Langmuir 2000, 16, 1825-1833
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Thermodynamic Study on the Langmuir Adsorption of Various Bile Salts Including Taurine and Glycine Conjugates onto Graphite in Water Gohsuke Sugihara,*,† Dai-Suke Shigematsu,† Shigemi Nagadome,† Sannamu Lee,† Yasushi Sasaki,‡ and Hirotsune Igimi§ Department of Chemistry, Faculty of Science, Fukuoka University, Jonan-ku, Fukuoka 814-0180, Japan Received March 26, 1999. In Final Form: October 4, 1999 The adsorption isotherms of various free and conjugated bile salts (BS) onto the surface of graphite (Gr) powder in aqueous borate buffer solution at pH 10 were obtained as a function of temperature ranging from 20 or 25 to 42 °C. Analysis by Langmuir plot was made within the concentration range where the Langmuir adsorption took place, and from it the maximum amount of monolayer adsorption (Nm) and the Langmuir constant (KL), i.e., the ratio of rate constants of adsorption and desorption (KL ) ka/kd), were determined for each BS at different temperatures. The present study shows the KL to be the reciprocal of equilibrium concentration (C*) at half surface coverage, as KL ) 1/C*, and in addition, KL is equal to the adsorption equilibrium constant, Kad, which was defined by a thermodynamic consideration. For determination of KL or Kad, a more reliable method was proposed by to more easily examine the accuracy of the measured points. From the van’t Hoff plot of Kad, the enthalpy changes (adsorption heats, ∆HQad) were determined and the entropy changes (∆SQad) were calculated from the Gibbs energy changes (∆GQad). These data were compared among BS species and the correlation with hydrophobicity index (HI) was discussed. The so-called entropy-enthalpy compensation phenomenon was observed throughout BS species. (The compensation temperature was determined to be 304 K). The enthalpy term was found to be overwhelmingly dominant compared to the entropy term in the adsorption of BSs onto Gr in water.
1. Introduction Since bile salts (BSs) and their analogues are the most important biosurfactants acting like detergents occurring in the living body, many studies have been designed to compare BSs with typical anionic surfactants and/or to see whether BSs might possess some distinctive physicochemical properties which would lead to an understanding of their physiological functions.1 These studies have suggested that a major action of BSs during fat digestion is to bring the products of pancreatic lypolysis, i.e., fatty acids, monoglycerides and cholesterol (Ch), into a mixed micellar solution, and that this process reflects the distinctive surfactant properties of BSs.2 A variety of species of bile acid (BA) salts and their analogues are slightly different from each other in number, location and orientation of hydroxyl group.3 The slight difference, however, has been known to result in greatly different behavior with respect to micelle formation and solubilization. It is worth noting here that pure bile salts are not emulsifiers, as reviewed by Carey, but dilute mixtures of all three biliary lipids; that is bile salts, phosphatidilcholine, and cholesterol can become powerful emulsifiers only when they are heteroaggregated.4 Even in the case of gallstone dissolution, gallstones being mainly composed of Ch, the dissolution mechanisms of * To whom correspondence should be addressed. † Fukuoka University. ‡ San-Ei-Gen FFI Inc. § Institute of Systematic Medical Treatment. (1) (a) Small, D. M. In The Bile Acids; Nair, P. P., Krichevsky, Eds.; Plenum Press: New York, 1971 Vol. 1, pp 249-536.(b) Carey, M. C. In Sterols and Bile Acids; Denielson, H., Sjo¨vall, J., Eds.; Elsevir: Amsterdam, 1985; pp 345-403. (2) Hofmann, A. F. Gastroenterology 1965, 48, 484. (3) Hofmann, A. F. Hepatology 1984, 4, 484. (4) Carey, M. C. In Phospholipids and Atherosclerosis; Avogado, P., et al., Eds.; Raven Press: New York, 1983; pp 33-63.
chenodeoxycholic acid (CDC) and ursodeoxycholic acid (UDC) are different.5 Therefore, from the medical and physicochemical viewpoints, much attention is being devoted to these BSs in connection with Ch solubilization or gallstone dissolution. It should be noted that gallstone dissolution by BSs is initiated by the adsorption of BSs onto the gallstone surface, so that an adsorption study of BSs on Ch crystals in water will give us some important information connecting the gallstone dissolution mechanism or Ch solubilization. In regard to this, we have examined the adsorption behavior of four sodium salts of bile acids (BAs); sodium cholate (NaC), -deoxycholate (NaDC), -chenodeoxycholate (NaCDC), and -ursodeoxycholate (NaUDC), on Ch crystals in water.6 The results obtained from the study on the BSs/Ch combinations, however, suggested that we should evaluate the substantial hydrophobic-hydrophilic balance of the respective BAs, so we needed to choose such a solid system as graphite (Gr) having a simpler hydrophobic surface structure compared with crystals of Ch, which has a hydroxyl group. In the meantime, we have reported the monolayer formation of four species of BAs [cholic acid (CA), β-muricholic acid (β-MCA), CDC, and UDC] and of CA/ β-MCA and CDC/UDC mixtures.7 In the monolayer study,8 it was found that the mean molecular surface area and the attitude (the gradient of the plane of the steroidal skeleton) of the molecules floating on the water surface are dependent mainly on the magnitude of the hydrophilicity of the BAs, which follows the order β-MCA < UDC < CDC < CA, and inversely, the (5) Igimi, H.; Carey, M. C. J. Lipid Res. 1980, 21, 72. (6) Sugihara, G.; Hirashima, T.; Lee, S.; Nagadome, S.; Takiguchi, H.; Sasaki, Y.; Igimi, H. Colloids Surf. B 1995, 5, 63. (7) Shibata, O.; Miyoshi, H.; Nagadome, N.; Sugihara, G.; Igimi, H. J. Colloid Interface Sci. 1991, 146, 594. (8) Miyoshi, H.; Nagadome, S.; Sugihara, G.; Kagimoto, H.; Ikawa, Y.; Igimi, H.; Shibata, O. J. Colloid Interface Sci. 1992, 149, 216.
10.1021/la990358c CCC: $19.00 © 2000 American Chemical Society Published on Web 12/07/1999
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Figure 1. Structural formulas of bile salts studied.
gradient decreases in the order β-MCA > UDC > CDC > CA. Furthermore various monolayer studies have been performed on mixed systems of different conjugated bile acids (glyco- and tauro-chenodeoxycholic acids, GCDC and TCDC; glyco- and tauro-ursodeoxycholic acids, GUDC and TUDC),9 and mixed systems of Ch with deoxycholic acid (DC)10 and Ch with above conjugated BAs11 on the substrate of 5 M aqueous NaCl solution at pH 1.2 and 25 °C. Based on the above monolayer studies as well as the adsorption studies of BSs-Ch crystals6 and BSs-graphite (Gr) systems,12 our adsorption study has been extended to the systems of four BSs-activated carbon (AC),13 in addition to a temperature study on the adsorption behavior of the above four BS species onto Gr in water.14 The amounts of adsorbed BSs were estimated by measuring the BS concentration in bulk solution (tetraborate(9) Sugihara, G.; Yamato, Y.; Yamamoto, S. K.; Lee, S.; Sasaki, Y.; Nagadome, S.; Shibata, O. Colloids Surf. B 1996, 6, 91. (10) Yamamoto, S. K.; Shibata, O.; Sakai, M.; Sasaki, Y.; Lee, S.; Sugihara, G. Colloids Surf. B 1995, 5, 249. (11) Sugihara, G.; Yamamoto, S. K.; Nagadome, S.; Lee, S.; Sasaki, Y.; Shibata, O.; Igimi, H. Colloids Surf. B 1996, 6, 81. (12) Sasaki, Y.; Igura, T.; Miyasu, Y.-I.; Lee, S.; Nagadome, S.; Takiguchi, H.; Sugihara, G. Colloids Surf. B 1995, 5, 241. (13) Sasaki, Y.; Miyasu, Y.-I.; Lee, S.; Nagadome, S.; Igimi, H.; Sugihara, G. Colloids Surf. B 1996, 7, 181. (14) (a) Sasaki, Y.; Nagata, H. D.; Fujii, Y.-K.; Lee, S.; Nagadome, S.; Sugihara, G. Colloids Surf. B 1997, 8, 81. (b) Sugihara, G.; Sasaki, Y. In Current Topics in Colloid & Interface Science; Reserch Trends: Trivantrum, 1997; Vol. 1, pp 31-50.
carbonate buffer at pH 10; ionic strength 0.15; temperature 37 °C except for the case of the thermodynamic study14) at equilibrium by using the same method as in a previous solubilization study.15 In a previous study on the BSs-Gr system, all the isotherms obtained for Na salts of C, UDC, DC, and CDC enabled us to construct both the Langmuir and the BET (Brunauer-Emmett-Teller) plots, and calculate that the maximum amount of monolayer adsorption, Nm, was found to decrease in the order DC > CDC > C > UDC.12 This resultant order was different from that found in these BSs’ adsorption onto Ch crystals (DC > CDC > UDC > C). In the previous temperature study on BSs-Gr system,14 however, there remained a problem, that is, whether the constant determined from the Langmuir isotherm, i.e., the ratio of rate constants of adsorption and desorption (ka and kd, respectively) may be used for thermodynamic analysis or not. In other words, whether the constant (we call this the Langmuir constant, and express it as KL in this paper) can be regarded as a thermodynamic equilibrium constant. In this paper, on the basis of collections of adsorption data determined more accurately at different temperatures, a thermodynamic examination has been made especially on the temperature dependence of the Langmuir constants for various BSs including taurine and glycine (15) Nagadome, S.; Miyoshi, H.; Sugihara, G.; Kagimoto, H.; Ikawa, Y.; Igimi, H. J. Jpn. Oil Chem. Soc. (Yukagaku) 1992, 41, 376.
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conjugates of deoxycholate. As for the analysis of Langmuir adsorption, a new treatment of the measured data will be proposed. 2. Experimental Section Materials. We used sodium salts of four free and two conjugate BA salts in this study: sodium deoxycholate (NaDC), sodium ursodeoxycholate (NaCDC), sodium cholate (NaC), sodium taurodeoxycholate (NaTDC), and sodium glycodeoxycholate (NaGDC) (Figure 1). All these salts, which were obtained from CalbiochemNovabiochem, San Diego, CA, were used without further purification except for NaDC. The purification of NaDC was performed by means of repeated recrystallization from hot ethanol. Graphite (Nacalai Tesque, Japan, Lot M3A8672), was used as received. All other inorganic chemicals (purchased from Nacalai Tesque, Kyoto, Japan) were of analytical grade. Thrice distilled water was used throughout the present studies. Enzabile‚ 2 was obtained from Daiichi Pure Chemicals Co., Japan. Method. The BS was dissolved in tetraborate carbonate buffer solution (0.05 M Na2B4O7 + 0.05 M Na2CO3) at pH 10 in the concentration range below the CMC and the solutions were placed together with a fixed amount of Gr (0.100 or 0.200 g) in test tubes fitted with ground glass stoppers. The stoppered test tubes were sealed hermetically with Parafilm. The tubes were shaken for 24 h at 150 min-1 at constant temperatures: 20 or 25, 30, 37, and 42 °C. The incubated solutions were first centrifuged for 20 min at 3000 rpm, and the supernatant solutions were then used for the assay at room temperature, ca. 25 °C. From a concentration analysis of the BSs, we determined the amount of adsorbed BSs on Gr powders; the concentration of BSs at adsorption equilibrium was assayed by an enzymatic method.16,17 For the assay, Enzabile‚ 2 was used. Measurements were carried out with use of a Jasco Unidec-320 spectrophotometer. For the determination of the surface area of the adsorbent, we used the iodine method.18 That is, from the Langmuir plot of the iodine adsorption, the surface of Gr used for the present study was determined as 12.9 m2g-1, showing a good linearity with a regression of 0.999 at 30 °C.
3. Results In the previous adsorption study of BSs on Gr, the Langmuir adsorption equation or its plot was confirmed to be applicable for the present four bile salts as well as the Brunauer-Emmett-Teller (BET) adsorption or the BET plot.19 Similarly, the adsorption isotherms were obtained for NaTDC and NaGDC at different temperatures, as are shown in Figure 2. In the plot of adsorbed amount N (mol per gram of adsorbent) against equilibrium concentration of adsorbate CB (mmol‚dm-3), the curves at some temperatures demonstrate a further increasing trend which resembles that of BET adsorption, similar to the previous adsorption study.12 It is not yet known if the so-called admicellization or hemimicelle formation takes place or not. And anyway, whether such a further increase appears or not is likely to depend on the species as well as the temperature. In this study, we focus on the adsorption at the lower concentration range, that is, the monolayer adsorption or the Langmuir adsorption. So the measured points at the lower concentration range were obtained in greater numbers and more precisely and accurately than in the previous works. Meanwhile, as for the Langmuir plot, it was found to have a trend of good linearity with a high regression (even if measured values involved some minor errors), but simultaneously to result in inaccurate values of the Langmuir constant and the amount of maximum adsorp(16) Mashige, F.; Yamanaka, M. Jpn. J. Clin. Chem. 1979, 8, 191. (17) Mashige, F.; Tanaka, N.; Maki, A.; Kanei, S.; Yamanaka, M. Clin. Chem. 1981, 27, 1352. (18) Kondou, S.; Ishikawa, T.; Abe, I. In Kyuchaku no Kagaku; Maruzen: Tokyo, (in Japanese) 1991. (19) Moor, W. J. In Basic Physical Chemistry; Prentice-Hall: Englewood Cliffs, NJ, 1983.
Figure 2. Examples of the adsorption isotherms obtained for NaGDC and NaTDC onto graphite in tetraborate-carbonate buffer solution at pH 10 at different temperatures.
tion. Therefore, needless to say, the more reliable result requires more accurately measured points. The respective measured points in Figure 2 were determined by at least three measurements. Here, the Langmuir adsorption isotherm is well-known to be expressed as the following equation
CB CB 1 ) + N KLNm Nm
(1)
where Nm is the amount of maximum monolayer adsorption and KL is the ratio of the rate constants of adsorption (ka) and desorption (kd), being expressed as KL ) ka/kd.18,19 Equation 1 implies that the slope and the intercept of a linear relation between CB/N and CB can simultaneously let us determine Nm and KL; this is known as the Langmuir plot.19 Examples of the Langmuir plot are given for NaDC, NaGDC, and NaTDC in the frames of the top, middle, and bottom of Figure 3, respectively, in which the regression value (R) is indicated for each system. All the Langmuir plots for different BSs at the respective discrete temperatures gave Nm and KL values with a high regression of at least 0.999. The results are tabulated in Table 1. The Nm values determined clearly indicate the species dependency but little change with temperature for each BS, so that the values may be averaged for each species. Interestingly, both of the weaker adsorbates, NaC and NaUDC, have smaller values ranging around 7.9 × 10-6 mol‚g-1, while the stronger adsorbates, various deoxycholates, have larger values ranging around 1.0 × 10-5 mol‚g-1. The KL values show a systematic decrease with temperature for the respective BSs. 4. Discussion To treat thermodynamically the data of temperature dependent Langmuir constants, let us first consider the Langmuir adsorption relation at kinetic equilibrium. The
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adsorption sites are occupied by adsorbate molecules, the Clausius-Clapeyron plot should give the thermodynamic quantity of the heat of desorption. Note that eqs 4 and 5 suggest that the enthalpy change on adsorption can be estimated from the slope in a van’t Hoff plot of the Langmuir constants.
[
∂ ln KL ∂(1/T)
]
)
p
[
]
∂ ln CB* -∆HQad )R ∂(1/T)
(5′)
p
That is, eqs 5 and 5′ are basically the same except for the sign (lnKL is for adsorption and -lnKL ) lnCB* is for desorption). In this sense, the Clausius-Clapeyron plot is essentially the same as the van’t Hoff plot. Next, turning our viewpoint to a thermodynamic interpretation, the chemical potential (µA) of an adsorbate per area given for its one mole at solid-water interface may be assumed as
µA ) µQA + RT ln θ
(6)
where µQA is the standard chemical potential, when the coverage is completed. In the bulk solution the chemical potential of the adsorbate is considered to be expressed as Figure 3. The Langmuir plots of three bile salts adsorbed onto graphite in tetraborate-carbonate buffer solution at pH 10 and 30 °C.
relation is derived from eq 1 as
kaCB(1-θ)Nm h kdθNm or kaCB(1-θ) ) kdθ
(2)
where the coverage θ is defined as θ ) N/Nm. The former relation refers to the event of adsorption-desorption taking place per gram of adsorbent (or per a given surface area). At adsorption equilibrium, eq 2 leads to the following relation
ka θ 1 KL ≡ ) kd 1 - θ CB
(
)
(3)
(4)
Equation 4 tells us that the Langmuir constant has a dimension of the inverse of concentration and thus KL-1 can be defined as the half coverage concentration CB*. (Note that the KL value itself depends on the units employed for concentration). If this half coverage is employed as a reference common to the systems concerned, and the characteristic concentration CB* is determined, (KL-1 is determinable from the Langmuir plot) as a function of temperature, a variant of the Clausius-Clapeyron equation enables us to evaluate the heat of desorption (∆Hdes) as follows
d ln CB* d(1/T)
)-
∆Hdes R
(7)
where µQB is taken as the standard chemical potential assuming θ ) 0 and CB ) 1 mol dm-3. In this relation, the factor of (1 - θ) may be regarded as a kind of activity coefficient in the case where an adsorbent solid coexists, meaning that the chemical potential of the adsorbate depends on its bulk concentration and the coverage of solid surface as well. The molar Gibbs energy change ∆G h ad on adsorption is given as the difference between µA and µB.
∆G h ad ) µA - µB ) (µQA - µQB) + RT ln θ -
Especially at one-half of coverage (θ ) 1/2), an important relation is obtained as
KL ) 1/CB* C*B ) 1/KL
µB ) µQB + RT ln CB(1 - θ)
(5)
where R denotes the molar gas constant and T the Kelvin temperature. As long as a standardized reference is regarded as the bulk concentration of a given adsorbate at equilibrium with a solid surface on which 50% of the total number of
RT ln CB(1 - θ) ) ∆GQad + RT ln θ/(1 - θ)CB Here, we have the following relations, since ∆G h ad is taken as zero at equilibrium.
∆GQad ) µQA - µQB ) -RT ln Kad ) RT ln CB[(1 - θ)/θ] (8) where Kad is the equilibrium constant of adsorption. Then, recalling θ ) N/Nm, the standard Gibbs energy change ∆GQ is expressed as
(
∆GQad ) RT ln CB
Nm -1 N
)
(9)
Equation 9 tells us that the term CB (Nm/N - 1) should be constant irrespective of changes in CB or N, because ∆ GQad is a constant at a constant temperature and pressure. It is noted again that ∆G h ad corresponds to the molar Gibbs energy change from the state that one mole of adsorbate at 1 mol dm-3 in concentration to the state of complete monolayer coverage (θ ) 1) on a surface area needed for occupation by one mole of adsorbate. In addition when N is Nm/2 or a half of coverage, the logarithmic term in eq 9 becomes equal to ln CB*. Therefore, we obtain the relation
Kad ) KL )
(
)
N 1 1 ‚ ) CB Nm - N CB*
(10)
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Table 1. Maximum Amount of Monolayer Adsorption (Nm/10-6 mol g-1), the Langmuir Constant (KL/dm3 mol-1 × 103), the Thermodynamical Constant of Adsorption Equilibrium (Kad/dm3 mol-1 × 103), the Half Coverage Concentration (CB*/ mmol dm-3), and the Mean Value of CB(Nm/N - 1)/mmol dm-3 a T/°C
Nm/10-6 mol‚g-1
KL/dm3 mol-1‚103
Kad/dm3 mol-1‚103
CB*/10-2‚mmol dm-3
CB(Nm/N - 1)/10-2‚mmol dm-3
NaDC
25 30 37
9.89 9.84 9.56
69.8 63.4 57.9
70.3 67.4 57.5
1.43 1.58 1.73
1.42 1.48 1.74
NaCDC
25 30 37
54.7 45.3 41.6
50.3 44.6 38.4
1.83 2.21 2.40
1.99 2.24 2.60
NaUDC
25 30 37 42
7.87 7.67 7.68 7.80
55.8 48.2 45.1 40.0
50.8 48.0 43.4 40.8
1.79 2.07 2.22 2.50
1.97 2.08 2.30 2.45
NaC
25 30 37 42
7.61 7.87 7.60 8.11
33.0 28.5 26.5 24.3
30.3 27.3 25.8 22.5
3.03 3.51 3.78 4.12
3.30 3.67 3.88 4.45
NaTDC
20 25 30 37 42
30.2 28.8 27.1 23.3 21.7
30.6 28.7 26.8 23.3 21.3
3.31 3.47 3.69 4.29 4.61
3.27 3.52 3.73 4.29 4.69
NaGDC
20 25 30 37
61.5 57.6 48.9 42.7
57.2 48.6 47.2 41.2
1.63 1.74 2.05 2.34
1.75 2.06 2.12 2.43
species
10.2 10.5 11.2
10.7 10.8 10.3 10.4 10.6 9.72 9.93 9.99 9.94
a All the data were determined for aqueous Na salts of bile acids at pH 10, meaning that the table does not include data for bile acids at lower pH values.
This means that the Langmuir constant may be regarded as a thermodynamic equilibrium constant. In fact, the Langmuir constant (Moore has called this the adsorption coefficient19) has been shown to be employed for estimates of the adsorption heat.20,21 The meanings of the Langmuir constant are described in detail based on statistical mechanics;22-24 however, consideration based on statistical mechanics is at present given up for conciseness. To evaluate confidence of our data used for determining the Langmuir constant (or CB*), the constancy of CB (Nm/N - 1) term was examined for each BS by plotting it against CB. The examples are shown for NaGDC at discrete temperatures in Figure 4 and for different BAs (at 25 °C) in Figure 5, respectively; a good constancy is seen over a wide concentration range for almost all the systems. The horizontal line in each frame indicates the mean value corresponding to 1/Kad. The mean value itself and a calculated Kad value are listed for each system in Table 1. In this table, C* values calculated from the Langmuir constants are included for comparison with CB (Nm/N 1) values. These show a good coincidence with each other, and furthermore, a good but not perfect agreement is also seen between KL and Kad for the respective systems. Looking at the temperature dependence in KL and Kad, generally they show a decreasing trend with raised temperature, suggesting that the adsorption is an exothermic process. When the enthalpy changes on adsorption are estimated from the van’t Hoff plots or Clausius-Clapeyron plots, the slight disagreement results in different values. This (20) Atkins, P. W. In Physical Chemistry, 3rd ed.; Oxford Univ. Press: Oxford, U.K., 1986. (21) Tsubomura, H. In Shin-Butsuri Kagaku (Physical Chemistry); Kagakudojin: Kyoto, 1994. (22) Vold, R. D.; Vold, M. J. In Colloid and Interface Chemistry; Addison-Wesley Publishing Co.: London, 1983. (23) Hunter, R. J. In Foundations of Colloid Science; Clarendon Press: Oxford, U.K., 1986. (24) Hiementz, P. C. In Principles of Colloid and Surface Chemistry; Marcel Dekker: New York, 1977.
difference is within the error for the present experiment. Trials of the van’t Hoff plots of KL and Kad were made for the respective BSs; some samples are shown in Figure 6 and Figure 7, respectively. The enthalpy changes determined from both plots are listed in Table 2. According to eq 9, the Gibbs energy changes ∆GQad were calculated and then the entropy changes, (∆SQ) were also calculated from the relation ∆SQad ) (∆GQad - ∆HadQ)/T. It is noted that when ∆GQad is calculated according to eq 9, the value of concentration must be molarity (mol‚dm-3), because the standard chemical potential is taken at C ) 1 mol‚dm-3. All the thermodynamic parameters are tabulated in Table 2. The values with no parenthesis are those estimated from the Langmuir constants determined from the Langmuir plot. In regard to ∆GQ, interestingly, its dependency on temperature is almost negligible, and the species dependence of is also so small that it does not allow us to compare them by relating to the species difference in hydrophobic-hydrophilic balance. Comparing ∆HQ values determined from KL and Kad, they are in poor agreement with each other except for NaDC and NaCDC, in particular, 20% and 40% of differences are found for NaGDC and NaUDC, respectively (see Table 2). As mentioned above, the values determined from Kad are more trustworthy compared with those from KL. Hereafter, we assume that values are -13 (NaDC), -17 (NaCDC), -10 (NaUDC), -13 (NaC), -13 (NaTDC), and -13 (NaGDC) kJ mol-1. It is noted that the absolute value ∆HQ of is the largest for NaCDC and the lowest for NaUDC while that for NaC is comparable with NaDC and NaTDC. The highest value of NaCDC seems to reflect the highest geometrical hydrophobic index (HI) offered by Miyajima et al.25 NaUDC, one of the weaker adsorbates, exhibits the smallest ∆HQad; this probably comes from its having the lowest hydrophobicity. In fact, its geometrical HI25 and (25) Miyajima, K.; Machida, K.; Taga. T.; Komatsu, H.; Nakagaki, M. J. Chem. Soc., Faraday Trans. 1988, 184, 2537.
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a
b
c
d
Figure 4. The constancy of CB(Nm/N - 1) term or its independence from the change in bulk concentration (denoted as “Equilibrium concentration” in the figures) CB, observed for NaGDC adsorption at different temperatures.
the empirical HI (by Heuman26) is the lowest among the species examined. On the other hand, NaC, one of the weaker adsorbates, has a comparatively high ∆HQad value; this may be ascribed to NaC’s wide limiting surface area (A0) determined from a monolayer study,7,8 in which A0 in nm2 has been reported as 1.49 for NaC and as 1.23 for NaUDC. The A0 value of NaC is much larger than NaDC (A0 ) 1.18 nm2). Therefore, compared with NaCDC’s ∆HQad the lower value for NaDC, which is almost the same as NaC, may be interpreted by the narrower contacting area. (The present authors have considered that the substantially contacting surface area with hydrophobic surfaces is almost the same as A0.12-15) With respect to the accuracy of the present study, the authors acknowledge the necessity of discussion. We have previously reported that the ∆HQad values determined from the van’t Hoff plot are 15 ( 2 kJ mol-1 for NaDC, 20 ( 2 kJ mol-1 for NaCDC, 17 ( 3 kJ mol-1 for NaC, and 9 ( 3 kJ mol-1 for NaUDC, and described that the Langmuir plot was easily affected by a small experimental error at each measured point in the dilute concentration region or by the number of measured points. This is because the KL value itself inherently contains a large error and accordingly the adsorption heat value estimated from the van’t Hoff plot is obliged to have a large error margin. In any case, the adsorption heat ranges from -10 to -20 kJ mol-1 corresponding to hydrophobic interaction18 and it can be considered that the species dependency of the value reflects the respective substantial area of hydrophobic surface of the β-side of the bile salt molecules. Here, we have noteworthy references: one is a study using immobilized artificial membrane (IAM) chroma(26) D. M. Heuman. J. Lipid Res. 1989, 30, 719.
tography27 and the other is a study using flow adsorption microcalorimetry (FAMC).28 To predict bile salt-membrane interactions physiologically, Cohen and Leonard used an IAM-HPLC column that contained dimyristoyl-phosphatidylcholine molecules covalently linked to a silica microsphere. From the van’t Hoff plots, demonstrating the influence of temperature on IAM-HPLC capacity factors for various bile salts species, they determined interaction enthalpies ranging from -2.86 kcal mol-1 (12.0 kJ mol-1) to -7.67 kcal mol-1 (32.1 kJ mol-1). In addition, they reported that interaction enthalpies were substantially better correlated than HI by octadecylsilane-HPLC (Heuman’s empirical HI26) with equilibrium binding to small unilamellar vesicles, but not with bile salt functions that do not require phospholipids (e.g., micellar cholesterol solubilization).27 The objective and systems of the present study are different from those of the literature,27 so naturally, the stories are not in accordance with each other, but it should be noted that the IAM-HPLC study resulted in an accuracy of three significant figures (our study’s enthalpy values are restricted to only two significant figures). In the FAMC studies Groszek and Partyka have reported not only the surface areas of hydrophilic and hydrophobic sites in carbons and zeolites but also the integral heats of 1-butanol adsorption (for example) on solids in its aqueous solutions.28 This method may enable us to measure the adsorption heats of BSs bound onto graphite to reveal more clearly the species dependence than the method of the present study, but it should be noted that FAMC might not measure the real equilibrium (27) Cohen, D. E.; Leonard, M. R. J. Lipid Res. 1995, 36, 2251. (28) Groszek, A. J.; Partyka, S. Langmuir 1993, 9, 2721.
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a
b
c
d
e
Figure 5. The plot of CB vs CB(Nm/N - 1) for the respective bile salts at 25 °C; all the systems indicate a constancy.
enthalpy because the systems examined are of a dynamic process. If an FAMC study is performed, it may show a similar increasing order in line with the empirical HI. It is considered that an attempt of FAMC will lead to new information. In the present study, we found in relation to Nm that, first, Nm is more accurately determinable, compared with KL, with a good reproducibility and with more than three nines of regression, but a slight error in Nm affects KL greatly, due to a very small intercept (1/Nm KL), and second, when the temperature dependence of Nm is marked (or Nm is very different from each other at different temperatures) the data should be regarded as being poor in accuracy. Recently, we have examined the adsorption behaviors of a few proteins onto hydroxyapatite in water, in which we found that in order to determine the constant KL ) ka/kd the Scatchard plot can give us more reliable
values than the Langmuir plot (for Nm determination the Langmuir plot is more favorable than the Scatchard one) and also found that a KL value differs by 10% at most between both plots. Averaging KL and Nm values obtained from both plots are likely to produce in more reliable data (Nagadome et al. Unpublished data). The reliability of KL data can be confirmed by checking whether the calculation of CB (Nm/N - 1) shows a good agreement with CB* or not. In addition, the confidence level for all the data can be examined by the extent of constancy in the relation of CB (Nm/N - 1) with CB as mentioned above. In this sense, our data for NaUDC is the lowest in reliability among the bile salts studied. The Gibbs energy change estimated from Kad will be more reliable than that from KL, but, anyway, the calculated entropy value may involve somewhat large error in parallel with the error of the enthalpy. Here, noting
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Langmuir, Vol. 16, No. 4, 2000
Sugihara et al. Table 2. Thermodynamic Parameters Determined from KL (and Those in Parentheses Determined from Kad) of Bile Salts Adsorption onto Graphite Surface species NaDC NaCDC NaUDC
NaC
NaTDC
Figure 6. The van’t Hoff plots of the Langmuir constants (KL) for the respective bile salts in the adsorption onto graphite powder surfaces in aqueous buffer solution at pH 10.
Figure 7. The van’t Hoff plots of the adsorption constants (Kad) for the respective bile salts; from the slope the adsorption heats are determinable.
comments by Atkins, the value of KL can be used to obtain a value of ∆GQad, and then, that value can be combined with ∆HQad to obtain an entropy of adsorption ∆SQad, however, that raises some tricky features of interpretation.20 Irrespective of the problem with entropy pointed out here, the relation between ∆SQad and ∆HQad was examined for BSs by plotting ∆SQad against ∆HQad at all the temperatures studied. The result is given in Figure 8, showing the so-called entropy-enthalpy compensation phenomenon. The compensation temperature (the reciprocal of the slope) was calculated as 304 K with a regression of 0.953. The compensation phenomena have been observed for those of micelle formation of various surfactants in water 29-32 and for the different behaviors shown by biological substances.33 Figure 8 tells us that the energy (enthalpy) term is dominant compared to the entropy term in the adsorption process of BSs onto Gr surface, and shows (29) (a) Kresheck, G. C.; Hargraves, W. A. J. Colloid Interface Sci. 1974, 48, 481. (b) Kresheck, G. C. In Water, a Comprehensive Treatise; Franks, F., Ed.; Plenum Press: New York, 1975; pp 95-167.
NaGDC
T/°C
∆H/kJ mol-1
∆G/kJ mol-1
∆S/J K-1 mol-1
25 30 37 25 30 37 25 30 37 42 25 30 37 42 20 25 30 37 42 20 25 30 37
-13.3 (-13.1)
-27.6 (-27.7) -27.9 (-28.0) -28.3 (-28.3) -27.0 (-26.8) -27.0 (-27.0) -27.4 (-27.2) -27.1 (-26.9) -27.2 (-27.2) -27.6 (-27.5) -27.8 (-27.8) -25.8 (-25.6) -25.9 (-25.7) -26.3 (-26.2) -26.5 (-26.3) -25.1 (-25.2) -25.5 (-25.4) -25.7 (-25.7) -25.9 (-25.9) -26.2 (-26.1) -26.9 (-26.7) -27.2 (-26.7) -27.2 (-27.1) -27.5 (-27.4)
48.1 (48.9) 48.1 (49.2) 48.3 (48.9) 33.3 (32.0) 32.7 (31.9) 33.3 (32.0) 43.2 (55.9) 42.8 (56.0) 43.3 (55.9) 43.0 (55.9) 41.9 (43.2) 41.4 (43.0) 41.8 (43.5) 41.8 (43.0) 39.7 (42.2) 40.1 (42.4) 40.3 (42.5) 40.1 (42.3) 40.2 (42.2) 33.7 (44.3) 34.1 (43.8) 33.7 (44.3) 33.8 (44.2)
-17.1 (-17.3) -14.2 (-10.2) -13.3 (-12.7) -13.5 (-12.8)
-17.0 (-13.7)
Figure 8. The enthalpy-entropy compensation phenomenon observed in the adsorption of bile salts onto graphite in aqueous buffer solution at pH 10. The compensation temperature (the reciprocal of the slope of straight line) Tc and the regression value R are indicated in the figure. The diameter of the closed circle for each bile salt involves the data values at different temperatures.
that a great contrast is found between NaCDC and NaUDC reflecting the difference in the orientation of hydroxyl group at position 7 of the steroid skeleton. Considering that the Gr is composed of carbon atoms and has a simple hydrophobic surface, Gr is the most favorable adsorbent to study the hydrophobic interaction of BSs. Hydrophobic bonding is a force involved in the adsorption of BSs to the carbon in aqueous solution. Water molecules form a cluster around the hydrophobic areas of BS molecules, the so-called iceberg structure; the system becomes energetically unstable due to the decreased (30) (a) Oda, H.; Nagadome, S.; Lee, S.; Ohseto, F.; Sasaki, Y.; Sugihara, G. J. Surf. Sci. Technol. 1998, 14, 1. (b) Nakamura, A. A.; Hisatomi, M.; Sugihara, G.; Fujiwara, M.; Okano, T. J. Surf. Sci. Technol. 1998, 14, 23. (c) Araki, Y.-I.; Hisatomi, M.; Lee, S.; Sugihara, G. J. Jpn. Oil Chem, Soc. 1999, 48, 307. (31) Chen, L.-J.; Lin S-Y.; Huang, C.-C.; J. Phys. Chem. B 1998, 102, 4350. (32) Sugihara, G.; Hisatomi, M. J. Colloid Interface Sci. 1999, 219, 31. (33) Lumry, R.; Rajener, S. Biopolymers 1970, 9, 1125.
Thermodynamics of Langmuir Adsorption of Bile Salts
entropy resulting in an increase of free energy. However, if the water cluster separates from the hydrophobic region, i.e. if the hydrophobic surface of BS contacts directly with (adsorbs onto) the carbon surface, the iceberg structure disappears and the total system becomes more stable due to the increase of entropy.34-36 In regard to BSs adsorption onto Gr, however, this effect seems rather small. In contrast, it may be considered that the dispersion force in the van der Waals force plays an important role. This dispersion effect correlates inversely with the sixth power of the distance between the two molecules. Therefore, in the case where this affinity exerts its maximum effect, the Gr and BSs should be very close together and adhere to each other over as wide an area as possible.37 In conclusion, the adsorption heat ranges from10 to 20 kJ mol-1 corresponding to hydrophobic interaction18 and (34) Abe, I.; Hayashi, K.; Kitagawa, M. J. Jpn. Oil Chem, Soc. (Yukagaku) 1976, 25, 145. (35) Frank, H. S.; Evans, M. W. J. Chem. Phys. 1959, 13, 507. (36) Kauzmann, W. Adv. Protein Chem. 1959, 14, 1.
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the Gibbs energy change ranges from - 25 to - 28 kJ mol-1 on keeping a compensation relation between ∆HQad and ∆SQad. And it can be considered that the species dependency of the value reflects the respective substantial area of hydrophobic surface of the β-side of the bile salt molecules. Acknowledgment. This work was in part supported by grants from the Ministry of Education, Culture and Science of Japan (Grant in Aid for Scientific Research, C-07680729 and that on Priority Areas 09261240), the Central Institute of Fukuoka University and Shionogi Co. Ltd., Osaka, and Tokyo Tanabe Co. Ltd., Tokyo. The authors are grateful to Mr. Y. Fujii for his technical contribution. LA990358C (37) Abe, I.; Hayashi, K.; Kitagawa, M.; J. Jpn. Oil Chem. Soc. (Yukagaku) 1977, 26, 355.
