Double layer electrical conductivity as a stability criterion for concentrated colloidal suspensions

Double layer electrical conductivity as a stability criterion for concentrated colloidal suspensions

Colloids and Surfaces A: Physicochem. Eng. Aspects 520 (2017) 9–16 Contents lists available at ScienceDirect Colloids and Surfaces A: Physicochemica...

2MB Sizes 0 Downloads 4 Views

Colloids and Surfaces A: Physicochem. Eng. Aspects 520 (2017) 9–16

Contents lists available at ScienceDirect

Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa

Double layer electrical conductivity as a stability criterion for concentrated colloidal suspensions Robinson C.D. Cruz a , Ana M. Segadães b,∗ , Rainer Oberacker c , Michael J. Hoffmann c a b c

University of Caxias do Sul, Instituto de Materiais Cerâmicos (IMC), 95765-000 Bom Princípio, Brazil University of Aveiro, Department of Materials and Ceramics Engineering (CICECO), 3810-193 Aveiro, Portugal Karlsruhe Institute of Technology, Institute for Applied Materials, Ceramics in Mechanical Engineering, 76131 Karlsruhe, Germany

h i g h l i g h t s

g r a p h i c a l

a b s t r a c t

• Relationship between particle elec• • • •

trical conductivity and DLVO colloidal stability. Identified processing window for the stability control of concentrated suspensions. DLVO secondary attractive minimum lies at 1.5 kT for the equilibrium conductivity. At the minimum reversible distance (∼7 nm) particles conductivity is zero. More accurate measurement of static ␨–potential at the isoconductivity point.

a r t i c l e

i n f o

Article history: Received 7 October 2016 Received in revised form 13 January 2017 Accepted 20 January 2017 Available online 23 January 2017 Keywords: Colloidal interactions Particle conductivity DLVO Electrokinetics Alumina

a b s t r a c t The slightly attractive inter–particle equilibrium potential associated with electrostatically stabilized suspensions of minimum viscosity is described by the DLVO theory and commonly gauged by static ␨-potential measurements, plagued with experimental uncertainties. In this work, the electrokinetic mobility of alumina particles was measured in suspensions prepared with selected solids content and ionic strength, as well as was the electrical conductivity of each suspension and suspending liquid. Particles electrical conductivity was then calculated and related to the colloidal stability described by the DLVO theory, enabling the identification of a processing window for the stability control of concentrated suspensions. The maximum repulsive potential and distance between particles (∼46 nm) corresponds to the particles maximum conductivity. When the particles conductivity is zero, the diffuse layer is fully collapsed and they stand at the minimum reversible distance (∼7 nm). At the equilibrium conductivity, a potential curve is produced with a secondary attractive minimum of ∼1.5 kT at an inter–particle distance of ∼17 nm, as suggested by the DLVO theory and the Equipartition of Energy theorem. The condition for accurate measurement of static ␨-potential occurs at the isoconductivity point between particles and suspending liquid. © 2017 Elsevier B.V. All rights reserved.

1. Introduction ∗ Corresponding author. E-mail address: [email protected] (A.M. Segadães). http://dx.doi.org/10.1016/j.colsurfa.2017.01.059 0927-7757/© 2017 Elsevier B.V. All rights reserved.

The manipulation of nanoscale particles often requires the control of the mobility of suspended particles, which is the underlying

10

R.C.D. Cruz et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 520 (2017) 9–16

feature of many processing methods in a variety of key applications. These range from catalysis and biosensing to remediation of surface and subsurface oceanic oil spills, through centuries old slip casting of ceramic suspensions [1–7]. The key challenge in such processing methods is the ability to prepare stable suspensions of the starting powders, so they all rely on the comprehension of colloidal interactions and stability of concentrated suspensions. Colloidal interactions are determined by inter–particle forces and can be manipulated by changes on the electrolyte (suspending liquid) or by surface functionalization, in order to promote specific characteristics (e.g. protein, cell or bacteria adsorption on surgical tools and medical implants, particle wettability by conflicting solvents, environmentally benign stable emulsions, electrophoretic deposition of films and coatings). Particularly, it is important to know how the individual powder particles are spatially arranged within the suspension, for how long that arrangement is kept (i.e. colloidal stability) and how it propagates through the consolidation method into the green body, after removal of the suspending liquid. The need to remove the suspending liquid also explains why concentrated suspensions are generally preferred. Colloidal electrostatic stability is characteristic of dispersed suspensions with comparatively low solids loads [1–4] and is usually explained by the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory for the interactions between charged particle pairs [8,9]. Upon immersion in a polar liquid, adsorption or desorption of ionic species in solution, as dictated by the reaction constants of the corresponding dissociation equilibria, results in the development of electrical charges at the particles surface. As a consequence, ions of opposite charge are sequentially attracted to the particle surface, causing the development of a charged electrical double layer (internal Stern layer and outer diffuse layer) enveloping each particle. According to the DLVO theory, the total potential interaction energy between particle pairs results from the balance established between the repulsive potential, due to the electric charges present in the particles electrical double layer, and the attractive potential, due to the ever present long range London–van der Waals interactions (dispersion forces). When the repulsive potential is high, the total potential remains positive even for long separation distances and these suspensions are stable and unlikely to coagulate. If the repulsive potential decreases, a shallow attractive secondary minimum can be observed and particles tend to cluster at this distance (but strong short-range repulsive forces keep the particles from direct contact). By manipulating the ionic strength of the suspending liquid, hence, the thickness of the electrical double layer, the repulsive potential can be reduced enough as to destroy the repulsive energy barrier that opposes coagulation. This destabilizes the system and leads to flocculation (particles fall into a deep attractive primary minimum). The stability of dispersed suspensions was found to begin at the equilibrium inter–particle distance that corresponds to the net electrical potential within the DLVO shallow attractive secondary minimum and is usually associated with minimum viscosity. In essence, the diffuse layer controls particle interactions and its electrical potential is estimated, in practice, in electrokinetic particle mobility tests carried out as function of varying pH. In these experiments the potential value at the “interface” between double layer and electrolyte, called zeta–potential (␨–potential), is measured. Suspensions stability is associated with high ␨–potential, whereas flocculation is bound to occur at the isoelectric point (zero ␨–potential) [10–17]. Commonly, static (electrophoresis) ␨–potential is used but the values obtained are very sensitive to the experimental procedures. To overcome the experimental-related uncertainties encountered in static ␨–potential measurements, different models, usually complex and with different limitations, and alternative measurement

techniques were proposed to describe and calculate the value of ␨–potential. The measurement of particles mobility in Electrokinetic Sonic Amplitude (ESA) ␨–potential tests offers the access to changes in the ionic envelope of the particles double layer and the choice of calculation model [12,15]. Generally, the Helmholtz-Smoluchowski model is used, the major assumption in which is that particles are non–conducting, electrical conduction being carried out only by the suspending liquid. The model requires that the ionic strength is high enough to ensure thin double layers and proposes a limiting value ␬a > 100 (a is the particle radius and ␬−1 , the inverse Debye length, is its double layer thickness). In such cases, changes in the conductivity through the electrical double layer and the effects of the presence of added counter–ions and nonspecific adsorption become less important and might be neglected [10,11]. Other models were developed to describe ␨–potential for dilute suspensions and thick double layers (␬a ≈ 1), to include the effects mentioned above and other observed deviations from the original DLVO model [18–24]. Among those, O’Brien’s model, which considers both the electrical conductivity contribution of the diffuse layer and that of the suspending liquid, is frequently the preferred alternative [21]. Despite the different assumptions, both Helmholtz-Smoluchowski’s model and O’Brien’s propose a decrease of ␨–potential with increasing ␬a (increasing ionic strength in the suspending liquid) as the result of the compression of the diffuse layer. Changes in ionic strength in the suspending liquid also result in changes in its electrical conductivity. Electrical conductivity phenomena are less affected by the measurement technique [25–27] and can be described by generally simpler models. Previous work [28] carried out with aqueous suspensions of commercial ␣-alumina (1–35 vol.% solids) showed that the change in the conductivity of the suspension KS relative to that of the suspending liquid KL (i.e. relative conductivity, KS /KL ) could be described by Maxwell’s model for the conductivity of a mixture of two phases (such as suspensions, made of the continuous suspending liquid and the dispersed particles) as a function of the ratio ␣ between the particles conductivity KP and that of the electrolyte KL (i.e. conductivity ratio ␣ = KP /KL ) and the solids volume fraction ␾. More elaborate analytical models have been devised to theoretically predict the relationships between the relative conductivity and particle volume fraction and salt concentration [29] but Maxwell’s approach, which remains essentially correct, offers the benefit of experimental simplicity. In Maxwell’s model, for a given ␣, the relative conductivity varies according to KS /KL = 1 + K·␾;, i.e. linearly with ␾. Three special cases can be considered for the line slope K, depending on ␣: (1) when KP « KL (insulating particles, ␣ → 0), then K = −1.5; (2) when the particles and the electrolyte have equal conductivities (␣ = 1), K = 0; and (3) when KP » KL , (conductivity of the particles much higher than that of the electrolyte, ␣ → ∞), K = 3. Thus, an increase in the solids content might decrease, not affect, or increase the suspension conductivity, which can be lower than, equal to, or higher than that of the suspending liquid. In other words, Maxwell’s model for the conductivity of suspensions shows that paradoxical effects can occur: the addition of dielectric particles can result in increased suspension conductivity. The slope of the straight line in Maxwell’s model for the relative conductivity, K = (KS –KL )/(KL ·␾), which is called relative conductivity rate or electrical conductivity increment, was interpreted in terms of the DLVO theory and the particles double layer parameter ␬a. As ␬a changes in response to the changes in the ionic strength of the suspending liquid, so does the conducting to insulating character of the particles (expressed by ␣) and, as such, their contribution to the suspension conductivity (expressed by K). This work is aimed at throwing further light into the use of K as a suspension stability criterion and its interpretation in the light

R.C.D. Cruz et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 520 (2017) 9–16

Fig. 1. Effect of pH on the static ␨–potential (␮e ) of alumina suspensions (0.004 vol.% solids, 0.01 M KCl) in the as–prepared condition (AP) and after dialysis (AD).

of the DLVO theory, by relating the electrokinetic mobility of suspended particles with: (1) the electrical conductivities of particles, suspending liquid and suspension, (2) the electrolyte ion concentration (ionic strength) and (3) pH. 2. Experimental The ceramic powder used throughout this work was the commercial 99.97% pure RC-HP-DBM ␣-Al2 O3 (Baikowski Malakoff Industries, Inc, Reynolds, USA) whose density was taken as 3.98 g/cm3 . Particle size was calculated from specific surface area (SSA) measurements (N2 adsorption 5 point BET, Gemini 2370, Micromeritics, USA), given that light scattering–based techniques tend to over–estimate the particle size by favoring larger particles. Distilled water was used as suspending liquid (measured average conductivity of 1.0 ␮S/cm). Suspensions production started with the preparation of a purified, concentrated (35 vol.% solids) mother–suspension at pH = 6. The purifying process essentially involved a combined dialysis operation under slow magnetic stirring using ion exchanger beads (Merck Amberlite MB 6113 resin beads enclosed in Roth Nadir cellulose membrane dialysis tubing, with 50 mm diameter and 2.5–3.0 nm average pore size). Samples were collected at intervals and centrifuged, and the purifying process was considered complete when a constant low conductivity value was obtained for the suspending liquid (ion concentration < 0.001 M). Further details on the procedure can be found elsewhere [28]. Conductivity and pH measurements were carried out using the appropriate set of electrodes (WTW GmbH, Germany, TetraCon 325/inoLab, Cond Level2 at 400 Hz, and SenTix HW/inoLab, Ion Level2, respectively). Having prepared the mother–suspension, various diluted suspensions with selected solids load and pH could be produced just by adding distilled water and adjusting the pH value with HCl or KOH (Merck, Germany). For each solids loading, the desired ionic strength was obtained by adding the appropriate amount of KCl (Merck, Germany). This salt was selected because the two ions, K+ and Cl− , show similar ionic mobilities (respectively 7.62 and 7.91 × 10−8 m2 /sV) [30]. An additional advantage is that KCl dissociates completely in water and its hydrolysis behavior is little sensitive to the pH of the liquid. A KCl solution was used as reference electrolyte to obtain a calibration curve to translate the measured electrical conductivity values into ion concentration. In the concentration range used (0–40 mM), the conductivity of the solution was found to increase linearly with the KCl concentration, a direct consequence of the similar ionic mobility of the two ions.

11

Fig. 2. Effect of suspending liquid electrical conductivity KL on the dynamic ␨–potential (␮d ) of dialyzed alumina suspensions (2 vol.% solids, pH = 6) calculated from ESA measurements: (a) using O’Brien’s model; and (b) using Helmholtz-Smoluchowski’s model. Suspending liquid conductivity values (␮S/cm) are indicated at relevant points in curve (a).

The electrophoretic (static) mobility ␮e was determined on very diluted suspensions (0.004 vol.% solids) in the pH range of 3–12 (Laser-Doppler-Electrophoresis, Delsa 440SX, BeckmanCoulter GmbH, Germany). As before, KCl was added to vary the ionic strength. The dynamic electrokinetic mobility ␮d was determined from ESA measurements (AcustoSizer IIs, Colloidal Dynamics Inc., USA) on diluted suspensions (2 vol.% solids) in the pH range of 3–12 and frequency range of 1–20 MHz. Again, the ionic strength was varied with KCl. To convert ESA mobility data to zeta-potential [21], the solid density mentioned above was used, and the properties of the liquid were taken as those of water at 25 ◦ C. 3. Results and discussion 3.1. Contributions of electrolyte and particles to the electrical conductivity of suspensions The alien ions that always accompany commercial powders dissolve in the suspending liquid and affect the particles electrophoretic mobility ␮e and ␨–potential. As mentioned before, the removal process of those alien ions enables, later, the precise knowledge of the type and content of the ions in solution [28]. Fig. 1 compares the static ␨–potential vs. pH curves for the same alumina suspension (0.004 vol.% solids, 0.01 M KCl) in the as–prepared condition (AP) and after dialysis (AD). The HelmholtzSmoluchowski’s model states that ␨–potential should fall as the ionic strength increases but the two curves show significant differences, particularly for pH values below 5.7. Because those differences can often be accommodated within the experimental error range, this observation is generally dismissed as such. In fact, if the observed behavior of the AD suspension is not attributed to experimental uncertainty, it cannot be described by Helmholtz-Smoluchowski’s model. Therefore, because the model assumes non–conducting particles, changes in the conducting character of the particles and their electrical double layers might be at work in the absence of alien ions. If this is the case, that change should be detected by O’Brien’s model, which considers both the electrical conductivity contribution of the suspending liquid and also that of the diffuse layer. In other words, for any given dialyzed suspension, differences should be observed between the dynamic ␨–potential curves (␮d ) calculated from ESA measurements using the HelmholtzSmoluchowski’s model or O’Brien’s, as a function of increasing suspending liquid electrical conductivity KL (ionic strength). Fig. 2

12

R.C.D. Cruz et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 520 (2017) 9–16

illustrates this for dialyzed alumina suspensions with 2 vol.% solids equilibrated at pH = 6. The first point to note in Fig. 2 is that, from the same experimental results, the two models render different ␨–potential values, those calculated using the Helmholtz-Smoluchowski’s model (curve (b) in Fig. 2) being systematically lower. This supports the idea that there is an effective electrical conductivity contribution of the particles diffuse layer to ␨–potential. In the Helmholtz-Smoluchowski’s curve, the ␨–potential goes through a maximum in the low conductivity region as the conductivity of the suspending liquid increases. Given that this model proposes a continuous decrease of ␨–potential with increasing ionic strength of the suspending liquid, curve (b) in Fig. 2 indicates that the Helmholtz-Smoluchowski’s model can only be considered valid when the liquid conductivity is higher than 642.5 ␮S/cm (from d␨/dKL = 0 in curve b). This condition can now be compared with the limiting ␬a > 100 specified by this model. After the combined dialysis and surface cleaning process, the alumina specific surface area increased from the original 7.64 m2 /g (as–received powder) to 9.06 m2 /g, leading to a final calculated particle size dBET = 166 nm. Thus, if an average particle radius a = 83 nm is considered, the ion concentration needed to reach the ␬a > 100 specified by the Helmholtz-Smoluchowski’s model would be 134 mM KCl, corresponding to an electrolyte conductivity of 18.97 mS/cm. According to this model, only above these values the double layer would be thin enough for the particles electrical contribution to be negligible. The fact that, in curve (b) in Fig. 2, the maximum ␨–potential occurs at a much lower conductivity value (642.5 ␮S/cm) suggests that either selective ion adsorption at the particles surface is occurring and the double layer is shrinking much faster than predicted by the model, or that the limiting value specified by the model is overestimated. The ␨–potential curve calculated using O’Brien’s model (curve (a) in Fig. 2) can be interpreted as follows. In the dialyzed condition the suspending liquid, clean of alien ions, has low conductivity (55 ␮S/cm). Suspended particles acquire charge (a thick double layer that hinders particle mobility is formed) [21] and display a high ␨–potential (88.4 mV). As the ionic strength begins to increase (added KCl), charged particles attract any available counter–ions (Cl− ) that replace the water molecules previously adsorbed and specific adsorption occurs (formation of the inner Helmholtz layer), partially shielding the positive charge at the particles surface. As a result, the ␨–potential falls almost linearly from the initial value to a first minimum of 75.9 mV, when the conductivity is 121 ␮S/cm. As the ionic strength increases, the outer Helmholtz layer of co–ions (K+ ) builds up, the thickness of the diffuse layer decreases and the electrokinetic mobility of the particles increases towards a maximum ␨–potential of 83.5 mV (when the electrolyte conductivity is 277 ␮S/cm), where the outer Helmholtz layer becomes complete. Further increase in the ion concentration in the suspending liquid will only contribute to further compression of the diffuse layer and ␨–potential decreases again towards a minimum of 71.4 mV (corresponding to an electrolyte conductivity of 1416 ␮S/cm). Thus, the ␨–potential curve calculated with O’Brien’s model in Fig. 2 shows that the conducting character of particles and their double layer envelope changes with the ionic strength of the suspending liquid. This being the case, the contribution of particles to the suspension conductivity should also be dependent on the suspension solids content. Thus, the conductivities of suspensions and those of the corresponding suspending liquids were measured as the solids content increased, from diluted (5 vol.% solids) to concentrated suspensions (35 vol.% solids). Fig. 3 shows the striking effect of alien ions dissolved in the suspending liquid and the dialysis efficiency in removing them: the conductivity of the natural (as–prepared) suspension (AP) is always much higher than that of the corresponding dialyzed sus-

Fig. 3. Effect of solids volume fraction ␾ and attached alien ions on the electrical conductivity of the suspension (continuous lines) and corresponding centrifuged over–laying liquid (dashed lines), at pH = 6, for the as–prepared suspension (AP) and after dialysis (AD).

pension (AD). When soluble alien ions brought in with the solids are not removed from the suspension (AP condition), their content in the suspending liquid increases its ionic strength and increases with the solids content. As a result, the conductivity of the suspending liquid increases faster with the solids content than that of the suspension. On the contrary, although the alien ions have been removed by dialysis, the electrical conductivity of the dialyzed suspension (AD) still increases with the solids content and the conductivity of the suspending liquid is consistently lower than that of the suspension. Therefore, Fig. 3 shows that there is indeed an effective contribution of suspended particles and their double layer envelopes to the suspension conductivity, which changes with both the ionic strength (salinity) of the electrolyte and the suspension solids content. Dialyzed suspensions with solids contents varying from 5 to 35 vol.% were prepared, to which increasing KCl additions were made (0.4 mM < cKCl < 23.7 mM). The suspensions measured electrical conductivities KS and those of the corresponding suspending liquids KL are shown in Fig. 4. Fig. 4-A shows that the electrical conductivity of the dialyzed suspension obviously increases with the added salt content. For any given salt content, however, while the conductivity of all the suspending liquids (KL ) is very much independent of the solids content, the conductivity of the suspensions (KS ) not only varies with the solids content but also can be lower than, equal to, or higher than that of the corresponding electrolyte. This readily brings to mind Maxwell’s model for suspensions conductivity [28], according to which the relative conductivity KS /KL should vary linearly with the solids content ␾ (i.e. for a given ␣ = KP /KL , KS /KL = 1 + K·␾). Fig. 4-B shows, for the same suspensions presented in Fig. 4-A, how the relative conductivity KS /KL changes in response to changes in the solids content at a given ionic strength. Maxwell’s model for non–conducting particles (i.e. ␣ → 0) returns a straight line with a negative slope K, as shown by the dashed line. However, Fig. 4-B clearly shows that the salt content not only affects the K value in linear relationships (high ionic strength region II), but can also lead the dependency away from linearity (low ionic strength region I). Of course particle crowding, as the solids load increases, might have some influence on the non–linearity of the curves, particularly when the ionic strength is low (thicker double layers), i.e. for suspensions with K > 0. However, the conducting character of particles mostly depends on the characteristics of the electrical double layer, which are exclusively determined by the ions concentration in the liquid cKCl .

R.C.D. Cruz et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 520 (2017) 9–16

13

Table 1 Calculated values of double layer parameter ␬a, particle conductivity KP (calculated using Maxwell’s model [28]), intrinsic conductivity [K]␾=0 , and relative conductivity rate K = (KS − KL )/(KL ·␾), for dialyzed suspensions with different ionic strengths cKCl and solids contents ␾. cKCl (mM)

0.4 1.2 2.8 5.3 23.7

␬a

5.2 9.5 14.4 19.9 42.1

KP (␮S/cm)

142.67 224.85 307.31 293.36 59.73

Volume fraction of solids, ␾ 0.00

0.05

0.10

0.15

[K]␾=0

Relative conductivity rate, K = (KS − KL )/(KL ·␾)

0.94 0.27 −0.26 −0.78 −1.46

1.31 0.35 −0.25 −0.77 −1.43

2.32 0.75 −0.22 −0.71 –

2.47 – – – –

0.20

2.92 0.98 −0.17 −0.69 −1.34

0.25

0.30

0.33

0.35

3.40 – −0.16 −0.66 −1.30

4.28 1.30 – – –

– – −0.13 −0.63 −1.26

4.60 1.51 – – –

Fig. 6. Effect of solids volume fraction ␾ and the particles double layer parameter ␬a on the relative conductivity rate K (for the sake of clarity, only the K vs. ␬a curves for the limiting solids contents are plotted).

Fig. 4. Effect of solids volume fraction ␾, and salt concentration cKCl (mM), on: (A) the electrical conductivity of dialyzed suspensions (KS , continuous lines) and of the corresponding centrifuged over–laying liquids (KL , dashed lines); and (B) the relative conductivity KS /KL . For comparison, the dashed line in (B) represents Maxwell’s model for non–conducting particles.

Fig. 5. Effect of solids volume fraction ␾ and salt concentration cKCl (mM) on the relative conductivity rate K. The extrapolated intercept for ␾ = 0 is the suspension intrinsic conductivity [K]␾ = 0 .

Fig. 5 shows how the relative conductivity rate values K (extracted from the curves in Fig. 4-B and listed in Table 1) change with the liquid salinity. For any given salt concentration cKCl , Fig. 5 also shows that K varies linearly with the solids content ␾, which means that the solids effect on K can be “removed” if each K vs. ␾ line is extrapolated to ␾ = 0, as also shown in Fig. 5. By doing so, the relative conductivity rate K can be treated as a property of the liquid alone. Thus, the concept of intrinsic conductivity [K]␾=0 is introduced, as the hypothetical relative conductivity rate that a given suspension would have when its solids volume fraction is ␾ = 0 (values also listed in Table 1). The relationship between the relative conductivity rate K and the double layer parameter ␬a can now be investigated as the solids content varies (0.05 < ␾ < 0.35). The calculated ␬a values are also listed in Table 1 (the relevant equations can be found elsewhere [28]) and the resulting K vs. ␬a curves are plotted in Fig. 6 (for the sake of clarity, only the K vs. ␬a curves for the limiting solids contents are plotted). Fig. 6 shows that for any given solids content, the relative conductivity rate K tends to decrease and level off as the ion concentration in the liquid cKCl , hence ␬a value, increases. However, the effect of different solids content is only noticeable when the particles have thick double layers (low ␬a values) and that effect quickly wears off as the double layers get compressed (higher ␬a values). Moreover, there is a threshold ␬a value above which the K values become essentially independent of the solids content. In other words, when the particles electrical double layer is thin enough, their contribution to the suspensions conductivity becomes negligible. From this point onwards, the ␨–potential experimental determination becomes less sensitive to external factors fluctuations and calculations can be carried out with the Helmholtz-Smoluchowski’s model.

14

R.C.D. Cruz et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 520 (2017) 9–16

Fig. 7. Effect of particles double layer parameter ␬a on the suspension intrinsic conductivity [K]␾=0 and particle relative conductivity ␣ (␣ = KP /KL ). KP values were calculated using Maxwell’s model [28].

Fig. 7 shows the relationship between the intrinsic conductivity [K]␾=0 and the particles electrical double layer parameter ␬a. A trend similar to that of the relative conductivity rate (Fig. 6) can be observed, and the intrinsic conductivity becomes zero for ␬a = 12. Referring back to Fig. 6, this ␬a value should be that threshold value mentioned then, above which the particles contribution to the suspensions conductivity becomes negligible. These results indicate the existence of different conduction paths in the suspension (through the suspending liquid and through the particles electrical double layer). This being the case, which conduction path is dominant will be determined by the particle relative conductivity ␣ (i.e. ␣ = KP /KL ), which was calculated and is also represented in Fig. 7 (the relevant equations can be found elsewhere [28]). It can be seen that particles can, indeed, be conductive (␣ > 0), and that ␣ decreases exponentially (from 2.4 to 0.02) with increasing ␬a, sweeping nearly the entire conductivity range that is described by Maxwell’s model, from conducting to non–conducting particles (␣ = 0). Also, it can be seen that the ␬a = 12 corresponds to the condition at which particles conductivity equals that of the suspending liquid (␣ = 1, isoconductivity [27]). Given that the conductivity of the suspending liquid is hardly dependent on the solids content, as seen earlier in Fig. 4-A, the ␬a = 12 also separates the region in which the conductivity of the suspension is always higher than that of the suspending liquid (␣ >1, KS /KL > 1), from that in which it is always lower than that of the suspending liquid (␣ <1, KS /KL < 1), as seen in The suspending liquid conductivity at the ␬a = 12 value for the isoconductivity point (ICP) in Fig. 7 was found to be KL = 277 ␮S/cm, which coincides with that for the ␨–potential maximum calculated with O’Brien’s model (curve (a) in Fig. 2). In other words, the ICP occurs when the compression of the diffuse layer is about to begin. This finding clearly overcomes the limitations of ␨–potential determination and might have very important implications in colloidal consolidation methods.

3.2. Electrical conductivity in the light of the DLVO theory When the particles conductivity KP for each ion concentration is plotted against the ␬a values, as shown in Fig. 8 (KP values calculated with Maxwell’s model [28] are also listed in Table 1), it can be observed that the particle conductivity first increases linearly with ␬a, for low ␬a values, and then, for high ␬a values, decreases, presumably also linearly, when ␬a increases. The extrapolated intersection of the two lines should represent the ␬a value for maximum particle conductivity (␬a = 16, KP,Max = 335 ␮S/cm) and the

Fig. 8. Effect of double layer parameter ␬a, on the particles conductivity KP (calculated using Maxwell’s model [28]). Open symbols are extrapolated points and represent the ␬a values for maximum and zero particle conductivity (KP,Max and KP,0 , respectively).

Fig. 9. Effect of electrolyte conductivity KL on ␨–potential and particle conductivity KP (calculated using Maxwell’s model [28]). IHP and OHP are the inner and outer Helmholtz planes, respectively.

extrapolation towards high ␬a produces the ␬a value at which the particle conductivity is zero (␬a = 47, KP,0 ). Seeking a relationship between the particles conductivity and ␨–potential, the calculated KP curve can now be superposed on the O’Brien’s ␨–potential curve in Fig. 2, as shown in Fig. 9. It can be seen that: (1) the ␨–potential maximum at KL = 277 ␮S/cm occurs at the ICP (KP = KL ); and (2) for a while after the ICP, although the Stern layer is already complete (decrease in ␨–potential, as stated by the models), the particles conductivity is still increasing. The particles maximum conductivity occurs for an electrolyte conductivity KL = 500 ␮S/cm (after the ICP and O’Brien’s ␨–potential maximum, but before the Helmholtz-Smoluchowski’s maximum, at 642.5 ␮S/cm) and can, thus, be used to detect the effective beginning of the diffuse layer compression. From this, the conducting character of particles and their double layer envelopes can be directly related with the electrostatic potential described by the DLVO theory. If the particles maximum conductivity occurs after the Stern layer is complete, as shown in Fig. 9, it should correspond to maximum repulsive potential between particles (i.e. when the total electrostatic potential is always positive and there is no secondary minimum in the particle interaction potential curve). Thus, from the condition of KP,Max , the inter–particle distance can be shortened (denser particle packing) to a slightly attractive equilibrium value and the suspensions viscosity should decrease towards the desired minimum for ideal processing conditions [2].

R.C.D. Cruz et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 520 (2017) 9–16

Fig. 10. (A) Calculated inter–particle total interaction potential curves (DLVO) for selected values of particle conductivity, namely KP,Max , KP,0 and KP,Eq , as a function of the inter–particle distance (for the sake of clarity, full representation of the potential curves is shown only in the inset); (B) Effect of the particle conductivity KP on the relative intensity of the repulsive and attractive peaks in the inter–particle total interaction potential curves.

Fig. 10-A presents the calculated total particle interaction potential curves, based on the DLVO theory [31], for various particle conductivity values between the limiting KP,Max and KP,0 . The inset in Fig. 10-A shows that the potential curve for the condition at which the particles conductivity is maximum (cKCl = 3.5 mM, ␬a = 16) presents the expected high repulsive interaction (large separation between particles), with a very intense repulsive maximum (∼282 kT) and a nearly flat attractive minimum (∼ 0.2 kT) at an inter–particle distance of ∼46 nm (outside the Figure range). Fig. 10-A also shows that, beyond KP,Max , as the particle conductivity drops towards zero and the inter–particle equilibrium distance shortens, the height of the repulsive maximum decreases faster than the depth of the attractive secondary minimum increases. When the particle conductivity is zero, the double layer is fully collapsed and particles stand at the closest reversible distance (critical ionic strength for coagulation), i.e. the inter–particle distance is at the brim of the total potential primary minimum. The potential curve for the condition of KP,0 (cKCl = 30.5 mM, ␬a = 47) shows a much smaller repulsive maximum (∼12 kT) and a deep attractive secondary minimum (∼5 kT) at an inter–particle distance of only ∼7 nm. These results show that the accepted limiting value ␬a > 100 for the Helmholtz-Smoluchowski’s model corresponds to a condition at which the particles conductivity is zero and the very diluted suspension is actually overflocculated. The slightly attractive inter–particle equilibrium distance generally associated with electrostatically stabilized suspensions of minimum viscosity, below which charged particle crowding becomes excessive and the viscosity of the suspension increases again, has to be somewhere between the limiting potential curves for KP,Max and KP,0 . The observed marked changes in the total potential curves and the relative intensities of the repulsive and attractive

15

peaks can be used to help finding that equilibrium potential curve and the corresponding particle conductivity KP,Eq . From the KP,Max and KP,0 curves and two intermediate conditions chosen between them, represented as thinner lines in Fig. 10-A, the relative intensity of the four repulsive peaks (linearly normalized between 0 and 1 by the most intense among the four), as well as the relative intensity of the four attractive peaks (again, normalized by the most intense), were plotted as function of KP as shown in Fig. 10-B (curves (a) and (b), respectively). The KP value at the intersection of the relative peak intensity curves corresponds to the total potential curve that separates the conditions where particles repulsion dominates from those where particles attraction dominates, and might be regarded as an equilibrium particle conductivity, KP,Eq . From that KP value, the ion concentration in the suspending liquid was extracted (cKCl = 13.2 mM, ␬a = 34) and a new total potential curve was constructed (KP,Eq , also plotted in Fig. 10-A). The curve constructed for KP,Eq displays an intermediate repulsive maximum (∼127 kT) and an attractive secondary minimum (∼1.5 kT) at an inter–particle distance of ∼17 nm. The depth of this attractive minimum is very much in agreement with the literature [2], according to which particles in stable electrostatically dispersed suspensions with minimum viscosity remain in the shallow secondary minimum of the DLVO potential curve that corresponds to a net attractive potential of 1–2 kT [1]. Moreover, the equilibrium between the thermal energy of Brownian motion of particles and their average kinetic translation energy, or the energy involved in the random movement of particles around that inter–particle distance (Equipartition of Energy theorem), is expected to be ∼1.5 kT [13]. Given the clear coincidence between the DLVO calculated attractive potential minimum and the values generally accepted by the literature, it is to be expected that the foreseen relationship between particle conductivity and suspension rheology might also be proven true. Further research work is being carried out to demonstrate this reasoning and will be the object of a forthcoming paper.

4. Conclusions In this work, the suspension preparation procedure and the use of the electrokinetic sonic amplitude (ESA) method for the measurement of particles mobility enabled the identification of relationships between ␨–potential and electrolyte conductivity. Those relationships, in turn, were interpreted in terms of the changes in the electrical conductivity of the enveloped alumina particles, calculated with Maxwell’s model, due to changes in the corresponding electrical double layers. Although based on a simplified model, this strategy enabled the identification of a processing window for the stability control of concentrated suspensions, between the particles maximum and zero conductivities (KP,Max and KP,0 , respectively), which corresponds to the formation of the shallow secondary attractive minimum of the DLVO theory and can be assessed through the relationships between electrical conductivity and ionic strength. For the alumina suspensions investigated, KP,Max (i.e. maximum repulsive potential between particles) is reached at ␬a = 16 after the Stern layer is complete and can, thus, be used to detect the effective beginning of the diffuse layer compression (which is not detected by classical electrokinetic mobility measurement techniques). In the total potential curve, between KP,Max and KP,0 (at ␬a = 47) the depth of the secondary minimum changes from ∼0.2 to ∼5 kT while the height of the repulsive maximum changes from ∼282 to ∼12 kT and the inter–particle distance from ∼46 to ∼7 nm. The slightly attractive inter–particle equilibrium distance generally associated with electrostatically stabilized suspensions of minimum viscos-

16

R.C.D. Cruz et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 520 (2017) 9–16

ity occurs between particles maximum and zero conductivity, at ∼17 nm, when ␬a = 34. The isoconductivity point (ICP) between particles and suspending liquid was identified at ␬a = 12, coincides with the O’Brien’s ␨–potential maximum and separates electrical conductivity preferential paths: through the particles electrical double layer (before the ICP), or through the suspending liquid (beyond the ICP). Electrical conductivity measurements can detect such changes with better measurement accuracy, providing a deeper understanding of suspensions structure, stability and rheology with important implications in colloidal suspensions manipulation and consolidation methods. Acknowledgements Authors appreciate the financial support received from the Brazilian Research Agency CAPES (R.C.D. Cruz, Ph.D. grant) and from Deutsche Forschungsgemeinschaft (DFG Research Unit FOR 371) and the very enlightening discussions with P.Q. Mantas from the University of Aveiro, Portugal. References [1] W.M. Sigmund, N.S. Bell, L. Bergström, Novel powder–processing methods for advanced ceramics, J. Am. Ceram. Soc. 83 (2000) 1557–1574. [2] J.A. Lewis, Colloidal processing of ceramics, J. Am. Ceram. Soc. 83 (2000) 2241–2259. [3] H. Guldberg-Pedersen, L. Bergström, Stabilizing ceramic suspensions using anionic polyelectrolytes: adsorption kinetics and interparticle forces, Acta Mater. 48 (2000) 4563–4570, http://dx.doi.org/10.1016/S13596454(00)00242-1. [4] B. Ferrari, R. Moreno, EPD kinetics: a review, J. Eur. Ceram. Soc. 30 (2010) 1069–1078, http://dx.doi.org/10.1016/j.jeurceramsoc.2009.08.022. [5] K.G. Neoh, E.T. Kang, Combating bacterial colonization on metals via polymer coatings: relevance to marine and medical applications, ACS Appl. Mater. Interfaces 3 (2011) 2808–2819, http://dx.doi.org/10.1021/am200646t. [6] F. Akhtar, L. Andersson, S. Ogunwumi, N. Hedin, L. Bergström, Structuring adsorbents and catalysts by processing of porous powders, J. Eur. Ceram. Soc. 34 (2014) 1643–1666, http://dx.doi.org/10.1016/j.jeurceramsoc.2014.01.008. [7] J. Dong, A.J. Worthen, L.M. Foster, Y. Chen, K.A. Cornell, S.L. Bryant, T.M. Truskett, C.W. Bielawski, K.P. Johnston, Modified montmorillonite clay microparticles for stable oil-in-seawater emulsions, ACS Appl. Mater. Interfaces 6 (2014) 11502–11513, http://dx.doi.org/10.1021/am502187t. [8] B.V. Derjaguin, L. Landau, Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes, Acta Physicochim. 14 (1941) 633–661. [9] E.J.W. Verwey, J.ThG. Overbeek, Theory of the Stability of Lyophobic Colloids, Elsevier, Amsterdam, 1948 (Also available as a Dover reprint, 1999). [10] P.C. Hiemenz, Principles of Colloid and Surface Chemistry, second ed., Marcel Dekker, New York, 1986. [11] S. Usui, DLVO theory of colloid stability, in: H. Ohshima, K. Furusawa (Eds.), Electrical Phenomena at Interfaces: Fundamentals, Measurements, and Applications, Surfactant Science Series, vol. 76, second ed., Marcel Dekker, New York, 1998, pp. 101–118.

[12] B.W. Ninham, On progress in forces since the DLVO theory, Adv. Colloid Interface Sci. 83 (1999) 1–17, http://dx.doi.org/10.1016/S00018686(99)00008-1. [13] M.D. Haw, Colloidal suspensions, brownian motion, molecular reality: a short history, J. Phys. Condens. Matter 14 (2002) 7769–7779, http://dx.doi.org/10. 1088/0953-8984/14/33/315. [14] A.V. Delgado, F. González–Caballero, R.J. Hunter, L.K. Koopal, J. Lyklema, Measurement and interpretation of electrokinetic phenomena (IUPAC technical report), J. Colloid Interface Sci. 309 (2007) 194–224, http://dx.doi. org/10.1016/j.jcis.2006.12.075. [15] S. Wall, The history of electrokinetic phenomena, Curr. Opin. Colloid Interface Sci. 15 (2010) 119–124, http://dx.doi.org/10.1016/j.cocis.2009.12.005. [16] B. Vincent, Early (pre-DLVO) studies of particle aggregation, Adv. Colloid Interface Sci. 170 (2012) 56–67, http://dx.doi.org/10.1016/j.cis.2011.12.003. [17] J. Lyklema, Joint development of insight into colloid stability and surface conduction, Colloids Surf. A: Physicochem. Eng. Aspects 440 (2014) 161–169, http://dx.doi.org/10.1016/j.colsurfa.2012.09.013. [18] W.R. Bowen, P.M. Williams, Quantitative predictive modelling of ultrafiltration processes: colloidal science approaches, Adv. Colloid Interface Sci. 134–135 (2007) 3–14, http://dx.doi.org/10.1016/j.cis.2007.04.005. [19] R.W. O’Brien, The electrical conductivity of a dilute suspension of charged particles, J. Colloid Interface Sci. 81 (1981) 234–248, http://dx.doi.org/10. 1016/0021-9797(81)90319-2. [20] D.A. Saville, Electrical conductivity of suspensions of charged particles in ionic solutions: the roles of added counterions and nonspecific adsorption, J. Colloid Interface Sci. 91 (1983) 34–50, http://dx.doi.org/10.1016/00219797(83)90312-0. [21] R.J. Hunter, R.W. O’Brien, Electroacoustic characterization of colloids with unusual particle properties, Colloids Surf. A: Physicochem. Eng. Aspects 126 (1997) 123–128, http://dx.doi.org/10.1016/S0927-7757(96)03964-7. [22] I. Szilagyi, A. Sadeghpour, M. Borkovec, Destabilization of colloidal suspensions by multivalent ions and polyelectrolytes: from screening to overcharging, Langmuir 28 (2012) 6211–6215, http://dx.doi.org/10.1021/ la300542y. [23] S. Chakraborty, S. Padhy, Anomalous electrical conductivity of nanoscale colloidal suspensions, ACS Nano 2 (2008) 2029–2036, http://dx.doi.org/10. 1021/nn800343h. [24] K.G.K. Sarojini, S.V. Manoj, P.K. Singh, T. Pradeep, S.K. Das, Electrical conductivity of ceramic and metallic nanofluids, Colloids Surf. A: Physicochem. Eng. Aspects 417 (2013) 39–46, http://dx.doi.org/10.1016/j. colsurfa.2012.10.010. [25] L.G. Bunville, Commercial instrumentation for particle size analysis, in: H.G. Barth (Ed.), Modern Methods of Particle Size Analysis, Chemical Analysis, vol. 73, Wiley, New York, 1984, pp. 1–91. [26] R.J. Hunter, Zeta Potential in Colloid Science. Principles and Applications, Academic Press, London, 1981. [27] H. Matsumura, Surface conductivity, in: H. Ohshima, K. Furusawa (Eds.), Electrical Phenomena at Interfaces: Fundamentals, Measurements, and Applications, Surfactant Science Series, vol. 76, second ed., Marcel Dekker, New York, 1998, pp. 305–321. [28] R.C.D. Cruz, J. Reinshagen, R. Oberacker, A.M. Segadães, M.J. Hoffmann, Electrical conductivity and stability of concentrated aqueous alumina suspensions, J. Colloid Interface Sci. 286 (2005) 579–588, http://dx.doi.org/10. 1016/j.jcis.2005.02.025. [29] J. Cuquejo, M.L. Jiménez, Á.V. Delgado, F.J. Arroyo, F. Carrique, Numerical and analytical studies of the electrical conductivity of a concentrated colloidal suspension, J. Phys. Chem. B 110 (2006) 6179–6189, http://dx.doi.org/10. 1021/jp057030e. [30] P. Atkins, J. Paula, Atkins’ Physical Chemistry, ninth ed., Oxford University Press, New York, 2010. [31] J.N. Israelachvili, Intermolecular and Surface Forces, second ed., Academic Press, London, 1992.