Influence of charge exchange in acidic aqueous and alcoholic titania dispersions on viscosity

Advances in Colloid and Interface Science 226 (2015) 138–165

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Historical Perspective

Influence of charge exchange in acidic aqueous and alcoholic titania dispersions on viscosity Jarl B. Rosenholm ⁎, Per Dahlsten Laboratory of Physical Chemistry, Center of Excellence for Functional Materials, Åbo Akademi University, FIN 20500 Åbo (Turku), Finland

a r t i c l e

i n f o

Available online 19 October 2015 Keywords: Solvent/acid adsorption Solvent/acid dissociation Surface-induced dissociation (SIED, SILD, SIAD) Charge exchange Dispersion stability

a b s t r a c t Charging effects resulting from adsorption of acid, acid anions, and protons on titania (anatase) surfaces in anhydrous or mixed alcohol–water dispersions is summarized. The suddenly enhanced conductivity as compared to titania-free solutions has previously been modeled and explained as surface-induced electrolytic dissociation (SIED) of weak acids. This model and recently published results identifying concurrent surface-induced liquid (solvent) dissociation (SILD) are evaluated with experimentally determined conductivity and pH of solutions, zeta-potential of particles, and viscosity of dispersions. Titania (0–25 wt%)–alcohol (methanol, ethanol, and propanol) dispersions mixed with (0–100 wt%) water were acidified with oxalic, phosphoric, and sulfuric acids. It was found that the experimental results could in many cases be condensed to master curves representing extensive experimental results. These curves reveal that major properties of the systems appear within three concentration regions were different mechanisms (SILD, surface-induced liquid dissociation; SIAD, surfaceinduced acid dissociation) and charge rearrangement were found to be simultaneously active. In particular, zeta-potential – pH and viscosity – pH curves are in acidified non-polar solvents mirror images to those dependencies observed in aqueous dispersions to which hydroxyl is added. The results suggest that multiple dispersion and adsorption equilibria should be considered in order to characterize the presented exceptionally extensive and complex experimental results. © 2015 Elsevier B.V. All rights reserved.

Contents 1. 2. 3. 4.

Introduction . . . . . . . . . . . . . . . . Surface chemistry model . . . . . . . . . . Experimental . . . . . . . . . . . . . . . Results and discussion . . . . . . . . . . . 4.1. Potentiometry (pH) measurements . . 4.1.1. Summary of observations . . 4.2. Conductivity measurements . . . . . 4.2.1. Dilute oxalic acid dispersions . 4.2.2. Concentrated oxalic acid range 4.2.3. Summary of observations . . 4.3. Zeta-potential measurements . . . . . 4.3.1. Dilute oxalic acid range . . . 4.3.2. Concentrated oxalic acid range 4.3.3. Summary of observations . . 4.4. Viscosity measurement . . . . . . . . 4.4.1. Summary of observations . . 5. Conclusions . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . .

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⁎ Corresponding author at: Laboratory for Physical Chemistry, Åbo Akademi University, Porthansgatan 3-5, FI-20500 Åbo (Turku), Finland, Tel.: +358 2 2154254; fax:+358 2 2330228. E-mail address: Jarl.Rosenholm@abo.fi (J.B. Rosenholm).

http://dx.doi.org/10.1016/j.cis.2015.10.007 0001-8686/© 2015 Elsevier B.V. All rights reserved.

J.B. Rosenholm, P. Dahlsten / Advances in Colloid and Interface Science 226 (2015) 138–165

1. Introduction Solids can exist in different crystal forms which may catalyze chemical reactions and chemisorb solvent molecules and ionic species. Whereas oxide surfaces may act as ligands for cations in solution, the specific adsorption of anions or weak acids occurs by substitution of hydroxyls on the oxide surface. The effect of multivalent anions on the surface charging is sparsely investigated. Chelating acids such as oxalate, phosphate, and sulphate may replace mono-coordinated groups on the surface, which in aqueous dispersions is exhibited within 3 b pH b 4 [1,2]. Obviously, this is the optimum pH-range for anion adsorption in aqueous solutions. The reactivity of surface hydroxyl groups toward anion substitution decreases as the acid character of these groups increases. Doubly and triply coordinated metal hydroxyls are more acidic and carry negative charges which do not favor electrostatic attraction with anions. The symmetry of anion charge plays an important role in its adsorption and its mode of coordination. Specific adsorption of anions is a surface complexation reaction and, as a rule, anions do adsorb more efficiently if their complexing nature is high in solution. In addition, these groups form bonds with surface cations that are more covalent in nature than the bonds formed with mono-coordinated hydroxyl groups. Their replacement is therefore more difficult. The chelating or bridging effect, which reinforces the complexing nature of the anion in solution, also stimulates adsorption [1,2]. The adsorption is dependent on whether anion affinity for the surface is greater than solvation of the surface or the acid anion [3,4]. In aqueous dispersions, the adsorption is predominated by charge neutralization, Brϕnsted acid–base and hydrogen bond interaction. The role of Lewis acid–base and van der Waals interaction is enhanced when the water content is reduced. Chelation may lead to a considerable increase of surface element dissolution (extraction). Oxalate anions adsorb through condensation with surface hydroxyl groups, but also via hydrogen bonding to the carbonyl groups [1,2]. Both the adsorption to mono-dentate surface complexes and the free carboxylic acid group enable a proton release. This effect seems to be specific to surface coordination because it is not observed with mononuclear complexes in aqueous solution. The dissociation constants of oxalic acid in water are [5] pK1 = 1.25 (1.1), pK2 = 4.29 (4.0), the value in parenthesis representing an ionic strength of pI= 1 (0.1 mol/dm3). Oxalate replaces mono-coordinated hydroxyl groups on the surface, but seems in some cases to be capable to chelate also doubly and triply coordinated hydroxyl groups [1,2]. Phosphate and sulfate replace monocoordinated groups on the surface and possess a bridging coordination mode at around 3 b pH b 4. For phosphate, this is only slightly more than the first dissociation constant of phosphate in water (pK1 = 2.15, pK2 = 7.21, pK3 = 12.34) [5]. Sulfate anions are usually doubly coordinated on hydroxylated surfaces due to complexation. Since the acid constants of sulfate is very low in water (pK1 = −3, pK2 = 1.94) [5], both protons are dissociated. However, due to bi-dentate surface complexation, two hydroxyl groups are consumed. As a result sulfate only neutralizes surface charges at hydroxylated surface sites. The charging is obviously dependent on both pH (acidity) and pI (ionic strength). Only the mono-coordinated hydroxo groups are replaced. Phosphate replaces all mono-coordinated groups on the surface because it is a strong complexant [1]. Only one hydroxyl group remains active for excess charging upon adsorption.

We have previously reported on the mutual influence of metal cations as well as some anions on SiO2, TiO2, ZrO2, Al2O3, Fe2O3, CaCO3, and some other particles in aqueous dispersions [1,6–49]. Moreover, investigations on charge interactions of multiprotic acids (H2C2O2, H3PO4, H2SO4) with such colloidal particles in low-dielectric suspensions, such

139

as ionic liquids [50–54] have been made. Properties of hydrocarbon [55–57] and alcohol (CH3OH, C2H5OH, C3H7OH)–water dispersions [58–63] have been published. It was concluded that acids reside in alcohol-rich suspensions mainly in molecular form. This is due to order of magnitude reduced dissociation. For example, the acid constants of oxalic acid are shifted from pK1 = 1.25, pK2 = 4.29 in water to pK1 = 4.2, pK2 = 8.2 in anhydrous ethanol [58–63]. The pKi are depressed as the dielectric constant of the solvent decreases, e.g. as a function of the alcohol chain length. Due to the reduced ionic character the solubility of oxalic acid is enhanced almost two times to 2.07 mol/dm3. In alcoholic solutions of multiprotic acids, the concentration of preexisting ions is therefore expected to be low. In the presence of dissolved multiprotic acids, adsorbed surface complexes may form and induce a dissociation of solvated protons or anions to the solution. The enhanced proton release is observed as an enhanced conductivity and a charge reversal denoted surface-induced electrolytic dissociation (SIED) [58–63]. It is opposite to the “normal” reduction in conductivity in the presence of particles due to adsorption of protons and anions. Thus, the measured conductivity and charging of dispersions may be enhanced or depressed as a result of two processes acting in opposite directions. The aim of this report is to review and extend some of our results published previously [58–63] by inter-correlating key parameters characterizing ionic interactions in mixed and non-aqueous methanol, ethanol, and propanol suspensions. Titania dispersions serve as model systems. Moreover, the influence of water as a mixed solvent is of particular interest. Since the conductivity of proton is substantially higher than other ionic species, the conductivity has been assumed to be directly proportional to the presence of protons in titania suspensions. The potentiometrically determined pH represents, however, the true proton concentration (activity) in bulk solution/suspension. This enables calculation of surface proton excess concentration and surface charge density which represent the charging (potential) at the particle surface. The effective surface potential (ζ-potential) is dependent on the proton exchange at surface hydroxyl sites. Finally, viscosity may be used to relate the effective surface charging to the stability of titania suspensions. Experimentally, the following four interlinked properties are measured or calculated.

Conductivity is a measure of ion (proton) and zeta (ζ ) potential a measure of particle transport in an external field. On the other hand, dispersed proton concentration and protons adsorbed to particle surface (surface charge density) are equilibrium properties. Obviously, the amount of adsorbed ions are interlinked to ζ-potential as particle properties while equilibrium proton concentration (pH) and conductivity are dispersion properties. Viscosity provides a mean to relate charge exchange to the overall suspension stability. 2. Surface chemistry model In non-aqueous and aqueous alcohol suspensions, alumina surface has been found to cataly–tically dissociate adsorbed ethanol to ethanolate anions on Lewis acid surface sites and protons on Lewis base surface sites [64]. The assumption is that surface is Lewis or Brϕnsted active. The reaction occurs as a two-step process illustrated as the top reaction scheme in Fig. 1. First, ethanol adsorbs on the surface sites as neutral molecules and then ethanolate anions desorb from the surface into bulk dispersion. As a result, the surface is rendered a positive surface charge. The catalytic autoprotolysis of ethanol solvent on

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J.B. Rosenholm, P. Dahlsten / Advances in Colloid and Interface Science 226 (2015) 138–165

alumina enhances positive charging since protons remain adsorbed on Lewis base sites [64]. We denote this process a surface-induced liquid dissociation (SILD). Previously we have reported that addition of weak acids to low-dielectric dispersions induces a surface-induced electrolytic dissociation (SIED) in which case the anion remains adsorbed and protons are released. As an extension of the previously introduced SIED concept [58–63], we denote this surface-induced acid dissociation (SIAD). The primary network of reactions is illustrated in Fig. 1. The first equilibrium constant KLI represents adsorption of neutral ethanol molecules on the surface (state LI). The generalized equilibrium concentration of alcohol liquid (L = HRO) remaining in dispersion (d) is thus: [HRO]d = [HRO] − [SHRO]s. s

K LI ¼

½SHRO ½HRO ½S½HRO

d

ð1Þ

where [SHRO]s = [S*H+RO−]s denotes a surface complex. The positive surface charging is due to a subsequent release of alcoholate anions into suspension (state LII). This release may be described by the following generalized equilibrium constant. K LII ¼


þ s SH ½RO− d ½SHROs

ð2Þ

In the presence of an acid, the adsorption of neutral liquid ethanol (KLI) and neutral acid (KAI) occur in parallel (middle reaction in Fig. 1). Depending on the relative affinities of protons and anions for particle sites, this may be followed by a release of acid anions (KAII) as in SILD process. However, instead of anion release which is characteristic for the surface-induced liquid dissociation (SILD), protons are released (bottom reactions in Fig. 1) in the surface-induced acid dissociation (SIAD). The release equilibrium (state AIV) is represented by equilibrium constant KAIV as K AIV ¼


d ½SAc− s H þ ½SHAcs

ð5Þ

For some solids (particles), there may be adsorption of alcoholate anions (KLIV) as in SIAD process. The affinity of acid anions to the surface is then greater than the affinity of protons which are released to the suspension. The assumption is that the surface is Lewis or Brϕnsted active. For charged surfaces, the distribution of protons between surface and bulk is determined by Boltzmann distribution as
þ s
þ b − Fψ0 H ¼ H e RT :

ð6Þ

The overall SIAD equilibrium is represented by As shown, it is assumed that the affinity for protons exceeds that of alcoholate anions which results in a positive particle surface charge. For charged surfaces, the distribution of alcoholate anions between surface and bulk is determined by Boltzmann distribution as − s

− d −

½RO  ¼ ½RO  e

Fψ0 RT

ð3Þ

where F = Farady's constant, ψ 0 = surface potential, R = gas constant, T = Kelvin temperature. The surface-induced liquid dissociation (SILD) is represented by the equilibrium between first reactants and last products represented by constant KLIII . It involves simultaneous adsorption of protons and release of alcoholate anions to bulk suspension. K LIII ¼ K LI  K LII ¼


þ s SH ½RO− d ½HROd ½S½HRO

ð4Þ

These reactions occur in the absence of added acid. The adsorption of neutral molecules on the surface (sites) may enhance pH (reduced H+ concentration) due to a small shift in acid dissociation equilibrium.

K AV ¼ K AI  K AII ¼


d ½SAc− s H þ ½HAcd ½S½HAc

ð7Þ

where [SHRO]s = [S*H+RO–]s. If both reaction schemes are simultaneously active, neutral solvent (ethanol) result from the excess protons and alcoholate anions (KLVI and KAVI) as ½HROd K LVI ¼
d H þ ½RO− d

½HAcd ⇔ K AVI ¼
d : Hþ ½Ac− d

ð8Þ

Note that disregarding proton adsorption the proton neutralization in dispersion (d) is assumed to equal dissociation equilibrium in bulk (b) liquid without particles. This should be taken into account both when considering conductivity and proton concentration balances. The reactions included in Fig. 1 are reduced to a minimum and exclude a number of optional reactions. The exchange of protons with hydroxylated surface sites [1] is not considered. Instead the network is kept reasonably simple in order to maintain comparability with SILD and SIAD models referred to. The following considerations have been omitted:

Fig. 1. Related reactions when solvent alcohol and added acid reacts with particle surface sites.

J.B. Rosenholm, P. Dahlsten / Advances in Colloid and Interface Science 226 (2015) 138–165

• When brought into contact with water (liquids), the surface sites may hydrolyze to form aquo-, hydroxo-, and oxo surface groups or alternatively metals and oxides may dissolve (lyotropic annihilation). • Impurities (inorganic and organic) may leach out from or adsorb onto particle surface and compete with SILD and SIAD reaction. Washing removes impurities but may result in adsorption of acids and bases used in washing process. • CO2\\H2CO3 equlibrium and adsorption induces long-term (pH, redox-potential, conductivity) changes in dispersion. • Redox-potential of dispersion and extraction may cause changes in oxidation state (z+) of the metal over extended time. • Thermal treatment (annihilation) before contact with water changes the nature and the occurence of hydroxylated) surface sites. In this report, we restrict us to the influence of (mono-dentate) acids dissolved in alcohol mixed with an increased amount of water inducing SILD and SIAD processes illustrated in Fig. 1. The dependence of proton equilibrium on acid concentration is investigated by converting the change between the initial (i) and final (f) pH of dispersions (d) and particle-free bulk liquids (b) to relative proton (H) concentrations as cH ≈ 10−pH 

cdH ¼ cHf −ciH cbH

¼



ð9aÞ  dis



  3 ; mol=dm

cHf −ciH ; bulk

csH ≈ cdred;H



3

mol=dm

ð9bÞ



ð9cÞ

  3 ¼ cdH −cbH ; mol=dm

ð9dÞ

where d (dis) = dispersion b(bulk) = bulk liquid (no particles) s = surface excess

i = initial f = final red = reduced

Note that final state is measured after completion of SILD and SIAD. The reduced concentration represents the surface excess of adsorbed protons. In order to normalize the concentration scale to represent different particle loads, it is expressed as amount of protons per surface area denoted normalized concentrations:   Γ HAc ¼ ðV=AÞ cHAc ; mol=m2

141

density may be calculated as Faraday constant multiplied by difference in normalized oxalic acid (σrel = F ΓHs) as       − cHf −ciH σ rel ≈ F Γ sH ¼ F Γ dH −Γ bH ¼ F ðV=AÞ cHf −ciH dis bulk     μC=cm2 ¼ 10−2 C=m2

ð11Þ

Note that the difference between normalized concentration of added acid and dispersion, the normalized excess proton concentration,     Γ ex;H ¼ Γ HAc −Γ dH ; mol=m2 ;

ð12Þ

does not account for the degree of acid dissociation which according to molar conductivity ratio dereases from 0.25 in dilute oxalic acid solutions (0.64 mmol/dm3) to less than 0.05 at 23 mmol/dm3. In the same way as for protons conductivity may be reduced by subtracting the conductivity of the corresponding particle-free solvent. However, since the initial conductivity is (nearly) zero only bulk liquid conductivity is considered. κ red ¼ κ dis −κ bulk ; ðmS=cmÞ ¼ 10−1 ðS=mÞ

ð13Þ

With the purpose to consolidate extensive results, the conductivity may further be divided by surface area of titania as   Ω ¼ κ E =A; 10−1 S=m3 ;

ð14aÞ

  Ωred ¼ κ red =A ¼ ðκ dis −κ bulk Þ=A; 10−1 S=m3 :

ð14bÞ

The experimental molar conductivity expressed as Λ m ¼ κ E =cHAc ;

h

 i   3 ¼ 10−4 Sm2 =mol : ðmS=cmÞ= mol=dm

ð15Þ

The molar conductivity of the suspension may be reduced by subtracting the molar conductivity of particle-free ethanol–water solutions of equal oxalic acid concentrations as Λ red ¼ Λ dis −Λ bulk ;

h

 i   3 ¼ 10−4 Sm2 =mol : ð16Þ ðmS=cmÞ= mol=dm

The extrapolated limiting molar conductivity (limΛm = Λ∞) allows for a simple method to estimate the degree of dissociation as α¼

Λm : Λ ∞m

ð17Þ

ð10aÞ

It is then assumed that the acid (salt) is fully dissociated at infinite dilution which is not the case for the alcohol–water solutions. For binary

    ; mol=m2 Γ dH ¼ ðV=AÞ cdH ¼ ðV=AÞ cHf −ciH

ð10bÞ

Table 1 Physical properties of solvents and species investigated at infinite dilution at 25 °C [65].

  Γ bH ¼ ðV=AÞ cbH ¼ ðV=AÞ cHf −ciH

ð10cÞ

dis

bulk

Γ sH

≈ Γ dred;H

¼

Γ dH −Γ bH ;



2

mol=m



  ; mol=m2

ð10dÞ

Note that the acid (HAc) is considered to be mono-dentate, releasing only one proton in dispersion. For simplicity, it is assumed that dissociation degree of acid added to dispersion is independent of particle load. With these constraints, the normalized amount of adsorbed protons, i.e. surface excess (ΓsH) was calculated as the difference between normalized proton concentration in dispersion and in bulk solution at the same acid and particle concentration. The relative surface charge

Solvent

Water

Methanol

94 % ethanol

εr η(cP) Λm(H+) 10−4

78.5 0.892 349.65

32.6 0.541 49⁎

26.5 (100%, 24.3) 1.317 (100%, 1.074) 40.2⁎ (10.2⁎⁎)

Λm(A–) 10−4 .Sm2mol−1 349.65 198 40.2 74.11 36 57 52 80

D(A–) 10−5 cm2s−1 9.311 5.273 1.070 0.987 0.959 0.759 1.385 1.065

Λm(H+A–) 10−4 Sm2mol−1 – 547.65 389.85 423.76 385.65 406.65 401.65 429.65

Sm2mol−1 Proton and anion H+ OH– HC2O–4 ½ C2O2– 4 H2PO–4 ½ HPO2– 4 HSO–4 2– ½ SO4

⁎ Assumed values. ⁎⁎ Adjusted assumed value. εr(PrOH) = 20.1.

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J.B. Rosenholm, P. Dahlsten / Advances in Colloid and Interface Science 226 (2015) 138–165

alcohol–water solutions, the limiting equivalent molar conductivity (limΛeq) may be subdivided into contributions of proton and anions (A−) as

This equals reversed process (8, KHAc = 1/KLVI). In dilute state, dissolved neutral acid molecules adsorb to surface sites 1 as ¼ Ti þ HAc ⇔ ¼ Ti–HAc

Λ ∞eq

Λ∞ ¼ m ¼ Λ ∞Hþ þ Λ ∞A− : z

½¼ Ti1 −HAcs ½¼ Ti1 ½HAcd

:

ð20Þ

ð18Þ

The molar conductivities of liquid species reported in Table 1 refer to infinite dilution. Recently, an adsorption model was suggested [66] to account for the release of protons into solution upon addition of acids to alcohol dispersions. If TiO2 is chosen as metal oxide the following reactions was suggested to dominate SIED process [66]. The dissociation of acid is assumed to be independent on the presence of particles in dispersion:

HAc ⇔ Ac– þ Hþ

K1 ¼

K HAc ¼


d ½Ac− d H þ ½HAcd

ð19Þ

This equals process (1) for acid adsorption. Increasing acid concentration to state AII acid molecules which adsorb dissociate releasing protons to dispersion as ¼ Ti þ HAc ⇔ ¼ Ti–Ac– þ Hþ

K2 ¼


d ½¼ Ti2 −Ac− s H þ ½¼ Ti2 ½HAcd

:

ð21Þ

This is nearly, but not quite equal, to process (7). The analysis was focused on changes in conductivity (SIED process) while dispersed and adsorbed proton concentration was chosen to represent SIAD process. The chemical potential of protons was expressed in terms of conductivities and written as h i μ H ≈ RT lncH ∝2:3RT logκ E ≈ 2:3RT log cdH Λ ∞H :

ð22Þ

Table 2 Identification of symbols in figures indicated. In the presence of both TiO2 (wt%) and H2O (wt%), combined symbols apply. TiO2

Symbol

0 1 2 5 10 0 1 2 5 10

1 2 5 10

0 1 2 5 10 1 2 5 10 1 2 5 10 2 2 2 2 2 2 2 2 2 2 2

ΓHAc ΓdH ΓdH ΓdH ΓdH ΓsH ΓsH ΓsH ΓsH ΓbH ΓbH ΓbH ΓbH

H2O

Symbol

0 0 0 0 0 10 20 30 40 50 60 70 80 90 100 6 10 20 30 40 60 80 6 6 6 6 6 6 6 6 6 6 6 6 6 6 10 20 30 40 50 60 70 80 90 100

Filled-diamond Filled-square Filled-circle Filled-up-triangle Filled-down-triangle Filled-square Filled-circle Filled-up-triangle Filled-down-triangle Filled-diamond Filled-left-arrowhead Filled-right-arrowhead Filled-hexagon Filled-star Filled-pentagon Filled-square Open-square Plus-square Cross-square Minus-square Dot-square Bottom-shaded-square Plus-square Filled-square Open-square Top-shaded-square Plus-square (filled) Filled-circle Open-circle Top-shaded-circle Plus-circle (filled) Filled-up-triangle Open-up-triangle Top-shaded-up-triangle Plus-up-triangle (filled) Filled-square Filled-circle Filled-up-triangle Filled-down-triangle Filled-diamond Filled-right-arrowhead Filled-left-arrowhead Filled-hexagon Filled-star Filled-pentagon Dot-filled-circle

Symbol

-circle -circle -circle -circle -circle -circle -circle

Symbol

-up-triangle -up-triangle -up-triangle -up-triangle -up-triangle -up-triangle -up-triangle

Symbol

-down-triangle -down-triangle -down-triangle -down-triangle -down-triangle -down-triangle -down-triangle

Figure 17 4–27 (selected) 4–27 (selected) 4–27 (selected) 4–27 (selected) 3, 4, 14, 22, 23 3, 4, 14, 22, 23 3, 4, 14, 22, 23 3, 4, 14, 22, 23 3, 4, 14, 22, 23 3, 4, 14, 22, 23 3, 4, 14, 22, 23 3, 4, 14, 22, 23 3, 4, 14, 22, 23 3, 4, 14, 22, 23 6, 8 5, 6, 7 5, 6, 7, 8 5, 6 5, 6, 7, 8 8 8 10 6 6 6 6, 10 6 6 6 6, 10 6 6 6 6, 10 15, 16 15, 16 15, 16 15, 16 15, 16 15, 16 15, 16 15, 16 15, 16 15, 16 15, 16

J.B. Rosenholm, P. Dahlsten / Advances in Colloid and Interface Science 226 (2015) 138–165

Fig. 2. The first dissociation constant (pKI, squares) and dielectric constant (divided by ten, crosses) of phosphoric acid in methanol and pH (diamonds) of oxalic acid in methanol as a function of wt% water. First dissociation constant (pKI, spheres), dielectric constant (divided by ten, asterisk), and pH (triangles) of oxalic acid in ethanol as a function of wt% water [73–76].

The model was successfully fitted to conductivity versus oxalic acid curves representing 94% by weight ethanolic titania dispersions. The following sum was minimized [66]: X


 2 logκ E ð expÞ− log cH ðcalcÞ  Λ ∞H ;

ð23Þ

where Λ∞ H = molar conductivity of protons at infinite dilution which is assumed to be 40.2⁎10− 4 m2S/mol for 94% by weight ethanol (Table 1). An improved fit was, however, obtained when the molar conductivity was adjusted to 10.2⁎10−4 m2S/mol. Λ∞ H was assumed to remain constant over the entire concentration range. The limiting molar conductivity was thus considered to be a fit parameter. The two adsorption reactions (20,21) were assumed to occur at different non-defined

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surface sites (1,2) having specific surface site densities (σ/nm2) and equilibrium constants (K). The calculated concentration of protons was derived by adjustment of the state 1 site density σs1 (free + HAc) (HAc = H2C2O4, H3PO4) representing adsorbed neutral acid molecules and state 2 site density σs2 (free + Ac–)/nm2 (Ac– = HC2O–4, H2PO–4) representing adsorbed acid anions. Each total site density fraction may thus be considered as site occupancy. Finally, equilibrium constants (K1, K2) and site densities were calculated by interpolation based on chosen Λ∞ H and KHAc values. The concurrent release of solvent molecules upon adsorption, the exchange of protons from surface hydroxyle groups (sites), and the contribution of surface potential (the Boltzmann distribution) to the proton release were disregarded in the model. For oxalic acid in 94 wt% ethanol TiO2 dispersions, the extracted equilibrium constants were found to be pKIs = − 5.19 and pKIIs = − 0 .122 [66]. The corresponding calculated surface concentrations were (σIs = 0.458/nm2) and (σIIs = 0.420/nm2), respectively. The sites are a decade lower than published site densities for anatase and rutile [67]. Although K2s〈〈 K1s for almost equal site densities (σIIs ≈ σIs) equilibrium 2 was considered to represent the main charging mechanism (the SIED effect). The adsorption constant for the third equilibrium (K3 = K2/K1) that is pK3 = − 0.0235 shows that concurrent proton dissociation from adsorbed neutral acid molecules may occur. Recently, the averaged time dependence (20 min b t b 3 h) of SIED reaction was evaluated with different conductivity sensors [68]. It was found that that time and type of sensor have an influence on conductivity. A slow equilibration process follows the fast initial equilibrium (t b 8 s). In order to explain the results, an additional proton release reaction was introduced to replace reaction (21) [68]:

¼ Ti−HX þ HAc ⇔ ¼ Ti−HAc þ Hþ þ X−

K2 ¼


d ½¼ Ti2 −HAcs Hþ ½X − d ½¼ Ti2 −HX d ½HAcd

ð24Þ

Fig. 3. Dependence of pH on oxalic acid concentration in methanol at various TiO2 and water weight fractions (10, 20,30, 40 wt% water in 0, 1, 2 5, 10 wt% TiO2 dispersions, upper-left diagram), in ethanol (10, 20, 30, 40, 50, 60, 70, 80, 90, 100 wt% water in 0, 1, 2 5, 10 wt% TiO2 dispersions, upper-right diagram), and water-free propanol (in 1, 2 5, 10 wt% TiO2 dispersions, lower-left diagram). Symbols are identified in Table 2. Dependence of pH on sulfuric acid concentration in 94 wt% ethanol in TiO2 dispersions (lower-right diagram). Symbols (bottomupwards): square—0, square—1, square—2, square—5, square—10 wt% TiO2.

:

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This reaction represents an exchange of pre-adsorbed acidic impurity (HX) by neutral acid. The impurity was considered a stronger acid in dispersion but has a lower affinity to surface sites. The nature of the impurity (inorganic, CO2/H2CO3, organic) was, however, not analyzed. The conductivity enhancement increased with decreased amount of water and averaged dielectric constant. Replacement of reaction (21) with reaction (24) produced an equally fair fit as compared to original fits. The most disturbing observation was that the conductivity of supernatant from which particles were removed by centrifugation was found to be equal to conductivity of dispersion. This was considered inconsistent with SIED process in which the presence of particles was necessary for enhanced conductivity and charge neutralization of solvated protons. On the other hand, the conductivity of solvent with a corresponding amount of acid but no particles was two orders of magnitude lower than dispersion. It remains unclear whether the experimental conditions were sufficient to detect the small conductivity differences between supernatant

and dispersion. In order to account for dissociation of stable titania complexes, the following chelation reaction was considered [68]: h i2x−2y x TiO2 þ y H2 Ac ⇔ ðTiOÞx ðAcÞy þ x H2 O þ 2ðy−xÞHþ

ð25Þ

The activity of TiO2 and H2O are assumed constant in order to focus on the contribution of protons. Reaction (25) was rewritten as
−z þ z Hþ x TiO2 þ H2 Ac þ ðz−2ÞH2 O ⇔ ðTiOÞx ðAcÞðOHÞz−2

ð26Þ

Combining reactions (20) and (26) produced again an equally fair fit (when z = 4) as previous reactions. Although metals are known to dissolve from MxOy at particular pH ranges, TiO2 was found to be stable at 4 b pH b 9 as found previously [7–9]. Therefore, reaction (26) is improbable in the present case. The concentration of Ti in supernatant was found to be smaller by four

Fig. 4. Dependence of pH on normalized oxalic acid concentration at various TiO2 and water weight fractions (10, 20, 30, 40 wt% water in 1, 2, 5, 10 wt% TiO2 methanol dispersions, upperleft diagram; 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 wt% water in 1, 2, 5, 10 wt% TiO2 ethanol dispersions, upper-right diagram; and 1, 2 5, 10 wt% TiO2 propanol dispersions, lower-left diagram). Symbols are identified in Table 2. Dependence of pH on normalized phosphoric acid concentration at various TiO2 and water weight fractions (10, 20, 40 wt% water in 1, 2, 5, 10 wt% TiO2 methanol dispersions, middle-left diagram; and 6, 20, 40, 60 wt% water in 0, 1, 2, 5, 10 wt% TiO2 ethanol dispersions, middle-right diagram). Dependence of pH on sulfuric acid concentration in (94 wt%) ethanol TiO2 dispersions (lower-right diagram). Symbols (top-downwards): square—1, square—2, square—5, square—10 wt% TiO2. Expanded scales for inserts indicated.

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orders of magnitude than concentration of protons. Since the assumed impurity influencing the long-term conductivity remained unidentified, the extended evaluation produced no improvement to the original analysis. Perhaps the most confusing neglect in the design of the model is the absence of surface hydroxyls which during adsorption contribute to the proton equilibrium. There are numerous methods to quantify the adsorption equilibrium which would provide site densities and equilibrium constant for comparison with those extracted from model fits. Concerns on the key assumption of the model remain whether conductivity is indeed proportional to proton concentration (activity) in dispersion at all experimental conditions. 3. Experimental Aeroxide (P-25) from Degussa was used as obtained. It is a relatively pure anatase (with admixture of rutile); it consists of particles 30 nm in diameter with a specific surface area of 50 m2/g. The specific surface area of TiO2 was determined by a Micromeritics ASAP 2010 gas sorption instrument (Micromeritics Instrument Corporation, Norcross, GA, US) and was found to be 55.64 m2/g. The pristine pHiep in aqueous solutions is about 6.5. Water was freshly obtained from a MilliQ device. Ethanol (94 wt%) was supplied by Altia, Finland. Methanol (N 99.8%, b 0.02% water) was from Baker and propanol (N 99.5 %, b0.1 % water) were

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from Sigma–Aldrich. Oxalic acid dehydrate (N99.5%), phosphoric acid (85%) and sulfuric acid were delivered by Fluka. All chemicals were used as obtained. Acoustosizer IIs (Colloidal Dynamics, Warwick, USA) with a built-in pH-meter, conductivity meter, and thermometer was used to measure the pH, conductivity, and electrokinetic potential in dispersions containing 1–10% of titania by mass. All solid-to-liquid ratios in this paper are expressed in terms of mass fractions. The instrument was used in “polar solvent” mode for aqueous dispersions and in “non-polar solvent” mode for organic dispersions. A flow-through system and vigorous stirring were used to prevent sedimentation, and the dispersions were kept at 25 ± 1 °C. The instrument was kept in a fume hood. An external thermostat was used to keep the solutions and dispersions at 25 °C. Data points were taken in titration mode every 2 min. and 4 mL of titrant solution was added in 40 equally spaced portions to 170 mL base dispersion containing no oxalic acid. Thus, in course of titrations, titania suspensions were diluted by the titrant to final concentration of about 98% of the initial fraction of titania particles. Previous experiments with longer equilibration times showed an insignificant effect of the titration rate on ζ-potentials. The instrument software produced two types of ζ-potential results. The Hückel (Smoluchowski for aqueous dispersions) ζ-potentials were calculated from the dynamic mobility at one frequency. The full analysis was

Fig. 5. Dependence of normalized dispersed proton concentration (ΓdH) on normalized oxalic acid concentration at various TiO2 and water weight fractions (10, 20, 30, 40 wt% water in 1, 2 5, 10 wt% TiO2 methanol dispersion, upper-left diagram, insert scale indicated) and of normalized adsorbed proton concentration (ΓsH surface excess, upper-right diagram). Expanded diagram for 10, 20, 30, 40 wt% water in 10 wt% TiO2 methanol dispersion (dispersed protons, lower-left diagram) and adsorbed (surface excess protons, lower-right diagram). Symbols are identified in Table 2.

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performed by the instrument software using dynamic mobilities measured at different frequencies. The full analysis was shown to be unstable, while the Hückel–ζ-potentials produced smooth electrokinetic curves. Viscosity measurements were carried out on 10, 15, and 25 wt% dispersions with a Bohlin VOR rheometer. A C14 and a C25 cup-piston systems were used with five torsion-bars with constants from 0.33 to 11.1 gcm. The selection of torsion bar and cup depended on the viscosity. For low viscosities, a C25 cup-system in combination with a torsion bar with a low constant was needed. In opposite, a high viscosity required a C14 cup-system and a high torsion bar constant. Shear rates

were scanned from low to high and back again in the range of 0.0921– 367 s− 1 at 20 °C. The maximum shear rate was dependent on the tension range of the torsion bar and therefore sometimes lower. The relatively low temperature and a Teflon lid were used to prevent evaporation. For comparison, selected shear rates at 0.581, 5.81, and 58.1 s−1 were used. In contrast to acoustic titrations, the viscosity measurement were carried out in batches. Before the measurements, the dispersions were stirred for 20 minutes and thereafter relaxed in the measurement cup for another 5–10 minutes before starting the measurements. For details of experimental conditions, the reader is advised to consult original publications.

Fig. 6. Dependence of normalized dispersed proton concentration (ΓdH), adsorbed (ΓsH, surface excess), and in bulk (ΓbH) on normalized oxalic acid concentration in 1, 2 5, 10 wt% TiO2 ethanol dispersion (upper-left diagram) and expanded scales (upper-right, scale indicated). Normalized dispersed proton concentration (middle-left diagram) and normalized adsorbed proton (surface excess, middle-right diagram) concentration in 6 wt% H2O dispersions. Expanded diagram for 6, 20, 30, 40 wt% water in 10 wt% TiO2 ethanol dispersion (dispersed protons, lower-left diagram) and adsorbed (surface excess protons, lower-right diagram). Symbols are identified in Table 2.

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4. Results and discussion In previous investigations, the characteristic sudden conductivity enhancement (SIED effect) has been related to the release of protons to dispersion. In order to highlight the main features of the system, it is therefore necessary to determine the amount of protons released to dispersion and adsorbed on the particles as a function of added acid. The obvious choice is to measure the changes in pH and convert it to changes proton concentration (activities). The potentiometric measurement is considered quite specific to protons. The overall properties of the system are discussed with focus on: • • • •

Surface proton excess (surface charge density) Conductivity ζ-potential Viscosity

The results are first discussed for the dilute acid solutions/dispersions with reference to concentrated dispersions. The experimental results are identified with symbols collected in Table 2. 4.1. Potentiometry (pH) measurements In low (20 b εr b 30) and non-polar (εr b 10) liquids, the affinity of solvent for protons is at least as important as that for other cations

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and anions. Two features deserve particular attention when considering the influence of acids on particle charging and suspension stability: • Small ions cannot be solvated in non-polar solvents. Charges can be created only if large ions are formed, keeping charges sufficiently apart. Small ions (cations) prefer high dielectric solvents which results in a preferential dissolution of large ions (anions) in low-polar liquids. As large ions have stronger preference for non-polar solvents, the small ions (protons) tend to have a stronger tendency to adsorb on particle surfaces and charge them positively. • In most non-aqueous solvents, the solubility of electrolytes is much less than in water. This results in a very thick double-layer and small field strength according to DLVO theory [69–72]. The charges at particle surfaces are thus poorly screened. It is generally considered that due care has to be taken when measuring pH in non-aqueous liquids and mixed solutions of reduced water content. However, according to an investigation for IUPAC, the pH values measured potentiometrically for oxalate in methanolic and ethanolic solutions (Fig. 2) are sound [73]. The dissociation of weak acids in water–alcohol mixed solvents has been extensively investigated [73–76]. The first dissociation constant (pK1) of oxalic acid in mixed ethanol–water solutions is plotted as a function of pH of 0.01 mol/kg HOx–LiOx solutions in ethanol– and methanol–water solutions in Fig. 2.

Fig. 7. Dependence of normalized dispersed proton concentration on normalized phosphoric acid concentration at various TiO2 and water weight fractions (10, 20, 40 wt% water in 1, 2 5, 10 wt% TiO2 methanol dispersion, upper-left diagram, insert scale indicated) and of normalized adsorbed proton concentration (surface excess, upper-right diagram). Expanded diagram for corresponding 10, 20, 40 wt% water in 10 wt% TiO2 methanol dispersion (dispersed protons, lower-left diagram) and adsorbed (surface excess protons, lower-right diagram). Symbols are identified in Table 2.

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Fig. 8. Dependence of normalized proton concentration on normalized phosphoric acid concentration at various TiO2 and water weight fractions (6, 20, 40, 60, 80 wt% water in 1, 2 5, 10 wt% TiO2 ethanol dispersion, upper-left diagram, scale of insert indicated) and of normalized adsorbed proton concentration (surface excess, upper-right diagram). Expanded diagram for corresponding 6, 20, 40, 60, 80 wt% water in 10 wt% TiO2 ethanol dispersion (dispersed protons, lower-left diagram) and adsorbed (surface excess protons, lower-right diagram). Symbols are identified in Table 2.

Fig. 2 reveals that pK1 of oxalic acid is reduced with increased water concentration. The pKa1 follows pH of the mixture over a wide composition range indicating that it controls the solution acidity. Only at the extremes, pKa1 diverges from the measured pH of the 0.01 mol/kg HOx–LiOx solutions [73]. The dissociation constants of oxalic acid in water are [5] pKa1 = 1.25 (1.1), pKa2 = 4.29 (4.0), the value in

parenthesis representing an ionic strength of pI = 1 (0.1 mol/dm3). In anhydrous ethanol, the deprotonation is reduced to pKa1 = 4.2, pKa2 = 8.2 which agrees with the extrapolated value for 0 wt% water. The conclusion that oxalic acid occurs mainly as molecular monodentate acid (HOx) and hydro-oxalic anions (Ox−) in ethanol–water mixtures is supported by these results. It was therefore considered

Fig. 9. Normalized dispersed proton concentration in 1 (squares), 2 (circles), 5 (upright triangle), 10 (inverted triangle) wt% TiO2 94 wt% ethanol dispersion (dispersed protons, left diagram) and adsorbed (surface excess protons, right diagram) as a function of normalized sulfuric acid concentration.

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Fig. 10. Dependence of normalized proton concentration dispersed (ΓdH, filled chaki squares), adsorbed (ΓsH, surface excess, filled blue circles) and in bulk (ΓbH, purple triangles) on oxalic acid concentration in 10 wt% TiO2 ethanol dispersion. Three ΓdH ranges are identified. For comparison, normalized oxalic acid concentration is included (purple plus-squares). Rigt diagram: Same plots on expanded ΓH scale. Symbols are identified in Table 2.

safe to convert the measured pH values to equilibrium proton concentration in solution. The pH measured as a function of acid concentration at various water contents is presented in Fig. 3. The spread of pH in Fig. 3 is diminished to master curves when plotted as a function of normalized acid concentration in sets depending mainly on wt% TiO2 but also on H2O. The pH is plotted as a function of normalized oxalic, phosphoric, and sulfuric acid in Fig. 4. Increasing the particle content, the curves are separated to lower pH levels. The pH dependence on water is reduced in oxalic acid–methanol dispersions as compared to ethanol dispersions. The dependence on water of normalized phosphoric acid systems seems to nearly equal those of oxalic acid systems. The reversed reaction from proton release (lower pH) to proton consumption (pH increase) is visible only for H3PO4–MeOH/EtOH and H2C2O4–PrOH systems. H2SO4–EtOH system represents strong acid behavior and resembles H2C2O4–MeOH/EtOH systems. The dependence of pH on oxalic acid concentration in nonaqueous propanol and on sulfuric acid in non-aqueous ethanol dispersions are presented as limiting references. Propanol dispersions represent the behavior of non-polar systems with a reversal of pH from a declining to an increasing dependence on ΓH2C2O4. Sulfuric acid is strong and exhibits a continuously reduced pH which is enhanced as a function of ΓH2SO4 and wt% TiO2. Recalculating pH to proton concentration (activity) enables plots of normalized dispersed proton concentration (d) and adsorbed on particle surfaces (surface excess, s) against normalized acid (HAc) concentration

(Figs.5–9). Magnitudes of ΓdH and ΓsH illustrate the affinity of protons to solvent (solvation) and to particle surfaces (adsorption) and the exchange equilibrium between these states. The systems presented are H2C2O4–MeOH–H2O (Fig. 5), H2C2O4–EtOH–H2O (Fig. 6), H3PO4– MeOH–H2O (Fig. 7), H3PO4–EtOH–H2O (Fig. 8), and H2SO4–EtOH (Fig. 9) titania dispersions. As shown, normalized proton concentrations consolidate the dependencies on normalized acid concentration. The 1, 2, 5, 10 wt% titania ΓdH–ΓHAc plots did not result in master curves but reveal a number of particular dependencies: • The break point corresponding to onset of SIAD process (ΓdH increase) is common but less developed at increasing water content. Simultaneously, a negative minimum develops for ΓsH which increases with wt% H2O. • The SIAD process is characterized by an extensive ΓdH and ΓsH enhancement. • These reactions are followed by a break point to a nearly constant ΓdH plateau and a maximum followed by a declining ΓsH. For 1 and 2 wt% TiO2 dispersions, these effects are less developed. Protons are released from the surface but its influence on proton concentration in dispersion is marginal. • An increased water content counteracts SIAD process strongly. The maximum in ΓdH is exchanged for a break point after which it continues to increase. The ΓsH maximum disappears and is replaced by flat plateau following the negative minimum. The minimum is deeper

Fig. 11. Left diagram: Dependence of conductivity (filled-open symbols) and ζ-potential (dotted symbols) of 0 and 1% TiO2 on oxalic acid concentration in methanol (asterisk-diamonds), ethanol (crosses-squares) and propanol (plus-triangles) dispersions. Right diagram: Dependence of conductivity and pH of 0 (asterisk/cross) and 1 (square/triangle) wt% Al2O3 on hydrochloric acid in ethanol dispersions [64]. The change in ζ-potential (divided by ten) is indicated with a dashed line.

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and the plateau occurs at a lower ΓsH and higher ΓHAc when wt% H2O increases. This behavior resembles that of strong acids (eg. H2SO4).

4.1.1. Summary of observations Three significant changes are clearly revealed. Range I: Prior to SIAD effect, there is a decrease in proton surface excess which is more visible the stronger the acid and the more polar solvent (higher water content) is. The increase of ΓdH is regulated by free protons in particle-free bulk solutions (ΓbH). As shown in Fig. 10, a full dissociation in particle-free solutions exceeds that in dispersion (ΓbH) at equal ΓHAc which may be identified as different dissociation. The SIAD in range II results in an almost exponentially enhanced ΓdH and ΓsH, which indicate that SIAD is a progressively cooperative process. Note that they increase linearly at the final SIAD stage. Range III is characterized by a break point to a nearly constant ΓdH and a maximum followed by a linearily declining ΓsH. Since ΓsH = ΓdH–ΓbH, its linear reduction must be due to the linear increase of ΓbH with ΓH2C2O4. Comparing with the linear ΓdH increase and simultaneous almost linear ΓsH decrease of sulfuric acid (Fig. 9) in this ΓHAc range, the constant normalized proton concentration in dispersion (ΓdH) depends obviously on the larger degree of oxalic acid dissociation in bulk. Increasing water fraction reduces the SIAD effect and the ΓbH dependence changes successively to the linear strong acid behavior. The dependence of surface excess (ΓsH) on water content is even more dramatic. The minimum at low acid concentration becomes deeper and wider extending SILD over the entire SIAD range. A reference is again provided by H2SO4 dispersions where the ΓsH decline extends over entire ΓH2SO4 Range III. Obviously, the minimum is due to a change in acid dissociation from surface sites. Thereafter, the change in positive or negative surface excess is relatively small, but the ΓsH-level diminishes with wt% H2O. The reduction of ΓsH and simultaneous constancy

of ΓdH must be due to displacement of protons from the surface (1/ KLII) due to anion adsorption (KAIV) followed by a shift of dissociation equilibrium (KLVI and KAVI) in dispersion. All processes are dependent on the strength of acids and polarity (dielectric constant) of the solvent. It should, however, be kept in mind that all proton concentrations are based on the assumption that pH can be measured potentiometrically in alcohol liquids and dispersions and that it can be converted to concentration of protons dispersed in bulk liquid and dispersion. 4.2. Conductivity measurements The conductivity of titania dispersions plotted as a function of oxalic and phosphoric acid concentration change gradually from “normal” reduced to “reversed” enhanced conductivity with higher amounts of acid. A break in the conductivity curve may be observed at low acid concentration indicating the onset of a SIAD reaction. 4.2.1. Dilute oxalic acid dispersions In order to properly understand reaction mechanisms, we focus first on the change in conductivity and pH when a very strong acid (HCl) is added to Al2O3 suspensions (right-hand diagram in Fig. 11 [64]). In particle-free suspensions, conductivity increases almost linearly with the strong hydrochloric acid concentration. The change in conductivity is mainly a result of extensive proton dissociation, since the ion mobility of all other ions is five-to-seven times smaller (Table 1). In the presence of 1% Al2O3, however, conductivity remains constant (almost zero) until a critical concentration (1 mmol/dm3) after which the conductivity change almost equals that of particle-free suspensions. All protons are obviously adsorbed in the initial SILD process. For increasing (constant) HCl concentration, the (vertical) difference between conductivity of particle-free and 1% Al2O3 suspensions increases within 0 b cHCL/ (mmol/dm3) b 1. The amount adsorbed may be deducted as the

Fig. 12. Conductivity of TiO2 dispersions in the presence of 0 (asterisk/cross/plus), 1 (squares), 2 (triangles), 5 (spheres), and 10 (diamonds) wt% TiO2 in methanol (upper-left diagram), (94 wt%) ethanol (upper-right diagram), and propanol (lower-left diagram) as a function of oxalic acid concentration. Bottom-right diagram; conductivity of 0,59 (diamonds) and 3,52 (triangles) mmol/dm3 oxalic acid in 1% (filled symbols), 2% (shaded symbols), 5% (dotted symbols), and 10% (open symbols) titania dispersions as a function of relative dielectric constant of 2-propanol, 1-propanol, ethanol, and methanol.

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Fig. 13. Conductivity of 0 (diamonds), 1 (squares), 2 (circles), 5 (upright triangles), and 10 (inverted triangles) wt% TiO2 dispersions in methanol (upper diagrams), (94 wt%) ethanol (uppermiddle diagrams), and propanol (lower-middle diagrams) plotted as a function of oxalic acid concentration (left diagrams) and as a function of normalized oxalic acid concentration (right diagrams). Extension of Fig. 18 diagrams indicated. Bottom diagrams 94 wt% ethanol as a function of sulfuric acid (left diagram) and normalized sulfuric acid (right diagram, increasing wt% TiO2 right-to-left) concentration.

(horizontal) difference between HCl concentration of 1% Al2O3 and particle-free suspensions at constant conductivities. This concentration difference remains relatively constant. The pH of particle-free solutions drop instantaneously by four units and remains thereafter nearly constant. For 1 wt% Al2O3 suspensions, the pH reduction is more gradual as HCl is added until the critical HCl concentration (1 mmol/dm3), after which the change becomes minimal [64]. Thus the pH difference is reduced linearly in this range. The amount of adsorbed acid may be derived from the (horizontal) difference between HCl concentration of 1 wt% Al2O3 and particle-free suspensions at constant pH. This concentration difference diminishes with decreasing constant pH level.

The adsorption of protons in dispersions of strong acids, such as HCl is supported by an increased positive ζ-potential reaching a maximum at the critical HCl concentration [64]. The chance in hydrochloric acid consumption at constant conductivity and pH do, however, not entirely agree. While conductivity of particle-free solutions increases with cHCL, pH remains constant after the initial drop. Since pH measurement is specific to protons in bulk solution, this suggests that conductivity is significantly influenced by the presence of other ion species than protons in suspension. For weak acids such as oxalic acid (left diagram in Fig. 11), the presence of 1% TiO2 enhances the relatively concentration-independent conductivity level from particle-free dispersions. The greatest conductivity

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Fig. 14. Dependence of conductivity on normalized acid concentration at various TiO2 and water weight fractions (10, 20, 30, 40 wt% water in 1, 2, 5, 10 wt% TiO2 methanol–oxalic acid dispersions, upper-left diagram; 10, 20, 40 wt% water in 1, 2, 5, 10 wt% TiO2 methanol–phosphoric acid dispersions, upper-right diagram; 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 wt% water in 1, 2, 5, 10 wt% TiO2 ethanol–oxalic acid dispersions, lower-left diagram; and 6, 20, 40, 60 wt% water in 1, 2, 5, 10 wt% TiO2 ethanol–phosphoric acid dispersions, lower-right diagram). Symbols are identified in Table 2. Inserts indicates expanded scales.

Fig. 15. Normalized conductivity of 2% by weight TiO2 methanol (left-side diagrams) and ethanol (right-side diagrams) dispersions plotted against mole fraction of water and normalized oxalic acid (upper diagrams) and phosphoric acid (lower diagrams) concentrations. Symbols identified in Table 2.

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Fig. 16. Side view enlargement of normalized conductivity of 2% by weight TiO2 dispersions (Fig. 15) plotted as a function of amount (mole) of acid (horizontally) and amount (mole) of water (vertically) emphasizing the conductivity emerging from the SIAD effect observed at low mole fraction of water and the increased normalized conductivity (dissociation) in solution resulting from increased water content. Symbols are the same as in Fig. 15 (identified in Table 2).

enhancement is observed for methanol dispersions. For ethanol dispersions, the conductivity increase is about half and it is very small for propanol dispersions. Simultaneously, pH is initially reduced (Fig. 3) alike for Al2O3 systems, after which it remains rather constant. The dependence of ζ-potential on oxalic acid concentration is largest for propanol and smallest for methanol shifting the isoelectric concentration (ciep, ζ = 0) to higher cHAc values as PrOH b EtOH b MeOH. The adsorption of acid anions results in charge reversal (Fig11), suggesting that there must be an increased specific adsorption of anionic species (KAIV) onto TiO2 particles. As shown for the Al2O3–EtOH–HCl system, this trend is opposite since HCl is a strong acid.

The role played by particle fraction may be investigated by plotting conductivity for increasing particle fraction as a function of oxalic acid concentration. This is illustrated together with the κ E depression of oxalic acid dissociation with decreasing polarity (εr) in Fig. 12. The onset of conductivity increase is delayed (shifted to higher oxalic acid concentration) by a larger particle fraction (1–10 wt%). This suggests that the SILD effect is indeed dependent on the total surface area (surface sites) available for adsorption. Since the conductivity change after the break point exceeds changes in the SILD range the SIAD effect is much greater. Obviously, KLIV b b KAIV when the SIAD effect is

Fig. 17. Molar conductivity of 94% by weight ethanol TiO2 (anatase) dispersions as a function of normal (left) and normalized (reduced molar, middle) and expanded normalized (right) oxalic acid concentration. Symbols; 1 (squares), 2 (circles), 5 (upright triangles), and 10 (inverted triangels) at 25oC.

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Fig. 18. Extrapolated limiting molar conductivity (limΛ = Λ∞) plotted as a function of weight fraction water for particle-free ethanol–oxalic acid ( squares), ethanol–phosphoric acid ( spheres), methanol–oxalic acid ( upright triangles), methanol–phosphoric acid (downright triangles), and ethanol–sulfuric acid ( diamonds)–water solutions. Scale of insert indicated.

initiated. Note that the acid constant for hydrochloric acid in water (pKC1 = − 7) exceeds that of sulfuric acid (pKS1 = − 3), of oxalic acid (pKO1 = 1.25) and of phosphoric acid (pKP1 = 2.16) [5]. A reduced dielectric constant suppresses conductivity probable because loss of solvation power of the increasingly hydrophobic solvents. Obviously, the SIAD (KAIV) is strongly depressed in these dilute non-polar dispersions.

4.2.2. Concentrated oxalic acid range The observed changes in conductivity are mainly opposite to reduction in conductivity found for “normal” aqueous suspensions exhibited by H2SO4 in EtOH (lowest diagrams in Fig. 13, range of diagrams in Fig. 12 indicated). When SIAD is activated, the conductivity is suddenly enhanced within a rather narrow oxalic acid concentration range (cooperative process) more the higher the particle solid fraction is. This is a clear demonstration of the SIAD effect characterized by proton dissociation resulting from neutral acid adsorption. The polarity of solvent is reflected in the κE-value. The propanol conductivity is only one-tenth of the methanol system. The overall trends remain, however, equal. Plotting conductivity of H2SO4 in EtOH as a function of normalized acid concentration (lowest diagrams in Fig. 13), the 10 wt% TiO2 plot has the steepest almost linear slope which diminishes with lower particle content (area). The initial dependence of conductivity on ΓH2C2O4 is independent on the particle fraction but levels off after a break point (constant plateaus for κred, Fig. 19) with increasing wt% TiO2. Fig. 14 shows the influence of an increasing concentration of water. As compared to changes in pH (Fig. 4), the curves are opposite and more spread. There is a dependence on both wt% TiO2 and wt% H2O. A reasonable plateau is found only for 5 and 10 wt% TiO2 in presence of phosphoric acid. In all cases, titania and water enhances the conductivity, but the shapes of κE remain. For constant 2 wt% TiO2, the dependence of conductivity on oxalic acid concentration can be brought to a master curve if both conductivity and acid concentration are normalized. Normalization enables a reasonable modeling of extensive experimental data. The normalized conductivity is plotted as a function of both the mole fraction of water and the normalized oxalic acid concentration in Fig. 15. The SIAD equilibrium observed for nearly anhydrous alcohol solutions [small x(H2O)] at low oxalic acid concentrations is successively concealed by the increased acid dissociation (larger slopes) induced

Fig. 19. Reduced conductivity (upper-left diagram), normalized dispersed proton concentration (upper-right diagram), and reduced normalized conductivity (lower-left diagram) plotted as a function of normalized oxalic acid concentration in 1 (squares), 2 (spheres), 5 (triangles), 10 (inverted triangles) wt% TiO2 (94 wt%) ethanol dispersions. Reduced normalized conductivity (lower-right diagram) plotted as a function of normalized dispersed proton concentration. Ranges I-III indicated.

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by the increased water content. In order to highlight this effect, a side view (mole fraction of water perpendicular to observator) enlargement of normalized conductivity of 2% by weight titania suspensions is plotted as a function of the normalized oxalic acid concentration in Fig. 16. The ionic transport in non-aqueous liquids is less extended. The solubility is low, and weak acids mostly appear in its molecular forms. The solubility of oxalic acid in anhydrous ethanol is 2.07 mol/dm3 which is almost two times higher than the solubility in water. The molecular form of oxalic acid is more stable, and the hydrogen oxalate anion is less stable in anhydrous ethanol, resulting in a reduced solubility. For example, the solubility of potassium hydrogen oxalate in water is 0.415 mol/dm3 and in anhydrous ethanol only 0.0033 mol/dm3. The molar conductivity plotted as a function of oxalic acid concentration is plotted in Fig. 17. The molar conductivity is characterized by a maximum which occurs at a lower concentration than the break point of the conductivity versus concentration (Fig. 13). When the reduced molar conductivity is plotted against the normalized concentration, all curves are almost superimposed. A closer inspection (right insert) reveals, however, that the maximum was slightly dependent on wt% TiO2. The extrapolated limiting molar conductivity (limΛ = Λ∞) for binary ethanol–water solutions is plotted as a function of water content in Fig. 18. The extrapolation was made to zero oxalic acid concentration (squares) and to zero square root of concentration (diamonds) from the lowermost experimental points. The solubility in pure ethanol was omitted due to low solubility. The average limiting molar conductivity for 94% by weight (x(H2O) = 0.140) and 90% by weight (x(H2O) = 0.221) oxalic acid solution was found to be 5.4 10−4 m2S/mol and 16.0 10−4 m2S/mol, respectively. The value used for protons in the model [66], Λ(H+) = 40.2 10−4 m2S/mol corresponds to about 25 wt% water solutions. The extrapolated average value in pure water (Λ∞ = 459 10−4 m2S/mol) is somewhat lower than 547.65 10−4 m2S/mol for

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water referred to (Table 1). In Fig. 19, the reduced and normalized conductivity is plotted against both pH and concentration of dispersed protons. Subtracting conductivity of particle-free solutions (Fig. 13) results in an almost concentration-independent reduced conductivity plateau within Range III. A master curve is produced when both conductivity and concentration are normalized with the total surface area of the particles. Both within the SIAD range (II) for surface-induced acid dissociation (rising Ωred) and at the plateau (constant Ωred) there is, however, a slight dependence on particle fraction. The master curve is slightly improved if Ωred is plotted against ΓdH but the plateau for the 5 and 10 wt% TiO2 systems appears as a single point

4.2.3. Summary of observations A summary of the experimental observations is presented in Fig. 19. Overall, the behavior agrees with the dependence of dispersed proton concentration although the influence of wt% TiO2 is opposite. It is no surprise that the reduced normalized conductivity (Ωred) is a master curve against both ΓH2C2O4 and ΓdH. Consequently, the conclusions drawn on concentration ranges I (SILD), II (SIAD), and III apply also for conductivity. This behavior represents a typical titration curve. The break point to a plateau represents the end point of titration of a weak base with a weak acid. The surface site saturation can be regarded as a Langmuir type adsorption to monolayer site coverage. The overall Ωred–ΓHAc dependence within Range III suggests that at least a third equilibrium (association constant KAVI) should be included in the discussed fitting procedure. As shown, the Ωred changes resemble but do not match those of normalized dispersed proton concentration. This explains the shortcomings of the suggested model [66]. Moreover, when developing models [66,68], any fit should preferably be made to master curves.

Fig. 20. Zeta-potentials of TiO2 dispersions in the presence of 1% (squares), 2% (triangles), 5% (circles), and 10% (diamond) titania in methanol (upper-left diagram), 94% ethanol (upperright diagram), and propanol (lower-left diagram) as a function of oxalic acid concentration. Bottom-right diagram; zeta-potential of 0.59 (filled symbols) and 3.52 (open symbols) mmol/ dm3 oxalic acid in methanol (diamonds), ethanol (squares) and propanol (triangles) titania suspensions as a function of particle fraction.

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4.3. Zeta-potential measurements As indicated in the Introduction, both conductivity and ζ-potential are transport properties, while pH represents the equilibrium chemical potential. Conductivity and pH (ΓdH and ΓsH) represent solution properties while ζ-potential characterizes charging of particles. The effective charge of particles represented by zeta-potential is a key property determining the macroscopic stability (viscosity) of dispersions. It also provides indirect information on the nature of charge exchange and specificity at particle surfaces. The surprisingly large ζ-potentials found in anhydrous alcohols are remarkable since the dielectric

constant is rather low (20 b εr b 35, Fig. 12, Table 1). Due to preferential solvation of large acid anions in non-aqueous solvents, protons are adsorbed on particle surfaces (SILD) providing them with a positive charge. The catalytic autoprotolysis model [64] explains the substantial positive ζ-potential found already in acid-free suspensions. An accurate determination of the absolute surface charge density is very difficult and therefore points of zero charge are difficult to determine experimentally. The best technique is determination of ζ-potential which enables an equalization of point of zero charge with isoelectric point. The interpretation of double layer of the DLVO model [69–72] is simple. Since the field strength is small due to a very low ionic strength, zeta-potential

Fig. 21. Zeta-potential of 1 (squares), 2 (circles), 5 (upright triangles), and 10 (inverted triangles) wt% TiO2 in methanol (upper diagrams), ethanol (upper-middle diagrams), and propanol (lower-middle diagrams) plotted as a function of oxalic acid concentration (left diagrams) and normalized oxalic acid concentration (right diagrams). Open symbols represent zeta-potentials measured for 10-25 wt% TiO2 dispersions. Zeta-potential of ethanol dispersions plotted as a function of sulfuric acid (lower-left diagram) and normalized sulfuric acid (lower right) concentration. Note different expansion of ΓHAc scale.

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provides an accurate representation of surface potential. Because of the low-dielectric constant, only a few charges suffice to yield a potential that is of the same magnitude as for aqueous systems. Large ζpotentials have indeed been reported in low-dielectric solvents in which the amount of ionic species is low [55–63,77,78]. Impurities have, however, a profound influence on charging [55]. A small interparticle interaction force means that the pair interaction between particles may be modeled by Coulombs law. It is thus of interest to investigate how ζ-potential is related to conductivity and proton concentration and whether this can provide some insight to the exceptional charging phenomena observed. 4.3.1. Dilute oxalic acid range As done with conductivity (Figs.11 and 12), we focus first on the change in ζ-potential as a function of acid concentration and pH in order to properly understand the reaction mechanisms. In Fig. 20, ζ-potential of methanol, ethanol, and propanol TiO2 suspensions is plotted as a function of acid concentration. Fully in line with increased conductivity (ionic strength) of alcohol suspensions, the surface potential is first screened by adsorbed oxalic acid molecules (KAI, Fig. 1). The ζ-potential is thereafter reversed from positive to negative for the lowest particle loadings due to specific anion adsorption (KAIV), but the effect is delayed for high particle fractions due to incomplete surface site saturation. The total range of ζ-potential change is greatest for propanol and smallest for methanol suspensions due to the lower solubility of ions and higher solubility of neutral acid in liquids of decreasing dielectric constant. The break point of ΓdH and maximum ΓsH conductivity occur roughly at the isoelectric concentration of zero ζ-potential. As shown in Fig. 20, the ζ-potential increases almost linearly with wt% TiO2, except for 1 wt% particle dispersions having a proportionally lower ζ-potential. It seems that both dielectric constant and particle fraction determine the properties of dilute particle dispersions. All critical

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concentrations are shifted to higher oxalic acid concentration with increased particle fraction. On the contrary, charge reversal is shifted to lower acid concentration with a reduced dielectric constant (MeOH to PrOH). 4.3.2. Concentrated oxalic acid range Although the main events occur in dilute suspensions an extended concentration range provides a better separation of the main properties for each system (Fig. 21, range for diagrams in Fig. 20 indicated). The reduction of ζ-potential from its positive value in oxalic acid-free solutions (SILD effect) to negative values must ascribed to the SIAD reaction (KAIV) due to adsorbed oxalate anions. The dependence of ζ-potential on oxalic acid concentration in methanol resembles that of the sulfuric (strong) acid system. The initial relatively linear and large concentration dependence is successively enhanced for ethanol and propanol systems. Normalization of concentration brings the dependencies to a master curve. Note the strong dependence of ζ-potential on normalized acid concentration below Γiep, which indicates that different mechanisms are active on each side of it. Two examples of influence of water on ζpotential are presented in Fig. 22. The initially constant ζ-potential observed for oxalic acid systems is expanded for phosphoric acid systems. A general observation is that an increased titania content enhances the zeta-potential. Curves representing constant fractions of titania, but increasing water content enhance zeta-potential at low acid concentrations but depresses it at high acid concentrations. The curves intersect roughly at ζ = 0 (isoelectric concentration) as a function of oxalic acid concentration. The common intersection point is above it (ζ N 0) as a function of phosphoric acid concentration indicating specific adsorption. All constant wt% H2O curves seem to be nearly superimposed when plotted against acid concentration. Although pH is not an ideal measure of proton exchange, the peculiarities in particle load and water fraction become obvious in Fig. 23.

Fig. 22. Zeta-potential at various TiO2 and water weight fractions (10, 20, 40 wt% water in 1, 2 5, 10 wt% TiO2) methanol–phosphoric acid (upper-left diagram) and normalized phosphoric acid (upper-right diagram) dispersions. Zeta-potentials of (10, 20, 30 ,40, 50, 60, 70, 80, 90, 100 wt% water in 1, 2 5, 10 wt% TiO2) ethanol–oxalic acid (lover-left diagram) and ethanol– normalized oxalic acid (lover-right diagram) dispersions. Symbols are identified in Table 2.

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Fig. 23. Dependence of zeta-potential on pH at various TiO2 and water weight fractions (10, 20, ,30, 40,50, 60, 70, 80, 90, and 100 wt% water in 1, 2 5, 10 wt% TiO2) methanol–oxalic acid (upper-left diagram), methanol–phosphoric acid (upper-right diagram), ethanol–oxalic acid (middle-left diagram), ethanol–phosphoric acid (middle-right diagram), ethanol–sulfuric acid (lower-left diagram), and propanol–oxalic acid (lower-right diagram) dispersions. Symbols are identified in Table 2.

In order to rationalize these observations, the non-specific and specific changes of ζ-potential in aqueous solutions of ions are presented in Fig. 24. The upper-left figure represents normal indifferent screening by cations (left side) and anions (right side) both neutralizing, but not reversing the ζ-potential. The upper-right figure shows how anions (left side) and cations (right side) reverse ζ-potential charge by specific adsorption. The lower-left figure illustrates that the curves correspond to particles to which both anions (low pH) and cations (high pH) are specifically adsorbed to the extent that zeta-potential is reversed (mirror picture). An increased particle fraction (larger surface area) causes a reduction of pHiep without changing the shape of the curve to a great extent. The lower-right mirror picture shows how an increase of water concentration initially enhances pHiep and ζ-potential before an increasingly abrupt charge reversal. This effect is enhanced in less polar solvents and for weaker acids. Absence or low amount of water leads to a peculiar bending (buffering) of ζ-potential back toward higher pH after surface site saturation (Fig. 23). Note that the curves extrapolate to an almost common ζ-pH point for highest acid concentrations (lowest ζ-potentials). When the isoelectric pHiep is extracted from Fig. 23 and converted to isoelectric concentration of dispersed protons (cdH)iep, the pattern becomes clearer. As shown in Fig. 25, pHiep and (cdH)iep have opposite

dependencies on wt% H2O and on wt% TiO2. The isoelectric point (pHiep) is particularly high between about 20 b wt% H2O b 50 pHiep while (cdH)iep is compressed to nearly constant in this range. Above wt% H2O N 50 pHiep declines and (cdH)iep begins successively to increase. Both pHiep and (cdH)iep are almost linearly dependent on wt% TiO2. Equal water content collects all systems to master curves which are distinguishable from each other. Obviously the influence of wt% H2O b wt% TiO2, but both have a systematic influence on the isoelectric point (surface charging). This corresponds to the conditions at equivalence point and surface saturation. The dependence of ζ-potential on adsorbed proton concentration is shown in Fig. 26 for 94 wt% EtOH dispersions. When tilted, the curve resembles the plot of csH plotted as a function of normalized acid concentration (Fig. 10). The plot of ζ-potential against csH decreases almost linearly within the (SIAD) Range II and decreases almost linearly within Range III. The dependence increases with particle load. The ζ-potential change is larger at (csH)iep and more extended for phosphoric acid dispersions. The curves become more condensed, but not overlapped (master curve) when ζ-potential is plotted against surface excess (ΓsH). The spread of the curves is again larger for phosphoric acid system. The ζ-potential thus responds to the dispersion charging and surface charging by different mechanisms. The reduction of surface excess (surface charge density) at negative ζ-potentials is rather extensive.

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Fig. 24. Schematic illustration of typical changes in zeta-potential due to changes of pH, ionic strength (pI), and specific ion concentration (pM). Upper-left diagram represents normal (non-specific) and upper-right diagram represents non-coulombic (specific) ion effects. Lower diagrams show (Fig. 35) reversed (mirror) dependence on pH of 1, 2, 5, 10 wt% TiO2 (curves from right to left) in 90 wt% methanol–oxalic acid (lower-left diagram) and in 90 wt% methanol–phosphoric acid (lower-right diagram). The dotted line represents 60 wt% methanol– phosphoric acid dispersions. Increased acid concentration is directed opposite to pH.

In order to establish whether surface charging can equally well be represented by conductivity, the ζ-potential is also plotted against the reduced (κred) and normalized reduced conductivity (Ωred) (Fig. 27). All curves resume a similar sigmoid shape, but the presence of a plateau, the dependence on reduced conductivity almost ceases at isoelectric point for negative ζ-potentials. The reduced normalized conductivity (Ωiep) is particularly effective in producing a master curve. Obviously, the dependence of ζ-potential (particle property) on the adsorbed proton concentration on the one hand and on the reduced (normalized) conductivity on the other hand (dispersion property) is clearly related but differs

substantially from each other particularly at high acid and proton concentrations (plateau region). 4.3.3. Summary of observations Zeta-potential dependence on pH corresponds to specific anion (low pH—negative ζ-potential) and proton (high pH—positive ζ-poential) adsorption to the extent that the potential is reversed. As shown, the ζ-pH curves are mirror pictures of the dependence of ζ-potential on pH in aqueous dispersions. The ζ-pH dependence is related to solvent polarity and acid strength in a complex way. Dependence of ζ-potential

Fig. 25. Dependence of isoelectric pHiep on wt% (H2O, upper-left diagram) and wt% (TiO2, upper-right diagram). Dependence of isoelectric dispersed proton concentration (cdH)iep on wt% (H2O, lower-left diagram) and on wt% (TiO2, lower-right diagram). Symbols: MeOH–H2C2O4 (diamonds), MeOH–H3PO4 (squares), EtOH–H2C2O4 (triangles), EtOH–H3PO4 (circles), EtOH– H2SO4 (shaded asterisk), and PrOH–H2C2O4 (shaded plus) dispersions. Left diagrams: 1 (filled), 2 (low-shaded), 5 (open), and 10 (raster) wt% TiO2. Right diagrams: 6/10 (filled), 20 (lowshaded), 30 (open) and 40 (raster), 50 (right-shaded), and 60 (left-shaded) wt% H2O.

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Fig. 26. Zeta (ζ) potential plotted as a function change in adsorbed proton concentration (left diagrams) and surface excess of protons (right diagrams) from oxalic acid (upper diagrams) and phosphoric acid (lower diagrams) in 1 (squares), 2 (spheres), 5 (triangles), 10 (inverted triangles) wt% TiO2 (94 wt%) ethanol dispersions. Ranges I-III are indicated.

Fig. 27. Zeta (ζ) potential plotted as a function of reduced conductivity (left diagrams) and reduced normalized conductivity (right diagrams) for 1 (squares), 2 (spheres), 5 (triangles), 10 (inverted triangles) wt% TiO2 (94 wt%) ethanol suspensions with oxalic acid (upper diagrams) and phosphoric acid (lower diagrams).

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Fig. 28. Schematic illustration of the dependence of viscosity on acid concentration (pH), ionic strength (pI), and specific ion concentration (pM). Left-diagram shows the influence of nonspecific adsorption of ions (ionic strength) and right-diagram the influence of specifically adsorbed ions. A master line may usually be found prior to isoelectric point (pHiep), but an increasing residual viscosity after isoelectric point. Reference behavior at low ionic strength is illustrated by the solid lines. A decade higher viscosity is usually found in the presence of a decade smaller concentration of specifically bound ions. Moreover, due to overcharging, the viscosity maximum may shift and turn to a break point for continuously increasing viscosity. Range I (SILD), Range II (SIAD), and Range III are indicated.

on the selected equilibrium (pH, cdH, ΓdH, ΓsH) and transport (κ(red), Ω(red)) properties of the dispersion medium suggests that three equilibria are involved (Ranges I–III). Each of them can be easily distinguished experimentally. A plot of ζ-potential against the surface excess of adsorbed protons (ΓsH) is a tilted image of its dependence on normalized acid concentration. The reduced (normalized) conductivity also reveals three equilibrium ranges, but different dependencies on solution and

surface charging are clearly discerned particularly in the plateau region. The multiple mechanisms contributing to the overall properties become particularly observable when ζ-potential is plotted as a function of pH for different particle loads and water contents. It is obvious that both SILD and SIAD processed are active and coupled as illustrated in Fig. 1. Obviously ζ-potential depends primarily on adsorbed ion species rather than dissolved ions.

Fig. 29. Viscosity ratio (η/ηmax measured at 0.51 s−1, triangle, 5.81 s−1, circle, 58.1 s−1, square shear rate), zeta-potential (diamonds), and pH (asterisk) of 10 wt% H2O–H2C2O4 (upper diagrams), 25 wt% EtOH–H2C2O4 (middle diagrams) and 25 wt% EtOH-H2PO4 (lower diagrams) TiO2 dispersions plotted as a function of normalized acid concentration (left diagrams) and pH (right diagrams).

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Fig. 30. Surface excess of protons (inverted triangles, 0 b ΓsH/(μmol/m2) b 0.7, 10 wt% TiO2), viscosity (diamonds, 25 wt% TiO2 recorded at 58.1 s−1 shear rate), and model fit to viscosity (dotted line, [12]) as a function of oxalic acid in 94 wt% ethanol. Broken-dot lines illustrate the two possible viscosity maxima.

4.4. Viscosity measurement Viscosity provides an ideal test for the nature and stability of suspensions. A maximum viscosity is expected to emerge at or near isoelectric (ζ = 0) pH or concentration [19,20,25]. Moreover, if the viscosity does not return to its initial value after isoelectric point is a sign of specific ion adsorption (Fig. 28). Fig. 28 illustrates how viscosity maximum is related to changes in ζ-potential and pH [19,20,25]. Since the viscosity is strongly dependent on the particle load, nature of solvent, and type of acid, it is divided by the (extrapolated) maximum viscosity to yield a viscosity ratio (η/ ηmax). The viscosity ratio is plotted against normalized acid concentration and pH in Fig. 29. Plots of viscosity against pH were (like ζ-pH curves) mirror images of aqueous dispersions (Fig. 28). Indeed, the maximum viscosity agrees with the isoelectric point (pHiep). The viscosity decline above pHiep (SIAD range) follows reasonably well a master curve for all share rates. A spread of η-pH dependencies is observed at pH b pHiep, probably due to specific anion adsorption. Evaluation of adsorption specificity from viscosity peak symmetry is not possible due to truncation as a result of buffering at pH b pHiep. In order to relate the general behavior, the adsorbed proton concentration (surface excess), viscosity (diamonds 25 wt% TiO2 recorded at

58.1 s−1 shear rate), and a model fit to viscosity (dotted line, [12]) are in Fig. 30 plotted as a function of normalized oxalic acid concentration in 94 wt% ethanol. The onset of viscosity enhancement seems to coincide with the onset of ΓsH increase. The less acidic side of isoelectric point is characterized by a neglectable viscosity (SILD Range I) followed by a common viscosity ratio increase (SIAD Range II). The appearance of a break point for ΓdH and maximum for ΓsH (Figs. 6,8,10) correspond to two alternative viscosity maxima out of which the latter coincide with isoelectric point. The two maxima can be extracted from intersections of linear viscosity ratio segments near isoelectric point. Obviously, the ion adsorption and solvent/acid dissociation equilibria influence the macroscopic properties of dispersions. Specific adsorption may be identified from the symmetry of the viscosity peak as a function of pH. A substantial non-relaxed viscosity remains indeed after isoelectric concentration. The normalized surface excess of protons matches with the viscosity maximum. Fig. 31 illustrates the dependence of maximum viscosity on normalized acid concentration and the relationship between normalized acid concentration at maximum viscosity and normalized isoelectric concentration at increasing shear rates. As shown, maximum viscosity depends strongly on shear rate, nature of solvent and concentration of acid. The high viscosity found at lowest shear rate is due to shear enforced structure which is removed at high shear rate or continuous shearing [26,45]. Despite the exceedingly low ηmax values found at high shear rates, the dependence of viscosity ratio on normalized acid concentration agree mutually surprisingly well. The concentration at maximum viscosity is somewhat smaller but follows relatively close the rather constant isoelectric concentration. Model considerations based on DLVO theory [12,45] predicts that viscosity ratio should be proportional to squared ζ-potential. In addition, it is expected that both branches are then superimposed to a master line (Fig. 32). A reasonably straight line to η/ηmax = 1 is found slightly off isoelectric point (ζ = 0). Alike the plots of viscosity against pH, there is a strong truncation of curves due to reduced stability close to isoelectric point which appears as reduced and fluctuating viscosity ratios. A much higher ζ-potential is required for 10 wt% H2O–H2C2O4 and 25 wt% EtOH–H2PO4 as compared to 25 wt% MeOH–H2C2O4 and 25 wt% EtOH–H2C2O4 systems to obtain full suspension stability (η/ηmax = 0). However, it seems that DLVO theory is capable to model the dependence of viscosity ratio on square of ζ-potential despite the nonrelaxed viscosity above isoelctric concentration (Γiep) or below pHiep [12]. It was previously stated that zeta-potential is the best technique to determine interactions within double layer in medium and low-dielectric

Fig. 31. Left diagram: Maximum viscosity in Pas measured at different at 0.581 s−1 (triangles), 5.81 s−1 (circles), and 58.1 s−1 (squares) shear rates (increasing rate, filled, and decreasing rate, dotted) for 10 wt% H2O–H2C2O4 (at 1,43 μmol/m2), 25 wt% MeOH–H2C2O4 (at 2,00 μmol/m2), 25 wt% EtOH–H2C2O4 (at 1.25 μmol/m2), and 25 wt% EtOH–H2PO4 (at 1.66 μmol/m2) titania dispersions. Right diagram: Normalized concentration at maximum viscosity (dotted symbols) and normalized isoelectric concentration (filled symbols) for H2O–H2C2O4 (diamonds, 1.64 b Γiep/(μmol/m2) b 1.66) MeOH–H2C2O4 (triangles, 2.08 b Γiep/(μmol/m2) b 2.11) EtOH-H2C2O4 (triangles, 1.80 b Γiep/(μmol/m2) b 1.83) and EtOH–H2PO4 (circles, 1.92 b Γiep/(μmol/m2) b 1.97) TiO2dispersions as a function of increasing shear rate.

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Fig. 32. Viscosity ratio (η/ηmax measured at 0.51 s−1, triangle, 5.81 s−1, circle, 58.1 s−1, square shear rate) of 10 wt% H2O–H2C2O4 (upper-left diagram), 25 wt% MeOH–H2C2O4 (upper-right diagram), 25 wt% EtOH–H2C2O4 (lower-left diagram), and 25 wt% EtOH–H2PO4 (lower-right diagram) titania suspensions plotted as a function of squared ζ-potential.

suspensions. Since the field strength is small due to a very low ionic strength, ζ-potential provides an accurate representation of surface potential. Because of the low-dielectric constant only a few charges suffice to yield a potential that is of the same magnitude as for aqueous systems.

As found here, large ζ-potentials have previously been reported in lowdielectric solvents in which the amount of ionic species is low [55–64, 73,74]. A small interparticle interaction force means that the pair interaction between particles is completely described by Coulombs law. For

Fig. 33. Viscosity ratio (η/ηmax measured at 0.51 s−1, triangle, 5.81 s−1, circle, 58.1 s−1, square shear rate of 10 wt% H2O–H2C2O4 (upper-left diagram), 25 wt% MeOH–H2C2O4 (upper-right diagram), 25 wt% EtOH–H2C2O4 (lower-left diagram), and 25 wt% EtOH–H2PO4 (lower-right diagram) titania suspensions plotted as a function of εraζ2/1000.

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systems where Coulombic repulsion rather than the repulsion due to slowly decaying electrical double-layer overlap, expressions for stability ratio (W = k D2 /kR2 = 105, D = diffusion-controlled and R = repulsion barrier-controlled coagulation) have been derived [69–72]. The stability ratio may be expressed as a ratio of second-order rate constant for diffusion-controlled (rapid) coagulation and electrical repulsion controlled (slow) coagulation. Based on the expression for stability ratio and assuming W = 105 for stable dispersions Morrison [78] found that the ratio εraψ20/1000 N 1 for dispersion stability where a [μm] and particle radius and surface potential ψ0 = ζ [mV]. Viscosity ratio (η/ηmax) is plotted against (εraψ20/1000) in Fig. 33. As expected from Fig. 32, the linearity prevails slightly off isoelectric point. However, the stability ratio has to be somewhat modified for each system in order to match with the break point from stable suspensions (η/ηmax = 0) to increasing viscosity ratio when isoelectric point is approached. Only 25 wt% EtOH–H2PO4 system performs close to the expectation. The instability close to isoelectric point is successfully explained by the model, since εraψ20/1000 is less, but not in excess of unity. In these calculations, zeta-potentials determined for 10–25 wt% TiO2 dispersions were used which may diverge from reference zetapotentials determined in more dilute dispersions. Due to the semipolar nature of alcohols, the stability ratio needs adjustments. 4.4.1. Summary of observations Plots of viscosity against pH were (like ζ-pH curves) mirror images of aqueous dispersions to which non-specific alkali (OH) is added. The common viscosity increase occur at pH N pHiep and a spread of η-pH dependencies are observed at pH b pHiep, probably due to diminished stability as a result of specific anion adsorption. An evaluation of adsorption specificity from viscosity peak symmetry is not possible due to truncation as a result of buffering at pH b pHiep. However, the expected viscosity is available when plotted as a function of (normalized) acid concentration revealing clearly Range I (SILD), Range II (SIAD), and Range III (specific and neutralization reactions). The viscosity peak is reproduced by surface excess of protons supporting their predominating role in surface charging and suspension stabilization. Two viscosity maxima may be extracted at or near isoelectric concentration of acid. Both viscosity maxima are strongly dependent on particle load, nature of solvent, and type of acid, but also on the shear rate. These dependencies can largely be accounted for by dividing viscosity with maximum viscosity to produce a viscosity ratio (η/ηmax). The specificity of ion adsorption can be evaluated from the symmetry of viscosity peak by plotting viscosity ratio as a function squared ζ-potential. Symmetry of the viscosity peak depended on the concentration scale used and is also influenced by buffering of acids. Previously tested DLVO-based models [12,45] agreed fairly well with plots of η/ηmax against ζ2 and εraψ20/1000 which provide an experimental evaluation of the stability of the system. With some adjustments of fit parameters, both the DLVO and Coulomb interaction based models seem to equally well describe the features of the 20 b εr b 35 solvent suspensions. 5. Conclusions • Equilibrium (pH and proton concentrations) and transport properties (conductivity, zeta-potential, and viscosity) are closely related but respond differently to the different states of the suspensions. Note that the changes occur within 2 b pH b 4 which is a wider range than 3 b pH b 4 identified as optimal for acid complexation in aqueous dispersions. From a close analysis of dependencies, it becomes obvious that proton concentration is not fully proportional to (reduced, normalized) conductivity. • The extensive experimental results were successfully condensed to master curves which reveal three major proton (cation) and anion exchange ranges characterizing SILD (I), SIAD (II), and recombination (III) processes. Overall the conductivity curves represent titration of

a weak base with a weak acid. • The results exhibit the shortcomings of the suggested model [66]. Model fits should be made to proton (or anion) surface excess curves rather than to conductivities. Moreover, master curves representing a wide range of experimental data are needed in order to improve the evaluated models [66,68]. • Zeta-potentials correspond to specific both anion and cation (proton) adsorption to the extent that the potentials are reversed. Since acids are added, the ζ-pH curves are thus mirror pictures of the dependence of ζ-potential on pH in aqueous dispersions. The ζ-pH dependence is related to solvent polarity and acid strength in a complex way. Isoelectric point (concentration and pH) of ζ-potential was successfully related to cdH-, ΓdH-conductivity break points and to ΓsH maxima. The dependencies showed that several mechanisms were determining particle charging when concentration of acid was increased. • Viscosity is particularly useful to provide an overall evaluation of the influence of charge interactions on dispersion stability. In alcohol dispersions, two viscosity maxima could be identified. Only one of them matched fully with the isoelectric point (acid concentration, pH and proton concentration). Plots of viscosity against pH were (like ζ-pH curves) mirror images of aqueous dispersions. The common viscosity increase occur at pH N pHiep and a spread of η-pH dependencies are observed at pH b pHiep, probably due to a decreased stability as a result of specific anion adsorption. An evaluation of adsorption specificity from viscosity peak symmetry is not possible due to truncation as a result of buffering at pH b pHiep. Viscosity as a function of squared ζpotential gave also information on specific adsorption of ions and the range of stability and instability of dispersions. Acknowledgements Academy of Finland (contract nr. 116466), Center of Excellence for Functional Materials (FunMat) and Graduate School of Materials Research (GSMR) are acknowledged for financial support. References [1] Rosenholm JB, Kosmulski M. Adv Colloid Interface Sci 2012;51:179–82. [2] Jolivet J-P. Metal oxide chemistry and synthesis. Chichester, West Sussex, UK: John Wiley & Sons Ltd.; 2000. [3] Fowkes FM, Mostafa MA. Ind Eng Chem Prod Res Dev 1978;17:3. [4] Rosenholm JB. In: Tadros ThF, editor. Colloid Stability: The Role of Surface Forces –, Colloids and Interface Science Series. Weinheim, Germany: Wiley-VCH; 2007. p. 1. [5] Ringbom A. Complexation in analytical chemistry. New York, USA: WileyInterscience; 1963[Appendix]. [6] Rosenholm JB, Lindén M. In: Birdi KS, editor. Handbook of Surface and Colloid Chemistry. 3rd Ed. Boca Raton, USA: CRC Press; 2008. p. 439–97 [Ch.10.]. [7] Harju M, Halme J, Järn M, Rosenholm JB, Mäntylä T. J Colloid Interface Sci 2007;313: 194. [8] Harju M, Järn M, Dahlsten P, Rosenholm JB, Mäntylä T. Appl Surf Sci 2008;254:7272. [9] Harju M, Järn M, Dahlsten P, Nikkanen j-P, Rosenholm JB, Mäntylä T. J Colloid Interface Sci 2008;326:403. [10] Harju M, Areva S, Rosenholm JB, Mäntylä T. Appl Surf Sci 2008;254:5981. [11] Rosenholm JB, Rahiala H, Puputti J, Stathopoulos V, Pomonis P, Beurroies I, et al. Colloids Surf 2004;A250:289. [12] Dahlsten P, Kosmulski M, Rosenholm JB. Colloids Surf 2011;A376:42. [13] Rosenholm JB, Manelius F, Strandén J, Kosmulski M, Fagerholm H, BymanFagerholm H, et al. In: Smart RSt C, Nowotny J, editors. Ceramic Interfaces: Properties and Applications. London, UK: IOC Communications Ltd.; 1998. p. 433–60. [14] Gustafsson J, Nordenswan E, Rosenholm JB. J Colloid Interface Sci 2003;258:235. [15] Gustafsson J, Nordenswan E, Rosenholm JB. Colloids Surf 2003;A212:235. [16] Rosenholm JB, Manelius F, Fagerholm H, Grönroos L, Byman-Fagerholm H. Progr Colloid Polym Sci 1994;97:51–8. [17] Kosmulski M, Rosenholm JB. J Phys Chem 1996;100:11681. [18] Shojai F, Pettersson ABA, Mäntylä T, Rosenholm JB. Prog Colloid Polymer Sci 1997; 105:1. [19] Kosmulski M, Gustafsson J, Rosenholm JB. J Colloid Interface Sci 1999;209:200 [Erratum 1999;209:449]. [20] Kosmulski M, Gustafsson J, Rosenholm JB. Colloid Polym Sci 1999;277:550. [21] Kosmulski M, Durand-Vidal S, Gustafsson J, Rosenholm JB. Colloids Surf 1999;A157: 245. [22] Kosmulski M, Eriksson P, Gustafsson J, Rosenholm JB. J Colloid Interface Sci 1999; 220:128. [23] Shojai F, Pettersson ABA, Mäntylä TA, Rosenholm JB. Ceram Int 2000;26:133. [24] Kosmulski M, Eriksson P, Gustafsson J, Rosenholm. Radiochim Acta 2000;88:701.

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