Langmuir 1992,8, 1587-1593
1587
Adsorption Isotherms and Overloaded Elution Profiles of Phenyl-n-alkanes on Porous Carbon in Liquid Chromatography Moustapha Diack and Georges Guiochon' Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996-1501, and Division of Analytical Chemistry, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 -6120 Received December 18,1991. In Final Form: March 6, 1992 The adsorption isotherms of phenyltridecane,phenylundecane,phenyldecane,and phenyloctanebetween acetonitrile and graphitized carbon have been measured by frontal analysis. Like the isotherm of phenyldodecanepreviously reported, all of these isotherms exhibit two inflection points and can be empirically accounted for by the s u m of a quadratic and a Langmuir term. The elution profiles of large size samples of these hydrocarbons are calculated from the experimental isotherms, using the equilibrium-dispersive model of chromatography. In spite of the complexity of the profiles, the results of the calculations are in excellent agreement with the experimental band profiles.
Introduction Adsorption on graphitized carbon black exhibits some unusual features.'P2 Of greatest potential interest for the analysts is a retention mechanism which is very different from the one observed on conventional reversed-phase materials. Because of the lack of any functional group on the hard, smooth carbon surface, this mechanism is based essentially on the number of heavy atoms (i.e., all common atoms but hydrogen) which can come into close contact with the carbon surface.' As a consequence, selectivity is essentially controlled by the geometrical structure of the analyte molecules, somewhat by their polarizability, and little by their polarity.' This explains the unique stereochemical selectivity and the high potential of graphitized carbon adsorbent to separate positional isomers.3 Although most work has been carried out so far in gas chromatography, scattered results suggest that a pure carbon phase could complementmost usefully the variety of stationary phases currently available in liquid ~hromatography.~~~ The development of a graphitic carbon adsorbent suitable for use as a stationary phase in HPLC has been extremely difficult. This adsorbent must satisfy several requirements which have turned out to be nearly incompatible. First, the particles should have the mechanical strength to withstand without breaking the high pressure (i.e. a t least up to 700 bar) applied during packing and operation of the column. Second, these particles should be available in a size range suitable for high-performance liquid chromatography (HPLC), Le., 5-20 pm. Finally, besides offering good chemical resistance to hostile eluents, they should be highly porous and have a homogeneous surface and a relatively large specific surface area.596 The particles of graphitized thermal carbon black used successfully in gas chromatography's2 are agglomerates
* Author to whom correspondence should be sent, at the University of Tennessee. (1)Kiselev, A. V.; Yashin, I. A. Gas Solid Chromatography; Plenum Press: New York, 1970. (2)Vidal-Madjar, C.; Guiochon, G. In Separation and Purification Methods: Perry, E. S., Van Oss, C. J., Eds.; Marcel Dekker: New York, 1973;voi. 2,p i . (3)Siouffi, A.; Colin, H.; Guiochon, G. Anal. Chem. 1979,51, 1661. (4)Unger, K. K. Anal. Chem. 1983,55,361A. (5)Colin, H.;Guiochon, G. J. Chromatogr. 1976,226,43. (6) Colin, H.;Eon, C.; Guiochon, G. J . Chromatogr. 1976,122,223.
which have no mechanical stability in a liquid.6 They can be consolidated into stable particles by pyrolysis of hydrocarbon^.^^^ Although the particles obtained after this treatment have a high specific surface area and a very homogeneous surface, it has not been possible to produce particles with a diameter less than ca. 20-25 km.6+6,8By high-temperature treatment of fine particles of activated carbons, Unger et al.4*9have prepared 5-pm carbon particles which are very strong but do not have a sufficiently large specific surface area, only a few m21g. Finally, Knox et al.'OJ1 have prepared carbon particles which are small enough (ca. 7 pm), are mechanically resistant, and have a large specific surface area (ca. 109150 m2/g). The surface of these particles is not entirely homogeneous, however, but includes some sites which selectively adsorb n-alkanes or compounds with long nalkyl chains. Because of these different limitations, few investigationsof the adsorptive properties of this new type of adsorbent and of its behavior in liquid chromatography have been published so far. We have recently measured the adsorption isotherm of phenyldodecane in the system acetonitrilelgraphitized carbon a t 50 OC, using frontal analysis and elution by characteristic points (ECP).12 This work was undertaken as part of a study on the relationship between elution band profiles in chromatography and equilibrium isot h e r m ~ . ~We ~ - ~were ~ expecting to find an isotherm exhibiting one inflection point at low concentrations, due to strong adsorbate-adsorbate interactions between the alkyl chains' and to record the kind of band profiles predicted for an S-shaped isotherm,13which have never been studied in detail. (7)Barmakova, T.V.; Kieelev,A.V.; Kovaleva, N.V. Kolloid Zh. 1974, 36, 133. (8)Colin, H.;Guiochon, G. Carbon 1978,16,145. (9)Unger,K. K.;Roumeliotis,P.;Mueller,H.;Gotz,H. J. Chromatogr. 1980,202,3. (10) Gilbert, M. T.; Knox, J. H. Chromatographia 1952,16,138. (11)Knox, J. H.;Kaur, B.; Millward, G. R. J. Chromatogr. 1986,352, 3. (12)Diack, M.; Guiochon, G. Anal. CheM. 1991,63,2608. (13)Guiochon, G.;Golshan-Shirazi, S.; Jaulmes, A.Anal. Chem. 1988, 60,1856. (14)Golshan-Shirazi, S.;Guiochon, G. J. Chromatogr. 1990,506,495. (15)Golshan-Shirazi, S.;Guiochon, G . Anal. Chem. 1988,60,2634. (16)Katti, A. M.; Ma, Z.;Guiochon, G . AIChE J. 1990,36,1722. (17)Jacobson, S.;Golshan-Shirazi, S.; Guiochon, G. J. Am. Chem. SOC. 1990,112,6492. (18)El Fallah, Z.; Guiochon, G. Anal. Chem. 1991,63,859.
0743-7463/92/2408-1587$03.00/00 1992 American Chemical Society
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1588 Langmuir, Vol. 8, No. 6, 1992
We found that the isotherms of phenyldodecane has two inflection points. The isotherm data were well accounted for by the sum of a quadratic and a Langmuir term. The Langmuir term has a very high initial slope and a very low column saturation capacity. It corresponds to the adsorption of phenyldodecane on sites which are highly selective of the n-alkyl groups and cover a very small fraction of the surface area. These could be surface defects (e.g., microporosity of the adsorbent or functional groups existing at the edges of the aromatic sheets and called edge groups). The quadratic term accounts for the S-shape of the isotherm at moderate and high concentrations. Because the interaction energy between two nalkyl chains lying on the surface and close to each other is high, the adsorption energy of the second molecule is higher than that of the first one. These adsorbate-adsorbate interactions would explain an isotherm which is convex downward at moderate concentrations and exhibits an inflection point when a certain surface coverage is reached and the isotherm turns toward saturation. A second inflection point, at lower concentrations, results from the addition of the quadratic and the Langmuir term. In spite of the complexity of the profiles recorded, a good agreement was observed12 between the experimental band profiles of phenyldodecane and those calculated by using the equilibrium-dispersive model of c h r ~ m a t o g r a p h y . ~ ~ J ~ J ~ ~ ~ ~ Although our original goal had been reached, we thought it useful, from both experimental and theoretical viewpoints, to study the behavior of other members of the n-alkylbenzene series, to determine the influence of the length of the alkyl substituents on the parameters of the adsorption isotherms and the shape of the experimental band profiles. We expected to loose the inflection points a t short lengths of the alkyl group, because the intensity of molecular interactionsbetween n-alkyl chains decreases rapidly with decreasing length. In this paper, we report and discuss the adsorption isotherms of four other of the six n-alkylbenzenes whose equilibrium isotherms from acetonitrile can be measured. Phenylheptane is almost not retained, while phenyltetradecane is too strongly retained, making isotherm measurements long, tedious, and inaccurate. We also discuss the elution band profiles of these four compounds in relation with the isotherm behavior.
Experimental Section I. Equipment. Adsorption data and elution profiles of high concentrationbands were acquired with an HP1090 liquid chromatograph (Hewlett-Packard, Palo Alto, CA), as previously described.12 11. Materials. Stationary Phase. The sample of microcrystalline porous graphitic carbon (PGC) used in this study was supplied by Professor John H. Knox (Wolfson Liquid Chromatography Unit, Department of Chemistry, University of Edinburgh, UK). It is different from the one used in our previous investigation.12 It presents a better mechanical robustness and performs well at packing pressures up to 6000 psi. The spherical particles are finer (ca.5 pm in diameter)and their sizedistribution is narrower. As a consequence the column obtained exhibits improved performances regarding its efficiency and lifetime and the reproducibility of the data. The packing porosity is approximately 80%, and the adsorbent has a specific surface area of about 109 m2/g, measured with nitrogen, using the BET method.lOJ1 (19) Glueckauf, E.,Proc. R. Soc. London, A 1946, A186, 35. (20) Aris, R.;Amundson, N. R. Mathematical Methods in Chemical Engineering; Prentice Hall: Englewood Cliffs, NJ, 1973.
_._ ...... !
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300
time (min)
350
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Figure 1. Comparison of the breakthroughcurves obtained for the successive injection of a positive and a negative concentration step of the same height. This comparison illustratesthe problems encountered in the determination of an isotherm point when using classical and reverse frontal analysis in the vicinity of inflection points (phenyltridecane). Column Packing. A 0.46 X 10 cm stainless steel column (1.66 mL volume) was packed using the same slurry technique as described previously.l2 The only changes were the uses of a 2-propanol slurry of a mixture of ethanol and 2-propanol (3:l (v/v)) as pushing solvent and of a packing pressure of 6000 psi. Column Characteristics. The column void volume (1.25 mL) was measured using deuterated water. The reason of this choice was discussed previously.12 The column efficiency for nonretained and for moderately retained compounds waa 2200 plates (e.g., acetone, k' = 1.2) and dropped for more 'strongly retained compounds (e.g., 1900plates for naphthalene, k' = 4.5). Mobile Phase and Chemicals. All experiments were performed under isocratic conditions, using pure acetonitrile aa the mobile phase (Baxter H. T., IL). Phenyltridecane (98%grade), phenyldecane(98%grade),and phenyloctane (99%grade) were purchased from Aldrich (Milwaukee WI), and phenylundecane was purchased from TCI America (OR). All of these compounds were used without further purification. 111. Procedures. The same procedures as previously described12were used, except that the more efficient column could be used at higher flow rates, and some changes were made aa reported. Determination of the Isotherm. Only classical frontal analysis21m22 was used for the determination of all the equilibrium isotherms. Thirty-two points were recorded for each isotherm. In the case of phenyltridecane,the breakthrough curvesrecorded using classical frontal analysis were more diffuse (Figure 1) in the intermediate concentration range between the two inflection points (0.17-1.20 mM) and presented a pronounced shoulder in the vicinity of the inflection points making difficult an accurate determinationof the isotherm. Theseexperimentalobservations confirm the reversal of the spin of the isotherm curvature. When the classical frontal analysis procedure is followed,the breakthrough curve exhibitsa gteep front followedby a shoulder, a long concentrationplateau, and another steep front (Figure 1). The two steep fronts correspond to the two segments of the isotherm which are convex upward, the shoulder (diffuse boundary) to the part which is convex downward. To the diffusefrontal boundary correspondsa steep boundary (shocklayer) in the rear profile and to the two steep fronts,two diffuseboundaries (Figure 1). Rear profile frontal analysis in the concentration range of the steep rear boundary in Figure 1permits an accurate determination of the isotherm data in the region where the isotherm is convex downward.
Results and Discussion I. Modeling of the Adsorption Isotherms. The equilibrium isotherms determined by frontal analysis are reported in Figure 2 (symbols). The solid lines show the best theoretical representation of these isotherms, using (21) James, D.H.;Phillips, C. S. G. J. Chem. SOC.1954, 1066. (22) Schay, G.; Szekely, G. Acta Chim. Hung. 1954,5, 167.
Langmuir, Vol. 8, No. 6,1992 1589
Phenyl-n-alkanes on Porous Carbon
4
8
12
18
20
Conc.(mM)
Figure 2. Equilibrium isotherms of phenyltridecane (11, phe-
nylundecane (2), phenyldecane (3), and phenyloctane (4) in the systemporous graphitized carbon/pureacetonitrile: experimental points, symbols; best fits of the composite isotherm model, solid lines. The correspondingvalues of the isotherm parameters are in Table I (model 2). Experimental conditions: column, L = 10 cm, i.d. = 0.46 cm. Temperature = 50 O C . Mobile phase flow rate = 1.1 mL/min.
the sum of a quadratic and a Langmuir term (model 212)
C.(mM)
Figure 3. Equilibrium isotherms of phenyltridecane (a), phenylundecane(b),phenyldecane(c),and phenyloctane(d)between graphitized carbon and acetonitrile. Same data as in Figure 2, but plots of q/C versus C. Table I. Parameters of the Adsorption Isotherm Models Model 1: Q.lC(b1 + 2bzC)/(l+ blC + b2C2) Model 2: Q.lC(b1 + 2bzC)/(1+ blC + b2O) + Q1zb3C/(1+ bsC) homologouscompounds models Q.1 bl bz Q1z bs CH,(CHz)6xH3
1
phenyloctane
2
291.7 0.025 0.0003 219.4 0.030 O.OOO6
2.5 0.51
CHz-(CHz)a~h
1 2
149.7 0.110 0.0009 147.2 0.087 0.0100
6.0 1.69
1 2
139.9 0.175 0.0300 122.4 0.103 0.0320 17.0 1.78
1 2
114.3 0.476 0.267 102.9 0.363 0.309
phenyldecane
where Q8,1 and Q8,2 stand for the saturation capacities of the two isotherm terms and bl, b2, and bs are numerical coefficients. This model has been chosen for reasons explained in the next section. The parameters giving the best fit are reported in Table I. Figure 3 represents the plots of q/C versus C for the four compounds studied and shows the variation of the slope of the isotherm chord with increasing mobile phase concentration. These plots are hyperbolic for a Langmuir isotherm. The adsorption behavior of the four components is quite different but still present a number of similarities. A t low concentrations, the slope of the chord decreases rapidly with increasing concentration and the isotherm is convexupward, as a Langmuir isotherm. This effect takes place in such a low concentration range that it is not clearly visible on the isotherms in Figure 2. It is better illustrated in Figure 3. At concentrations below 0.1 mM, all the isotherms could be accounted for by the Langmuir equation (eq 2). At a certain intermediate concentration, however, there is an inflection point for some of them (Figure 3a-c) and a reversal of the isotherm curvature takes place. Between approximately 0.17 and 1.2 mM (phenyltridecane, Figure 3a) or 2 mM (phenylundecane, Figure 3b), the slope of the chord increases with increasing mobile phase concentration, suggesting strong adsorbate-adsorbate interactions. A t high concentrations, a second inflection point is observed and the isotherm becomes convex upward again, and q tends toward the saturation capacity. As seen in Figure 3, the concentration range in which the isotherm is convexdownward decreases with decreasing
CHz-(CHz)$-CH3
phenylundecane
CHT(C+),,~H3 phenyllridecane
7.0 4.66
chain length, from phenyltridecane (Figure 3a) to phenyldecane (Figure 3c). The simplest model for isotherms with an inflection point is provided by the quadratic isotherm (eq 2). A nonlinear least-squares fit of this model to the experimental data gives satisfactory results only at high concentrations, above ca. 3 mM for phenylundecane (Figure 4, inset 2). The parameters of a least-squares fit of the experimental data to this model are reported in Table I (model 1). Also presented in Figure 4 are the plots of the best Langmuir isotherm (inset 1)and of the best composite isotherm obtained by adding a Langmuir and a quadratic term (main figure). Figure 4 shows clearly that, for phenylundecane, the former model is unacceptable, while an excellent agreement with the experimental results is obtained with the composite model. The same results are obtained with phenyltridecane (Figure 3a). Similar results were previously reported for phenyldodecane.12 A systematic evolution of the adsorption isotherm with decreasing length of the alkyl chain is observed (Figures 2 and 3). The isotherms of phenyltridecane, phenyldodecane,12and phenylundecane have two inflection points, but these points become closer and closer when the chain length decreases (parts a and b of Figure 3). Only one inflection point is observed for phenyldecane (Figure 3c) and none for phenyloctane (Figure 3d).
Diack and Guiochon
1590 Langmuir, Vol. 8, No. 6, 1992
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Figure 4. Comparison between experimentalisotherm data for phenylundecane (symbols) and the best fit of three isotherm models to these data (solid lines), plot of q / C versus C: main figure, composite isotherm model (values of the parameters in Table I, model 2); inset 1,Langmuir model (a = 35.6, b = 0.09); inset 2, quadratic model (values of the parameters in Table I, model 1). Experimental data are the same as in Figure 3b. For phenyloctane, the isotherm is nearly linear in the whole concentration range studied, instead of being curved before tending toward a saturated limit (Figure 2). However, the adsorption isotherm of phenyloctane still cannot be accounted for by a linear isotherm, nor a Langmuir isotherm, nor the combination of a Langmuir and a linear term, nor the combination of two Langmuir terms, as illustrated by Figures 3d and 5 (insets). The main Figure 5 shows the plot of q/C versus C for phenyloctane using the isotherm model given in eq 6. An excellent agreement is obtained between the isotherm model and the experimental data. 11. Discussion of the Isotherm Model. Simple statistical thermodynamics suggests an adsorption isotherm which is the ratio of two related polynomials of the same The Langmuir isotherm25is the simplest, first order such model. The second-order model is the quadratic isotherm. The model proposed earlier12is the sum of a Langmuir and a quadratic term. I t agrees with thermodynamics provided we assume that the surface is heterogeneous. The Langmuir isotherm assumes that the solution is ideal, the adsorbate forms an ideal monolayer, there are no adsorbate-adsorbate interactions in this monolayer, and adsorption is localized. Although these conditions are not met in most practical cases, the Langmuir isotherm remains a satisfactory empirical model for fitting adsorption data at low to moderate ~oncentrations.2~ While the Langmuir isotherm is always convex upward, the quadratic isotherm may be convex downward close to the origin and exhibit an inflection point when approaching (23) Hill, T. L. Introduction t o Statistical Thermodynamics; Addison-Wesley: Reading, MA, 1960. (24) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984. (25) Langmuir, I. J . Am. Chem. SOC.1916,38, 2221.
10
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20
C.(mM)
C.(mM)
Figure 5. Comparison between experimentalisotherm data for phenyloctane (symbols)and the best fit of three isotherm models to these data (solidlines): main figure, composite isotherm model (eq 6); inset 1,Langmuir model; inset 2, sum of a Langmuir and a linear term. Experimental data are the same as in Figure 3d. saturation. This model can be used to account for adsorption when one of the basic assumptions of the Langmuir model falters, especially when adsorbate-adsorbate interactions are significant and the isotherm has an inflection point. Adsorbent surfaces are often inhomogeneous.26Several different types of sites may coexist on a surface and have different adsorption behavior for a given ~ o m p o u n d . ~ ~ * ~ ~ In general, the adsorption on these different types of sites is not c ~ o p e r a t i v and e ~ ~a multiterm isotherm is useful to account for the adsorption behavior observed with such surfaces, each term accounting for the adsorption on a given type of sites. The experimental isotherm data are consistent with eq 1 and with the model of the carbon surface presented previously.12 This general agreement does not constitute a sufficient proof that the model is not purely empirical, however. The variation of the isotherm coefficients with the chain length suggests that our model has some physical sense. The surface of graphitized carbon is mainly made of the 001 basal planes of graphite, but is not homogeneous.lOJ1 The lack of crystalline order at long distances does not affect the adsorption properties of the surface.lP2 However, a small fraction of the surface has a higher energy and is highly selective for the alkyl groups. Originally,12 we suggested that this part of the surface was mainly made of micropores in which the alkyl chain could enter but not the phenyl group. This suggestion is not supported by the results reported here. The specificsaturation capacity of the Langmuir term depends rather strongly on the length of the alkyl chain, increasing 3 times from phenyloctane to phenyltridecane (Table I). (26) Jaroniec, M.; Madey, R. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, 1988. (27) Andrade, J. D. In Surface and Interfacial Aspects of Biomedical Polymers; Andrade, J. D., Ed.; Plenum Press: New York, 1985; Vol. 2, p 35.
Phenyl-n-alkanes on Porous Carbon
Langmuir, Vol. 8, No. 6,1992 1591
Such a dependence does not make much physical sense. The values in Table I are given in millimoles adsorbed per unit volume of adsorbent. The number of molecules needed to cover agiven adsorbent surface area with a dense monolayer should decrease with increasing molecular size. Thus, as expected, the specific saturation capacity of the quadratic term decreases linearly with increasing length of the alkyl chain. However, a linear regression of l/Qs,l versus the number of alkyl carbon gives a slightly negative intercept (area of the phenyl group), which is not acceptable. I t is well-known that the retention volume of homologs increases exponentially with the length of the alkyl chain.' In agreement with this anticipation, the logarithm of the coefficients bl and b~ increase linearly with the number of carbons in the chain. The shape of the quadratic isotherm and ita curvature at low concentrations depend strongly on the alkyl chain length. Because of its shape, the phenyl ring contribution --.to molecular interactions between adsorbed molecules is S 10 12 14 very small.lI2 On the contrary, interactions between alkyl time (min) chains laying parallel on the graphite surface are strong. Figure 6. Comparison between an experimental band profile Adsorbatefadsorbate interactions increase with increasing (symbols) and the profiles calculated with the equilibriumchain length, causing the curvature of the quadratic dispersive models, using the best Langmuir isotherm (dashed isotherm to increase. The coefficient b2 increases with line), the best quadratic isotherm (dotted line), and the beet increasing chain length (Table I). Linear regressions with composite isotherm (solid line). Experimental conditions are the chain length and the square of the chain length give the same as for Figure 2. Sample volume was 150 pL. equally satisfying results. 0 The influence of the presence of a long alkyl chain on the adsorbate-adsorbate molecular interactions is confirmed by the results obtained with hexamethylbenzene. The isotherm of this compound has a steep initial slope but no inflection point (unpublished results), demonstrating strong adsorbate-adsorbent interactions, with a high retention at infinite dilution, but weak adsorbate/ adsorbate interactions as expected with a star-shaped molecule.' One can expect to loose entirely the S-shape feature of the isotherm in the case of phenylheptane or phenylhexane. However, these two compounds were not retained under our experimental conditions. 111. Experimental Band Profiles. The profiles of high concentration bands were recorded for a series of samples of increasing sizes, phenyloctane, phenyldecane, phenylundecane, and phenyltridecane. These experimental profiles are shown in Figures 6-10 (symbols). Obviously, they are compatible with the respective isotherms previously discussed. The existence of an inflection point of the isotherm causes a major change in the shape of the profiles when the band concentration increases above i 2 3 4 the concentration of this inflection point, as illustrated by time (min) these figures. Figure 7. Comparison between the experimentalelution band The ideal model of chromatography, which assumes an profiles (symbols) of phenyloctane and the calculated profiles infinite efficiency for the column, shows that a velocity is (solid lines): isotherm model 2, numerical coefficienta in Table associated to each c o n c e n t r a t i ~ n This . ~ ~ velocity ~ ~ ~ ~ ~is~ ~ ~ ~I. Experimentalconditionsare the same as for Figure 2. Sample volumes were (1) LO pL, (2) 30 p L , (3) 60 p L , (4)90 pL, ( 5 ) 120 inversely proportional to 1 + F dq/dC. When the pL, and (6)150 pL. associated velocity increases with increasing concentration (Le., d2q/dC2 < 0, convex upward isotherm), the high reverses and the side of the band on which a shock grows concentrations move faster than the low ones. The high with increasing sample size changes. concentrations cannot pass the low ones, however. They Although column efficiencies are always finite, the pile up behind, and a discontinuity is formed. The band results of the ideal model permit a simple explanation of front has a shock, the band rear is diffuse. The opposite our observations. Because of the finite rate of mass is true for a convex downward isotherm (d2q/dC2> 0): in transfers in the column, the concentration shocks are this case, the band front is diffuse and the band rear has slightly dispersed. Steep fronts (or rears), called shock a shock. At an inflection point, the isotherm curvature layers, replace the shocks.20s29However, these shock layers propagate at the velocity calculated by the ideal model for (28) Rouchon, P.; Schonauer, M.; Valentin, P.; Guiochon, G. Sep. Sci. the shock propagation. Technol. 1987. 22. 1793. The band profiles of compounds having an S-shape (29) Lin, B.;Ma,Z.; Golshan-Shirazi, S.; Guiochon, G. J . Chromatogr. 1990,500, 185. isotherm have two shock layers, one in the front, one in
Diack and Guiochon
1592 Langmuir, Vol. 8, No. 6, 1992
m~
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-
11
time (min) Figure 8. Comparison between the experimentalelution band profiles (symbols) of phenyldecane and the calculated profiles (solid lines): isotherm model 2, numerical coefficients in Table 1. Experimental conditionswere the same as for Figure 2. Sample volumes were the same as for Figure 7. ul
i
S
10
12
14
16
time (min) Figure 9. Comparison between the experimentalelution band profiles (symbols)of phenylundecane and the calculated profiles (solid lines): isotherm model 2, numerical coefficients in Table I. Experimental conditionswere the same as for Figure 2. Sample volumes were the same as for Figure 7. the rear, and the concentration dependence of their shape is complex (Figures 6 and 8-10). A t low concentration, the equilibrium concentration in the adsorbed monolayer increases faster than the concentration in the solution, the isotherm exhibits a region which is convex downward, and the high concentrations move slower than the low ones. A rear shock develops and grows until an inflection point of the isotherm is reached. An inflection point takes place at an intermediate surface coverage since the monolayer capacity is finite. Beyond this inflection point, the equilibrium concentration in the monolayer increases more slowly than the concentration in the solution and a new shock layer forms on the band front. Since the concentration of a band must return to
13
18
19
22
5
time (min) Figure 10. Comparison between the experimentalelution band profiles (symbols)of phenyltridecaneand the calculatedprofiles (solid lines): isotherm model 2, numerical coefficients in Table I. Experimental conditionswere the same as for Figure 2. Sample volumes were (1)10 pL, (2) 20 pL, and (3) 60 pL. zero, however, the same rear shock layer is observed for all sample sizes exceedingthe one for which the front shock layer is first observed. These considerations explain the main features of the series of profiles recorded, their two shock layers, one on the front and the other on rear of the band profiles, and the stability of the rear front at high sample sizes. The intensity of these features increases progressively, from phenyloctane to phenyltridecane, paralleling the changes in the isotherm shape. The high concentration bands, particularly in the case of phenyltridecane (Figure lo), exhibit another important feature, which is not explained by a quadratic isotherm. This is the Langmuirian shape of the bands at moderate concentrations and the appearance of a front shoulder at higher concentrations. This characteristic is explained by the Langmuir term of the isotherm, which is dominant at low concentrations. Finally, the complexity of the experimental band profiles increases with increasing length of the alkyl chain, i.e., with increasing intensity ofthe adsorbate-adsorbate molecular interactions. For example, the front shoulder observed at moderate concentrations is more pronounced in the case of phenyltridecane than in the case of phenyldodecane12and it almost disappears in the case of the other members of the series. IV. Comparison between Experimental and Predicted Band Profiles. The elution profiles of high concentration bands can be calculated by numerical integration of the system of mass balance and kinetic equations of ~ h r o m a t o g r a p h y . ~ 3 J 4 ~In* ~the - ~ present ~~~ work, we study the elution profiles of pure component bands, we use a pure solvent as the mobile phase, and the column efficiencylargely exceeds a few hundred p l a t e ~ . ' ~ J ~ Thus, we can use the simplified equilibrium-dispersive model which includes only the isotherm of the adsorbate studied and its differential mass ba1an~e.l~ To perform the calculations required for the present work, we have used the calculation procedure based on the semi-ideal (30)Czok, M.; Guiochon, G. Anal. Chem. 1990, 61, 1 2 8 9
Phenyl-n-alkanes on Porous Carbon model of chromatography which has been previously described13J4and discussed.2g30 In Figure 6 we compare the highest concentration band profile recorded for phenylundecane (symbols) with the profiles calculated using the Langmuir isotherm (dashed line), the quadratic isotherm (dotted line), and the combined isotherm (solid line). Only this last isotherm accounts completely and accurately for the band profile. This result is general. In Figures 7-10, we compare the experimental band profiles (symbols) recorded for different size samples of phenyloctane (Figure 7), phenyldecane (Figure 81, phenylundecane (Figure 9), and phenyltridecane (Figure 10) with the band profiles calculated for the same injected amounts (solid lines). The calculations were performed using the equilibrium-dispersive model13 as described above and the composite isotherm (sum of a Langmuir and a quadratic term), with the parameters given in Table I, and assuming a rectangular pulse injection profile. As reported previously12and as explained by the detailed comparison illustrated in the case of phenylundecane (Figure 6), the quadratic isotherm model alone cannot account for either the front shoulder observed at moderate concentrations (a shoulder which could be mistaken for a poorly resolved impurity) or the tail which is characteristic of all the elution band profiles of all the phenylalkanes studied in the present and the previous12 work. This tail has a definite Langmuirian look and a Langmuir term is needed in the isotherm to take it into account. The profiles are characterized by their two shock layer boundaries. In the case of phenyltridecane, phenylundecane, and phenyldecane, the rear shock layer does not move when the sample size increases above the size needed for the band maximum to exceed the concentration corresponding to the second inflection point of the isotherm (phenyldecane is a limit case where the two inflection points take place at nearly the same concentration). On the contrary, the rear part of the phenyloctane profile is never stationary, confirming the absence of an inflection point on the isotherm of this compound. In all cases, a very good agreement is observed between the profiles of the experimental bands and the profiles predicted by the theoretical calculations. Of particular significance are the front shoulders exhibited by the profiles of the high concentration bands of phenyltridecane. These shoulders are well accountedfor by the model. They are a somewhatunexpected contribution of the Langmuir term of the isotherm. We note also the much closer agreement between the experimental and calculated band tails in the case of phenylundecane, phenyldecane, and phenyloctane as compared to the case of phenyltridecane. This is explained by the greater difficulty of an accurate determination of the adsorption isotherm of this compound.
Conclusion Further to our previous publication dealing with the profiles of high concentration bands of a compound having
Langmuir, Vol. 8, No. 6,1992 1593
an isotherm with an inflection point,12 our goal in the present work was a study of the behavior of phenylalkane homologs, focusing on the influence of the length of the alkyl chain on the parameters of the adsorption isotherms and on the shape of the experimental bands. As expected, we lost the S-shape behavior of the isotherm of the phenylalkanes by decreasing the chain length, as the adsorbateadsorbate molecular interactions decrease. The same composite isotherm model as successfully used for phenyldodecane could account for the adsorption behavior of all its homologs. Our results demonstrate that phenyltridecane, phenyldodecane, phenylundecane, and phenyldecane exhibit an isotherm with two inflection points in the system acetonitrile/graphitized carbon. Phenyloctane has a convex upward isotherm with no inflection point and a nearly linear arc, at intermediate concentrations. In all five cases, the sum of a quadratic and a Langmuir term gave the best representation of these isotherms. It permitted an excellent agreement between the experimental band profiles and those calculated with the equilibrium-dispersivemodel of nonlinear chromatography. Although the numerical dependencies of the column saturation capacities for the quadratic and the Langmuir term on the chain length are difficult to explain, especially for the Langmuir term, the variations of the other isotherm parameters on this length are as expected, reflecting the known variation of the limit retention times of adsorbates at infinite dilution (i.e., under analytical conditions) and the anticipated dependence of the adsorbate-adsorbate interactions on the length of each alkyl chain. Finally, an excellent agreement was observed between the experimental band profiles and those calculated using the best representation of the isotherms available and the equilibrium-dispersive model. This result contributes to the validation of the theory of nonlinear chromatography.
Acknowledgment. We thank John H. Knox (Wolfson Liquid Chromatograpy Unit, Department of Chemistry, University of Edinburgh, U.K.) for the generous gift of samples of microcrystalline porous graphitic carbon. We are grateful to the Hewlett-Packard Corp. for the gift of a 1090A liquid chromatograph with its data system. This work was supported in part by Grant CHE-8901382 from the National Science Foundation and by the cooperative agreement between the University of Tennessee and the Oak Ridge National Laboratory. We acknowledge support of our computational effort by the University of Tennessee Computing Center. Registry No. Phenyltridecane, 123-02-4; phenylundecane, 6742-54-7; phenyldecane, 104-72-3; phenyloctane, 2189-60-8; benzene, 71-43-2; acetonitrile, 75-05-8.
