Anal. Chem. 1997, 69, 183-189
ACN Clusters in a Water/ACN Mixture, with Implications for the RPLC Weak Polar Solute Retention Yves Claude Guillaume* and Christiane Guinchard
Laboratoire de Chimie Analytique, Faculte´ de Me´ decine et Pharmacie, Place Saint Jacques, 25030 Besancon Cedex, France
Recently, a model was proposed to describe the existence of pockets of ACN called clusters in an ACN/water mixture. Using this mixture as a mobile phase, a novel mathematical theory is presented to describe the variation of the retention factor, k′, of alkyl benzoate esters in reversed-phase liquid chromatography. For the first time, using this model, enthalpy, entropy and the Gibbs free energy were determined for two physicochemical processes: (i) the transfer of the alkyl benzoate ester from a pure aqueous mobile phase to the stationary phase and (ii) the alkyl benzoate ester solvation by the ACN clusters. These thermodynamic data indicate that the main parameter determining retention is distribution of the alkyl benzoate esters to clusters of ACN, while the interactions with the stationary phase play a minor role. The effect of the mobile phase composition on the selectivity and retention mechanism in reversed-phase liquid chromatography (RPLC) is usually described through the hydrophobic effect1-3 or by the use of the partitioning model.4-7 Usually, the mobile phase is a binary or a ternary mixture. For ternary mobile phases, empirical modeling approaches have been published by Kowalska8-10 and Xie et al.11 Other methods of selectivity characterization include principal component analysis12 and a thermodynamic treatment using a displacement mechanism to model the sorption of solvents into the bonded phases.13,14 For a binary mixture, organic modifier (OM)/water, a change in the organic modifier (i.e., OM ) methanol changed to OM ) ACN) caused variations in the retention mechanism.15,16 To study this difference, thermodynamic property trends for a series of (1) Horvath, Cs.; Melander, W. R. J. Chromatogr. 1976, 125, 129. (2) Melander, W. R.; Horvath, Cs. In High Performance Liquid Chromatography, Advances and Perspectives; Horvath, Cs., Ed.; Academic Press: New York, 1980; Vol. 2, p 113. (3) Horvath, Cs.; Melander, W. R. Am. Lab. 1978, 17. (4) Martire, D. E.; Boehm, R. E. J. Phys. Chem. 1983, 87, 1045. (5) Dill, K. A. J. Phys. Chem. 1987, 91, 1980. (6) Dill, K. A.; Naghizadeh, J.; Marquisee, J. A. Annu. Rev. Phys. Chem. 1988, 39, 425. (7) Dorsey, J. G.; Dill, K. A. Chem. Rev. 1989, 89, 33. (8) Kowalska, T. Chromatographia 1989, 28 (7-8), 354. (9) Kowalska, T. Chromatographia 1989, 29 (7-8), 389. (10) Kowalska, T. Chromatographia 1991, 31 (3-4), 119. (11) Xie, M.; Zhou, C.; Ren, Z.; Luo, T. J. Chromatogr. 1991, 555 (1-2), 33. (12) Coenegracht, P. M. I.; Smilde, A. K.; Benak, H.; Bruins, C. H. P.; Metting, H. J.; De Vries, H.; Doornboos, D. A. J. Chromatogr. 1991, 550 (1-2), 13. (13) Jaroniec, M.; Lin, S.; Gilpin, R. K. Chromatographia 1991, 32 (1-2), 13. (14) Gilpin, R. K.; Jaroniec, M.; Lin, S. Chromatographia 1990, 30 (7-8), 393. (15) Guillaume, Y.; Guinchard, C. Chromatographia 1995, 41, 84. (16) Guillaume, Y.; Guinchard, C. Anal. Chem. 1996, 68, 2869. S0003-2700(96)00679-8 CCC: $14.00
© 1997 American Chemical Society
benzodiazepines15-18 were determined in the methanol/water or ACN/water mobile phase. It was found that differences between the molecular structures of the benzodiazepines contributed more significantly to changes in the retention process in the CH3OH/ water than in the ACN/water mixture.16 These differences are supported by the fact that the methanol solution is dominated by competitive hydrogen bonding, whereas the ACN solution is governed by the formation of aggregates of ACN molecules called clusters.19-21 The systems involving water-rich mobile phases have been the most difficult to describe, particularly those containing >90% water. This lack of correlation has been attributed to the probable solvation of the stationary phase by the organic component of the mobile phase, which becomes more significant in the water-rich mobile phase. Therefore, if equations have been proposed relating the mobile phase conditions to the solute retention factor, no single equation has been adequate to describe the retention process over the entire mobile phase composition. This paper studies the usefulness of an equation that describes the variation of the retention factor for a series of alkyl benzoate esters in an ACN/water mixture with a C18 column. This equation is expressed in terms of fractions of both free acetonitrile (not in a cluster) and water in the ACN/water mixture. This new mathematical model is explicitly derived from three equilibria, i.e., (i) equilibrium between free ACN and ACN clusters; (ii) solute M solvation equilibrium by ACN clusters; and (iii) equilibrium between solute M and the stationary phase ligand, Ls. This equation is tested over a wide range of water fractions, Φ (0.20 e Φ 0.70), and column temperatures, T (5 e T e 50 °C) for six different alkyl benzoate esters. A thermodynamic study is then carried out to evaluate the retention mechanism. THEORY The retention behavior of a weak polar solute in RPLC is based on the partitioning of the samples between the ACN/water mixture and the stationary phase. In the ACN/water mixture, the ACN molecules are organized in agreggates or loosely defined clusters.19-21 An equilibrium model has been developed to describe this molecule association.16 It has been represented by
nACN H U
(1)
(17) Guillaume, Y.; Guinchard, C. J. Liq. Chromatogr. 1994, 17 (13), 2809. (18) Guillaume, Y.; Guinchard, C. Chromatographia 1995, 40, 193. (19) Stalcup, A. M.; Martire, D. E.; Wise, S. A. J. Chromatogr. 1988, 442, 1. (20) Lowenschuss, A.; Yellen, N. Spectrochim. Acta 1975, 31A, 207. (21) Rowlen, K. L.; Harris, J. M. Anal. Chem. 1991, 63, 964.
Analytical Chemistry, Vol. 69, No. 2, January 15, 1997 183
[ACN]0 is given by16
with
U ) (ACN)n
[ACN]0 ) d(1 - Φ)/Mw
(2)
n ) 120 is the ACN molecule number in a cluster U.16 The weak polar solute molecule M solvation by p clusters is represented by the equilibrium
M + pU H M‚pU
(3)
Combining eqs 13 and 14 yields
k′ ) γKM‚Ls/(1 + KM‚pUKUpynpdnp(1 - Φ)np)/Mwnp)
(4)
(15)
From eq 11, ynp is given by
ynp ) (1 - y)p/(λpnp(1 - Φ)p(n-1))
The equilibrium of the species M with the stationary phase ligand Ls is
M + Ls H M‚Ls
(14)
(16)
Substitution of eq 16 into eq 15 yields
k′ ) γKM‚Ls/(1 + KM‚pUΨp(1 - y)p(1 - Φ)p)
(17)
The equilibrium constants for eqs 1, 3 and 4 are
KU ) [U]/[ACN]n
(5)
where Ψ is a constant function of d, Mw, and n:
Ψ ) d/(Mwn) p
KM‚pU ) [M‚pU]/([M][U] )
(6)
KM‚Ls ) [M‚Ls]/[M]
(7)
(18)
Taking the logarithm of eq 17 leads to
ln k′ ) ln KM‚Ls + ln γ - ln(1 + KM‚pUΨp(1 - y)p(1 - Φ)p) (19) If γ is the column phase ratio (volume of the stationary phase divided by the volume of the mobile phase),22 the retention factor k′ of the species M is given by
k′ ) γ[M‚Ls]/([M] + [M‚pU])
For a low water fraction:
Φ f 0 and y f 0
(8) therefore,
and using the constants (5-7), then, the retention for the species M is
k′ ) γKM‚Ls/(1 + KM‚pU[U]p)
x ) KM‚pUΨp(1 - y)p(1 - Φ)p . 1
(20)
(9) Using the approximation
ln(1 + x) = ln x for x . 1
(21)
ln k′ ) ln k′ACN - p ln(1 - y)(1 - Φ)
(22)
If [ACN]0 is the total concentration of ACN and y the fraction of free ACN (not in a cluster) in the ACN/water mixture, then eq 19 leads to
y ) [ACN]/[ACN]0
(10)
It has been demonstrated previously that y and the fraction of water Φ in the ACN/water mixture are related by the equation16
1 ) y + λnyn(1 - Φ)n-1
(11)
where λ is a constant16 function of n, KU, acetonitrile density d, and its molecular weight, Mw:
λ ) KUdn-1/Mwn-1
(12)
(22) Sentell, K. B.; Dorsey, J. G. J. Liq. Chromatogr. 1988, 11, 1875.
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Analytical Chemistry, Vol. 69, No. 2, January 15, 1997
ln k′ACN ) ln KM‚Ls - ln KM‚pU - p ln Ψ + ln γ (23) For a high water fraction:
Φ f 1 and y f 1 therefore,
x ) KM‚pUΨp(1 - y)p(1 - Φ)p f 0
Combining eqs 5, 9, and 10, the following is obtained:
k′ ) γKM‚Ls/(1 + KM‚pUKUpynp[ACN]0np)
k′ACN is the solute retention factor in a pure ACN mobile phase:
(13)
(24)
Using the approximation
ln(1 + x) = x for x f 0
(25)
eq 19 leads to
ln k′ ) ln k′w - KM‚pUΨp(1 - y)p(1 - Φ)p
(26)
k′w is the solute retention factor in a pure aqueous water mobile phase:
ln k′w ) ln KM‚Ls + ln γ
(27)
Subtracting eq 23 from eq 27 yields
ln k′w - ln k′ACN ) ln KM‚pU + p ln Ψ
(28)
If
ξ ) k′w/k′ACN
(29)
ln ξ ) ln KM‚pU + p ln Ψ
(30)
then
If ∆G°M‚pU, ∆H°M‚pU, ∆S°M‚pU, and ∆G°M‚Ls, ∆H°M‚Ls, ∆S°M‚Ls are the Gibbs free energy, enthalpy, and entropy, respectively, for the solute solvation by ACN clusters and solute transfer from the mobile to the stationary phase, then the Van’t Hoff plot equations are
ln KM‚pU ) -∆G°M‚pU/(RT)
(31)
∆G°M‚pU ) ∆H°M‚pU - T∆S°M‚pU
(32)
ln KM‚pU ) -∆H°M‚pU/(RT) + ∆S°M‚pU/R
(33)
ln KM‚Ls ) -∆G°M‚Ls/(RT)
(34)
∆G°M‚Ls ) ∆H°M‚Ls - T∆S°M‚Ls
(35)
ln KM‚Ls ) -∆H°M‚Ls/(RT) + ∆S°M‚Ls/R
(36)
with
then
and
then
Substitution of eq 36 into eq 27 leads to
ln k′w ) -∆H°M‚Ls/(RT) + ∆S°M‚Ls/R + ln γ
(37)
Substitution of eq 33 into eq 30 gives
ln ξ ) -∆H°M‚pU/(RT) + ∆S°M‚pU/R + p ln Ψ
(38)
As can be seen from eq 37, ∆H°M‚Ls and ∆S°M‚Ls represent the enthalpy and entropy of transfer of the solute from a pure aqueous mobile phase to the stationary phase. Equation 38 shows that ln ξ versus 1/T is a Van’t Hoff plot. From the slope, the solute solvation by the ACN cluster enthalpy, ∆H°M‚pU, can be determined, and, from the intercept, the solute solvation by ACN cluster entropy, ∆S°M‚pU, can be calculated if the constant pln Ψ is known. Nevertheless, the determination retention time for a weak polar solute with a mobile phase containing 100% water is very difficult to obtain due to both the very high spread of the peaks and a high elution time. Therefore, to circumvent the measurement of the retention time in a pure water mobile phase, eqs 32, 33, 35, and 36 were used to determine the thermodynamic data. EXPERIMENTAL SECTION Apparatus. The HPLC system consisted of a HPLC Waters pump 501 (Saint Quentin, Yvelines, France), an Interchim rheodyne injection valve, Model 7125 (Montlucon, France), fitted with a 20 µL sample loop, and a Merck 2500 diode array detector (Nogent-sur-Marne, France). A Lichrocart 125 mm × 4 mm i.d. RP18 column (5 µm particle size) was used with a controlled temperature in an Interchim oven, TM No. 701. The mobile phase flow rate for all experiments was 1 mL/min. Solvents and Samples. HPLC grade acetonitrile (Merck) was used without further purification. Water was obtained from an Elgastat option I water purification system (Odil, Talant, France) fitted with a reverse-osmosis cartridge. The variation range of the water fraction (v/v) was 0.20-0.70. The chromatographed compounds were alkyl benzoate esters. The straightchain esters, methyl (1), ethyl (2), propyl (3), and butyl (4) were purchased from Interchim. The branch chain esters, isopropyl (5) and 2-methyl-1-propyl (6), were synthesized in our laboratory by an esterification reaction: 0.01 mol of thionyl chloride was added to 0.06 mol of the corresponding alcohol. The reaction mixture was stirred at room temperature and then refluxed for 2 h. The solvent was removed under reduced pressure, and the esters were recrystallized from a methanol/water mixture. All the compounds were diluted in acetonitrile at a concentration of 10-80 mg/mL. Each solute or a mixture of these when the six compounds were well resolved was injected, and the retention times were measured. Temperature Studies. Compound retention factors were determined over the temperature range 5-50 °C. The chromatographic system was allowed to equilibrate at each temperature for at least 1 h prior to each experiment. To study this equilibrium process, the compound retention time of the methyl ester was measured every hour for 7 h and again after 20, 21, and 23 h. The maximum relative difference of the retention time of this compound between these different measurements was always 0.5%, making the chromatographic system sufficiently equilibrated for use after 1 h. RESULT AND DISCUSSION Validation of the Theoretical Model (Eq 17). To obtain the constants KM‚Ls, KM‚pU, and p at 25 °C, the retention factor of each of the six alkyl benzoate esters was determined for a wide variation range of water fractions (0.20 e Φ e 0.70). Eleven Φ values were included in this range (0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, and 0.70). For each Φ value, the corresponding value of the fraction of free ACN, y, in the ACN/ Analytical Chemistry, Vol. 69, No. 2, January 15, 1997
185
Table 1. KM‚Ls and KM‚pU Parameter Values for Eq 17, Relating Retention Factor, k′, with the Fraction of Water, Φ, and the Corresponding Free ACN, y, at 25 °C with Standard Deviations (in Parentheses) for the Six Benzoate Alkyl Esters compound
KM‚Ls
KM‚pU
methyl ester (1)a ethyl ester (2) propyl ester (3) butyl ester (4) isopropyl ester (5) 2-methyl-1-propyl ester (6)
7.58(0.3) 8.36(0.2) 19.75(0.4) 50.67(0.6) 17.18(0.5) 46.15(0.7)
38.05(0.8) 60.71(0.7) 99.72(0.8) 170.36(0.9) 91.95(0.7) 160.71(0.8)
a
Represents the compound number.
water mixture had been previously16 determined. All the experiments were repeated three times. The coefficients of variation of the k′ values were
