Applied Clay Science 184 (2020) 105393
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Research Paper
Kinetic determination of sedimentation for GMZ bentonite colloids in aqueous solution: Effect of pH, temperature and electrolyte concentration
T
Zhen Xua,1, Yalou Suna,1, Zhiwei Niua,b, Yang Xua, Xiaoyan Weia, Ximeng Chena, ⁎ ⁎ Duoqiang Pana,b, , Wangsuo Wua,b, a b
School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China Key Laboratory of Special Function Materials and Structure Design, Ministry of Education, Lanzhou 730000, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Stability Bentonite colloids Sedimentation DLVO theory
Bentonite colloids are readily generated by eroding the compacted bentonite blocks with flowing groundwater and facilitate the transport of radionuclides due to their high mobility. The geological fate of colloids is highly relevant to the aggregation and sedimentation of colloids in porous media. In the present work, the week-scale stability of bentonite colloids concerning sedimentation was determined by photon correlation spectroscopy (PCS) as a function of pH, temperature, and electrolyte concentration. The related mechanisms governing colloidal stability were elucidated by employing the DLVO model. The results showed that the alkaline condition was favorable for bentonite colloidal stability, while high temperature and high salinity destabilized colloids due to the decrease in repulsive potential energy. Ca2+ contributed more significantly to colloid sedimentation than Na+ because of the favorable replacement in the Stern layer. The critical coagulation concentration (CCC) values calculated theoretically from DLVO theory were applicable to predict the stability of bentonite colloids. Knowledge from the present work provides deep insight into the stability of bentonite colloids and has potential implication for understanding the detailed physico-chemical processes governing colloid migration under various subsurface environments.
1. Introduction In China, bentonite from the Gaomiaozi region (GMZ bentonite) is expected to be used as the buffer material in high-level radioactive waste repositories due to its low permeability, excellent swelling ability and high adsorption capacity (Wang et al., 2009; Sun et al., 2018). The migration of radionuclides escaping from a damaged canister should or is expected to be retarded by bentonite as well as host rocks (Pan et al., 2011; Wang et al., 2015; Pan et al., 2017). However, colloids with superior mobility and reactivity are easily generated by eroding the compacted bentonite blocks with flowing in situ groundwater (Bessho and Degueldre, 2009; Albarran et al., 2014) which poses the risk that the mobile colloids associated with radionuclides may drive the transport of radionuclides toward the biosphere (Möri et al., 2003; Missana et al., 2008; Albarran et al., 2011; Bouby et al., 2011). The aggregated colloidal particles are readily settling in porous media because of the increased steric effect and deposition velocity, thus impede the transport of colloids as well as radionuclides (Xie et al., 2012; Haliena et al., 2016). Therefore, further understanding on the stability of colloidal
particles concerning sedimentation in the vicinity of a geological repository is of great significance for assessing the performance and safety of the repository (Geckeis et al., 2003; Wan et al., 2004; Pan et al., 2019). Colloidal stability is highly related to environmental factors such as ionic strength, acidity and temperature, which will alter the surface potential and thus the interaction energy between colloidal particles. Aggregation and sedimentation may occur when the repulsion between colloidal particles decreases (Adamczyk and Weroński, 1999; Tombácz and Szekeres, 2004; Wang et al., 2013; Zhang et al., 2017; Tan et al., 2018). Colloids are easy to disperse under low-ionic-strength conditions (Garcia-Garcia et al., 2006; Garcia-Garcia et al., 2007), whereas in highionic-strength systems, the diffuse double layer of colloidal particles is compressed, and the repulsive forces decrease each other; thus colloids are prone to aggregate and deposit (Croll, 2002; Martines et al., 2008). The aggregation process usually occurs very quickly, while within a relatively longer time scale, sedimentation of colloids would take place, in which the deposition velocity may vary. In repository environments, the surrounding temperature will increase up to ~80 °C due to the heat
⁎
Corresponding authors at: School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China. E-mail addresses:
[email protected] (D. Pan),
[email protected] (W. Wu). 1 These authors contributed equally to this work. https://doi.org/10.1016/j.clay.2019.105393 Received 14 August 2019; Received in revised form 26 November 2019; Accepted 28 November 2019 0169-1317/ © 2019 Elsevier B.V. All rights reserved.
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the hydrodynamic diameter as time passed, and the stock bentonite colloid dispersion could be stable for at least 30 days in deionized water (Xu et al., 2018). The size distribution and zeta potential of the bentonite colloid dispersion were measured by the Zetasizer Nano ZS analyzer (Malvern, United Kingdom) equipped with a 4 mW HeeNe laser (λ = 633 nm). XRD patterns were obtained on D/max-2400 (Rigaku, Japan, 40 kV/100 mA) using a Cu-Kα radiation source (λ = 0.154 nm) with a scan rate of 2°/min and a step of 0.02°, covering a range between 3 and 90°. The morphology of GMZ bentonite colloidal particles was observed by atomic force microscopy (AFM, Asylum Research Cypher, Cypher S, United States) and transmission electron microscopy (TEM, Tecnai G2 F30 S-Twin, FEI, United States).
released from radioactive decay, which is evolutionary in terms of time and distance from the radioactive source. In general, a temperature increase will increase the colloid movement and collision efficiency and thus the potential aggregation. However, increasing stability as the temperature increase has also been reported (Garcia-Garcia et al., 2006). The layer structure and the charges on platelets confer particular characteristics to bentonite, the particle size, shape and clay mineralogy can effectively affect the clay fabric formation (Palomino and Santamarina, 2005), which may display a decisive effect on the involved interaction forces and the temperature dependence (GarciaGarcia et al., 2006). Thus, a description of the influence of temperature on the stability of bentonite colloids is in demand. The colloid aggregation mechanism can be qualitatively interpreted with the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, which includes a balance between the Van der Waals attractive force and the stabilizing repulsive force derived from the electrostatic charge (Missana and Adell, 2000; Adamczyk, 2003; Hoek and Agarwal, 2006; Liang et al., 2007; Martines et al., 2008; Bendersky and Davis, 2011). The main contribution to the surface charge of bentonite colloids is permanent defects arising from isomorphic substitutions in the crystal lattice, while the charge at the edges is only ~1% of the total charge (Sondi et al., 1997; Tombácz and Szekeres, 2004). Therefore, bentonite colloids are usually treated as particles with identical surfaces, and the electrostatic force is mainly from the permanent charge. The repulsive electrostatic potentials are sensitive to the solution conditions. For instance, an increase in the electrolyte concentration will result in a decrease in the Debye length and thus have a decisive impact on the involved interaction forces (Grasso et al., 2002; Bostrom et al., 2006). A safety assessment of geological repositories for high-level radioactive waste is highly related with stability of colloid. The stability of bentonite colloids concerning aggregation on an hour scale has been widely investigated (Adamczyk and Weroński, 1999; Bhattacharjee et al., 2000; Missana and Adell, 2000; Huynh and Chen, 2011; Furman et al., 2013; Huangfu et al., 2013). However, the situations in the relatively longer term concerning sedimentation, especially under different temperatures, are still unknown. Therefore, the specific objectives of the present work are to (1) investigate the week-scale stability of bentonite colloids concerning the sedimentation process; (2) elucidate the related mechanisms governing colloidal stability by employing the DLVO model; and (3) understand the geological fate of colloids as well as colloid-carried radionuclides.
2.3. PCS experiments Photon correlation spectroscopy (PCS) was employed to determine the particle concentration of colloid dispersion. All experiments were conducted under ambient conditions. Three milliliters of dispersion was piped into a quartz cuvette, and the measurement was initiated. The hydrodynamic diameter of the colloid was determined by measuring the translational diffusion coefficients from the intensity of scattered light (Baik and Lee, 2010). The signal obtained from PCS was the count rate (Cr), which was proportional to the combination of the concentration and hydrodynamic diameter of colloidal particles in the dispersion. If the hydrodynamic diameter of the colloid remained constant, the count rate could be directly used to determine the colloid concentration. To verify the feasibility of this method, a verification experiment on the count rate vs. particle concentration was conducted at different pH values with bentonite colloid concentrations varying from 0.4 to 0.8 g·L−1, which were dispersed in a 1.0 × 10−3 mol·L−1 NaCl solution under ambient conditions at room temperature. The ion concentrations in all experiments refer to the concentration of the background electrolyte ions without including the mineral dissolved ions. The change in the hydrodynamic diameter of the bentonite colloid was monitored during the experiment. The zeta potential values of the bentonite colloid under different conditions were measured by the PCS. To observe the temperature effect, sedimentation under different temperatures was performed, with the stock dispersion being equilibrated in an oil bath at the desired temperature. Before executing PCS measurements, the surrounding temperature of the sample holder in the instrument was set and preequilibrated at the desired temperature, which remained constant during the measurement. The electrophoretic mobility of colloidal particles was converted to a zeta potential value by using the Helmholtz-Smoluchowski equation.
2. Materials and methods 2.1. Materials The bentonite used in this work, sourced from Gaomiaozi County (Inner Mongolia, China), was transformed to Na type and then washed with deionized water until no Cl− was detected in supernatant (Pan et al., 2011; Xu et al., 2018). Bentonite colloids were prepared from Na bentonite under ambient conditions at room temperature by following the reported procedures (Xu et al., 2018). In brief, the bentonite powder (< 44 μm) was dispersed in deionized water via ultrasound (24 h) to obtain a well-dispersed system. Then, the dispersion was centrifuged at 8000 rpm (6347 ×g) for 30 min to remove larger particles. The supernatant, which contained the colloidal fraction, was finally collected as a colloidal stock dispersion. The concentration of bentonite colloids was determined to be 0.8 g·L−1 by gravimetric analysis. The electrical conductivity of supernatant of original and Na-type bentonite were 42 μS/cm and 10 μS/cm, respectively. All other chemicals used in the experiments were purchased in analytical purity and used without any further purification.
2.4. Sedimentation experiments The aggregation of colloids can be considered as a bimolecular reaction following second-order kinetics (Garcia-Garcia et al., 2006):
A + A → A2
(1)
For reaction (1), the reaction rate can be expressed as:
−
d[A] = 2k [A]2 dt
(2)
where k is the rate constant of the sedimentation process and [A] is the concentration of bentonite colloids. The integration of Eq. (2) leads to:
1/[A]t = 1/[A]0 + 2kt
(3)
The second-order rate constant (k) is determined from the slope of the plot of 1/[A]t vs. t. Because the count rate is used to denote the colloid concentration when the colloid size remains constant, the rate constant could be derived from the slope of the plot of 1/Cr vs. t. The week-scale sedimentation kinetic experiments were carried out
2.2. Characterization The stability of the colloid dispersion was determined by monitoring 2
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at different pH values, temperatures and electrolyte concentrations to determine the stability of GMZ bentonite colloids. The desired pH values of the suspension were adjusted by adding 0.1 mol·L−1 NaOH or HCl solutions. For the temperature effect experiment, the colloid dispersion was equilibrated in an oil bath at the desired temperature, and the electrolyte concentrations of the colloid dispersion was adjusted by adding aliquots of 1.0 or 0.1 mol·L−1 NaCl or CaCl2. All sedimentation experiments were conducted in a cylindrical plastic container (10 cm in height) that contained a 250 mL colloid dispersion. Samples of 2 mL dispersion were periodically taken with a pipette at a depth of ~1.0 mm below the liquid level to determine the size, concentration and zeta potential of colloidal particles. The sedimentation under different pH values and temperatures was measured for 16 days and 6 days, and sedimentation in NaCl and CaCl2 solutions was performed for up to 35 days. The uncertainty was analyzed by determining the rate constant of aggregation in three identical dispersions.
Table 1 The parameters related to the theoretical calculation. Parameter ε0 (F·m ) εr (F·m−1) γ2 κ (m−1) e (C) NA kB (J·K−1)
The total interaction energy (VT) as a function of the particle distance was calculated from the repulsive and attractive energy between two particles when approaching each other. In the current work, the geometry of colloidal particles was assumed to be spherical (Bhattacharjee et al., 2000; Hoek and Agarwal, 2006; Martines et al., 2008), and the face-to-face association rather than the edge-to-edge or edge-to-face association was predominant at high pH in the calculation process (Keren et al., 1988; Tombácz and Szekeres, 2004). Therefore, the total potential energy of bentonite colloids can be expressed as shown in Eq. (4) (Missana and Adell, 2000; Martines et al., 2008).
VA = −
VT =
64πrn 0 kB T 2 Ar γ exp(−κh)‐ κ2 12h
(10)
(11)
(12)
κh = 1 Substituting Eq. (12) into Eq. (10) leads to.
κ3 =
768000πNA CCCC kB Tγ02 (13)
Ae
Substituting Eq. (7) into Eq. (13) and solving the equation, the CCC can be obtained as follows:
(7) 23
CCCC = 1.51 × 1080
where NA is Avogadro's Number, 6.0 × 10 ; Ci is the electrolyte concentration; ε0 is the permittivity in vacuum, 8.9 × 10−12 C2·(J·K)−1; and εr is the dielectric constant of water. The γ factor is a parameter dependent on the surface potential ψ0 according to Eq. (8).
( )−1 exp ( )+1
108 10−19 1023 10−23
Solving for Eq. (11), the relation between h and k can be deduced as follows:
1/2
exp
10−12
(9)
Ar 64πrn 0 kB T 2 γ exp(−κh)‐ =0 κ2 12h dVT 64πrn 0 kB T 2 Ar =‐ γ κ exp(−κh) + =0 dh κ2 12h2
where r is the particle radius, n0 is the number of background anions and cations, which can be determined from the molar concentration of the background electrolyte, kB is the Boltzmann constant, 1.4 × 10−23 J·K−1, T is the temperature in Kelvin, A is the Hamaker constant, h is the distance between the surfaces of particles, and the reciprocal of the Debye length, κ, is given by Eq. (7) (Grasso et al., 2002).
γ=
108 10−19 1023 10−23
8.9 × 61 0.95 1.1 × 1.6 × 6.0 × 1.4 ×
VT =
(6)
1000e 2NA Σi2 Ci ⎞ κ = ⎜⎛ ⎟ ⎝ ε0 εr kB T ⎠
10
T = 353 K
Thus, Eq. (9) can be expressed as Eq. (11) (Zhang et al., 2015)
(5)
Ar 12h
108 10−19 1023 10−23
8.9 × 70 0.97 1.1 × 1.6 × 6.0 × 1.4 ×
−12
The total interaction energy of two sphere particles can be expressed as follows (Garcia-Garcia et al., 2006):
(4)
64πrn 0 kB T 2 γ exp(−κh) κ2
10
T = 323 K
VT = 0 dVT =0 dh
where VR is the repulsion electrostatic potential, as given in Eq. (5) (Garcia-Garcia et al., 2006).; VA is the component of the Van der Waals attraction, as given in Eq. (6) (Croll, 2002).
VR =
8.9 × 78 0.98 1.0 × 1.6 × 6.0 × 1.4 ×
−12
that should be taken into account in the calculation. The value from reference (Helmy, 1998) (2.3 × 10−20 J) was used to model the aggregation process of bentonite colloids. The parameters related to the theoretical calculation were summarized in Table 1. When the background electrolyte concentration approached the critical coagulation concentration, that is, the minimum concentration of counter ions that induce colloid coagulation, the CCC value was calculated based on the interaction energy of two colloidal particles. At the critical coagulation concentration, the repulsive energy was less than or equal to the attractive energy. Therefore, the maximum total interaction energy (VT) was equal to zero (Zhang et al., 2015). Consider the following:
2.5. DLVO modeling
VT = VR + VA
T = 298 K
−1
(ε0 εr )3 (kB T )5γ04 1 NA e 2A2 Z6
(14)
3. Results and discussion
zeψ0
2k B T
3.1. Characterization
zeψ0
2k B T
(8)
The bentonite colloid was stable in a pure water system (Xu et al., 2018), and the mean hydrodynamic diameter of the bentonite colloid in deionized water determined by the PCS was 201.4 nm, with a particle dispersion index (PDI) of 0.17 (Fig. 1a). The XRD patterns in Fig. 1b indicated that the main components of bentonite were montmorillonite (PDF 29–1498) and quartz (PDF 43–0596). AFM and TEM images of the bentonite colloids (Fig. 1c and d) showed that the colloidal particles were well dispersed and basically exhibited a non-uniform shape. The size of the bentonite colloids was approximately 200 nm, which falls in
where ψ0 is the surface potential of colloidal particles, z is the charge of the background ions and e is the elementary charge, 1.6 × 10−19C. In the modeling calculation, the radius of the bentonite colloids was assumed to be 200 nm. In general, the surface potential of bentonite colloids was considered equal to the zeta potential value for most colloidal systems (Missana and Adell, 2000); thus, the zeta potential of bentonite colloids was used to calculate the double layer repulsion energy. In addition, the Hamaker constant is an important parameter 3
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Fig. 1. Characterization of GMZ bentonite and bentonite colloids. (a) The size distribution of bentonite colloids in pure water. T = 25 °C, pH = 7.8. (b) XRD patterns of bentonite. (c) TEM and (d) AFM images of bentonite colloids.
(Fig. 2a). The colloid size from PCS at different colloid concentrations was almost identical (Fig. 2b), suggesting that multiple scatter originating from the colloidal heterogeneity did not take place (GarciaGarcia et al., 2006). The hydrodynamic diameter of the colloid remained constant, and large aggregates were not detected in the current system. Therefore, the count rate from direct PCS measurement was dependent merely on the number of particles and thus could be used as
line with that determined by the PCS technique.
3.2. Effect of pH The PCS verification experiments in the 1.0 × 10−3 mol·L−1 NaCl solution showed that the count rate, mega counts per second (Mcps), was proportional to the colloid concentration at different pH values
0.4
250
(a)
pH= 8.5 pH= 9.0 pH=9.5
Mean hydrod. diam.(nm)
Count rate (Mcps)
0.5
0.3
0.2 0.3
0.4
0.5 0.6 0.7 0.8 Concentration (g/L)
Mean hydrod.diam.(nm)
-1
(c)
pH=8.5 pH=9.5
5 1/Cr (Mcps )
100 50 0.4
250
6
4 3 2 1 0
150
0
0.9
2
4
6 8 10 time (day)
12
14
16
0.5 0.6 0.7 Concentration (g/L)
(d)
0.8
pH=8.5 pH=9.5
200 150 100 50 0
0
pH=8.5 pH=9.0 pH=9.5
(b)
200
0
2
4
6 8 10 time (day)
12
14
16
Fig. 2. The PCS verification experiments (a, b), and the effect of pH on the sedimentation of bentonite colloids: (c) the inverse of the count rates versus time; (d) size versus time. T = 25 °C, CNaCl = 1.0 × 10−3 mol·L−1. 4
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an indicator of the relative colloid concentration. The colloid aggregation process was considered a bimolecular reaction in which the colloidal particles collided with each other and formed large aggregates, which then caused the sedimentation process. The sedimentation rate constant (k) is directly related to the stability of the colloid. The slopes of the plot of inverse count rate (1/Cr) vs. time at different pH values were presented in Fig. 2c. The 1/Cr ratio increased with increasing time, suggesting that the sedimentation process for bentonite colloids can be well described by the second-order kinetics, which are based on the assumption of a bimolecular reaction. The slopes were proportional to the sedimentation rate constants, and the higher k value reflected the unstable colloidal system, in which the fast sedimentation process existed (Garcia-Garcia et al., 2006). From Fig. 2c, the slope for pH 8.5 (5.1 × 10−5 Mcps−1 min−1) was greater than that for pH 9.5 (4.7 × 10−5 Mcps−1 min−1), indicating that the bentonite colloid was more stable at pH 9.5, which falls in line with the results in the literature (Missana and Adell, 2000; Missana et al., 2003; Baik and Lee, 2010). In general, the acidity in the liquid-solid interface played two specific roles: 1) neutralizing the permanent negative charges of the dominant electric double layer on mineral planes and 2) providing chemical species (H+ and OH−) for the surface proteolytic reactions on the edge sites (Tombácz and Szekeres, 2004). One possible interpretation was that the latter role of pH in the aqueous medium formed the pH-dependent hidden electric double layer and further affected the colloidal stability. The size evolution as time passed up to 16 days was monitored in Fig. 2d, and no significant change was found in the mean particle size with increasing time, suggesting that sedimentation did not occur or was not enough to be detected at the time scale studied.
Table 2 Slopes for the count rate and concentration of bentonite colloids at different temperatures. pH = 9.5, CNaCl = 1.0 × 10−3 mol·L−1. Temperature (°C)
Slope (Mcps−1 × min−1) × 105
R2a
80 50 25
21 ± 3 11 ± 8 4.0 ± 0
0.91 0.97 0.98
a
R2 is the coefficient of determination
fluctuation in colloid size was observed as time passed. Furthermore, the rate constant for the sedimentation process appeared to be dependent on temperature, and the effect of temperature on the corresponding slopes of the curves was summarized in Table 2. The greater curve slope at 80 °C (2.1 × 106 Mcps−1·min−1) than that at 25 °C (4.0 × 105 Mcps−1·min−1) suggested that the bentonite colloid was relatively unstable at higher temperatures, and thus, the sedimentation process was fast. A plausible explanation was that for a bimolecular reaction, the thermal energy of particles increased as the temperature increased, then a higher collision frequency between colloidal particles enabled the fast aggregation and sedimentation process. However, the mechanism of the effect of temperature on the sedimentation process is complicated. In contrast, enhanced stability at higher temperatures was also reported, which was attributed to the increased Brownian force of the colloid at higher temperatures, accordingly the colloid aggregation process was disturbed (Ni and Zhang, 2009). As the temperature increases and time passes, mineral dissolution and mineral structure changes may occur and influence the stability of the colloid (GarciaGarcia et al., 2006). The effect of temperature on the hydrodynamic diameter of bentonite colloid as time passed was shown in Fig. 3b. The variation in colloid size at different temperatures was not significant over time. The measured hydrodynamic diameter of the colloidal particles varied by approximately 50 nm between 25 and 80 °C, and this variation fell within the error of measurement and was probably attributed to the system heterogeneity.
3.3. Effect of temperature The inverse count rate (1/Cr) of bentonite colloids versus time at different temperatures was plotted in Fig. 3a. The 1/Cr increased as time passed, and the slopes increased with increasing temperature. The colloid size as time passed was synchronously monitored in Fig. 3b. The hydrodynamic diameter was approximately 200 nm, and no significant
3.4. Effect of electrolyte concentration Coexisting ions are ubiquitous in the subsurface environment and show a significant influence on colloidal stability (Albarran et al., 2014; Xu et al., 2018). The influence of typical electrolyte ions, including Na+ and Ca2+, on bentonite colloid sedimentation was shown in Fig. 4. The inverse of the count rate for bentonite colloids at different NaCl and CaCl2 concentrations was plotted as a function of time in Fig. 4a and c, respectively, and the size evolution of the bentonite colloids in the NaCl and CaCl2 solutions as time passed was shown in Fig. 4b and d, respectively. The aggregation of bentonite colloids was considered as a bimolecular reaction, thus the sedimentation process in NaCl or CaCl2 followed the second-order kinetics. The second-order kinetic rates for sedimentation derived from the plot slopes were presented in Table 3 and Table 4. The ascending slopes as the ion concentration increased reflect that the sedimentation was kinetically fast at high electrolyte concentrations. The calcium played a more effective role in accelerating the colloid sedimentation due to the higher positive charge, which was in accordance with the Schulze-Hardly rules in the aggregation process. No significant change in the hydrodynamic diameter of bentonite colloids was observed as time passed up to 35 days in NaCl (3.0 × 10−3 mol·L−1) and CaCl2 (3.0 × 10−5 mol·L−1) solutions (Fig. 4b and d), suggesting that the sedimentation process of bentonite colloids was kinetically slow and that the week-scale stability of the colloids was considerable under low electrolyte concentrations. In addition, the fabric formation can affected the settlement, rheological behaviors and shear strength of mineral particles (Palomino and Santamarina, 2005). To further qualitatively evaluate the counter ion effect on the
Fig. 3. Effect of temperature on the sedimentation of bentonite colloids: (a) the inverse of the count rates versus time; (b) the size of the bentonite particles versus time. The error bar represents the standard deviation. pH = 9.5, CNaCl = 1.0 × 10−3 mol·L−1. 5
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Fig. 4. Effect of cations on sedimentation of bentonite colloids: inverse of the count rates versus time in (a) NaCl and (c) CaCl2; the mean size versus time in (c) 3.0 × 10−3 mol·L−1 NaCl and (d) 3.0 × 10−5 mol·L−1 CaCl2. The error bar represents the standard deviation. T = 25 °C, pH = 9.5. Table 3 Second-order slopes for the sedimentation kinetics of bentonite colloids at different concentrations of NaCl. NaCl (mol·L−1) 1.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 1.0 2.0 a
× × × × × × × × × ×
−3
10 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−2 10−2
Slope (Mcps−1 × min−1) × 105
R2a
Zeta potential/(mV)
1.8 2.1 2.4 2.6 2.9 3.0 3.2 3.8 4.2 6.5
0.94 0.95 0.98 0.96 0.98 0.99 0.98 0.97 0.91 0.93
−33 −34 −38 −36 −35 −40 −35 −31 −34 −36
± ± ± ± ± ± ± ± ± ±
0.2 0.2 0.1 0.2 0.1 0.1 0.2 0.3 0.5 0.7
± ± ± ± ± ± ± ± ± ±
2 2 4 2 1 6 3 1 3 2
R2 is the coefficient of determination
Table 4 Second-order slopes for the sedimentation kinetics of bentonite colloids at different concentrations of CaCl2. CaCl2 (mol·L−1) 3.0 4.0 5.0 6.0 7.0 8.0 a
× × × × × ×
10−5 10−5 10−5 10−5 10−5 10−5
Slope (Mcps−1 × min−1) × 105
R2a
Zeta potential/(mV)
2.2 2.9 3.0 4.0 5.4 5.8
0.95 0.96 0.95 0.99 0.99 0.99
−36 −34 −35 −35 −36 −36
± ± ± ± ± ±
0.2 0.2 0.3 0.2 0.2 0.3
± ± ± ± ± ±
Fig. 5. The log k of bentonite colloids versus the square root of the ionic strength in (a) NaCl and (b) CaCl2. The total potential energy (VT) versus the square root of the ionic strength in (c) NaCl and (d) CaCl2.
0 1 1 1 2 2
Hückel theory was not applicable for all colloid sedimentation systems. Other qualitative analysis methods (e.g., DLVO modeling) are still in demand.
R2 is the coefficient of determination
3.5. Zeta potential
sedimentation kinetics of the bentonite colloid, the logarithm values of the rate constants in Table 3 and Table 4 were plotted against the square root of the ionic strength as described in the Debye-Hückel theory. From Fig. 5a and b, the log(k) had a good linear relationship with the square root of the ionic strength ( I ). To elucidate the theoretical relevance of this linear correlation, the total potential energy of a bentonite colloid as a function of I in NaCl and CaCl2 was calculated and was displayed in Fig. 5c and d, respectively. The curve of the total potential energy (VT) vs. square root of the CaCl2 concentration was linear, while that for NaCl was not linear, indicating that the Debye-
The zeta potential of the bentonite colloid was monitored throughout the sedimentation experiments. Subtle deviation of the zeta potential of the bentonite colloids was observed at the considered pH values as time passed (Fig. 6a), and the zeta potential remained almost consistent (approximately −35 mV) with increasing time at different temperatures (Fig. 6b). The negative charges derived from permanent defects in the bentonite structure were insensitive to pH but not to temperature, therefore, the zeta potential of bentonite colloids originated mainly from the permanent structural charges instead of variable charges at the edge sites. Although the conditionally charged 6
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the interaction energy would vary with the particle distance. The total potential energy (VT) is the sum of the attractive potential (VA) and repulsive potential (VR). Fig. 7 showed the DLVO calculation results of the potential energy at different temperatures and cation concentrations. The maximum total potential energy (VT) for the bentonite colloids was considered an energy barrier that particles had to overcome to collide and aggregate. In Fig. 7a, the repulsive interaction (VR) between particles remained dominant and was larger than the attractive interaction (VA) at all temperatures, which resulted in a constant positive total potential energy (VT). The total potential energy (VT) decreased as the temperature increased, indicating that the decrease in repulsion potential as the temperature increased contributed to the interior colloidal stability and thereby caused fast aggregation and sedimentation. At higher temperatures, the more intense Brownian force provided more drive for motion, which promoted the probability of particle collision and then destabilized the colloidal system. The potential energies at different background electrolyte concentrations as a function of the particle distance were shown in Fig. 7b and Fig. 7c. Both repulsive potential energy and total potential energy decreased with increasing electrolyte concentration. At the same electrolyte concentration, the total energy in CaCl2 was smaller than that in the NaCl solution (Fig. 7d). When the particles approached each other, the diffusion double layers of the particles overlapped, and the effect of colloidal particles on the overlap region could not be completely shielded by the counter ion atmosphere. The increase in counter ion concentration and charge would destroy both ion balance and electrostatic balance in the diffusion layer. The former induced the diffusion of ions from the overlap region with high concentration to the nonoverlapping region and then produced a permeable repulsive force, while the latter led to a decrease in electrostatic repulsive force between colloidal particles. Specifically, when the electrolyte concentration increased, the thickness of the diffuse electric double layer was compressed, and the repulsive force was reduced. The particles repelled each other less effectively, and aggregation was favored, then fast sedimentation was observed. The DLVO theory could be used to predict CCC under diffusioncontrolled conditions, in which the electrolyte concentration was higher than the CCC value. To elucidate the theoretical relevance of the sedimentation mechanisms, the CCC values of bentonite colloids in NaCl and CaCl2 were theoretically determined with the aid of DLVO theory. The calculated CCC values for NaCl and CaCl2 were 0.17 M and 0.003 M, respectively, the order of magnitude of which was consistent with that obtained by other methods. The CCC values determined from the experiment were 0.25 M for NaCl and 0.002 M for CaCl2 (Frey and Lagaly, 1979; Tombácz et al., 1989). The CCC values determined from DLVO theory were usually higher than those from other methods, as the calculated total potential energy in the diffusion-controlled conditions remained positive under the assumption of DLVO, while in other CCC determination methods, the inherent factors, such as size and particle shape, might change when the electrolyte concentration approaches or exceeds the CCC values (Osakai et al., 2004; Garcia-Garcia et al., 2007).
Fig. 6. Effect of (a) pH and (b) temperature on the zeta potential of bentonite colloids over 16 days and 6 days, respectively. The error bar represents the standard deviation. T = 25 °C, CNaCl = 1.0 × 10−3 mol·L−1.
amphoteric edge sites would enable the alternation of surface charge due to protonation and deprotonation reactions, their contributions were subtle because of the low proportion of the edge charge in relation to the total charge (~1%) (Sondi et al., 1997; Tombácz and Szekeres, 2004). The zeta potential values could be used as a representative of the colloid surface potential (French et al., 2009), but the surface potential was usually a rough estimation since not all of the electrophoretic mobility was converted to zeta potential. Note that the zeta potential of the bentonite colloid was slightly higher at 80 °C than at 25 °C (insert Fig. 6b). The increase in surface potential with increasing temperature decreased the electrostatic repulsion and thus enabled more effective aggregation at higher temperatures, which was consistent with the fast sedimentation in the kinetic experiments. The average zeta potentials of the bentonite colloids at different electrolyte solutions were listed in Table 5. The zeta potential values of the bentonite colloids in CaCl2 were less negative than in the NaCl solution, suggesting that the calcium influenced the surface charge property more significantly. With higher affinity to bentonite, Ca2+ was easier to replace the initially adsorbed cation in the Stern layer and compensate for the negative structural charge; thus the lower repulsion between colloidal particles was responsible for the fast sedimentation in the CaCl2 solution, as shown in Fig. 4.
3.6. DLVO modeling 4. Conclusions To further understand the sedimentation process, DLVO theory was employed to illustrate the evolution of total potential energy in the sedimentation process. When bentonite colloidal particles approached each other, the diffuse double layers of the particles would interact, and
The week-scale stability of bentonite colloids with regard to the sedimentation process was estimated in the present work. The effects of pH, temperature and electrolyte concentration on the sedimentation kinetics of bentonite colloids were systematically investigated. The related mechanisms governing colloidal stability were elucidated by employing the DLVO model. The repulsive potential between colloidal particles decreased under high acidity and high salinity conditions; thus, the stability of bentonite colloids decreased, and sedimentation was considerable. Calcium ion with higher z/r ratio than that of sodium ion played a more significant role in colloid aggregation and sedimentation because Ca2+ could more easily replace the original cation in the Stern layer and compensate for the negative structural charge. At
Table 5 Average values of zeta potentials for bentonite colloids in different electrolyte solutions. Electrolyte
Order of magnitude/(mol·L−1)
Average zeta potential/(mV)
NaCl CaCl2 CaCl2
1.0 × 10−3 – 2.0 × 10−2 3.0 × 10−5 – 8.0 × 10−5 1.0 × 10−3 – 2.0 × 10−2
−36 ± 4 −36 ± 2 −11 ± 2
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Fig. 7. Potential energy curves of interaction as a function of separation distance for bentonite particles at different (a) temperatures; (b) NaCl concentrations; (c) CaCl2 concentrations; and (d) electrolytes. pH = 9.5.
high temperature, the promoted collision probability was responsible for the fast aggregation and sedimentation. Under the assumption of a bimolecular reaction, the aggregation and sedimentation process agreed with the DLVO model. The critical coagulation concentration values calculated from DLVO theory were comparable with those from other determination methods; thus they were applicable for the prediction of colloidal stability. The results in the present work provide insight into the stability of bentonite colloids and thus have essential implications for understanding the detailed physico-chemical processes governing the migration of colloids in various subsurface environments.
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Declaration of Competing Interest The authors declared that they have no conflicts of interest to this work. Acknowledgements This work was supported by the National Natural Science Foundation of China (U1730245, 21806063); the Double First Class Funding-international Cooperation and Exchange Program (27560001); the Fundamental Research Funds for the Central Universities (lzujbky2017-96); the DSTI Foundation of Gansu (2018ZX-07). Author contributions Zhen Xu: Writing the article, collection and assembly of data. Yalou Sun: Collection, assembly and analysis of data. Zhiwei Niu: Assembly and analysis of data. Yang Xu: Data analysis and interpretation. Xiaoyan Wei: Collection and assembly of data. Ximeng Chen: critical revision of the article. Duoqiang Pan: Research concept and design, critical revision of the article. Wangsuo Wu: Research concept and design. References Adamczyk, Z., 2003. Particle adsorption and deposition: Role of electrostatic interactions.
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