pH Gradient Reversed-Phase HPLC - American Chemical Society

Anal. Chem. 2004, 76, 749-760

pH Gradient Reversed-Phase HPLC Roman Kaliszan,* Paweł Wiczling, and Michał J. Markuszewski

Department of Biopharmaceutics and Pharmacodynamics, Medical University of Gdan´ sk, Gen. J. Hallera 107, 80-416 Gdan´ sk, Poland

pH gradient HPLC is reported, which is a new original mode of reversed-phase high-performance liquid chromatography applicable to ionogenic analytes. The method consists of programmed increase during the chromatographic run of the eluting strength of the mobile phase with respect to the acid/base analytes separated. Unlike the well-established conventional gradient HPLC, where the eluting power of the mobile phase is increased with time due to the increasing content of organic modifier, in the pH gradient HPLC that is realized by linearly increasing (in the case of acids) or decreasing (in the case of bases) the pH of the eluent of a fixed organic modifier content, thus providing functional increase in the degree of analyte dissociation and, hence, a decrease in its retention. The pH gradient mode has typical features of gradient HPLC, such as reduced peak width and minimized peak-tailing due to peak compression, which is especially advantageous in the case of organic base analytes. It may be of special value for separation of those analytes which are susceptible to the higher concentrations of organic solvents, as many bioanalytes are. A theory of the pH gradient HPLC has been elaborated, and its full mathematical formalistic is presented step by step in a comprehensive manner. Although fundamental relationships at the basis of pH gradient HPLC are more complex than in the case of the organic gradient variant, the resulting mathematical model is easily manageable. Its applicability to predict changes in retention and separation of test mixtures of analytes accompanying the changes in chromatographic conditions has been demonstrated experimentally in both gradient and isocratic HPLC. The proposed model supplies a rational basis for modifications of eluent pH aimed at optimization of separations and for convenient assessment of chromatographically relevant physicochemical parameters of analytes, such as pKa. Gradient mode of high performance liquid chromatography (HPLC) allows for separations of mixtures of analytes which are normally not attainable with the standard isocratic mode. The term “gradient HPLC” refers to a programmed change (usually linear) of the eluting power of the mobile phase during the chromatographic run, whereas isocratic HPLC is carried out with constant composition of the eluent. Normally, the change (increase) of * Corresponding author. Telephone: ++48 58 3493260. Fax: ++48 58 3493262. E-mail: [email protected]. 10.1021/ac034999v CCC: $27.50 Published on Web 12/31/2003

© 2004 American Chemical Society

eluting strength of the mobile phase is provided by adding a stronger solvent B (organic) to a weaker solvent A (usually water). Such organic solvent gradient elution in so-called reversed-phase HPLC has been described in rigorous theoretical terms.1-4 It is more and more often used for routine chemical and biomedical assays.5 Retention of ionogenic analytes in reversed-phase HPLC is known to strongly depend on the pH of the eluent. The retention factor, k, of a nondissociated form of an acid or base may be 1020 times larger than that of the respective dissociated form at given composition of the water-organic mobile phase. That offers a convenient means to rationally modify separation of ionizable compounds, provided that a stringent theory is available. Such a theory for isocratic systems was first presented and tested for a buffered water mobile phase by Horvath at al.6 Next, Van de Venne at al.7 extended the studies on the relationships between eluent pH and analyte retention to the methanol-water mobile phases. A complete mathematical formalistics to model retention in isocratic mode of reversed-phase HPLC as a function of pH at given mobile phase compositions has been reported by Lopes Marques and Schoenmakers.8 Rules of selection of pH of the mobile phase to optimize separations of mixtures of analytes have recently been reported by Snyder and co-workers.9 The results of exhaustive studies on the effects of organic modifiers on acid-base equilibria in mobile phases, along with a critical review of a vast amount of literature on the subject, have been presented in a most competent and comprehensive report by Roses and Bosch.10,11 An excellent upto-dated presentation of the subject has recently been published by Barbosa et al.12 The effect of pH on retention of bases was also recently examined by LoBrutto at al.13 (1) Snyder, L. R.; Kirkland, J. J.; Glajch, J. L. Practical HPLC Method Development, 2nd ed.; Willey-Interscience: New York, 1997. (2) Jandera, P.; Churacek, J. Gradient Elution in Column Liquid Chromatography, Elsevier: Amsterdam, 1985. (3) Snyder, L. R.; Dolan, J. W. Adv. Chromatogr. 1998, 38, 115-185. (4) Dolan, J. W.; Snyder, L. R.; Wolcott, R. G.; Haber, P.; Ba¸ czek, T.; Kaliszan, R. J. Chromatogr., A 1999, 857, 41-68. (5) Ba¸ czek, T.; Kaliszan, R.; Claessens, H. A., van Straten, M. A. LC-GC Europe 2001, 14, 304-313. (6) Horvath, C.; Melander, W.; Molnar, A. Anal. Chem. 1997, 49, 1142-154. (7) van de Venne, J. L. M.; Hendrikx, L. H. M.; Deelder, R. S. J. Chromatogr. 1978, 167, 1-16. (8) Lopez Marques, R. M.; Schoenmakers, P. J. J. Chromatogr. 1992, 592, 157182. (9) Jupille, T. M.; Dolan, J. W.; Snyder, L. R.; Molnar, J. J. Chromatogr., A 2002, 948, 35-41. (10) Roses, M.; Bosch, E. J. Chromatogr., A 2002, 982, 1-30 and references therein. (11) Espinosa, S.; Bosch, E.; Roses, M. Anal. Chem. 2002, 74, 3809-3818.

Analytical Chemistry, Vol. 76, No. 3, February 1, 2004 749

All of the literature reports on the use of pH modifications to affect HPLC separations refer to the pH value which is kept constant during the whole chromatographic run. Recently, we found it technically feasible to carry out reversed-phase HPLC with a linearly changing pH of the water (buffer)-organic eluents of fixed organic solvent contents.14-16 That kind of gradient HPLC was initially introduced with the aim of assessment of pKa values of drug candidates, often produced as mixtures by the modern methods of chemical synthesis, such as combinatorial chemistry methods. At the same time, we realized that the pH gradient HPLC could be of practical analytical (especially bioanalytical) importance, because many bioanalytes undergo structural and functional changes at the presence of higher concentrations of organic solvents, whereas most such bioanalytes tolerate well the changes in pH of their environment. We succeeded in describing the pH gradient HPLC retention in rigorous terms, avoiding oversimplifying assumptions, and we got an agreement between the experimental and the theoretically predicted chromatographic patterns. Bellow we report our approach. Theory. At the usual isocratic conditions (i.e., with the composition of the eluent kept constant during the whole chromatographic run) the retention time, tR, and retention volume, VR, of an analyte are described by the equations:

tR ) t0(1 + k)

(1a)

VR ) V0(1 + k)

(1b)

where t0 and V0 are dead (void) time or volume, respectively, of a nonretained (and nonexcluded) marker. The retention factor of the analyte at given chromatographic conditions is defined as

k)

tR - t0 tR′ VR′ ) ) t0 t0 V0

100; and S is a constant that is characteristic for a given analyte when chromatographed in a given HPLC system. For liquid chromatography with gradient elution (Figure 1), the fundamental equation describing analyte retention is19-21

dx )

dV V0(1 + ka(V, x))

where V is the volume of mobile phase that has passed through the column since the beginning of the gradient and ka is the instantaneous analyte retention factor, corresponding to the composition of the mobile phase in that part of the column in which the analyte band is actually present. That composition is the same as that of the mobile phase entering the column at the volume V - xV0 from the beginning of the gradient separation. Hence,

dx )

dV V0(1 + ki(V - xV0))

(3)

where kw corresponds to the retention factor, which would be provided by neat water eluent (φ ) 0); φ is the volume fraction of solvent B (organic modifier) in eluent, which is equal to %B/ (12) Sanli, N.; Fonrodona, G.; Barro´n, D.; Ozkan, G.; Barbosa, J. J. Chromatogr., A 2002, 975, 299-309 and references therein. (13) LoBrutto R.; Jones A.; Kazakevich, Y. V.; McNair, H. M. J. Chromatogr., A 2001, 913, 173-187. (14) Kaliszan, R.; Haber, P.; Snyder, L. R. Book of Abstracts, 23rd International Symposium HPLC 99, Granada, Spain, L/043. (15) Kaliszan, R.; Haber, P.; Ba¸ czek, T.; Siluk, D. Pure Appl. Chem. 2001, 73, 1465-1475. (16) Kaliszan, R.; Haber, P.; Ba¸ czek, T.; Siluk, D.; Valko, K. J. Chromatogr., A 2002, 965, 117-127.

Analytical Chemistry, Vol. 76, No. 3, February 1, 2004

(4a)

where ki represents the retention of the analyte independent of the composition of the mobile phase entering the column. Substituting V′ ) V - xV0, where V′ represents volume of the mobile phase that has passed through the band of the compound, the following can be obtained:

V0 dx + V0ki(V - xV0) dx ) dV

(4b)

V0ki(V - xV0) dx ) dV - V0 dx

(4c)

V0ki(V′) dx ) dV′

(4d)

dx )

750

(4)

(2)

where t′R and V′R are called the reduced retention time and volume, respectively. The last two terms of eq 2 are equivalent because V0 ) Ft0 and VR ) FtR, where F denotes the mobile phase flow rate. The relationship between composition of binary waterorganic eluent and isocratic k for a given analyte is considered in reversed-phase HPLC to be adequately described by the linear Snyder-Soczewiski relationship17,18

log k ) log kw - SΦ

Figure 1. Schematic presentation of basis of gradient elution.

dV′ V0ki(V′)

(4e)

Because for the whole column ∑ dx ) 1, eq 4e leads to eq 5a. In the upper integration limits of eg 5 appear the reduced retention volume (V′R ) VR - V0). (17) Schoenmakers, P. J.; Billiet, M. A. M.; de Galan, L. J. Chromatogr. 1981, 218, 261-284. (18) Ba¸ czek, T.; Markuszewski, M.; Kaliszan, R.; van Straten, M. A.; Claessens, H. A. J. High Resolut. Chromatogr. 2000, 23, 667-676. (19) Freiling, E. C. J. Am. Chem. Soc. 1955, 77, 2067-2071. (20) Snyder, L. C. Chromatogr. Rev. 1964, 7, 1-51. (21) Hansch, C.; Fujita, T. J. Am. Chem. Soc. 1964, 86, 1616-1626.

∫

VR′

1 dV )1 V0 ki

0

(5a)

ki represents the retention factor corresponding to the composition of the mobile phase at the beginning of the column. Analogously,

∫

tR′

0

1 dt )1 t0 ki

(5b)

with t′R ) tR - t0, denoting the reduced retention time. Snyder and Dolan3 solved eq 5b, arriving at the formula describing the retention time, tR, in organic-gradient mode of reversed-phase HPLC

tR ) (t0/b)log(2.303k0b + 1) + t0 + td

(6)

where b ) t0∆φS/tg denotes gradient steepness; k0 is analyte retention factor corresponding to the mobile phase composition at the start of gradient; td is the chromatographic system’s dwell time; ∆φ is the change in mobile phase composition during the whole gradient run; S is the constant characteristic for the defined analyte and the HPLC system applied; and tg is time of the gradient program. To get eq 6, Snyder and Dolan3 combined the linear relationship between the logarithm of the retention factor and the volume percent of the organic modifier in the mobile phase with linear change of modifier content with time (LSS theory: linear solvent strength theory). For the sake of comprehension, we will show below how one can arrive at eq 6. At first, it is assumed that eq 3 can be applied to determine the ki at gradient conditions after rewriting that equation in the following form

t log ki ) log k0 - b t0

(7)

t′R

0

10bt/t0 dt )1 k0t0

k ) f[HA]k[HA] + f[A-]k[A-]

(9a)

k ) f[BH+]k[BH+] + f[B]k[B]

(9b)

and for bases,

where f denotes mole fractions of specific forms. There are known relationships,

Now, eq 7 can be substituted into eq 5b, giving

∫

Actually, eq 6 needs corrections if k0 for the analyte is low or high. For low values of k0, a preelution of the analyte will take place, which will be the higher the longer td is and the lower k0 is. For the high values of k0 (when tR is longer than the sum of t0 + td + tg), eq 6 also needs correction. Equation 6 comprises two constants which are characteristic for the analyte and for the HPLC system (column and eluent) employed. These are k0 and S, which can be obtained by solution of a set of two equations of the type of eq 6. Because empirical solution is not possible, the set of equations is solved by numerical analysis. Appropriate procedures are included into available chromatographic softwares (e.g., DryLab, LC Resources, Walnut Creek, CA, used in our laboratory). Previously,15,16 we demonstrated application of eq 6 to determine from two organic-gradient reversed-phase HPLC runs the parameter log kw, considered commonly to be the most convenient and reliable chromatographic measure of analyte lipophilicity.21,22 pH gradient HPLC is obviously more difficult to describe theoretically than the standard organic modifier gradient mode. The reason is a complex (nonlinear) change of retention of ionizable compounds with the linearly changing pH of the mobile phase. However, a rigorous theoretical treatment is possible, as will be demonstrated below. It has been well-established that for ionizable compounds, the HPLC retention factor, k, is a weighted average of the retention factors of the nondissociated and the dissociated forms.6-11 Hence, for acids,

(8)

f[HA] )

1 Ka/[H+] + 1

f[A-] ) 1 - f[HA]

Solving eq 8,

∫

t′R

0

(10a) (10b)

t

10bt dt ) k0t0 0

[ ] t

t010bt0 2.303b

(8a)

t'R

0

) k0t0

(8b)

t′R

10b t0 - 1 ) k02.303b

(8c)

t′R ) (t0/b)log(2.303k0b + 1)

(8d)

one receives

After adding of the system dwell time to eq 8d, one eventually gets eq 6.

where Ka is the dissociation constant and [H+] denotes the hydrogen ion concentration. Equations 10a and 10b are for acids. Analogous equations hold for bases. In the treatment below, we will employ symbols pKa and pH in the meaning of swpKa and swpH (or sspKa and sspH) as defined by IUPAC, that is, referring to the data measured in the waterorganic solvent system actually employed and related to water (or actual solvent). Obviously, the sspKa and sspH values differ from the standard reference wwpKa and wwpH parameters10,11 obtained in water in the absence of organic modifiers. Although not fundamentally correct, this is the only realistic choice for the present project. Equations 9a and 9b can be transformed to the following wellestablished relationships.6-11 For acids, Analytical Chemistry, Vol. 76, No. 3, February 1, 2004

751

k)

k[HA] + k[A-](10pH-pKa) 1 + 10pH-pKa

)

k[A-] + k[HA](10pKa-pH) 1 + 10pKa-pH

(11a)

for bases,

k)

k[BH+] + k[B](10pH-pKa) 1 + 10pH-pKa

)

k[B] + k[BH+](10pKa-pH) 1 + 10pKa-pH

(11b)

In our pH gradient HPLC method, the value of pH changes linearly with time,

pH ) pH0 + at

(12)

where pH0 is the starting pH and a is the programmed rate of pH change. It is extremely difficult (if at all possible) to get an appropriate buffer that would give ideally linear pH changes, especially when mixing with organic modifier. Therefore, it should be mentioned here that eq 12 is of an approximate nature. Howewer the nonlinear pH changes are minimal and can be neglected. Hence, for retention factor, ki, at pH ) pH0 + at, eqs 11a and 11b can be rewritten in the forms of eqs 13a and 13b for acids and bases, respectively.

ki )

ki )

k[A-] + k[HA](10pKa-(pH0+at)) 1 + 10pKa-(pH0+at) k[BH+] + k[B](10

(13a)

Figure 2. Changes of instantaneous retention factor, ka, during pH gradient elution for a hypothetical base of pKa ) 7.

Now, one has to note that during the pH gradient elution, the actual pH of the mobile phase in the column at time t is delayed for a value of the HPLC system dwell time, td (Figure 2). Therefore,

pH ) pH0 when 0 < t < td

pH ) pH0 + a(t - td) when td < t < tg + td (16b) pH ) pH0 + atg when t g tg + td

(13b)

Substituting eqs 13a and 13b into eq 5b results in the following fundamental equations for pH gradient HPLC. For acids,

1 + 10

t′R 1

t0 k

0

[A-]

∫

t′[HA]

+ k[HA](10pKa-(pH0+at))

dt ) 1

∫ t′

1 + 10pKa-(pH0+a(t-td))

t′R

td

[A-]

+ t′[HA](10pKa-(pH0+a(t-td)))

dt ) 1

∫ t′ 1 td

dt +

[HA]

∫

1 + 10pKa-(pH0+a(t-td))

tg + td

t′[A-] + t′[HA](10pKa-(pH0+a(t-td)))

td

(14a)

∫

1

t′R

tg + tdt′ [A ]

dt +

dt ) 1 when t′R g tg + td (17c)

In the case of bases,

1 + 10(pH0+at)-pKa

t R′ 1

0

dt +

(17a)

when td < t′R < tg + td (17b) 0

pKa-(pH0+at)

1

td

and for bases,

∫

1 dt ) 1 when t′R e td t′[HA]

0

0

∫

∫

t′R

1 + 10(pH0+at)-pKa

(16c)

where pH0 denotes the pH at the beginning of the gradient run, and a is the rate of pH change (equal to ∆pH/tg). Eventually, taking gradient delay into account, the following equations describe retention time in pH gradient HPLC. In the case of acids,

(pH0+at)-pKa

)

(16a)

t0 k

[BH+]

(pH0+at)-pKa

+ k[B](10

)

dt ) 1

∫

(14b)

∫ t′1 td

0

Substituting t′ ) kt0 in eqs 14a and 14b, one arrives at, for acids,

∫

t′R

1 + 10pKa-(pH0+at) pKa-(pH0+at)

0

t′[A-] + t′[HA](10

)

dt ) 1

(15a)

t′R

0

dt +

[B]

∫

1 dt ) 1 when t′R e t t′[B] 1 + 10(pH0+a(t - td))-pKa

t′R

t′[HB+] + t′[B](10(pH0+a(t-td))-pKa)

td

(18a) dt ) 1

when td < t′R < tg + td (18b)

∫

td

0

1 dt + t′[B]

∫

1 + 10(pH0+a(t-td))-pKa

t g + td

t′[HB+] + t′[B](10(pH0+a(t-td))-pKa)

td

∫

t′R

tg + td

dt +

1 dt ) 1 when t′R g tg + td (18c) t′[BH+]

and for bases,

∫

0

752

t′R

1 + 10(pH0+at)-pKa

t′[BH+] + t′[B](10(pH0+at)-pKa)

dt ) 1


(15b)

Equations 17a and 18a describe analyte retention at constant pH conditions (isocratic with respect to pH) when t′[HA] and t′[B] do not change with time. To these equations, reduce eqs 15a and

15b, respectively, because the large difference between pH0 and pKa at t′R e td allows cancellation of the exponential terms. Equations 17a and 18a refer to a situation when the analytes are eluted from the column before pH gradient starts. Thus, eqs 17a and 18a account for the isocratic part of the chromatographic run and are relevant in the case of substances of low k and high (bases) or low (acids) pKa. Such a situation is of no actual theoretical pH gradient HPLC concern. Equations 17b and 18b account for the situation when analyte retention time is between the start and the end of the gradient. These equations are sums of two integrals. The first parts concern isocratic retention, as described by eqs 17a and 18a, respectively. The second parts reflect the retention at the actual pH gradient conditions. As a matter of fact, in situations when values of t′[HA] and t′[B] are relatively large (as often happens in practice), the first part in the second integral of eqs 17b and 18b can be neglected, and then the solution simplifies. Nevertheless, the solution of complete eqs 17b and 18b is also possible, and we will provide it below, step by step, for the sake of comprehension of the example of bases (eq 18b). After solving the first integral in eq 18b and rearrangement, one gets

td 1 + t′[B] t′[HB+]

1 + 10(pH0+a(tg-td))-pKa dt ) 1 td t′[B] 1+ (10(pH0+a(tg-td))-pKa) t′[HB+]

∫

t′R

(19)

td 1 1 + t′[B] ln 10 at′[HB+] 2A

[∫

(2A - 1)

(20a)

dy ) a10[pH0+a(t-td)]-pKa ln 10 dt

(20b)

dt )

1 ln 10 a(10[pH0+a(t-td)]-pKa) dt )

dy

(20c)

1 dy ln 10 ay

(20d)

t′R

td

t′R

td

A dy 1 + Ay

)] ) 1

(2A - 1)(ln|y| - ln|1 + Ay|)]tt'dR ) 1 td 1 1 + ln|y + Ay2| + t′[B] ln 10 at′[HB+] 2A

[

2A ln

|

| | |] | |]

y y - ln 1 + Ay 1 + Ay

td 1 1 y + ln(1 + Ay)2 + 2A ln t′[B] ln 10 at′[HB+] 2A 1 + Ay

[

[

td 1 1 + ln(1 + A10(pH0+a(t-td))-pKa)2 + t′[B] ln 10 at′[HB+] 2A

[

2A ln

|

10(pH0+a(t-td))-pKa

1 + A10

t′[B]

A)

|]

(pH0+a(t-td))-pKa

one can rewrite eq 19 as follows:

td 1 + t′[B] ln 10 at′[HB+]

∫

1+y dy ) 1 y + Ay2

t′R

td

(22)

td 1 1 + t′[B] ln 10 at′[HB+] 2A

[∫

∫

(

t′R

td

)

1 + 2Ay 2A - 1 + dy ) 1 y + Ay2 y + Ay2

+ 2Ay + y + Ay2

t′R1

td

(2A - 1)

(1y - 1 +AAy) dy] ) 1

t′R

)1

td

10(pH0+a(t′R-td))-pKa

]

1 + A10(pH0+a(t′R-td))-pKa 2A ln )1 10pH0-pKa 1 + A10pH0-pKa

Now, the pH value of the mobile phase at which the analyte leaves the column is denoted by pH**, that is, pH** ) pH0 + a(t′R - td). Hence,

[

]

10pH**-pKa 1 + A10pH**-pKa 1 + A10pH**-pKa 2 ln + 2A ln )1 pH0-pKa 1 + A10 10pH0-pKa 1 + A10pH0-pKa

[

td 1 1 1 + A10pH**-pKa + + log t′[B] at′[HB+] A 1 + A10pH0-pKa log

The following sequence of mathematical steps is performed next.

)1

)1

td

td 1 1 1 + A10(pH0+a(t′R - td))-pKa + 2 ln + t′[B] ln 10 at′[HB+] 2A 1 + A10pH0- pKa

(21)

t′[HB+]

t'R td

t'R

td 1 1 × + t′[B] ln 10 at′[HB+] 2A

Now, after denoting

td 1 1 + t′[B] ln 10 at′[HB+] 2A

(∫ 1y dy - ∫

td 1 1 [ln|y + Ay2| + + t′[B] ln 10 at′[HB+] 2A

The following substitutions can be applied:

y ) 10[pH0+ a(t-td)]-pKa

+ 2Ay dy + y + Ay2

t′R1

td

10pH0-pKa(1 + A10pH**-pKa)

1 + A10pH**-pKa 1 + A10pH**-pKa 1 log log + A 1 + A10pH0-pKa 1 + A10pH0-pKa log

( )

]

10pH**-pKa(1 + A10pH0-pKa)

(

)1

)

td 10pH**-pKa ) 1at′[HB+] pH0-pKa t′ 10 [B]

1 1 + A10pH**-pKa - 1 log + pH** - pH0 ) A 1 + A10pH0-pKa td 1at′ (23) t′[B] [HB+]

(

)


753

Equation 23 holds for bases. An analogously derived equation describing the pH gradient HPLC of acids has the form

( )

1 1 + A10pKa-pH** - 1 log + pH0 - pH** ) A 1 + A10pKa-pH0 td at′ (24) - 1t′[HA] [A-]

(

)

Now let us consider the third situation in pH gradient HPLC, accounted for by eqs 17c and 18c. That situation takes place when the analyte’s reduced retention time is longer than the sum of gradient time, tg, and gradient delay time, td. The meaning of the first two terms in eqs 17c and 18c remains as discussed above. The third interval describes analyte retention after completing gradient program, that is, at isocratic pH conditions at the final pH, denoted as pHF, which maintains the full ionization of the analyte. Solution of eqs 17c and 18c is like that given above for eqs 17b and 18b with one difference, namely the pH0+ a(t - td) for the time of chromatographic run t g tg + td equals the pH at the end of gradient program, that is, pHF. In effect, the general equations are for acids,

( )

1 1 + A10pHF-pKa - 1 log + pHF - pH0 ) A 1 + A10pH0-pKa td t′R - tg - td 1at′[HB+] (25) t′[B] t′[HB+]

(

)

and for bases,

( )

1 1 + A10pKa-pHF - 1 log + pH0 - pHF ) A 1 + A10pKa-pH0 td t′R - tg - td at′[A-] (26) - 1t′[HA] t′[A-]

(

)

The above derived equations describing pH gradient HPLC can be used for prediction of retention of individual analytes and, hence, for rational optimization of the separation conditions both in gradient and in isocratic liquid chromatographic modes. Solution of the equations is done numerically, employing standard mathematical programs, such as Excel. To use the appropriate equation in separation practice, one needs to carry a preliminary experiment at a constant pH, providing full suppression of analyte ionization but applying an organic-water gradient. From that experiment, an appropriate organic modifier concentration may be evaluated from the Snyder LSS theory,1 allowing for a range of well-measurable retention factors of the analyte under study. Then a programmed pH gradient run is performed with a constant concentration of organic modifier but at the pH range which provides a complete suppression of ionization of the analyte at the beginning of the gradient and its full ionization at gradient end. One additional injection of the analyte after completing the pH gradient program is required to get the retention factor of its ionized form. EXPERIMENTAL SECTION Equipment. The HPLC systems applied were LC Module I Plus (Waters Associates, Milford, MA) of dwell volume, Vd, of 754


4.3 mL equipped with a variable wavelength UV-vis detector and a Merck-Hitachi LaChrome System (Darmstadt, Germany, San Jose, CA) of Vd of 1.4 mL, equipped with a diode array detector. Chromatographic data, obtained with organic modification gradients, were processed using the DryLab program (LC Resources, Walnut Creek, CA). The columns were XTerra MS C-18, 150 × 4.6 mm i.d., particle size 5 mm (Waters Corporation, Milford, MA), packed with octadecyl-bonded silica and PRP-1, 150 × 4.1 mm i.d., particle size 5 µm (Hamilton Company, Reno, NV), packed with cross-linked polystyrene(divinylbenzene). Mobile phases contained methanol as organic modifier. Water or buffers of fixed pH formed the aqueous component of the eluent. NaNO3 (1%) was used as the dead time marker. The dead volumes of columns thus determined were 1.36 ( 0.2 mL for the PRP-1 and 1.64 ( 0.02 mL for the XTerra MS. The injected sample volume was 10 µL. The analytes were dissolved in methanol at concentration of 0.5 mg/mL. The chromatographic measurements were done at either 25 °C (PRP-1 column) or 35 °C ((1 °C) (XTerra MS column) with an eluent flow rate of 1 mL/min on the PRP-1 column and of 1.5 mL/min on the XTerra MS column. All of the reagents and analytes employed were of the highest commercially available quality. Mobile Phase. Universal buffer used consisted of parts I and II. Part I was formed by three acids, phosphoric, acetic, and boric, all at concentrations of 0.004 M. Part II, 0.02 M sodium hydroxide, was added to part I at amounts necessary to obtain the required pH. The wwpH of the buffers was measured at 25 °C before mixing with organic modifier, and the swpH of the mixtures of various buffer-metanol compositions were measured afterward. The measurements were performed using an HI 9017 pH meter (Hanna Instruments, Bedfordshire, U.K.). Linearity of changes in swpH was tested following the addition of part II of the buffer (0.02 M NaOH) to the solution of acids (part I) and methanol, with the volume fraction of methanol in water ranging from 0 to 50%. For that purpose, to a flask thermostated at 25 °C and containing 100 mL of a mixture of methanol and part I of the buffer at various proportions, part II of the buffer in 2 mL portions was added (in cases when initial percentage of methanol exceeded 45% v/v, the portions of part II added were 1 mL). The values of swpH were measured with a pH meter calibrated with regard to the standard reference aqueous buffers. The measurements were carried out within the range of pH (wwpH) of the universal buffer used of 3.00-10.50 pH units. The relationship between the variables swpH, percent B (content of methanol), and composition of universal buffer, expressed by the volume ratio of its parts II and I, is presented in Figure 3. The following regression equation best describes the relationship illustrated in Figure 3.

pswH ) 1.55 + 9.48(II/I) + 0.0269(%B) 0.0266(II/I)(%B) (27) For eq 27, the multiple correlation coefficient is R ) 0.9930, and the standard error of estimation is s ) 0.27; all of the variables are significant at significance level p < 0.01. Equation 27 describes satisfactorily the relationship among the variables considered. It allows one to assume that the presence of methanol does not affect significantly the linearity of the swpH

Table 1. Experimental Data Used for Calculation of s wpKa Values of Test Analytes Chromatographed on PRP-1 Columna

Figure 3. Relationships between swpH of the mixture, volume percent of methanol (%B), and composition of universal buffer (volume ratio of part II to part I).

changes with changing composition of the universal buffer. Therefore, the linear pH gradient elution can be realized with the mobile phases proposed. It must be noted here, however, that adding methanol evidently changes the pH (i.e., swpH) of the aqueous buffer. For example, adding 50% (v/v) of methanol to aqueous universal buffer of wwpH ) 3.00 produces a swpH of the resulting water-buffer solution of 4.00; in the case of buffer of w s wpH ) 10.50, an analogous operation gives wpH ) 10.60. That behavior is explained well in recent literature.10,11 That must be taken into consideration when applying pH gradient HPLC for determination of the standard pKa of analytes, namely wwpKa. However, for pH gradient retention modeling in a given HPLC system, it is of no direct relevance. Determination of wwpKa will be a subject of an independent study. Determination of log kw Values by Isocratic and by Gradient Elution. Two organic modifier gradients of 5-100% B at gradient times tg of 20 and 60 min were carried out. On the basis of the retention times from two gradient runs with different b values for each compound, the log kw values were derived by the DryLab w program. DryLab software also predicted the isocratic retention parameter, k, corresponding to a defined percent of organic modifier. Determination of pKa Values by Gradient Elution. The pH gradient of the aqueous component of the mobile phase was programmed for the selected k value of each compound. Percent of organic modifier was kept constant during the chromatographic run, while composition of buffer components was linearly changed during a programmed gradient time. For the basic test compounds studied, the pH was 10.50 at the start and 3.00 at the end of the gradient (∆pH 7.5). RESULTS AND DISCUSSION Having in mind the known disturbing effects of free silanols on retention (in particular, of basic analytes),23,24 we started verification of our theory on a polymeric column PRP-1 instead of the typical high-performance silica-based reversed-phase materi(22) Nasal, A.; Siluk, D.; Kaliszan, R. Cur. Med. Chem. 2003, 10, 381-426. (23) Vervoort, R. J. M.; Debets, A. J. J.; Claessens, H. A.; Cramers, C. A.; de Jong, G. J. J. Chromatogr., A 2000, 897, 1-22. (24) Vervoort, R. J. M.; Ruyter, E.; Debets, A. J. J.; Claessens, H. A.; Cramers, C. A.; de Jong, G. J. J. Chromatogr., A 2002, 964, 67-76.

analyte

t[B]b

t[HB+]b

tRb

s wpKa exp

w wpKa,lit

aniline p-anisidine 2-methylbenzimidazol

51.87 68.10 44.13

6.53 4.24 3.36

27.41 25.39 21.28

4.94 5.58 6.36

4.63 5.34 6.19

a Retention data were obtained on an PRP-1 column with the mobile phase containing 30% (v/v) of methanol flowing at a rate of 1 mL/min at 25 °C. Values of swpKa calculated for these conditions and the wwpKa data taken from literature were used for retention predictions at all the other conditions applied. b t[B] and t[HB+] are isocratic retention times (in min) of nondissociated and dissociated forms, respectively; tR is the pH gradient retention time determined using a pH gradient from 10.50 to 3.00 formed within a gradient time of 25 min.

als. Another obvious reason to prefer the PRP-1 to the silica-based column is the instability of the latter at the initial pH of 10.50. For three representative organic bases, we were able to reliably measure the requested gradient retention times at 25 °C. First, we applied two standard methanol gradients, keeping the pH of the eluent constant and high enough to prevent the analytes’ dissociation (wwpH of the buffer was 10.50). That way, we derived retention factors of nonionized forms of analytes. Next, on the basis of organic-gradient HPLC theory (eq 6), we estimated the content of methanol in the mobile phase, providing appropriate retention at the start of pH gradient. Then a programmed pH gradient run was performed with one additional injection of the analyte after completing the pH gradient program. That way, all the data requested for calculation of swpKa values of analytes was derived. These values were then used to predict pH gradient retention parameters at other chromatographic conditions. The starting data, namely, isocratic retention times of nondissociated, t[B], and dissociated, t[HB+], forms of test bases, along with the pH gradient retention times of the analytes, tR, all determined at the concentration of methanol in the mobile phase of 30% (v/v), are collected in Table 1. Values of tR, along with the programmed pH gradient parameters and the HPLC system parameters, served to calculate the pH** value necessary for solving eq 23. The requested isocratic retention time of the fully dissociated form of the analyte, t[HB+], corresponding to a given content of methanol in the eluent, may be obtained by injecting the analyte after completing of the pH gradient. It was found experimentally that some 5-min delay was necessary after completing the pH gradient program to get stable t[HB+] data. The reason for that delay is gradient-rounding previously described25 for regular organic gradient mode and responsible for the increase in retention times of bands eluting near the end of the gradient. On the basis of the experimental data given in Table 1, the swpKa parameters were calculated for individual test analytes by numerically solving eq 23. Such determined swpKa data are collected in Table 1, along with the standard reference wwpKa values. The performance of both types of pKa parameters in retention prediction was next compared. It must be noted here that using the wwpKa or swpKa values for prediction of analyte retention at a methanol content different from that used in the pKas determination is an approximation. It is so because the addition of methanol changes (25) Quarry, M. A.; Grob, R. L.; Snyder, L. R. J. Chromatogr. 1984, 285, 1-18.


755

Table 2. Isocratic Retention Times (min) of Nondissociated, t[B], and Dissociated, t[HB+], Forms of Test Analytes on an PRP-1 Column in Relation to the Content of Methanol in the Mobile Phase % (v/v) MeOH 25

30

35

analyte

t[B]a

t[HB+]

t[B]a

t[HB+]

t[B]a

t[HB+]

aniline p-anisidine 2-methylbenzimidazol

(69.59)b

7.09 4.53 3.55

51.87 (50.69) 68.10 (57.52) 44.13 (42.85)

6.53 4.24 3.36

36.37 (37.03) 43.52 (40.99) 28.83 (29.52)

6.00 3.92 3.23

(80.19)b (62.49)a

a In parentheses are data calculated by DryLab on the basis of two initial methanol gradient runs of 5-100% (v/v) B at gradient times, t of 20 g, and 60 min. b Not determinable experimentally.

Table 3. Experimental, tR,exp, and Calculated, tR,calcd, pH Gradient Retention Times (in min) of Test Analytes on a PRP-1 Column for Three Concentrations of Methanol in the Mobile Phase and for Various Gradient Times, tg 25% (v/v) MeOH tga 20

30

tr,calcd using analyte

tr,exp

s wpKa

aniline p-anisidine 2-methylbenzimidazol mean rel error (%)

24.32 22.16 19.07

24.36 21.84 18.87 0.53

w wpKa

22.47 24.95 19.28 4.26

40

tr,calcd using tr,exp

s wpKa

w wpKa

32.51 30.03 25.09

32.61 29.67 25.47 0.60

30.6 33.76 26.13 4.49


s wpKa

w wpKa

40.21 37.57 30.64

40.34 37.14 31.7 0.99

38.35 41.83 32.54 4.43

30% (v/v) MeOH tga 15

25


tr,exp

s wpKa


19.39 17.60 15.44

19.39 17.50 14.84 0.89

w wpKa

17.98 19.83 15.17 4.34

30


s wpKa

w wpKa

27.41 25.39 21.28

b b b

26.18 28.36 21.83 3.75


s wpKa

w wpKa

31.20 29.07 23.97

31.2 29.20 24.31 0.37

30.13 32.3 24.94 3.72

35% (v/v) MeOH tga 15

20

tr,calcd using

b

analyte

tr,exp

s wpKa


17.01 15.89 14.61

18.35 16.7 14.1 3.29

w wpKa

17.17 18.79 14.43 4.08

25


s wpKa

w wpKa

22.51 20.93 17.63

22.18 20.46 17.08 1.37

21.07 22.91 17.5 3.32


s wpKa

w wpKa

26.11 24.51 20.16

25.71 24.04 19.81 1.04

24.8 26.59 20.3 2.84

a Gradient retention times were calculated using either s pK parameters here determined (Table 1) or wpK values taken from literature. w a w a Experimental gradient retention times were used to calculate these swpKa values (see Table 1).

the value of swpKa. Despite that, as far as minor differences in methanol content are concered, the effect of swpKa can be neglected. For rational optimization of chromatographic separations a knowledge of the dependence of separation patterns of individual analytes on the changes in chromatographic conditions is required. In gradient HPLC, the modifications of separations are often obtained by varying gradient time, tg. Normally, that is done by a trial-and-error approach. Our model of pH gradient HPLC allows for reliable predictions of analyte retention times at designed gradient times. We tested the predictions of pH gradient 756 Analytical Chemistry, Vol. 76, No. 3, February 1, 2004

retentions at several gradient times, tg, for fixed concentrations of methanol in the eluent. In Table 2, the requested isocratic retention times of nondissociated and dissociated forms of test analytes are given for 25, 30, and 35% (v/v) of methanol in the eluent. In the case of the nondissociated form, the t[B] values may either be determined experimentally or evaluated from LSS theory (eq 6). As can be seen in Table 1, there is a satisfactory agreement between the experimental values and those calculated by DryLab software t[B] values, except for p-anisidine. Therefore, the evaluated data can be used if the experimental ones are not measurable, such as in the case of PRP-1 column washed with mobile phases

Figure 4. Experimental and theoretically predicted chromatograms of test mixtures of analytes on XTerra MS column at a content of methanol in the mobile phase of 3% (v/v) with the pH gradient time, tg, of 25 min (a); 7% (v/v) of methanol with pH gradient time of 20 min (b); 11% (v/v) of methanol with pH gradient time of 11 min (c); 15% (v/v) of methanol with pH gradient time of 10 min (d); and the swpH ranging from 10.50 to 3.00. Analytes are numbered: 1, aniline; 2, p-anisidine; 3, 2-amino-5-nitropiridyne; 4, 2-methylbrnzimidazol; 5, morphine.

containing 25% (v/v) of methanol or less. For very approximate pH gradient retention time predictions, one can assume that dissociated forms of analytes are not retained by the column, and their t[HB+] values are about the dead times. It remains to be determined what would be the value of such approximate predictions. By now, to test our theoretical model, we employed t[B] and t[HB+] data determined experimentally for individual contents of methanol in the mobile phases.

Results of pH gradient retention prediction on PRP-1 column are given in Table 3. For the calculations, the input data t[B] and t[HB+] from Table 2 were used, along with either swpKa or wwpKa values from Table 1. Analyzing the data from Table 3, one will find good agreement between the observed and the predicted pH gradient retention times. In general, the predictions obtained when using swpKa parameters for solving eq 23 are better than those obtained Analytical Chemistry, Vol. 76, No. 3, February 1, 2004

757

Table 4. Experimental Data Used for Calculation of s wpKa Values of Test Analytes Chromatographed on XTerra MS Column analyte

t[B]a

t[HB+]a

tRb

s c wpKa,exp

w c wpKa,lit

aniline p-anisidine 2-amino-5-nitropyridine 2-methylobenzimidazol morphine

8.67 11.41 16.37 23.09 42.08

1.76 1.84 1.65 2.96 2.05

8.16 8.59 7.52 8.93 7.79

4.87 5.29 6.83 6.32 7.43

4.63 5.34 7.22 6.19 8.21

a t [B] and t[HB+] are isocratic retention times (in min) of nondissociated and dissociated forms, respectively. b tR is the pH gradient retention time determined with pH gradient from 10.50 to 3.00 formed within gradient time, tg, of 8 min. Retention data were obtained on XTerra MS column with mobile phase containing 7% (v/v) methanol flowing at a rate of 1.5 mL/min at 35 °C. c Values of swpKa calculated for these conditions and the wwpKa data taken from literature29-31 were used for retention predictions at all the other conditions applied.

employing the wwpKa data. That is as theoretically expected, because the actual organic-water mobile phase used has different acidity from neat water. On the other hand, the available literature w wpKa values can be used to roughly evaluate changes in analyte retention accompanying the changes in chromatographic conditions. Polymeric columns, such as PRP-1, are of a limited specific analytical use. On a regular basis, the silica-based reversed-phase materials are used in analytical applications for HPLC. Therefore, practical utility of the pH gradient technique depends on its applicability to the modern HPLC columns packed with chemically bonded hydrocarbonaceous silica stationary phases. A representative of such high performance and high stability columns is XTerra MS. The column is especially suitable for pH gradient mode because it can be operated at a wide pH range (from 1 to 12). The column is also reported to show limited free silanols activity.25-27 Experiments on XTerra MS were carried out at 35 °C. Increasing the temperature to 35 °C eliminated technical problems caused by precipitation of the universal buffer components within the HPLC system, especially at higher contents of organic modifier in the eluent. A series of measurements of pH gradient retention for a set of five basic test analytes was performed. Organic bases were chosen because such analytes tend to interact specifically with the accessible silanols on the stationary phases, and hence, with such analytes, the actual predictive potency of our theoretical model can be even more rigorously tested.

In Figure 4, exemplary pH gradient chromatograms of a test mixture of analytes are compared as determined experimentally and calculated from our model. It is evident from Figure 4 that the pH gradient, like the organic-modifier-gradient,1,28 provides relatively narrow, symmetrical peaks of approximately the same width with minimized tailing. The reduced peak tailing is especially valuable for basic analytes for which the tailing is a serious analytical problem with the standard HPLC procedures. Reduced peak tailing is probably due to peak compression28 and may be explained as follows. The pH of eluent gradually decreases over time during the pH gradient chromatography of bases. At any site in the column, the analyte molecules passing through it are exposed to a weaker eluent than the molecules which pass through it later. A stronger eluent (lower pH) pushes bases faster than a weaker one (higher pH). Thus, the tail is permanently being pushed back into the main peak, and peak tailing is reduced. On the basis of the necessary experimental data, that is, the retention times of dissociated and nondissociated forms and s wpKa calculated from a single pH gradient run (Tables 4 and 5), the expected pH gradient retention times can be calculated for changing chromatographic conditions. In Table 6, good agreement is observed between the experimental and the calculated retention times. That is clearly evidenced by the low mean relative errors of the predictions. Obviously, the model proposed is able to follow the changes in elution sequences where these are experimentally observed. Comparing the predictions collected in Tables 3 and 6, one will note that with the XTerra MS column, it is even more evident that the swpKa parameters chromatographically determined account much better than the standard wwpKa values for the differences in analytes’ dissociation in the actual organicwater mobile phases. In a separate series of experiments ,we tested the applicability of the data generated in the pH gradient mode to predict isocratic retention at a fixed eluent pH (and methanol content). Reliable predictions of that sort would allow one to design the pH of the eluent to optimize isocratic separations. Employing the swpKa values determined by pH gradient HPLC (Table 4) and the retention times of nondissociated and dissociated of methanol in the mobile phase (Table 5), we calculated the isocratic retention times expected for the three selected swpH of the eluent (Table 7). The measured data are in reasonable agreement with the calculated data. Naturally, the agreement tends to be better the larger the difference is between the eluent pH and the analyte pKa.

Table 5. Isocratic Retention Times (in min) of Nondissociated, t[B], and Dissociated, t[HB+], Forms of Test Analytes on XTerra MS Column in Relation to the Content of Methanol in the Mobile Phase % (v/v) MeOH 3%

7%

11%

15%

analyte

t[B]

t[HB+]

t[B]

t[HB+]

t[B]

t[HB+]

t[B]

t[HB+]

aniline p-anisidine 2-amino-5-nitropyridine 2-methylobenzimidazol morphine

11.87 18.80 25.76 36.80 (62.49)a,

2.12 2.32 1.98 4.75 3.36

8.67 11.41 16.37 23.09 42.08

1.76 1.84 1.65 2.96 2.05

6.72 7.79 11.33 16.00 22.61

1.65 1.56 1.39 2.13 1.12

5.44 5.76 8.40 11.76 13.89

1.60 1.49 1.25 1.73 1.09

a Not determinable experimentally; calculated by DryLab on the basis of two initial methanol gradient runs of 5-100% (v/v) B at gradient times, tg, of 20 and 60 min.

758


Table 6. Experimental, tR,exp, and Calculated, tR,calcd, pH Gradient Retention Times (in min) of Test Analytes on XTerra MS Column for Four Concentrations of Methanol in Mobile Phase and for Various Gradient Times, tg 3% (v/v) MeOH tg 7

10


tr,exp

s wpKa

w wpKa

15


aniline 8.65 8.39 8.58 10.80 p-anisidine 8.85 8.66 8.62 11.15 2-amino-5-nitropyridine 7.79 7.40 7.06 9.73 2-methylobenzimidazol 10.45 9.92 10.03 13.41 morphine 9.47 8.40 7.70 11.97 mean rel error (%) 5.31 7.10

20

tr,calcd using

25

tr,calcd using

30

tr,calcd using

t, calcd using

s wpKa

w wpKa

tr,exp

s wpKa

w wpKa

tr,exp

s wpKa

w wpKa

tr,exp

s wpKa

w wpKa

tr,exp

s wpKa

w wpKa

10.27 10.86 9.22 11.78 10.17 7.99

10.49 10.80 8.73 11.93 9.16 10.16

12.00 14.16 12.13 15.87 14.35

11.74 14.16 12.07 14.84 13.05 3.64

11.79 14.07 11.35 15.07 11.54 6.69

11.73 16.29 14.40 17.76 16.55

11.86 16.75 14.70 17.80 15.86 2.08

11.86 16.67 13.77 18.11 13.85 5.22

11.68 17.65 16.48 20.21 18.91

11.87 18.22 17.09 20.65 18.59 2.49

11.87 18.17 15.98 21.02 16.10 5.29

11.71 18.29 18.29 22.64 21.49

11.87 18.66 19.22 23.34 21.24 2.55

11.87 18.64 17.99 23.78 18.27 4.99

7% (v/v) MeOH tg 5

10

15

tr,calcd using

tr,calcd using

tr,calcd using

20 tr,calcd using

analyte

tr,exp

s wpKa

w wpKa

tr,exp

s wpKa

w wpKa

tr,exp

s wpKa

w wpKa

tr,exp

s wpKa

w wpKa

aniline p-anisidine 2-amino-5-nitropyridine 2-methylobenzimidazol morphine mean rel error (%)

6.83 6.75 6.05 7.33 6.35

6.51 6.56 5.76 7.03 6.01 4.35

6.64 6.53 5.51 7.10 5.51 6.27

8.45 9.55 8.75 10.03 8.75

8.57 9.73 8.62 10.17 8.92 1.63

8.61 9.68 8.14 10.33 7.93 4.52

8.59 10.93 10.56 12.51 11.04

8.67 11.22 11.10 13.12 11.70 3.91

8.67 11.20 10.44 13.35 10.20 3.77

8.59 11.31 12.27 14.75 13.25

8.67 11.39 13.15 15.81 14.32 4.81

8.67 11.39 12.37 16.10 12.34 3.69

11% (v/v) MeOH tg 3

5

tr,calcd using

7

tr,calcd using

11

tr,calcd using

15

tr,calcd using w wpKa

20

tr,calcd using

analyte

tr,exp

s wpKa

w wpKa

tr,exp

s wpKa

w wpKa

tr,exp

s wpKa

w wpKa

tr,exp

s wpKa


5.28 5.14 4.83 5.39 4.75

4.84 4.92 4.76 4.74 4.27 4.12 5.00 5.04 4.09 3.77 9.69 11.29

6.40 6.50 5.90 6.61 5.83

6.09 6.12 5.46 6.31 5.29 6.39

6.19 6.09 5.22 6.39 4.77 8.52

6.72 7.31 6.91 7.79 6.83

6.65 7.16 6.56 7.57 6.43 3.37

6.68 7.13 6.23 7.67 5.70 6.20

6.83 7.84 8.61 9.89 8.75

6.71 6.72 6.80 6.72 6.72 6.72 6.72 6.72 7.76 7.76 7.92 7.79 7.79 7.81 7.79 7.79 8.47 8.00 9.84 9.90 9.39 10.67 10.87 10.50 9.93 10.10 11.76 12.00 12.20 13.73 14.03 14.24 8.56 7.44 10.59 10.53 9.03 12.77 12.78 10.86 1.40 5.36 1.21 5.17 0.88 4.10

tr,exp

s wpKa

w wpKa

tr,calcd using s wpKa

tr,exp

w wpKa

15% (v/v) MeOH tg 3

5

7

tr,calcd using

tr,calcd using

tr,calcd using

analyte

tr,exp

s wpKa


5.07 5.07 4.67 5.07 4.67

4.64 4.54 4.12 4.66 3.97 10.76

w wpKa

4.72 4.53 3.97 4.70 3.66 12.29

tr,exp

s wpKa

w wpKa

5.36 5.36 5.36 6.16 5.36

5.38 5.52 5.24 5.95 5.09 2.81

5.40 5.50 5.00 6.02 4.58 5.38

10

tr,exp

s wpKa

w wpKa

5.47 5.73 6.64 7.41 6.64

5.44 5.74 6.21 7.15 6.13 3.68

5.44 5.74 5.90 7.25 5.43 6.45


s wpKa

w wpKa

5.49 5.81 7.49 8.88 7.97

5.44 5.76 7.35 8.76 7.56 2.03

5.44 5.76 7.00 8.90 6.60 5.15

Gradient retention times were calculated using either swpKa parameters here determined (Table 4) or wwpKa values taken from literature.

CONCLUSIONS pH gradient HPLC is a new separation mode extending the analytical versatility of liquid chromatography. It appears to be (26) Kaliszan, R.; van Straten, M. A.; Markuszewski, M.; Cramers, C. A.; Claessens, H. A. J. Chromatogr., A 1999, 855, 455-486. (27) Buszewski, B.; Jezierska, M.; Wełniak, M.; Berek, D. J. High Resolut. Chromatogr. 1998, 21, 267-278. (28) Dolan, J. W. LCGC North America 2003, 21, 612-616. (29) CRC Handbook of Chemistry and Physics, 67th ed.; CRC Press: Boca Raton, FL, 1986.

especially suitable and effective for separation of ionogenic substances and may be a method of choice for separation of those bioanalytes which are sensitive to higher concentrations of organic solvents which are normally employed in regular organic gradient HPLC. When retention of analyte take place at actual pH gradient (30) The Merck Index, 11th ed.; Merck & Co., Inc.: Rahway, NJ, 1989. (31) Craig, P. N. In Comprehensive Medicinal Chemistry; Hansch, C., Sammes, P. G., Taylor, J. B., Eds.; Pergamon Press: Oxford, 1990; Vol. 6, pp 237991.


759

Table 7. Experimental, tR,exp, and Calculated, tR,cald, Isocratic Retention Times (in min) of Test Analytes on XTerra MS Column for a Constant Concentration of Methanol of 11% (v/v) and Three Different pswH of the Mobile Phase s wpH

8.08

6.82

5.57

analyte

tr,exp

tr,calc

tr,exp

tr,calc

tr,exp

tr,calc

aniline p-anisidine 2-amino-5-nitropiridine 2-methylobenzimidazol morphine

6.96 8.13 9.33 16.77 18.85

6.71 7.78 10.80 15.76 18.68

6.48 6.72 3.04 7.79 2.53

6.66 7.61 6.30 12.66 5.36

5.15 3.76 1.79 3.36 1.92

5.88 5.64 1.91 4.22 1.41

conditions (td

pH Gradient Reversed-Phase HPLC - American Chemical Society

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