Anal. Chem. 1987, 59,854-860
854
also corrects for particle refractive index in a single collection angle instrument. The high-power dependence of the light scatter signal upon particle size limits the dynamic range of the measurement; it is not possible to simultaneously display upon the multichannel analyzer the light scatter signal generated by widely spaced particle size distributions. It is anticipated that a nonlinear electronic amplifier may be placed before the multichannel analyzer to improve the dynamic range of the measurement. For example an amplifier with a logarithmic or six root response may be employed to produce a nearly linear relationship between the amplified light scatter signal and particle size. The incorporation of the nonlinear amplifier would simultaneously improve the dynamic range of the measurement and also produce a more nearly linear response between amdified signal and Darticle size.
LITERATURE CITED Greenless, G. W.; Clark, D. L.; Kaufman, S. L.; Lewis, D. A,; Tonn, J. F.; Broadhurst, J. H. Opt. Commun. 1977, 2 3 , 236-239. Pan, C. L.; Prodan, J. V.: Fairbank, W. M.; She, C. Y. Opt Lett. 1980, 5 ,459-461. Hirschfeid, T. Appl. Opt. 1976, 15, 2965-2966. Dovlchi, N. J.; Martin, J. C.; Jett, J. H.; Kelier, R. A. Science 1983, 219, 845-847. Nolan, T. G.; Dovichl, N. J. I€€€ Circuits Devices Mag. 1986, 2 , 54-56. Burgi, D. S.; Nolan, T. 0.;Risfelt, J. A,; Dovichi, N. J. Opt. Eng. 1984, 23,756-758. Zarrin. F.: Dovlchl. N. J. A m / . Chem. 1985, 57, 1826-1829. Zarrln. F.: Dovichi, N. J. Anal. Chem., previous article in this issue. Kaye, W. Anal. Chem. 1973, 45, 221A-225A. Mullaney, P. F.;Van Dilla. M. A,; Coulter, J. R.; Dean, P. N. Rev. SQ. Instrum. 1969, 4 0 , 1029-1032.
(25) (26) (27) (28)
Hercher, M.; Mueller. W.; Shapiro, H. M. J. Histochem. Cytochem. 1979, 27, 350-352. Loken. M. R.; Parks, D. R.; Herzenberg, L. A. J. Histochem. Cytochem. 1977, 25, 790-795. Crosland-Taylor, P. J. Nature (London) 1953, 1 7 1 , 37-38. Salzman, G. C.; Wilder, M. E. Jett, J. H. J. Histochem. Cyfochem 1979, 27, 284-267. Croweil, J. M.; Hiebett, R. D.; Salzman, G. C.; Price, B. J.; Cram, L. S.; Mullaney, P. F. I€€€ Trans. Blomed. Eng. 1978, BME-25, 519-526. Bartholdi, M.; Salzmann, G. C.; Hiebert. R. D.; Seger, G. Opt. Lett. 1977, 1 , 233-235. McConnel, M. L. Anal. Chem. 1981, 53, 1007A-1018A. Cintre, M.; Cambon, S.; Leclerc, D.; Dodds, J. Anal. Chem. 1986, 5 8 , 86-89. Livesey, P. J.; Billmeyer, F. W. J. Colloid Interface Sci. 1969, 3 0 , 447-472. Wims, A. M. J. Colloid Interface Sci. 1973, 4 4 , 361-368. Hershberger, L. W.; Callis, J. E.; Christian, G. D. Anal. Chem. 1979, 51, 1444-1446. Kelly, T. A.; Christian, G.D. Anal. Chem. 1981, 53,2110-2114. Kelly. T. A.; Christian, G. D. Anal. Chem. 1982, 5 4 , 1444-1445. Dovichi, N. J.; Martin, J. H.; Jett, J. H.; Trkula. M.; Keller, R. A. Anal, Chem. 1984, 56, 348-354. Harris, J. M.; Lylte, F. E.; McCain, T. C. Anal. Chem. 1976, 4 8 , 2095-2098. Wickramasinghe, N. C. Light Scattering Functions for Small Particles ; Adam Hiiger: London, 1973; Chapter 3. Born, M.; Wolfe, E. Principles of Optics; 5th ed.; Pergamon: Oxford, 1975; 633-664. Hodkinson, J. R. Appl. Opt. 1966, 5 , 839-844.
RECEIVED for review May 20,1986. Accepted November 12, 1986. The authors gratefully acknowledge funding from the following organizations: Xertex, Inc., The American Heart Association of Wyoming, The National Institutes of Health, and the Biomedical Research Support Grant Program of the University of Wyoming.
Laser Doppler Velocimetry for Particle Size Determination by Light Scatter within the Sheath Flow Cuvette Fahimeh Zarrin,' D a r r y l J. Bornhop: a n d Norman J. Doviehi**
Department of Chemistry, University of Wyoming, Laramie, Wyoming 82071
Laser Doppler veloclmetry may be used to measure partlcle slre with high precision. A continuous wave laser beam Is spHt Into two nearly equal Intmsfty beams which are crossed and focused by uslng a lens, generating a set of Interference fringes. A modulated burst of light scatter Is generated as a particle p a w s through the frlnge reglon. The sheath flow cuvette Is necessary to align precisely the particle stream with respect to the fringe region center. A microscope collects and a photomultiplier detects the light. A band-pass filter rejects low-frequency noise In the background light scatter signal while a full wave rectifier demodulates the light scatter signal. A small angle cdlectlon geometry produces a monotonic relationship between partlcle size and light scatter intensity, detects 175 nm radlus particles, and easily resolves partlcle mlxtwes differing by 12% In radius. A right angle collectlon geometry produces a nonmonotonic relationship between light scatter amplitude and partlcle size but detects 45 nm radlus particles.
The previous paper in this journal considered single particle light scatter determination using a Gaussian laser beam light source and a sheath flow cuvette (2). This instrument provides very good results: particles as small as 88-nm radius are detected and mixed particle suspensions differing in size by a few percent are resolved into individual components. The performance of the single beam instrument is limited by neither shot noise in the scattered light signal nor the inherent particle size distribution of the particle standards but rather by noise elsewhere in t h e system. In particular, laser intensity noise in the 1-100 kHz region may limit the system performance. Consider the light scatter signal generated by a single particle passing through a Gaussian laser beam. The light scatter signal temporal behavior mimics the radial intensity profile of the laser beam. The intensity profile is Gaussian; therefore, the time domain signal generated in light scatter instruments is also Gaussian (Figure 1A)
I ( t ) = I(0)e-2(t-to)*/(W/U)2 Present address: Department of Chemistry, Colorado State University, F o r t Collins, C O 80523. Present address: Department of Chemistry, University of Alberta, Edmonton, Alberta, T6G 2G2 Canada.
(1)
where I(t)is the time-dependent light scatter signal, t is time, tois the time when the particle passes through the axis of the laser beam, Z(0) is the light scatter intensity when the particle
0003-2700/87/0359-0854$01.50/00 1987 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 59, NO. 6, MARCH 15, 1987
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Figure 2. Laser Doppler velocimetry. The laser beams are crossed at an angle 0 to produce interference fringes with spacing D .
TIME
-vm
-v/2w
0 v/2w FREQUENCY
VRLl
Figure 1. Light scatter signal generated by a single small particle as it passes through a Gaussian laser beam. t o corresponds to the time when the particle passes through the beam center, w is the laser beam spot size, and Vis the linear velocity of the particle. (A) Time domain. (B) Frequency domain.
passes through the beam axis, w is the laser beam spot size, and u is the velocity of the particle. Unfortunately, the Gaussian temporal shape of the particle light scatter signal suggests sensitivity to low-frequency noise. By use of Bracewell's definition of the Fourier transform (2), the frequency spectrum of the light scatter signal may be found for a single particle passing through the center of a Gaussian laser beam (Figure 1B)
where u is frequency. Note that the light scatter signal is centered at dc and has a bandwidth of approximately u / w hertz. Typically, a laser-beam spot size of 10 pm and a flow velocity of l m/s is employed for light scatter measurements of particle size within the sheath flow cuvette. These parameters produce a light scatter signal that is centered a t dc and has significant components beyond 50 kHz. Unfortunately, the light scatter signal overlaps with significant noise sources in continuous wave (CW) lasers, including harmonics of line frequency, l / f noise, and mode beating within the laser cavity ( 3 ) . Very low frequency noise components may be removed with a high-pass filter, albeit with a slight decrease in light scatter amplitude. However, noise sources in the 1-100 kHz region are particularly important in light scatter measurements using a single Gaussian laser beam. It would be advantageous to modulate the light scatter signal in order to shift the signal to a more quiet portion of the noise spectrum of the laser. For example, signals generated at higher frequencies produce near shot noise limited absorbance measurements ( 4 ) . Similar improvements in performance may be expected for light scatter measurements. However, simply modulating the laser-beam power is not useful in light scatter measurements since both signal and noise are shifted in frequency by an identical amount.
T
1 -V/D -VU0 VnLl V/D FREQUENCY Flgure 3. Light scatter signal generated by a single small particle as it passes through the interference fringes for laser Doppler velocimetry. t o corresponds to the time when the particle passes through the beam center, w is the laser beam spot size, D is the fringe spacing, the V is the linear velocity of the particle. (A) Time domain. (B) Frequency domain.
Laser Doppler velocimetry is an attractive method of modulating the light scatter signal without modulating the noise components of the background signal (5). In this light scatter technique, a laser beam is split into two nearly equal intensity beams which are recombined at the focus of a lens, Figure 2. Constructive and destructive interference generates a set of light and dark fringes within the interaction volume. The fringe spacing is given by
D = X/[2 sin (0/2)]
(3)
where X is the wavelength of light in the medium and 0 is the intersection angle of the two interfering beams. The fringe region is an ellipsoid of revolution, with major axis given by 2lI2w/sin (012) and with minor axis given by 21/zw/cos (012) (5). At the intersection of the two laser beams, the light intensity is given by the product of a Gaussian function times a sinusoidal function for the intensity fringes. The light scatter intensity generated as a particle passes through the center of the fringe volume is given by (Figure 3A)
~ ( t=)I(O)[I + cos (29(t - t o ) u / ~ ) ~ e - 2 ( t - t a ) 2 / ( u(4) /U) where I ( 0 ) is the light scatter intensity generated when the particle is in the center of the fringe volume. The light scatter
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ANALYTICAL CHEMISTRY, VOL. 59, NO. 6, MARCH 15, 1987
Figure 4.
Experimental diagram. Light from a helium-cadmium laser
is split into two nearly equal intensity beams with a cube beam splitter. The beams are combined at their focus with a lens. A sheath flow
cuvette constrains the sample to flow through the intersection region of the two beams. Scattered l i i t is collected in both forward and right angles with microscopes. The microscopes utilize an objective and eyepiece. A pinhole is located in the eyepiece to block background light scatter from the cuvette windows. A photomultiplier detects the light.
of laser Doppler velocimetry is primarily a result of the sensitivity of the instrument to particle trajectory through the fringe region; particles which pass off axis generate smaller modulated signals than particles which pass through the center of the fringe region. The broad particle size distribution generated as particles pass through the entire fringe region may be partially compensated with a numerical deconvolution algorithm (16). However, narrow light scatter distributions appear to have not been reported by using Dopper velocimetry. On the other hand, the sheath flow cuvette appears to be very well suited for particle size determination using laser Doppler velocimetry. The narrow sample stream may be centered in the fringe region, providing consistent modulation shape for all the particles in the distribution. Furthermore, since the particles are traveling with a well-defined velocity, the band-pass filter in the demodulation circuit may be optimized for the modulation frequency generated by laser Doppler velocimetry. Such optimization is not possible in simultaneous measurements of particle size and velocity.
EXPERIMENTAL SECTION signal consists of a Gaussian envelope with a superimposed modulation component with frequency u/D. As ita name suggests, laser Doppler velocimetry is primarily utilized as a nonintrusive measure of velocity (5). Here, small particles are seeded into a flowing stream. Light scatter is collected and the modulation frequency of the signal is extracted with a bank of band-pass filters. The modulation frequency is linearly proportional to velocity; knowledge of the fringe spacing allows precise determination of flow velocity. However, the modulation theorem of the Fourier transform suggests an advantage of laser Doppler velocimetry for particle size analysis. The Fourier transform of the laser Doppler velocimetry generated light scatter signal is given by (Figure 3B)
By passage of the particles through the center of the fringe region produced a t the intersection of two laser beams, the light scatter intensity spectrum consists of a Gaussian component centered at dc and sidebands generated at a frequency u / D . By use of an electronic band-pass filter center a t the modulation frequency, i t is possible to reject low-frequency noise components while passing the modulated light scatter signal. Near shot noise limited light scatter determination of individual particles appears possible with laser Doppler velocimetry. Laser Doppler velocimetry has been used for simultaneous particle velocity and size determination since at least the early 1970s (6-23). However, these applications have produced poor resolution of light scatter distributions. The poor performance
The optical portion of the laser Doppler apparatus is shown in Figure 4. A 5-mW beam at 442 nm is produced by a heliumcadmium laser, Omnichrome. The beam is split into two parallel beams with a 25 mm square beam splitter, Melles Griot. The beam splitter is not optimized for this wavelength nor orientation so that the beams differ in intensity by about 20%. The distance between the beams is adjusted by translating the cube perpendicular to the laser beam axis. Beam separations of 1 to 25 mm may be obtained. The parallel beams are focused and crossed with a 25 mm focal length biconvex lens. Typical fringe spacing is 2 to 3 pm. The sheath flow cuvette is from an Ortho cytofluorograph and has a 250 pm square bore flow chamber with 1.5 mm thick windows. Two collection optic geometries are employed. In a small angle geometry, the collection optic is aligned at about 1 2 O from the plane containing the laser beams in the plane perpendicular to the bisector of the beams. Typically, a 7X and 0.20 numerical aperture objective and a 20x eyepiece are employed. In the right angle geometry, light scatter is collected at right angles with a microscope, typically using a 18X and 0.45 numerical aperture objective and 20X eyepiece. The eyepiece is fitted with a small pinhole, typically 0.4 mm in diameter, to restrict the field of view of the photodetector to the sample stream-laser beam intersection region. An RCA 1P28 photomultiplier, wired with fast response (24),is used t o detect the scattered light. The small angle geometry typically uses a relatively low photomultiplier voltage, 550 V, while the right angle geometry uses a higher voltage, 1150 V. Samples are introduced into the sheath flow cuvette with a low-pressure syringe pump, Hazeltine, whereas a high-pressure liquid chromatography pump provides the sheath fluid. Particle suspensions are made from polystyrene standards, Duke and Polyscience, in filtered (0.20 pm),deionized water. The sheath water is also filtered by an in-line, 0.20-pm filter. The light scatter electronic circuit is shown in Figure 5. The signal from the photomultiplier is amplified with an Ortec Model
-12v
Figure 5. Electronic diagram. PMT is a photomultiplier, Amp 1 is an Ortec Model 450 amplifier, filter is a variable frequency band-pass filter, the first set of electronic components form a full wave rectifier, the second set of components form a four-pole low-pass fitter, amp2 is an Ortec Model 440A amplifier, and MCA is an EGGOrtec Model 7150 multichannel analyzer. D is a 1N914 diode: OA 1-OA3 are LF351 bifet operational amplifiers. All resistor values are in ohms.
ANALYTICAL CHEMISTRY, VOL. 59. NO. 6. MARCH 15. 1987
TIME
TIME
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F@me 8. Dependence 01 laser Doppler velocimetry timwesobed signal upon posnion 01 sample wlthin ihe binge regbn: (A) sample 70 pm horn hinge center; (E) sample 5 0 pm hom hinge center; (C)sawla 30 pm horn hinge center: (0) sample 10 pm lrom hinge center; (E) sample
at fringe center. 450 amplifier. The shaping filters on the amplifier are employed in a wide hand-pass configuration to remove much of the lowfrequency component of the signal. An lthico narrow hand-pass filter. Model 4210, is centered on the laser DoDDler velocimetw modulation frequency, and typically operating whh a Q of 10. This filter eliminates noise generated outside the band of the modulated light scatter signal. The signal is demodulated with a locally constructed circuit also shown in Figure 5. The signal is buffered with an operational amplifier. full wave rectified hy two half-wave rectifiers of opposite polarity, and combined with a differential amplifier. Diodes 1 and 1’ are used to compensate the forward voltage drop of diodea 2 and 2’ hy providing 0.6 V to bias the second diodes at the threshold of conduction (25). The elimination of diode drop is important for demodulation of low-amplitudelight scatter signals. A full wave rectifier provides twice the signal of a half wave rectifier. The rectified signal is filtered with a four-pole low-pass filter with 10-kHzcutoff. The demodulated light scatter signal is amplified, Ortec Model M A , and quantitated with a multichannel amplifier. O w Model 7150. operating in the pulse height analysis mode. The signals are recorded photographically
RESULTS AND DISCUSSION Equation 4 will he valid only when the particle passes through the center of the fringe region. Particles passing away from the center of the fringe region will generate incompletely modulated signals, leading to broadening of the light scatter distribution. Figure 6 shows the time-resolved light scatter signal produced by 300 nm radius particles passing at various distances away from the fringe region center. T h e ratio of the sample and sheath stream volume flow rates was about 0.015, producing a 10 pm radius sample stream (26).Figure 6A shorn, the light scatter signal generated by a single particle passing 70 pm from the center of the fringe region. T w o peaks are observed on the aSeiUmpe trace corresponding to passage of the particle through the individual, noninterfering laser beams. Note that one beam is ahout 20% more intense than the other beam, due to imperfect action hy the beam splitter. Figure 6B shows the light scatter signal as an individual particle passes 50 pm from the fringe intersection region. Weak interference produces a small amount of modulation upon the two Gaussian peaks corresponding to the individual laser beams. Figure 6C presents the light scatter signal
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stream radius. generated 30 pm from the heam center. More interference is generated, and the Gaussian peaks begin to merge. Figure 6D presents the light scatter generated by a particle passing 10 pm from the center of the fringe volume. The light scatter signal is slightly distorted, even for particles passing within 10 pm of the fringe region center. Figure 6E presents the light scatter signal generated by a particle pawing very near the center of the fringe region. The signal is nearly symmetric about the maximum. A significant Gaussian pedestal is present, a result of the unequal beam intensities. The difference in the two heam intensities is directly proportional to the intensity of the pedestal. These figures demonstrate the very narrow acceptance region of the laser Doppler velocimetry instrument; particles must pass within a few micrometers of the fringe intersection region to produce a nondistorted, uniform modulation. A large sample stream will pass through different portions of the fringe region, resulting in a broadened particle size determination. Figure I represents the relative standard deviation of the light scatter distribution generated as a function of sample stream radius for 4 5 0 nm radius particles. The data were collected with a right angle geometry; similar results were obtained for the forward angle collection geometry. The sample stream radius was changed by varying the sample stream flow rate at constant sheath stream flow rate. T h e
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ANALYTICAL C M M I S T R Y . VOL. 59. NO. 6. MARCH 15. 1987
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ratio of sample and sheath stream flow rates was used to compute the sample stream radius (26).A constant increase in the full width a t half-maximum is noted as the sample radius increases. The best data are obtained with a sample stream about 3 r m in radius. T h e laser-beam spot size was about 10 rm. To generate narrow particle size distributions. it is neceSSary to transport particles in a stream much narrower than the laser-beam spot size. A portion of the light scatter distribution certainly is due to particles passing through different intensity regions of the laser heam. It is interesting that laser Doppler velocimetry instrumentation produces less stringent requirements on sample stream size than the single-beam light scatter instrument (26). It is not clear what produces this decreased sensitivity to sample stream radius. Possibly, the axes of the two laser beams do not cross within the sample, effectively generating a uniform set of fringes over a wide area. We have noted that the two laser beams do not cross coaxially; as the sheath flow cuvette is moved perpendicular to the laser beams, one beam and then the other is o b s e ~ e dto intersect the cuvette window. Also, the two beams may not cross a t their heam waist. A larger spot size laser heam will produce a larger acceptance volume. The relationship between particle size and light scatter intensity was investigated for both forward angle and right angle collection geometries. The forward angle geometry produced a smooth, monotonic variation of signal with particle size for particles ranging in radius from 175 to 545 nm, Figure 8. Also shown is the Mie scattering intensity for forward angle collection over the microscope objective aperture ( I . 27). Note that the laser Doppler velocimetry signal closely follows the Mie scattering calculation. However, the modulated intensity will decrease from the single beam Mie scattering values for larger particles due to the nonuniform intensity profile of the laser heam (6, 7). The variation from simple Mie scatter theory occurs as the particle radius approaches the laser fringe spacing; in this instrument, significant deviation is expected for particles larger than a micrometer in radius. Unfortunately, suspensions of very small particles failed to generate a signal; a very large background signal was observed in the forward angle instrument. The background signal appeared to be due to light scatter generated a t the sheath streamcuvette window interface. The pinhole located in the microscope objective failed to reject liiht scattered a t the cuvette windows. To prevent damage to the photomultiplier, low supply voltage, 550 V, and relatively low collection efficiency microsocope objectives, NA = 0.20, were employed. T h e light scatter signal was measured as a function of particle size for the right angle geometry. Fortunately, the background signal was very low in this configuration, allowing higher collection efficiency and higher photomultiplier supply voltage. A plot of light scatter intensity as a function of particle size reveals a complicated behavior, Figure 9. Also
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shown is the Mie scatter intensity expected for this collection geometry and single laser beam excitation. Unfortunately, the curve is not monotonic, suggesting that particles of different size will generate the same light scatter signal. It appears that the right angle collection geometry is not suited for particle size determination in the 150-250 and 3 W 3 5 0 nm range. The log-log plot demonstrates, on the average, a slope of 2.1. This slope is less than that observed with the forward angle collection geometry and suggests that the right angle collection geometry will be better suited for small particle detection. Figure 10 presents the light scatter distribution generated by 45 nm radius particles using the right angle collection geometry. The distribution is barely resolved from the background counts and probably represents the smallest detectable particle size with our instrument. The large relative standard deviation in the data, 16%. appears to be primarily a result of the distribution of particle size within the standard. The manufacturer's value of the relative standard deviation, 6.4%, accounts for most of the observed light scatter width, when the quadratic dependence between particle size and intensity is considered. We have not investigated smaller particles. However, the light scatter signal from smaller particles presumably will merge with the background signal. It is interesting to note that 45 nm radius particles have been detected on the basis of light scatter in a single heam instrument using the sheath flow cuvette (28). However, the earlier report utilized a factor of 20 higher laser power in a single-beam instrument. The modulated signal generated by laser Doppler velocimetry appears to produce a significant improvement in signal to noise ratio for right angle collection. The light scatter distributions obtained for particles larger than 175 nm radius using forward angle collection have 1 % to 4% relative standard deviation. The measurements appear to be determined hy the particle standards employed. The particle standards are not monodisperse but instead typically have a 1% relative standard deviation in size. Consideration of the dependence of light scatter intensity with particle size
ANALYTICAL CHEMISTRY. VOL. 59. NO. 6. MARCH 15, 1987
INTENSITY Flgue 11. Laser Doppler velocimeby light scatter htenslty d!sbibuI!m for a rnixhne of 205. 230. and 300 nm radius particles.
INTENSITY Flgue 12. Laser Doppler vehximeby light scatter ihtenohy dkbibutbn for a mixture of 350. 455. and 545 nm radius particles.
suggests that the light scatter distribution is determined by the finite size distribution of particle size in our standards. The high precision light scatter measurement produced by the laser Doppler velocimetry instrument suggests application in the study of mixtures of particles with similar size. Figure 11presents a histogram of counts vs. pulse height for a mixture of 205,230, and 300 nm radius particles using forward angle collection geometry. Baseline resolution is obtained between the individual distributions. Figure 12 presents a pulse height analysis of a mixture of 350, 455, and 545 nm diameter particles for forward angle collection geometry. T h e light scatter peaks are very well separated and the distribution width is apparently limited by the particle standards themselves. Unfortunately, we do not have access to intermediate size particles to demonstrate resolution of a larger number of components. Also, the dynamic range of the measurement is limited by the strong dependence of light scatter intensity upon particle size. A lower amplification gain setting was used in this photograph compared to the previoua example. The peak at low intensities corresponds to small amplitude events generated by background light scatter. The cursor marks the limit of this background signal. In general. the forward angle collection geometry employed for the laser Doppler velocimetry instrument appears best suited for particle size determination in the 175545 nm range. Very narrow distributions are obtained compared with the single-heam instrument ( 1 ) . For example, the single-beam instrument produces a factor of 2 wider distribution than the laser Doppler instrument for 300 nm radiua particles. Similar results were found for other size particles: laser Doppler velocimetry produces greater precision than single detection. Multicomponent mixtures are easily resolved, even for sus-
859
pensions differing by a few percent in size. T h e right angle collection geometry appear best suited for size determination of very small particles, less than 175 nm in diameter. The low background produced in this configuration. along with the weaker dependence of light scatter signal upon particle size, appears to be responsible for the excellent performance of the right angle collection geometry for small particle size analysis. Unfortunately, the complicated dependence of light scatter intensity upon particle size limits study of particles larger than 175 nm radius with the right angle collection geometry. The laser Doppler velocimetry instrument, like other single-particle light scatter instruments, suffers from two drawbacks: in addition to particle size, the signal is influenced by both the particle shape and refractive ivdex. The hydrodynamics of the sheath flow cuvette provide an interesting property for the study of nonspherical particles. The shear forces associated with the laminar flow profile within the cuvette act to orient particles so that the long axis is aligned along the flow direction (29). Presumably, particle size determination are dominated by the longest dimension of the particle. The refractive index of the particle also influence the laser Doppler instrument. Placement of an additional detection a t shallow angles to the fringe region should allow determination of particle size independent of refractive index for spherical particles (30). However, the expense associated with a second detector is not desirable. Instead, an interesting property of laser Doppler velocimetry signals may be used the ratio of the modulated to unmodulated component of the signal is monotonically related to particle size over a large range of particle sizes for right angle collection optics (G23). Inclusion of a low-pass filter and fast ratio circuit in our instrument should allow the precise determination of particle size independent of refractive index over a relatively large range in particle size. The dynamic range of the laser Doppler instrument appears to be limited, for small particles, by the small number of photons in the light scatter signal. A higher power and shorter wavelength laser, a higher numerical aperture collection optic, and a high quantum yield photomultiplier are required for detection of smaller particles. However, the very high order dependence of light scatter intensity upon particle radius suggests that particles smaller than about 10 nm in radius will be very difficult to detect by single-particle light scatter. The dynamic range is limited, for larger particles, by the fringe spacing. As the particle radius approaches the fringe spacing, the depth of modulation of the light scatter signal decreases; to first approximation, the light scatter intensity is proportional to the laser intensity integrated over the particle area. For the fringe spacing used in this instrument, the largest particle size that can be analyzed falls in the 1-2 r m range. However, larger particles could be analyzed simply by increasing the fringe spacing. Increasing the fringe spacing produces a proportional decrease in modulation frequency, possibly increasing the system noise. A dual fringe system could be employed where two different fringe regions are formed within the sample stream; one fringe spacing would be optimized for small particles and the other for larger particles. Ultimately, the largest particles that can be studied would he limited by flow channel plugging. In this cuvette, 100-pm particles are the largest practical size to be analyzed. In the current instrument, dynamic range is limited by the highly nonlinear relationship between particle size and light scatter intensity. With a 512-channel multichannel analyzer, particles differing in size by roughly a factor of 4 can be displayed simultaneously by the analyzer. However, this limitation in dynamic range primarily reflects the limitation
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ANALYTICAL CHEMISTRY, VOL. 59, NO. 6, MARCH 15, 1987
in the electronic circuit used in the instrument and does not reflect fundamental limitations in the measurement. For example, a nonlinear amplifier could be used to compress the light scatter amplitude for larger particles. It is interesting to compare the results of the single-particle light scatter instruments with other techniques for particle size determination. The resolution of the laser Doppler instrument is excellent and appears to be limited by the inherent size distributions of the particles themselves. Particles differing in size by a few percent are base-line resolved into individual components and dynamic range ultimately could span 4 orders of magnitude, from 10 nm to 100 pm in radius. In comparison, the best separation technique for particle characterization in the 0.01-1 pm range appears to be timedelayed exponential force-field sedimentation field-flow fractionation (TDE-SFFF) (31). The field flow fractionation technique produces excellent resolution. Particles from about 5 nm to 2 pm in radius are studied, although the dynamic range of the instrument for any given set of experimental parameters is limited to about a factor of 6 difference in particle size. The instrument produces a fractogram where in particles are eluted over a period of time, typically over an hour. On the other hand, the light scatter instrument analyzes the particle suspension very rapidly; depending upon the particle concentration, particle size analysis may be performed in a few seconds to minutes. All of the light scatter data shown in this and the previous paper took less than 5 min to generate. The rapid particle size determination combined with the potentially very large dynamic range of laser Doppler velocimetry would appear to be quite useful in a number of applications.
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(11) (12) (13) (14)
RECEIVED for review May 20,1986. Accepted November 12, 1986. The authors gratefully acknowledge funding from the following organizations: Xertex, Inc., the American Heart Association of Wyoming, the National Institutes of Health, and the Biomedical Research Support Grant Program of the University of Wyoming.
