pubs.acs.org/Langmuir © 2010 American Chemical Society
Acoustic Spectroscopy of Colloids Dispersed in a Polymer Gel System Prasad S. Bhosale and John C. Berg* Department of Chemical Engineering, University of Washington, Seattle, Washington 98195 Received July 20, 2010. Revised Manuscript Received August 16, 2010 The technique of acoustic spectroscopy offers some significant advantages over conventional techniques, such as dynamic light scattering and differential sedimentation (centrifugation), for the characterization of colloidal dispersions in that it does not require that the systems be highly dilute and transparent. Another advantage of the method may derived from the fact that in applications, the relative motion between any particle and the medium is very small, at the most being comparable to the particle size. It may thus be suited, within limits, to the study of dispersions in polymer gels, without the additional limitation of conventional methods to transparent media (matching refractive index of polymer and liquid). The present work seeks to probe experimentally the limits of the technique and its current theory for the determination of particle size distributions in gel media. Experiments measuring acoustic attenuation have been conducted on dispersions of silica particles of varying size in aqueous hydroxylpropyl cellulose (HPC) gels of varying cross-link density. The particle size distribution (PSD) was successfully measured by acoustic attenuation theory for dispersions in Newtonian media provided that the hydrodynamic particle diameter was less than the hydrodynamic mesh size of the gel, as given by simple rubber elasticity theory (mesh size/particle size J1.5). The same results were obtained at particle loadings of up to 15 wt %. If the particles are larger than the mesh size, then a viscoelastic response from the gel matrix is observed that cannot be interpreted to yield the particle size using the existing theoretical framework.
Introduction Particles dispersed in a gel system (gel-trapped colloids1 or hydrogel nanocomposites2) are widely used for a number of applications, including separations2,3 (gel electrophoresis), the growth of high-quality crystals/particles for suspending particles4 (in the food and pharmaceutical industries), and drug delivery.5 However, techniques for characterizing gel-trapped or gel-suspended particle sizes and dynamics remain rather limited primarily because of two problems: (1) nonhomogeneity in the gel matrix and (2) optical contrast between particles and the gel medium.5 Conventional light scattering requires special conditions such as low particle concentration and the use of transparent gels (matching refractive indexes of polymer and liquid) to characterize the particles. Acoustic spectroscopy is a novel, noninvasive technique used for particle surface charge and particle size distribution (PSD) determinations in dense dispersions.6,7 Acoustic techniques can potentially overcome the limitations of the conventional techniques and provide a simple alternative for the characterization of the opaque colloidal dispersions in polymer gels. In acoustic spectroscopy, a monochromatic longitudinal ultrasound wave (1-100 MHz) is passed through a colloidal dispersion, and the loss of amplitude (attenuation) and the speed of sound are measured to predict the PSD. The loss of acoustic energy (amplitude) is due to viscous, thermal, electrokinetic
transport processes occurring at the interfaces and scattering by the particles as well as intrinsic absorption by the system.7 For solid submicrometer particles, the viscous losses are most dominant.7,8 As the acoustic pressure wave passes through the dispersion, liquid and the particles move at different velocities because of inertial effects. A part of the acoustic energy is absorbed to facilitate this relative motion (viscous losses) that is expressed in terms of acoustic attenuation. The attenuation or viscous losses are a function of the particle size, density difference, and frequency. A number of previous studies6,8,9 have shown that the viscous losses are greatest when the shear wavelength (the relaxation distance of the velocity profile at the particle surface or the viscous shear depth) generated by the acoustic pressure wave is comparable to the size of the particle; the relative motion of the particle with respect to the liquid medium is also greatest at this point. The frequency at which this happens is known as the critical frequency. At low frequencies, both the particles and liquid can follow the sound wave with little relative motion, whereas at very high frequencies there is little motion of the particles or the liquid molecules. Many fundamental studies in the 1940s9,10 and 1950s11,12 and in particular those by Allegra et al.8 in the 1970s correlated the attenuation of the signal (R) by viscous losses to the particle radius (R), density contrast, and frequency (ω). For a model system of monodisperse submicrometer spherical particles dispersed in a Newtonian fluid at low-to-intermediate frequencies,8
*To whom correspondence should be addressed. Tel: þ1 206 543 2029. Fax: þ1 206 543 3778. E-mail:
[email protected].
2 R 1 2 2 F Fp ¼ ωR -1 φ 9 cμ F
(1) Laxton, P. B.; Berg, J. C. Langmuir 2008, 24, 9268–9272. (2) Hill, R. J. J. Colloid Inerface Sci. 2007, 316, 635–644. (3) Wanga, M.; Hill, R. J. Soft Matter 2008, 4, 1048–1058. (4) Grassmann, O.; Lobmann, P. Chem.;Eur. J. 2003, 9, 1310–1316. (5) Grimm, A.; Nowak, C.; Hoffmann, J.; Schartl, W. Macromolecules 2009, 42, 6231–6238. (6) Dukhin, A. S.; Goetz, P. J. Langmuir 1996, 12, 4987–4997. (7) Dukhin, A. S.; Goetz, P. J. Ultrasound for Characterizing Colloids: Particle Sizing, Zeta Potential, Rheology; Elsevier: Amsterdam, 2002; Vol. 15.
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ð1Þ
(8) Allegra, J. R.; Hawley, S. A. J. Acoust. Soc. Am. 1972, 51, 1545–1564. (9) Lamb, H. Hydrodynamics, 6th ed.; Dover: New York, 1945. (10) Urick, R. J. J. Acoust. Soc. Am. 1948, 20, 283. (11) Busby, J.; Richardson, E. G. Proc. Phys. Soc., London 1956, B69, 193. (12) Epstein, P. S.; Carhart, R. R. J. Acoust. Soc. Am. 1953, 25, 553–565.
Published on Web 08/20/2010
DOI: 10.1021/la102892e
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experimentally and explore its limits. The polymer mesh size relative to the particle size is systematically varied to explore the effects on particle mobility. Experiments are also conducted at high particle loading to test the technique in dense dispersions.
Materials and Methods
Figure 1. Particles confined in a polymer gel system: (a) particles smaller than the mesh size and (b) particles larger than the mesh size.
where φ is the volume fraction of the particles, c is the speed of sound, μ is the viscosity of the medium, and F and Fp are the medium and particle densities, respectively. Low-to-intermediate frequencies are those for which the particle diameter exceeds the viscous shear depth. In the 1980s13 and 1990s, Dukhin and Goetz6,7 and others14 developed the models further using numerical methods to characterize dispersions with polydispersity, strong interparticle interactions, and multicomponent systems. A typical modern acoustic spectroscopy instrument yields the attenuation versus frequency curve for the system, which is then fitted by the relevant model considering different types of losses and scattering mechanisms to predict the particle size distribution. Acoustic spectroscopy has been used to measure the bulk viscosity of polymer gels.15 Strybulevych et al.16 have used ultrasound attenuation to characterize large air bubbles (0.4-0.2 mm) and polystyrene beads (0.25 mm) embedded in an agar gel matrix. Recently, Wang and Hill17 provided a theoretical framework in which to correlate the dynamic electrophoretic mobility18,19 obtained in acoustic electrophoresis7 experiments to the viscoelastic properties of the system and the physicochemical characteristics of the particle-polymer interface.3,20 However, to the best of our knowledge acoustic spectroscopy has not been applied to characterize colloids dispersed in polymer gels. Here, we have applied acoustic spectroscopy to characterize particle size distributions in hydroxylpropyl cellulose (HPC) gel systems containing silica nanoparticles. HPC is widely used in various food and pharmaceutical products, for example, as a binder in tablets,21 a thickener or stabilizer in food products, and a rheology modifier in artificial tears.22 Because the particle motion with respect to the medium is very small in acoustic testing (at maximum attenuation, it is comparable to the particle size), we speculate that when the particles are smaller than the hydrodynamic gel mesh size their mobility should be identical to that found in pure solvent, as suggested in Figure 1. It may then be used to predict the hydrodynamic size of the particles or the PSD in the gel medium using current acoustic attenuation theory derived for Newtonian media. The objective of this letter is to probe this hypothesis (13) Gibson, R. L.; Toksoz, M. N. J. Acoust. Soc. Am. 1989, 85, 1925–1934. (14) Hipp, A. K.; Storti, G.; Morbidelli, M. Langmuir 1999, 15, 2338–2345. (15) Bonacucinaa, G.; Cespia, M.; Palmieri, G. F. Int. J. Pharm. 2009, 377, 153–158. (16) Strybulevych, A.; Leory, V.; Scanlon, M. G.; Page, J. H. Soft Matter 2007, 3, 1388–1394. (17) Wanga, M.; Hill, R. J. J. Fluid Mech. 2009, 640, 357–400. (18) O’Brien, R. W.; Jones, A.; Rowlands, W. N. Colloids Surf., A 2003, 218, 89–101. (19) O’Brien, R. W. J. Fluid Mech. 1990, 212, 81–93. (20) Hill, R. J.; Ostoja-Starzewski, M. Phys. Rev. Lett. 2008, 77, 011404. (21) Weiner, M. L.; Kotkoskie, L. A. Excipient Toxicity and Safety; Marcel Dekker: New York, 1999. (22) Wikipedia hydroxypropyl cellulose. http://en.wikipedia.org/wiki/ Hydroxypropyl_cellulose, July 7, 2010.
14424 DOI: 10.1021/la102892e
Three different silica particle types of different sizes were used: Ludox SM-30, Ludox HS-30, and Ludox TM-40, all from Grace Davison (Columbia, MD). The particle hydrodynamic dimensions were first determined by dynamic light scattering (DLS) using the Zeta-PALS instrument from Brookhaven (Brookhaven Instruments Corp., Holtsville, NY). Samples for acoustic testing were prepared by mixing the desired quantity of Ludox particles with a 0.5 wt % solution of hydroxylpropyl cellulose (HPC, 1 000 000 MW) from Sigma-Aldrich (St. Louis, MO) in a 20 mM NaOH solution. The HPC solutions were cross linked to varying degrees using divinyl sulfone (DVS) (Sigma-Aldrich, St. Louis, MO). The pH was adjusted to 12.3 by the addition of a 1 M NaOH solution. The solution (50 mL) was then poured into the test cell of a DT-1201 AcoustoPhor Acoustic & ElectroAcoustic spectrometer (Horiba Instruments Inc., Irvine, CA), where it was allowed to gel for 30 h before testing. The attenuation cell was sealed to minimize evaporation losses. HPC gel without added particles was first tested to measure the attenuation and speed of sound, which was used to calibrate the background signal. The HPC polymer gel mesh was characterized in each case by bulk oscillatory rheological measurements using a vane tool in a Physica MCR 300 rheometer (Anton Paar, Ashland, VA). Following gelation, a strain sweep was performed to determine the limits of linear viscoelasticity for each sample type. Then a frequency sweep (1- 100 Hz angular frequency) was performed within the linear viscoelastic range to measure the storage modulus, and it was found to be constant over the range of 1-10 Hz. It has been shown that the measured storage modulus, G0 , obtained over a range of low frequency in which it is constant can be correlated to the mesh spacing (ξ) using simple rubber elasticity theory1,23 in which the polymer gel is assumed to be a collection of interconnected entropic springs. The mesh size is given by ξ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p 3 kB T=G0
ð2Þ
where kB is the Boltzmann constant and T is the temperature. The first measurements were made with particles of increasing size (6 wt % 15.9, 20.8, and 29.6 nm) dispersed in a 0.5 wt % HPC gel prepared using 100 mM of the DVS cross linker. The measured acoustic attenuation in each case was compared to that obtained for the 6 wt % particle dispersions in pure water. In the second set of measurements, the particle size was kept constant at 29.6 nm, using the Ludox TM-40, and the cross-link density of the gel was increased by increasing the concentration of DVS from 75 to 400 mM. Again, the measured attenuation response was compared with the attenuation of the dispersion in water. Finally, the HPC gels with 100 mM DVS with different particle loadings (2-15 wt %) were investigated to probe the response in dense dispersions.
Results and Discussion DLS measurements of the hydrodynamic sizes of the silica particles used gave diameters of 15.9, 20.8, and 29.6 nm for Ludox SM-30, HS-30, and TM-40, respectively. Figure 2 shows the attenuation curves obtained as a function of frequency for 6 wt % silica dispersions of the different Ludox particles in water and in the 0.5 wt % HPC gel obtained using a 100 mM concentration of the cross linker, DVS, which produced a hydrodynamic mesh size in accordance with eq 2 of ξ = 56.8 nm. Numerical results for this series are summarized in Table 1. In all cases, the attenuation (23) Edwards, S. F.; Vilgis, T. A. Rep. Prog. Phys. 1988, 51, 243–297.
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Letter Table 2. Mean Particle Diameters as Inferred from Acoustic Attenuation Data for a 0.5 wt % HPC Gel with Different Cross-Linker Concentrations and Gel Loaded with 6 wt % of 29.6 wt % Silica Nanoparticles acoustic attenuation measurements cross-linker mesh size indicated conc. (nm) from diameter in (mM) eq 2 water (nm) 75 100 200 400
70.8 56.8 45 19.1
30 ( 1 30 ( 1 30 ( 1 30 ( 1
indicated mean diameter diameter in by light gel (nm) scattering (nm) 29.1 ( 1.2 29.7 ( 1.5 31.7 ( 1.1 71 ( 0.9
29.6 ( 1.8 29.6 ( 1.8 29.6 ( 1.8 29.6 ( 1.8
Figure 2. Acoustic attenuation at various frequencies through a 0.5 wt % HPC gel with 100 mM DVS cross-linker concentration loaded with 6 wt % silica nanoparticles of different sizes (15.9, 20.8, and 29.6 nm). Table 1. Mean Particle Diameter Obtained from Acoustic Attenuation Data for a 0.5 wt % HPC 100 mM Cross-Linker Concentration Loaded with 6 wt % Silica Nanoparticles of Different Sizes (15.9, 20.8, and 26.9 nm) acoustic attenuation measurements mean particle particle diameter by light type scattering (nm) Ludox SM-30 Ludox HS-30 Ludox TM-40
HPC gel indicated mesh size diameter in (nm) water (nm)
indicated diameter in HPC gel (nm)
15.9 ( 2.3
56.8
22 ( 1
18 ( 2
20.8 ( 2
56.8
26 ( 0.5
24.3 ( 1.5
29.6 ( 1.8
56.8
30 ( 1
29.7 ( 2
Figure 3. Acoustic attenuation at various frequencies through a 0.5 wt % HPC gel (75 mM DVS) and water loaded with 6 wt % silica nanoparticles (26.9 nm). The experimental data were fitted using the Allegra et al.8 model, plotted as a line, to predict a particle size of 30 nm (inset). Background attenuation signals from water and the HPC gel are represented by the empty symbols.
increases with increasing particle size, in accordance with theory. In Figure 3, the attenuation curve for the 29.6 nm particles is replotted together with the background curves for pure water, for the 0.5 wt % HPC gel in the absence of particles, and for the particle dispersion in the absence of gel. The inset in Figure 3 shows the particle size distribution with a mean diameter of 30 ( 1 nm as Langmuir 2010, 26(18), 14423–14426
Figure 4. Acoustic attenuation at various frequencies through a 0.5 wt % HPC gel with different cross-linker concentrations (75, 100, 200, and 400 mM DVS) in comparison with particles in water. All of the dispersions are loaded with 6 wt % silica nanoparticles (26.9 nm).
calculated by the instrument software based on the model developed by Dukhin and Goetz.6,7 This is very close to the mean diameter measured using light scattering (29.6 nm). The mean particle diameters measured for each particle size in water and in the HPC gel are recorded in Table 1. For the remaining particle sizes shown in Figure 2, the attenuation curves for the gel system yielded values for particle size very close to those corresponding to the values measured in water by DLS. This indicates that the particles were experiencing only the water medium upon acoustic vibration, a possible response because the particles were smaller than the gel mesh size, which was measured to be 56.8 nm for this gel. To explore the case of particles trapped in the gel (i.e., for mesh sizes smaller than the particle size), we systematically varied the cross-linker DVS concentration from 70 to 400 mM, producing mesh sizes in the 0.5 wt % HPC gel as summarized in Table 2: 70.8, 56.8, 45, and 19.1 nm at 75, 100, 200, and 400 mM DVS, respectively. Figure 4 shows the corresponding attenuation curves. The particle mean diameters as computed by acoustic attenuation theory are recorded in Table 2, which show that for mesh sizes larger than the particle size (29.6 nm) the attenuation spectra were almost identical to those of silica particles dispersed in water. However, at 400 mM DVS (mesh size 19.1 nm) the indicated diameter was 71 nm, which is much larger than the actual size. Particles in such a gel are trapped, as suggested in Figure 1b. The increase in attenuation was due to excess acoustic energy absorbed by the particles in moving against the viscoelastic gel medium. Such a response cannot be accurately interpreted to yield the particle size using the traditional models developed for DOI: 10.1021/la102892e
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the corresponding curves for the same weight percentages of silica in water. The measured mean particle diameters (and particle size distributions) as determined by acoustic spectroscopy were accurate, repeatable, and almost the same as the particle diameter measured by light scattering (Table 3), showing that the techniques can be used in dense dispersions confined in gels, provided that the particle size is less than the mesh size. In theory, the technique can be applied in Newtonian media to even higher concentrations,7,14 but the present experiments were limited to a particle loading of 15 wt % because higher loadings resulted in polymer precipitation and phase separation.
Figure 5. Acoustic attenuation at various frequencies through a 0.5 wt % HPC gel with 100 mM DVS cross-linker concentrations loaded with 2, 6, and 15 wt % silica nanoparticles (20.8 nm). Table 3. Mean Particle Diameter Obtained from Acoustic Attenuation Data for 0.5 wt % HPC 100 mM Cross-Linker Concentration Loaded with 2, 6, and 15 wt % Silica Nanoparticles (21 nm) acoustic attenuation measurements particle wt %
mesh size (nm)
indicated diameter in water (nm)
indicated diameter in gel (nm)
2 6 15
56.8 56.8 56.8
25 ( 0.7 25 ( 0.5 21.6 ( 1
25.3 ( 1 24.3 ( 0.8 25.2 ( 0.5
Newtonian media. As noted earlier, Wang and Hill17 provided a theoretical framework in which to correlate the dynamic electrophoretic mobility obtained in acoustic electrophoresis experiments to the viscoelastic response of a hydrogel medium for colloidal particles embedded in hydrogels (with a particle size comparable to or higher than the gel mesh size). The findings of the present work may potentially be extended to describe electroacoustic measurements and their dependence on the ratio of particle to mesh size of the gel medium. Gel systems at higher particle loadings were also investigated. Figure 5 shows the attenuation curves for a 0.5 wt % HPC gel (100 mM DVS) with 2, 6, and 15 wt % silica loadings and
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Conclusions Experiments measuring acoustic attenuation have been conducted on dispersions of silica particles of varying size in aqueous hydroxylpropyl cellulose (HPC) gels of varying cross-link density to determine the apparent particle size distribution (PSD) as given by acoustic attenuation theory for dispersions in Newtonian media. The indicated PSD was found to be identical to that in pure water provided that the hydrodynamic particle diameter, as given by dynamic light scattering, was less than the hydrodynamic mesh size of the gel, as given by simple rubber elasticity theory (mesh size/particle size J1.5). The same results were obtained at particle loadings of up to at least up to 15 wt %, beyond which measurements could not be made for the systems studied. If the particles are larger than the mesh size, then a viscoelastic response from the gel matrix is observed that cannot be interpreted to yield particle size using the existing theoretical framework. Current models would need to be extended to account for the elastic response of the medium and to predict the PSD for geltrapped colloids. If such models are successfully developed, then acoustic attenuation can be used to probe the viscoelastic properties (microrheology) of the polymer gel matrix at megahertz frequencies. Acknowledgment. This work was financially supported by the U.S. Department of Energy’s Office of Technology Innovation and Development (EM-30) through the Pacific Northwest National Laboratory (PNNL), Richland, WA. We gratefully acknowledge Dr. Philip Goetz for helpful discussions and Horiba Instruments, Inc. for the use of the DT-1201 instrument.
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