I
A. B. LOEBEL Research Laboratories, National Starch Products, Inc., Plainfield, N. J.
Determination of Average Particle Size of Synthetic latices by Turbidity Measurements T H E increasing interest in synthetic latices in the paper, paint, and other industries has created need for a rapid and reproducible method of measuring the average particle size of polymeric dispersions, as correlations between performance and particle size have been shown to exist. The use of Tyndall spectra-the variation of scattered light with wave length-as a measure of particle sizes was first suggested by Heller and others (2-4). In general, the turbidity, T , of any system is an exponential function of the wave length, A, such that T = f ( l / h n ) . Theoretically, n = 4 for particles smaller than 0.1 X. Above this diameter, n decreases with increasing particle diameter. The value of n can be determined by measuring the turbidity a t various wave lengths using a spectrophotometer, and plotting log 7 us. log A . The slope of the straight line is equal to n. I t is possible by using monodisperse samples of known diameter to correlate n with the particle diameter, D , and thus calibrate the technique. A linear relationship exists between n and log D. Examination of the calibration curve would indicate that a particle diameter of 1600 mp ( n = 0), represents the upper limit of this technique. For calibration, the Dow monodisperse polystyrene latices have been used ( 7 ) . Because latices prepared by the usual
Table I.
1/1
1/250 1/2500 1 /5200 1/40,000
LS-040-A 15-N-23 LS-055-A LS-057-A 15-N-7 LS-061-A LS-063-A LS-067-A
n 4.37 3.73 3.20 3.02 2.29 2.63 1.58
88
138 188
264 340 365 557 1171
..
zk 0 . 1 7 =k
0.03
=t 0.08
0.03 0.11 =t 0 . 1 0 ;t ;t
zk 0.08
..
emulsion polymerization techniques are not monodisperse, but have a distribution of particle sizes, it is necessary to determine what type of averaging is affected by this technique. Consequently, mixtures of the Dow monodisperse latices were prepared and the apparent particle size was determined from the plot of log T us. log X. The number, b,, weight, b,, and z, b,, averages were calculated, ZniDi
6,==
-
Zn.D.4
D , = Zni A Di3
bz
Z n i Di6 Zni Di4
~
The I average most closely correlated with the apparent particle size (Table 1). The effect of this type of average is such that a relatively few (in number) large particles can give an average many times greater than the mean. For example, one 600-mp particle in 5000 particles of 90-mp diameter will give a
Wt. of 560-Mp Particles Wt. of 90-Mg Particles
b,
1/0.004 1/1 1/10 1/21 1/161
325 90 90 90 90
6,
E,
bobad
Millimicrons 560 325 135 110 95
560 495 270 195 110
500 430 270 185 105
Number Average Particle Diameters of Synhetic Latices Related t o n Electron Micrograph Tyndall Spectra s o . of
Polymer Composition Styrene Vinyl acetate Vinyl acetate-ethyl acrylate Vinyl chloride-acetate Vinyl acetate
1 18
Sample
Particle Dia.. M p
Particle Diameters for Mixtures of Monodisperse Latices
No. of 560-Mg Particles No. of 90-Mg Particles
Table II.
Dow
particles counted 75 115 75 50 50 50 25
INDUSTRIAL AND ENGINEERING CHEMISTRY
b,,
bll,
mp
35 45 90
92 120 250 400
n
4.0 zk0.13 3 . 4 zko.10 2.95 0.05 2 . 6 7 i0 . 0 5 2 . 5 7 zk 0 . 0 5 1 . 6 5 0.05 1.25 i 0 . 0 5
* *
mg 120 180 250 300 330 630 840
z average of 200 mp. In practice, latices do not consist of large and small particles, but rather have a continuous skew distribution. A mixture of this type was prepared and gave the expected results. The question of the limitations of this type of averaging is somewhat minimized by the fact that extremely large-Le., greater than 1600mp-particles do not affect the value of n appreciably, and latices prepared in the usual manner will all have approximately the same distribution. Therefore, we can feel confident that samples showing larger z average particle size will have an equivalently larger mean particle size. -4series of emulsions prepared by the usual polymerization techniques was examined by electron-photomicrography, the particles counted, and D,’s calculated. Calculation of D, is not practical, because the high order dependency would require sampling an extremely large population. Because practical interest is in the number average, a calibration curve was set up correlating 6, with n (Table 11). A straight line is once again obtained with the same intercept but a somewhat different slope. This difference in slope might be attributed to the difference between b, and b,. Conclusions
Determination of the particle size of synthetic latices from the slope of the plot log turbidity us. log wave length appears to yield an average strongly weighed by the diameter (D‘ - D 9 . However, particles above a certain limiting size (ca. 1500-mp diameter) are not counted in the population. A number average can be obtained by calibrating the slope against a set of samples whose number average particle size is known, and assuming the size distribution is similar for all samples. The change in slope with particle size is proportional to the particle size. Literature Cited (1) Bradford, E. E., Vanderhoff, J. W., J . Appl. Phys. 26, 865 (1955). (2) Heller, W., Klevens, H. E., Oppenheimer, H., J.Chem. Phys. 14, 566 (1946). (3) Heller, W., Vassy, E., Zbid., 14, 565 (1946). (4) Heller, W., Vassy, E., Phys. Rei. 63, 65 (1943).
