Structure, Ion Transport, and Rheology of Nanoparticle Salts

Article pubs.acs.org/Macromolecules

Structure, Ion Transport, and Rheology of Nanoparticle Salts Yu Ho Wen, Yingying Lu, Kerianne M. Dobosz, and Lynden A. Archer* School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, United States S Supporting Information *

ABSTRACT: Above a critical surface chemistry-dependent particle loading associated with nanoscale interparticle spacing, ligand−ligand interactionsboth electrostatic and stericcome into play and govern the structure and dynamics of charged oligomer-functionalized nanoparticle suspensions. We report in particular on the structure, ion transport, and rheology of suspensions of nanoparticle salts created by cofunctionalization of silica particles with tethered sulfonate salts and oligomers. Dispersion of the hairy ionic particles into medium and high dielectric constant liquids yields electrolytes with unique structure and transport properties. We find that electrostatic repulsion imparted by ion dissociation can be tuned to control the dispersion state and rheology through counterion size (i.e., Li+, Na+, and K+) and dielectric properties of the dispersing medium. Analysis of small-angle X-ray scattering (SAXS) structure factors and the mechanical modulus shows that when the interparticle spacing approaches nanometer dimensions, weakly entangled anchored ligands experience strong and long-lived topological constraints analogous to those normally found in well-entangled polymeric fluids. This finding provides insight into the molecular origins of the surprisingly similar rubbery plateau moduli observed in hairy nanoparticle suspensions and entangled polymers of the same chemistry as the tethered ligands. Additionally, we find that a time−composition superposition (TCS) principle exists for the suspensions, which can be used to substantially extend the observation time over which dynamics are observed in jammed, soft glassy suspensions. Application of TCS reveals dynamical similarities between the suspensions and entangled solutions of linear polymer chains; i.e., a hairy particle trapped in a cage appears to exhibit analogous dynamics to a long polymer chain confined to a tube. stability. Recently, Schaefer et al.18 used a variation of this approach to create silica nanoparticles that were cofunctionalized with poly(ethylene glycol) chains and lithiated sulfonate molecules. These authors showed that because of the high grafting density of lithium salt to the particles, dispersion of the cofunctionalized particles in a moderate dielectric constant medium produces electrolytes with improved conductivity and ion transport characteristicsanalogous to what would be achieved upon addition of a conventional molecular salt to an electrolyte solvent. Unlike a molecular salt, where the ionic conductivity originates from motion of the dissociated cation and anion, the authors found that their nanoparticle salts behave as approximate single-ion conductors with more than 90% of the ionic conductivity originating from motion of the Li+ cation associated with groups tethered to the nanoparticles. Nanoparticles stabilized by a combination of electrostatic and steric forces, as illustrated in Figure 1a, are of additional interest for fundamental studies of colloidal stability and polymer confinement. 19,20 Created by tethering sulfonate salts (−SO3−M, where M = Li+, Na+, or K+) and neutral ligands (polyetheramines) to nanometric silica particles, these cofunctionalized particles exhibit attractive colloidal stability (Figure 1b) in a range of fluids, even at high particle loadings. This feature facilitates their use as model systems for

1. INTRODUCTION Polymer-functionalized particles, consisting of an inorganic core and tethered charged/neutral molecules, are indispensible in many complex fluids and are promising candidates for various emerging technologies,1,2 e.g., electrolytes,3,4 lubricants,5,6 fuel cells,7 optoelectronic devices,8 etc. These nanocomposites are attractive because they retain desirable properties from their individual constituents, and therefore, permutations among the vast library of core/tethered materials chemistries allow for an increasing number of novel materials with functionalities appropriate to contemporary innovations. Uncoated particles are commonly stabilized through attaching either neutral ligands (steric),9−12 charged groups (electrostatic),13 or ionic oligomers (electrosteric)14 to their surface. Because of a high surface area to volume ratio of nanometer-sized particles, perennial dispersion challenges associated with the strength of the interparticle dispersion force frustrate many of these tested solutions for larger colloids and limit their potential applications.2,15 Incorporation of an explicit charge onto hairy nanoparticles provides an attractive solution as it can impart enhanced stabilization from both electrostatic and steric forces. Reports by Rodriguez et al.16 and Agarwal et al.17 disclose a novel family of sterically stabilized nanoparticles in which short polymer chains bearing amino groups are tethered by reaction with sulfonic acid groups covalently grafted to the particles. The authors showed that under some conditions it is possible to synthesize highly grafted particles that form solvent-free nanoparticle suspensions that exhibit long-term colloidal © 2014 American Chemical Society

Received: February 25, 2014 Revised: June 10, 2014 Published: June 25, 2014 4479

dx.doi.org/10.1021/ma5004002 | Macromolecules 2014, 47, 4479−4492

Macromolecules

Article

bonded to a polymer25−29 or particle3,18,30 substrate, and the mobile cations ionically coupled to the substrate hop between immobilized anions and act as charge carriers. Single-ion conductors based on both materials designsionomers and nanoparticle saltscan attain high cation transference number approaching unity but generally are insufficiently conductive for straightforward use in batteries at room temperature. Poor conductivity arises from electrostatic correlation effects between neighboring ionic groups and low dissociated ion fractions.31 The structure and dielectric properties of the electrolyte near the substrate and their effect on ion-pair dissociation are important aspects of understanding these systems, but the effects remain largely unexplored in electrolytes based on nanoparticle salts. Indeed, contrary to usual expectations, our dielectric relaxation measurements reveal that high ion dissociation fractions (∼0.1 at 70 °C) can be attained even in a low dielectric constant suspending medium.

2. EXPERIMENTAL SECTION 2.1. Synthesis of Nanoparticle Salts. Nanoparticle salts used in the study were synthesized using the following multistep procedure. First, a dense layer of 3-(trihydroxysilyl)-1-propanesulfonic acid (Figure 1a; Gelest, Inc.) was grafted on bare silica nanoparticles (Ludox SM colloidal silica, Sigma-Aldrich) in aqueous media using a previously reported approach.16,17 The SM particles were found to have a number-average diameter, ⟨D⟩n ≈ 7.8 ± 2.4 nm from dynamic light scattering measurements (Figure S1 in Supporting Information). The purified surface functionalized particles obtained after rigorous dialysis of the raw product were protonated through ion exchange, and the average concentration of the immobilized sulfonic acid groups on the particles was determined by titration. The grafting procedure is very efficient and leads to high ligand coverage on the particles (typically approximately 2 ligands/nm2 or around 390 active sulfonic acid groups per particle). The grafting density is determined by the ligand molecular weight and the organic content of the functionalized particles from TGA. The second step of the synthesis involves stoichiometric reaction of the purified particles with neutral copolymer chains, polyetheramines (CH3(C2H4O)19(C3H6O)3NH2), with Mw ≈ 1000 Da and Rg ≈ 1.3 nm (Figure 1a; Huntsman Corp.), followed by neutralization of the particles by exchanging the acidic H+ counterions with alkali metal ions (Li+, Na+, or K+) of different size. In this study, the number ratio of sulfonate salts to neutral ligands is fixed at unity (approximately 1 salt molecule/nm2 and 1 copolymer chain/nm2). Finally, before drying the particles to remove water, an appropriate amount of aprotic solvent, mPEG (methoxy poly(ethylene glycol), Mw ≈ 350 Da, εmPEG ≈ 14), or PC (propylene carbonate, εPC ≈ 65 at 25 °C),32 was added to the aqueous particle suspensions as an ultimate suspending medium. The suspensions were dried in a convection oven at 80 °C for 24 h and then vacuum-dried at 60 °C for another 24 h to get rid of the last traces of water. The sample preparation method reported here is specifically designed to suppress particle aggregate formation during drying. Additionally, because it does not involve drying the particles and redispersing the dried particles in the suspending medium, the method yields electrolytes of reproducible structure and composition. The core volume fraction, ϕc, is determined from gravimetric analysis of the final electrolyte product, but to some extent can be controlled, as the evaporation of mPEG is insignificant during the drying procedure and the sample mass of the dried suspensions was confirmed to be within ±1% of target weight. Because of a lower boiling point of PC (∼240 °C), however, we typically used double the desired amount of the solvent prior to water removal. After 24 h of drying at 80 °C, we found that for dilute suspensions an additional drying step is required to remove excess PC, whereas for concentrated ones an additional amount of the solvent has to be repeatedly added to the suspensions to ensure no concentration overshoot, by monitoring the sample mass. The procedures took another 24 h before vacuum drying and minimize the influence of solvent evaporation on the target ϕc. A range of charged and neutral

Figure 1. (a) Schematic drawing of nanoparticle salts created by cofunctionalization of nanometric silica particles with tethered sulfonate salts (−SO3−M) and neutral ligands (polyetheramines), where M represents counterions (Li+, Na+, or K+) that either associate with −SO3− or dissociate into the bulk. The grafting densities are ca. 1 salt molecule/nm2 and 1 copolymer chain/nm2. (b) TEM image of the Li-neutralized charged particle suspension (ϕc = 0.06).

investigating suspension structure and polymer dynamics in highly filled polymer−particle composite systems. As all anions are covalently anchored to the surface of much larger particles (i.e., no free anions in the bulk), these nanoparticle salts are also potentially advantageous for studying the impacts of different counterions and dielectric media on electrostatic forces and hence colloidal interactions. Small-angle X-ray scattering (SAXS) results discussed later suggest that electrostatic repulsion provided by the dissociated ion-pair restricts particle−particle contacts and stabilizes suspension electrolytes based on these salts. Additionally, at high nanoparticle salt loadings, the combined attributes (colloidal stability and singleion transport) provide opportunities for designing electrolytes with controlled rheological and mechanical properties for applications. The demand of portable energy has drawn much attention to rechargeable lithium batteries.21,22 Electrolytes that provide high ion mobility and single-ion conduction by mobile cations are understood to provide important advantages in terms of cell efficiency and suppression of undesirable concentration polarization,23 and stabilization of electrodeposition of metals,24 such as lithium, and to reduce the growth rate of dendrites. In most single-ion conducting electrolytes, fixed anions are covalently 4480


Macromolecules

Article

Figure 2. SAXS intensity spectra, I(q), for (a) neutral and (b) Li-neutralized charged particles in mPEG; for clarity, scattering curves are shifted upward with respect to that of the dilute suspension (ϕc = 0.01). particle suspensions was made with ϕc = 0.010−0.148 (i.e., 5−52 wt % nanohybrids) and ϕc = 0.010−0.175 (i.e., 5−82 wt % nanohybrids), respectively; still higher particle loadings pose difficulties in performing measurements. 2.2. Material Characterization. SAXS intensity spectra were collected at Sector 12-ID-B of Argonne National Laboratory. The point-collimated beam has an incident energy 7.9−14 keV and a q range of 0.06−7 nm−1. A custom-built sample holder connected to a temperature controller was used for the gel and waxy samples at measurement temperature 70 ± 5 °C. Scattering data were averaged over five consecutive exposures, 1 s each, and no radiation damage was found after repeated measurements. Background and solvent scattering was subtracted from the samples’ scattering. An in-house instrument (SAXSess, Anton Paar) was also used to perform SAXS measurements for some samples. The instrument produces a line-collimated beam at a wavelength 0.154 nm. A paste sample holder with Kapton window was used to hold the samples at measurement temperature 70 °C. The generalized indirect Fourier transformation (GIFT) method was employed to desmear line-collimated scattering intensity.33,34 A controlled stress rheometer (MCR301, Paar Physica) outfitted with cone-and-plate fixtures (cone diameter 10 mm and cone angle 2°; cone diameter 25 mm and cone angle 1°) was utilized to measure bulk rheological response of all particle suspensions at 70 °C, unless otherwise mentioned. Prior to data collection, the materials were presheared by applying a variable shear strain ramp (strain sweep) with strains in the range 0.1% ≤ γ ≤ 200%, until reproducible data were obtained. The zero-shear-rate viscosity of the concentrated, jammed particle suspensions at shear rates smaller than 10−5 s−1 was obtained using constant shear stress (creep) measurements on the presheared materials. For each measurement, the stress was maintained until a linear relationship between strain and time is attained and an effective shear rate determined from the slope of the strain versus time plot. A Novocontrol broadband dielectric spectrometer applying 0.1 Vrms ac voltage was used to study the linear electrical response of nanoparticle salts. Isothermal frequency sweeps in the range 10−1−107 Hz were carried out from 70 to 0 °C. The sample geometry was set by a Teflon spacer with a thickness of 0.75 mm and an inner diameter of 6.7 mm. Samples were sandwiched between gold-plated copper electrode disks of 30 mm diameter.

impacts of tethered ligandsboth charged and neutralon colloidal interactions over a range of particle loadings (0.01 ≤ ϕc ≤ 0.175), we performed SAXS measurements to determine the structure of the suspensions; the scattering intensity spectra, I(q), are shown in Figures 2a,b (Figure S2 in Supporting Information for Na- and K-neutralized counterparts). All scattering profiles show a scaling relationship, I(q) ∼ q−4, in the high q regime (i.e., qa ≫ 1). This is the expected result from an ideal two-phase model scatterer (Porod law).35 The scattering length density of the tethered ligand is similar to that of mPEG; the two-phase model scattering at high q then suggests that there is a sharp boundary between the nanocores and the liquid phase. For a well-dispersed particle suspension, one expects a sharp peak at intermediate q ≈ 2π/dpp, where dpp is the mean interparticle distance for nearest neighbors. Figures 2a,b, however, reveal only a broad shoulder. This is presumably a result of suppressed constructive scattering interferences due to the adhesive particles. We will address this structural feature in more detail shortly. Since I(q) profiles do not plateau at low q, the formation of a certain population of large clusters cannot be precluded in both neutral and charged particle suspensions, in agreement with the transmission electron microscopy (TEM) image (Figure 1b). It is useful to retrieve the structure factor, S(q), from the scattering spectra (Figure 2) to understand the microscopic structure resulting from electrostatic and steric interactions imparted, respectively, by the tethered salt and neutral ligands. The S(q) was determined by overlaying the high-q scattering data for a concentrated suspension with that of a dilute, noninteracting (as evidenced by the disappearance of the nearest-neighbor peak in I(q)) suspension with ϕc = 0.01, the so-called form factor,36,37 as summarized in Figures 3a,b (Figure S3 in Supporting Information for Na- and Kneutralized counterparts). Although the form factor may change slightly upon further dilution, the one with ϕc = 0.01 suffices for present purpose as the peak position of S(q) depends weakly on the form factor chosen. Let us first consider the structure of neutral particle suspensions, where particles interact via excluded volume and

3. RESULTS AND DISCUSSION 3.1. Impacts of Tethered Sulfonate Salts on Structure: Electrostatic Stabilization. To first understand the general 4481


Macromolecules

Article

Figure 3. Experimental structure factors, S(q), for (a) neutral and (b) Li-neutralized charged particles in mPEG. Lines are fits to the square-well (SW) potential with interaction width of 0.12 nm and depth of 30 kBT; a log-normal distribution with mean core radius of 3.9 nm and width of 0.1 is assumed. For clarity, data are shifted upward with respect to that of the dilute suspension (ϕc = 0.06). (c) Interparticle distance, dpp, determined from the first interaction peak of structure factor, and the prediction of dpp = 2a(0.63/ϕc)1/3.

van der Waals (vdW) forces. It can be seen in Figure 3a that as ϕc increases, the position of the regular (first) interaction peak remains essentially invariant at q ≈ 0.6 nm−1, indicating strong particle correlation and a nearly constant interparticle spacing. The estimated dpp (≈ 2π/q) from the peak values are summarized in Figure 3c, together with a theoretical prediction, dpp = 2a(0.63/ϕc)1/3, that assumes uniform spatial distribution of spheres in the suspending fluid. The comparison clearly indicates that the actual dpp is substantially smaller than the prediction, implying that the particle suspensions are not homogeneous, even at low ϕc = 0.06 where metastable clusters and voids might coexist. As seen in Figure 3c, nanoscale surface-to-surface spacings, dss, are inferred from the structure factor (i.e., dss = dpp − ⟨D⟩n ≈ 2.5 nm), and the mean particle separation is close to 2Rg, where Rg ≈ 1.3 nm is the radius of gyration of tethered neutral ligands under the assumption that they form Gaussian coils. This result suggests that there exists an attractive force between particles that strongly correlates

their center-to-center locations and that the attractive forces that correlate the particles are balanced only by the steric forces between the overlapping/compressed tethered polymer brush, which produces small weakly bonded, metastable clusters, and prevents wholesale aggregation.38,39 The attractive force between the surface functionalized particles can originate from multiple sources. It can arise from interactions between the strong dipoles produced by the ether oxygens along the tethered polymer backbone. It may also originate from the hydrophobicity of the tethered copolymer chains. Specifically, the three hydrophobic propylene glycol monomers, (C3H6O)3, of the copolymer (Figure 1a) might attract each other in the hydrophilic solvent, mPEG. As discussed later, linear viscoelastic measurements indicate that the particle suspensions manifest little aging immediately after rejuvenation (Figure S4 in Supporting Information), indicating that the particle clusters evident from the SAXS measurements are “metastable” and the attractive interactions that bring them 4482


Macromolecules

Article

Figure 4. Desmeared SAXS intensity spectra, I(q), for Li-neutralized charged particles in mPEG (a) and PC (b) collected on the SAXSess instrument; for clarity, scattering curves are shifted upward with respect to that of the dilute suspension (ϕc = 0.01). (c) Structure factor, S(q), for Lineutralized charged particles in mPEG and PC. Inset shows interparticle distance, dpp, in the two solvent systems.

second peak is more prominent (i.e., second-order Bragg reflection at q ≈ 4π/dpp). This could be attributed to the polydispersity of core size and the clustering of adhesive particles. Overall, the theory/data comparison of S(q) provides clear evidence in support of our earlier observation that metastable clusters may be formed in the neutral particle suspensions. Structure factors for charged particles are more complicated, and smaller counterion size is found able to effectively increase suspension stability. Using the same potential parameters as in Figure 3a, we find in Figure 3b that the calculated S(q) obviously overestimates the low-q upturn. This indicates that attachment of salts, the lithium salt (−SO3−Li+) in particular, seems able to keep particles further apart, as shown in Figure 3c. Cluster formation is evident from the upturn of S(q) at q → 0,41 especially in the K-neutralized charged particle suspensions. As the charge density goes down from Li+ to K+ due to increasing counterion size, the ability of the tethered salt to overcome interparticle attractions appears to decrease as the charge density is lowered. In other words, K-neutralized charged particles behave like the “neutral” or uncharged

together are compensated by the repulsive forces that arise from compression of the dense ligand brush. This observation suggests that particles are in a nearly equilibrium state in the suspensions, as is further evidenced by the measurable Newtonian viscosity (a characteristic of an equilibrated fluid) in high-volume fraction suspensions, which exhibit characteristics associated with soft, jammed matter. In Figure 3a, theoretical predictions of the square-well (SW) structure factor are presented for comparison.40 The purpose of fitting the experimental S(q) is to understand the low-q upturn that may signify long-range particle correlations. Since the silica particles investigated are slightly polydisperse, as often encountered for nanometric colloids, S(q) is evaluated using a log-normal distribution for the SW radius with ∼10% polydispersity. The SW potential with interaction width of 0.12 nm and depth of 30 kBT reasonably describes the low-q data, and the depth is close to the value typical for weakly flocculated suspensions (≈ 20 kBT).13 Additionally, the position of the first interaction peak in the calculated S(q) does not change with ϕc, reflective of the sticky ligands that bond neutral particles together. Another interesting feature in Figure 3a is that the 4483


Macromolecules

Article

tethered to our particles are dissociated in solution. Figure 5a reports the DC conductivity, σDC, for the lithiated nanoparticle

particles in some sense due to their bulky counterions that may screen electrostatic repulsion of the particles, which counteracts the vdW ligand−ligand attraction. Thus, our S(q) analysis suggests that Li-neutralized charged particles possess appreciable electrostatic repulsion due to the smaller cations, which effectively increases suspension stability. To estimate the effective range of electrostatic interactions, we calculate the double layer thickness, κ−1, which can be estimated using the modified Debye length, κ2 = (e2/ εε0kBT)[(2z2nb − 3Qzϕc/ae)/(1 − ϕc)],13,42 if no addition of electrolyte (i.e., nb → 0) and a uniform density of free counterions are assumed, where Q is the surface charge per unit area of particle surface. Here, 10% ion dissociation (at 70 °C) is assumed, and hence Q ≈ −0.016 C/m2. The estimate yields a double layer thickness κ−1 ≈ 2 nm at ϕc = 0.10 and roughly sets an upper bound at low particle loadings, in agreement with what is observed in Figure 3c, whereafter particle crowding induces the interpenetration of tethered copolymer chains. The estimate also implies that even in the absence of an explicit electrolyte, the Debye length of the particles is small. It is worth briefly mentioning the general consensus on melt ionomers that charged groups attached to polymer melts can induce dipole−dipole attraction that leads to the formation of ionic aggregates, especially in the low dielectric medium of themselves (typically, 2 < εmelt < 5).43,44 In addition, it is thought that the reversible ionic cross-links formed as a result of these attractive forces remain intact if ionomers are plasticized with small molecules of low polarity (i.e., low ε). This situation appears to be quite different from what we observe here for particles, wherein in intermediate dielectric solvent, εmPEG ≈ 14, the formation of ionic cross-links and larger particle clusters is not favored. Dielectric spectroscopy analysis discussed in the next section suggests an explanation for this difference. It indicates that because the ether oxygen and/or hydroxyl groups in mPEG can interact specifically with and solvate Li+, there is a nonclassical enhancement in counterion dissociation, which would account for an absence of ionic cross-links. 3.2. Impacts of Dielectric Medium on Structure and Ion-Pair Dissociation. 3.2.1. Electrostatic Repulsion Enhanced in High Dielectric Suspending Medium. It is generally accepted that repulsive electrostatic interactions become more long-range with increasing dielectric constant of a suspending medium. The Bjerrum length, lB (= e2/4πεε0kBT), is defined as the separation at which electrostatic interaction between two elementary charges is equal in magnitude to thermal energy. The values of lB are 3.5 and 0.7 nm in mPEG and PC, respectively (εmPEG ≈ 14 and εPC ≈ 65). Thus, ion pairs dissociate more readily in PC. Figures 4a,b show I(q) for Lineutralized charged particles in the two solvents with quite distinct ε, and Figure 4c compares calculated S(q) in the two solvent systems using the GIFT method to approximate the scattering spectra using a hard-sphere model with the Percus− Yevick closure relation.33 We find that the mean interparticle separation is larger in PC than in mPEG (inset to Figure 4c), and the modified Debye length is estimated to be κ−1 ≈ 4 nm in PC at ϕc = 0.10. Thus, the comparison suggests that particles may be more negatively charged in PC due to a higher Li+ dissociation fraction, and as a result, the enhanced Coulombic repulsion reduces particle−particle correlations. 3.2.2. Mobile Ion Concentration. The ionic conductivity and mobile ion concentration in a dielectric medium provide additional means for assessing the extent to which the ion pairs

Figure 5. (a) DC conductivity, σDC, (b) calculated ion mobility, μ, and (c) calculated ion dissociation fraction, α, as a function of T for lithiated nanoparticle salts in mPEG (open) and PC (closed). VFT fits of σDC shown as lines, with parameters compiled in Table S1.

salts in two solvents (mPEG and PC); here σDC is assessed from the plateau value of the real part of complex conductivity. It is evident from the figure that σDC in PC is 1−2 orders of magnitude higher than in mPEG at most of the temperatures studied and that whereas σDC decreases consistently with particle concentration for PC, it exhibits a complicated dependence on particle concentration for mPEG. As the DC conductivity of an electrolyte is proportional to the 4484


Macromolecules

Article

concentration of mobile ions p in the electrolyte and the mobility μ of the ions (i.e., σDC = eμp), these observations require knowledge of p and μ. The viscosity of neat propylene carbonate is measured to be around 6 times lower than that of mPEG at 70 °C, implying that the ion mobility in PC would be substantially higher. Additionally, the conductivity displays Vogel−Fulcher−Tammann (VFT) dependence, σDC = σ∞ exp(−B/(T − T0)), where any temperature dependence of ion dissociation is omitted. Here, σ∞ is the conductivity at T → ∞; B is the effective activation energy barrier for coupled ion and local polymer segmental motions/breathing modes, with units of temperature; T0 is the Vogel temperature at which conductivity goes to zero (fitted parameters compiled in Table S1). The good agreement to the VFT model displayed by the results in Figure 5a implies that at all ion concentrations ion motion is coupled with molecular motions of tethered chain segments and solvent molecules. To consider the effect of PC and mPEG solvents on ion-pair dissociation, we use a simple model for electrode polarization for single-ion conductors with low to moderate conductivity to analyze ion dynamics in the two solvents. We fit the tan δ peak (= ε″/ε′) deduced from frequency-domain dielectric relaxation measurements (Figure S5) using the expression, tan δ = ωτEP/ (1 + ω2τEPτσ), where τEP is the electrode polarization time and τσ the ion diffusion time.25 The assumption here is that because the electrolytes contain no molecular salt and exhibit modest ionic conductivities (σDC < 10−3 S/cm), dielectric polarization at low frequencies is directly reflective of ion dynamics of the free (unpaired) Li+ counterions. The model also ignores interaction between ions and hence is more accurate for lower ion concentrations.45,46 The ion mobility and mobile ion concentration can be calculated from the fitted parameters, μ = eL2τσ/4τEP2kBT and p = σDC/eμ, where L is the sample thickness. The ion mobility and mobile ion concentrations deduced from this analysis are reported in Figures 5b,c. The higher ion mobility obtained for PC (see Figure 5b) is consistent with the much lower viscosity of PC relative to mPEG. On the other hand, the generally higher ion dissociation fractions, α (= p/p∞), computed for mPEG relative to PC (Figure 5c) are unexpected on classical grounds because the dielectric constant for mPEG is 4−5 times lower than that for PC. Strong coordination of localized mPEG dipoles with Li+ has been long advocated; our results may be considered additional proof that this nonclassical effect can lead to enhanced ion-pair dissociation. It is understood that the more numerous, but larger lithium−mPEG complexes will encounter much greater resistance than might be inferred from the viscosity of the neat solvents, which would explain the much higher ionic conductivity of the PC-based electrolytes. The negatively charged surface, however, could be somewhat screened due to the formation of lithium−mPEG complexes around the periphery of particle surface, as neutralizes the particles and leads to smaller interparticle spacing as observed in the inset to Figure 4c. As shown in Figures 6a,b, contrary to the assumption made earlier in fitting the conductivity data, the mobile ion concentration is temperature-dependent. In the case of PC (Figure 6b), the behavior at low nanoparticle salt concentrations is captured reasonably well by the Arrhenius equation p = p∞ exp(−Ea/RT), where p∞ is the mobile ion concentration as T → ∞ and Ea is an activation energy for ion hopping. The inset to Figure 6b shows that extrapolation of the dissociated

Figure 6. Calculated mobile ion concentration, p, as a function of T for nanoparticle salts in (a) mPEG and (b) PC. Except for the inset to (b), the Arrhenius (dashed) and VFT (solid) fits were forced to intersect p∞, whose values are determined from stoichiometry and marked in the inset.

ion fraction in the limit, T → ∞, yields a p∞ value that is roughly consistent with expectations from stoichiometry of the particle salts, especially at low particle concentrations where the EP model is most accurate. An Arrhenius temperature dependence of p can be explained in straightforward terms based on thermal dissociation of ion pairs. The results for mPEG are, however, more complex as the mobile ion fraction exhibits noticeably stronger temperature dependence at high temperature and particle concentrations. Arrhenius fits at the lowest nanoparticle salt concentrations suggest a comparable binding energy of ion pairs in both solvents, i.e., Ea = 8.9 ± 2.9 kJ/mol in mPEG and 10.6 ± 0.5 kJ/mol in PC; these values are lower than reported for Li-neutralized ionomer melts, i.e., Ea = 25.2 ± 0.5 kJ/mol.25 The presence of solvent in the current systems provides the most obvious explanation of this difference. The strong dependence of Ea on particle content for the mPEG system and the clear deviation from Arrhenius behavior at moderate temperatures are also unexpected. We suspect that this behavior may reflect the specific role played by mPEG chain conformation in promoting ion-pair dissociation. A crude assessment of this idea is given in Figures 6a,b where the solid lines are VFT fits to the calculated data. The parameters used for the fits are provided in Table S2 of the Supporting Information. Although the fits are somewhat improved, suggesting that the ion dissociation in mPEG may indeed be coupled with its conformational dynamics, some of the parameters in Table S2 do not support this conclusion. In 4485


Macromolecules

Article

(G′ ∼ ω0) with increasing ϕc (Figure S6 in Supporting Information for Na- and K-neutralized counterparts). It is commonly believed that as G′ becomes frequency-independent at high particle loadings, individual particles are topologically constrained in cages created by their nearest neighbors and therefore are unable to relax. The cage constraint imposes long-lived dynamic correlations between particle centers and an exceedingly large amount of time is needed for cage escape and suspension relaxation.17 The soft glassy rheology (SGR) model quantifies the extent of jamming in such suspensions by a noise temperature, x, which can be extracted from the slope of G′ in the frequency domain (i.e., G′ ∼ ωx−1 for 1 < x < 3).47,48 The noise temperature takes on a limiting value of unity; i.e., G′ becomes independent of frequency when the system undergoes dynamic arrest and transitions to a glassy state. It is apparent from Figure 7c that the transition to a glassy behavior occurs at a relatively low ϕc for charged particles (ϕc ≈ 0.10), irrespective of the size of the counterion employed. This behavior is thought to reflect the electrostatic repulsion imparted by the tethered sulfonate salts, which increases the effective range of the particle cages. That the transition is observed at lower particle loadings for Li-based particle salts is consistent with the greater ease of solvating the Li+ by PEG, which produces particles with higher degree of surface charging. The fact that K-based particle salts jam sooner, but apparently less completely (x > 1), than Na-based materials can be rationalized in terms of the larger size of K+ ions and hence shorter association lifetime, which leads to easier solvation but better screening of the particle surface charge. Large-amplitude oscillatory shear (LAOS) measurements provide a complementary tool for characterizing viscoelastic mechanics of a jammed suspension. The method can be used to obtain information about the strength of the nanoporous network of cages and the conditions required for breakdown of the structure. In particular, at a shear strain γ ≫ γy, it is possible to break the interparticle cages and engender yielding and flow in a jammed material. At such strains, the conventional linear material functions, G′(ω0) and G″(ω0), are insufficient to characterize the material response because it is nonlinear.49 However, for all nanoparticle salt suspensions studied, the stress contributions from the second and third harmonics (at 2ω0 and 3ω0, where ω0 is the excitation frequency) are noted to be insignificant in the strain range from 0.01 to 200%. Thus, the first harmonic component of the loss modulus (G″ at ω0) can represent the intrinsic material response beyond yielding. It is apparent in Figure 8 that the Li-neutralized charged particles exhibit pronounced yielding at γy ≈ 5% (where G″ shows a maximum), consistent with a burst of dissipation and a transition to fluidlike behavior upon cage breakup, whereas neutral particles and K-neutralized charged particles yield at higher particle loadings. For Li-neutralized charged particles, the jamming can be detected at ϕc as low as 0.100, which is consistent with the critical ϕc inferred from the noise temperature (Figure 7c). 3.4. Impacts of Counterion Size and Dielectric Medium on Particle Interactions. It is evident in Figure 9a that at a fixed particle concentration G′ becomes smaller as the counterion size increases from Li+ to K+. This is due to the progressively weakened electrostatic repulsion as a result of bulky counterions. The figure also shows the effect of solvent dielectric properties on the jamming transition for neutral and Li-based nanoparticle salts. In particular, it is seen that whereas

particular, while the apparent activation energies deduced from the fits are consistent with those obtained from the VFT fits of the conductivity data, the T0 values are not. 3.3. Soft Glassy Rheology. The effect of nanoparticle content on suspension rheology is comparatively less complex and provides additional insights into the structure and dynamics of suspension electrolytes based on these nanoparticle salts. Small-amplitude oscillatory shear measurements were performed and used to quantify the viscoelastic behaviors of the suspensions. As seen in Figures 7a,b, there is a clear transition from a liquid-like state (G′ ∼ ω2) to a solid-like state

Figure 7. Linear response of storage modulus, G′, at a reference temperature T = 70 °C for (a) neutral and (b) Li-neutralized charged particles in mPEG. (c) Noise temperature, x, extracted from G′ vs ω. 4486


Macromolecules

Article

on PC (εPC ≈ 65) manifest consistently lower elastic moduli than those based on mPEG (εmPEG ≈ 14) at comparable particle loadings. Considering the much smaller Bjerrum length in PC versus mPEG, this result might at first seem surprising. It is consistent with the empirical findings reported in Figure 5c, which clearly show that despite its much lower dielectric constant, mPEG is more effective than PC in dissociating the tethered salts. It is possible to take this analysis one step further to retrieve an effective repulsive interparticle potential, U(r), for particles ′ values in with different surface properties. In particular, the G∞ Figure 9a can be used to extract U(r) by assuming an appropriate potential form through G∞ ′ = (Nϕm/5πr)(∂2U(r)/ 2 50,51 ∂r ), where N is the number of nearest neighbors per particle and ϕm is the volume fraction at which particles touch. The relation follows from the Zwanzig−Mountain equation,52 where the radial distribution function (RDF) can be replaced by a delta function if a suspension is in an ordered state; here a BCC array is assumed and therefore N = 8 and ϕm = 0.68. For simplicity, we employ a purely repulsive U(r) commonly used for describing particles with stretched, grafted brushes:

Figure 8. First harmonic of loss modulus, G″, at ω0 = 10 rad/s divided by its linear response value in the limit γ → 0 for neutral and charged particles in mPEG.

the elasticity in the neutral case is unaffected by medium dielectric constant at high particle loadings, suspensions based

⎧∞ , r < 2a ⎪ ⎪ ⎡ ⎤ 1 9 1 3 (1 − y 6 )⎥ , 2a < r < 2(a + H ) U (r ) = ⎨U0⎣⎢ −ln y − (1 − y) + (1 − y ) − ⎦ 5 3 30 ⎪ ⎪ r < 2(a + H ) ⎩ 0,

where U0 is the potential strength and y = (r − 2a)/2H with H being the contour length of polymer chains (or brush height).9 Here, U0 is a function of several structural parameters characterizing grafted polymer brushes, and the only adjustable ′ can only parameter is the contour length, H. We find that G∞ be described reasonably when U0 is treated as an adjustable parameter, possibly due to the stickiness of the ligands and the jamming of particles that substantially increase suspension elasticity (hence U0). Thus, we treat U0 and H as floating ′ in simplex optimizations. The parameters while fitting G∞ extracted U(r) are plotted in Figure 9b, and the best fits of G′∞ and the associated parameter values are provided in the inset to the figure. We find that the overall interaction is enhanced with decreasing counterion size and that an additional increment ∼1 nm of the effective brush height can be achieved for Lineutralized charged particles, as compared to H ≈ 2.9 nm for neutral particles. We also find that the range of the repulsive interactions in mPEG is larger than in PC, again reflecting the greater ion-pair dissociation in the former due to enhanced/ nonclassical solvation of Li+ due to specific interactions with PEG chains. 3.5. Structural and Dynamical Similarities to Entangled Polymers. 3.5.1. Structure: Confinement of Tethered Ligands and Nanoscale Interparticle Spacing. Closer inspection of Figure 9a reveals an important result. Irrespective of surface properties of the nanoparticle salts and dielectric constant of the solvent, G′ is observed to approach a fixed value of around 1 MPa at high ϕc. It follows from the

discussion thus far that this modulus reflects the compressive strength of the swollen, interdigitated polymer brush anchored to the particles. Consistent with a recent observation,19 the magnitude of the limiting storage modulus is also seen to be within a factor of 2 of the plateau modulus (Ge = 1.8 × 106 Pa at 80 °C) for entangled PEO melts.53,54 To understand the physical consequences of these observations, we use the relation Ge ≈ b2kBT/v0dt2 ≈ (1 − ϕc)G∞ ′ to estimate an apparent tube diameter, dt, for the tethered ligands in solution from the polymer contribution to the measured G′∞ (Figure 9a), the known Kuhn length (b = 1.1 nm), and Kuhn monomer volume (v0 = 0.21 nm3) of a PEO melt.54 The dt values thus estimated are summarized in Figure 9c to be smaller for Libased particle salts as a result of their better dispersion state revealed by SAXS and interparticle potential analyses. We also find that these values approach the tube diameter of PEO melts, dt,PEO = 3.7 nm, at high particle loadings. This implies that the tethered ligands experience their surface and geometrically constrained neighborhood on the particles in an analogous manner to a “weakly entangled” polymer, despite the fact that their molecular weight (≈1200 Da) is smaller than the entanglement molecular weight (Me,PEO ≈ 1700 Da). A similar observation has been reported recently for self-suspended suspensions created using silica−polyisoprene hybrid nanoparticles.19 Notwithstanding this confirmation, it is surprising that dt computed for the particle suspensions are generally larger than dt,PEO, and therefore, the inorganic silica cores may not contribute appreciably to G∞ ′ , possibly due to a low ϕc 4487


Macromolecules

Article

studied (ϕc ≤ 0.175). In general, the addition of nanofillers into polymer matrix55 or the presence of solvent is known to dilute the entanglement network around long chain molecules. Given that the dt values are close to both the melt tube diameter and the interparticle spacing for homogeneously distributed particles (i.e., dss), we conclude schematically in Figure 9d that the confinement effects produced by (1) tethered ligands19 and (2) nanoscale interparticle spacing on the test chain may produce topological constraints analogous to those conventionally associated with entangled polymers. 3.5.2. Dynamics: Particle in a Cage vs Polymer in a Tube. There appears to be an additional analogy between dynamics of tethered particles in a cage and long polymer chains in a tube. We consider this analogy next to understand the short-time particle dynamics (i.e., shorter than the cage escape time). We first construct a linear viscoelasticity (LVE) plot for neutral particle suspensions at different loadings using time−temperature superposition (TTS), as summarized in Figure 7a. It is worth mentioning that TTS does not hold true for the nanoparticle salt suspensions, presumably due to the strong temperature dependence of ion dissociation as seen in Figure 6a. Because the frequency-dependent moduli are measured at small shear strains (γ ≪ γy), the results in Figure 7a allow us to see how the plateau develops and how its width changes with ϕc. A notable feature in Figure 7a is that irrespective of the particle loading, G′ seems to approach a limiting plateau value in the high frequency regime. This is reminiscent of the linear viscoelastic response of entangled polymer melts, for which polymers of different chain lengths attain a melt plateau modulus in the high-frequency regime, as exemplified in Figure S7 for monodisperse polystyrene melts.56,57 For entangled polymers, the plateau is understood to reflect the paucity of molecular relaxation due to confinement of individual chains in a conceptual tube;58 the plateau ends at low frequency when the chains escape their confining tubes and relax by reptation. It has been already pointed out that the jamming transition in a suspension of particles at a critical ϕc arises from a conceptual cage produced by surrounding particles that restricts their independent motions. As ϕc further increases, the effects of the cage become more important and long-lived. Consequently, the plateau is dominant, spans a wider frequency domain, and assumes a nearly ϕc-independent value, and the cage escape time increases substantially. Figure S7 is a wellknown result, namely that a master curve can be obtained by horizontally shifting the linear viscoelastic spectra for entangled polystyrene melts with different chain lengths, with respect to the sample with the highest number of entanglements.57 The shift factors, aMw, used for creating the master curve over the frequency domain are found to manifest a scaling law, aMw ∼ Mw3.4 (inset to Figure S7), which follows the familiar scaling relation for both the tube escape time τd and zero-shear-rate viscosity, η0, implying that it is the self-similar dynamics of molecules with differing molecular weights that are responsible for the superposition. Surprisingly, as shown in Figure 10a, a similar master curve can be created for nanoparticle suspensions using time−concentration superposition (TCS) of the data in Figure 7a; the reference sample is the material with ϕc = 0.175, and the shift factors, aϕc, are given in Figure 10b. Though the master curve is not perfect (smooth), it reveals the dynamic response of suspensions over an extremely wide (nearly 18 decades) time range. The corresponding time spectrum is from 10−5 up to 1013 s (ca. 0.3 million years),

Figure 9. (a) High-frequency limit of G′ (ω = 112 rad/s) for charged and uncharged particles in mPEG and PC. (b) Interparticle potential, ′ for sample suspensions; the inset shows the U(r), extracted from G∞ best fits and the associated parameter values, (U0/kBT, H). (c) Apparent tube diameter, dt, against ϕc. Surface-to-surface distance, dss = 2a[(0.63/ϕc)1/3 − 1], estimated from core radius a = 3.9 is shown for comparison. (d) Schematic drawing illustrating the two confinement effects: (1) weakly entangled ligands and (2) nanoscale interparticle spacing. 4488


Macromolecules

Article

Figure 7a shows that each suspension attains the same G′∞, implying that the terminal/material relaxation time, τ (= η0/ G′∞), is proportional to the zero-shear-rate viscosity η0. Overall, for nanoparticle suspensions we find aϕc ∼ η0 ∼ τ, and the scaling relation has obvious similarities to what has been found for entangled polymers, for which aMw ∼ η0 ∼ τd ∼ Mw3.4. Thus, TCS may provide a simple scheme not only for studying slow dynamics but also for characterizing the concentration dependence of viscosity in suspensions near the jamming/soft glass transition. Flow curves for the suspensions studied are shown in Figures 11a,b (Figure S8 in Supporting Information for Na- and Kneutralized counterparts). The results show that a zero-shearrate viscosity, η0, is accessible even in systems for which x ≈ 1, i.e., for jammed particle suspensions. Taken together with the structural features inferred from the SAXS results, the Newtonian fluid flow behavior indicates that charged and neutral particles may form metastable clusters and stay in their equilibrium states, as is also evidenced by aging measurements, where insignificant variation of dynamic moduli after ∼14 h is observed (Figure S4 in Supporting Information). The flow curves in Figures 11a,b are also seen to exhibit power-law behavior in the shear thinning regime, η ∼ γ̇−m; the values of m are plotted against ϕc in Figure 11c. It is commonly reported that m = 1 is characteristic of jammed particles. By comparing Figures 7c, 8, and 11c, we find that the critical particle loadings at which jamming occurs are basically independent of the flow kinetics exploited (i.e., frequency, strain, and rate sweeps). Additionally, we find that the values of ηr increase with ϕc only up to a critical value, whereafter they become nearly ϕcindependent, as seen in Figure 11d. The mean relaxation times, τ, for the jammed particle suspensions can be estimated using the relation, τη0 = η0/G∞ ′, and are given in Figure 11e, where the relaxation times are found to be virtually independent of ϕc (i.e., τη0 ≈ 5 × 103 s). The τη0 is, however, about an order of magnitude smaller than the inverse critical shear rate beyond which shear thinning commences; presumably as a result of cage relaxation, i.e., τcage ≈ 105 s (Figures 11a,b). Thus, we conjecture that for our particles the τη0 estimated from the viscosity is reflective of the orientation relaxation of anchored ligands, at times shorter than the cage escape time. At longer time scales (t ≫ τη0), relaxed ligands may lubricate overlapping particles facilitating relaxation. This conclusion that τη0 corresponds to the ligand relaxation time rather than the cage relaxation time can be supported by further evidence: (a) A terminal relaxation time, τterm, can be estimated from the inverse of the crossover frequency at which G′ and G″ intersects (Figure 10a) and is found to be much larger than the ligand relaxation time. (b) In creep experiments, the total accumulated strain applied to the jammed suspensions to attain quasi-steady simple shear flow is noted to be substantially smaller than the yield strain (Figure S9 in Supporting Information). (c) As schematically illustrated in Figure 9d, the independence of the ligand relaxation time on concentration stems from a constant interparticle distance (Figure 3c), as a result of the incompressibility of dense tethered ligands. Finally, it is worth mentioning that for the jammed suspensions, due to its very small yield strain (γy ≤ 5%), “steady-state” shear flow cannot be reached but “quasisteady” shear flow (i.e., γ < γy in the creep experiments). Unless

Figure 10. (a) Time−composition superposition (TCS): master curve obtained at ϕc = 0.175 using TCS for neutral particles in mPEG at a reference temperature T = 70 °C. (b) aϕc and ηr vs ϕc; line gives the Krieger−Dougherty equation, ηr = (1 − ϕc/ϕm)−[η]ϕm, with ϕm = 0.163 and [η] = 33.7.

simultaneously showing that cage escape is remarkably slow, but that it can be captured in real-time experiments in systems of progressively reduced concentration, which allow the cage constraint around particles to be slowly dismantled in space. Similar to entangled polymers, the shift factors, aϕc, for the suspensions aresurprisinglyfound to overlay quite well with their reduced viscosities, ηr, except at the two highest particle concentrations where jamming occurs (Figure 10b). The Krieger−Dougherty equation, ηr = (1 − ϕc/ϕm)−[η]ϕm, is a popular choice for fitting viscosity,59 where the densest possible packing, ϕm, and the intrinsic viscosity (or Einstein coefficient), [η], are considered to be fitting parameters. The reasonable fit apparent in Figure 10b yields ϕm = 0.163 and [η] = 33.7; for hard spheres, ϕm = 0.63 and [η] = 2.5. As the overlap volume fraction, ϕ*, is inversely proportional to [η], we know that ϕ* is 13.5 times smaller in our particle suspension than in a hard sphere suspension. Accordingly, the brush height, H, is estimated to be 1.3a (i.e., ∼5 nm) and falls in between the radius of gyration (Rg ≈ 1.3 nm) and the contour length (L ≈ 7.8 nm) of the fully stretched out neutral ligand. The result Rg < H < L has been reported previously from the dielectric loss amplitude for PI-tethered SiO2 nanoparticles;19 its observation here provides additional support for the applicability of the TCS principle for studying long-time dynamics of jammed suspensions. 4489


Macromolecules

Article

Figure 11. Flow curves for (a) uncharged and (b) Li-neutralized charged particles in mPEG (inset: creep experiment). (c) Power-law exponents, m, vs ϕc. (d) Reduced viscosity, ηr, vs ϕc; line gives the Krieger−Dougherty equation, ηr = (1 − ϕc/ϕm)−[η]ϕm, with (ϕm, [η]) = (0.163, 33) and (0.108, 75) for neutral and Li-neutralized charged particle suspensions, respectively. (e) Mean relaxation time, τη0, determined from zero-shear-rate viscosity.

by dispersing hairy nanoparticles cofunctionalized with oligomers and tethered alkali metal sulfonate salts. Measurements are reported in mPEG (εmPEG ≈ 14) and propylene carbonate PC (εPC ≈ 65) to explore the role of solvent dielectric properties on suspension structure, ion transport, and rheology. The structure factors deduced from SAXS indicate that tethered lithium salts (−SO3−Li+) can effectively impart electrostatic stabilization that counteracts vdW ligand−ligand attraction, which destabilized the suspensions. We also find that despite its modest dielectric constant, high ion dissociation fractions (∼0.1) can be achieved in mPEG, presumably due to a combination of factors: (i) its specific ion-solvating power toward lithium ions and (ii) better solvency for neutral ligands.

the applied deformation rate is substantially smaller than the relaxation rate of cage escape (i.e., γ̇ ≪ τcage−1 ≈ 10−7 s−1), we are only able to measure the stress response mainly from tethered ligands. This may explain why η0 obtained from the flow curve (η0 ≈ 1010 Pa·s) is different from that from the relation η0 = lim G″/ωω→0 (≈ 1013 Pa·s) using the TCS plot. ω→ 0

We therefore conclude that the relaxation time estimated from the viscosity may be associated with the orientation relaxation of tethered chains and is noted to be much smaller than the time required for cage escape in our soft, jammed suspensions.

4. CONCLUSIONS We have systematically investigated the structure, ion-pair dissociation, and rheology for suspension electrolytes created 4490


Macromolecules

Article

Through rheological analysis, we further find that nanoparticle salts based on Li+ counterions exhibit longer-range interactions than those based on uncharged particles as well as charged particles with Na+ or K+ counterions. Remarkably, we find that irrespective of the counterion size or particle charge, at high particle loadings the suspensions manifest nearly the same high-frequency elastic modulus. Tellingly, the magnitude of the high-frequency modulus for suspensions based on these particleseither charged or neutralis of comparable magnitude to the plateau modulus for entangled polymers of similar chemistry as the tethered ligands. This characteristic is thought to stem from the confinement/compression of the tethered ligand brush carried by each particle in nanoscale channels produced by the hard walls of neighboring particles. It is further found that a time−composition superposition (TCS) procedure can be used to create a dynamic map of the suspension dynamics that span many decades in time. Similarities in the scaling relations for the shift factor, viscosity, and terminal relaxation time deduced from TCS imply that selfsimilar dynamics exist in the suspensions as the nanoparticle content is changed. These observations altogether appear to suggest that oligomeric molecules with specific functionalities anchored to nanoparticles can increase suspension stability, impart physical properties of interest, and facilitate broad understanding of the roles individual constituents in hybrid materials play in observed behaviors.

■

(6) Shahar, C.; Zbaida, D.; Rapoport, L.; Cohen, H.; Bendikov, T.; Tannous, J.; Dassenoy, F.; Tenne, R. Langmuir 2009, 26, 4409−4414. (7) Warren, S. C.; Messina, L. C.; Slaughter, L. S.; Kamperman, M.; Zhou, Q.; Gruner, S. M.; DiSalvo, F. J.; Wiesner, U. Science 2008, 320, 1748−1752. (8) Tikhomirov, G.; Hoogland, S.; Lee, P. E.; Fischer, A.; Sargent, E. H.; Kelley, S. O. Nat. Nanotechnol. 2011, 6, 485−490. (9) Mewis, J.; Wagner, N. J. Colloidal Suspension Rheology; Cambridge University Press: New York, 2012. (10) Kim, S. Y.; Zukoski, C. F. Macromolecules 2013, 46, 6634−6643. (11) Kumar, S. K.; Jouault, N.; Benicewicz, B.; Neely, T. Macromolecules 2013, 46, 3199−3214. (12) Krishnamurthy, L.-n.; Weigert, E. C.; Wagner, N. J.; Boris, D. C. J. Colloid Interface Sci. 2004, 280, 264−275. (13) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: New York, 1989. (14) Fritz, G.; Schädler, V.; Willenbacher, N.; Wagner, N. J. Langmuir 2002, 18, 6381−6390. (15) Fernandes, N. J.; Wallin, T. J.; Vaia, R. A.; Koerner, H.; Giannelis, E. P. Chem. Mater. 2013, 26, 84−96. (16) Rodriguez, R.; Herrera, R.; Archer, L. A.; Giannelis, E. P. Adv. Mater. 2008, 20, 4353−4358. (17) Agarwal, P.; Qi, H.; Archer, L. A. Nano Lett. 2010, 10, 111−115. (18) Schaefer, J. L.; Yanga, D. A.; Archer, L. A. Chem. Mater. 2013, 25, 834−839. (19) Agarwal, P.; Kim, S. A.; Archer, L. A. Phys. Rev. Lett. 2012, 109, 258301. (20) Kim, S. A.; Archer, L. A. Macromolecules 2014, 47, 687−694. (21) Croce, F.; Appetecchi, G. B.; Persi, L.; Scrosati, B. Nature 1998, 394, 456−458. (22) Sadoway, D. R.; Mayes, A. M. MRS Bull. 2002, 27, 590−596. (23) Wright, P. V. MRS Bull. 2002, 27, 597−602. (24) Tikekar, M. D.; Archer, L. A.; Koch, D. L. J. Electrochem. Soc. 2014, 161, A847−A855. (25) Klein, R. J.; Zhang, S.; Dou, S.; Jones, B. H.; Colby, R. H.; Runt, J. J. Chem. Phys. 2006, 124, 144903. (26) Klein, R. J.; Welna, D. T.; Weikel, A. L.; Allcock, H. R.; Runt, J. Macromolecules 2007, 40, 3990−3995. (27) Bronstein, L. M.; Karlinsey, R. L.; Stein, B.; Yi, Z.; Carini, J.; Zwanziger, J. W. Chem. Mater. 2006, 18, 708−715. (28) Tierney, N. K.; Register, R. A. Macromolecules 2003, 36, 1170− 1177. (29) Kreuer, K.-D.; Wohlfarth, A.; de Araujo, C. C.; Fuchs, A.; Maier, J. ChemPhysChem 2011, 12, 2558−2560. (30) Zhang, H.; Zhang, X.; Shiue, E.; Fedkiw, P. S. J. Power Sources 2008, 177, 561−565. (31) Doi, M. Soft Matter Physics; Oxford University Press: New York, 2013. (32) Xu, K. Chem. Rev. 2004, 104, 4303−4418. (33) Bergmann, A.; Fritz, G.; Glatter, O. J. Appl. Crystallogr. 2000, 33, 1212−1216. (34) Srivastava, S.; Shin, J. H.; Archer, L. A. Soft Matter 2012, 8, 4097−4108. (35) Roe, R.-J. Methods of X-ray and Neutron Scattering in Polymer Science; Oxford University Press: New York, 2000. (36) Pedersen, J. S. Adv. Colloid Interface Sci. 1997, 70, 171−210. (37) Kohlbrecher, J.; Buitenhuis, J.; Meier, G.; Lettinga, M. P. J. Chem. Phys. 2006, 125, 044715. (38) Zhang, Q.; Archer, L. A. Langmuir 2002, 18, 10435−10442. (39) Zhang, Q.; Archer, L. A. Macromolecules 2004, 37, 1928−1936. (40) Pontoni, D.; Finet, S.; Narayanan, T.; Rennie, A. R. J. Chem. Phys. 2003, 119, 6157−6165. (41) Liu, Y.; Chen, W.-R.; Chen, S.-H. J. Chem. Phys. 2005, 122, 044507. (42) Larson, R. G. The Structure and Rheology of Complex Fluids; Oxford University Press: New York, 1999. (43) Eisenberg, A.; Kim, J.-S. Introduction to Ionomers; WileyInterscience: New York, 1998.

ASSOCIATED CONTENT

S Supporting Information *

Figures S1−S9; Tables S1 and S2. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (L.A.A.). Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Science Foundation, Award DMR-1006323, and is based on work supported as part of the Energy Materials Center at Cornell, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award DESC0001086. The work made use of the electrochemical characterization facilities of the KAUST-CU Center for Energy and Sustainability, which is supported by the King Abdullah University of Science and Technology (KAUST) through Award KUS-C1-018-02. Electron microscopy facilities at the Cornell Center for Materials Research (CCMR), an NSF supported MRSEC through Grant DMR-1120296, were also used for the study.

■

REFERENCES

(1) Sperling, R. A.; Parak, W. J. Philos. Trans. R. Soc., A 2010, 368, 1333−1383. (2) Kumar, S. K.; Krishnamoorti, R. Annu. Rev. Chem. Biomol. Eng. 2010, 1, 37−58. (3) Villaluenga, I.; Bogle, X.; Greenbaum, S.; Gil de Muro, I.; Rojo, T.; Armand, M. J. Mater. Chem. A 2013, 1, 8348−8352. (4) Srivastava, S.; Schaefer, J. L.; Yang, Z.; Tu, Z.; Archer, L. A. Adv. Mater. 2014, 26, 201−234. (5) Kim, D.; Archer, L. A. Langmuir 2011, 27, 3083−3094. 4491


Macromolecules

Article

(44) Wang, W.; Liu, W.; Tudryn, G. J.; Colby, R. H.; Winey, K. I. Macromolecules 2010, 43, 4223−4229. (45) Wang, J.-H. H.; Colby, R. H. Soft Matter 2013, 9, 10275−10286. (46) Wang, Y.; Sun, C.-N.; Fan, F.; Sangoro, J. R.; Berman, M. B.; Greenbaum, S. G.; Zawodzinski, T. A.; Sokolov, A. P. Phys. Rev. E 2013, 87, 042308. (47) Sollich, P.; Lequeux, F.; Hébraud, P.; Cates, M. E. Phys. Rev. Lett. 1997, 78, 2020−2023. (48) Sollich, P. Phys. Rev. E 1998, 58, 738−759. (49) Hyun, K.; Wilhelm, M.; Klein, C. O.; Cho, K. S.; Nam, J. G.; Ahn, K. H.; Lee, S. J.; Ewoldt, R. H.; McKinley, G. H. Prog. Polym. Sci. 2011, 36, 1697−1753. (50) Buscall, R.; Goodwin, J. W.; Hawkins, M. W.; Ottewill, R. H. J. Chem. Soc., Faraday Trans. 1 1982, 78, 2889−2899. (51) Buscall, R. J. Chem. Soc., Faraday Trans. 1991, 87, 1365−1370. (52) Zwanzig, R.; Mountain, R. D. J. Chem. Phys. 1965, 43, 4464− 4471. (53) Fetters, L. J.; Lohse, D. J.; Richter, D.; Witten, T. A.; Zirkel, A. Macromolecules 1994, 27, 4639−4647. (54) Rubinstein, M.; Colby, R. H. Polymer Physics; Oxford University Press: New York, 2003. (55) Kim, D.; Srivastava, S.; Narayanan, S.; Archer, L. A. Soft Matter 2012, 8, 10813−10818. (56) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Oxford University Press: New York, 1986. (57) Onogi, S.; Masuda, T.; Kitagawa, K. Macromolecules 1970, 3, 109−116. (58) de Gennes, P. G. J. Chem. Phys. 1971, 55, 572−579. (59) Krieger, I. M.; Dougherty, T. J. Trans. Soc. Rheol. 1959, 3, 137− 152.

4492


Structure, Ion Transport, and Rheology of Nanoparticle Salts

Recommend Documents