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a Dep. of Land, Air, and Water Resources, University of California, Davis, CA 95616
b Institute of Soil, Water, and Environmental Sciences, Agricultural Research Organization (ARO), The Volcani Center, P.O. Box 6, Bet Dagan 50250, Israel
* Corresponding author (geshel{at}ucdavis.edu).
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONParticle-Size Distribution...The Effects of Nonsphericity...MATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Abbreviations: LD, laser diffraction • PIDS, polarization intensity differential of scattered light • PSD, particle-size distribution • RI, refractive index
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONParticle-Size Distribution...The Effects of Nonsphericity...MATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Particle-Size Distribution Determination Methods Employed in Soil Science |
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TOPABSTRACTINTRODUCTIONParticle-Size Distribution...The Effects of Nonsphericity...MATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Numerous techniques for the determination of PSD, other than these classical ones, were developed, mainly for industrial applications such as the determination of the homogeneity of powders and gels (Buurman et al., 1997). Among those techniques, LD (or laser light scattering) was occasionally applied to soil material (e.g., Cooper et al., 1984; Levy et al., 1993; Buurman et al., 1997; Muggler et al., 1997; Konert and Vandenberghe, 1997; Chappell, 1998; Beuselinck et al., 1998). In this latter method the forward diffraction of a laser beam by the particles is used to determine their size distribution. The angle of diffraction is inversely proportional to particle size, and the intensity of the diffracted beam at any angle is a measure of the number of particles with a specific cross-sectional area in the beam's path. Two optical models are commonly used to calculate PSD, the Fraunhofer diffraction model and the Mie theory. The former is based on the approximation that the laser beam is parallel and the detector is at a distance that is very large compared with the size of the diffracting particle. The Mie theory is a solution of the Maxwell equations (i.e., a set of four fundamental equations governing the behavior of electric and magnetic fields) describing propagation of the electromagnetic wave of light in space. The theory provides a solution for the case of a plane wave (i.e., the wavefronts of which are planes) on a homogeneous sphere of any size (Jonasz, 1991). In addition, it takes into account phenomena other than diffraction (e.g., transmission through the particle) and therefore requires knowledge of the RI of the material tested. The Mie theory thus offers an exact solution to the scattering of light from a homogeneous sphere (but not from an irregularly shaped particle). The resultant PSD computed by either the Fraunhofer diffraction or the Mie theory is a volume (rather than mass) based size distribution. Early generation LD instruments for PSD determination suffered from a size detection limit >0.5 µm. In addition, they employed mainly the Fraunhofer diffraction, which is inaccurate for particles smaller than d = 10
(where is wavelength) (Bayvel and Jones, 1981; de Boer et al., 1987); for the Beckman–Coulter LS-230 it would be particles <7.5 µm in diameter. In newer LD apparati, the lower detection limit was extended to approximately 0.04 µm.
Main advantages of the LD technique for PSD determinations include: short time of analysis (5–10 min per sample), high repeatability, small size of sample needed (
1 g), and a wide range of size fractions into which the entire range of particle sizes can be divided. The latter point is of particular importance because the availability of a continuous PSD, rather than an arbitrary division of the particles among a limited number of size fractions (as is obtained by the pipette method), enables a more detailed data analysis and a simultaneous use of the same data sets for classification of the analyzed samples under different national classification systems. Furthermore, PSD is used for the prediction of soil hydraulic properties (e.g., Bloeman, 1980; Arya and Paris, 1981). Because porosity and pore-size distribution in soils or other porous media are key parameters in the calculation of hydraulic properties, direct determination of PSD in terms of volume percentage by LD, rather than in terms of mass percentage as is the case in the pipette method, eliminates the need to adopt the rough approximation of a single value for soil particle density in the prediction process.
Main disadvantages are high cost of the LD instrument and insufficient confidence in the results due to the relatively low number of LD analyses of soils as compared with the enormous number of analyses performed by the classical methods. Entire texture-based classifications of soils are dependent on correlations that were established between soil properties and PSDs derived by classical methods. Correlations between PSDs obtained by LD and soil properties are yet to be established.
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The Effects of Nonsphericity and Uncertainty in Participle Density on Particle-Size Distribution Analysis |
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TOPABSTRACTINTRODUCTIONParticle-Size Distribution...The Effects of Nonsphericity...MATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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In the case of sieving, for example, the likelihood of a nonspherical particle to pass through or be retained on a sieve of a given mesh size depends on the particle's shape and the probability of the particle to assume, during the time allotted for sieving, an orientation relative to the sieve that will allow it to pass through. Such an orientation exists for particles whose smallest cross-section can clear through the sieve's aperture. The net outcome of the nonsphericity of soil particles is, as a rule, that a coarser population is retained by the sieve than the actual population of particles with apparent diameters corresponding to the sieve size (Mathews, 1991). Exceptions to this rule may occur, for example, when the soil sample contains a significant quantity of very flat disk-shaped particles with a diameter exceeding that of the sieve aperture.
In sedimentation-based techniques the particle shape has the following effect. The most stable position of a settling nonspherical particle is the one in which the maximum cross-sectional area is perpendicular to the direction of motion (Krumbein, 1942). This position increases the expected particle drag, which, in turn, results in a decrease in the settling velocity (Mathews, 1991). Thus, the fine size fraction is overestimated.
When wet sieving through a sieve with a 53-µm effective opening and sedimentation are combined for the determination of PSD (as is the case in the pipette method), an overestimation of the silt plus clay fraction at the expense of the sand fraction usually occurs during the sieving stage. Thereafter, during the sedimentation stage, the clay fraction is overestimated at the expense of the silt fraction.
An additional source of error in the sedimentation-based techniques is the heterogeneity in the particles' density. For soil and earth materials, particle density is commonly taken as 2.65 Mg m–3. Yet, Clifton et al. (1999) found that the density of marsh sediment particles can vary between 1.66 and 2.99 Mg m–3. The uncertainty regarding the actual density of the particles may strongly bias the size distribution in the sedimentation analysis.
Unlike PSDs derived from sedimentation-based techniques, a PSD measured by the LD method is independent of the density of the particles. On the other hand, LD derived PSD is also affected by the shape of the particles. The projected cross-sectional area of a nonspherical particle averaged over all the particle's possible orientations relative to the direction of the beam is larger than that of a sphere with an equal volume (Jonasz, 1991). This may lead to the assignment of a measured particle to a larger size fraction than it actually belongs to on the basis of its apparent radius; that is, a shift of the PSD toward its coarser fractions. It should be borne in mind however that for particles with an equivalent spherical diameter 0.1 µm, the projected cross-sectional area becomes nearly the same as that of a sphere of equal volume (Jonasz, 1987).
In the present study, we performed a critical evaluation of the LD method and the combined sieve–pipette method for determining PSD of soils and assessed (i) whether a functional relationship existed between the two types of methods for determining PSD, and (ii) the suitability of LD as a routine procedure for PSD determination in soil science.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONParticle-Size Distribution...The Effects of Nonsphericity...MATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Pipette Method
Forty-gram samples were dispersed overnight in a 50-g L–1 sodium hexametaphosphate solution. Thereafter, the sand-size particles were separated from the suspensions by wet sieving through a 53-µm sieve. The fraction retained by the sieve was dried and then weighed. The clay fraction was determined using the pipette method as described by Janitzky (1986). The silt fraction was determined by difference. Analyses were performed in triplicate.
Laser Diffraction
A Beckman–Coulter LS-230 with a 750-nm laser beam was used for PSD analysis; software version 3.01 was used for the calculation of the PSD. The instrument measures particle size over the range of 0.045 to 2000 µm. The laser beam accurately measures particles of an apparent cross-sectional diameter >0.4 µm (Buurman et al., 1997). For particles with an apparent cross-sectional diameter 0.4 µm, the LS-230 employs the polarization intensity differential of scattered light (PIDS) system, which uses polarized beams of 450-, 600-, and 900-nm wavelength. The PIDS system determines particle sizes between 0.1 to 0.6 times the wavelength of the polarized beam, thereby extending the measurement limit to 0.045 µm (Coulter Co., 1994).
The calculation module offers the use of two optical models, the Fraunhofer diffraction model and the Mie theory. Because the Fraunhofer model is not accurate enough for the determination of the clay-size fraction (Bayvel and Jones, 1981; de Boer et al., 1987), calculations based on the Mie theory were used. It should be borne in mind that the Mie theory applies rigorously to spherical, homogeneous particles and fits less satisfactorily nonspherical or nonhomogeous particles (Jonasz, 1991) as are commonly found in soil. The Mie theory model requires, as an input parameter, the RI, which is a complex number comprised of (i) a real part (nr) which represents the change in the velocity of light through the tested material compared with the velocity of light in vacuum; and (ii) an imaginary term (ni) which represents the transparency and absorptivity of that material. Different RI values were tested to obtain the most suitable PSD.
For the PSD analysis, 0.1 to 0.5 g of soil was dispersed overnight in a 20-mL scintillation vial containing 10 mL of a 50-g L–1 hexametaphosphate solution. Thereafter, individual dispersed samples were transferred to the fluid module that contained 1.7 L of deionized water (nr = 1.33 at 20°C) and subjected to a 1-min ultrasonication at energy level 3. Three to five replicate samples of each soil were then subjected to three consecutive 1 min runs at a pump speed of 8 to 12 L min–1.
To further compare the pipette method with the LD technique, we chose surface horizon samples from three representative soils varying considerably in their PSD: Clear Lake Series Fine, smectitic, thermic Xeric Endoaquerts; Yolo Series Fine-silty, mixed, superactive, nonacid, thermic Mollic Xerofluvents; and Auberry Series Fine-loamy, mixed, semiactive, thermic Ultic Haploxeralfs (Table 1: Soils No. 2, 22, and 35, respectively). From these soils we extracted the silt + clay fraction by wet sieving with a 53-µm sieve. The <53-µm particles were then placed in a 1-L settling cylinder as used in the pipette method. Immediately after homogenizing the suspension in the cylinder a sample was taken with a pipette and placed in the LD analyzer for PSD measurement. Thereafter, we rehomogenized the suspension in the cylinder and allowed for particles >2 µm to settle. A sample was then taken with a pipette from a depth of 10 cm (to include only particles <2 µm) to the LD analyzer and PSD analysis was performed. All measurements were performed in two replicates for each soil.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONParticle-Size Distribution...The Effects of Nonsphericity...MATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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0.4 µm that are determined by the PIDS procedure. Because the projected cross-sectional area of nonspherical small particles (<0.1 µm) is similar to that of equivalent spherical particles, the aforementioned need to choose a lower nr no longer exists. In addition, the clay-size particles are frequently coated with oxides and organic matter whose nr is higher than that commonly considered for clay minerals. Therefore, it might be advantageous to increase the nr in the 0.4-µm range to approximately 1.6. For the investigated soils, adopting the larger nr value for the lower range of the PSD affected the curve's shape only in the part of the curve corresponding to clay particles <1 µm (Fig. 3)
. It led to a decrease of 0.7, 1.1, and 1.9% in the total volume of the clay fraction of the Auberry, Yolo, and Clear Lake soils, respectively. Even though the magnitude of the total clay fraction did not change substantially in the present case by the application of a larger nr to the size region in which the PIDS procedure is employed, it is suggested that whenever this option exists a higher nr value should be adopted in the PIDS as it may have a significant effect on the PSD in some cases (e.g., soils rich in oxides or organic matter).
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The above discussion about the relation between pipette and the LD data refers only to the clay-size fraction. To evaluate all three size-classes, we calculated the relative error, that is the absolute value of the difference between measured and calculated LD values (based on the equation presented in Fig. 4 for each size class) expressed as percentage of the measured value, for the sand, silt, and clay fractions (Table 3). The results indicated that even if the relative error was small for one size fraction, as was the case for the clay fraction in soils 5, 10, 15, and 27, the relative error was still high for one or both of the other fractions (Table 3). These observations strongly suggest that in individual studies LD data could at times be satisfactorily correlated with pipette data for a given size fraction, but no universal relation between PSD obtained by LD and that obtained by the pipette method can be formulated for the entire PSD range.
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To further examine the differences in PSD between the pipette and the LD methods, we examined the PSD using the LD of the silt + clay (<53 µm) and clay fractions (<2 µm) of the Auberry, Yolo, and Clear Lake soils that were isolated by wet sieving and the pipette method, respectively (Table 4). In all three soils, after sieving, the volume percentage of the <53-µm fraction was <100%, thus indicating, as discussed above, that during the sieving part of the combined sieving–pipette method, particles >53 µm passed through the sieve and were thus no longer considered as sand particles. Concerning the clay-size fraction (<2 µm), only approximately 57% by volume of the samples were determined to be within the clay-size fraction, while approximately 43% of the particles were in the size fraction >2 µm (Table 4). These results are similar to those of Clifton et al. (1999), who analyzed marine sediments and found that approximately 35% of the clay-size particles obtained by settling were considered coarser than 2 µm by a LD determination. These results further highlight the consistent lack of agreement regarding the clay fraction between the sedimentation-based pipette method and the LD technique.
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The difference between a PSD obtained by LD and the one obtained by sedimentation for a given soil is dependent in a complex fashion on the properties of the soil and especially on its mineralogy (that determines, e.g., the RI and the density) and morphology (that affects the shape, or deviation from sphericity) of the soil particles. The overall consequence of the predictable, procedure-dependent sources of error inherent in the PSD determinations by the two methods and the harder to estimate soil-dependent sources of error is that no consistent relationship between PSDs derived by LD and PSDs derived by sedimentation methods can be formulated. This is so, despite some recurring features of the differences in the derived PSDs (e.g., a lower clay fraction produced by the LD method).
Finally, it should also be born in mind that disparities between measured PSDs may also occur when different LD apparati are used. Loizeau et al. (1994), for example, reported a discrepancy between PSDs obtained by two LD instruments for particles <10 µm. This discrepancy was probably the result of using two instruments with different detection limits. Not only may LD instruments differ in their detection systems, but the optical model employed for PSD determination may also be different. In some studies the Fraunhofer diffraction model was used (e.g., Loizeau et al., 1994; Konert and Vandenberghe, 1997; Beuselinck et al., 1998), while in others the Mie theory was used (e.g., Buurman et al., 1997; Muggler et al., 1997). Differences inherent in the two optical models, and especially the fact that the Fraunhofer model has difficulties in calculating the magnitude of particles in the size range of the laser beam wavelength or smaller, may affect the outcome of the PSD determination for a given sample.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONParticle-Size Distribution...The Effects of Nonsphericity...MATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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It should be realized that there is no method for PSD determination of soil materials that can serve as a universal yardstick, because all available methods, whether classic (e.g., pipette) or new (e.g., LD), suffer from some inherent flaws. The choice between methods depends, therefore, on the balance between the pros and cons of each. Advantages of the LD procedure over the pipette method include (i) need for only a small sample, (ii) short time of analysis, and (iii) a continuous PSD curve.
Compared with the pipette method, the LD procedure suffers from two main disadvantages. One is the high cost of the instrumentation. However, with the increase in cost of labor and the constant pressure for greater reliability, reproducibility, and speed of analysis, the attractiveness of LD apparati is expected to grow. The second disadvantage is the lack of a database that correlates LD-derived PSDs with soil properties, similar to the very extensive database existing for pipette-derived PSDs. Nonetheless, should the LD method become more accepted in the soil science community, the well needed database will gradually be established.
We believe that the LD method and the resultant expression of PSD based on volume is a valid method even though it does not provide data that are fully comparable with data derived by classical methods. Because of the speed, small sample size, and range of output options available with laser diffraction, we foresee the method becoming more widely used for PSD.
Received for publication April 9, 2003.
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TOPABSTRACTINTRODUCTIONParticle-Size Distribution...The Effects of Nonsphericity...MATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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