Calculation of Retention Volumes in Gradient Elution Adsorption Chromatography Milan Popl, Vladimir Dolansk?, and Jiii Mosteckjl Department of Petroleum Technology andPetrochemistry, Institute of Chemical Technology, Suchbatarova 5, Praha 6, Czechosloaakia CALCULATION OF RETENTION VOLUMES of solutes determined by gradient elution was not dealt with in detail until now. Published procedures d o not allow for calculating retention volumes for the general case of a solvent gradient, i.e., any desired dependence of solvent composition on elution volume (or time). The calculation of the retention volumes of components in the analyzed mixture is advantageous, particularly for primary consideration of separability of the individual components, and allows adjusting the gradient course, without experimental data to achieve an optimum separation. In this paper is presented a simple method for calculation of retention volumes in gradient elution using the basic equations presented by Snyder and coworkers (1-3). A method for calculation of retention volumes in the case of linear dependence of solvent strength E" on the eluate volume was published by Snyder (I). A similar approach can be used for stepuise elution by solvents of growing elution strengths (2). At the present time, specialized gradient pumps are available for mixing two or three solvents and keeping total flow-rate constant. By means of these devices it is possible to select any course of solvent gradient. In this case it is difficult or even impossible to obtain a n explicit expression for the solvent strength-eluate volume dependence. The basic relationship (3) for calculation of the equivalent retention volume R" ( d i g ) , in the adsorption elution chromatography is given by Equation 1 :
log R"
=
log V ,
+ CY(SO- €"A8)
where Vu and CY are parameters relating t o the adsorbent; CY, the adsorbent activity; V,, the adsorbent surface volume (ml/g), S o , sample adsorption energy; A , , sample effective molecular area; c" is a parameter of the eluent, so-called solvent strength. Values of eo for different solvents and adsorbents have been published (3). As solvent strength of pentane is defined E O = 0, for a solute eluated by pentane Equation 2 can be written: log R ,
=
log V ,
+ aSo
(2)
Using an eluent with a higher solvent strength than pentane, the equivalent retention volume must be calculated by Equation l. By substracting and rearranging Equations l and 2, relationship 3 is obtained:
Table I. Equivalent Retention Volumes, R,, Adsorbents, and Solutes Parameters Alumina Acid Neutral a = 0.1269, a = 0.846, log v, = log v, = - 2.1641 -2.3042 So AS Solute R, (mllg) R, (ml/g) 0.25 1.86 6.0 Benzene 0.18 1.87 3.10 8.1 Naphthalene 1.16 2.65 3.72 9.7 Biphenyl 1.80 4.34 10.2 50.80 Anthracene 18.26 5.58 13.4 264.W p-Terphen yl 72.60 a Calculated by Equation 1.
where Nb is molar fraction of the solvent B in the binary solvent mixture, n, is effective molecular area of a n adsorbed solvent molecule B , and en is the solvent strength parameter of the eluent with the higher solvent strength. The retention volumes are obtained by multiplying the value of Ro and weight of adsorbent W . R,W
(1) L. R. Snyder, J . Chromatogr., 13, 415 (1964). (2) L. R. Snyder and D. L. Saunders, J . Clzromatogr. Sci., 7, 195 (1969). (3) L. R . Snyder, "Principles of Adsorption Chromatography," Marcel Dekker, New York, N. Y., 1968. 2082
V,
=
V,, X IOaEnbA'
(5)
Equation 5 permits the calculation of the retention volume V,, for the compound of interest using a binary eluent mixture of a known solvent strength value cab, under the assumption that the retention volume of the compound V , for elution by pentane, the adsorbent activity CY, and the sample parameter A , are known. Values A , can be calculated for most compounds (3). In the case of gradient elution, a continuous change of the value of e n b occurs under condition of constant eluent flowrate. Under this assumption and by inserting Eabinstead of the term 10PEnbAa into Equation 5 , Equation 6 can be written as follows :
1 V
v p =
(3)
When a mixture of two solvents A and B is used, the solvent strength c a b is calculated by Equation 4, which was derived by Snyder (3) under certain simplifying assumptions. I n this case the resulting solvent strength cab also depends on the adsorbent activity a as follows:
=
EubdVg
(6)
where V , is retention volume of a solute in gradient elution. As far as compounds with identical values of A , are concerned, it is necessary to solve only one function. I n the case of a mixture of compounds with different values A , , a separate function corresponds to each of the different A , values. Solution of Equation 6 is obviously difficult. I n the present work, a numerical solution of the integral o n the right side of Equation 6 has been employed. The desired upper limit of the integral represents a n eluate volume required to elute the sample by the given gradient.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 12, OCTOBER 1972
4
10
a
n 0
w
C
5 9 8-
8
r,==10.2 kq- 9.7
77 6-
6
E 4
ELUATE VOLUME (mi) I
0
1
3
9
18
36
L8
64
100 100 x)( OIO VOL. B
Figure 1. Gradient course for neutral alumina 1, naphthalene; 2, biphenyl; 3, anthracene; 4, terphenyl
I.-
80 100 120 ELUATE VOLUME (mt) I
0
1
3
Figure 2.
9
18
36
L8
61
?OO 100 Hx OIO VOL. B
Gradient course for acid alumina
1, naphthalene; 2, biphenyl; 3, anthracene; 4, terphenyl
EXPERIMENTAL
Materials. Alumina Neutral and Alumina Acid (Woelm Eschwege) were used as the adsorbent. The adsorbents were first activated at 400 "C for 8 hr and then deactivated by addition of 2 x wt of water. Columns. Glass columns, 12, 24, and 36 inches long with an inner diameter of 4 mm, possessing a device for introducing the sample were used. The pump was a programmed gradient pump, Dialagrad Model 190, manufactured by the firm ISCO. A UV spectrophotometer SP 800 B (Pye Unicam) with a flowthrough quartz cell of 10-mm path length and a dead volume of 0.2 ml was used for the detection. A gradient of n-pentane-ethylether was used for the elution. For experimental verification of this problem, model mixtures benzene-naphthalene-anthracene and benzene-biphenyl-g-terphenyl were used. For these compounds, retention volumes V , were measured on both adsorbents using the course of gradient given in Figures 1 and 2. Also for all the components, equivalent retention volumes R,, were measured on both adsorbents using n-pentane as solvent (Table I). Based on the obtained values R, and known values So (3), adsorbent parameters CY and log V, were calculated according to Equation 1. In the case of the terphenyl on the acid alumina, the R , value was calculated from Equation 1 after preliminary determination of a and log V,. Values for E,* and Ea, were calculated from Equations 4 and 5, respectively, for both the adsorbents of interest. Ob-
tained values of In E,, us. eluate volume were plotted in graphs (see Figures 1 and 2). The elution volumes, V,, resulting from the measurements were compared with values of V,, calculated on the basis of numerical integration Equation 6 using Simpson's one-third rule, by means of the HewlettPackard 9100 A calculator. The numerical integration may be used for any course of the dependence of E,, on the eluate volume. However, in certain cases, this dependence can be approximated by one or more defined curves. The entire course of the dependence of Ea,o n the eluate volume has been divided into three parts (see Figures 1 and 2). The first part and the third one were approximated with a good precision by a curve of the form y = axb whereas the second one was approximated by a straight line. The whole treatment of the problem--i.e., calculation of Ea, and In Enb,preparation of graphs, and integration for the four above-mentioned compounds and one adsorbent takes about 1.5 to 2 hr using a calculator. RESULTS AND DISCUSSION
Table I1 exhibits a relatively good agreement of both measured and calculated volumes of model mixture components. The larger relative differences between values V , and Vu,for naphthalene and biphenyl, may be attributed to the low value
ANALYTICAL CHEMISTRY, VOL. 44, NO. 12, OCTOBER 1972
2083
~~
Table 11. Measured and Calculated Retention Volumes (GEAC: rz-pentane-ether, eluent flowrate 65 ml/hour. Column length, 36 inches, weight W = 13.8 g) Alumina neutral Solute v, vo 1 (A 2 3 1 Naphthalene 13.2 14.7 11.4 20.7 18.5 Biphenyl 18.0 19.0 5.6 24.3 22.0 Anthracene 46.5 48.0 3.2 52.2 54.8 p-Terphenyl 49.5 54.0 9.1 59.0 59.2 Vo = measured retention volume; Vor = calculated retention volume using Simpson’s d e ; (A%),
=L
v
- Vo
vo
x
-10.6 -9.5 5.0 0.3
100
of the integral where a remarkable effect is faced with, for example, a subjective error encountered when reading off the data in the graph. F o r this reason retention volume for benzene was not calculated. On the other hand, for compounds with higher retention volumes, such as anthracene and p-terphenyl, the relative deviation is remarkably smaller. When integrating a n analytically expressed dependence of Eabus. V,, the fact should be taken into account that the gradient curve is only approximated by a mathematical function. Another reason for difference between measured V , values and those obtained by calculation may be in a worse precision of measuring the retention volume or of charging the stronger eluent. Those differences are markedly manifested in the region of higher elution volumes where a very high value of In Eaboccurs. Thus, the whole procedure shows requirements for a high precision a t all stages, for continuous control of the eluent flow-rate and for accurate calculations. The graphical integration based o n Simpson’s rule is relatively rapid. It is easy to check the possibility to approximate the course of the gradient by one or more curves. Whenever this is practicable, the whole calculation can be facilitated and made essentially more rapid.
SYMBOLS USED
solvents A and B, where B is the stronger :olvent adsorbed solute effective area (units 8.5 A*) lOaao.bda, see Equation 6 adsorbed solvent B effective molecular area mole fraction of solvent B in a binary solvent mixture solute linear isotherm equivalent retention volume (mlig) value of R”for elution with pentane solute adsorption energy, pentane solvent adsorbent surface volume (ml/g) retention volume for elution with mixture of solvents A , B retention volume for elution pentane measured retention volume for gradient elution calculated retention volume for gradient elution total weight of the adsorbent in the bed (g) adsorbent activity function solvent strength parameter values of e o for solvents A , B, A-B RECEIVED for review December 6, 1971. Accepted May 22, 1972.
A Thermal Analysis-Mass Spectrometric Technique for lderitifying Trace Impurities in Gas Samples Rudolf Schubert Bell Telephone Laboratories, Incorporated, Columbus, Ohio 43213
OFTENIT IS of interest to determine the trace amount and chemical composition of various unknown impurities in a gas sample. Many techniques with varying sensitivity exist for a large range of compounds ( I ) . Recently, utilization of the physical properties of the gases themselves (2) and improvements in gas chromatography (3) have extended detection limits for certain impurities. Gas chromatographs (GC) and mass spectrometers (MS) singularly or in combination detect and identify the broadest range of compounds. (1) “Air Pollution,” A. C. Stern, Ed., Academic Press, New York, N.Y.. 1968. Vol. I. 11. and 111. (2) L. B. Kreuzer, J.’App/. Phys.. 42, 2934 (1971). (3) R. K. Stevens and A. E. O’Keeffe, ANAL.CHEM.,42(2), 143A (1970). 2084
When the composition of the pollutants is unknown or one is interested in a variety of impurities, the usage of GC and/or MS presents problems. GC analysis of trace amounts of pollutants requires different traps, columns, packings, and detectors for different classes of impurities. Interpretation of MS analysis is difficult because of overlapping mass spectra. Possible reactions in a concentrated sample, or with traps and containers, can present additional complications. This paper describes a freeze-out (4)-thermal analysis-mass spectrometric technique which is particularly useful for de(4) M. Shepherd, S. M. Rock, R. Howard, and J. Stormes, ANAL. CHEM.,23, 1431 (1951).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 12, OCTOBER 1 9 7 2
