Anal. Chem. 1995,67, 2119-2128
Thermodynamics of Solute Partitioning into Immobilized Artificial Membranes Shaowei Ong and Charles Pidgeon* Department of Medicinal Chemistty, school of Phatmacy, Purdue Universiiy, West Lafayeite, Indiana 47907
The solute retention mechanism on immobilized artificial membranes (IAMs) was studied using three Merent IAM.PC phases. IAMs were prepared by immobilizing either single-chain or double-chain phosphatidylcholine (PC) ligands. Solute affinity for the single-chainIAM.PC columns (with a ligand density of 127 pmol of PC/g of IAM)was 3-fold lower compared to solute affinity on the double-chainIAM.PC column (with a ligand density of 98 pmol of PC/g of IAM). "his suggests that the solute retention on IAMs is dominated by a solute partitioning mechanism. Temperature-dependentstudies indicated that the thermodynamics of solute partitioning is similar on both the single-chain and double-chain IAM.PC surfaces. For a set of phenol derivatives,the partitioning into IAM.PC surfaces is both enthalpy and entropy driven. For p-blockers, the partitioning into IAM.PC surfaces is entropy driven. The free energy of solute partitioning into IAMs correlates very well with the free energy of solute partitioning into liposomes. Immobilized artificial membrane ( M A ) chromatography surfaces have been used in a variety of chemical and biological applications.'-'Z One of the most promising applications of IAM surfaces resides in their ability to predict drug permeability through membranes and drug absorption in tissues and animals.3~~ In addition, a recent report demonstrated that IAMs can predict pharmacokinetic parameters including drug binding to proteins,13 which was unexpected because IAMs emulate lipid surfaces not protein surfaces. Nevertheless, these applications of IAMs involve (1) Pidgeon, C. US. Patent 4,931,498,1990. (2)Pidgeon, C.; Stevens, J.; Otto, S.; Jefcoate, C.; Marcus, C. Anal. Biochem. 1991, 194,163-173. (3)Ong, S.; Liu, H.; Qiu, X; Bhat, G.; Pidgeon, C. Anal. Chem. 1995.67,755762. (4)Pidgeon, C. US. Patent 4,927,879,1990. (5)Pidgeon, C.; Ong, S.; Liu, H.; Qiu, X; Pidgeon, M.; Dantzig, A H.; Munroe, J.; Homback, W. J.; Kasher, J. S.; Glunz, L.; Szczerba, T.J. Med. Chem. 1995,38,590-594. (6)Ong, S.;Cai, S. J.; Bemal, C.; Rhee, D.; Qiu, X.;Pidgeon, C. Anal. Chem. 1994,66,782-792. (7)Qiu, X.;Ong, S.; Bemal, C.; Wee, D.; Pidgeon, C.J. Og.Chem. 1994,59, 537-543. (8) Rhee, D.; R, M.; Chae, W. G.; Qiu, X.; Pidgeon, C.Ana1. Chim. Acta 1994, 297,377-386. (9)Thumhofer, H.; Schnabel, J.; Betz, M.; Lipka, G.; Pidgeon, C.; Hauser, H. Eiochim. Eiophys. Acta 1991,1064, 275-286. (10)Cohen, D. E.;Leonard, M. R; Leonard, A N.; Donovan; Carrey, M. C. Gnstroenterology 1993,104,A889. (11) Pidgeon, C.; Cai, S.; Bemal, C., submitted for publication in/. Chromatogr., A. (12) Pidgeon, C.; Venkatarum, U. V. Anal. Biochem. 1989, 176,36-47. (13) Kaliszan, R;Nasal, A; Bucinski, A Eur. 1.Med. Chem. 1994,29,163170. 0003-2700/95/0367-2119$9.00/0 0 1995 American Chemical Society
the chromatography of small drug molecules on IAM highperformance liquid chromatography surfaces. Elucidating the molecular reasons responsible for IAM predictions of drug transport and drug partitioning requires that the mechanism of solute retention on IAMs be understood from a fundamental perspective. Solute retention on IAMs and all other chromatographic surfaces is facilitated by understanding the temperaturedependent solute retention of the capacity factor, k'w, that is calculated according to
k;m= (t, - t J / t o
(1)
where tois the retention time for an unretained compound and tr is the retention time of solute. During the chromatographic process, there is an equilibrium between the solute in the mobile phase and solute in the stationary phase; for IAM surfaces, this equilibrium constant or distribution constant is denoted as Kw. The k h capacity factor is proportional to the KW partition coefficient,
where $I = V,/V,, V, is the stationary phase volume, and V , is the mobile phase volume in the column. In eq 2, CIA, is the molar solute concentration in the IAM interphase and CM is the molar solute concentration in the mobile phase. Equation 2 defines the relationship between the chromatographically measured kiAM value to the biologically relevant immobilized artificial membrane equilibrium constant Kw. The key concept is that when solute retention is dominated by a partitioning mechanism, the distribution constant K w is called the IAM partition coefficient. The Gibbs free energy of transfer, AGO, of solute transfer from the mobile phase to the stationary phase is related to KW as follows:'4 AGO = -RT In K
m
(3)
where R is the gas constant and T is temperature. Equation 4 shows how the temperature dependence of a solute's capacity factor k ' can ~ be used to obtain thermodyamic quantities
AS0 I n k $ , = - - AH0 -+In$
(4) R where AHo is the partial molar enthalpy change for the transfer of the solute from the mobile phase to the stationary phase and A 9 is the associated change in entropy. If AHo and ASo are independent of temperature, a linear plot of In k' vs 1/T (the van't Hoff plot) is obtained, the slope equals AHo, and the intercept
RT
(14)See, for example: Edsall, J. T.; Gutfreund, H. Eiothermodynamics: me Study ofEiochemica1 Processes at Equilibrium; Wiley: New York, 1983.
Analytical Chemistry, Vol. 67, No. 73,July 1, 1995 2119
Chart 1. Structures of Three Different IAM.PC Bonded Phases'
Double Chain IAM.PC
Single Chain IAM.PC
Ether linkage
f
f
+
-0. / o
i'""'" oyo-P*,
/
0,
/Ester
ilnkago
c=o
a
The double-chain IAM.PC has a nonbonded, conformationally free hydrocarbon chain.
equals the sum of ASo/R plus a constant that depends on the phase ratio (ln 4). These thermodynamic constants (AHo,ASO) are useful in assessing the thermodynamic driving force responsible for solute retention. Our goal is to obtain thermodynamic parameters to elucidate solute retention on JAM surfaces. The intent is to understand why IAM surfaces are more accurate than all existing experimental models in predicting drug membrane partitioning. The effect of the lipid structure on the thermodynamics of solute partitioning was studied. Differences in lipid structure are shown in Chart 1. One of the major factors influencing solute retention is the number of alkyl/acyl chains on the immobilized phospholipid ligands shown in Chart 1. The IAM bonded phases were (i) a single-chain ether PC ligand (e*erIAM.PCC10/C3), (ii) a single-chain PC ligand that lacks a glycerol backbone (6WM.PCC1O/C3), and (iii) a diacylated or doublechain PC ligand (esterIAM.PCC10/C3). Siglechain IAM.PC denotes either e*p?AM.PCC10/C3 or 6GIAM.PCC10/C3;doublechain IAM.PC denotes esterM.pCClO/C3. EXPERIMENTAL SECTION Chemicals. The following chemicals were purchased from Sigma: phenol, pcresol, pethylphenol, pn-propylphenol, pflorophenol, $-chlorophenol, pbromophenol, piodophenol, propranolol, alprenolol, oxprenolol, metoprolol, pindolol, nadolol, atenolol, and phosphatebuffered saline (FBS). pn-butylphenol was purchased from Lancaster. Synthesis of IAM.PC Bonded Phases. Detailed procedures for the synthesis of IAM.PC bonded phases have been described for the etherIAM.PCC10/C3 phase,* the 6GIAM.PCc10/c3 phase? and the esterIAM.PCC10/c3 phase.12 6GIAM.PCc10/c3 is currently com2120 Analytical Chemistfy, Vol. 67,No. 13, July 1, 1995
mercialized as an IAM.PC.DD column (Regis Chemical Co.). The ligand densities (in pmol/g of IAM;PC:ClOC3) are 127:2860 for etherIAM.PCC10/C3, 127:4836 for dGIAM.PCc10/c3, and 98:48.6:28 for esterIAM.PCC10/C3. The ligand densities (in mg/g of IAM; (PC:ClO:C3) are 59.7:3.92.5 for e*erIAM.PCC10/C3, 48.5:6.7:1.5 for 6GIAM.PCc10/c3, and 70.06.7:1.2 for eskrM.PCC10/C3. The bonded ligand densities on IAMs were measured as describede6 IAM Chromatography. IAM.PC chromatographicparticles suspended in acetone (10% w/v) were packed at Regis Chemical Co. AU IAM HPLC columns were 0.46 x 3 cm and contained a void volume V , of -0.415 mL. For water-soluble solutes, the injection volume was -10 pL of the solute solution (1pg/pL) in aqueous solsution. The two solutes piodophenol and p-n-butylphenol have low solubility in water and were dissolved in methanol; these compounds were injected in -10 pL of methanol and (1 pg/pL). The flow rate was 1mL/min for e*erIAM.PCC10/C3 6GIAM.PCClO/C3 columns and 3 mL/min for an esterIAM.PCC10/C3 column. High flow rates were needed for the esterIAM.PCC10/C3 column because the solute retention times are longer on a doublechain ester IAM.PC column compared to the single-chain IAM.PC columns. Solute detection was at 220 nm. The buffered aqueous mobile phase was 0.01 M PBS at pH 7.4 (which contains 0.027 M KCl and 0.137 M NaCl). Chromatograms were obtained as de~cribed.~ The volume of the stationary phase (Vd is assumed to be the the volume of sum of the volume of bonded PC ligands and the volume of bonded C3 groups bonded C10 groups The IAM interfacial thickness is unknown, and it is therefore difficult to accurately calculate Vs;approximations are thus made. To calculate Vs on M s , we used Cole's method of
(e3).
(el0)
(Ec),
Table 1. Chemical Structures of Phenol Derlvitlves and @-Blockers
Group 1
phenol
Structure Group 2
F-phenol
Et-phenol
C1-phenol
Br-phenol
Q
6
q C H 3
Pr-phenol
Bu-phenol
q C H 2 C &
qCbCH2CH3
I-phenol
6 6 6
sfructure
CI
F
Group 3
cresol
atenolol
pindolol
x
Br
nadolol
= -OCH,CHCI+NHCH(CH3)2 OH I
calculating V, on C18 columns.15 The volume of each individual bonded ligands was thus calculated as the weight of the ligand divided by ligand's density.
The density of the PC ligands bPc)is -1.01 g/mL.16 The density of hydrocarbons (eC1O, sc3>is -0.86 g/mL.17 A typical 0.46 x 3 cm IAM.PC column contains0.277 g of packing material. Based on the ligand densities, the calculated values of V, are 0.0189 mL for e*erIAM.PCC10/C3, 0.0144 mL for dGIAM.PCc10/c3, and 0.0220 mL for esterIAM.PCC10/C3, The dead volume (Vd in a 0.46 x 3 cm IAM.PC column is 0.415 mL, and approximate values of the phase ratio (4 = V,/Vd are 0.046 for e*erIAM.PCC10/C3, 0.035 for dGIAM.PCc10/c3, and 0.053 for esterIAM.PCC10/C3. The temperature dependence of solute retention on IAM columns was performed by placing the IAM column in a Rainin Eldex CH-150 temperature controller. Temperature was varied from 25 to 50 "C. The temperature was controlled to an accuracy of 0.1 "C, and the time allowed for temperature equilibration was always greater than 30 min. RESULTS AND DISCUSSION Sixteen solutes used in this study are shown in Table 1. Group 1 solutes are a homologous series of pakylphenols including phenol, pcresol, pethylphenol,pn-propylphenol, and p-n-butylphe nol; &e only structural difference is the hydrocarbon chain length. Group 2 solutes are a homologous set of p-halophenols including pflorophenol, #chlorophenol, p-bromophenol, and piodophenol; the only structural difference is a halogen atom. Group 3 solutes are a set of &blockers including atenolol, pindolol, nadolol, metoprolol, oxprenolol, alprenolol, and propranolol. Figure lA-C compares the retention k h values of these 16 solutes on three different IAM.PC columns at 298 K There is almost a perfect correlation (+ > 0.99) between kim values (15) Cole, L. A; Dorsey, J. G. Anal. Chem. 1992,64, 1317-1323. (16) Katz, Y.; Diamond, J. M. 1.Membr. Bid. 1974,17,69-86. (17) Cheng, W. Anal. Chem. 1985,57, 2409-2412. (18)Betageri, G. V.; Rogers, J. A Inf. J. Pharm. 1987,36,165-173.
I
metoprolol
oxprenolol
alprenolol
propranolol
Y sz - 0 C y C H C H2NHC(C 6H
obtained on the e*erIAh4.PCC10/C3 column and km values obtained on the 6GAM.PCc10/c3 column (Figure lA). Similar results were found when correlating solute retention between esterIAM.PCC10/C3 and e*erIAM.PCC10/C3 columns Figure 1B) and esterIAM.PCC101C3 and 6GAM.PCc10/c3 columns (Figure 1C). More important, the slope of 0.91 in Figure IA indicates that YAM retention factors measured on singlechain 6GAM.PCc10/c3and etherIAM.PCC10/C3 columns are virtually identical. However, the slopes of -4 in (B) and (C) indicate that the doublechain esterIAM.PCC10/C3 column has -4fold higher k i i values compared to the singlechain IAM columns. The K m value reflects the distribution of solute between the stationary phase and the mobile phase. The phase ratio and kiw were used to calculate KIAMaccording to eq 2. At pH 7.4, phenols exist mostly in un-ionized form whereas both ionized and unionized forms of #?-blockersexist. ,%blockers contain ionizable functional groups (i.e., the amino groups), and the pKa values are 9.55 for atenolol, 8.80 for pindolol, 9.67 for nadolol, 9.70 for metoprolol, 9.50 for oxprenolol, 9.70 for alprenolol, and 9.45 for propranolol.18 The ionized species usually does not participate in membrane binding or partitioning. Thus, for ,&blockers KIAM only measures the partitioning of the un-ionized forms and needs to be corrected as follows:18
K~ = K ~ ( I +w ~ a - 7 . 4 )
(6)
The KIAMvalues obtained on each IAM column correlate with the KIAMvalues obtained with the other two IAM columns ( F i i r e 1D-F); excellent linear correlations (72 = 0.982-0.998) were always obtained. It should be noted that the affinity of solutes for the esterIAM.PCC1O/C3 surface is -3 times the &ity of solutes for the etherIAM.PCC10/C3 surface (Figure lE,F). These results are significant and provide insight into the mechanism of solute retention as further discussed below. Solute-IAM interactions may be dominated by partitioning, adsorption,or both. Partitioning implies that the solute molecule penetrates the head-group region of IAM and is embedded within the hydrocarbon region, whereas adsorption implies that the solute molecule is simply in surface contact with the polar lipid Analytical Chemistry, Vol. 67, No. 13, July 1, 1995
2121
400x1 O3
400
/
m -
m -
e
Y 0
6
0 r
300
300
0
0
0
4
4
5
z a
200
200
al L..
L!!
al
c u)
c
m
S = 2.71f0.10
100
5
loo
--
r = 0.982
Y
0
1
0
20
40
1
'Ic3)
FAM
I
I
120x1oJ
40
0
80
60
k ' (?AM.PCC1
1
(601AM.PCc1' I c 3 )
n
(3
$
400~10~
m
Y 0
300
r
0
0
0
4
300
5
200
4
5 200 4
L.!
L a l-
--2-
0
c 8
CI
m
In
100
5
x
s
r = 0.998
04 2 o the:'
kt(
100
0
6%101&?
IAM.PC
)
1004
160x1O3
-
n
e (3
F
"e
F
0
4
0
60
5
a
0-
140
v-i 0 0
80
0
40
r
fa
(ro
Y
W
-5- 20
5
s
Y
0
120 -
100 80
-
40 60
20 0-
1
1
1
2p(
k
the?'
I
1
1
6%10/8P
IAM.PC
)
1
1
1
'
1
1
1
1
loo
Figure 1. (A-C) Correlation of the IAM capacity factors (NAM) of 16 solutes on the single-chain and double-chain IAM.PC columns at 298 K. (D-F) Correlation of the equilibrium distribution constants of 16 solutes on the single-chain and double-chain IAM.PC columns at 298 K.
Chart 2. Partitioning: The Dominating Retention Mechanism on IAMs
head groups. The outer most surface of IAM.PC contains a monolayer of PC head groups, and underneath these polar lipid head groups resides the hydrocarbon chains of the immobilized PC ligands and the C10 or C3 alkyl groups as shown in Chart 2. 2122 Analytical Chemistry, Vol. 67, No. 13, July 1, 1995
If solute adsorption dominates retention, then the amount of immobilized PC head groups determines kfm.The density of PC head groups on the este~IAM.PCCIO/Q column (98 pmol of PC/g of IAM,Table 1) is lower than the densities of PC head groups on etherIAM.PCC10/C3 or 6GIAM.PCc10/c3 (127 pmol of PC/g of WLI). Based on PC head-group density, an adsorption retention mechanism predicts that the esterIAM.PCC10/C3 column should have the shortest solute retention values. However, Figure lA-C demonstrated the opposite effect; i.e., the eterIAM.PCC10/C3column has the longest retention factors. This indicates that., for these solutes, a partitioning mechanism controls solute retention on the IAM phase and not solute adsorption. Thus, the solute actually
100
1 nn
n n
:
80
2
-L
E
0
4
0 60
4
5
.5
p6gdm
E 40 3 20
c
p'
0
0
3
= -0.26k1.04
I
I
1
1
I
0
20
40
60
80
0 0
20
40
AsO
60
(Othe\AM,pCC1
80
100
01~3)
Aso (s?AM.PCC10'C3) 4 4 "n
g
e i r
I
0-
E
/-0
=
-4-
G'
-8-
c
L 0
3 -15
-12-
3 -16-
S = 1.03f0.06 = -0.27f0.39 = 0.957
.
= 0.57f0.99
I
l
-16
'
l
'
-12
i
-8
'
l
'
-20
-15
-10
A G ~(ether,AM.pCc101c3)
-5
0
l
4
I -5
0
I
I
I
I
-25
-20
-15
-10
AGO
'
0
JY
-25
l
-4
1
('?AM.PCC10'C3)
Figure 3. Correlation of thermodynamic properties (A@ at 298 K, AH", A F ) for partitioning of 16 solutes between a single-chain
Figure 2. Correlation of thermodynamic properties (A@ at 298 K, AH", AS') of 16 solutes partitioning on the single-chain IAM.PC columns.
aGIAM.PCC10/c3 column and a double-chain esterlAM.PCC10/C3 column.
penetrates beyond the interfacial PC head groups and is embedded within the IAM.PC bonded phase (Chart 2). For this reason, the distribution constantK m of a solute between IAMs and mobile phase is the partition coefficient of the solute between IAMs and the mobile phase. As discussed above, Figure 1E,F demonstrated that solute partitioning into the doublechain ester PC column is -3 fold more favorable compared to solute partitioning into the singlechain IAM column. The higher partitioning on the ester column may be the result of the following: (i) a lower immobilized PC density exhibits a lower interfacial barrier to solute transport into the IAM hydrocarbon region, and (ii) immobilized doublechain ester PC ligands (98 pmol of PC/g of IAM) contain -50% more hydrocar-
bon compared to the singlechain PC ligands (both were 127pmol of PC/g of IAM). The higher hydrocarbon density on the est~~IAM,PCC1O/CJ column would increase the Van der Waals interactions between the hydrophobic solutes and the bonded phases and, therefore, increase the solute affinity to the bonded phase. Using eq 4, the KIAMvalues measured at T = 298 K were used for calculating the free energy AGO of solute partitioning into IAM columns. Temperature-dependent solute retention was used to obtain Maand AS" for the partitioning process. AHO was obtained from the slope of van't Hoff plots, which are plots of In kim vs 1/T. The values for AS' were calculated as follows: Analytical Chemistfy, Vol. 67,No. 13,July 1, 1995
2123
Table 2. Thermodynamlcs of Partltlonlng of Group I Solutes (pAlkylphenols), Qroup 2 Solutes (pHalophenols), and Group 3 Solutes (/?.Blockers)into IAY.PC Columns*** efherIAMpCClO/CS
solute phenol cresol $ethylphenol $-n-propylphenol $-n-butylphenol
pfluorophenol pchlorophenol $-bromophenol $-iodophenol atenolol pindolol nadolol metoprolol oxprenolol alprenolol propranolol
dGm,PCClO/C3
esterm,pCClO/C3
AS" U/mol K,
Kwil 52.9 118.2 258.7 626.7 1838.2
-9.83 -11.82 -13.77 -15.96 -18.62
-6.54 -7.02 -7.42 -7.57 -7.38
11.04 16.10 21.31 28.16 37.72
Group 1 69.1 -10.50 140.6 -12.25 293.1 -14.07 733.2 -16.35 2194.3 -19.06
-6.65 -7.26 -7.48 -8.56 -7.26
12.90 16.76 22.12 26.14 39.61
94.1 244.6 653.5 1960.7 6102.5
-11.26 -13.63 -16.06 -18.78 -21.60
-4.90 -5.35 -5.61 -6.14 -8.95
21.32 27.79 35.06 42.44 42.45
80.4 282.4 409.0 719.0
-10.87 -13.98 -14.90 -16.30
-7.07 -9.48 -9.44 -11.66
12.76 15.11 18.31 15.57
Group 2 100.4 -11.42 330.1 -14.37 494.7 -15.37 870.7 -16.77
-7.27 -9.94 -10.92 -12.63
13.94 14.88 14.95 13.90
171.1 733.5 1221.1 2364.3
-12.74 -16.35 -17.61 -19.25
-5.70 -9.62 -10.96 -12.63
23.64 22.58 22.32 22.20
5316.1 5122.0 12536.9 22250.2 21336.4 79741.4 102642.7
-21.25 -21.16 -23.38 -24.80 -24.70 -27.96 -28.59
-1.76 -5.99 -1.26 0.22 -0.42 -3.06 -5.46
65.41 59.93 74.24 84.06 81.48 83.57 77.61
Group 3 7375.5 -22.06 7505.9 -22.11 17786.0 -24.25 24128.5 -25.00 25206.8 -25.11 78745.8 -27.93 122935.8 -29.04
66.93 51.59 71.12 87.02 78.43 87.43 76.76
6710.9 9924.6 22040.1 44210.9 4862 1.1 240600.0 317686.2
-21.83 -22.80 -24.78 -26.50 -26.74 -30.70 -31.39
-2.12 -6.73 -3.05 0.93 -1.74 -1.88 -6.16
-0.93 -8.94 -5.06 1.96 0.58 -2.49 -1.03
70.14 46.49 66.16 91.62 91.68 94.68 101.87
K w and AGO are the values at T = 298 K (25 OC). AHo and AS" were obtained from the linear regression of van't Hoff plots. The fitting parameters for linear regressions of van't Hoff plots (Le., slopes, intercepts, and linear correlations) are available as supplementary material. (I
(AH"- AGo)/T (7) Table 2 shows AG", AH",and AS" values for solute partitioning AS" =
into three different IAM.PC columns. For all solutes tested, increasing the temperature causes a decrease in kim (data not shown). With few exceptions, the test solute gave excellent correlations on van't Hoff plots regardless of the IAM.PC column used for the analysis (72 0.9-0.99, data not shown). The compounds that give a poor correlation are oxprenolol and metoprolol on etherIAM.PCC10/C3, alprenolol on 6GIAM.PCC10/C3,and oxprenolol, metoprolol, and atenolol on esterIAM.PCC10/C3 (data not shown). Poor correlations occurred for these compounds because a very weak temperature dependence of retention was observed. Weak temperature dependence results in small slopes for van't Hoff plots and small AH" values, which cause the poor correlation. Nevertheless, decreasing k i f with increasing temperature results in positive slopes for van't Hoff plots, and positive slopes on van't Hoff plots correspond to negative values for AH'. Most of the compounds tested had a negative value for AH'. The thermodynamic parameters (AGO, AH", AS") for solute partitioning on the two different singlechain IAM.PC surfaces are compared in Figure 2; for all parameters, a perfect correlation between the two single-chain IAM.PC columns was obtained (Le., etherIAM.PCC10/C3 and dGIAM.PCc10/c3columns). Most important, the intercepts are almost zero and the slopes for all of the plots are very close to unity. When intercepts are -0, and slopes are -1, eqs 8-10 indicate that the values of AGO, AH', and AS" are similar on the two columns,
-
+
AGo,umn.l= slope x (AG;olumn.2) intercept
(8)
PC ligands that contain a glycerol backbone and an 0-methyl tethered to the glycerol backbone, whereas the 6GIAM.PCc10/c3 surface lacks these structural features. However, since AGO, AH", and A 9 are similar on the e*erIAM.PCC10/C3 vs 6GIAM.PCc10/c3 columns (Figure 2), these structural differences are apparently unimportant regarding the solute partitioning process. Thermodynamic properties between single-chain and doublechain IAM.PC columns were also compared. Figure 3 compares the eskrIAM.PCC10/C3 vs dGIAM.PCc10/c3 column. For all parameters (AGO, AH", AS") there is almost a perfect correlation and the slopes are -1. However, unlike the comparison of the singlechain IAM.PC columns where the intercepts were -0, the intercepts in Figure 3 significantly deviate from zero. Equation 11 applies to the data in Figure 3, which compares the doublechain ester IAM.PC column to the single-chain 6GIAM.PC column. AGzster= slope x (AG'SG)
+ intercept
(11)
The intercept of -1.50f 0.76 kJ/mol in Figure 3 indicates that the ester column has -1.50 f 0.76 kJ/mol more favorable free energy of partitioning compared to the single-chain 6G column. The thermodynamic reason for the more favorable free energy of partitioning is attributed to a more favorable entropy contribution on the doublechain ester column. This is based on the intercepts of the plots in Figure 4B and C. Equations for the AH" data shown in Figure 4B are
AHgster= slope x (AHOSG)
+ intercept ester = slope x ( A P S G ) + (0.57 f 0.99) (12)
and equations for AS" data shown in Figure 4C are
+ intercept AS:,, = slope x (ASOSG) + (9.17 f 3.45) (13) The intercept of + 0.57f 0.99 kJ/mol for AH" corresponds to
AgSte, = slope x (ASOSG)
+
AS;olumn-l= slope x (AS:olumn.2) intercept
(10)
The structural differencebetween the two singlechain IAM.PC columns is that the e*erIAM.PCC10/C3 surface contains immobilized 2124
Analytical Chemistry, Vol. 67, No. 13, July 1, 1995
a small difference in the AH" between ester and 6G columns. However, the intercept of 9.17 f 3.45 for AS" corresponds to a
- - 10n
E
\-127
5 - 1 4-
' :1
- 161 4 d- I4
1.0 1.2 1.4 1.6 1.8 2.0 2.2 Halogen Van der Waal's Radius (A)
I
=-6.56kO.42 = 1.71f0.77 =0.992
6-
1.0 1.2 1.4 1.6 1.8 2.0 2.2 Halogen Van der Waal's Radius (A)
1
-1
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Figure 4. Structural effects on thermodynamic properties of partitioning of phenols into a 6GIAM.PCC10'c3 column: (A) dependence of free energy of partitioning, AGO at 298 K, on hydrocarbon chain length for group 1 solutes (palkylphenols); (B) dependence of entropy contributions to partitioning, TA.9 at 298 K on hydrocarbon chain length tor group 1 solutes (palkylphenois); (C)dependence of free energy of partitioning, AGO at 298 K, on the halogen size of group 2 solutes (phalophenols); (D) dependence of enthalpy, AH", on the halogen size of group 2 solutes (phalophenols).
2.73 f 1.01 kJ/mol (TAS") difference in the entropy contribution to the partitioning process between the ester and the 6G column. Thus, there is a signi6cant entropy contribution TAP that favors solute partitioning into doublechain IAM columns. Similarresults were obtained for comparisons between esterIAM.PCC10/C3 and etherIAM,PCC10/C3. In other words, both singlechain IAM.PC columns give virtually identical results when compared to the doublechain IAM.PC ester column. Thus, the key iindmg from these results is that the more favorable solute partitioning is into doublechain IAM columns compared to singlechain columns, which is probably due to an increase in entropy of the doublechain surface during the partitioning process. Solute partitioning can be discussed relative to the functional groups associated with each solute. Three groups of solutes were studied, and within each group the compounds were rank ordered according to their AGO values, as shown in Table 2. The general rank order of solute partitioning into the IAM surfaces is group 1 p-alkylphenol -AGO (kJ/mol) 9.83-21.60
-- p-halophenols group2 10.87-19.25 5
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