent complexes. The data suggest that self-association, when it occurs, has a greater significance in the more lipophilic cases and this may partly explain why the variability in measurements of octanol-water partition coefficients between laboratories tends to be larger and significant for more lipophilic solutes. 1. Introduction Self-association is a process by which a solute complexes with itself to form multimers or n-mers. There is recognition of its importance in liquid phases, especially in the biochemical and pharmaceutical sciences.1-5 There has been little attention paid to it, especially for nonionic organic compounds, in the interpretation of the measurements of the octanol-water partition coefficient.6,7 This, a key measure of lipophilicity,8 is significant in hazard and fate assessments of xenobiotic chemicals in the environment, so accurate measurement is important. Hydroxylic solvents such as water and 1-octanol also undergo self-association,4 but our concern here is primarily with the solute. There are many reasons why measurements of octanol-water partition coefficients for lipophilic solutes have proved to vary considerably between laboratories.6 Pontollilo and Eaganhouse9 describe these in detail for DDT and DDE; they attribute much variability to poor experimentation. There are also phenomena, within the system comprising octanol, water, and the solute, which are not well understood, and self-association is one of these. Edelbach and Lodge10 measured partition coefficients of acrylate esters over a range of concentration and they interpreted their results by invoking self-association of the esters in the 1-octanol phase. Charman and co-workers11 invoked selfassociation of nicotinamide in the aqueous phase to interpret * To whom correspondence should be addressed. E-mail: klodge@ d.umn.edu. † Department of Chemical Engineering. ‡ Department of Chemistry. Present address: Shire PLC, 11200 Gundry Lane Owings Mills, MD 21117.
their measurements of its octanol-water partition coefficient and other properties. For ionizing organic compounds within nonionic phases, association phenomena have been known for a long time.12 Our purpose here is to examine self-association as a source of discrepancy between measurements of the octanol-water partition coefficients made in various ways. We develop a monomer-single-multimer model to judge whether there is significant self-association of an organic solute distributed between 1-octanol and water, and we apply this to our results of measurements for the octanol-water partition coefficients of toluene, p-xylene, and biphenyl made over as wide a range of concentration as we found possible to measure, from the upper limit of the aqueous solubility down to a low concentration, determined by analytical sensitivity. As part of the same work, one of us did equivalent measurements, not presented here in detail, for ethylbenzene and naphthalene.13 There appear to be few reported studies over a wide range of solute concentration. We reanalyzed the reported data for nicotinamide11 and the isomers of hexachlorocyclohexane14 using the monomer-single-multimer model. 2. Theory Consider the distribution of a solute A between the two immiscible liquids, water (w) and 1-octanol (o), at constant temperature and pressure:
Aw h Ao The equilibrium constant Kow for this process is called variously the distribution constant, the partition ratio, the
10.1021/jp907752w 2010 American Chemical Society Published on Web 03/31/2010
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partition coefficient or intrinsic partition coefficient; it is defined as
Kow ) (concentration of A in 1-octanol)/ (concentration of A in water) ) Co /Cw (1) These concentrations represent those of the freely dissolved or unassociated solute. We postulate the existence of self-association equilibria of the solute A in 1-octanol (Ao) and in water (Aw). In 1-octanol, the self-association is
associated forms, eqs 3 and 5. Unless special methods are used, the total concentrations of solute in each phase are measured, and this is indeed the case in this work. To interpret measurements, we consider various cases of self-association. By significant self-association, we mean that the concentrations of the freely dissolved forms, Co and Cw, are small with respect to the concentration of the multimers, and so the total concentrations may be written, using eqs 2, 4, and 1, as
Ao + Ao + Ao + ... h (Ao)n with the equilibrium constant for the self-association given by:
Kn,o ) Cn,o /(Co)n
Ct,o ) Co + nCn,o
(3)
In water the self-association is:
(9)
There are various limiting cases. 1. The Limit of Infinite Dilution (All Chemical Unassociated), or No Self-Association at All. In this case selfassociation is not important in the limit that Co and Cw approach zero, or there is no self-association at all. In other words: Ct,o ≡ Co and Ct,w ≡ Cw, so
or
(4)
where Cm,w is the concentration of the multimer, and m is the degree of self-association of A in the aqueous phase. The total concentration of all solute species in water is
(5)
This treatment does not consider the formation of intermediate self-association complexes; for example, if tetramers are formed, the treatment does not consider the existence of trimers. In other words, it is a monomer-single-multimer approach. Despite the severity of this approximation, this treatment provides a sufficient framework, in our view, to judge the existence of selfassociation, and this is the primary purpose here. The intractable nature of a fuller treatment including intermediate complexes has been recognized for a long time,3 and there are various approximate methods, one of which is used in work cited here.11 If the monomer-single-multimer approach leads to good fit of the data, then it should be concluded that there is a preponderance of the multimer in the equilibrium mixture. The observed partition coefficient is
Kobs ) Ct,o /Ct,w
(8)
Kobs ) Kow ) a constant
The equilibrium constant for the self-association is:
Ct,w ) Cw + mCm,w
Ct,w ≈ mCm,w ) mKm,w(Cw)m
Cw ) {Ct,w /(mKm,w)}1/m
Aw + Aw + Aw + ... h (Aw)m
Km,w ) Cm,w /(Cw)m
(7)
A useful form of the latter equation is:
(2)
where Cn,o is the concentration of the multimer, and n is the degree of self-association of A in the octanol phase. The total concentration of all solute species in 1-octanol is:
Ct,o ≈ nCn,o ) nKn,o(Co)n ) nKn,o(KowCw)n
(6)
The distinction between the true, or intrinsic, partition coefficient defined in eq 1 and that observed is critically important. The total concentrations in each phase include the
log Kobs ) a constant or log Ct,o ) log Ct,w + log Kow (10) For a system in this region, the plot of log Kobs versus log Ct,w should yield a horizontal line; the partition coefficient is independent of concentration. Also, a plot of log Ct,o against log Ct,w should yield a line with slope of unity. 2. Significant Self-Association in the 1-Octanol Phase Only. In this case there is no self-association in the aqueous phase. The use of eqs 6 and 7 leads to
log Kobs ) (n-1) log Ct,w + log Kow + log[nKn,o(Kow)n] log Ct,o ) n log Ct,w + log Kow + log[nKn,o(Kow)n]
(11) For a system in this region, the plot of log Kobs versus log Ct,w should yield a line with slope n - 1. The plot of log Ct,o against log Ct,w should yield a line with slope n, the degree of self-association in the 1-octanol phase. 3. Significant Self-Association in the Aqueous Phase Only. In this case there is no self-association in the octanol phase. The use of eqs 6, 1, 8, and 9 leads to
log Kobs ) {(1-m)/m} log Ct,w + log[Kow(mKm,w)-1/m]
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log Ct,o ) (1/m) log Ct,w + log[Kow(mKm,w)-1/m]
(12) For a system in this region, the plot of log Kobs versus log Ct,w should yield a line with slope (1 - m)/m. The slope is expected to range from -0.5 for dimerization (m ) 2) to -1 for a high degree of self-association as m f ∞. The plot of log Ct,o against log Ct,w should yield a line with slope 1/m, the reciprocal of the degree of self-association in the aqueous phase. The slope is expected to range from 0.5 for dimerization (m ) 2) to 0 for a high degree of self-association as m f ∞. 4. Significant Self-Association in Both Phases. The use of eqs 1, 6, 7, 8, and 9 leads to
importance in each phase, if we observe the general behavior represented by the curves in Figure 1, although we may not be able to identify the limiting forms represented by eqs 11-13 exactly. In other words, the general picture in Figure 1 is applicable when the monomer-single-multimer approach is not quantitatively appropriate. If there is significant self-association then the measured partition coefficient will depend upon the concentration of the solute used, and the usual practice of measuring the partition coefficient at a single concentration, often unspecified, provides an incomplete picture. We find evidence for self-association, or the lack thereof, by inspecting the plots of log Kobs and log Ct,o versus log Ct,w. Greenwald and co-workers used log concentration plots in a similar way to find the critical micelle concentrations of nonionic surface agents distributed between water and iso-octane.15
log Kobs ) {(n-m)/m} log Ct,w + log[nKn,o(Kow)n(mKm,w)-n/m] -n/m
log Ct,o ) (n/m) log Ct,w + log[nKn,o(Kow) (mKm,w) n
] (13)
For a system in this region, the plot of log Kobs versus log Ct,w should yield a line with slope (n - m)/m. The plot of log Ctc,o against log Ctc,w should yield a line with slope n/m, the ratio of the degree of self-association in the 1-octanol phase to that in the aqueous phase. Figure 1 shows schematic plots representing the various cases; Figure 1a shows the plot of log Kobs versus log Ct,w, and Figure 1b shows the corresponding plot of log Ct,o versus log Ct,w. It is reasonable, in our view, to conclude the existence of selfassociation and to make qualitative statements about its relative
Figure 1. Expected behavior for various cases of self-association of a solute in 1-octanol and water. The graph in panel A shows the logarithm of the measured partition coefficient plotted against the logarithm of the total concentration in the aqueous phase; the graph in panel B contains the logarithm of the total concentration in octanol as the ordinate. s: no self-association; s s s: self-association only in aqueous phase; - s - s: self-association only in the octanol phase; - - -: self-association in both phases with a higher degree of self-association in the octanol phase.
3. Experimental Section Chemicals. Toluene, p-xylene, biphenyl, ethylbenzene, and naphthalene were obtained from the Aldrich Chemical Co. and were used without further purification. Methanol, HPLC grade, was obtained from Fisher Scientific. Ultra pure water was prepared with a Barnstead II purification system. Octanol-Water Partition Coefficients. We determined these by a “shake-flask” method for toluene and a “slow-stir” method for p-xylene, biphenyl, ethylbenzene, and naphthalene; we prepared partitioning experiments for each concentration in duplicate, and the equilibration of the vials or centrifuge tubes occurred in an environment controlled at 25 °C. After equilibration, we analyzed both phases for the solute using HPLC (BioRad) with fluorescence detection. We did experiments for as wide a range of concentration as possible, from the aqueous solubility limit down to as low a concentration as possible, dictated by analytical sensitivity. The shake-flask experiments were performed in 15 mL capped disposable glass centrifuge tubes (Kimble 73785) using 10 mL of ultrapure water and 1.5-2.0 mL of the octanol solution of the chemical. For shaking the contents of each tube, a vortex mixer (Fisher Genie 2) was used on its highest setting for 1 min. Then, each tube was centrifuged for at least 15 min at 900g in a refrigerated centrifuge (Fisher Marathon 22KBR), whose temperature was controlled at 25 °C. For chemical analysis, an aqueous sample was withdrawn using an HPLC syringe. Immediately after withdrawal, the needle was wiped with a tissue moistened with mobile phase to remove any droplets of octanol solution. This sample was promptly injected into the HPLC. The sequence of shaking, centrifugation, and chemical analysis of the aqueous phase was repeated another two times. Thereby, it was demonstrated that equilibrium is attained after the second sequence. Tubes were kept in the centrifuge until the final analyses of the octanol and aqueous phases. Slow-stir experiments were carried out in 10 mL reaction vials (Ace Glass 9591-48); these vials have a capped side arm. Approximately 10 mL of ultrapure water was dispensed into each vial along with a clean Teflon-coated stirring bar (Fisher 14-511-95C). The octanol solution of the chemical, 1.5-2.0 mL, was placed on top of the water with great care, thereby ensuring that the side arm was only filled with aqueous phase. The vials were clamped over magnetic stirrers (Fisher Electronic Stirrer 2003) and placed in a water bath controlled at 25 °C. The stir bars were rotated at 50 rpm. The approach to equilibrium was monitored by withdrawing a sample of aqueous phase from the side arm using an HPLC syringe and injecting
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J. Phys. Chem. A, Vol. 114, No. 15, 2010 5135 TABLE 1: Partition Coefficients and Self-Association Constants for Toluene and Nicotinamide from Limiting Formsa equations of limiting forms toluene
log Kobs ) 2.80 log Kobs ) -1/2 log Ct,w + 0.85 log Kobs ) log Ct,w + 5.37
nicotinamide
log Kobs ) -0.443 log Kobs ) -2/3 log Ct,w - 0.80
log Kobs ) -1/2 log Ct,w - 0.85b
Figure 2. Behavior of toluene in 1-octanol and water. The graph in panel A shows the logarithm of the measured partition coefficient plotted against the logarithm of the total concentration of toluene in the aqueous phase; the graph in panel B contains the logarithm of the total concentration of toluene in octanol as the ordinate. Data (n ) 24, individual duplicates shown) s: no self-association. The slope of the line is zero in A and unity in B; s s s: self-association in the aqueous phase only. The slope of the line is -1/2 in A and +1/2 in B; - - -: self-association in both phases with a higher degree of self-association in the octanol phase. The slope of the line in A is unity and is 2 in B. The vertical arrow (v) represents the aqueous solubility.
the sample on the HPLC. Forty-eight hours proved sufficient time for equilibrium to be attained. Lodge16 originally applied these methods for octanol-water partitioning studies of 16 C-7 hydrocarbons. The slow-stir method17,18 was developed for very lipophilic solutes with the intent of minimizing the production of micelles. These are thought to be produced by the shake-flask method, which was developed from the classic extraction-flask procedure of organic chemistry. Lodge16 demonstrated that the slow-stir and shakeflask methods give the same results for log Kow < 3.8, and toluene falls well within this range. 4. Results and Discussion Figure 2 contains the results of the determination of octanol-water partition coefficients for toluene. Figure 2a shows the plot of log Kobs versus log Ct,w and Figure 2b shows the plot of log Ct,o versus log Ct,w. The range corresponds to 3 orders of magnitude in the total aqueous phase concentration. The vertical arrow in the lower right quadrant represents the aqueous solubility of toluene19 (5.71 mmol dm-3 at 25 °C). The figures that display the data for the other solutes have a similar format. By inspection and comparing these plots to those in Figure 1, we can draw three lines through the data from which we identify three limiting forms. These are: (1) the horizontal line in Figure 2a, corresponding to the line of unit slope in the Figure 2b. This means that there is a region of concentration-independent behavior as infinite dilution is approached, eq 10, and this corresponds to log Kow ) 2.80 (the accepted value20 is 2.73) and we take this to represent the infinite-dilution value. (2) A line with slope of -1/2 through data in the middle of Figure 2a that corresponds to the line with slope of +1/2 in Figure 2b. These lines indicate a region of significant self-association in
Kow ) 631 the estimates directly from the equations K2,w ) 3970 dm3 mol-1 K4,o ) 23.3 dm9 mol-3 the optimized values K2,w ) 1030 dm3 mol-1 K4,o ) 2.46 dm9 mol-3 Kow ) 0.362 the estimate directly from the equation K3,w ) 3.98 dm6 mol-2 the optimized value K3,w ) 2.78 dm6 mol-2 the estimate directly from the equation K2,w ) 3.29 dm3 mol-1 the optimized value K2,w ) 1.74 dm3 mol-1
a Equation 10 gives Kow. Equation 12 leads to the estimate of Km,w. Equation 13 leads to the estimate of Kn,o. b Figure 6 does not show the line corresponding to this equation.
the aqueous phase only, eq 12, with 1/m ) 0.5, so the degree of self-association is two. (3) A line with slope of +1 through data in the right of Figure 2a that corresponds to line with slope +2 in Figure 2b. These lines indicate a region of significant self-association in both the octanol and the aqueous phase, eq 13, with n/m ) 2, so the degree of self-association in octanol is four. We conclude that there is significant dimerization in the aqueous phase and significant tetramerization in the octanol phase. Table 1 contains the equations of the lines corresponding to the plot of log Kobs in Figure 2. These permit us to estimate the self-association constants for dimerization in the aqueous phase, K2,w, and tetramerization in the octanol phase, K4,o, using eqs 12 and 13, respectively, and Table 1 contains these estimated values. We further optimized these estimations by fitting the data to the model function for Kobs, eq 6. This required the use of eqs 1, 3, and 5; and the infinite-dilution value of Kow and the self-association constants, K2,w and K4,o, were the sole adjustable parameters with the estimations taken as their initial values. This is possible in the case of dimerization because there is an exact solution for the freely dissolved concentration of solute, Cw, in eq 5. The direct minimization of the sum of the squares of the differences between the measured and model values of the measured partition coefficients, using “Solver” in an Excel spreadsheet, led to the optimized values of K2,w and K4,o. The curves in Figure 3 represent the calculations of log Kobs using the estimated and optimized values. The resulting optimized self-association constants are K2,w ) 1.03 × 103 dm3 mol-1 and K4,o ) 2.46 dm9 mol-3. Neighboring or overlapping data points in Figure 2 represent partitioning experiments that were set up with the same initial composition, two in each case. The figures showing our measurements for the other solutes have the same structure. The results indicate variations, representing precision, in both the aqueous and octanol phase compositions. Table 2 contains a summary and estimates of uncertainty for the all the data presented here. The treatment of the data as simple repetitions of the measurement of a single quantity, corresponding to no association, leads to a standard deviation of 0.19 in log Kobs for toluene. The optimized association model leads to a standard error of the estimate of 0.10 in log Kobs.
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Figure 3. Measured octanol-water partition coefficients for toluene plotted as a function of the total concentration in water assuming that toluene forms dimers in the aqueous phase and tetramers in the octanol phase. O: data (n ) 24, individual duplicates shown); - - -: model using the estimates of the self-association constants from limiting forms; s: model using optimized values of the self-association constants.
Figure 4 contains the results of the determination of octanol-water partition coefficients for p-xylene. The vertical arrow represents the value of the aqueous solubility19 (1.53 mmol dm-3 at 25 °C). The range corresponds to about 3.5 orders of magnitude in the total aqueous phase concentration. We can draw two lines through the data from which we identify two limiting forms. These are: (1) the horizontal line in Figure 4a, corresponding to the line of unit slope in Figure 4b. This means that there is a region of concentration-independent behavior as the limit of infinite dilution is approached, eq 10, and this corresponds to log Kow ) 3.06 (the accepted value20 is 3.15). (2) A line with slope of +0.13 through data in the right of Figure 4a corresponding to the line with slope +1.13 in Figure 4b. We see two possible interpretations: (1) there is self-association in the system but the monomer-single-multimer approach for each phase is inappropriate in this system in contrast to toluene. (2) In the monomer-single-multimer approach n/m ) 0.13. If the degree of self-association is high, say m ) 100, then n ) 130. The first interpretation is more likely. In either case we conclude self-association is more important in the octanol phase. Figure 5 contains the results of the determination of octanol-water partition coefficients for biphenyl. The vertical arrow represents the value of the aqueous solubility21 (39 µmol dm-3 at 25 °C, standard deviation 6%). Our largest measured aqueous concentration is 50 µmol dm-3, about 28% larger; however, our largest concentration is in water that is saturated with 1-octanol. The range of our data corresponds to about 3.5 orders of magnitude in the total aqueous phase concentration. We can draw only a single line through the data, which indicates a single regime. This is the horizontal line in Figure 5a, corresponding to the line of unit slope in Figure 5b. This means that the partition coefficient is independent of concentration across the whole range of the measurement and this corresponds to log Kow ) 4.02 (the accepted value20 is 4.01). The possibility that there is self-association in both phases that is essentially the same is unlikely. Charman and co-workers11 measured octanol-water partition coefficients for nicotinamide at 15, 25, and 32 °C, and they presented their data by plotting the measured coefficient, Kobs, versus the total concentration in octanol, Ct,o. In Figure 6 we have plotted their data measured at 32 °C, and their data at the other temperatures show similar behavior. The range corresponds to about 3.5 orders of magnitude in the total aqueous phase concentration. The value of the aqueous solubility,22 represented by the vertical arrow, is 7.5 m at 23-25 °C. We can draw two lines through the data from which we identify two limiting forms. These are: (1) the horizontal line in Figure
Lodge and Egyepong 6a, corresponding to the line of unit slope in Figure 6b. This means that there is a region of concentration-independent behavior as the limit of infinite dilution is reached, eq 10, and this corresponds to log Kow ) -0.443 (the accepted value20 is -0.37), and we take this to represent the infinite-dilution value. (2) A line with slope of -2/3 through data in the right of Figure 6a that corresponds to the line with slope +1/3 in Figure 6b. These lines indicate a region of significant self-association in the aqueous phase only, eq 12, with 1/m ) 1/3 and so the degree of self-association is three, representing trimerization. Table 1 contains the equations of the lines corresponding to those in the plot of log Kobs in Figure 6. These permit the estimation of the self-association constant for trimerization in the aqueous phase, K3,w, and Table 1 contains the estimated and optimized values, the latter being determined using a similar procedure to that used for toluene. Our treatment confirms the conclusion made by Charman and co-workers11 that the nicotinamide in the octanol phase is monomeric. However, they used a dimerization model to interpret their data and we have also applied our approach assuming dimerization only, and Table 1 contains the corresponding results. Figure 7 contains the plot of the data for log Kobs, and the model fits for dimerization and trimerization using the optimized values of the self-association constants. Table 2 contains the corresponding standard errors of the estimates. The monomer-single-trimer model provides a better fit to the data than the monomer-single-dimer model; the standard errors of the estimates are 0.026 and 0.075, respectively. Paschke and Schu¨u¨rmann14 measured coefficients for the four isomers of hexachlorocyclohexane at 25 °C, and they presented their data by plotting the measured coefficient, Kobs, versus the log of the total concentration in water, log Ct,w. In Figure 8, we have plotted their data for the δ isomer and for the γ isomer (lindane) in the same graphs. The range corresponds to about 5-6 orders of magnitude in the total aqueous phase concentration. The vertical arrows represent the values of the aqueous solubility14 (35 and 51 µmol dm-3 for δ and γ isomers, respectively). We can not discern regions of concentration-independent behavior in Figure 8 when we compare the data with the predicted model behavior, Figure 1, and the observed behaviors of toluene, Figure 2, and biphenyl, Figure 5. However, the region of concentration-independent behavior, if any, is expected at low concentrations, so to aid in interpretation we draw horizontal lines in Figure 8a and lines of unit slope in the Figure 8b that are slightly above the respective levels of quantitation.14 These lines correspond to log Kow ) 4.76 and log Kow ) 3.91 for the δ and γ isomers, respectively. Lines through the data have slopes of -0.17 for the δ isomer and -0.045 for the γ isomer in Figure 8a and for clarity, the corresponding lines are not shown in Figure 8b. We see two possible interpretations: (1) there is selfassociation in the system but the monomer-single-multimer approach for each phase is inappropriate. (2) In the monomersingle-multimer approach (n - m)/m ) -0.17 for the δ isomer and (n - m)/m ) -0.045 for the γ isomer. If the degree of self-association is high, say m ) 100, then n ) 83 for the δ isomer and n ) 95 or 96 for the γ isomer. The first interpretation is more likely. In either case we conclude the self-association is more important in the aqueous phase. The data14 for the R and β isomers, not shown here, show a similar pattern; (n m)/m ) -0.046 for the R isomer and (n - m)/m ) -0.054 for the β isomer. We do not include the data here for ethylbenzene and naphthalene; Egyepong reported these elsewhere.13 The results are summarized in Table 2. The data for ethylbenzene span only
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TABLE 2: Summary of Results and Estimates of Uncertainty
solute toluene p-xylene biphenyl nicotinamide δ-HCH γ-HCH ethylbenzeneb naphthaleneb
all data optimized model all data line all data all data optimized dimer model optimized trimer model all data line all data line all data all data
mean log Kobs
standard deviation in log Kobs
No. of data points
2.80
0.19
24
3.28 4.02 -0.684
0.20 0.08 0.215
standard error of the estimate in log Kobs
infinite dilution log Kow
0.10
2.80
0.11
3.06
2.73
32
3.15
38 18
4.01 -0.37 0.075 0.026
4.34
0.32
17
3.78
0.07
12
accepteda value of log Kow
-0.443 -0.443
0.10 3.70 0.02 3.16 3.34
0.12 0.11
22 29
3.15 3.30
a Accepted values are the “log P*” values taken from ref 20, except for the value for γ-HCH that is taken from the data compilation of Xiao and co-workers, ref 23. b Data are taken from the thesis of Egyepong, ref 13.
Figure 4. Behavior of p-xylene in 1-octanol and water. The graph in panel A shows the logarithm of the measured partition coefficient plotted against the logarithm of the total concentration of p-xylene in the aqueous phase; the graph in panel B contains the logarithm of the total concentration of p-xylene in octanol as the ordinate. O: data (n ) 32, individual duplicates shown); s no self-association. The slope of the line is zero in A and is unity in B. - - -: significant self-association in the octanol phase. The slope of the line in A is 0.13 and is 1.13 in B. The vertical arrow (v) represents the aqueous solubility.
2 orders of magnitude in the total aqueous phase concentration owing to analytical limitations, and the data for naphthalene span 3.5 orders of magnitude in the total aqueous phase concentration. Naphthalene appears to behave in a similar way to biphenyl with more scatter in the data than for biphenyl, and this is shown by the standard deviations given in Table 2. There is evidence for the self-association of these and similar solutes in the gas phase. Borba and co-workers24 recently reported studies of the self-association of nicotinamide in the gas phase. Law and co-workers25 studied dimers of benzene, toluene, and benzene-toluene in supersonic jets. Chipot and co-workers26 reported calculations for benzene and toluene dimers in the gas phase. The evidence for self-association in organic phases is summarized by Grant and Higuchi,4 and this
Figure 5. Behavior of biphenyl in 1-octanol and water. The graph in panel A shows the logarithm of the measured partition coefficient plotted against the logarithm of the total concentration of biphenyl in the aqueous phase; the plot in panel B contains the logarithm of the total concentration of biphenyl in octanol as the ordinate. O: data (n ) 38, individual duplicates shown); s: no self-association. The slope of the line is zero in A and is unity in B. The vertical arrow (v) represents the aqueous solubility.
includes dimers, trimers, tertramers, and pentamers. Edelbach and Lodge10 interpreted their measurements on acrylate esters in terms of dimerization and tetramerization in the octanol phase; however, the concentrations used spanned a smaller range than used in this work, and they were with within about 2 orders of magnitude of the solubility limit.27 Here, tetramerization for toluene in the octanol phase is apparent within an order of magnitude below the solubility limit. In contrast, self-association in the aqueous phase, when it occurs, appears as the concentrations increase from infinite dilution. The self-association in octanol, when it occurs, appears as the aqueous solubility limit is reached. Approximately, the regions of concentration-independent behavior in the aqueous phase end as mole fractions are increased above 10-3 for nicotinamide, 10-6 for toluene, 10-8 for p-xylene, and 10-12 for the hexachlorocyclohexanes. In the latter case we do not clearly discern regions of concentration-independent behavior
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Figure 6. Behavior of nicotinamide in 1-octanol and water. The graph in panel A shows the logarithm of the measured partition coefficient plotted against the logarithm of the total concentration of nicotinamide in the aqueous phase; the graph in panel B contains the logarithm of the total concentration of nicotinamide in octanol as the ordinate. O: data at 32 °C (n ) 18); s: no self-association. The slope of the line is zero in A and is unity in B; s s s: self-association in the aqueous phase only. The slope of the line is -2/3 in A and is +1/3 in B. The vertical arrow (v) represents the aqueous solubility.
Figure 7. Behavior of nicotinamide in 1-octanol and water and selfassociation models. The logarithm of the measured partition coefficient is plotted against the logarithm of the total concentration of nicotinamide in the aqueous phase. O: data at 32 °C (n ) 18); s: trimerization with K3,w ) 2.78 dm6 mol-2; s s s: dimerization with K2,w ) 1.74 dm3 mol-1.
and the mole fraction corresponds approximately to the smallest concentrations in these cases. As the solute becomes more lipophilic, the region of concentration-independent behavior ends at a smaller composition for those cases exhibiting selfassociation. The self-association of lipophilic solutes, or lipophilic groups within large molecules, in water, has been of keen interest for a long time. Its role in the behavior of proteins,1 drugs,5,28 micelles, and membranes2 is significant. In these contexts, the self-association of lipophilic solutes in water is called the “hydrophobic interaction” or the solutes are said to exhibit “hydrophobicity”.8 The unique properties of the water-water interaction29,30 are paramount, affecting whether solutes will exhibit hydrophobicity or not. In hindsight it is not surprising that the hydrophobic effect would be manifest in the octanolwater system.
Lodge and Egyepong
Figure 8. Behavior of δ- and γ-hexachlorocyclohexane (δ- and γ-HCH) in 1-octanol and water. The graph in panel A shows the logarithm of the measured partition coefficient plotted against the logarithm of the total concentration of HCH in the aqueous phase; the graph in panel B contains the logarithm of the total concentration of HCH in octanol as the ordinate. ): data for δ-HCH (n ) 17); O: data for γ-HCH (n ) 12); s: no self-association for δ-HCH; - - -: no self-association for γ-HCH. The slopes of the lines are zero in A and are unity in B for no self-association. s s s: predominant selfassociation in aqueous phase only for δ-HCH. The slope of the line is -0.17 (the corresponding line is not shown in B); s - s -: predominant self-association in aqueous phase only for γ-HCH. The slope of the line is -0.045 (the corresponding line is not shown in B). The vertical arrows (v) represent the aqueous solubilities.
The dimerization of benzene was regarded as a prototype for the hydrophobic interaction by Tucker and Christian.31 They interpreted their measurements of Henry’s law constants for benzene between water vapor and liquid water in terms of benzene dimers in the aqueous phase. Later, Tucker and coworkers32 reported a dimerization constant for benzene in water of 0.50 dm3 mol-1 in the range 15-45 °C. Chipot and co-workers26 also reported calculations for benzene and toluene dimers in aqueous solution, and they calculated dimerization constants for various molecular orientations in water with the following ranges; 0.16-3.07 for benzene; and 4.39-14.8 dm3 mol-1 for toluene. Our dimerization constant for toluene is about 100 times larger, and this may be due to the octanol that is dissolved in the water. Nicotinamide, toluene, and the hexachlorocyclohexanes exhibit self-association in water or hydrophobicity. The protonated form of nicotinamide probably predominates under these conditions; the protonation constant33 is 2500 dm3 mol-1 at 298 K and at an ionic strength of 0.24 mol dm-3, so hydrogen bonding is expected to play a role. Other studies provide evidence for the self-association of nicotinamide in the aqueous phase, and Charmin and co-workers11 described these, including additional evidence from their own freezing-point depression studies. We think that the behavior of the hexachlorocyclohexanes34 indicates a different type of self-association. In the system comprising 1-octanol and water there are the cosolvents. These are the octanol dissolved in water and the water dissolved in octanol, and the approximate concentrations7 are 3-7 mmol dm-3 and 2 mol dm-3, respectively. It is unlikely there will be a region of concentration-independent behavior, if the solute associates significantly with the solvent or cosolvent, these both
Self-Association of Nonionic and Other Organic Solutes being present in much higher concentration than the solute. This suggests that self-association involves the solvent (Si) and possibly the cosolvent (Sj) in each phase and we may represent this generally as:3,4
nAi + mSi + pSj h (Ai)n(Si)m(Sj)p The propensity for hexachlorocyclohexanes34 to exhibit hydrogen-bonding would assist in this type of self-association. Cosolvency effects that increased with lipophilicity were observed by Edelbach and Lodge10 in their experiments with acrylate esters in which they measured both the concentration of octanol in water and water in octanol. p-Xylene and the more lypophilic biphenyl do not exhibit self-association in the aqueous phase. For biphenyl the twisted conformation of the benzene rings (the angle35 of intersection of the planes containing the rings is 42°) may account for its behavior. This leads to following general idea that we think has not been appreciated in the use and measurement of octanol-water partition coefficients. It is important to distinguish between lypophilicity and hydrophobicity. Strictly, the application of an octanol-water partition coefficient measured at a single concentration is justified only for biphenyl because it does not exhibit hydrophobicity, although it is very lipophilic. For the hazard and fate assessments of xenobiotic chemicals in the environment, typical uncertainties in log Kow of ( 0.3 are regarded as acceptable.6 The magnitude of the effects studied here fall approximately within this range of uncertainty, as can be seen from Table 2. However, the chemicals that cause particular concern are more lipophilic than those studied here. The analytical effort required in detailed measurements usually increases dramatically with the lipophilic character of the solute, so it is better to see if we observe self-association of solutes for which the analytical effort is reasonable; this is the philosophy behind this work. However, the data discussed here lead to the following idea that deserves further attention because of its potential impact on the use of octanol-water partition coefficients in environmental and other applications. The dimerization constant for toluene in water (K2,w ) 1030 dm3 mol-1, log Kow ) 2.80) is greater than the trimerization constant for nicotinamide (K3,w ) 2.78 dm6 mol-2, log Kow ) -0.443) in water. The implication is that self-association constants in water, or hydrophobicity, may increase with the lipophilicity of the solute. The results for the hexachlorocyclohexanes also show this. The data for δ and γ isomers show that the self-association has a greater influence for the more lipophilic δ isomer because the slope of line in the plot of log Kobs versus log Ct,w is more negative for the δ isomer. Over similar total ranges of aqueous concentrations, the net change in the log Kobs is about 1.0 and 0.3 for δ and γ isomers, respectively. Hexachlorocyclohexanes represent well the types of compounds for which there is a need for accurate partition coefficients in environmental applications. Chessells and co-workers36 reviewed the measurements of log Kow for 40 different solutes (including chlorinated compounds), done by various methods and groups. They found the standard error of the mean increased quadratically with the mean value, becoming significant, greater than 0.3, above 5.5. We can see from Table 2 that uncertainties even less than 0.3 can be explained by self-association. Pontollilo and Eaganhouse9 found that published data for the water solubility and the octanol-water partition coefficients of DDT and DDE spanned 2-4 orders of magnitude. We can not help but conclude that
J. Phys. Chem. A, Vol. 114, No. 15, 2010 5139 self-association must be a significant part of the explanations for these observations. Acknowledgment. E.J.E. is grateful to the Department of Chemistry for a teaching assistantship. We thank Paul Siders (Chemistry) for useful discussions, the Department of Chemical Engineering for equipment and supplies, and Duane Long for technical assistance. The comments of the reviewers were helpful. References and Notes (1) Kauzmann, W. AdV. Protein Chem. 1959, 14, 1–63. (2) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed.; Wiley: New York, 1980; pp 233. (3) Connors, K. A. Binding Constants: the Measurement of Molecular Complex Stability; Wiley: New York, 1987; pp 411. (4) Grant, D. J. W.; Higuchi, T. Solubility BehaVior of Organic Compounds; Techniques of Chemistry; John Wiley & Sons: New York, 1990; pp 600. (5) Martin, A. N.; Bustamante, P. Physical Pharmacy: Physical Chemical Principles in the Pharmaceutical Sciences; Lea & Febiger: Philadelphia, 1993; pp 622. (6) Dearden, J. C.; Bresnen, G. M. Quant. Struct. Act. Relat. 1988, 7, 133–144. (7) Sangster, J. Octanol-Water Partition Coefficients: Fundamentals and Physical Chemistry; Wiley: Chichester; New York, 1997; Wiley Series in Solution Chemistry; v. 2; pp 170. (8) IUPAC. Compendium of Chemical Terminology, 2nd ed.; Blackwell Scientific Publications: Oxford, 2009; Vol. 2009. XML on-line corrected version: http://goldbook.iupac.org (2006) created by M. Nic, J. Jirat, B. Kosata. We use terminology following the IUPAC definitions: Lipophilicity represents the affinity of a molecule or a moiety for a lipophilic environment. It is commonly measured by its distribution behaviour in a biphasic system, either liquid-liquid (e.g., partition coefficient in 1-octanol/water) or solidliquid (retention on reversed-phase high-performance liquid chromatography (RP-HPLC) or thin-layer chromatography (TLC) system). The hydrophobic interaction is the tendency of hydrocarbons (or of lipophilic hydrocarbonlike groups in solutes) to form intermolecular aggregates in an aqueous medium, and analogous intramolecular interactions. The name arises from the attribution of the phenomenon to the apparent repulsion between water and hydrocarbons. However, the phenomenon ought to be attributed to the effect of the hydrocarbon-like groups on the water-water interaction. Hydrophobicity is the association of non-polar groups or molecules in an aqueous environment which arises from the tendency of water to exclude non-polar molecules. (9) Pontolillo, J.; Eganhouse, R. P. The Search for Reliable Aqueous Solubility (SW) and Octanol-Water Partition Coefficient (KOW) Data for Hydrophobic Organic Compounds: DDT and DDE as a Case Study. WaterResour. InVest. Rep. (U. S. Geol. SurV.) 2001, 01-4201, 1–51. (10) Edelbach, D. J.; Lodge, K. B. Phys. Chem. Chem. Phys. 2000, 2, 1763–1771. (11) Charman, W. N.; Lai, C. S. C.; Finnin, B. C.; Reed, B. L. Pharm. Res. 1991, 8, 1144–1150. (12) Leo, A.; Hansch, C.; Elkins, D. Chem. ReV. 1971, 71, 525–616. (13) Egyepong, E. J. Detailed Measurements of Octanol-Water Partition Coefficients of Alkyl Benzenes; M.S. Thesis, University of Minnesota: Duluth, 2004. (14) Paschke, A.; Schu¨u¨rmann, G. Chem. Eng. Technol. 2000, 23, 666– 670, Water solubilities were calculated from the saturated mole fractions in Table 1 of this reference. (15) Greenwald, H. L.; Kice, E. B.; Kenly, M.; Kelly, J. Anal. Chem. 1961, 33, 465–468. (16) Lodge, K. B. J. Chem. Eng. Data 1999, 44, 1321–1324. (17) Brooke, D. N.; Dobbs, A. J.; Williams, N. Ecotoxicol EnViron Saf 1986, 11, 251–260. (18) de Bruijn, J.; Busser, F.; Seinen, W.; Hermens, J. EnViron. Toxicol. Chem. 1989, 8, 499–512. (19) Sanemasa, I.; Araki, M.; Deguchi, T.; Nagai, H. Bull. Chem. Soc. Jpn. 1982, 55, 1054–1062. (20) Hansch, C.; Leo, A.; Hoekman, D. H. Exploring QSAR; American Chemical Society: Washington, DC, 1995; “Accepted” refers to the log P* values in this reference. (21) Banerjee, S.; Yalkowsky, S. H.; Valvani, C. EnViron. Sci. Technol. 1980, 14, 1227–1229. (22) Good, D. J.; Rodriguez-Hornedo, N. Cryst. Growth Des. 2009, 9, 2252–2264. (23) Xiao, H.; Li, N.; Wania, F. J. Chem. Eng. Data 2004, 49, 173– 185.
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(24) Borba, A.; Albrecht, M.; Gomez-Zavaglia, A.; Lapinski, L.; Nowak, M. J.; Suhm, M. A.; Fausto, R. Phys. Chem. Chem. Phys. 2008, 10, 7010– 7021. (25) Law, K. S.; Schauer, M.; Bernstein, E. R. J. Chem. Phys. 1984, 81, 4871–4882. (26) Chipot, C.; Jaffe, R.; Maigret, B.; Pearlman, D. A.; Kollman, P. A. J. Am. Chem. Soc. 1996, 118, 11217–11224. (27) Edelbach, D. J. The Variation of the Octanol-Water Partition Coefficient for Thirteen Acrylates; M.S. Thesis, University of Minnesota: Duluth, 1992. (28) Connors, K. A. Thermodynamics of Pharmaceutical Systems: An Introduction for Students of Pharmacy; Wiley-Interscience: Hoboken, N.J., 2002; pp 344. (29) Frank, H. S.; Evans, M. W. J. Chem. Phys. 1945, 13, 507–532.
Lodge and Egyepong (30) Ben-Naim, A. Hydrophobic Interactions; Plenum Press: New York, 1980; pp 311. (31) Tucker, E. E.; Christian, S. D. J. Phys. Chem. 1979, 83, 426–427. (32) Tucker, E. E.; Lane, E. H.; Christian, S. D. J. Solution Chem. 1981, 10, 1–20. (33) Sharnin, V. A.; Dushina, S. V.; Zevakin, M. A.; Gushchina, A. S.; Grazhdan, K. V. Inorg. Chim. Acta 2009, 362, 437–442. (34) Ouvrard, C.; Lucon, M.; Graton, J.; Berthelot, M.; Laurence, C. J. Phys. Org. Chem. 2004, 17, 56–64. (35) Almenningen, A.; Bastiansen, O. Kgl. Norske Videnskab. Selskabs. Skrifter 1958, 1, 16. (36) Chessells, M.; Hawker, D. W.; Connell, D. W. Chemosphere 1991, 22, 1175–1190.
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