effect of particle shape on the spectral absorption of colloidal silver in gelatin
TRANSCRIPT
Effect of Particle Shape on the Spectral Absorption of Colloidal Silver in GelatinDavid C. Skillman and Chester R. Berry
Citation: The Journal of Chemical Physics 48, 3297 (1968); doi: 10.1063/1.1669607 View online: http://dx.doi.org/10.1063/1.1669607 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/48/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Formation and optical absorption property of nanometer metallic colloids in Zn and Ag dually implantedsilica: Synthesis of the modified Ag nanoparticles J. Appl. Phys. 113, 034304 (2013); 10.1063/1.4775820 The effect of plasmonic particles on solar absorption in vertically aligned silicon nanowire arrays Appl. Phys. Lett. 97, 071110 (2010); 10.1063/1.3475484 Focusing surface plasmon polariton trapping of colloidal particles Appl. Phys. Lett. 94, 063306 (2009); 10.1063/1.3072610 Shape effects in plasmon resonance of individual colloidal silver nanoparticles J. Chem. Phys. 116, 6755 (2002); 10.1063/1.1462610 Optical absorption of nanoscale colloidal silver: Aggregate band and adsorbate-silver surface band J. Chem. Phys. 108, 4315 (1998); 10.1063/1.475831
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SUBLIMATION OF NiCI2, NiBr2, AND Nil! 3297
and Cromer,28 i.e., 1.86 A, one calculates for a linear molecule a rotational contribution of 21.37 eu. And for the two vibrational frequencies, 515 and 417 cm-t, one calculates 2.32 and 2.72 eu, respectively. Hence, there remains 85.4-39.65-21.37-2.72-2.32=13.3 eu which must be attributable to unaccounted vibrational and electronic degrees of freedom. Brewer, Somayajuhi, and Brackett27 have attempted to account for such larger internal entropies in terms of the energy states for the ~f2+ ion and a relative small bending frequency, ,....,50 cm-I . Clearly one recognizes that more definitive experimental results are needed in place of these speculations. As a first step one recognizes that the fact that nickel dichloride vapor absorbs strongly at several places in the visible region indicates that there exists a significant electronic contribution to the entropy. In some of these regions the absorption appears to be continuous.
The observation to the effect that the extent of reaction between NiCh and Ni was not detectable within the precision of the weighed amount of solid nickel chloride sublimed permits an evaluation of the upper limit for the dissociation energy of NiCI(g). For this reaction one writes that IlHd=RT InPNiCI+TIlS/+
28 J. T. Waber and D. T. Cromer, J. Chern. Phys. 42, 4116 (1965).
THE JOURNAL OF CHEMICAL PHYSICS
IlF, (Ni, c) +IlF/(CI) -tIlF/ (NiCh, s). For the ratio of the effusion rates of NiCI(g) to NiCI2 (g), we estimate a maximum value of 0.002. For the entropy of dissociation we estimate the molecular parameters, w=424 cm-I, re =1.86,28 to obtain a value of 64.9 eu. With these estimates one finds that a value less than 4 eV is indicated for the dissociation energy of gaseous NiCl. Hence, the value of 7.3 eV given by Herzberg29
is too large; the value given by Gaydon,30 5±2 eV is also somewhat too large.
ACKNOWLEDGMENTS
The measurements reported herein represent the culmination of the efforts of several persons, two of whom have accomplished completed preliminary measurements of the mass effusion of nickel dichloride with a vacuum balance. These persons are E. Plante and B. R. Conard. We particularly acknowledge the efforts of O. B. Fletcher who made modifications of the equipment used in these studies cited immediately above. And we thank Cathy Kloog for typing the manuscript.
29 G. Herzberg, Molecular Spectra and Molecular Structure. [. Spectra of Diatomic Molecules (D. Van Nostrand Co., Inc., New York, 1950).
30 A. G. Gaydon, Dissociation Energies and Spectra of Diatomic Molecules (Chapman and Hall Ltd., London, 1947).
VOLUME 48, NUMBER 7 I APRIL 1968
Effect of Particle Shape on the Spectral Absorption of Colloidal Silver in Gelatin
DAVID C. SKILLMAN AND CHESTER R. BERRY
Research Laboratories, Eastman Kodak Company, Rochester, New York
(Received 1 September 1967)
Small prolate spheroids of silver (between 140 and 400 A av diam) were produced by photographic development of fine-grain silver bromide embedded in gelatin. The shape and size distributions of the silver particles were determined from electron micrographs of thin sections. The average axial ratios of these spheroids had values for different preparations between 0.3 and 0.9. The optical absorption was measured and a shift of the main absorption peak (near 400 mJt) to shorter wavelengths, and of a secondary peak to longer wavelengths, with elongation of the particles was found to be in good quantitative agreement with the theory of Gans. The position of the main peak can be brought into even better agreement with the theory by taking account of the finite average particle size (by using the Mie theory) and by selecting the most appropriate set of optical constants for chemically prepared silver. Small departures from spherical shape affect the spectral absorption of colloidal silver much more than changes in size or refractive index.
The optical properties of spherical silver particles in gelatin have been studied by Klein and Metz,l who reported quite good agreement between experimental spectral-absorption curves and the Mie2 theory. The possibility of making a similar quantitative examination of the nonspherical silver particles of colloidal size which are normally present in processed photographic materials was considered by Van Veelen3 and
1 E. Klein and H. J. Metz, Photo Sci. Eng. 5, 5 (1961). 2 G. Mie, Ann. Physik 25, 377 (1908). • G. F. Van Veelen, Photo Korr. 101, 149, 165 (1965).
thought to be impossible at that time. A qualitative study of elongated silver particles, somewhat larger than those in this report, was made recently by Solman,4 who observed a shift in the absorption maximum to shorter wavelengths, with decreasing particle size. The possibility that the refractive index of the small particles may not be the same as that of bulk silver was emphasized by Van de Hulst.5
4 L. R. Solman, J. Photo Sci. 14, 171 (1966). 'H. C. van de Hulst, Light-Scattering by Small Particles (John
Wiley & Sons, Inc., New York, 1957), p. 400.
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3298 D. C. SKILLMAN AND C. R. BERRY
, • " , , • .. "JIlt '" :/<- ,.
l' -' ... )\, ~ , 4f11!1' . . 4
I ./ , ~
··~I··· , .....
.' ,'f'}";:' ~_~t;:, <Ie
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SPECTRAL ABSORPTION OF COLLOIDAL SILVER 3299
80
60
o Ag (mg/cm2)
40-
FIG. 2. Spectral optical density at constant silver concentration measured with a Cary 14 double-beam spectrophotometer of samples (a)-(d) of Fig. 1, before sectioning. The reference sample was identical, but contained no developed silver.
It will be shown that large changes in optical absorption, especially at wavelengths near 400 m~ where there is a pronounced absorption peak, can be explained very well by relatively small departures from spherical shape, as treated in the extension of the Mie theory by Gans.6
EXPERIMENTAL METHOD
The silver particles were produced by applying photographic developers and fixers to a dispersion of small silver bromide particles in a gelatin matrix. The specular density was measured with a Cary 14 spectrophotometer in the wavelength interval from 270-2000 m~. The mass of silver per unit area was determined by x-ray fluorescence. Cross sections (400±100 A) of the gelatin matrix were made with a glass-knife microtome and photographed at a magnification of 80 000 X in a Siemens electron microscope. Sample preparation
6Q.°r------ -- 1- -J --~-- J-~ ~,- l 40n
l -
";~'ooli_ ,: _,_ " ,!l " \ Cv 221%
I // \. I~-=,~,...··· _ .. -.. --:"<~-L-''-/:-.l_ _ ~--",',-o 100 200 300 0 400 500
Equivalent sphere diameter (A)
FIG. 3. Arithmetic size-frequency distributions for samples (a)-(d) of Fig. 1.
6 (a) R. Gans, Ann. Physik 47, 270 (1915); (b) 37, 881 (1912).
by sectioning avoids the changes in the particles themselves and errors in their distributions which were detected when the electron-microscope samples were prepared from aqueous suspensions. It also provides a measure of the particle separation in the bulk samples. The silver particles were apparently pushed aside and not cut in the sectioning.
The electron micrographs were projected to 320 OOOX, and the length and width of the particles were measured to the nearest 3 A. Examination indicated that all
-15, ~---,----- ---,-----,- --I --~T 4.0 \ \ \ \ \
\ I \ I
I -10- I
-5
o
I I I
20
10
___ :=-0 __ = _________ _
+5~3a~O~-~-~40~O--~-~50~O---L-~a
Thin film Ag A(mj-L)
Chemically ~--- prepared Ag
2nk
FIG. 4. Optical constants of silver; m2 = (n2-k2) -i(2nk). The continuous dashed-curve values are those used in the present study of photographically developed silver.
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3300 D. C. SKILLMAN AND C. R. BERRY
TABLE 1. Measured values of colloidal silver samples.
Equiv. Coeff. Peak Average sphere of position, Optical
axial ratio diam variation Amax density Ag Sample b/a (1)
1 (a) 0.366 243.5 2 0.450 244.3 3 0.457 293.0 4 (b) 0.473 365.3 5 0.537 274.5 6 0.664 182.2 7 0.670 309.9 8 (c) 0.743 166.3 9 0.781 274.4
10 0.783 321.7 11 0.830 314.0 12 0.840 189.2 13 0.840 168.9 14 0.847 138.9 15 0.849 231.0 16 0.852 265.7 17 0.857 186.9 18 (d) 0.889 328.6 19 0.920 185.5 20 (e) 0.568 407.7
particles approximated prolate spheroids in shape, so the axial ratio and diameter of a sphere of equal volume were calculated for each silver particle. Since the length of a prolate spheroid measured in projection is less than its actual length, except when the long axis is exactly normal to the projection direction, a small correction was applied to the measured axial ratios. In this correction, it is assumed that the long axis of each particle was oriented at an angle to the projection or electron-beam direction which is the average angle for randomly oriented particles. The corrected axial ratio X and the measured axial ratio Yare related then by
Y = 2X(1- X2)1/2/[arc sin(1-X2)1/2+ X(l- X2)1/2],
where the ratio of minor to major axis, bfa, is used for X and Y. The magnitude of this correction is at a maximum when the measured b/a=0.600, giving a corrected b/a=0.515. An appropriate correction was applied to the average of the measured axial ratios of each sample. About 250 particles were measured on most samples. The size-frequency, axial ratio-frequency, and axial ratio-size distributions were plotted on arithmetic and probability graphs for evaluation.
RESULTS
Electron micrographs which are representative of the ran!2;e of particle shapes and sizes obtained are presented in Figs. 1 (a) -1 (e). The corresponding absorption curves are given in Fig. 2, where the curve for sample "e" is omitted for clarity since it is essentially flat (D/Ag=27.0±O.5) from 365-820 mJL.
('10) (mIL) DmaI (mg/it')
24.1 372 1. 94 30.5 27.3 380 2.19 43 24.3 380.5 2.94 55 22.7 383.5 1. 90 33 33.0 384 5.27 106 26.4 396 4.86 86 31.2 398 4.75 80 23.1 407 5.55 91 56.4 425.8 2.99 48 35.0 409 2.92 SO 34.5 430 5.90 80 16.2 414 4.98 71.5 50.2 415 5.70 125.5 50.9 417 5.45 65 17.4 422.5 4.01 74 27.5 430 4.39 133 30.5 422 3.92 107.5 18.5 434.5 3.35 33 27.1 423 7.14 88 47.6 4.52 152.5
The distributions of particle size for samples "a-d" are shown in Fig. 3. Except for the tails on the smallparticle side, the distributions are relatively symmetrical. Because of the tendency of certain development conditions to accentuate this small-particle tail, the coefficient of variation (C) exceeded 50% on some samples.
A plot of axial ratio vs cumulative frequency on a log probability graph gave a good straight line for sample "b," which indicated a log-normal distribution. Other samples, however, showed deviations from a straight line which resulted from different development conditions. For samples "a" and "b," the axial-ratio vs particle-size graphs showed monotonically increasing elongation of the particles with size until a maximum was reached near the 90-percentile point. Other samples showed a relatively constant axial ratio over a broadsize range. These results were also dependent on development conditions.
In Table I, the measured values of particle size and shape are given, along with some of the optical and x-ray fluorescence measurements, for twenty samples which include those previously designated "a-e." The samples have been numbered in the order of increasing axial ratio (approaching spheres), except for sample 20, which differs from all the other samples in that it has no absorption maximum. An obvious correlation is the shift of the main absorption maximum to longer wavelengths as the elongation of the particles decreases. This appears to be a contradiction of the statement by Doremus7 that the absorption band would
7 R. H. Doremus J. Chenl. Phys. 42, 414 (lY65).
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SPECTRAL ABSORPTION OF COLLOIDAL SILVER 3301
TABLE II. Optical constants of silver: m2 = (n2-k2) -i(2nk).
A 1Il2 A 1Il' A m'
280 0.85-i3.99 480 -7. 22-iO. 270 700 -21.34-iO.698
290 1.20-i3.75 490 -7. 72-iO. 279 710 -22.14-iO.725
300 1.87-i3.20 500 -8.23-iO.288 720 -22. 96-iO. 753
310 2.08-i1.66 510 -8.78-iO.300 730 -23.80-iO.781
320 1.04-iO.680 520 -9.30-iO.314 740 -24.65-iO.809 330 -0.18-iO.390 530 -9.85-iO.326 750 - 25. 50-iO. 838 340 -1. 2S-iO. 510 540 -1O.42-iO.342 760 -26.34-iO.868 350 -1. 78-iO.562 550 -11.01-iO.360 770 -27.18-iO.900 360 -2.27-iO.51S 560 -11.60-iO.379 780 - 28. 02-iO. 935 370 -2.87-iO.470 570 -12.22-iO.398 790 -28.86-iO.972 380 -3.29-iO.407 580 -12.84-iO.417 800 -29.70-il.010 390 -3.57-iO.340 590 -13.48-iO.438 810 -30. 56-i1.046 400 -3.83-iO.300 600 -14. 14-i0.459 820 -31. 44-i1. 082 410 -4.16-iO.285 610 -14.81-iO.480 830 -32.34-i1.118 420 -4.52-iO.281 620 -15 .48-iO .501 840 -33.26-i1.154 425 -4.73-iO.278 630 -16.16-iO.523 850 -34.20-i1.190 430 -4.96-iO.276 640 -16.86-iO.546 860 -35.12-il.226 435 -5.18-iO.273 650 -17.56-iO.570 870 -36.02-i1.262 440 -5.39-iO.270 660 -18. 28-iO. 594 880 -36.92-i1.298 450 -5.83-iO.266 670 -19.02-iO.619 890 -37.81-i1.334 460 -6.28-iO.264 680 -19.78-iO.645 900 -38.69-i1.370 470 -6.73-iO.266 690 -20.56-iO.671
shift to shorter wavelengths as the particles became more spherical with annealing. An examination of the theory will resolve this question.
THEORY
In 1915 Gans6 extended the Mie2 theory to both prolate and oblate ellipsoids of revolution. The calculation applies exactly to infinitesimally small ellipsoids only but should be approximately correct for particles in the Rayleigh range, where the particle radius p~ O.lA. The spectral absorption calculated by Gans for five shapes of prolate ellipsoids from spheres to infinitely long needles showed immediately an obvious similarity to our experimental results. Since the optical constants for silver used by Gans were those of Hagen and Rubens8 and were found by Klein and Metz1 to be less appropriate than the later determination by Schulz,9 it was expected that the use of more recent constants in the Gans theory would improve the agreement with our experiments.
In a study by Morriss and CollinsIO of the optical properties of multilayer colloids (silver on gold nuclei), it was found that the optical constants for thin films determined by Huebner, et at.ll fitted the experimental data better than did the constants for bulk silver determined by Ehrenreich and PhilippP Unfortunately, the
8 E. Hagen and H. Ruhens, Ann. Physik 8, 1, 432 (1902). 9 L. G. Schulz, Adv. Phys. 6, 102 (1957); J. Opt. Soc. Am. 44,
357,362 (1954). 10 R. H. Morriss and L. F. Collins, J. Chern. Phys. 41, 3357
(1964) . 11 R. H. Huebner, E. T. Arakawa, R. A. MacRae, and R. N.
Hamm, J. Opt. Soc. Am. 54,1434 (1965). 12 H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622
(1962) •
thin-film values were restricted to the range 250-370 mJL, but it is believed that the values of Minor13 and Schulz are applicable above this range since they lie between the thin-filmll and bulk-silverIO values in this range and were determined for chemically deposited13
as well as evaporated9 silver films. In Fig. 4 are presented the real and imaginary parts
of the square of the complex refractive index for bulksilverIO (solid curves) and for thin-film silver (dashed curves) with an interpollation between the values for air-exposed thin films below 370 mJLll and the values of Schulz and Minor above 410 mJL. The continuous dashed-curve values are given in Table II and are the ones which were used in our computations. Additional determinations of the optical constants from 270-580 mJL of air-exposed, evaporated silver were published by Meyer, et al. 14 after our calculations had been made. These values14 are very close to the ones which we used, including those in the wavelength range from 370-410 mJL where our values were interpolated. The shift in position of the maximum at about 400 mJL correlates better with the thin-film values than with the bulksilver values, even though the differences are small in this region where the curves intersect. Actually, the agreement between experiment and theory would be further improved if values for chemically developed silver in gelatin could be shown to depart from those for bulk silver by slightly greater amounts.
With the set of optical constants in Table II, the curves of absorption coefficient vs A were determined
13 R. Minor, Ann. Physik 10, 581 (1903). 14 E. Meyer, H. Frede, and H. Knof, J. Appl. Phys. 38, 3682
(1967). .
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3302 D. C. SKILLMAN AND C. R. BERRY
xlO"
20
K/cm
. I:IG. 5. C~lcula~ed absorption curves for prolate spheroids of mdlcated aXial ratIO. Only three curves are included here for clarity; the dashed curve is the envelope of the maxima.
by using an IBM 360 computer for eleven shapes of prolate ellipsoids from spheres to needles (Fig. 5). Here, the absorption coefficient K = (67r IA') 1m ( - al) , where A'=A/mo and mo= 1.538 for gelatin, the surrounding medium. 1m signifies that only the imaginary part of al i{taken.
A d· - t G _1 '+2" h ccor mg 0 ans, al- aal aal, were
m'2-1 a '- ---------1- 3+ (3P'/47r) (m'L1)
xl06 18,-----,--------,---,------,--,-----,---"
16
14
12
K/cm 10
8
6
4
2
o~-~-
380 400 420 440 460 480 500 520
A(mj.L)
FIG. 6. Calculated absorption for spheres of indicated diameter.
and
" m'2-1 a - ---------
I - 3+ (3P"/47r) (m'2-I) ,
with P'+2P"=47r, and m'=mlmo, where m is the complex refractive index of silver. For prolate spheroids (ellipsoids of revolution),
P' = 47r[ (1-e2) je2] ( (l/2e) In[ (1 +e) I (I-e) J-1)'
where e= (a2-b2Jl /2Ia. From this, the relation between the axial ratio bla and 3P'/47r is obtained.
If the curves of Fig. 5 are compared with those of Gans (Fig. 2, Ref. 6a), it can be seen that the envelope of the curve maxima is of the same shape, but the magnitudes of our values at all wavelengths are about four times greater because the real part of the refractive index used by Gans was much too large. As the average shape of a distribution of particles becomes more
--I --- - I --- I
! - ---- [ 40 50
Diameter (mf-L)
_______ J 60 70
FIG. 7. Absorption maximum vs sphere diameter, calculated from Mie theory.
elongated, the main absorption shifts to shorter wavelengths, and a secondary peak appears at longer wavelengths. The major change produced by the use of the new constants for silver is in the reduced width of the peaks on the long-wavelength side of the sphere peak and the increased rate of splitting of the sphere peak with increasing axial ratio. Thus, for a given departure from the spherical shape, the result would be a broader main absorption peak and less absorption at the longer wavelengths.
A correction for finite particle size was considered desirable before the shift in the calculated absorption maximum from Fig. 5 was compared with the experimentally observed shift with changing axial ratio. Since the wavelength of the absorption peak was given by Klein and Metzl for spheres as small as 40 mJ.! in diameter only, computations made with the Mie2 equations were extended down to spheres of zero size. Values for the first electric partial wave were computed for ten values of a.2 from O-D.5 (a.=7rdmo/A, where d is the
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SPECTRAL ABSORPTION OF COLLOIDAL SILVER 3303
FIG. 8. Calculated (curve), observed (0), and size-corrected (.) positions of absorption maximum vs average axial ratio of prolate spheroids.
1.0
.9
8 -
. 7
5/0
.6
0
6' 0
0
sphere diameter) and 22 values of A from 330-520 m}.!. The results were replotted for eleven values of Ii from 0-60 m}.! of which seven are reproduced in Fig. 6. The values of wavelength at the positions of maximum absorption are given in Fig. 7 for spheres of different diameter.
The values of Amax for spheres of the same volume as the average particle in each of nineteen samples are given in Table III. From these values the observed shift in Amax is obtained and compared with the shift predicted by the Gans theory, replotted in terms of Amax vs axial ratio in Fig. 8. The average difference of only 0.7 m}.! in the observed minus the theoretical shift indicates that the refractive index of silver at A= 425 m}.!
35°1 360
I I ,------,- I I I I
-------------------------~----
425 _I I .. _._~J.__ ... L. __ L 500 600 700 800 900 1000 1100 1200
Armx(mj-L )
FIG. 9. Position of main absorption maximum C\nax) vs longwavelength maximum (Amax') for prolate spheroids of increasing axial ratio. Curve is calculated for particles of zero size by Gans theory. Circles are measured values.
--,---- T---- --,- - ~-- --,---
Infinitesimal particles
• • o
•
• • •
•
_~ __ LI_ 380 370 360
(which was used) is approximately correct. Also, the scatter of the observed values (±5.9 m}.!) from the theoretical curve is not much greater than would be expected from experimental error. The use of a size correction based on the average equivalent sphere diameter results in what appears to be an over correction. A rigorous solution for an ellipsoid of arbitrary size has been published by Moglich,15 but the treatment is much more complicated.
Another comparison of experiment and theory is presented in Fig. 9, where the position of the main absorption maximum is plotted against the position of the long-wavelength absorption maximum for prolate spheroids of increasing axial ratio. The displacement of the experimental values from the theoretical curve is in the direction that would be expected from the effect of the finite size. However, the amounts by which the experimental points depart from the theoretical curve are not correlated well with the measured sizes of the different specimens.
We have computed synthetic absorption curves for some samples from their measured axial ratio-frequency distributions. With a density match at the longer wavelengths, the computed main absorption peaks are too high by a factor of about 2, and the minima near 500 m}.! are too low by the same factor. These discrepancies can also be ascribed to the effect of finite size since the main difference in the sample "e," which has no maximum or minimum, and the other samples is a slightly larger average size. Probably the broad size distribution is an added factor in smoothing the absorption of sample "e."
The amount of silver per unit area in sample "e" is higher than in other samples. Therefore, the effect of
15 F. Moglich, Ann. Physik 83,609 (1927).
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3304 n. C. SKILLMAN ANn C. R. BERRY
TABLE III. Wavelengths of absorption maxima for colloidal silver samples.
Corrected average Mie theory
axial (sphere) ratio Amax
Sample b/a (mIL) -----------
1 (a) 0.299 434.8
2 0.373 434.8
3 0.380 439.1 4 (b) 0.394 446.6
5 0.453 437.4 6 0.580 430.3
7 0.588 440.8
8 (el 0.665 429.3
9 0.710 437.4
10 0.713 441.9
11 0.769 441.1
12 0.782 430.7
13 0.783 429.5
14 0.791 428.1
15 0.794 433.8
16 0.798 436.6
17 0.804 430.5
18 (d) 0.846 442.6
19 0.890 430.5
silver-particle concentration on the spectral absorption was investigated. A series of five preparations with increasing thickness and gelatin content were made. After a constant exposure, a sample from each step in the series was treated uniformly in one of three developers which produce different average particle shapes. The range of volume concentrations of the resulting silver in the gelatin was from 0.02%-6.1%. The position of the main absorption peak, for those series of samples with a given development, had an average variation of less than 4 mIL. It is probable that at higher silver concentrations significant spectral effects would be encountered. However, since the particle-shape studies were done at intermediate concentrations, the effect of the range of silver concentrations in these experiments is considered to be negligible.
Although the preceding discussion has considered silver particles in the shape of prolate spheroids, it should be mentioned that the theory includes spheroids of oblate shape as well. If the experimental curves of WiegeP6 for plate-shaped silver particles are compared with the calculations of Gans (Fig. 3, Ref. 6a), the expected shift of the main absorption maximum to
'" E. Wiegel, Z. Physik 136, 642 (1954); see Fig. 4, p. 649.
Observed shif 1 of Am", from Galls theory positioll for shift in Oos-calc
fini te spheres Arnax A (mIL) (mIL) (mIL)
"."--"--------
62.8 54.4 +S.4 54.8 50.9 +3.9
58.6 50.4 +8.2
63.1 49.6 +135
53.4 45.6 +7.8
34.3 34.0 +0.3
42.8 33.3 +9.5
22.3 26.0 -3.7
11.6 22.1 -10.5
32.9 21.8 +11.1
11.1 17.4 -6.3
16.7 16.4 +0.3
14.5 16.3 -1.8
11. 1 15.6 -4.5
11.3 15.4 -4.1
6.6 15.0 -8.4
8.5 14.6 -6.1
8.1 11.3 -3.2
7.5 8.0 -0.5
i.i=+0.7
Ii [=±5.9
longer wavelengths with increasing departure from spherical shape is observed. The presence of a secondary maximum on the short-wavelength side which shifts to shorter wavelengths in agreement with the theory can also be observed. It is probable that Doremus7
was referring to silver particles of oblate shape when he predicted the direction of shift of the absorption maximum to shorter wavelengths with annealing.
For silver particles in the Rayleigh region of absorption and scatter, the effect of a 10% departure from spherical shape (b/a=0.9) is a shift in the absorption maximum which is larger than that which results from doubling the average particle size from 100 A to 200 A.
When the appropriate optical constants for silver are used, the Gans theory predicts a shift of the main absorption maximum to shorter wavelengths with increasing elongation of prolate spheroids which is in good quantitative agreement with experimental values.
ACKNOWLEDGMENTS
We wish to thank Dr. D. C. Shuman for helpful discussions, Mr. J. L. Pabrinkis for the computer programs, and Mr. C. F. Oster, Jr., for the electron micrographs.
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