COMPLEX REFRACTIVE INDEXOF COLLOIDAL SILVERBROMIDE microwave region cannot be explained as the relaxation losses of rotating permanent dipoles. Possible relaxation mechanisms, not depending on molecular dipole rotation, that might be associated with the short relaxation times of the nonpolar acetylacetonates will be discussed in another paper. The reasons for the differences between the present solution results and those of Wright and his coThe disagreement between w o r k e r ~are~ unknown. ~~~~ the two sets of data is greater than can be accounted for by the absolute errors in the polarization values reported in this work. Two differences between the studies are the concentration ranges used for the solution measurements and the number of solutions examined at each temperature. The concentration range employed in the present investigation for p-dinitrobenzene and ferric acetylacetonate was two and four times greater, respectively, than that used for the same sub-
1523
stance in the earlier work. The number of solutions measured previously was either four or five, as compared to seven examined in all cases in this work. In addition to these experimental differences, another point deserves consideration; Le., the assumption employed by Wright, et al., that the distortion polarization of a molecule is independent of the conditions under which it is measured. To our knowledge there is no conclusive experimental evidence to justify the assumption that the distortion polarization in the solid state does not differ significantly from that in the liquid,'* particularly for molecules with very flexible structures and many polar bonds. A study dealing with the above question has been ~ t a r t e d . ~ (26) The relaxation time observed for aluminum acetylacetonate in benzene solution at 46' (ca. 3 x 10-12 sec) is much smaller than would be expected for simple rotational orientation of a rigid polar molecule of the same size and shape.
Complex Refractive Index of Colloidal Silver Bromide in the Near-Ultravi~let~ by E. J. Meehan and Jerry K. Miller School of Chemistry, University of Minnesota, Minneapolis, Minnesota
(Received September 6 , 1967)
66466
'The complex refractive index of silver bromide in the form of colloidal particles in aqueous suspension has been measured by a combination of light scattering and absorption methods, a t the wavelengths 366, 405, and 436 mp. The radius of the smallest particles investigated was about 4 mp. The real part of the refractive index appears to be the same for colloidal material and for bulk. However, the imaginary part, proportional to the absorption coefficient, for colloidal particles is definitely different from that of bulk, that of the particles being ca. 50% smaller, 10% larger, and 60% larger a t wavelengths 436, 405, and 366 mp, respectively.
This paper describes the use of light-scattering measurements to obtain the complex refractive index of silver bromide in the form of colloidal particles in aqueous suspension. The results show that the absorption by small colloidal particles is different from that by material in bulk form. The complex refractive index, f i ~of, an absorbing substance in bulk is given by
2,
=
n B
- inB'
in which TLB is the real part and n B ' bulk absorption coefficient, Y B , by
(1) is related to the
In eq 2, Ioand 1 are intensities incident upon and trans-
mitted (corrected for reflections) by thickness x , and XV is the vacuum wavelength. Equations identical in form to eq 1 and 2 connect the corresponding values of rip, n p , n p ' , and yp of material in the form of colloidal particles. Obviously, it is necessary to consider whether the latter set of values depends upon particle size. The scattering and absorption by a spherical particle of radius r, suspended in a nonahsorbing medium of refractive index YLM, cas1 be calculated from exact Mie theory, given the values of 7% and (Y
n~ 7n = - nx
.nP'
2-
=
m - im' = m ( l - ik)
nM
(3)
(1) Taken from the Ph.D. thesis of J. K. Miller, University of Minnesota, Minneapolis, Minn., 1966.
Volume 7.8, Number 6
M a y 1968
1524
E. J. MEEHANAND JERRYE(. NILLER 2ar - 27rnwr
a=---
Xnr
XV
(4)
ri2, is the complex refractive-index ratio,2 and XV and Xnl are wavelengths i n vacuo and in the medium, respectively. Conversely, ri2, can be calculated from suitable scattering and transmission measurements if CY is known. This procedure is used in the present paper. Additionally, as is described in the section on Calculations, nz may be derived in some cases by measurement of the refractive-index increment. Values of n B ‘ for silver bromide have been determined by several workers down to XV 264 mp, but n B has been measured only over the range 436671 mp.314 Direct measurements at shorter X are complicated not only by the relatively strong absorption but also by the photosensitivity. Yo data exist in the literature on absorption by colloidal silver bromide. Silver bromide is transparent, or practically so, above 436 mp, and it has been shown already by comparison of results of scattering and electron microscopy that n p = n ~at, least for T greater than about 100 mp.j The question of a possible dependence of n p on r has been considered critically. All the data presented in this paper can be accounted for satisfactorily on the assumption that n p = n B down to the smallest sizes investigated.
Experimental Section Transmission measurements were made using either a Beckman DU or Cary 1 5 spectrophotometer. Tenmillimeter cell compartments were used with 4-mm apertures to limit the angle of view. The geometry of the light beam is different in the two instruments, but the values of log I o / I always agreed within 0.003. The turbidity r is calculated from 1 l o r = -1n-
I
I
where 1 is the path length in centimeters. The specific turbidity, r / c , for monodisperse spherical particles is related to the total extinction coefficient, K T ~by,
where c is the concentration of the suspension (g ml-I) and D is the density of the part,icle. The values of r / c were extrapolated to c = 0. Angular scattering measurements were made with a Brice-Phoenix instrument. The relative intensity G(0) of the vertically polarized scattered component of unpolarized incident light was measured for various mercury wavelengths Over the range 30-900 and to e = 0 to obtain G(0). I n order to obtain absolute scattering intensities from G(O), the instrument was calibrated with “small-particle” 'Judex' As by Deielic and Krahtovi17 the Ludox was centrifuged at The JOUTnal of Physical Chemistru
12,000 rpm for 90 min. The suspension was poured off and 1-, 2-, 3-, and 10-ml portions were diluted to 100 ml with 0.05 M sodium chlorideE and were filtered through a 0.45, Millipore filter. The value of i46/i136 was 1.07 and the wavelength exponent was 3.9, in good agreement with the closest approach to smallparticle scattering previously ~ b s e r v e d . ~The turbidities of the Ludox suspensions were measured spectrophotometrically. The ratio G(O)/r was plotted us. r and extrapolated to = 0. This procedure eliminates the effect of secondary scattering. For small particles, the relation between r and the Rayleigh ratio, R8, for the vertically polarized scattered component of unpolarized incident light, is given byg
(7) In this way the forward-scattered intensity per unit solid angle, per unit volume of suspension, and per unit illumination is found. Calling this quantity V(O),and using the notation of Gumprecht and Sliepcevich,1°one obtains
for a suspension containing N particles per milliliter. The specific forward scattering, V(O)/c (compare eq 6), is given by
The difference in the refractive index of the colloidal suspension and the medium (ie., water containing the same concentrations of dissolved electrolytes), Ap, was measured with a Brice-Phoenix differential refractometer. For work at 366 mp a plate of uranium glass was placed at the focal plane of the projection lens, and the displacement of the fluorescent slit image was measured. The instrument was calibrated by visual measurements as usual with sucrose solutions (2) H. C. van de Hulst, “Light Scattering by Spherical Particles,” John Wiley and Sons, Inc., New York, N.Y., 1957, pp 130, 269; see also 1’. Latimer and F. D. Bryant, J . O p t . SOC.Amer.. 55, 1554 (1965). (3) T. F. W. Barth, Amer. J . Sci., 19, 135 (1930). (4) H. Schroter, 2. P h y s i k . , 67, 24 (1931). ( 5 ) E. J. Meehan and W. H. Beattie, J . P h y s . Chem., 64, 1006 (1960). (6) Definitions of KT and related quantities are given in ref 2 , P 127f. The quantity KT is called Q e x t by van de Hulst. Also see D. Sinclair, J . Opt. S O C .Amer., 37, 475 (1947).
(7) Gj, Deielic and J. P. Krahtovil, ~ ~ z l z., ~ i173, d 38 (1960). (8) D. A. I. Goring, M. Senea, B. Melanson, and M. M . Huque, J . Colloid Sci., 12, 412 (1957). (9) W. F. H. M. klommaerts, ibid.,7, 71 (1952). (10) R. 0. Gumprecht and C. M . Sliepcevich, “Tables of LightScattering Functions for Spherical Particles,” Engineering Research Institute, University of Michigan, Ann Arbor, Mioh., 1951.
COMPLEX REl?RACTIVE INDEX
OF
COLLOIDAL SILVER BROMIDE
at 546 mp, the displacement of slit image, Ad, is proportional to .&: a t 546 mp Ap646
= k~Ads46
-
0
kX =
M646 k546-
MA
435 8 9.705
0.30
0.15
where M is the magnification. Values of M are supplied by the manufacturer at 589, 546, and 436 mp. Since M varies very little with X, a short extrapolation to shorter X seems entirely reliable. The values used were 546.1 9.686
0.40
0.35
and a t any wivelength
XV
1525
404.7 9.712
0.10 rM (mu)
Figure 1. Determination of m from transmission measurements on a heterogeneous suspension.
366.1 9.72
of YB a t 366 mp is 6.0 X lo3 cm-1.14 This corresponds (using the value of np derived in this paper) Chemicals were as described before." b9easurements t o D?B' = 1.3 x 10-2 and k g = 7.0 x low3. Mie were made on a variety of sols. Small-particle sols calculalions were made for values of k p smaller than, having a radius of 5 10 mp were made in a rapid-mixing equal to, and larger than k B , up to 0.1, which proved apparatus, described elsewhere, l2 in which mixing was to be larger than the actual value. Similar calculacomplete in 0.006 sec or less. hleasurements on SOIS tions were made (with appropriately smaller k ) for with radius cn. 7 mp were made in the rapid-mixing 405 and 436 mp. apparatus either during flow or with stopped flow. Tables 1-111 contain a few examples, selected from Sols with radii 7-10 mp were prepared in the same the very extensive calculations for homogeneous susapparatus; the effluent was collected and stabilized pensions, which illustrate the principles used in obat a given radius by addition of a solution of polyviriyltaining &. pyrrolidone (I'VP),11 which either prevented particle Scattering measurements are considered first. K S growth entirely or made growth so slow that any determines the total scattering and il(0) is proporchange in radius could be corrected for easily. Sols tional to forward-scattered intensity, eq 8. Table I of radius 10-30 mp were prepared using a mechanical shows that for small particles, CY 5 0.5,15the scattering stirrer ant1 stabilized with PVP. Radius was deteris practically independent of k up to k = 0.01. Even mined by scattering and transmission measurements for k = 0.1, which corresponds to very strong absorpover the range XV 436-800 mp, assuming that np = n ~ . ' ~tion,16 the scattering differs by only a few per cent The validity of this assumption is confirmed by the from that of a nonabsorbing substance. Of course fact that the values of r thus found were the same the scattering for small a is sensitive to m, as is shown within a few per cent over the entire range of wavein Table 11. Therefore, measurements of forward length. Equation 6 was used to obtain a from meascattering in homogeneous sols of small radius serve surements of transmission, which yielded r / c , combined to determine m, no matter what the value of k is (up with Alie theory values of KT. Radius was found to the above-stated limit at least). from a: by eq 4. Equation 9 was used to obtain a: The quantity Re &*(O) given in Table I is the real from scattering measurements extrapolated to 0") part of the complex forward-scattering function which which yielded V(O)/c, combined with XIie theory determines il(0) values of i(0). All the small-particle sols were relail(0) = /Re il*(0) iIm il*(0)l2 tively homogeneous, as shown by the fact that even (10) ca. 30 min after mixing, at which time the radius in There is no general uniformity of notation among the absence of stabilizer was much larger than Rayleigh size, measurements over this range of wavelength (11) E. J. Meehan and G. Chiu, J. Phys. Chem., 70, 1389 (1966). (12) E. J. Meehan and J. K. Miller, ibid., in press. gave the same radius within a few per cent. I n addi(13) The experimental values of 1 2 ~extend only up to 671 mfi, but a tion, some heterogeneous sols containing larger parshort extrapolation to 800 mp should be reliable. The value of 1zp ticles (modal radius, 48 mp; see Figure 1) were preused for 800 mp was 2.210, corresponding to mp = 1.664. pared by ordinary mixing, as described earlier. l1 (14) Y. Okamoto, Naehr. Akad. Wiss. GBtt., IIA, 275 (1956); F. M
+
Calculations Values of the scattering coefficient, Ks,the total extinction coefficient, KT, and forward scattering were calculated from exact Mie theory for many values of nz and k (see eq 3), at intervals of 0.05 in CY. The value
Moser and F. Urbach, Phys. Rev., 102, 1519 (1956); F. Moser, Eastman Kodak Co., Rochester, N. Y., personal communication, 1964. (16) At XV 366 mfi, 123% = 1.346, and a = 0.5 corresponds to r = 21.7 mp. (16) A layer 0.1-mm thick of a substance having k = 0.1 and CB = 1.87 X 1.346 (compare eq 2 and 3) would transmit only 0.02% at XV 366 mfi.
Volume 78, Number 6 May 1068
1526
E. J. MEEHANAND JERRYI
