3042
Ind. Eng. Chem. Res. 2001, 40, 3042-3047
Measuring Particle Diameter and Particle-Particle Gap with Nanometer Precision Using an Optical Microscope Prasanna K. Thwar and Darrell Velegol* Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802-4400
A simple optical microscopy method has been developed for measuring particle diameters and particle-particle gaps with a precision of a few nanometers. The method uses an inexpensive and straightforward image-processing technique to examine optical microscope images of the particles, which can be wet or dry. The technique is demonstrated on polystyrene latex and silica particles with diameters greater than 450 nm suspended in KCl solutions, and the measured particle diameters compare to within a few percent with those measured by electron microscopy and light scattering. In addition, changes in the gap between two colloidal spheres were measured with nanometer precision, a result that will have important implications for measuring colloidal force profiles between two Brownian particles. Introduction Particles with diameters of 500 nm and greater are pervasive in many applications. Such systems are commonly studied using optical microscopy, and a frequent requirement is that the particle diameter and its standard deviation be known. Although size can be measured accurately and reliably using transmission electron microscopy (TEM),1,2 scanning electron microscopy (SEM)1, or photon correlation spectroscopy (PCS),3,4 the most convenient method for measuring particle size would often be the optical microscope itself. The purpose of this paper is to demonstrate that, for spherical particles with diameters greater than about 500 nm, optical microscopy can often be used to measure diameters as accurately as either electron microscopy or light scattering. The technique can be used for either dry or wet samples. In addition, changes in the gap between two solid colloidal spheres can be measured with nanometer precision. Such measurements are highly useful in evaluating colloidal force profiles in which the gap between particles can fluctuate with time over nanometer distances. Standard techniques such as EM or PCS can require a significant amount of sample preparation to measure particle size.2 For facilities not already equipped with these apparatuses, several days might be required before a size measurement can be taken. In addition, researchers often must rely on others to make the measurements because the preparation for EM or PCS requires time and skill. For laboratories that are already equipped with an optical microscope and digital video equipment, optical microscopy provides several advantages for particle sizing: (1) easy sample preparation and rapid measurement time, (2) inexpensive equipment, (3) ability to measure particle size either wet or dry, and (4) simple calibration. In addition, optical microscopy allows one to measure changes in the gap between two colloidal particles (even Brownian particles). Thus, optical microscopy provides a straightforward method for measuring particle size with inex* Darrell Velegol can be contacted at
[email protected]; Penn State University, Department of Chemical Engineering, University Park, PA 16802-4400; phone (814) 865-8739; or fax (814) 865-7846.
pensive equipment, which can be critical for projects in which the measurement of particle size is important but not central to the research project. In this paper, we explain the experiments for measuring particle diameters using the technique of digital video microscopy (DVM), and we compare the results with those obtained from other techniques, including TEM, SEM, and PCS. Methods and Materials The DVM technique for measuring particle diameters is based on the processing of digital images of the colloidal particles.5,6 These images consist of an array of pixels, and computational processing can give the center, major and minor axes, angle, and area of objects within the images. This section describes the methods that we used to obtain the center-to-center distance (L) between two particles. For particles 1 and 2 that are touching (a “doublet”), L gives the average diameter [(2R1 + 2R2)/2]. For almost-touching particles that are undergoing Brownian motion, our method gives changes in the interparticle gap (2δ) as a function of time. We know that 2δ ) L - R1 - R2, and so ∆(2δ) ) ∆L for rigid particles. We studied both polystyrene latex particles (obtained from Interfacial Dynamics Corporation, Portland, OR) and amorphous silica particles (obtained from Bangs Laboratories Inc., Fishers, IN). The polystyrene particles were transparent (n ) 1.591), and the silica particles (n ) 1.47-1.55) were semi-transparent to visible light. Whereas the polystyrene particles alter only the phase of the transmitted light, the silica particles alter both the phase and amplitude of the transmitted light; however, this does not seem to affect the experimental results. The manufacturers’ information about the particles is given in Table 1. Our images were taken using a Cohu 4910 monochrome CCD camera (8-bit video camera) connected to a Nikon Eclipse TE 300 inverted biological microscope. This camera collected photons in an array of 640 × 480 at 10 frames per second (fps), although the shutter was open in each frame for only 1/150 s. The images were stored directly into digital memory. The particles were suspended in 10-100 mM KCl solution and drawn by capillary action into a 0.2 × 2.0
10.1021/ie000664h CCC: $20.00 © 2001 American Chemical Society Published on Web 04/05/2001
Ind. Eng. Chem. Res., Vol. 40, No. 14, 2001 3043 Table 1. Manufacturers’ Information on the Particles Used in Our Experimentsa particle code
nominal diameter (µm)
nominal coefficient of variation (%)
% solids
PSL 1 PSL 2 PSL 3 PSL 4 Si
4.60 2.40 1.00 0.45 2.30
6.5 5.9 2.4 1.1 4.3
8.4 8.6 8.2 4.0 10.2
a PSLs 1, 2, and 3 had negatively charged sulfate groups on their surface, whereas PSL 4 had negatively charged carboxyl groups. The plain silica particles were listed as being “hydrophobic”.
mm i.d. borosilicate glass capillary tube (Vitrocom, Mountain Lakes, NJ), which was then waxed to a glass slide for observation on the microscope. Alternatively, a drop of the suspension was sometimes placed on a 1 × 25 × 75 mm slide under a square cover slip (0.17 mm thick). For either case, the slide was observed by brightfield microscopy with a Plan Fluor 100× oil objective (NA ) 1.30) and polychromatic light from a halogen bulb. The field diaphragm aperture was set for proper Koehler illumination, and the aperture stop was opened so that the entire field of view was just illuminated. For the smallest particles (PSL 4), an intermediate 2× multiplying lens was used. The captured images were analyzed using Scion Image, the PC version of the image-processing program NIH Image. The initial calibration was performed using a micrometer scale (Nikon reticle) to find the equivalent pixel size, which for our equipment was 1 pixel ) 98 nm in both directions. The micrometer accuracy is quoted to be (2% by the manufacturer, and this ultimately limits the accuracy (not the precision or repeatability) of our measurements. The particles were in salt solution and formed doublets (and some higher-order aggregates) in the capillary. After the doublets settled to the bottom of the capillary, we recorded the diffraction images (Figures 1 and 2). As shown in the figures, the experiments are easier and more accurate for larger particles (although the data in Table 2 show that the method works fairly well on 450-nm particles). The diffraction images of two touching or almost-touching particles appear as two Airy patterns, which consist of a central Airy disk surrounded by several diffraction rings.7 The diffraction rings can be treated using Fraunhofer diffraction7 principles, as the theory of diffraction for circular phase objects can also be applied to spherical objects (at least, for the PS latex spheres).8 Thus, in principle, it might be possible to size individual colloidal spheres (i.e., not doublets) from their Airy patterns, although we do not pursue such an approach in this paper. Rather, the key in our experiments is to determine the locations of the central Airy disks of the two touching spheres (Figure 1c). Image processing has been used to locate the centers of the spheres,9-14 including the 3-D position of the particle.15 We thresholded the diffraction images (Figure 1b), and then blackened the diffraction rings (Figure 1c). The algorithm for calculating the centers from the resulting image is5
∫S∫xf(x) dS 〈x〉 ) ∫S∫f(x) dS
(1)
Figure 1. Images of a PSL1 doublet. (a) Raw image taken from the microscope. (b) Thresholded image, showing first diffraction ring. (c) Inverted image with the diffraction rings whited out, leaving the Airy spots. By calculating the centers of the two spots, one obtains the center-to-center distance, which for touching particles is the average diameter.
Figure 2. Images of a PSL 4 doublet. (a) Raw image, (b) thesholded image, (c) resulting Airy disks from thresholded image.
where 〈x〉 is the vector (x,y) center of the particle in the image, S is the area of the object, and f(x) is the gray level value at dummy position x (see Figure 3). For example, if we have a dark image (dark ) 255 for 8-bit
3044
Ind. Eng. Chem. Res., Vol. 40, No. 14, 2001
Table 2. Average Particle Diameters and Standard Deviations between Particles Based on the Measurements of a Statistically Significant Number of Particlesa diameter (µm)
PSL 1
PSL 2
PSL 3
PSL 4
Si
nominal TEM SEM PCS DVM
4.60 ( 0.299 4.28 ( 0.110 4.30 ( 0.077 4.30 4.26 ( 0.117
2.40 ( 0.142 2.34 ( 0.084 2.37 ( 0.077 2.30 2.30 ( 0.079
1.00 ( 0.024 0.99 ( 0.020 1.05 ( 0.018 1.01 0.98 ( 0.032
0.45 ( 0.005 0.45 ( 0.014 0.47 ( 0.012 0.45 0.45 ( 0.017
2.30 ( 0.100 2.33 ( 0.052 2.38 ( 0.036 2.32 2.41 ( 0.059
a The precision for a single particle is not given in this table. The accuracy of our DVM measurements compares well with results from electron microscopy and dynamic light scattering (PCS).
Figure 3. Finding the particle centers. The two objects are the Airy disks, shown in black. A time stamp appears in the upper left. The (x,y) position varies from (0,0) in the upper left to (639,479) in the lower right. The gray level f ) 1 inside the Airy disks and 0 outside. Thus, the particle-finding algorithm would identify two objects here, at the center of each disk.
Figure 4. Two PSL 3 particles “stuck” together with no relative motion between particle centers as a function of time (or frames). Note that the differences between the points are discrete because of the center-finding algorithm. The rms variation is about 5 nm, which might be reduced by using a vibration-isolation table.
images) on a white background, we let f ) 1 for a “dark” pixel. Because a video image consists of a discrete number of pixels, eq 1 can be approximated by the sum
〈x〉 )
∑S xif(xi) ∑S f(xi)
(2)
where S is defined by a closed path of dark pixels (e.g., the perimeter of a circle) that defines an object. The computer algorithm in Scion Image calculates 〈x〉 to within 0.01 pixels (∼1 nm), in principle, although the data are usually noisier than this. To obtain the images in parts b and c of Figure 1, a threshold value (TV) must be chosen. For our 8-bit camera, the gray scale values (GV) range from 0 to 255, and the threshold value sets all pixels with GV g TV as black, and all with GV < TV as white. Experimentally, the calculations for the particle centers depend little on the precise TV used. An exception to this is for small particles, where only a few pixels appear in the thresholded image (see Figure 2c). Once the centers (x1 and x2) of particles 1 and 2 are known (i.e., the centers of their central Airy disks), the following equation is used to obtain the center-to-center distance (L):
L ) x(x2 - x1)‚(x2 - x1)
(3)
If the two particles are touching, L is the average diameter of the two particles. Whether or not the particles are touching can be determined by examining L(t) (i.e., over many images, as in Figures 4 and 5). If L
Figure 5. Relative position between the centers of two almosttouching PSL 1 particles. The relative motion between the particles is barely visible to the eye, but the video technique shows relative motion easily.
is constant over time (as in Figure 4), the particles are probably touching. If L varies with time, then one is, in fact, measuring changes in the interparticle gap as the two particles undergo relative Brownian motion (see Figure 5), perhaps in a DLVO “secondary energy minimum”.16 One case that could not be detected is if two particles were to adhere to the glass surface with a small but finite gap between them. In this case, the particles would be stationary but not touching. In our experiments, we typically recorded 50 images of each doublet, and we examined 10-20 doublets for each particle type in Table 1. For doublets with touching spheres, the variation in L from image to image was small; the standard deviation between the images for a single doublet was typically 3-5 nm (see Figure 3), and the standard error of the mean was less than 1 nm. For
Ind. Eng. Chem. Res., Vol. 40, No. 14, 2001 3045
PSL 4, this standard deviation between images was larger (as high as 15 nm), and the standard error was still less than 5 nm. A previous estimate of the uncertainty in measuring particle position is 10 nm;14 however, this estimate represents the uncertainty arising from a single image. Because we used the average obtained from many images, our uncertainty in particle positions was reduced. This standard error in diameter for a single doublet is much less than the variation from doublet to doublet and, thus, serves as an estimate of the precision (but not the accuracy) of our technique. That is, when we measured the diameter of the same doublet many times, we obtained a value consistent to within a few nanometers. Much of this small variation is due to vibration in the room; we did not use a vibration-isolation table for these experiments. For touching spheres, measurements of L for many doublets also gives the standard deviation of the particle diameters (d). To assess the accuracy of our particle diameter measurements, we compared them to measurements taken using TEM, SEM, and PCS on the same population of particles. For the TEM experiments, 5 µL of the colloidal dispersion was pipetted onto 200 hex copper grids coated with Formvar and carbon. The grids were then dried overnight and observed using a JEOL 1200 EXII transmission electron microscope. The images of the electron diffraction pattern were captured using a Gatan Bioscan camera and analyzed for particle size using standard image-processing software. The SEM samples were prepared in a manner similar to the TEM sample preparation, and they were gold-coated. The dried samples were observed using a Philips XL 20 scanning electron microscope, and the magnification was adjusted to provide good contrast between the particles and the background. The images of the particles obtained by the reflection of the incident electron beam in the CRT monitor were then analyzed for the particle size using the in-built software interfaced with the equipment. For the PCS experiments, the colloidal dispersion was poured into a test tube and placed in the sample holder of a 2030 AT variable-angle Brookhaven dynamic light scattering apparatus. The “mean diameter” readings were obtained from the instrument since the particles were nearly monodisperse in size. The apparatus does not give the standard deviation of particle diameter. Results and Discussion Table 2 shows a comparison of particle diameters measured using TEM, SEM, dynamic light scattering (PCS), and digital video microscopy (DVM). The DVM measurements were recorded for particles that are touching, and this measurement was averaged over 1020 doublets (20-40 particles) for each particle type. Thus, for each particle, we obtained the diameter by averaging over many images, so the “(” represents the standard deviation of diameter among the particles. It is clear from the data in Table 2 that DVM can size large particles with an accuracy comparable to that of electron microscopy and dynamic light scattering. It is also apparent from the data that the particles do not deform significantly when they touch, as DVM gives values very close to those from the other methods; such deformation could skew the results for soft particles. Figure 6 shows SEM images of the PSL 1 and Si particles. In understanding these measurements, it is important to distinguish the “optical resolution” of a microscope
Figure 6. SEMs of two particles in Table 1. (a) PSL 1 and (b) Si.
from the ability to determine the center of an object. The optical resolution refers to the ability to distinguish two nearly touching objects.7,17 Various measures exist (e.g., the Rayleigh limit, the Sparrow limit), but they are all similar: The optical resolution (h) is given by h ) λ/2NA, where the wavelength of light (λ) is roughly 500 nm and the numerical aperture (NA) of our oil immersion objective is 1.30. In our case, h ≈ 200 nm. Although the Rayleigh criterion depends on the ability of the observer to distinguish gray levels (i.e., a 16-bit camera gives a better optical resolution than the human eye), the essence of the limit remains. On the other hand, if the shape of the object is known to be a sphere, then the particle center can be determined with accuracy better than the optical resolution9,18 since the surface topography is known on a length scale that is much finer than the diffraction limit. Even for small spheres (190-nm polystyrene beads), previous researchers have used computationally intensive methods to calculate the center to within 1 nm.9 It is probable that the central Airy disks of two nearby colloidal spheres might overlap and skew the estimation of the distance between them.12 This overlap is increased when the particles are not in perfect focus and when the system is not Koehler-illuminated, but the results in Table 2 indicate that any bias introduced by overlap is small compared to the particle sizes measured. Figure 4 shows the plot for two particles that are stuck together, such that the interparticle gap was not changing with time. The figure reveals the excellent precision inherent in the DVM technique. Figure 5 shows the plot for two particles that were not stuck together and were undergoing a slight amount of Brownian motion. By eye, one can see an extremely small amount of relative motion between the particles. These figures are the type that enable us to distinguish doublets that are touching from those that are not.
3046
Ind. Eng. Chem. Res., Vol. 40, No. 14, 2001
Each of the techniques used in this study for sizing the diameter of particles (DVM, PCS, SEM, and TEM) has advantages and limitations. Two advantages of EM are that the technique has a proven history of reliability and that it can visualize details of the particle surface. EM methods utilizing a short-wavelength electron beam provide much higher resolution than the optical microscope, even though they have some inherent characteristics that limit the practically attainable resolution (e.g., convolution of the aberration coefficient,17 size of the scanning electron probe, and finite size of the effective interaction volume as in SEM19). However, the accuracy is still dependent on the error involved in measuring the magnification. An internal standard such as the lattice parameter of an ionic crystal (e.g., NaCl) can be used to calibrate the instrument, but this calibration typically limits the accuracy (not the resolution) of TEM and SEM to 1-2%. However, for colloidal sizing purposes, an important limitation of EM is that the samples must be dried and placed in a vacuum; therefore, no in vitro measurements can be made. Like EM, dynamic light scattering (PCS) has proven to be a reliable measurement technique for particle diameters. However, as a bulk technique, PCS is not as well equipped to study polydisperse or nonhomogeneous dispersions of particles. Also whereas DVM is better suited to larger particles (i.e., for particles 1 µm and greater, the measurements are very straightforward), PCS is more difficult for larger particles. Finally, PCS measurements depend on the knowledge of other system variables, including the fluid viscosity and refractive index, which are temperature-dependent. A key advantage of PCS is that it gives quick and accurate measurements of particle size, especially in facilities that already have this equipment. DVM has several advantages, which were listed in the Introduction section. In addition, it has the advantages that, because the optical path in a microscope is not overly complicated (compared with EM), the errors are small when the microscope is refocused or the sample remounted. Also, DVM is not subject to large errors from the environment, such as temperature changes. The precision of our experiments could be improved in a number of ways. (1) Vibration in the laboratory is a significant source of variation in the center-to-center measurements from frame to frame. A vibration-isolation table would reduce this greatly. (2) Improving the optics of the system would help, especially for the smaller particles where the Airy disks begin to overlap. Blue light would improve the optical resolution over our current polychromatic light. (3) A better camera, in terms of both spatial resolution (e.g., 1000 × 1000 pixels) and gray-scale resolution (e.g., 12-bit camera), would improve the technique. The experimental accuracy could be improved by a better calibration of the pixel size, which currently is limited by the accuracy of the reticle ((2%, according to the manufacturer). Conclusions Digital video microscopy is not a replacement for electron microscopy or photon correlation spectroscopy in determining particle diameters, but rather, it can be used as an additional tool for measuring the diameters of large particles or the gaps between two large particles. DVM has a precision of less than a few nanometers, which is important when measuring the standard
deviation of particle sizes. In addition, we have shown that, in measuring the diameters of large particles, its accuracy is comparable to that of EM and PCS measurements. The technique could be especially valuable to researchers who have video microscopy equipment in their laboratories already; reasonably accurate particle size measurements can be taken in much less than an hour. An important feature of DVM is the ability to measure interparticle gap as a function of time with nanometer precision.20-23 Previous researchers have used the technique to measure large separations of small particles;24 however, for large particles, the technique can detect changes in small separations with a resolution of 10 to 20 nanometers.14 This has important implications in measuring colloidal force profiles (e.g., with differential electrophoresis25 or a thermal motion technique20-22,24) and interparticle distances in colloidal crystal lattices.26,27 Acknowledgment Professor J. Larry Duda has a gift for telling entertaining stories and for helping people to feel welcome and appreciated. His unfailing confidence in others has inspired many of us to higher standards. D.V. thanks Professor Duda. The authors also thank the National Science Foundation for CAREER Grant CTS 9984443 and the Petroleum Research Fund for type G Grant 35400. Literature Cited (1) Goodhew, P. J.; Humphrey, F. J. Electron Microscopy and Analysis, 2nd ed.; Taylor and Francis: London, 1988. (2) Williams, D. B.; Carter, C. B. Transmission Electron Microscopy: A Textbook for Materials Science; Plenum Press: New York, 1996. (3) Berne, B. J.; Pecora, R. Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics; Wiley: New York, 1976. (4) Pecora, R. Dynamic Light Scattering: Applications of Photon Correlation Spectroscopy; Plenum Press: New York, 1985. (5) Russ, J. C. The Image Processing Handbook, 2nd ed.; CRC Press: Boca Raton, FL, 1995. (6) Inoue, S.; Spring, K. R. Video Microscopy: The Fundamentals, 2nd ed.; Plenum Press: New York, 1997. (7) Born, M.; Wolf, E. Principles of Optics, 6th ed.; Pergamon Press: Elmsford, NY, 1983. (8) Ali, S. A.; Sengupta, M. Correction to Microscopically Determined Particle Size According to Diffraction Correction Theory. J. Colloid Interface Sci. 1999, 220, 205. (9) Gelles, J.; Schnapp, B. J.; Sheetz, M. P. Tracking kinesindriven movements with nanometre-scale precision. Nature 1988, 331, 450. (10) Schaertl, W.; Sillescu, H. Dynamics of Colloidal Hard Spheres in Thin Aqueous Suspension LayerssParticle Tracking by Digital Image Processing and Brownian Dynamics Computer Simulations. J. Colloid Interface Sci. 1993, 155, 313. (11) Grasselli, Y.; Bossis, G. Three-Dimensional Particle Tracking for the Characterization of Micrometer-Size Colloidal Particles. J. Colloid Interface Sci. 1995, 170, 269. (12) Crocker, J. C.; Matteo, J. A.; Dinsmore, A. D.; Yodh, A. G. Entropic Attraction and Repulsion in Binary Colloids Probed with a Line Optical Tweezer. Phys. Rev. Lett. 1999, 82, 4352. (13) Crocker, J. C.; Valentine, M. T.; Weeks, E. R.; Gisler, T.; Kaplan, P. D.; Yodh, A. G.; Weitz, D. A. Two-Point Microrheology of Inhomogeneous Soft Materials. Phys. Rev. Lett. 2000, 85, 888. (14) Crocker, J. C.; Grier, D. G. Methods of Digital Video Microscopy for Colloidal Studies. J. Colloid Interface Sci. 1996, 179, 298. (15) Ovryn, B.; Izen, S. H. Imaging of transparent spheres through a planar interface using a high-numerical-aperture optical microscope. J. Opt. Soc. Am. A 2000, 17, 1202.
Ind. Eng. Chem. Res., Vol. 40, No. 14, 2001 3047 (16) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: New York, 1989 (with corrections, 1991). (17) Sarikaya, M. Evolution of Resolution in Microscopy. Ultramicroscopy 1992, 47, 1. (18) Denk, W.; Webb, W. W. Optical measurement of picometer displacements of transparent microscopic objects. Appl. Opt. 1990, 29, 2382. (19) Joy, D.C; Pawley, J. B. High-resolution Scanning Electron Microscopy. Ultramicroscopy 1992, 47, 80. (20) Prieve, D. C.; Luo, F.; Lanni, F. Brownian Motion of a Hydrosol Particle in a Colloidal Force Field. Faraday Discuss. Chem. Soc. 1987, 83, 297. (21) Prieve, D. C. Measurement of Colloidal Forces with TIRM. Adv. Colloid Interface Sci. 1999, 82, 93. (22) Walz, J. Y. Measuring particle interactions with total internal reflection microscopy. Curr. Opin. Colloid Interface Sci. 1997, 2, 600.
(23) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Direct Measurement of Colloidal Forces Using an Atomic Force Microscope. Nature 1991, 353, 239. (24) Crocker, J. C.; Grier, D. G. Microscopic Measurement of the Pair Interaction Potential of Charge-Stabilized Colloid. Phys. Rev. Lett. 1994, 73, 352. (25) Anderson, J. L.; Velegol, D.; Garoff, S. Experimental Studies of the Forces between Colloidal Particles. Langmuir 2000, 16, 3372. (26) Larsen, A. E.; Grier, D. G. Like-charge attractions in metastable colloidal crystallites. Nature 1997, 385, 230. (27) Gast, A. P.; Russel, W. B. Simple Ordering in Complex Fluids. Phys. Today 1998, 51, 24.
Received for review July 19, 2000 Revised manuscript received December 1, 2000 Accepted December 4, 2000 IE000664H
