Langmuir 1985,1,373-379

Light-Scattering and Aerodynamic Size Measurements for Homogeneous and Inhomogeneous Microspherest

373

E. James Davis* and Ravindran Periasamy Department of Chemical Engineering, BF-IO, University of Washington,

Seattle, Washington 98195

Received December 28,1984. In Final Form: February 8, 1985

A combination electrodynamic balance/lightcscattering chamber was used to suspend single small particles in a laser beam to obtain light-scattering data for silicate particles and coated microspheres. The light- scattering data for the silicate particles, which had been exposed to temperatures near their melting points, were analyzed by applying the Lorenz-Mie theory to determine the particle sizes and refractive indices as a function of wavelength. The data for microencapsulated ink were used to estimate the optical properties of the polymeric coating. The microencapsulated spheres contained a core phase consisting of a solution of crystal violet lactone in a mixture of mono-/di- polybenzylated xylenes with a coating of etherified

the particles, which provide an independent measurement of the particle size. The drag force measurements were made by using the electric field to maintain the suspended particle at the null point of the balance while exposed to a jet of nitrogen passed through the picobalance.

methylolmelamine polymer. The light-scattering d/ ata are supplemented by aerodynamic drag data for

Introduction The theory of scattering of electromagnetic radiation

from spheres has been widely used since the pioneering work of Lorenz' and Mie2 at the turn of the century, but, as Kerker3 has pointed out, the mother lode of the Lor- enz-Mie equations is still yielding nuggets of new phe- nomena. Furthermore, new instruments are available for precise measurement of new and old phenomena. Of particular interest here is the application of the electro- dynamic balance for the stable suspension of single par- ticles in a laser beam or other excitation source to perform light-scattering measurements. With this instrument particles in the size range of about 0.1-100 pm can be effectively studied. Two applications will be treated (i) the determination of the size and complex refractive index of aerosol particles generated when soil is exposed to very high solar energy fluxes and (ii) the measurement of the characteristics of the polymeric shell of a microencapsu- lated solution.

As light scattering from a homogeneous sphere is just the limiting case of zero coating thickness for a coated sphere, we shall review only the latter, and more general, problem. Aden and Kerker4 formulated and solved the problem of light scattering from two concentric spheres for a plane wave incident upon a sphere with a concentric spherical shell, and Espenscheid et al.5 prepared and measured the light-scattering characteristics of silver chloride spheres encased in a concentric shell of linolenic acid fixed by oso2. The theoretical treatments of these authors will be followed here.

Calculations of scattering from coated spheres based on Aden and Kerker's analysis have been performed by Scharfman? Fenn and Oser,' Pilat,B and Morriss and Collinsg compared that theory with measured extinction coefficients for gold spheres coated with silver. Wyatt'O-" used a combination electrostatic balancellight-scattering photometer to measure the refractive indices of the core and coating of spores (bacillus sphaericus) and water- coated fly ash particles, and Meyer and Brunsting12 applied the theory of Aden and Kerker to determine the mor- phology of nucleated biological cells from light-scattering data. Wang13 reviewed the application of the Lorenz-Mie

'Presented at the symposium on 'The Chemical Physics of Aer- ocolloidal Particles". 188th National Meeting of the American Chemical Society, Philadelphia, PA, Aug 26-3i, 1984.

theory to light scattering by spherical and nonspherical multilayered particles.

The geometry and coordinates of the system under consideration are shown in Figure 1. The incident plane wave is propagated in the z direction, and for the exper- iments described below the electric field vector was po- larized verticaly to the direction of the observation, the photodetector being rotated around the sphere in the y-z plane. They coordinate for Figure 1 is normal to the plane of the paper. The intensity function for this configuration has been solved for by Aden and Kerker in terms of the dimensionless size parameters a and 0 and the complex refractive indices m(l), m(2), and m(3) of core, shell, and surroundings, respectively. The refractive indices may be written

mG) = mj - ikj, j = 1, 2, 3

Where is the dimensionless size of the sphere defined by 0 = 2?rb/X, and a is the dimensionless core size defined by a = 2?ra/X, where X is the wavelength of the incident radiation. It is convenient to define a dimensionless shell thickness by

6 = 2?r(b - a)/X = - a ( 2 )

When we set 6 = 0 and m(l) = m@) the classical solution for a homogeneous sphere is recovered. To interpret light-scattering data it is necessary to invert the phase function (intensity function) to obtain the unknown pa- rameters, such as the radii a and b and one or more of the indices of refraction. The inverse problem is formidable, so forward calculations using assumed values of the pa- rameters and followed by an iterative procedure is the

(1) Lorenz, L. Skr. Nor. Videmk.-Akad. [Kl.] I : Mat.-Naturuidemk.

(2) Mie, G. Ann. Phys. (Leipzig) 1908,217, 377. (3) Kerker, M. Aerosol Sei. Technol. 1982, I , 275. (4) Aden, A. L.; Kerker, M. J. Appl. Phys. 1951,22,1242. (5) Espenecheid, W. F.; Willis, E.; Matijevic, E.; Kerker, M. J. Colloid

(6) Scharfman, H. J. Appl. Phys. 1954,25, 1352. (7) Fenn, R. W.; Oser, H. Appl. Opt. 1965,4, 1504. (8) Pilat, M. J. Appl. Opt. 1967, 6, 1555. (9) Morriss, R. H.; Collins, L. F. J. Chem. Phys. 1964, 41, 3357. (10) Wyatt, P. J. Spores, 1972, V, 61. (11) Wyatt, P. J. Appl. Opt . 1980, 19, 975. (12) Meyer, R. A.; Brunsting, A. Biophys. J. 1975, 15, 191. (13) Wang, D.-S.Y., Ph. D. Dissertation, University of Utah, 1979.

1890, 6, 405.

Sci. 1965, 20, 501.

0 1985 American Chemical Society

374 Longmuir, Vol. I . No. 3,1985

ELECTRIC VECTOR - E

Davis and Periasamy

WYNTING'S

SURROUNDINGS 131

S H ~ L L ( 2 1

Figure 1. Geometry and coordinates for a multilayer sphere.

Fmre 2. Effect of the dimensionless shell thickness on the intensit of the scattered light for m('1 = 1.696 - io, m(" = 1.610 - io, m(J = 1.OOO - io, and a = 5.0.

more tractable approach used here. Figure 2 illustrates the calculated effect of 8 on the light-scattering phase function (intensity vs. angle profile) for a coated droplet with m('] = 1.696 -io, m(2] = 1.610 - io, m@] = LOO0 - io, and 01 = 5.0. The complicated topology shown in the figure indicates that the phase function is greatly affected by a variation in 8, for the relative magnitudes of the peaks depend strongly on 8 even though the angular variations due to 6 are not too great. Hence it should be possible to determine 8 from measured intensity profiles. For a ho- mogeneous sphere of unknown composition the only pa- rameters to be determined are a and m"].

Apparatus and Experiments The electrodynamic balance described by Davis and

Ravindran" was modified to provide flow of a metered jet of nitrogen upward along the axis of the light-scattering chamber. The experimental system is shown in Figure 3. The scattered light was recorded as a function of angle using a photomultiplier tube which was rotated in the horizontal midplane of the balance. The solid particles, in the form of a very dilute suspension in water, were charged and injected into the balance from a capillary tube connected to a microliter syringe. The capillary was electrified to 2-5 kV dc to cause a droplet partially formed at the tip to drop into the balance, and the peak-to-peak ac voltage used to focus the particle was preset to about lo00 V. After injection of the particle the dc voltage Vo was set to balance the gravitational field, following the equation

Va = -mgzo/Coq (3)

where m is the particle mass, q is ita charge, g is the gra- vitational acceleration constant, and Co and zo are geo-

PbRTICLE INJECTOR

GAS EXIT

DYE LAISER

TELESCOPE - RAYLEIG

HORN

I I TO PHI

GAS CYLINDER " H C ~ ~ ~ $ N T

Figure 3. Combination electrodynamic balanc+ght-smttering cell used for the experiments.

metrical constanta of the balance. After the water evap orated, as indicated by no further change in Vo, light- scattering data were taken by actuating a stepping motor used to rotate the photodetector. Voltages from the stepping motor and photomultiplier tube were recorded on an X-Y plotter and were digitized and stored on magnetic disks using a MINC-23 data acquisition system. The digitial computer was also used to analyze these in- tensity-vs.-angle data to obtain the particle size.

An independent determination of particle size was made by measuring the aerodynamic drag force on the micro- sphere. After the particle was balanced stably at the midplane of the balance and the light-scattering data had been obtained, nitrogen was introduced through a hole in the bottom electrode. As the flow rate was increased the dc voltage Vdc required to maintain the object at the midplane was adjusted and recorded. If U is the velocity of the jet at the center of the balance, the drag force for the conditions used here is given by

(4)

where p is the gas viscosity, D is the particle diameter, and Re is the Reynolds number defmed by Re = DpU/p. Here p is the gas density.

The electrostatic force, FE, required to balance the drag force and gravity is given by

FE = CoqV,/zo = BlrpDU(1 + 3Re/16) - mg (5) When the flow rate is increased to the point that the

aerodynamic drag balances the gravitational force no dc voltage is required for suspension, and eq 5 can be used to determine the diameter. In this ease with m = l rpp /6 , where pp is the particle density, the diameter is given by

D = 27U:/lSp& + [(27U~/16p&)2 + 18pU,/p&]'/2 (6)

FD = -3lrpDU(1 + 3Re/16)

and for Re < 0.1 this reduces to

D = [18pU,/p&]'l2 (7)

Thus, the diameter can be calculated from the m e a s d critical velocity, U,, required to balance gravity. The ac- curacy of this technique is limited by the accuracy of the calibration of the jet velocity, which waa performed using liquid dropleta of known refractive index and polystyrene latex (PSL) spheres. The droplet diameters were deter- (14) Davis, E. J.; Ravindrm. P. Aerosol Sei. Technol. 1982, I, 337.

Light-Scattering and Aerodynamic Size Measurements

Pigurs 4. h n i n g electron micrograph of the micrmncapsulated spheres.

mined by light scattering. We shall compare the diameter obtained by drag force measurement with that extracted from the light-scattering data.

Sample Preparation The microencapsulated particlea used in the experiments

were prepared by coacervation, an emulsion polymer- ixation process reviewed by Speiser16 and Watanahe and Haysashi.16 The internal phase (core) consisted of a so- lution of crystal violet lactone (CVL) dinsolved in a mixture of mono- di- polybenzylated xylenes (Santosol-150). The shell was formed from a mixture of melamine and form- aldehyde. The continuous phase of the emulsion consisted of 67 g of a mixture of commercially available emulsifiers (35 g of a 10% aqueous solution of EMA-31 and 32 g of a 20% aqueous solution of EMA-1103) added to 150 g of water. The pH of this solution was adjusted to 4.0 by adding a 20% solution of NaOH, then 80 g of a 0.5% solution of CVL in Santosol-13l and 20 g (16 g dry) of the melamic+formaldehyde mixture were introduced into the continuous phase. The total mixture was milled at high speed to obtain droplets of about 3-pm diameter in the resulting emulsion.

During the emulsification process the condensation products (methylolmelamines) of the polymerization re- action formed a resinous skin around the core material. After a stable emulsion was formed the shell was cured by stirring and heating to 55 OC. A scanning electron mi- crograph (SEM), shown in Figure 4, indicates that the resulting microcapsules are indeed spherical. The micro- spheres were observed to vary in size from about 0.3 to 4 pm in diameter. By material balance it is estimated that if the core and shell materials were uniformly distributed among the microcapsules and if complete reaction oc- curred the ratio of the m w of the shell to that of the core should he 0.2.

As we shall show from lightscattering data and aero- dynamic drag measurements, appreciable coagulation of the microcapsules murred during storage, so before their injection into the picobalance the concentrated suspension was diluted in a ferric chloride solution a t pH 1.4 and placed in an ultrasonic bath for dispersion of the particles. The dilute suspension was introduced to the syringe for injection into the light-scattering chamber.

The silicate particles examined were obtained from solar furnace experiments in which high thermal fluxes were generated to create a dust cloud similar to that encoun- tered in thermonuclear blasts. Aerosol fdtera were installed at various vertical positions in the solar furnace to sample

(15) Sllebr, P. 'Dm and Pharmaeautid Science.": Nixon. J. R.. . . Ed.; Mark1 Dekker: New York, 1976: Vol. 3.

Nhon, J. R.. Ed.; Mareel Dekker: New York. 1976; Vol. 3. (16) Watanabe. k: Hayashi. T. ' b a n d Pharmaeeutid S e n a s ;

Langmuir, Vol. 1. No. 3, 1985 375

'oor--T--r 1 \

Be.[ .\ w w r

z

D 11.4519 ""I . L..eBOnm

MIE THEORY -

Figure 5. Light-scattering data and the Lorenz-Mie theory for a dust particle ohtained at two different wavelengths for run 60.

the particulate matter, and wall wipings were also collected. In general, particle sizes and shapes varied greatly, as indicated by SEM, and many of the dust particles melted and formed spheres or nerar-spheres with protuberances due to outgassing. Samples ohtained from the upper, and cooler, part of the solar furnace showed few spherical particles, and the unmelted crystalline or partly amorphous materials had irregular shapes.

The very rapid heating and cooling sequence associated with the thermal wave in the solar furnace might he ex- pected to lead to amorphous spheres for those particles that melted, and the SEM results show no observable crystallinity of the spheres. Microcrystals formed within the spherical particles would he expected to affect the light mttering if they are of the order of the wavelength of light, and in this event the spheres could not he considered to be homogeneous.

The silicate particles studied were washed from the filters and injected into the electrodynamic balance as discussed above. X-ray analyses (EDAX) of the particles demonstrated that mast were mixed silicates of AI, Ca, Fe, K, Mg, and Na. In a few samples small amounts of copper were detected.

Experimental Results Figure 5 shows raw data of normalized intensity M.

scattering angle obtained a t two wavelengths, 457.9 and 488.0 nm, for a typical silicate particle. Also shown are the theoretical predictions from the Lorenz-Mie theory which 'best fit" the data. Considering that some deviations from a perfect sphere are likely and the data are noisy, the agreement between theory and experiment is satisfactory. Davis and Ravindran" described the method of data analysis used here. which was based on a multiparameter optimization algorithm. For the results presented in Figure 5 and for a third run using a wavelength of 514.5 nm the dimensionless radii a, obtained by using the three wave- lengths, were 12.60, 12.77, and 12.89, respectively. These values correspond to calculated radii of 0.918,0.992 and 1.056 F, with a mean of 0.989 pm and a mean deviation of 4.8%, which is fairly representative of the results for about 50 light-scattering runs involving various samples. The complex refractive indices obtained by data analysis are 1.551 - i0.003, 1.525 - i0.004, and 1.508 - i0.005, respec- tively, for these same data. The imaginary component is so low here that there is large uncertainty in the values reported. When phase functions are computed setting k, = 0 the agreement between experimental and theoretical results is less satisfactory (statistically) than when the optimized parameters are used, hut one must place little confidence in the numerical values of k, reported here.

376 Langmuir, Vol. 1, No. 3, 1985 Davis and Periasamy

Table I. Complex Refractive Index and Size of Silicate Particles for Three Wavelengths

refractive index

run wavelength, nm a radius, um m, ki

57

60E

60F

69

104

107

108

136

138

1180

457.9 488.0 514.5 457.9 488.0 514.5 457.9 488.0 514.5 457.9 488.0 514.5 457.9 488.0 514.5 457.9 488.0 514.5 457.9 488.0 514.5 457.9 488.0 514.5 457.9 488.0 514.5 457.9 488.0 514.5

12.60 12.77 12.89 5.008 4.910 5.378 4.604 4.841 4.618

12.53 11.84 11.44 12.23 12.18 12.38 13.65 12.40 12.53 12.75 12.88 13.08

12.40

14.14 14.59 15.06 9.61 9.20 9.30

0.918 0.992 1.056 0.365 0.381 0.440 0.335 0.376 0.378 0.913 0.919 0.937 0.891 0.946 1.014 0.994 0.963 1.026 0.929 1.000 1.071

0.963

1.030 1.133 1.233 0.700 0.714 0.761

1.551 1.525 1.508 1.705 1.590 1.571 1.626 1.600 1.633 1.562 1.557 1.490 1.601 1.593 1.573 1.594 1.574 1.559 1.529 1.510 1.481

1.582

1.723 1.674 1.613 1.719 1.716 1.709

0.003 0.004 0.005 0.054 0.049 0.018 0.036 0.030 0.026 0.003 0.005 0.012 0.024 0.007 0.008 0 I 006 0.007 0.005 0.005 0.005 0.007

0.002

0.007 0.010 0.000 0.029 0.001 0.026

The results obtained for m,, the real component of the refractive index, are consistent and suggest that ml de- creases with an increase in wavelength, but for a set of runs using different wavelengths the scatter is too large to permit a dispersion relation to be formulated for ml from the data.

Results for about 30 light-scattering runs for silicate particles in the micrometer size range are summarized in Table I. The range of values of ml obtained are in agreement with handbook values for bulk minerals such as andesine (1.549), wollastonite (1.616), kaolinite (1.561), orthoclase (1.518)) enstatite (1.650), gehlenite (1.669), kyanite (1.712), and other mixed silicates, but only ele- mental analyses of the particles examined have been de- termined. Data are not available in the literature for values of k, with which to compare, but for the reasons discussed above little confidence can be placed in the values listed in Table I. The numerical values of kl are given only to indicate the "best fit" parameters obtained by optimiza- tion. Greater confidence can be placed in the radii and real component of the refractive index, for the calculated phase functions are highly sensitive to size and moderately sensitive to m, in the ranges encountered here.

Larger particles (a > 20) have a much more complicated light-scattering profile than those shown in Figure 5, and the optimization procedure used to determine the size and complex refractive index becomes unsatisfactory as CY in- creases because the number of data points that must be used increases and convergence problems abound. Figure 6 shows phase functions calculated for DBP for a = 30, 50, and 100. Because of the strong dependence of the phase function on size indicated in the figure it is most desirable to have either a simpler method of determining the size or a better estimate for the trial value of size used to initiate the computations. Measurement of the drag force provides a reliable alternative to light scattering for size determination, and a simple rule of thumb for size

80

60

4 0

20

0

tbs

-. I

LI I i

!L 0 40' 50' SCATTERING 60' ANGLE 70' 80' 90'

Figure 6. Phase functions calculated for various dimensionless sizes for DBP, m(') = 1.491 - io.

v MICROSPHERES

P I N E N E 0 S I L I C A T E S P H E R E S

Y

v)

Y 0

f 40

/ i

20

0

J -I

d 100 loo0

0 . DIMENS'ONLESS OPTICAL S I Z E

Figure 7. Number of peaks between 40' and 90° for refractive indices in the range of interest here.

estimation can be obtained from the Lorenz-Mie theory calculations for a wide range of sizes. As a increases the number of peaks over some finite range of angles increases, and that number is less sensitive to the refractive index. Figure 7 is a composite plot of the number of peaks in the range 40' < 6 < 90' as a function of CY for the refractive indices of microspheres (1.590), pinene (1.466)) DBP (1.491), DOP (1.48718 and silicate particles (1.481-1.719). By simply counting peaks on a stripchart recording of intensity vs. angle one may obtain an accurate estimate of a.

Figure 8B is a stripchart record of intensity vs. angle obtained with the rotating photomultiplier tube for a silicate particle substantially larger than those listed in Table I. The incident beam from a tunable dye laser had a wavelength of 605 nm. The number of major peaks in the range 40-90' is just over 10, and from Figure 7 we estimate a = 40. The upper part of Figure 8 shows the theoretical phase function calculated from the results of the optimization program, which yielded CY = 41.9 (D = 8.07 pm) and m(l) = 1.517 - iO.001. Although the exper- imental results have not been corrected for the background

Light-Scattering and Aerodynamic Size Measurements Langmuir, Vol. 1, No. 3, 1985 317

500

- -301

40" 50' 60° 70° SOo 90' SCATTERING ANGLE

Figure 8. Comparison between raw light-scattering data and the Lorenz-Mie theory for a silicate particle.

intensity and the experimental and theoretical results have different scale factors for the intensity, there is excellent agreement between the raw data and theory with respect to the positions and relative heights of the peaks. Agreement between measured and calculated phase functions supports the assumption that the silicate par- ticles are homogeneous spheres, lacking crystallinity, a t least on a size scale that affects light scattering.

Drag force measurements were also made for the silicate particles and liquid droplets, and Figure 9 is a typical plot of the dc voltage required for suspension at the null point of the picobalance as a function of the nitrogen flow rate for three droplets. The flow rate for which Vd, = 0 cor- responds to the balance between the gravitational force and the drag force, and from calibration of the jet velocity as a function of flow rate and from knowledge of the droplet density the aerodynamic diameter was calculated from eq 6. Table 11 compares the diameters measured by aerodynamic drag measurements with the peak-counting results for a number of solid particles and liquid droplets. There is good agreement between the two methods, par- ticularly for the larger particles, and these results lend confidence to the radii reported in Table I.

The accuracy of the size determination by aerodynamic drag measurement depends on the accuracy of calibration of the jet velocity, which showed significant scatter (mean deviations of about 10%) for flow rates below 2 mL/min with the rotameter and jet used. For flow rates greater than 10 mL/min mean deviations were less than 5%. Better reproducibility is achievable with a more accurate low-range flow meter.

The experiments with coated particles followed the procedure used for the dust particles, but the unknown parameters in this case are the refractive index of the shell, m(2), the dimensionless core diameter, a, and the dimen- sionless outer diameter, 0 (or, alternatively, the dimen- sionless shell thickness, 6). The refractive index of the liquid core was measured independently with an Abbe refractometer to give 1.696 at room temperature, the tem-

,/ DOP 1 I J 0 DBP I

- -40/ 50 0 10 20 30 40 50 60 70

NITROGEN FLOW RATE, ml/min

Figure 9. Dc voltage required to suspend liquid droplets as a function of N2 flow rate.

Table 11. Comparison between Measured Aerodynamic Radii and Light-Scattering Radii for Liquid Droplets and

Silicate Particles aerodynamic light-scattering

particle radius, pm radius, pm pinene 9.20 9.15

pinene 14.7 14.9 DBP 21.3 21.5 DBP 18.1 18.0 DBP 15.1 17.1 silicates, run

pinene 11.9 12.0

57 3.78 2.89 60A 10.0 9.87 60B 3.30 3.19 60C 2.83 2.89 60D 4.18 4.04 104A 3.85 4.14 104B 3.85 3.56 136A 3.31 3.76 136B 3.85 3.47 138A 5.97 5.78 138B 3.26 4.04 1180A 4.18 4.04 1180B 3.02 2.70

perature of all experiments. The maximum value of 6 corresponds to the case of complete polymerization of the melamine and formaldehyde, so the trial value of 6 used in the optimization procedure was calculated from the amounts of core solution and monomers used in the sample preparation.

Figure 10A shows typical light-scattering data for sus- pended particles obtained from a sample of microspheres. The phase function data shown in Figure 10A are signif- icantly different from those shown in Figures 5 and 6, for there is more backscattering and there is stronger scat- tering in the vicinity of 90°. Furthermore, the data appear noisier than the results shown in Figures 5 ,6 , and 8. The optimization algorithm failed to find satisfactory agree- ment with the Mie theory for this particle and others with a similar phase function structure. Many of the particles

378 Langmuir, Vol. 1, No. 3, 1985 Davis and Periasamy

c

.k \\I AGGLOMERATED MICROSPHERES i

( B ) i SINGLE PARTICLE

40' 60" 80' 100" ANGLE

Figure 10. Light-scattering data for a microencapsulated particle.

Table 111. Results for Coated Microspheres particle @ D, pm 6 6,, m ( 2 )

117 15.6 3.14 0.62 0.600 2.125 - i0.023 118 23.0 4.63 0.14 0.885 2.300 - i0.13 119 18.3 3.68 0.13 0.704 2.542 - io 911 20.7 4.17 0.034 0.796 2.302 - i0.034

examined, including the one corresponding to Figure 10A, showed greater backscattering than that predicted from the Mie theory computations, so aerodynamic drag mea- surements were made to determine the particle size. Typical aerodynamic diameters were found to be 8.66 and 9.42 pm, which are considerably larger than expected from the SEM (most particles less than 2 pm in diameter). This suggests that the paricles examined were agglomerations of microspheres, and in the initial experiments all of the light-scattering data appeared suspect.

To examine the question of agglomeration the micro- spheres were diluted and supended in a ferric chloride solution with pH 1.4. A small sample of the suspension was injected by means of the hypodermic needle and trapped in the light-scattering chamber. Figure 10B is a typical experimental phase function for a microsphere obtained from the treated sample of microspheres. This phase function is more like Mie theory predictions for a single sphere, and the optimization procedure was used to analyze data of this type.

Figure 11 is a representative comparison of the Mie theory and data for a coated particle for which the opti- mization routine converged, and Table I11 lists the pa- rameters p, 6,6,, n~@), and the microsphere outer diam- eter, D, determined for four such microspheres. These data were obtained using a helium-neon laser with a wavelength of 632.8 nm. The diameters measured for these micro- spheres are less than half (3.1-4.6 pm) the aerodynamic diameters measured for the particles that were suspected of being agglomerated (8.7-9.4 pm), which suggests that agglomeration was likely. Attempts to measure the aero- dynamic diameter of the single microspheres generally led to the microsphere being expelled from the chamber as soon as the nitrogen flow was turned on. The particles were too small to be suspended in the nitrogen stream with the flow control system used. Again this is an indication that the particles were smaller than the particles not

0 -I

1 - MIE THEORY

4 0 DATA FOR RUN 119

l o o t v a, 0 I I

40' 500 60' 70' 80' 90' loOD 110' 120° _. SCATTERING ANGLE

Figure 11. Comparison between experimental and calculated phase functions for microencapsulated particle number 119 with 0 = 18.3, 6 = 0.13, and m(') = 2.542 - io for the theoretical com- putations.

treated with the ferric chloride solution. The dimensionless shell thickness, a,,, listed in Table

I11 was calculated on the assumption that all of the mel- amine and formaldehyde were used to form the shell and that the ratio of the mass of the shell to the mass of the core was 16:80, which corresponds to the amounts of CVL solution and monomers used in the formulation. Table I11 shows that, except for particle number 117, all of the estimated shell thicknesses were well below this theoretical value. The wide range of thicknesses determined from the light-scattering data casts doubt on the physical signifi- cance of the numerical values.

The real part of the refractive index of the polymeric shell, m(2), averaged 2.317, a relatively large refractive index compared with the core material (m(l) = 1.696 - io). The imaginary part of m(') varied greatly (0-0.132), but these values cannot be considered significant because the de- termination of four parameters from the phase function data is not sufficiently sensitive to variations in the im- aginary part of m(2) to place confidence in its determina- tion. Use of K 2 = 0 in the calculations yields phase func- tions not greatly different from the results of the opti- mization.

Discussion of Results Light-scattering results for liquid droplets, solid

spherical silicate particles, and coated microspheres all indicated that the number of peaks in a suitably large range of scattering angles is a good indicator of particle size for dimensionless sizes greater than about 15. Aero- dynamic drag force measurements yield aeroynamic sizes in good agreement with the light-scattering results.

The agreement between phase functions measured for coated microspheres and those calculated from the Mie theory is not as good as results obtained for homogeneous solid spheres and liquid droplets. One source of error is noise in the data due to laser intensity fluctuations. Figure 10B clearly shows the noise superposed on the phase function. A second source of disagreement is nonuni- formities in shell thickness, and to explore this possibility a sample of coated particles was frozen, microtomed, and examined with a scanning electron microscope. Figure 12, an SEM obtained in this way, shows that the shell wall of the particles was, indeed, thin, and it appears that the shell thickness is not uniform. It is not possible to obtain ac- curate quantitative data from such micrographs, for the process of freezing and cutting the sample causes much distortion of the particles. The thin shell wall shown in the figure lends support to the values of wall thickness estimated from light-scattering data, but it must be con-

Langmuir 1985,1,379-387 379

which generally gave diametera of 3-4 pm. The stability characteristics of a particle in the electrodynamic balance depend on the charge on the particle and the amplitude and frequency of the ac voltage used to trap a particle, and it is likely that the smaller miemspheres were unstable for the ac field used in the experiments. The sensitivity of the particles to the initial transient state of the nitrogen flow when the microvalve was opened indicates that the 34" particles were near an unstable state, for they were readilv lost when the forces on the particle were perturbed

Figure 12. Scanning electron micrograph of a eample of mi- croencapsulated particles that was frozen and microtomed.

cluded that for the thin-walled layered spherea examined here there is ambiguity associated with quantitative in- terpretation of the light-scattering data because of the difficulty in determining four parameters (a, 6, and the two components of m(*)) from the light-scattering data. As in the case of the silicate spheres one can place more confi- dence in the size and real component of the refractive index than in the shell thickness and the imaginary com- ponent of ita refractive index.

Figure 12 also shows many particlea with diameters less than 1 in contrast with lightscattering measurements,

due to the flow. For silicate ~artiela and liouid dronlets with diameter8

greater than pm there is g& agreement between the aerodynamic diameter and the light-scattering diameter, and modifications to the flow system and jet diameter should permit aerodynamic drag measurements to be made with smaller particles.

Acknowledgment. Part of this -cb wan supported by the Defense Nuclear Agency under Contracta DNA 001-82-C-0224 and DNA 001-&L-C-0293. We are grateful to Donald Churchill and Richard Bowman of Appleton Papers Inc. for preparation of the encapsulated ink mi- crospheres.

Electrodynamic Balance Stability Characteristics and Applications to the Study of Aerocolloidal Particlest

E. James Davis Department of Chemical Engineering, BF-10, University of Washington,

Seattle, Washington 98198

Received December 28,1984. I n Final Form: February 8,1985

The theory of the electrodynamic balance, a device used for the study of single aerosol particles in the size range 0.1-100 lun, is extended to aualyze the particle's &ability chmacterktica with and without feedba& contmL A new analytical approximation is obtained for the de electric field strength for the bihyperboloidal electrodynamic balance, and the results are applied to the equations of particle motion to examine the marginal stability envelope. On the basis of the stability theory, it is shown that the aerodynamic drag can be determined by measuring the onset of instability. The drag force can ala0 be measured directly by suspending the particle in a jet of air flowing at various velocities, and experimental results are reported for spherical droplets and nonspherical particles. The dc voltage required to maintain the particle position against the opposing forces of aerodynamic drag and gravity was measured to determine the drag force.

Introduction The electrodynamic balance has become an important

instrument for the study of the chemical physies of single aemlloidal particles. Although the device dates from the electric mass filter of Paul and Ftaether' in 1955, only in the past 5 years has its potential for aerosol research been recognized. With this device a single charged droplet or particulate is suspended stably by superposition of ac and de electric fields in a cell consisting of two endcap elec- trodes and a ring electrode located midway between the endcaps. The simplest form, used by Straubel? consists of two flat plates with a ring located at the midplane be- tween the plates. An ac potential applied to the ring focuses the particle, and a dc potential difference applied to the endcaps is used to balance the gravitational force.

In thin way a particle in the size range of about 0.1 to 100 pm can be suspended stably in a laser beam with or without gaa flow through the chamber.

Davis3 haa reviewed the development of the electrody- namic balance and its applications to lighhcattering measurements, particle mam and charge measurements, droplet evaporation, and other aerosol phenomena. The symposium for which this paper has been prepared in- volves more than a dozen applications of the balance, in- cluding Raman, infrared, and photophoretic spectroscopy of single droplets or particulates, gas/particle chemical reactions, and droplet solution behavior. New applications of the balance are appearing frequently.

It is the purpose of this paper to extend the existing theoretical analyses of the electrodynamic balance and to

'Pressnted at the Symposium "The Chemical Phpica of Aero- colloidal Particles". 188th National Meeting of the American Chem- ical Society, Philadelphia, PA, Aug 26-31, 1984.

0743-7463/85/2401-0379$01.50/0 0 1985 American Chemical Society