LETTER pubs.acs.org/Langmuir
Electroacoustics of Particles Dispersed in Polymer Gel Prasad S. Bhosale,† Jaehun Chun,‡ and John C. Berg*,† † ‡
Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States Pacific Northwest National Laboratory, Richland, Washington 99352, United States ABSTRACT: This study examines the electroacoustics of particles dispersed in polymer hydrogels, with the particle size either less than or greater than the gel mesh size. When the particles are smaller than the gel mesh size, their acoustic vibration is resisted by only the background water medium, and the measured dynamic electrophoretic mobility, μd (obtained in terms of colloid vibration current, CVI), is the same as that in water. For the case of particles larger than the gel mesh size, μd is decreased due to trapping, and the net decrease depends on the viscoelastic properties of the gel. The gel mesh size was varied by varying its cross-link density, with the latter being characterized as the storage modulus, G0 . The dependence of mobility on G0 , for systems of a given particle size, and on particle size, for gels of a given G0 , are investigated. The measured mobility remains constant as G0 is increased (i.e., mesh size is decreased) up to a value of approximately 300 Pa, beyond which it decreases. In the second set of measurements, the trapped particle size was increased in a gel medium of constant mesh size, with G0 being approximately 100 Pa. In this case, the measured μd is found to be effectively constant over the particle size range studied (14120 nm); that is, it is independent of the degree of trapping as expressed by the ratio of the particle size to the mesh size.
’ INTRODUCTION Particles dispersed in polymer gels (i.e., gel-trapped particles or composite hydrogels) have widespread application in the food and pharmaceutical industries; for example, weak polymer gels are commonly used as particle suspending media or thickening agents.1 Hydrogel scaffolds are used to grow size-controlled particles2,3 in biominerlization processes.4 Composite hydrogels are also under investigation for use in gel electrophoresis.57 However, for such dispersions, available techniques for characterizing particle size distribution and electrical properties are rather limited, especially for the dense or opaque systems that are industrially more relevant. Conventional light scattering or centrifugation techniques have been developed only for Newtonian media and require both transparency (matching refractive index of polymer and liquid) and low concentrations.8 Thus, electroacoustics is a promising alternative for characterizing these systems.911 Theoretical models have suggested that, in particular, it might be used to characterize the electrokinetic properties of particles in viscoelastic media.1214 However, to the best of our knowledge, there have been no experimental studies investigating electroacoustics of gel-trapped particles. In electroacoustics, the colloidal particles are subjected to oscillatory motion using longitudinal ultrasound waves (120 MHz), which produce an alternating polarization of the electric double layer around the particles. The alternating current (colloid vibration current, CVI) or voltage (ultrasonic vibration potential, UVP) generated by the double layer polarization is used to determine dynamic electrophoretic mobility, μd, analogous to the classical electrophoretic mobility, uE. The dynamic mobility μd may be used to calculate the electrical properties of r 2011 American Chemical Society
the particles such as zeta potential or surface charge density.9 In a previous study, we have shown that if the particles are smaller than the gel mesh size during acoustic vibration at 1100 MHz, they experience only the background Newtonian medium.2 In such systems, the oscillatory motion of the particle is very small compared to its diameter.2,15,10 Therefore, one would expect that in electroacoustics the dynamic electrophoretic mobility of the particles suspended in the gel would be the same as in the background medium if the particles are smaller than gel mesh size, but the case of gel-trapped particles may be more complicated. Recently, Wang and Hill13 proposed a model for the dynamic electrophoretic mobility of gel-trapped particles at frequencies up to 1 GHz. They assumed that the viscous component of the gel was the same as that of the background medium, η, and the polymer network contributed only to the elastic component of the gel medium. Their analysis suggested that, at sufficiently high frequency (>1 MHz), the fluid phase would carry the larger part of the stresses until, at very high frequencies, inertial forces would dominate the motion.13,16 Specifically, it was suggested that at high enough frequencies, and shear moduli less than approximately 10 kPa, the dynamic electrophoretic mobility of the particles should be independent of the elasticity of the gel medium (presumably whether or not the particles are trapped). For higher gel moduli, μd was predicted to drop. Since most of the commercial instrumentation available for implementing Received: April 19, 2011 Revised: May 20, 2011 Published: May 27, 2011 7376
dx.doi.org/10.1021/la2014495 | Langmuir 2011, 27, 7376–7379
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LETTER
electroacoustics operates in the 120 MHz frequency range, the detected particle motion, for systems of low modulus, should thus be mediated solely by the viscosity of the medium and independent of the elastic properties of the gel. This study investigates the electrokinetic behavior of particles in viscoelastic gel media, with the particle size either less than or greater than the gel mesh size, using electroacoustics as implemented with commercial instrumentation. Specifically, it seeks (1) to examine the hypothesis that if the particles are smaller than the gel mesh size, particle dynamic electrophoretic mobility (as measured in terms of the colloid vibration current, CVI) is the same as that in the background medium, and (2) to investigate, for the case of gel-trapped particles, the dependence, if any, of the dynamic mobility μd on the gel storage modulus, G0 , for a given particle size, and on the particle size for a gel of given G0 .
’ MATERIALS AND METHODS For the case of particles smaller than the gel mesh size, a well characterized system of hydroxypropyl cellulose (HPC) gel with silica particles was selected.2 The HPC polymer does not adsorb onto the silica particles and is uncharged, so no additional electrokinetic effects on the particle μd were expected. For the case of gel-trapped particles, polyacrylamide was selected for the medium because it provided fast gelation times17 (avoiding sedimentation problems) as well as the very small mesh sizes (611 nm)18 needed to ensure trapping. The cross-linker and monomer concentrations were varied to alter the cross-link density (i.e., gel mesh size) of the gels. Specifically, the concentration ratio was varied from 100:1 to 10:1, for monomer concentrations of 3 wt %. Further increases in cross-link density were achieved by increasing the monomer concentration to 5 and 10 wt %, respectively, at a monomer-to-cross-linker concentration ratio of 60:1. The gel cross-link density in each case was characterized in terms of the storage modulus, G0 , measured by oscillatory rheometry at a frequency of 1.0 Hz, so that a correlation could be established between the dynamic electrophoretic mobility and G0 . In a second set of experiments, the degree of trapping of the particles, as expressed by the ratio of the particle size to the mesh size, was varied by changing the gel-trapped particle size in a gel medium of given G0 . Oscillatory rheometry was performed to measure the viscoelastic properties of the polyacrylamide gel using a vane tool in a Physica MCR 300 rheometer (Anton Paar, Ashland, VA). Following gelation (after 80 min), a strain sweep was performed at 1 Hz to determine the limits of linear viscoelasticity for each sample type. Then a frequency sweep (1100 Hz angular frequency) was performed within the linear viscoelastic range to measure the storage modulus, G0 . Monodispersed silica particles of different sizes were used, specifically Ludox HM-30 and Ludox TM-50 from W. R. Grace & Co. (Columbia, MD) and NexSil 85 and NexSil 125 from Nyacol Nanotechnologies, Inc. (Ashland, MA). The hydrodynamic dimensions of the particles were determined in each case by dynamic light scattering (DLS) using a Brookhaven Zeta-PALS instrument from Brookhaven Instruments Corp. (Holtsville, NY). The HPC gel (30 mL) was prepared by mixing the desired amount of silica particles (9 wt % Ludox TM-50) with a 0.5 wt % HPC polymer solution (106 MW) in 20 mM NaOH solution. The HPC solutions were cross-linked using divinylsulfone (DVS) 200 mM, allowing 20 h for gelation. The HPC polymer and DVS cross-linker were obtained from Sigma Aldrich, Inc. (St. Louis, MO). The polyacrylamide gels were prepared using the acrylamide monomer, the cross-linker bisacrylamide, reaction initiator ammoniumpersulfate (APS), and catalyst N,N,N0 N0 tetramethylethlyenediamine (TEMED), all obtained from Bio-Rad Laboratories (Hercules, CA). Silica particles (9 wt %) were mixed with
Figure 1. Change in dynamic electrophoretic mobility (μd) of silica particles during the hydroxylpropyl cellulose (HPC) gelation process. The solution contains 0.5 wt % of HPC gel with 200 mM of DVS crosslinker and 9 wt % 30 nm silica particles. the acrylamide monomer solution (310 wt %) containing the desired amount of cross-linker bisacrylamide (total solution volume 30 mL). APS (300 μL of 10% solution) and TEMED (60 μL) were then added to initiate and catalyze polymerization. Monodispersed silica particles of different sizes were trapped in 3 wt % polyacrylamide gel with a 20:1 monomer-to-cross-linker concentration ratio. Measurements with higher particle sizes (>250 nm) were avoided because of sedimentation problems.10 The total monovalent ionic strength was approximately 18 mM for the NexSil 85 and 125 silica particle dispersions and 30 mM for the Ludox HM-30 and TM-50 dispersions, producing Debye lengths (k1) of 2.26 and 1.75 nm, respectively. The dispersions to be studied were placed in a 100 mL Teflon beaker, and the electroacoustics probe of a DT 310 ZetaPhorElectroAcoustic spectrometer from Dispersion Technology, Inc. (New York, NY) was placed inside the beaker. The device measures the colloidal vibration current (CVI), the oscillatory current flowing between a pair of concentric electrodes in the dispersion subjected to ultrasound waves of frequency 3.4 MHz. The measured CVI yields, through the use of instrument software, the dynamic electrophoretic mobility (μd) of the individual particles in accord with CVI ¼ Aφμd
Fp Fm Fm
ð1Þ
where φ is particle volume fraction, Fp and Fm are the densities of the particles and the medium, respectively, and A is an instrument constant.
’ RESULTS AND DISCUSSION The storage modulus of all polyacrylamide gels varied directly with the expected cross-link density, and while it increased with frequency, it was found to be constant over the range of 0.11 Hz in all cases. This low-frequency value of G0 was taken as the quantitative measure of the cross-link density. The hydrodynamic sizes of the silica particles measured by DLS were 14, 30, 67, and 120 nm for Ludox SM-30, Ludox TM-40, NexSil 85, and NexSil 125, respectively. Particle Size Less than Gel Mesh Size. The mesh size obtained using 0.5 wt % HPC with 200 mM DVS has been reported to be 56.8 nm, approximately.2 Oscillatory rheometry gave G0 = 40 Pa at 1 Hz for this gel. The silica particles used, Ludox TM-50, with a diameter of 30 nm, were smaller than the gel mesh size, so that as hypothesized upon acoustic vibration the particles should experience only the background water medium. Figure 1 shows the mobility μd of the silica particles measured 7377
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Figure 2. Change in dynamic electrophoretic mobility (μd) of silica particles during the polyacrylamide gelation process. The solution contains 5 wt % acrylamide monomer, with a 60:1 monomer-to-crosslinker concentration ratio and 9 wt % 30 nm silica particles.
during the HPC gelation (20 h). It is seen to remain constant at a value of 3.7 ( 0.2 (μm/s)/(V/cm), the same as that measured for the particles suspended in water at the same loading. This result is consistent with Wang and Hill13 analysis, which predicts that in weak hydrogels (shear modulus
