ADAMCHOUAND MILTON KERKER
562
Vol. 60
THE REFRACTIVE INDEX OF COLLOIDAL SOLS’ BY ADAMCHOUAND MILTONKERKER Department of Chemistry, Clarkson College of Technology, Potsdam, N . Y . Received August d6, 1966
The refractive index of sulfur hydrosols of various particle sizes has been measured and the intrinsic refractive index computed. The experimental values are in agreement with the requirements of the Zimm-Dandliker theory,
Zimm and Dnndliker2 have developed a relation between the scattering and refractive index of a colloidal sol which involves the Mie3scattering functions. This relation is more general than the mixture rules discussed by Heller4 since it is not restricted to systems of small particles with a refractive index close t o that of the medium. In this paper, we will compare the results of our observations on sulfur hydrosols with the requirements of the Zimm-Dandliker theory. We have found it convenient to work with
- n = [nlc = 3R(& *)c nap.= n’ 7 n’ 2ci D
where nsp. n n [n] C
= =
CY
D
= = = =
TABLEI SCATTERING FUNCTIONS A N D INTRINSIC REFRACTIVE INDEX AS A FUNCTION OF CY FOR m = 1.50 a
R(il*)
In] X 10’
a
0 1 2 4 6 8
...
2206 2598 2324 336 -393 47 37 12
20 30 40 50 75 100 200 400
0.3461 2.4767 2.8666 -11.286 3.2061 10 4.8675 15 5.4333
= specific refractive index = refractive index of the sol = refractive index of the medium
R(il*) =
r X
(1)
Sliepcevi~h,~.~ we have computed R(il*) for refractive index m = 1.50 over a wide range of a values. This refractive index is applicable to sulfur hydrosols. These computations and the corresponding intrinsic refractive indexes are presented in Table I. Figure 1 illustrates the variation of the intrinsic refractive index with a.
intrinsic refra,ctiveindex concentration of sol in g./ml. scattering function 2~r/h radius of colloidal particle wave length of light in the medium density of the colloidal particles
+
*
L
I’,
PARTICLE SIZE,
a=2nr/a.
Fig. 1.-Intrinsic refractive index versus
a!
2‘0
[nl X 10‘
33.571 -315 46.716 -128 47.449 - 5.56 143.21 - 8.60 273.20 - 4.86 367.84 - 2.76 990.91 - 0.93 -1646.0 - 0.193
where F(cY)d a is the fraction of particles with CY values between CY and (a da). When the colloidal particles are sufficiently small so that the Rayleigh law of scattering is applicable
+
In]
; t s‘
R(ai*)
If the system is polydisperse, the intrinsic refractive index is given by
The above utilizes the refractive index increment, n’ - n, rather than the differential refractive index, dnldc, employed by Zimm and Dandliker.
f-aL
-
&I
for m = 1.50.
The intrinsic refractive index, [n],depends upon the scattering function, R(il*),which in turn is dependent upon the size, shape and refractive index of the colloidal particles. For spherical particles, R(i1”)is obtained from the Mie theory. The available Mie theory functions have been reviewed recently.6 Using the tables of Gumprecht and (1) This work has been supported in part by grants from Reaearch Corporation and the Atomic Energy Commission, Contract AT(30-1)1801. (2) B. I€. Zimm and W. B. Dandliker, THISJOURNAL,IS, 644 (1954). (3) G. Mie, A n n . Physilc, 26,377 (1908). (4) D. Sinolair and V. K. La Mer, Chem. Revs.,44, 246 (1949). (5) M. Kerker, J . Optical Soc. A m . , in 46, lOSl(1955). (6) R . 0. Gumprecht and C . M. Sliepcevich, “Tables of Functions of First and Second Partial Derivatives of Legendre Polgnomials,” Engineering Research Institute, University of Michigan, Ann Arbor, 1951.
3(m9 - 1) 2)
= 2D(m2
+
(3)
for polydisperse as well as monodisperse sols. m is the refractive index of the colloidal particles relative t o that of the medium. Use of La Mer Sols.-Zimm and Dandliker have suggested that their theory may be tested with the sulfur hydrosols studied by La Mer and cow o r k e r ~and ~ * ~it was this suggestion that interested us in this work. These sols, which may be prepared by treating dilute sodium thiosulfate (0.0010.003 M ) with dilute hydrochloric acid (0.0020.006 M ) are monodisperse and thus offer a method of observing the influence of particle size on the intrinsic refractive index without the complicating effects of polydispersity. Unfortunately, the particle concentration in the La Mer sols is much too low to observe refractive index increments even for those sols consisting of small particles. For sols somewhat more concentrated than those of La Mer (0.02 t o 0.04 M thiosulfate and 0.06 t o 0.12 M acid), we did observe a change in refractive index in the (7) R. 0. Gumprecht and C. M . Sliepcevich, “Tables of Light Scattering Functions of Spherical Particles,” Engineering Reaearch Institute, University of Michigan, Ann Arbor, 1951. (8)I. Johnson and V. K. La Mer, J . A m . Chem. Soc., 69, 1184 (1947). (9) M. Kerker and V. K. La Mer, ibid.,72, 3516 (1950).
REFRACTIVE INDEXOF COLLOIDAL SOLS
Mq,1956
563
TABLE I1 HYDROSOLS OF VARIOUS PARTICLE SIZES INTRINSIC REFRACTIVE INDEXFOB SULFUR Partiole
me
I I
I I I1 I1 I1 I1 I11 I11 I11
Concn. &/mi.
Conan. of NaCl, g./d.
0.0070 .0065 .0056 .0024 0.00305 .0063 .00061 .0390 O.oO067 .oO099 .00095
0.00167 .00158 .00084 .00045 0 . oO080 .00568 .oO078 .03100 0.00012 .00009 .00010
of
s
course of the growth of t h e sols but were able to relate this to changes in homogeneous salt concentrations rather than to colloidal particles. We assumed that the principal reaction waslo HCl
+ NalSzOa+NaHSOs + NaCl + S
and that the refractive index of a growing sol was the sum of the refractive indexes of each of the components when separate and a t the appropriate concentration. The refractive index at any stage of the reaction was found to be the sum of the values for each of the homogeneous components. Therefore, even for these concentrations, the sulfur content was too low for a determination of the intrinsic refractive index. In order t o determine this quantity, it is necessary to work with sols of very high sulfur concentrations and with present techniques this means abandoning monodisperse systems. Fortunately it is possible to obtain some information about the relation between intrinsic refractive index and particle radius even from systems which are not highly monodisperse, provided they have a sufficiently high particle concentration. Examination of Fig. 1 indicates three regions of particle size convenient for testing. For sols whose particles are less than a! = 2, the intrinsic refractive index is insensitive to particle radius, only varying from 0.22 to 0.26. The intrinsic refractive index is practically zero for sols with particles greater than a! = 4. It is only in the intermediate range that the intrinsic refractive index is sensitive to particle radius and, for a polydisperse system, to size distribution. A system with the bulk of its particles in this intermediate range should have an intrinsic refractive index between 0 and 0.22. We have calculated the effect of size distribution on the intrinsic refractive index of a sol with a normal distribution of particle sizes and aav= 3. For standard deviations Q = 0,0.2,0.5 and 1.0 the respective values of the intrinsic refractive index were 0.102, 0.098, 0.087 and 0.058. Preparation of Sols .-We have prepared sols, designated as types I, I1 and 111, whose size distributions correspond to the three ranges described above. Type I sols consist of small particles (CY< 2) and are prepared by the fractional coagulation technique of Oden." They are nearly clear, yellow, quite stable, of high concentration and can be diluted without apparent decomposition. (10) E. M. Zaiser and V. K. La Mer, J . Colloid Sci., 3, 571 (1948). (11) 8. Oden, Noua Acta Regiae SOC.Sci. Upaaliensis, Ser. IV, 3, N. 4 (1913).
n'
-n
0.00235 .00190 .00180 ,00094 0 . ooO65 .00104 .oO000 .00554 -0.00009
-
.00008
.00010
n'
1.33482 1.33435 1.33413 1,33321 1.33304 1,33415 1.33232 1.34173 1.33214 1.33213 1.33209
[n
0.25 .22 .24 .29 0.16 .12 .OO f 0 . 6 .ll -0.10 f 0 . 0 5 - . O 6 f .04 - .08f .04
Type I1 sols were those for which the bulk of the colloidal material was in the size range CY = 2 t o 6. These were repared by a modification of Oden's technique. Tlkee volumes of 3 M sodium thiosulfate were added dropwise to concentrated sulfuric acid and the resulting solution made 0.25 M with respect to NaCl. The sulfur was centrifu ed out at 8,000 r.p.m. for half an hour in a Sorvall Type S k l centrifuge and the centrifugate was redispersed in warm water and centrifuged again. The su ernatant was then fractionated by coagulation with Na81 in the manner described b Oden to form sols which we have referred to as type I. &e second centrifugate was then redispersed in warm water and a second series of sols containing particles in the size range for type I1 was obtained by continual centrifugation and redispersion of the centrifugates. These sols were milky. Electron microscope examination indicated the bulk of the sulfur was in the size range 01 = 2 to 6 although there were always a considerable number of very small particles and sometimes some large ones present. A seeding technique was used to prepare type I11 sols, L e . , those with particles greater than CY = 4. A ten to one ratio of 0.03 M sodium thiosulfate and an Oden sol, which provides condensation nuclei, were mixed and the resulting solution was made 0.1 M with respect to HCl by addition of the concentrated acid. After standing for half an hour, the solution was centrifuged and the residue redispersed in warm water. These sols were free of the background of small particles which characterized the Oden type sols and they contained a sufficiently high sulfur concentration for an accurate analysis. The size could be controlled by the time between the initial mixing and the centrifuging. We found ten minutes to half an hour provided a convenient range for our purpose.
Experimental The particle sizes were examined by both electron microscopy and light scattering. The electron microscope samples were prepared by placing a droplet of sol on a water cast collodion film and drying in air. The unprotected sulfur articles could be seen to evaporate in the electron beam of t i e microscope and just as in the case of sulfur aerosol particles12 this could be inhibited by sandwiching between two collodion films. I n practice we did not find this sandwiching necessary because the evaporated droplets always left a mark on the film which indicated its size. Measurement of the disymmetry of the light scattering a t 45 and 135' and the polarization at 90' indicated whether the sols consisted of small particles or not. This technique was used to confirm the ty e I sols. I n order to carculate the intrinsic refractive index from equation 1, i t is necessary to know c , n' - n, and n. c was determined by evaporating the sol to dryness, weighing the residue, igniting and weighing the final residue. The final residue was principally sodium chloride and the weight of sulfur was obtained by subtraching it from the weight of the initial residue. This analysis was checked by oxidation of the sol to sulfate with bromine-nitric acid and precipitation of barium sulfate. The difference in refractive index between the sol and water was measured with a Brice-Phoenix differential re(12) M. Kerker, A. L. Cox and M . Sohoenberg, J . CoEloid Sei., 10, 413(1955).
564
T. E. MOORE,R. W. GOODRICH, E. A. GOOTMAN, B. S. SLEZAK AND P. C. YATES
fractometer using the 5461 A. mercury line. From this was subtracted the difference in refractive index between water and sodium chloride solution of concentration equal to that in the sol. This second difference gives n~- n. F~~n, the refractive index of the medium, the value for the abovementioned sodium chloride solution was used.
Results The results are presented in Table 11. The intrinsic refractive indexes for type I sols range from 0.22 t o 0.29. The principal error for this group was in the analysis of the sulfur concentration which we estimate to be within 10%. The results are in agreement with the requirements of the theory for this size range. Oden measured the refractive index of some of his sulfur sols and from his data we have calculated an intrinsic refractive index of 0.25 which would indicate his sols also consisted of small particles. The results of type I1 and I11 sols (Table 11) also agree with equation 1. In the latter group and for one sol of the former, the experimental error arises principally in the measurement of the very
Vol. 60
small differential refractive index. The estimated are given in the tables for these cases, all the other cases the limiting error is in the sulfur analysis. A check on the consistencv of eauation 1 can be obtained from dilution exp&iment$. For a given size distribution, the intrinsic refractive index should be independent of concentration. Table I11 shows the effect of dilution on three sols. The intrinsic refractive index does remain constant in the course of the dilution which in one case is nearly 30-fold. TABLE I11 EFFECT OF DILUTION ON INTRINSIC REFRACTIVE INDEX Sol 5 Concn.
s 0.0030 of
[n1
.0024
0.16 .15
.0020
.17
.0014
.17
Sol 8 Concn.
of
s
0.039 .029 .022 .015
In1
0.11 .10 .ll .10
so1 12 Concn. of s
0.0151 .0059 ,0023 .00144 .OW56
[n1 0.26 -26 .26 .25 .25
EXTRACTION OF INORGANIC SALTS BY 2-OCTANOL. 11. COBALT(I1) AND NICKEL(I1) CHLORIDES AND BROMIDES. EFFECT OF ELECTROLYTES' BY T. E. MOORE,R. W. GOODRICH, E. A. GOOTMAN, B. S. SLEZAK AND PAULC. YATES Contribution from the Department of Chemistry, Oklahoma A . and M . College, Stillwater, Oklahoma Received September 1 , 1066
An analysis of the distribution coefficients of CoClz and NiCh between 2-octanol and aqueous mixtures with HC1 a t constant concentration has been made by studying the variations in the non-aqueous and aqueous phase activity coefficients with salt concentration. In approximately 5 molal acid the octanol-rich phase activity coefficient for CoC12remains nearly constant while that for NiC12increases rapidly, thus accounting for the difference in the extractability of the two salts and also their separation by 2-octanol extraction. Study of the effect of different valence-type chlorides upon the distribution coefficient of CoClz showed a marked de endence u on the s ecific extraction-promoting chloride present. The order of promoting effectiveness is HC1> LiCl > 8 a C b > Al& or (Cl&NCl. This parallels the order of extraction of the promoting electrolytes themselves. As predicted by the Born equation for ion charging, the distribution coefficients of CoBrz are greater than those of CoCl2 at the same concentrations because of the larger anion. The extraction of CoBrz from aqueous mixtures with LiBr, CaBrz, and AIBra does not depend greatly upon the valence-type of the promoting salt at equivalent concentrations (in contrast with the case of CoC12). An explanation for the separation of CoClzfrom NiClz by 2-octanol extraction is suggested.
The original experiments of Garwin and Hixson2 on the separation of C0C12 from NiC12 based upon the preferential extraction of C0C12 by 2-octanol from aqueous mixtures containing HC1 or CaC12 at high concentrations led to investigation of some of the factors affecting this and related 2-octanolsalt-water partition equilibria. One of the most important of these is the promotion of extraction by electrolytes having a common anion. The distribution coefficient k d for a solute is easily shown to be proportional to the ratio of the activity coefficients of the solute in the two phases h c KYIIYZ (1) where K is the equilibrium constant and y1 and y2 are the appropriate stoichiometric activity coefficients in the aqueous and non-aqueous phases, respectively. Since the distribution coefficient usually increases with increasing concentration of (1) Supported under Contract AT(11-1)-71 No. 1 with the U. 8. Atomic Energy Commission. (2) L. Garwin and A. N. Hixson, Ind. Eno. Chem., 41, 2208 (1040).
both the extracted salt under consideration and the extraction-promoting electrolyte, a study of the variation with concentration of y1 relative to y2 provides information about the nature and the relative importance of the interactions occurring in the aqueous and non-aqueous phases. The distribution coefficients of CoC1, and NiC12 in mixtures with HC1 (at constant concentration) were determined by equilibration of the aqueous mixtures with octanol. Ratios of the aqueous phase activities to the non-aqueous phase concentrations (equal to y 2 / K ) were then calculated from equation 1. In making the calculations the octanol phase salt concentrations were expressed as moles per 1000 g. of octanol water, and negligible solubility of the octanol in water was assumed. Activity coefficients of the solutes in the aqueous phases were taken from the data of Moore, et a2.8 Figure 1 shows the results obtained from equili-
+
(3) T.E. Moore, E. A. Gootman and P. Soc., 77, 298 (1055).
C. Yates, J . Am. Chem.
