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Cite this:DOI: 10.1039/c5cp03431k

Precipitation and surface adsorption of metalcomplexes during electropolishing. Theory andcharacterization with X-ray nanotomographyand surface tension isotherms†

Maryana I. Nave,a Yu-chen Karen Chen-Wiegart,b Jun Wangb andKonstantin G. Kornev*a

Electropolishing of metals often leads to supersaturation conditions resulting in precipitation of complex

compounds. The solubility diagrams and Gibbs adsorption isotherms of the electropolishing products

are thus very important to understand the thermodynamic mechanism of precipitation of reaction

products. Electropolishing of tungsten wires in aqueous solutions of potassium hydroxide is used as an

example illustrating the different thermodynamic scenarios of electropolishing. Electropolishing products

are able to form highly viscous films immiscible with the surrounding electrolyte or porous shells

adhered to the wire surface. Using X-ray nanotomography, we discovered a gel-like phase formed

at the tungsten surface during electropolishing. The results of these studies suggest that the

electropolishing products can form a rich library of compounds. The surface tension of the electrolyte

depends on the metal oxide ions and alkali-metal complexes.

Introduction

Electropolishing is a popular inexpensive method for smoothingmetal surfaces, micromachining, and sharpening metal wires.1–3

In electropolishing, the metal is immersed in an electrolytesolution and, upon application of a voltage, the metal undergoesan electrochemical reaction resulting in material removal. As aresult, a rough metal surface can be significantly smoothed outand the wire tips can be sharpened to nanometer radii.4–10

Currently, the available electropolishing techniques take advantageof convection-limited electropolishing (CLE) when the flowingelectrolyte facilitates the removal of ions from the metalsurface.4,6,11–14 In many cases, the flowing film is oversaturatedwith the products of the electrochemical reaction and may forma phase which is immiscible with the surrounding electrolyte.In attempts to reduce the influence of the flowing film onelectropolishing, researchers have used magnetic field,15,16

rotating electrodes,17,18 and some other means.1,2

This work aims to understand how the solution propertieschange during electropolishing. Tungsten was chosen as an

example of an important metal: tungsten wires are used to makesharp probes for scanning tunneling microscopy,19 atomic forcemicroscopy,13 field ion microscopy, Raman spectroscopy,20 nano-lithography,21 micro/nano welding,22 etc.13,23 At the same time,electropolishing of tungsten wires is a challenging task. Tungstenelectropolishing in an aqueous environment leads to the for-mation of a rich library of compounds. These compounds affectthe process efficiency which depends on the thermodynamicstability of electrolytes and their surface properties.

Therefore, in this paper, the main attention is given to theion concentrations corresponding to the conventional conditionsof tungsten electropolishing in aqueous solutions of potassiumhydroxide.14 We construct the solubility diagrams and discuss theconditions leading to precipitation of tungsten-based compounds.The changes of surface tension of these electrolytes are related tothe conditions of phase separation.

In electropolishing of tungsten wires in aqueous solutions ofpotassium hydroxide, the tungsten wire is connected to a powersupply and serves as an anode. As suggested by Kelsey,24 theanodic and cathodic electrochemical reactions can be summar-ized as follows: 6H2O + 6e�- 3H2(g) + 6OH�, W(s) + 8OH�-

WO42� + 4H2O + 6e�. Tungsten is oxidized with the continuous

release of tungstate ions WO42� into water changing the electro-

lyte composition. As shown recently, the amount of potassiumhydroxide in solution influences the rate of electropolishing andsignificantly influences the solution stability: one can observeprecipitation of different tungsten oxides and hydrates in the

a Department of Materials Science and Engineering, Clemson University, Clemson,

SC 29634, USA. E-mail: KKORNEV@clemson.edub Photon Sciences Directorate, Brookhaven National Laboratory, Upton,

New York 11973, USA

† Electronic supplementary information (ESI) available: Composition and thermalanalysis of the precipitates are presented with EDS, XRD, DSC and TGA data. SeeDOI: 10.1039/c5cp03431k

Received 15th June 2015,Accepted 27th July 2015

DOI: 10.1039/c5cp03431k

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form of flakes and nuclei.23 Since the surface and capillary effectsare important for obtaining smooth and sharp tips of the tungstenwires,14 one has to pay special attention to the change of surfacetension of the electrolyte during electropolishing.

By knowing the dependence of surface tension on theconcentration of the electrolyte constituents one can obtainadsorption isotherms.25–37 It is known that the electrolyte–airinterface can either repel or attract ions to its surface.29,35,38 Ifthe ions are repelled, the adsorption of ions to the interface iscalled negative; this effect is manifested through an increase ofsurface tension. If the ions are attracted to the surface of theelectrolyte, then the adsorption is called positive; in this casethe surface tension decreases.36 As the salt concentrationincreases, the surface tension does not always increase ordecrease monotonously; sometimes it can go through a minimum.This Jones–Ray effect was discovered by Jones and Ray andcontinues to be an unsolved controversy.39–48 Thus, adsorptionof multiple ions on the electrolyte surface is poorly understoodand, to the best of our knowledge, it has never been studied inelectropolishing applications.

ExperimentalSolution preparation

Solutions were prepared by electropolishing of tungsten plates bythe CLE technique described in ref. 14 and 23. The tungstensquare plate (15� 15 mm) with a thickness of 1.5 mm served as ananode. The stainless steel rod with 15 mm diameter and 50 mmlength was used as a cathode. Both electrodes were placed into aglass beaker with a diameter of 20 mm and a height of 25 mm andconnected to a potentiostat (CHI 660D, CH Instruments, Inc.).Then, 1 ml of the freshly prepared 2 M KOH electrolyte solutionwas added to the beaker using a 1 ml syringe. In order to preparesolutions with different concentrations of the reaction products,tungsten was electropolished at a DC potential of 10 V for differentperiods of time. The salt concentration of 2 M KOH and theapplied potential of 10 V are typically used in conventionalmethods of formation of tungsten probes.14,23 Therefore, wefollowed the most common conditions to reproduce the productsof electrochemical reactions. Each time, at the end of the electro-polishing, solutions were carefully collected and transferred intothe glass vial using a 1 ml syringe. The dependence of currentversus time was saved for each experiment for further calculationsof the mass loss of tungsten. Each experiment was performed witha freshly prepared KOH solution, every time in a new beaker.

When electric current passes through the electrolytic cell,the number of moles liberated during the reaction can be

estimated using Faraday’s law as: NWO42� = Q/zF, where Q is

the total charge at time t, z = 6 is the tungsten valence number,and F = 96485 C mol�1 is Faraday’s constant. The total chargeQ is found by integrating the current: Q ¼

ÐIðtÞdt. The concen-

tration is determined as follows: CWO42� = NWO4

2�/V, where

CWO42�, is defined as the amount of moles of the solute, NWO4

2�,divided by the volume of the solution, V. The number of moleswas estimated from the overall electrochemical reaction

W + 2OH� + 2H2O - WO42� + 3H2 which shows that the

reaction proceeds with oxidation of one mole of tungsten toone mole of tungstate ions. The concentration of tungstateions WO4

2� released into electrolyte during electropolishing

was calculated as follows: CWO42� = Q/zFV.

Measurements of volumetric mass density

The density measurements were performed using a microbalanceand a micropipette. For each solution, a drop of V = 30 ml was placedon the pan of the microbalance to measure the weight in mg. Foreach solution, five drops were measured to obtain the standarddeviation of the measurements. The densities were calculated usingthe equation r = m/V. The measured density of the 2 M KOHsolution was equal to r2M KOH = 1.0990� 0.0024 g cm�3 and wasin good agreement with the density found in the literature.49

Surface tension measurements

The surface tension measurements were performed using a KrussDSA10 instrument with 1.25 mm needle diameter for all solutions.Once a glass syringe was filled with the solution a pendant drop wasproduced and images were recorded using the Kruss DSA softwarefor further analysis. All measurements were carried out at roomtemperature. Five measurements were taken for each solution to getthe standard deviation. The surface tension of water measured withthis technique was equal to sw = 71.82 � 0.38 mN m�1. The surfacetension of the 2 M KOH was equal to s2M KOH = 75.17� 0.1 mN m�1.This value of surface tensions agrees fairly well with the surfacetensions reported in the literature.28–30,35,50

pH analysis

The pH was measured using a pH meter (UltraBASIC US-10,Denver Instrument) and double checked with the pH strips.

SEM-EDS

The precipitates in solutions were filtered out and washed5 times with DI water. After that, they were left to dry in theair at room temperature for 24 h. The precipitates appeared tohave a dull white color. They were analyzed using the FESEM-Hitachi S4800 scanning electron microscope equipped with anOxford INCA Energy 200 energy dispersive spectroscope (EDS).The precipitates were mounted on aluminum stubs with carbon–graphite tape for fixation.

XRD

The X-ray diffraction (XRD) patterns were acquired using aRigaku Ultima IV powder diffractometer equipped with Cu Karadiation (l = 1.5418 Å) in the angular range from 101 to 801 2y.The XRD measurements were carried out at room temperature.The data were analyzed using PDXL software version 1.4.0.0.

Thermal analysis

Thermal gravimetric analysis (TGA) was performed on TAInstruments TGA Q5000 V3.13 Build 261 with a ramp rate of10 1C min�1 from 25 1C to 400 1C in nitrogen gas. First thesample was equilibrated at room temperature under nitrogen

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purge for 10 min prior to heating. Differential scanning calori-metry (DSC) was performed on TA Instruments DSC Q1000 V9.9Build 303. First the sample was equilibrated at 25 1C followedby an increase in temperature with a ramp rate of 10 1C min�1

to 400 1C in helium gas. To analyze the data, the TA InstrumentsUniversal Analysis 2000 V3.9A and 4.7A software was employed.

TXM nanotomography

Nanotomography was performed with a transmission X-ray micro-scope (TXM) on the samples prepared with the CLE technique atbeamline X8C of National Synchrotron Light Source, BrookhavenNational Laboratory.51 The schematic of the setup is shown inFig. 1, where the X-ray beam with the 8960 eV energy is focused bya capillary condenser on the tungsten wire. A Fresnel zone platewas used as an objective lens to form an image onto the CCDdetector (2048� 2048 pixels) with the camera binning 2� 2 pixelsor 4 � 4 pixels with a single pixel size of 20 nm. The images werecontinuously collected with the 1 s exposure time. This runresulted in the collection of 1441 projections with the 40 �40 mm2 field of view. After the measurements, the backgroundwas subtracted and an automatic alignment using the run-outcorrection system was applied. A standard filtered back-projectionreconstruction algorithm was used to construct the 3D images.52

Volume rendering was applied to the reconstructed image stacksusing the Avizos program, VSG, version 8.0.

TheoryStability of the tungsten compounds in aqueous solutions

The stability of different tungsten compounds in aqueous solutionsof potassium hydroxide can be determined using the thermo-dynamics of chemical reactions.37,53–55 First, all possible chemicalreactions are written down in the following form:

n0A0 + n1A1 +. . .+ nrAr = m1B1 +. . .+ msBs, (1)

assuming that N0 moles of A0 solvent molecules are mixed withN1,. . .,Ni moles of A1,. . .,Ar solute molecules that react on the

left side, producing N01,. . .,N0j moles of B1,. . .,Bs solute mole-cules that react on the right side. In eqn (1), symbols n0,n1,. . .,nr and m1,. . .ms are assigned for the stoichiometric coeffi-cients of the reacting molecules from left and right sides. If n0 =0 then the solvent is not involved in the chemical reaction andif n0 a 0 then the solvent is involved in the reaction. In dilutesolutions the equality Ni { N0 holds true. If we assume that thesolution is an ideal solution, then the chemical potential ofspecies i, mi, can be represented as follows:

mi = m0i + RT ln[Ci], (2)

where the activity of the species i is defined as [Ci] = Ci/C0i ,

where Ci is the molar concentration and C0i is the molar

concentration of species i in the standard state. In chemicalphysics of solutions, the standard state of a solution is consi-dered as a state where there are no interactions between speciesand their behavior can be assumed as ideal. The standard stateis chosen at C0

i = 1 M.53

The equilibrium conditions are obtained using the relationof the Gibbs free energy, DG0, and the constant of chemicalreaction, K, as53

DG0 = �RT ln K (3)

where R is the gas constant and T is the absolute temperatureand the equilibrium constant is expressed using the activitiesof the species as

K ¼ B1½ �m1 . . . Bs½ �ms

A0½ �n0 A1½ �n1 . . . Ar½ �nr(4)

In this work, all experiments were performed at roomtemperature T = 25 1C, and hence eqn (1) is simplified as DG0 =A log10 K, where A = �5.71 kJ mol�1.55–61 The Gibbs free energiesof all possible compounds are collected in Table 1.

Consider dissolution of the solid tungsten compounds in anaqueous solution. During dissolution in an aqueous solution,tungsten can form a variety of tungstate ions,53,62,63 such asHW6O21

5�, H2W12O4210�, W6O21

6�, W7O246�, W12O41

10�,

Fig. 1 Schematic of the sample positioning on the transmission X-ray microscope (TXM). A tungsten wire was immersed in a Kapton tube filled with theelectrolyte. The wire was connected to a battery and was placed on the sample stage. By rotating the stage, one acquires the necessary images furtherused for reconstruction of a 3D volume.

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H2W12O406�, W12O39

6�, and W10O324�. Due to the limited avail-

ability of the Gibbs free energy data and the fact that the HW6O215�

ion has the lowest Gibbs free energy among the known polytungstateions, we have restricted ourselves to the analysis involving only thision. Hence only reactions depending on its presence were chosenfor the construction of the diagrams (Table 2). Possible solidcompounds and their aqueous products are listed in Table 1.Using the equilibrium conditions for the reactions of tungstenwith water, the stability of the compounds can be studied.

It can be noticed that the equilibrium boundaries separatingdifferent aqueous solutions are represented in the form

apH = b log[WO42�] + d log[HW6O21

5�] + g (5)

where constants a, b, d, g are given in Table 2 for the particularchemical reactions.

Now, equilibrium conditions are plotted in Fig. 2(a–c) wherelog C = log[WO4

2�] if tungstate ions WO42� are involved in the

reaction, or log C = log[HW6O215�] if the polytungstates

HW6O215� are involved in the reaction. The regions marked

with WO3, WO3�H2O or WO3�2H2O specify the concentration-versus-pH conditions when these compounds can be stable withrespect to water, meaning that these compounds will stay solidand would not dissolve in water. The regions marked with thepolytungstates HW6O21

5� specify the concentration-versus-pHconditions when the solid compounds WO3, WO3�H2O or WO3�2H2O will react with water producing the polyions and willeventually dissolve in water producing polytungstates HW6O21

5�

and vice versa. The regions marked with the tungstate ions WO42�

specify the concentration-versus-pH conditions when the polyionsHW6O21

5� and WO3�H2O will react with water producing thetungstate ions. The straight lines represent the boundariesalong which both species from each side of the line can coexistin equilibrium. The OH� and H+ lines represent equilibrium

conditions at which hydroxyl ions or hydrogen ions will bestable with respect to water.

As an illustration of the application of these diagrams, we useFig. 2(a) and follow the horizontal dashed arrows from the right tothe left. Assume that a solid WO3 compound is added to an aqueoussolution which is maintained at pH 14. As follows from thisdiagram, the WO3 compound will be dissolved in this solutionproducing the tungstate ions WO4

2� which are the only stablespecies at pH 14. If some acid is added to this solution and pH islowered, say to pH 7.6, the tungstate ion will react with hydrogenions producing polytungstate ion HW6O21

5� and both tungsten ionswill be in equilibrium with each other at this pH point. However, ifpH is lowered even more, say to pH 6, then the tungstate ions willreact to produce polytungstate ions and only polytungstate ions willbe present in the system when the system reaches equilibrium. Byadding more acid to this solution and lowering the solution pH topH 2, one can force the polytungstate ions to react with thehydrogen ions to produce the tungsten trioxide. The latter willprecipitate out as a solid particle. Below this pH, all the polytung-state ions will react to form solid tungsten trioxide.

It is instructive to interpret the effect of ion concentration onthe thermodynamic state of the solution following the verticalarrows. If a small amount of the solid tungsten trioxide isadded to the beaker with the pure water (pH 7), the chemicalreaction will proceed with the formation of the tungstate ionsand the hydrogen ions. By increasing the amount of solidtungsten trioxide, one would produce more tungstate ions untilthe concentration of the tungstate ion will reach the criticalconcentration �log C = �log[WO4

2�] = 3.8 or [WO42�] = 10�3.8 M

beyond which the tungstate ions will start reacting with hydrogenions producing the polytungstate ions. Above this critical concen-tration, the tungsten trioxide will continue to react with water,forming polytungstate ions instead.

From these diagrams, one infers that the composition ofthe solution is influenced by the concentration of the ionsproduced in the electrochemical reaction. Fig. 2(d) shows a threedimensional diagram where the planar boundary represents theequilibrium between the polytungstate ions and tungstate ions.Below this boundary, the tungstate ion will convert into thepolytungstate ion and vice versa to reach equilibrium.

By analyzing these diagrams, we conclude that the ionicproducts of tungsten electropolishing will precipitate in theform of tungsten trioxide monohydrate as the pH level is loweredbelow BpH 8 with the concentration of tungstate ions around�log[WO4

2�] E 2.4. On decreasing the pH below pH 1, one expectsto observe the tungsten trioxide dihydrate as a solid precipitate.

Table 1 List of considered compounds and their standard partial molarGibbs energies. ((s) – solid, (l) – liquid, (aq) – aqueous)

Name Species (state) D�G0

i (kJ mol�1) Ref.

Tungsten(VI) trioxide WO3(s) �763.9 53 and 54Tungsten(VI) trioxidemonohydrate

WO3�H2O(s) �1020.9 64

Tungsten(VI) trioxidedihydrate

WO3�2H2O(s) �1220.0 53

Tungstate(VI) ion WO42�(aq) �916.7 53

Polytungstate ion HW6O215�(aq) �5175.6 53

Water H2O(l) �237.2 53Hydrogen ion H+(aq) 0.0 53Hydroxide OH�(aq) �157.3 53

Table 2 The list of a, b, d, g coefficients

Compound pairs Chemical reactions a b d g

WO3(s)/WO42�(aq) WO3 + H2O = WO4

2� + 2H+ 2 1 0 14.8WO3(s)/HW6O21

5�(aq) 6WO3 + 3H2O = HW6O215� + 5H+ 5 1 0 20.9

HW6O215�(aq)/WO4

2�(aq) HW6O215� + 3H2O = 6WO4

2� + 7H+ 7 6 �1 67.8WO3�H2O(s)/WO4

2�(aq) WO3�H2O = WO42� + 2H+ 2 1 0 18.3

WO3�H2O(s)/HW6O215�(aq) 6(WO3�H2O) = HW6O21

5� + 3H2O + 5H+ 5 1 0 41.7WO3�2H2O(s)/WO4

2�(aq) WO3�2H2O = WO42� + 2H+ + H2O 2 1 0 11.6

WO3�2H2O(s)/HW6O215�(aq) 6(WO3�2H2O) = HW6O21

5� + 9H2O + 5H+ 5 1 0 1.7

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These diagrams suggest that electropolishing should proceedwith a change of the electrolyte composition, and, most important,with a possibility of phase separation. In electropolishing of tung-sten wires, the wire is submersed in the electrolyte. The CLE regimeof electropolishing significantly relies on the complex physico-chemical phenomena occurring under the meniscus formed bythe electrolyte/air interface around the wire.14 Since the surfacetension is very sensitive to the electrolyte composition,37,65 it istherefore instructive to develop a theoretical basis for interpreta-tion of the experimental data on the surface tension changes.

Gibbs adsorption isotherm

At constant temperature and pressure, the Gibbs adsorptionequation is given as65

ds ¼ �Xi

Gidmi; (6)

where Gi is the surface excess of the compound i concentrated atthe air/liquid interface and measured with respect to the concen-tration of some compound at a reference surface, mi is its chemicalpotential and s is the surface tension of the electrolyte. In order togo further and interpret the Gibbs adsorption equation for ourcase, we first need to specify all possible ions present in the system.

When discussing adsorption phenomena, we cannot ignore apossibility for potassium hydroxide to alter the thermodynamicpathway of chemical reactions. As mentioned, the surface pro-perties of electrolytes are very sensitive to any contaminants.

Therefore, while potassium containing compounds are knownto quickly dissociate in aqueous solutions,53,58,60 their effect onsurface properties of solutions is important to investigate.

Effect of potassium hydroxide

In electropolishing of tungsten in potassium hydroxidesolution, tungsten consumes hydroxyl groups OH� producingtungstate ions WO4

2�:24

W + 2OH� + 2H2O = WO42� + 3H2 (7)

Potassium hydroxide dissociates into potassium ions andhydroxide groups; hence positively charged potassium is able toassociate with negatively charged tungstate ions to form ahighly water soluble compound K2WO4:66,67

2K+ + WO42� = K2WO4 (8)

The total concentration C of dissolved species is

C = C1 + C2, (9)

where Ci is the concentration of the i-th compound, i = 1, 2,C1 = CKOH, C2 = CK2WO4

, measured in mol l�1. Following thestoichiometry of the reactions, the total concentration of ions isexpressed as follows:

C = CK+ + COH� + CWO42� = n1CKOH + n2CK2WO4

, (10)

where the coefficient n1 is equal to the total number of K+ and OH�

ions in the KOH compound and n2 is equal to the total number of

Fig. 2 Dependence of �log C on pH, considering the thermodynamic stability of (a) WO3, (b) WO3�H2O and (c) WO3�2H2O compounds. (d) Threedimensional graph showing the dependence of �log[WO4

2�] and �log[HW6O215�] on pH. The concentration C represents the concentration of the ions

in the system as explained in the text.

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K+ and WO42� ions in the K2WO4 compound. If n1K+, n1OH�, n2K+,

n2K+, n2WO42� represent the number of ions involved in the process

of dissociation of the KOH and K2WO4 compounds, we have n1 =n1K+ + n1OH� = 1 + 1 = 2 and n2 = n2K+ + n2WO4

2� = 2 + 1 = 3. Takinginto account all reactions occurring in this electrolyte solution, onewrites the electro neutrality condition for the solution as H+ +2OH� + 3K+ + WO4

2� = 0. Now, eqn (10) can be rewritten in thefollowing form: C = n1CKOH + n2CK2WO4

= 2CKOH + 3CK2WO4. This

form prompts one to operate with the concentration of neutralKOH and K2WO4 compounds rather than ions.

Motomura used this idea in his studies of complex mixtures.68,69

In Motomura’s model, the concentration of one ionic component ofthe mixture is assumed non-changing during adsorption. Thisassumption is not applicable to the electropolishing case, because,as shown in the previous section, tungsten ions undergo a complexchain of chemical reactions forming different compounds. There-fore, the concentration of the tungsten containing component maynot stay unchanged at the air/electrolyte interface. Below, theMotomura model was augmented to take into account this effectof change of the concentration of potassium and tungstate contain-ing compounds at the air/electrolyte interface.

Following Motomura, we introduce the mole fractions ofions associated with potassium hydroxide (X1) and potassiumtungstate (X2) measured with respect to the total concentrationof these ions in these two compounds. Using the definedstoichiometry coefficients, one obtains

X1 ¼n1CKOH

C¼ 2CKOH

2CKOH þ 3CK2WO4

(11)

and

X2 ¼n2CK2WO4

C¼ 3CK2WO4

2CKOH þ 3CK2WO4

(12)

The introduced mole fractions of ions satisfy the massbalance condition X1 + X2 = 1.

Using these definitions and assuming that the solution is ideal,one can write the differentials of the chemical potentials of the ions as

dmOH� ¼ RT d lnCX1

n2

" #¼ RT

CdC þ RT

X1

dX1: (13)

From the mass balance condition X1 + X2 = 1 one can findthe relation X1 = 1 � X2 and hence rewrite eqn (13) as

dmOH� ¼RT

CdC � RT

X1

dX2: (14)

Following the same logic and using eqn (2), the chemicalpotential of the WO4

2� ions is written as

dmWO42� ¼ RT

CdC þ RT

X2

dX2 (15)

The chemical potential of the K+ ions is then written as

dmKþ ¼RT

CdC � RT

n1Kþ

n1� n2Kþ

n2n1Kþ

n1X1 þ

n2Kþ

n2X2

dX2 (16)

With these chemical potentials, we can derive the Gibbsadsorption isotherm of aqueous solutions of tungsten andpotassium mixtures.

Gibbs adsorption isotherm of complex mixtures

Assuming constant pH (this assumption will be verified later inexperiments), the Gibbs adsorption equation H2O + H+ + 2OH�

+ 3K+ + WO42� = 0 is expressed as follows:

ds ¼ �GHH2O

dmH2O� GH

OH�dmOH� � GHWO4

2�dmWO42� � GH

KþdmKþ ;

(17)

where the superscript H represents an adsorbed quantity at the

air–liquid interface, and the symbols GHOH� ; G

HWO4

2� ; GHKþ repre-

sent the number of moles of the adsorbed ions OH�, WO42�,

K+ per unit area at the air–liquid interface.Due to convention, adsorption of water molecules GH

H2Oat

the air/electrolyte interface is set as zero,65,70 and thus eqn (17)is rewritten as

ds ¼ �GHOH�dmOH� � GH

WO42�dmWO4

2� � GHKþdmKþ (18)

The total Gibbs adsorption of all ions at the air–liquidinterface is represented as

GH ¼ GHOH� þ GH

WO42� þ GH

Kþ ; (19)

where GHKþ is defined as

GHKþ ¼ n1KþG

H1 þ n2KþG

H2 ; (20)

and GHOH� and GH

WO42� are defined as

GHOH� ¼ n1OH�G1

H ; (21)

and

GHWO4

2� ¼ n2WO42�GH

2 (22)

The total adsorption of compounds 1 and 2, GH, is written as

GH = GH1 + GH

2 (23)

The mole fraction of the K2WO4 compound at the air–liquidinterface is then

XH2 ¼

GH2

GH(24)

Using the stoichiometry coefficients, the mole fraction ofions at the air–liquid interface is found as

XH

2 ¼GHWO4

2� þ n2cGH2

GH: (25)

Substituting the differentials of the chemical potentialsdmOH�, dmWO4

2�, dmK+ (eqn (14)–(16)) into the Gibbs adsorption

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eqn (18), one obtains

ds ¼ � GHOH�

RT

CdC � RT

X1

dX2

� �� GH

WO42�

RT

CdC þ RT

X2

dX2

� �

� GHKþ

RT

CdC � RT

n1Kþ

n1� n2Kþ

n2n1Kþ

n1X1 þ

n2Kþ

n2X2

dX2

264

375:

(26)

Collecting the same differentials and using eqn (19) and(25), the Gibbs adsorption equation for the complex mixturecontaining potassium and tungstate ions is written as

ds ¼ �GHRT

CdC

þ GHRTX2 � X

H

2

X1X2

1� n1Kþn2Kþ

n1Kþn2X1 þ n2Kþn1X2

� �dX2:

(27)

The Gibbs adsorption equation in this form is convenient touse for a practically important case when the concentration ofpotassium hydroxide does not change significantly. In particular,at the beginning of tungsten electropolishing, the concentrationof potassium hydroxide can be considered constant because theconcentration of potassium tungstate goes to zero, X2 - 0.We discuss this important case below.

Evaluation of the total amount of adsorbate at the air/electrolyte interface at a low concentration of potassiumtungstate

Assuming a constant concentration of potassium hydroxide,CKOH, the differential of eqn (12) is written as

d(X2C) = n2dCK2WO4(28)

Accordingly, the differential of total concentration of com-pounds is rewritten in the form

dC = n2dCK2WO4(29)

Therefore, eqn (28) is expanded as X2n2dC2 + CdX2 = n2dC2,leading to the following relation:

n2dCK2WO4¼ dC ¼ � C

X2 � 1� �dX2;);

dC

C¼ � dX2

X2 � 1� � (30)

Substituting eqn (30) into the first term on the right handside of eqn (27), one obtains

ds

dX2

¼ GHRT

X2 � 1� �þ GHRT

X2 � XH

2

X1X2

1� n1Kþn2Kþ

n1Kþn2X1 þ n2Kþn1X2

� �(31)

At a low concentration of potassium tungstate, when X2 - 0,eqn (31) is simplified as

ds

dX2

����X2¼0¼ �GHRT þ GHRT

X1

1� n1Kþn2Kþ

n1Kþn2X1

� �����X1¼1

; (32)

to provide the total amount of adsorbate GH as

GH ¼ ds

dX2

1

RT �1þ 1

X1

� n1Kþn2Kþ

n1Kþn2X12

� ���������X1¼1

¼ � ds

dX2

n1Kþn2

RT � n1Kþn2Kþ(33)

Plugging n1 = n1K+ + n1OH� = 1 + 1 = 2 and n2 = n2K+ + n2WO42� =

2 + 1 = 3 into this equation, the total Gibbs adsorption GH at theair/electrolyte interface in this limiting case is calculated as

GH ¼ � ds

dX2

� 3

2RT(34)

Thus, in order to evaluate the total amount of adsorbate, oneneeds to find the slope ds/dX2 of the surface tension versuspotassium tungstate concentration at a low concentration ofthe latter.

Results and discussion

The solutions prepared using the CLE regime with tungstenplates electropolished in KOH solution were used to conductthe proposed studies on change of solution properties upondissolution of tungsten. Table 3 shows the following datacollected from the electropolishing experiment at time t: totalcharge Q, mass of the electrochemically removed tungsten mW

calculated using Faraday’s law, density r of the solution mea-sured using a microbalance and a micropipette, concentrationCWO4

2� of the reaction products WO42� calculated using Faraday’s

law, surface tension measured using the drop shape analyzer, theconcentration of KOH, C1, in the electrolyte, the concentration ofK2WO4, C2, where C2 = CK2WO4

= CWO42�. The parameters C, X1, and

X2 were calculated using the equations presented above ((10), (11)and (12), respectively).

Fig. 3 collects the results of the surface tension and pHmeasurements of the tungstate solutions prepared by electro-polishing of tungsten in the potassium hydroxide electrolyte.The insets in Fig. 3 show a sequence of images of the solutionsprepared by electropolishing of tungsten in the 2 M KOH electro-lyte for different periods of time. Remarkably, the pH of thepotassium hydroxide with tungstate ion solutions remains almostconstant when the surface tension visibly decreases. The con-stancy of pH provides the solid ground for the theory of the Gibbsadsorption isotherm that we derived (eqn (34)).

Manifestation of thermodynamic instability of electrolytesduring electropolishing

The pH drops from pH 14 to pH 9 at the 0.65 M concentrationof the tungstate ions when the surface tension has alreadystabilized. These observations confirm the presence of precipi-tates as suggested by the phase diagrams that we constructedearlier. These diagrams also suggest that the tungstate ionsshould form the WO3�H2O precipitates when pH drops belowpH 8, which is in agreement with the observations.

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As shown in the ESI,† the results from the EDS analysispoint to the presence of tungsten oxides/hydrates in the preci-pitates. The thermal analysis revealed the presence of structurallybound or hydrated water. This indicates that the precipitates aremost likely consisting of tungsten hydrates that are present in theamorphous form.

The presence of precipitates significantly changes the rheo-logical properties of the electrolyte especially near the wiresurface. As shown in ref. 14, in the CLE, a thin liquid film withdistinguishable properties is formed near the wire surface. Wefollowed the same CLE protocol to X-ray film the process. Thetungsten wire was electropolished until the lower part ofthe wire immersed into the liquid was dropped off and themeniscus that was originally created on the wire slid off thewire exposing the needle to the air. At this moment, the wirewas imaged using TXM mosaic mode, where 15 images with40 � 40 mm2 field of view were collected consequently and

combined together automatically to form an expanded image that isshown in Fig. 4(a). After that the wire was left undisturbed in thetube for 1 h for stabilization of the electrolyte; then the X-raynanotomography was performed. The result of the nanotomographyis shown in Fig. 4(b).

In contrast to the recently discovered regime of electro-polishing leading to the formation of a porous shell,23 thenanotomography of the CLE tip reveals a smooth surface of thetungsten tip without any porous shell (Fig. 4). Surprisingly, wedetected a micrometer thin (diameter d B 2 mm) bridgeconnecting the suspended part of the wire with the free surfaceof the liquid spanning about 70 mm distance of the observationspot. The bridge appeared to have some trapped nuclei thatremained intact during the nanotomography scan. It should benoted that the bridge was present in the mosaic image that wastaken immediately after the meniscus had slid down andremained stable until the end of the nanotomography scan.

Table 3 Experimental data and calculated parameters for the tungstate solutions

t (s) Q (C) mW (g) r (g cm�3) CWO42� (mol l�1) s (mN m�1) C1 C2 C %X1 %X2

0 0 0.000 1.085 0.00 75.18 2.00 0.00 4.00 1.00 0.0050 11 0.003 1.091 0.02 74.70 2.00 0.02 4.07 0.98 0.02100 19 0.006 1.101 0.06 74.28 2.00 0.06 4.19 0.95 0.05200 37 0.012 1.109 0.10 73.81 2.00 0.10 4.30 0.93 0.07300 51 0.016 1.127 0.19 73.56 2.00 0.19 4.57 0.88 0.12600 91 0.029 1.170 0.34 72.98 2.00 0.34 5.03 0.80 0.20470 150 0.047 1.149 0.28 73.30 2.00 0.28 4.84 0.83 0.171000 182 0.057 1.206 0.49 73.20 2.00 0.49 5.47 0.73 0.272000 332 0.105 1.228 0.58 73.57 2.00 0.58 5.74 0.70 0.306100 356 0.113 1.224 0.65 73.26 2.00 0.65 5.96 0.67 0.33

Fig. 3 Surface tension (black triangles) and pH (red diamonds) as a function of K2WO4 concentration. The insets are optical images of the mixtures.

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Prior to the X-ray scanning, the tube with the suspendedwire was left in the air. It can be assumed that water from thebridge evaporated during this period of time. According to ouranalysis of thermodynamic stability of these solutions, evapora-tion of water, resulting in an increase of the ion concentration,should also lead to the precipitation of tungsten compounds.This explains the presence of particles in the bridge.

If we assume that the bridge has the same surface tension asthat of the electrolyte, then using Fig. 4 one can estimate theYoung’s modulus E of the bridge balancing the capillarypressure with the radial stress srr E E. Therefore, the orderof magnitude estimate gives

E ¼ 2sd¼ 2� 73 mN m�1

2 mm¼ 73 kN m�2 (35)

Such a value of the Young’s modulus corresponds to a gel-like structure. For example alginate hydrogels have the sameorder of magnitude moduli.71,72 This estimate suggests that thebridge is not completely dried but is formed from a gel-likestructure of polytungstates reinforced with the nuclei of differ-ent tungsten compounds and bound water. If the bridge weremade of tungsten oxides or hydrates, the Young’s moduluswould be much greater.

Analysis of surface composition of electrolytes

Now, using eqn (34) and knowing the slope ds/dX2 = �0.019from Fig. 3, the Gibbs adsorption can be estimated as GH = 1.2� 10�5 mol m�2. Thus, the Gibbs adsorption appears positivein contrast to the initial Gibbs adsorption of the KOH solutionwhich is negative.29,30 This means that the tungstate ions wereadsorbed at the surface decreasing the surface tension of theentire mixture.

Knowing the value of the total Gibbs adsorption at the initialpoint when X2 = 0, area A at the surface occupied by a single ioncan be found using the following equation:

A ¼ 1

NA � GH¼ 0:14 nm2; (36)

where NA is the Avogadro’s number NA = 6.02 � 1023 mol�1.

Average area of the tungstate ion

The tungstate ion is a polyatomic ion that consists of four oxygenatoms that surround one tungsten atom that is positioned in thecenter of the ion. When ions are formed, the atoms arrangethemselves in a way to lower the internal energy of the system.73

To achieve that, they form the three dimensional units, arrangingatoms using covalent bonding with the shortest length. In the caseof tungstate ion, we have four atoms of oxygen and the optimalconfiguration for this ion is a tetrahedral arrangement of atomswhich is shown in the inset of Fig. 3. The ionic radii of oxygen andtungsten ions can be found in the literature: rO2� = 0.13 nm,55 rW6+ =0.042 nm.73 The tungstate ion radii then can be approximated asrWO4

2� = rW6+ + 2rO2� = 0.302 nm.Assume one tungstate ion positioned at the air–liquid inter-

face with one oxygen atom pointing out towards the air with therest of the oxygen atoms pointing inwards and the next tung-state ion sitting at the air–liquid interface with three oxygenatoms pointing towards the air and one oxygen atom pointinginto the liquid. In this case, the area occupied by two tungstateions at the interface can be approximated by the cross sectionof the four oxygen atoms. The cross section of a single oxygenatom was found as AO2� ¼ prO2� 2 ¼ 0:053 nm2. Now, two tung-sten ions situated at the air–liquid interface would occupy thearea A2ions = 4AO2� = 0.212 nm2. Thus, the average area occupiedby a single tungstate ion is Aion = 0.106 nm2. Comparing theaverage area occupied by a single ion at the air–liquid interfaceestimated from the Gibbs adsorption isotherm eqn (36) and theaverage area of the tungstate ion situated at the air–liquidinterface, we conclude that the ions are closely packed at thefree liquid surface.

Conclusions

Theoretical analysis of thermodynamic equilibrium of three solidcompounds of tungsten in aqueous solutions of potassium hydro-xide allowed one to obtain the solubility conditions of thesecompounds. In a basic solution with the pH level around pH 14,no precipitates can form. When the pH is lowered to pH 8, thetungsten trioxide monohydrate WO3�H2O might precipitate in thesolution. If the pH is lowered further to pH 4, the tungsten trioxideWO3 might precipitate. And if the pH drops below pH 1, thetungsten trioxide dehydrate WO3�2H2O has a chance to precipitate.We went further to analyze the Gibbs adsorption isotherms ofthese electrolytes modifying the Motomura theory of surfaceadsorption of ions at the liquid surfaces.

In order to check the predictions of the derived phasediagrams and analyze the surface tensions of electrolytes, weconducted a series of different experiments. The complex

Fig. 4 The TXM mosaic image on the left (a) depicts the region where thenanotomography was performed. The image in the red box (b) is a 3Dvolume rendering view of the reconstructed CLE prepared tip with a bridgeconnecting the tip with the electrolyte surface.

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multicompound ionic mixtures consisting of dissociated KOHand tungstate ions in water were studied. With the increase ofthe concentration of tungstate ions, the initially clear solutionsbecame turbid indicating the onset of phase separation. Alongwith this visible change of the solution composition, the surfacetension changed as well; it decreased and then stabilized at a lowervalue relative to the initial level corresponding to the aqueoussolution of KOH. Using the Gibbs adsorption isotherm, we pro-vided an estimate of the packing density of ions at the air/liquidinterface.

The Gibbs adsorption of potassium ions at the water/airinterface is negative. This implies that the ions are repelledfrom the surface increasing the surface tension as the KOHconcentration increases. When analyzing the surface tension ofthe mixture after electropolishing of tungsten in potassiumhydroxide solutions, the Gibbs adsorption of tungstate ions wasfound to be positive. Thus, the tungstate ions produced duringelectropolishing are attracted to the air–liquid interface changingthe surface adsorption and the surface tension of the mixture.

Characterization of the precipitates revealed that the pre-cipitates possibly consist of amorphous tungsten hydrates.X-ray diffraction revealed the amorphous nature of the preci-pitates and energy dispersive X-ray spectroscopy showed thepresence of oxygen in the sample. Finally, thermal analysisrevealed the presence of structurally bound water implying thatthe precipitates consist of some type of tungsten hydrate.

Also, using transmission X-ray nanotomography we discoveredthat the boundary layer of the electrolyte, which has distinguish-able physical properties, can flow down the electropolished tipand, when exposed to air, it forms a long living gel-like bridge. Thisbridge showed a remarkable stability: it remained unbroken forabout two hours after the electrochemical reaction had beenstopped. Thus, the oversaturated solution of the products of theelectrochemical reaction of tungsten and an aqueous solution ofpotassium hydroxide is able to form a gel-like long living structure.

Acknowledgements

We would like to acknowledge the help of Dr Colin McMillenwith the XRD experiments, George Wetzel for his assistancewith the SEM and EDS techniques, and Kim Ivey for her help withthe thermal analysis techniques. We thank Ella Marushchenko forthe drawing of Fig. 1. Use of the National Synchrotron LightSource, Brookhaven National Laboratory, was supported by theU.S. Department of Energy, Office of Science, Office of BasicEnergy Sciences, under Contract No. DE-AC02-98CH10886.

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