Fiber optic dynamic light scattering from concentrateddispersions. 3: Particle sizing in concentrates

John C. Thomas and Victoria Dimonie

We describe measurements of particle size during the course of a latex emulsion polymerization reaction usingfiber optic dynamic light scattering (FODLS). These measurements are compared to results from dynamiclight scattering (DLS) measurements performed in the usual way on diluted samples. It is shown that theFODLS measurements follow the DLS results and reliably track the growth of the latex particles throughoutthe reaction. It thus appears that the FODLS technique is useful for the measurement of particle size inhighly concentrated samples, such as is found in latex production.

1. IntroductionOver the last several years a number of groups have

used optical fiber components instead of the usualoptical components in dynamic light scattering (DLS)experiments.1 -6 The primary interest has been to ob-tain more compact, more robust, and cheaper opticalsystems. However, it was realized that there was an-other potential application of fiber optic systems, i.e.,the study of concentrated colloidal dispersion.2 4 6 In-deed, by using an optical fiber system incorporating adirectional coupler, one can readily make DLS mea-surements on the backscattered light from these dis-persions. 2 '6

Performing DLS measurements on concentratedsamples is attractive because it allows insight into thephysics of the samples, and it admits the possibility ofdoing particle sizing without dilution. If the need fordilution can be eliminated, industrial particle sizingwith DLS will be viable for on-line determinations andmeasurements may also be made on samples for whichdilution is not possible, e.g., because the nature of thesample changes with dilution.

Dynamic light scattering measurements on concen-trated dispersions are complicated by the potential for

John Thomas is with Brookhaven Instruments Corporation, 750Blue Point Road, Holtsville, New York 11742, and V. Dimonie iswith Lehigh University, Emulsion Polymers Institute, Bethlehem,Pennsylvania 18015.

Received 8 March 1990.0003-6935/90/365332-04$02.00/0.C 1990 Optical Society of America.

multiple scattering, particle interactions, and, as wehave shown,6 a changing heterodyne/homodyne mix inthe detected signal. Despite these complicating fac-tors, useful information may be obtained from mea-surements of this type. In the following we outline themethod for fiber optic dynamic light scattering(FODLS) measurements and demonstrate its poten-tial by showing the results of particle size measure-ments over the course of a latex polymerization reac-tion using this technique. The FODLS results arecompared with corresponding results obtained fromDLS on the dilute samples.

II. Basic Theory of DLSThe fundamental quantity measured in a DLS ex-

periment is the photocount autocorrelation function(ACF) of the scattered light:

(2) =(n(0)n())g r= (n)2 (1)

where n(r) is the photon count measured at time delayr. The dynamics of the scattering system are mani-fested in the electric field ACF, g(l)(r), and the rela-tionship between g(l)(r) and g(2)(r) is determined bythe method of detection.

The fiber optic system used generates a significantbackscattered signal from reflections at the fiber end-face and from scattering within the coupler. This actsas a local oscillator signal which beats with the lightscattered from the colloidal suspension and gives riseto a heterodyne component in the detected signal. Ingeneral, there will be a mixture of homodyne and het-erodyne components in the measured g(2)(T) and

(2)g(21(T) = 1 + b[2(n,~nj og(1)(,) + (n )'Ig 1)(,)1219 ~~~~~ n)-2

5332 APPLIED OPTICS / Vol. 29, No. 36 / 20 December 1990

Here b is an instrumental constant of the order of 1,nLO is the (constant) local oscillator count rate, (n,) isthe an erage scattered light count rate, and

(n) = nLO + (ne) (3)

is the total photon count rate.For a dilute suspension of monodisperse noninter-

acting spheres,

lg')(-)l = exp(-rT).

The decay constant is

r = KID,

where D is the particle diffusion coefficient and

K = 4irn sin(0/2)'o

is the magnitude of the scattering vector. Here n is therefractive index of the suspending liquid, 0 is the scat-tering angle, and X0 is the laser wavelength. Forspheres, D is related to the particle radius r by theStokes-Einstein relationship

kBT

D=76 *7

Here kB is the Boltzmann constant, T is the absolutetemperature, and q is the viscosity of the suspendingliquid. This equation provides the basis for particlesizing with DLS.

In view of the complex nature of FODLS measure-ments on concentrated dispersions, we are unable tomodel the ACF precisely. Instead we resort to simplydetermining a mean decay constant P via the methodof cumulants.6-8 This is then used to calculate anapparent diffusion coefficient Dapp and particle sizeusing Eqs. (5) and (7), respectively.

Ill. Experimental ArrangementFigure 1 shows the optical setup used in this work.

It is based on a three-port single-mode fiber opticsystem containing a 1:1 beam splitting directional cou-pler. The output of the 5-mW He-Ne laser is coupledinto the fiber on the two-port side and passes throughthe coupler, out the fiber on the one-port side, and intothe sample being measured. Backscattered light fromthe sample returns up the same fiber to the coupler, atwhich point half goes back toward the laser and is lost,and half goes to the photomultiplier detector. Theoutput of the photomultiplier goes through an amplifi-er-discriminator and on to a Brookhaven InstrumentsBI-2030AT digital correlator. The correlator com-putes the ACF of the scattered light.

Previously6 we used this system to make measure-ments of Dapp on an 170-nm diam latex sphere sam-ple as a function of volume fraction 0 over the range 5.8X 10-5-0.43. A pronounced variation of Dapp with was observed, and we were able to draw a number ofconclusions.

At very low concentrations (less than a few percent)the inherent local oscillator signal from the fiberswamps the light scattered from the spheres. The

(4)

(5)jot

Fig. 1. Experimental setup for FODLS measurements.

(6)

time dependence of g(2)(r) is then determined by thesecond (heterodyne) term in Eq. (2); i.e., heterodynedetection occurs. With increasing concentration, (n,)increases, whereas nLO remains constant, so that thethird (homodyne) term in Eq. (2) becomes more im-portant at the expense of the second term. Eventuallythe homodyne term dominates and homodyne detec-tion occurs. At still higher concentrations, changes inDapp are due to the dynamics of the concentrated dis-persion per se rather than the changing heterodyne/homodyne mix. Between the extremes of concentra-tion there is a region extending over 2 orders ofmagnitude in 0 in which Dapp is fairly constant andwithin 10-20% of the value of the diffusion coefficientthat would be measured in a dilute suspension. Henceit should be possible to determine a reliable particlesize in this region.

IV. MaterialsThe goal of the experimental work was to measure

the evolution of latex particle size during a typicalemulsion polymerization directly in the reaction ves-sel. The reaction was a standard styrene-acrylonitrileemulsion copolymerization to prepare an -30% solidscontent latex. An anionic surfactant, Dowfax 8174(C12 alkylated diphenyloxide disulfonate from DowChemical Co.) was used as the emulsifier. The follow-ing materials were charged into the polymerizationreactor: 100 g of distilled deionized water; 0.625 g ofDowfax 8174 (45.6% active substance); 32 g of styrene;8 g of acrylonitrile.

The reactor was thoroughly purged with nitrogenand heated to 70°C. After the reactor reached a con-stant temperature, 0.02 g of potassium per sulfate ini-tiator was added, and the polymerization began. Af-ter the initiator was added, aliquots were drawnperiodically from the reactor.

Initial attempts to make FODLS measurements di-rectly in the reactor were unsuccessful, because thesample was being stirred and the probe was initiallyfouled by coagulum on the tip. Consequently, theFODLS measurements were made directly on the un-diluted samples as they were withdrawn from the reac-

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Table 1. Latex Particle Size Variation with Reaction Time

Time (min) dDLs(nm)1 dFODLS(nm)P

15 58 78+730 73 68+ 145 91 74±260 96 78 185 108 84 + 2

105 117 89 + 3135 124 103 + 3180 121 113 + 2240 125 113 + 4300 126 256 + 7

a Determined by dynamic light scattering measurements on dilut-ed samples with a BI-90 particle sizer.

b Determined by fiber optic dynamic light scattering on the undi-luted samples.

tor. Dynamic light scattering measurements werethen made on a diluted portion of these samples. TheDLS measurements were made with a BrookhavenInstruments BI-90 particle sizer.

V. Results and DiscussionTable I shows the latex particle size (diameter) de-

termined by FODLS, dFODLS and DLS, dDLS as a func-tion of reaction time. The FODLS data are the meanof five 3-min measurements, whereas the DLS resultsare from a single 3-min measurement at each time. Itcan be seen that, with the exception of the data at 15and 300 min, both dFODLS and dDLS increase steadilywith time until a plateau is reached after -140 min.This corresponds to the final size of the latex particles.Clearly the FODLS results parallel the DLS resultsand reliably follow the growth of the latex particlesduring the reaction. This is more readily seen fromFig. 2, which shows the two sets of particle size data as afunction of reaction time.

We return now to the FODLS data at 15 and 300min. Fifteen minutes into the reaction the latex parti-cles are quite small (-58-nm diameter), and their con-centration is low. Indeed, most of the styrene is stillcontained in large (up to millimeters in size) dropletsof the monomer. Thus light scattering from the latexparticles is relatively weak and only about twice theinherent local oscillator signal (-30 kcps) of the fiber.Consequently, the ACF will contain heterodyne andhomodyne components of similar amplitude. Thepresence of the slower decaying heterodyne termmeans that the data analysis, which assumes homo-dyne detection, will yield a smaller average decay con-stant and, therefore, a larger particle size than expect-ed. Thus we believe that the FODLS result at 15 minis artificially high because of heterodyning in the sig-nal. Note that from this point on both the particle sizeand concentration increase rapidly so that the scat-tered light increases rapidly, and homodyning willquickly dominate.

At 300 min the reaction is complete, and the particlesize and concentration are at their maximum. Thescattered light is 15-30 times the local oscillator level,

150

130

ES.

110

90 -

70 .

500 100 200 300 400

Reaction Time (minutes)

Fig. 2. Latex particle size as a function of reaction time [, deter-mined by standard (very dilute) DLS measurements; O. determined

by FODLS measurements directly on an undiluted sample].

and homodyne detection is assured. In this case thesharp increase in dFODLS clearly cannot be due to heter-odyning and thus must be the result of particle interac-tions in a concentrated dispersion. Note that, afterthe particle size peaks at -140 min, the particle con-centration continues to increase, and the sample at 300min is much more viscous than at 240 min. Note alsothat dFODLS is typically -10% smaller than dDLS. Wehave no explanation for this at present except to sug-gest that this may reflect the different intensityweighting of the particle size distribution at a 90 and1800 scattering angle. Larger particles scatter rela-tively more light toward the forward direction so thatmeasurements at 900 are weighted more toward largersizes than the measurements at 1800. Thus one ex-pects a smaller average size to result from measure-ments at 1800.

VI. ConclusionIn general, the interpretation of results from

FODLS experiments is not straightforward. Howev-er, as the present work has shown, there are a numberof situations in which useful and reliable informationcan be readily obtained from these measurements.Dynamic light scattering has inherent simplicity andspeed advantages as a particle sizing technique, but itsapplication is restricted to dilute suspensions (010-4). The FODLS technique presents the possibilityof characterizing concentrated dispersions with theattendant ease and convenience of DLS.

References1. R. G. W. Brown, "Optical Fibre Sensing Using Light Scattering

Techniques," J. Phys. E 20, 1312-1320 (1987).2. H. Auweter and D. Horn, "Fiber-Optical Quasi-Elastic Light

Scattering of Concentrated Dispersions," J. Colloid Interface Sci.105, 399-409 (1985).

3. R. Falciai, E. Piano, and C. Pontiggia, "Use of Optical Fiber toMeasure Dynamic Light Scattering," Appl. Opt. 25, 3983-3984(1986).

4. J. C. Thomas and S. C. Tjin, "Fiber Optic Dynamic Light Scatter-ing (FODLS) from Concentrated Suspensions," J. Colloid Inter-face Sci. 129,15-31 (1989).

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-i DLS

-- FODLS

-|

5. H. Dhadwal and B. Chu, "A Fiber-Optic Light-Scattering Spec-trometer," Rev. Sci. Instrum. 60, 845-853 (1989).

6. J. C. Thomas, "Fiber Optic Dynamic Light Scattering from Con-centrated Disprsions. 2. Concentration Dependence of the Ap-parent Diffusion Coefficient," Langmuir 5, 1350-1355 (1989).

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