Refined Direct Transmission Photometry of Translucent Sheet Chromatograms Some Aspects of Partition Chromatography Affecting Interpretation of Measurements J. W. H. LUGG Department o f Biochemistry, University of Western Australia, Nedlands, Western Australia EDWARD McEVOY-BOWE Department of Biochemistry, University o f Malaya, Sepoy lines, Singapore
b Currently used direct methods are subject to large random errors especially with two-dimensional chromatograms. In the minimum transmission (or maximum density) methods, most suitable on theoretical grounds, a small densitometer aperture assists discrimination but enhances errors due t o sheet textural irregularities. The subject i s discussed on theoretical lines and studied experimentally with amino acid-ninhydrin bands on filter paper sheets. Solution of the key problem requires precise positional replacement of sheet material in the densitometer after bleaching band and background colorations. A suitable instrument is described. With it the mean of triplicate assays is as reliable as the mean of some twelve replicates obtained otherwise. Several equations are derived. Departure from linearity of the relationship between computed band absorbance and amount of substance these can be reduced by restoring reflected light with the a i d o f instrument accessories. Under specified conditions, neglecting reflected light, a semiempirical equation, Q = k"' [ ( l / T ) .- l ] , relates Q (quantity of a substance chromatographed) with T (computed transmittance), k " ' being constant.
THL
,-iiit M ork deals mainly n ith thcoretical ')lC tieatmmt of the assuniptionq and mcasuremcnts involved in using dircct photometry to detcrmne the concentration of substances on paiier chiomatograins 'The emphasis is placed on instrumentation, on the ph? sical significance of the galvanometer readings, and on the statistical significance of the results Xumerous publications have described piocedures for the estimation of substances separated out on sheet (primarily filter paper) partition chromatograms and employing instrumental J
3
photometry as the final step. These procedures fall into three main groups. Those of the first depend upon elution of the substances from the sheet with prior, or subsequent, conversion into colored compounds and densitometry of the liquid eluates (3, 6, 8). Those of the second employ strip-scanning photometry of the colored bands on the sheet itself (5, 16). Those of the third (1, 2, 12, 17) involve direct photometry of the bands on the sheet in the regions of minimum transmission. Procedures of the first group can often yield precise results but are time consuming and require relatively large amounts of substances for satisfactory work. They can be seriously inaccurate if bands overlap appreciably, or if the presumptive band positions must be ascertaiiicd from duplicate chromatograms. Procedurcs that rely upon strip-scanning, nith integration over the number of framcs required to cover the visible limits of a band, appear very satisfactory with one-dimensional chromatograms if the bands are of reasonably uniform density across the strip and do not overlap seriously. Thus, even applying spots instead of stripes, on very narrow strips of paper, Redfield and Barron (16) could claim a mean coefficient of variation for single results of 4.36y0 over a fairly wide range of levels of nine amino acids. They seem ill adapted to the far more highly resolving two-dimensional chromatograms, for it can be shown that, unless the visible bands have density distributions independent of their orientation (not to be expected on theoretical grounds), the values of integrals must vary with orientation relative to the scanning slit. Even with a fixed orientation of amino acid-ninhydrin bands, the authors found the mean of ten replicates untrustn-orthy. Procedures of the third group seem
capable of satisfactory adaptation to two-dimensional chromatograms. If the densitometer aperture is circular and if the photocell is of uniform response across its effective face, the reading in the region of minimum transmission will be independent of band orientation. Furthermore, with an aperture of sufficiently small diameter, even appreciable overlapping of band peripheries may have only a small effect if chromatographic displacement has not obtruded appreciably, or in ordinary (elution) partition separations if concentrations are low (13). The use of a small aperture, however, brings into more serious question the effects of textural irregularities in the sheet. Earlier work ( 1 , 2 ) with amino acidninhydrin bands has not been reassuring, the coefficients of variation of means of twelve replicates being as Exploratory work high as 10 to 15yOb. (9) indicated that inadequate control in earlier steps and vitiation of the photometry by sheet irregularities each contributed much to the variability. One phase (9) was thus directed toward improving the direct photometry of these bands. This involved finding means of correcting adequately for sheet textural irregularities, and for background coloration which was somewhat variable and of more serious consequence with small amounts of amino acids. Chromatograms were used in the work and it is therefore necessary to consider first the distribution of materials on the sheets. DISTRIBUTIONS OF BAND AND BACKGROUND SUBSTANCES O N SHEET CHROMATOGRAMS
If the initial spot of solution of the mixture of substances is so applied as to be of fixed area and shape on a sheet of a t least grossly uniform texture and physical thickness, if the grain of irregularities is small compared with the area of the VOL. 33, NO. 4, APRIL 1961
535
spot (the effects of noncompliance, however, are largely eliminated during a run) , and if the conditions of running are closely reproducible, then, apart from the textural irregularities, density distributions of the substances on the dried sheets should be reproducible in both one- and two-dimensional procedures. These conclusions follow from the theoretical and practical studies of Martin and Synge (14) and Consden, Gordon, and Martin (7) and might be expected of adsorption as well as of liquid-liquid partition chromatograms. With the ordinary (elution) partition sheet-chromatogram (even the so-called “single-phase” paper chromatogram is believed to be of this type, the single phase functioning as two when associated with the fibers) , however, the density of a substance in a specified region of any one band should be directly proportional to its quantity in the initial spot, if its coefficient of distribution between stationary and mobile phase and its diffusion constants in both are constant. This conclusion follows from three considerations : Martin and Synge’s (14) theoretical treatment of the column partition chromatogram for solutes having constant coefficients of distribution between the phases; the effects of diffusion, including the lateral spreading of bands on a wide sheet, can be derived from the equation for heat loss from a source by conduction ( 4 ) ; and the microscale angle channelling of mobile phase between fibers, while increasing the lateral spreading of bands, would be sensibly independent of the (low) concentrations of solutes. In a one-dimensional run each solute is distributed beyond its original position through the full length of traverse of the mobile phase, and in a two-dimensional run also along the full length of traverse of the second mobile phase. I n most work the amounts outside the immediate vicinities of the visible bands are minute and contribute little to the general background, essentially because of substances inherently present in the fibers or introduced during treatment [with amino acid-ninhydrin paper chromatograms ammonia may be largely responsible (3,S ) ] . Possible Nature and Effects of Textural Irregularities. It has been assumed that the area of the initial spot, b u t not t h a t of t h e densitometer aperture, is large enough t o represent t h e mean properties of a sheet of grossly uniform texture and physical thickness. Textural irregularities might be in granular physical thickness for uniform packing of fiber, or granular denseness of packing for minutely uniform physical thickness, or both together. The cross-sectional areas of mobile phase, stationary phase, and fiber would
536
ANALYTICAL CHEMISTRY
be in fixed ratios in purely physical thickness irregularities, and the density of substance in and upon the fibers of the dried sheet would not be affected: the amount of substance would be proportional to the amount of fiber in an irregularity. For irregularities purely in fiber packing, the cross-sectional areas of stationary phase and fiber would be in the same virtually constant ratio as before but that of the mobile phase in relation to the other two would be increased with loose and decreased with dense packing. Relative to the mean density of substance in and upon the dried fibers in the region, the density n-ould be low with dense and high with loose packing, the effect increasing with the RF value; and the amount of substance in an irregularity would not be proportional to the amount of fiber there. Regarded as grossly uniform over the sheet, the background in a textural irregularity may, from earlier comments, be proportional simply to the amount of fiber. Formally Derived Relationships. Several equations are developrti t o correct for background and for textural irregularities, and to relate the corrected band transmittance to t h e amount of substance in the original spot. The basis for the theoretical development is valid for all sheet chromatograms provided the physical conditions mentioned earlier are observed. Two-dimensional chromatograms have been used bccause of their high resolving power. The preliminary assumptions are that the sheet material, functioning both as a medium itself and as a vehicle for bands and background, possesscs constant optical properties except for the nonuniformity within textural irregularities, that the absorption of monochromatic light is, in effect, in accordance with the laws of Lambert and Beer, and that absorbances are strictly additive. Transmissions of “entering” lightviz., that fraction of the incident light which actually enters the sheet and is not irretrievably lost by reflection back from it-are r for the band plus background on the sheet, b for the sheet alone in that place, r’ for background on another part of the sheet, and b’ for the sheet alone there. The transmittances of band plus background and of background alone (both relative to the sheet where measured) are r/b and r’lb’, respectively, and the corresponding absorbances are log(b/r) and log(b’/r’). The absorbances of sheet alone in the two positions, log(l/b) and log(l/b‘), are assumed to be proportional to the amount of fiber there. The absorbance of band material alone is D = log(b/r) log(b’/r’) (log l/b)/(log l/b’), if back-
ground absorbance in an irregularity is proportional to amount of fiber; but, as b and b‘ are of similar magnitude, this reduces to D = log (b7’/b’r) as a close approkimation if the background is not too obtrusive, rb’lr’b being the corrected band transmittance. It is also the valid equation if b and b’ happen to be equal andlor i f the background absorbance, however great. is independent of irregularities. Its validity is presumed in what follon-s. Only trro of the various possibilities are considered: First, the amount of band material present in an irregularity is proportional to the amount of fiber there as well as to the quantity, Q, of substance in the initial spot, whence
Q
=
k’D(l0g 1 %+)/(log I/%)
(I)
Second, the amount of band material is proportional to Q but not to the amount of fibpr, and happens to be (for whatever reason) , sensibly constant n ithin irregularities. whence Q
=
LtfD
(2)
and b + may be regarded as the geometric mean of numerous hypothetical b values for places randomly distributed over the sheet. The multiplier of 12’ reduces to that of k” if b happens to equal b+. Mean k‘ = mean 12” for large samples, though the variabilities of k’ and k” (determined by those of their respective multipliers) may differ. For sheets all of constant gross texture and each of grossly uniform physical thickness, the conditions imposed imply that for constant Q the concentration of a substance in the two phases in the vicinity of the initial spot would be inversely proportional to the grossly uniform thickness of any sheet, the amount transferred to a specified region of its band being independent of this thickness. The important principle follows that for reasonably small variations in thickness betvieen individual sheets of a batch, k’ and k” n-ould not change because their multipliers should remain constant for constant Q. TRANSMISSION PHOTOMETRY OF MATERIALS DISTRIBUTED ON (FIBROUS) TRANSLUCENT SHEETS
The quantities r, b, r‘, and b’ cannot be measured n-ith as negligible systematic errors as occur in the photometry of solutions. It is normal to use a standardized, stable light source, but whereas in work with solutions the loss of light by reflection back from components of the examined system (solvent vehicle and solute) is small and sensibly constant, the sheet which acts as a vehicle for the color substances is itself a strongly absorbing medium and, furthermore, reflects so much light back
C
B--
e LI,1
1
2
3
4
2 c.
1
I
Scale in i n c h e s .
xr Z’ Figure 1 . Sectional front elevation of densitometer on Y-Y
Key to Symbols in Figures 1 , 2, and 3 6-volt, 15-watt lamp bulb Platform Bulb-socket insulator Terminal nut 653. Adjustable screw far centering lamp filament C. Light-proof cover and warm-air vent CSF, CSH. Cavities (with free glass bottoms) in sliding carrier for standardizing filter and sheet holder, respectively G1, G2. Guides for transversely sliding sections, G 2 acting also as clearance support for carrier OP. Opaque plate which fits flush with negative collecting ring of photocell OPA. Aperture in opaque plate P. Base plate to which mechanical stage is clamped Ph. Selenium barrier-layer photocell S. Shim(s) for adjustment of stage and carrier movement SC. Sliding carrier SCE. Sliding carrier extension to which mechanical stage movement is screwed SSC. Stepped circular cavity in slide for reception of diffuser and/or color filter TS. Transversely sliding sect ions which bridge carrier and exclude external light V. Ventilation air inlets in lamp house W W a l l of tunnel in which carrier moves
6. 6P. 6S1. 652.
from the system that the intensity of entering light (as already defined) does not approximate that of incident light. The facts that band material may be distributed in and upon fibers, that an appreciable fraction (decreasing with the amount of band material) of the incident light may be lost in reflection back, and that the “transmitted” light may be, in part, light emerging after repeated reflections between fiber surfaces, renders extension of the formal treatment speculative even for monochromatic incident light, Optical Properties of Sheets, Consequences for Densitometry. Measurementq were made of the fraction, eriiergent incident light intensity, with sheets of K h a t n i a n S o . 1 filter paper employed throughout, using greenfiltered and unfiltered light (diffused and dircct) from an incandescent filament source a t T arious high temperatures but below maximum rating (to preserve the lamp rharacteristics) within a blackwalled lamphouse, and a selenium barrier-layer photocell. Results were very similar: 0.322, 0.162, 0.110, 0.076, 0.055, and 0.039 for 1, 2, 3, 4, 5, and 6 sheets, respectively. Obviously, there is
f
Yf-
Y
Figure 2.
Sectional plan of densitometer on X - X
Figure 3. Sectional side elevation of densitometer on Z-Z
considerable loss of incident light by reflection back into the lamphouse, chiefly, but not solely, from the more superficial fibers of the first sheet; by reflected light a pencil line on the second sheet is faintly visible through the first. Only after the third sheet has been entered does the absorption of light with thickness closely follow a law of the Lambert form. This finding permits the ratio of entering to incident light to be calculated for a single sheet interposed between source and photocell (for the third and subsequent sheets it is close to unity), and vindicates the earlier assumption that the “absorbance” of sheet material in the path is proportional to the amount of fiber. K i t h a galvanometer giving deflections proportional to the intensity of light reaching the photocell we have, where E is the deflection for entering light (as already defined), R is that for sheet with band and background, B that for sheet alone there, R’ that for another part of the sheet with background only, B’ that for the sheet alone there, and B+ the geometric mean of numerous B values for the sheet, r = R / E , b = B / E , r’ = R’/E, b’ = B’/E, and b+ =
B+/E. For constant E, Equations 1 and 2 thus yield, respectively, Q = h’log(BR’/B’R) (log E / B + ) / ( l o gB I B ) (3)
Q
=
k“ log (BR’IB’R)
(4)
Virtual constancy of E, even with greatly varying densities of band and background, might be contrived by restoring t o the test sheet light reflected back from it, by employing a suitable reflector, one or more backing sheets between test sheet and source, or both means together. The densitometer (to be described) is furnished Kith the necessary accessories. EXPERIMENTAL WORK
Densitometer. The design of the instrument and accessories is as given in Figures 1 to 7 and the accompanying legends. Detailed specifications and descriptions of use are available elservhere (11). Informative outlines, only, are provided here, together with performance data not previously published. The sliding carrier of the instrument may be racked horizontally in two dimensions over the 3-mm. diameter VOL. 33, NO. 4, APRIL 1 9 6 1
537
Figure 4.
Sheet holder
A, B, C. Front elevstion, plon, and side elevation. respectively, o f sheet holder in inverted position D. Plan o f wedge E. Insertable gloss square far retention of backing sheetM in well 1. lnioid giass bottom 2. Well of holder 3. Channel in woII of well for iniertion of hooked retracting probe 4. Perrpex frame 5. Slot for wedge
I" I . 1 _ " . . 1 . 1 _ .
I
/ I
A 3
C
sei are, piat.
. C.
1. 2.
Fmnt elevation of stamper Spring clip Raised back of dotform
reflector assembly A, C.
D. 1. 2. 3. 4. 5,
538
a.
Elevation and plan, rerpectiveiy, of sdlimator-reflector assembly Perspex light Conductor Spacing ring Support with m e w hder, for attachment beneath lamp house C0llimotor Reflector Coliimotor extension with well for reception of diffuser and/or color filter 6. Channels in wall of well and edge of well depression for insertion o f hooked retracting probe
ANALYTICAL CHEMiSTRY
"\Iy.~~ ..lyy" y
1"1~"
graduated (vernier) scales. One cavity in the carrier carries a filter of ahsorbance comparable with that of unused sheet [and backing sheet($, if used] in the test cavity, for recurrent checking and adjusting of the filament source intensity via coarse and fine resistances in series with the lamp. The galvanometer (with its resistr ances) is selected to give deflections sensibly proportional t o current, and the photocell (as supplied hy Evans Electroselenium Ltd.) is simnltaneously shunted to furnish a current proportional to intensity of impinging light, which is filtered if a filter is to he used though these cells have a fairly flat spectral response over 425 t o 625 mp. The sheet examined is a 1 X 1 inch inch from square creased along a line a n edge, located, oriented, and fixed by a wedge on the sheet-holder in a perfectly restorable way. It lies between the bottom of the inverted holder and the glass bottom of the carrier cavity. With bands, the position of minimum transmission is found hy trial and error racking of the stage, and the two scale readings are recorded together with the value of R. B is determined for that setting after bleaching. R' is measured for any arbitrary setting of a background square, and B' for that setting after bleaching. Backing sheets, when used, may be inserted with a test sheet or (less effective, hut better protected) in the well of the holder wherein they are clamped at the edges by a n inserted small glass square. They shonld he selected for uniformity of optical properties (tested in the instrument) and are best prepared hy cementing several thin sheets to&her at the edges. The collimator - reflector assembly comprises a support, a short collimator, a reflector that may he used therewith (it replaces a spacing ring), and a collimator extension. With galvanometers of low sensitivity, a Perspes light conductor may he inserted in the full length of the collimator and a diffuser in the well of the extension.
"""U'YJ
a"
Y l l r
n',rrY
I'%iylln
'UUlr
Lii'Llll
fourfold hut slightly spreads the beam at the periphery. Instrument Performance Data. Tests using near-white incident light with t h e full collimator-reflector assembly (with and without the light conductor) and with and without a hacking sheet similar i n optical properties to a blank test sheet (Whatman No. 1 filter paper) have been interpreted as follows: For "entering" light the fraction transmitted is ea. 0.70 per sheet. The reflector restores 35% of the reflected light in a first restoration, representing some 42% cumulative restoration and 22% increase in transmitted light, if the test sheet alone is interposed, and some 47% cumulative restoration and 32'% increase in transmitted light when a backing sheet is in contact with the test sheet. The percentage cumulative restoration is that percentage of the initiallv reflected liaht contained in the sum 07 terms of a;l infinite geometric series, both the first term and common ratio of which are 0.35 times the percentage of incident light initially reflected hack. With the reflector in use, the absorption of light by the test sheet will conform closely with a law of the Lambert form if a.n equivalent thickness of hacking sheet is in contact with it, or if about 1 1 / 2 equivalent thicknesses are used in the well of the holder. Choice of Optical System. For work t o be based upon Equation 5 (discussed later), which mas established only for near-white light and Whatman No. 1 filter paper, neither diffusers in the slide, hacking sheets, nor collimator - reflector assembly mould he used. For work to be based upon Equation 3 or 4, backing sheets should he used, preferably with the refleetor. The authors believe that the collimator extension should be employed with the reflector, but any filter required must then he inserted with diffuser in the extension well because the extension projects through the slide. The theoretical approach to measnrement of band absorbances has, almost
necessarily. presumed the use of monochromatic light. The optical properties of clean sheet (Khatman No. 1 filter paper) have been determined for greenfiltered and near-white light and were found similar for both. The behayior of the instrumental accessories has been tested only with near-Jvhite light, but the findings should be essentially valid for any part of tlie visible spectrum. Depending upon owr-all treatment, some amino acid-ninhydrin bands differ sufficiently in absorpiion spectra to furnish a yisual aid to identification. Such treatment was cmployed in this study. But. the pcri-atiing tint is subject to slight \-ariation, even with close cont,rol of color dcwlopment, with time of storage and possibly ot'her factors. I:innlly, t,he provision of high intensities of monochromatic. light is costly and troublcsoine. For tlicse reasons t,lic systematic densitoiiictry ol the bands Iyas commenced with n c a r - ~ h i t e ratlicr than greenfiltered light, and with the simplest of thc optical sj-stems as the instrunicntal accessories had not then been de~.elopcd. The practice was continued whm it n-as discovered that although results did not agree well with Equation 4 over a wide range of Q: a semiempirical rclstionship (Equation 5j! admirable for assay purposes, esist,eil between Q and a simple fuiictiori of tlie correct'ed band transniittance. RB'lR'B, ovcr a range of Q from 2 to 20 mpnioles. Thc accumulated data serve to demonstrate thci great superiority of the bleaching and precise replacement procedures ovcr those formerly available and to illustrate the use of Equation 5 . Chromatograms. It, is not the purpose here to discuss details of t h e chromatographic anti color-development procedures; it is sufficient t o say t h a t t h e runs 11-ere made at 29.5 3: 0.5' C., the escursions of mobile phases being approximately 16.5 em. in either dimension past the initial positions of substance.?, that the initial spot \vas a disk of 5.0-mni. diameter, that the same five substances mere resolved on each chromatogram, and finally that quantities of color substances produced could reasonably be assumed proportional to those of the substances chromatographed. Seven experiments, each in triplicate, were made a t the 2and 20-mpmole levels of application and others a t intcrniediate levels, but only the extremes are considered here. hIeasuremeiits were made under condit'ions of fairly uniform but rather high humidity and temperature. Some stabilization of otherwise fluctuating conditions is indicated, especially Tvith hygroscopic. color substances.
v)
.-2 L
0
P
I
.
U
RESULTS
l h e five substances resolved on the Chromatograms mere glycine, taurine, P-aniinoisobutyric acid, alanine, and glutamine. D-.Sminoisobutyric acid, occupying an intermediate position as regards variability of results (Table 11), has been selected for detailed consideration of this aspect (Table I). VOL. 33, NO. 4, APRIL 1961
Table II.
Statistics of Values of a for Five Substances, with Analyses of Variance of a for Each Substance and Derived Data (21 triale, 7 triplicates)
Substance Glycine Taurine @-Aminoiso-
butyric acid Alanine
Q,
Glutamine
Analysis of Variance
hlpmoles
Mean a
2.00 20.0 2.00 20.0 2.00 20.0 2.00
0.1147 1.0868 0.1187 1.2477 0.1171 1.1556 0.2128 1.8861 0.1476 1.3297
20.0
2.00 20.0
Table I is largely self-explanatory. Table I1 has been drawn up for all five substances, and involved the use of Equation 5 but is otherwise largely selfexplanatory. DISCUSSION
Table I. From the positions of the over-all means within t h e ranges, t h e distributions of B, B’, and R’ eshibit negative skewness, corresponding with positive skenness of the reciprocals and expected at least of B and B’ if the paper thicknesses [proportional to log(E/B) and log(E/B’)] are normally distributed, because for these measurements reasonable constancy of E must prevail as well as “in effect” conformity of the absorption of E with Lambert’s law. For constant E, band transmittance corrected for background and textural irregularities is T = RB’/R’B, the absorbance being D . The transmittance of band plus background corrected for irregularities is T’ = RIB, the absorbance being D’. The transmittance of band plus background, relative to unused sheet [as measured, for example, by Block ( I ) ]is uncorrected for irregularities. Designated as T”,it is almost perfectly represented by RIB’, the absorbance being D”. Quantities in Table I have been computed as if E were constant. Tests for skewness shon- the distributions of T and T” values to be positively skewed, especially a t the 2-mpmole level. To serve the needs of statistical analysis by normalizing, but also to facilitate discussion of the physical significance of differences between means, simple logarithmic transformations of these variates were made; and values of T’ and of R’/B’ (background transmittance relative to sheet) were 540
e
ANALYTICAL CHEMISTRY
Coefficient of Variation, yo Within expt., Total,
Range of a 0.082-0.150 0.853-1.214 0.094-0.140 0.929-1.483 0.072-0.143 1.004-1.253 0.171-0.268 1.649-2.140 0.118-0.198 1.217-1.584
S,2
0.0345 0.019 0.0348 0.052 0.0323 0.0250 0.0380 0.052 0.0360 0.0274
s:
0,0333 0.0238 0.0310 0.0248 0.0324 0.0233 0.0346 0.0290 0.0319 0.0255
similarly transformed though their distributions were not first tested. The resulting symbols have been prefixed by a negative sign, and in effect the four transmittances have thus been transformed into absorbances. A feature of the distributions of -log(R’/B’) values at both values of Q is the large between-experiment and relatively small within-experiment contribution to total variances. Compared with the D’ variances these are small, even at the 2-mpmole level, so correction for background (which yields D ) cannot be expected to diminish much the variances of D compared with those of D’. Three of the four comparisons available in Table I actually show increases, but all are of very low statistical significance. X factor operating in this direction, however, is that random errors in standardizing the light and zeroing the galvanometer are involved only twice in determining D’ (or D ‘I ) but four times in determining D . iit both levels, the mean D’ mean log(R’/B’) values correspond very closely with those of mean D, as expected with large samples. The small negative value of sf - s i for D values at the 2-mpmole level is properly attributed to chance in sampling. The over-all view is that: for D and D’ a t both levels the within-experiment contributions to total variance have been of major consequence; as between D and D’ the departures of variance ratios from unity are of low statistical significance; and the variances are much greater a t the 20 than a t the 2-mpmole level. At both levels, especially the 2mpmole, s i and sf values for D” are much larger than for D or D’. Judging from the F and P values, the differences are real and demonstrate, in respect to smallness of variability, the
+
:S
0.0336 0.0278 0.0222 0,019 0,0324 0.0238 0.0356 0.022 0.0331 0.0261
cvu
16 5.7 8.4 5.6 13 5.0
10 5.0 9.2 5.6
cz‘ 1
17 8.1 12 11
13 5.3 11
7.8 12 5.9
Std. Dev.
of Means of 3,
n-ithin
Expt.
9.2 3.3 4.9 3.2 7.5 2.9 5.5 2.9 5.3 3.2
decided superiority of both D and D’ over D” as measures of absorbance, and thus of T and T’over T” as measures of transmittance. D” - log(B’/R’) = log(R’/R) is D” corrected for background, and is the form of corrected absorbance often employed in stripscanning densitometry. Its s: and sf values, like those of D” itself, are high compared with those of D, as may be deduced from Table I. The variability of k“ a t constant Q is determined entirely by that of D (Equation 4). Whether the variability of k’ with these sheets is greater or less than that of k” has not been determined for lack of B” values (Equation 3)) but the geometric mean of B values for all bleached bands on a sheet might serve as a n approi5mation to B f . Differences between the mean D’ and D t t values (6% a t the 2 and 2% a t the 20-mpmole level) are attributed to the effects of substance residues upon the B values, the background (plus excess reagent) residue effects being regarded common to B and B’. If reasonable allowance is made for the substance residue effects by adding to mean D’ the corresponding log (mean B’lniean B ) values, the adjusted values differ from the mean D” values by only 0.4 and O.OS%, respectively. In preliminary trials, with chlorine gas to bleach band and background colors without detectably affecting unused sheet, it was concluded that residue effects must be small, if real. Accumulated data reveal the reality and smallness of these effects upon D’ (and thus D ) values. The foregoing analysis is completely valid only for monochromatic light and if all assumptions (including constancy of E ) are correct. Successful reflection photometry of sheet chromatograms attests to variation of E with Q if reflected light is not restored. Compared
with B and B’ values, those of R’ have therefore been slightly overestimated and those of R more so, especially a t the 20-mpmole level. For these reasons, and apart from the facts t h a t near-white instead of monochromatic light was used and t h a t the solute might not have behaved ideally, close accordance of the data with Equation 4 could not be expected. The variability comparisons, however, are not vitiated. Table 11, Simple Semiempirical Relationship. The failure of the d a t a for p-aminoisobutyric acid t o accord well with Equation 4 (k” = 42.1 a n d 60.0 a t the 2- and 20-mpmole levels. rwpectively, and slightly more dirergent if corrected for substance residue effects) mas repeated by the data for the other four substances chromatographed. It is of interest that the restoration of reflected light would have tended to correct the departure of k’’ from constancy. Examination of the data for all five substances a t levels of 2, 4, 10, and 20 nipmoles showed close linear regressions betn-een & and 1/T values. Similar findings have been made with chromatograms of sugar mixtures ( I O ) . Equation 5 is derived from these facts, the function, a, satisfying the conditions that it tends to zero with Q and increases continuously with &.
+
+
+
where a = A A2 d 3 etc. = A/(1 - A ) = 9 / T = ( I / T ) - 1 = (BR’/RB’) - 1,,4 being the absorptance of the band-vis., 1 - T. Mean values of a (and the ranges) a t the 2- and 20-mpmole levels for each substance are shonn in Table 11, together with an analysis of their variances, coefficimts of variation (cv, and cct) for within-e\periment and total variabilities, and standard deviations (errors) of means of within-experiment triplicates. Clearly, values of k’” ( = & / a ) for any one substance are very similar at both levels. There is no evidence of consistency in skewness in the distributions of a (and hence k’”) values. The coefficients of variation are usually much larger at the 2- than a t the 20-mpmole level. The extent to which the coefficients would have been increased by using instead of 1/T to compute a, the variate R’/R which, like 1/T corrects for background but, unlike it, not for irregularities. might be assessed adequately from the p-aminoisobutyric acid data. -4t the 2- and 20-mpmole levels, respectively, and adjusted for substance residue effects, mean (R’IR) - 1 = 0.1177, 1.1573; s i = 0.00124, 0.0098; s: = 0.00117 (use 0.00124), 0.0106; cum = 28%, 8.470; cut = 2870, 8.8%. As expected, the means agree closely with
those of a, but the variances are much greater and the differences are of high statistical significance [F (14 d.f.) = 5.2, 3.0; P‘, 0.002, 0.024; F (20 d.f.) = 5.2, 2.8; P’, 0.001, 0.0131. The high eou. and cut values are unaffected by the residue adjustment, and at the 2-mpmole level those of a are only 46YGas large and a t the 20-m,uniole level only 60y0 as large; these very substantial reductions in variability result from a single refinement (correction for sheet textural irregularities) in the photometry. K i t h this refinement, the mean of triplicate assays is as reliable as the mean of about twelve replicates lacking it, as in the method of Block (1) and siniilar methods nhich do not zero the instrument on bleached band in the same position. The authors realize that time is consumed in the bleaching process, but this is short and the position for a measurement after bleaching is fixed by predetermined stage-scale settings instead of time-consuming trial and error. Y = number of bands. For 12 Let i replicates, 12 S 1 measurements are required by other methods. For three 1) = 6 S 6 replicates, 3 X 2 ( N measurements are required n-ith this method for comparable precision. The advantage is already realized n-ith this method when S = 1, and increasingly so for larger A-.
( 7 ) Consden. R.. Gordon. A. H.. Martin.
work. (11) McEvoy-Bowe, E., Lugg, J.
IT. H., Australian Patent .Ippl. 44466 iIS%), 51256 (1959). (12) McFarren, E. F., Mills, J. A , -4s.~~. CHEM.24, 650 (195%). (13) Martin, A . J. P., ”Partition Chromatography,” Symp. Bzochem. Soc., So. 3, p. 4, (,l949). (14) Martin, 8.J. P., Synge, R. L. l f . , Biochem. J . 35, 1358 (1941).
(15) Pearson, E. S., Hartley, H. O., “Biometrika Tables for Statisticians.” Vol. 1, Cambridge Univ. Press, Cambridge, Eng., 1954. (16) Redfield, R. R., Barron, E. S. G., Arch. Biochem. Biophys. 35, 443 (1952). 1171 Salander. R . C.. Piano. ?*I..Patton. A.R., A N ~ LC. H E 25, ~ 1532 (1953). RECEIVEDfor review August 17, 1959. Resubmitted November 14, 1960. Accepted Kovember 14, 1960.
+
+
+
Correction Alternating Current Voltammetry with Controlled Alternating Potential
ACKNOWLEDGMENT
The authors are indebted to Lim Yen Hing, University of Nalaya, and Alan Mitchell, Lniversity of Western Australia, for technical help, especially in constructing the instrument; to S. E. Williams, J. E. Alderson, R. S. Crisp, and G. A. Rooke, University of Ifrestern Australia, for certain optical measurements; and to K. S. Stenhouse and staff, Commonwealth Scientific and Industrial Research Organisation Regional Laboratories, Kestern Australia, for statistical calculations. This n ork embodies part of a thesis submitted by E. NcEvoy-Boa-e for the Ph.D. degree in the University of Rfalaya.
LITERATURE CITED
(1) Block, R. J., AXAL. CHEM.22, 132T (1950). (2) Block, R. J., Durruni, E. L., Zweig, G., “A Manual of Paper Chromatography and Paper Electrophoresis,” 4cademic Press, S e w York, 1958. (3) Boissonnas, R . A., Helz;. Chim. Acta. 33, 1975 (1950). (4)Brimlev. R. C.. Suture 163. 215 ” , (1949). (5) Bull, H. B., Hahn, J. W., Baptist, V. H., J. Am. Chem. SOC.71, 550 (1949). (6) Clarkson, T. W.,Ilench, J. E., Biochem. J . 62,361 (1956).
I n this article by D. E. Kalker, R . S. Adams, and J. R . Alden [ ~ K A L .CHEN. 33, 308 (1961)], on page 309, column 3, the following Acknonledgment should be added: Kork supported by Grant 3476 5038 of the General Research Funds of the University of Kansas and partially by the L-,P. Atomic Energy Commission through Contract AT(111)686, and this support is gratefully acknodedged.
Correction Recorder-Integrator Errors in Gas Chromatography Area Measurements I n this article by Charles H. Orr [ANAL.CHEM.33, 15s (1961)] Equation
15 should be changed from P,
=
( X 100) = 100
to P, = ( R
x 100) -
100
VOL. 33, NO. 4, APRIL 1961
541
