Extended Thermodynamic Approach to Ion Interaction

Apr 28, 2001 - The present extended thermodynamic approach reduces to stoichiometric or electrostatic retention models if the surface potential or pai...
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Anal. Chem. 2001, 73, 2632-2639

Extended Thermodynamic Approach to Ion Interaction Chromatography T. Cecchi,* F. Pucciarelli, and P. Passamonti

Universita` degli Studi di Camerino, Dipartimento di Scienze Chimiche, Via S. Agostino 1, 62032 Camerino, Italy

The chromatographic behavior of charged analytes in ion interaction chromatography (IIC) is theoretically investigated. The chemical modifications of the stationary and mobile phases in the presence of ion interaction reagent (IIR) are theoretically shown to change the partition coefficient for charged molecules. The most reliable literature experimental results concerning retention behavior of charged molecules in IIC were used to test the new theory. Retention equations are compared with those that can be obtained from the most important retention models in IIC. The present exhaustive retention model, which is well-founded in physical chemistry, goes further than the previous ones whose retention equations can be viewed as limiting cases of the present theory. The present extended thermodynamic approach reduces to stoichiometric or electrostatic retention models if the surface potential or pairing equilibria are respectively neglected. Moreover, it is able to quantitatively explain experimental evidences that cannot be rationalized by the existing retention models. When an ion interaction reagent (IIR), which is a large lipophilic ion, is added to the mobile phase, ionized species of opposite charge are separated on reversed-phase columns with enhanced retention. This is the chromatographic approach of reversed-phase IIC. The influence of IIRs on retention of oppositely and similarly charged analytes has been well studied.1-12 The great number of names (e.g., ion-pair chromatography, dynamic ion-exchange chromatography, hetaeric chromatography, soap chromatography),1 that were given to IIC, points to the uncertainty concerning the retention mechanism. * Fax: +39-737-637345. E-mail: [email protected]. (1) Cecchi, T. Dekker Encyclopedia of Chromatography, Marcel Dekker Inc.: New York, in press. (2) Gennaro, M. C. Adv. Chromatogr 1995, 35, 343-381. (3) Bidlingmeyer, B. A.; Deming, S. N.; Price, W. P.; Sachok, B., Jr.; Petrusek, M. J. Chromatogr. 1979, 186, 419-434. (4) Bidlingmeyer, B. A. J. Chromatogr. Sci. 1980, 18, 525-539. (5) Thomlinson, E.; Jefferies, T. M.; Riley, C. M. J. Chromatogr. 1978, 159, 315-358. (6) Hung, C. T.; Taylor, R. B. J. Chromatogr. 1980, 202, 333-345. (7) Knox, J. H.; Hartwick, R. A. J. Chromatogr. 1981, 204, 3-21. (8) Bartha, A.; Stahlberg, J. J. Chromatogr. A 1994, 668, 255-284. (9) Stahlberg, J. J. Chromatogr. A 1999, 855, 3-55. (10) Cantwell, F. F. J. Pharmaceut. Biomed. Anal. 1984, 2, 153-164. (11) Chen, J.-G.; Weber, S.; Glavina, L. L.; Cantwell, F. F. J. Chromatogr. A 1993, 656, 549-576. (12) Strahanan, J. J.; Deming, S. N. Anal. Chem. 1982, 54, 2251-2256.

2632 Analytical Chemistry, Vol. 73, No. 11, June 1, 2001

Stoichiometric models, which are a majority of the proposed models, suggest that the oppositely charged analyte ion and IIR form a complex according to a clear reaction scheme either in the mobile phase (ion-pair model) or at the stationary phase (dynamic ion exchange model). Knox and Hartwick7 demonstrated that both of the models lead to an identical retention equation. The reader is referred to their paper for a more extensive discussion of the stoichiometric models. These models, though of practical and intuitive value, are not well-founded in physical chemistry. The pioneering, even if qualitative, work of Bidlingmeyer3,4 demonstrated that IIRs adsorb onto the stationary phase, forming a primary charged ion layer. The corresponding counterions in the diffuse outer region form an electrical double layer together with the charged stationary phase, which more strongly retains analyte ions of the opposite charge. The multibody interaction and long-term forces which are involved in IIC were better described by the electrostatic, nonstoichiometric approach developed by Ståhlberg and coworkers.8-9 The model applies the Gouy-Chapman electrostatic theory to describe the interactions between charged species, and it does not assume the formation of any chemical complexes. The adsorption of the IIR onto the stationary phase establishes a certain electrostatic surface potential, because its counterion has a lower adsorption tendency. An electrical double layer develops, and a difference in electrostatic potential is created between the electroneutral bulk of the mobile phase and the net charged surface. The intuitive view of the effect of the IIR on retention is an electrostatic repulsion or attraction of the analyte to the charged stationary phase surface, according to the analyte and IIR charge status. The total free energy of adsorption of the solute is partitioned into a chemical free energy, considered constant, and an electrostatic free energy. A series of approximations have to be made to obtain a relationship between the analyte capacity factor and the mobile phase concentration of IIR, which is of interest for practical work. Cantwell and co-workers10,11 proposed a surface adsorption, diffuse layer ion-exchange double-layer model in which they emphasized the role of the diffuse part of the double layer by assigning a stoichiometric constant for the exchange of ions. They share the view that the chemical part of the free energy can be considered constant after the addition of the IIR. The influence of the diffuse layer on organic ions retention was, however, demonstrated to be residual.8 10.1021/ac001341y CCC: $20.00

© 2001 American Chemical Society Published on Web 04/28/2001

Stranahan and Deming12 proposed a thermodynamic model for IIC in which electrostatic effects are accounted for via a simplified activity coefficient in the stationary phase and not in an explicit, rigorous way. An interfacial tension decrease with increasing IIR concentration was considered responsible for the appearance of maxima in the plot k vs IIR concentration; however, a behavior that runs counter to the known surfactant chemistry was obtained. It is the aim of this work to present and assess an extended thermodynamic approach to the theoretical modeling of IIC. The theory was developed on the basis of the following idea: pure electrostatic interactions cannot completely model charged solute retention. The importance of chemical equilibria can be recovered from stoichiometric models, but thermodynamic, and not stoichiometric, equilibrium constants must be used to take into account the chemical and physical modification of the interface. THEORY Because the behavior of neutral13 and zwitterionic14 analytes in IIC has already been dealt with from a theoretical point of view, we will now focus on the IIC of charged, nonzwitterionic eluites. The basis for the present thermodynamic theory of IIC is the Stern-Gouy-Chapman model of the electrical double layer.8,9,15 The adsorbed IIR ions are responsible for the electrical potential difference, Ψo, between the surface and the bulk solution. Two regions are distinguishable in the double layer: the compact layer, in which the potential decays linearly; and the diffuse layer, in which the potential decays almost exponentially because of screening effects. The higher the ionic strength, the faster the potential decays. From stoichiometric models7 we obtained the importance of the reaction scheme, even if the equilibrium constants which will be considered below are not stoichiometric but thermodynamic. For charged analytes, we may reasonably neglect interfacial tension effects and the modifications of the stationary phase that, on the contrary, as demonstrated,13 must be taken into account if the analyte is neutral and strong electrostatic interactions with the charged stationary phase are missing. A number of secondary effects are neglected in the present model, for example, dipolemonopole interactions, dipole-charged surface interactions, image forces, dielectric saturation, etc. In IIC systems, for an eluite the main equilibria are the following: (i) adsorption of the eluite E onto the stationary phase site L (hydrocarbonaceous ligand) KLE

L + E 98 LE

(1)

(ii) adsorption of the IIR H onto L KLH

L + H 98 LH

KLE/KLH

E + LH 98 LE + H

(iv) ion pair formation in the mobile phase (EH) if the charge status of the analyte and IIR are opposite KEH

E + H 98 EH

(4)

(v) ion pair formation in the stationary phase (EHL) if the charge status of the analyte and IIR are opposite KEHL

E + H + L 98 EHL KEHL/KLH

E + LH 98 ELH KEHL/KEH

EH + L98 EHL

(5) (6) (7)

If the charge status of the analyte and IIR are the same or if the eluite is neutral, equilibria 4-7 do not apply. Equilibria 3, 6, 7 are not independent of other equilibria; hence, for the condition of equilibrium, it holds that

µLE ) µL + µE

(8)

µLH ) µL + µH

(9)

µEHL ) µE + µH + µL

(10)

µEH ) µE + µH

(11)

where µ represents the electrochemical potential for each species. The electrochemical potentials are the following

µLE ) µ°LE + RT ln aLE + zEF Ψ°

(12)

µE ) µ°E + RT ln aE

(13)

µL ) µ°L + RT ln aL

(14)

µH ) µ°H + RT ln aH

(15)

µLH ) µ°LH + RT ln aLH + zHF Ψ°

(16)

µEHL ) µ°EHL + RT ln aEHL

(17)

where µ° represents the electrochemical potential for the standard state, F is the Faraday constant, and zE and zH are the charges of E and H, respectively. By combination of eqs 8-17 the following expressions are obtained for the thermodynamic equilibrium constants:

KLE )

aLE exp(zEFΨ°/RT) aLaE

(18)

KLH )

aLH exp(zHFΨ°/RT) aLaH

(19)

aEH aEaH

(20)

aEHL aEaHaL

(21)

(2)

(iii) displacement of H by E (13) Cecchi, T.; Pucciarelli, F.; Passamonti, P. Chromatographia 2001, 53, 2734. (14) Cecchi, T.; Pucciarelli, F.; Passamonti, P.; Cecchi P. Chromatographica, in press. (15) Grahame, D. C. Chem. Rev. 1947, 41, 441-501.

(3)

KEH ) KEHL )

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Eqs 18 and 19 parallel the nonthermodynamic, stoichiometric (or concentration-based) constants of stoichiometric models (see eqs 1 and 3 of ref 16), which neglect the importance of the electrostatic potential. Stoichiometric relationships8 are different from thermodynamic ones, because the former cannot be related to the thermodynamic quantity ∆µ°. They only represent the ratio of equilibrium concentrations. It is clear that a stoichiometric equilibrium constant is not constant8 after the addition of the IIR in the mobile phase, because it alters the surface potential, 8,9,17 which in turn modulates the influence of increasing IIR concentration. That’s why Stahlberg underlines that electrostatic interactions “cannot be described by stoichiometric relationships”.8 In their stoichiometric approach, Knox and Hartwick7 considered the counterions to ensure the balance of electrical neutrality in the adsorption process. In this case, they were allowed to neglect the presence of the surface potential in the expression of the equilibrium constants. We believe that their approach is not acceptable on the basis of the wide experimental evidence that a surface potential develops just because ions have different adsorbophilic attitudes.11,17 That is why we did not include nonadsorbophilic counterions in our adsorption equilibria. Eqs 18 and 19 do not deliberately take into account the role of a counterion, because the extent to which an ion migrates toward the oppositely charged surface with a counterion that is not lipophilic is often negligible. They are able to take into account the modification of the stationary phase potential that modulates the influence of increasing IIR concentration. The capacity factor of the eluite, k, is defined in the usual way as

Course of the Eluite Retention upon IIR Concentration in the Mobile Phase. The combination of eqs 18-23 yields k) γL γE γE γH γ L exp(-zEFΨ°/RT) + KEHL [H] γLE γEHL γE γH γL γH 1 + KEH [H] 1 + KLH exp(-zHFΨ°/RT)[H] γEH γLH KLE

φ[L]T

(

)(

)

(24)

where [L] is the surface concentration of free adsorption sites and [LH] is the surface concentration of the IIR Because the eluite is present in the mobile phase at concentrations much smaller than those of any other component, only a negligible fraction of the IIR is in the form of a complex; hence, its concentration [H] in the eluent can be considered to be invariant.16 Even if [H] may not be locally constant, the prompt restoration of local concentration of IIR ensures that both the pairing ion isotherm and the surface potential are unchanged by the presence of the sample ion.11,18

The first term in the numerator of eq 24 describes the modification of the adsorption of the eluite onto a stationary phase in the presence of the IIR. If the charge status of the eluite and the IIR are the same, k is expected to decrease with increasing IIR concentration, but the opposite is predicted for the oppositely charged analyte and IIR. The second term in the numerator of eq 24 accounts for ionpair formation in the stationary phase. It is easily predicted to increase retention. Obviously, this term is missing if the charge status of the analyte and IIR is the same or if the analyte is neutral, because equilibrium 5 does not apply. The second term in the left factor of the denominator of eq 24 accounts for ion pair formation in the mobile phase, which withdraws the eluite from the stationary phase toward the eluent; it is expected to reduce retention, because that has been demonstrated.19 Hence, the intuitive view of the classical ion-pair model is quite misleading. This term is missing if the charge status of the analyte and IIR is the same or if the analyte is neutral, because equilibrium 4 does not apply. The right factor of the denominator of eq 24 accounts for adsorption competition between the analyte and the IIR. It is noteworthy that the potential that develops at the stationary phase always runs counter to further adsorption of the IIR, because Ψ° is of the same sign as zH. The following two arguments lend strong support to the new theory. First, if surface potential is not taken into account, eq 24 reduces to eq 2 of the stoichiometric model of Knox and Hartwick7, except that their equilibria contain the counterions necessary to ensure the balance of electrical neutrality. The present approach, which underlines the importance of a charged stationary phase to which the eluite ion migrates without a counterion, is better founded in experimental evidence.3-4,11,17 On the other hand, if pairing equilibria are neglected, eq 24 reduces to the pure electrostatic approach (see eq 26 of reference 8), because the second term in the numerator and the second term of the first factor of the denominator are missing. However, although eq 26 of reference 8 predicts only one KLH for different analytes, we have shown13 that KLH itself depends on equilibria 1 and 3 because of displacement phenomena; hence, its numerical value may depend on the analyte, whose retention data are fitted. If adsorption competitions are also negligible, eq 24 reduces to eq 4a of reference 8. It is rewarding to see that if the analyte is neutral, eq 24 reduces to the previously developed retention equation for uncharged eluites.13

(16) Horvath, C.; Melander, W.; Molnar, I.; Molnar, P. Anal. Chem. 1977, 49, 2295-2305. (17) Cantwell, F. F.; Puon, S. Anal. Chem 1979, 51, 623-632.

(18) Liu H.; Cantwell F. F. Anal. Chem. 1991, 63, 2032-2037. (19) Terweij-Groen, C. P.; Heemstra, S.; Kraak, J. C. J. Chromatogr. 1979, 185, 225.

k)φ

[LE] + [EHL] [E] + [EH]

(22)

where φ is the phase ratio of the column and [LE], [EHL], [E], and [EH] are, respectively, the surface concentration of the eluite, the surface concentration of the complex EH, the mobile phase concentration of E and the mobile phase concentration of the complex EH Because the extent of binding of the eluite with the stationary phase accessible sites is expected to be small and the total ligand concentration [L]T is conserved, it can be written7,16 that

[L]T ) [L] + [LH]

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Analytical Chemistry, Vol. 73, No. 11, June 1, 2001

(23)

It is evident that the course of retention upon IIR concentration in the eluent can be very complex and variable, because it depends on a number of factors. Increasing amounts of adsorbed IIR cause a change in the chemical character of the stationary phase surface and, consequently, a change in the electrochemical potentials of the adsorbed phase and their activity coefficients. Although their evaluation in the mobile phase is straightforward, the activity coefficients in the adsorbed phase are not easily estimated. To obtain an expression for a practical test, as a first approximation, we may assume that the activity coefficient ratios are almost constant. This is a good approximation, because the experimental results, which will be used to test the new theory, were obtained at constant ionic strength. To obtain the rigorous relationship for the surface potential, the porous nature of the particles packed in a column would require the solving of the Poisson-Boltzmann equation in cylindrical coordinates. Usually, if the ionic strength is high enough and the inverse Debye length is low, we can use a planar surface geometry.20 The following is a rigorous relationship for the surface potential21

Ψ° ) 2RT F

ln

{

[HL]‚|zH|F

(80rRT

∑c

+ 1/2

0i)

[

([HL]‚zHF)2

80rRT

i

∑c i

]}

+1

0i

|zH|F (80rRT

∑

(25)

(26) c0i)1/2

i

where f (m2/mol) is a constant which can be evaluated from experimental conditions. In a number of cases, if the IIR concentration in the mobile phase is not too high, the rigorous, potential-modified, Langmuir adsorption isotherm reduces to the Freundlich isotherm22

[LH] ) a[H]

γLγE c1 ) φ[L]TKLE γLE

(29)

This means that c1 is the retention factor when the IIR is not present in the eluent (k0), and it can be obtained by experimental results. In the exponent of the first term of the numerator, the plus sign applies for oppositely charged analytes and IIR, and the minus sign applies for analytes possessing the same charge as the IIR. Their retention is predicted to decrease with increasing IIR concentration; they may eventually come out faster than a nonretained compound, as expected.

c2 ) φ[L]TKEHL

γEγHγL γEHL

(30)

γEγH c3 ) KEH γEH

(31)

γLγH γLH

(32)

c4 ) KLH

1/2

where 0 is the electrical permittivity of vacuum, r is the dielectric constant of the mobile phase, and ∑ci is the mobile phase concentration (mol/m3) of electrolyte ions, which are assumed to be singly charged. Ψ° must be considered positive or negative, according to the charge status of the IIR. For low surface potentials the above expression can be easily linearized.8 For the sake of simplicity, we will indicate

f)

where

b

If k0 is known, eq 28 is a three-parameter equation. Course of the Eluite Retention upon IIR Concentration in the Stationary Phase. From eqs 18-23 and 27, we have the following expression for the dependence of retention upon the IIR concentration in the adsorbed phase

KLE k)φ

KEHL γEγHγL γLγE exp(-zEFΨ°/RT) + 1/b [LH]1/b γLE γ a EHL × KEH γEγH 1/b 1 + 1/b [LH] γEH a

(

)

([L]T - [LH]) (33) Again, the second term in the numerator and the second term in the denominator are missing if the charge status of the analyte and IIR is the same, because equilibria 5 and 4 do not apply. Under similar hypotheses, by substitution of eqs 25 and 26 into eq 33, we obtain

k)

d1([LH]f + (([LH]f)2 + 1)1/2)(2|zE| + d2[LH]1/b (1 + d3[LH]1/b)

×

(d4 - [LH]) (34)

(27)

where a and b are constants. The Freundlich isotherm approximation was considered good enough for all isotherm data taken from selected data sources (r >0.998). By substitution of eqs 25, 26, and 27 into eq 24, we obtain

where, in the exponent of the first term of the numerator, the plus sign applies for oppositely charged analytes and IIR, and the minus sign applies for similarly charged analyte and IIR as expected, and

d1 ) φKLE

k) c1(a[H]bf + ((a[H]bf)2 + 1)1/2)((2|zE|) + c2[H] (1 + c3[H])(1 + c4[H](a[H]bf + ((a[H]bf)2 + 1)1/2)(-2|zH|)) (28)

γLγE γLE

(35)

This means that d1 is equal to k0/d4; hence, it is not an additional fitting parameter if ko is known. If adsorption competiAnalytical Chemistry, Vol. 73, No. 11, June 1, 2001

2635

Table 1. Summary of Data Sources, Surface Potentials, Parameter Estimates, Correlation Coefficients, Standard Errors, and Number of Data Pointsa,b ref

IIR

eluite

Ψ° max (eq. 25) mV

c1

7; fig. 4 left, fig. 3 7; fig. 4 left, fig. 8 7; fig. 4 left 7; fig. 3 7; fig. 8 7; fig. 4 left

decylsulfate decylsulfate decylsulfate octylsulfate octylsulfate decylsulfate

tyrosine amide normetadrenaline adrenaline tyrosine amide normetadrenaline naphthalene-2-sulfonate

-135 -135 -135 -115 -115 -135

0.43 0.27 0.16 0.46 0.31 7.16

a

c3 1/mM

c3/(a1/b)

r

SSE

no. points

0.25 0.22 0.27 0.11 0.09

0.09 0.09 0.1 0.43 0.37

0.99812 0.99847 0.99802 0.99969 0.99852 0.9946

1.7671 0.6286 0.2386 0.0696 0.2455 0.4859

9 9 9 8 9 9

Best fit of retention data digitized from ref 7, as indicated, by eq 28. b No data for c2 or c4.

Table 2. Summary of Data Sources, Surface Potentials, Parameter Estimates, Correlation Coefficients, Standard Errors, and Number of Data Pointsa,b ref

IIR

eluite

Ψ° max (eq. 25) mV

d1

7; fig. 4, right 7; fig. 4 right, fig. 8 7; fig, 4 right, fig. 9 7; fig. 8 7; fig. 9 7; fig. 4 right, fig. 9 7; fig. 9

decylsulfate decylsulfate decylsulfate octylsulfate octylsulfate decylsulfate octylsulfate

tyrosine amide normetadrenaline adrenaline normetadrenaline adrenaline naphthalene-2-sulfonate naphthalene-2-sulfonate

-135 -135 -135 -115 -115 -135 -115

0.41 0.26 0.16 0.32 0.19 7.35 7.03

a

d3 (m2 µmol-1)1/b 0.09 0.08 0.1 0.39 0.38

r

SSE

no. points

0.99601 0.99562 0.99428 0.9977 0.99857 0.99635 0.99719

3.6788 1.7665 0.6453 0.3763 0.0962 0.3541 0.2499

9 9 9 9 9 9 9

Best Fit of Retention Data Digitized from Ref 7, as Indicated, by Eq 34. b No data for d2 or d4.

tions are negligible, [HL] may be neglected with respect to [L]T, and the latter is included in d1; hence, d1 ) k0

KEHL γEγHγL a1/b γEHL

d2 ) φ

(36)

Again, if [HL] is negligible with respect to LT, the latter is included in d2; hence, d2 ) c2/(a1/b).

d3 )

KEH γEγH a1/b γEH

(37)

hence, d3 ) c3/(a1/b).

d4 ) [L]T

(38)

The fitting of eq 34, if k0 is known, requires the optimization of only three parameters. DISCUSSION The proposed new expressions have been tested on a data set that is generally considered one of the most reliable in the field.7 We have considered only experimental results obtained (i) for IIR concentration below the critical micelle concentration (CMC)23 (hence, in the following, data relative to lauryl sulfate will not be discussed) and without adsorbophilic counterions; (ii) at constant (20) Stahlberg, J.; Bartha, A. J. Chromatogr. 1988, 456, 253-265. (21) Stalberg, J. J. Chromatogr. 1986, 356, 231-245. (22) Davies, J. T.; Rideal E. K. Interfacial Phenomena; Academic Press: New York and London, 1961; Chapter 4. (23) Bartha, A.; Vigh, Gy.; Varga-Puchony, Z. J. Chromatogr. 1990, 499, 423434.

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ionic strength and IIR counterion concentration. This way, saltingout effects were ruled out, and when IIR concentration was changed, only the relative concentrations of IIR and its counterion were altered, and the surface potential increase was not influenced by ionic strength effects; moreover, the activity coefficient ratios were almost constant; (iii) at constant organic modifier concentration in the eluent. From the eluent composition (water:methanol, 80:20; estimated dielectric constant of the mixture, 70;24 pH 6.0, constant ionic strength), f was estimated to be 2.31 × 106 m2 mol-1. By numerically fitting eq 27 to the adsorption isotherms of Figure 1 of ref 7, with permission from Elsevier Science, the a constant was found to be 1.3818 for decylsulfate and 0.5530 for octylsulfate. In a similar way, b was found to be 0.3330 for decylsulfate and 0.4352 for octylsulfate. In the fitting of literature data by eq 28 or 34, the fitting parameters, which proved to be important to contemporaneously obtain a good fit of retention data plotted against both the mobile and surface concentration of the IIR, are reported in Tables 1 and 2, respectively. If a parameter is missing, this means that it was unreasonable to include it (e.g., a negative estimate, correlation coefficient not increased by its inclusion); that is, in the chromatographic system, its influence is negligible. The number of adjustable parameters was two at maximum, and their numerical estimate is very reasonable in all cases. Let us start with the comment of Figure 4 of the work of Knox and Hartwick7 (see Figure 1). The appearance of maxima in the plot of k vs [H] has been explained by Stahlberg8 by the adsorption competition between the analyte ion and IIR for a limited surface area. We will demonstrate that, in the present case, this is not (24) Marcus, Y.; Kertes, A. S. Ion exchange and Solvent Extraction of Metal Complexes; Wiley-Interscience: London, 1969; Chapter 2.

Figure 1. Dependence of k, for various solutes, upon concentration of decylsulfate in standard eluent. Left, k vs [H]; right, k vs [LH]. Tyr-amd, tyrosine amide; Normet, normetadrenaline; Adr, adrenaline; BzOH, benzyl alcohol; NpS, naphthalene-2-sulfonate. Reprinted from Figure 4 of Knox, J. H.; Hartwick, R. A. “Mechanisms of Ion-Pair Liquid Chromatography of Amines, Neutrals, Zwitterions, and Acids using Anionic Hetaerons”; J. Chromatogr. 1981, 204, 3-21, with permission from Elsevier Science.

correct, and a pure electrostatic theory is not able to model these retention data. Strahanan’s12 analysis of Knox and Hartwick’s7 data focused on interfacial tension effects, but the trend in parameter estimates was the opposite of what can be predicted on the basis of surfactant behavior. Because it was not possible, because of the small scale, to differentiate the k0 value of the three analytes, we decided to leave it as a fitting parameter. Its estimates are, however, excellent. Experimental results for analytes having the same charge as the IIR are very well fitted, as outlined in Table 1, by the pure electrostatic potential term, as easily predicted, because the very strong electrostatic repulsion prevents adsorption competitions. If the latter are considered, a negative estimate of KHL is obtained, thereby indicating that they are not operating. The experimental behavior of oppositely charged analytes (Table 1) confirms that adsorption competitions are not responsible for the foldover at higher IIR concentration. If only electrostatic interactions and adsorption competitions are considered, eq 24 reduces to eq 26 of reference 8. In this case, the estimate of KLH corresponds to a very high ∆G° (∆G° ) -31.7 kJ/mol, estimated from data of adrenaline) for the adsorption of H onto the stationary phase, and this is not realistic, especially if one takes into account the percentage (20%) of methanol in the eluent. Moreover, with the same number of fitting parameters, a determination coefficient lower than that reported in Table 1 (0.88788 for tyrosine, 0.92805 for normetadrenaline, and 0.87220 for adrenaline) and a completely wrong estimate of k0 (2.6 for tyrosine, 1.6 for normetadrenaline, and 1.1 for adrenaline) were obtained. On the contrary, almost a perfect biparametric fit was obtained by taking into account electrostatic interactions and ion pair formation in the eluent. Ion pair formation in the mobile phase does cause a decrease, not an increase, of retention, and it is responsible for the foldover of the curves. The fit of the same retention data, plotted against the surface concentration of the IIR (Table 2), confirms this conclusion.The parameter d3 compares very well with the ratio c3/(a1/b). This lends further support to the hypothesis that the foldover is caused by

ion pairing in the eluent and not by adsorption competitions. We can reasonably expect that adsorption competitions are (i) mostly important for neutral compounds,13 because strong electrostatic interactions are not operating; (ii) less important for similarly charged analytes because electrostatic repulsion may prevent adsorption competitions; and (iii) often negligible if the charge status of the analyte and the IIR are opposite, because in this case, mutual attraction in the stationary phase may also lead to the formation of a dynamic multilayer. To definitively rule out the importance of adsorption competitions in determining the foldover, we want to discuss the retention data that was obtained for the same analyte with a different IIR. We would emphasize that every pure electrostatic retention theory, including the multisite occupancy model,25 predicts only one theoretical curve to exist for all IIRs when eluite retention is plotted against the surface concentration of the IIR. Hence, not every pure electrostatic retention theory, which can only explain maxima as the result of adsorption competitions, is also useful to rationalize the experimental evidence of Figure 2 and 3. The curves for octyl- and decylsulfate, which were considered “nearly coincidental” by Knox, are in fact completely coincidental only if the analyte (naphthalene sulfonate, Figure 3) and the IIR are similarly charged. In this case, pairing equilibria are obviously missing. As it may be observed in Tables 1 and 2, adsorption competitions are also negligible, and eq 24 reduces to eq 4a of reference 8; hence, predictions of the electrostatic retention model8 are correct. If the amount of the adsorbed IIR is the same, the electrostatic potential is the same, and only one curve is expected for different IIRs. The pure electrostatic theory works well if the analyte and the IIR are similarly charged. Unfortunately, IIC is mostly used to separate oppositely charged analytes. We may observe that for them (normetadrenaline, Figure 2, and adrenaline, Figure 3), the curve of k vs surface concentration of octylsulfate always lies below the one relative to decylsulfate. For the neutral eluite (benzyl alcohol, Figure 3), (25) Narkiewicz-Michalek, J. Chromatographia 1993, 35, 527-538.

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Figure 2. Dependence of k for Normetadrenaline on concentration of alkylsulfates of different chain lengths in standard eluent. Full lines, plot of k vs [H]; broken lines, plot of k vs [LH]. Reprinted from Figure 8 of Knox, J. H.; Hartwick, R. A. “Mechanisms of Ion-Pair Liquid Chromatography of Amines, Neutrals, Zwitterions, and Acids using Anionic Hetaerons”; J. Chromatogr. 1981, 204, 3-21, with permission from Elsevier Science.

Figure 3. Dependence of k for positively charged, neutral, and negatively charged solutes (for identification, see Figure 1) on concentration of alkylsulfates of different chain lengths in standard eluent. Reprinted from Figure 9 of Knox, J. H.; Hartwick, R. A. “Mechanisms of Ion-Pair Liquid Chromatography of Amines, Neutrals, Zwitterions, and Acids using Anionic Hetaerons”; J. Chromatogr. 1981, 204, 3-21, with permission from Elsevier Science.

adsorption competitions were demonstrated13 to be important, and an opposite trend is observed. It has already been explained in terms of the displacement equilibrium 3, which is obviously more effective for octyl- than for decylsulfate: higher retention is obtained for the former IIR.13 If the charge status of the IIR and analyte are opposite, it is difficult to expect a strong displacement 2638

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of the IIR by the analyte. Moreover, if displacement equilibria were operating, the same trend as that observed for neutral compounds would be expected; that is not so in the present case. The experimental evidence of Figures 2 and 3 can be rationalized in the following elegant and quantitative way. If the surface concentrations of octyl- and decylsulfate are the same, the mobile phase concentration of octylsulfate is higher than that of decylsulfate (as may be observed in Figure 1 of ref 7). For a given analyte, even if the pairing constant KEH for octylsulfate is lower than that for decylsulfate, as is expected and as may be observed from parameter c3 in Table 1, a higher d3 parameter is obtained when the IIR is octylsulfate, as may be seen in Table 2. It can be calculated that the second term of the denominator of eq 34 is always higher for octylsulfate with respect to decylsulfate. This means that the analyte is more strongly withdrawn toward the mobile phase to form ion pairs, and a lower retention is obtained for octlylsulfate, even if the surface concentration, hence the surface potential, is the same as that of decylsulfate. It is noteworthy that the new retention equations are able to quantitatively predict experimental evidence that cannot be rationalized by the electrostatic retention model.8-9 The electrostatic retention model8,9 for ion interaction chromatography predicts that the kE1/kE2 ratio (E1 and E2 are two different analytes) will be independent of the surfactant concentration. It has been shown25 that this is not true. A multisite occupancy model of the electrostatic theory of ion-pair chromatography25 implements the pure electrostatic retention model of IIC by taking into account analytes’ surface requirements. It does predict that, when the surface area occupied by two analytes is the same, the kE1/kE2 ratio will be independent of the surface concentration of the surfactant. We decided to test this prediction that was not experimentally confirmed in the original paper.25 It can be observed that for isomers of the same molecular area,26-29 this prediction is not true; hence, the electrostatic theory needs an extension different from that offered by the multisite occupancy model. The present theory is completely able to theoretically explain the change of the ratio kE1/kE2 with increasing IIR concentration. Because KEH, KEHL, andKLH are all different if the analyte is not the same, the ratio kE1/kE2 calculated via eq 24 for both eluites, even if they are two isomers, can obviously change with increasing IIR in the eluent. This is also true even if two analytes are both of the same charge status as the IIR.29 Even if eq 24 reduces to eq 26 of reference 8, the effectiveness of the displacement equilibrium 3 can be different. This, at variance with a pure electrostatic theory, leads to a different KLH if the analyte is different. We may conclude that the foundations of the IIC for neutral molecules are clearly far more complex than it has been presumed. If one takes into account the complex behavior of both charged and neutral13 analytes, the hypothesis that the adsorption of the IIR does not alter any property of the stationary phase other than its electrical potential, which is the basis of the electrostatic theory,9 proves to be incorrect. (26) Van De Venne, J. L. M.; Hendrix, J. L. H. M.; Deelder, R. S. J. Chromatogr. 1978, 167, 1-16. (27) Rotsch, T. D.; Pietrzyk, D. J. Anal. Chem. 1980, 52, 1323-1327. (28) Petterson, C.; Schill, G. Chromatographia 1989, 28, 437-444. (29) Bartha, A.; Stahlberg, J.; Szokoli, F. J. Chromatogr. 1991, 552, 12-22.

According to the present extended thermodynamic model, the extent to which electrostatic interactions, ion pair formation in the adsorbed and in the mobile phases, and adsorption competitions are predominant depends on experimental conditions.30 For example, we will quantitatively show in a subsequent paper that the ion pair formation in the stationary phase exponentially decreases with increasing methanol concentration in the eluent.31 The present theory is very useful to track the versatility of IIC and to give new insights into IIC. From the epystemiological point of view, it is important to underline that the new retention model (30) Cecchi, T.; Pucciarelli, F.; Passamonti, P. Anal. Chem., submitted. (31) Cecchi, T.; Pucciarelli, F.; Passamonti, P. In preparation.

is able to quantitatively predict experimental evidence not previously rationalized, and this supports the claims for a superior theory. ACKNOWLEDGMENT We thank MURST and CNR for financial support. Permissions granted from Elsevier Science and discussions with Prof. J. H. Knox are gratefully acknowledged. Received for review November 16, 2000. Accepted March 4, 2001. AC001341Y

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