Anal. Chem. 2001, 73, 3467-3471
Particle Characterization and Separation by a Coupled Acoustic-Gravity Field Takashi Masudo and Tetsuo Okada*
Department of Chemistry, Tokyo Institute of Technology, Meguro-ku,Tokyo 152-8551, Japan
A coupled acoustic-gravity field is proposed as a novel external field for particle separation and characterization. When a standing plane ultrasound wave is generated, particles move to the node of the wave along the ultrasound force gradient. If the particles also undergo a sedimentation force, they aggregate at the equilibrium position, where these two forces are balanced. The equilibrium position, which is determined by the density and compressibility of a medium and particles, characterizes the particles. The local ultrasound energy, which is necessary for quantitative discussions, is evaluated by using a standard particle, the physical parameters of which are unambiguously determined; aluminum particles are used in the present study. The local ultrasound energy makes possible the determination of the compressibility of unknown materials. Nonporous particles of inorganic and polymeric materials, the particle sizes of which range from 3 to 100 µm, follow a derived model, suggesting that the local ultrasound energy and a derived model be valid. The proposed external field can be used for separation of particles having different acoustic natures. Separation is a fundamental science, which has contributed to the development of research in various fields including physics, life sciences, and geosciences as well as chemistry and its related practices. Chromatography is, for example, a very versatile and efficient tool, which covers separation of various sizes of molecules, ranging from monatomic molecules to macromolecules having molecular weights of ∼106.1 The invention of novel separation modes and the development of new types of separation media have enhanced its versatility and applicability. There are two possible approaches, which enable further development of separation sciences; one is to improve existing methods and the other is to introduce a new separation principle or concept into them. The former is necessary for continuous advances, while the latter is expected to realize a breakthrough in this important branch of science. The authors believe that the efficient involvement of external fields may permit innovations in separation sciences. In most of the conventional separation techniques, chemical interactions * Corresponding author. Phone and Fax: +81-3-5734-2612. E-mail:
[email protected]. (1) Hagel, L.; Janson, J.-C. In Chromatography: fundamentals and applications of chromatography and related differential migration methods, Part A”; Heftmann, E., Ed.; Elsevier: Amsterdam, 1992; Chapter 6. 10.1021/ac001354b CCC: $20.00 Published on Web 06/06/2001
© 2001 American Chemical Society
occurring in particular phases or at an interface are the driving force for separation and are usually modified by varying chemical variables, such as types of solvents, pH, salt concentrations, etc. In contrast, external fields are capable of not only affecting chemical interactions but also separating substances through physical interactions. The possibility to control separation from outside of the system should be a great advantage of external fields over the usual separation based only on chemical interactions. Field flow fractionation (FFF) is a well-known example of separation, where external fields are successfully utilized.2-7 In FFF, an external field applied perpendicular to the flow direction has allowed the separation of large macromolecules and even particles that cannot be separated by chromatography. Temperature, gravity, flow, and electric fields have been successfully employed in FFF.2 Similar but slightly different utilization of external fields in separation has been reported for particle separation. Nomizu, for example, invented magnetic chromatography and showed that separation of hematite from magnetite is feasible.8 Imasaka and co-workers9,10 presented another interesting separation mode, in which optical radiation force is utilized for particle separation. This method, named “optical chromatography”, is an application of so-called “optical forceps” or “laser trapping” to separation. While various external fields, such as electric, magnetic, optical, temperature, and gravity fields, have been employed to develop new separation techniques, the utilization of acoustic fields is limited. Yasuda and co-workers 11,12 reported that particle separation is feasible by coupling an ultrasound standing wave with an electric field and analyzed their results based on an ultrasound theory.13 They horizontally applied the acoustic and electric fields and attempted the vertical observation of particle behavior. However, particles having a density different from that of a surrounding medium are subject to sedimentation, which makes (2) Giddings, J. C. Anal. Chem. 1981, 53, 1170A. (3) Wang. X.-B.; Yang. J.; Huang, Y.; Vykoukal, J.; Becker, F. F.; Gascoyne, P. R. C. Anal. Chem. 2000, 72, 832. (4) S. A. Suslov, S. A.; Roberts, A. J. Anal. Chem. 2000, 72, 4331. (5) Viebke, C.; Williams, P.A. Anal. Chem. 2000, 72, 3896. (6) Niem Tri, N.; Caldwell, K.; Beckett, R. Anal. Chem. 2000, 72, 1823. (7) Hassello ¨v, M.; Lyve´n, B.; Haraldsson, C.; Sirinawin, W. Anal. Chem. 2000, 72, 3497. (8) Nomizu, T.; Nakashima, H.; Sato, M.; Tanaka, T.; Kawaguchi, H. Anal. Sci. 1996, 12, 829. (9) Kaneta, T.; Ishidzu, Y.; Mishima, N.; Imasaka, T. Anal. Chem. 1997, 69, 2701. (10) Makihara, J.; Kaneta, T.; Imasaka, T. Talanta 1999, 48, 551. (11) Yasuda, K.; Umemura, S.; Takada, K. J. Acoust. Soc. Am. 1996, 99, 1965. (12) Yasuda, K.; Takeda, K.; Umemura, S. Jpn. J. Appl. Phys. 1995, 34, 2715. (13) Yoshioka, K.; Kawashima, Y. Acustica 1955, 5, 167.
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Figure 1. Schematic representation of a coupled gravity-acoustic field.
it difficult to accomplish stable separation with such arrangements. This leads to the idea that the acoustic field should be vertically applied, and in that case, we can couple a gravity field with an acoustic field. In this paper, we demonstrate that this coupled field is successfully utilized to the characterization and separation of particles and analyze the obtained results on the basis of an acoustic theory. EXPERIMENTAL SECTION Particle behavior was studied in a cell having a 1.5-mm channel between two 5.54-mm quartz walls. This cell was designed for a 500-kHz ultrasound transducer; both the cell wall thickness and channel width are equal to the half-wavelengths of the ultrasound of 500-kHz frequency. A PZC transducer (500 kHz, Fuji Ceramics) was attached to the bottom of the quartz cell with epoxy glue and connected to an ac high-speed power amplifier, model 4015 (NF Electric Co.), to which appropriate sine curves were fed from a function generator, model WF1946 (NF Electric Co.). The cell was installed to allow the acoustic field to compete with the gravity field as schematically shown in Figure 1. The effective coupled field for separation occurred in the lower half of the cell, because the densities of particles studied in this work were higher than that of a separation medium. Particle behavior was observed through a microscope (Olympus). Microscope views were monitored by a CCD camera, and digital data were acquired and stored on a computer via a video board. Polystyrene latex (mean diameter, 3 µm) and poly(acrylonitrileco-vinyl chloride-co-methyl methacrylate) (wet-expandable spheres having 5-8-µm diameter) were purchased from Aldrich. Alumina (mean diameter, 10 µm) was a gift from Sumitomo Chemicals. Silica gel particles were Wakogel LP-40 (particle size 20-40 µm) and Wakogel C-100 (75-100 µm). Aluminum and quartz powder were prepared from their bulk. MilliQ water was used as a separation medium after sufficient deaeration to prevent cavitation. THEORY When a plane ultrasound standing wave is formed in a fluid, the ultrasound radiation pressure is given by
∆p(z) ) p0 sin(2 πz/λ) cos(2πft)
Analytical Chemistry, Vol. 73, No. 14, July 15, 2001
pressure node, and λ and f are the wavelength and frequency of the ultrasound, respectively. This equation indicates that the ultrasound radiation pressure becomes zero when z ) nλ/2. According to Yoshioka and Kawashima,13 a particle in the fluid undergoes the following ultrasound radiation force (Fac):
Fac ) -
8π2 3 4πz R EacA sin 3λ λ
A)
( )
5F′ - 2F γ′ 2F′ + F γ
(2) (3)
where R is the radius of the particle, Eac is the density of an ultrasound energy, F and F′ are the densities of the medium and particle, respectively, and γ and γ′ are the compressibility of the medium and particle, respectively. When A is positive, the particle moves to an ultrasound node, where the particle does not undergo ultrasound gradient forces, whereas particles move to a loop for negative A. For most solid particles, this parameter is positive. When the ultrasound wave is vertically radiated from the bottom of the cell, a particle in the cell simultaneously undergoes an upward radiation force and a downward (if F < F′) sedimentational force as shown in Figure 1. The balance of these two forces determines the vertical equilibrium position, where the particle should stay. The sedimentational force can be written as
Fsed )
4 πR3(F - F′)g 3
(4)
where g is the gravity acceleration. If the behavior of particles can be described by classical physics, the vertical position (z) can be given by combining eq 2 with eq 4; i.e. Fac ) Fsed.
z)
{
}
(F - F′)gλ λ sin-1 4π AEac2π
(5)
(1)
where p0 is the pressure amplitude, z is the distance from a 3468
Figure 2. Distribution of ultrasonic radiation forces inside the observation cell. (A) Ultrasound force in the absence of gravity. (B) Sum of ultrasound and gravity force, applied to 3-µm polystyrene particles. Eac ) 1.0 J m-3. Other parameters necessary for the calculation are listed in Table 1.
Figure 2 illustrates the distributions of the acoustic force (500 kHz) against 3-µm polystyrene particles inside the cell (1.5-mm channel width). The nod appears at the center of the cell (z ) 0)
Table 1. Parameters of Particles Tested
a
material
F′/103 kg m-3 a
γ′/10-10 Pa-1 a
A
Vth/V
Eth/J m-3
aluminum alumina silica glass PS PANVCMM
2.669 (2.70)b 3.698 (3.5-3.9) 2.694 (2.635-2.660) 1.052 1.200
1.36947 0.0377295 0.0269921 2.3753 2.5 c
1.4966 1.9558 1.72635 0.52987 0.62877
5.10 5.61 4.74 1.41 2.65
5.20 6.29 4.49 0.40 1.40
water
0.997 (0.997)
4.56454
Taken from refs 14 and 15. b Values in parentheses taken from ref 16. c Determined by the present method.
Figure 4. Relation between V and the equilibrium positions of aluminum particles. Solid curve shows the result of calculation (see the text).
Figure 3. Aggregation of alumina particles under different acoustic field strengths. (A) V ) 7.0 V; (B) V ) 10.0 V; (C) V ) 17.0 V.
when the sedimentation force is negligible (Figure 2A). In contrast, in the presence of gravity, the equilibrium position shifts to the bottom of the cell (Figure 2B). If a number of particles exist in the cell, a diffusion force also affects their distribution and equilibrium position. However, even in such cases, the center of the particle band is given by eq 5 because the statistical distribution of particles should follow the Gaussian distribution. For simplicity, the diffusion force is thus neglected for the following discussion. It should be noted that the equilibrium position is independent of particle sizes and determined only by A and Eac. RESULTS AND DISCUSSION Figure 3 shows the digital images of the aggregated alumina with different applied voltages, i.e., V ) 7.0, 10.0, and 17.0 V. The equilibrium position approaches the bottom of the cell with decreasing V and in turn Fac. In the present study, an ultrasound node is formed at the center of the channel of the quartz cell. The physical parameters for samples are summarized in Table 1.14-16 The A values for the samples are positive, suggesting that they are aggregated at the center of the channel regardless of the nature of the materials in the absence of the sedimentation force. The present setup allows us to couple the sedimentation force with the acoustic force. Under this coupled field, an (14) Kagakubinran (Chemical Index); Maruzen: Tokyo, 1993. (15) Cho-onpabinran (Ultrasound Index); Maruzen: Tokyo, 1999. (16) Lange’s Handbook of Chemistry; 13th ed.; Dean, J. A., Ed.; McGraw-Hill: New York, 1985.
equilibrium position for a particular particle should be somewhere between the center of the channel and the bottom of the cell, depending on the magnitude of the ultrasound force and the A values. The ultrasound force, in turn the mean ultrasound energy, should be known to compare the above theory with experimental results. Yasuda attempted to determine the mean ultrasound energy by measuring temperature increases.12 Although temperature measurements gave the mean ultrasound energy in the entire cell, the local energy was not known. The observation of particle behavior has indicated that the ultrasound energy varies from one point to another and should differ for the position, where particle behaviors are observed. We therefore determined the local ultrasound energy by the following approach. The equilibrium position of a particle is determined solely by Eac (eq 5), if its density and compressibility are known. Eac should be a function of the voltage applied to the ultrasound transducer (V).
Eac ) aV2
(6)
where a is a proportional constant. Thus, if we determine a for a standard particle with unambiguous density and compressibility, we can simply calculate the local Eac from the applied voltage and thus predict the behavior of the particles. Aluminum particles were selected for a standard for determining a, because both F′ and γ′ for this material are unambiguously determined. Figure 4 shows the relation between the equilibrium position of aluminum and V. It can be intuitively understandable that particles completely settle down when Eac is lower than a particular critical value (Eth ) aVth2). The relation shown in Figure 4 should be described by eqs 5 and 6, and thus, a can be evaluated by curve fitting, Analytical Chemistry, Vol. 73, No. 14, July 15, 2001
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Figure 6. Relation between V and the equilibrium positions of two types of Wakogel LP40 (A) and C100 (B). Broken curves are obtained with acoustic parameters for silica glass. Solid curves show the results calculated with γ′ ) 1.636 × 10-10 Pa1- for Wakogel LP40 and γ′ ) 1.559 × 10-11 Pa1- for Wakogel C100. Details are given in the text.
Figure 5. Relation between V and the equilibrium positions of (A) alumina, (B) silica glass, (C) PS, and (D) PAAVCMM. Solid curves are the results of calculation based on eqs 5 and 6 with a ) 0.2.
which gave a ) 0.2. We can thus estimate the local ultrasound energy density; e.g., Eac ) 20 J m-3 for V ) 10.0 V and Eac ) 5 J m-3 for V ) 5.0 V. The mean ultrasound energy density with the same applied voltage was 34.4 J m-3 for V ) 10.0 V, which was determined by temperature measurements; the difference between the local and average ultrasound energies implies the spatial distributions of the ultrasound intensity in the cell. To verify the validity of the parameter, a, the behaviors of other particulate materials, i.e., alumina, polystyrene (PS), silica glass, and poly(acrylonitrile-co-vinyl chloride-co-methyl methacrylate) (PAVCMM), were also simulated with eqs 5 and 6 and a ) 0.2 and compared with experiments. The density and compressibility of alumina, PS, and silica glass are available in the literature. As shown in Figure 5A-C, the behavior of these particles can be well simulated by the above equations and the parameter of the local ultrasound energy density. Thus, we can determine reliable local ultrasound energy density using appropriate standard materials. The literature compressibility for PAVCMM is unknown. Compressibility of polymers possibly depends on their chemical 3470 Analytical Chemistry, Vol. 73, No. 14, July 15, 2001
compositions and manufacturing processes. Curve fitting by the above equations gave its compressibility (γ′ ) 2.5 × 10-10 Pa-1). The densities of unknown materials can be determined by measuring their swelling volume and weight in a rather easy way, whereas their compressibility measurements are generally much more difficult. The present acoustic-gravity field can thus provide a very simple way to evaluate the compressibility of particulate materials. The behavior of most particulate materials under the present acoustic-gravity field was reasonably explained by the above theory. However, obvious deviations were detected for porous materials. Figure 6 shows the V dependence of the equilibrium positions for two types of silica gel, which is usually used as the chromatographic stationary phase. The above calculations cannot explain their behavior (shown by dotted curves), when F′ and γ′ for silica glass were used as parameters. Water can penetrate into the pores of silica gel and be entrapped in the pores. The imbibed water should move together with the silica skeletons. It is well known that the mobile phase in liquid chromatography basically flows through the interparticle spaces, and no flows occur inside the particles. Under typical chromatographic conditions, the pressure drop is ∼1 × 106 Pa along the entire length of the column (e.g., 10 cm) packed with 10-µm porous particles; this corresponds to 100 Pa per particle. In the present acoustic field, the acoustic pressure for a 10-µm particle is lower than 30 Pa (eq 2). Water imbibed by porous particles cannot be pushed out or into the pores by the acoustic pressure. Thus, porous particles should be characterized by different F′ and γ′ from those of base materials. If the porous silica particles can be regarded as composed of the silica skeletons and imbibed water, the apparent density of
particle (Fa) can be written as
Fa ) F + (1 - )F′
(7)
where is the porosity of the particle. The porosities of the silica gel particles were determined by titration according to the literature;17,18 ) 0.659 for Wakogel LP40 and ) 0.643 for Wakogel C100, and thus, Fa ) 1.562 and 1.588 g cm-3, respectively. The compressibility is equal to the reciprocal of the product of the density and the squared sound velocity in the medium. It was assumed that the average sound velocity (va) in a mixed medium, such as porous silica gel, is given by the following relation:
1 1 - ′ ) + va v v′
(8)
where v and v′ are the sound velocity in water and in the particle skeleton, respectively. The va values for Wakogel LP40 and C100 are 1978 and 2010 ms-1, and thus, γ′ ) 1.636 × 10-10 Pa-1 and γ′ ) 1.559 × 10-11 Pa-1, respectively. These values can explain the z-V curves of the porous silica gel as shown in Figure 6. Table 1 shows that the materials tested have different A values (eq 3), suggesting the possibility of material separation by the present method. Also, the comparison of z-V curves shown in Figures 4-6 clearly indicates that the particulate materials tested in this study are actually aggregated in the different equilibrium positions. Figure 7 shows separation of PS and PAVCMM; discrete two bands are obtained. This figure verifies the applicability of this method to particle separation. In conclusion, the acoustic-gravity fields can provide some physical parameters for particulate materials, e.g., density, com(17) Innes, W.B. Anal. Chem. 1956, 28, 332. (18) Mottlau, A.Y.; Fisher, N.E. Anal. Chem. 1962, 34, 714.
Figure 7. Separation of PAAVCMM (A) and PS (B) particles. V ) 3.22 V.
pressibility, and porosity, and make separation of particles possible. In the present instrument, it is difficult to observe the behavior of a single particle if its radius is smaller than 10 µm, and thus, rather concentrated particle solutions should be used. This high population of particles causes their coagulation and makes difficult separation between different materials. However, the present approach has potential advantages over other external fields; e.g., the coupling with other fields is rather easy, acoustic field is unambiguously evaluated using standard particles such as aluminum, etc. We may advance a new separation system based on the present versatile approach. Studies on other fields coupled with an acoustic field are now in progress in our laboratory. ACKNOWLEDGMENT This work has been partly supported by a Grant-in-Aid from the Ministry of Education, Science, Culture, and Sports, Japan. Received for review November 20, 2000. Accepted April 16, 2001. AC001354B
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