ASTM Carbon Black Reference Materials: Particle Sizing Using a Brookhaven Instruments BI-DCP, Disc Centrifuge Photosedimentometer Walther W. Tscharnuter, Lily Zu, Bruce B. Weiner, Brookhaven Instruments Corporation, 7 Blue Point Road, Holtsville, New York 11742-1832 USA, E-mail: bruce@bic.com William Bernt, Particle Characterization Laboratories, 32 Seventh Street, Novato, California 94945 USA, E-mail: bernt@bic.com Abstract The principles of particle sizing using a disc centrifuge photosedimentometer are reviewed. The importance of the extinction correction for accurate measurements is emphasized. Results on the ASTM A4 through F4 series of reference blacks is presented. Comparisons between reference materials are made. Different sample preparations are discussed. Stability of such preparations with time is shown. Introduction The commercial importance of carbon black is a foregone conclusion with anyone attending this conference. It is used as an abrasion-resistant filler in the manufacture of tires and in the production of many other rubber materials. Carbon black is also used as a pigment in coatings and lacquers, plastics, printing inks, and tinting blacks (1). Since the particle size distribution (PSD) of aggregates of carbon black is strongly correlated with the thermal and mechanical properties of dispersions (2), the measurement of a carbon black PSD is an important part of quality control. The typical size range for nonagglomerated carbon black is from nm to over 0 nm. Although often unimodal, except for mixtures, the typical carbon black PSD is broad, typically covering more than one decade in size, sometimes two. Given the small sizes involved, the breadth of a typical distribution, a disc centrifuge photosedimentometer (DCP) has been the instrument of choice for more than 25 years (3). It is a rugged instrument, the theory of which is well developed. Provided all corrections are made, the accuracy of the DCP is unsurpassed. Following a brief review of the theory, including the importance of the light scattering correction, the results on ASTM reference materials are presented.
Theory: Stokes s Law in a Centrifuge The theory was presented during the last conference held in Japan and will be summarized here. It is also available in the literature (4,6). There are two techniques used with a DCP: the line start and the homogeneous start. In this paper we will discuss only the line start. With this technique, a small volume of the dispersion is injected onto the meniscus of a rotating, hollow disc filled with liquid. The liquid is called the spin fluid. Typically, it contains a gradient to prevent hydrodynamic instabilities, surfactants to match those in the dispersion, and a very thin layer of a low vapor pressure liquid to prevent evaporative cooling and thermal inversions. After injection, assuming the particle density is larger than the liquid density, all the particles of various sizes start sedimenting radially outward at the same time. This line start technique provides the most resolution. An equation of motion is written for a particle of diameter D p, mass m p, and density ρ p moving radially outward in a liquid of density ρ f and viscosity η f, while the disc is spinning with an angular velocity of ω. After taking into account the buoyancy and frictional terms, and assuming a steady-state solution, the result is: 18η ln rd f t = S 2 ω ρ D 2 p Here t is the time it takes the particle to travel from the meniscus, with radial distance S, to the detector, with radial distance r d. S is easily calculated from the volume of the injected spin fluid and the internal dimensions of the disc cavity. The difference in density between the particle and fluid is given by ρ = ρ p - ρ f. For ρ > 0, as is the case with carbon black in water, the particles sediment radially outward and the detector is placed near the internal perimeter of the disc. For ρ < 0, as is the case with oil droplets in water, the particles sediment radially inward and the detector is placed just below the meniscus. In this case the homogeneous start technique is used. The measured time at which particles cross the detector yields the particle size through Stokes s Law. To complete the PSD determination, the amount of material at that time is required. This is calculated from the turbidity τ, which is obtained from the measured voltages with and without particles. To obtain the volume distribution, corrections must be applied. One of these, the extinction correction, is worth repeating since it was systematically ignored in many earlier DCP investigations.
The differential volume distribution (equivalent to the differential weight distribution assuming all particles have the same density) is given by: dv / dd = C τ / p Q ext Here C is a constant for a fixed detector position. Q ext is the extinction efficiency that is calculated from Mie scattering theory, given the wavelength of the light (6 nm for a BI- DCP), the particle size (determined by Stokes s Law above), and the refractive index of the particle and liquid (4). Although there are minor variations (5) in the refractive index of carbon blacks, a suitable average value for particle sizing is n = 1.84-0.85i. Figure I shows the extinction efficiency versus particle diameter from 0 to 2 microns. The calculations are discussed in a previous publication (4). 3.0 2.5 Extinction Efficiency 2.0 1.5 1.0 0.5 0.0 0 200 400 600 800 00 1200 1400 1600 1800 2000 Figure I: Extinction correction for carbon black Note the linear increase from zero to about 200 nm. Note also the curve is asymptotically approaching a flat line with a limiting value of 2 as the size increases. This is the limiting value predicted by Fraunhofer diffraction theory, also known as forward angle light scattering theory. In this size range, no refractive index is required and instruments based on Fraunhofer diffraction are suitable. Below this range, where the extinction correction
is required for accuracy, the particle refractive index is required and Fraunhofer theory no longer applies. The relationship between turbidity, Q ext, and the volume distribution is given by (6): τ = 3 c Qext dn / dd D = c Qext dv / dd Here the number-weighted, differential PSD is dn/dd; the volume-weighted differential PSD is dv/dd (also equal to the differential weight distribution when all the particles have the same density); and the factors c and c are normalization constants which drop out of the final analysis. The number- and volume-weighted, cumulative PSDs are obtained by integrating dn/dd and dv/dd, respectively. This equation holds for a fixed detector position and was obtained after integration over a finite detector slit width. Before integration, the surface area-weighted size distribution is proportional to τ/q ext. Treasure (7) was the first to point this out. After integration the volume-weighted size distribution, dv/dd, is proportional to τ/q ext. Since carbon blacks are neither homogeneous spheres nor monodisperse, it is impossible to prove experimentally using carbon black that the theory is correct. However, work with both polystyrene latex and BCR66 (quartz powder) have shown the excellent agreement between theory and experiment (4) using both the Treasure correction and the appropriate extinction efficiency. Sample Preparation and Centrifuge Run Conditions Approximately mg of the carbon black powder is added to 2 ml of 0% ethanol in a 20 ml, screw-cap, dilution vial. The suspension is sonicated in a 30 mw sonic bath for 5 minutes to wet the sample. To cool the capped vial, it is placed in an ice-water bath for 3 minutes. After cooling, it is sonicated again while 6 ml of a 0.1 vol% TritonX-0 (DuPont) aqueous solution is slowly added to the suspension to disperse the particles. However, to fully break apart the more strongly bound agglomerates, vigorous mechanical energy is still needed. The resulting 8 ml suspension is sonicated with a 375 watt sonic probe at 40% power with a % duty cycle for minutes while surrounded by an ice bath to prevent boiling and evaporation. A pipette is used to withdraw the suspension, taking care not to collect any undispersed particles stuck to the glass walls of the original vial. The contents of the pipette is emptied into a clean, 20 ml vial. Finally, the suspension is de-gassed for five minutes using the de-gas mode of a sonic bath (not constant sonic mode). While capped, it is allowed to warm up to room temperature. For each measurement about 0.2 ml of this suspension is injected into the centrifuge. The measurements were made with a Brookhaven Instruments BI-DCP, disc centrifuge photosedimentometer, using the following procedures.
About 0.2 ml of 0% ethanol is injected into the non-spinning disc to act as a buffer layer which rises through the spin fluid. The disc is then spun at 8,000 rpm. Immediately 15 ml of a 0.1 vol% TritonX-0 aqueous solution, the spin fluid, is injected into the spinning disc, followed immediately by the injection of about 0.1 ml of 0% dodecane to prevent evaporative cooling. It is important to prepare the spin fluid and dodecane liquids and syringes prior to the ethanol injection in order to prevent evaporation and thermal gradients. A flat voltage vs. time response after a minute or two ensures the system has reached thermal equilibrium. Then about 0.2 ml of the carbon black suspension described in the first paragraph is injected. A typical run time takes about 45 minutes. Though not required, it was found useful to inject NIST-traceable, narrow latex standards, both before and after each of the carbon black samples, to verify both gradient and thermal stability as well as the temperature inside the disc. Stability was excellent and multiple injections over the same gradient were possible for up to four hours. Results The volume-weighted, cumulative undersize and differential PSD for ASTM carbon black reference material A4 is shown in Figure II with and without the extinction correction. The uncorrected distribution is shifted to larger sizes. The d is shifted by %, from 96.6 nm with the full light scattering correction to 6.5 nm with no correction. 0 Cumulative Undersize and Differential Size Distribution 80 70 60 40 30 20 No correction 0 0 0 1 200 2 Figure II: Effect of light scattering correction.
The volume-weighted, cumulative undersize and differential PSDs for ASTM A4, B4, C4, D4, E4, and F4, including the light scattering and Treasure corrections are shown in Figures III and IV, respectively. Cumulative Undersize Distribution 0 80 70 60 40 30 20 A4 C4 B4 F4 E4 D4 0 0 0 200 300 400 0 600 700 800 Figure III: Volume-weighted, cumulative undersize distribution. 0 Differential Size Distribution 80 70 60 40 30 20 B4 C4 A4 F4 E4 D4 0 0 0 200 300 400 0 600 700 800 Figure IV: Volume-weighted, differential particle size distribution.
Table I shows the th, th, and th percentile diameters by volume for these six ASTM reference materials. The span, defined as d Span = is one of many possible measures of relative width for a unimodal distribution. d d Table I. ASTM Reference Materials: Particle Size in nanometres ASTM d d Span Name (nm) (nm) (nm) A4 61.1 96.6 136 0.775 B4 73.2 118 175 0.863 C4 59.5 96.5 143 0.865 D4 165 283 455 1.025 E4 134 230 347 0.926 F4 140 225 332 0.853 Six repeats of A4 produced a 95% confidence limit of 1.5 nm on d. This 1.5% reproducibility is a fair estimate for all the other numbers in the table too. This number is used to guide the rest of the comparison. The six samples may be divided into two groups: small sizes (A4, B4, C4) and large sizes (D4, E4, F4). The six samples have an average relative width, as measured by the span, of 0.88 with only a 16% deviation above and below this value encompassing all six samples. However, at the 1.5% reproducibility level, there are significant differences. Sample D4 is the broadest; sample A4 is the narrowest; and samples B4, C4, and F4 have nearly the same relative widths. While d and d of samples A4 and C4 are equal within the random error of the measurements, d of sample C4 is larger. This accounts for sample C4 s greater relative width. While d of samples E4 and F4 are equal within the random error of the measurement, the d and d are not, with sample E4 spread to slightly lower and slightly higher sizes than F4. This accounts for sample E4 s greater relative width. Since carbon blacks tend to agglomerate, the sample preparation involves dispersion with a sonic probe. It is natural to ask if the sample preparation is sufficient to break apart agglomerates. Results are shown in Figure V on sample A4 prepared with the normal and four times the normal duration of sonic energy. The results are indistinguishable within the random error of repeated measurements. d
Cumulative Undersize and Differential Size Distribution 0 80 70 60 40 30 20 0 0 0 1 200 2 Figure V: Different durations of sonic (probe) energy to test sample preparation on A4. Cumulative Undersize & Differential Size Distribution 0 80 70 60 40 30 20 0 0 0 200 300 400 0 600 700 800 Figure VI: Stability of sample F4 one year later.
The results presented here were actually determined in February of 1999, shortly after the December meeting in Japan. To test the stability of the dispersions, sample E4 and F4 were measured again in January of 2000 with only mild sonication (30-40 W, 3-5 minutes) applied. These were not freshly prepared samples; these were the same suspensions prepared a year earlier and left sitting in the lab. The agreement is within the 1.5% random error of the measurement for th, th, and th percentiles of the volumeweighted, cumulative undersize distributions for both E4 and F4, except the th percentile for E4 was 4.4% lower a year later. The volume-weighted, cumulative undersize and differential PSD s are shown for F4 in Figure VI. The agreement is excellent. Note that all scales are linear. Most size distribution analyses are presented on logarithmic scales and this often masks poor resolution. Discussion For accurate results on carbon blacks, a light scattering correction in the form of Q ext is required for transforming turbidity-weighted centrifuge results into volume-weighted PSD results whenever the particle size is less than a few microns. Likewise, a light scattering correction is also required for any other type of experiment where light is used to detect the amount of particles. This applies to dynamic light scattering, column hydrodynamic fractionation, field-flow fractionation, and various forms of high angle light scattering, the extension of Fraunhofer diffraction into the colloidal size range. It is a mistake to assume the correction is linear over the entire range of interest for carbon blacks. The best approach is to use the exact correction as shown here. The adequacy of the sample preparation technique is demonstrated in two ways. First, increasing the duration of sonic energy to disperse the agglomerates (8) gave the same results, suggesting the method is sufficient as it stands. Secondly, samples run one year later, after sitting in the lab, require only mild bath sonication to ensure reproducibility within the random error of the measurement. Tables of the volume-weighted, cumulative undersize and differential particle size distributions for these ASTM reference materials are available from the authors.
References 1. Voll, M. & Kleinschmit, P., Black Pigments (Carbon Black), in Industrial Inorganic Pigments, edited by G. Buxbaum, VCH Publishers, New York, 1993. 2. Patel, A.C. & Lee, K.W., Characterizing Carbon Black Aggregate via Dynamic and Performance Properties, Elastomerics, Communication Channels Inc., Atlanta, March 19. 3. Redman, E., Heckman, F.A., & Connolly, J.E., Rubber Chemical Technology, 51:00, 1977. 4. Weiner, B.B., Fairhurst, D., & Tscharnuter, W.W., Particle Size Analysis with a Disc Centrifuge: Importance of the Extinction Correction, in Particle Size Distribution II: Assessment and Characterization, edited by T. Provder, ACS Symposium Series 472, American Chemical Society, Washington D.C., 1991, Chapter 12. 5. Medalia, A.I. & Richards, L.W., Journal of Colloid and Interface Science, 1972, 40, 233. 6. Devon, M.J., Provder, T., & Rudin, A., Measurement of Particle Size Distribution with a Disc Centrifuge, in Particle Size Distribution II: Assessment and Characterization, edited by T. Provder, ACS Symposium Series 472, American Chemical Society, Washington D.C., 1991, Chapter 9. 7. Treasure, C.R.G., Whiting and Industrial Powder Research Council, Welwyn, U.K., Tech. Paper No., 1964. See reference 5 above for a more modern development of the Treasure correction. 8. The authors distinguish between primary particles, aggregates (strongly bonded), and agglomerates (weakly bonded: edges and corners).