Anal. Chem. 1904, 56,88-9 1
a0
accurate exptrapolation and interpolation of the a values. With tv and the retention time of one analyte, tA, the retention time of the other analytes can be predicted from eq 1. This has been done for a series of snow melt samples. The results are summarized in Table 11. In all cases the agreement is within &3% RSD which is equivalent to the experimental precision.
LITERATURE CITED
Laub, R. J.; Purnell, J. H. J. Chromafogr. 1975, 112, 71.
(4) Laub, R. J.; Purnell, J. H. Anal. Chem. 1976, 4 8 , 1720. (5) Dernming, S. N.; Turoff, M. L. Anal. Chem. 1978, 5 0 , 546. (6) Price, W. P., Jr.; Demrnlng, S. N. Anal. Chlm. Acta 1979, 108, 227. (7) Price, W. P., Jr.; Edens, R.; Hendrlx, D. L.; Dernming, S. N. Anal. Blochem. 1979, 93, 233. (8) Sachok, B.; Strawahan, J. J.; Demming, S.N. Anal. Chem. 1981, 53,
70. (9) Jenke, D. R.; Pagenkopf, G. K. Anal. Chem. 1982, 5 4 , 2603. Jenke, D. R. Ph.D. Thesis, Montana State University, 1983. (10)
RECEIVED for review Mav 31.1983. AcceDted October 11.1983. project A-138 MONT.
Models for Prediction of Retention in Nonsuppressed Ion Chromatography Dennis R. Jenke and Gordon K. Pagenkopf*
Department of Chemistry, Montana State University, Bozeman, Montana 5971 7
The retention behavior of Br-, NO,-, CI-, SO:-, and S2O;- in nonsuppressed Ion chromatography Is studied as a functlon of changlng eluent composltlon. Three models, multlple specles.eluent, single species eluent, and single Interaction sles, are utlllzed to predlct chromatographic Fhavlor. While all three are based on a thermodynamic equllibrlum conslderatlon of the Ion exchange process, they dlffer in their characterlzatlon of the analyte/eluent competltlon or the ion/resin Interaction. Desplte thls dlff erence in approach, all three models effectlveiy characterlre the behavior of the analytes under elution condltlons which are of practlcai importance. The relative utlllty of each model Is discussed.
Ion chromatography has rapidly evolved into an accepted method for the determination of solute species in liquid samples (I, 2), and correspondingly characterization and modeling of the separation process are critical for method optimization and subsequent development. The current models are based upon an equilibrium distribution of analyte and eluent between the mobile phase and the resin ion exchange sites ( 3 , 4 ) . These models differ through the definition of the number of active components in the mobile phase that participate in the chromatographic separation. The single active species model (3) for nonsuppressed anion chromatography utilizes the phthalate dianion as the active eluent. A multiple active species model (5) has been used to predict the chromatography of arsenate and orthophosphate. Three models, multiple species eluent, single species eluent, and single interaction sites have been utilized to predict. the chromatographic behavior of chloride, bromide, nitrate, sulfate, and thiasulfate. These models are an extension of the ion-exchange theory developed by Mayer and Tompkins (6) with appropriate modifications. Multiple Species Eluent. The equations used to model the multiple eluent treatment are similar to those previously developed for suppresed ion chromatography (4). There are four basic considerations. (1)The reduced retention volume of the analyte, U, is equal to the volumetric distribution coefficient (6). In this case 0003-2700/84/0356-0088$0 1.50/0
UA = DA
(1) where UA is equal to the observed retention volume minus the void volume, DA is the ratio of analyte in the resin and solution phases associated with a given theoretical plate. (2) All of the "available" exchange sites are occupied by eluent anions and therefore the effective column capacity is given by
Q, = Cm[Ex"-I
(2)
X
where m is the ionic charge. (3) Electroneutrality is maintained during the elution process by exchange of charged species. (4)For anions interacting with a strong base anion exchanger, the following equilibrium is established at the resin sites. The equilibrium constant for this reaction is defined as the selectivity coefficient, KA-E.
(A"-)
+ n/rn(E-Rn)
= n/m(E"-)
+ (A-Rn)
(3) (4)
Experimental observations were made with phthalate eluents. For the multiple eluent treatment, HP-and P2- are assumed to be active eluents and eq 2 becomes
&e = AHP-R~
2AP-Rn
(5)
Use of eq 4 to describe eluent/eluent and analyte/eluent exchange and substitution into eq 5 provides
The volumetric distribution coefficient for analyte A is expressed as
DA = KA-~(D~)"/" and for a monovalent eluent-divalent analyte
0 1983 American Chemlcal Society
(7)
ANALYTICAL CHEMISTRY, VOL. 56, NO. 1, JANUARY 1984
Solution of eq 6 for AHp-h and substitution into eq 8 provides
(9) Experimental conditions are quoted in terms of total eluent concentration and hydrogen ion activity. For the phthalate system ET
= [HZP]
+ [HP-] + [P2-]
(10)
By use of the a notation, [HP-] = ETCYHP, AHP = fHpETaHp, and AP = fpE@p where fHp and fp are the mean ionic activity coefficients (7). Substitution into eq 10 and use of the second acid dissociation constant for phthalic acid provides
and in the same manner
(12)
Single Species Eluent. When the only active eluent species is P2-,Qe becomes Qe = 2Ap-h and a derivation similar to that presented above provides
u,,= KA-PQe ETfPaP UlS =
(-)
KA-PQ~' I 2
2ETfPaP
Single Site Interaction. The resin used in these studies had a silica support and quaternary exchange sites. From the column capacity (4.9 X mol), weight of the resin (2.9 g), and surface area 95 m2/g, the average surface area per site is calculated to be 94 A2 (8). The area occupied by analyte and eluent anions is significantly less than this, approximately 30 A2, and thus if the exchange sites are evenly distributed, a divalent ion is too small to simultaneously interact with more than one adjacent site a t any given time. In this situation, species charge will not affect the total number of column/ species interactions which can occw but w i l l affect the stability of the interaction. Under these conditions the effective column capacity becomes (15) = AHP-~n+ AP-R~ which when coupled with a derivation similar to those used previously yields Qe
EXPERIMENTAL SECTION The chromatographicsystem consisted of a Perkin-ElmerSeries 3B liquid chromatograph, a Vydac Model 3021 C4.6 anion separator column, a Vydac Model 6000 CD conductivity detector, and a Sargent Welch strip chart recorder. The injection loop was 0.100 mL. The chromatographic components were thermally insulated to minimize short-term temperature variations (9).The eluent was prepared from reagent grade potassium hydrogen
89
Table I. Retention Times of Analytes total retention time,= min phthalate, so,*- s,o,zpH NO,C1Br10-3 M 3.75 6.97 4,87 6.21 40.42 52.67 1.0 1.0 4.60 4.87 3.23 4.21 12.75 17.00 9.50 13.27 5.07 4.32 2.85 3.75 1.0 8.13 11.44 1.0 5.57 4.13 2.69 3.53 7.26 9.77 1.0 6.01 3.82 2.58 3.29 2.0 3.85 5.44 3.66 4.69 18.70 23.58 9.47 12.37 2.0 4.53 4.18 2.83 3.62 6.25 8.76 2.0 4.94 3.58 2.41 3.11 5.04 7.15 2.0 5.40 3.48 2.26 2.98 4.65 6.61 5.82 3.29 2.19 2.85 2.0 4.57 2.71 5.47 2.5 5.39 2.41 3.88 2.5 5.95 2.38 3.56 2.5 9.37 13.65 3.82 4.02 2,79 3.53 3.0 5.76 7.45 4.54 3.30 2,32 2.90 3.0 4.71 6.39 4.80 3.09 2.16 2.71 3.0 3.52 4.80 5.42 2.91 1.96 2.53 3.0 3.42 4.68 5.89 2.82 1.93 2.47 3.0 4.61 2.41 4.33 3.5 5.14 2.26 3.26 3.5 5.85 2.16 2.81 3.5 9.00 15.03 3.82 5.29 3.01 3.15 4.0 6.69 10.20 4.26 4.66 2.66 2.78 4.0 5.35 8.33 4.60 4.31 2.41 2.54 4.0 4.38 6.75 5.00 4.03 2.26 2.33 4.0 3.68 5.79 5.38 3.88 2.14 2.25 4.0 3.35 5.18 5.95 3.82 2.09 2.21 4.0 6.33 8.30 3.75 3.18 2.36 2.84 5.0 3.75 4.70 4.54 2.55 1.95 2.35 5.0 3.08 3.88 4.96 2.42 1.84 2.19 5.0 2.70 3.42 5.39 2.37 1.77 2.14 5.0 2.45 3.13 5.98 2.35 1.73 2.10 5.0 2.18 3.69 4.14 6.0 2.08 2.98 4.60 6.0 1.98 2.65 4.79 6.0 a Flow rate of 3 mL/min. phthalate with pH being monitored after degassing under vacuum and controlled by addition of KOH. When eluent solutions were changed, the system was flushed at 2 mL/min for at least 1 h. Stock solutions (0.10 M) of NaC1, NaN03,Na2S04,Na2S203,and KBr were prepared from their reagent grade salts. The standard solutionswere diluted with the desired eluent in order to minimize solvent dips in the chromatograms. All samples were analyzed in triplicate with a flow rate of 2-3 mL/min. Activity coefficients were predicted by the extended DebyeHuckel equation. The pK, values for phthalic acid are 3.10 and 5.40 (7). The retention times for the analyte ions were obtained from the graphical display and are corrected for the dead volume equivalent. The latter was considered to be equal to the time required for the cations to move through the column. The reduced retention volume (Vi) was converted. to the retention time by addition of the void volume and dividing by the eluent flow rate. All concentrations and the column capacity are expressed in terms of interaction equivalent, the moles of exchange sites per 100 /IL of sample, and moles of eluent per 100 /IL.
RESULTS AND DISCUSSION Multiple Eluent Species. The elution behavior of the five analyk anions at various elution concentrations and pH values is listed in Table I. In general the retention times decrease as pH and total eluent increase. Modeling of the robserved chromatographic behavior with eq 11and 12 requires an evaluation of the analyte-eluent and eluent-eluent selective coefficients. These constants may be obtained from batch experiments (IO),calculated with other mathematical theories (11-16), or obtained from observed retention times. The latter was used in these studies. The observed retention times and the maximum column capacity are substituted into eq 11 and 12 providing a sequence of
90
ANALYTICAL CHEMISTRY, VOL. 56, NO. 1, JANUARY 1984
Table 11. Selectivity Coefficients for Multiple Eluent Speciek Model'" constant value constant value K,i.Hp 0.916 i. 0.046 K ~ p p 20.0 i 1.0 0.0500 i 0.0025 K B r - ~ p 1.384 * 0.069 K p ~ p KNO,-HP 1.707 c 0.085 KSO,-HP 0.0844 i. 0.0055 KS,O,-HP 0.125 i. 0.008 mol/interaction equiv. a See eq 4, &le = 1.51 X Interaction equivalent = moles of exchange sites per sample volume (100 pL). equations with two unknowns. This set of equations is solved by iterative minimization of the variability in KA-Hpfor a given value of KHp-p. The values of the selective coefficients are summarized in Table 11. The magnitude of the constants increases as one goes from chloride to bromide to nitrate. This is expected since it parallels the order of elution. The greater the value of the constant, the greater the interaction with the resin and thus a longer retention time. Comparison of the divalent analyte-monovalent eluent constants indicates that P2-is preferentially bound by the column with Sz032-being retained more extensively than S042-. For the latter two this is in agreement with the observed retention times. Since P2- is preferentially bound to the column, it takes many void volumes for the column to reach equilibrium with the eluent as the pH is lowered. A comparision of predicted and observed retention times for bromide using the multiple species eluent treatment provides a slope of 1.00, intercept = 0.01, R = 0.991, and av RSD = 2.6%. A similar comparison for sulfate using the multiple species eluent treatment yields a slope of 0.96, intercept of 0.14, R = 0.998, and av RSD = 2.69%. The RSD values for chloride, nitrate, and thiosulfate are 2.3, 2.5, and 4.1 %, respectively. The model does a particularly poor job of predicting the retention time a t the lowest eluent concentrations and lowest pH values. In these cases the model predicts retention times much longer than those observed. Experimental observations indicate that the column does not have as much capacity at the low eluent, low pH conditions. This could be caused by resin swelling within a confined volume. As the resin swells some sites could become unavailable for interaction with the eluent and the analytes. Experimentally it is noted that there is a 13% decrease in void volume over the range of a eluent concentrations used and implies an increase in resin volume. It also has been observed that nonexchange adsorption and resin invasion can occur as the eluent concentration increases (17). In summary this model is applicable provided the total eluent concentration is greater than 2 x M and the pH is greater than 4. Single Eluent Species. At an eluent pH of 6, phthalate speciation is dominated by the Pz-ion and anal@ elution can effectively be described by eq 13 and 14. Since the resin selectivity for P2-vs. HP- is large, P2-controls analyte elution behavior even under conditions where the eluent is dominated by HP-. The elution behavior of both Br- and SOf approach linearity above a pH 4.6 Below this pH, HP- contributes to analyte elution and the model becomes ineffective. Elution behavior and eluent compositions for the eluents whose pH is greater than 4.6 have been used to generate the respective selectivity coefficients. The values of KA-p are summarized in Table 111. These coefficients cannot be directly compared to those obtained for the multiple species eluent treatment since the analytes are only related to P2-. The magnitude of the coefficients for a given analyte charge accurately reflect the observed elution sequence. However, there is no continuity in trend with varying analyte charge since the mathematical forms of eq 11 and 12 differ.
Table 111. Selectivity Coefficients for Single Species Eluent Model constant value'" constant valuea KC1-p 16.2 i 2.2 Kso,.~ 1.48 i 0.22 2.14 i. 0.26 KBr-p 34.4 i 5.9 K~,o,-p KNo,-p 41.7 i 7.0 a Values obtained by using data with a pH of 4.6 or greater. Table IV. Selectivity Coefficients for Single Site Exchange Model constant value constant value K c ~ p 0.80 i 0.09 K B r - ~ p 1.21 i. 0.12 KNO,-HP 1.49 c 0.14
Kp-~p
2.33 c 0.20'" 6.67 t 0.8Bb KSO,-HP 4.93 i 0.69 KS,O,-HP 6.82 i. 0.90 a Calculated by use of monovalent analyte ions. Calculated by use of divalent analyte ions. The agreement between predicted and observed retention time for sulfate provides an av RSD = 5.0% for the data with a pH of 4.6 or greater. Extreme deviation is observed when the pH is less than 4.6 due to the contribution of HP- to the elution process. Similar agreement was obtained for the other four anions. Single Site Interaction. Equation 16 describes the relationship between eluent composition and retention volume under single site interaction conditions and, coupled with elution behavior and eluent composition data, can be used to generate selectivity coefficients as described previously. For a sample set which contains all analytes regardless of charge, the calculated value of Kp-Hp is (4.50 f 0.75). Use of this value to predict analyte retention results in significantly poorer agreement than that observed with the other models. Under such conditions observed and predicted analyte retention behavior differ by k7.7% and k6.1% RSD for Br- and S042-, respectively. If the data are divided into two sets as a function of charge, selectivity coefficients are calculated that produce better agreement between predicted and observed retention times. Once again, the magnitude of these coefficients, as documented in Table IV, accurately reflects the elution sequence of the analytes. The agreement between observed and predicted behavior using these coefficients provides a slop = 1.05, R = 0.958, and av RSD = 3.55% for bromide. For eluents with a phthalate concentration greater than 2 X M, the fit is similar to that obtained with the single eluent model but is inferior to that obtained for the multiple species eluent model. Both the single site and multispecies models are unable to accurately model the chromatographic behavior at low pH and 1 X M total phthalate eluent. As observed previously, it is suggested that this behavior reflects variability in the effective column capacity. It is not known why two values of Kp-Hpprovide a better fit for this model. Possible explainations could include the presence of charge specific sites or potassium playing a role as a counterion in the interaction between dissimilarly charged species.
CONCLUSIONS None of the proposed models is capable of predicting chromatographic behavior under low eluent, low pH conditions. Specifically the retention times are overestimated and can be attributed to a decrease in column capacity with these conditions. The agreement between observed and predicted retention times when total phthalate concentration is greater than 2 X M and a pH greater than 4.6 is best for the multiple species eluent model by a factor of approximately
Anal, Chem. 1984, 56,91-96
Table V. Ratio of ICAxIPCoefficients mathematical treatment used multiple single species eluent species eluent single site 0.41 t 0.11 0.55 * 0.11 Cl-/NO,0.54 r 0.05 0.67 * 0.14 0.67 * 0.07 0.50 t 0.15 Cl-/Br0.86 ?: 0.13 0.82 r 0.13 Br-/NO,0.81 r 0.06 S0,2-/S2032-
0.68
?:
0.09
0.73
* 0.17
0.75 i: 0.20
2. The single site and single eluent models are comparable; however, the applicable pH range for the single site approach is larger. The mathematical treatments for these models provide selectivity coefficients that differ widely in magnitude. There is consistency within the models as evidenced by the ratios of the selectivity coefficients, Table V. The values for a particular pair are not statistically different. The results obtained for the other anions are comparable to those shown for bromide and sulfate. Registry No. Br-, 24959-67-9; NO3-, 14797-55-8;Cl-, 1688700-6;SO-,; 14808-79-8; S2032-, 14383-50-7; phthalic acid, 88-99-3.
91
LITERATURE CITED Fritz, J. S.; Gjerde, D: T.; Pohlandt, C."Ion Chromatography"; Heuthig: Heidelburg, 1982. Pohl, C. A.; Johnson, E. L. J . Chromatogr. Sci. 1980, 18, 442. Gjerde, D. T.; Schmuchkler, G.; Frltz, J. S. J . Chromatogr. 1980, 187, 35. Hoover, T. B. Sep. Sci. Technoi. 1982, 17,295. Hoover, T. B.; Yager, G. "Ion Chromatography of Anions"; EPA-600/ 4-80-020; Environmental Protection Agency: Washington, DC, 1980. Mayer, S. W.; Tompkins, E. R. J . Am. Chem. SOC. 1947, 69, 2866. Pagenkopf, G. K. "Introduction to Water Chemlstry"; Marcel Dekker: New York, 1978. Harrison, K., The Separations Group, Vesperis, CA, personal communication, 1982. Jenke, D. R.; Pagenkopf, G. K. Anal. Chem. 1982, 54,2603. Kunin, R. "Elements of Ion Exchange"; Reinhold: New York, 1960. Davidson, A. W.; Argerringer, W. J., Jr. Ann. N Y . Acad. Sci. 1953, 57, 105. Giueckauf, E. Proc. R . SOC.London, Ser. A 1952, 214, 207. Freeman, D. H. J . Chem. Phys. 1961, 35, 189. Soldano, B. A.; Larson, Q. V.; Meyers, G. E. J . Am. Chem. SOC. 1953, 77,1338. Marinsky, J. A.; Reddy, M. M.; Amdur, S. J . Phys. Chem. 1973, 77, 2126. Gregor, H. P. J . Am. Chem. SOC. 1951, 73,642. Diamond, R. M.; W h y , D. C. I n "Ion Exchange"; Marissky, J., Ed.; Marcel Dekker: New York, 1966; pp 227-274.
RECEIVED for review May 31,1983. Accepted October 11,1983.
Computer Simulation of Light Transmission through Scattering and Absorbing Chromatographic Media I. E. Bush* and H. P.Greeley
Research Service, Veterans Administration Medical and Regional Office Center, White River Junction, Vermont 05001
Quantltative densitometry and fluorometry of thin-layer chromatograms and other planar separatlon medla still depend for the most part on emplrlcal management of the problems caused by light scatterlng. The degree of deviation from linear callbration curves reported in the literature varles considerably. To Investigate thls problem, a computer model was developed whlch slmuiates the Kubelka-Munk dlfferentiai equations and allows a varlabie number of Iteratlons. The results from thls model are compared with solutlons of the same equatlons obtained by conventlonal methods of lntegratlon. Wlth simulated layers more than 100 particles thick, the results obtained are lndlstlngulshabie from the Integral solutlons of the Kubdlka-Munk equations for scatterlng powers between 0 and 20. With layers thinner than 40 particles, the model predicts slgnlflcant devlatlons from the Integral solutions over the same range of scatterlng powers. I t seeme likely that thin medla commonly used for paper and thln-layer chromatography are often better approximated by the discrete step model with thlcknesses equlvalent to 10-40 particles, thus explalnlng much of the reported variability in the literature.
In their classical analysis of light transmission through absorbing and scattering media, Kubelka and Munk (1) proposed the pair of simultaneous differential equations -dI/dx = -(S + K ) I + SJ (la) d J / d x = -(S
+ K ) J + SI
where I is the intensity of light traveling inside the specimen away from its illuminated surface, J is the intensity of light traveling inside the specimen toward its illuminated surface, S is the coefficient of scatter per unit thickness, K is the coefficient of absorption per unit thickness, and x is the distance from the unilluminated surface of the specimen. Although solution of these equations is difficult and requires further simplifying assumptions (e.g., Kubelka (2)),the Kubelka-Munk (K-M) theory has been used extensively in industrial applications with considerable empirical success (3). Its applications in analytical chemistry and to luminescence in turbid materials, however, still present difficulties (e.g., ref 4). Thus, Vaeck (5) first applied the K-M theory to the densitometry of chromophores on paper chromatograms, and Ingle and Minshall(61, Kortiim (3,and Goldman and Goodall (8) demonstrated reasonable correspondence between the concentration of material in paper and thin-layer chromatograms (TLC) and the absorbance predicted by the theory. However, Treiber (9) observed better correspondence with a combination of the Beer-Lambert equation with the Kubelka and Munk theory. Hurtubise ( I O ) found that Goldman's later application of the K-M theory to luminescence on thin-layer chromatograms (11)was only partidy satisfactory and pointed out the dearth of experimental work testing these and other theoretical approaches that had been suggested following Goldman's work. Goldman and Goodall (8)first emphasized the theoretical weakness of direct photometry of paper and thin-layer chromatograms with the instruments then current. They suggested that two requirements were mandatory for precise measurement by this method: (1) correction of absorbances
This article not subject to U.S. Copyright. Publlshed 1983 by the American Chemical Society
