Measurement of Mobile-Phase Volume in Reversed-Phase Liquid

HPLC grade acetonitrile, methanol, and tetrahydrofuran were obtained from Kanto ... Test solutions were prepared by dissolving analyte compounds in th...
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Anal. Chem. 2007, 79, 6279-6286

Measurement of Mobile-Phase Volume in Reversed-Phase Liquid Chromatography and Evaluation of the Composition of Liquid Layer Formed by Solvation of Packing Materials Masami Shibukawa,* Yuji Takazawa, and Kazunori Saitoh

Department of Applied Molecular Chemistry, College of Industrial Technology, Nihon University, 1-2-1, Izumi-cho, Narashino, 275-8575, Japan

The mobile-phase volumes (Vm) in reversed-phase liquid chromatography (RPLC) with alkyl-bonded silica, defined as the difference between the total volume of eluent in the column (V0) and the volume of the eluent solvent layer formed by solvation of the bonded phase (VL), are determined by the method derived from the eluent electrolyte effect on the retention of ionic analytes. The validity of the Vm values obtained is evaluated by comparing them with the retention volumes of various organic compounds and inorganic ions, which have been suggested as unretained markers, and those obtained from a linear dependence of the logarithmic retention factor on the carbon numbers of homologous series. From the results obtained, it has been concluded that the solvated liquid phase on a column packing material should be assigned to a part of the stationary phase and the method developed for determination of the Vm value based on the ion partition model gives the most reasonable value as the mobilephase volume in RPLC. The volume and the solvent composition of the solvated liquid phase on C1, C8, and C18 bonded silica are estimated, and the effects of organic modifiers and the physicochemical structures of the packing materials on these values are discussed. It has been recognized that an exact definition and measurement of the mobile-phase volume in liquid chromatography is essential for an accurate determination of the retention factor, k, which is directly related to the thermodynamic fundamentals of the separation process.1 The retention factor is used for determination of the distribution coefficient, Gibbs free energy, enthalpy, and entropy for distribution of solutes in a chromatographic system. It is also used for determination of separation factor, which allows the comparison of selectivity of various stationary phases and eluents. However, in reversed-phase liquid chromatography (RPLC), the method for determination of the true mobile-phase volume has not yet been established although many methods have * Corresponding author. Tel: +81-48-858-3520. Fax: +81-48-858-3520. Email: [email protected] Present address: Graduate School of Science and Engineering, Saitama University, 255 Shimo-Okubo, Saitama 338-8570, Japan. (1) Rimmer, C. A.; Simmons, C. R.; Dorsey, F. G. J. Chromatogr., A 2002, 965, 219-232. 10.1021/ac0701839 CCC: $37.00 Published on Web 07/14/2007

© 2007 American Chemical Society

been proposed.2-27 Much of the controversy over the definition and determination of the mobile-phase volume arises from the position of the boundary between the mobile and the stationary phases. A column packing material in liquid chromatography is solvated by components of the eluent, and the phase volume ratio depends on the assignment of the solvated or adsorbed solvents to the mobile phase or the stationary phase.1 Yun et al.2 have presented concise definitions for void volume and mobile-phase volume as follows: “void volume” is the volume of the liquid in the column up to the physical surface of the solid, whereas “mobile-phase volume” is the volume of the bulk liquid out from the Gibbs dividing surface. That is, the void volume is defined as the total volume of eluent in the column and the mobilephase volume as the difference between the void volume and the (2) Yun, K. S.; Zhu, C.; Parcher, J. F. Anal. Chem. 1995, 67, 613-619. (3) Knox, J. H.; Kaliszan, R. J. Chromatogr. 1985, 349, 211-234. (4) McCormick, R. M.; Karger, B. L. Anal. Chem. 1980, 52, 2249-2257. (5) Melander, W. R.; Erard, J. F.; Horvath, Cs. J. Chromatogr. 1983, 282, 211228. (6) Engelhardt, H.; Muller, H.; Dreyer, B. Chromatographia 1984, 19, 240245. (7) Bidlingmeyer, B. A.; Warren, F. V.; Weston, A.; Nugent, C.; Froehlich, P. M. J. Chromatogr. Sci. 1991, 29, 275-279. (8) Fini, O.; Brusa, F.; Chiesa, L. J. Chromatogr. 1981, 210, 326-330. (9) Stanley, B. J.; Foster, C. R.; Guiochon, G. J. Chromatogr., A 1997, 761, 41-51. (10) Oumada, F. Z.; Roses, M.; Bosch, E. Talanta 2000, 53, 667-677. (11) Nowotnik, D. P.; Narra, R. K. J. Liq. Chromatogr. 1993, 16, 3919-3932. (12) Wells, M. J. M.; Clark, C. R. Anal. Chem. 1981, 53, 1341-1345. (13) Jinno, K.; Ozaki, N.; Sato, T. Chromatographia 1983, 17, 341-344. (14) Jinno, K. Chromatographia 1983, 17, 367-369. (15) Hearn, M. T. W.; Grego, B. J. Chromatogr. 1981, 203, 349-363. (16) Van der Houwen, O. A. G. J.; Van der Linden, J. A. A.; Indemans, A. W. M. J. Liq. Chromatogr. 1982, 5, 2321-2341. (17) Rustamov, I.; Farcas, T.; Ahmed, F.; Chan, F.; LoBrutto, R.; McNair, H. M.; Kazakevich, Y. V. J. Chromatogr., A 2001, 913, 49-63. (18) Vit, I.; Popl, M.; Fahnrich, J. J. Chromatogr. 1983, 281, 293-298. (19) Kazakevich, Y. V.; McNair, H. M. J. Chromatogr., A 2000, 872, 49-59. (20) Li, L.; Carr, P. W.; Evans, J. F. J. Chromatogr., A 2000, 868, 153-167. (21) Krstulovic, A. M.; Colin, H.; Guiochon, G. Anal. Chem. 1982, 54, 24382443. (22) Mo ¨ckel, H. J. J. Chromatogr., A 1994, 675, 13-28. (23) Berendsen, G. E.; Schoenmakers, P. J.; de Galan, L. J. Liq. Chromatogr. 1980, 3, 1669-1686. (24) Al-Thamir, W. K.; Purnell, J. H.; Wellington, C. A.; Laub, R. J. J. Chromatogr. 1979, 1739, 388-391. (25) Laub, R. J.; Madden, S. J. J. Liq. Chromatogr. 1985, 8, 173-186. (26) Perkins, T. W.; Root, T. W.; Lightfoot, E. N. Anal. Chem. 1997, 69, 32933298. (27) Riedo, F.; sz. Kova´ts, E. J. Chromatogr. 1982, 239, 1-28.

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volume of the solvated phase. It should be noted here that the solvation layer may also be formed in a single-solvent system although the Gibbs dividing surface is usually defined for a two or more component system. The void volume, V0, can be determined by measuring the retention volumes of isotopes of all the components of the eluent according to the following equation:

V0 )

∑φ

m i VR,i

(1)

where φm i is the volume fraction of the component i in the eluent and VR,i is the retention volume of isotopically labeled component i. This method was proposed by Knox and Kaliszan3 and is based on the assumption that the partial molar volume of any eluent component in the solvated phase is the same as that in the bulk phase. On the other hand, the mobile-phase volume, Vm, of a liquid chromatographic system can be obtained from the retention volume of any solute that is neither adsorbed onto the packing material nor penetrates the Gibbs dividing surface. Some investigators believe that there is no distinct boundary between the bulk liquid phase and the solvated phase so that it is impossible to determine the mobile-phase volume.3,27 Even so, the solvent molecules incorporated in the solvated phase may exhibit an interaction with a solute different from that of the bulk solvent molecules, and thus, the solvents in the solvated phase should be assigned to a part of the stationary phase. Many researchers have advocated that deuterated water can be regarded as an ideal marker for determination of the mobilephase volume in RPLC columns packed with alkyl-bonded silica particles or hydrophobic polymer particles such as poly(styrenedivinylbenzene) copolymer (PS-DVB) gels.2,4-7 Many other compounds such as thiourea,8 uracil,7,9 and inorganic anions10-16 have also been proposed as unretained markers, though most of them have been shown to exhibit retention volumes different from that of deuterated water. However, it has not necessarily been proved that water does not form any solvation layer on the surface of RPLC packing materials. We have shown that some inorganic ions exhibit retention volumes less than the total volume of water in the column or the retention volume of deuterated water when eluted on various kinds of hydrophilic and hydrophobic polymer columns with aqueous solutions containing an electrolyte.28-33 This result cannot be ascribed to either electrostatic exclusion or size exclusion but is interpreted by partition between the bulk water phase and the water incorporated in the polymer matrix or aqueous polymer solution. We have also shown that the retention of inorganic anions such as nitrate and iodide ions on a PS-DVB column depends on the eluent electrolyte when eluted with acetonitrile-water; in a certain electrolyte system, they retain less (28) Shibukawa, M.; Ohta, N. Chromatographia 1988, 25, 288-294. (29) Shibukawa, M.; Ohta, N.; Onda, N. Bull. Chem. Soc. Jpn. 1990, 63, 34903494. (30) Shibukawa, M.; Aoyagi, K.; Sakamoto, R.; Oguma, K. J. Chromatogr., A 1999, 832, 17-27. (31) Baba, T.; Shibukawa, M.; Heya, T.; Abe, S.; Oguma, K. J. Chromatogr., A 2003, 1010, 177-184. (32) Baba, T.; Sakamoto, R.; Shibukawa, M.; Oguma, K. J. Chromatogr., A 2004, 1040, 45-51. (33) Shibukawa, M. Bunseki Kagaku 2006, 55, 149-162.

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on the column than deuterated water.28 This suggests that water can be a component of the solvated phase even on the RPLC packing materials. We clarified the retention mechanism of ionic solutes in partition chromatography34,35 and proposed an original method for determination of the mobile-phase volume in liquid chromatography based on the ion partition model presented.28 It has been demonstrated that the method gives a reasonable value as Vm in RPLC as well as in normal-phase liquid chromatography (NPLC) not only in a water-organic solvent mixture but also in a pure water system.28 This method has also been applied successfully to the determination of the mobile-phase volume and the volume of hydrated phase in various kinds of hydrophilic and hydrophobic polymer gels in water.29-33 The idea of this method is based on the fact that the ratio of the retention factors of two analyte ions with the same charge is constant regardless of the eluent electrolytes. This is the case for a system where the activity coefficients of the analyte ions can be regarded as the same as each other both in the mobile phase and in the stationary phase.34,35 The mobile-phase volume is then given by the following equation:

Vm )

VAYXVBWZ - VAWZVBYX VAYX + VBWZ - VAWZ - VBYX

(2)

where A and B represent analyte ions and YX and WZ eluent electrolytes.16 This equation reveals that the mobile-phase volume can be calculated from the retention volumes of two equally charged analyte ions determined in two eluent electrolyte systems. In a dilute aqueous solution of strong electrolytes of which the ionic strength is 0.1 M or less, the activity coefficient of an ion can be assumed to depend only on the total ionic strength of the solution and the valency of the ion.34,36 Therefore, this method can be applied to the systems where the association of an analyte ion with counterions can be neglected, the concentration of an analyte ion is negligibly smaller than that of eluent electrolyte, and the stationary phase into which an analyte ion partitions can be regarded as made up of one homogeneous phase. More than 10 years ago, just after we had presented this method, we tried to determine the Vm values of several commercially available alkyl-bonded silica columns according to eq 2. However, we failed in obtaining reasonable Vm values. The calculated values were scattered depending on the combinations of analyte ions and eluent electrolytes used; some of the values were negative and others were larger than the total liquid volume in the column.37 This result was supposed to be due to the interaction with unreacted silanols on the silica surface. Actually, it was also impossible to obtain a reasonable Vm value for a silica column in normal-phase mode, the scattering of the calculated values being much greater than that observed for the alkyl-bonded silica columns. In recent years, however, silica-based packing materials with virtually no residual silanols have been developed by new technologies such as polymeric end capping or polymer coating (34) Shibukawa, M.; Ohta, N.; Kuroda, R. Anal. Chem. 1981, 53, 1620-1627. (35) Shibukawa, M.; Ohta, N. Chromatographia 1986, 22, 261-267. (36) Davies, C. W. J. Chem. Soc. 1938, 2093-2098. (37) Shibukawa, M., unpublished results.

of a silica support.38-41 We have thus tried again to apply our method to the determination of the mobile-phase volumes in several commercially available alkyl-bonded silica columns using aqueous solutions of acetonitrile, methanol, and tetrahydrofuran as eluents. In this paper, the validity of the Vm values calculated from eq 2 are evaluated by comparing them with the values obtained from the retention volumes of various organic and inorganic compounds, which have so far been suggested as unretained markers, and those obtained on the basis of a linear dependence of the logarithmic retention factor on the carbon numbers of homologous series. The amount and composition of the eluent solvent layer formed by solvation of the bonded phase were also estimated from the Vm values, and the relationship between these properties of the solvent layer and the structure of the packing material was discussed. EXPERIMENTAL SECTION Chemicals. All chemicals used in this study were obtained from commercial sources and were of reagent-grade unless otherwise stated. HPLC grade acetonitrile, methanol, and tetrahydrofuran were obtained from Kanto Chemicals (Tokyo, Japan). Deuterated compounds for water (D2O), methanol (CD3OH), acetonitrile (CD3CN), and tetrahydrofuran (C4D8O) for NMR use were purchased from Wako Pure Chemicals (Tokyo, Japan). Water was purified subsequently with an Auto Still WG 202 (Yamato, Tokyo, Japan) and an Autopure WR 600A (Yamato). The columns used were Inertsil ODS-3V (GL Sciences, Tokyo, Japan), L-column ODS (Chemicals Evaluation and Research Institute, Tokyo, Japan), and Capcell Pak C1 UG120, C8 UG120, C18 UG80, C18 UG120, and C18 UG300 (Shiseido, Tokyo, Japan). The particle size of all the packing materials used in this study was 5 µm. The column size, 150 × 4.6 mm, was also the same for all the columns used. Chromatographic Conditions. Chromatographic measurements were performed on an HPLC system consisting of a Nihon Dionex (Tokyo, Japan) model AIP-1 pump, a Rheodyne (Cotati, CA) model 9725 loading injector fitted with a 20-µL sample loop, a Senshu Scientific (Tokyo, Japan) model SSC UV detector, and a Tosoh (Tokyo, Japan) model RI-8020 refractometric detector. The columns were thermostated at 313 K using a Waters model CHM column oven. Water or aqueous solutions of acetonitrile, methanol, or tetrahydrofuran were used as eluents. For determination of the Vm value of a column according to eq 2, the eluents containing sodium chloride and sodium perchlorate with ionic strength of 0.1 M were used. All the eluents were filtered through a 0.45-µm membrane filter JHWPO 4700 obtained from Nihon Millipore (Yonezawa, Japan) and degassed with an aspirator in a Yamato Scientific (Tokyo, Japan) model 2510J-MT ultrasonic bath before use. Elutions were carried out at a constant flow rate of ∼0.5 mL min-1. The exact values of the volumetric flow rate were measured using a buret designed to prevent the vaporization of the solvent. The extracolumn volume was determined by measuring the elution volume of a sample solute through the system from which (38) Shirota, O.; Ohtsu, Y.; Nakata, O. J. Chromatogr. Sci. 1990, 28, 553-558. (39) Kobayashi, S.; Tanaka, I.; Shirota, O.; Kanda, T.; Ohtsu, Y. J. Chromatogr., A 1998, 828, 75-81. (40) http://www.cerij.or.jp/06_05_english/Chromato/En_L_spec.html. (41) http://www.shiseido.co.jp/e/hplc/column/html/col_abou.htm.

Table 1. Retention Volumes (mL) of Univalent Inorganic Ions Used as Probe Ions on an Inertsil ODS-3V Column concentration of acetonitrile (% w/v) eluent electrolyte

probe ion

0

2

5

10

15

20

40

NaClO4

IO3BrNO3ISCNIO3BrNO3ISCN-

1.74 1.78 1.82 1.86 2.11 1.80 1.87 1.93 2.02 2.43

1.69 1.73 1.76 1.83 2.06 1.78 1.87 1.92 2.05 2.50

1.65 1.70 1.71 1.78 1.97 1.73 1.84 1.88 2.02 2.41

1.62 1.66 1.68 1.73 1.87 1.68 1.78 1.82 1.94 2.24

1.58 1.62 1.63 1.68 1.78 1.65 1.74 1.78 1.90 2.10

1.54 1.57 1.58 1.63 1.71 1.63 1.72 1.75 1.87 2.04

1.48 1.49 1.51 1.53 1.57 1.44 1.51 1.53 1.61 1.67

NaCl

the column had been removed. The weight of the each column packing material in the column was determined after the packing was quantitatively transferred into a glass filter and then dried in an oven at 363 K until a constant weight was reached. Test solutions were prepared by dissolving analyte compounds in the eluent to be used. Inorganic anions, uracil, thiourea, and phloroglucinol were detected with the UV detector, while n-alcohols, D2O, CD3CN, CD3OH, and C4D8O were monitored with the refractometric detector. The detection signal was fed into a CAC data analysis system (Nihon Filcon, Tokyo, Japan). RESULTS AND DISCUSSION Determination of the Mobile-Phase Volume. The retention volumes of IO3-, Br-, NO3-, I-, and SCN- obtained on an Inertsil ODS-3V column by elution with 0-40%(w/v) acetonitrile-water containing 0.1 M NaCl or NaClO4 are listed in Table 1. The ionic strength of the eluent was set at 0.1 M in order to suppress the Donnan exclusion due to the possible presence of residual silanol groups. By substituting the retention volumes of the inorganic anions into eq 2, we can obtain the Vm value and the results are tabulated in Table 2. As can be seen from Table 2, the Vm values calculated from each combination of two analyte ions are in excellent agreement with one another. This indicates that the activity coefficients of these inorganic anions can be regarded as the same as one another not only in the mobile phase but also in the stationary phase, and then the ratio of the retention factors of two singly charged ions is constant regardless of the background eluent electrolytes although the retention factors themselves depend on the type of the eluent electrolyte. We have thus evaluated the validity of the Vm value calculated according to eq 2 by comparing the Vm values shown in Table 2 with those obtained by the use of various marker compounds that have been suggested as unretained solutes as well as by linearization of the retention data of a homologous series. A lot of organic compounds and inorganic ions have so far been suggested as unretained solutes for use as a mobile-phase volume marker.1,2,4-18 Among them, we adopted phloroglucinol, thiourea, uracil, NO3-, and D2O. The retention volumes of these markers are shown in Figure 1 together with the Vm value obtained by eq 2 as a function of the concentration of acetonitrile in the eluent. The retention volumes of NO3- shown in Figure 1 are the values obtained in the eluent systems containing 0.1 M NaClO4. Analytical Chemistry, Vol. 79, No. 16, August 15, 2007

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Table 2. Vm Values (mL) Calculated from Eq 2 for an Inertsil ODS-3V Column concentration of acetonitrile (% w/v) probe ion

0

2

5

10

15

20

40

IO3-/BrIO3-/NO3IO3-/IIO3-/SCNBr-/NO3Br-/IBr-/SCNNO3-/INO3-/SCNI-/SCN-

1.62 1.63 1.65 1.64 1.65 1.67 1.64 1.69 1.64 1.59

1.62 1.61 1.60 1.60 1.59 1.57 1.58 1.56 1.58 1.59

1.60 1.60 1.59 1.58 1.60 1.57 1.57 1.55 1.56 1.57

1.58 1.58 1.57 1.57 1.58 1.57 1.56 1.57 1.55 1.54

1.54 1.54 1.53 1.53 1.49 1.51 1.51 1.52 1.51 1.49

1.49 1.49 1.48 1.48 1.52 1.47 1.46 1.43 1.44 1.44

1.49 1.50 1.50 1.50 1.45 1.47 1.47 1.49 1.49 1.43

average (SD)

1.64 ((0.03)

1.59 ((0.02)

1.58 ((0.02)

1.57 ((0.01)

1.52 ((0.02)

1.47 ((0.03)

1.48 ((0.02)

A lot of researchers have shown that a linear dependence of the logarithmic retention factor, log k, on the carbon number of successive members of the homologous series, nc, is observed in RPLC, being represented as

log k ) anc + b

(3)

where a and b are constants.7,8,11,19-25 Therefore the mobile-phase volume could be obtained from the retention volumes of members of the homologous series if the relationship given by eq 3 exists. For three consecutive homologues, nc ) n, n + 1, n + 2, we can write

kn+1/kn ) kn+2/kn+1

(4)

where kn is the retention factor of the homologous compound of nc ) n and is calculated from the equation

kn ) (Vn - Vm)/Vm

Figure 1. Dependence of the retention volumes of some marker compounds and the Vm value on concentration of acetonitrile in the eluent. Column: Inertsil ODS 3V. Eluent: acetonitrile-water solution. Column temperature: 313 K. Symbols: (∆) phloroglucinol, ([) uracil, (0) thiourea, (]) D2O, (2) NO3-, and (O) Vm. See text for discussion.

The results shown in Figure 1 indicate that all the markers used give retention volumes greater than the Vm value calculated from eq 2. Particularly, phloroglucinol and uracil show very strong retention in the eluent systems with acetonitrile concentration of 20% (w/v) or less, and in some cases, their retention volumes exceed even the total column volume. It should be noted that D2O, which is usually assumed as an ideal compound as the Vm marker in RPLC, has a retention volume larger than that of NO3- as well as the Vm value obtained by eq 2. This reveals that D2O cannot necessarily give the true mobile-phase volume. Although the retention volume of NO3- is very close to the Vm value obtained by eq 2 in the range of acetonitrile concentrations studied, it must be noted that the retention of ionic solutes depends on the eluent electrolyte as shown in Table 1, indicating that they are retained on the RPLC column. Therefore, inorganic ions such as NO3cannot also be regarded as an ideal Vm marker. 6282

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(5)

where Vn is the retention volume of the homologue. Substituting eq 5 and the corresponding equations for kn+1 and kn+2 into eq 4, we obtain

Vm )

VnVn+2 - Vn+12 VnVn+2 + 2Vn+1

(6)

We used normal alcohols with the carbon number of 1-8 for determination of the Vm value by eq 6. The retention volumes of the alcohols obtained on the Inertsil ODS-3V column by elution with 15-50% (w/v) acetonitrile-water and the Vm values calculated from eq 6 are given in Tables 3 and 4, respectively. It is evident from Table 4 that the Vm value calculated from eq 6 changes significantly with a change in the carbon number of the alcohols examined. In order to circumvent this problem, Laub and Madden25 introduced a graphical method of determining the bestfit Vm value. This method consists of plotting the correlation coefficient, r, of plots of log k versus nc against candidate Vm value, and the plot with the highest r determines the Vm value. The Vm values determined according to their method are tabulated in Table 5. As well as the Vm values calculated for the entire series

Table 3. Retention Volumes (mL) of n-Alcohols on an Inertsil ODS-3V Column

m L Table 6. VD2O, VCD3CN, V0, VL, φCH , and φCH Values 3CN 3CN Determined for an Inertsil ODS-3V Column

concentration of acetonitrile (% w/v)

CH3OH C2H5OH C3H7OH C4H9OH C5H11OH C6H13OH C7H15OH C8H17OH

15

20

40

50

2.01 2.28 3.21 5.71 12.89

1.95 2.14 2.80 4.32 8.07

1.69 1.97 2.23 2.65 3.32 4.48 6.41 9.67

1.81 1.93 2.11 2.35 2.71 3.25 4.07 5.31

Table 4. Vm Values (mL) Calculated from Eq 6 for an Inertsil ODS-3V Column concentration of acetonitrile (% w/v) carbon no. of n-alcohols nc ) 1, 2, 3 nc ) 2, 3, 4 nc ) 3, 4, 5 nc ) 4, 5, 6 nc ) 5, 6, 7 nc ) 6, 7, 8

15

20

40

50

1.91 1.72 1.86

1.87 1.62 1.78

8.97 1.52 1.55 1.70 1.61 0.62

1.60 1.26 1.63 1.69 1.57 1.71

Table 5. Vm Values (mL) Determined for an Inertsil ODS-3V Column by Linearization of Retention Data of n-Alcohols (Laub and Madden’s Method) concentration of acetonitrile (% w/v) carbon no. of n-alcohols chromatographed nc ) 1-5 nc ) 2-5 nc ) 1-8 nc ) 2-8 nc ) 3-8

15

20

1.86 1.77

1.81 1.67

40

50

1.35 1.59 1.63

1.58 1.59 1.64

studied, the values for its segments obtained by eliminating methanol or methanol and ethanol are also listed for comparison. This method apparently reduces the scatter, and the values obtained appear to be more reasonable than those obtained by the use of some marker compounds. However, the Vm value obtained by this method is still affected rather substantially by the choice of which set of homologues is used for the calculation, and some values are too small or too large to be accepted as the mobile-phase volume. These results described above suggest that the Vm value calculated from eq 2 is the most reasonable one as the mobilephase volume. Figure 1 shows that the Vm value gradually decreases with increasing concentration of acetonitrile. This can be attributed to the increase in the volume of the eluent solvent layer formed on alkyl-bonded silica. As shown in Table 1, the retention of the each anion is greater in the NaCl eluent system than in the NaClO4 system. This eluent electrolyte effect on the retention of an anionic solute is similar to that observed in a PSDVB column28 and can be ascribed to the difference in partition coefficient of the coion, i.e., chloride ion and perchlorate ion, into the eluent solvent layer.

concentration of acetonitrile (% w/v)

VD2O (mL) VCD3CN (mL) V0 (mL) VL (mL) m φCH 3CN L φCH 3CN

0

10

15

20

1.96

1.89 2.49 1.97 0.40 0.13 0.30

1.83 2.38 1.96 0.44 0.19 0.40

1.79 2.24 1.91 0.44 0.26 0.46

1.96 0.32

100 2.01 2.01

Table 7. Vm, VL, φim, and φiL Values Determined for an Inertsil ODS-3V Column Equilibrated with Aqueous Mobile-Phase Systems Containing 10% (w/v) Organic Modifiers

Vm (mL) VL (mL) φm i φLi

methanol

acetonitrile

tetrahydrofuran

1.62 ( 0.05 0.37 0.13 0.13

1.57 ( 0.01 0.40 0.13 0.30

1.49 ( 0.01 0.45 0.11 0.34

As well as the retention of the each inorganic anion, the difference in the retention between these anions decreased with increase in concentration of acetonitrile in the eluent so that the precise determination of the Vm value according to eq 2 was difficult for the system with an acetonitrile-water composition of 40% (w/v) acetonitrile or above. Actually, some Vm values obtained for 40% (w/v) acetonitrile system are larger than the retention volumes of IO3- and Br-. This may be due to poor precision caused by the extreme closeness of the retention volumes of the probe ions or some effect of eluent electrolyte on the state of the solvent layer formed on alkyl-bonded phase at high concentrations of acetonitrile. Evaluation of the Composition of the Solvent Layer Formed on the Surface of an Alkyl-Bonded Phase. The total liquid volume in the column or the void volume is obtained by eq 1 by measuring the retention volumes of the isotopically labeled eluent components. Therefore, the volume and the composition of the solvent layer formed on the surface of the alkyl-bonded phase can be calculated according to eqs 7 and 8, respectively.

VL ) V0 - Vm φLi ) φm i

(VR,i - Vm) VL

(7) (8)

where VL is the total volume of the solvent layer formed on the surface of the alkyl-bonded phase in the column and φLi is the volume fraction of the eluent component i in the layer. The V0 and VL values calculated for 0-100% (w/v) acetonitrilewater eluent systems are given in Table 6 together with the retention volumes of D2O (VD2O) and CD3CN (VCD3CN). The V0 values obtained are approximately constant independent of the composition of the eluent, giving V0 ) 1.96 ( 0.04 mL. The L φCH values calculated according to eq 8 are also listed in 3CN m Table 6 together with φCH values. As seen in Table 6, the 3CN Analytical Chemistry, Vol. 79, No. 16, August 15, 2007

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L H Table 8. Vm, VL, VH, V0, φCH , and φCH Values Determined for C1, C8, and C18 Silica Columns Equilibrated with 20% 3CN 3CN (w/v) Acetonitrile-Water

C1 silica 1: Capcell Pak C1 UG120 C8 silica 2: Capcell Pak C8 UG120 C18 silica 3: Inertsil ODS-3V 4: L-column ODS 5: Capcell Pak C18 UG80 6: Capcell Pak C18 UG120 7: Capcell Pak C18 UG300

Vm (mL)

VL (mL)

VH (mL)

V0 (mL)

1.72

0.39

0.54

1.71

0.35

1.47 1.66 1.46 1.61 2.01

0.44 0.33 0.29 0.30 0.19

concentration of acetonitrile in the solvated liquid layer is greater than that in the eluent or the mobile phase as expected from the difference from water in affinity to alkyl groups. It must be noted, however, that water is also a component of the solvent layer on C18 silica, and even in pure water system, water molecules form a solvated layer, which functions as a stationary phase. We consider that there is little possibility that the formation of the solvated water layer could be attributed to the residual silanol groups. If the solvated water phase is formed on the silanol groups and acetonitrile is adsorbed on alkyl groups, there should be two different stationary phases leading to mixed retention mechanisms, which would make it impossible to determine the Vm value according to eq 2. As described above, we could not obtain reasonable Vm values for the alkyl-bonded silica columns containing a substantial amount of residual silanols.37 In order to examine the effect of organic modifier on the solvation of the alkyl-bonded silica, the volume and the solvent composition of the solvated liquid layer was determined for methanol-water and tetrahydrofuran-water eluent systems using the same Inertsil ODS-3V column. The Vm, VL, φLi , and φm i obtained were tabulated in Table 7 together with the data for acetonitrile-water system. All these data are those obtained for the eluent systems containing organic modifier of 10% (w/v); the solubility of NaCl is lower than 0.1 M in the tetrahydrofuranwater mixture at the concentration of 20% (w/v) or more. The VL values were calculated from the V0 values determined using the corresponding isotopically labeled compounds, i.e., D2O, CD3OH, CD3CN, and C4D8O. Again, in methanol-water and tetrahydrofuran-water systems, the Vm values calculated from each combination of two probe ions were in excellent agreement with one another. D2O and CD3OH both coeluted with a system peak in a 10% (w/v) methanol-water system so that we calculated the V0 and L φCH values by assuming that the retention volumes of D2O 3CN and CD3OH were identical to that of the single observed peak. As can be seen from Table 7, the volume of the solvated liquid layer and the volume fraction of organic modifier in the layer increase with increase in hydrophobicity or eluting strength of the organic solvent in RPLC. These results suggest that the liquid layer on the alkyl-bonded phase may be formed by adsorption of the organic solvent as well as formation of a structure of water around the hydrophobic moieties different from that of the bulk water. Dependence of the Volume and Composition of the Solvated Liquid Layer on the Physicochemical Structure of 6284

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L ΦCH 3CN

H ΦCH 3CN

2.11

0.41

0.30

0.55

2.06

0.42

0.27

0.77 0.70 0.75 0.64 0.37

1.91 1.99 1.75 1.91 2.20

0.46 0.45 0.46 0.43 0.46

0.26 0.21 0.18 0.20 0.24

L the RPLC Packing Material. We determined the VL and φCH 3CN values for a C8 and a C1 silica column as well as five commercially available C18 silica columns with different pore size and surface area in order to investigate the dependence of these values on the chemical and physical structures of the packing materials. The L VL and φCH values as well as Vm and V0 obtained for all the 3CN columns equilibrated with 20% (w/v) acetonitrile-water are L summarized in Table 8. It is very interesting that the φCH 3CN value does not depend on the type of column, and even the C1 and C8 silica columns exhibit nearly the same solvent composition in the solvated liquid phase as that for the C18 silica columns, L although the φCH values for the C1 and C8 silicas are a little 3CN lower than those for the C18 silicas. This indicates that the solvent composition in the solvated layer primarily depends on the surface chemical structure, which is in contact with the eluent solvents. If it can be assumed that alkyl chains bonded on silica particles form a homogeneous phase involving water and an organic modifier, then the volume of the homogeneous phase, VH, and the volume fraction of solvent i in the phase, φH i , are evaluated according to the following equations.

VH ) VL + Vb m φH i ) φi

(VR,i - Vm) VH

(9) (10)

where Vb is the volume of the alkyl-bonded phase in the column. H values for the columns studied are given in The VH and φCH 3CN L Table 8 for comparison with VL and φCH . The Vb value was 3CN calculated by the following equation assuming that the densities of the alkyl groups are identical to that of n-octadecane at 301 K, FC18, being estimated to be 0.766 g cm-3 according to a modified Rackett equation:42

Vb ) (wCn - wsilica)/FC18

(11)

where wCn (n ) 1, 8, or 18) and wsilica are the weights of the packing material and of the base silica gel in the column, respectively. We estimated the wsilica value from wCn and the carbon content, C%, as follows by assuming that the origin of carbon of the packing material is only alkyl groups:

C% 2n + 1 C% H% ) w [1 + + 1)] [ (100 100)] 100 ( 12n

wsilica ) wCn 1 -

Cn

(12)

Table 9. Values of Surface Area and Pore Diameter for C1, C8, and C18 Silica Columns Studied c Aa dporea Ac dpore (m2 g-1) (nm) (m2 column-1) (nm)

C1 silica 1: Capcell Pak C1 UG120 C8 silica 2: Capcell Pak C8 UG120 C18 silica 3: Inertsil ODS-3V 4: L-column ODS 5: Capcell Pak C18 UG80 6: Capcell Pak C18 UG120 7: Capcell Pak C18 UG300 a

290

12.0

338

9.7

290

12.0

337

9.4

427 340 344 290 149

10.2 12.0 8.1 12.0 30.0

505 378 428 346 124

4.6 8.7 26.6

Manufacturers’ data.

where H% is the hydrogen content. As can be seen from Table 8, H varies from one column to the other, contrary to the φCH 3CN H L φCH3CN. It is expected that an identical φCH value should be 3CN given for all the C18 columns if the octadecyl group forms a homogeneous phase consisting of the alkyl chain, water, and acetonitrile. This result suggests that the stationary phase in reversed-phase liquid chromatography may rather be regarded as an alkyl-bonded layer covered by an eluent solvent layer formed by solvation of the bonded phase. We infer that the solvated liquid phase consisting of acetonitrile and water is accessible to inorganic ions, whereas the alkyl-bonded phase is not. On the other hand, the VL value also varies from one to the other. This result suggests that the volume or the thickness of the liquid layer depends on the physical structure of the packing material. Table 9 gives specific surface areas, A, and average pore diameters, dpore, for the alkyl-bonded silica packings studied. These values are given for base silica gels, and the A values are expressed in units per gram of silica gel. Therefore, the surface area expressed in units per column, Ac, is given by

Ac ) Awsilica

(13)

Although the surface area may also be decreased by chemical modification of the base silica, we assumed that the Ac value of

Figure 2. Relationship between VL and Ac values for the C18 silica columns. The numbers denote the columns shown in Tables 8 and 9. See text for discussion.

the alkyl-bonded silica was the same as that of the base silica in the following discussion. The pore diameter for the bonded silica should be smaller than those for the bare silica due to chemical derivatization of the alkylbonded phase. The pore diameters of the bonded silica, dcpore, for the column packings of Capcell Pak series were thus estimated by the following equation:

dcpore ) dpore - 2Vb/Ac - 2ls

(14)

where ls denotes the thickness of the silicone polymer layer coated on the base silica ()0.7 nm41). The dcpore values for Inertsil ODS3V and L-column ODS could not be calculated because of the lack of the quantitative data for surface modification. The calculated values of the Ac and dcpore values are also given in Table 9. Figure 2 illustrates the relationship between the VL and the Ac values for the C18 silica columns. As can be seen from Figure 2, the plots for Inertsil ODS-3V, L-column ODS, and Capcell Pak C18 UG120 approximately fall on a straight line going through the origin. On the other hand, the plot for Capcell Pak C18 UG300 shows the VL value larger than that expected from the straight line obtained from the plots for the three columns, while the plot for Capcell Pak C18 UG80 gives a smaller VL value than the one expected. The pore diameters of Inertsil ODS-3V, L-column ODS,

c Figure 3. Plots of VL/Ac against dpore for the Capcell Pak columns. The numbers denote the columns shown in Tables 8 and 9. See text for discussion.

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and Capcell Pak C18 UG120 are nearly the same, while Capcell Pak C18 UG300 and UG80 have larger and smaller dcpore values than those of the former three packing materials, respectively. Therefore, the result shown in Figure 2 reveals that the VL value depends not only on the surface area but also on the pore size of the packing material. Figure 3 illustrates the plots of VL/Ac versus dcpore for the Capcell Pak columns including the C8 and C1 silicas as well as the C18 silica columns. As seen in Figure 3, The VL/Ac value increases with increase in the dcpore value until it reaches the maximum, 1.6 nm, and at dcpore of 10 nm or above, the dependence of VL/Ac value on dcpore becomes small and eventually constant independent of dcpore. This suggests that the thickness of the solvated liquid phase formed in the 20% (w/v) acetonitrilewater system can be regarded as ∼1.6 nm, and the full formation of the solvated liquid phase is restricted in narrow pores. The dcpore values given in Table 9 are the average values and the base silica gels have pore size distribution. The fact that the VL/Ac does not reach the maximum even on a packing material that has dcpore value of 10 nm may be ascribed to the presence of small pores of which the diameter is less than the average. In addition, we estimated the Ac values from the manufacturers’ data for the base silicas. The surface area of the alkyl-bonded silica may be smaller than that of the base silica. Therefore the thickness of the solvated liquid phase should probably be larger than 1.6 nm. CONCLUSIONS We have concluded that the solvated liquid phase on a column packing material should be assigned to a part of the stationary phase and the method developed for determination of the Vm value based on the ion partition model gives the most reasonable value as the mobile-phase volume in RPLC as well as in NPLC. The idea of this method is based on the fact that the ratio of the retention factors of two analyte ions with the same charge is constant regardless of the eluent electrolytes. Small inorganic anions used as the analyte ions can be regarded as probes that differentiate between the bulk liquid phase and the solvated liquid (42) Reid, R.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill; New York, 1987; p 67.

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layer. It has been shown that the Vm determinations by the use of marker compounds and by linearization of the retention data of a homologous series do not give accurate and precise Vm values. We calculated the volume of the solvated liquid phase formed on alkyl-bonded silica particles from the mobile-phase volume and the void volume determined by the method proposed by Knox and Kaliszan.3 Furthermore, the solvent composition of the solvated liquid phase was estimated from the VL value and the retention volumes of the isotopically labeled eluent components. It has been demonstrated that the VL value and the volume fraction of organic modifier in the solvated liquid layer on the alkyl-bonded silica increase with increase in hydrophobicity and concentration of the organic solvent. We have also shown that, even in a pure water eluent system, the solvated water phase is formed on the surface of alkyl-bonded silica. All the commercially available C1, C8 and C18 silica columns used exhibited approximately the same solvent compositions in the solvated phase, while the VL value strongly depends on the physical structure such as pore size and specific surface area of the RPLC packings. From the results obtained, we have concluded that the stationary phase in reversed-phase liquid chromatography may rather be regarded as an alkyl-bonded phase covered by an eluent solvent layer formed by solvation of the bonded phase. The thickness of the solvated liquid phase formed on the alkyl-bonded silica in a 20% (w/v) acetonitrile-water system has been estimated to be ∼1.6 nm or more. ACKNOWLEDGMENT This research was supported by a Grant-in-Aid for Scientific Research No. 18550081 from Ministry of Education, Culture, Sports, Science and Technology, Japan, and a grant from High Technology Research Center, College of Industrial Technology, Nihon University.

Received for review January 30, 2007. Accepted June 19, 2007. AC0701839