MEASUREMENT O F PARTICLE SIZE O F LATEX
357
gives high values for the apparent solubility in neutral solution, probably owing to peptization of the precipitates. REFERENCES Compt. rend. 207, 6327 (1038). (2) JOHNSON ASD HULETT: J. Am. Chem. SOC.55,2258 (1933). (3)_hIEES A N D PIPER:Phot. J. 52, 221 (1914).
BEDEL: EL:
ADSORPTION AREAS I N T H E SOAP TITRATION OF LATEX FOR PARTICLE-SI ZE MEASUREMENT E. A . WILLSOT\’, J. R . hIILLER,
AND
E. H. ROWE
The R . F . G o o d n c h C o m p a n y , Research Center, Biecksvzlle, Ohio Keceii ed M a y 6 , 1948 INTRODUCTION
There are several soap titration methods for measuring the particle size of a latex. They have been described by Harkins and Adinoff ( 5 ) , by Maron, Elder, and Ulevitch (9), by Williams, Meehan, and Kolthoff (ll),and by Klevens (8). The quantity of adsorbed soap as measured by the several methods of soap titration is nearly the same, except for experimental differences, since the end point in each titration is a concentration of soap in solution equal to the critical micelle concentration (C.M.C.). The importance of subtracting the soap in solution from the total soap to obtain the quantity of adsorbed soap was first pointed out by Maron (9). Translating the quantity of adsorbed soap to a value for interfacial area involves the assignment of an adsorption area for the soap molecule. The adsorption area for sodium stearate mas assumed by n I m n (9) to be khat of an oriented, close-packed, straight-chain hydrocarbon molecule (21 sq. A.), and he experimentally determined the adsorption areas of other soap molecules by comparing them with sodium stearate. Klevens (8) used the value of 28 sq. for sodium myristate, which was the cross-sectional area of this molecule in a soap micelle as determined by x-ray diffraction. Corrin and Harltins c3) have an experimentally determined value for potassium myristate of 56 sq. A., based on the quantity of soap adsorbed on a lcgown graphite surface. This laboratory has used in the past %: value of 29 sq. A. for S.F. flakes, obtained by calcula1,ing the area of latex particles from electron micrograph measurements. With improvement in techniques it seemed worthwhile to repeat this lastmentioned approach in order to obtain a better value for use in calculating the interfacial area of a latex system.
A.
EXPERIMENTAL PROCEDURES
Average diameter by soap titration Particle-size measurement of a latex by a soap titration method is based on the hypothesis that the quantity of soap adsorbed a t a selected end point is pro-
358
E. -4. WILLSON, J. R . MILLER .XED E. IT. ROWE
portional to the interfacial area of a unit volume of part8icles. If the average adsorption area of the soap molecule for these conditions is known, an average diameter can be calculated from the quantity of soap adsorbed. This average diameter of the particles is the ratio of the cube of the volume average diameter to the square of the area average diameter since:
A = nad:
and d ,
=
( z g ? ) ’ i ?
Dividing equations 1 by equations 2:
number of particles volume average diameter area average diameter volume-area average diameter V = volume of polymer particles A = area of polymer particles
where n d, d, dvs
= = = =
Latices examined For the determinations of adsorption area a series of five latices was prepared with each soap by successive seeding. The first lates in the series was prepared by polymerization of the monomers, butadiene and styrene, in a solution of the soap to be studied. A volume of this latex, which contained one part of polymer used as seed, mas mixed with four parts of monomers and polymerized to form the second latex. By using conditions that limited growth to the seed particles, the latex formed had an average particle volume approximately five times that of the seed particle. New particles were not initiated if the concentration of soap in solution was less than the critical micelle concentration. Coalescence of the seed particles was prevented by careful mixing, the use of as large a quantity of soap as consistent with the requirements for preventing initiation of new particles, and a moderate reduction in the quantity of watjer in the seeded polymerizations. Then, using the second latex as seed, the next lates in the series \vas prepared in the same manner. This operation was repeated so that a related series of latices was made having i-olurne average diameters approaching the relative values: 1, W, W 3 ,5, and 54’3. X small correction must be macle to these values, owing to the fact that the latices were shortstopped a t conversions that varied between 91 and 97 per cent. The examination of such a series offers the advantage of enabling one t o correlate the relative average diameters calculated from soap adsorption data and the volume average diameters from electron microscope data with the relative volume average diameters from calculations based on growth. Separate series were prepared using Armour’s
3IEASVREMEKT O F PARTICLE SIZE O F L.\TEX
359
RI,-17-12 oleic acid, Einier antl Amend's -4-21G oleic acid, antl Eastman Ilodak's S o . 111G myristic acid.
Coductonictric soap iitrnfion The quantity of adsorbed soap was determined 113' ;\Iaron's conductometric soap titration technique with ,z conductivity cell \i.hich essentially duplicated the one described in llaron's paper (9). -4nenclosed-s\vitoh Leeds S: Northrup Wheatstone bridge (4760), an A . c. Leeds & Sorthrup galvanometer (2370), and n water bath tliermost~atetla t 41.18"c'. i 0.02" \\.ere used in the conductivity measurements. The t'itration \vas performed by adding increments of 0.2 -4r ;soap to the contluctivity cell containing 100 ml. of latex of known concentration. The soap addition \\.as mixed into the latex by pumping the latex in the cell with air passed through Ascarite tubes. Equilibrium was established as soon as the soap \vas thoroughly mixed with tlie latex. A plot of t'he milliliters of added soap versus conducti.i.ity gives two intersecting straight lines whose junction is the end point of the titration. The sharp break in the conduct'ivity curve is assumed to indicate the point at which the concentration of unadsorbed soap, i.e., t,he soap in solution, is the same as the critical micelle concentfration, and the soap in solution is in equilibrium with a monomolecular layer of adsorbed soap. The conductometric soap titrations have a precision of k0.G per cent of t,he tot,al soap value for the latex of smallest particle size. The uncertainty increases as the particle size of the latex increases and is It3.0 per cent for the latex of largest particle size. For the latex of smallest particle size in each series the salt effect of the potassium persulfat'e catalyst and potassium hydroxide added to neutralize reduced peiwilfiite was very small. Although the quantity of electrolyte in each lates jvithin a series was nearly the same, the ratio of the quantity of electrolyte to quantity of soap a t the titration end point increased with increasing particle size, onting to the smaller quantity of adsorbed soap. As this ratio increased, tjhe concentration of soap in solution a t the end point of the titration decreased. In older t'o find the concentration of soap in solution a t the end point, use was made of hlaron's device (9) of plotting the results of several conductometric titrations of the same latex a t different dilutions (the milliliters of added soap per liter of lates versus the grams of polymer per liter of latex) and estrapolating to zero grams of polymer. It has been assumed generally by the users of soap titration methods of measwing pilrticle size that the average adsorption area of tlie soap molecule a t the conductometric break is constant, even though the concentration of soap in solution has been reduced by the presence of salts. This seems like a reasonable assumpiion, since conditions that, would favor the association of soap in solution tjo form micelles a t lower concentrations of soap \\-odd also favor the adsorption of soap on the surface of latex particles. If this is not strictly true, a t least the error int,rodiiced should be very small in the range of salt effects encountered in the series of latices studied. In the latex of largest particle size in the sodium myristate series the total
360
E. A. WILLSON, J. R. MILLER AND E. H. ROWE
quantity of soap varied so widely with dilution, owing to the relatively large quantity of soap in solution compared with the adsorbed soap, that it was necessary to keep the salt effect essentially constant by adding sodium chloride with the dilution water. This was done on the basis that the ratio of moles of added cation to the total moles of soap was maintained regardless of dilution.
Treatment of latices for preparation of electron micrographs The copolymer of butadiene and styrene is made up of carbon and hydrogen atoms. These atoms of lorn mass scatter electrons poorly and hence tend to give electron micrographs of low contrast. The fact that copolymer particles are plastic permits them to merge and flatten out on the supporting film. They appear in the electron microscope as large, hazy, irregular-shaped bodies. Thus, three difficulties are to be overcome before accurate measurements can be made on particle sizes of these latices: namely, poor contrast, flattening, and coalescence. Methods of preparing latices of this type for the electron microscope have been given. One method, published by Kelsey and Hansen (7), involves surrounding the latex particles with a water-soluble plastic material such as polyvinyl alcohol. This method claims to prevent flattening of the particles but it does not help the contrast. The shadow-casting technique of Williams and Wyckoff (12) was not used, because considerable coalescence of the particles occurs on drying the sample. Another method, that of Brown (l),is capable of solving these problems and was therefore used in this study. This method is simply t o add bromine atoms to the unsaturated butadiene component of the copolymer molecules, which is done by passing a stream of dry gaseous bromine across a diluted drop of latex. A small part of the drop of brominated latex is placed on a screensupported Parlodion film and examined with the electron microscope. Such a preparation gives the hard spheres with high contrast needed for accurate particle-size determinations. One correction must be applied to the measurements, however, and that is the swelling of the particles caused by bromination. The amount of swelling was experimentally determined by adding an excess of bromine water to a latex sample, followed by centrifuging to give a heavy paste. This paste was washed by making a slurry in distilled water and centrifuging again. The operation was repeated until the wash water was bromine-free. The dried paste was analyzed for density and per cent bromine, and the increase in volume was calculated to be 0.G per cent of the diameter of a spherical particle. This correction is readily made in the magnification.
Calibration of magnification Several methods have been suggested in the literature for determination of an electron microscope magnification (2, 4, 10). The method used for the first trials of the oleate-A and myristate series was to prepare a replica of a 30,000 lines per inch grating and use it as an internal standard. This method was abandoned in the subsequent trials, however, because of distortions resulting
MEASUREMENT O F PARTICLE SIZE O F L A T E X
36 1
from unequal stresses as the samples were dried on the replica films. The remaining trials of these series were calibrated by using a replica film with no sample on it. With this method, trial evaluations of a complete latex series were run in the same day in order to eliminate as much as possible changes in the microscope itself. For the oleate-B series, the decision was made to use a copper disk the size of the specimen screen with a small hole punched in it. This hole was measured with an optical microscope and was used to calibrate the electron microscope. To avoid errors due to lens hysteresis, the lenses were snapped on and off several times tefore each sample was micrographed. Calibrations were made both before and after the latex series measurements and averaged. The microscope used was the R.C.A. type B. PREPARATION O F LATICES
Polymerizations were conducted in 32-oz., cron-n-cap bottles with the ingredients added in the proportion of twice the weight in grams of the recipe parts in table 1. The first latex in each series was prepared by charging the bottle with the aqueous soap and potassium persulfate solutions. The solution of styrene containing the mercaptan modifier was weighed and added carefully to the bottle so that it layered over the soap solution. Finally, butadiene was weighed into the botlle with a few grams escess, which was allowed to vent to the correct weight, and then the bottle was quickly capped. Polymerization was carried to over 90 per cent conversion. The subsequent latices in the series were charged by taking one-fifth of the preceding latex weight and mixing carefully with the solution of soap and catalyst. The seed latices, at conversions of 90 per cent and over, were transferred without appreciable loss of residual monomers. Styrene with modifier was then layered over the diluted lhtex a t room temperature, followed quickly by the butadiene. Emulsification was started immediately with end-over-end agitation to minimize any tendency for water-in-oil emulsification. Polymerization was conducted in a mater bath at 50°C. and conversions determined by Houston’s (6) hypodermic syringe technique. A uniform charging ratio of monomers, butadiene-styrene 60-40, was employed. The portions of the latices set aside for seeding were stored without shortstopping a t room temperature until use. The latex samples used for soap adsorption and electron microscope measurements were shortstopped with 0.1 per cent hydroquinone on the weight of monomers charged, the conversions were determined by the hypodermic syringe technique, the i*esidual monomers were removed by steam stripping, and the rubber contents were calculated from determinations of total solids. COKDUCTOMETRIC SOAP TITRBTION DATA
Oleate-A and oleate-B series
The conductometric soap titration results of the oleate-A series of latices are plotted in figure 1 and the oleate-€3series are plotted in figure 2 with the straightline extrapolations to zero grams of polymer to give the free soap values. Table
362
E. -4. WILLSON, J. R. MILLER . W D E . H. ROWE
2 and table 3 show the results of calculations for the quantities of adsorbed soap for the oleate-A and oleate-B series, respectively.
Myristate series The conductometric soap titration results x i t h 0.2 N potassium myristate of the sodium myristate series of latices are plotted in figure 3 with the straightTABLE 1 L a t e x i.ecipes Latex No . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Seeded with latex 30. . . . . . . . . . . . . . . . . . P a r t s seed polymer and monomer.. . . . . P a r t s seed latex.. . . . . . . . . . . . . . . . . . . . . . Added ittalerial: P a r t s butadiene.. . . . . . . . . . . . . . . . . . . . P a r t s styrene.. . . . . . . . . . . . . . . . . . . . . . . . P a r t s DDM*. . . . . . . . . . . . . . . . . . . . . . . . . . P a r t s potassium persulfate.. . . . . . . . . . . P a r t s sonpt. . . . . . . . . . . . . . . . . . . . . . . . . . . Parts water.,. . . . . . . . . . . . . . . . . . . . . . . . P a r k alkali$. . . . . . . . . . . . . . . . . . . . . . . . . Total ]isits charged. . . . . . . . . . . . . . . .
I Sone None None 60. 40. 0.40
0.30 5.00 180.
I1 I 20. 57.14
111 I1 20. 50.50
4s. 32. 0.32 0.24 1.00 114. 0.05
32. 0.32 0.24 0.60 120. 0.05
--285.70
252.51
4s.
___
V IV
IV I11 20. 50.34
20. 50.31
48. 32. 0.32 0.24 0.60 120. 0.05
48. 32. 0.32 0.24 0.24 45. 0.05
--
--
251.71
251.53
176.16
Polymerization temperature, "C.. . . . . . . .
50
50
50
50
50
Per cent conversion oleate-A series . . . . . Per cent conversion oleate-B series . . . . . Per cent conversion myristate series.. . .
92.8 92.6 94.3
95.0 94.3 92.9
93.7 95.3 94.7
95.9 96.5 91.9
92.7 93.8 91.2
Polymerization time oleate-A, h r . , . . . . . . Poljmerization time oleate-B, hr.. . . . . . . Polymerization time myristate, hr. . . . . .
22.0 24.5 17.5
24.5 28.0 20.0
40.5 45.0 41.5
116.5 94.5 82.0
193.0 164.5 209.0
_ _ _ _ _ _ ~ ~ ~
* Hooker DDM, 14.05 per cent SH sulfur.
t Oleate-A series: sodium oleate from Armour's
RL-1762 oleic acid. Oleate-B series: potassium oleate from Eimer and Amend's A-216 oleic acid. h l y s t ~ i s t n t eseries: sodium inyristate from Eastman Kodak's No. 1116 myristic acid. 3 Oleate-A nnd myristate series : sodium hydroside. Oleate-B series: potassium hydroside.
line est,rapolationsto zero grams of polymer to give the free soap concentrations 2 L t the conductometric break. The rather large salt effect in latex V combined with the large values for free soap attending the use of myristate soaps created the condition of giving a different value of free soap for each latex dilution. This showed up in a plot of free soap by yielding a curve instead of the usual straight line. The results giving a straight-line plot for latex V shown in figure 3 were obtained by keeping the molar cation concentration (in excess of that associated with the soap) in the
MEASUREMENT O F PARTICLE SIZE O F LATEX
363
same ratio to the total moles of soap by estimated additions of sodium chloride. It was calculated that the most concentrated sample, 25.93 g. of latex diluted to
l
0
70
-I
L
-
1
I
1
I
I
I
I
I
,
'
,
'
I
I
0-
I
20
0
I
I
I
I
'
80
60
40
GRAMS
I
I 100
-
'
I
I
120
OF POLYMER PER LITER OF LATEX
FIG.1; Determinations of C.M.C. values from extrapolations of conductometric soap titration d a t a . Oleate-A series.
0 0
I
'
IO
'
I
I . '
'
'
' ' '
50
'
I
60 70 GRAMS OF POLYMER PER LITER OF LATEX
20
30
40
I
'
80
FIG.2. Determinations of C.il1.C. values from extrapolations of conductometric soap titration data. Oleate-B series.
100 ml., had 0.58 mole of excess cation per mole of total soap and this proportion was maintained for the more dilute samples.
364
E. A . WILLSON, J. R. MILLER AND E . H. ROWE
Table 4 lists the results of the calculations for adsorbed soap in the myristate series of latices. TABLE 2 Calculations f o r quantity of adsorbed soap: oleate-A series
'
LATEX
I Latex I . .. , . . . . . , . 6.51
~
ADSORBED SOAP'
! 0.205 0.201
~
0.034 0.030 0.028 0.032
0,177 0.177 0.177 0.177
0.348 0.348 0.351 0.352
~
,I
Average.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . , . . . . . . . . Latex I1 . . . . . . . . .
19.22 18.13 35.93
~
5.31 5.10 9.89
~
0.185 0.177 0.157
~
0.036 0.037 0.019
0.350 ~
0.218 0.209 0.207
0.069 0.069 0.069
0.211
Average
'
Latex 111
1
38.32 22.46
9.87 5.78
'j
0.074 0.082
0.015 0.026
1
0.129 0.126 0.128 0.129
0.070 0.070
Average. . .
0.128
Latex I V . . . . . . . . , .
~
~
38.81 24.32
11.30 7.06
i
I
0.054 0.062
I 1
0.013 0.022
~
0.075 0.074
0.034 0.034
0.075 Latex V . , , . , , . .
I
'
26.58 20.00 13.64
1 1
1
6.35 4.78 3.26
,
1 1
0.041 0.047 0.061
0.020 0.027 0.041
0.045 0.046 0.016 0.045 0.045
0.025 0.025 0.025
Average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
* Millimoles of sodium oleate per gram of polymer.
0.045 _
_
ELECTRON MICROSCOPE DATA
Results of the electron microscope analysis of the particle sizes of the two oleate series and the myristate series of latices are shown in table 5. Four separate trials were made on the oleate-A and the myristate series, while only one trial was made on the oleate-B series. Each trial represented a count of 150 or more particles. Figures 4a through 4e are electron micrographs of the myristate series of five latices made a t the same magnification and illustrate the
~
Lntcs I
:ivcl,:lg.e,
, ,
, , ,
.... ..,..
Lntes 11, . . . . . .
1 I
,
.
19.111
,
,
.. . .. . . . . . . . .
,
i:3.m S.05T ~B.MI 1G.183
~
~
2.227 (i.170 4.102
,
, ,
., .....................
0.220 0.247 0,250 0.214 0.240
~
0.039 0.000
0.01s
1
.
0.25:: 0 . 253 0.253 0.248 0,23
0.066 0.060 0 .000 0.060 0.06G .
-~
~
0,253 ~-
0 . 101 U.15G
0.155 0.142 0.150 0.154 -~
~
0.094 0.090 0.095 0.095 0,094
0,095 0,057 0 . 050
Discirssion o,/' )ri icroscopc errors E i ~ ( ~ i of , h c:tlitii,ntion include inacciiixcy of the standaid, in,zcciiincies of nieusiiiwueiit of tlic htnnd:xrtl, ,znd nicclinnicnl niitl electiicnl inconhistencies of the
30G
E. A. n'ILLSOS, J.
R. hIILLER .4ND E. H. ROWE
iiiiviuhvo1)c. iiic~iitioueclwrlicr, tlie ii1:tgilific:tt'iuils uf t'lie o l c : t l ~ - ~~ l i c l i n ~ ~ r i s ~serics : t ~ o \\'ere cdil~i,ittc~.l \\.it11 i t rq)licit gyatitlg usctl :is :t nioitrlt iiig film. (The gxtting of 30,000 lines per inch \vas supplied by G. 13. Dielre of John$ Hopliins University.) At first it iv:ts thought t,hat errors of the replica due t'o shrinkage from stresses cliiring drying of the diliited latex sample could be eliminated by cnlihxting the replica with an optical microscope. It was soon decided that the clifficrdt'y of focussing sharply on the barely visible replica film was :LI~ inlierent tlisadImtage of this nietliocl. Tlie other trials of these series relied on tlie reproducibilit'y of the electron microscope for constant niagnificat'ion ~intla ivellprepared Formvar replica grating w:w used for calibration. For tlie oleate-B series, a small hole punched1in a copper disk \vas measured with an opt8icalmicroscope niid \vas used for cnli tirating the electron microscope. Reproducible I
x
I
I
I
I
I
I
I
I
I
I
I
I
I
I
1 7 -
-
P4 80-
I
25
0
IO
2.0
30
40
GRAMS OF POLYMER
50 PER
LITER
60 70 OF LATEX
80
FIG.3. Deteriiiitiatioiis of C.hI.C'. \,nlues from e s t i ~ ~ ~ p o l a tofi o contluctoriictrjo ~i~ soap titrstiori data. hlyristnte series.
results \\.ere oht'slined by this method. Errors of calibration were estimated t o he from 3 to 5 per cent. Extreme care must be esercised to assure fair sampling, because the \\.eight of polymer in a given field of view is about g., and each field is of t8heorder of sq. cm. in area. This is pnrtictilndy true in samples of broad t1ist)rit)iition. Fortunately, in t'liese particular experiments t'he latices of large particle size cnn he considered extremely uniform. Dist'ribution curves to show this uniformity are given in figure 5 for the five 1at)icesof the myristate series. The cur\'es are drawn through the midpoints of the measuring cell. Esperience indicates that a ninsiniiim vnrintion of about 10 per cent in tliameter lietwey two samples of a lntes c i ~ nbe expected. With particle sizes greater than 1000 *\. much of this error mny be attributed to sampling. With repented sanipling this can be reduced. The estiniatecl 10 per cent error on a single t'rial was cut to 5 per cent' when four trirtls \Yere used. This \vas assumed for d l
367
MEhSURERfENT O F PARTICLE SIZE O F LATEX
samples. I n the case of small particles other effects, such as contaminat'ion, loiv contrast, and poor resolution, are added t o t#hesampling error. Subsequent
~
LATEX
1
LATEX WEIGHT
. . . . . . . . . .. !
' ~
'I
--
1
POLYNER WEIGHT
ADDED SOAP'
13.60 25.18 12.12 31.93
i
1
1
1
I
, -~
I
3.366 4.383 6.220 2.990 7.787
0.254 1 0.384 0.231 1
1
0.219 1 0.168 0.115 j 0.247 0.003
0 216 0 216 0 216 0 216 0 216
'
L:ites I I . ,. . . . . . .
,~
1
~
1
16.77 15.00 21.12 28.57
1
4.26G
I
0.277
,
3.81F 5.373 7.26s ,
0.301 0.240 0.205
~
12.46
i
1
17.87
1
~
~
i
0.086
0.180 0.123
0.086
'
1 ~
~
0.086 O.OS6
I
0.088
~
i
1
0,063 0.193
~
1
0.073 0.135
1 ~
0.0G3
0.063 0.063
Average.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
___
_____
Latex IV . . . . . . . . . . i
17.6; ' 25.05 2G.51 1
4.60s
12.G3
3.265
~
~
'
~
__-
7.251 G.853
1
~
'
0.174 0.119 0.125 0.232
~
~
1
I
0 355
j
0,120
1 ~
I
0.035 I 0.035 1
0.196
~
0.206 0.206
0.090
0.035
0.203
1
0.055
~
0.204 0.208 0.207
I
0.135 0.084 1
i
0.119
0.120 0.121 0.120 0.071 0.070
0.068 0.069
-~
. . . . . . ..I.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
L:ites
~
0.159 '
3.435 4.027
1
0.356 0.357 0 353 0 353 0 354
I
Ave1,:ige. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lntes I11
1
1
.\ver:ige., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ _ _ _ _ ~
'
17..
........
i i
~
,
15.00
i
10.13
1
14.33 20.16 26.93
~
~
2.712 2.582 2.722 5.140 6.610
~
I
0.163 0.237 0.171 I 0.127 i
0.141 0.213 0.149 0.105
0.103
0.080
~
1 ~
I
~
. . . . . . . .
i ~
I
1
0.018 0.01s
0.018
0.018 0.018
i\vet,:rye.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.040 ~
~
~
~
0.042 0.040 0.040 0.041 0.041
correlations indicate thnt much larger eri'ors than those atti4il)utnhle t o these causes occui-i~etli n the nieizhrii*ementof the latices of small pniticle size.
FIG.4 a, 11, c 368
NE.-\SGRERIEKT
309
O F P.\RTIC'LE SIZE O F L.ATES
ADSORPTIOS ARE.LR O F SOAP RIOLECYLES
The series of lat'ices prodriced by succes4i.e seeding pelmi t' cnlculation of yelative volume diameters Iinsed on the n,ssuniption that polymer gi*o\\,tli\\.>as limited to the seed particles 2nd coalescence of particles \\.:IS negligilile. For example, compared to nn average diameter of 1 f o r lntes I t'lie relnti\,e \.olwne average
1
//v
e
FIG.4 d,e FIG.4. Electron inicrographs of the inyistnte sciies: ( a ) late\; I ; (I))l n t e s 11; (c) lntes 111; (tl) lates IV; (e) lntes V.
diameter of lntes I1 is equal to 51'3times the conversion of late\: I1 tli\.ided by the con\yersion of latex I. The rehtive d , of each lntes in the three series, as calculated from espected growth of the particles, is listed in table 6. The correlations bet\\-een the calculated relati\Te yohime average diameters and the electron microscope volume a\.erage diameters are shown Iiy the plot in
I
LATEX
~
T R I A L I*
,
T R I A L ll*
A. latex latex latex latex latex
I . .. . , . . . . , . . . . . 11.. . . . . . . , . . , . . 111... . . . . . . . . . IV... . . . , . . . . , . V...., . , , . . . , , .
Oleate-B latex Oleate-B latex Oleate-B latex Oleate-B l a t e s Oleate-B latex
I . .. . . . . , . . . , . . , 11.. . , . . . . , . . . . . 111.., , . . . . . . , , . IV... . , . . . , . . . . V..... . . .. . , . , .
Oleate-A Oleate-A Oleate-h Oleate-A Oleate-A
~
720 1105 1010 3270 4710
T R I A L Ill*
TRIAL IV*
A.
2.
2.
1100 1710 2720 4430
790 1230 1780 2860 4600
875 1230 1650 2900 4610
1
AVERAGE
AVERAGE
do
dvst
A.
A. 705 1165 1760 2940 4590
850 1215 1825 3035 4615
680 1065 1560 2410 4030
710 1135 1610 2440 4050
671 1130 1630 2525 4150
755 1220 1690 2680 4150
I
1
1 ~
~
I
-I D_3 hlyristnte latex 111., . . . . . . . . . . Atyristate l a t e s I V . . . . . , . . . , . .
* d , is the volulne average diaiiiet,er =
000 1680 2570 4220
1080 1520 2560 4100
1600 2510
(x;$)
620 1110 1730 2460 4270
' ~
~
1/ 3
End3 t d , , is the voluiiie surface avernge diameter = %id2 -,
LATEX
CONVERSION
RELA-
E L E C T R O N MICROSCOPE
CIVEd,,*
dt,s
1
1
'i
dus/du
1
705 llG5
1.OG9 1.043
1
2010
1.032
do
SOAP TITRATION
!
drat
per cent
Oleate-A latex Oleate-A lntes Oleate-h latex Oleate-X latex Oleate-A latex
I ..... . . . . . , I1. . . . . . . . , . I11 . . . . . . . . , I V . ,. . . . . . . V..., .., , ..
92.8 05.0 03.7 0G.5 92.3
2.03 5.06 8.53
1825 3035 4615
Oleate-B latex Olettte-B latex Oleate-B latex Oleate-B latex Oleate-B lntes
I . .. . . . . . . . . 11. . . . . . . . . . 111.. . . . . , . . 1Ir... . . . . . . IT., ...., . .
02.6 04.3 05.3 06.5 93 .8
1. 1.72 2.95 5.07 8.55
7 10 1135 1G10 2440 4050
2.25. IC1 3.71 6.20 10.40 17.64
1. 1 .70 2.03
755 1220 1600
2.50. I
