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Vol. 14, 9525–9533, 2014 www.aspbs.com/jnn

Optimization of Polymeric Dispersant Concentration for the Dispersion-Stability of Magnetite Nanoparticles in Water Solution Geun-Dong Song, Mun-Hwan Kim, and Wan-Young Maeng∗ Department of Nuclear Materials Development, Korea Atomic Energy Research Institute, 111 989 Gil Yuseong, Deajeon, Korea Fouling of various Fe oxide particulates on heat transfer tubes in the coolant of the secondary system of a nuclear power plant has been known to reduce the heat transfer performance and degrade the integrity of system components. Thus, in order to mitigate such a fouling problem, an addition of polymeric dispersant has been proposed to remove the oxide partculates. In this paper, experimental studies was conducted for evaluating the effect of polymeric dispersants (PAA: Polyacrylic acid, PMA: Polymethacrylic acid, PAAMA: Polymaleic acid-co-acrylic acid) on the dispersion stability of magnetite nanoparticles (MNPs, Fe3 O4 ) for the reduction of fouling and corrosion of carbon steel by the settling test, the transmittance, zeta-potential, and particle size measurements, and the electrochemical corrosion tests. It was observed that the critical concentration for maximizing the dispersionstability of MNPs was in the range of concentration ratio (dispersant/MNPs) of 0.1 to 0.01 and the dispersion-stability of MNPs was not improved when the dispersant concentration is above this critical value. This non-linearity above a critical dispersant concentration may be explained by the agglomerations between MNPs. While there is no significant increase of corrosion rate with an addition of up to 10 ppm PAA, the addition of 100 ppm PAA increases the growth rate of oxide layer rapidly and deteriorates the formation of protective oxide on carbon steel. It is thus reasonably stated that the optimization of polymeric dispersants variables and its impacts on the corrosion of structural materials is necessary for the best application at plants.

Keywords: Fouling, Magnetite, Polymeric Dispersant.

1. INTRODUCTION Fouling is a deposition of undesirable materials on the surface of structural materials, and is the source of the trouble of several problems in various locations such as heat exchange tubes, venturi flow tubes, and water purifying membranes, etc. At power plants, the deposition of various oxide particulates on heat exchange tube causes a significant decrease on the efficiency of power production. A similar fouling problem has been also observed on steam generator tubes of the secondary system of nuclear power plants. MNPs from the corrosion products of feed water pipe are deposited on the surface of heat exchange tubes of steam generator and caused the high corrosion and heat transfer reduction.1 In order to prevent such a problem, a method using polymer dispersants for the removal ∗

Author to whom correspondence should be addressed.

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of MNPs has been recently proposed.2 A polymer dispersant adsorbed on the surface of MNPs produces steric and electrical repulsion,3 and MNPs are not aggregated by steric and electrical repulsion. It is therefore possible to remove the MNPs more easily and consequently reduce the fouling phenomena.4 Thus, it is necessary to evaluate the effective application of polymeric dispersant and optimize the dispersion characteristics of MNPs.5 6 The polymer used as a dispersing agent must be selected in consideration of the cationic or anionic depending on the zeta-potential of MNPs.7 In the case of the secondary system of a nuclear power plant, a basic environment of pH 9 or higher, because the zeta-potential of MNPs is negative in this environment,8 an anionic polymer should be selected to increase the electrostatic repulsive force.9 10 Most anionic polymers contain an acidic group, for example, a typical anionic polymer contains a carboxyl

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doi:10.1166/jnn.2014.10174

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Optimization of Polymeric Dispersant Concentration for the Dispersion-Stability of MNPs in Water Solution

group (–COOH) or sulfonic group (-SO3 H). There is the possibility that functional groups contained in the polymer dispersant may affect the dispersion of MNPs. However, when considering the effect of dispersants on the corrosion of substrate, a polymeric dispersant that contains a carboxyl group, which is weakly acidic, must be selected. In this study, the three different anionic polymers containing a carboxyl group were selected for the purpose of improving the dispersion-stability of MNPs. The dispersion characteristics of MNPs with polymeric dispersants were evaluated by performing a settling test and measuring the transmittance, zeta-potential, and hydrodynamic particle size of the colloid solutions. In addition, the free immersion and electrochemical corrosion tests were conducted to evaluate the effect of polymeric dispersants on the corrosion of carbon steel.

2. EXPERIMENTAL DETAILS 2.1. Materials In this study, polymethacrylic acid (PMA) (Sigma aldrich, Mw : 5 kg/mol, 99.99%) and polyacrylic acid (PAA) (Sigma aldrich, Mw : 100 kg/mol, 99.99%), poly (acrylicacid-co-methacrylicacid) (PAAMA) (Mw : 3 kg/mol, 99.99%) are used as dispersants to improve the dispersion of MNPs. The typical structure of a polymeric dispersant for this studyisillustratedin Figure 1. Specimens of carbon steel tubes (SA 106 Gr.B) are used for corrosion tests. 2.2. Condition of Test Solution Test solutions for the dispersion characteristic analysis are shown in Table I. A 0.01 M NaOH was used for pH adjustment of the aqueous solution. The pH of the test solution that was reduced by the injection of the dispersant was maintained at approximately 9.5 through additional injection of pH adjuster. MNPs in an aqueous solution prepared in accordance with the test conditions were dispersed using

Poly(acrylic acid)

Poly(methacrylic acid, sodium salt)

Poly(acrylic acid-co-maleic acid)

Figure 1.

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The structure of anionic polymer.

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Table I. Condition for the dispersion characteristic measurement. Anionic polymer concentration (ppm) Magnetite (Fe3 O4 ) concentration (ppm) pH Temperature

0, 0.1, 1, 10, 100, 1000 100, 1000 9–9.5 25 C

ultrasonic waves first. All experimentals were performed in a given solution at pH 9.0–9.5 at room temperature. The corrosion tests performed only in the presence of PAA. The electrochemical corrosion test was conducted at 40 and 93 C, and the free immersion corrosion test was conducted at mean 40 , 65 , and 93 C. 2.3. Dispersion Characteristic Analysis 2.3.1. Settling Test The settling test was conducted to determine the effect of various polymer dispersants in the dispersion behavior of MNPs. This experiment was conducted as follows. First, each of prepared MNP test solutions was injected into a 20 ml vial. Second, the test solutions in a 20 ml vial were dispersed using ultrasonic waves. Finally, the dispersion behaviorwas evaluated by comparing the dispersion state, which varies depending on the time. 2.3.2. Measurement of Transmittance To quantify the dispersion behavior and measure the transmittance of the test solution, a Turbiscan (AGS, Fomulaction, FRA) apparatus utilizing the principle of multiple light scattering was used the dispersion analyzed is contained in a cylindrical glass cell. The light source is an electrical luminescent diode in the near infrared ( = 880 nm). Two synchronous optical sensors receive light transmitted through the sample, and backscattered by the sample.11 The dispersed MNP test solutions using ultrasonic waves were then used to measure the transmittance as a function of time (once per hour for 24 hours). The conditions of all experiments were measured twice to confirm the reproducibility. 2.3.3. Measurement of Zeta-Potential The zeta-potential is a characteristic of the solid substrate/ electrolyte solution system and can be used for determining the electrical repulsive force between the particles. The zeta-potential of a given particle of metal oxide or hydroxide depends on metal element, oxidation state, degree of oxide hydration and H+ /OH− concentrations.12 In this study, the zeta-potential was measured on the principle of electrophoresis by using a zeta/particle analyzer (zeta plusBIC, USA) apparatus. The zeta-potential was then calculated after measuring the electrophoretic velocity of MNPs.13 14 2.3.4. Measurement of Particle Size Measurement of MNP size was performed using the same apparatus as the zeta-potential measurement. It is J. Nanosci. Nanotechnol. 14, 9525–9533, 2014

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important to measure the particle size to determine the effect of polymer dispersant on the aggregation behavior of MNPs in an aqueous solution. The particle size of MNPs was measured as a function of time. Dependence of time on particle size has been reported previously.15 Measurement after 12 and 24 hours was done after shaking the test solution by hand to prevent the aggregate particle from breaking by the use of ultrasonic waves. Measurements were then taken three times to confirm the reproducibility under all test conditions.

Where : Icorr = A/cm2 K = combination of several conversion terms (12866 × 105 , for mpy) = equivalent weight (27.92 gram/equivalent) = metal density (7.86 gram/cc) A saturated calomel electrode (SCE) was used as a reference electrode and a high density graphite rod as a counter electrode. 2.4.2. General Corrosion Test A general corrosion test was performed in a free immersion test cell with reference to ASTM G31. The corrosion rate is calculated by the weight loss of the specimen before and after testing. The specimen was placed vertically in a test vessel and the test solution was added. In order to exclude the influence of dissolved oxygen, a high purity argon gas was purged for about 2 hours (2 L/min). The temperature of the test vessel was raised using a water bath. The free immersion test was performed for a total of 14 days. The test specimen after the free immersion for a certain period of time was treated and analysed with reference to ASTM G1. The corrosion rate then was calculated as follows: KW Corrosion rate = (2) ADT

2.4. Corrosion Test 2.4.1. Electrochemical Corrosion Test To evaluate the effect of a polymeric dispersant on the corrosion of carbon steel (SA 106 Gr. B: Cmax 0.3, Mn 0.29–1.06, Simin 0.1, Pmax 0.035, Smax 0.035, Cumax 0.4, Nimax 0.4, Crmax 0.4, Momax 0.15, Vmax 0.08), the electrochemical corrosion measurements were performed, with reference to ASTM G3. The test specimen (20 mm × 5 mm × 1 mm) was polished to at least 0.0025 mm (0.0001 in.) before testing. Test specimens were placed vertically in an electrochemical test cell, and the test solution was then added. The desired temperature was achieved using a heating mantle covering the test vessel. In order to exclude the influence of dissolved oxygen, a high purity argon gas was purged for about 2 hours before potentiodynamic polarization. The potentiodynamic polarization measurement (scan rate: 0.5 mV/s) was performed using a potentiostat (EG&G 273A, S/W: Powersuite). The corrosion current density was determined using a linear polarization method and the corrosion rate was calculated by the following equation: Corrosion rate =

Icorr K

Where : K = Constant K in Corrosion Rate Equation (345 × 106 for mpy) T = time of exposure in hours to the nearest 0.01 h, A = area in cm2 to the nearest 0.01 cm2 , W = mass loss in g D = density in g/cm3 , (see Appendix X1 of ASTM Practice)

(1)

(a)

(b)

(c) Figure 2.

Results of the settling test by anionic polymer concentration: (a) PAA, (b) PMA, and (c) PAAMA.

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3. RESULTS AND DISCUSSION 3.1. Dispersion-Stability 3.1.1. Settling Test The effect of polymeric dispersants on the dispersionstability of MNPs is shown in Figure 2. The left side photos of Figure 2 show the dispersion state of MNPs immediately after using ultrasonic waves treatment, and the right side ones illustrate the state of dispersion after 24 hours.

0 ppm-1 1 ppm-2 10 ppm-1 100 ppm-1 1000 ppm-1

(a) 100


T (%)

80 60 40 20 0 0

5

10

15

20

25

Time (h) 0 ppm-1 1 ppm-2 10 ppm-1 100 ppm-1 1000 ppm-1

(b) 100


T (%)

80 60 40 20 0 0

5

10

15

20

25

Time (h) 0 ppm-1 1 ppm-2 10 ppm-1 100 ppm-1 1000 ppm-1

(c) 100


T (%)

80 60 40 20 0 0

5

10

15

20

25

Time (h) Figure 3. Time-dependent transmission on the anionic polymer dispersant concentration: (a) PAA, (b) PMA, and (c) PAAMA.

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Figure 2(a) shows the effect of PAA concentration on the dispersive behavior of MNPs. The dispersion states of MNPs immediately after ultrasonication were very similar, but after 24 hours, it is clearly observed that the dispersed state of MNPs strongly depends on the concentration of PAA. The dispersion-stability of MNPs is improved in the solutions with PAA comparing to the solution without PAA. But the dispersion-stability of MNPs was not improved in proportion to the PAA concentration. The best dispersion-stability of MNP was formed in the test solution with an addition of 10 ppm PAA and followed by an addition of 100 ppm PAA. The dispersion-stability of MNPs was improved with the increase of PAA concentrations up to 10 ppm. When the PAA concentration was above 10 ppm, the dispersion-stability of MNPs decreased compared with 10 ppm PAA. Figure 2(b) shows the effect of PMA concentration on the dispersive behavior of MNPs. The results with an addition of PMA showed a similar tendency as the results of PAA addition. The best dispersion-stability of MNP was also observed in the solution containing 10 ppm PMA. When the PMA concentration was above 10 ppm, the dispersion-stability of MNPs decreased compared with 10 ppm PMA. The extent of the dispersion-stability attenuation of MNPs was lower than in the condition of PAA addition. Figure 2(c) shows the effect of PAAMA concentration on the dispersive behavior of MNPs, showing a similar tendency as the result of other polymeric dispersant; the best dispersion-stability of MNP in the solution containing 10 ppm PAAMA. When the PAAMA concentration was above 10 ppm, the dispersion-stability of MNPs decreased compared with an addition of 10 ppm PAAMA. The extent of the dispersion-stability attenuation of MNPs was larger than in the condition of PAA addition. 3.1.2. Transmittance Measurement The dispersion-stability of MNPs was compared quantitatively using the numerical results obtained by transmittance measurements. At the initial stage, no precipitation of MNPs occurs and the value of transmittance is close to 0%. But, the transmittance gradually increases as a function of time with the increase of the precipitaion in the solution. Figure 3 shows the effect of dispersant concentration on the transmission behavior of MNPs. The lowest transmission value was measured when 10 ppm of dispersant was added, suggesting that the transmittance measurement is in a good agreement with visual observation, as shown in Figure 2. The transmittance variation (after 24 hours) as a function of concentration for the three dispersants are represented in Figure 4. The lowest value of transmittanceis in the concentration of 10 ppm for all three dispersants. It is well known that a polymeric dispersant has a significant impact on the dispersion-stability J. Nanosci. Nanotechnol. 14, 9525–9533, 2014

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100

PAA PMA PAAMA

90 80

T (%)

70 60 50 40

The decrease in zeta-potential with the increase of dispersant concentrations indicates an increase in repulsive force between MNPs. However, the dispersion-stability of MNPs was reduced in a concentration ratio of 0.01 or more in spite of the increase of the value of the zeta-potential in negative direction. It is considerd that the reduction of the dispersion-stability above the ratio (dispersant/MNPs) of 0.01 may be controlled by another interaction of the

30 20

0

1

10

100

1000

Dispersant concentration (ppm) Figure 4. Transmission behavior as a function of concentration of various polymer dispersants after 24 hours.

of nanoparticles in an aqueous solution. While the dispersant addition tends to improve the dispersion-stability of MNPs, the dispersion statbiliy of MNPs does not increase linerly with an increase in the polymeric dispersant concentration. It is considered that the most effective condition for the dispersion-stability improvement is at the dispersant concentration ratio (dispersant/magnetite) of around 0.01 (considering that the dispersant concentration is 10 ppm, and the concentration of MNPs is 1000 ppm). 3.1.3. Zeta-Potential Measurement Figure 5 shows the variation of zeta-potential as a function of polymeric dispersant concentration. The zeta-potential of MNPs showed about −35 mV in basic aqueous conditions (pH 9 ∼ 9.5), and decreased in proportion to the polymeric dispersant concentration. This trend indicates that the adsorption of polymeric dispersant increases on the surface of the MNPs with the increase of dispersant concentration.

650 600 550 500

0 ppm 0.1 ppm 1 ppm 10 ppm 100 ppm

450 400 350 300 250 200 0

12

24

Time (h) (b) 700 Hydrodynamic diameter (nm)

0

Hydrodynamic diameter (nm)

(a) 700

10

650 600 550 500


450 400 350 300 250 200 0

12

24

Time (h)

PAA PMA PAAMA

Zeta Potential (mv)

–20 –30 –40 –50 –60 –70 –80

Hydrodynamic diameter (nm)

(c) 700 –10

650 600 550 500


450 400 350 300 250 200 0

–90 0

0.1

1

10

100

12

24

Time (h)

Dispersant Concentration (ppm) Figure 5. Zeta-potential of MNPs as a fuction of concenratio of various polymer dispersants at 25 C.


Figure 6. Time-dependent particle size as function of time on the concentration of various polymer dispersants: (a) PAA, (b) PMA, and (c) PAAMA.

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dispersant adsorbed on the surface of MNPs. More studies and analysis are needed for a better understanding of this discrepancy. 3.1.4. Time-Dependent Particle Size Measurement The effect of polymer dispersants as a function of time on the variation of MNPs particle size is shown in Figure 6 (in this case MNPs concentration is 100 ppm). In the case of PAA addition (Fig. 6(a)), the change in particle size is smaller in the solution of dispersant concentration of 1 ppm (the ratio of dispersant/MNPs is 0.01) compared with the other solution of dispersant concentrations. This may reflect the highest dispersion stability in the solution of the ratio of dispersant/MNPs is 0.01. An addition of PAAMA also showed a similar trend to PAA addition (Fig. 6(c)). As for the PMA addition (Fig. 6(b)), the particle size increased sigificantly for the solution of 1 ppm. The different behavior with an addition of 1 ppm PMA is not clearly understood and more analysis are needed. 3.1.5. The Critical Concentration for Maximizing the Mnps Dispersion-Stability Based on the experimental results (Figs. 2∼4), the most effective condition for the dispersion-stability improvement is obtained when the dispersant concentration ratio (dispersant/MNPs) is around 0.01 (dispersant concentration: 10 ppm). Considering the fact that the zeta-potential decrease at a concentration ratio of 0.01 or more, there may be another interaction to offset the force of repulsion by zeta-potential between the particles. The polymer absorbed on the particles can flocculate by the bridging mechanism. This bridging mechanism occurs

Figure 7.

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by the interaction of polymer chains adsorbed onto different particles as shown in Figure 7.16 The flocculation occurs when the polymer chains are very long and the surface coverage by adsorbed polymer is so high that the adsorption sites are scarce, and the probability for the polymer extension between the particles is low.17 18 The MNPs dispersion stability is determined by the two influencing factors of zeta-potential of MNPs and flocculation mechanism. Zeta-potential is influenced by solution properites and the flocculation is affected by the specific dispersant’s charateristics. Therefore, it is required to established the critical concentration for maximinzing the MNPs dispersion stability for the effective application of polymeric dispersants considering the solution and specific dispersant properties. 3.2. Corrosion Test 3.2.1. Electrochemical Corrosion Test The results of electrochemical corrosion measurements to evaluate the effects of the polymer dispersant on the corrosion of carbon steel are shown in Figure 8 and summarized in Table II. At 40 C, the corrosion current density slightly increased with the increase of polymeric dispersant concentrations. At 93 C, as the concentration of PAA increases, the corrosion current density significantly increases. The corrosion rate was calculated using Eq. (1) and is shown in Figure 9. In addition, when 100 ppm of PAA was added, the corrosion rate increased, compared to the conditions of 1 and 10 ppm of PAA. It is obvious that an addition of 100 ppm PAA significantly inreased the corrosion rate of carbon steel at both temperatures, much higher rate at 93 C.

Two different types of polymer adsorption on a particle.16


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(a)

(b)

1.0

10 ppm PAA

1.0

10 ppm PAA

0.0

Without PAA 100 ppm PAA

Potential(V vs SCE)

Potential (V vs SCE)

1 ppm PAA

0.5

0.5 1 ppm PAA

0.0

–0.5

–0.5

Without PAA 100 ppm PAA

–1.0

–1.0 1E-7

1E-6

1E-5

1E-4

1E-3

1E-8

1E-7

A/cm2 Figure 8.

1E-6

1E-5

1E-4

1E-3

A/cm2

Potentiodynamic polarization behavior of carbon steel as a function of concetration of PAA: (a) 40 C and (b) 93 C.

3.2.2. General Corrosion Test General corrosion tests were carried out to evaluate the effects of the polymer dispersant to the corrosion of carbon steel. The calculated corrosion rate by weight loss is shown in Figure 10. Corrosion rate increases as the dispersant concentration increases in the test environment. While there is no significant increase of corrosion rate up to 10 ppm PAA, it is interesting to note that the addition of 100 ppm PAA increases significantly the corrosion. Table II. Corrosion current density by linear polarization method for SA 106 Gr.B.

Material SA106 Gr.B

Temperature ( C)

PAA concentration (ppm)

Icorr (A/cm2 )

40

100 10 1 0 100 10 1 0

1516 0651 0635 0530 6605 1118 0820 1045

93

In the solution of 100 ppm PAA, the growth behavior of oxide layer was influenced greatly. The high concentration of dispersant deteriorates the formation of protective oxide on carbon steel as shown in Figure 11. In the solution containing PAA 1 ppm, 10 ppm and without PAA at 93 C, a dense oxide layer of about 0.3 m was formed uniformly on the surface of the test specimen, while with an addition of PAA 100 ppm at 93 C, a coarse oxide layer (thickness: 5 m) having cavities and pores was formed on the surface of the specimenIt is considered that the dispersants significantly influences the growth mechanism of the oxide layer on the carbon steels. It is determined that was interfered with the formation of a uniform oxide layer by the dispersant surrounding nucleus of the oxide layer. Therefore, it can be seen that the corrosion rate has increased by the non-uniform formation of a protective oxide layer. The injection of high concentration dispersant should be applied after a careful consideration of the impact on the corrosion integrity of the plants.

6

Corrosion rate (mpy)

4.5 4.0

0 ppm 1 ppm 10 ppm 100 ppm

5

Corrosion rate (mpy)

5.0

3.5 3.0 2.5 2.0

0 ppm PAA 1 ppm PAA 10 ppm PAA 100 ppm PAA

4 3 2

1.5 1

1.0 0.5

0 40

0.0 40

93

65

93

Temperature (ºC)

Temperature (ºC) Figure 9. Corrosion rate of carbon steel specimen (the corrosion current density was estimated from Fig. 8).


Figure 10. Effect of dispersant (PAA) concentration on the corrosion rate of carbon steel at different temperatures (calculated from the weight change).

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(b)

(c)

(d)

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Figure 11. Effect of dispersant (PAA) concentration on the surface oxide formation of carbon steel after testing at 93 C: (a) without PAA, (b) 1 ppm, (c) 10 ppm, and (d) 100 ppm.

4. CONCLUSION The effect of the polymeric dispersants on the dispersionstability of MNPs in a water solution was evaluated by conducting the settling behavior of MNPs and measuring the transmittance, zeta-potential and particle size. Corrosion tests were also carried out to confirm the influence of dispersant and its concentration on the corrosion behavior of carbon steel. It was observed that the dispersion-stability of MNPs was not improved linearly in proportion to the concentration of dispersants. This suggests that a critical concentration may exist for maximizing the dispersion-stability. From this study, it is considered that a critical concentration of dispersant for the improvement of dispersionstability of MNPs is in the range of concentration ratio (dispersant/MNPs) of 0.1 to 0.01. The zeta-potential of MNPs was measured to decrease with an increase of polymeric dispersant concentrations, but the results of the particle size measurement showed that the MNPs were aggregated above a concentration ratio around 0.01. This discrepancy indicates that the interaction between the adsorbed polymer on other particles counteracts the electrical repulsion by the zeta-potential. 9532

At 40 C and 65 C, there is no significant effect of PAA concentration on the corrosion rate of carbon steel, while with an addition of 100 ppm PAA at 93 C, the corrosion rate increased significantly. It is considered that, when the dispersant is saturated in a given test solution,the dispersant may act as a hazardous material for deteriorating the formation of a stable protective oxide layer on carbon steel. However, it is recommended that, for the reduction of fouling without a deleterious impact on components, the optimum conditions of dispersants should be developed for the effective application of polymeric dispersants at plants.

References and Notes 1. K. Fruzzetti, Nuclear Plant J. 42 (2009). 2. J. K. Lee, J. S. Moon, S. K. Yoon, and W. Y. Maeng, Trans. of the Korean Society of Hydrogen Energy. 22, 546 (2011). 3. K. Holmberg, Surfactants and Polymers in Aqueous Solution, John Wiley & Sons, Inc., New York, USA (2002). 4. R. J. A. Tippett, R. Crovetto and C. J. McDonough, Dispersant Application for Mitigation of Steam Generator Fouling, NACE International, San Antonio, Texas, USA (2010). 5. S. J. Jung, S. I. Lee, and H. M. Lim, J. Kor. Ceram. Soc. 40, 293 (2003). 6. E. Tombacz, I. Y. Tóoth, D. Nesztor, E. Illées, A. Hajdúu, M. Szekeres, and L. Véekáas, Col. Surf. A. 435, 91 (2013).


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7. E. Illées and E. Tombáacz, J. Colloid Interface Sci. 295, 115 (2006). 8. A. Hajdúu, E. Illées, E. Tombáacz, and I. Borbáath, Col. Surf. A. 347, 104 (2009). 9. A. Hajdúu, M. Szekeres, I. Y. Tóoth, R. A. Bauer, J. Miháaly, I. Zupkóo, and E. Tombáacz, Col. Surf. B. 94, 242 (2012). 10. P. C. Heimenz, Principle of Colloid and Surface Chemistry, Marcel Dekker, Inc., New York and Basel (1986). 11. M. Wisniewska, K. Terpilowski, S. Chibowski, T. Urban, V. I. Zarko, and V. M. Gun’ko, Powder Technology 233, 190 (2013). 12. R. J. Hunter, Zeta Potential in Colloid Science, Academic Press, Academic Press, New York (1981).

13. Sze, D. Erickson, L. Ren, and D. Li, J. Colloid Interface Sci. 261, 402 (2003). 14. P. Leroy, C. Tournassat, and M. Bizi, J. Colloid Interface Sci. 356, 442 (2011). 15. N. A. Clark, J. H. Lunacek, and G. B. Benedek, Am. J. Phys. 38, 575 (1970). 16. B. J. Lee, M. A. Schlautman, E. Toorman, and M. Fettweis, Water Research 46, 5696 (2012). 17. G. J. McFann, K. P. Johnston, and S. M. Howdle, Aiche J. 40, 543 (1994). 18. M. J. Rosen, Surfactants and Interfacial Phenomena, John Wiley & Sons, Inc., New York, USA (1978).

Received: 8 January 2014. Accepted: 7 March 2014.


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