Tuning friction and slip at solid-nanoparticle suspension interfaces by electric fields

We report an experimental Quartz Crystal Microbalance (QCM) study of tuning interfacial friction and slip lengths for aqueous suspensions of TiO2 and Al2O3 nanoparticles on planar platinum surfaces by external electric fields. Data were analyzed within theoretical frameworks that incorporate slippage at the QCM surface electrode or alternatively at the surface of adsorbed particles, yielding values for the slip lengths between 0 and 30 nm. Measurements were performed for negatively charged TiO2 and positively charged Al2O3 nanoparticles in both the absence and presence of external electric fields. Without the field the slip lengths inferred for the TiO2 suspensions were higher than those for the Al2O3 suspensions, a result that was consistent with contact angle measurements also performed on the samples. Attraction and retraction of particles perpendicular to the surface by means of an externally applied field resulted in increased and decreased interfacial friction levels and slip lengths. The variation was observed to be non-monotonic, with a profile attributed to the physical properties of interstitial water layers present between the nanoparticles and the platinum substrate.

were obtained from US Research Nanomaterials (stock numbers US7071 and US7030; Houston, TX 77084, USA). These stock solutions were further dispersed in deionized water to obtain the desired concentrations. Measurements were conducted within 48 h of preparing the suspensions. No nanoparticle aggregation was observed during this period. Some sedimentation was, however, detected for suspensions left overnight that could be reversed by stirring and sonication. The suspensions were therefore stirred and sonicated for 10-15 min immediately before each experimental measurement, and all measurements were completed within 60 min of this procedure.
The values of the physical properties of the suspensions and nanoparticles employed in this study are listed in Table 1. The viscosity is estimated by Einstein's equation 38 where η 0 is the viscosity in the absence of nanoparticles and η nf is the viscosity of a suspension with volume fraction concentration ϕ of nanoparticles. Surface tension values for the suspensions were obtained from ref. 39 . The total surface charge per particle q p was estimated using the approach described in ref. 40 . At concentrations of 0.67 wt% the particle densities in the TiO 2 and Al 2 O 3 suspensions were respectively 1.2 × 10 20 m −3 and 4.7 × 10 19 m −3 , and the average particle-to-particle distances were respectively 4.05 × 10 −7 m and 5.54 × 10 −7 m. The average mass of the particles were respectively 1.42 × 10 −16 g and 5.59 × 10 −17 g and the mass per unit area of monolayers of the NP attached in close-packed lattice would respectively be ρ 2 = 1.02 × 10 −5 g/cm 2 and ρ 2 = 7.17 × 10 −6 g/cm 2 .  The QCM crystals (Fil-Tech Inc., Boston, MA) were 5 MHz AT-cut (Temperature compensated transverse shear mode type A) quartz, 1" in diameter with liquid-facing Pt surface electrodes that were ½" in diameter and rear-facing electrodes of ¼" in diameter. The Pt electrodes were deposited atop Ti adhesive layers on overtone-polished surfaces. A QCM's sensitivity zone is characterized by the shear-wave penetration depth into the liquid given by δ = (2η/ωρ) 1/2 . For the crystals employed here the penetrations depths for all fluids are close to 244 nm 41 . Methods. QCM data were recorded with a QCM100 system (Stanford Research Systems, Sunnyvale, CA, USA) employing a Teflon sample holder that exposed one side of the QCM to the surrounding liquid 42 . QCM resonant frequency f and conductance voltage V c are the measured output signals. The "motional resistance", or effective additional electrical resistance to the circuit δR upon immersion of a QCM crystal in a liquid is directly proportional to shifts in the oscillator's inverse quality factor δ(Q −1 ) with a proportionality factor of the order of ~10 −6 , as described in detail in ref. 29 . Shifts in frequency and inverse quality factor Q −1 respectively reflect the mass of the material dragged along with the oscillatory motion and the frictional forces impeding the QCM's motion. For exposure of one oscillating electrode of the QCM to mass loading and/or a surrounding fluid they are related to the acoustic impedance Z R X = − i acting on the electrode as 43 : where ρ q = 2.648 g cm −3 and μ q = 2.947 × 10 11 g cm −1 s −2 are respectively the density and the shear modulus of quartz. Other parameters commonly employed in the literature to represent the system dissipation are the unitless damping factor D f , the unitless dissipation D, and the half bandwidth at half maximum Γ that has units of Hz. These parameters are mutually related as δ δ Γ Changes in f and V c . were recorded for QCM crystals mounted in sample holders under ambient conditions and then immersed in DI water. TiO 2 or Al 2 O 3 nanoparticles from the stock suspensions were added next while continuing to record changes in f and V c . Changes in the conductance voltage were converted to those in motional resistance according to the relation = − − R 10 75 42 . Data were recorded for nanoparticle concentrations ranging from 0 to 1 wt% in equal intervals of 1/6 wt % first without any external fields (i.e., zero field conditions), and next in constant (both attractive and repulsive) or slowly varying electric fields at fixed nanoparticle concentrations of 0.67 wt%. For the latter experiments a second identical QCM mounted in the identical Teflon holder was positioned within the suspension at a distance of 1.5 cm to serve as a grounded counter electrode (Fig. 1). This arrangement allowed the two electrode surfaces to be kept parallel to each other and facilitated uniformity of the electric field in the region between two electrodes. The arrangement was selected for its convenience. A suitably shaped platinum counter electrode could also have been utilized. A bias voltage was then applied to the sensing electrode while maintaining the counter electrode at ground. The applied potential of ±1.5 V (peak or constant) produced an electric field of ±100 N/C in the region between the electrodes. Measurements were carried out at least 5 times each for the case of static electric fields and for at least 5 cycles for the slowly alternating electric field.
Contact angle measurements were performed in air on the QCM Pt electrodes via a drop shape analysis method 44 . In this method, the contact angle θ is defined as tan(θ/2) = h/d, where h and d are respectively the height and the diameter of sessile droplets deposited onto the surface of interest. AFM measurements were recorded to characterize rms surface roughness levels σ(L) as a function of the lateral scan size L, generating values for the self-affine roughness exponent and the lateral correlation lengths 29 . theoretical Analysis Approaches QcM data analysis. QCM data were analyzed using available theories that considered several models for film and/or bulk phases in contact with the oscillating electrode under slip and non-slip boundary conditions (Fig. 2) 27 . These idealized limiting cases reveal scenarios for starting conditions that could be used for more detailed theoretical modeling. Intermediate cases, for example systems falling between Fig. 2c,e, would require more extensive computational methods, as analytic solutions have not been reported in the literature. Figure 2 depicts QCM motion with velocity amplitude V q immersed in suspensions (a) along with various slip conditions displaying vectors that represent the difference in the velocity amplitudes of the fluid with the QCM electrode (b-f). A no-slip boundary condition corresponds to V − V q = 0 at the electrode surface. Slippage is characterized by a non-zero value of V(t) -V(t) q at the surface electrode and a slip length λ s , which is distance below the surface that the velocity extrapolates to zero (Fig. 2c).
For a no-slip boundary condition and in the thin film limit, the acoustic impedance Z R X = − i 2 2 2 of an adsorbed film on a QCM electrode with mass per unit area ρ 2 is purely imaginary: 45

R X
Slippage of the film in response to the oscillatory motion of the electrode is treated mathematically by introducing an interfacial friction coefficient η 2 defined by F f /A = −η 2 (V − V q ) and related a characteristic slip time as τ = ρ 2 /η 2 46 . The real and imaginary components then become: 46 www.nature.com/scientificreports www.nature.com/scientificreports/ which reduce to the Eq. (2) expressions for the no-slip boundary condition by setting τ = 0.
For a QCM immersed in a bulk fluid with no film adsorption and no-slip boundary conditions, V = V q , and the real and imaginary components of the acoustic impedance are equal and related to the fluid properties as: 32 where ρ and η are respectively the bulk fluid density and dynamic viscosity. Boundary slip is incorporated into the model by inserting the velocity of the monolayer adjacent to the surface obtained from the friction law The acoustic impedance is obtained by solving the system equations of motion via Eq. (5) and after some rearrangement of terms it can be expressed as: 27,33 where a is the ratio of the slip length λ s to the penetration depth δ of the oscillations in a liquid. For fluids with uniform density the parameter a is related to η 2 as λ s = η/η 2 . Other parameters commonly employed in the literature to represent the boundary slip of a liquid are the slip parameter s = 1/η 2 , which has units of cm 2 s/g, and the parameter χ τ = 1/ , which has units of s −1 . QCM data were then compared to "bulk suspension", "electrolyte", and "adsorbed film" models for the acoustic impedance in the idealized limiting cases discussed above. The "bulk suspension" model has no film phase and predicts Eq. (4) or Eq. (6) respectively for no-slip and slip conditions. The "electrolyte" model incorporates both a film and bulk phase, but allows the slip to occur only at the upper boundary of the film with the fluid phase (  In the case of a no-slip boundary condition at the film-fluid boundary, a = 0 and the response reduces to the sum of the separate non-slipping film and bulk contributions, Eqs. (2) and (4).
The "adsorbed film" model allows for the slippage at the boundary of the film with the QCM electrode. Mistura et al. considered the case of a dense thin film in a contact with a low density vapor phase and obtain expressions for the combined slipping film plus the vapor phases 34 . While this model was not originally developed for the case of immersion in a liquid, it is potentially applicable to the case of nanoparticles forming a dense compact phase that slips at the boundary with the substrate. The total system impedance in this model includes a contribution from the frictional energy dissipation at the interface parameterized by η 2 . In the limit where the adsorbed film thickness is much less than the penetration depth, d ≪ δ, and the bulk acoustic impedance π ηρ f of the surrounding fluid is far less than that of the film phase, the acoustic impedance components are described by: The mass per unit area of the film in Eq. (8) is written as ρ 2 = ρ film d, where d is the thickness and ρ film is the three dimensional density of the film phase. The measured values of the acoustic impedance can be used to solve for ωρ film d, which can be substituted into the left-hand side of Eq. (8) to obtain the interfacial viscosity η 2 and the slip length λ s = η/η 2 46,47 . For the analysis employed here, we set R R X X ≡ ≡ ; v f luid v f luid and then explore whether any physically realistic solutions could be obtained.

Alternate analysis approaches for determining slip lengths and/or apparent slip lengths.
The results of the QCM data analyses were compared with two independent approaches for estimating slip lengths. The first relates the contact angle θ of a liquid atop a substrate to its predicted slip length 27 , and the second estimates the magnitude of the slip length that would be inferred from apparent slippage associated with reduced fluid density levels near the boundary 27,[48][49][50] .
For the contact angle method, we utilized the parameters for water (σ = 0.276 nm, r = 0.385 nm) and also the relation reported by Ellis et al.: 48 where the term αA is on the order of σ 2 , the molecular diameter squared, r is the center to center distance between molecules in the sheared liquid and γ lv is the liquid vapor surface tension 27,48,49 . This approach, first suggested by Tolstoi and later extended by Blake 50 , is based on an observation that mobility of the liquid molecules adjacent to a solid surface should be linked to the equilibrium contact angle. In particular, the theory suggests that liquid molecules immediately adjacent to a surface will have the same mobility as the bulk for the case of complete wetting (θ = 0°) and mobility greater than the bulk for the case of partial wetting (θ > 0°). The enhanced mobility associated with non-zero contact angle in turn would give rise to a non-zero slip length. The method provides a means to independently and qualitatively rank the magnitude of the slip lengths in the systems studied, but has been found to consistently underestimate slip lengths [48][49][50] . Slip lengths obtained from analysis of the QCM data recorded here are therefore expected to have the same rank ordering, but different magnitudes from those obtained from Eq. (9). The response of a QCM to the true slip is identical to that for the systems with density variations within the penetration depth. For a thin liquid film whose three-dimensional density is ρ film and whose three-dimensional viscosity is η film , the slip length appears to be: 27 www.nature.com/scientificreports www.nature.com/scientificreports/ The values for the saturated AFM roughness is σ rms = 1.8 nm, with a lateral correlation length of 110 nm. This places the sample in the "slight" roughness regime categorized as σ rms /δ≪1. The response of the QCM is therefore theoretically predicted to be very close to that given by Eq. (4) when immersed in water 27 .

QCM response in zero, static, and varying external electric fields. Figures 4 and 5 display QCM
frequency and resistance data for concentrations ranging from 0 to 1 wt% under zero external field conditions (Fig. 4a,b), for attractive and repulsive external fields applied to 0.67 wt% suspensions of TiO 2 (Fig. 4c,d) and Al 2 O 3 (Fig. 4e,f), and for slowly varying electric fields applied to the same suspensions (Fig. 5). The zero-field data were recorded upon immersing the electrode in water -the conditions under which platinum surfaces develop a negative charge 51 ; therefore, the interfacial properties for the oppositely charged suspensions are expected to vary significantly from each other. The QCM data sets are indeed very different for the oppositely charged NP's without an external electric field present, and are also quite responsive to the presence of the field. Overall, the nanoparticle systems behave as anticipated for attractive and repulsive fields: the QCM parameters trend in opposite directions under attractive and repulsive fields (Fig. 4c-f). Time constants displayed in Fig. 4(c-f) are obtained from fitting the data to an exponent approaching a limiting value. The motion of nanoparticles towards the surface is slower than the motion away from the surface. This is consistent with slowing of the Brownian motion of nanoparticles near surfaces 52,53 .
It is worthwhile to note here that the QCM data are not described by variations in concentration of the surrounding fluid under the no-slip conditions, Eq. (4). In this scenario the zero-field resistance (frequency) data (Fig. 4a,b) would monotonically increase (decrease) with the nanoparticle concentration. The resistance data for TiO 2 actually go in the opposite direction when the particles are added, thus, clearly violating Eq. (4). Variations in concentration also fail to explain the alternating field data (Fig. 5), which displays distinct features associated with approach and retraction of the particles. The results as a whole are attributable to a complex interface, where changes in suspension density, particle uptake, interfacial slippage and friction levels, as well as changes in the slip plane location and the electric double layer configuration collectively contribute to the QCM response.
We begin the data analysis by comparing the zero field response to attractive and repulsive electric field conditions for 0.67 wt% suspensions, the nanoparticle concentration producing the greatest reduction in frictional drag forces for the TiO 2 suspension. The dashed lines in Fig. 4(a,b) mark the frequency and the resistance response at 0.67 wt%, and fall close to (−15 Hz, +2.5 Ω) and (−5 Hz, −2.75 Ω) respectively for Al 2 O 3 and TiO 2 . The average of multiple runs, along with the error bars, are depicted in Fig. 4(c-f), with the zero field average coinciding with the values marked in Fig. 4(a,b). The average values for an immersion in pure water were −727 Hz and +329 Ω. Frequency and resistance shifts for the suspensions relative to air under zero field conditions therefore respectively totaled (−742 Hz, 331.5 Ω) and (−732 Hz, 326.25 Ω) for Al 2 O 3 and TiO 2 . Values for the suspensions exposed to constant attractive and repulsive fields after 100 s are also listed in Table 2. The corresponding real and imaginary components of the acoustic impedance, along with other relevant parameters are also listed in Table 2. Equations (1), (2) and (4) were used to obtain the proportionality constant between R exp (Ω) and  exp (g cm −2 s −1 ), employing the experimentally measured value of  for water obtained from the frequency shift data and Eq. (1). The measured frequency shift of −727 Hz for pure water was 6.3% higher than the theoretical value for a planar surface, −684 Hz (Eqs. 1 and 4, using the values in Table 1), an increase that is commonly reported in the literature and attributed to the surface roughness 29 . There is, however, no unified theory predicting the overall system response to roughness for both  fluid and  fluid . We therefore assumed a universal 6.3% www.nature.com/scientificreports www.nature.com/scientificreports/ increase for the Table 2 values for both, i.e.  fluid =  fluid πρη ≡ .
⋅ f 1 063 s s , where ρ s and η s are respectively the density and viscosity of the fluid or suspension.
The QCM data presented in Table 2 reveal several interesting features. One notable observation is the similarity of the QCM response for TiO 2 suspensions in an attractive field with Al 2 O 3 data under zero field conditions (light grey columns). Data for the Al 2 O 3 in repulsive fields are similarly comparable to TiO 2 data recorded under zero field conditions (dark grey columns). Since the Pt surface at normal pH would have a negative charge without any applied external field 51 , the qualitative implication is that the repulsive field lifts Al 2 O 3 particles from the electrode surface reaching a condition that is very similar to the TiO 2 particles in the absence of such a field. Directing the TiO 2 particles towards the surface by an electric field meanwhile results in a QCM response similar to that of Al 2 O 3 in the absence of the field. Additional features in the Fig. 5 data might then be attributed to the physical properties of interstitial water layers present between the nanoparticles and the Pt substrate, or a lack thereof if the double layer does not remain intact.
The data reported in Table 2 were next compared to the limiting models of Fig. 2 by substituting the experimental parameters into Eqs. 4, 6, 7 or 8. Some of the models were found to be in clear contradiction with the experimental parameters while others allowed for the equations to be solved with reasonable physical parameters. Table 3 summarizes the results of substituting the Table 2 data in cases where the data did not contradict the models. All Table 2 data, with the exception of Al 2 O 3 system in attractive field conditions, contradicted the Eq. 4 non-slipping bulk suspension model (Fig. 2b), which requires = fluid f luid X R . For the Al 2 O 3 system in attractive fields the model predicts an unrealistic increase in the suspension concentration (~8 wt%). All of the Table 2 data contradicted the slipping bulk suspension model (Fig. 2c). Two systems, Al 2 O 3 in the zero field and TiO 2 in an attractive field, yielded realistic solutions to the no-slip film and no-slip bulk suspension model (Fig. 2d). All other Table 2 data contradicted the model. Three systems, TiO 2 in the zero field and both Al 2 O 3 and TiO 2 in attractive fields, yielded realistic solutions to Eq. 7 with a >0, the no-slip film with slipping bulk suspension model (Fig. 2e). Equation 8 corresponding to the slipping adsorbed film model could also be solved for the three systems ( Fig. 2f) but only one of these, the Al 2 O 3 suspension under attractive field conditions, yielded physically realistic parameters. Two others systems, Al 2 O 3 in the zero field and TiO 2 in an attractive field, yielded solutions corresponding to only trace levels of the film uptake. These were ruled out as physically unrealistic since the model assumes a dense film is present.
Slip lengths for the three systems that matched the slipping film-fluid boundary model are in the range of 20-22 nm. This is greater than the slip length that would arise from a density variation artifact associated with the pure water near the surface ( Table 3,      www.nature.com/scientificreports www.nature.com/scientificreports/ order 10 −10 s, which is also physically realistic as the typical values range from 10 −12 to 10 −8 s 46 . A slip length of 30 nm was obtained for the Al 2 O 3 under the attractive field conditions employing the "adsorbed film" model that attributes all increases in resistance to a slippage at the film-substrate boundary. One possible interpretation of the results obtained with these models is that an interstitial layer of water is present between the TiO 2 particles and the substrate but not the Al 2 O 3 layers under zero field conditions because the negative charge on both the NP and the substrate would act to stabilize the double layer. As the TiO 2 (Al 2 O 3 ) particles are directed into (or retracted from) the surface, water might be squeezed out (or reformed), resulting in additional non-monotonic features in the data associated with the physical properties of the confined molecules 54,[56][57][58][59] . No-slip boundary conditions and/or high interfacial friction levels would then be linked to the absence of the interstitial water layer(s). This interpretation is consistent with fact that some fine features is observed in the data for the TiO 2 suspensions for both retraction and approach, but only for the Al 2 O 3 suspensions in retraction. The features in the data are not readily attributable to electrolysis, as no bubbles were observed either visually or in a form of the characteristic QCM response in water or the nanoparticle suspensions themselves. It is known, however, that the voltage levels corresponding to the electrolysis are closely linked to the thickness of the oxide layers on the platinum surface and significantly increase the voltage threshold at which the steady-state electrolysis first occurs 60,61 . It is also well known that water molecules can reorient and also solidify under the influence of external fields. The latter phenomenon is expected to have a great impact on the interfacial friction 58 .
In summary, although the origins of the physical phenomena reported here have yet to be fully illuminated, the results are reminiscent of the variations in friction observed in SFA as molecular layers are squeezed out from an interface 54 . Numerical simulations of nanodiamond systems with positive and negative charge have revealed the presence of the interstitial water layers 56 , but simulations of the present systems under tunable external electric fields remain to be reported. Such computational studies would be also highly valuable for further development of this method. The present results nonetheless demonstrate the sensitivity of the QCM technique to identify molecular repositioning near interfaces and suggest that the charged nanoparticles can be actively repositioned to explore interfacial properties and nanoscale interactions in geometries inaccessible to optical and micromechanical probes.

Data availability
The datasets generated during and/or analyzed during the current study are available at https://doi.org/10.7910/ DVN/YRTIM1.  Table 3. Solutions to the various models' equations employing the data reported in Table 2.