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ANTHONY
J. PETRO
Vol. 64
the entropy change of reaction 1 a t 650', measured cies can be estimated from the force constants of BiC13 with Badger's rule. The frequencies estiby this study. The absolute entropies of the two gaseous species mated in that way are 210(1), 91(1), 155(2) and (Sumbers in parentheses are the can be calculated from estimated molecular con- 65(2) cm.-'. stant data. For BiBr the internuclear distance degeneracies of the vibrational mode.) The absohas been estimateds to be 2.48 A., and the funda- lute standard entropy of BiBra gas calculated from mental vibration frequency has been m e a ~ u r e d . ~those molecular constants is 116 e.u. a t 650'. When combined with the experimental values3 It was ,mumed that there was no electronic contribution to the entropy. These lead to a cal- for Bi, these entropies for BiBr and BiBra lead to a culated absolute standard entropy of 73.6 e.u. calculated entropy change at 650' for reaction 1 of 17 e.u. This is in good agreement with the for BiBr gas a t 650'. For I3iBrs the internuclear distances have been experimental value and provides additional evimeasured.'O The fundamental vibration frequen- dence that reaction l was indeed the equilibrium studied, and BiBr was the only important sub(8) D. I'. Stevenson, J . Chem. Phys., 8 , 898 (1940). halide species. (9) G. Heriberr:, "Molecular Spectra and Molecular Structure," Acknowledgment.-The author is grateful to Mr. Vol. I. 2nd Ed.. El. Van Nostrand Co., New York, N. Y.,1950. William E. Robbins who performed the experimen(10) H. A. Skinner and L. E. Sutton, Trans. Faraday Soc., 8 6 , 681 tal work. (1940).
PARTICLE SIZE DISTRIBUTION IN MOSODISPERSE SULFUR HYDROSOLS' BY ANTHONY J. PETRO Chemicals Research Division, Esso Research and Engineering Company Received April $8, 1960
The particle size distribution in monodisperse sulfur hydrosols has been investigated by a new instrument, the Coulter Counter. The hydrosols were prepared by the acid decomposition of dilute thiosulfate solutions and the particle sizes were measured independently by the Higher Order T-yndall Scattering method. Distribution curves were ronstructed from Counter data obtained a t increments of 0.02 p diameter. The results indicate that the distribution of particle sizes in these systems is relatively broad but single-peaked. Higher Order Tyndall Scattering was found to exist for mixtures of two monodisperse sols and it is concluded that this method is a measure only of the most populated particle size.
Introduction Monodisperse sulfur hydrosols, or colloidal suspensions of sulfur with a very narrow distribution of particle sizes, were first prepared by Barnes and LaMer in 1946.2 Further work by LaMer and his associates established the light scattering,3,4 and electrokinetic&properties of these systems, and the mechanism6-$ and kinetics'O of their production. The bulk of .the data indicates a very sharp distribution of prirticle sizes. Until recently there has been no method available which could be used to determine successfully the particle size distribution of these sulfur sols. The electron microscope is inapplicable because osmotic effects cause the particles, in the form of supercooled liquid A-sulfur droplets, t o rupture during preparation of specimens." In the past several (I) Portions of 1,his paper were read before the American Chemical Society, Division of Colloid Science, Boston, Massachusetts, April, 1959. (2) V. K . LaMer and M. D. Barnes, J . Colloid Sei.. 1, 71,79 (1946). (3) M. 13. Barnis, A. S. Kenyon, E. M. Zaiser and V. K. LaMer, ibid., 2 , 349 (1947). (4) I. Johnson rind V. K. LaMer, J. A m . Chem. SOC.,69, 1184 (1947). (5) R. €K. Smellie, Jr., and V. K. Lahler, THIS JOURNAL,68, 583 (1954). (6) V. K.LaMer and A. S. Kenyon, J . CoZloid Sei., 2 , 257 (1947). (7) E. M. Zaiser and V. K. Lahler. ibid., 3, 571 (1948). (8) V. K. Lahler and R. H. Dinegar. J . A m . Chem. Sac., 73, 4847 (1950). (9) H.Reiss and V. K. Lah'Ier, J. Chcm. P h y a . , 18, 1 (1950). (10) R. H. Dinegar, R. H. Smellie, Jr., and V. K. LaMer, J. A m . Chcm. SOC.,7 8 , 2050 (1951). (11) V. K. LaMer, private communication.
years a novel method has been developed for measuring particle size. The method is referred to as the Coulter Method, the instrument used being the Coulter Counter. 12,13 This method was used in the present work to determine the actual distribution of particle sizes in these preparations. Experimental Preparation of Sols.-Sols were prepared by adding to 480 ml. of distilled water, 10 ml. of 0.1 M HC1 and 10 ml. of 0.1 M Wa2S201,thus making the concentration of each reagent 0.002 M . The flask was thoroughly shaken and placed in a water-bath thermostated at 25 ==! 0.1' for the desired length of time, usually 8-12 hours. After the sol had developed, a sample was removed and the particle size was determined by the Higher Order Tyndall Scattering (HOTS) Method according to Johnson and Lahler.' Another sample was treated as described below for measurement of particle size distribution by the Coulter Counter. Particle Size by Light Scattering.-Monodisperse sols were observed3 to scatter white light into its component colors, the number and position6 of the red hues being a function of the particle size of the suspended sulfur.' Bx referring the angular positions of the scattered red "orders to a set of standard curves, measurement of particle size by this method can be accomplished in less than one minute to within 0.01 pin diameter. The scattering curvea used in the present work were those of Petro and Sme1lie.l' This set of curves is somewhat different from that published by Johnson and LaMer,4 but i t waa found to be completely reproducible (12) W. C. Coulter, "High Speed Sutomatic Blood Cell Counter and Cell Size Analyzer," paper presented a t the National Electronics Conference, Chicago, Illinois, 1956. Also, R. H. Berg, ASTM Special Tech. Publ. No. 234,245 (1959). (13) "Theory of the Coulter Counter," Coulter Induatrial Sales Co.. Elmhurst, Illinois, 1957. (14) A. J. Petro and R. H. Smellie, Jr., to be ~iublished.
Oct., 1960
P a R T I C L E SIZE
DISTRIBUTION Ih’ %f OKODISPERSE S U L F U R HYDROSOLS
as long as two precautions were taken in preparing sols: namely, stock solutions of thiosulfate more than 5 days old could not be used, and the stock solutions must be prepared with freshly boiled distilled water. Otherwise, completely non-reproducible particle sizes are obtained, the scattering data corresponding to two different sizes. This scattering data has been verified independently’s by measuring light transmission as a function of wave length. Particle Size by Coulter Counter.-The main feature of the Coulter Counter is the tiny aperture drilled through a sapphire wafer which is cemented into the wall of a glass tube. This aperture allows completion of the electrical between an inner and an outer electrode through an electrolyte solution. In the present work, an aperture 30 1 in diameter was used. As a particle passes through the aperture it displaces its own volume of conducting electrolyte solution, causing a momentary change in conductivity of the circuit. The pulse is amplified and counted if its magnitude is above a preselected threshold value. The particles are made to pass through the aperture by establishing a pressure differential across the orifice as a result of displacing the mercury in a manometer connected in series. As liquid (and particles) flows through the aperture, the mercury returns to equilibrium and in so doing interrupts the start-stop connections in the manometer. In this way a reproducible sample volume is counted and each count is automatic. A typical count, a t a given threshold setting, taken with the 30 p aperture and on a 50 pl. sample volume, requires ea. 15 sec. for completion and may register ae many as 100,000 counts. The Counter was calibrated with a sample of monodisperse polystyrene latex obtained from the Dow Chemical Company. The particle diameter was reported to be 1.171 p with a standard deviation of 0.0133 p. However, upon comparing the HOTS of this material with the data of Plesner and LaMer’S the diameter appeared to be 0.94 p. This apparent discrepancy was resolved when it was realized that the scattering angles of Plesner and LaMer were the supplements of the angles read on the apparatus used in the present work and in previous work on sulfur s0ld.~J4 The present instrument defines 180’ as complete transmission and 0” as complete reflection. The number of particles counted a t a given threshold setting was the average of a t least four trials, the electrode polarity being reversed after each count. The particle size corresponding to the threshold setting was calculated by the relation~hip’~ d = kt’/a where d is the diameter, t is the threshold value in dial units, and k is a proportionality constant which was found to be 1.30. Differential particle size-distribution curves were constructed by plotting t A.n/Ad us. d . For the present work, a sample of sulfur sol was diluted with three times its own volume of 0.9% NaCl solution. This dilution ratio was chosen in order to obtain optimum values of conductivity ancl particle concentration. Counts were taken on the solution a t intervals of ca. 0.02 I.( diameter. Two types of sols were produced for study. One had a “poor” scattering spectrum, i.e., there was no correspondence to a set of angles for a single particle size, and the second type had a “good” spectrum. The former was prepared merely by not boiling the distilled water prior to preparing the stock thiosulfate solution.
Discussion In order to interpret the results of this work it is desirable to review briefly some of the pertinent aspects of monodisperse sulfur hydrosols. Immediately upon mixing the reagents, elemental sulfur begins to be produced. This sulfur, however, remains in solution until a critical, reproducible, supersaturation level (ca. 3.1 X lo4 g. at./1.)lo is attained. At this stage, spontaneous nucleation occurs, producing ca. 4 X lo6 particles/ml. Continued formation of sulfur is so slow, because of the low concentrations of reagents, that further nuclea(15) R. Toggenburger. M.S. Thesis, Trinity College, 1956. (16) I. W. Plenner and V. K.LeMer. J . PoEymer Sei.. Pa, 147 (1957).
1201
I
HOTS I
loo--
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I
I
I
I
I
,
I
I
0.9
1.0
1.1
1.2
1.3
I
I 1
1
I
0
0.7
0.8
d
Fig. 1.-Particle size distribution curve for “poo_r” sol. HOTS results; -, Coulter Counter results. d is in microns.
-,
I
I
I
I
I
d .
Fig. 2.4’article size distribution curve for “poor” sol. -, HOTS results; -, Coulter Counter results. d is in microns.
tion does not take place. The particles already formed grow uniformly by diffusion of newly-produced sulfur onto the particle surfaces. The key to monodispersity, then, is the control of the rate of reaction so that nucleation occurs once, or only over a very brief span of time. One experimental problem had to be resolved before completely accepting the results obtained in this work. The Counter requires a conducting medium for operation. The effect of salts on the electrokiiietic properties5 and the kinetics of the reaction5J7would lead one to suspect that dilution of the sol with NaC1 solution may significantly alter the system. To answer this question, a sample of counting solution was rechecked by the HOTS two hours after preparation and was found to show exactly the same spectrum as did the original undiluted sol. That is, not only was agglomeration undetectable as was any particle size increase due to salting-out dissolved sulfur, but the pH (17) R. H. Dinegar and R. 13. Smellie. Jr., J. Colloid Sci., 7 , 370 (1952).
ANTHONY J. PETRO
1510 I
I
I
I
-
d .
Fig. 3.-Particle size distribution curve for “goo$” sol. -, HO‘I’S results; -, Coulter Counter results. d is in microns. 5c
I
I
a
d.
Fig. 4.-Particle size distribution curve for sol grown while ssirred slowly. --, HOTS results; -, Coulter Counter resultri. d is in microns.
44-
30
e 0 06
0.8
IO
1.2
1.4
1.6
-
1.8
20
2.2
2.4
2.6
d .
Fig. 5.--Parf;icle size distribution curve-for sol gromq in the presence of 0.15 M (0.9%) NaC1. d is in microns.
increase (2.8 to 3.4) resulting from dilution by the salt solution effectively stopped the formation of
Vol. 64
further sulfur and, hence, stopped further growth of the particles.’’ Therefore, the length of time taken for the complete counting of the sample was immaterial. Figures 1 and 2 show typical distributions obtained for “poor” sols. The diameter values measured by the HOTS are indicated by the dotted lines, the smaller values corresponding to obtuse (90
