Materials Letters 60 (2006) 666 – 673 www.elsevier.com/locate/matlet
The investigations of influence of BDTDACl and DTABr surfactants on rheologic, electrokinetic and XRD properties of Na-activated bentonite dispersions E. Günister a , N. Güngör a,⁎, Ö.I. Ece b a
İ.T.Ü., Faculty of Science and Letters, Dept. of Physics, Maslak 34469 Istanbul, Turkey b İ.T.Ü., Faculty of Mines, Mineral.-Petrog. Division, Maslak 34469 Istanbul, Turkey Received 27 July 2005; accepted 28 September 2005 Available online 13 October 2005
Abstract The influence of cationic surfactants benzyldimethyltetradecyl ammonium chloride (BDTDACl) and dodecyltrimethylammonium bromide (DTABr) on flow behaviors and electrokinetic properties of soda activated bentonite suspensions (3 wt.%) were studied. Surfactants were added to the bentonite water system in different concentrations in the range of 10− 5 – 10− 2 mole/L. The interactions between clay minerals and surfactants in water-based Na-activated bentonite dispersions (3 wt.%) were examined in detail using rheologic parameters, such as viscosity, yield point, apparent and plastic viscosity, hysteresis area, and electrokinetic parameters of mobility and zeta potentials, and XRD analyses also helped to determine swelling properties of d-spacings. Besides, the influence of pH and particle size distributions was also evaluated. XRD studies revealed that d-spacings expanded about 1.98 and 3.49 A° after the interactions of bentonite + DTABr and bentonite + BDTDACI complex, respectively. © 2005 Elsevier B.V. All rights reserved. Keywords: Clay minerals; Bentonite; Cationic surfactants; Composite materials; Characterization methods
1. Introduction Bentonite with higher ion exchange and surface area is widely used as an industrial raw material in sorption, catalytic and rheologic applications. It is very important to measure rheological properties, like viscosity, yield point, thixotropy, and electrokinetic properties of mobility and zeta potential for determining of specific industrial application areas. The interactions between each other of charged clay particles and water molecules have strong influence on flow properties. During the interactions, the quantity and amount of exchangeable cations have an important role on the shape and size of clay particles, and those cations control electrical charges, pH of solution and many characteristic properties [1–3]. Investigation of macroscopic properties of bentonite dispersions, such as rheological and electrokinetical properties, as a function of particle size, type of the structure, pH of slurry and charge ⁎ Corresponding author. Tel.: +90 212 285 32 15; fax: +90 212 285 63 86. E-mail address:
[email protected] (N. Güngör). 0167-577X/$ - see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2005.09.055
distributions on the clay surfaces reveals for the better understanding of the interaction behaviors between clay particles. Adsorption of surfactants by clay surface can change rheological and electrokinetic properties and greatly improve their adsorption capacities. Investigation of electrokinetic and rheological properties on bentonite–water colloidal dispersions has been a subject of a special interest to scientists and engineers. During the last decades, many researches have been performed on the interaction of organic additives with smectite group minerals [4–11]. The main purpose of this study is first to characterize mineralogical and chemical properties of natural and Naactivated bentonite samples. Second, is to interpretate the influence of two different cationic surfactants and their electrokinetic properties on the interactions between clay particles by determining particle size distributions, flow and electrokinetic properties, the degree of dispersions on these properties (solid percentage) and their effects on different pH's.
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2. Experimental studies The clay sample was collected from the bentonite deposits in Lalapaşa-Edirne, Thrace, Turkey (courtesy of Bensan Corp.). Samples were taken from three sections at random locations. A Philips PW 1040 model X-ray diffractometer instrument was used to determine the clay mineral types. The dominant clay mineral was found to be dioctahedral montmorillonite (98%) with minor amounts of illite (0.5–1%), calcite (1–2%), feldspar (0–1%), quartz (0–0.2%). Major industrial usage of this bentonite is cat liter, foundry and detergent industries; also it can be used as drilling mud after soda activation. The natural sample has been identified as Ca-bentonite. The Na-activated bentonite was obtained from natural bentonite (35% humidity) by treating the clay with 4% (w/w) NaHCO3 solution. Natural bentonite is labeled CaLB and activated clay as NaLB. The chemical composition of the samples was determined by atomic absorption spectroscopy (Perkin Elmer 3030 model) except for silica, which was determined gravimetrically. Chemical analysis of the clays is given in Table 1. The particle size distributions of the bentonitic clays were determined by the sedimentation technique method. A photo centrifugal Particle Size Analyser SA-CP2 model Shimadzu; Corp., was used for particle size measurements. The natural pH value of NaLB was found 10.7. For studies on the effect of pH on the colloidal and rheological behavior of the Na-bentonite + cationic surfactant dispersions, the pH of the dispersions was adjusted by addition of dilute HCl or NaOH. The samples were shaken for 1 h, and the pH was adjusted several times until the required pH was obtained. A WTW InoLab pH-Cond Level 1 pH-meter was used to measure the pH value of the dispersions. A stable colloidal dispersion coagulates when a certain amount of salt is added. The minimum salt concentration that is needed to cause coagulation of a colloidal dispersion is called critical coagulation concentration, cK. The critical concentration of the organic salts (surfactant) was determined by visual inspection of the behavior of bentonite dispersions. For this purpose, diluted (0.25% w/w) bentonite dispersions prepared at different DTABr and BDTDACl concentrations in test tubes at room temperature. The minimum salt concentration that coagulates the dispersion was recorded as critical coagulation concentration. The critical coagulation concentration values of NaLB for BDTDACl and DTABr have been found to be 0.1 mmol/L, 5 mmol/L, respectively. The cK of long chain organic molecules generally decreases with the chain length [12]. The flow behavior of the dispersions was measured in a Brookfield DVIII+ type low-shear rheometer. The sample was dispersed in water (2% w/w) and shaken for overnight. An adsorption time of 24 h was adopted for the surfactants. The Table 1 Chemical analyses (wt.%) of clay samples Sample
SiO2
Al2O3
CaO
Na2O
MgO
Fe2O3
K2O
TiO2
A.Z.
CaLB NaLB
61,06 56,77
19,91 19,27
3,12 3,5
0,01 4,54
5,27 4,48
2,26 2,33
0,20 0,41
0,18 0,22
7,99 8,48
Fig. 1. Particle size distribution of CaLB and NaLB samples.
rheological behavior of the clay suspensions was obtained by shear stress–shear rate measurements within 0–350 s− 1 shear rates. Rheological measurements were carried out in duplicate. Zeta potential measurements were carried out using Malvern Instruments, Zetasizer 2000. The Zeta potential measurements were carried out using a Malvern, Instruments, Zetasizer 2000. The optic unit contains a 5 mW He–Ne (638 nm) laser. In this instrument to make an electrophoretic mobility measurement, laser beams of are caused to cross at a particular point in the cell. These beams illuminate particles in the cell. At the crossing point of the beams, Young's interference fringes are formed. Particles moving through the fringes under the influence of the applied electric field scatter light whose intensity fluctuates with a frequency that is related to the particle velocity. The photons detected by photomultiplier are fed to a digital correlator, the resulting function being analysed to determine the frequency spectrum, from which the mobility and hence the zeta potential are calculated. The measured electrophoretic mobilities were converted to zeta potential using established theories. Before the measurements, all the dispersions were centrifuged at 4500 rpm for 30 min then supernatants were used for zeta potential measurements. The molecular weight of BDTDACl (C23H42 NCl; Mw = 368.05 g/mol) and DTABr (C12H25N(CH3)3Br, Mw = 308.35 g/mol) were purchased from Fluka. All other chemicals used in this study were analytical grade. 3. Results The particle size distribution in the CaLB and NaLB dispersions is shown in Fig. 1. These studies have done at natural pH 10 using 3 wt.% clay dispersions. It is observed from Fig. 1 that 12.5% of the particles are bigger than 6 μm at CaLB. Coarser than 3 and 0.8 μm particle size fractions are about 53.5% and 87.4% in CaLB dispersions, respectively and no particle size are observed less than 0.8 μm. In contrast, coarser than 40 and 0.6 μm particle size fractions are 9.3% and 75.4% in NaLB dispersions, respectively. For this reason, particle size distribution of NaLB dispersion has a wide variety, so its distribution is very heterogeneous. The comparison of particle size distributions curves in both samples show that relatively small and coarse fractions are present in NaLB dispersions (Fig. 1).
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concentration (solid content) is due to the increase of number of clay particles in the dispersion (Fig. 2a and b). The thixotropic behavior increased strongly with an increase in solid content (Fig. 2c). The area of the hysteresis loop of the flow curves, which is a measure of the degree of hysteresis, is accepted to be positive if the behavior of the system is thixotropic, and to be negative if the behavior is antithixotropic [2,4]. The hysteresis area curves are drawn against solid ratios (Fig. 2c) and flow curves belong to 6 wt.% dispersion, which display a large area indicates that network formed as the result of combination of clusters that were formed by the interactions between clay within dispersion. The influences of pH on rheologic and electrokinetic properties of clay dispersions have been investigated and its effectiveness has been proved [2,6,13–18]. Fig. 3 shows the change in zeta potential with pH for NaLB dispersions. Dispersion displays deflocculating effect in natural pH value (zeta potential—45 mV). A cation–exchange reaction depends on the negative charge of the clay minerals, which can be divided into two types: permanent charge, which is independent of pH, and variable charge, which depends strongly on pH of the solution [6,12]. When the acid is added into the dispersion, the proton of the Al– OH group at the edge surface of the clay crystal is not easily dissociated and even excess proton is adsorbed as follows: Al–OH + H+→Al–OH2. Hence, the negative charge on the edge surface is reduced. System exhibit flocculate structure when the repulsion power weakens between clay particles, double layers shrink and zeta potential values reduce. However, at that time, net charge of particles is negative. For this reason, possible approaches of clay minerals are in surface–surface type. No zero point was found in the study interval of pH 2–11.7. When the dispersion has been made basic by the NaOH addition, the proton of the Al–OH group of the clay crystal dissociates as follows: Al–OH + OH−→ AlO− + H2O. Thus, the negative charge increases. In other words, the polarity of the electrical double layer on the edge surface may change with pH. Fig. 4a, b, c and d show the changes in rheological parameters containing 3 wt.% NaLB dispersion at different pH. All flow curves adjust with pseudoplastic Bingham plastic flow model and all viscosity curves showed that they can be described as thinning flow (Fig. 4a and b). The degree of clusters formed in different pH values dispersions
Fig. 2. The effect of clay concentration on a) the flow curves, b) plastic viscosity (or yield value) versus solid content and c) hysteresis area—solid content.
Rheological parameters are sensitive to solid content. The flow and apparent viscosity-shear velocity curves of the % 1, 2, 3, 4, 5, and 6 of dispersions that have been prepared with the NaLB sample, have been drawn and the flow models are illustrated (Fig. 2a). The value of the rheologic parameters has been increased by the solid ratio and, the thinning flow and thixotropy characters of the system could be clearly examined (Fig. 2a, b and c). The dispersions exhibit nearly Newtonian flow at the concentration of % 1 and 2, but the flow becomes pseudoplastic as dispersion concentration increases. The increase in the rheological parameters (viscosity and yield value) with clay
Fig. 3. The variation of the zeta potential versus pH for 3% w/w NaLB dispersion.
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reflect on the behavior of flow curves. Shear stress value of the system is 0.0113 Pa and hysteresis area is 8.42 Pa/s in natural pH condition. The experimental values, which are so close to each other, indicate that dispersions exhibit maximum deflocculate structure at these pH values (Fig. 4a and c). Zeta potential is about −43 mV in natural pH condition and this zeta value indicates the presence of deflocculated structures in dispersion. Clay particles are highly negative charged in the system and they are separated from each other in deflocculated situation. After the addition of HCl, system started to change acidic environment and rheologic parameters show significant increase in early stage. As continue to add HCl in the system, a decrease was observed on rheologic parameters, because negative charge of clay surfaces diminished as attaching of H+ ions increase. Zeta potential–pH curves reflects a decrease on the negativity of charges (Fig. 3). The zero point couldn't obtain in this study, because clay particles never became completely neutral. The repulsion power between clay particles decreases with decreasing in pH, which reflects on rheologic parameters that causes continuous dropping. The degree of hysteresis increases with increasing pH (Fig. 4c). This indicates that at this pH, the degree of hysteresis is dependent of charge density. Formation of the different networks in the bentonite–water systems depends on the size and shape of particles, exchangeability of cations, layer charge and pH. Rheologic parameters reached the highest values in the pH interval of 7.2–8.0. The reason of reaching the highest values at this interval is related to the increasing in the interaction of clay particles, which indicate the forming of cluster, network structure, in dispersion. However, it is not possible to say that the interactions of all clay
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particles are surface-to-edge attachments. The zeta potential measurements in this interval show that surface charges, even they are gradually diminishing, have negative values. These negative charges repulse clay particles making far from each other which cause inactive or motionless particles against each other that enables an increase in rheological parameters [16]. This is not a stable balance. It is possible to mention about structural changes in dispersion between pH intervals of 8–10.7. A decrease in the rheological parameters suggests breaking down or decomposition of the presence of interactions (Fig. 4). Zeta potential measurements also support this conception. Besides, mobility and zeta potential values are increasing in this interval. Berna et al. [6] studied the effect of pH on the rheological behavior of three purified sodium bentonite suspensions. Each clay sample is studied as a function of pH, at a chosen concentration. The influence of pH on yield stress values of three bentonite suspensions showed that similar values are obtained. It reaches a minimum before it increases sharply, at very high basic medium. When the pH decreases, the yield stress increases and reaches a maximum for pH in weakly acidic media before decreasing again. In a very highly acidic medium, these values decrease and as the result, the structures of the clays probably attach. At acidic medium, there is a dominance of the attractive forces between particles. It is interpreted that ionic forces are very high, double layers squeezed and consequently, EF attractive forces reduced and card-house structure broke down. At high basic medium, yield stress values suddenly increase, interparticle interactions lead to a card-house-like structure based on edge-to-edge, edge to face and face-to-face repulsion, instead of attraction. In these pH values, all edges are negatively
Fig. 4. The variation of a) shear stress–shear rate, b) viscosity–shear rate and c) hysteresis area, d) yield stress curves with 3% w/w NaLB samples at different pH.
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and revealed that face-to-face interactions are virtually independent of pH, whereas edge-to-edge interactions are most attractive at the isoelectric point of edges (pH ∼7). They also reported that significant variations occur in face-to-edge potential energy with strong attraction at acidic media. The yield stress decreases up to an order of magnitude between pH 3 and 7, with a much slower rate of decrease in the 7–11 pH interval. Duran et al. [22] found that face-to-edge attraction is the predominant interaction in the acid pH interval and determines the internal structure of the gel in these conditions. At basic pH, the attraction between different surfaces is weaker and a more relaxed internal structure of the system is predicted [22]. Hysteresis area — pH and yield stress-pH diagrams (Fig. 4c and d) are found from the flow curves of dispersions, which exhibit parallel behaviors to the curves of rheological parameters (Fig. 2). Thixotropic properties of the dispersion increases when the working range of pH's of dispersion are 6, 7 (in this pH, thixotropic gel reaches to maximum level) and 8. Nevertheless, maximum gel property is observed at pH 7.2 in our experiments. Addition of surfactants into the bentonite dispersion does effects the rheological behavior of the system (Fig. 5). The degree of interaction between bentonite particles and surfactant molecules depends on the surfactant concentration in the dispersion. First additions to the bentonite dispersions do not change the rheological parameters significantly. Further additions of surfactants, however, the results of the rheological parameters sharply and continuously increase. Also, the
Fig. 5. The changes of the rheological parameters of NaLB dispersions with DTABr and BDTDACl surfactants added to dispersions; a) yield value b) hysteresis area.
charged and diffused double layers highly squeezed and Van der Waals attractive force is not dominant. However, electrostatic attraction force is not possible, only electrostatic repulsive force between particles are present in edge-to-edge and face-to-face forms [6]. Negative charges further away each clay particle from other by repulsive force that causes unattractive stationary suspension, results an increase in rheological parameters [18,19]. After reducing in rheological parameters, clay structures changed and the forms of aggregations broke down. The values of zeta potential also support these measurements. Bern et al. [6] reported that rheological parameters reach minimum values at pH 10, these parameters increase after pH 11 and their results are comparable with our studies. There are two proposed models by which a gel of smectites can be formed from the starting suspension. Model-1; Van Olphen [17] attributed gel formation to the electrostatic attraction between negatively charged faces and positively charged edges of clay particles (E–F). Model-2; Norrish [18], Callanghan and Ottewil [19] and Moan [20] assumed that gel formation is due to the long-range electrostatic double-layer repulsion (E–E and F–F).Moreover, Norrish [18] argued that these two ideas may operate together and these processes particularly depend on pH [6]. Sakairi et al. [21] calculated the yield stress of electrostatically dispersed Na-montmorillonite suspensions a function of the volume fraction of clay and ionic strength of background NaCl solution. They found that as rapid increase in yield stress values when volume fraction of clay increases and, in contrast, it decreases with an increase in ionic strength. Duran et al. [22] described the rheology of Na-montmorillonite suspensions as a function of pH, at constant ionic strength
Fig. 6. The changes of flow curves and apparent viscosity–shear rate curves in 8 and 10 mmol/L BDTACI and 5 and 8 mmol/L DTABr surfactants containing NaLB (3% w/w) dispersions.
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continuous increase is an indicator of a growing net structure in the environment. Both surfactants containing with 3 wt.% have flocculants effect in solution. Especially, when DTABr surfactant added, the system shows rapid and continuous increase in viscosity and yield point values. The interaction difference between these two surfactants and clay particles are related to the difference between chemical compositions of these surfactants (7, Fig. 6). BDTDACI surfactant contains benzene structure, which is covered by electron clouds, and by the reason of this structure, the electrostatic interaction became more difficult between clay particles and negative charges of surfactant. However, Br ion located in DTABr surfactant can easily released from its structure and this property makes easy the interaction of surfactant with clay particles. The properties of thixotropic gel are measured after adding both surfactants in 3 wt.% dispersions. After adding of 10 mM surfactants, hysteresis areas for BDTDACI and DTABr surfactants are found as 40.9 Pa/s and 75.25 Pa/ s, respectively. Both surfactants have showed the same effects on the yield point and apparent viscosity values (Fig. 5a and b). However, DTABr surfactant behaves more effective than the parameters of BDTDACI. The measured yield point values show an increase for DTABr after adding 1 mmol/L and for BDTDACI after adding 3.6 mmol/L especially, yield point value shows rapid and continuous increase in DTABr containing slurries. Hysteresis area reaches to the maximum value after adding 6 mmol/ L surfactant in 2 wt.% dispersion, but 3 wt.% NaLB containing dispersion reaches to the maximum value after adding 10 mmol/L (Fig. 5b). After adding 10 mmol/L DTABr, the hysteresis area 9 times increased, up to 75 Pa/s, compared to the dispersion without additive. The shape of curves shows synchronizes with the changes in surfactant concentration and the values of viscosity and yield point. Both figures, (Fig. 5a and b) indicate that thixotropic gel structure increase with an increase in surfactant concentration.
Fig. 7. Chemical of formulas of DTABr and BDTDACl surfactants.
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Fig. 8. The changes of the zeta potential of NaLB dispersions with DTABr and BDTDACl surfactants added to dispersions.
When 8 and 10 mmol/L BDTDACI were added in 3 wt.% NaLB containing dispersion, the behaviors on the changes of flow curves and apparent viscosity—shear rate relations are illustrated in Fig. 6a and b. These results have in good agreement with the behaviour of hysteresis area and plastic viscosity of bentonite dispersion. The influence of effects of surfactants on zeta potential of dispersions using natural pH conditions is given in Fig. 7 and the results are adjustable with the results of rheological studies. Both surfactants show the flocculants effect on the 3 wt.% clay containing dispersions. However, surfactants are not able to cover up completely clay surfaces. Especially, DTABr surfactant is very effective in these experiments. In the dispersion, which shows alkaline property in natural pH, the adsorption of cationic surfactant through cation– exchange reaction is greater than that in acidic solution. Particle size distribution measurements have been done on 8 and 10 mmol/L BDTDACI and 7.5 and 10 mmol/L DTABr containing NaLB dispersions and detected that particle sizes are decreasing in dispersions after the addition of both surfactants (Fig. 8). These observations clearly indicate that additives disperse present clusters and by this way, additives create more dispersed slurries. These observations are compared with the results of other dispersions, which showed flocculated systems after adding surfactants, based on rheological and
Fig. 9. Particle size distribution of NaLB or CaLB treated samples with DTABR and BDTDACI surfactants.
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electrokinetic measurements, and concluded that the new forming gel structure is a repulsive gel. Those surfactant molecules, which attach on clay surfaces as a result of partial interaction with their charges, develop a new second layer after adding of additives. As a result of these reactions, the repulsions between these new layers and between surface charges of clay particles, which are not reacted with surfactants, create a repulsive gel structure. 8 mmol/L BDTDACI containing clay particles are caused a decrease in particle size fractions. However, those fine clay particles, after addition of 10 mmol/L BDTDACI, came together and grew again like foam flocculation due to wrapping around the polar tales of organic molecules. It was concluded that new forming gel is repulsion gel from the comparison of the above result with the rheologic and electrokinetic measurements, which showed that they were flocculated, of DTABr containing dispersion. In addition, particle size distribution curves of 7.5 and 10 mmol/L DTABr containing NaLB dispersions also showed that clay particle sizes became smaller after addition of additives. Surfactants clearly dispersed well enough clay particles and finer clay particles became more abundant. In original NaLB dispersion, coarser than 10 μm fractions are 49.8%, but no clay particle above 10 μm was found after addition of additives. As the result of experiments, we concluded that surfactant containing dispersions contain much smaller clay particles due to their strong dispersion performance. Besides, in order to understand whether added surfactants enter into the interlayer of clay minerals or not, XRD analyses were done to measure d(001)-spacing. The sheets in clay structures bound to each other with covalent bonds and therefore, their crystal structure are stable. In contrast, the layers bound with Van der Waals bonds and water or organic molecules expands the layers when it introduces the interlayers. In this way, the distance between basal spacings increased. An increase in basal spacing is considered as a criterion for the degree of swelling of clay minerals due to introducing of organic molecules. Whether surfactant molecules introduce into smectite layers or not, can be determined based on d(001)-spacing measurements with XRD after the addition of each additives. Basal d(001)-spacings of the films are shown as a function of surfactant concentrations in Fig. 9. It was measured during XRD studies that basal d(001)-spacing was 12.98 A° in natural NaLB sample, but it shifted to 14.71 A° after the addition of 0.8–4 mmol/L BDTDACI and d(001)-spacing reached to 16.44 A° after increasing of surfactant up to 4–10 mmol/L (Fig. 9). These values shifted to 14.98 A° after the addition of 0.25 mmol/L DTABr and shifted to 14.36 A° when 10 mmol/L was added. Swelling of basal d(001)-spacing increased about 3.46 A° after the addition of BDTDACI and 1.98 A° after the addition of DTABr. XRD studies clearly indicate that adsorption performance of BDTDACI is better than DTABr due to the differences in their molecular structures.
4. Conclusions These studies showed that both surfactants have flocculants effect on 3 wt.% containing dispersions. Also, dispersions gained more thixotropic properties after the addition of these surfactants. It has been determined that forming of thixotropic gel is depending on the shape and size of clay particles, solid ratio in dispersions, pH of slurries, molecular structure and concentration of surfactants, which are also associated with particle-to-particle reactions. In this study, it was determined that both surfactants have flocculants affect on dispersions, but they were not able to cover clay surfaces completely. The intercalation of surfactants with bentonite slurries have been examined by X-ray diffraction and
Fig. 10. The changes of the d(011) in bentonite–water systems with DTABr and BDTDACl added to suspensions.
found that additives partially increase the interlayer spacings (Fig. 10). In this study, the flow and surface properties of BDTDACI and DTABr surfactants containing dispersions in different conditions are depending on the rheological and electrokinetic properties of dispersions and clay particle size distributions. Acknowledgement This research project is supported by Istanbul Technical University, Turkey, Research Fund (Project No: 30451). References [1] Th.F. Tadros, Solid/Liquid Dispersions, Academic Press, New York, 1987. [2] N. Güven, Rheological aspects of aqueous smectite suspensions, in: N. Güven, R.M. Pollastro (Eds.), CMS WorkShop Lectures, Boulder, CO, 1992, p. 82. [3] F.P. Luckham, S. Rossi, Advances in Colloid and Interface Science 82 (1999) 43. [4] G. Lagaly, Applied Polymer Science 4 (1989) 105. [5] G. Chen, B. Han, H. Yan, Journal of Colloid and Interface Science 201 (1998) 158. [6] M. Benna, N. Kbir-Ariguib, A.F. Magnin, F. Bergaya, Journal of Colloid and Interface Science 218 (1999) 442.
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