Topics in..
. Chemical instrumentation
Edited by S. Z. LEWIN, N e w York University, N e w York 3, N. Y.
T / m e urlicles, most of which are lo be contributed by gue-st by calling atlention aulhors, are intended lo serve the readers of this JOURNAL to new developments i n the theory, design, or availability of chemical laboratory instrumentation, oi b~ presenting uscful insights and explanalias of topics that are of practical importance to lhose who use, or leach the use oj, modern inslrurnentation and inslrumenlal techniques.
XIV. Some Problems of Quantitative Analysis in Gas Chromatography h i s Condal-Bosch, Inrtifuto Quimico de b r r i a , Translation from the Spanish by S. Z. Lewin
Barcelona, S p i n .
.L. Condal-Borch is Profesor of Physical
The characteristics of vapor phase chromatography that have contributed most t,o its rapid development have been, without doubt, ita enormous separalin and a possibility of puantitatiw precision quite rare among separation techniques. The methods used for quantitat,ive determinations in gas chramatography do not differ essentially from those used in other types of analysis, but this does not mean that the chemist, upon being confronted with his first quantitative determinations by gas chromatography, will not find himself faced with a group of new technical problems that can readily lead him into considerable errors or utter failures. The basic objective of the present work is to present a review and discussion of a number of those problems, in order to clsrify certain concepts and techniques for the chemist who wishes to become familiar with quantitative chromatography, which is so full of exciting possibilities for the solution of chemical problems. The majority of the quantitative methods employ, as the basic eompuiat i a a l pammetw, the area enclosed by each chromatographic peak, and its corresponding baseline. The substitution of the peak height for this area is a less frequently used approach that is useful in specific cases, and is based fundamentally upon the more exact parameter. The first part of this treatment is devoted to the various methods employed for t,he determination of areas, with special attention t o non-automatic methoda, for it is in those that the role played by the ehemist is of major importance. The second part is devoted to the analytical methods that are always the central part of every quantitative determination. Since this is a subject that is too long to treat in detail here, we will start by giving same idea of the nature and classification of the various methods. in
order to devote the third part to that aspect which is of prime importance for the quantitative methodology of gas chromatography; viz., the problem of sensitivity factors.
Determination of Areas The methods employed for the determination of area8 in gas chromatography can be classified into two main groups, as shown in Table 1. The manual methods are carried out after the ordinary chromatographic record has been made, and even in the ease of the most mechsniired of these techniques (viz., the utilization of the planimeter), the role played by the operator is fund%mental. The automatic methods are characterized by the fact that the operator plays only Table 1.
Chemistry ond of Instrumento1 Methods of Anolysis a t the Chemicol Institute of Sorri&, Borcelono, Spain. He studied rimultaneoudy ot the Chemisol Institute of Sorria, and Ihe University of Borcelono, receiving the degree of Chemical Engineer fmm the former institution in 1946, and the license in chemigtry from tho latter in 1947. He received the DSc. from the Univerrity of Madrid in 1950. His principal research activities a t present are in the fields of electrochemical and optical methods, electronic instrumentotion, gas chromatography, and analogue computation.
require nothing more than ordinary drafting equipment, or, a t most, relatively inexpensive instruments of the type of the micrometer magnifier, or the polar planimeter.
Methods for Determination of Peak Areor
Manual (performed subsequent to recording)
Instrumental: Graphical:
Automated (~erformed simultaneouslv .. with recording)
Mechanical: Electromechanical: Electronic:
a secondary role (e.g., he merely notes the magnitude of theread-out, pushesa button to start the measurement, etc.). From the technical point of view, the automatic methods are nearly always preferihle became of their ease of use and precision, and their relative freedom from ineonvenienee and limitations. Their only disadvantage is the cost of the requisite accessories and instrumentation, which can amount to a substantial part of t,he total enst of the installation. The majority of manual methods, hy eompaxison,
Balance and scissors Planimeter Classical methods Triangulation Ball-and-disc Low inertia motors Linearized motors Analogue Digital
Another essential characteristic of the automatic methods is the f a t that the integration is carried out simultaneously with the ordinary recording of the data. Based upon the nature of the principle exdoited for the inteeration. the mrt,hod~ ~-~ can he classified &: A,' mechanical, B. electromechanical, and C. electronic. There is in practice only a single memher nf the group of automatic mechanical integrators; vis., the hall-and-disc device. ~~
(Continued on page A236)
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Tliis rcmpuncnt ran he rcadily d a p t e d to any servomechanism recorder, and can he arranged to inscribe the result of the integration on the same segment of chart paper as the ordinary recording; this result is usually drawn in the farm of a sig-oaa line d o n -g the border of the chart - . p:y. The electromechanical integrators nre based upon a simple mechanical counter coupled to a n electric motor, the velocity of which is made as proportional as possible to its input signal. To this end, t,he low inertia motors employed in elertrochemistry as current integrators (eoulameters) represent a very economicd means of effecting this type of measurement., although it is essential that the operator be present to activate and deactivate the motor a t the proper instants. In order to automate the recording of the integral, it is necessary to complicate the instrumentation considerably, and the resulting greater cost makes it practied to utilize motors the velocities of which are linearized by negative feedback through the use of a tschometer-generator. The mathematical operation of integration based upon t,he use of a voltage is one of the fundamental operations of every analogue cowpulor, and is areomplished 11.v means of a capacitor coupling to a do amplifier. In principle, this "nu-electronic" met,hod is very attractive, but there are difficulties in practice, such as the problem of coupling to a. suitable recorder, and of the automat,isation of the integration factor, which are generally complicated and expensive to solve. As a consequence of these ronsiderations, digital cornputma are at present looked upon with more favor in the field of all-electronic integrators for gas ehromatography. Despite their coarplexityand present rehtively high cost, they are murh more flexible than the analogue eomputors, and a great deal can be expected of them in the not too distant. future. Fundamentally, digital integrators eonsist of an electronic decimal counter, very similar to those currently employed in nuclear instrumentation, preceded hy an i m p u h generator, t h e output rate of which is proportional to the input. voltage signal.
Manual Inlegrotion The manual methods can he divided into two groups, according to whether they require only ordinary drafting equipment, or a more expensive instrument (e.g., a balance or planimeter). The "balance method" consists of rutting oul the chromatographic peaks with a scissors, and weighing the resulting pieces of paper with the quantitative halance. Aside fmm the well-known problems sssoriated with the necessity of using paper of great. uniformity, and the nuisance of rutting accurately d o n g a curved surface, there is the additional serious rlifirnlty that the technique results in the destruction of the chromatographic data, which are so valuable as a permanent record. This last difficulty can be cinu~nvented by using photographic paper to make n contact print of the chromntnpa~n; this also has the advantage that the gmph is (Conlintred on page .(?40)
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Chemical Instrumentation thereby transferred to a. thicker paper which can then he cut and weighed with greater ease. As a. general rule, it sulnces to employ a balance that can be read to tenths of a milligram; the use of contact printing paper represents an approximate doubling of the weight compared to t,he majority of recorder chart papers. The planimeter method may be przcticable in those laboratories in which there are already available the requisite instrument, as well a8 persons experienced in its manipulation, but in the absence of these conditions, the acquisition of t,he device is rarely justified. In order that a planimeter give results that can be relied upon, it is necessary to acquire considerable practice in its manipulation, and a t the very least to make all measurements in duplicate. The sensitivity (smallest division of t,he nonius) oi a normal planimeter isusually iOmma, whichis in many cases insufficient for analytical purposes in gas chromatography; hence it may be necessary t,o employ a planimeter with a constant minor (havine a sensitivitv of
obtained by other methods. When a chemist who is somewhat familiar widh the methods of grrtphical or numerical integration attempts to apply these to the determination of chromatographic peak aress, he may expect to receive two surprises. I n the first place, the general methods, which are adequate far the great majority of cases, prove to be inadequate, or of limited applicability. The counting of squares of millimeter or ruled paper is more aggravating than any other mct,hod imaginable, and it is quite surprising that this method is cited in several books and papers on chromatog raphy. Simpson's rule, or the trapezoid simplification, is extremely difficult to apply to the tall, narrow farms of the majority of peaks; in addition, i t ia not a simple method t,o use. The methods based on the summing of several selected ahcissae (Gauss' method) do not improve the situation either; nor does inverting the approach (using selected ordinates) prove any more practical despite the fact that it is feasible and precise.
Triangulation The second surprise consists in the great possibilities with respect to precision and si~nplicit,y (compared with automated methods of much greater cost) bhat can be achieved when one dispenses with the general methods, and attempts to develop s p e d methods based upon the particular form of the chromatographic peaks. I n this way, it is possible to arrive a t a. series of methods that we may combine under the name of triangulation methods, and that are very simple and precise if rert,ain necessary precautions are taken. The first triangulation method (Fig. 1) consists in extending the approximately straight aegments about the inflection points; these two lines, together with the (Continued on page A242:
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baseline, constitute a triangle the area of which is obtained as onehalf the product of the base t,imes the altitude. I n this way, one obtains a n area that is equal to 97% of the actual area of the chromstographic peak, if the shape of the curve is that of the Gauss error function. This triangulation method is a t once simple and intuitive, and has been much utilized since the very beginnings of gas chromatography. However, i t has two serious disadvantages that frequently limit its precision. First, the parameters required for the calculation are dofined by a, geametrical construction that is not always easy to accomplish with the desired precision. Secondly, the assumption concerning the shape of the peak is not valid in certain specific eaatses (e.g., asymmetric peaks, unresolved peaks, etc.).
Figure 1. Triangulation method applied to 0 Gousion curve b y extension of the straight-line segmentratthe inflection points.
The first difficulty can he solved by relinquishing the intuitive part af the method and seeking parameters (among those that accomplish a triangulabion) that are defined by the curve with a minimum of geometric construction. Thus, one arrives a t the procedure of Figure 2, in which the area is obtained as the product of the peak height times the half-width (width a t half the peak height,). The only geometric construction necessary consists in drawing the baseline, measuring
Figure 2. Area computed ms peak height multiplied by half-width ir 90qlo of actual peak
oreo.
(Continued on page A244)
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llle peak height, noting a t the same time its midpoint, drawing a horizontal through this point, and measuring the peak width nn this horizuntal. Both measurements (but especially the uidth) enn be made wit,h r nolahle improvement in precision with the help of a magnifying lens that incorporates a micrometer 8calo. The nrex enlculated in this way (Fig. 2 ) correspunds to 01% of the acbual area for s (:aussinn curve. This diflerenre of 10% (as well a8 the 3% dilrcrenw in the first triangulation method dcseribed) is not important, since ordinarily the areas of d l the peaks (including those of the calihrntion substsnres when these are used) are determined by the same procedure, and all the areas are diminished to the same degree. In cases where these conditions do not apply, and one has to mix data obtained by different methods, it is necessary to apply the appropriate carrect,ion factor, multiplying by 1.03 in the first procedure, and by 1.11 in the second.
F ' q ~ r e3. A r r o computed from peak height ond .nlenerlion of srro'gnt-l'ne exlropoloton *:In b o x .me ir 80% of o d u o l peak area.
I t is appropriate to note here that one occasionally encounters in the literature s procedure intermediate between the two previous ones (el. Fig. 3), in which the projected base found by the first method is taken, but the altitude is taken to be the peak height, as in the second method. I n this mse, one obtains n result that is 80% of the area of a Gaussian curve. We believe that this procedure corresponds to stopping. in the middle of the road on the way to a definite improvement,, and that its use is not justified. In the rase of asymmetric peaks, that consequently ditrer from the Gauss curve, the triangulation methods described until now ran lend to considerable errors, especially when the various peaks of the 8sme chromatogram do not all have the same asymmetry. Hence, we are faced with the problem of modifying the triangulation method so that i t will be equally applicable to the asymmetric peaks, which are intermediate between (,he Gauss curve and the negative exponenbial curve, without having to deal with or determine asymmetry coefficients. It is evident that the only modification that does not complicate the method eonsists in taking the peak width a t somt. other location than the half-height.
(Continued on page AZ46)
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A mathematical a n a l y k of this problem, assisted by experimental tests, shows that this can be achieved by taking the
question: what is the possibility of a triangulation method which gives the area, without requiring any correction factor a t all, and how will it apply to curves of every degree of asymmetry?
Trapezoid Construction From the preceding discussion it is evident, that such an approach is not possible on the bask of a single width parameter, and it is necessary to resort to taking into consideration two widths (at dinerent heights) or, in other words, to convert the triangle into a trapezoid. As is shown in Figure 5, tbis is achieved
graphical procedure and template are utilized (Fig. 6)to determine the two locations a t which to measure the widths. Since in ordinary chromatograms the widths of chromatographic peaka increase in proportion to the retention time, it can prove to he rapid and adequate to tske onc it, p l : w of tlnc ml.er, i.e., t:tkin~I I W ~ r u d u r tof 1l.r pcnk hc1rl.r time8 the rrrmlton rime. Tlrir give? rhe area rnultinlied by 0.4 of the square root of the numder of plates (Fig. 7). This procedure is beset with numeroue sources of error (variable number of plates throughout the length of the chromatogram, peaks widened by saturation or by slow response of the re-
Figure 4. Area computed from peak height and Width ot one-quarter of p e a k height ir 133% of actual peak area.
width a t one-quarter of the peak height, as shown in Figure 4. This gives 133Y0 of t,he actual area of the peak. The idea of multiplying the peak height by some specific width opens new horizons in the triangulation procedure and immediately suggests the question: a t what locations should the width be taken in order that the ares, obtained hy the triangulation be exsctly equal to that of the peak? A simple mathematical ealculation shows that the fraction of the peak height a t which the width should be taken is 0.45 for 8. symmetrical Gaussian curve, m d 0.37 for an asymmetric curve with an exponential type boundary. These small computations lead us to pose a double
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Figure 5 . Tropezoid construction, in which area i s computed from peak height and widths at two selected plocer on the altitude.
by taking one width a t 0.15 and the other a t 0.85 of the peak height. The formula for the area is half of the sum of the widths multiplied by the peak height. This method is rapid, especially if a
corder, a8ymmetric peaks, etc.), but it can give good service, pnrticularly in cases where high precision is not required, as (Continued on page A2521
-
is no doubt t h a t the primary method Chemical h S f l ~ m e f I f a f i 0 ~ isthere the method, whirh involves the G~SOLU~,
use of appropnate "sensitivity fartors"
Figure 6. Principle of technique for rapid location of the 0.15 and 0.85 h positions on the altitude. The liner moy be ruled on a transparent sheet thot can be laid over the chramotographic record.
well as in those instances where the peaks are narrow enough t o create confidence in the liability of their widths.
(i.e., grams ur moles). I n gas chromatography, these factors are never absolute qusntities in the strict sense of the wwd.
Quantitative Methods
Tob!e 2.
ClarsiRcotion of Quontitofive Methsdoiogy
There exist in the literature some ten to fifteen different designations for the
Amount of Sample Injected:
Knmm which the remainder are derived, add this classification is shown in Table 2. From the theoretical point of view, to convert area8 into absolute quantities
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Calibration methods Sensitivity factors
Calibrittidn curves Ahsulute met,hods
Tinknown Internit1 standard Internal normalination
which ilnplies t h a t such quantities are deducible i n n basic theory; rather, they are the result of practical measurements, whose use is extended by means of theoretical considerations to apparatus and conditions quite distinct from those by means of which they have been determined. This criterion distinguishes the absolute met.hods from the calibration methods (whirh are relative methods). .48 is the case in many other types of analysis, the result can be obtained by a. rornparison with knowns under conditions that are as similar as possible; this i~ usuallv done bv the construction of caliprocedure permits better precision to be achieved than is characteristic of the absolute method. Both the absolute method based on sensitivit,y f:tetars, and the relative method hased on calihration curves, $ve for each component an ah.solute puantzty contained in the injected sample and, eoneequently. it is necessary to know the amount of material involved in this injection, st) that the results of the analysis can be expressrd in pweenlages. The small size of the injected sample often means that its sire cannot be known with sufficient precision to permit the aforementioned calculation. Hence, i t is necessary t o ~ e e ka solution for the vase which we can call "unknown puanlil:/ injected," although this really means t h a t the injected quantity is knuwn with less precision than t h a t which is needed for the calculation of the analgt(('ontinued on page .4?54)
Figure 7. Peak areor may be estimated from the peak height and retention time. Area is equoi to product of there parameters, divided by two-fifths of the square root of the number of theoretical plater.
icxl results, nr less than that with ahieh response (RMR), generally taking benzene the areas, sensit,ivity factors, and ralihraas having RMR = 100. tion data are determined. 1>here are instances when it is not pclssiWhen it is desired t,o make use of sensiIde t o hase the i d r u l a t i m o n the suppvsitivity factors, and if it may he asumed t i m that all the wvnpnnents are present. in the vhrrnnat,ogram, for this is not in fact that all of t,he components of the sxmplo are prosent in the chromatogram, the size so; such situations arise in the analysis of the sample ran he obthined hy summing of minor components under runditiuns up the components, and the individual surlt that the major p e s t s do not register quantities are referred t o bhis sum. This adequately, or in the use of dotortors that proredwe is termed inlernal nornzaliznlion, are not sensitive to certain rrrmponents, etr. In such cases, the only sulution is and prohably represents the most widely used method. In this rme, thc sensitivity tu etTect a comparison within the ehnnn:~fartors can be relative quantities (taking toprem itself, adding a referenre suhstanre one subst,anre as a reference), and hmre in n known m o u n t t,o t,he mixture to he i t is common to s p e d of t,he relntirir molar (~onlinrrerlon page A?.i6) -
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nnn1yi;ed hefore taking the sample to he injected. This method has heen given the name nf inlrmal standard, and correctly used it permits the lhest precision of any of the methods cited.
Sensitivity Factors From the preceding considerations it is evident thst the use of sensitivity factor8 is involved in the majority of rhmmatographic methods, and since they play s11c11 an important ride, some further considerations conrerning them are warranted. \Ve do not include here the absolute sensibivities utilized for the testing of the various types of detectors, or t,he sensitivity factors derived from them and used for absolute methods. \re will comment solely on the relative molw responses, such as are employed in the internal norn~aliant,ionand internal standard mot,liods, fr,r with the aid of these R3lIl's it is possible to obtain much more prerisr results than is commonly believed t,o be the case. In the second place, and in order not tn extend ourselves unnecessarily, wc will limit ourselves to the thermal condurtivity (hot wire or thermistor) and the flsmr ionization (ionization current,) detecturs, which me the most commonly used tyllcs. Adhering to these lirnitnt,ians, we ran nav thst there are thme degrees of rcl%tive sensitivity factors, each one being m o w perfect t h m the preceding one. .4. Sirnplr democracy (the simplest, dcgrer). ISven the most, cursory eran~in:~t,ion of the literature of g'as cl~ronmtwraphy shows the great (and disproportionate) esteem paid to that system which consists in considering all substnnces : ~ s having equal wsponse. At t,he start of gas cliromatogmphy, and for the use of t,he thermal conductivity deteet,ors, il. appeared that (except for those subst,.zneea of verv low moleculi~rweight) the inst:mt,aneous response of the detector and hence the area m d e r the recorded pwk should he proportional to t,he molar concent,rstion. This assumption is incorrect in its basic premise, for the response of this type of detector does not rorresponrl only to degree of suhstilution of the molerules of the carrier gas by the much heavier molecules of the substance to be detected, but there also exists (and is a t times the major factor) an additional effect tlxd consists in the diminution of the mean free path (and hence the thermal conductivity) of d l the moleeules of the carrier gas. I t is a t present recognized that tho assumption of equal molar response is not. correct, and this hss been replaced hy that of equal mass T e s p a s e , and thus wt. cnn say thst the degree of simple demncracy far tllerrnal detectors consists in assuming proportionality between areas and weights. I n the case of flitme ionization detectors an analogous situation exists which consists in assuming that the area is proportional to the amount of carbon present in the corresponding substance; this assumption is ndequztely exact if only hydrocarbons are treated. R. ?'heoreticadEzperimental EstGna(Continued on page A 2 S )
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Chemical Instrumentation lions (the broadest degree). The previous ~rrcthodof simple democracy yields prerisions that ; r e rather poorer than those with whirh meas can he determined in those r:rses in which mixtures o i s u l ~ st:maes belonging to different classes are treated. The errors are particularly large fur hnlogenntctl deriv.ztivrs with thermal conductivity detectors and far orggensted nr nitroeenated substmces with Hame
and to summarize it in some rule or simple irmnuln that will permit the prediction of the ItAlIt of new mhstanres. A nombn. o i v e T interesting works are currently nppenrinp in the litersture un this suhjeet, and there is only space here for citing one e x ~ m p l eof the simplest rules for each of the two mast romrnon detectors. For thermal eandurtivity dptoctora, thc follo~ingformula:
in which J l is the mdeaular weieht, and d is the density of the liquid a t :my ternprrature, yields values with an ermr of less than lo1/, in the great majority of c:lsea rrf very ditlerent types. Less univenul, but mare pre?ise is the use o i ;I linear fr,rmuln of t,he t,vpc: ItlllZ = o bn in which "n" is the nurnher of r w h m tltorna, and "a" and "h" arc specific constants for each h m i l of srthstanrea. For the i l i w of Hnrne innisntion detertors, the R l I R is made eqml t o the numher o i carbc,ns that remain in the molerule after the eliminittion of all the oxygen in thr form of moleroles (or fractions) of cnrbnn dioxide. For this 1)-pe of detector there me alsu inellu~dfiof nbtaining the RhIR hv means of nrlditive pro
