Effect of surface hydroxyl groups on the dispersion of ceramic powders

Effect of surface hydroxyl groups on the dispersion of ceramic powders

Materials Chemistry and Physics xxx (2016) 1e5 Contents lists available at ScienceDirect Materials Chemistry and Physics journal homepage: www.elsev...

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Materials Chemistry and Physics xxx (2016) 1e5

Contents lists available at ScienceDirect

Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys

Materials science communication

Effect of surface hydroxyl groups on the dispersion of ceramic powders Tse-Hsing Ho a, Shinn-Jen Chang b, Chia-Chen Li a, * a

Institute of Materials Science and Engineering, and Department of Materials & Mineral Resources Engineering, National Taipei University of Technology, Taipei 10608, Taiwan b Material and Chemical Research Laboratories, Industrial Technology Research Institute, Hsinchu 30011, Taiwan

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

 Effect of surface hydroxyl group on the dispersity of oxides was explored.  Larger amount of dispersant was required for dispersing hydroxylated oxides.  Organic additives became more competitive to adsorb on the hydroxylated oxides.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 4 September 2015 Received in revised form 15 January 2016 Accepted 23 January 2016 Available online xxx

The effect of surface hydroxyl groups (eOH) on the dispersity of ceramic powders was explored using the common ceramic powder barium titanate (BaTiO3) as the study model. To simulate the presence of eOH on the powder, which is generally formed because of atmospheric storage, oxidative hydroxylation with hydrogen peroxide was used to produce and adjust the concentration of surface eOH. Owing to the presence of a lot of surface eOH, BaTiO3 particles aggregated because of hydrogen bonding and required a large amount of dispersant such as the ammonium salt of poly(acrylic acid) (PAA-NH4) for its dispersion stabilization. In addition, the commonly used binder poly(vinyl alcohol) (PVA) became more competitive with PAA-NH4 for adsorption onto the hydroxylated BaTiO3, thereby reducing the efficiency of the dispersant and impeding the dispersion of the powder. © 2016 Elsevier B.V. All rights reserved.

Keywords: Ceramics Oxides Adsorption Surface properties

1. Introduction Most ceramic powders have characteristics of both ionic and covalent bonding; therefore, they are usually polar, particularly when the ionic character is more significant, as in the case of barium titanate (BaTiO3), alumina (Al2O3), zirconia (ZrO2), and titania (TiO2) [1,2]. Because of their significant polarity and large

* Corresponding author. E-mail address: [email protected] (C.-C. Li).

surface area, ceramic powders easily absorb water vapor from the atmosphere during storage. In general, water vapor does not simply adsorb physically but tends to be transformed by hydration upon chemical adsorption, thereby producing hydroxyl groups (eOH) on the surface of the powder [3e6]. Because hydration is a chemical reaction, it is irreversible; regular drying in an oven does not easily remove the produced eOH. Hydrogen bonds (Hebonds) between surface eOH groups of powders (caused by hydration) tend to initiate powder aggregation and make subsequent dispersion processes more difficult. The resultant poor dispersity and low compatibility of the powder with other materials will restrict its

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applications. BaTiO3 is a popular dielectric material in the industry of passive electronic components [7e10]. It is the most essential dielectric ceramic for commercial products consisting of multilayered ceramic capacitors (MLCCs). In the fabrication of MLCCs, BaTiO3 powder is blended with other additives in a solvent to form homogeneous slurry in the initial steps. Several studies [11e15] report the importance of using water as a solvent for the preparation of ceramic slurries for economic and environmental reasons. Because BaTiO3 is generally stored under ambient conditions prior to processing, it tends to undergo hydration due to water vapor in the air. Furthermore, it may be hydrated by water from the aqueous process during fabrication. Both the above hydration routes irreversibly produce surface eOH. This phenomenon is more severe with nanosized powders; yet, such powders are in high demand for the development of small electronic devices. In preliminary research [15e17], we found that mild oxidative conditions could produce eOH on the surface of BaTiO3 particles. As the corresponding technique and mechanism of BaTiO3 hydroxylation have been established and well studied, hydroxylated BaTiO3 is suitable for use as a study model to explore the effect of surface eOH on the dispersity of ceramic powders. The interaction between the surface eOH of BaTiO3 and organic additives, such as the dispersant and binder, was also investigated. Results of this investigation closely correlated to the dispersion of ceramic powders. 2. Materials and methods High-purity BaTiO3 powder (99.8%; Fuji Titanium, trace-metal basis, Japan) having ~0.63 mm median size, 3.7 m2/g surface area, and 0.997 barium/titanate ratio was used. An aqueous solution of hydrogen peroxide (H2O2; 50.38%, Echo Chemical Co., Taiwan) was used for the hydroxylation of BaTiO3. The dispersant used was ammonium poly(acrylic acid) (PAA-NH4; Darvan-821A, R. T. Vanderbilt, Norwalk, CT) with molecular weight of 6000 g/mol. The binder used was poly(vinyl alcohol) (PVA; 88.0% hydrolysis, Chang Chun Petrochemical, Taiwan) with molecular weight of 27,000e32,000 g/mol. Deionized water was used as the dispersion medium. For hydroxylation, 1 g of BaTiO3 powder was refluxed in a specific volume of H2O2(aq) at 106  C for 4 h [15e17]. After reflux, the hydroxylated BaTiO3 was filtered and washed with deionized water until the filtrate reached a pH higher than 6.5. It was then rinsed with acetone to extract most of the moisture. The powder was dried and stored in a vacuum desiccator for at least one day. In the dispersion experiments on adsorption and in rheology measurements, aqueous suspensions with 5 wt% and 10 vol% BaTiO3 powder (based on the weight of solvent) were respectively prepared by mixing powder with PAA-NH4 and PVA at various concentrations (based on the weight of BaTiO3). The suspensions were then mixed and de-agglomerated by ball-milling with 10 mm Y2O3-stabilized ZrO2 media for 72 h. The adsorptions of PAA-NH4 and PVA on BaTiO3 were respectively measured by potentiometric titration [11,13] and thermogravimetric analysis (Q50, TA Instruments Ltd., UK). The apparent viscosities of the powder suspensions were measured at various shear rates by using a concentric cylinder rheometer (AR1000, TA Instruments Ltd., UK). Cone-plate geometry fixtures with a diameter of 20 mm and cone angle of 1 were chosen for the steady-shear rotation tests. Also, the respective viscosities of two aqueous solutions of 1 wt% PAA-NH4 and 10 wt% PVA were measured at various shear rates for the further calculations of relative viscosities of powder suspensions. The interaction between PAA-NH4 and PVA was characterized by Fourier transform infrared (FT-IR) spectroscopy (DA 8.3, Bomen, Canada) using a sample of the mixture at a 1:1 weight ratio.

3. Results and discussion To simulate the presence of eOH on BaTiO3 caused by hydration under ambient conditions, BaTiO3 was mildly hydroxylated by surface treatment with H2O2 [15e17]. Fig. 1 compares the FT-IR spectra of BaTiO3 powders hydroxylated with H2O2 at various concentrations. As-received BaTiO3 (labeled as PBT) was dried at 80  C for 24 h before FT-IR characterization; however, it exhibited slight IR absorption corresponding to eOH stretching at 3000e3600 cm1 [18]. This result shows that eOH, which is mostly due to hydration of the powder, was chemically bonded and could not be easily removed. For the hydroxylated BaTiO3 powders that were surface-treated with H2O2 at concentrations of 10, 25, 40, 60, 90, and 120 mL/g BaTiO3 (mL/g BT) (labeled as HBT-10, HBT-25, HBT-40, HBT-60, HBT-90, and HBT-120, respectively), the IR absorption of eOH (3000e3600 cm1) significantly increased with increasing the H2O2 treatment concentration. This increase demonstrated that oxidative hydroxylation by H2O2 could simulating the varied eOH concentration on the BaTiO3 surface. Fig. 2(a) shows the adsorbed amount of the dispersant PAA-NH4 on various BaTiO3 powders as a function of the equilibrium concentration of PAA-NH4 in the suspension. In all cases of adsorption on the various BaTiO3 powders, the adsorbed amount of PAA-NH4 initially increased and then reached a saturation limit, showing the characteristic behavior of monolayer adsorption [11,13,19,20]. This result indicates that the mechanism of PAA-NH4 adsorption on the powders was not affected by the increased concentration of surface eOH. Nevertheless, more hydroxylated BaTiO3 exhibited a higher saturation limit for PAA-NH4. As the increase in polarity, resulting from the greater degree of hydroxylation of BaTiO3, enhanced the polarepolar and ionepolar interactions, more hydroxylated BaTiO3 may have increased the adsorption of PAA-NH4. Fig. 2(b) shows the

Fig. 1. FT-IR spectra of (a) as-received BaTiO3 and of hydroxylated BaTiO3 surfacetreated with H2O2 with concentrations of (b) 10, (c) 25, (d) 40, (e) 60, (f) 90, and (g) 120 mL/g BT.

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Fig. 2. Amounts of (a) PAA-NH4 and (b) PVA adsorbed on various BaTiO3 powders as functions of equilibrium concentrations.

adsorbed amount of the commonly used binder PVA on various BaTiO3 powders as a function of the equilibrium concentration of PVA. Similar to the results for PAA-NH4 adsorption, PVA adsorbed as a monolayer on the powder, and this behavior remained unchanged even when BaTiO3 was highly hydroxylated. The saturation limit of PVA adsorption also increased with increased concentration of surface eOH on BaTiO3. This resulted from the availability of Hebonds between hydroxylated BaTiO3 and PVA [15], i.e., more hydroxylated BaTiO3 favored PVA adsorption. Based on the results shown in Fig. 2(a) and (b), both the dispersant PAANH4 and binder PVA clearly adsorbed preferentially to hydroxylated BaTiO3. The adsorption preference of PVA and PAA-NH4 may cause their competitive adsorption on the hydroxylated BaTiO3 and affect the dispersion efficiency of PAA-NH4. Furthermore, the adsorptions of PAA-NH4 and PVA on various BaTiO3 powders can be analyzed using the data of Fig. 2 based on the Langmuir monolayer adsorption equation [Eq. (1)] [20].

Ce =As ¼ Ce =Cm þ k=Cm

(1)

where Ce is the equilibrium concentration of the polymer, such as PAA-NH4 or PVA, in solution, As is the adsorption amount of the polymer, Cm is the monolayer adsorption amount of the polymer, and k is a constant. Using Eq. (2), the resulting Cm from Eq. (1) can be utilized to calculate the gyration size (rg) of the adsorbed polymer, which is also the radius of the occupied area of each polymer chain on the particle [20].

Cm ¼

SA M pNr2g

(2)

where SA is the specific surface area of the powder, M is the average molecular weight of the polymer, and N is Avagadro's number. The calculated rg values for PAA-NH4 and PVA on various BaTiO3 powders are listed in Table 1. Both rg values of PAA-NH4 and PVA decreased with the increased hydroxylation of BaTiO3, indicating that the adsorption conformations of both polymers varied for different powders. The smaller rg values of the polymers on the more hydroxylated BaTiO3 suggested that the polymer chains in the adsorbed layer were more erective and compact. The dispersion properties of aqueous suspensions containing 10 vol% of various BaTiO3 powders in the presence of different concentrations of PAA-NH4 ([PAA-NH4]) were revealed by rheological analyses [Fig. 3(a)]. For comparison, all viscosities were obtained at a shear rate of 25 s1. Without the addition of PAA-NH4, aqueous suspensions of HBT-90 and HBT-120 underwent shear thinning and

Table 1 Gyration sizes (rg) of PAA-NH4 and PVA, and the adsorption thicknesses (d) of PAANH4, PVA, and the mixture of PAA-NH4 and PVA (PAA-NH4 þ PVA) on various BaTiO3 powders. BaTiO3

Polymers 1 wt% PAA-NH4

PBT HBT-10 HBT-25 HBT-40 HBT-60 HBT-90 HBT-120

10 wt% PVA

1 wt% PAA-NH4 þ 10 wt% PVA

rg (nm)/d (nm)

rg (nm)/d (nm)

d (nm)

3.0/6.8 2.2/13.2 2.0/13.8 1.7/32.3 1.5/33.4 1.3/45.8 1.2/41.3

3.1/4.0 2.3/33.3 2.1/49.8 2.0/45.4 1.7/50.4 1.7/48.4 1.6/51.8

34.1 52.6 62.4 72.8 72.7 94.5 96.0

showed a viscosity higher than that of PBT; in contrast, the aqueous suspension viscosities of HBT-10, HBT-25, HBT-40, and HBT-60 were lower than that of PBT. The lower aqueous suspension viscosities of HBT-10 to HBT-60 resulted from the improved affinity of the less hydroxylated powders in the dispersion medium. The higher viscosity of HBT-90 and HBT-120 was caused by the presence of Hebonds in HBT-90 and HBT-120 that may have resulted in severe agglomeration of powders. Furthermore, the viscosity of all suspensions decreased as [PAA-NH4] increased until stable minimum was reached. The critical concentration of PAA-NH4 ([PAANH4]c) required for the stabilization of various BaTiO3 powders was within 0.3e0.5 wt% for PBT, HBT-10, HBT-25, HBT-40, and HBT-60 and was within 0.7e1.0 wt% for HBT-90 and HBT-120. The increased [PAA-NH4]c with increasing eOH concentration on BaTiO3 indicated more aggregation of the hydroxylated powder due to Hebonding. Fig. 3(b) shows a comparison of the viscosities of aqueous suspensions containing 10 vol% of various BaTiO3 powders in the presence of 10 wt% PVA and various [PAA-NH4]. When PAA-NH4 was not added, the PBT suspension exhibited the lowest viscosity. The viscosity of the suspensions increased with increasing eOH concentration on BaTiO3. Comparison of the viscosities of suspensions at [PAA-NH4] ¼ 0 in Fig. 3(b) (with the presence of 10 wt% PVA) to those in Fig. 3(a) (with absence of PVA) showed that only the suspensions with PBT and HBT-10 had lower viscosity. This result indicated that PVA had the ability to disperse BaTiO3 but became less efficient when the eOH concentration on BaTiO3 increased. It is interesting to note that more hydroxylated BaTiO3 had greater adsorption of PVA but resulted in poorer dispersion. For most dispersants, a higher adsorbed amount on powders generally

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Fig. 3. Viscosity of 10 vol% aqueous BaTiO3 suspensions at a shear rate of 25 s1 as a function of the concentration of PAA-NH4 added in the (a) absence and (b) presence of 10 wt% PVA.

facilitates the dispersion of the powder because the dispersant has better surface coverage, which provides sufficient electrostatic or steric repulsion for powder dispersion. As PVA is neutral, it does not dissociate in the same manner as most polyelectrolyte-type dispersants. Its higher adsorption on the more hydroxylated BaTiO3 [Fig. 2(b)] did not aid in increasing electrostatic repulsion. In addition, PVA possesses abundant eOH, which prefers to form Hebonds. Polymer bridging rather than steric hindrance between particles dominated the dispersion behavior of the powders, i.e., the powders agglomerated via polymer bridging, resulting in poorer dispersion (Fig. 4). Fig. 3(b) also shows that the viscosity of suspensions decreased as [PAA-NH4] increased, suggesting that the dispersing effect caused by adsorption of PAA-NH4 was more significant than the agglomerating effect caused by PVA adsorption. For the suspensions with the more hydroxylated BaTiO3, such as HBT-90 and HBT-120, the required [PAA-NH4]c (1.5 wt%) was much greater than that of the suspensions containing less hydroxylated BaTiO3 (0.7 wt%). This result revealed that the adsorption competitiveness of PAA-NH4 decreased when the eOH concentration on BaTiO3 increased, which impeded the dispersion of suspensions. In contrast, the viscosity of the PBT and HBT-10 suspensions initially increased and then decreased with the continuous increase in [PAA-NH4]. Although the initial increase in viscosity may have been caused by competitive adsorption, it more likely resulted from a specific interaction between PAA-NH4 and PVA that is not yet discussed in the literature. To evidence whether a specific interaction occurred between PAA-NH4 and PVA, further information about the layer thickness of the adsorptions of the polymers was analyzed by the viscometric

method [19,20] using the data of the apparent viscosity (h) measured with a shear rate of 250 s1. Relative viscosity (hr) of the suspensions was attained by dividing h of suspensions with the viscosity of the continuous phase (h0). The relation between hr and the apparent hydrodynamic volume fraction of the dispersed phase (f) that contains the particle and its adsorbed polymer was approximated by the modified Einstein equation [Eq. (3)], which was proposed by Doroszkowski and Lambourne [20,21]. The effective volume of the adsorbed layer (Df) was calculated from the difference between the apparent volume and actual volume of the dispersed phase, and the average layer thickness of the adsorbed polymer (d) was then be determined by Eq. (4) [20].

hr ¼ 1 þ 3f þ 23f2

(3)

d ¼ Df=SA

(4)

The resultant d values of PAA-NH4, PVA, and the polymer mixture of PAA-NH4 and PVA on various BaTiO3 are listed in Table 1. Note that the relative viscosities used for calculations corresponded to the suspensions with saturated additions of polymers, which were 1 wt% for PAA-NH4 and 10 wt% for PVA (Fig. 2). The diameter of the free polymer chain coil in solution can be approximated by the square root of its molecular weight (M1/2), and they were 7.7 nm and 17.9 nm for PAA-NH4 and PVA, respectively. For the adsorption of PAA-NH4 on PBT, rg was 3.0 nm and d was 6.8 nm. The values of 2rg and d were close to the diameter of the free PAA-NH4 coil; therefore, the adsorbed PAA-NH4 on PBT exhibited almost the same geometry as it did in the dispersion medium. For the adsorption of

Fig. 4. Schematic agglomeration of hydroxylated BaTiO3 caused by polymer bridging of surface adsorbed PVA.

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suspensions [Fig. 3(b)] should be attributed to the chemical interaction between PAA-NH4 and PVA in the aqueous suspension. 4. Conclusions

Fig. 5. FT-IR spectra of (a) pure PAA-NH4, (b) pure PVA, and the(c) PAA-NH4/PVA blend.

PVA on PBT, rg was 3.1 nm and d was 4.0 nm; both were smaller than 17.9 nm, indicating that the conformation of the adsorbed PVA may not be coil-shaped, which should be relevant to the intramolecular Hebonding of PVA and the lesser interaction of PVA with PBT. In addition, the d of 34.1 nm for the co-adsorption of the polymer mixture on PBT is much larger than the 6.8 nm for PAANH4, 4.0 nm for PVA, and the summated 10.8 nm for PAA-NH4 and PVA. The larger d for the co-adsorption of polymer mixture demonstrated that the conformations of the two polymers on PBT were more extended. The only possible cause for the more extended conformation was the high affinity of the two polymers, i.e., some kind of specific interaction may have occurred between the co-adsorbed PAA-NH4 and PVA. In contrast, the decreased rg and increased d for both PAA-NH4 and PVA with the increased hydroxylation of BaTiO3 indicated altered conformations of the adsorbed polymers. The variation in their adsorbed conformations was caused by the different interactions of polymers with BaTiO3 having differing surface chemistries. For adsorptions on various HBT powders, d of the polymer mixture approximated to the summated d from the individual PAA-NH4 and PVA, suggesting that the competitive adsorption between PAA-NH4 and PVA remained. Moreover, the FT-IR spectrum of the PAA-NH4/PVA blend at a 1:1 weight ratio was characterized and compared with those of pure PVA and PAA-NH4, as shown in Fig. 5, to qualify the interaction between PAA-NH4 and PVA. The broad band of PAA-NH4 [Fig. 5(a)] centered at 3130 cm1 was attributed to eOH stretching [18]. The characteristic peak at 1710 cm1 resulted from C]O stretching, and peaks at 1560 and 1400 cm1 were attributed to CeOeH bending [18,22]. The broad band of PVA [Fig. 5(b)] at 3295 cm1 and the peak at 2941 cm1 were associated with eOH stretching and CeH stretching [18], respectively. The peaks at 1735 and 1658 cm1 respectively resulted from C]O stretching and CeO stretching from the acetate groups in PVA [18,23]. The IR spectrum of the PAANH4/PVA blend [Fig. 5(c)] was markedly different from that of pure PAA-NH4 and PVA. The decrease in significance of eOH stretching at 3000e3700 cm1 and the shifting of the peak for C]O stretching to a lower wavenumber (1686 cm1) indicated that PAA-NH4/PVA was not simply a mixture but rather a chemical product. In other words, the initial increase in viscosity of the PBT and HBT-10

Hydroxylated BaTiO3 was used as a model ceramic powder to study of the effect of surface eOH on the dispersion behavior of ceramic powders. The eOH on BaTiO3 in this investigation was derived using surface hydroxylation with H2O2 treatment. More aggregation of BaTiO3 was observed with increased surface hydroxylation due to Hebonding of eOH, and the amount of PAA-NH4 required for powder dispersion increased. In contrast, the commonly used dispersant and binder, PAA-NH4 and PVA, had a higher tendency to adsorb on the more hydroxylated BaTiO3. Their preference for adsorbing on the hydroxylated BaTiO3 resulted in more competitive adsorption between them and an increased amount of PAA-NH4 required for stabilizing the dispersion. We observed that the co-existed PVA chemically interacted with PAANH4 (via viscosity characterization and FT-IR), thereby affecting the dispersion stability and increasing the viscosity of the corresponding suspensions. Acknowledgments The authors are grateful for the financial support by the Ministry of Science and Technology of the ROC under Grant No. 103-2221-E027-011 and by the Material and Chemical Research Laboratories of Industrial Technology Research Institute. References €ttger, Dielectric properties of polar oxides, in: R. Waser, U. Bo € ttger, [1] U. Bo S. Tiedke (Eds.), Polar Oxides: Properties, Characterization, and Imaging, Wiley-VCH, Weinheim, Germany, 2005, pp. 11e37. [2] M.W. Barsoum, Fundamentals of Ceramics, Mc-Graw-Hill, Boston, 2000. [3] H. Manzano, R.J.M. Pellenq, F.J. Ulm, M.J. Buehler, Adri C.T. van Duin, Langmuir 28 (2012) 4187e4197. [4] K.C. Hass, W.F. Schneider, A. Curioni, W. Andreoni, Science 282 (1998) 265e268. [5] J.M. Wittbrodt, W.L. Hase, H.B. Schlegel, J. Phys. Chem. B 102 (1998) 6539e6548. [6] V. Shapovalov, T.N. Truong, J. Phys. Chem. B 104 (2000) 9859e9863. [7] D.H. Yoon, J. Ceram. Process. Res. 7 (4) (2006) 343e354. [8] B.I. Lee, P. Badheka, V. Magadala, X. Wang, D. Yoon, J. Ceram. Process. Res. 5 (2) (2004) 127e132. [9] G.N. Howatt, R.G. Brekenridge, J.M. Brownlow, J. Am. Ceram. Soc. 30 (8) (1947) 237e242. [10] D. Yoon, B.I. Lee, J. Ceram. Process. Res. 3 (2) (2002) 41e48. [11] J.H. Jean, H.R. Wang, J. Mater. Res. 13 (8) (1998) 2245e2250. [12] Z.G. Shen, J.F. Chen, H.K. Zou, J. Yun, J. Colloid Interface Sci. 275 (1) (2004) 158e164. [13] Z.C. Chen, T.A. Ring, J. Lemaître, J. Am. Ceram. Soc. 75 (12) (1992) 3201e3208. [14] U. Paik, J. Korean Phys. Soc. 32 (1998) S1224eS1226. [15] C.C. Li, C.H. Chang, J. Am. Ceram. Soc. 96 (2) (2013) 436e441. [16] S.J. Chang, W.S. Liao, C.J. Ciou, J.T. Lee, C.C. Li, J. Colloid Interface Sci. 329 (2009) 300e305. [17] C.C. Li, S.J. Chang, J.T. Lee, W.S. Liao, Colloids Surf. A 361 (1e3) (2010) 143e149. [18] G. Socrates, Infrared Characteristic Group Frequencies d Tables and Charts, John Wiley and Son, England, 1994. [19] E. Kissa, DispersionseCharacterization, Testing, and Measurement, Marcel Dekker, New York, 1999. [20] T. Sato, R. Ruch, Stabilization of Colloidal Dispersions by Polymer Adsorption, Marcel Dekker, New York, 1980. [21] A. Doroszkowski, R. Lambourne, J. Colloid Interface Sci. 26 (1968) 214e221. [22] B.P. Singh, S. Nayak, S. Samal, S. Bhattacharjee, L. Besra, Appl. Surf. Sci. 258 (2012) 3524e3531. [23] S.N. Alhosseini, F. Moztarzadeh, M. Mozafari, S. Asgari, M. Dodel, A. Samadikuchaksaraei, S. Kargozar, N. Jalali, Int. J. Nanomed. 7 (2012) 25e34.

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