Langmuir 1997, 13, 3913-3914
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High-Precision Measurement of Submicrometer Particle Size Distributions Philip J. Wyatt* and David N. Villalpando Wyatt Technology Corporation, Santa Barbara, California 93103 Received April 4, 1997. In Final Form: June 6, 1997X Submicrometer particles (polystyrene latices, for example) are often used as size standards for the calibration of various instruments and substrates. Ideally, the size distribution of such standards should be extremely narrow. However, the current method of choice for such classification, transmission electron microscopy (TEM), is fraught with problems rendering the reported size distributions uncertain. A far more precise and practical method consists of fractionating the particle sample prior to measurement by light scattering. A nominal 100 nm diameter NIST sample has been so-analyzed and yields a full width at half maximum of less than 0.5 nm, far below the resolution of TEM. The fractionation/light scattering protocol for so narrow a standard is confirmed by repeating the measurement using a broader sample fractionated under identical conditions.
Introduction The establishment of precise submicrometer particle size standards for many diverse applications requires the use of transmission electron microscopy (TEM), the socalled “gold standard” of measurement.1,2 Applied to submicrometer polystyrene latex (PSL) spheres (an important calibrant, for example, for the semiconductor industry), TEM measurements of several hundred to a few thousand of such particles are used to determine the size distribution characteristics of a large batch. Such samples, measured and sold by the National Institute of Standards and Technology (NIST), are often used subsequently by other manufacturers of similar particles to produce their own “NIST traceable” standards. The trouble with the TEM approach is that this “gold standard” method is fraught with problems! We report here the confirmation of a new, simpler, and far more precise method which combines a chromatographic separation followed by a multiangle light scattering (MALS) measurement. Discussion TEM measurements of simple submicrometer particles are flawed in various ways including the introduction of artifacts (e.g., shrinkage, distortion, etc.) during the preparation of samples for measurement. For such analyses, reference to a length, generally obtained from a ruled grating, of the spherical diameters measured on the same photomicrograph presents its own uncertainties. The most significant of these is related to the difficulty of delineating each particle’s true equatorial plane to which its accurate diameter would correspond. Once each particle in the electron micrograph has been so measured, the resulting collection of values is presented generally as a histogram, each bar of which has a width characteristic of the measurement resolution, often several nanometers. As these measurements are usually performed manually, the inaccuracy of the distribution measurement is further exacerbated for lack of sufficient numbers of determinations within each detected size interval. Finally, these measurements are best applied to samples of very narrow distribution since the characterization of broad distributions would require inordi* Author to whom correspondence should be addressed. Fax: (805) 965-4898, e-mail:
[email protected]. X Abstract published in Advance ACS Abstracts, July 1, 1997. (1) Maron, S. H.; Moore, C.; Powell, A. S. J. Appl. Phys. 1952, 23, 900. (2) Bradford, E. B.; Vanderhoff, J. W. J. Appl. Phys. 1955, 26, 864.
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nately large samples: far beyond the current limits of technician fatigue. Classical multiangle light scattering (MALS) measurements of single latex particles were shown many years ago3 to produce extremely accurate sizes since the scattering from such simple structures depends only on the particle diameter, its refractive index relative to the surrounding media, and the wavelength of the incident (vertically polarized) light. Given the latter two, the size is easily and precisely deduced from the measurement. The reference of measurement now is the laser wavelength: often known to five significant figures. A similar measurement from an ensemble of identical particles will produce the same result since (in the absence of multiple scattering) the identical scattering properties of the identical particles are just superimposed. The strategy by which the size distribution of a suspension of submicrometer particles would be measured is straightforward: by chromatographic or mechanical means separate the particles into aliquots each of which is comprised of an essentially single size. As has been confirmed recently,4,5 such a separation may be achieved by using cross flow field flow fractionation6,7 (CfFFF). Figure 1 shows the structure of such a fractionator comprising a ribbon-like channel along whose length a laminar flow stream is confined. Typically, the channel is 28.5 cm long, 2.0 cm wide, and 0.25 mm thick. Top and bottom surfaces of the channel are comprised of permeable ceramic frits through which a secondary transverse flow is introduced. Along one of these surfaces (the “accumulation wall”) lies a membrane of effective pore size small enough to prevent the particles from passing through. Particles are introduced at one end of the channel in a small aliquot which then flows within the laminar stream while acted upon by the transverse stream. Diffusion causes the particles to move away from the accumulation wall while the transverse Stokes’ forces push them toward the wall. Each particle size group, therefore, establishes its own equilibrium distribution above the wall: smaller particles, having an equilibrium position higher into the laminar stream, elute first. Connecting the CfFFF fractionator output to a MALS (3) Kerker, M.; Cooke, D. D. Croat. Chem. Acta 1973, 45, 235. (4) Roessner, D.; Kulicke, W.-M. J. Chromatogr., A 1994, 687, 249. (5) Shortt, D. W.; Roessner, D.; Wyatt, P. J. Am. Lab. 1996, 11, 21. (6) Caldwell, K. In Modern Methods of Particle Size Analysis; Barth, H. G., Ed.; John Wiley and Sons: New York, 1984; p 211. (7) Giddings, J. C. Science 1993, 260, 1456.
© 1997 American Chemical Society
3914 Langmuir, Vol. 13, No. 15, 1997
Letters
Figure 3. Differential number fraction distributions for the samples shown in Figure 2. The NIST standard has a fullwidth at half-maximum value of 0.34 nm. Figure 1. Diagram of the cross flow field flow fractionator showing its main components. A cross flow toward the accumulation wall produces a Stokes’ force opposing the particle diffusion. The particles establish, therefore, equilibrium positions above the wall: the smaller particle equilibrium position is farther from the wall corresponding to a greater laminar channel flow and thus these particles elute first.
Table 1. Relation of Flow Field-Flow Fractionation Cross Flow to Retention Volume and Diameter Resolution at 100 nm cross flow (mL/min)
retention volume (mL)
dD/[dV]a (nm/mL)
0.4 0.8 1.0
9.043 18.443 23.523
4.24 5.16 4.82
a Where dD/[dV] is the change in diameter with respect to elution volume at 100 nm.
Figure 2. Plot of the hydrodynamic radius versus elution volume for broad (Duke 3301-1) and narrow (NIST 1963) polystyrene standards, exhibiting the ability of the fractionator to separate the samples by size. Run conditions for both samples: solvent ) water; channel flow ) 1.5 mL/min; cross flow, 0.8 mL/min; laser λ ) 632.8 nm. Injected mass for the NIST and Duke standards was 3.92 × 10-5 and 3.00 × 10-4 g, respectively.
unit8 permits the measurement of the scattered light from each eluting fraction (“slice”). From these measurements, the average hydrodynamic diameter (or radius) of the particles present in that fraction is readily calculated, as well as the differential number fraction distribution of the entire sample. Figure 2 shows the measured particle radius as a function of elution volume for two PSL samples: a NIST (1963) standard reference material, 100 nm diameter particles, and a Duke Scientific (3100-01) broad distribution sample of average diameter 100 nm. Also shown for comparison are the respective MALS signals at 90°. The corresponding differential number fraction distributions are shown in Figure 3. The extremely narrow distribution (about 0.34 nm fullwidth at half-maximum) derived for the NIST standard is far less than the value quoted by them (NIST Standard (8) Wyatt, P. J. Anal. Chim. Acta 1993, 272, 1.
Reference Material 1963 Certificate of Analysis). A common “explanation” for this overly monodisperse result is that the fractionator did not actually separate the sample and, therefore, the eluting peak represented, for the most part, a dilution without separation. Referring to the broad Duke standard of Figure 2, however, we confirm that the fractionator does separate effectively over a broad range of sizes including those that might be present in the NIST standard. The derived distributions of Figure 3 are correct. If one defines the resolution of the channel for particles near 100 nm by the slope of the elution curve at 100 nm, then by increasing the cross flow relative to the channel flow, the resolution of the channel may improve.6 However, as the cross flow reaches some optimum value, the resolution about a particular size (say 100 nm) may even diminish, as shown in Table 1. The data of Table 1 further confirm that flow conditions, under which the results of Figure 2 were generated, were more than sufficient to detect a larger range of sizes in the NIST sample were they indeed present. Conclusions Light scattering measurement following fractionation is confirmed as a suitable and precise means for the characterization of submicrometer homogeneous spheres. Each scattering particle registers its own signature based on exposure to a “perfect” ruler: the laser. No subjective judgments are required, as is always the case with TEM. The reproducibility of the MALS measurement is extremely high and the measurement is direct; i.e. no auxiliary reference standards are required. Finally, the determinations may be made in most laboratories without reference to any standards measured by other laboratories. LA9703508
