Inhibition of Homogeneous Formation of Magnesium Hydroxide by

Feb 3, 2015 - The homogeneous crystallization of magnesium hydroxide (Mg(OH)2) was carried out at 97 °C in the absence and presence of low molar mass...
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Inhibition of Homogeneous Formation of Magnesium Hydroxide by Low-Molar-Mass Poly(acrylic acid) with Different End-Groups Ali A. Al-Hamzah,†,‡ Erica J. Smith,† and Christopher M. Fellows*,† †

School of Science and Technology, The University of New England, Armidale, NSW 2351, Australia Desalination Technologies Research Institute (DTRI), P.O. Box 8328, Al-Jubail 31951, Kingdom of Saudi Arabia

‡

ABSTRACT: The homogeneous crystallization of magnesium hydroxide (Mg(OH)2) was carried out at 97 °C in the absence and presence of low molar mass (Mn ≤ 2000) poly(acrylic acid) (PAA) terminated with different end groups. A significant decrease in Mg(OH)2 crystal growth was found in the presence of PAA, with relatively hydrophobic end-groups being most effective. The end-groups that were most effective were decyl isobutyrate which are more hydrophobic than the hexyl isobutyrate end-groups previously shown to be maximally effective in inhibiting calcium carbonate and calcium oxalate scaling. Poly(maleic acid)13−15 and poly(maleic acid-co-acrylic acid)16 have shown some effectiveness in inhibition of precipitation of Mg(OH)2, though again they have been reported to be less effective than against CaCO3 scale. In this work the effectiveness of poly(acrylic acid) (PAA) of low molar mass (Mn ≤ 2000) in retarding the homogeneous crystallization of Mg(OH)2 was determined using conductivity measurements in calcium-free solutions containing nonequivalent concentrations of Mg2+ and OH¯ ions ([Mg2+]/[ OH¯] > 15) at elevated temperature (T = 97 °C). The effect of different endgroups, previously investigated in scale inhibition in the CaCO3,17,18 CaSO4,18 and CaC2O419,20 systems, on the effectiveness of PAAs in Mg(OH)2 scale inhibition was also investigated.

1. INTRODUCTION In thermal desalination processes such as multistage flash (MSF) desalination, magnesium hydroxide is a major component of the alkaline (or “soft”) scale formed at lower temperatures than the “hard” calcium sulfate scale. While Mg(OH)2 formation depends on the concentration of Mg2+ and the pH of the process stream, deposits of brucite (Mg(OH)2) usually appear in MSF desalination at temperatures above 80 °C and predominate in alkaline scale above 100 °C.1−4 Mg 2 + + 2OH− ⇌ Mg(OH)2 ΔGf⊖ = −80.82 kJmol−1 at 100 °C

(ΔG value obtained from refs 5 and 6). 2+

− 2

K sp = [Mg ] × [OH ]

−12

K sp = 4.8 × 10

2. SYNTHESIS AND CHARACTERIZATION OF POLY(ACRYLIC ACID) A number of PAAs with different end-groups and molar masses were synthesized by atom transfer radical polymerization (ATRP) of t-butyl acrylate followed by hydrolysis of the poly(t-butyl acrylate) produced with trifluoroacetic acid as previously described.19 PAAs were characterized by 1H and 13C NMR spectroscopy (Bruker-300) and gel permeation chromatography (GPC, Waters 1525 HPLC, Waters autosampler 712 WISP, and Waters 2414 RI detector). The following low-molar-mass PAAs were used (Figure 1); details of their synthesis and characterization have previously been reported:19 a. carboxymethyl-1,1-dimethyl-PAA (CMM-PAA, Mn = 2106, Đ = 1.3) b. ethyl isobutyrate-PAA, (EIB-PAA Mn = 1669, Đ = 1.3) c. hexyl isobutyrate-PAA (HIB-PAA, Mn = 1403) d. cyclohexyl isobutyrate-PAA (CIB-PAA, Mn = 1689, Đ = 1.4) e. decyl isobutyrate-PAA (DIB-PAA, Mn = 2422)

at 100 °C (1)

Several methods have been used to determine the Ksp value of Mg(OH) 2 such as hydrogen electrode measurements,7 conductivity titration,8 and glass electrode titration,9 with Ksp values between 2 × 10−9 and 1.2 × 10−11 reported at room temperature. Gjaldbaek7 suggested that Mg(OH)2 may be present in two different crystalline forms, an unstable amorphous form of relatively high solubility (Ksp is (0.4−1.4) × 10−9) which forms initially and then undergoes recrystallization to form the low solubility (Ksp is (1.6−4.2) × 10−11) polymorph.7,10 Although this phenomenon is clearly readily amenable to experimental investigation, we have been unable to find any later references to it. The effect of two phosphonate additives (aminotris(methylenephosphonic acid) and N,N,N′,N′-ethylenediaminetetramethylenephosphonic acid) on the growth of seed crystals of Mg(OH)2 was studied by Liu and Nancollas.11 While a significant reduction in crystal growth of Mg(OH)2 was observed, the effect of phosphonate scale inhibitors was much less pronounced than in the case of the other common scaleforming minerals CaCO3 and CaSO4 under the same conditions. Similar results of the relative ineffectiveness of phosphonate inhibitors were reported by Linnikov et al.12 © XXXX American Chemical Society

Received: December 15, 2014 Revised: February 3, 2015 Accepted: February 3, 2015

A

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Figure 2. Experimental apparatus for conductivity measurements.

of low molecular mass of PAA with different end groups. At the experimental conditions employed, the supersaturation level (SL) of Mg(OH)2 was calculated to be 44.9 (SL = (Qip/Ksp)). The inhibition efficiency of PAA was determined by applying ⎡ a(PAA) ⎤ ⎥ × 100 % IE = ⎢1 − ⎢⎣ a(blank) ⎥⎦

(2)

where a(PAA) and a(blank) are determined by the logarithmic fitting equation (N = a × ln(t) + b) for the normalized conductivity curve in the presence and absence (blank) of PAA, respectively, as shown in Figure 3. Each set of experimental conditions was repeated at least three times

Figure 1. Poly(acrylic acid) end-groups investigated.

f. hexadecyl isobutyrate-PAA (HDIB-PAA, Mn = 1687)

3. EXPERIMENTAL DETERMINATION OF CONDUCTIVITY AT 97 °C Stock solutions of 0.823 M (20000 ppm) Mg2+ as MgCl2·6H2O and 0.20 M OH¯ as NaOH were prepared daily. These solutions and the R/O water used were filtered and degassed using a 0.45 μm Millipore solvent filter. The boiling point of dilute aqueous solutions at ambient pressure at the elevation at which the experiment was carried out is 97 °C. Filtered deionized water (346.4 mL) was placed in a magnetically stirred 500 mL three-neck vertical round-bottom flask containing two platinum conductivity probes (3 mm × 3 mm) under a water-cooled glass condenser open to the air, and 1.4 mL of MgCl2 solution was then added to give a final [Mg2+] concentration of 3.292 mM (80 ppm). When the solution began to boil, 1.75 mL of aqueous PAA solution and 0.45 mL of OH¯ as NaOH were then added to give a final [PAA] = 5 ppm and [OH¯] = 0.2571 mM, respectively, and data recording was begun. The initial pH of the PAA solutions before the addition of NaOH was 2.8−3.0 indicating that the PAA was fully protonated. The experimental apparatus is shown in Figure 2. Conductivity was measured using a Beta 81 conductivity meter (CHK Engineering). Analogue outputs from the conductivity meter were digitally converted using a Picolog Analog/Digital Converter 16 (16 Bit) and Picolog recording software, and data was acquired every 300 s.

Figure 3. Reduction in conductivity (normalized to a value of 1 at time = 0) for homogeneous formation of Mg(OH)2 in the absence of PAA at 97 °C.

4.1. In the Absence of PAA (Blank). The conductivity curve of homogeneous formation of Mg(OH)2 in the absence of PAA showed an increase in conductivity for the second sampling compared to the first due to the addition of OH¯ solution. As the experiment continued conductivity decreased as shown in Figure 3, indicating the removal of ions from solution through the formation of Mg(OH)2. The conductivity measurements of Mg(OH)2 formation in the absence of PAA were analyzed over the period 5−50 min. The decline of normalized conductivity (N) could be fit to a logarithmic curve (N = a × ln(t) + b) with a good correlation coefficient (R2 = 0.98). However, the system did not reach a steady state even when the experiment continued more than 3 h (Figure 3), indicating the slow rate of Mg(OH)2 formation under these conditions. Although the formation of Mg(OH)2 under the experimental conditions used is thermodynamically

4. RESULTS AND DISCUSSION Conductivity of the solutions containing [Mg2+] = 3.292 mM (80 ppm) and [OH¯] = 0.2571 mM in the absence and presence of [PAA] = 5 ppm (T = 97 °C) was measured as a function of time to determine the inhibition efficiency (% IE) B

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Figure 4. Dehydration of Mg2+ and formation of Mg(OH)2.

favorable (ΔG = −11.8 kJ mol−1),5 the disruption of the aquated Mg2+ complex is enthalpically unfavorable and the transition state where these bonds are broken is likely to correspond to a high activation energy (Figure 4).3 The activation energy may be estimated at approximately 50 kJ mol−1 on the basis of literature data on the kinetics of Mg(OH)2 dissolution.21 4.2. In the Presence of PAA. All experiments in the presence of low molar mass PAAs with different end groups showed a significant decrease in the conductivity between the initial and second conductivity measurements (Figure 5). In

groups in PAA¯. As the experiment continued the conductivity decreased logarithmically for all PAA. The theoretical residual concentrations of [OH¯] and [Mg2+] ions in the presence of 5 ppm of PAA were calculated on the basis of the number of carboxylic acid units present, with the assumption that the quantitative reaction of OH¯ with PAA and of PAA n− with Mg 2+ occurs. The values of residual concentration of [OH¯] and [Mg2+], the change in normalized conductivity over the first 5 min (ΔNExp), and supersaturation level (SL, = QIP/KIP) are summarized in Table 1. The ratio of complexation taking place between carboxylate groups in PAA¯ with Mg2+ can be determined by applying %RC =

(ΔKExp)ave (ΔKEtheor)ave

× 100

(3)

where (ΔKEtheor)ave is the average theoretical reduction in conductivity when the complexation is 100%, equal to 0.0380, and (ΔKExp)ave is the average experimental reduction in conductivity for the first sampling after OH¯ ions were added to Mg2+ solution disregarding the contribution of the conductivity of OH¯ ions which was equal to 0.0116. The results suggest that approximately 70% of carboxylate groups in PAA¯ were not complexed by Mg2+. Note that only 0.9 ppm from 80 ppm of Mg2+ were complexed with carboxylate groups in PAA¯ at 5 ppm. It should be noted that the complexation of PAA may significantly alter its adsorption behavior, but at 30% complexation the PAA chains will still bear a strong negative charge. The % IE of low molar mass PAA (Mn ≤ 2000) was calculated using eq 1 with results given in Table 2 and Figure 6. All PAAs gave some control of scale deposition of Mg(OH)2 with significant differences depending on the nature of the endgroup. In all cases it was observed that the incorporation of a hydrophobic end-group gave better inhibition efficiency with the lowest % IE found for the hydrophilic CMM end group. This result parallels results previously found for CaCO3 and CaC2O4 scaling under similar conditions.17−20 Again paralleling these previous results, the most effective result is found not for the shortest hydrophobic end-group (EIB, % IE 58) nor the longest hydrophobic end-group (HDIB,

Figure 5. Normalized conductivity measurements for solutions initially containing 3.292 mM [Mg2+], 0.2571 mM [OH¯], and 5 ppm of PAA with different end groups (Mn ≤ 2000). The solid lines represent the data fit to N = a × ln(t) + b.

addition to formation of Mg(OH)2, the decreasing conductivity may be attributed to two possible reactions: the neutralization reaction between carboxylic acid groups in PAA with OH¯ ions and the complexation reaction between Mg2+ and carboxylate

Table 1. Residual Concentrations of [OH¯] and [Mg2+], ΔNExp and Supersaturation Level (SL) in the Presence of 5 ppm of PAA with Different End Groups, Assuming Quantitative and 30% Complexation of Carboxylate Groups in PAA¯

end groups of PAA

Mn

blank CMM EIB CIB HIB DIB HDIB

2106 1669 1689 1403 2422 1687

ΔNExp

[Mg2+] × 10−3

[Mg2+] × 10−3

[OH¯] × 10−4

SL

N0 min − N5 min

M (100%)

M (30%)

M

30%

± ± ± ± ± ±

3.292 3.154 3.160 3.168 3.171 3.168 3.179

3.292 3.251 3.252 3.255 3.256 3.255 3.258

2.571 1.882 1.912 1.949 1.965 1.952 2.008

45 24 25 25 26 26 27

0.0139 0.0097 0.0161 0.0104 0.0079 0.0087

0.0013 0.0033 0.0037 0.0020 0.0020 0.0027 C

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Industrial & Engineering Chemistry Research Table 2. Effect of PAA with Different End Groups on Mg(OH)2 Formation at 97 °C, where a Is Determined by the Logarithmic Fitting Equation N = a × ln(t) + b end groups of PAA blank CMM EIB CIB HIB DIB HDIB

Mn

−a

b

R2

2106 1669 1689 1403 2422 1687

0.0110 ± 0.0010 0.0076 ± 0.0030 0.00464 ± 0.00067 0.0073 ± 0.0030 0.0046 ± 0.0011 0.00287 ± 0.00032 0.0057 ± 0.0027

1.03131 0.99860 0.99803 0.99692 0.99746 0.99723 1.00083

0.978 0.998 0.994 0.983 0.982 0.977 0.985

% IE 0 31 58 33 58 74 48

± ± ± ± ± ±

12 8 14 14 8 23

Figure 7. Model of a Mg(OH)2 crystal where the lighter shading indicates a lower (more negative) interaction energy of Mg(OH)2 surfaces with polyethylene as calculated from molecular dynamics simulations23 (a) in the absence of an edge-active scale inhibitor; (b) postulated behavior in the presence of an edge-active scale inhibitor.

adsorption of PAA is essentially irreversible and is unaffected by subsequent loss of the end-group. Preferential behavior in adsorption of monatomic ions and small polymers at different surfaces of Mg(OH)2 has been demonstrated computationally.22,23 Previous atomistic dynamics simulations of Ca2+ and Cl− on Mg(OH)2 planes have given negative adsorption energies indicating that adsorption is energetically favorable for both ions.22 However, the adsorption energies were not equivalent for each plane studied; it was found to be energetically more favorable for Ca2+ ions to be adsorbed on the (001) plane and the Cl− to be adsorbed on the (101) plane. The adsorption order for the Ca2+ and Cl− were (001) > (100) > (101) > (110) and (101) > (100) > (001) > (110), respectively. Zhang et al. recently carried out molecular dynamics simulations to calculate interaction energies between polyethylene molecules and Mg(OH)2 surfaces, as well as the internal binding energy of the total system and the nonbonding van der Waals and electrostatic interactions.23 The internal binding energy was found to be much smaller than the nonbonding energies; and the electrostatic force played a more significant role than the van der Waals interaction indicating that there is formation of ionic bonds between the polyethylene and the Mg(OH)2 surfaces. However, Zhang et al. also found that the polyethylene interacted preferentially with different surfaces, interacting most strongly with the (001) surface and most weakly with the (110) surface.23 Figure 7 shows the relative interaction energies of polyethylene with the four surfaces studied. The darker shading indicates higher interaction energy hence a weaker binding of the polyethylene molecules. Detailed electronic structures of the surfaces indicated that the (001) surface possesses an external OH group and has low polarity, whereas the (110) surface has the Mg atom and OH group on the same level. It was also reported that the interaction energy of the polyethylene became more negative as the chain length of the polymer increased indicating that the binding force increases with polymer length.23 4.3. The Estimation of Order and Crystal Growth Rate for Mg(OH)2 Formation. Liu and Nancollas have proposed a model for Mg(OH)2 crystallization growth rates as a function of supersaturation level (eq 2).11 The supersaturation level is a very important factor in determining the rates of nucleation and crystal growth.24 The

Figure 6. % IE of Mg(OH)2 formation by PAA with different end groups (Mn ≤ 2000), (● = CIB).

% IE 48), but for an end-group of intermediate hydrophobicity (DIB, % IE 74). In the CaCO3 and CaC2O4 systems, where % IE are significantly greater for these PAA antiscalants under similar conditions, HIB was found to be the most effective suggesting that the hydrophobicity for maximum effectiveness shifts to greater values as overall effectiveness of the scale inhibitor declines. While the PAA may affect both nucleation and crystal growth, the increasing divergence in results over time observed in Figure 5 suggests that PAA has a greater effect on growth than on nucleation. Hydrophobic end groups may discourage desorption of the PAA chains from the nuclei of Mg(OH)2 as fast as PAA with hydrophilic end groups, delaying the growth of the Mg(OH)2 nuclei, but the differences in overall hydrophobicity of the chains are minimal so it is hard to see this having a significant effect. An alternative hypothesis we have suggested is that hydrophobic end-groups may direct the adsorption of PAA preferentially to the edges of faces in the growing crystallites where a more highly charged face meets a less highly charged face, thus retarding growth at a lower antiscalant concentration than one which adsorbs less selectively (Figure 7(b)). Such behavior would only be expected for well-defined crystallites, and not for the amorphous precursor phase formed on initial nucleation. It should be noted that at pH ∼10 and 100 °C, hydrolysis of the terminal ester group may be significant over the time scale of the experiments.19 However, no discernible convergence of the rates of change of the conductivity curves can be seen in Figure 5. This may mean the hydrolysis is not occurring to a significant extent, that a reduced concentration of inhibitor shows similar effectiveness in inhibition, and/or that initial D

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Industrial & Engineering Chemistry Research model proposed by Liu and Nancollas11 for Mg(OH) 2 crystallization (eq 4) was used to estimate the order and rate of crystal growth for Mg(OH)2 formation by analysis of the conductivity data obtained in this study. −d[Mg 2 +] = dt n ⎧ ⎛ K sp ⎞1/3⎫ ⎪ ⎪ − 2 1/3 2+ ⎟⎟ ⎬ kcS ⎨([Mg ] × [OH ] ) − ⎜⎜ 2 f1 × f2 ⎠ ⎪ ⎪ ⎝ ⎩ ⎭

(4)

In this model kc is the rate coefficient for crystal growth, S is a function of the number of effective nucleation sites, f1 and f 2 are the activity coefficients for OH− and Mg2+, respectively, and n is the order of crystal growth with respect to supersaturation of Mg(OH)2.11 The estimation of n was done by approximating f1 = f 2 = 1 and plotting log (−d[Mg2+]/dt) versus log (([Mg2+] × [OH¯]2)1/3 − (Ksp)1/3) (Figure 8). Note that n was found to

Figure 9. Plot of log {([Mg2+]i − [Mg2+]o)/([Mg2+]t − [Mg2+]o)} versus time (t) for the crystal growth of Mg(OH)2 in the absence of PAA.

Table 3. Conductance of Mg2+, Na+, OH¯, and Cl¯ at 25 and 97.2 °C26,27 ions 2+

Mg OH¯ Na+ Cl¯

(S·m2) × 10−4 (25 °C)

(S·m2) × 10−4 (100 °C)

106 198 50 76

266 468 125 191

The rate of crystal growth for homogeneous formation of Mg(OH)2 significantly decreased in the presence of PAA, with different values seen for different PAA (Figure 10). Figure 8. Plot of log −d[Mg2+]/dt versus log(([Mg2+] × [OH¯]2)1/3 − (Ksp)1/3) to determine n for the crystal growth of Mg(OH)2 in the absence of PAA.

be less than 1 under all conditions, in contrast to the results of Liu and Nancollas11 where under “slow” growth conditions n ≈ 1. This suggests that the surfaces of the forming crystallites were strongly positively charged and could repel incoming Mg2+ ions sufficiently to retard growth.25 The rate of crystal growth for Mg(OH)2 was determined from plots of log {([Mg2+]i − [Mg2+]o)/([Mg2+]t − [Mg2+]o)} versus time (t) where, [Mg2+]i, [Mg2+]t and [Mg2+]o are the initial concentration, the concentration at t, and the concentration at equilibrium of Mg2+, respectively (Figure 9). The concentration [Mg2+]i was set as equal to the residual concentration of Mg2+ ions in solution after all OH¯ ions reacted with Mg2+ to form Mg(OH)2 at equilibrium (the equilibrium constant value of Mg(OH)2 formation at 97 °C was estimated as Keq = 2.06 × 1011).6 The concentration of Mg2+ at time (t) was calculated from conductivity data over the course of the experiment using ionic conductance values of Mg2+, OH¯, Cl¯, and Na+ at 97 °C (shown in Table 3)26 which were estimated from their ionic conductance values at 25 °C using eq 5 λi0, T = λi0,25 ° C[1 + α(T − 25 °C)]

Figure 10. Plot of log {([Mg2+]i − [Mg2+]o)/([Mg2+]t − [Mg2+]o)} versus time (t) for the crystal growth of Mg(OH)2 in the presence of PAA with different end groups.

The results of the order and crystal growth for homogeneous formation of Mg(OH)2 in solution containing nonequivalent concentrations of Mg2+ and OH¯ ions in the absence and presence of PAAs are summarized in Table 4. The order of Mg(OH)2 formation with respect to supersaturation in the absence and presence of PAAs was found to be 0.72 and 0.66, respectively. The small difference between the values may be due to the reduction in concentration of Mg2+ and OH¯ ions in

(5)

where α is a temperature coefficient with a value for all ions ≈ 0.02 deg−1 except H3O+ (≈ 0.0139 °C−1) and OH− (≈ 0.018 °C−1).27 E

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with a trend to lower n with increasing Mg2+:OH− ratio that has previously been observed. The conductivity data in the presence of PAAs with different end groups suggest that in the initial stage after the addition of PAA two consecutive reactions occurred. The first reaction was the neutralization of carboxylic acid groups in PAA by OH¯ ions. The second reaction was the complexation of carboxylate groups in PAA¯ with Mg2+, which we estimate to have proceeded to approximately 30% complexation for all PAA. The results show that the hydrophobicity of the end group of the low molar mass PAA inhibitor can affect the rate of Mg(OH)2 deposition in a similar manner as we have previously observed for CaCO3 and CaC2O4 deposition.17,19 Low molar mass PAA with a long hydrophobic (decyl isobutyrate) end group gave the highest inhibition efficiency, while low molar mass PAA with a hydrophilic end group (carboxymethyl-1,1dimethyl) gave the lowest inhibition efficiency. The order and rate of crystal growth with respect to the supersaturation of Mg(OH)2 crystallization were estimated based on the expression of Liu and Nancollas11 for Mg(OH)2 formation at low temperature. The results showed a significant decrease in crystal growth of Mg(OH)2 in the presence of PAA with different end groups. Some of the decrease in crystal growth may be due to the increasing ratio of [Mg2+]/[OH¯] in the presence of PAA, as the rate of crystal growth has been reported to decrease in the presence of excess magnesium ions, but this is insufficient to explain the differences observed between PAAs. The more likely explanation is the adsorption of PAA onto the active surface of Mg(OH)2 crystallites which appear clearly in the different values of the rates of crystal growth in the presence of PAA with different end groups. These end-groups can influence the adsorption/desorption behavior of PAA and may direct selective adsorption to the edge of the (100) face of growing crystallites where they can effectively retard crystal growth at low concentrations.

Table 4. Order (n) and Rate of Crystal Growth for Mg(OH)2 Crystallization end groups of PAA blank CMM EIB CIB HIB DIB HDIB

n 0.72 0.65 0.65 0.65 0.66 0.66 0.66

rate of crystal growth (min−1) 1.491 1.015 0.613 1.012 0.601 0.378 0.773

× × × × × × ×

−3

10 10−3 10−3 10−3 10−3 10−3 10−3

% retardation

[Mg2+]/[OH¯]

0 32 59 32 60 75 48

12.8 17.3 17.0 16.7 16.6 16.7 16.2

the presence of PAA as a result to neutralization and complexation reactions. These results agree with the results obtained by Dabir et al.24 who observed “the kinetics of Mg(OH)2 are a sensitive function of pH”, whereas the order of Mg(OH)2 formation decreased when the concentration of OH¯ ions decreased. The order of Mg(OH)2 formation in the presence of excess magnesium ions (20%) has been reported to be 1.0 ± 0.3 at room temperature;24 under the conditions used in this work, the excess of Mg2+ over OH¯ ions was considerably greater (Table 4). The decrease in Mg(OH)2 formation may be due to two effects. The first is the increasing ratio of [Mg2+]/[OH¯] in the presence of PAA arising from the more quantitative reaction of PAA with OH− than PAAn− with Mg2+. Larson and Buswell28 proposed that the Mg2+ ions in the supersaturated solution “are more strongly adsorbed by the crystal surface than [OH¯] ions and when the latter are in excess, the rate constant for crystal growth is increased”. Those results agree with the results that were obtained by Liu and Nancollas11 in which the rate of crystal growth decreased in the presence of excess magnesium ions. The second possible effect is the adsorption of PAA on the active surfaces of Mg(OH)2 nuclei. This effect may be clearly seen in the different values of the rates of crystal growth in the presence of PAA with different end groups, whereas if the first effect was the only reason for the decreasing rate of crystal growth, the rate of crystal growth value would be approximately the same in all cases. The trends in retardation observed, in which the PAA with end-groups of moderate hydrophobicity are (EIB, HIB, and DIB) are more effective than PAA with hydrophilic end-groups (CMM) and long hydrophobic endgroups (HDIB), parallel results we have reported in the calcium oxalate19,20 and calcium carbonate17,18 systems and have, as we hypothesized for those systems, been provisionally attributed to selective adsorption of PAA on edges between more and less positively charged surfaces. The computational studies summarized above22,23 suggest that the hydrophobic endgroups of PAA, which are functionally identical to PE oligomers, should preferentially absorb to the (100) face which would localize the highly effective decyl isobutyrateterminated PAA inhibitor to the edges between this face and the others.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +61 2 6773 2470. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Shams El Din, A. M.; El-Dahshan, M. E.; Mohammed, R. A. Inhibition of the Thermal Decomposition of HCO3− A Novel Approach to the Problem of Alkaline Scale Formation in Seawater Desalination Plants. Desalination 2002, 142, 151. (2) Shams El Din, A. M.; El-Dahshan, M. E.; Mohammed, R. A. Scale Formation in Flash Chambers of High-Temperature MSF Distillers. Desalination 2005, 177, 241. (3) Mubarak, A. A Kinetic Model for Scale Formation in MSF Desalination Plants. Effect of Antiscalants. Desalination 1998, 120, 33. (4) Hillier, H. Scale Formation in Sea-Water Distilling Plants and Its Prevention. Proc. Inst. Mech. Engrs. (London) 1952, 1B, 295. (5) King, E. G.; Ferrante, M. J.; Pankratz, L. B. Thermodynamic Data for Magnesium Hydroxide (Brucite); Bureau of Mines: Pittsburg, PA, 1975; p 13. (6) Physical Constants of Inorganic Compounds. In Handbook of Chemistry and Physics, 70 ed.; Weast, R. C., Lide, D. R., Astle, M. J., Beyer, W. H., Eds.; CRC Press: Boca Raton, 1989. (7) Gjaldbaek, J. K. An Investigation of the Solubility of Magnesium Hydroxide. II. The Solubility Product and the Dissociation Constant of Magnesium Hydroxide. Z. Anorg. Allg. Chem. 1925, 144, 269.

5. CONCLUSIONS The inhibition efficiency of low molecular mass (Mn ≤ 2000) PAA with different end-groups to prevent Mg(OH)2 formation in solution containing nonequivalent concentrations of Mg2+ and OH¯ ions at 97 °C was studied using conductivity measurements. The order of crystal growth, n, was found to be 0.66−0.72, lower than previously reported, but this is consistent F

DOI: 10.1021/ie504869e Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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DOI: 10.1021/ie504869e Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX