Electroacoustic Spectroscopy of Nanoparticle-Doped Hydrogels

This paper probes the nanoparticle (NP) interaction with hydrogels using ..... The ratio d/ξ is a dimensionless measure of the overall degree of NP e...
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Electroacoustic Spectroscopy of Nanoparticle-Doped Hydrogels Vahid Adibnia and Reghan J. Hill* Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, QC H3A 0C5, Canada S Supporting Information *

ABSTRACT: This paper probes the nanoparticle (NP) interaction with hydrogels using electroacoustic spectroscopy at MHz frequencies. We measured dynamic electrophoretic mobility spectra of silica NPs in polyacrylamide gels for a variety of NP sizes and gel concentrations. The spectra are exquisitely sensitive to NP entrapment, size, and charge as well as to gel rheology and gelation kinetics. For NPs that are large compared to the gel mesh size, many of these influences can be quantified using electrokinetic theory, which furnishes the apparent NP ζ-potential and a complex gel shear modulus at MHz frequencies. The methodology provides new insights into the NP−hydrogel interaction, since it noninvasively probes the nanostructure and the combined influences of particle and gel properties. Electroacoustic spectroscopy may therefore be a valuable new tool for characterizing soft nanocompositesone that complements other noninvasive methods, such as bulk rheometry and microrheology.

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INTRODUCTION Hydrogels are water-swollen cross-linked polymer networks that are often biocompatible, with widespread scientific, technological, and commodity applications.1,2 Recently, nanoparticles (NPs) have been found to enhance hydrogel mechanical properties,3−6 also imparting novel biological and physicochemical characteristics.7−9 Such enhancements are due to covalent and hydrogen bonding and hydrophobic and electrostatic interactions.3,10−12 The NP−hydrogel interaction is especially important in drug delivery, where NPs are used to deliver specific agents to prescribed tissues.13 Despite its fundamental significance, the NP−hydrogel interaction is poorly understood, partly due to the challenge of noninvasively probing the heterogeneous nanostructure. In this work, the NP−hydrogel interaction is probed using electroacoustic spectroscopy, which was originally developed to measure NP size and charge in Newtonian solvents,14,15 but has recently been extended to complex fluids.16,17 We systematically explore how the gel elastic modulus and the ratio of the NP size to the gel mesh size influence the particle dynamics at frequencies in the MHz range. These data help to elucidate the silica NP interaction with polyacrylamide (PA) gels, also furnishing insight that establishes more general properties of NP−hydrogel interactions at the nanoscale. In one form of electroacoustic experiment, the sample, which ideally comprises charged NPs dispersed in a continuous medium, is subjected to an alternating electric field at MHz frequencies. This sets the particles into oscillatory motion, producing sound waves, the amplitude and phase of which can be measured using a pressure transducer.18 When normalized with respect to the electric field, the pressure signal is termed the electrokinetic sonic amplitude (ESA). This encodes the © XXXX American Chemical Society

particle size and charge and can be used to ascertain the NP dynamic electrophoretic mobility from electrokinetic theory.19,20 In practice, however, the NP size is often obtained from the acoustic attenuation, while the ESA spectrum furnishes the particle charge. Fundamental studies of NP-doped gels could benefit tremendously from knowledge of the dynamic mobility spectrum. For NPs with known size in a prescribed Newtonian electrolyte, a single mobility amplitude at a single frequency is often sufficient to furnish a ζ-potential. However, the mobility spectrum may help to unravel the many combined influences that a polymer network has on the NP dynamics, including the effects of entrapment, nanoscale viscoelasticity, NP surface charge, and electroosmotic flow. Theories that relate dynamic electrophoretic mobility to particle and media properties customarily focused on Newtonian electrolytes.19,21 However, Wang and Hill22 recently proposed a theory for charged spheres trapped in uncharged hydrogels, predicting that the mobility spectrum transits from a low-frequency elastic regime, where the particle amplitude is in phase with the electric field, to a high-frequency regime, where the velocity is in phase with the electric field. These physics lead to low-amplitude mobilities at kHz frequencies and mobilities that are comparable to those in the solvent at MHz frequencies. The authors also showed that the mobility of sufficiently large particles at high frequencies is well approximated by earlier theories for Newtonian electrolytes Received: September 30, 2014 Revised: October 30, 2014

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Silica NP Characterization. Silica NPs were adopted because they are spherical and commercially available over a broad range of welldefined sizes. Here, we used Ludox TM50 (50 wt % colloidal suspension, diameter d ≈ 30 nm, Sigma-Aldrich Inc.), NexSil-85 (40 wt % colloidal suspension, d ≈ 60 nm, Nyacol Nanotechnologies Inc.), and NexSil-125 (40 wt % colloidal suspension, d ≈ 100 nm, Nyacol Nanotechnologies Inc.). Hydrodynamic diameters were measured using acoustic attenuation, which is integrated into the electroacoustic instrument (AcoustoSizer II, Colloidal Dynamics LLC). These diameters were well reproducible over a period of more than 6 months and are in good agreement with literature values from dynamic light scattering (DLS) (d = 34 nm for Ludox TM5023 and 30 nm for Ludox TM40;17 d = 67 and 120 nm for NexSil-85 and NexSil-125, respectively17) and scanning electron microscopy (SEM) (d = 29 nm for Ludox TM5023). NP-doped PA hydrogels were synthesized by mixing the monomer, cross-linker, APS, colloidal silica, and reverseosmosis (RO) water so that the final silica NP concentration in the pregel solution was 5 wt %. Dissolved oxygen was removed by bubbling N2 gas through the mixture for ∼5 min before adding TEMED. Subscripts 30, 60, and 100 attached to identifiers S1−S6 denote gels bearing d ≈ 30, 60, and 100 nm NPs, respectively. SB identifies a sample that mimics the background electrolyte by mixing RO water, 5 wt % silica NPs, APS, and TEMED. These background solution data help to distinguish the effects of the gel from those of the interstitial electrolyte, which comprises ions from the initiator (TEMED) and catalyst (APS). Electroacoustic Spectra. Dynamic mobility spectra were obtained using an AcoustoSizer II instrument (Colloidal Dynamics LLC) and its integrated software (AcoustoSizer IIX, version 3.28) following the manufacturer instructions with minor modifications to accommodate gels. For each sample, 20 mL of pregel or background solution was injected into the ESA cell. The instrument measures the ESA at 13 frequencies in the range 1−20 MHz and converts this to the dynamic electrophoretic mobility M according to

when the familiar Newtonian shear viscosity is replaced by a complex value η* = η − iμ*ω−1

(1)

where η is the solvent viscosity, μ* is the skeleton shear modulus, and ω is the angular frequency. (Implicit in eq 1 is a complex phase vector that varies as eiωt with the complex unit i.) As shown below, such a simplification expedites fast and convenient fitting of analytical formulas to ESA spectra. Moreover, we will demonstrate that the dynamic mobility spectra for large silica NPs in PA gels (at MHz frequencies) infer a shear-thinning skeleton viscosity at MHz frequencies. Bhosale et al.17 measured the closely related colloidal vibration current (CVI) at a single frequency of 3.4 MHz to ascertain the dynamic mobility amplitude of silica nanoparticles in hydroxypropyl cellulose (HPC) gels. By systematically varying the mesh size, they demonstrated that the dynamic mobility also reflects NP trapping by the mesh. Thus, when NPs are smaller than the mesh size (as estimated from the bulk elastic modulus of the gels), the particle mobility is independent of the hydrogel elastic modulus, suggesting that the NPs respond predominantly to the viscous stresses of the solvent. In stiffer gels, however, mobilities decrease with increasing stiffness, suggesting that the particle dynamics are hindered by the skeleton elasticity, as predicted by the theory of Wang and Hill.22 However, because that CVI instrument did not provide a spectrum, quantitative analysis of the viscous and elastic forces could not be undertaken. Nevertheless, on the basis of the difference between the mobility magnitude in weak gels (storage modulus 1−300 Pa) and in water, Bhosale et al. suggested that the skeleton has a significant intrinsic viscosity. We will show that this difference could also result from physicochemical interactions of the particles with the polymer, which modify the apparent surface charge.

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ESA = A(ω)

Hydrogel Synthesis and Characterization. PA gels were synthesized from acrylamide (monomer) available as a 40 wt % solution (Fisher Scientific), bis(acrylamide) available as a 2% w/v solution (Fisher Scientific), ammonium persulfate (APS) powder (Fisher Scientific), and N,N,N′,N′-tetramethylethylenediamine (TEMED, GE Healthcare Life Science, Germany). To synthesize gels with a prescribed elasticity, the acrylamide to bis(acrylamide) weight ratio was varied in the range 19:1−99:1 with monomer concentrations in the range 3−10 wt %, as summarized in Table 1.

Table 1. Hydrogel Compositions AAm:Bis

acrylamide (%)

S1 S2 S3 S4 S5 S6

19:1 19:1 19:1 19:1 39:1 99:1

10 7 4 3 3 3

(2)

where A(ω) is a frequency-dependent factor that is determined by calibration using a potassium tungstosilicate (KSiW) electrolyte (provided by the manufacturer). Parameters ze and zs are the acoustic impedances of the electrode backing material and suspension, respectively. For homogeneous materials, the acoustic impedance equals the density times the sound speed in that material, but zs is determined by the instrument using an acoustic measurement following every ESA measurement.14 Thus, even though eq 2 was derived for Newtonian media,21 it applies equally to linearly viscoelastic media. The particle volume fraction ϕ, solvent density ρ ≈ 998 kg m−3, and particle density ρ + Δρ ≈ 2200 kg m−3 are prescribed by the user. Note that the ESA signal in eq 2 is normalized with the electric field strength E, which is automatically selected by the instrument to maximize the signal-to-noise ratio and eliminate signal distortion and nonlinear electrokinetic effects.

MATERIALS AND METHODS

sample

zsze Δρ ϕ M zs + ze ρ

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RESULTS AND DISCUSSION As detailed in the Materials and Methods section, PA was selected as the hydrogel because its gelation kinetics expedite injection of the pregel solution to the ESA cell. Electroacoustic spectroscopy and dynamic rheology were performed on the series of PA gels listed in Table 1. Silica NPs were selected because of their spherical shape and well controlled size. NPs with a nominal diameter d (nm) were dispersed into pregel solutions, forming hydrogel nanocomposites with a prescribed gel composition and NP size; e.g., nanocomposite S660 denotes a composite synthesized from 3 wt % acrylamide (AAm) with acrylamide (AAm) to bis(acrylamide) cross-linker (Bis) weight ratio 19:1, containing d ≈ 60 nm NPs.

Also added to the precursor mixture were 10 μL of APS (10% w/v solution) as initiator and 3 μL of TEMED per mL of pregel solution as catalyst (Bio-Rad Laboratories Inc., technical note). To monitor gelation dynamics, the storage modulus was measured under oscillatory shear at ω = 10 rad s−1 with 5% strain (ARES-G2, TA Instruments). Next, a frequency sweep in the range ω = 0.1−100 rad s−1 at 5% strain was performed, followed by a strain sweep in the range 0.1−100% at ω = 10 rad s−1. All rheological and ESA measurements were performed at ≈21 °C. B

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Gel Rheology. The time-dependent rheology indicates that gelation begins approximately 2−5 min after mixing the precursor materials. Following this incubation period, the modulus increases on a time scale ∼30 min before reaching a plateau. Storage modulus time series G′(t) are plotted in Figure 1 for PA gels with monomer concentrations and monomer to

Figure 3. Mobility magnitude |M| (blue circles) and storage modulus G′ (green line) time series for nanocomposite S5100 (at frequencies f = 14.1 MHz and ω = 10 rad s−1).

cross-linker ratios producing terminal moduli G′∞ ≈ 0.0015− 21 kPa. Each time series begins immediately following an initial incubation period, during which the modulus is below the instrument detection limit (∼0.01 Pa) and then plateaus to a constant, G′∞. Storage moduli are frequency-independent in the range 0.1−100 rad s−1 and were verified to be independent of the prescribed strain. Mobility Magnitude. Mobility magnitude |M| spectra of negatively charged silica NPs in PA at several time points during gelation are plotted in Figure 2 for nanocomposite S5100. The mobility decreases and, similarly to the storage modulus, reaches a plateau after ≈70 min. To highlight the close correspondence between the time dependence of the dynamic mobility and bulk storage modulus, Figure 3 shows time series of |M| at f = 14.1 MHz and G′ at angular frequency ω = 10 rad

s−1. These suggest, but do not prove, that the decreasing mobility is a direct result of the increasing elastic modulus. Another possibility is that the polymer hinders electroosmotic flow, thereby decreasing the apparent surface charge or apparent ζ-potential. Whereas the storage modulus G′ is a bulk property, the NP mobility can reflect an averaged local NP environment. Thus, in the terminal stages of gelation, when pores may still be developing, such changes seem to have a much weaker influence on the bulk rheology than on the particle mobility. This may explain why the mobility takes longer to reach its terminal value than the bulk storage modulus, also bringing attention to the variety of configurations that may exist between NPs and the hydrogel pores. Terminal mobility spectra for gels containing d ≈ 60 nm NPs are shown in Figure 4. When in gels, the mobility magnitude for NPs of this size is low at low frequencies but increases substantially when increasing the frequency. When the same particles are dispersed in the background electrolyte, the mobility is considerably larger and decreases only slightly with increasing frequency (black). This reflects the viscoelasticity of the hydrogel network, which produces NP dynamics that are

Figure 2. Mobility magnitude |M| spectrum for nanocomposite S5100 at the times (advancing top to bottom) identified by the symbols in Figure 3.

Figure 4. Terminal mobility magnitude |M∞| spectra for d ≈ 60 nm NPs in PA gels with various terminal storage moduli: SB (black), S6 (red), S5, S4, S3, S2, S1 (blue) (modulus increasing from red to blue).

Figure 1. PA storage moduli time series G′(t) during gelation of S1− S6 (top to bottom). Terminal storage moduli G′∞ ≈ 21, 7, 1.1, 0.27, 0.12, and 0.0015 kPa.

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dominated by elastic stresses at low frequencies and viscous stresses at high frequencies. The transition is elaborated upon below when we examine the mobility argument spectra. Here, spectra were measured for three separately prepared samples, furnishing error bars that show the standard deviation from the respective mean value. For the softest gels, the mobility is practically independent of the storage modulus until the modulus exceeds a critical value (G′∞ ≈ 0.27 kPa), beyond which the mobility decreases continuously with a further increase in stiffness, consistent with Bhosale et al.17 for 30 nm silica NPs in PA. Experiments were also undertaken with gels containing d ≈ 30 and 100 nm NPs. To highlight the correlation between the NP and gel mesh sizes, Figure 5 shows the terminal mobilities Figure 6. Scaled terminal mobility magnitude |M∞|/|M0| of d ≈ 100 nm (blue), 60 nm (green), and 30 nm (red) NPs versus the scaled terminal mesh size ξ/d.

attenuated according to ξ and d with the mobilities of smaller particles being attenuated more than for large particles. This suggests that the attenuation is principally governed by the gel modulus rather than the degree of confinement. As illustrated schematically in Figure 7, our results suggest that NPs reside in a variety of elastic coupling configurations,

Figure 5. Terminal mobility magnitude |M∞| (at f ≈ 14.1 MHz) of d ≈ 100 nm (blue), 60 nm (green), and 30 nm (red) NPs versus the terminal storage modulus G′∞. Solid lines are to guide the eye, and dashed lines are the mobilities in the background electrolyte.

at f ≈ 14.1 MHz plotted versus the terminal storage modulus. For the two smaller (d ≈ 30 and 60 nm) NPs, there is an ostensible plateau for the NPs embedded in soft gels, whereas the largest (d ≈ 100 nm) NPs exhibit a monotonic decrease over the entire range of gel stiffnesses. As the gel stiffness increases, the fraction of NPs that elastically couple to the network increases, thereby decreasing the average mobility. Note that the displacements have subangstrom amplitude at the prevailing MHz frequencies, so the response is in a linear regime where the microstructure is weakly perturbed from the state that prevails in the absence of an electric field, e.g., NPs in fluid domains have insufficient time to electrophoretically collide with the skeleton. To highlight the role of entrapment at the nanoscale, Figure 6 shows the terminal mobilities versus the mesh size

Figure 7. Schematic representations of soft (left) and stiff (right) NP− hydrogel composite microstructures bearing small (top) and large (bottom) NPs. Color identifies NPs that are predominantly coupled to the gel by elastic (red) or viscous (green) forces.

′ )1/3 ξ = (kBT /G∞

which reflect the NP size and geometrical features of the nanostructure that principally depend on the polymer density and cross-linking ratio. Note that the gel may also modify the diffuse double layer and, therefore, vary the apparent ζpotential. For example, polymer may preferentially accumulate at the particle surfaces, forming a layer that hinders electroosmotic flow that drives electrophoretic motion. Alternatively, the gel may modify the electrical forces by changing the local ionic strength and dielectric constant. These possibilities are assessed below when we theoretically interpret the mobility

where kBT is the thermal energy. The ratio d/ξ is a dimensionless measure of the overall degree of NP entrapment. Note that we have attempted to remove the nonsteric effects by normalizing the terminal mobilities with |M0| obtained when the NPs are dispersed in the background electrolyte. The mobilities when d ≪ ξ plateau to a value that is ≈7% lower than in the electrolyte, suggesting that nonsteric influences also hinder electroosmotic flow, attenuating the apparent ζpotential. On the other hand, when d ≫ ξ, the mobility is D

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spectra for nanocomposites with the largest, completely trapped NPs. The foregoing inferences are consistent with Rose et al.,23 who used diffusing-wave spectroscopy and dynamic light scattering to ascertain microstructural elasticity and NP diffusivities in gels. Their data show the diffusion coefficient of d ≈ 30 nm silica NPs in PA decreasing with a decrease in mesh size until diffusion is completely arrested at ξ ≈ 9 nm. From Figure 5, the critical mesh size for trapping d ≈ 30 nm NPs is ξc ≈ 15 nm. Similarly to the critical mesh size of Rose et al.23 (ξc ≈ 9 nm), this is notably smaller than the particle diameter (ξc ≈ 0.5d), suggesting a network that is much more heterogeneous than the ideal networks underlying the theoretical connection of the measured modulus to the mesh size. Note also that the mobility magnitudes for d ≈ 30 nm NPs are qualitatively consistent with those of Bhosale et al.,17 with the principal quantitative difference manifesting in different trapping moduli. Their critical modulus G′∞ ≈ 0.3 kPa is considerably lower than our G′∞ ≈ 1.1 kPa, highlighting again the sensitivity of the nanostructure to the sample preparation and loading protocols for the electroacoustic and rheometry measurements. Mobility Argument. Having explored the mobility magnitude, we now turn to the phase angle, also termed the mobility argument, ∠M. Phase spectra at several time points during gelation are shown in Figure 8 for the same sized NPs

Figure 9. Terminal mobility argument spectra (solid lines) for d ≈ 30 (top), 60 (middle), and 100 nm (bottom) NPs in PA gels with various terminal storage moduli: S1 (blue), S6 (red), and SB (green). Dashed lines show the mobility argument immediately after injecting the pregel solution into the ESA cell.

Figure 8. Mobility argument spectra for nanocomposite S5100 at the same times as for the mobility magnitude spectra in Figure 2.

and gel as in Figure 2. Similarly to the magnitude, the argument deviates most from the pregel solution at low frequencies, where the elastic forces are accentuated relative to the viscous forces. Note that a perfectly elastic response would furnish a 90° phase angle, so the considerably smaller angles here suggest that viscous stresses still play a significant role. To highlight the network formation, initial (dashed) and terminal (solid) spectra are compared in Figure 9 for NPs with various sizes in viscous (SB) and gel/viscoelastic media (S1 and S6). Spectra for the background electrolyte (SB) are consistent with the classical dynamic mobility; i.e., larger particles adopt a phase lag that increases with frequency because of inertial forces, and smaller, highly charged particles adopt a phase lead because of diffuse layer polarization.20 Here, there is a slight drift in the phase angle, which correlates with a drift in the conductivity, due to reactions involving APS and TEMED (details available as Supporting Information). For the particles

in gels (S1 and S6), the phase angle is much more sensitive to the frequency, and there are significant temporal changes that increase the phase angle, particularly at low frequencies. The weak temporal changes at high frequency suggest that the dynamics are dominated by the viscous stresses of the electrolyte, as expected from the constitutive eq 1. These are all hallmarks of a developing elastic network. Quantitative insights are provided by the reciprocal viscoelastic time scale τv−1 = μ/η. For the softer gel (S6, red), τv−1 ≈ 1.5 kHz when μ = G′∞, whereas the spectra in Figure 9 indicate that the viscous and elastic stresses balance when the frequency f ∼ 10 MHz, as indicated by the overlap of the initial and terminal spectra. This suggests that the local environment is less compliant than inferred by the bulk storage E

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modulus, again implying an heterogeneous nanostructure in which NPs adhere to the walls of macropores. For the stiffest gel (S1, blue), τv−1 ≈ 21 MHz when μ = G′∞, which is consistent with inferences drawn from the spectra in Figure 9. Thus, the stiffest gels seem to present a microstructure that is more homogeneous and representative of the bulk viscoelastic properties. Theoretical Interpretation. A network viscosity is readily incorporated into the theory of Wang and Hill22 by adopting a complex-valued shear modulus

μ* = μ + iμi

(3) −1

where the shear viscosity is μiω . Since the theory is for spherical colloids embedded in uncharged gels, with no-slip between the particle and gel, it can be applied to interpret our experiments with the largest d ≈ 100 nm NPs. According to the theory, for large particles at MHz frequencies, the shear modulus is the single independent gel parameter that affects the particle dynamics, since draining and compressibility (captured by the hydrodynamic permeability and skeleton Poisson ratio) are active only at much lower frequencies. However, the NP mobility is affected by the surface charge and electrolyte ionic strength, which together set the apparent NP ζ-potential. Note that we use the term apparent ζ-potential because there are many factors that can influence the apparent surface charge, including softness, surface roughness, porosity, and heterogeneity.24−26 Brooks27 experimentally and theoretically showed that the electrical properties of NPs dispersed in uncharged polymer solutions can be different from those in the pure electrolyte. He showed that κ → κe−β/2, where β is a parameter that can be linked to the polymer concentration and interaction energies among the polymer, solvent, and ions. For adsorbed polymer layers, β > 0 due to expansion of the diffuse double layer by the polymer excluded volume. In addition, adsorbed polymer can decrease the NP surface charge by neutralizing charged groups.28 Finally, adsorbed polymer can decrease the apparent NP charge by shifting the shear plane.27 With a prescribed solvent and NP size and density, the dynamic mobility depends on four model parameters: the ζpotential, Debye length κ−1, and the real and imaginary parts of the skeleton shear modulus μ*. Here, we present the results of nonlinear least-squares fitting of the Wang and Hill22 theory to the terminal mobility spectra for d = 100 nm NPs in gels S1−S4 with all four variables as fitting parameters (available in Table 2). Other model parameters were prescribed the values

Figure 10. Terminal mobility magnitude (top) and argument (bottom) spectra for the largest, i.e., fully trapped with d ≫ ξ, NPs (d ≈ 100 nm) in PA gels with various terminal storage moduli: S1 (yellow), S2 (magenta), S3 (blue), S4 (red), and SB (cyan). Circles are experimental data, and solid lines are the theory of Wang and Hill22 evaluated with the fitting parameters provided in Table 2. SB parameters are ζ = −2.6kBT/e, κa = 20.5, and μ = 0. Other prescribed model parameters: ρ = 997 kg m−3 (solvent density), ρp = 2,200 kg m−3 (NP density), η = 9 × 10−4 Pa s (solvent viscosity), D = 2 × 10−9 m2 s−1 (ion diffusivities), T = 294 K.

The fitting parameters in Table 2 reveal real and imaginary parts of μ* that both increase with increasing polymer concentration. The magnitude has the same order of magnitude as the shear modulus ascertained from bulk rheometry on pure gels but is quantitatively lower and has a much weaker dependence on the polymer concentration. A lower magnitude may reflect heterogeneity, with NPs preferentially occupying softer domains, perhaps even adhering to the surfaces of larger pores. The smaller imaginary part of the shear modulus manifests in viscous stresses that are comparable to those of the solvent at MHz frequencies, i.e., μiω−1 ∼ 1 mPa s when ω ∼ 106 rad s−1. This supports the general assertion of Bhosale et al.,17 which was drawn from dynamic mobility data at a single frequency. The ζ-potentials are substantial, decreasing modestly with increasing polymer concentration, possibly due to absorption of polymer chains at the NP surfaces, further hindering electroosmotic flow. As expected by the theory of Brooks,27 the apparent diffuse layer thickness κ−1 increases with the polymer concentration. Together, these results show that the PA skeleton modulates the particle dynamics through its influence on the viscoelastic properties of the medium and the

Table 2. Model Parameters for the Theory in Figure 10 sample

PA (wt %)

S1 S2 S3 S4

10 7 4 3

μ* (kPa) 3.80 2.26 1.21 1.06

+ + + +

1.60i 1.07i 0.71i 0.71i

−ζe/kBT

κa

1.9 2.0 2.1 2.3

4.6 10.8 13.4 15.3

available in the caption of Figure 10, which also compares the model spectra with ESA data. Note that other fitting strategies (involving fewer fitting parameters) produced less satisfactory results (available as Supporting Information). Prescribing the diffuse layer thickness based on the measured conductivity also produced comparable fits and fitting parameters to those shown here (available as Supporting Information). F

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in-situ free-radical polymerization in PNIPA-clay nanocomposite hydrogels. Macromolecules 2005, 38, 3482−3490. (4) Okay, O.; Oppermann, W. Polyacrylamide-clay nanocomposite hydrogels: rheological and light scattering characterization. Macromolecules 2007, 40, 3378−3387. (5) Wang, Q.; Hou, R.; Chenga, Y.; Fu, J. Super-tough doublenetwork hydrogels reinforced by covalently compositing with silicananoparticles. Soft Matter 2012, 8, 6048. (6) Ye, L.; Tang, Y.; Qiu, D. Enhance the mechanical performance of polyacrylamide hydrogel by aluminium-modified colloidal silica. Colloids Surf., A 2014, 447, 103−110. (7) Schexnailder, P.; Schmidt, G. Nanocomposite polymer hydrogels. Colloid Polym. Sci. 2009, 287, 1−11. (8) Zhu, M.; Zhu, Y.; Zhang, L.; Shi, J. Preparation of chitosan/ mesoporous silica nanoparticle composite hydrogels for sustained codelivery of biomacromolecules and small chemical drugs. Sci. Technol. Adv. Mater. 2013, 14, 045005. (9) Gaharwar, A. K.; Peppas, N. A.; Khademhosseini, A. Nanocomposite hydrogels for biomedical applications. Biotechnol. Bioeng. 2014, 111, 441−453. (10) Samoshina, Y.; Diaz, A.; Becker, Y.; Nylander, T.; Lindmana, B. Adsorption of cationic, anionic and hydrophobically modified polyacrylamides on silica surfaces. Colloids Surf., A 2003, 231, 195− 205. (11) Petit, L.; Bouteiller, L.; Brulet, A.; Lafuma, F.; Hourdet, D. Responsive hybrid self-assemblies in aqueous media. Langmuir 2007, 23, 147−158. (12) Arends, F.; Baumgartel, A.; Lieleg, O. Ion-specific effects modulate the diffusive mobility of colloids in an extracellular matrix gel. Langmuir 2013, 29, 15965−15973. (13) Panyama, J.; Labhasetwar, V. Biodegradable nanoparticles for drug and gene delivery to cells and tissue. Adv. Drug Delivery Rev. 2003, 55, 329−347. (14) O’Brien, R. W.; Cannon, D. W.; Rowlands, W. N. Electroacoustic determination of particle size and zeta potential. J. Colloid Interface Sci. 1995, 173, 406−418. (15) Carasso, M. L.; Rowlands, W. N.; O’Brien, R. W. The effect of neutral polymer and nonionic surfactant adsorption on the electroacoustic signals of colloidal silica. J. Colloid Interface Sci. 1997, 193, 200−214. (16) Dukhin, A.; Goetz, P. Evolution of water-in-oil emulsion controlled by droplet-bulk ion exchange: acoustic, electroacoustic, conductivity and image analysis. Colloids Surf., A 2005, 253, 51−64. (17) Bhosale, P. S.; Chun, J.; Berg, J. C. Electroacoustics of particles dispersed in polymer gel. Langmuir 2011, 27, 7376−7379. (18) Hunter, R. J. Recent developments in the electroacoustic characterisation of colloidal suspensions and emulsions. Colloids Surf., A 1998, 141, 37−65. (19) O’Brien, R. W. Electroacoustic effects in a dilute suspension of spherical particles. J. Fluid Mech. 1988, 190, 71−86. (20) Mangelsdorf, C. S.; White, L. R. Electrophoretic mobility of a spherical colloidal particle in an oscillating electric field. J. Chem. Soc., Faraday Trans. 1992, 88, 3567−3581. (21) O’Brien, R. W.; Jones, A.; Rowlands, W. N. A new formula for the dynamic mobility in a concentrated colloid. Colloids Surf., A 2003, 218, 89−101. (22) Wang, M.; Hill, R. J. Dynamic electric-field-induced response of charged spherical colloids in uncharged hydrogels. J. Fluid Mech. 2009, 640, 357−400. (23) Rose, S.; Marcellan, A.; Hourdet, D.; Creton, C.; Narita, T. Dynamics of hybrid polyacrylamide hydrogels containing silica nanoparticles studied by dynamic light scattering. Macromolecules 2013, 46, 4567−4574. (24) Hill, R. J.; Saville, D. A. ‘Exact’ solutions of the full electrokinetic model for soft spherical colloids: Electrophoretic mobility. Colloids Surf., A 2005, 267, 31−49. (25) Delgado, A. V.; González-Caballero, F.; Hunter, R. J.; Koopal, L. K.; Lyklema, J. Measurement and interpretation of electrokinetic phenomena. J. Colloid Interface Sci. 2007, 309, 194−224.

electrical properties of the NP inclusions, as predicted by the theory of Wang and Hill.22

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CONCLUSIONS Electroacoustic spectroscopy has been applied to study the interaction of silica NPs with PA gels, as a simple model of a more general class of NP−hydrogel nanocomposites. To highlight the close correspondence between the time dependence of the dynamic mobility and the bulk storage modulus, storage modulus time series were compared to mobility magnitude spectra at several time points during gelation. The slower development of the NP mobility shows that NP mobilities are more sensitive to the developing microstructure than the bulk rheological properties. Terminal mobility magnitude spectra suggest that NPs occupy a variety of elastic coupling configurations, from detached, through partially attached, to fully trapped. This is also evident from the nonuniversal manner in which NP mobilities are related to their radius and the gel mesh size, again highlighting nanoscale heterogeneity. The mobility phase angle spectra highlighted the significant roles of viscous and elastic dynamics in the MHz range, with clear indications of elastic network formation at lower frequencies and viscous dominated dynamics at high frequencies. The theory of Wang and Hill22 was fitted to dynamic mobility spectra for d = 100 nm NPs trapped in gels with various polymer concentrations, using the ζ-potential, diffuse layer thickness, and complex skeleton shear modulus as fitting parameters. This suggests that PA influences NP dynamics by modifying the viscoelastic environment and electrical properties. These changes occur in a systematic manner with respect to changes in polymer concentration and are qualitatively consistent with theory.

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ASSOCIATED CONTENT

S Supporting Information *

Conductivity analysis; nonlinear least-squares fitting of theory to electroacoustic spectra. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (R.J.H.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from NSERC Discovery and NSERC Research Tools and Instruments programs is gratefully acknowledged. V.A. is supported, in part, by a McGill Engineering Doctoral Award (MEDA). We thank Dave Cannon (Colloidal Dynamics LLC) for advice on operating the AcoustoSizer II.

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