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Comprehensive Study of the Chelation and Coacervation of Alkaline Earth Metals in the Presence of Sodium Polyphosphate Solution Arash Momeni† and Mark Joseph Filiaggi*,†,‡ †

School of Biomedical Engineering, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5 Faculty of Dentistry, Department of Applied Oral Sciences, Dalhousie University, 5981 University Avenue, Halifax, Nova Scotia, Canada B3H 3J5

‡

S Supporting Information *

ABSTRACT: The effect of chelation of three alkaline earth metals (Ca, Sr, and Ba) by polyphosphates on the pH and viscosity of the solution is examined and correlated to the phosphate glass properties. Also, the impact of the polyphosphate average degree of polymerization (Dp) as well as the type and amount of chelated divalent cation on the degradation rate of the chains is studied. Subsequently, the number of divalent cations required for polyphosphate chain agglomeration to form a coacervate, and the resulting composition of these coacervates, was investigated. A decrease in polyphosphate solution pH during chelation was routinely obtained, with a sudden shift in the rate of pH drop occurring around a divalent cation/phosphorus molar ratio of 0.18. Longer chains or cations with a smaller ionic radius accelerated the rate of Dp reduction. The number of divalent cations required for coacervation depends on different variables such as the polyphosphate concentration, the Dp, and the type of divalent cation. The formed coacervate retains the Dp of polyphosphate originally used for coacervation, and the resulting Ca/P molar ratio depends largely on the amount of calcium being used during coacervation. Overall, this article helps one to understand the coacervation of polyphosphates in order to exploit their potential as a biomaterial.

1. INTRODUCTION Monovalent phosphate glasses are represented by xR2O−(1 − x)P2O5, where R stands for a monovalent cation such as Na+. The value of x determines the type of phosphate network present in the glass. For 0.5 ≤ x ≤ 0.67, the glasses are composed of phosphate chains without any branching points. These phosphate glasses dissolve in the presence of water with minimum degradation, resulting in a solution of inorganic polyphosphate chains. Polyphosphate solutions are widely used as a water-softening agent due to the very well known ability of polyphosphate chains to chelate multivalent cations.1 However, a very interesting phenomenon happens when an excess number of © 2014 American Chemical Society

multivalent cations are added to the polyphosphate solution: large cations (Ba2+, Sr2+, Pb2+, Ag+, Bi2+, ZrO2+, UO22+, and Hg22+) in excess give flocculent, solid precipitates, whereas smaller cations (Ca2+, Mg2+, Zn2+, Mn2+, Ni2+, Co2+, Fe2+, Fe3+, Cr3+, Hg2+, and Cu2+) give a highly viscous liquid or coacervate that is immiscible with water.2 The term coacervation is used to describe a process in which aqueous colloidal solutions separate, upon alteration of the thermodynamic condition of state, into two liquid phases: one rich in colloid, i.e., the Received: February 5, 2014 Revised: March 21, 2014 Published: April 21, 2014 5256

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solution having a Dp of 100 ± 1 and a phosphate concentration of 0.098 M. Subsequently, these cation-loaded polyphosphate solutions were titrated at 25 °C ± 0.5 between a pH of 3.5 and 10 in order to determine the acid dissociation constant (pKa). In the resulting titration curves, two inflection points were identified and then the pH at the halfway point was reported as the pKa of the hydrogen atoms at the end of the chains. In all pH studies, freshly boiled water was used and pKa measurements were carried out rapidly to minimize the effect of CO2 on titration. 2.2.2. Liquid 31P NMR Studies. NMR studies were conducted at three stages. First, investigations of the degradation rate of a pure NaPP solution in relation to its Dp was studied at 80 °C since degradation is so slow at lower temperature; NaPPs with Dp values of 402 ± 15 and 100 ± 1 were dissolved in water in triplicate at a phosphate concentration of 0.86 M and maintained at 80 ± 1 °C for up to ∼35 h. The pH was kept constant at 6.5 close to the NaPP pKa using 1 M NaOH. At predetermined time intervals, the Dp was determined by a Bruker AV300 MHz NMR spectrometer at 101.26 MHz using a 15° pulse, 65 536 (64 k) data points giving a 0.8 s acquisition time, a 7.0 s repetition rate, and greater than 100 scans. Spectra were reported using the d scale, with positive values downfield, and were referenced to an 85% solution of H3PO4 in H2O. The peaks around 0 and −9 ppm represent the Q0 (orthophosphates) and Q1 (end-of-chain phosphorus atoms) respectively, and the peaks around −21 ppm represent Q2‑middle (middle of chain phosphorus atoms in polyphosphates) and Q2‑meta (middle of ring phosphorus atoms).24 The Dp of NaPP was determined by the following equation based on the area under the peaks:

coacervate, and the other containing little colloid.3 Polyphosphate coacervates could have multiple applications as a biomaterial or as a glass precursor for coating.4−8 There are several reports on coacervates of polyphosphates with cations such as Mn2+,9 Ni2+,10,11 Co2+,10,11 Fe3+,12,13 Mg2+,5,14−16 Ca2+,4−8,12,14−20 Al3+,13,15 and Zn2+.21,22 Although several groups have reported on coacervate formation, no one has investigated or described this phenomenon in any great detail, resulting in some cases in confusing or misleading statements in the literature. For instance, it has been erroneously mentioned that acidic conditions are required for the coacervation of polyphosphates.22 Our group has recently become interested in the coacervation of polyphosphates given its potential use in injectable in situ forming systems for bioapplications such as drug delivery. In order to understand this system better and exploit its potential for different bioapplications, we deemed it necessary to comprehensively study the reactions between polyphosphate solutions and three alkaline earth metals, namely, Ca, Sr, and Ba. First, the chelation of these cations by polyphosphates and their impact on the stability of polyphosphate chains is studied by means of liquid 31P nuclear magnetic resonance (NMR), pH, and viscosity measurements. Then, the exact number of these divalent cations required for coacervation under different conditions is examined and discussed based on polyelectrolyte theories. Finally, the composition of the resulting polyphosphate coacervates and their dependence on the coacervation process are assessed. Our observations and subsequent analyses are valuable not only in understanding the coacervation of polyphosphates but also in describing some of the unique properties of phosphate glasses.

Dp =

2 × (Q 1 + Q 2 ‐ middle) Q1

(1)

In the second part of the NMR experiments, the degradation of a 0.860 M solution of NaPP with a Dp of ∼86 was studied this time at different M2+/P molar ratios. The degradation of these polyphosphate chains loaded with divalent cations was followed in triplicate for up to 14 days (37 °C, pH 6) by measuring the Dp at predetermined time intervals as described above. The effect of the chelated cation on the chemical shifts in the NMR spectra was investigated. Also, the effect of the chelated cation on the width at half height of the Q2‑middle peak was examined by fitting a Lorentzian curve to the peak using Bruker TopSpin 1.3 software. In the third part of NMR studies, polyphosphate solutions at 0 Ca/ P molar ratio at different pHs between 3.5 and 10.25 were prepared by adding NaOH to a 0.1 M NaCl NaPP solution having a Dp of 100 ± 1 and a phosphate concentration of 0.098 M. The chemical shift of the Q1 site highly depends on its protonation.25 The chemical shift is plotted against the pH of the solution, and the pH at the inflection point in this plot is equal to the pKa.26 2.2.3. Viscosity Studies. A DV3 cone−plate rheometer (Brookfield, USA) was used to measure the viscosity of a NaPP solution with a Dp of ∼17 000 at a phosphate concentration of 0.171 M for divalent cation to phosphorus molar ratios of 0, 0.05, 0.10, 0.125, 0.15, 0.175, and 0.20 at a temperature of 25 ± 0.1 °C and a shear rate of 750 s−1. NaPP with a very large Dp was chosen in order to achieve viscosities high enough to measure the viscosity accurately. The viscosity was also measured for the same NaPP sample at different Ca/P molar ratios but at very low phosphate concentrations in order to plot the specific viscosity/concentration (ηsp/C) against concentration (C). 2.3. Coacervation Studies. 2.3.1. Turbidity Studies. Turbidity studies were carried out to determine the exact amount of divalent cation required for coacervation and its relation to the NaPP concentration, Dp of the NaPP, type of divalent cation, solution pH, and the presence of NaCl in the solution. NaPP solutions with phosphate concentrations ranging from 0.001 to 3 M were prepared. Divalent chloride solutions (1 or 0.1 M) were added dropwise using a micropipet while the temperature was kept constant at 37 ± 0.5 °C. After each drop, the turbidity of the solution was measured using a Micro 100 turbidity meter (Scientific, Inc.). At a certain M2+/P molar ratio, a sudden shift in the turbidity of the solution occurs. This point

2. EXPERIMENTAL SECTION 2.1. Starting Materials and Sodium Polyphosphate Processing. Sodium polyphosphates (NaPP) with different average degrees of polymerization (Dp) were prepared as comprehensively reported.23 Briefly, NaPPs with Dp < 500 were produced by holding NaH2PO4· H2O (Sigma-Aldrich) at 700 °C for 1 h to obtain an NaPP glass, followed by acetone fractionation to yield NaPPs with a narrow size distribution. NaPPs with Dp >500 were produced by holding KH2PO4 (Sigma-Aldrich) at 775 °C for different time periods to obtain a potassium Kurrol salt, followed by an ion exchange process to replace potassium with sodium. Following the acetone fractionation and ion exchange processes, the NaPP solutions were freeze-dried to yield NaPP powder that was subsequently stored at −20 °C for later studies. A commercial NaPP with Dp = 27 was also used in these investigations (ICL Performance Products LP, Missouri, USA). Chloride salts of calcium, strontium, and barium (Sigma-Aldrich) were used as the sources for divalent cations in the solutions. All other materials were of reagent grade. 2.2. Chelation Studies. 2.2.1. pH Studies. The addition of divalent cations to NaPP solutions causes the pH of the solution to drop. To understand this phenomenon better, NaPPs with different Dp were dissolved in water at 25 ± 0.5 °C at a phosphate concentration of 0.3 M, and the pH of all solutions was adjusted to 7 using a 1 M NaOH solution. Subsequently, 1 M Ca, Sr, or Ba solutions were added dropwise using a micropipet, and the pH was monitored using an Accumet Basic AB15 pH meter (Fisher Scientific, Boston, MA, USA) until the solution became cloudy, indicating precipitation and subsequent coacervate formation. pH measurements were carried out in triplicate for each sample, and the average pH value and standard deviation were reported against the divalent cation to phosphorus (M2+/P) molar ratio (M stands for the divalent cation). In addition, polyphosphate solutions at 0, 0.05, 0.10, 0.15, 0.20, and 0.25 Ca/P and 0.15 Sr/P and Ba/P molar ratios were prepared by adding the required number of divalent cations to a 0.1 M NaCl NaPP 5257

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Figure 1. (a) pH decrease as calcium is added to polyphosphate solutions with different Dp ([phosphate] = 0.3 M, STD bars shown just for one sample for clarity, the large STD might be due to the presence CO2). (b) pH decrease for different divalent cations in a polyphosphate solution with a Dp of 47 ([phosphate] = 0.3 M, positive STD error bars shown only for clarity, negative error bars are equal to positive error bars). Insets show the rate of pH drop. The temperature in all pH studies was 25 ± 0.5 °C. The rate of pH drop refers to the slope of the titration curves.

Table 1. Summary of the Key Features from the Titration Curves of a Polyphosphate Solution with Dp of 100 at 0.15 (Sr or Ba)/ P Molar Ratios and at Different Ca/P Molar Ratios Lower than Ca* sample

pH at first inflection point

pH at second inflection point

pH at halfway = pKa

volume of 0.1 M NaOH between two inflection points (μL)

0 Ca/P 0.05 Ca/P 0.10 Ca/P 0.15 Ca/P 0.20 Ca/P 0.25 Ca/P 0.15 Sr/P 0.15 Ba/P

4.88 4.79 4.62 4.31 4.15 4.01 4.39 4.41

8.70 8.61 8.25 8.06 8.17 7.75 8.42 8.67

6.5 6.25 5.95 5.55 5.25 5 5.7 5.9

169 165 163 161 164 164 165 172

is known as the cloudy point and the value of the M2+/P ratio at the cloudy point is known as the demixion point27 (M*), which is reported here. Tris(hydroxymethyl)aminomethane (Tris, 0.05 M) and 2-(N-morpholino)ethanesulfonic acid (MES, 0.05 M) buffer solutions were used to stabilize the pH at 7.4 and 5.5, respectively. 2.3.2. Chemical Composition of the Coacervate. NaPP (100 mg) with Dp of 402 ± 15 was dissolved in 1 mL of water. All of this 1 mL solution was added at once to 4 mL of water having 93.6, 163.8, 234, 334, 393, 468, and 936 μL of 1 M Ca resulting in mixtures with 0.10, 0.175, 0.25, 0.357, 0.42, 0.50, and 1 Ca/P molar ratios, respectively. At Ca/P molar ratios higher than or equal to 0.357, which is the M* under these conditions, the coacervate formed spontaneously; at lower Ca/P molar ratios, coacervate formation was subsequently induced by adding 47 mL of acetone. These mixtures were agitated for 5 min using a magnetic stirrer, and the coacervate was collected and stored at −20 °C until analysis. To evaluate the composition and chain length, the coacervates were subsequently dissolved using 200 mM ethylenediaminetetraacetic acid (EDTA) at a pH of 10. The volume of EDTA required for dissolution was determined based on having a minimum of 1.2 mol of EDTA for each mole of Ca; at this EDTA/Ca molar ratio and pH, polyphosphate chain degradation is kept to a minimum.28 After dissolution, the Ca/P molar ratio of the coacervate was determined using inductively coupled plasma optical emission spectroscopy (ICP) (Optima 7300 V ICP-OES, PerkinElmer Instruments, USA). Dp was measured using liquid 31P NMR as described above. The amount of calcium and phosphorus remaining in the supernatant solution was also determined by ICP. To assess if the mixing time affected the Ca/P molar ratio or the resulting Dp of the coacervate, experiments with longer mixing times (15, 30 min, and 1 h) were also conducted. All sample groups were evaluated in triplicate.

amount of pH drop is directly related to the NaPP chain length. As an example, in an NaPP fraction with a Dp of 279, the pH decreases from 7.10 ± 0.00 at a Ca/P molar ratio of zero to 6.50 ± 0.05 at its Ca* = 0.293. In contrast, for a NaPP fraction with a Dp of 47, the pH drops from 7.08 ± 0.01 at a Ca/P molar ratio of zero to 6.08 ± 0.05 at its Ca* = 0.313. The shape of the pH curves is also interesting; the pH decreases at an almost constant rate until a Ca/P molar ratio of ∼0.18 is reached, at which point a sudden increase in the rate of pH drop occurs. This behavior could be more clearly seen in the inset of Figure 1a, which shows the rate of pH drop for different NaPPs. This behavior was observed in all NaPPs except for the commercial unfractioned NaPP with a Dp of 27. The amount of pH drop in the NaPP solution is also affected by the type of divalent cation being used (Figure 1b), with decreases in pH from 7.08 ± 0.01 to 6.08 ± 0.05, 7.09 ± 0.01 to 6.71 ± 0.05, and 7.08 ± 0.01 to 6.77 ± 0.01 for Ca, Sr, and Ba, respectively. The shape of the pH curves remains similar between different divalent cations, but the sudden increase or inflection in the rate of the pH drop is slightly shifted to lower divalent cation/P molar ratios in cations with a higher ionic radius (Figure 1b inset). The most important features of the titration curves of polyphosphate solutions loaded with calcium at different Ca/P molar ratios are summarized in Table 1 (with the actual titration curves provided as Supporting Information). The values of pH at inflection points reported in Table 1 are not perfectly accurate due to the difficulties in determining the accurate inflection point. In contrast, the value of pH at the halfway point, which is equal to the pKa, is more accurate (accuracy error 0.357 (Ca*) it was assumed that the penetration of remaining calcium into the coacervate requires time. Figure

Ca* was significantly higher than Ba*. The differences between Ca* and Sr*, or Sr* and Ba*, were not significant for most of the phosphate concentrations studied, though a general trend suggested that fewer divalent cations with the larger ionic radius were required for coacervation. Another figure in the Supporting Information shows the effect of ionic strength on M* using a 0.05 M tris buffer solution and a 0.05 M tris buffer saline solution. The addition of NaCl and the resulting increase in the ionic strength of the solution causes Ca* to decrease at phosphate concentrations higher than 0.03 M and to increase at phosphate concentrations lower than 0.03 M. Finally, there is a figure in the Supporting Information that shows the effect of pH on Ca* for two different NaPP batches (Dp values of 80 and 20 000). Overall, Ca* decreases in acidic pH, indicating that less calcium per chain is needed to form a coacervate under acidic conditions. 3.5. Chemical Composition of the Coacervates. Sr addition to polyphosphate solution at values higher than Sr* results in flocculation. These particles are not sticky and can be integrated with each other only when pressed by hand; even after pressing, the resulting mass easily breaks up when pulled. On the other hand, the addition of Ba at values higher than Ba* 5261

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Figure 5. (a) Ca/P molar ratio in the coacervate in comparison to the original Ca/P molar ratio that was used during mixing. (b) Mole percentage of calcium and phosphorus that is not incorporated into the coacervate. (c) Effect of mixing time on the Ca/P molar ratio of the coacervate. (d) Dp of polyphosphates inside the coacervates in comparison to the original Dp of polyphosphate at different Ca/P molar ratios. Numbers show the average, and bars show the STD (n = 3).

acid−base equilibrium can be considered; therefore, the pKa determined by titration refers to this reaction:

5c shows the result of these experiments for the 0.50 Ca/P ratio. On the basis of single-factor ANOVA analysis, the mixing time was found to have no significant effect on the Ca/P molar ratio of the coacervate. Figure 5d describes the Dp of polyphosphates in the coacervate in comparison to that of the original NaPP solution. No significant drop in Dp was noted. Increasing the mixing time from 5 min to 1 h also did not cause any significant drop in the chain length of polyphosphates inside the coacervate (data not shown). As mentioned, at 0.357 (Ca*), a significant percentage of phosphates remained in the solution, which were presumably the shorter-chain polyphosphates. Interestingly, only at this Ca/ P molar ratio was an increase in the Dp of the coacervate observed; if some of the short chains from the original NaPP do not get incorporated into the coacervate, then the Dp inside the coacervate could become higher than the original Dp .

Since CO2 dissolution and conversion to H2CO3 is very slow, the effect of CO2 on titration in this study is minimal. Indeed we have shown that the number of Q1 phosphate sites in NaPP solutions as determined by titration, using the same procedure as described in this study, is not different from the number of Q1 sites determined for that same solution using liquid 31P NMR.23 This confirms the accuracy of titration studies and shows that the effect of CO2 under the conditions of these studies is minimal. In addition, the pKa as determined for a 0 Ca/P sample by liquid 31P NMR was very close to the value obtained by titration. This again shows that the effect of CO2 on titration under the conditions of these studies is minimal. The chelation of divalent cations by polyphosphate chains caused the pH of the solution to decrease, an effect previously reported by several researchers.21,31,32 We showed that the pKa value of hydrogen atoms at the end of the chains also decreases during chelation. This pH effect can be explained, therefore, by the dissociation of hydrogen atoms at the chain ends. Since chains with larger Dp values have a fewer number of end-group phosphates, they have correspondingly fewer hydrogen atoms at their ends to be released into the solution, resulting in less of

4. DISCUSSION There is a relatively weak hydrogen at each end of a phosphate chain, but the middle phosphate groups in either chains or rings do not have such weak hydrogens. Therefore, in the absence of Q 0 , the number of base equivalents used to titrate polyphosphate solution between pH 4.5 and 9 is equal to the moles of Q1 sites in the solution.1,30 In a long polyphosphate chain where the dissociation of a hydrogen atom at one end does not affect hydrogen dissociation at the other end, a single 5262

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In the limit of infinite dilution, the fraction of condensed counterions (θ) is given by41

a pH drop. The extent of any decrease in the pH and pKa values of polyphosphates loaded with divalent cations seems to be directly related to the stability of the complex forming between that cation and the chain; it is known that the dissociation constant and the stability of the complexes of Ba, Sr, and Ca with tripolyphosphate, tetrapolyphosphate, or longer chains decrease as the ionic radius increases.33−35 The other possible explanation for the pH decrease during chelation is the hydrolysis of the chelated divalent cation, which is partially hydrated, forming hydroxyl complexes as shown in the following reaction. This reaction has been reported for alkaline earth metals that are chelated by tripolyphosphates.36

1⎛ 1 ⎞ ⎜1 − ⎟ Z⎝ Zξ ⎠

θ=

(for Zξ > 1) (2)

where Z is the valence of the counterion and ξ = λB/b (where b is the distance between two charged groups on the polyion and λB is the Bjerrum length defined as the distance at which the Coulomb interaction between two unscreened elementary charges is equal to the thermal energy, which is equal to 7.135 Å for a water medium at 25 °C41). In a polyphosphate chain, b = 2.5 Å;41 therefore, the charge density (ξ) of a polyphosphate chain in water is 2.85. From eq 2, at infinite dilution, the fraction of condensed counterions (θ) for a divalent counterion is 0.41. This means that at extremely low ionic strength, in dissolved calcium polyphosphate (Ca(PO3)2), 41% of calcium ions are chemically attached (Ca/P molar ratio ≈ 0.20). Yet, in most situations, the fraction of condensed counterions in a polyphosphate solution is lower than this theoretical value due to the presence of polyphosphate chains and other ions in the solution, which screen the charge on the chains.44 So overall, based on the Manning theory, divalent cations are condensed on the chains up to a 0.16−0.20 M2+/P molar ratio; above this threshold these cations enter into the diffuse layer, leading to anomalies in the behavior of the polyphosphate−divalent cation system. The second part of these chelation studies focused on the relation between the NaPP chain length and its degradation and the effect of alkaline earth metals on the rate of degradation. The degradation of pure NaPP solutions has been well studied.45−48 Degradation proceeds through three pathways: cleavage of orthophosphates from the chain ends, random scission in the middle of the chain, and cleavage of trimetaphosphates from the end and middle of the chains. Their reaction rates are governed by the following equations, respectively,48

The immersion of alkaline phosphate glasses into water instantly leads to a rapid decrease in pH.20,37 This pH drop is fundamentally similar to the pH decrease that was observed here in polyphosphate solutions. It is expected that the extent of this drop is related to the type of modifier cation in the glass. For instance, more calcium in a Na2O−CaO−P2O5 glass system should result in a larger pH drop.38 This study also revealed a sudden increase in the rate of pH drop when the M2+/P molar ratio exceeds ∼0.18. This kind of anomaly has been previously reported in Raman spectroscopy and extended X-ray absorption fine structure (EXAFS) studies of polyphosphate−divalent cation systems, where shifts in behavior always happen around 0.16−0.20 M2+/P.11 It is interesting that this anomaly also happens at the same ratio in alkaline phosphate glasses.39,40 There are three possible explanations for this behavior. First, Filho et. al19 using europium luminescence spectroscopy have shown that at low Ca/P molar ratios, Ca2+ would be located in cagelike sites with a coordination number of 6 provided by phosphate units of the polyphosphate chain. However, when the Ca/P ratio exceeds ∼0.17, Ca2+ ions begin to occupy a second family of sites where they can interact with water molecules. The transition between these two sites could be the cause of the observed anomalies. A second explanation is based on the coordination number of the cation (CN) and the number of terminal oxygen atoms (MTO) on the phosphate chain;40 Ca2+ has a CN of 6;19 therefore, at a Ca/P molar ratio of 1/6 (∼0.17) all of the terminal oxygen atoms are bonded and remaining Ca2+ ions either end up sharing the terminal oxygen atoms or satisfy their CN with water molecules, leading to changes in behavior of the system at this ratio. The third explanation is based on the Manning theory, which states that counterions exist in three different states in a polyelectrolyte solution.41−43 The first group includes counterions that are chemically site bonded to the polymer chain; this group is known as condensed counterions. In the second group, the counterions are still in close proximity to the polymer chain but they are not chemically condensed. These counterions, making up a diffuse layer, are able to move along the axis of the polymer chain and are entrapped in the vicinity of the polyion due to electrostatic forces. Finally, the last group consists of counterions that are freely scattered in the solution.

d[Q 0] dt d[Q 1] dt

= kE1[Q 1] = 2kME[Q 2 − middle] +

d[Q 2 − meta] dt

(3)

2k O3[Q 2 − meta] (4)

3

⎛ [Q 1] ⎞ = kMO⎜[Q 2 − middle] − ⎟ 2 ⎠ ⎝ + kEO([Q 1] − 2([P2] + [P3] + [P4 ])) −

k O3[Q 2 − meta] 3

(5)

where kE1 and kEO are specific rates for the formation of Q0 and trimetaphosphate from Q1 groups, kME and kMO are specific rates for the formation of Q1 and trimetaphosphate from Q2‑middle groups, and kO3 is the specific rate for the hydrolysis of trimetaphosphate to tripolyphosphate. [P2], [P3], and [P4] represent the concentrations of pyrophosphate, tripolyphosphate, and tetraphosphate, respectively, which do not participate in the formation of trimetaphosphate. In our results, the rate of formation of ortho and trimetaphosphates were much higher in the shorter fraction. This could be explained based on eqs 3 and 5, where the rates of formation of these two species depend mainly on [Q1], which is higher in the shorter fraction. One should note that in eq 5 the value of kMO is significantly smaller than kEO48 and 5263

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and decreasing electrostatic repulsion forces until Ca* is reached; above this threshold, precipitate forms, followed by aggregation to form coacervate. That M* continuously decreases as the concentration of NaPP in the solution increases could be explained based on the entropy of the system; soluble NaPP has a higher entropy compared to NaPP trapped in a coacervate, so for a coacervate to form, there is an entropy gap to be overcome. This entropy gap is overcome by other forces that are present in this system, including hydrophobic and electrostatic forces. This entropy gap is larger at low NaPP concentration than at high NaPP concentration, and as a result, at low NaPP concentrations more divalent cations are needed to overcome the entropy and form a coacervate. We also saw that, at the same phosphate concentration, M* is lower for NaPPs having a higher Dp and that this difference is more significant at low phosphate concentrations (≤0.3 M). This observation can also be explained based on entropy; at the same phosphate concentration, a solution of shorter chains has a higher entropy compared to a solution of longer chains. Therefore, a larger entropy gap for shorter chains must be overcome in order to form a coacervate, meaning more divalent cations are required. M* also depends on the type of divalent cation or, more specifically, their ionic radius. The general trend observed was that fewer divalent cations possessing a larger ionic radius were required for coacervation. This originates from the ability of the divalent cation to compete with Na+ or other monovalent cations in the solution; presumably in the presence of Na+, Ba2+ and Sr2+ are more capable of forming hydrophobic complexes than Ca2+. The presence of Na+ has two effects in polyphosphate solutions: it could screen the charge on a polyelectrolyte or compete with the divalent cation forming a nonhydrophobic monovalent−polyphosphate complex. The former promotes precipitation and is effective at high phosphate concentrations, while the latter prevents precipitation affecting low phosphate concentrations. In contrast, rising [H+] caused M* to decrease independently of phosphate concentration probably because H+ screens only the charge on the chains and does not compete with Ca2+ as effectively as does Na+.

therefore could be neglected. On the other hand, the rate of formation of end groups was much higher in the longer fraction. This could be explained by eq 4 and the greater number of Q2‑middle groups in the longer fraction. Moreover, it has been shown that the kME value increases with an increase in the Dp ,48 suggesting more rapid random scissions in the middle of longer chains.49 Our results further show that the rate of degradation of polyphosphates depends on the M2+/P molar ratio, similar to previous reports.50−52 Trimetaphosphate was the main degradation byproduct of the polyphosphates loaded with calcium, and its formation was highly accelerated at a Ca/P molar ratio of ≥0.15. Presumably at low Ca/P molar ratios the chains are not coiled effectively to cleave into trimetaphosphate rings. Ca also had a more significant ability to degrade polyphosphates compared to Sr or Ba. The viscosity of polyphosphate solutions profoundly decreases when divalent cations are chelated by the chains. Cations with a larger ionic radius have a greater ability to coil the polyphosphate chain on itself, reducing its viscosity in solution. A similar relationship between the viscosity of the polyphosphate solutions and ionic radii of the divalent cation has been previously reported, but no explanation has been provided.53−55 This viscosity phenomenon is common with polyelectrolytes,56 and the possible explanation could be based on the hydrated ionic radii. Unlike anhydrous ionic radii, the hydrated ionic radii decrease from Ca2+ to Ba2+.57 The less hydrated the ion, the more strongly it interacts with the polyelectrolyte and the larger effect it exerts on the charge state and coiling of the chain on itself.56 It is very interesting that the same relationship exists in phosphate glass melts. Toyoda et al.58 have shown that the viscosity of polyphosphate glass melts is inversely related to the ionic radii of the modifier divalent cation. Finally, we focused on the quantity of alkaline earth metals required for coacervation. The precipitation of polyelectrolytes in the presence of multivalent cations has been the subject of several publication by Delsanti and colleagues.27,59,60 This group realized that the nature of the condensation phenomenon described in the Manning theory should be differentiated into two criteria based on the functional group of the polyelectrolyte. The first criterion consists of polyelectrolytes with anionic functional groups having high dissociation constants with divalent cations, such as sulfonate on poly(vinyl sulfonate) (PVSF). Here, the condensation reaction is basically electrostatic. In contrast, if the polyelectrolyte functional group is an anion that has a low dissociation constant with a divalent cation, such as carboxylate on poly(acrylic acid) (PAA) or phosphates in NaPP, then the condensation reaction is chemical. The presence of chemical condensation is necessary for the precipitation of polyelectrolytes by divalent counterions. As a result, divalent cations do not induce the precipitation of PVSF solutions but do so for PAA27,59 or NaPP solutions. In a divalent cation−polyanion system, factors acting against precipitation are the entropy of the polymer, the steric excluded volume, and electrostatic repulsion between negatively charged polymers. In contrast, factors acting in favor of precipitation are the hydrophobicity of the chemically condensed phase and the electrostatic interaction between negatively charged free monomers and those monomers possessing an effective positive charge due to the condensation of the divalent cation.27,59 As calcium is being added to the NaPP solution, Ca(PO4)2 dicomplex forms, resulting in increasing hydrophobic forces

5. CONCLUSIONS pH, viscosity, and NMR studies were carried out to better understand the chelation of alkaline earth metals by polyphosphates. The pH decrease in polyphosphate solutions during the chelation is due to the decrease in the pKa value of hydrogen atoms at phosphate chain ends or possibly hydroxyl complex formation. Longer chains or larger cations cause a smaller pH drop. The sudden shift in the rate of pH drop around a divalent cation/phosphorus molar ratio of 0.18 is similar to previously reported anomalies for polyphosphate solutions and glasses, and it was explained based on Manning theory, the cation coordination number, and the different sites available for the cation. The extent of viscosity decrease in polyphosphate solutions, such as phosphate glass melts, depends directly on the ionic radius of the divalent cation. Furthermore, the degradation rate of these polyphosphate chains is a function of the type and quantity of divalent cation as well as the polyphosphate Dp . The coacervation of polyphosphate chains is the result of a low dissociation constant between the phosphate group and the divalent cation, which is basically similar to the precipitation of 5264

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(11) Silva, M. c. A. P.; Franco, D. F.; C. de Oliveira, L. F. New Insight on the Structural Trends of Polyphosphate Coacervation Processes. J. Phys. Chem. A 2008, 112, 5385−5389. (12) Masson, N. C.; de Souza, E. F.; Galembeck, F. Calcium and iron(III) polyphosphate gel formation and aging. Colloids Surf., A 1997, 121, 247−255. (13) Fatima de Souza, E.; Bezerra, C. C.; Galembeck, F. Bicontinuous networks made of polyphosphates and of thermoplastic polymers. Polymer 1997, 38, 6285−6293. (14) Umegaki, T.; Kanazawa, T. Viscosity behavior of coacervates of magnesium and calcium highpolyphosphates. Bull. Chem. Soc. Jpn. 1975, 48, 1452−1454. (15) Kanazawa, T.; Umegaki, T.; Kitahima, Y.; Ogawa, T. A solubility study of coacervate of magnesium, calcium and aluminum highpolyphosphates in acid solutions. Bull. Chem. Soc. Jpn. 1974, 47, 1419− 1421. (16) Umegaki, T.; Kanazawa, T. Degradation of Magnesium and Calcium Highpolyphosphate Coacervates. Bull. Chem. Soc. Jpn. 1979, 52, 2124−2126. (17) Sinyaev, V. A.; Shustikova, E. S.; Levchenko, L. V.; Sedunov, A. A. Synthesis and Dehydration of Amorphous Calcium Phosphate. Inorg. Mater. 2001, 37, 619−622. (18) Gomez, F.; Vast, P.; Llewellyn, P.; Rouquerol, F. Dehydroxylation mechanisms of polyphosphate glasses in relation to temperature and pressure. J. Non-Cryst. Solids 1997, 222, 415−421. (19) Dias Filho, F. A.; Carlos, L. D.; Messadeq, Y.; Ribeiro, S. J. L. Spectroscopic Study and Local Coordination of Polyphosphate Colloidal Systems. Langmuir 2005, 21, 1776−1783. (20) Lee, I.-H.; Shin, S.-H.; Foroutan, F.; Lakhkar, N. J.; Gong, M.-S.; Knowles, J. C. Effects of magnesium content on the physical, chemical and degradation properties in a MgO−CaO−Na2O−P2O5 glass system. J. Non-Cryst. Solids 2013, 363, 57−63. (21) Willot, G.; Gomez, F.; Vast, P.; Andries, V.; Martines, M.; Messaddeq, Y.; Poulain, M. Preparation of zinc sodium polyphosphates glasses from coacervates precursors. Characterisation of the obtained glasses, and their applications. C. R. Chim. 2002, 5, 899−906. (22) Palavit, G.; Montagne, L.; Delaval, R. Preparation of zinc— sodium phosphate glass precursors by coacervation. J. Non-Cryst. Solids 1995, 189, 277−282. (23) Momeni, A.; Filiaggi, M. J. Synthesis and characterization of different chain length sodium polyphosphates. J. Non-Cryst. Solids 2013, 382, 11−17. (24) Van Wazer, J. R.; Callis, C. F.; Shoolery, J. N.; Jones, R. C. Principles of Phosphorus Chemistry. II. Nuclear Magnetic Resonance Measurements1. J. Am. Chem. Soc. 1956, 78, 5715−5726. (25) Yoza, N.; Ueda, N.; Nakashima, S. pH-dependence of 31P-NMR spectroscopic parameters of monofluorophosphate, phosphate, hypophosphate, phosphonate, phosphinate and their dimers and trimers. Fresenius’ J. Anal Chem. 1994, 348, 633−638. (26) Handloser, C. S.; Chakrabarty, M. R.; Mosher, M. W. Experimental determination of pKa values by use of NMR chemical shift. J. Chem. Educ. 1973, 50, 510. (27) Sabbagh, I.; Delsanti, M. Solubility of highly charged anionic polyelectrolytes in presence of multivalent cations: Specific interaction effect. Eur. Phys. J. E 2000, 1, 75−86. (28) Tischendorf, B.; Otaigbe, J. U.; Wiench, J. W.; Pruski, M.; Sales, B. C. A study of short and intermediate range order in zinc phosphate glasses. J. Non-Cryst. Solids 2001, 282, 147−158. (29) de Oliveira Lima, E. C.; Moita Neto, J. M.; Fujiwara, F. Y.; Galembeck, F. Aluminum Polyphosphate Thermoreversible Gels: A Study by31P and27Al NMR Spectroscopy. J. Colloid Interface Sci. 1995, 176, 388−396. (30) Callis, C. F.; Van Wazer, J. R.; Arvan, P. G. The Inorganic Phosphates as Polyelectrolytes. Chem. Rev. 1954, 54, 777−796. (31) Wazer, J. R. V.; Campanella, D. A. Structure and Properties of the Condensed Phosphates. IV. Complex Ion Formation in Polyphosphate Solutions. J. Am. Chem. Soc. 1950, 72, 655−663.

PAA under the same conditions. The formed coacervate possesses a similar Dp to that of the polyphosphate originally used for coacervation, but its Ca/P molar ratio depends largely on the amount of calcium being used and not on the mixing time. We are currently focusing on the biodegradation of the coacervate and its potential applications as a biomaterial.

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ASSOCIATED CONTENT

S Supporting Information *

Titration curves of polyphosphate solutions, Q1 chemical shift at different pH values, Q1 peaks at different divalent cation to phosphorus mole ratios, NMR spectra of polyphosphate solutions at different time points, bar graphs showing the M* value under different conditions, and a table showing the width at half height for the Q2 peak at different divalent cation to phosphorus molar ratios. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +1902 494 7102. Fax: +1902 494 6621. E-mail: filiaggi@ dal.ca. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge funding from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the NSERC CREATE BioMedic program (AM).

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REFERENCES

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