Anal. Chem. 1987, 59, 2816-2818
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in situ from AgN03 solutions by laser illumination. We have been able to increase the Ag concentration in the photocolloid SERS by a factor of 4.2 over the Ag concentration in conventional colloids. The photocolloid SER spectra have better signal-to-noise ratios than their conventional Ag colloid counterparts. Although the quality of the photocolloid SER spectra is comparable to that obtained for conventional Ag colloids, the photocolloids cannot always be used to probe low analyte concentrations. While laser-generated Ag colloids are unlikely to replace conventional Ag colloids for d applications, we believe this simple method for obtaining enhanced Raman spectra can aid in the development of SERS as a more general analytical technique.
(5) b o . x.; Wan, c.; He, T.; Li, J.; Xin, H.; Liu, F. Chem. ~ h p Lett. .
1884. 112. 465-468. (6) Laist.' J. W.Comprehensive Inorganic Chemistry; D. Van Nostrand Co.: New York. 1954; Vol. 2, pp 165-168. (7) Garrell, R. L. Ph.D.Thesis, University of Michigan, 1984. (8) Creighton, J. A.; Bbtchford, C. G.; Albrecht, M. G. J . Chem. Soc., Faraday Trans. 2 1878, 75, 790-798. Bumm, L. A.; Callaghan, R.; Biatchford, C. G.: Kerker, M. (9) Siiman, 0.; J . Phys. Chem. 1983, 87, 1014-1023. IO) Garreli, R. L.; Ahern, A. M., unpublished work, University of Pittsburgh. 1987. 11) Kerker, M.;Wang. D.-S.; Chaw, H.; Siiman, 0.;Bumm, L. A. In Surface Enhanced Raman Scattering; Chang. R. K., Furtak, T. E., Eds.; Plenum: New York, 1982; pp 109-128. 12) Tadayyoni, M. A. PhD. Thesis, Purdue University, 1984. 13) M w . Mahnnav .-, Cnnnav ---..-,, R. .. P.,. Hnward . .-..-.-, .... _.., ....-..-..-,, M .... R...,. Marnalrnh ...-...--a,, T. . p .. Chem. Phys. Lett. 1881, 79, 459-464. (14) Mernaugh, T. P.; Cooney, R. P.; Turner, K. E. Chem. Phys. Lett.
.
4a-a
,we..,
ACKNOWLEDGMENT We thank Sanford A. Asher for helpful discussions. Registry No. AgN03, 7761-88-8; Ag, 7440-22-4; pyridine, 110-86-1;sodium citrate, 68-04-2; (+)-biotin, 58-85-5; acetone1,3-dicarboxylicacid, 542-05-2; pyridine N-oxide, 694-59-7. LITERATURE CITED (1) Seki, H. J . E k h o n Spectrosc. Re&. phenom. 1888, 39, 289-310. (2) Moakovits, M. Rev. Mod. phvs. 1885, 57, 783-626. (3) WS, C. E. K. The Theory of the phofcgraphic Process; Macmillan: New Yark. 1942; Chapter IV. (4) Walls. J. H.;Amdge, A. A. Basic Photo Sclence; Focal Press: London, 1977; pp 93-118.
,+A I I",
C I P C.44 .Iuv-*1 I .
Angela M. Ahern Robin L. Garrell* Department of Chemistry University of Pittsburgh Pittsburgh, Pennsylvania 15260 RECEIVED for review April 13, 1987. Accepted July 30, 1987. We gratefully acknowledge support for this work from a National Science Foundation Presidential Young Investigator Award (R.L.G.) (DMR-8451962),from the Eastman Kodak Co., and from the PPG Foundation.
txcnange OT Gomments on a New I ecnnique in memicai Assay Calculations Sir: A long step toward an unified practice for general use in quantitative chemical analysis has recently been taken with the publication of Cardone's companion articles in this journal (1,2). The scope of the subject explains why anyone interested in analytical method development and validation is prompted to refine upon another's contribution whenever the subject emerges. However, some additional comments on this matter seem to be justified in the present case. The corrigible error correction (CEC) technique advanced by Cardone (2,3) is designed to ferret out one after another the constant component of bias and the proportional component of bias in the end user's evaluation studies. This aim has been satisfactorily reached for the constant-error correction. The paragraph on page 1285 (3), starting "A directly determined blank ... * and ending " ... Youden (S)," settles conclusively the issue. Unfortunately, the situation is not so satisfactory on the proportional-error-correction side. Here we find a couple of misconceptions which, we believe, seriously impair the CEC technique at ita present stage of development. On the other hand, it is apparent that the best way to cope with the proportional-error correction is the method of standard additions (MOSA) technique in the user's hands as in situ normalization of the proportional error (2). But, again, some misunderstandings about the MOSA functionality are evident in ref 2; we shall try to clear them away.
DISCUSSION CEC Shortcomings in the Proportional-Error Correction. The proportional-error component of bias is usually thought of as due, at least in part, to a matrix effect. If such an effect exists, then the fact that the matrix varies in the
Youden one-sample plot (left side in Figure 5B of ref 2) whereas it is constant in the MOSA plot (right side in Figure 5B), must not be overlooked. We believe that this objection invalidates Figure 5B of ref 2. Another weak point in the CEC technique is the use of a proportional-error-correction factor P, defined as the ratio of the MOSA slope, mM,to the standard-response-curve slope, m,. The way P is handled in ref 2 requires the fulfillment of the following assumptions (1)the only source of proportional error is the matrix effect and (2) the matrix effect when present is always harmful. Should assumption 1fail because some other sources (instrumental, etc.) of proportional error exist, and assuming that there is no interaction between them and the matrix source, then all the effects but that from the matrix cancel out in P and remain uncorrected in the analytical result. On the other hand, if we consider interaction, the problem becomes too much involved. This unpleasant situation arises because P is obtained from two different series of measurements. The reason why the total Youden blank (TYB) is the proper solution in the constant-error correction follows from the fact that it is obtained from just one series of measurements on just the laboratory sample ( 4 ) . For second assumption, that of a harmful effect of the matrix on the analytical results, it can be said that, although unexpected, a favorable effect cannot be ruled out. We have recently come across this possibility (5) while applying a stoichiometric technique (a gravimetry); the slope of the MOSA plot was closer to the expected stoichiometric value than the standard-response-curve slope. In this seemingly unusual situation the use of the correction factor P, as it is done in ref 2, would spoil the analytical result instead of improving it.
0003-2700/87/0359-2616$01.50/00 1987 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 59, NO. 23, DECEMBER 1, 1987
By giving up the correction factor P, we lose the possibility of a diagnosis of the proportional-error component of bias (3). We are left only with the MOSA technique as a way of obtaining in situ corrected analytical results. It is interesting to note that the reverse situation holds in the constant-error correction. Here we have a freestanding technique, the Youden one-sample plot, which is a diagnostic tool for the true blank, i.e., the TYB (3),expressed in analytical response units, but we do not have any freestandingtechnique yielding in situ either blank-corrected results or blank-corrected responses. MOSA and Blank Diagnosis. In ref 2 we are told that “the MOSA technique ... can be and is used as a freestanding technique ... although ... its functionality is not freestanding”. As a matter of fact, the MOSA technique cannot be a freestanding one, because it only works when it is fed with blank-corrected analytical responses. No MOSA results are possible without knowing the blank-correction, preferably the TYB. Accordingly, in Figure 3 of ref 2 the symbol a should be substituted for the A’s. Test Portion, Spiked Sample, and Treated Sample. After having pointed out the wrong labeling of ordinates in Figure 3 of ref 2, we shall deal with another misconception affecting the label of abscissas in Figure 3B of ref 2. This is a more elusive question and its proper discussion requires making a point of several specific analytical terms. The test portion (TP) is defined (4) as the actual material weighed or measured for the analysis, the spiked sample is the solution containing the TP and a given amount of added standard, ready to be submitted to the analytical method, and the treated sample (TS) is ( 4 ) the solution used for the measurement of a property related to the original analyte, the analytical response being the result of such a measurement. The MOSA procedure chosen by Cardone in his survey ( I ) is case 1among the nine discussed by Bader (6). The T P is dissolved, quantitatively transferred to a volumetric flask, spiked, treated with the reagents, if any, and diluted to the mark; the solution in the flask or the pipet content, if an aliquot is taken, is the TS. Once the analytical response is obtained from measurement in the TS, the constant-error component is eliminated by applying the blank correction, i.e., substracting the TYB. The blank-corrected analytical response is the label of ordinates when drawing the MOSA plot, from which the analyst is expecting to obtain the final analytical result by dividing the intercept b (a,never A, in Cardone’s notation, Glossary in ref 2) by the slope m (Cardone’s mM). Therefore, the label of abscissas should be so chosen that C, = b/m, C, (Cardone’s C ) being the analyte concentration in the TP. We adopt Bader’s notation because his approach facilitates a more simple and effective discussion and, also, because Cardone’s U p s introduce much ambiguity in the topic under consideration. The equivalences between both notations will be indicated whenever necessary. Focused MOSA Plot. The immediate aim in Bader’s generalized discussion is not to find an analytical result but to consider several MOSA cases under the same MOSA functionality. This is why he chooses N as the label for abscisaas. N is a running integer 0, 1,2, etc. indicating how many times a unit volume, V,, of solution of standard has been taken to spike the TP volume, V,. Equation 3 in Bader’s paper gives the C, value as C, = bV,C,/mNV, where mN is the slope in Bader’s plot, which he notes as m while we retain m for the slope in the MOSA plot used by the practising analyst, C, is the stock concentration of standard, and the other symbols have already been defined. V , is a volume in fluid samples, but if the laboratory sample from which the T P is drawn is a solid, V , ( Wz,uin Cardone’s no-
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tation, mass meaning) is usually expressed in weight units. Now, the label of abscissas in the practical MOSA plot should be such that
C, = bV,C,/mNVx = b / m Accordingly
(3) Equation 3 means that the scale factor (SF) to be applied to the label of abscissas in order to convert Bader’s MOSA plot into the practical one is SF = V,C,/ V,, so the label NV,C,/ V , should be substituted for N , Bader’s labeL The new label is the added standard concentration in TP. Besides, eq 3 indicates that the MOSA slope will become larger as the amount V, increases. On the other hand, since b/V, is a constant or nearly so, C, does not depend upon V,, as eq 2 shows. A MOSA calculation approach such as this, with added standard concentration in T P on abscissas, was used by Foster et al. (7)when they introduced the MOSA calculation technique. The quantity on ordinates was an internal-standard corrected analytical response; the blank correction was probably taken care of with a method blank (21, Le., the background intensity as measured on the spark-spectrograph plate. Actually they did not use a MOSA plot but applied instead an equation derived for just one addition of standard. By use of Cardone’s own model problem data to draw a plot, with “B-corrected response on ordinates and added standard concentration referred to the TP on abscissas, the ratio blm gives 0.125 for C, (Cardone’s C), which is the expected result. It does not depend upon the wimple size, being the same for either 62.4746 or 82.7915. Therefore, Figure 3B in ref 2 would be correct if, besides substituting a for A , we substitute W,/ WE,ufor W,. A German standard (8) to determine cadmium in water by atomic absorption (AA)uses a MOSA plot with raw response on ordinates and added standard concentration in T P on abscissas, but the final result is not the intercept of ordinate = zero but that of ordinate = blank. In another standard (9) used to determine lead, the complete information is written on the label, where one reads “Massenkonzentrationin ng/mL bzw. pg/L bezogen auf die Original-Wasserprobe”. Physical Meaning of the Abscissa Intercept. The negative nature of the intercept on the abscissa in the MOSA plot is not a physically meaningless result, because the anal@ concentration in TP, C,, may be viewed (IO) as that related to a “negative” standard addition with No times V,, so that
C,
+ N,,V,C,/Vx
=0
(4)
and
C, = -N,V,C,/V, No is less than zero because it belongs to a “standard substraction”; its negative nature compensates for the explicit minus sign in eq 5, so C, is positive. Constant-Slope MOSA Plot. We turn now to another variation of the MOSA plot, which is also considered in ref 2. This variation was introduced by Foster and Horton (11). Here the blank-corrected analytical response is plotted vs. the amount (mass) of added standard, i.e., in Bader’s notation, vs NV,C,. Therefore the scale factor on abscissas required to change Bader’s plot into ours is SF = V,C,, and the relationship between slopes is in this case
Substituting into eq 1,we obtain (7)
Anal. Chem. 1087, 59, 2818-2822
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and
b / m = C,V, So now the MOSA extrapolation does not yield C,, but C,V,, the analyte amount run through the test. Equation 6 shows that in this MOSA variation the slope m does not depend upon V,, but b / m does, as shown by eq 8. The C,V, here are the Q's in Figure 3C of ref 2. The fact that C,V, changes with TP (Cardone's sample size, W,,", mass meaning) does not impair the usefulness of this constant-slope MOSA variation, because C,V,, Le., Q,is not the analytical result C, (Cardone's C) but rather the mass of analyte involved in the test. The constant-slope MOSA plot is accurately described in ref 12.
FINAL REMARKS We can trace now the source of the confusion about Figure 3B in ref 2. According to the Glossary, the W's stand for either mass or concentration. This is only possible if there is a proportionality between both quantities. In that case the change of mass for concentration and vice versa, in terms of the W's, will have the same effect as the introduction of a scale factor. This means that the slope of the MOSA graph will be altered, but not so the shape of the whole plot. In the case under consideration the plot is necessarily of the constantslope type, because one of the two equivalent meanings given by Cardone to the Ws is the mass of added standard. On the other hand, mass and concentration are proportional only if the related volume is constant. The only possible constant volume in the MOSA technique, as it is sketched by Cardone ( I ) , is the final specified volume reached by diluting after spiking and, perhaps, treating with reagents, Le., the TS volume. Therefore, the concentration which is equivalent to the mass of added standard is not that in TP but that in TS, so the slope of the straight lines remains unaltered when the
Sir: It is gratifying to note that Ferrus ( I ) accepts the Youden one-sample regression plot (2) (a good convention by Ferrus since it differentiates from the Youden Plot (a twosample technique) that is discussed in ref 2) as the only procedure for the correct determination of the constant error, i.e., method blank and the method of standard additions (MOSA) as the best procedure for the in situ normalization of the proportional error ( 3 , 4 ) . However, Ferrus raises some questions about the corrigible error correction (CEC) technique. ABSCISSA UNITS OF RESPONSE FUNCTIONS One of the major underlying misconceptions throughout Ferrus's commentary concerns the abscissa units for the symbols W,, W,, W,, and Wz,uthat are used in presenting the CEC technique (3-5)in the various response functions as either a concentration or mass term, a choice that is actually normally dictated by the type of measurement system involved in the method. There is no problem with my symbolization since it represents accepted common practice. For example, Figure 5A of ref 4 is a typical generic standard response curve where S, could be the absorbances of a series of standard solutions of corresponding concentrations W, in any unit of concentration such as milligrams per liter. If one preferred, one could use the corresponding mass of the standard taken thereby plotting absorbance, SI,vs milligrams, W,. In such a case, the only 0003-2700/87/0359-2818$0 1.50/0
TP (sample size, W,+, mass meaning) varies. Putting W, (read as either added standard mass or added standard concentration in TS) as the abscissa label is not compatible with the focused MOSA plot depicted in Figure 3B of ref 2. The focused plot holds only if the label of the abscissas is the added standard concentration referred to TP. As an example of MOSA plot with added standard concentration in TS on abscissas we have ref 13. ACKNOWLEDGMENT The author thanks Mario J. Cardone for indicating to him ref 4 and 6 and for sending a copy of the former. LITERATURE CITED (1) Cardone, M. J. Anal. Chem. lB86, 58, 433-438. (2) Cardone. M. J. Anal. Chem. 1966, 58. 438-445. (3) Cardone, M. J. J. ASSOC.Off. Anal. Chem. lS83, 66, 1283-1294. g Anelytfccel Chemlsby; IUPAG (4) Horwitz. W. Nomendehve of S ~ n p / hh Comissbn, Vol. 3, Analytical Nomenclature. Provisional Proposal, 14th Draft, 1986, 16 May. (5) Ferrlis, R.; Torrades, F., unpublished work, Terrassa, 1986. (6) Bader, M. J . Chsm. €duc. 1980, 57. 703-706. (7) Foster, J. S.; Langstroth. G. 0.; McRae. D. R. Roc. R . SOC.London, A 1935, 153, 141-152. (8) DIN 38406, Besflmmung von Cadmium; Beuth: Berlin, 1980; Teil 19. (9) DIN 38406, BesUmmung yon Blel; Beuth: Berlin, f08l; Teil 8. 10) Caulcutt, R.; Boddy, R. Sfet/st/cs for Analytlcel C h m l s b ; Chapman and Hall: London, 1983; Chapter 13. 11) Foster, J. S.; Horton, C. A. Roc. R . SOC. London B 1937, 123, 422-430. 12) Kolthoff. I . M.; Sandell, E. B.; Meehan, E. J.; Bruckensteln, S. Ouantltatlve Chedcal Anaksls, 4th ed.;Macmlllan: London, 1969; Chapter 15. 13) DIN 38406, Bestlmmung von Chrom; Beuth: Berlin, 1085; Tell 10.
Ricard Ferrtis Escola dEnginyers Universitat PoliGcnica de Catalunya 08222 Terrassa, Spain
RECEIVED for review June 9,1986. Accepted July 22,1987.
effect would be a magnitude change in the value of the slope that results. Since, for example, in spectrophotometry, one reads an absorbance, the functionality A = abc makes it simpler to plot such standard curves with the concentration term, c, rather than a mass unit as the abscissa. Now looking at the MOSA part of Figure 5B from ref 4, any units of concentration or mass or a dimensionless term may be used for W, (added). If a concentration term were selected for the W, units in the standard curve, it would be simplest to select the same W , units in the MOSA; however, it is not mandatory but would eliminate the need for an appropriate scale factor. Obviously, it is most convenient to be consistent in the units selected for the standard curve, Youden one-sample curve, and the MOSA curve, either a concentration, mass, or dimensionless term throughout. No one in the model problems survey had any difficulties with these basic fundamentals (6). It was also uniformly understood by the respondents that the abscissa units were those for the aliquot (treated sample, TS as defined by Horwitz (7)). It was quite clear that the concentration of the analyte, W, in the original sample (test portion, TP (7)) when read (calculated) from the standardization plots (in W, units) becomes W,/ W , for the standard curve and single-point-ratio (SPR) techniques or W,/ Wz,ufor the MOSA technique. However, an explicit example using data from the literature follows ( 3 ) . The data for CPM (from Tables 5, 6, and 7 of ref 3) used a concentration term for the respective response 0 1987 American Chemical Soclety
