Langmuir 1995,11, 80-86
80
Layer Formation on Microdroplets: A Study Based on Resonant Light Scattering James L. Huckaby and Asit K. Ray* Department of Chemical Engineering, University of Kentucky, Lexington, Kentucky 40506-0045 Received July 1, 1994. I n Final Form: October 14, 1994@ A technique for determining the absolute size and refractive index, as well as small size and refractive index changes, of a microdroplet has been presented. The technique utilizesthe wavelengths ofthe intensity peaks (resonances)of light scattered by a droplet observed in the planes parallel and perpendicular to the plane of incident light polarization and unambiguously distinguishes droplet growth by the formation of a layer from homogeneous growth on the basis that the formation of a layer results in substantially different spectral shifts of the scattered transverse electric (TE) and transverse magnetic (TM) mode resonances. The technique has been applied to study absorption and layer formation on single droplets exposed to a vapor of a nearly immiscible component. Wavelengths of TE and TM resonances measured by scanning with a laser are used to determine the size and wavelength-dependent refractive index of a droplet prior to exposure to the vapor. The spectral shifts of two resonances,one TE and another TM, after the exposure are used to calculate size changes due to the absorption and layer formation. The experimental data show good agreement with the theory, and the results suggest that the presence of a monolayer on a droplet can be detected by the technique.
Introduction The formation of multicomponent, multiphase droplets is a process of interest in many areas, such as cloud formation, spray drying, droplet combustion, removal of fine particles in eMuent gases by water vapor condensation, and pesticide and pharmaceutical aerosols. Multiphase droplets exist either as layered or as emulsion droplets. Layered droplets can form by the interaction of single phase droplets and vapor of a component that is partially or nearly immiscible with the droplet phase. Initially, vapor molecules absorb in the droplet phase and, subsequently, form an immiscible layer on the droplet surface by heterogeneous nucleation which may be preceded by the formation an adsorbed monolayer.' Such a process is likely to be responsible for the presence of organic layers found in atmospheric aerosol^.^^^ The formation of an immiscible layer on a droplet has not been examined critically due to the lack of precise experimental tools for characterization of layered particles. Since the experimental verification of size and refractive index dependent resonances (i.e., intensity peaks) in light scattered by a sphere, resonant scattering has been extensively used in size and refractive index (i.e. composition) determination of homogeneous droplet^.^-^ Despite the availability of an accurate theory to describe scattering by a concentrically layered sphere, developed by Aden and Kerker,lo scattering resonances, however, have only
* Author to whom correspondence
should be sent. Abstract published inAdvance ACSAbstracts, J a n u a r y 1,1995. (1) Van Der Hage, J. C. H. J. Colloid Znterfme Sci. 1984,101, 10. (2) Husar, R. B.; Shu, W. R. J . Appl. Meteorol. 1975,14, 1558. (3)Gill, P. S.; Graedel, T. E.; Weschler, C. J . Reu. Geophys. Space Phys. 1983,21,903. (4) Richardson, C. B.; Hightower, R. L.; Pigg, A. L. Appl. Opt. 1986, 25,1226. ( 5 ) Fung, K.H.; Tang, I. N.; Munklewitz, H. R. Appl. Opt. 1987,25, 1282. (6) Taflin, D. C.; Zhang, S. H.; Allen, T.; Davis, E. J . AICHE. J . 1988, 34, 1310. (7)Ray, A. K.;Johnson, R. D.; Souyri, A. Langmuir 1989,5, 133. (8) Lin, H.-B.; Huston, A. L.; Eversole, J. D.; Campillo, A. J.Opt. SOC. Am. B 1990,7,2079. (9) Ray, A. K.; Souyri, A.; Davis, E. J.;Allen, T. M. Appl. Optics 1991, 30,3974-3983. (10)Aden, A. L.; Kerker, M. J. Appl. Phys. 1951,22,1242. @
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been used in a few studies8J1J2involving evaporation of layered droplets. Techniques used in those studies are applicable to droplets that undergo significant size changes. In a recent study,13we have shown that minute size and composition changes of a homogeneous droplet due to the absorption of a sparingly soluble vapor can be detected from the positions of two resonances before and aRer the change and suggested on theoretical bases that a similar scheme can be adopted to detect a layer on the surface of a droplet. In this paper, we provide experimental data on scattering from a single droplet exposed to a nearly immiscible vapor and show that the formation of a layer, as thin as one monolayer, on the droplet surface can be detected by the technique presented. In the following section we present the theoretical basis of the experimental scheme used in this study by briefly reviewing the theory of light scatteringby a concentricallylayered droplet.
Light Scattering by Concentric Spheres When a spherical particle, homogeneous or layered, is illuminated by a linearly polarized monochromatic light beam of intensity Ii and wavelength A, the intensity of light scattered by the particle in the plane perpendicular to the plane of incident beam polarization is given by14-16
where r (>+A)is the distance from the center of the sphere, and 8 is the scattering angle measured from the backside of the particle. The scattered intensity Iz, in the plane parallel to the plane of polarization, can be obtained from (11)Hightower, R. L.; Richardson, C. B.; Lin, H.-B., Eversole, J. D.; Campillo, A. J. Optics Lett. 1988,13, 946. (12) Ray, A. K.; Devakottai, B.; Souyri, A.; Huckaby, J. L. Langmuir 1991,7, 525. (13)Ray, A. K.; Huckaby, J. L. Langmuir 1993,9,2225. (14) van de Hulst, H. C. Light Scattering - by . Small Particles; Dover: New York, 1981. (15)Kerker, M. The Scattering o f l i g h t a n d Other Electromagnetic Radiation; Academic Press: New York, 1983. (16) Bohren, C. F.;Huffman, D. R.Absorptionand Scatteringoflight by Small Particles; Interscience: New York, 1983.
0 1995 American Chemical Society
Langmuir, Vol. 11, No. 1, 1995 81
Layer Formation on Microdroplets the above expression by interchanging the angle-dependant functions n, and t,, which are defined by n,(@ =
Pi(cos 8 ) sin 8
where Pk(cos8) is the associated first-order Legendre function of the first kind of degree n. The scattering coefficients, a, and b,, may be written in the following forms:17
An an = A n
b, =
+ LC,
Bn Bn + a n
(3) (4)
For a homogeneous sphere of radius a, the scattering coefficients, a,'s of the transverse magnetic (TM) and bn)s of the transverse electric (TE) modes, depend on the size parameter, defined byx = 2naI4 and the refractive index of the sphere relative to the surrounding medium, m. The parameters An, Bn, Cn, and D,, in eqs 3 and 4, are related to the Riccati-Bessel functions of the first and second kinds of order n with arguments x and mx.17 For a concentric sphere of core radius a, and outer radius a, the scattering coefficients depend on the core and outer size parameters, defined byx, = 2na& andx = 2nal2, and the core and outer layer refractive indices m, and m , relative to the surrounding medium. The expressions for A,, B,, C,, and D, for a concentric sphere are as follows:
where
and w,(x) and ~ , ( x )are the Riccati-Bessel functions of the first and second kinds of order n, respectively. The scattered intensity from a homogeneous sphere at a fixed scattering angle as a function of size parameter shows sharp peaks, called resonances, superimposed on a slowly varying intensity profile. A resonance occurs for values of x and m for which the imaginary part of the denominator of one of the scattering coefficients goes to zero and the coefficient itself attains a maximum value of 1. The locations of resonances can be computed from (17)Huckaby, J. L.; Ray, A. K.; Das, B.AppZ. Optics, in press.
the roots of C , = 0 for a TM mode coefficient (i.e., a,) and D, = 0 for a TE mode coefficient. These resonances are identified by the mode number, n, and an order number, C, where the first root is labeled t = 1. The intensity of light scattered by a concentric sphere also shows resonances similar to those found in scattering by homogeneous spheres; however, their locations depend on x, x,, m , and m,. Hightower and Richardson'* and Locklghave theoretically examined resonances from concentric spheres. An experimental intensity versus time spectrum obtained from an evaporating homogeneous or layered droplet illuminated by a fixed-wavelengthlight shows a series of resonances due to the variation of the size parameterb). For a given refractive index (or indices) and scattering angle, 8,the shape of an intensity spectrum is unique and depends on the size parameter interval(s). Several investigators have obtained the size of a homogeneous d r ~ p l e t or ~ -the ~ core and outer radii of a layered droplet11J2 by matching the shape of an experimental spectrum with a theoretical spectrum. The fixed wavelength technique is applicable to situations where the size of a droplet changes significantly since about 12 resonance peaks are needed for an unambiguous identification. For a homogeneous droplet with time invariant size, the size parameter can be varied only by varying the wavelength of the incident light. In such a scattered intensity versus wavelength spectrum, the wavelengths at which resonances are observed depend on the size and refractive index of the droplet. By aligning the observed resonating wavelengths with theoretical values, the size of the droplet and its refractive index can be determined with high precision.17 When the droplet undergoes a homogeneous size change due to, say, the absorption of a vapor, the position of each ofthe resonating wavelengths change. The shift of a resonance (i.e., the difference between the final and initial wavelengths ofthe resonance) depends on the size and refractive index changes and is different from the shift that occurs when the same size change results from the incorporation of a layer on the droplet. This fact forms the basis of the method used in the present study to determine size changes of homogeneous and layered droplets. To understand the foundation of the method used, consider a homogeneous droplet of component A illuminated by a tunable laser beam. Initially, the droplet has a radius of 20 pm, and its refractive index is mA = 1.400. By scanning the laser with appropriate detection schemes, two theoretical resonances of mode number 226 and order number 12 (i.e., one of TM mode coefficient a&, at x = 215.541 56 and the other of TE mode coefficient b!j!6, at x = 215.278 81) are detected at wavenumbers v = 17 152.25 cm-' (Le., 2 = 583.7254 nm) and Y = 17 131.34 cm-l, respectively. The droplet is then exposed to avapor of a miscible component, B, and it grows by absorption. The growth causes the spectral positions of the resonances to shift to lower wavenumbers. To calculate the shifts, we assume that the volume change due to the mixing of A and B occurs according to the ideal solution law and that the refractive index of the homogeneous solution droplet is given by
where U B is the volume fraction of B in the droplet. Figure 1 shows the theoretical shifts in wavenumbers (i.e., the difference between the initial and final wavenumbers) of the TE and TM mode resonances as functions of droplet (18)Hightower,R. L.;Richardson, C. B.AppZ.Optics 1988,27,4850. (19)Lock, J. A.Appl. Optics 1990,29,3180.
82 Langmuir, Vol. 11,No.1, 1995 120
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Figure 2. Calculated shifts of TE and TM mode resonances as functions of layer thickness on a droplet for various values of layer refractive index.
size change due to the absorption of B, the refractive index of which is varied from mg = 1.200 to 1.600. The calculations for mg = 1.400 (i.e., mA = mg) denote growth of the droplet without any change in the refractive index. For such situations, the size parameter values of the resonances remain at the same initial values throughout the growth process, and the resonances of both TE and TM modes shift according to the relation
the droplet the two resonances, initially at 17 152.25 and 17 131.34 cm-', shift to lower wavenumbers. In Figure 2, we have plotted the calculated shifts of the TE and TM mode resonances as functions of layer thickness for various values of m. The results show that for a given layer thickness the TE and TM mode resonances shift differently. When the layer refractive index is less than the core refractive index (Le., m < m,),the TM mode resonance shifts more than the TE mode resonance, and the opposite happens when m > m,. For a given layer thickness the difference between the shifts of the TE and TM mode resonances increases as the difference between the core and layer refractive indices (i.e., Im - m,l) increases, and also for given refractive indices the difference between the shifts increases as the layer thickness increases. Even for a very thin layer, a significant relative difference between the shifts of TE and TM resonances exists when the core refractive index differs considerably from the layer refractive index. For example, the formation of a 10 i% layer ofrefractive index 1.600on a core droplet of refractive index 1.400 causes the TE and TM resonances, in the present example, to shift by 1.109 and 1.394 cm-l, respectively, whereas a 10 i% size change of the homogeneous droplet by the absorption of a material with the same refractive index as the layer, as in the previous example, results in shifts of 1.212 and 1.216 cm-l, respectively. The difference of about 0.38 cm-l between the shifts of the TE and TM resonances, resulting from the layer formation, is quite significant considering the fact that the absolute shifts of the resonances are on the order of 1 cm-l. This difference in the properties of homogeneous and layered droplet resonances provides a basis for an unambiguous discrimination between homogeneous and layered droplets and, in fact, suggests the possibility of detection of a monolayer on the surface of a spherical particle. I t should be pointed out here that a significant difference only exists between the shifts of a TE and a TM mode resonances of a layered droplet but not between two TE or two TM resonances of the same droplet. Thus, to implement an experimental method to determine size changes and to distinguish a homogeneous growth from a layer formation, one needs to devise a way to measure TE and TM mode resonances independently.
-Aa _ -- AL a0
Lo
where LO is the position of a resonance wavelength at the initial radius ao, and AL is the shift of the resonance when the droplet size changes by Aa. If the initial positions of the TE and TM mode resonances are not too far apart, as in the example used in Figure 1, eq 12 shows that both of the resonances shift almost identically due to a size change. Figure 1 shows that when the absorbing component has a higher refractive index (i.e., for mg > mA) both the TE and TM resonances shift more than the shift that occurs when mg = mA and that the inverse is true when mg < mA. Even though the magnitude of the shift depends on the refractive index of the absorbing material, the shifts of the TE and TM mode resonances do not differ significantly. For example, for a 0.10 pm size increase with mg = 1.200 (Le., where the maximum difference appears in Figure l ) , the TM resonance shifts by 50.29 cm-l while the TE resonance by 49.68 cm-l. Thus, the separation between the resonances increases only by 0.61 cm-'. The difference between the shifts, though detectable, is relatively small compared to the total shift of about 50 cm-' and is insignificant compared to the difference, as discussed below, that results from the formation and subsequent growth of a layer. Now to examine the effects of a layer formation and its growth on resonances, consider a droplet, identical to the initial droplet in the previous example (i.e., a, = 20 pm, and m, = 1.4001, exposed to a supersaturated vapor of component B, but B is now completely immiscible with the droplet phase. The liquid phase refractive index of B is denoted by m. When a layer of component B forms on
Layer Formation on Microdroplets
f
my AR Figure 3. Schematic of experimental system.
In the present study, we have used the technique developed by Ray and Huckaby13 for the independent determination ofTE and TM mode resonances in scattered light, using two detectors. The technique is based on the fact that in the vicinity of 8 = 90")the angle dependent functions n:s are negligible compared to zn's for n 2 x . Thus, the terms associated with TE mode coefficients (i.e., bnW in eq 1dominate over the terms associated with TM mode coefficients, and only the TE mode resonances can be detected in the scattered intensity measured at 8 = go", in the plane perpendicular to the plane of polarization. Similarly, only TM mode resonances appear at 8 = go", in the plane parallel to the plane of polarization. Thus, the TE and TM resonances can be detected independently by using two detectors placed at about 8 = 90")in the planes parallel and perpendicular to the polarization of the incident beam. This is the scheme used in the present experimental system. Experimental Section Experiments were conducted on single Santovac 5 (polyphenol ether) droplets suspended in a stream containing Fomblin (perfluorinatedpolyether) vapor inside an electrodynamic balance. Figure 3 shows a schematic of the experimental system which has been described in detail by Ray and Huckaby13 and Huckaby.20 Here we briefly review the salient features of the system. An electrodynamicbalance is housed in a temperaturecontrolled cylindrical chamber. An ac potential driving the two central electrodes of the balance focuses a charged droplet at the center,while dc potentials ofopposite polarity applied across the two endcap electrodes, located above and below the central electrodes, balance the verticalforceson the droplet. "he droplet is illuminated by a linearly polarized tunablering dyelaser beam entering vertically through a window at the bottom of the cm-l and chamber. The beam has a line width of about 2 x (20) Huckaby, J. L. Ph.D. Thesis, University of Kentucky, 1991.
Langmuir, Vol. 11, No. 1, 1995 83 can be scanned continuously over a wavenumber range from 16 500 to 17 700 cm-1. The wavenumber ofthebeam is measured with an accuracyofbetterthan 0.001cm-l. Two photomultiplier tubes (PMT's), in the planes parallel and perpendicular to the electric field vector of the incident beam, are used to detect intensities of light scattered by the droplet at about 0 = 90". A vapor free or Fomblin vapor laden air stream flows past the droplet. Fomblin vapor is introduced into the air stream by passing a dry air stream through a column packed with fomblincovered steel wool. The air stream leaving the column is saturated with Fomblin vapor at the column temperature. The coppertubing from the outlet ofthecolumnleadingto the chamber is also maintained at the temperature of the column. When the columntemperature is higher than the temperature of the balance chamber, the air stream upon entering the chamber becomes supersaturated with Fomblin vapor. In all the experiments the balance temperature was maintained at 25 "C. The experimental procedure consisted of the following sequential steps: (i)a Santovac droplet was suspended in a dry air stream; (ii) the laser was scanned from 16 900 to 17 600 cm-l, while scatteredlight intensity data was collected,with detection by two PMT's, at 0.1667 cm-1 intervals; (iii) the laser was rescanned around the regions where sharpresonance peaks were detected by the PMT's, and data were collected at 0.008 33 cm-l intervals to establish the positions of the resonances more precisely;(iv)from the resonances with well-defined sharp peaks observed in the intensity spectra,two closely located resonances, one from each PMT, were chosen for further monitoring; (v) an air stream saturated with Fomblin vapor was introduced into the chamber; (vi) after the system attained a steady state, as evidenced by no further movements of the peaks, the new positions of the two resonances were established by scanning the laser; (vii)the previous step was repeated after the introduction of an air stream supersaturated with Fomblin vapor at the chamber temperature.
Data Reduction Experimentally observed resonances are analyzed by using light scattering theory to determine the initial size of a pure Santovac droplet and its size changes after exposures to Fomblin vapor at saturated and supersaturated levels. The sharp TE and TM mode resonance peaks detected in the scattered intensity spectrum from an initially pure droplet form the basis for its absolute size and refractive index determination. Unlike fixed wavelength intensity spectra, in the present wavelengthdependent intensity spectra, the refractive index of the droplet varies with the wavelength of the incident light due to the dispersion. To account for the change in the refractive index we have used the following threeparameter Cauchy dispersion formula:
To determine the droplet radius and the constants of the dispersion formula, we have followed the procedure developed by Ray and Huckaby13 and subsequently improved by Huckaby et a1.l' The procedure is based on the alignment of experimental resonances with resonances computed from the individual scattering coefficients and does not require any a priori visual comparison between experimental and theoretical intensity spectra. Only a validation of the procedure is obtained by comparing the experimental spectra with theoretical spectra calculated with the size and dispersion relation obtained from the alignment procedure. Here we briefly review the procedure. Typically, about 20-25 sharp resonances (about 10-13 from each detector), observed while the laser was scanned, their positions subsequently being determined with high resolution laser scans, are used in the determination procedure. The peaks are first sorted and labeled vi,ofor i = 1to N, in ascending wavenumbers. From the separation distances between the observed resonances,
84 Langmuir, Vol. 11,No.1, 1995
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droplet. we then establish an upper limit, aH, and a lower limit, aL, of the droplet radius, as well as its upper limit, mH, and lower limit, mL, for its refractive index. Since for a given size parameter only a resonance with a mode number in the range x < n < mx can appear in an intensity spectrum, only those resonances whose mode number lie in the range 2 n a ~ v 1o,corresponding to the first observed peak a t ~ 1 , The ~ . second observed resonance at the higher wavenumber V Z , ~is then aligned with a computed resonance that gives the refractive index mzxO, which is higher than ml,o. This step provides an estimate of dispersion per wavenumber. Each subsequent observed resonance at vi,o,is aligned with a calculated resonance in the group that gives a refractive index closest to the refractive index calculated at the wavenumber vi+, from m1,o and the dispersion estimate. Thus, by aligning all the observed peaks with scattering coefficients peaks in this manner, a set of misoversus vi,o data is generated. The data set is then fitted to eq 13, using a least squares method, to obtain best estimates of the dispersion parameters. Theoretical peak positions vi,e)sfor the assumed droplet size are then iteratively calculated, using the resulting dispersion relation. An estimate of alignment errors between the observed and calculated peak positions is obtained from the following relation: N
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For the same droplet size, the procedure is repeated by aligning the first and second observed resonances with all physically acceptable combinations of calculated resonances in the group. For each combination, the subsequent observed resonances are aligned to calculated resonances according to the dispersion estimate for that combination. The combination of resonances that produces the minimum value of the objective function, in eq 14,is chosen as the optimum alignment for the assumed droplet size.
The above procedure, in its entirety, is repeated by incrementing the droplet size. The global minimum in the objective function 4 is assumed to be associated with the best determination ofthe droplet size and its dispersion relation. By aligning the sharp resonances observed in the experimental TE and TM mode intensity spectra shown in Figure 4, we find that the minimum of the objective function or the minimum in the alignment errors occurs at a = 24.1258 pm. At this radius the dispersion formula obtained by regressing the refractive versus wavelength data obtained by aligning observed resonances with calculated resonances is given by
m(v)= 1.595314
+ 9.89548 x 10-"v2 + 5.8933 x 10-20v4 (15)
Figure 4 shows a comparison between the experimental spectra and theoretical spectra calculated for the radius a = 24.1258 pm with the dispersion formula given by eq 15. The observed peak positions as well as the shapes of the experimental intensity spectra agree remarkably well with those of the calculated spectra, thus demonstrating the validity of the alignment procedure.
Results and Discussions After collecting data on a pure Santovac droplet, the droplet was exposed to air streams containing Fomblin vapor at saturated or supersaturated levels. The positions of two sharp peaks, one from each PMT, were monitored. For the droplet for which the intensity spectra is shown in Figure 4, the two indicated peaks associated with the 29 a2,2 and b i x scattering coefficients were monitored. Figure 5 shows the positions of these peaks prior to the exposure to Fomblin vapor (i.e., S = 0) and their positions after exposures to Fomblin vapor at saturated (S = 1)as well as at supersaturated (S > 1)levels. When the droplet was exposed to air saturated with Fomblin vapor, both the TE and TM mode resonance peaks shiEted by an identical amount of 0.58 cm-', as shown in Figure 5. The identical shifts indicate that the droplet remained homogeneous and its growth was due to the absorption of Fomblin vapor. Figure 5 also shows that, after the exposure to Fomblin vapor at a supersaturated level, the TE and TM mode resonance peaks shifted by 5.55 and 8.51 cm-', respectively. The significant difference in the peak shifts suggests the presence of a layer on the droplet. In principle, as discussed earlier, the observed shifts of two resonance peaks of different modes are sufficient to
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Langmuir, Vol.11, No.1, 1995 85
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