Contrast Measures for Spectrographic Plates SIR: As a result of differing publication schedules in different journals, the first printed appearance of the parameter G introduced by the writer for the characterization of emulsion response (7) occurs in a Scientific Communication by M. H. Hunt (3). The definition of G given by Hunt differs in important respects from that of the writer, and the following clarification is intended to aid the users of spectrographic response plots. G, as defined by the writer, is the slope of the extended linear region on a logarithmic-probability plot of exposure, E , and relative transmission, TR. This slope is measured in terms of “transform units” (numerical values of a modified normal probability deviate) per logarithmic cycle of E . The probability deviate was modified by a constant numerical factor in order that the slope measure at TR = 0.5 on the probabi1it.y paper would be numerically the same as that on a corresponding plot with the ordinate scale linear in log (1/TR - 1). The relative transmission, TR, is the transmittance, T , of the processed emulsion re-expressed as a fraction of the transmittance range between the processing fog transmittance level, To,and the minimum or saturation level, T,, of transmittance that is achieved at large exposure. The algebraic definition of TR is
Tz
(
1
- T o - T , ) + T - i =1 O 2 TOT,
(4)
Application of Equations 3 and 4 reveals only minor numerical differences between G and H in the cwe of Hunt’s silver bromide plates 386 and 387. The values of H , To, and T , for the Q-2 plate 385 are 0.81, 0.83, and 0.03, respectively. The positive value of T satisfying Equation 4 for this case is 0.284, and the corresponding value of TR is 0.317. The result 0.96 for G is obtained by substitution in Equation 3 and illustrates an important numerical difference between G and H . The G derived from Hunt’s data on Q-2 plate 385 is in excellent agreement with the representative value 0.98 obtained by the author (7) for several Q-2 plates from four different emulsion lots with To and T, levels of 0.84 and 0.018, respectively. When the value of T, for processed Q-2 plates is below 0.005, G usually displays a higher value around 1.2. The author’s choice of G as a symbol for the constant in Equation 2 and the corresponding slopes of linear regions on response curves was based on the phonetic similarity between G and the Greek letter y . The conventional contrast measure y for a photographic emulsion is defined as the slope dD/d log E in the straight region about the inflection point on a plot of log E and the ordinate log ( 1 / T ) or D, the optical density. If Equation 2 applies strictly 1
for all T between - (To 2
+
T,) and
dE, the relation follows without any approximation ( 5 ) . As T, approaches zero, Equation 5 shows that y and G approach a common value and Equations 3 and 4 show that H simultaneously approaches the same value. Because the plots on which G is measured as a slope are linear or nearly linear ( 6 ) , y can be determined from G without the judgment factor involved in select.ing the maximum slope of the characteristically S-shaped plot of log E and D. In the nomenclature of Reed and Berkson (8), data satisfying Equation 2 show a logarithmic-logistic relationship between E and T R . Such data will plot linearly on a logarithmic-logistic grid; but when a logarithmic-probabilit,y grid is used, the resulting plot, Figure 1 , is an extremely shallow S curve. G is given by the slope of this curve at T R = 0.5, the inflection point, and is some 7% greater than the slope of the dotted straight line that represents a good approximation to the S curve shown. If only a limited number of data points cover the T R range between 0.05 and 0.95, shallow S curvature is difficult to perceive; as a result, the natural tendency will be to represent the data by a straight line regardless of whether a logarithmic-logistic grid or a logarithmic-probability grid h w been used. Small differences in slope values will be introduced by the choice of grid
Hunt identified with G will be denoted by H in the present article. The parameter G and H are related through Equation 1 and the differential equation d log ( ~ / T R 1) = G d log E
(2)
that applies to the linear central region on a plot with log E as abscissa and either the modified probability deviate or log ( l / T R - 1) as ordinate. The result is contained in the equations
when the values of T and T Rcorrespond to the inflection point on a plot of log E and log ( 1 / T - 1 ) . The condition for inflection, obtained by equating the second derivative d210g( l / T - l)/d(log E)2 to zero, is the quadratic 1402
ANALYTICAL CHEMISTRY
Figure 1
.
A logarithmic-logistic relation plotted on a logarithmic-probability grid
in such practical cases and values of G should be accompanied by a statement of the particular plotting technique used for the determinations. Reed and nerkson made a suggestion that is currently very pertinent to the nomenclature of emulsion response plots. They gave several examples, none from the field of spectrography, of forms of the logistic function in use under a variety of specialized names, and strongly urged that scientists should learn to recognize forms of the logistic function and rcfcr to them by the generic term “logistic.” The technique of making a logarithmic-logistic response plot of E and T by plotting log E and the ordinate log (1/T - 1) was first presented by Baker ( 1 ) . Common use of the symbol A for log (1/T - 1) by both I3aker and Seidel has suggested strongly to the author (4) that Seidel, who frequently is given credit for the technique, merely retrieved Ijakcr’s innovation from the literature and did not make even an independent rediscovery. The equations given by Hull (@) for the ion-response of Q-2 plates provided, for the first time, forms of the logistic function that gave a good fit
with response data at low transmittances approaching a T, that differed appreciably from zero. If densitometer sensitivity controls are arbitrarily adjusted to refer transmittances to the processing fog level as unity, then these equations become equivalent to integrated forms of Equation 2 and the parameter R of Hull’s work and G are algebraically the same. The author supports Fked and Herkson on terminology and recommends adoption of the usagcs logarithmic-logistic (or loglogistic) plot and logarithmic-logistic function where these entities occur in spectrographic work. Mr. Hunt is to be congratulated for the investigation of the vapordeposited silver bromide film as an ion detector. This detector shows values of T o , T,, and G that are preferable to those obtained with conventional, emulsionbased detectors. The author’s paper (7) contained only a verbal descrip tion of relative transmission without formal presentation of its algebraic definition, Equation 1 ; and confusion between the parameter G and the ded l o i ( l / T - l) rivative unfortunately d log E
has resulted. This communication is submitted to prevent propagation of confusion and to detail explicitly some prolarties of G in relation to other contrast measures for spectrographic emulsions. LITERATURE CITED
( 1 ) Baker, E. A., Proc. Roy. SOC.Edin. 45, 166 (1925). (2) Hull, C. W., Mass Spectrometry Conf., New Orleans, Paper No. 72, June 3-8, 1962. (3) Hunt, M. H., ANAL. CHEM.38, 620 (1966). (4) McCrea, J. M., “Developments in
Applied Spectroscopy,” Vol. 4, E. N. Davis, ed., p. 501, Plenum, New York, 1465 -I--.
(5) McCrea, J. M., 4th National Meeting,
Society for Applied Spectroscopy, Denver, Paper No. 157, Aug. 3GSept. 3, 1965.
(6) McCrea, J. M., Speclrochem. Acta 21,
1014 (1965). (7) McCrea, J. &I., 12th Annual Conf.
on Msss Spectrometry and Related Topics, Montreal, Paper No. 92, June
7-12, 1964; A p p l . Speclr. 20, 181 (1966). (8) Reed, L. J., Berkson, J., J . Phys. C h a . 33, 760 (1929). J. M. MCCREA
Applied Research Laboratory United States Steel Carp. Monroeville, Pa. 15146
Polarographic Determination of Iron in Concentrated Phosphoric Acid SIR: Wet process phosphoric acid produced from Florida rock contains between 0.5 and 1.5’% FeOs, with both ferrous and ferric iron usually present. I n order to study the relationship between the iron couple and various kinetic properties of the system, it is advantageous to measure simultaneously the concentrations of both oxidation states in situ, without significantly sffecting the Fe(II)/Fe(III) ratio or the reaction of either ion with the substrate. The standard methods of analysis generally measure only Fe(II), Fe(III), or total iron concentration. A polare graphic method, originally described by von Stackelberg and von Freyhold (S) and later by Lingane (2), was applied by Doumas ( 1 ) to the determination of iron in phosphoric acid. Although the method measures the concentrations of both ions, the procedure involves a dilution of the sample, complexation of the iron with oxalate, and addition of potassium chloride to reduce the migration current. Concentrated phosphoric acid, per se: is in fact an ideal solvent for the polarographic analysis of dissolved iron in that it provides a self-contained s u p porting electrolyte and a complexing
medium in which the anodic wave for ferrous iron is as well defined as the cathodic wave for iron 111. These reactions are reversible at the dropping mercury electrode, and the contaminants which commonly occur in wet process phosphoric acid, including aluminum, do not interfere with the polarographic waves for iron. EXPERIMENTAL
Apparatus. A Sargent Model X X I Recording Polarograph was used with a 10-ml. Heyrovsky cell containing a mercury pool anode. The open circuit characteristics of the D.M.E. were: t = 6.14 and 6.64 sec. in 41.5 and 74y0 H3Y04, respectively, and m = 0.941 mg. set.-' at h = 41.5 cm. No special precautions were taken to
Table 1.
thermostat the solutions; ambient temperature was 22” f 1” C. Reagents. Aqueous 0.5.U stock solutions were prepared from reagent grade FeS04(NH4)2S04. 6 H 2 0 and FeNHI(SOI)S.12H20. Ferrous salt solutions were maintained under a nitrogen atmosphere until final dilution with aqueous solutions of phosphoric acid. Reagent grade 85% H3P04was used in preparing the calibrating solutions. Procedure. Calibration data were obtained on a series of solutions containing 1 X 10-5 to 5 X 10-2M Fe+a and 1 X 10-5 to 5 X 10-*M Fe+2 in both 41.5 and 74% HSPO,. Solutions were deaerated with tank nitrogen and polarograms scanned from +0.5 to -1.5 volts us. the mercury pool. Anodic ferrous iron diffusion currents were measured at +0.1 to f0.2 volt
Diffusion Current Constants of Ferrous and Ferric Iron in 4 1.5 and Phosphoric Acid
Iron concn. range 0. ooo2-0.01 0. ooo2-0.05 0.00054.20 0 . 0002-0.20
-
Oxid. state +2 +2 +3 +3
HaPo,, % 41.5 74 41.5 74
74%
Av. id/C f std. dev.
(amp.-L/mol) 1441 z!L 100 531 f 18 931 f 24 479 f 24
VOL 38, NO. 10, SEPTEMBER 1966
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