Determination of Particle Size-n-particle Size Distributions

7/29/2019 Determination of Particle Size-n-particle Size Distributions

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148 Part. Part. Syst. Charact. 12 (1995) 148-157

Comparative Test of M ethodstoDetermine Particle Size andParticle Size Distribution in the Submicron RangeHeinz L ange*Dedicated toProfessor Klaus Elgeti on the occasion of his 60th birthday(Received:7 February 1994;resubmitted: 2 January 1995)

AbstractAmong the most important characteristic properties of dispersesystems such as latices, pigments, ceramic materials or drug for-mulations are the particle size and the particle size distribution.To measure these quantities, several methods and measuring in-struments based on different physical principles are available.These include turbidimetry, dynamic and static light scattering,electron microscopy with image analysis, ultra- and disc cen-trifugation, light diffraction and the electrical sensing zonemethod. A ll these measuring techniques are doubtless necessarybecause of the large product variety and the broad particle sizerange. However, some problems arise if different techniques areused and the results are compared uncritically without consider-ing to the application range and the resolution of the methods.An extensive comparative test was therefore carried out usingseven latices in the submicron range with defined monomodal,

1 Introduction and MethodsAmong the most important characteristic data for dispersesystems such as latices, pigments, ceramic materials or drug for-mulations are the particle size and the particle size distribution.In order to measure these quantities, several methods and meas-uring instruments based on different physical principles areavailable. These include turbidity measurements, dynamic andstatic light scattering, electron microscopy with image analysis,ultra- and disc centrifugation, light diffraction and the elec-trical sensing zone method.All these measuring techniques are doubtless necessary becauseof the large product variety and the broad particle size range ofabout 10' to lo6nm. However, some problems arise if differenttechniques are used and the results are compared uncriticallywithout considering the application range and resolution of themethods.In order to achieve some improvements in this field, an exten-sive comparative test was carried out in which the most impor-tant methods to determine average particle size values and parti-cle size distributions were tested and compared with regard totheir efficiency in the submicron range').

* Dr. H. Lange, Bayer AG, ZF-TPF 2, E 41, 51368 Leverkusen (Ger-many).1) For comparative tests with particle diameters larger than 1pm, see[l-41.

bimodal and hexamodal particle size distributions. The mostimportant methods of determining average particle size valuesand particle size distributions were tested and compared. Of themethods to determine only average particle sizes, turbidimetryis the most efficient, followed by dynamic light scattering withcumulants evaluation. Static light scattering only yields ac-curate results for small particles with narrow particle sizedistributions. Of the methods to determine particle sizedistributions, ultracentrifugation and, somewhat less, disc cen-trifugation and electron microscopy with image analysis are themost efficient. Dynamic light scattering only yields reliableresults in the case of small particles with narrow distributioncurves. L ight diffraction and the electrical sensing zone methodare less suitable for the submicron range.

This test involved 17 laboratories within the Bayer Group world-wide, using all the methods mentioned above. Each laboratorywas sent seven test samples (latices) with defined particle sizedistributions, unknown to the participants. They were asked tomeasure the average particle size values and particle sizedistributions routinely without special effort.

2 Test LaticesThe test latices were chosen in such away that the eff iciency ofthe methods could be examined and evaluated for both smalland relatively large particle diameters of about 100and 800nmand for a large distribution range between about 100 and1600nm. T he efficiency of the methods was also tested forlatices of different chemical composition.The test latex set therefore consisted of two almost monodis-perse polystyrene latices, two bimodal polystyrene latex blends,one hexamodal polystyrene latex blend and two latex blendsof polystyrene and polybutadiene and of poly(styrene-co-buta-diene), polystyrene and polychloroprene. The detailed data(composition, modality, particle diameter and distributionrange) of the test latices are given in Table 1.

0 VCH Verlagsgesellschaft mbH, D-69469Weinheim, 1995 0934-0866/95/0306-0148$5.00+.25/0


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Part. Part. Syst. Charact. I 2 (1995) 148-157 149Table1: Test latices.test substance compo- modality d, U d P f d 3.1 Determination of Average Particle Size Valueslatex sition (nm) (nm) (nm)

3 Results

(070) The first part of this paper discusses the results of thosepolystyrene 100polystyrene 100polystyrene 50polystyrene 50polystyrene 10polystyrene 90polystyrene 16.67polystyrene 16.67polystyrene 16.67polystyrene 16.67polystyrene 16.67polystyrene 16.67polystyrene 33.33polybutadi-ene 66.67poly(styrene- 33.33co-butadiene)

1 2131 815

1372 2136052 81513721332755268151,550213

36380

2

7.9 2137.8 8157'0 1757.97.87.07.9

10.47.87.9

8.9 794

9*0 599

-313

--polystyrene 33.33 3 113 - 132polychloro-prene 33.33 200 -

The particle size (diameter d,) and the standard deviation ( 0 ) of thepolystyrene test latices except the last constituent of latex E and themiddle constituent of latex G are data from the supplier Serva,Heidelberg, based on electron microscopic measurements. The particlesize of the last constituent of latexE was measured in the laboratory 11(see Table4)by electron microscopy and the particle size of the secondconstituent (polybutadiene) of latexF andof all constituents of latex Gwere determined in the laboratory 2 (see the same table) by ultracen-trifugation [lo]. All test latices were sent to the participating labora-tories as 10ml samples with 10% solids content together with a smallamount of the emulsifier K30 (sodium alkanesulfonate) for furtherdilution with a defined dispersion medium (0.2 g/l K30 in distilledwater). dppFals the weight-average particle diameter calculated from thed, values and the compositions.

Table2: Results of the comparative test: particle size average values.

methods which are able to determine only average particle sizevalues and not particle size distributions. These methods areturbidimetry [5-71, dynamic light scattering with cumulantsevaluation [8] and static light scattering with evaluation of theangle dependence of the scattered intensity [9 ] . The results ofthese methods are shown in Table 2 and Figures 1-6.3.1.1 Test Latex ATest latex A with aparticle diameter of 213 nm and a very nar-row monomodal particle size distribution (see thick full l ine inFigure 1) is characterized very well by turbidimetry and dy-namic l ight scattering with cumulants evaluation. The valuesobtained by static light scattering are slightly too high (seeTable 2 and Figure 1).3.1.2 Test Latex BTest latex B with aparticle diameter of 815 nm and avery nar-row monomodal particle size distribution (see thick full line inFigure 2) is also characterized very well by turbidimetry inlaboratories 2 and 3 and by dynamic light scattering withcumulants evaluation in laboratories 4, 8 and 9. Only turbidi-metry in laboratory 1 and dynamic light scattering in labora-tories 5, 6 and7 yield values which aretoo low (see Table 2andFigure 2). The static li ght scattering measurements could not beevaluated because of the curvature of the resulting Zimm plots.3.1.3 Test Latex CTest latex C is a blend of two latices with small particle dia-meters of 137 and 213 nm and a mass ratio of l : l. From this,the weight-average particle diameter 4,al was calculated as175 nm (see thick full lines in Figure 3) and the Z-average as183 nm. These average values are characterized very well by tur-

laboratory equipment ~p,meas(nm)ethodtest latex A B C D E Fd,,, (nm) 213 815 175 794 599 313

2 Photometer 1 220 800 180 800 700 2903 Photometer 2 206 796 179 748 449 252dynamic light scattering 4 Goniometer 1 211 840 187 769 266 249(cumulants evaluation) +Correlator5 Measuring instrumentD1 227 616 198 766 283 2626 Measuring instrumentD1 226 451 204 533 286 2617 Measuring instrumentD1 220 692 197 698 279 2658 Measuring instrumentD1 217 814 192 744 323 2569 Measuring instrumentD1 213 769 197 773 408 236Measuring instrumentD2 214 779 190 785 291 256Measuring instrumentD3 224 875 208 820 395 341static light scattering (evalua- 10 Measuring instrumentS1 246 - 217 - - 136

turbidimetry 1 Photometer 1 210 700 180 700 700 -

- -ion of the angle dependence) Measuring instrument S2 246 - 224 -


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150 Part. Part, Syst. Charact. 12 (1995) 148-157

d p nmlFig. 1: Particle size distribution (mass distribution) and the measuredaverage particle diameters dp,meass. Table 2) of test latex A(polystyrene; monomodal; d, =213 nm, o =7.9 nm).

500 600 700 800 900 1000d s [mlFig. 2: Particle size distribution (mass distribution) and the measuredaverage particle diameters dp,me,, s. Table 2) of test latex 5 (poly-styrene; monomodal; d, =815 nm, o =7.8 nm).

80706050

0, 4030

-xI$la- 2o-I E0 10

0 0 100 200 300 400 500dp nml

Fig. 3: Particle size distribution (mass distribution) and the measuredaverage particle diameters (s. Table 2) of test latex C (poly-styrene; bimodal; d, ] =137 nm, o1=7.0 nm; dp,z=213 nm,o2=7.9 nm; mass ratio 1 :1).

- I . t

500 600 700 800 9W 1000dp " n lFig. 4: Particle size distribution (mass distribution) and the measuredaverage particle diameters d,,,,,, (s. Table2) of test latex D (poly-styrene; bimodal; d , , =605 nm, o, =8.9 nm; d,,, =815 nm,(5 =7.8 nm; mass ratio 1: ).

--5 12

QIQ

02 8E *-

-IE0 4

0 0 400 800 1200 1600 2000d lnml

Fig. 5 : Particle size distribution (mass distribution) and the measuredaverage particle diameters dp,meass. Table 2) of test latex E (poly-styrene; hexamodal; d , ]=137 nm, o, =7.0 nm; dp,*=213 nm,o2=7.9 nm; dp,3=327 nm, o3=9.0 nm; d, , =552 nm, o 4 =10.4 nm;dp,5=815 nm, a5=7.8 nm; d,, =1,550 nm, EM ; mass ratio1 : 1 : 1 :1: 1: 1).

Fig. 6: Particle size distribution (mass distribution) and the measuredaverage particle size diameters dP,,,,, (s. Table2) of test latex F (poly-styrene, polybutadiene; bimodal; d,,] =213 nm, 6 )=7.9 nm;d, , =363 nm, UC; mass ratio 1 :2).

bidimetry and well by dynamic light scattering with cumulantsevaluation. The values obtained by static light scattering areslightly too high (see Table 2 and Figure 3).3.1.4 Test L atex DTest latex D is a blend of two latices with relatively large particlediameters of 605 and 815 nm and a mass ratio of 1:9. Fromthis, the weight-average particle diameter dp,al was calculatedas 794 nm (see thick full lines inFigure 4) and the Z-average as799 nm. These average values are characterized very well byturbidimetry in laboratories 2 and 3and by dynamic light scat-tering with cumulants evaluation in laboratories 4, 5 , 8 and 9.Only turbidimetry in laboratory 1and dynamic light scatteringwith cumulants evaluation in laboratory 7 yield values whichare slightly too low and in laboratory 6 values which are too low(see Table 2 and Figure 4). See Section 3.1.2 for resultsof staticlight scattering.3.1.5 Test Latex ETest latex E is a blend of six latices with particle diameters of137, 213, 327, 552, 815 and 1550nm and a mass ratio of1:1:1:1:1:1. From this, the weight-average particle diame-ter dp,calwas calculated as 599 nm (see thick ful l lines in Fig-ure 5 ) and the Z-average as 986 nm. These average values can-not be characterized well. Tho of the turbidimetric results arebetween the two average values and one is too low. The results


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Part. Part. Syst. Charact. 12 (1995) 148-157 151Table3: Efficiency evaluation of themethods to determine average particle sizes.method small particles large particles large particle particles of different advantages disadvantagessize region chemical composition

d, 5 2,000nmd,s 50 0 nm d, 2 500nm dpz 100nm d, s 500 nmd, 5 1,000nmnarrow distributions narrow distributions narrow distributionsmonomodal bimodal monomodal bimodal hexamodal bimodal~turbidi- ++ ++ + +metry (+I small,inexpensiveinstrumentation

dynamic ++ + + +lightscattering(cumulantsevaluation)static light + (+I -- --scattering(evaluationof the angledependence)

+ no parametersof the particlesneeded, veryfast methodno parametersof the particlesneeded

refractive index ofthe particles andat low particlesizes additionallythe concentrationand the densityof theparticlesneeded, sphereequivalent particlediametersphere equivalentparticle diameter

method moreappropriate forpolymers insolution+ + very good, + good, (+) less good, - bad, - - very bad appropriate for thedetermination of average particle sizes. This efficiency evaluationis exclusively related to the results of the present comparative test.

of dynamic light scattering with cumulants evaluation are toolow overall (see Table 2 and Figure 5). See Section 3.1.2 forresults of static light scattering.

3.1.6 Test Latex FTest latex F is a blend of two latices with chemically differentparticles of polystyrene and polybutadiene. T he particle dia-meters are213 and 363 nm and the mass ratio is l : . From this,the weight-average particle diameter ap,cals calculated as313 nm (see thick full lines in Figure 6) and the Z-average as329 nm. These average values are characterized well. Turbidi-metry and dynamic light scattering with cumulants evaluationyield values which are only slightly too low. T he exception is theresult of the light scattering measurement with the measuringinstrument D3. The value obtained by static light scattering ismuch too low (see Table2 and Figure 6).

3.1.7 Efficiency Evaluation of the Methods to DetermineAverage Particle SizesSummarizing the results given in Table 2 and Figures 1-6, theefficiency evaluation of the methods to determine average par-ticle sizes is as follows (see Table 3).Turbidimetry [5-71 with its small and inexpensive instrumenta-tion yields nearly the exact average particle diameters over thewhole submicron range. Only the results for the latices with avery wide particle size distribution vary considerably betweenthe laboratories and the mesured values for the latices withchemically different particles are slightly too low.

Similar good results are obtained using the very fast method ofdynamic light scattering with cumulants evaluation [8]. Only inthe case of the latex with avery wide particle size distributionare the measured values too low.The static light scattering method [9], which is more suitable forcharacterizing macromolecules in solution, yields useful resultsonly in the case of latices with very small particles and narrowparticle size distributions.

3.2 Determination of Particle Size DistributionsThe second part of this paper discusses the results of thosemethods which are able to determine particle size distributions.These methods include electron microscopy with image ana-lysis, ultra- and disc centrifugation [lo, 111, dynamic ligth scat-tering with non-negative least-squares fit (NNLS) evaluation[8], light diffraction [12, 131 and the electrical sensing zonemethod [14].The results of these methods are shown in Tables4and 5 and Figures 7-26. In all these figures the plotting scalesare linear in order to illustrate the different efficiency of themethods clearly. Because of the very broad distribution curvesobtained by the methods of light diff raction and electrical sens-ing zone in this small particle size range, no plots of the resultsof these methods are shown in the figures.3.2.1 Test Latices A and BThe particle size distribution of test latexA (see thick full linesin Figures 7-9) is characterized very well by electron micro-


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152 Part. Part. Syst. Charact. I2 (1995) 148-157Table4: Results of the comparative test: particle size distribution of test latices A, B, C, and D.method laboratory equipment resultslatex A latex B latex C latex Dd, ( ma) mass ratio d, (max) mass ratio d, (mu) mass ratio d, ( ma) mass ratio

(nm) W) (nm) (Oh) (nm) (Yo) (nm) (70)electronmicroscopy 11

12132

144

5

6999

15

Electron microscope I+ image analysis 1Electron microscope 2+ image analysis 2Electron microscope 2+ image analysis 3Ultracentrifuge+ in-house method [lo]Disc centrifuge

230 -218 -204 -

836 - 892208089211897

93-

=70=30-----=37=63-51=49-

148214139210-145215153220195

189165165-150=160=145---

6108365 5 5805545814580843567815=800

=830=1800=650=6305 670=650=750=630=850=690

-

-

815 -810 -

ultra-centrifugationdisccentrifugationdynamic l ightscatteringevaluation)(NNLS*)

212 - 815 -208 - 819 98=950 2820 -oniometer 1+ Correlator 208 -

Measuring instrument D1 215 -Measuring instrument D1Measuring instrument D3Measuring instrument L1Measuring instrument L2Measuring instrument L3

- -=950 -5 630 -5 720 -=595 =285 720 =72=620 =50=850 =50=750 -

- -light diffraction

electrical sensing 8 Measuring instrument Elzone method9 Measuring instrument E2

16 Measuring instrument E3*) NNLS =non-negative least-squares f it.

6050403020100 0 100 200 300 400 500d p"4

laboratory4 -labralory6 - -.laboratory 5 -----50 -40-

30 -20 -10 -

-% 2._-.; , , , , f0 100 200 300 400 50 0dp =

In

B

Fig. 7: Particle size distribution (mass distribution) of test latex A,given distribution (-) and the results of electron microscopy. Fig. 9: Particle size distribution (mass distribution) of test latex A,given distribution (-) and the results of dynamic light scattering.

lo150 -40 -30 -20 -

I :entrifugationlaboralmy 14 ----aboralmy 2-. .300 400 500'Od "nl0 100

Fig. 8: Particle size distribution (mass distribution) of test latex A,given distribution (-) and the results of ultra- (-) and disc (---)centrifugation. Fig. 10: Particle size distribution (mass distribution) of test latex B,given distribution (-) and the results of elecctron microscopy.


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a

Fig. 11: Particle size distribution (mass distribution) of test latex B,given distribution (-) and the results of ultra- (-) and disc (---)centrifugation.

604 ' ' ' I '

laboratory 4-4030 -20-10- I

I1 . , . ~ , . 3- --

,1__ .___ ___ . ' - - - - - - -O r , I 1 - 7 7 + k , 1 7 . .500 600 70 0 600 900 1000d [nml

Fig. 12: Particle size distribution (mass distribution) of test latex B,given distribution (-) and the results of dynamic light scattering.

605040302010

00 100 200 300 400 500dp nml

Fig. 13: Particle size distribution (mass distribution) of test latex C,given distribution (-) and the results of electron microscopy.

Fig. 14: Particle size distribution (mass distribution) of test latex C,given distribution (-) and the results of ultra- (-) and disc (---)centrifugation.

scopy with image analysis, by ultra- and disc centrifugation andby dynamic light scattering with NNLS evaluation in laboratory4. The distribution curves produced by the dynamic light scat-tering method in laboratories 5 and 6 aretoobroad. The latteris also true for the results of the light diffraction method (seeTable 4 and Figures 7-9).The particle size distribution of latex B (see thick full lines inFigures 10-12) is characterized well by electron microscopy withimage analysis and by ultra- and disc centrifugation and lesswell by dynamic light scattering in laboratory 4. The distribu-tion curves obtained using dynamic light scattering in labora-tory 9, light diffraction and the electrical sensing zone methodare partially bimodal and much too broad (see Table 4 andFigures 10-12).3.2.2 Test Latices C and DThe particle size distribution of test latex C (see thick full linesin Figures 13-15) is characterized very well by electronmicroscopy with image analysis and by ultra- and disc cen-trifugation. T he resolution of the two peaks of the distributioncurve is almost perfect using these methods. T he correlationwith the given particle sizes and the mass ratio of 1 :1 is alsovery good. Dynamic light scattering and light diffraction arenot able to resolve the two peaks and the distribution curvesobtained are monomodal and very broad (see Table 4 andFigures 13-15).The particle size distribution of test latex D (see thick full linesin Figures 16-18) is also characterized well by ultra- and disccentrifugation. These methods reproduce the given particlesizes and the extreme mass ratio of 1 :9very well. Dynamic lightscattering, light diffraction and the electrical sensing zonemethod are not able to resolve the two peaks of the given parti-cle size distribution. The curves obtained are partly monomodaland much too broad (see %ble 4 and Figures 16-18).3.2.3 Test LaticesE and FThe particle size distribution of test latex E with its six peaks(see thick full lines in Figures 19-21) is reproduced with onlylimited success by electron microscopy with image analysis.Only four (laboratory 11 ) or five(laboratory 12)constituents arefound. The largest particles are missed in the electron micro-scopic image because of their extremely small number. This andthe small overall number of particles (about500) for all the con-stituents together are also the reason for the lack of correlationbetween the measured and given mass ratios, since the numbersof particles of the constituents on the pictures taken are moreor less random and not always representative (see Table 5 andFigure 19). However, the ultra- and disc centrifugation methodsrecord all six constituents, not only with the right particlediameters but also with the right mass ratios (see Table 5 andFigure 20). Dynamic light scattering and light diffraction arenot able to resolve the six constituents of latex E. The distribu-tion curves obtained are partially monomodal and partiallybimodal and very broad (see Table 5 and Figure 21). The elec-trical sensing zone method cannot resolve the constituents oflatex E. This method yields a very broad monomodal distribu-tion curve with particle diameters larger than about 1 vm.The particle sizes of test latex F with its two chemically differentconstituents (see thick full lines in Figurs 22-24) are charac-terized very well by electron microscopy with image analysis.However, before the image is taken, the polybutadiene particleshave to be contrasted, e.g, with OsO,. The correlation with themass ratios is not so good, probably because of the relatively


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154 Part. Part. Syst. Charact. 12 (1995) 148-157~

Table 5: Results of the comparative test: particle size distribution of test latices E, F, and G.method laboratory ~ ~ ~equipment resultslatex E latex F latexGd, (ma) mass ratio d, ( ma) mass ratio d, (ma) mass ratio

(nm) (070) (nm) (@fo) (nm) (410)electronmicroscopy 11 Electron microscope 1+image analysis 1 155215

345565140205330550790150220345585825=1,750155213330565805

1,470=1,760180570=480

=820400610=525

=1,900=180=550

295~2,500

822 220 2544 375 75 =25022 110 =391212 213 4817 376 5247

60

12 Electron microscope 2+ image analysis 2

ultra- 2centrifugation Ultracentrifuge+ in-house method [lo] 181714161817121719171518

21 1377

3565

83 35198 31114 34

disc 14centrifugation Disc centrifuge 218263 973

dynamic l ightscattering( NNLS evalua-tion)

4 Goniometer 1+Correlator 252212

-360=320=280=250- 20-

-

3862=74

=26--=70=30=30=70--

5 Measuring instrument D1699

Measuring instrument D1Measuring instrument D3Measuring instrument L1ight diffraction9 Measuring instrument L2

1517

Measuring instrument L3Measuring instrument E3lectrical sensingzone method

20

10

e Icc I r o n microscopyl a h a t o n , 12 -----laboratory 5 -----laboratory6 -.-.-

I-100 200 300 400 500

E

2001xI%--I En 10

0500 600 700 800 900 1000d B b l0 dp"n l

Fig. 15: Particle size distribution (mass distribution) of test latex C ,given distribution (-) and the results of dynamic light scattering. Fig. 16: Particle size distribution (mass distribution) of test latex D,given distribution (-) and the results of electron microscopy.


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Part. Part. Syst. Charact. 12 (1995) 148-157 155

60-- 50 --5 40 -0x 30 -....2 a" 20 -

- l E o10 -

500 600 700 800 900 . 1000dp nml

' ' ' ' ' ' I L

I

20

16

12XI- 85Is

4I ED0

400 800 1200 16W 2000dp nml

Fig. 17: Particle size distribution (mass distribution) of test latex D,given distribution (-) and the results of ultra- (-) and disc (---)centrifugation.Fig. 21 : Particle size distribution (mass distribution) of test latex E,given distribution (-) and the results of dynamic light scattering.

20

z"? 120x21a-- I ' 4

00 400 800 1200 1600 2WO

dp"4Fig. 19: Particle size distribution (mass distribution) of test latex E,given distribution (-) and the results of electron microscopy.

20

- 16E0

-- 12xI 8213'-I- 4

00 400 800 1200 1600 2000d [nml

Fig. 20: Particle size distribution (mass distribution) of test latex E,given distribution (-) and the results of ultra- (-) and disc (---)centrifugation.

0 I OO 10o 300 400 miil Inml

Fig. 22: Particle size distribution (mass distribution) of test latex F,given distribution (-) and the results of electron microscopy.

I0 100 200 300 400 500

d,, l nml

Fig. 23: Particle size distribution (mass distribution) of test latex F,given distribution (-) and the results of ultra- (-) and disc (---)centrifugation.

- I

n 100 mi 3on 4oo sno


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156 Part. Part. Syst. Charact. 12 (1995) 148-157

- I n I1 0 1 ik;-, ~ , , , , I.--.n -... L...:+ .....* r0 100 200 300 300 500d,,lnml

Fig. 25: Particle size distribution (mass distribution) of test latex G,given distributions (-, ---, - .. ) and the results of electronmicroscopy.30

ce n t r i fu g a t i o n I tc

Fig. 26: Particle size distribution (mass distribution) of test latex G,given distributions(-, ---, - . ) and the results of ultracentri-fugation.

small number of particles investigated (see Table 5 andFigure 22). The results of the centrifugation methods have to beconsidered separately. The particle size distribution is charac-terized very well by ultracentrifugation. The disc centrifugationmethod records only the polystyrene particles because onlysedimenting particles can be measured by this method (seeTable 5 and Figure 23). Dynamic light scattering and light dif-fraction are not able to resolve the two peaks. The resultingdistribution curves are mostly monomodal and too broad (seeTable 5 and Figure24).

3.2.4 Test Latex GTest latex G with its three constituents of different chemicalcomposition of poly(styrene-co-butadiene) SBR), polystyreneand polychloroprene (see thick full and dotted lines inFigures 25-26) was investigated using only electron microscopyand ultracentrifugation. A fter contrasting the particles withOsO,, electron microscopy finds only two kinds of particles.On the one hand SBR and polychloroprene and on the otherpolystyrene. The first kind cannot be differentiated becauseboth constituents contain double bonds that add OsO,.However, the particle size distributions of all three constituentsare reproduced relatively well (see Table 5 and Figure 25). Incontrast, ultracentrifugation yields, after preseparation accor-ding to the different particle densities by preparative ultracen-trifugation, excellent results for particle size distribution andchemical composition (see Table 5 and Figure 26).

3.2.5 Efficiency Evaluation of the Methods to DetermineSummarizing the results given in Tables 4 and 5 andFigures 7-26, the efficiency evaluation of the methods to deter-mine particle size distributions is as follows (see Table 6).Electron microscopy with quantitative image analysis yieldscorrect particle size distributions with very high resolution inthe small and large particle size ranges and also in avery wideparticle size range. The condition for this, especially in the caseof a wide particle size distribution, is the investigation of anadequate large number of particles which accurately representsthe whole sample. However, this is not always achieved. Becauseof the restricted possibilities to contrast specifically, some pro-blems also arise with the identification of particles of differentchemical composition.With ultracentrifugation, very accurate particle size distribu-tions with very high resolution in particle size and accurate massratios are obtained, not only in the small and in the large parti-cle size range but also for very broad particle size distributions.Similar results are yielded by disc centrifugation, except in thecase of floating (not sedimenting) particles, which cannotmeasured by this method.Dynamic light scattering with NNLS evaluation yields differentresults. The particle size distributions are reproduced fairly wellfor small particle sizes and relatively narrow distribution curves.However, in the large and wide particle size ranges, the distribu-tion curves are too broad and partly bimodal and the resolutionis poor.Even worse results are obtained using light diffraction and theelectrical sensing zone method. These methods are more ap-propriate for the characterization of particles with diameterslarger than 1pm but not of those in the submicron range.

Particle Size Distributions

4 AcknowledgementsThe author thanks Drs.A. Becker,A. Biirkholz, bK J acobsen,G J unkers, A. Karbach, G. Klug, H . Krtimer, H. G. Miiller,T Miinzmay, E-M . Rateike,A. Schmidt, S. Storp, K . Siimmer-mann, H. G. Vogt and K. Wieser, Dip1.-Phys. E.-R Kops,Ing. R. Sneyders, Ch. van Roost, D. Pfiitzenreuther and theirco-workers for participating in the comparative tests and foruseful discussions.

5 References[l] I : Allen, R. Davies: Evaluation of Instruments for Particle SizeAnalysis. Report of Du Pont Engineering Services, 1987.[2].I . Davies,D. L . Colhs: Comparison of the Size Distributionof Bor on Powders as Measured by Malvern Diffractometer andCoulter Counter. Part. Part. Syst. Charact.5 (1988) 116-121.[3]A . BllrkholG R. Boeck: KompatibilitSlt unterschiedlicher Korn-gr(iBenme8verfahren. Report of Bayer AG, 1989.[4] l? J okela, l ? D. I. F letcher, R. Aveyard, J - R. Lu: The Useof Computerized M icroscopic Image Analysis to Determine EmulsionDroplets Size Distributions. J. Colloid Interface Sci. 134 (1990)

417.[5].IB. Bateman, E. J Weneck,D.C. Eshler: Determination of Parti-cle Size and Concentration from Spectraphotometric Ransmis-sion. J . Colloid Sci. 14 (1959) 308.[6] FK Heller, H . L. Bhatnagar,M. Nakagaki: Theoretical Investiga-tionson the Light Scattering of Spheres XI I I . T he WavelengthEx-ponent of Differential nrbidity Spectra. J . Chem. Phys. 36(1962)1163.


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Part. Part. Syst. Charact. 12 (1995) 148-157 157~ ~

Table 6: Efficiency evaluation of the methods to determine particle size distributions.method small particles large particles large particle particles of different advantages disadvantagessize region chemical compositiond, 2 100nmd, s 2,000nmd, 5 500nm d, 5 500nmd, s1,000nmnarrow distributions narrow distributions narrow distributions

monomodal bimodal monomodal bimodal hexamodal bi- and trimodal

d, s 500nm

electron ++ ++ ++ ++microscopy

ultra- ++ ++ ++ +centrifugation

disc ++ ++ ++ +centrifugationdynamic light (+) _ _ _ -scattering(NNLSevaluation)

_ - _ - _ _ _ -ightdiffraction

electricalsensing zonemethod

+

++

++

4-

++

no parametersof the particlesneeded, infor-mation aboutthe particleshapehigh statisticalsecurity

ditto

high statisticalsecurity, veryfast method

high statisticalsecurity, veryfast method

no parametersof the particlesneeded

low statisticalsecurity, limitedcontrastability ofparticles with dif-ferent chemicalcompositionrefractive indexand density ofthe particles andfor particles withdifferent chemicalComposition pre-separation accord-ing to particledensity neededditto, onlysedimenting par-ticles can bemeasuredrefractive index ofthe particlesneeded, sphereequivalent particlediameterin the submicronregion refractiveindex of the par-ticles needed,sphere equivalentparticle diameterlow statisticalsecurity

+ + very good, +good, (+)less good, - bad, - - very bad appropriate for the determination of particle size distributions. The efficiency evaluationis exclusively related to the results of the present comparative test.

[7] H. Lunge: Bestimmung von TeilchengrdDen aus Triibung undBrechungsinkrement. Kol loid-Z. Z. Polym. 223 (1968) 34-30.[8] B. J Berne, R. Pecoru: Dynamic L ight Scattering. Wiley, NewYork 1976.[9] H. A . Stuart: Die Physik der Hochpolymeren, Bd. 11. Springer-Verlag, Berlin, Gbttingen, Heidelberg 1953.

[lo] FK Scholtun,H.Lunge: Bestimmung der Tei l chengrbDenver t ei l ungvon Latices mit der Ultrazentrifuge. K olloid-Z. Z. Polym. 2.50(1972) 782-796.

1111 T Allen: Photocentrifuges. Powder Technol. 50 (1987) 193.[12] K. Leschonski, FKAlex, B. Koglzn: TeilchengrdI3enanalyse. Chem.-Ing. Tech. 47 (1975) Sonderdruck Berufspraxis.[13] R. Weichert:Untersuchungen zur photometrischen Charakterisie-rung von Partikelkollektiven. Habil itationsschrift, Univ. K arlsruhe1983.

[14] T Allen: Particle Size Measurement. Chapman and Hall , London,NewYork 1981.

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Determination of Particle Size-n-particle Size Distributions