Latex particle size analysis

JOUI~NAL OF COLLOID .~ND INTERFACE SCIENCE ~ 5 , 3 8 1 - 3 8 8

(1967)

Latex Particle Size Analysis I. Flow Ultramicroscopy JOHN A. DAVIDSON, CHRISTOPHER W. MACOSKO 1 AND EDWARD A. COLLINS The B. F. Goodrich Chemical Co. Development Center, Avon Lake, Ohio 44012 Received April 5, 1967; revised June 7, 1967

INTRODUCTION Accurate determination of particle size and size distribution of synthetic polymer latexes is vital to most latex research and development. Presently, the most commonly accepted absolute method of determining latex particle size is by electron microscopy. This method also offers direct observation of particle shape and clustering. However, there are several disadvantages and limitations. First and foremost is the fact that only dried latexes or replicas of them are examined. Other problems are the representative sampling, problems associated with instrument calibration and spherical aberration of the lenses, and dimensional changes of the particle in the electron beam (1, 2). Finally, the electron microscope is not especially suited for practical routine measurements. Classically ultramicroscopes have been used extensively in colloid studies to determine particle size. This was especially true before the advent of the electron microscope. With the use of the ultramicroscope, the number concentration and volume average particle size can be determined by counting the number of particles in a stationary volume. However, there are many inconvenienees and systematic errors, from Brownian motion and other sources, that have kept the ultramicroscope from wide-

spread use. Most of these difficulties disappear if the number of particles are counted in a knowrt volume flowing through the field of view of the ultramicroscope as reported by Derjaguin and Vlasenko (3). Although the flow ultramicroscope has been used to study the properties of aerosols and eolloidM suspensions, it has not previously been applied to the measurement of synthetic latex particle size. This paper reports such measurements on polystyrene, polyvinyltoluene, and polybutadiene-styrene latex, and in addition discusses particle statistics and measurement of errors involved in the technique. EXPERIMENTAL

The instrument used in this investigation is a modification of the flow ultramicroscope reported previously (3). Our instrument employs the conventional slit ultramicroscope optics and the flow cell design of Derjaguin and Vlasenko. The basic instrument is shown in Fig. 1. A schematic diagram of the principle is illustrated in Fig. 2. In the flow ultramicroscope a highly diluted latex is pumped at a known rate through a glass tube aligned along the optical axis of a microscope so that the particles are viewed as they move towards the observer. As the particles pass through the illuminated zone, a flash of light is perceived by the observer. By counting the 1Present address, Department of Chemical number of such flashes in a defined area for a Engineering and Chemical Technology, Imperial given time interval, the number concentraCollege, London, S.W.F. England (summer em- tion and a volume average particle diameter ployee, June-Sept. 1966). can be eMculated. 381

382

DAVIDSON, MACOSKO, AND COLLINS

The instrument consists of a Bausch and Lomb 160 ram. microscope tube (M) mounted on a specially constructed optical bench with the flow cell and slit assembly. The flow cell (F) is capable of movement in three directions and the microscope and cell

assembly can be displaced with respect to the slit. The light source (L) consists of a 1000 watt water-cooled high-pressure AH6 mercury lamp equipped with a parabolic reflector (R). The source is focused on an adjustable slit (S) the image of which is in

F~o. 1. Flow ultramicroscope

383

L A T E X P A R T I C L E SIZE ANALYSIS

~

Observer Retie le

l

(E)

ii lOx

z

Eyepiece

X i : ~y lOx Objective

FI ~ J i l l

Counting

Square

I~--

IiI '

-

~F)CeI! Dispersion

~-~..--I,

~P

Power Syringe ~Y)

Reticle

Pattern

FIG. 2. Flow ultramicroscope schematic

turn projected into the cell by a 10 N microscope objective (0). The counting area is defined by ~a reticle in the eyepiece (E). The colloid is driven through the instrument by a Bronwill Influsion pump (P) equipped with a special syringe (Y) which has an " 0 " ring sealed plunge~ in a precision glass tubing barrel. The qperation of the instrument is straightfg~w, ard. The latex to be measured is diluted with "colloid free" water, distilled under nitrogen and condensed at 80°C. in Teflon tubing. A suitable operating eoncentration gives about one particle every three seconds of flow through the counting square. Dilutions;therefore, range from 10-4 to 10-s g./em2 and should be freshly prepared. The pump is filled and its speed is normally set at 6.6 N 10-4 em2/sec. The slit width and the cell position are adjusted to obtain the best contrast in the microscope field. Low power (20X) is used to center the cell and is helpful in checking the latex for uniform mixture. A 10X objective and 10X eyepiece containing the crossed reticle are used for counting the particles. The counting square defines an area of 196 sq. microns. Counts are made by direct observation. The operator counts particles in 20 second in-

tervals using a hand counter and records each interval. Short intervals are best for preventing eye fatigue (4). Three hundred counts, requiring a time of about one-hMf hour, are usually taken per sample. The seven polystyrene latex samples ranging in size from about 0.17 to 1.20 g and the two polyvinyltoluene latex samples having a size of 2.0 g and 3.0 g used in this investigation were obtained from the Dow Chemical Co., Midland, Michigan. The butadienestyrene latexes were prepared from seeded recipes described elsewhere (5). The samples are listed together with their diameters in Table II. The particle diameters of all the latex samples used in this investigation were determined with an RCA EML electron microscope using a beam voltage of 50 kv. The microscope magnification was checked after each sample using a diffraction grating replica. Standard sample preparation techniques using copper grids covered with collodion and a light film of evaporated carbon were employed. Micrographs were taken at several different locations on the sample grid. Care was taken to expose each plate from a different grid opening. Particle diameters were determined from these mierographs with a Zeiss TGZ-3 Particle Size Analyzer counting 500-2000 particles. THEORY The particle concentration and average diameter can be determined from the flow ultramicroscope counts by simple fluid mechanics and geometric considerations. For the flow cell used in this study the Reynolds number was 0.3. Since the entrance effects for our system are negligible, the flow through the inner tube should be laminar. If we assume the particles flow at the fluid speed, their velocity profile should be parabolic. This parabolic distribution was verified experimentally and the results are shown in Fig. 3. The velocity v of the particles flowing through the counting square is computed from the bulk flow rate Q of the pump, the radius R; of the flow tube, and the assumption of laminar flow. The counting square of dimension 1 is set at the center of the inner flow tube and thus at a maximum

of the

384

DAVIDSON, MACOSKO, AND COLLINS

0 -"~ ~

average ultramicroscope diameter D ~ be found from

Experiment

can

Theory

1.2~

Substituting Eq. [4] into Eq. [3] and rearranging gives:

,oi-

3

D um -

).8__

6VC 7rNp "

[5]

If we now substitute for V and let n = N / t Eq. [5] reduces to

!0.6 --

3

Dum -

0,4--

6vl2C

~-np

,

[6]

and substituting v.... for v results in

.

3

d.

o,.

Dum -

o. . . . . . .

r (cms)

velocity profile. It is assumed that all the particles passing through the counting square are at v.... since this area is small with respect to the total cross section, that is, i2/TrR~ 2 < 2 X 10-5. From the Poiseuille equation 2Q 7rRi 2

[11

The volume V of solution that flows through the counting square in the counting time interval t is given by: V

= vl~t.

[2]

Using V, the concentration C of latex, the density p of the solid, and the number N of particles counted in the time interval, the average particle volume V~ can be computed from Eq. [3]. Vp -

VC Np "

[7]

or

FIG. 3. Velocity profile of particles in the flow ultramicroscope. The solid line represents a parabolic distribution as calculated from theory, the circles are points determined experimentally using Dow Polystyrene latex LS-449E. r is the distance (in centimeters) of the particle from the center of the flow tube.

Vm~ -

12I~QC Ir2Ri2pvt

[3]

If spherical particles are assumed, the

D~

=

,

[8]

where K = 1212/~r2R& The particle size D ~ so Obtained is an average volume diameter and is equivalent to

{ xN'-v: Dum =

ZNi

J

where N~ is the number of particles of diameter D~. The most commonly reported diameter obtained with the electron microscope is the number average D~ defined as: Dn =

Z N i D~ ZN~

COUNTING STATISTICS

In viewing the colloid a random distribution of particles is observed. It follows from this random pattern that the number of counts observed during any counting interval will also vary in some statistical manner. The best theoretical description of the variation in the counting interval is a Poisson distribution. This was verified experimentally over 191 counting intervals of 20 seconds each with a monodisperse polystyrene latex, and the results are shown in Fig. 4. Satisfactory agreement is obtained with a Poisson distribution.

385

L A T E X P A R T I C L E SIZE ANALYSIS

--

40--

....

E XPERII~ENTA THEORY

error in each variable in Eq. [7]. If it is assumed that the errors are independent, Taylor's expansion method can be used to find the total error in D~,~ according to:

L

(POISSON)

35--

S ) = f J S J + f d S d + . . . f~2Sn2, u) _J < :> cc w pz

[9]

where S~ is the standard deviation of the variable X and f~ is the partial derivative of D~m with respect to X. Taking the partials of Eq. [7] and simplifying terms results in:

30 ,---.

z5

2c z pz

=

i."

C-v [10]

o d

T -

4SR

S~

Sn 2\

I(

z

I ....

I 3

o NO.

I 4

I,

OF P A R T I C L E S

T

j ,[, B OBSERVED

IO

I[

12

13

IN ZOSEC. iNTERVAL

FIG. 4. Comparison of observed particle count with a Poisson distribution shown as counting intervals versus number of particles observed in 20 sec. interval determined with Dow Polystyrene latex LS-057A. at a concentration of 2.44 X 10-7 g./cm. 2 and a flow rate of 6.63 X 10-4 cm.3/see. To reduce the data to frequency % divide each interval by 191 and multiply by 100. Solid lines represent experimental data; dashed lines are calculated from a Poisson distribution.

In normal operation, concentrations and flow rates are adjusted to give 0.3 particle per second through the counting square. It was observed that the particles remained visible, i.e., passed through the light beam in less than one second. Particle coincidence is not important since at the low concentrations employed the probability of two partides' appearing as one is small. The apparent size of the largest particles appeared to be about 3 ~ in diameter in the microscope field. Using a Poisson model, the probability that one or more particles are obscured by a 3 ~ particle is 0.5 %. Thus, all average counts should be increased by this factor, however, since this increase was less than 1% in all eases, it was disregarded. INSTRUMENT PERFORMANCE

The total error for the ultramicroscope diameters can be estimated by finding the

The standard deviation of each variable was estimated as follows. The size of the counting square l was determined with a stage micrometer and is within 4-0.4%. The inner flow tube Ri was measured with a traveling microscope to i 0.5%. Much care was taken to calibrate the pump flow rates Q. It is important to eliminate any short-term oscillations in flow, since the counting intervals are only 20 seconds in length. The pump was connected to a precision bore capillary tube 30 inches long and 0.030 inch in diameter and the position of the meniscus of the fluid in this tube measured with a cathetometer as a function of time over intervals of 10-30 seconds. The flow rates calculated from these data had a variance of less than 2%. The reported values of density for polystyrene (2) and polyvinyltoluene (6) are 1.055 -4- 0.5 % and 1.026 4- 0.5%, respectively. A value of 0.933 4- 0.7 % was used for the butadienestyrene (7). The concentration C depends mainly on the accuracy of the total solids measurements. The error from dilution and total solids determinations was estimated to be 4-2.0%. There is also a possible error in centering the counting square at the peak of the velocity distribution, i.e., in the tube center. However, since a 10% centering error yields only a 1% error in v.... this was disregarded. The largest uncertainty'is in n, the average particle count/second, and is due to the statistical variation. For a normal 300 particle count, n will be known to 4-6 % at

386

DAVIDSON, MACOSKO, AND COLLINS

7 0 % cmflidence level or ± 1 2 % at 9 5 % confidence level. Solving Eq. [10], the u n c e r t a i n t y in D ~ was f o u n d to be + 2 . 3 % . This m e a n s t h a t it is possible to d e t e r m i n e a 3000A particle to w i t h i n + 7 0 A at a 7 0 % confidence in 300 counts, requiring less t h a n a half h o u r counting time. B y increasing t h e counts to 1000 for the same particle size it is possible to increase the accuracy to ± 4 5 A . TABLE I TYPICAL :RESULTS FOR LS 057A LATEX Conc. (g./c.c.)

Pumping speed (c.c./sec.)

Total number of particles counted

Operator 1, flow cell B, AH-6 lamp 2.44 X 10-7 6.46 X 10-4 93 5.09 X 10- 7 6.46 X 10-4 182 5.09 X 10-7 4.90 X 10-4 69 Average value obtained, trials weighted number of particles counted, is 0.275 ~.

Diameter ~u)

0.281 0.275 0.267 as to

Operator 2, flow cell A, 5 ampere carbon arc lamp 2.54 X 10-7 6.59 X 10-4 146 2.54 X 10-7 6.59 X 10-5 118 1.02 X 10-7 12.36 X 10-4 117 Average value obtained, trials weighted number of particles counted, is 0.274 ;~.

0.278 0.279 0.265 as to

T h e flow ultramicroscope with the A H 6 m e r c u r y light source has a lower particle size limit of a b o u t 1500A. A 5-ampere c a r b o n arc source was also tried w i t h no i m p r o v e m e n t in resolution a n d h a d t h e d i s a d v a n t a g e of being r a t h e r u n s t a b l e . P r e l i m i n a r y studies w i t h a laser light source i n d i c a t e d t h a t the range of the u l t r a m i c r o scope could be extended to latex particles well below 1000A. T o verify t h a t t h e flow t h r o u g h the i n n e r flow t u b e was t r u l y l a m i n a r , the particle velocities were d e t e r m i n e d at various p o i n t s across the t u b e d i a m e t e r using D o w polys t y r e n e LS-449E latex. T h e flow cell was m o v e d to various positions i n the X direction (refer to Fig. 2). T h e distance from the center was d e t e r m i n e d w i t h a precision micrometer. F r o m 30 to 70 counts were m a d e at each p o i n t a n d the velocity was calculated using the Poiseuille e q u a t i o n . T h e v.... was based on more t h a n 800 counts. T h e fit of the six e x p e r i m e n t a l points to the expected p a r a b o l a is s h o w n in Fig. 3. T e s t i n g the Poisson d i s t r i b u t i o n of the c o u n t i n g i n t e r v a l s was done with D o w LS-057A p o l y s t y r e n e latex. A c o n c e n t r a t i o n of 2.44 X 10-7 g./cm, a a n d a p u m p i n g speed of 6.63 X 10-~ cm2/sec, were used.

TABLE II COMPARISON OF ELECTRON MICROSCOPE AND F L O W ULTRAMICROSCOPE DIAMETERS Electron microscope data Ultramicroscope data Latex sample

D~ (~) Polystyrenes LS-055A LS-057A LS-061A LS-063A LS -449E LS -464E LS-1028E

Found

Dow reported

Du,neb Cu) [ No. of meas.

Dn (,u)

~

Dame (,")

No. of meas.

Aug Dum(~)

Total num berof count

0.1881 0.2638 0.3646 0.5567 0.7962 1.3046 1.0992

0.0076 0.0060 0.0079 0.0108 0.0083 0.0158 0.0159

0.1884 1,065 0.2640 557 0.3648 438 0.5569 373 0.7964 85 1.3049 142 1.0993 106

0.1770 0.2617 0.3499 0.5101~ 0.7646 1.0867 1.1827

0.0106 0.0144 0.0198 0.0267" 0.0624 0.2348 0.636

0.178 1,259 0.262 453 0.351 767 0.511 a 4,448 a,~ 0.769 269 1.126 1,280 1.186 645

0.171 1,215 0.2795 2,048 0.365 725 0.594 604 815 0.849 1.242 1,229 1.213 614

2.049 2.9583

0.0180 0.0150

2.0501 2.9588

2.0240 3.0356

0.1088 0.1904

2.032 3.048

583 572

2.211 3.128

625 702

0.2095 0.3865

0.02871 0.0428ii

1,198 650

0.255 0.443

692 748

Polyvinyl toluene:

L -6064-36 EP-1358-38

35 23

Polystyrenebutadiene

132-47-146B 132-47-147A

M

Average of 3 trials reported. b Supplied by J. W. Vanderhoff of the Dow Chemical Co.

.213 .392

LATEX PARTICLE SIZE ANALYSIS A good measure of the instrument performance is indicated by the data sho~ua in Table I. These data were obtained b y two operators over a period of several months. Different pumping speeds, concentrations, light sources, and flow cells were employed. However, the diameters determined have a deviation of less t h a n 60A. The particle diameters of the D o w polystyrene latexes as determined by electron

o

1,2

i1.0

E o.s

@ o.i

o.,

o.

/ I

0.2

I

I

0,4

i

0.6 Dume

0.8

I

1,0

I

1.2

microscopy in this investigation were in good agreement with the literature values (8) and are listed in Table II. Inspection of these data shows t h a t the standard deviations of our results are somewhat higher. To some extent this is due to the larger number of particles counted (9), This is especially true in the case of our sample of LS-464E, which was found t o contain a number of fine particles. A recalculation of the data for this sample leaving out all the particles not distributed symmetrically about the mean raised the D,~ value by only 0.064 ~ but reduced the a value from 0.2348 to 0.072 ~. The total number of particles counted was 1,280 and 1,178, respectively. Since the D~ value reported by Dow for this latex is higher than both our ultramicroscope and electron microscope values i the discrepancy is probably due to the different samples examined in each l a b o r a t o r y . The particle diameter results D~m obtained with the flow ultramicroscopes:for all the samples used in this investigatiofl a r e shown in Table II. Included in this table are: ultramicroscope volume averages D~,mlcalculated from electron microscope data. The correlation between the flow ultramicroscdpe and our electron microscope diameters is shown in Fig. 5. A least squares fit Of these data gives the equation.

[microns)

FIO. 5. Correlation of particle diameters deter-

D~m = 1.036 D u ~ ~- 0.03U micron,

mined with the flow ultramicroscope Du,~ and the electron microscope D~.... O--Polystyrene and polyvinyl toluene; ~--poly-butadiene-styrene.

with a z value of 0.016 and 0.020 for the slope and intercept, respectively. A t 90% con-

TABLE EFFECT

387

OF AGGLOMERATION

III

ON FLOW

ULTRAMICROSCOPE

DIAMETERS

Optical microscope data:

The0re:tical :

_ Latex sample

Dam

LS -449E

0.849

LS-464E LS-1028E L-6064-36

1.242 1.213 2.211

EP-1358-38

3.128

No. of separate particles counted

1189 647 858 969 1323 725 1628 846

Experimental

Frequency of aggregation in % by no. Number of particles in aggregate:

] Dnu~m ~ 1 Dam L'~mg 7 or more (%) (%)

~o-i

Singlets Doublets 1

?riplet 3

Etc. 4

76.92 80.35 71.5 98.15 89.0 90.6 91.6 93.3

3.55 4.33 7.45 0.1, 1.36 1.65 1.29 0.83

0.74 0.02 2.10

0.2

0.53 0.28 0.31 0.35

0.1 0.l 0.( 0.1

18.75 15.30 16.65 1.75 8.47 6.63 6.45 5.2

5

6

0.23

1.86

0.06 0.11

0.56 0.69 0.18 0.11

8.6 7.7 16.5 0.7 6.3 5.4 3.8 3.6

10.4 10.3 2.3 8.8 2.6

388

DAVIDSON, MACOSKO, AND COLLINS

fidence level the slope of this plot is greater than 1. One possible explanation for the larger diameters obtained with the flow ultramicroscope is the presence of agglomerates. It has not been possible to distinguish between agglomerates in the latex suspension and those formed during sample preparation for electron microscope examination. This same discrepancy between the relative particle volume average determined from polymerization particle growth calculations and the electron microscope volume averages has been previously observed in a series of seeded butadiene-styrene latexes (5). An optical microscope was used to examine the size and number of aggregates independently in the latex samples having a diameter greater than 0.848 micron. A drop of dilute latex was placed in a Spencer "Bright Line Hemacytometer" and the number of singlets, doublets, triplets, etc., were counted using 300X to 500X magnification. Only those aggregates which appeared to be permanent were recorded. The results of this study are shown in Table III. The agglomeration results for LS-464E are in good agreement with those reported by Gillespie (10). The existence of agglomerates in monodisperse polystyrene latex has also been suggested by the photo sedimentation studies of K a y and Jackson (9). These agglomeration data can be used to explain the discrepancy between experimentally determined flow ultramicroscope diameters D ~ and those calculated from electron microscope data D . . . . By assuming that D ~ , is based on a measurement of all particles as singlets, whereas D~m is based on a count of the aggregates, we can obtain a theoretical ratio of D ~ to D ~ according to: Theoretical

(D~,~/D~,~o) 3 Z ( n l ~ 2n2 . . . . in~) ~ ( n l + n~ ~- . . . . nil)

where nl = number of singlets; n2 = number of doublets; n3 = number of triplets, etc. The theoretical values are compared with the experimentally determined ratio in Table III. The reasonably good agreement indicates that agglomeration is of the right order of magnitude to account for the slightly higher particle diameters obtained with the flow ultramicroscope and suggests that the values so obtained represent more closely the true size of particles in the latex state. ACKNOWLEDGMENT The authors wish to acknowledge the assistance of Mr. F. Zemanek in the fabrication of the instrument and are indebted to the B. F. Goodrich Chemical Company for permission to publish this work. We also wish to thank Dr. John W. Vanderhoff of the Dow Chemical Company for supplying the Electron Microscope Volume average diameters of the Dow latexes used in this study and for

his constructive criticism of the manuscript. REFERENCES 1. BR.A-DFORD,E. B., AND VANDERHOFF, J. W.,

151st American Chemical Society Meeting, March 22, 1966, Pittsburgh, Pennsylvania. 2. McCoRMICK, I-I. W., J. Colloid Sci. 19, 173 (1964). 3. DERJAGUIN, B. V., AND VLASENKO, G. YA., J. Colloid Sci. 17, 605 (1962).

4. BVRRELLS, W., "Industrial Microscope in Practice," p. 92. Fountain Press, 1961. 5. WILLSON, E. A., MILLER, J. R., AND ROWE, E. H., J. Colloid Sci. 3,357 (1949). 6. BOTJNDV,R. H., ANDBOY~R, R. F., "Styrene; Its Polymer, Copolymers and Derivatives," p. 1239. Reinhold, New York, 1952. 7. BRANDRUP,J., AND IMMERGUT,E. H., "Polymer Handbook," p. vi-61. Interscienee Publishers, New York, 1966. 8. BRADFORD, E. B., AND VANDERHOFF, J. W., J. Appl. Phys. 26, 864 (1955). 9. KAY, B. I~., AND JACKSON,M. R., 151st Ameri-

can Chemical Society Meeting, March 22, 1966, Pittsburgh, Pennsylvania. 10. GILLESPIE,W., jr. Colloid Sci. 18, 35 (1963).