Langmuir 1993,9, 749-755
749
Theory of Ion-Pair Reversed-Phase Liquid Chromatography on Energetically Heterogeneous Solid Surfaces A. W. Marczewski Institute of Catalysis and Surface Chemistry of the Polish Academy of Sciences (Krakow), Laboratory for Adsorption and Physicochemistry of Interfaces, 20031 Lublin, Poland
M. Jaroniec* Department of Chemistry, Kent State University, Kent, Ohio 44242 Received January 2, 1992. In Final Form: December 14, 1992 The effect of adsorbent energetic heterogeneity on the retention of organic electrolytes in reversedphase liquid chromatography is studied in terms of ion-pair adsorption and electrical double layer models. The theoretical discussion is illustrated by the extensive model calculations.
Introduction Reversed-phaseliquid chromatography(RPLC) is often used for separation of ionic substances. The RPLC system consists of a nonpolar stationary phase and a polar mobile phase containing an ionic analyte, a counterion, and a co-ion. The changes in the concentration and hydrophobicity of the two last species regulate the analyte capacity factor. Some theoretical treatments were proposed to explain the retention mechanism of the ion-pair RPLC (e.g., refs 1-13). Two models are usually employed to explain the retention mechanism of an ion-pair chromatographic process. According to the first model, chromatographic process is represented by ion-pair equilibria (e.g., refs 1-5 and 9). The other model is formulated by assuming the concept of electrical double layer (e.g., refs 6-8, 10, and 13). In all of these treatments, the solid phase is assumed to be energetically homogeneous. To the best of our knowledge, there is no publication on ion-pair RPLC on heterogeneous surfaces. In this paper, a comprehensive description of ion-pair liquid chromatography on energetically heterogeneous solid surfaces is discussed with emphasis on ion-pair adsorption and electrical double layer models. This description permitted studies of the effect of solid phase heterogeneity on solute retention. Various adsorption equilibria are considered for different types of ion-pairs. The influence of different factors, including solution pH, on the retention of an organic ion is analyzed on the basis of model calculations. Theory General Considerations. For an infinitely low solute concentration, the net specific retention volume, VN= V R
- V Mis , associated with the adsorbed amount a as follows (e.g., ref 9)
-
V N /W = a/c for c 0 (1) where W is the amount of adsorbent in a column and c is the solute concentration. Defining the relative adsorption e as the ratio of the adsorbed amount a to the adsorption capacity a,, we can transform eq 1to the following form VN-= a,W
e
c
for c -
o
where a,W determines the adsorption capacity of the chromatographic column studied. Using such a transformation, one may investigate the intensive quantities independent on the column size. For simplicity, it is assumed in this paper, that a, W = 1mmol; it means that VN/a,W and VN are numerically identical, and the concentration values are expressed in mmol/L. Let us consider adsorption of one substance “i”from a dilute solution on a homogeneous solid surface. Such a process is described by the following type of adsorption isotherm (3) where the type of the function gi(Ci) depends on the adsorption model assumed (e.g., for nondissociable solutes gi(ci) = Kici, where Ki is the equilibrium constant). The values of the function gi(ci) are associated with the adsorption energy. The relative adsorption of the substance “i” from an n-component dilute solution on a homogeneous solid surface may be presented as follows6
* Author to whom all correspondence should be addressed.
(1) Knox, J. H.; Hartwick, R. A. J. Chromatogr. 1981, 204, 3. (2) Knox, J. M.; Laird, G . R. J. Chromatogr. 1976,122, 17. ( 3 ) Melander, W. R.; Horvath, Cs. J. Chromatogr. 1980,201, 211. (4) Horvath, Ca.; Melander, W.; Molnar, I. Anal. Chem. 1977,49,142, 2295. (5) Tilly-Melin, A.; Askemark, Y.; Wahlund, K. G.; Schill, G . Anal. Chem. 1979,51,976. (6) Stahlberg, J.; Hagglund, I. Anal. Chem. 1988,60, 1958. (7) Stahlberg, J. J. Chromatogr. 1986,356,231. (8) Bartha, A.; Stahlberg, J.; Szokoli, F. J. Chromatogr. 1991,582,13. (9) Sokolowski, A. Chromatographia 1986,22, 168, 177. (10) Stahlberg, J.; Bartha, A. J . Chromatogr. 1988,456,253; 1991,552,
13. (11) Hung, C. T.; Taylor, R. B. J . Chromatogr. 1980, 202, 333. (12) Liu, H.; Cantwell, F. F. Anal. Chem. 1991,63, 993, 2032. (13) Hearn, M. T. W. Ado. Chromatogr. 1980, 18, 59.
-
The retention volume V Nfor ~ the ith species is equal to
VNila,W = Bicn,/ci for ci 0 (5) where the forms of the functions gj(cj) for j = 1, 2, ..., n depend on the solute adsorption mechanism. In particular, if the substance “i” appears in various forms (neutral or ionic), then the function gi(ci) in the numerator of eq 4 should be replaced by the sum of suitable expressions gi,-
0743-1463/93/2409-0749$04.00/0Q 1993 American Chemical Society
Marczewski and Jaroniec
750 Langmuir, Vol. 9, No. 3, 1993 (cia),where the subscript a refers to the ath form of the ith substance. For an organic solute appearing at the different forms under given conditions, e.g., ionic, neutral, or associated, the concentrations of these forms are connected with the dissociation (or association) constant. For the acid-base equilibrium one obtains
ci = CiO + ci+ Cif
= D(Ci0, PH)
= giO(Ci0)
+ W),
(&+),(z-)d
(16b)
and
(&+I, (Q'),
+ (Q+),
+ W m+ CQ'),CS-),
(17a) (17b)
(6)
or
(7)
(18) The index m denotes the mobile phase, s the adsorbed (surface) layer, and d the layer adhered to the surface layer, Q+and S- denote the organic ions, and Z- denotes the inorganic ion (nonadsorbable). In the case when there is also a nondissociable form of organic substance Q in a solution (denoted as Qo) the suitable mechanism of adsorption and retention may be presented as follows:
where ci0 is the concentration of neutral form and Cif is the concentration of the ionic form; however, the type of the function D depends on the equilibrium type and on the composition of the liquid phase. Then, the function gi is given by
+ gi+(Ci+)
(8) If the conditions (i.e., pH) are identical for the whole chromatographic column, then the function gi(Ci) for both forms (ionic and neutral) can be expressed by one simple product as that for a nondissociated solute. Now, let us discuss the adsorption process of a mixture containing n solutes of similar properties of an energetically heterogeneous solid. For such a system, it is possible to assume that the distributions of adsorption energies are also similar (they differ only in the mean energies).lP16 Then, we obtain gi(Ci)
(Q'),
(Q'),
+ (S-&+ (Q+),(S-),
(Qo), + (Bo), (19) To keep a general character of these considerations, the problem of mutual relation between the concentrations of different forms of substance Q:Q+ and Qo in the mobile phase is not considered now. Taking also into account the adsorption equilibrium for the ion-pair S-R+: where R+ is an inorganic (nonadsorbable) ion, one can determine the mathematical forms
@-Im
+
(S3,
(20a)
+ (S-),(R+)d (20b) of the functions gi for a mixture of inorganic and organic ions Q+and S-. For a homogeneous surface these functions can be expressed as follows:
gQZ= KQZCQ + CZgQS
z(X*) = E(X*) -E; g,(ci) = gi(Ei,Ci)
(11)
E = e/RT; F e (0,l) (12) Above, e is the adsorption energy of the ith solute with respect to solvent, E is the reduced adsorption energy, E is the mean reduced energy, and E(X*) is the function inverse to the integral adsorption energy distribution function, X*(E). The function X*(E) is associated with the differential distribution X(E) by the following dependences: X*(E) = J E X(E*) dE* Emin
KQScg+ cs-
(21a) (21b)
(21c) gSR = KsRcs - cR+ gQa= KQOCQO (21d) For all energeticallyheterogeneous adsorbent the functions gi and the constants Ki should be replaced by gi and Ki. These values are connected with the mean adsorption energies corresponding to a given equilibrium (eqs 1620). If the solute Q is fully dissociated, the retention volume for the ion Q+ can be expressed as follows VNe/amW =
(13)
X(E) = dX*(E)/dE
(14) For energetically heterogeneous solids, eq 5 becomes
Ion-Pair Adsorption Model. The ion-pair adsorption model (e.g., eq 9) assumes that an organic ion is adsorbed on an adsorbent surface. With regard to the necessity of keeping electroneutrality, an organic or inorganic ion is also retained in the adsorption layer or in the layer adhered to it. This retention mechanism can be represented by the following quasi-chemical reactions:
(14)Marczewski, A. W.; Derylo-Marczewska, A.; Jaroniec, M. Chem. Scr. 1988,28, 173. (15) Marczewski, A. W.; Derylo-Marczewska,A.; Jaroniec, M. Tram. Faraday SOC.1 1988,84, 2951. (16) Jaroniec, M.; Madey, R. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, 1988.
where GQ+(cQ+) is the sum of -functions gi(Ci) describing the adsorption of ion Q+in different forms, however, G*Q+ is the sum of all remaining terms characterizing other equilibria which do not involve the ion Q+. In this case the terms associated with the neutral form of Q do not appear in eq 22. Analyzing the adsorption equilibrium of ion-pair Q'S(eqs 17 and 18),one can draw a conclusion that it is almost equivalent to an independent adsorption of organic ions Q+ and S- with lateral electrostatic interactions. For simplicity, one can omit the mechanism represented by eq 17b; this conclusion is confirmed partially by the experimental investigations of Sokolowski? Then, the functions G and G* in eq 22 are given as follows GQ+(cQ+) = &Zcg+cz-
(23a)
G*Q+= KSRCS-CR+ (23b) In the case when the solution contains many organic coions Q+, Q+I, ..., Q+,,, and co-ions s-,s-1,..., s - h , one can
Adsorbent Energetic Heterogeneity
Langmuir, Vol. 9, No. 3, 1993 751
easily generalize eqs 22 and 23
where
Let us consider now the pH effect of aqueous solution on the adsorption and retention of an organic cation being at the equilibrium with the neutral species KacQ+= cgocH+ (27) where Kais the acidic dissociation constant and CH+ is the concentration of ions H+. According to eqs 6-8 and 21, we obtain
physically realistic model of adsorption and chromatography of ions. In the current paper, the adsorption model based on the classical Gouy-Chapman theory of electrical double layer is considered and applied for describing solute retention in ion-pair RP chromatography. This model was used successfully by Muller et al.17 for the analysis and prediction of adsorption of the dissociable organics. It allows taking into account the surface charge resulting partially from dissociation of surface groups (q8) and partially from adsorption of organic ions (qads). Besides, it makes it possible to correlate the parameters that characterizeadsorption of organic substancesin the neutral and ionic forms. Let us discuss now the system containing an organic ion Q'. According to electrostatic theory17the function gQ(CQ) has the following form
(28)
If we denote CQ
= cQ++ CQO
(29)
then we have
where
(34)
KQ' KOexP(EQ*)
(35)
= exP(-zq$4,/RT)
(36)
where
VNQ/a,W =
+ KQOcQO+ G*Q) xQzcQ+cz+ KQOCQO et(KQzcQ+czKQZcQ+cz+ KQocQo+ G*Q cQ++ CQO
gQ*(cQ*) = RQ*cQ+,fq
and fq
Above, the constant KQ*describes the adsorption of ion ' Q on an electrically neutral surface, however, fq determines the effect of surface charge on adsorption process; is the charge of the organic ion , 'Q F is the Faraday constant, and & is the electrical potential of adsorbent surface in relation to solution. The expression ZQ*F& determines the work necessary to overcome the potential barrier between solution and adsorbent surface. The value of the potential & may be estimated from the equations describing the density of the diffuse double layer charge, ZQ*
qd qads
In the case when G*Q = 0 (the lack of other organic ions) eq 30 gives the following simple relationships:
VNQcQ/amW= et(pcQ) (33) Simple analysis of eqs 30 and 32 leads to the conclusion that for an organic ion the effect of pH on the retention and KQO.If KQZCZde ends on the ratio of values KQZCZ> then an increase in the pH causes a decrease in the Rf value (eq 31) and, consequently, a decrease in_the < KQO, retention volume VNQ(for CQ = const). If KQZCZthen an opposite behavior is observed. The above presented formulation allows taking into consideration also the other possible equilibria (for example, described by eqs 16 and 17) and study their influence on the state of adsorption or chromatographic systems. Electrical Double Layer Model. Now, the electrical double layer m o d e P o will be included to the equation describing the retention volume. To keep the condition of electroneutzality, the organic ions adsorbed on a surface have to be accompanied by the organic or inorganic ions of the opposite charge, retained in the adsorbed layer or in the solvent layer adhered to the adsorbed one. These species form an electrical double layer and determine the electrical potential difference between the solid surface and the liquid phase. This electrostatic surface potential is the important factor which should be considered in a
EQO,
+ qs + qd(4s) = 0
- Zdqd = [ S E J ~ T I I ~Sinh(ZdF&/%T) '~
(37) (38)
where Zd = Iz+l = (2-1 is the valence of ions forming the diffuse layer, c is the dielectric permittivity of solution, and I = (1/2)&izi2 is the ionic strength of solution.
Results and Discussion Ion-Pair Adsorption Model. It will be shown that the relationship vNQ,/c&= f(VNQ,CQ+) for c& # 0
(39)
is useful to study the dependence of the retention volume on the surface heterogeneity. If there is one organic ion Q+ in the solution, the course of the function (39) does not depend either on the organic ion concentration q+or on the concentration of inorganic counterion Z-, CZ-. Simultaneously,all the possible points corresponding to the different concentrations Q+ and Zmay be easily shown on one figure. For a homogeneous surface and any fixed concentration values of other components, this relationship is always linear. In Figure 1 the function (39) is presented for the system containing only ions Q+ and Z- and for the different dispersions of the adsorption energies associated with Gaussian distribution (G) (17) Muller, G.; Ftadke, C. J.; Prauenitz, J. M. J . CoZZoidZnterface Sci. 1985,103,466, 484.
Marczewski a n d Jaroniec
752 Langmuir, Vol. 9, No.3, 1993 A
\
a-W.1
B
KpZ4
81
I\\
6=2
\
\
\
I
I
'n
'b.'L.
I
Figure 1. Effect of the energetic heterogeneity on the retention of ion pair Q+Z-. Panel A shows the dependence (39)for different values of the energy dispersion u expressed in the RT units for Gaussian (G) distribution function; panel B presents this dependence for different energy distributions: Gaussian (G), square-shaped (Sq), and 6-Dirac (L) homogeneous surface) distributions taken with the dispersion u = 2.
Figure 3. Dependence (39)plotted for a model system containing various concentrations of the organic ions Q+z and S-. The symbols G and L refer to Gaussian and homogeneous surfaces, respectively. aW . 1.
.,.
0.5
1
C.,V,
4
+
Qr
Figure 2. Effect of the presence of other organic ions on the Q+1 ion retention. Panel A shows the dependence (39)plotted for a system containing an organic ion S-, whereas panel B presents this dependence for a system with the co-ion Q+z and the organic ion S-. Symbols G and L refer to Gaussian and homogeneous surfaces, respectively.
X ( E ) = (1/(2r)1/2u)expi-(E - E)2/2u21
(40)
These curves are compared with the straight line (L) obtained under assumption of energetic homogeneity ( a = 0) (part A). The characteristic limiting points of the relationship (39)are also drawn. For example, the Henry constant KQZ,H= RQZexp(u2/2)14J6changes when the energy dispersion u is changed. In Figure 1B the effect of shape of the adsorption energy distribution function on the concentration dependence of the retention volume is analyzed for two symmetricaldistributions: Gaussian (G) and square-shaped (Sq), characterized by the same values of the adsorption energy dispersion. The other model calculationsperformed for the Gaussian distribution are presented in Figure 2. This figure shows the influence of concentration of other organic ions on the retention of ion &+I. Figure 2A presenta the case when the presence of ions S-and R+ diminishes the retention volume VNQ,at a fixed value of cz-; however, it does not change the course of the dependence (39). Introduction
0.5
0
6=1 Kp,*:l
A
Figure 4. Dependence (39)plotted for a model system containing various concentrations of the counterion Z- and fixed concentrations of the organic ions Q2+ and S-. The symbols G and L refer to Gaussian and homogeneous surfaces, respectively.
of co-ion Q+2 to the system and then an increase in the concentration of co-ions S- causes a decrease in the retention volume of the ion Q+1 (see eq 28 and Figure 2B for CZ- = 100). The other problem arises when ion Q + 2 is added into solution. The retentions of Q + 2 and Q+1 are affected by the concentration of the same counterion Z-. In this case, a decrease in the difference between the plota (39) for homogeneous (L)and heterogeneous (Gaussian, G) surfaces are observed (cf. Figure 2B). It is due to the competitiveadsorption of ions Q+land Q + 2 on the surface. In Figure 3,analogously as in Figure 2, the effect of the small concentrations of ions Q+2 and S-on the retention of Q+I is presented for the fixed low concentration of counterion Z- and for Gaussian distribution with u = 1. At very low concentrations of ions Q+z and S- the dependence (39)is almost identical as in the case when there is only ion Q+l in the solution (Figure 1). When these concentrations increase, then the behavior of the dependence (39) is similar to that for a homogeneous surface (as in Figure 2). Figure 4 shows the effect of the concentration of the counterion Z-on the retention of Q+1for moderate (Figure 4A) and very low (Figure 4B) concentrations of organic ions S- and Q+2. The value of retention volume VNQ,
Adsorbent Energetic Heterogeneity Kpz,=l
K,,c,.c,=l
KsIcs.cR+:l
Kqz,=l
a5
0
Langmuir, Vol. 9, No. 3, 1993 753
1'.0
50
10
100 KQ2'cQ:cZ.
vUQ:cP:
Figure 5. Dependenceof the Q+Iion retention to VNQ+~CQ+~ (panel
A) and KQZ~CQ+~CZ(panel B) for various concentrations of Z- at the fixed concentrations of Qtz and S-. 1
'CI-
Figure 7. Effect of pH on the retention of the or anic cation Qt for a Gaussian surface (a = 1) at pK, = 9 and ~ Q =Z &a =
0.5
1. 4,rv 1
0
01
V% ,
Figure 6. Effect of pH on the retention of the cation Qt for a homogeneous surface (L) at pK, = 9 and KQZ= KQO= 1.
[
increases with CZ-; however, an increase in the concentrations of ions Q+2 and S- leads to a decrease in the retention volume. Figure 5 illustrates the possibility of the retention 0 analysis by using a simpler form of eq ~ , V N Qvs, VNQ~CQ~ (Figure5A), and the classicalone, V N Qvs~KQZ,CQ,CZ(Figure 5B). The first dependence has a great advantage in - 0.1 comparison to the classical one and it can be used for the chromatographic systems with the higher concentrations of substances competing with ion &+I. However, when concentrations of the ion, retention of which is analyzed, Figure 8. Dependence of the electrical potential & of an are much higher than that for the other components, eq adsorbent surface on the ionic strength Z (mol/L) for the 1:l 39 allows simplification of the analysis of a chromatosolvent-water electrolyte and different values of the surface graphic system. charges 9. and gads (C/m2). The model calculations were performed to investigate increasing the ionic strength I (the lower part in Figure the pH effect on retention of cation Q+ being at the 9B). The linear segments of the In f q vs log I dependence equilibrium with a neutral molecule Qo (eqs 21, 27, 28, refer exactly to the situation in the ion-pair adsorption and 30). We assumed the acidic dissociation constant pKa model.9 For 1:l electrolyte and I = c we have = 9 (and KQZ= RQO = 1). In Figures 6 and 7 the retention dependencesare presented for a homogeneous surface (L, u = 0) and for Gaussian distribution (G) with u = 1. The effect of the counterion 2-concentration on the shift of When the potential tpsand the adsorbed ions charge have retention curves is also shown in Figures 6 and 7. opposite signs (e.g. because of existence of the strong According to the dependences (30 and 31) one can observe surface charge qsor adsorption of other ionic organics, the that the slope of curves VNQ/CZdiffuse double layer charge can have the same sign as vs VNQCQ change proportionallytothe valueft'lcz- (eq31);however,their shapes adsorbed ions Q'), a strong increase in the adsorption do not change. If RQZ,CZ> RQo,then a decrease in pH forces is observed. This increase is depressed by an causes an increase in the retention volume. Simultaincrease in the ionic strength I (upper part of Figure 9A). neously, for the higher pH values (hydrolysis),the values In Figure 10 the data shown in Figure 9 are presented in the coordinates log(f,li) va log I in order to analyze the diminish with CZ- at a fixed value of VNQCQ. of VNQ/CZElectrical Double Layer Model. Figure 8 presents convergence of electrostatic and ion-pair adsorption modthe dependence of potential & [VI on ionic strength I eL9 Constant values of log(f,ll) (see eq 41) refer to their [mol/Ll at fixed values of the "spontaneous" surface charge perfect compatibility (see the lower part of Figure 10B qsand the surface charge qads. It is clearly visible that under the dashed line). Analyzing divergences and convergences between the and the diffuse double layer charge have always opposite electrostatic model and the ion-pair adsorption model, signs (eq 38). However, the analysis of the dependence of one may find that they are compatible at the relatively fq vs log I provide much more interesting results (Figure 9). For a diffuse layer charge q d having opposite sign to small concentrations of nonadsorbed counterions (CZ-) or, the charge qads, the electrostatic effect decreases with equivalently,at the small ionic strength (1%CZ-), especially
Marczewski and Jaroniec
754 Langmuir, Vol. 9, No.3, 1993
0)s
-5
-i
-j
-i
-i
b
Figure 11. Dependence on the extreme values of the potential
&on logl at the complete monolayer coverage (0 = 1).The value of qad. = 0.46 C/m2refers to the cross sectional area a. = 0.35nm2.
'
/
I
/
-4
-3
-2
-I
b1
Figure 9. Dependence of log f, on the logarithm of the ionic strength I for the different diffuse layer charge densities qd = -(q.& + qa). Panels A and B show respectively this dependence for the attractive (q.dJqd > 0) and repulsive ( q a d q d < 0) electrostatic forces.
0
a005
0.01 "NPCP
,
-aoL
-1
\
-4
-3
-Zl9,
-I
Figure 10. Dependencelog(fd0 vs log lplotted for the conditione
specified in Figure 9. The area in panel B from the dashed line to the left side refera to the functional convergence of the electrostatic and ion-pair adsorption models.
when the adsorbent has no yspontaneousnsurface charge (q8 = 0, q d = - q a d However, both models are not equivalent for strongly charged adsorbenta (e.g. with dissociable surface groups) having charge with opposite sign to that of the solute charge (qdqads< 0 and kd < lqadsl or qdqd > 0). In such casea the ion-pair adsorption model gives gQ+ CQ+CZ- while electroetatic model leads to gQ* C Q * / I (czI). Similarly, for a high concentration of inorganic, nonadsorbable ions (CZ- CR+ I, where Z-R+ form 1:l electrolyte) ion-pair adsorption model predicts gQ+ CQ+ CQ+CZ-, while an electroetatic model leads to gQ* CQ* what is equivalent to the lack of influence of electrolyte concentration change on adsorption and re'Q tention of. In order to estimate the limiting values of the electrostatic forces influencing adsorption of dieeociableorganica, the model calculations (Figure 11) were performed assuming the adsorbate surface deneity equalto the average cross-section area of simple aromatics (0.35 nm2).17 For lqadslthe value of 0.46C/m2was obtained for fully packed surface. Taking into account actual experimental conditione (ionic strength I and maximum relative coverage
- --- -
- -
Figure 12. Dependence VNQvs VNQCQ for different values of the ionic strength I on a homogeneous surface (L) and a Gaussian (G) heterogeneous surface ( a = 1). Calculations were carried out for KQ+= 1 (L/mmol), a,W = 1 m o l , and CQ+ expressed in L/mol. 8 reached on chromatographic column), together with poeaible spontaneous surface charging (e.g. for active carbons), one can easily find the extremum values of electrostatic potential qj8and then analyze the electrostatic effecta in solute retention. To complete the analyeisof properties of the electrostatic theory, model studies of the ionic strength I on the solute retention were performed at the fixed spontaneoussurface charge (as= 1)of a homogeneous (L)and heterogeneous (Gaussianwith u = 1)surfaces (Figure 12). These studies were carried out by assuming that only organic substance in solution is ion Q+. It ie clearly visible that an increase in the ionic strength causes a slower decrease in the retention volume VNQ. Figure 13 shows the influence of pH on the total retention of the ion Q+ and the neutral form Qo. For qe = 0, an increase in pH (more neutral species) causes a decrease in the ' Q concentration and consequently a decrease in the Q+ion adsorption and an increase in f,. Under assumption of the identical admeans sorption f o r m for &+ and Qospecies (KQ*= KQO) that adsorption energies are equal and when qja = 0 (i.e. f, = 11,a stronger adsorption and greater retention volume are observed. At the same time, the course of the VNQvs VNQCQcurves for VNQcQ/a,W' 1(id%eQ,t 1)is almost independent on the energetic heterogeneity when the mean adsorption energies are constant.
-
Adsorbent Energetic Heterogeneity
Langmuir, Vol. 9, No.3, 1993 755
chromatography showed that the energetic heterogeneity of the solid phase affects strongly the ion-pair retention. This effect is reduced considerably a t the higher concentrations of other organic ions, which compete with the ion Q+for the adsorption sites on the solid surface. However, a strong pH dependence observed for the ion-pair retention is almost not sensitive to changes in the adsorbent heterogeneity. The electrostatic model seems to be better than the adsorption model for studying different effects in the ionpair chromatography, such as dissociation, association, and surface charge effects. However, this model is less effective in studying the influence of different counterions on the ion-pair retention. Thus, a comprehensive description of the ion-pair chromatography on energetically heterogeneous solids should take into account adsorption and electrostatic effects. 0' Glossary a2 0.4 0.6 adsorption capacity of a solid am Figure 13. Dependence of VNQon VNQCQplotted for a homoC solute concentration geneous surface (L) and a Gaussian (G) heterogeneous surface E reduced adsorption energy (a = 1)at different values of H. Calculations were carried out for p ~ =. 9,qI = 0,I = 0.1, Rp+ = ~ p =o I (~/mmol), a , = ~1 minimum reduced adsorption energy Emin mmol, and CQ+expressed in L/mmol. E average reduced adsorption energy Faraday constant F surface change contribution f, model-dependent function of the solute conceng tration function g containing E as a parameter i? G sum of the g functions I ionic strength of solution equilibrium constant KI n number of components charge aseociated with adsorption on a surface gads Figure 14. Effect of the spontaneous surface charge q. on the double layer charge qd retention of Q+. Panels A and B show the dependence of the surface charge 9s relative retention VNQ+IvpJQ*,-on VNQCQ+for a homogeneous organic ion Q+ surface and a Gaussian ( u = 1)heterogeneous surface,reapectively, universal gas constant whereas, panel C presents the dependence of In VNQ+- on the R surface charge q8. The other parameters are as in Figure 13. R+ inorganic nonadsorbable ion absolute temperature T The last Figure 14 presenta the influence of the organic ion Sspontaneous surface charge (as)on retention of the Q+ion void retention volume VM (no neutral species). Parte A and B are drawn for net specific retention volume VN homogeneous (L, u = 0) surfaces, respectively, and for the corrected retention volume VR constant other parameters (I= 0). In order to compress mass of adsorbent in a column W the scale of the figure, the retention volumes are presented differential distribution function of adsorption X(E) as ratios VNe+/VNe+Mx where VNQ+, = [V~e+l,, 0. To energy complete Figure 14,part C,the values of In VNQ+~,= are X*(E) integraldistribution function of adsorption energy plotted against the spontaneous surface charge values qs. variable defied by eq 11 z The most violent changes in solute retention are observed charge of the organic ion for qs = 0 (see also inflection point for the dependence in ZQ Figure 14C),whereas for qs > 0 the retention volume is inorganic nonadsorbable ion Zmost stable though it assumes very low values (Figure Greek Symbols 14C). The curves for moderate qs< 0 (charge opposite to t adsorption energy the Q+-ion charge) show a slower decrease in comparison tP dielectric permittivity to that for qs = 0 and low values of vNQ+CQ+. For higher electrical potential of a solid surface values of VNQ+CQ+ (where qs+ qe& 0 and when the diffuse 4s double layer charge sign inversion is observed), these e relative surface coverage changes are much more visible. The shifting between L 0 dispersion of the energy distribution and G curves in Figure 12C refers to the ratio of the Henry constants of both isotherms: K H , G ~ ~ K =HexpM ~ ~Subscripts ~ ~ d layer adhered to the surface (u2/2) = 1.65 and, consequently, the difference in the logarithms of their retention volumes is constant equal to 1 ith component (u2/2) = 0.5 when u = 1. i jth component refers to the ath form of the ith component ia Conclusions refers to neutral form of the ith component io m mobile phase Theoretical considerations and extensive model studies s surface (adsorbed) layer presented in terms of the adsorption model of the ion pair V...C.
-
-
