Electrochemical Quartz Crystal Microbalance with Dissipation Real

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EQCM-D Real-Time Hydrodynamic Spectroscopy of Porous Solids in Contact with Liquids Sergey Sigalov, Netanel Shpigel, Mikhael D. Levi, Moshe Feldberg, Leonid Daikhin, and Doron Aurbach Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.6b02684 • Publication Date (Web): 20 Sep 2016 Downloaded from http://pubs.acs.org on September 21, 2016

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Analytical Chemistry

EQCM-D Real-Time Hydrodynamic Spectroscopy of Porous Solids in Contact with Liquids 1

1

*1

1

2

Sergey Sigalov, Netanel Shpigel, Mikhael D. Levi, Moshe Feldberg, Leonid Daikhin, Doron Aurbach

**1

1

Department of Chemistry, Bar-Ilan University, Ramat-Gan 5290002, Israel

2

School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 6997801, Israel

Abstract Using multiharmonic electrochemical quartz crystal microbalance with dissipation (EQCM-D) monitoring, a new method of characterization of porous solids in contact with liquids has been developed. The dynamic gravimetric information on the growing, dissolving, or stationary stored solid deposits is supplemented by their precise in-operando porous structure characterization on a mesoscopic scale. We present a very powerful method of quartz-crystal admittance modeling of hydrodynamic solid-liquid interactions in order to extract the porous structure parameters of solids during their formation in real time, using different deposition modes. The unique hydrodynamic spectroscopic characterization of electrolytic and RF-sputtered solid Cu coatings that we use for our “proof of concept” provides a new strategy for probing various electrochemically active thin and thick solid deposits, thereby offering inexpensive, noninvasive and highly efficient quantitative control over their properties. A broad spectrum of applications of our method is proposed, from various metal electroplating and finishing technologies to deeper insight into dynamic build-up and subsequent development of solid-electrolyte interfaces in the operation of Li-battery electrodes, as well as monitoring hydrodynamic consequences of metal corrosion, and growth of biomass coatings (biofouling) on different solid surfaces in sea water. Keywords: QCM-D, EQCM, lithium ion battery, electrodeposition, Sauerbrey’s mass, hydrodynamic correction, porous interfaces

*1

tel. +972 35317680, e-mail: [email protected] (M.D. Levi) tel. +972 35318317, e-mail: [email protected] (D. Aurbach)

**1

1 ACS Paragon Plus Environment


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Introduction 1

Porous solid deposits play a critical role in natural hydrogeological processes, water-purification 2

3

systems, capacitive deionization of water, metal corrosion

4,5

and growth of biomasses (biofouling) on

6

ship hulls and coastal buildings in contact with sea water. It is also commonly recognized that the mechanical and electrochemical properties of solid electrolyte interphases (SEI) formed on the surface of operating Li-battery electrodes are of key importance for healthy cycling performance.

7,8

Simultaneous

real-time characterization of mass changes related to SEI formation and growth on the surface of battery electrodes accompanied by changes in porous structure and viscoelastic properties remains a challenge in 9

the Li-ion battery and nanoporous carbon supercapacitor fields.

10,11

Dynamic measurements of this kind

are quite important in analytical applications such as electrodeposition of lead films and their dissolution in anodic stripping voltammetric experiments.

12

For generality, the characterization of porous solids based on the hydrodynamic study of liquid flow through the solid was included in the list of IUPAC “Recommendations for the characterization of porous solids”.

13

However, in view of the great difficulty in experimentally determining the required liquid

velocity profiles and finding analytical solutions to their distribution, such a hydrodynamic method was rejected as a practical means of porous solid characterization.

13

A 180-degree appraisal occurs when a stationary fluid flowing through a porous body of complex geometry is replaced by an oscillating movement of liquid (typically in the MHz-frequency range) through a thin porous solid layer rigidly attached to a quartz crystal surface. The major difference between these two alternatives is that in the latter case, the geometric characteristics of the porous solid simultaneously affect two easily accessible experimental quartz-crystal characteristics, namely, frequency and resonancewidth changes (∆F/n and ∆W/n, respectively). This approach was first advanced to describe the effect of the surface roughness of metallic coatings on their quartz-crystal admittance measured in fluid.

14-16

It was

later extended to describe the quartz-crystal admittance of porous supercapacitor and battery electrode coatings in contact with electrolyte solutions.

17-21

A concise description of the problem of fluid movement


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through a uniform solid porous layer and across larger asperities located on the external surface of electrode coatings rigidly attached to quartz-crystal surfaces is presented in the Supporting Information (SI). In our work, we carefully took into account all kinds of exceptionally important contributions to the theory and practice of electrochemical quartz-crystal microbalance (EQCM) technique on the fundamental oscillation frequency.

22-29

We have recently provided evidence that multi-harmonic EQCM with dissipation monitoring (EQCM-D) opens a new avenue for in-situ tracking of the adsorption and intercalation-induced deformations in supercapacitor and battery electrodes, respectively.

21

The fundamental harmonic method abundantly

reported in the literature excludes the overtone-order (n) dependence of the real and imaginary ~

28

components of the complex frequency change, ∆ F /n = ∆F/n + i ∆W/2n . In contrast, a significant advantage of the multi-harmonic measurements is the use of the dependence of complex frequency on n. The penetration depth (also called the decay length) of the transverse wave spreading from the oscillating crystal surface toward the contacting solution depends on the fluid’s viscosity-to-density ratio (η/ρ) and n (Fo, the fundamental frequency is constant for a given quartz crystal), and is given by

21,28,30

1/2

 η  δ =  ,  π nF0 ρ 

(1)

Equation 1 shows that for a given fluid (e.g. selected electrolyte solution) the penetration depth depends on the overtone order, n. The frequency (∆F/n) and resonance width (∆W/n) change with n, and hence with δ, when the quartz crystal coated with a porous solid layer is transferred from air to liquid. This can be regarded as in-situ hydrodynamic spectroscopy of the porous solid layer: the probing spectroscopic parameter is the penetration depth δ, appearing as a mesoscopic (submicron) probing length. Varying 21

the penetration depth, we can easily screen the entire variety of lateral pore sizes in the solid bulk, distinguishing between the trapped and moveable liquid in the narrow and wide pores, respectively. The porous structure parameters of the solid are obtained by fitting the experimental (∆F/n and ∆W/n)



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changes to the appropriate hydrodynamic admittance models, a powerful technique of the in-situ probing of rough/porous solid structures (SI). Inspired by the possibility of using EQCM-D for simultaneous gravimetric and hydrodynamic spectroscopic characterization of porous solid deposits in real time during their formation in a liquid environment, we focus on deriving a hydrodynamic correction to the Sauerbrey equation in a similar way to that used in introducing a viscoelastic correction to the mass effect for soft solid films.

28

The size of the correction

depends crucially on the porous structure parameters of the solid. In order to provide a proof of concept, we selected a simple model system, namely, the electrodeposition and electro-dissolution of thin porous layers of Cu on Au-coated quartz-crystal surfaces. The results obtained constitute the basis for a new strategy for simultaneous gravimetric and porous structure characterization of various practically important solid layers, such as SEI on the surface of Li-battery electrodes, battery anodes.

31

7,8

and conversion-type Li-

It can be also successfully used for hydrodynamic and viscoelastic monitoring of

intercalation-induced changes in specially-designed multilayered anodes for high-power applications,

32

and many other applications. Experimental Section Materials. CuSO4 (ReagentPlus®, ≥99%) and H2SO4 (puriss. p.a., 95-97%) were purchased from SigmaAldrich. The double-distilled water used to prepare a 0.1 M CuSO4 + 0.5 M H2SO4 solution to deposit Cu on an AT-cut Au-coated quartz crystal surface (fundamental frequency 4.95 MHz +/- 50 kHz, 14-mm diameter, 0.33 mm thick) was purchased from Biolin Scientific. The dynamic viscosity and density of the precursor solution for Cu deposition were measured on a clean Au crystal by EQCM-D at 25 °C and found -3

to be 1.12 cP and 1.067 g cm , respectively. Before Cu electrodeposition, the crystal was treated in Piranha solution, rinsed with double-distilled water, dried in a stream of pure N2 and finally subjected to oxygen plasma cleaning. The method of in situ hydrodynamic spectroscopic probing of a rough/porous structure of electrode coatings was described in detail in our recent papers.

17,19-21,33

Frequency and

resonance width changes were obtained for Cu deposits in contact with water and deposition solution (the mass of the coating in air was subtracted from the experimental frequency change in fluid).


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d

th

Instruments. Multiharmonic quartz-crystal measurements (overtone orders from 3 to 13 ) by QCM-D were performed using a Q-Sense E1 module (the entire experimental setup was purchased from Biolin Scientific). For data acquisition we used the QSoft401 software from Biolin Scientific. Electrochemical measurements were combined with QCM-D by means of a potentiostat/galvanostat BioLogic VSP-300, using the EC-Lab software. A leak-free Ag/AgCl (3 M KCl) electrode was used as reference electrode in the electrochemical measurements. For the counter electrodes (CE), a plate of pure Cu foil was used. Electrocrystallized Cu deposits of different porous structures were prepared by both linear potential sweeping and chronoamperometry, as specified in the Results section. Typically, for hydrodynamic characterization, we use deposits 130±10 nm thick (VEECO Dektak 150 profilometer). In addition to the electrocrystallized Cu deposits, we prepared radio frequency (RF)-sputtered Cu films (BESTEC, Germany) over 405 s (90 nm thickness) in order to ensure good uniformity and improved adhesion of the coated layer to the Au surface. AFM and SEM images were obtained using a Nanoscope V, MultiMode instrument (Bruker AXS) and FEI Inspec S instrument (FEI Company), respectively. We verified that the resonance peaks (i.e. the peaks of the quartz crystals conductance) of the RFsputtered and electrolytically-formed non-porous and porous Cu solid films are of similar shape and amplitude when measured with different overtone orders in air, signifying their rigid behavior in air (Figure S1, Supporting Information). No additional spurious modes appear in the energy spectrum of the coated crystals compared to that of the neat crystal. Both types of Cu coatings have almost the same F/ntype dependence on n as that of the neat-crystal testifying constant (i.e. n-independent) frequency change, due to solely “dry” mass loading on the crystals surfaces (Figure S2). Results and Discussion Weighing of Cu deposits in air and liquids: breakdown of the conventional gravimetric approach based on Sauerbrey’s equation At first glance, it may appear strange that for the demonstration of hydrodynamic corrections to the rigid mass loading onto quartz-crystal surfaces we have selected the electrodeposition of Cu, which is the



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recommended method for the calibration of quartz-crystals using Sauerbrey’s equation (Equation 2). The mass changes Δm are supposed to be proportional to the experimental frequency change due to the inertial mass load ΔFmass, rigidly attached to the quartz-crystal surface, and is given by the Sauerbrey’s equation:

(34)

Δm = -C∙ΔFmass/n,

(2)

where C is the mass sensitivity constant. The mass obtained from Equation (2) is often called Sauerbrey’s mass. The manual specifying calibration procedure of quartz crystals using the frequency change of the crystals during the electrodeposition of Cu does not take into account the fact that Sauerbrey’s equation adequately describes the mass change of the solid when it is completely non-porous and has a flat external surface. Figs. S3a and S3b mathematically and schematically demonstrate the following 35

fundamental statement (first proved during the early history of the EQCM method ): a thin, non-porous solid layer (with a flat external surface) rigidly attached to a quartz crystal surface has the same Sauerbrey mass when measured in air and in fluid. Complete discussion of this important issue is presented in the SI. When the solid layer on the crystal surface is intrinsically porous but still has a flat external surface (such as a solid, which is later called a homogeneous porous layer), the related frequency and resonance width changes for the response in liquid are expressed by Eqs. S1 and S2. If the morphology of the porous layer is complicated by the presence of micron-sized spherical bumps (asperities), the hydrodynamic response is expressed by Eqs. S3 and S4 for ∆F/n and ∆W/n, respectively. Assuming that Figure

represents an authentic electrolytically-deposited porous metallic layer, the

hydrodynamic correction to the mass effect can be roughly estimated (even without explicit use of hydrodynamic models) as follows: The mass of the deposited metal is translated into the related frequency change by the combination of the Faraday law and Sauerbrey’s equation: (ΔF/n)solid = -(ΔQ Mi)/ziCF, where Mi and zi are the molecular mass and charge of the electrolytic ion, ΔQ is the amount of charge passed during the deposition, and F is the Faraday constant.

11,12,18,19,36-39

The difference (ΔF/n) -

(ΔF/n)solid related to the total frequency change (ΔF/n) approximately quantifies the hydrodynamic


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correction to the mass effect. However, if the electrode particles contain narrow pores trapping fluid in their interior, the related contribution to the frequency change (ΔF/n)trapped should be assessed by explicit hydrodynamic modeling. Note that once (ΔF/n) - (ΔF/n)solid is assigned to the behavior of moveable liquid in relatively wide pores of the solid, a finite change in the resonance width ΔW/n = = ∆Whydrod/n should be observed as well. The following algorithm is used throughout the paper, namely, selecting a suitable admittance model (in this case, the equation for the resonance width change (Equation S2)) in order to first fit to the experimental values of ∆W/n = ∆Whydrod/n. In this way, two structural parameters of the homogeneous porous layer, ξ (lateral parameter) and h (vertical parameter along the penetration depth), are obtained. Thereafter, ∆Fhydrod/n is calculated using Equation S1 based on the evaluated parameters ξ and h. Thus, the frequency contribution due to the trapped fluid is calculated from a simple equation: (∆F/n)trapped = ∆F/n - (∆F/n)solid - (∆F/n) hydrod. The use of (∆F/n)solid together with (∆F/n)trapped accurately quantifies the hydrodynamic correction to the mass effect of an electrolytically-deposited porous solid (for further detail, see the SI). In-situ EQCM-D characterization of depositing/dissolving porous Cu layers Figure 1 shows a family of CVs related to Cu deposition/dissolution when cycling is performed between 0.5 V and a gradually decreasing limiting deposition potential ranging from 0 to -0.2 V (panel a), accompanied by the EQCM-D measurements (panel b). Panel c presents an enlarged view of ∆F/n and ∆W/n changes with time, for depositing the largest mass of Cu. The dash-dotted and dashed lines in panels b and c, designated as Ftheo, correspond to the frequency change calculated from the combined Faraday + Sauerbrey’s equations, as discussed above. We note that a certain small discrepancy between the values of Ftheo and the experimental total frequency change ∆F/n is observed, together with a small increase in ∆W/n: qualitative evidence of the significant hydrodynamic contribution to the measured EQCM-D characteristics. Interestingly, ∆W/n as a function of time has an approximately symmetric shape during the deposition and dissolution of thin Cu coatings (in relation to smaller deposition potentials). For thicker coatings, however, there is a clear break in the symmetry (Figure 1c). The shape of the time



dependence of ∆W/n qualitatively indicates that significant changes in the coating’s roughness take place: The formation of the Cu deposit results in the maximal change in ∆W/n when approximately 33% of Cu is deposited.

a 20

I (mA)

10

0

-10

-20 -0.2

0

b

0.2

0.4

E (V vs. Ag/AgCl)

1.00

0.00V -0.04V -2

0.75

-0.08V ∆Ftheo

0.50

-0.12V

-4 0.25

-0. 16V -6

-0.20V 0

50

100

150

c

∆W/n (kHz)

∆F/n (kHz)

0

200

0.00

250

t (s) 0.6

0

0.4

Deposition

-2

∆Ftheo -4

0.2

-6

∆W/n (kHz)

Dissolution

∆F/n (kHz)

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0.0 200

210

220

230

240

250

t (s)

Figure 1|Electrodeposition of Cu from 0.1 M CuSO4 + 0.5 M H2SO4 aqueous solution in linear voltammetry mode (the related CVs are shown in panel a) accompanied by frequency and resonance width changes rd th th (responses on 3 , 7 and 11 overtone orders are shown by blue, red and green solid lines in panel b). -1 The vertex negative potentials reached in consecutive voltammetric cycling at 20 mV s scan rate are indicated. The black dash-dotted line (designated as Ftheo) is the frequency change calculated from the


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passed charge (obtained by numerical integration of the related CVs) using the Faraday law and Sauerbrey’s equation. Panel c presents an enlarged view of the frequency and resonance width responses rd for a deposition/dissolution cycle between 0.5 and -0.2 V (for clarity, only the response on the 3 overtone is shown). Sketches in panel c schematically show the Cu deposition and dissolution processes.

Further decrease in ∆W/n as the deposition potential becomes more negative signifies that the deposit becomes denser (less porous), hence the contribution due to (∆W/n) hydrod is reduced. The dissolution of the Cu deposit demonstrates an interesting feature of the time-dependence of (∆W/n)hydrod: The resonance width increases until only a small part of the Cu deposit remains on the crystal surface. This signifies that the dissolution of a thick Cu deposit under chosen CV conditions occurs non-uniformly, creating a complicated geometric pattern of the deposit. The meaning of this important result is that the maximal change in (∆W/n) hydrod and (∆F/n) hydrod makes up only 3-4% of the frequency change due to the deposited mass of Cu. Hence, our spectroscopic EQCM-D measurements are sensitive enough to detect even small hydrodynamic corrections to the mass effect. Figure 2a presents the plots of ∆F/n and ∆W/n for the same set of data as functions of the charge passed during Cu deposition by a potentiodynamic sweep. The solid black straight line corresponds to Ftheo, which is the change in frequency calculated using the combined Faraday + Sauerbrey’s equation. If the mass effect is the only contribution to ∆F/n, then ∆W/n is equal to zero. When the deposit is not dense and flat enough, a small deviation of ∆F/n from Ftheo is observed, along with a simultaneous small increase in ∆W/n, which amounts to 3-4% of the hydrodynamic correction to the mass effect. In a second experiment, we replaced the potentiodynamic mode of the Cu deposition by the potentiostatic (i.e. cronoamperometric (CA) mode), aiming at changing the rough/porous structure of the Cu deposit prepared using the same amount of charge (see Figure 2b). The raw data showing frequency and resonance width changes together with the time dependence of the current passing during the potential step are presented in Figure S4. Indeed, the deviations of ∆F/n from Ftheo, as well as the increase in ∆W/n in CA deposition, are around 2-3%, which is less than in the case of Cu deposited by CV. This



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implies a denser Cu deposit obtained by CA due to a larger number of Cu nuclei (caused by high current density) favoring the formation of a less porous deposit (SEM images of both deposits confirming this conclusion are presented and discussed later).

Figure 2|Cu deposits obtained by electrodeposition from 0.1 M CuSO4 + 0.5 M H2SO4 solution by (i) sweeping the potential from 0.5 V to a set of values indicated in panel a, and (ii) applying the potential step from OCV to -0.15 V for 32 s (panel b). In panel a: for clarity, ∆F/n and ∆W/n are only shown as a function of electrode charge density for n = 3. The solid straight line (designated as F ) was calculated from the passed charge using the Faraday law theo

2

-1

and Sauerbrey’s equation; the crystal sensitivity was 56.6 Hz cm µg . The vertical blue and red lines show the deviation of ∆W/n from zero and the difference between ∆F/n and Ftheo. Sketches of deposit morphologies obtained at different potentials are shown in blue circles. rd

th

th

In panel b: The frequency and resonance width changes for 3 , 7 and 11 overtone orders are shown by black, blue and red circles, respectively, as a function of electrode charge density. The solid straight line (designated as F ) was calculated as explained above in the caption of panel a. The dashed straight line theo

parallel to Ftheo ideally approximates the experimental points for ∆F/n at the moderate values of charge density. The double arrows show the difference between Ftheo and ∆F/n (black) and the related deviation of ∆W/n from zero (blue).

A third experiment was conducted for a few initial cycles of Cu deposition/dissolution in the CV mode down to a potential of -0.16 V (Figure S5). Not surprisingly, the difference between ∆F/n and Ftheo, and the resonance width change ∆W/n simultaneously decreased. This implies that although the dissolution of Cu


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at the potential of 0.5 V was completed from a gravimetric point of view, Cu nuclei of tiny mass still survived, resulting in a moredense deposit during the subsequent half-cycle deposition, in agreement with the previously-discussed result for Cu deposits obtained by CV and CA.

In situ hydrodynamic spectroscopy of RF-sputtered and electrolytic Cu coatings We now switch from the surface charge density σ, as independent variable of the gravimetric analysis (used in Figure 2), to the penetration depth δ, the independent variable of the hydrodynamic spectroscopic analysis. In order to have an internal reference for our in situ hydrodynamic spectroscopic characterization of the deposits of complex geometry, we used an RF-sputtered Cu coating regarded as a dense layer with an almost ideally flat external surface on the scale of δ (the related AFM image is presented and discussed later). EQCM-D characterization of the RF-sputtered Cu deposit in distilled water results in almost ideally linear Kanazawa-type dependence of the normalized frequency and resonance width changes as a function of the penetration depth, δ (red spheres in Figure S6a, the “change” here means that the EQCM-D characteristics obtained in distilled water were referenced to the related characteristics in air). Such a linear relationship is also observed, of course, for a neat Au crystal in distilled water, in accordance with the viscous-type hydrodynamic interaction of a rigid flat surface with fluid (first member of the right-side expressions in Eqs. S1 and S2). Practically, this remarkable result means that the surface roughness of the RF-sputtered Cu film is much less than δ for n = 13 (68 nm), and that the film is dense and does not contain an appreciable amount of trapped water. When the same RF-sputtered Cu coating is immersed in 0.1 M CuSO4 + 0.5 M H2SO4, the normalized frequency change shows a progressive increase in frequency (constant ∆F/n shift for all overtone orders), with almost the same ∆W/n changes as a function of δ as those of the neat crystal (not shown in the treated data). Such characteristic behavior immediately implies the slow dissolution of the Cu deposit in 2+

this particular Cu -containing solution, without creation of significant surface roughness and, therefore, without additional contribution to the change in resonance width. When the experimental frequency



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changes for all n are corrected by the dissolved mass contribution, all the ∆Fhydrod/n and ∆Whydrod/n values (see blue spheres in Figure S6a) fall on the Kanazawa straight lines, as was the case with the Cu deposit in contact with water (red spheres in Figure S6a). The penetration depths in water and in 0.1 M CuSO4 + 0.5 M H2SO4 are, of course, different because of the different values of η/ρ. The straight line, however, is the same because the frequency and resonance width changes were normalized by the fluid density, making them solely a function of δ ̴ (η/ρ). An important quantitative result following from Figure S6a is that the multiharmonic EQCM-D measurements confirm that the frequency change due to the deposition of the non-porous RF-sputtered Cu on a flat surface are identical in air and water (Figure S3a and S3b). The dissolution of the RF-sputtered film performed in the potentiostatic mode (i.e. at a much higher rate than under the OCV condition considered above) shows essentially the same type of change in resonance width with time as the electrolytically-formed deposit (Figure S6b). However, the dissolution of this compact Cu coating occurs via the formation of a more rough/porous structure, as evident from the somewhat higher dispersion in the values of ∆F/n at different values of n and their larger deviation from Ftheo. Until now, the hydrodynamic correction to the gravimetric response for rough/porous Cu deposits was considered qualitatively, assuming that the measurable quantities (∆F/n) hydrod = (∆F/n) - (∆F/n)solid and ∆W/n = (∆W/n) hydrod are indeed linked to the quartz-crystal admittance of the porous solid in contact with fluid. We prove this assumption by showing that the selection of a suitable admittance model can return reasonable characteristic porous structure parameters of Cu deposits prepared under different conditions. Figure 3 shows normalized (by a constant factor of 10 /(ρFo )) values of (∆F/n) hydrod and (∆W/n) hydrod as a 9

2

function of the penetration depth δ for two types of deposits, namely, (i) an electrolytically-deposited Cu layer obtained by a linear potential sweep (to -0.16 V: blue spheres relate to this deposition potential, and red spheres relate to the deposit stripping at the potential 0.5 V), and (ii) the Cu layer obtained potentiostatically at the potential -0.15 V (black spheres relate to spectroscopic characterization at this potential).


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Figure 3 | In situ hydrodynamic spectroscopy of porous Cu deposits: red circles relate to ∆F/n and ∆W/n, changes after Cu dissolution at the potential 0.5 V (vs. Ag/AgCl) from the Au-coated crystal; the blue circles correspond to a Cu film obtained by a potential step from OCV to -0.15 V, whereas the black circles relate to Cu obtained by a linear potential sweep from OCV to -0.16. Theoretically calculated hydrodynamic response for rigid plane surface (using Kanazawa-type equation) is shown by the red dashed lines. Fitting the experimental ∆F/n and ∆W/n curves for the potentiostatically deposited coating to the uniform hydrodynamic porous layer model (solid blue line, Eqs. S1 and S2), the following structural parameters were returned: ξ = 45 nm, h = 80 nm, R = 1.05. The hydrodynamic response of a rougher Cu deposit obtained by a voltammetric scan fitted to the model of a porous layer + bumps (black solid curves, Eqs. S3 and S4), returned the following parameters: ξ = 40 nm, h = 95 nm, R = 1.12, r = 250 nm (average 2

bump’s radius) and bump surface coverage density m = 0.047 µm . Sketches of the crystal surface after Cu electrodissolution and of the electrodeposited Cu coatings related to their hydrodynamic spectroscopic curves are shown on the right side of the panel. The red spheres in Figure 3 ideally match the Kanazawa-type straight lines (described by first members on the right-hand side of Eqs. S1 and S2), implying that the EQCM-D response of the crystal completely stripped from the Cu coating is identical to that of the ideally flat neat crystal. The relevant hydrodynamic models that describe two other EQCM-D responses are selected taking into account the HR-SEM images of the Cu coatings obtained by CV and CA (Figure 4). Figure 4a shows that at a small deposition potential there is only a limited number of growing crystals. For the potentiodynamic deposition (at -0.16 V), the related SEM images are shown in panels b and c, whereas the image of the deposit obtained potentiostatically at -0.15 V is shown in panel d. We assign the relatively dense structure of the Cu deposit obtained potentiostatically to the formation of a uniform porous layer (Equations (S1) and (S2)), whereas



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a coarser Cu deposit obtained by CV reveals a uniform porous layer on top of which large semi-spherical particles are formed. In this case, we use a combined model of the uniform porous layer with the nonporous semi-spherical bumps on top of it (Equations S3 and S4). As discussed above, the uniform porous model has two geometric parameters, h and ξ. We added one more parameter, R, characterizing shallow roughness of the external surface of the porous layer. Non-porous bumps are characterized by two parameters: their radius r and the surface occupation density m. Fitting these hydrodynamic models to the experimental values of (∆F/n) hydrod and (∆W/n) hydrod provides good quality of fitting (the solid lines relate to fitted model in Figure 3 with fitting parameters listed in the figure caption). The downward deviation of the experimental frequencies from the calculated values (∆F/n)

hydrod

are assigned to the

contribution of the trapped fluid (∆F/n)trapped, as presented in Figure S3c and previously discussed in detail. Figure 4d shows an AFM image of the surface of the RF-sputtered Cu coating. This surface is obviously much flatter than that of the electrolytically-deposited Cu, in agreement with the fact that the EQCM-D response of this coating is identical to that of the ideally flat surface (Figure S6a). We have shown that the hydrodynamic factor affects both the frequency and resonance width changes in a rough/porous rigidly attached solid. Similar hydrodynamic corrections for a particular (shallow-type) roughness of viscoelastic deposits have been recently considered to provide good fitting to the experimental quartz-crystal impedance data.

40,41


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Figure 4|HR-SEM images of electrochemically deposited Cu (a-d) and AFM image of RF-sputtered Cu film (e). Cu coatings onto quartz-crystal were prepared by linear voltage sweeping to the negative deposition potentials of -0.04 and -0.16 V (a and b, c, respectively; inset in panel c shows occasional crack revealing Au-covered quartz crystal, pseudo-uniform porous Cu layer and bumps (aggregates) on top of its surface), and by chronoamperometry (d).

Conclusions In conclusion, we introduce a new approach to the simultaneous gravimetric and in-situ hydrodynamic spectroscopic characterization of rigid porous solid deposits (interfaces) formed dynamically on a quartzcrystal surface in contact with fluid. We show that hydrodynamic admittance models fitted to the experimental data, obtained by multiharmonic EQCM-D, return porous structure parameters and their minute potential-dependent changes in an approximately similar manner as resistance, capacitance and inductance (entering a complex equivalent electric circuit) are assessed by conventional electrochemical impedance modeling. This simplified modular principle of hydrodynamic quartz-crystal admittance modeling is potentially expected to increase the number of interested researchers dealing with the



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properties of physically different porous solid interfaces. The method we propose for the mesoscopic probing of the porous structure of solid interfaces in real time during their formation is unique, enabling the advanced gravimetric analysis of solvated solid layers/interfaces, separating between the dry-solid and trapped-solvent mass contributions to the total mass change. Finally, although this paper deals with rigid porous solid interfaces, we have started to adapt the hydrodynamic approach to typically soft solid layers. We believe that this approach will be very useful for a better understanding of the chemistry and mechanics of different types of electrochemically active solid layers and interfaces (Li-ion batteries electrodes, electroplated deposits, self-organized and patterned highly ordered interfaces, corrosion, etc.). Associated Content Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI.. Author Information Corresponding Authors: •

E-mail: [email protected] (D. Aurbach)

•

E-mail: [email protected] (M.D. Levi)

Author Contributions S.S. and N.S. performed the EQCM-D experiments, M.F. designed and produced the RF-sputtered Cu coatings onto a quartz-crystal surface, L.D. carried out the hydrodynamic modeling, and M.L. and D.A. contributed equally to the data treatment and the writing of the paper. Notes The authors declare no competing financial interests. Acknowledgements


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The authors gratefully acknowledge the funding from the USA-Israel Binational Science Foundation (BSF). We thank Prof. A. Arnau, Prof. Bund, Dr. A. Ispas, Dr. I. Efimov, and Dr. G. Ohlsson for the critical reading of this paper, providing us with important feedback. References

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Electrochemical Quartz Crystal Microbalance with Dissipation Real

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