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Colloids and Surfaces B: Biointerfaces 61 (2008) 262–269
Enhanced mixing in polyacrylamide gels containing embedded silica nanoparticles as internal electroosmotic pumps Marvi A. Matos a , Lee R. White a , Robert D. Tilton a,b,∗ a b
Center for Complex Fluids Engineering, Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, United States Center for Complex Fluids Engineering, Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, United States Received 24 May 2007; received in revised form 30 August 2007; accepted 30 August 2007 Available online 4 September 2007
Abstract Many biosensors, including those based on sensing agents immobilized inside hydrogels, suffer from slow response dynamics due to mass transfer limitations. Here we present an internal pumping strategy to promote convective mixing inside crosslinked polymer gels. This is envisioned as a potential tool to enhance biosensor response dynamics. The method is based on electroosmotic flows driven by non-uniform, oscillating electric fields applied across a polyacrylamide gel that has been doped with charged colloidal silica inclusions. Evidence for enhanced mixing was obtained from florescence recovery after photobleaching (FRAP) measurements with fluorescein tracer dyes dissolved in the gel. Mixing rates in silica-laden gels under the action of the applied electric fields were more than an order of magnitude faster than either diffusion or electrophoretically driven mixing in gels that did not contain silica. The mixing enhancement was due in comparable parts to the electroosmotic pumping and to the increase in gel swelling caused by the presence of the silica inclusions. The latter had the effect of increasing tracer mobility in the silica-laden gels. © 2007 Elsevier B.V. All rights reserved. Keywords: Electroosmosis; Mixing; Polyacrylamide; Biosensor
1. Introduction The dynamics of biosensor response to a change in analyte concentration represent a problem of chemical reaction with coupled mass transfer. The designs of biosensor devices often call for biomolecular recognition elements, such as enzymes, antibodies, or oligonucleotides, to be immobilized in or on a substrate [1–9]. Immobilization in hydrogels is commonly used to protect the sensing elements in applications involving exposure to fouling environments [10,11]. By minimizing convection, gel immobilization introduces a significant analyte mass transfer resistance, yet the structure of the gel precludes mechanical intra-gel mixing schemes. Similar issues are faced in microfluidic systems, where small spatial dimensions prevent high Reynolds number turbulent mixing [12]. The current investigation concerns the use of electrokinetic phenomena to promote mixing within gels. Variations on this basic strategy have been described for microfluidic devices. A
∗
Corresponding author. Tel.: +1 412 268 1159; fax: +1 412 268 7139. E-mail address:
[email protected] (R.D. Tilton).
0927-7765/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfb.2007.08.013
theoretical analysis by Qian and Bau described how mixing can be achieved by the application of oscillatory electric fields across channels with non-uniform zeta potentials [13]. Moctar et al. used electrohydrodynamic forces to promote mixing of two fluid streams in a channel with a T-shape geometry [14], while Oddy et al. studied the generation of instabilities in microfluidic channels with different geometries under applied electric fields [15]. Here we incorporate electrokinetics to enhance convective mixing in crosslinked polyacrylamide gels. Electrophoresis of charged solutes in polyacrylamide gels is commonplace, as in the use of gel electrophoresis as a diagnostic or preparative separations tool in molecular biology. Using electrophoresis to enhance transport in gels cannot be used as a general purpose technique, since it depends on molecular charge. Oppositely charged molecules are driven in opposite directions, and neutral solutes are not driven at all by electrophoresis, except under the influence of electroosmosis near any charged walls that bound the gel. Here we explore the use of temporally varying, non-uniform electric fields to generate electroosmotic flows from within a gel that has been doped with charged colloidal inclusions (Fig. 1). The charged colloids are immobilized by physical entrapment
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2. Experimental 2.1. Materials The fluorescent dye fluorescein-5-isothiocyanate (FITC ‘Isomer I’, λex = 490 nm, λem = 518 nm) and reagents for the polyacrylamide gel polymerization: acrylamide, N,N-methylenebisacrylamide, ammonium persulfate and tetra-methylethylenediamine (TEMED) were obtained from Sigma–Aldrich and used as received. Spherical silica nanoparticles with 7 nm diameter (Ludox SM) were obtained from Grace Davison. All water was de-ionized by reverse osmosis and subsequently purified by ion exchange and carbon adsorption columns on a Milli-Q Plus system (Millipore). Materials used for FRAP cell construction were sheets of transparent acrylic and black cast acrylic, obtained from McMaster-Carr, and Fisher brand (Fisher Scientific) plastic cover slips. 2.2. Preparation of polyacrylamide gels with silica inclusions Fig. 1. Schematic view of electroosmosis generated by negatively charged silica colloids trapped inside a neutral crosslinked gel. Application of an electric field across the gel exerts an electromotive force on counterions in the diffuse electrical double layers adjacent to the particle surfaces. This is transferred via viscous drag to a bulk flow of electrolyte solution parallel to the applied field direction.
within the gel. Electroosmosis is the bulk fluid motion induced by the electromotive force on the counterions residing in the diffuse electrical double layer surrounding a charged surface in response to a tangentially applied electric field. The electromotive force on the ions is transmitted to the fluid via viscous drag, resulting in bulk fluid flow that originates at the charged surface. The first reported examples of this electroosmotic internal pumping strategy were an experimental demonstration of electroosmotically enhanced solute fluxes across silica-laden polymer gels in dc electric fields [16] and an independent theoretical prediction of electroosmosis in gels with charged colloidal inclusions [17,18]. Since the electroosmotic flow depends only on the sign and magnitude of the surface charge on the colloidal inclusions, not on the solute charge, this mixing scheme should be useful regardless of the charge on the solute of interest; of course there will be a coupling between electroosmosis and electrophoresis (ionic conduction) for charged solutes. We propose that this strategy may be useful to induce convection in biosensors where transport barriers otherwise suppress it. We use fluorescence recovery after photobleaching (FRAP) with a charged fluorescent tracer to compare electroosmotically enhanced mixing with diffusive and electrophoretic mixing. Mixing is observed by the recovery of fluorescence intensity emitted from a photobleached spot in the gel, as unbleached tracers are transported into the bleached spot from unbleached regions of the gel. Here we demonstrate that the generation of electroosmotic flows in particle laden gels under temporally varying electric fields enhances intragel mixing compared to simple diffusive mixing or to mixing in particle-free gels with similar applied electric fields.
An aqueous stock solution of acrylamide monomer and bisacrylamide crosslinker at a 19:1 weight ratio was used. The monomer and crosslinker stock solution had a total acrylamide + bisacrylamide weight fraction of 0.40. The total percentage of monomer and crosslinker (%T) before polymerization was 15% with a crosslinker percent (%C) of 5.3%. The weight percent and crosslinker density were chosen so as to immobilize inclusions the size of typical proteins or larger inside the gel [19]. As described previously [16], the silica particle zeta potential in aqueous 1 mM KNO3 solutions was −68 mV. Silica stock suspensions were dialyzed overnight against de-ionized water before incorporation into the polymerization mixture. In order to make 5 mL of hydrogel, 1.875 mL of the monomer plus crosslinker stock solution were mixed with the silica nanoparticle stock suspension and de-ionized water and homogenized using a magnetic stir bar for 1 min at 180 rpm. The acrylamide and bisacrylamide concentration in the final solution were 2.08 M acrylamide and 0.04 M bisacrylamide. The stock suspension of silica particles had a silica weight fraction of 0.30. The volume of nanoparticle suspension added to each preparation depended on the desired final particle volume fraction. The balance of de-ionized water was added to give a total volume of 5 mL. Homogenization of the nanoparticle suspension with the pre-polymeric materials was found to be critical to ensure experimental reproducibility. After homogenization, the mixture was degassed for 10 min at a gauge pressure of −80 kPa in a vacuum oven. A 75 L aliquot of 0.1 g/mL ammonium persulfate solution and a 15 L aliquot of pure TEMED were added to 5 mL of the homogenized mixture and the suspension was mixed using a magnetic stir bar for ∼10 s at 180 rpm before dispensing between two 3 in. × 2 in. microscope slides spaced 2 mm apart. The reaction was allowed to proceed for 2 h at room temperature. For high silica particle volume fractions (φs = 0.05) the reaction was allowed to proceed overnight, in which case the gel casting slides were placed in a sealed jar with water added to control humid-
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ity. This water did not directly contact the gel material. After polymerization, the gels were stored in 1 mM aqueous KNO3 solutions for at least 24 h to equilibrate. This was essential for obtaining reproducible FRAP results. The conductivity of the KNO3 solution was 150 S/cm. After swelling in the KNO3 solution, the polymer volume fraction was 0.146 for gels with no particle loading (measured gravimetrically). Previous small angle neutron scattering measurements showed that the silica particles are dispersed uniformly in these gels [16]. 2.3. FRAP The water-soluble fluorophore fluorescein-5-isothiocyanate (FITC) was used as a photobleachable tracer solute. The swollen polyacrylamide gel slabs were soaked in 1 mM KNO3 solutions of FITC for another 24 h prior to starting a FRAP experiment. Due to differences in gel turbidity, the FITC concentration used in gels with no particles was 1 × 10−7 M while the concentration used in the more turbid gels with embedded particles was 1 × 10−6 M. Gel pieces measuring 20 mm × 4 mm × 2 mm were cut and placed in a gel-holding cell illustrated schematically in Fig. 2. Each piece of gel was photobleached more than once, by re-equilibrating the gel after bleaching for at least 3 h in FITC solution. Each experimental case was replicated at least three times using different gel pieces to account for possible gel composition or particle volume fraction variations. The two fluid compartments surrounding the gel slab were filled with the same solution in which the gels had been equilibrated. The cell was fabricated using an M-300 Laser Platform from Universal Laser Systems. The bottom part of the cell consisted of a transparent plastic cover slip. To help align the gel on the
microscope stage for FRAP experiments a circle was engraved on the cover slip. The transparent cast acrylic walls of the cell were cut to hold the gel slab by its edges. The upper part of the cell held the electrodes and was made with black cast acrylic to diminish intensity variations due to room light exposure. Aluminum wire electrodes were placed just outside the gel slab as described later. The FRAP experiments were conducted with a Nikon TE2000U inverted fluorescence microscope equipped with a high speed Cascade 512b ccd camera. In all experiments the intensity of fluorescence emission from dissolved FITC in the gel was monitored using a 10× objective before photobleaching. To minimize slow photobleaching during prolonged observation periods, the excitation light from the Xe lamp was attenuated 32-fold by neutral density filters. After a 30 s baseline monitoring period, we changed to a 40× objective and removed the neutral density filters in order to photobleach a 0.5 mm diameter spot in the gel for 60 s. The neutral density filters were then replaced and the objective was switched back to the 10× objective. The fluorescence intensity in the bleached region was recorded as a function of ccd pixel position and time. The field of view was 1 mm2 and images were recorded for 500 s at a rate of 1 frame/s. In electric field experiments, electrical potential gradients between the electrodes were produced by two phaselocked, programmable function generators (Agilent 33120A), as discussed in more detail below. 3. Results and discussion 3.1. Effect of silica loading on gel swelling The polymer volume fraction after swelling in the 1 mM KNO3 solutions was measured gravimetrically for gel samples containing different silica particle loadings. A wet gel sample was weighed and then placed in an 80 ◦ C oven overnight, after which the dry sample was weighed again. The polymer volume fraction in the gel was then calculated as: w p vp wp vp + (wt − wp )vw wp = wp+s − ws φp =
Fig. 2. Cell design for FRAP experiments. The 2 mm thick gel slab was placed vertically in the center and supported by indentations engraved in the transparent acrylic wall. The electrodes, placed immediately outside the gel slab in solution, were aluminum wires with a diameter ∼1 mm. These were inserted through small holes drilled in the opaque top acrylic block. The two sets of three wires were placed directly across the gel slab from each other. The horizontal distance between electrode centers on opposite sides of the gel was 3.5 mm, and the distance between centers of adjacent electrodes on the same side of the gel was 1.75 mm. The cell was secured by stainless steel screws. A microscope was focused inside the gel slab through the transparent coverslip that served as the bottom of the cell. Reference marks were engraved in the coverslip to ensure that the same part of the gel slab was bleached in every experiment. The gel was photobleached in a 0.5 mm spot, magnified at left, which was centered between the two sets of electrodes.
(1)
where wp is the dry polymer mass, ws the mass of the silica particles, wp+s the mass of the particles plus polymer (the dry gel sample mass), wt is the mass of the wet gel, vp the partial specific volume of polyacrylamide in water, and vw is the specific volume of water. The partial specific volume for polyacrylamide is reported to be 0.91 cm3 /g [20]. The weight of the particles, ws , was calculated using the known silica to polymer mass ratio established before polymerization. The effect of different silica loadings on gel swelling is shown in Fig. 3. The total polymer volume fraction in equilibrated gels decreased from 0.146 to 0.11 as the silica loading increased from 0% to ∼5 vol%. Note that the polymer volume fraction is reported on a “silica-free basis” (see Eq. (1)) and therefore represents the state of the swollen polymer network. The additional swelling observed in gels that contain silica inclusions is
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The horizontal line scan ran through the center of the photobleached spot, perpendicular to the gel edges. Fig. 6 also shows evolving raw intensity profiles along the line scan after photobleaching. The intensity at each position I(r,t) in each frame was normalized to account for light source variation as follows: IN (r, t) =
I(r, t) , IBP (r)
(2)
where IN is the intensity normalized for light source variations as captured by IBP , the intensity at position r before photobleaching. Further correction was required to account for slow photobleaching that was unavoidable during the prolonged observation of the spot recovery. Thus, a corrected intensity was defined as Fig. 3. Gel swelling increased with increased loading of 7 nm silica particles in the gel, as indicated by decreasing polymer volume fractions calculated on a particle-free basis.
attributed to the osmotic pressure contributed by counterions to the immobilized silica. 3.2. Effect of silica particles on tracer diffusion in gels The differing extents of equilibrium swelling for gels with φs > 0.02 suggest that the tracer mobility could depend on particle loading. Thus, FRAP experiments with gels containing 0% or 5% silica inclusions were performed without applied electric fields. For FRAP experiments, the photobleached spot was imaged at a focal plane lying approximately 1 mm inside the gel. Figs. 4 and 5 present photobleached spot image sequences for diffusive recoveries with φs = 0 and 0.05, respectively. The area shown represents a 1 mm × 1 mm view of the gel interior. Qualitatively, it is evident that the diffusive spot recovery is more rapid in the gel with φs = 0.05. Some image processing was required before quantitatively representing the FRAP results. Before photobleaching, the sampled area had a non-uniform illumination. This is evident in the line scan across a spot before photobleaching shown in Fig. 6.
IC =
IN (r, t) . IN,max (t)
(3)
IN,max is the maximum normalized intensity observed in the line scan and tends to decrease slowly over time due to photobleaching by the illumination light source. The slow photobleaching rate was found to be independent of position in the observed region. Mixing rates for different conditions were compared simply according to the rate at which the corrected fluorescence intensity increased at the center of the photobleached spot. The recovered fraction of corrected intensity after photobleaching was defined as: f (t) =
IC (0, t) − IC (0, 0) 1 − IC (0, 0)
(4)
where t = 0 corresponds to the first data point recorded immediately after the end of the photobleaching step. Examining the fractional recovery versus time in Fig. 7 indicates that the FITC tracer diffusion with and without silica inclusions was indistinguishable for φs = 0 and 0.01, but it did become increasingly rapid with further increases in φs . This increase in tracer mobility is attributed to the increased swelling of these gels that results in larger pores and greater permeabilities [19,21,22].
Fig. 4. Photobleached spot recovery in the absence of an electric field in gels with no particles.
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Fig. 5. Photobleached spot recovery in the absence of an electric field in gels with 5 vol% silica particles.
Quantitative analysis of this data is difficult because the rather long time required to create the photobleached spot (60 s) makes the initial condition for recovery not well established. The results are judged to be reasonable, in that the diffusion coefficient extracted from the expected time for 50% recovery, τ 1/2 , in a FRAP experiment with a circular bleached spot of radius w [23], D = 0.88
w2 4τ1/2
was ∼9 × 10−7 cm2 /s in the gel with φs = 0.05. This is of a similar magnitude as the diffusion coefficient for a comparably sized tracer, amino-methylcoumarin, measured in similar polyacrylamide gels, 3.3 × 10−6 cm2 /s [16]. 3.3. Electrokinetic mixing
,
(5)
Fig. 6. The raw intensity line scan data shown in (a) was normalized and smoothed using a running average method, with results shown in (b). Data is shown for various times after photobleaching. Gels contained 5% silica particles and no electric field was applied.
To generate time varying, spatially non-uniform electric fields inside the gel, the electrodes were driven by two phaselocked function generators, as shown in Fig. 8. The positive lead (at time zero) of the first function generator, defined as generator “1”, was connected to the middle electrode in the left side of the gel. The negative lead of function generator 1 was connected to the top and bottom left electrodes. The positive lead of the second function generator, defined as generator 2, was connected to the middle electrode of the right side of the gel. The negative lead of function generator 2 was connected to the top and bottom right electrodes. The terminals cycled between −10 V and +10 V. Function generators were at a phase-lock relation of 90◦ as shown in Fig. 8. The wave form was reasoned to improve mixing by repeatedly stretching and folding the bleached region
Fig. 7. Fraction of corrected intensity for the spot recovery as a function of time for gels with 0% to 5 vol% of silica particles.
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Fig. 8. At time zero, the + terminal and − terminal of each function generator are shown as dotted and solid lines, respectively. The function generators are phase-locked and programmed with the waveforms drawn above. The waveform is designed to create electroosmotic flows that periodically deform the concentration profile, as sketched at the bottom where arrows indicate the expected direction of electroosmotic flow around negatively charged silica inclusions. The spot would be stretched vertically (stage 1), folded to the right (stage 2), stretched horizontally (stage 3), and folded to the left (stage 4). The extent of deformation realized during each stage will depend on the local field strength and the waveform frequency ω.
in a way analogous to a dough or candy mixer. By stretching and folding the photobleached spot the contact area between the bleached and unbleached solution volumes is increased and mixing is enhanced. The photobleached spot recoveries under the action of the applied electric field were compared for gels with φs = 0 and 0.05 under oscillatory fields with a frequency ω = 0.1 Hz and voltage that cycled between −10 V and +10 V. In gels with no particles there was no evident enhancement of the spot recovery
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as shown in Figs. 9 and 10. The shape of the photobleached spot showed no discernable distortion, and the evolution of the normalized intensity across a horizontal line scan was similar in form to the simple diffusion recovery that was shown in Fig. 4. This indicates that in spite of the charge on the FITC tracer, electrophoretic migration was not significant under these applied field conditions. For the gel with φs = 0.05, the fluorescence recovery was significantly faster under this applied field at 0.1 Hz. As shown in Fig. 11, the spot was barely observable after just 30 s. This recovery was faster than either the particle-free gel under the applied field or the gel with φs = 0.05 under simple diffusive conditions with no applied field. Deformation of the spot was visibly evident, as also shown in the irregular evolution of the normalized intensity line traces in Fig. 12. Figs. 13 and 14 show the fractional recovery of normalized intensity over time, for gels with φs = 0 and 0.05. The results shown in each case are the average values for the fractional recovery of the intensity using three independent experiments. Results are shown for 0.1 Hz as well as for 1 Hz. For silica-laden gels, the recovery after 30 s (Fig. 13) was four times greater with the 0.1 Hz applied field than for diffusion in the same type of gel. The recovery after 30 s was 35 times greater for gels with φs = 0.05 in the 0.1 Hz applied field than the recovery for gels with no particles in the 0.1 Hz applied field and also 35 times greater than diffusive recovery in gels that contained no silica particles. This enhancement is therefore a combination of the electroosmotic flows and the increased permeability of the silicaladen gels. This conclusion is supported by previous research in which unidirectional flux measurements in DC fields indicated that electroosmotic flows was the dominant mechanism for enhanced tracer transport [16]. Mixing was also investigated at a frequency of 1 Hz. The electrode surface impedance decreases as frequency increases [24]. Thus, to maintain a constant current across the gel at different frequencies under the applied potentials, the maximum voltage was reduced for the higher frequency. The applied fields, and thus the current distributions in the gel, were highly non-uniform. To aid in adjusting the voltage needed to provide comparable currents for different frequencies, we measured the current between the center electrodes on opposite sides of the gel. Applying a 10 V potential difference at 0.1 Hz gave an rms current of 0.2 mA between these two electrodes. Then at 1 Hz the applied potential was reduced gradually from 10 to 7 V whereupon the current reached 0.2 mA. There was no mixing enhancement relative to diffusion in the silica-laden gels when the electric fields were applied at 1 Hz, as shown in Figs. 13 and 14. There are two possible explanations for the failure of the higher frequency. First, the extent of spot deformation during each stage of the waveform will be ∼10fold smaller at 1 Hz than at 0.1 Hz, since less time is allowed for electroosmotic flow in each cycle. There is no large scale folding of electroosmotic flow streamlines that would promote mixing. The second possibility is that the particles could not generate any electroosmotic flow at 1 Hz due to the nature of their confinement in the gel pore space. For electroosmosis to occur, the charged surfaces must be stationary. During each applied
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Fig. 9. Photobleached spot recovery as a function of time in gels with no particles under applied electric fields with ω = 0.1 Hz.
Fig. 10. Corrected intensity for the recovery of the spot for gels with no particles under applied electric fields with ω = 0.1 Hz.
Fig. 12. Normalized intensity for the recovery of the spot for gels with 5 vol% silica particles under applied electric fields with ω = 0.1 Hz.
field half cycle, the silica particles may be able to migrate electrophoretically some distance before the elastic polymer network halts their motion. Only then would electroosmotic pumping be established. At lower frequencies, the particles are allowed more time in their completely immobilized state to pump the electroosmotic flow. Higher frequencies may not allow sufficient time for complete particle immobilization, in which case the
particles would merely transit back and forth instead of pumping electroosmotic flow. It is notable that no spot deformation was observed at 1 Hz, another indication that electroosmotic flow was insignificant at that frequency. Finally, we note that in all types of mixing experiments, repeat measurements were performed on the same slab of gel in order to test whether the prolonged application of electric fields might
Fig. 11. Photobleached spot recovery as a function of time in gels with 5 vol% silica particles under applied electric fields with w = 0.1 Hz. The small dark spots shown in the image are unfocused dust particles between the gel and the bottom of the cell. Note the photobleached spot deformation.
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due to internally generated electroosmotic flows was estimated to be approximately four-fold relative to diffusion in the swollen gel. Applied field frequencies below 1 Hz were required to promote mixing. In order to achieve further mixing enhancement, one may choose to increase the inclusion volume fraction. This would both increase the density of electroosmotic pumping sites and increase solute mobility by the increased swelling of the gel. Acknowledgement
Fig. 13. Short time behavior of the fraction of corrected intensity for the spot recovery as a function of time and frequency for gels with 0% (filled symbols) and 5 vol% (open symbols) of silica particles with or without applied electric fields.
Fig. 14. Long time behavior of the fraction of corrected intensity for the spot recovery as a function of time and frequency for gels with 0% (filled symbols) and 5 vol% (open symbols) of silica particles with either no applied electric field, or applied fields at 0.1 Hz or 1 Hz.
cause any lingering effects on the gel transport properties. In all cases, there was no evidence that repeated field applications affected the mixing behavior, indicating that the gels remained unaltered after prolonged use. 4. Conclusions Mixing inside crosslinked polyacrylamide gels was studied under the application of temporally periodic, spatially non-uniform electric fields in gels with embedded 7 nm silica particles. Mixing rates were increased by as much as 35-fold, when comparing silica-laden gels and gels without embedded particles in non-uniform electric fields, although some of this enhancement must be attributed to the increased gel swelling and the corresponding increase in tracer mobility when silica is present at greater than ∼2 vol%. The enhancement in mixing
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