Electrostatic double layer interaction at the surface of rough cluster

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Electrostatic double layer interaction at the surface of rough cluster-assembled films: the case of nanostructured zirconia Francesca Borghi, Bianca Scaparra, Costanza Paternoster, Paolo Milani, and Alessandro Podestà Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b01387 • Publication Date (Web): 03 Aug 2018 Downloaded from http://pubs.acs.org on August 5, 2018

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Electrostatic double layer interaction at the surface of rough cluster-assembled films: the case of nanostructured zirconia

Francesca Borghi, Bianca Scaparra, Costanza Paternoster, Paolo Milani, Alessandro Podestà*

CIMaINa and Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy. * E-mail: [email protected]

Abstract We investigated the influence of the nanoscale surface morphology on the electrostatic double layer at corrugated surfaces in aqueous electrolytes. To this purpose, we have produced cluster-assembled nanostructured zirconium dioxide (ns-ZrOx, x ≈ 2) films with controlled morphological properties by supersonic cluster beam deposition (SCBD), and measured the double layer interaction using atomic force microscopy with colloidal probes. SCBD allowed tuning the characteristic widths of the corrugated interface (the rms roughness, the correlation length) across a wide range of values, matching the width of the electrostatic double-layer (the Debye length), and the typical size of nano-colloids (proteins, enzymes, and catalytic nanoparticles). To accurately characterize the surface charge density in the high-roughness regime, we have developed a two-exponential model of the electrostatic force that explicitly includes roughness, and better accounts for the roughnessinduced amplification of the interaction. We were then able to observe a marked reduction of the isoelectric point of ns-ZrOx surfaces of increasing roughness. This result is in good agreement with our previous observations on cluster-assembled nanostructured titania films, and demonstrates that the phenomenon is not limited to a specific material, but more generally depends on peculiar nanoscale morphological effects, related to the competition of the characteristic lengths of the system.

Keywords: DLVO interactions; IsoElectric Point (IEP); Atomic Force Microscopy (AFM); surface roughness; colloidal probes; Supersonic Cluster Beam Deposition (SCBD); cluster-assembled nanostructured materials; Zirconia.

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1. Introduction Systems based on the assembling of micro and nanoparticles of transition metal oxides are widely

used

for

applications

in

the

fields

of

biomedicine1,

catalysis2,3,

energy

production/conversion4,5, and environmental remediation2,6. Applications in turn rely on physical phenomena, which depend upon the surface charge density,7 and the resulting electrostatic double layer,8–10 in the aqueous medium. The reference theory to understand surface interactions between colloidal particles, and between particles and surfaces, immersed in a liquid11 was developed by Derjaguin and Landau12, Verwey and Overbeek13 (the DLVO theory). An important parameter to describe the electrostatic phenomena is the IsoElectric Point (IEP), which corresponds to the pH value at which the net charge of the compact part of the double layer is zero. At IEP, the ζ potential of the surface, which is responsible of the electrokinetic properties of particles in solutions14, is zero, provided we identify the boundary between the compact and the diffuse layers with the slipping plane14. The standard DLVO theory assumes ideally smooth surfaces. In practice, real surfaces are always rough to some extent. In particular, the surfaces of engineered nanoporous, nanostructured materials used for photoelectrochemical and biomedical devices, are characterized by surface roughness and porosity at the nanoscale. Consequently, the properties of the double layer predicted for ideally smooth surfaces by the theory8–10,15–17 do not in general provide the most accurate estimate of the real surface forces18. In particular, when two interacting surfaces are closer than a distance comparable or smaller than the typical screening length of the electrolytic solution (the Debye length, determined by the ionic strength of the solution), the overlap of the diffused layers determines complex charge regulation phenomena16. When regulation phenomena occur, the surface charge or the surface potential become a function of the separation distance between the two interacting surfaces, or equivalently of the degree of overlap of the corresponding double layers. This configuration brings the solution of the electrostatic problem far from the boundaries of the simplified linearized theory19,20, which strictly holds only at low surface potential, large distances, and low ionic strength8–10. A comprehensive review of the efforts to address the effects of the surface roughness on DLVO and other interfacial interactions has been recently presented by Thormann21. A crude approach to include surface roughness into the DLVO equations consists in assuming that there exist an “average plane of charges”, which produces the electrostatic double layer interaction, which is shifted backwards with respect to the points of first contact between the surface and an incoming probe18,22–28. In these works, the distance axis is typically translated by a distance equal to the rms surface roughness. In a recent work29, the presence of surface roughness not only suggested 2 ACS Paragon Plus Environment

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that the onset of the electric double layer interaction should be shifted as mentioned, but it also entails the inclusion of an additional exponential repulsive interaction taking into account the steric hindrance of the compressed asperities upon contact. In other works, simplified geometrical representation of the surface roughness have been used, such as mild periodic undulations (in the weak roughness regime, i.e. undulation amplitude small compared to the wavelength of the undulation)30–32, or collections of regions with different convexity and curvature33–37. In these works, it is recognized that the ratios of characteristic lengths of the system (Debye length, surface roughness, asperity separation…) influence the relative strength of different contributions to the interaction energy (van der Waals, electrostatic, Lewis acid-base acidity…). Duval et al. have also used a simplified representation of the surface morphology, but they have explicitly included in their calculations the charging mechanisms of the surfaces, developing a theoretical/numerical framework, which takes into account morphological and chemical heterogeneities19. A method for taking the surface roughness Rq explicitly into account is to adopt a statistical representation of the rough surface through the height distribution function, which is Gaussian, to a very good approximation. The advantage of a similar approach is that the height distribution can be characterized accurately with nanometer resolution by atomic force microscopy (AFM), together with the rms roughness and other morphological parameters. Following this approach, Daikhin et al. have considered different height distributions in the framework of the Poisson-Boltzmann equations (also outside the linear approximation) for the calculation of the double layer capacitance (a measurable electrochemical observable)38–40. This strategy was also recently exploited by Parsons et al.22, who presented a general approach to derive the energy function for the electrostatic component of the double layer interaction, assuming a single leading exponentially decaying contribution. The total energy was obtained as a Gaussian weighted average of electrostatic contributions from locally smooth regions, located at different distances D from the mean plane. Notably, the authors calculated the measurable electrostatic force in the limit of large distances and/or small roughness, and relatively low ionic strength: D/Rq >> Rq/λD, where λD is the Debye screening length. They showed that this model provides better results than the model for smooth surfaces in the case of rough titania (global Rq was 9.6 nm, although the local Rq was significantly smaller),22 and hafnia surfaces (Rq > 1 nm)23, respectively. So far, the experimental studies reported in the literature have focused primarily on the small roughness regime, while it would be interesting to explore also the high-roughness case, when Rq and λD are similar, and comparable to the typical dimensions of interacting particles (proteins, enzymes, and catalytic nanoparticles).


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The explicit consideration of the effect of surface roughness prompts for novel data acquisition and processing procedures. The statistical averaging approach to obtain an analytical model for the electrostatic interaction energy (and force) has considered so far only the leading exponential term proportional to exp(-D/λD), despite a two exponentials model would provide a more accurate description of the force when the condition D >> λD is not satisfied10,41,42. Several other aspects must be considered: i)

The points of first contact of the hundreds of force curves that are acquired across the rough surface are all different (they represent a subset of the right tail of the Gaussian distribution of all surface heights, i.e. the apices of the highest asperities). The distance axes of the force curves must therefore be aligned carefully in order to obtain an accurate averaged force curve with the maximal range of available distances for the fit.

ii)

If the AFM is used to characterize the double layer interaction, the hydrodynamic force due to the squeezing and confinement of the electrolyte in the probe surface gap, as well as within the rough interface, must be taken into account.

iii)

Since the probe-surface distance cannot be smaller than the rms roughness Rq (the protruding asperities keep the probe from penetrating deeply within the rough interface), and due to the fact in the vicinity of the isoelectric point (IEP) the net surface charge density tends to zero, the electrostatic interactions to be measured are significantly weaker than on smooth surfaces. It follows that the curve alignment and averaging, and the accurate estimation of the van der Waals and hydrodynamic contributions, are critical for the accurate characterization of the double layer interaction at rough surfaces. The scarcity of systematic experimental studies on double layer interactions at corrugated

interfaces limits the understanding of double layer phenomena in real systems. This is to a significant extent also a consequence of the difficulty of preparing and characterizing, at the nanoscale, interfaces with controlled morphology (in terms of rms roughness, average slope, correlation length, specific area, etc…). It is thus of primary importance to develop fabrication strategies for the accurate and controlled design of nanoscale morphological properties. Despite their high efficiency and low cost, conventional methods for the synthesis of nanostructured materials, like sol-gel, spray pyrolysis, micro-wave plasma processes, and sputtering43–45, allow a poor control over the resulting structure and topography, and on their reproducibility. Recently, we reported that nanostructured films can be fabricated by assembling neutral clusters from the gas phase onto suitable substrates; this bottom-up approach is called supersonic cluster beam deposition (SCBD).46 Clusters are produced by condensation in the gas phase and accelerated by a supersonic expansion46. This approach produces nanostructured thin 4 ACS Paragon Plus Environment

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ﬁlms with a nanoscale topography, whose root-mean-square roughness can be accurately controlled and varied in a reproducible manner47–50. The extremely precise control over nanoscale topography makes SCBD the ideal tool for supporting the systematic study of the influence of surface nanoscale morphology of nanostructured films on the electrostatic double layer. Here we present the results of a study of the influence of the nanoscale surface morphology on the electrostatic double layer at corrugated surfaces in aqueous electrolytes. We have produced cluster-assembled nanostructured zirconium dioxide (ns-ZrOx, x ≈ 2) films with controlled morphological properties by SCBD, and measured the double layer interaction using atomic force microscopy equipped with custom colloidal probes51. Cluster-assembled zirconia surfaces has been recently demonstrated as a very reach playground to study the influence of nanostructure on proteins and cells52–55. AFM is the technique of choice for sensing weak electrostatic forces in solution; when surface roughness effects could be neglected, the values of diffuse layer potentials measured by AFM and electrokinetic techniques have been found to be in good agreement18,56. It should be noted that the AFM probe senses the diffuse part of the electrostatic double 25,57

layer

. Therefore, by AFM it is possible to characterize the surface charge density projected on

the Outer Helmholtz Plane, at the onset of the diffuse layer, which is equal, by virtue of the electroneutrality principle, to the net surface charge density σS. The latter, in turn, is the sum of two contributions: the charge density due to the surface groups, and the charge density due to the specifically adsorbed ions from the electrolyte28. SCBD allowed varying the morphological properties of ns-ZrOx films across a wide range of values. We present a novel protocol for the investigation of double layer interactions by AFM, which is based on: i) the topographic correction of force curves, to account for the different contact points due to the surface roughness; ii) the assessment of the hydrodynamic force acting on the colloidal probe in the roughness-induced slip boundary conditions; iii) a two-exponentials model of the electrostatic force that explicitly includes roughness and extends the work of Parsons et al.22. We were thus able to observe a marked reduction of the isoelectric point of ns-ZrOx surfaces on increasingly rough surfaces. This result is in good agreement with our previous observations on cluster-assembled nanostructured titania films28, and demonstrates that the phenomenon is not limited to a specific material, but more generally depends on peculiar nanoscale morphological effects related to the competition of the characteristic lengths of the system.

2. Experimental section 2.1. Synthesis of ZrOx Nanostructured Thin Films by Supersonic Cluster Beam Deposition 5 ACS Paragon Plus Environment

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A Supersonic Cluster Beam Deposition (SCBD) apparatus equipped with a Pulsed Microplasma Cluster Source (PMCS) has been used to deposit nanostructured zirconia (ns-ZrOx) films by assembling clusters produced in gas phase58–62. The PMCS operation principle is based on the ablation of a target rod by an inert gas plasma jet (argon in this case), ignited by a pulsed electric discharge. The ablated species thermalize with argon and condense to form clusters61,62. The mixture of clusters and inert gas is then extracted into the vacuum through a nozzle to form a seeded supersonic beam60,63, which is collected on a set of round borosilicate glass coverslips (diameter 15 mm, thickness 0.13–0.17 mm) intercepting the beam in a deposition chamber. The clusters kinetic energy is low enough to avoid fragmentation and hence a nanostructured film is grown, leading to a highly porous, high-specific area material64,65. We deposited three different ns-ZrOx batches (samples SMP1–3). We have also produced a smooth zirconia film, deposited by means of an electron-beam evaporator (Kenosistec), to be used as reference sample (flat ZrOx). Immediately prior to AFM characterization (morphological and electrostatic) ns-ZrOx films have been thermally annealed for 2 hours at 100 °C in ambient air, in order to remove the organic contaminants, and to recover fully hydroxylated and hydrophilic surfaces. These mild annealing treatments do not modify the surface morphology of ns-ZrOx films, nor they affect the partially cubic phase present in the nanostructured film48. Borosilicate glass coverslips were used as substrates for the calibration of the colloidal probe surface charge density σT at different pH, in order to realize, together with the borosilicate glass colloidal probe, symmetrical systems for the DLVO measurements. To maximize the symmetry of the system, the glass substrates underwent a thermal annealing at 600 °C before use, i.e. at a temperature close to the temperature (780 °C) at which the colloidal probes are produced (it was not possible to anneal the thin glass coverslips at higher temperatures due to their tendency to bend significantly). 2.2. Characterization of ns-ZrOx films Morphology The surface morphology of ns-ZrOx films was characterized in air using a Multimode AFM equipped with a Nanoscope IV controller (BRUKER). The AFM was operated in Tapping Mode, using rigid silicon cantilevers mounting single crystal silicon tips with nominal radius 5–10 nm and resonance frequency in the range 250–350 kHz. Several 2 μm x 1 μm images were acquired on each sample with scan rate of 1 Hz and 2048x512 points. The images were flattened by line-by-line subtraction of first and second order polynomials in order to remove artifacts due to sample tilt and scanner bow.


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From flattened AFM images root-mean-square surface roughness Rq, the vertical width of the surface, was calculated as the standard deviation of surface heights (for relatively rough surface, the rms roughness is not strongly influenced by the finite tip radius). The specific area r was calculated as the ratio of surface area to the projected area (the specific area calculated from the AFM images is always underestimated because of the inability of the AFM tip to detect overhangs and because of its finite size). The correlation length ξ (the horizontal width of the surface) represents a statistical measure of the average peak-to-valley lateral dimension of the largest morphological surface features, and was calculated as the decay length of the height correlation function47. The film thickness was estimated from AFM images acquired across a sharp step produced masking the substrate before the deposition. 2.3. Force measurements by AFM We have used a Bioscope Catalyst AFM (Bruker) to measure the electrostatic force between custom colloidal probes (with radius R in the range 5500-8500 nm) and the sample surface in 0.1mM NaCl solutions at 20 °C with pH between 3 and 6. The NaCl electrolyte represents an appropriate choice, because at low concentrations ([NaCl] 0 the slip condition is obtained. Since the cantilever deflects more as the probe gets closer to the surface,

turns out to be a

function of the probe-surface distance D; this function has been evaluated explicitly, thanks to the fact that deflection and piezo displacements (from the z-sensor) can be acquired also as a function of time. We have characterized the hydrodynamic interaction, determining the parameter rs for each sample, in order to subtract this contribution from the total force when fitting the DLVO interaction. In order to characterize the hydrodynamic interaction between the colloidal AFM probe and the nsZrOx film surfaces, we have acquired force curves at room temperature in [NaCl] = 0.1mM electrolyte, at pH values close to the IEP values, in order to minimize the electrostatic interactions. Furthermore, in order to completely remove any residual electrostatic interaction, we have subtracted to each force curve recorded at an average approaching velocity of 8 µm/s a reference force curve acquired at a negligible velocity.

2.6. Electrostatic double layer force between rough surfaces Electrostatic and van der Waals forces in aqueous solution are considered additive in the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. In particular, the interaction between a sphere and a flat surface is approximated by the following equation10,42,41:

=

!"#$% &' &

(!)* )+ ,

%

%$-

-

+ /)!* + )!+ 0,

!%

%$2 #

3 1 − 4% !

(2)

where D is the sphere-plane first contact distance, R and σT are the radius and surface charge density of the sphere (the AFM colloidal probe), and σS is the surface charge density of the smooth (idealized) sample surface; ε is the dielectric constant of the medium (the aqueous electrolyte, we assume ε = 78.54), ε0 is the vacuum permittivity, λD is the Debye length, i.e. the screening length of the electrolyte, and AH in the van der Waals term is the Hamaker constant.


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The superscript cc in Eq. 2 indicates the constant-charge boundary condition for the electrostatic contributions. The constant charge condition is typically well satisfied on insulating surfaces. We have tested that this is actually the case for another transition-metal oxide material, titanium dioxide28. Another peculiarity of Eq. 2 is the presence of a second exponential term in the electrostatic contribution. This term, which decays over a length ½λD, is typically neglected in the analysis of the experimental data, although its explicit consideration provides more accurate fit of the doublelayer force in the small and intermediate distance regimes. When the effect of surface roughness is explicitly considered (the roughness-induced amplification of the electrostatic force, see below), the second exponential term turns out to be important. We have extended the model by Parsons et al.22 by including in it the second exponential term that appears in Eq. 2. We have not averaged the van der Waals term, which is typically negligible compared to the electrostatic term at distances from the mean plane larger than Rq (a theoretical treatment of the effect of roughness on dispersive forces can be found in Mazur et al.77). The topographic correction of the distance axes of the FCs however regards also the van der Waals term. In order to calculate the electrostatic DLVO interaction between a micrometer spherical tip and a rough surface, it is convenient to consider the distance d between the tip apex and the mean plane of the surface (Figure 2), instead of the distance D between the tip apex and the local first point of contact with the surface asperities. The mean plane is located at z = z0. If z’ is the distance from the mean plane of the point on the surface facing the AFM probe, then the distance of the probe from the surface is d - z’.

Figure 2. Schematic representation of the surface profile of a ns-ZrOx film and the approaching colloidal probe. The dotted line at z0 = 0 indicates the mean plane location, while the dot-dashed line indicates the quota of a generic point along the profile at distance z’ from the mean plane. The distance d between the sphere and the mean plane of the rough surface is also shown.


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The height distribution of nanostructured surfaces produced by SCBD is Gaussian to a very good approximation, with standard deviation equal to the root-mean square roughness Rq. In terms of the distance from the mean plane z’, p(z’)dz’ represents the fraction of points with height between z’ and z’+dz’, with: :)

8(9 =

;

√!"#=

,

-

! 9> !#=!

If the electrostatic force is described by (@ ) = A B

-

C DE

(3)

, the total electrostatic force is

obtained by integrating the contributions of all sets of points with different distances from the probe (this is equivalent to averaging with Gaussian weights the contributions from different distances):22 H

FG (H) = I-L J(H − 9: )8(9: )H9′ = M U

By substituting z’’= z/Rq + (

FG (H) = M

;

√!"

,

#=! !$! %

-

,

]"#$% )* )+

Setting A =

&' &

H

%$VE

L

I #=! (

%$L ; I , √!"#= '

#=! 9! N !O PHQ9NH! $% - !#=!

dz dz

(4)

– d)/Rq in (4), we obtain:

-H)/#=

,

-

/9>> 0 !

!

;

H9′′ = M ! ,

; #= ! ( ) !

%$,

-

H

%$XYJZ [

#=! -H

%$#=

\

(5)

, the electrostatic force between a smooth sphere and a rough surface, as a

function of the distance d from the mean plane, in the limit d≫$% , is:

FG (H) =

!"#$% )* )+ &' &

,

; #= ! ( ) !

%$H

%$-

,

#=! -H

%$XYJZ [

#=

\

(6)

If the second exponential contribution to f(d) equal to B B aU

same derivation with z’’= z/Rq + (

,b (H) =

!"#$% )* )+ &' &

,

; #= ! ( ) !

%$,

-

H

%$VE

– d)/Rq and B =

XYJZ [

#=! -H

%$#=

\+

-

C DE

is considered10,42,41, following the

!"#$% ()* ! )+ ! ) &' &

"#$% ()* ! )+ ! ) &' &

,

!(

#= ! )

%$, we obtain: -

,

!H

%$XYJZ [

!#=! -H

%$#=

\

(7)

Eq. 6 is compatible with the general energy function reported by Parsons et al.19 (Eq. S13 of their work).19 In the limit d/Rq >> Rq/λD Eq. 6 becomes Eq. 18 in Parsons et al.22. For Rq = 0, Eq. 7 turns into the electrostatic contribution of Eq. 2. In Figure 3 we show several FCs simulated using Eq. 7 for ideally flat and very rough (Rq=26nm) zirconia surfaces interacting with a borosilicate glass colloidal probe (R=5000 nm), by keeping two exponential terms, or only one.


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Figure 3. Theoretical electrostatic force curves simulated using Eq. 7, for Rq = 0 and Rq = 26 nm, respectively. The distance d of the sphere from the mean plane is reported on the abscissae. Other values of

the parameters used are: [NaCl] = 0.1mM, = 30nm, surface charge density σT =σS = 0.001 C m-2, R =

5000 nm. The vertical dotted line represents d = .

Figure 3 provides some insights on the effect of surface roughness on the double layer electrostatic interactions. The distance d is measured from the mean plane of the surface, therefore when comparing a smooth and a rough surface, the smooth surface is supposed to be located in the mean plane of the corrugated one. First, by comparing the smooth single-exponential curve to the smooth double-exponential curve, we see that the second exponential introduces significant deviations at distances as large as twice the Debye length. Since the best range for data fitting on smooth surfaces is typically between one and two Debye lengths, neglecting this term, as it is common habit, may lead to incorrect estimation of both and σS. Concerning the effect of

roughness, we see that at the same distance d, the electrostatic force turns out to be exponentially amplified on the rough surface, irrespective to the number of exponential terms considered. Comparing Eq. 2 to Eq. 7, the amplification factor is proportional in the case of a single exponential to ½(Rq/λD)2, and in the case of two exponentials to 2(Rq/λD)2; these factors depend on the ratio of the widths of the interface (Rq), and of the double layer screening (λD). The roughnessinduced amplification can be qualitatively understood by considering that in the case of the rough surface, given a distance d from the mean plane, a significant fraction of surface points, those protruding outwards, are actually closer to the probe than d, and their contribution to the total force is weighted exponentially more than that of the point around the mean plane, or below it.


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Figure 3 also shows that the second exponential term in Eq. 7 is important, especially in the presence of surface roughness. The reason is that the argument of the second exponential amplification factor is four times larger than that of the first factor, therefore in the presence of roughness, the relative importance of the second exponential term increases, despite the distances are larger. We have considered from each FC only the points up to the first contact. We have therefore not taken into account the elastic deformation of asperities, reported by Parsons and Valtiner in cases where the protruding surface asperities are heavily loaded by the probe22,29. In any case, the observed force necessary to mechanically break thorough the nanostructured zirconia interface with a probe with a 10 µm diameter, is about 100nN; at the employed forces, and at the considered distances, we are confident that deformation is negligible. Since we acquired a large number of FCs in different locations, we could sample a wide range of distances, and in particular we could probe also the inner part of the rough interface, at distances comparable to Rq. The Van der Waals force in Eq. 2 depends on the Hamaker constant AH of the surface/medium/probe system78. We have assumed for our experimental setup AH = 0.8 10-20 J for glass coverslip79–82 and AH = 1.25 10-20 J for ns-ZrO2 (versus borosilicate glass probe in aqueous solution)82.

Figure 4. A representative average force curve collected on a smooth glass borosilicate substrate in 0.1mM NaCl electrolyte, at pH = 6. The different contributions to the total force, determined as described in the Methods section, are shown. The distance d of the sphere from the mean plane is reported on the abscissae.


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Figure 4 shows a representative average force curve measured on a smooth borosilicate glass substrate, with roughness well below 1 nm (comparable to the typical roughness of the borosilicate glass colloidal probe). The total force FTOT in Figure 4 is composed of different terms: FTOT(d) = Fhydro(d-Rq)+ FvdW (d)+ Fel(d)

(8)

where the terms in the right end side of Eq. 8 have been introduced and discussed above. As mentioned, the van der Waals force is not averaged across the rough interface, although, as in the case of the electrostatic force, the onset of its interaction is shifted inwards by a distance Rq. The parameters for determining the hydrodynamic contribution are obtained according to the procedure described in the Methods, and are kept fixed in Eq. 8. For this reason we have fitted only the Fel(d) interaction (Eq. 7) to the data obtained by subtracting the Fhydro(d-Rq) and FvdW(d) contributions from the total experimental FCs. The fit provides the values of the charge density σS of flat ZrOx and ns-ZrOx surfaces, and of the Debye length λD. The radius R and the charge density

σT of the probe are previously calibrated, and kept fixed. The net surface charge density of the borosilicate glass probe (as a function of pH) is characterized by recording force curve in aqueous electrolyte, against a borosilicate glass smooth substrate, in order to realize a symmetrical system where σS ≈ σT. Eventually, once the surface charge density σS for the different samples have been obtained at all pH values, the pHIEP values are calculated by extrapolation between the closest experimental data with opposite signs28. The accurate determination of the van der Waals and hydrodynamic contributions according to the methodology described above is very important when fitting FCs acquired at pH values close to the IEP, when the electrostatic force is negligible. This is particularly true on rough surfaces, because in this case the available distance range is limited and shifted away from the surface, where the electrostatic interaction is exponentially weaker.

3. Results & Discussion 3.1. Surface Morphology of ns-ZrOx Films Figure 5 is a collage of representative AFM three-dimensional maps of the flat ZrOx and nsZrOx samples. As the deposition time increases, the thickness of the nanostructured film increases, as well as the vertical and lateral widths of the surface, represented by the rms roughness (the standard deviation of height values) and the lateral correlation length (the average peak to valley distance). 17 ACS Paragon Plus Environment

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Figure 5. Merging of three-dimensional views of AFM topographic maps of flat and nanostructured ZrOx samples (rms roughness increases from left to right). The vertical scale is 100 nm.

The morphology of ns-ZrOx films deposited by SCBD consists of a fine raster of nanometersized grains, with high specific-area depending on the film thickness47,59,64 and porosity of about 80%, at the nano and sub-nanometer scale. Incident clusters organize at the surface in high aspect ratio structures (the surface asperities, or grains), with diameter ranging from few nm up to hundreds of nanometer in the thickest films. In Table 1 the morphological parameters calculated from AFM topographic maps, and the ratios of the characteristic lengths of the interface, are reported. SAMPLE Flat SMP1 SMP2 SMP3

Thickness h [nm] // 55 ± 1 120 ± 2 282 ± 4

Roughness Rq [nm] 0.3 ± 0,1 18.4 ± 0.4 20.3 ± 0.3 26.4 ± 0.5

Specific Area r 1.01 ± 0.01 1.65 ± 0.05 1.76 ± 0.08 2.03 ± 0.05

Correlation length ξ [nm] 11 ± 1 39 ± 2 40 ± 2 42 ± 2

Slope 2Rq/ξ 0.05 0.94 1 1.17

(

γmeso

= 30 gh) 0.07 0.36 0.36 0.34

(

γmeso

= 9.5 gh) 0.022 0.091 0.092 0.088

Table 1. Morphological parameters of flat ZrOx and ns-ZrOx samples measured by AFM. The ratios of the characteristic lengths of the interface are also reported. γ is the mesoscopic fraction of the diffuse layer volume in each pore where overlap between adjacent diffuse electrostatic layers occurs, according to the model presented in Ref.28 Since the Debye length decreases at the lowest pH, we have calculated the value of γ for the two limit values of λD.

An advantage of SCBD is that the morphological parameters can be varied in a broad range by simply changing the thickness of the deposited films (i.e. the deposition time), without changing their surface chemistry, thanks to the existence of quantitative laws for the evolution of the interface widths, which takes place in the ballistic deposition regime48–50. In particular, we produced rough interfaces with values of both the rms roughness and the correlation length comparable with the Debye length of the electrolyte used in force spectroscopy experiments (Table 1), as well as to the 18 ACS Paragon Plus Environment

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typical size of nano-colloids (proteins, enzymes, and catalytic nanoparticles) interacting with surfaces in natural and engineered systems. By matching the surface lengths to the Debye length, it is possible to reproduce situation that is likely commonly occurring in natural corrugated interfaces: the diffuse electrostatic layers of adjacent portion of the same surface can overlap, intimately perturbing each other. Intuitively, the degree of (self) overlap increases when the slope of the pore walls, and the ratios of the vertical and lateral pore dimensions to the Debye length are large. We have recently tried to model the degree of self-overlap of the diffuse layer and found that it can be characterized by an adimensional parameter γ, representing the fraction of the total volume occupied by the two layers in the pore where overlap between the adjacent diffuse layers occurs.28. In general, the degree of overlap inside each pore increases when the two ratios 2∆┴/∆ ǁ (the slope of the pore walls, ∆┴ and ∆ǁ being the vertical and lateral half dimensions), and λD/∆ǁ increase. We can calculate a mesoscopic self-overlap factor γmeso by taking ∆┴ = Rq and ∆ ǁ = ξ, therefore considering the average surface slope 2Rq/ξ, and the ratio λD/ξ. The result is reported in the last column of Table 1. The degree of mesoscopic double layer self-overlap of nanostructured surfaces produced by SCBD is remarkable (about 40%). One should keep in mind, however, that γmeso represents only a lower limit for the local self-overlap factor. The local values of γ can be very large, if not completely saturated, because of the high aspect ratio of the smallest morphological units and the nanometer size of the smallest pores. Moreover, cluster-assembled nanostructured films are three-dimensional structures consisting of nano- and sub-nanometer sized pores, which can be fully permeated by the electrolyte, and therefore can host a fully self-overlapping and strongly regulated double-layer structure. This inner double layer structure is linked to the double layer of the external interface of the nanostructured film.

3.2. The evolution of surface charge density of ns-ZrOx surfaces Figure 6 a-d shows the electrostatic force curves measured at different pH on the flat ZrOx sample, and on the ns-ZrOx thin films. In order to interpret the trend observed in Figure 6, one has to consider that the systems are not symmetric. The pre-calibrated IEP of the colloidal glass probe lies between pH 3.5 and 3; this results agree with those reported also in Ref.28. For high values of pH, the nanostructured surfaces and the probe are both negatively charged and so their interaction is repulsive. Lowering the pH, the first IEP of the system (that of zirconia) is approached, therefore the value of the positive product of surface charge densities decreases, and becomes null at the pHIEP. Further lowering the pH, the charge density of nanostructured zirconia changes sign, and the interaction becomes attractive. The product of surface 19 ACS Paragon Plus Environment

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charge densities remains negative until the second IEP of the system (that of the probe) is reached (pHIEP-probe = 3.2). The charge density product is again null at pH = pHIEP-probe, then the interaction becomes repulsive again. Thanks to the pre-calibration of the surface charge vs pH curve of the AFM probe, we can accurately estimate the effective surface charge density σS of the zirconia surfaces. The trends of the measured nanostructured surface charge densities are shown in Figure 7a. The absolute value of the surface charge density of the evaporated flat zirconia sample is lower than the values measured on rough samples for all pH values. This result can be attributed to the different morphological properties of the flat and nanostructured surfaces, and to the analysis procedure. The increase of the charge density on rough surfaces is partially due to the increased specific area: the AFM probe sees more charge per unit projected area. The model does not account explicitly for the local specific area, or equivalently, it assumes that the rough surface is locally flat, like in the LEGO-like discrete model reported by Duval.19 Furthermore, the value of the surface charge density extracted by the fit of the electrostatic part of the force curves is strongly affected by the final rigid shift of +Rq of the distance axis (the last step of the topographic correction procedure described in this work), which exponentially amplifies the value of σS. The pHIEP values of the zirconia surfaces have been estimated from the data shown in Figure 7a by linearly extrapolating the pH values at which the surface charge density becomes zero, and reported in Figure 7b. We point out here that the accurate determination of the values of surface charge density is not critical for the assessment of the pHIEP, since the pHIEP is assessed based on the change of the sign of the charge, and this occurrence can be unambiguously determined in the force curves. Therefore, the above mentioned mechanisms that could affect the absolute values of

σS are not expected to reduce the accuracy of the estimation of the pHIEPs. The approximate linear extrapolation of pH values across the charge reversal condition provides the value of the pHIEP with satisfactory accuracy (as confirmed by the propagated errors in Figure 7b, and the larger difference between adjacent pHIEP values). In conclusion, we think that the identification of the pHIEP is rather accurate, and only to a minor extent it is affected by errors in the determination of the absolute values of the surface charge density.


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Figure 6. Average Fel curves acquired on (a) flat ZrOx, and (b-d) ns-ZrOx films with increasing surface roughness; for different pH values in [NaCl] = 0.1mM. The distance d of the sphere from the mean plane is reported on the abscissae.

The IEP of the flat zirconia surface is at about pH =5.1, in good agreement with the value reported in the literature obtained by AFM measurements74, and by other characterization techniques7,75,83. In the case of the roughest ns-ZrOx sample, the IEP is around pH = 3.5, and therefore the charges have always the same sign, except close to the pHIEPs, which are similar. We observe a shift of the IEP towards lower pH values (from 5.1 to 3.5) as the surface roughness increases (Figure 7b), approaching the value of the reference flat zirconia sample. This is a quite unexpected result, since the IEP is a surface property that usually depends on the local density (and nature) of surface active sites; this fact rules out the possibility that the observed shift of IEP on ns-ZrOx is due to the increase of specific area (i.e. of the available area) on rough samples. This trend was recently observed also on rough cluster-assembled titania surfaces28. The overall trend and the shift of the IEP across the same roughness interval for cluster-assembled titania and zirconia film is comparable (compare Figure 7b to Figure 6 in Ref.28). The differences between the two metal oxides materials could be explained in terms of different chemical and electronic atomic environments, as well as fine morphological differences, such as in the nano- and sub-nanoscale high porosity and overhangs, given that the overall scaling of the morphology is the same47,49,84. These fine differences cannot be detected by AFM due to its finite resolution; nevertheless, evidence of their existence also comes for example from surface morphology-related wettability experiments50,64.


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Figure 7. (a) Surface charge density vs pH and (b) pHIEP of flat ZrOx and ns-ZrOx samples with different rms roughness Rq.

The roughness-related shift of the IEP on two different materials strongly suggests that there are physical determinants underpinning the observed phenomena, which call into play some universal mechanisms related to the effect of nanoscale morphology on the fine structure of the electrostatic double-layer. This assessment required a second independent observation on a system that is chemically different, but possesses the same nanoscale morphology. In order to find reasonable explanations of the observed shift of the IEP towards lower values, we will consider firstly the possibility that the local chemical environment of the active charge-determining surface species can change with sample thickness, i.e. with increasing roughness. We recently showed that the size of nanograins in cluster-assembled zirconia does not evolve when the film thickness increases,48 as well as the overall stoichiometry and phase of nsZrOx surfaces (prevalently cubic at room temperature). Similarly to stoichiometry and crystalline phase, also the presence of chemical surface heterogeneities, distributed in the nanoporous matrix of the material, could in principle determine a change of the IEP with respect to the pristine material85. However, the effects of such chemically different nanoscale domains on IEP should not evolve with 23 ACS Paragon Plus Environment

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thickness nor with roughness, but rather stay constant, since the amounts of these surface domains should be all equally amplified as the specific area increases. We have also recently speculated28 that a strong perturbation of the double layer structure, can be provided by the self-overlap effect described earlier (γmeso in Table 1), because of the rough and porous surface. Because of the ballistic deposition49, characterized by reduced surface diffusion of the incoming clusters, the aspect ratio of the smaller asperities and pores can be very large, despite the average mesoscopic slope of the surface (approximately equal to 2Rq/ξ) remains relatively small. The nanoscale corrugation favors therefore the overlap inside the pores of the diffuse layers generated at the sidewalls, which interact and perturb strongly each other; this effect in turn leads to a modification of the local surface charge distribution and the surface potential, with very intense, and localized, electric fields, and strong gradients of ionic concentration. Duval et al.19 considered the double layer interactions between non-planar surfaces, and in particular highlighted how the specific ionic adsorption and/or the presence of charge-determining ions for the surfaces ensure the adjustment of charges and potentials upon double layer overlap. Within this picture, the rupture of the symmetry of cationic and anionic activities leading to a modification of the adsorption of electrolyte ions cannot be excluded15. Parks86 and Lyklema15 predicted how the IEP of metal oxides or partially oxidized metal surfaces can shift in response to specific adsorption of ions, even in the absence of an applied potential to the surface. The shift of the IEP towards lower pH values described in their works, due to the specific adsorption of ions, could explain our experimental evidence. Moreover, because of the above mentioned distortion of the double-layer structure, there could be a direct impact of the intense surface potential at the pore level on the dissociation constants of the surface groups, and therefore on the IEP87. All these effects would determine, in a morphology-dependent way, a readjustment of the effective charge inside the inner double layer, for a given pH, which is compatible with a change of the IEP. Although none of these effects is likely relevant when two planar, smooth surfaces interact, especially when relatively inert electrolytes are used, the strong morphology-induced local perturbation of the double-layer structure associated to the peculiar nanostructure of clusterassembled titania and zirconia surfaces could determine a much stronger enhancement of the abovementioned effects. Further studies are needed in order to proceed beyond the phenomenological understanding achieved to date, including performing electrokinetic measurements on powders obtained from cluster-assembled thin films deposited by SCBD. In our study, we could observe interesting phenomena since thank to SCBD, we managed to change the roughness and the other surface lengths, so that the interfacial width was comparable to the extension of the diffuse electrostatic layer. 24 ACS Paragon Plus Environment

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4. Conclusions We have carried out a systematic investigation of the effects of surface nanoscale roughness and morphology on the electrostatic double layer interactions. The production of suitable nanostructured templates with independently controlled morphological and chemical properties is crucial for the systematic investigation of interfacial phenomena. The use of SCBD for the production of the nanostructured zirconia films allowed tuning the characteristic lengths of the interface to the width of the electrostatic double layer, with a controlled degree of variability. Concerning the measurement of the interfacial forces and their analysis, our novel strategy was based on: i) The accurate re-alignment of force curves (the topographic correction, based on the contact points map and on the measured surface roughness), so that the origin of the distance axes is set at the surface mean plane. ii) An analytical, double-exponential model of the electrostatic force between a smooth colloidal probe and a rough surface, which extends the model proposed by Parsons et al.22 iii) A fitting procedure aimed at the determination of the surface charge density based on the precalibration of van der Waals and hydrodynamic forces, and on the characterization of the surface charge density (versus pH) and the radius of the probe. We observed a decrease of the IEP of cluster-assembled zirconia film with increasing roughness. This result is in agreement with previous results obtained by our group on cluster-assembled titania films28, using a simpler model of the electrostatic force in the presence of roughness. Our new results further support the hypothesis that the modification of the IEP is a consequence of profound modifications to the structure of the electric double layer induced by morphological effects. In particular, we think that the observed trend of the IEP is related to the increasing importance of nanoscale morphology-induced self-overlap of the local diffuse layers, leading to strong charge regulation effects, local enhancement of surface potential and ionic gradients, and overall deviation from the trends expected for the linearized Poisson-Boltzmann theory. At present, these effects are still poorly understood; our work sets a methodological ground for their systematic investigation. It would be very interesting to investigate further the modifications of the local structure of the electrostatic double layer induced by the peculiar topology of nanostructured surfaces. To this purpose, it is necessary to increase the resolution of the structural and morphological analysis of 25 ACS Paragon Plus Environment

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these interfaces, in order to use this information as input for the numerical integration of the complex equations of the regulated double layer. To this purpose, numerical simulations represent a promising route to produce in silico nanostructured films in the ballistic deposition regime88,89.

Acknowledgment We thank C. Piazzoni and E. Sogne for the deposition of ns-ZrOx films, and G. Malchiodi and F. Mazzorin for support in the AFM experiments.


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Benetti, G.; Caddeo, C.; Melis, C.; Ferrini, G.; Giannetti, C.; Winckelmans, N.; Bals, S.; Van Bael, M. J.; Cavaliere, E.; Gavioli, L.; et al. Bottom-Up Mechanical Nanometrology of Granular Ag Nanoparticles Thin Films. J. Phys. Chem. C 2017, 121 (40), 22434–22441.


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(a) A few contact points (CPs, red marks) from the complete map shown in (b) were superimposed to a representative topographic profile from a high-resolution AFM image of ns-ZrOx surface with Rq∼26 nm. (b) A complete array of 10x10 CPs, separated by 1000 nm, obtained from force curves acquired with a colloidal probe at pH∼6 and [NaCl] = 0.1 mM on the ns-ZrOx film. (c) The electrostatic component of the force curves aligned so that the origin of the distance axis is located in correspondence of the CP, or (d) aligned according to the procedure described in the Methods (the topographic correction), i.e. by re-summing the corrected relative CP map. The average curves are plotted in red color. (e) The average FCs shown in c-d, further translated by applying a +Rq rigid shift, as described in the main text, and fitted by Eq. 7. 160x126mm (300 x 300 DPI)

ACS Paragon Plus Environment

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Schematic representation of the surface profile of a ns-ZrOx film and the approaching colloidal probe. The dotted line indicates the mean plane location, while the dot-dashed line indicates the quota of a generic position along the profile. 85x52mm (300 x 300 DPI)


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Theoretical electrostatic force curves simulated using Eq. 9, for Rq = 0 and Rq = 26 nm, respectively. Other values of the parameters used are: [NaCl] = 0.1mM, λ_D=30nm, surface charge density σT =σS = 0.001 C m-2, R = 5000 nm. The vertical dotted line represents d = λ_D. 85x81mm (300 x 300 DPI)


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A representative average force curve collected on a smooth glass borosilicate substrate in 0.1mM NaCl electrolyte, at pH = 6. The different contributions to the total force, determined as described in the Methods section, are shown. The distance d of the sphere from the mean plane is reported on the abscissae. 154x153mm (300 x 300 DPI)


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Merging of three-dimensional views of AFM topographic maps of flat and nanostructured ZrOx samples (rms roughness increases from left to right). The vertical scale is 100 nm. 177x67mm (300 x 300 DPI)


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Average Fel curves acquired on (a) flat ZrOx, and (b-d) ns-ZrOx films with increasing surface roughness; for different pH values in [NaCl] = 0.1mM. The distance d of the sphere from the mean plane is reported on the abscissae. 66x236mm (300 x 300 DPI)


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(a) Surface charge density vs pH and (b) pH_IEP of flat ZrOx and ns-ZrOx samples with different rms roughness Rq. 67x126mm (300 x 300 DPI)


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TOC graphic 385x277mm (72 x 72 DPI)


Electrostatic double layer interaction at the surface of rough cluster

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