Solubilities of Three Phosphorus Flame Retardants in Selected

Article pubs.acs.org/jced

Solubilities of Three Phosphorus Flame Retardants in Selected Organic Solvents Guo-Min Yu,†,‡ Li-Sheng Wang,*,† Jian Sun,† and Lin-Kun Jiang§ †

School of Chemical Engineering and Environment, Beijing Institute of Technology, Beijing 100081, China School of Biochemical and Chemical Engineering, Nanyang Institute of Technology, Nanyang 473000, China § Department of Biology and Chemistry, Baoding University, Baoding 071000, China ‡

ABSTRACT: Using a static analytical method, the solubilities of phosphonic acid, P,P′-(1,4-piperazinediyl)bis-P,P,P′,P′tetraphenyl ester (PAPBE), N,N′-[1,3-phenylenebis(methylene)]bis(phosphoramidic acid)P,P,P′,P′-tetraphenyl ester (PNBE), and 4-(hydroxymethyl)-1-oxido-2,6,7-trioxa-1phosphabicyclo [2.2.2] octane (PEPA) were measured from 293.15 K to 343.15 K in four selected organic solvents. Several thermodynamic models were used to correlate the experimental solubility data, such as Scatchard−Hildebrand, Wilson, nonrandom two-liquid (NRTL), and UNIQUAC. The calculated results showed that all the models reproduced the experimental data very well, and the UNIQUAC equation gives the best correlation. Using the group contribution methods, the solubility parameters of phosphorus flame retardants can be calculated, which were compared with the previous values calculated with the Scatchard−Hildebrand model.

1. INTRODUCTION As a kind of important polymeric materials, engineering plastics are often used in industry and daily life, such as construction, electronics, automobiles, and biomaterials, and so forth. However, the flammability of polymeric materials is a severe fire hazard and limits their applications.1 In order to reduce the combustibility of the polymer materials, many kinds of phosphorus compounds were added into the polymer materials. They can effectively improve the flame retardant performances of polymer materials because of their efficient flame retardant performance, less smoke, and low toxicity. As one of the most commonly used polymer materials, epoxy resins have been widely applied in adhesive, coating, electronic appliances, aerospace, and so forth for its excellent chemical stability, heat resistance, electrical insulation, and good bonding performance.2,3 Therefore, the study of the flame retardant epoxy resins is very important. In the process of the flame retardant applications, some phosphorus compounds greatly enhance the fire resistance of epoxy resins. For example, the phosphorus flame retardants of phosphonic acid, P,P′-(1,4-piperazinediyl)bis-P,P,P′,P′-tetraphenyl ester (PAPBE), 4 N,N′-[1,3phenylenebis(methylene)]bis(phosphoramidic acid)P,P,P′,P′tetraphenyl ester (PNBE),5 and 4-(hydroxymethyl)-1-oxido2,6,7-trioxa-1-phoZ-sphabicyclo [2.2.2] octane (PEPA)6 (the formulas are shown in Figure 1) have been widely researched in recent years to enhance the fire resistance of epoxy resins.7−13 In industrial production, flame retardant polymer materials usually can be prepared by coating, injection molding, extrusion molding, solution casting, and so forth. As a well known, © XXXX American Chemical Society

convenient, and economical processing method, solution casting occupies a pivotal position in the materials processing. Usually, the insoluble flame retardants will easily migrate from the polymer materials because they are poorly dispersed in the polymer materials when the solid flame retardant particles are added. This results in some adverse effects such as increased brittleness and decreased mechanical strength of the materials. These adverse effects can be avoided by using the solution processing method. Thus, solubility data of flame retardants in basic information required for the application of the solution casting method. In the process of the epoxy resins materials, some organic solvents, such as acetone and toluene, are usually used to dissolve or disperse the flame retardants additives. However, the solubilities of PAPBE, PNBE, and PEPA in these common organic solvents are poor. Then, choosing appropriate solvents with larger dissolving capacity for these three kinds of flame retardants are very necessary. The alcohol ether solvents of 1-methoxy-2-propanol (MP), 1-propoxy-2-propanol (PP), 1-methoxy-2-propyl acetate (MPA), and 2-(2-methoxypropoxy) propanol (MPP) are usually used as solvents, dispersants, thinners, cleanser, and so forth. They have the strong solvency because of their alcohol ether structure. The big solvency tends to generate the large dispersion forces when the flame retardant additives are added into the polymer materials. Some researchers also used these Received: January 2, 2015 Accepted: May 18, 2015

A

DOI: 10.1021/je501173n J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Figure 1. Structures of PAPBE, PNBE, and PEPA.

solvents as the solvents and dispersants in the process of the epoxy resins materials. Zhang et al.14 researched a fireproofing epoxy resins composition that can be applied in manufacturing prepreg and copper clad laminate. In the process of manufacturing of the fireproofing epoxy resins composition, researchers used MP and MPA as the solvent dissolution and dispersion effect. Zhang15 used epoxy resins to synthesize a high-performance modified glass fiber-reinforced plastic coating material and MPA was used as a solvent to dissolve the epoxy resins and additives containing the flame retardant ingredients. Deng et al.16 using the epoxy resins polymer materials to prepare the flame retardant halogen-free heat dissipation insulation paint, and MPP acted as a solvent when flame retardants were added. Therefore, understanding the dissolve situation of flame retardants in the alcohol ether solvents could be helpful for the subsequent industrial production. The flame retardants of PAPBE, PNBE, and PEPA with high solubilities are important for the process of flame retardant epoxy resins. In this work, a static analytic method was employed to obtain the solubilities of PAPBE, PNBE, and PEPA in the four organic solvents. The measuring temperature ranged from 293.15 K to 343.15 K. The systematical and complete solubility measurement information on PAPTE, PNBE, and PEPA was performed. The solubilities measured results were correlated by Scatchard−Hildebrand, Wilson, nonrandom two-liquid (NRTL) and UNIQUAC models. Moreover, using the group contribution methods, the solubility parameters of PAPTE, PNBE, and PEPA were calculated according to the molecular structure of organic matters.

Table 1. Sources and Mass Fraction Purity of Materials chemical name

CAS registry numbers

PAPBEa PNBEa PEPAa MPa

34670-63-8 382596-16-9 5301-78-0 107-98-2

PPa

1569-01-3

MPAa

108-65-6

MPPa

34590-94-8

source synthesis synthesis synthesis Aladdin Chemistry Co. Ltd. Tokyo Chemical Industry Co., Ltd. Aladdin Chemistry Co. Ltd. Aladdin Chemistry Co. Ltd.

mass fraction purity

purification method

>0.9904 >0.9905 >0.9906 >0.990

recystallization recystallization recystallization none

>0.930

none

>0.990

none

>0.980

none

a

PAPBE refers to phosphonic acid, P,P′-(1,4-piperazinediyl)bis-,P,P,P′,P′-tetraphenyl ester. PNBE refers to N,N′-[1,3phenylenebis(methylene)]bis(phosphoramidic acid)P,P,P′,P′-tetraphenyl ester. PEPA refers to 4-(hydroxymethyl)-1-oxido-2,6,7-trioxa1-phosphabicyclo [2.2.2] octane. MP, PP, MPA, and MPP refer to 1methoxy-2-propanol, 1-propoxy-2-propanol, 1-methoxy-2-propyl acetate, and 2-(2-methoxypropoxy)propanol, respectively. These also are expressed in the other tables.

measurement, an excess solute was added into a known quality of solvent. The equilibrium cell was stirred and heated up to a constant temperature. After at least 3 h, the stirring would be stopped, and the solution would be kept still for 3 h during which a clear upper liquid was obtained. (In order to determine the equilibration time, the different dissolution times had been tested. The result showed that 3 h was sufficient time to reach the solid−liquid equilibrium.) Three clear saturated solution samples, of about 2 mL each, were withdrawn with a preheated on−off injector with a cotton filter. They were quickly transferred into previously weighed measuring vials; meanwhile, each vial was quickly and tightly closed. After weighing the vial, the mass of the sample would be determined. Each saturated solution was dried in a vacuum oven to evaporate all the solvents at 353 K. When the mass of the remaining solid reached a constant value, the final mass of the solute and the vial was measured. In the pure solvent, the solubilities of the solute in mole fraction x1 could be calculated by the following equation:19

2. EXPERIMENTAL SECTION 2.1. Materials. The description of the materials used in this paper are listed in Table 1, including PAPBE, PNBE, PEPA, 1methoxy-2-propanol (MP), 1-propoxy-2-propanol (PP), 1methoxy-2-propyl acetate (MPA), and 2-(2-methoxypropoxy) propanol (MPP). 2.2. Apparatus and Procedure. The protocol and experimental setup used for the solubility measurements were identical to those in the literature.17 A glass-jacketed equilibrium cell working volume 120 mL was equipped with a magnetic stirring device. A thermostat device (type 50 L, Shanghai Laboratory Instrument Works Co., Ltd.) was used to maintain the temperature ± 0.02 K. An analytical balance (type CPA225D, Sartorius.), which had an average deviation of 0.01 mg, was used for quality measurement. 2.3. Solubility Measurement. The solubilities measurement was performed by the gravimetric method.18 For each B



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Table 2. Mole Fraction Solubilities, x, Standard Deviations, SD, and Activity Coefficients, γ, of PAPTE in the Selected Solvents at 0.1 MPaa solvent

T

103x

γ

102 (x − xcalcd)/x

0.326 0.393 0.445 0.494 0.552 0.613 0.686 0.751 0.798 0.847 0.928 0.329 0.395 0.465 0.540 0.630 0.721 0.814 0.912 1.030 1.130 1.252 0.331 0.397 0.507 0.613 0.737 0.855 1.001 1.147 1.328 1.523 1.709 0.119 0.151 0.188 0.231 0.282 0.342 0.396 0.470 0.552 0.655 0.755

4.9478 −0.1746 −0.2557 1.068 0.8380 0.4673 −1.505 −1.854 0.2058 1.610 −0.5976 0.8210 −0.0894 0.1315 0.3938 −0.4739 −0.4828 −0.0046 0.5282 −0.6118 0.4964 −0.1522 −1.148 2.543 −1.468 −1.261 −1.760 0.2462 0.2703 1.301 0.3877 −0.4824 −0.0939 −0.9875 −1.076 −1.251 −0.8591 −0.9647 −1.515 1.667 1.415 1.298 −0.6766 −0.5213

K MP

PP

MPA

MPP

MP

PP

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 293.15

PAPBE 0.3560 0.4471 0.5885 0.7821 1.0188 1.3197 1.6756 2.1536 2.8239 3.6660 4.5726 0.3531 0.4445 0.5643 0.7147 0.8926 1.1212 1.4117 1.7739 2.1865 2.7494 3.3889 0.3510 0.4429 0.5172 0.6301 0.7623 0.9451 1.1485 1.4094 1.6953 2.0391 2.4822 0.9736 1.1658 1.3929 1.6713 1.9927 2.3624 2.9029 3.4419 4.0808 4.7426 5.6230 PNBE 0.6088 0.7585 0.9355 1.1357 1.3790 1.6928 2.0369 2.5537 3.0455 3.7365 4.3174 0.5083

C

29.67 31.72 33.94 36.55 39.03 40.88 43.35 43.80 46.18 47.02 50.50 35.54

−3.568 −1.686 −0.6837 −1.112 −1.384 −0.3854 −1.245 2.149 0.7373 2.274 −2.003 −4.631



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Table 2. continued solvent

T

103x

γ


37.81 41.47 43.08 44.36 48.01 48.56 51.75 54.21 55.58 58.34 5.664 6.454 7.377 8.468 9.833 10.90 12.48 14.15 15.78 17.52 18.93 6.756 7.273 7.912 8.531 9.211 9.699 10.65 11.23 12.12 12.74 14.00

−2.649 −4.581 −1.591 1.526 −0.9189 2.801 0.8207 0.0092 0.8740 −1.063 −2.875 −0.3592 1.032 1.241 −0.3921 1.911 0.3942 −0.8175 −0.8890 −1.0216 0.9803 −1.856 −0.8213 −1.120 −0.7744 −0.8144 1.415 −0.7809 0.8859 0.0685 1.628 −1.326

0.424 0.438 0.458 0.487 0.494 0.527 0.538 0.557 0.574 0.595 0.614 4.307 3.891 3.690 3.492 3.225 2.982 2.741 2.581 2.394 2.207 2.065 13.32 12.09 10.89

−2.926 −0.5241 0.08823 −1.235 1.675 −0.8771 0.7791 0.6562 0.7373 −0.0609 −0.6710 −3.605 0.3613 −0.7815 −1.961 −0.8309 −0.0135 1.250 −0.0398 0.0328 0.6195 −0.4415 −1.531 −0.7576 0.5195

K

MPA

MPP

MP

PP

MPA

298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 293.15 298.15 303.15

PNBE 0.6364 0.7656 0.9638 1.2132 1.4415 1.8187 2.1613 2.5944 3.1608 3.7370 3.1898 3.7283 4.3041 4.9027 5.4739 6.3494 7.0761 7.9004 8.9095 10.027 11.514 2.6741 3.3088 4.0132 4.8671 5.8438 7.1360 8.2889 9.9546 11.602 13.781 15.573 PEPA 19.507 23.146 26.921 30.641 36.296 40.611 47.294 53.989 61.633 69.602 78.602 1.9199 2.6034 3.3414 4.2690 5.5562 7.1804 9.2853 11.658 14.783 18.776 23.375 0.6206 0.8379 1.1312

D



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Table 2. continued solvent

T

103x

γ


9.636 8.902 8.390 7.632 6.748 6.305 5.597 5.046 0.734 0.774 0.815 0.856 0.893 0.915 0.950 0.969 1.004 1.053 1.077

3.529 2.118 −1.438 −1.565 1.042 −1.951 0.1134 0.5511 −1.024 −0.7568 −0.8185 −1.040 −1.0145 0.5364 0.476 1.718 1.184 −0.8087 −0.6142

K

MPP

308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

PEPA 1.5473 2.0132 2.5527 3.3353 4.4591 5.6142 7.4031 9.5685 11.263 13.092 15.132 17.421 20.058 23.398 26.801 31.041 35.241 39.353 44.833

a The standard uncertainty of the measurement temperature is u(T) = 0.02 K. The relative standard uncertainty of the solubility measurement is ur(x) = 2 %.

x1 =

m1/M1 (m1/M1) + (m2 /M 2)

(1)

Here, m1 and m2 refers to the mass of solute and solvent, respectively. M1 and M2 are the molar mass of solute and solvent, respectively.

3. RESULTS AND DISCUSSION 3.1. Correlation of Solubility Data in Pure Solvents. The mole fraction solubilities (x) of PAPBE, PNBE, and PEPA in four organic solvents are listed in Table 2, and the corresponding solubility curves are shown in Figures 2 to 4. From Figures 2 to 4, it can be seen that the solubilities of flame retardants in four organic solvents all increase with increasing temperature. At ambient temperature, the orders of the solubilities for the solutes are as the follows. PAPBE: MPP > MP > PP > MPA. PNBE: MPA> MPP > MP > PP. PEPA: MP > MPP > PP > MPA. From these data, it can be seen that the orders and capacity of the different solutes dissolving in the same solvent are different. The polarity of the solvents, intermolecular interactions, and hydrogen bonds between solvent and solute affect the solubility behaviors of solutes in the solvents.20,21 PNBE and PEPA contain the NH group and OH group in the molecular structure, respectively. The solubilities of PNBE and PEPA are larger than PAPBE when they dissolved in alcohol ether solvents. The structure of PEPA containing hydroxyl group also can increase the solubilities when the solutes dissolve in the solvents containing hydroxyl group. The solubilities of PEPA in MP and MPP are largest than other solubility values. From the solubility measurement data, it can be seen that the solubility value of PAPBE in MPP is 9.7363 × 10−4. The solubilities of PAPBE in toluene and acetone are 5.0597 × 10−4 and 4.2414 × 10−4, respectively, at 293.15 K.4 Similarly, PNBE can dissolve more in MPP and MPA. It is solubilities in MPP

Figure 2. Mole fraction solubilities of PAPBE in selected solvents. Experimental data: ■, MP; ●, PP; ▲, MPA; ▼, MPP; solubility curve calculated from eq 2.

and MPA are 2.6741 × 10−3 and 3.1898 × 10−3, respectively, larger than that in toluene, 5.9234 × 10−4, at 293.15 K.5 The solubility value of PEPA in MPP is 1.1263 × 10−2, which is larger than the value in acetone, 8.87 × 10−3, at 293.15 K.6 Most of the solubilities of these flame retardants dissolved in MPP, MPA, and MP are larger than the solubility in acetone and toluene. It indicates that these alcohol ether solvents are good for adding these flame retardants in the process of epoxy resins materials. The solubilities against temperature can be correlated using the following modified Apelblat equation:22 ln x1 = A + B /T + C ln T

(2)

where x1 is the mole solubility of the solute, T is the equilibrium temperature, A, B, and C are the parameters of the E



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Table 3. Parameters of Eq 2 and Root-Mean-Square Deviations of the Measured Solubility Calculated from Eq 3 for PAPTE in the Selected Solvents solvent

Figure 3. Mole fraction solubilities of PNBE in selected solvents. Experimental data: ■, MP; ●, PP; ▲, MPA; ▼, MPP; solubility curve calculated from eq 2.

A

MP PP MPA acetate MPP

−101.75 −115.67 −153.43 −107.78


−118.24 −105.44 −64.801 9.4926


−52.377 −92.910 −99.761 −54.565

ln(x1γ1) =

B

ΔfusH1 ⎛ 1 1⎞ 1 ⎜⎜ − ⎟⎟ − R ⎝ Tm,1 T ⎠ RT T ΔCp,1 1 + dT R Tm,1 T

∫

RSD %

16.515 18.236 23.492 16.691

1.79 0.45 1.24 1.16

18.371 16.468 10.002 −0.49426

1.79 2.44 1.29 1.15

8.5604 15.326 16.419 8.8061

1.21 1.36 1.65 0.97

∫T

T

ΔCp,1dT

m,1

(4)

where T is equilibrium temperature; Tm and ΔfusH are the melting temperature and enthalpy of melting of the solute, respectively, x1 and γ1 are the mole fraction and the activity coefficient of solute at equilibrium; R is the ideal gas constant; ΔCp is the difference of molar heat capacity of solute between solid state in measurement temperature to liquid state in melting point. The activity coefficients of PAPBE, PNBE, and PEPA in the four organic solvents can be described using the solid−liquid equilibrium eq 4. In eq 4, the three terms on the right-hand side are not of equal importance. The first term occupies the main position and the remaining two containing ΔCp, of opposite sign, have a tendency to cancel each other. Therefore, eq 4 can be derived from an approximation23,24

Figure 4. Mole fraction solubilities of PEPA in selected solvents. Experimental data: ■, MP; ●, PP; ▲, MPA; ▼, MPP; solubility curve calculated from eq 2.

ln

equation. The values of the parameters are listed in Table 3. The relative standard deviations (RSD) can be used to distinguish the difference between measured values and calculated values as the following equation: 2 1/2 ⎡ ⎛ N exp calc ⎞ ⎤ x x − 1 RSD = ⎢ ⎜⎜∑ i exp i ⎟⎟ ⎥ ⎢N⎝ xi ⎠ ⎥⎦ i=1 ⎣

C

PAPBE −17.293 1208.7 3528.7 1769.9 PNBE 1910.22 1274.15 663.37 −3690.9 PEPA −46.953 −110.03 −259.48 19.067

⎞ Δ H ⎛T 1 = fus ⎜ m − 1⎟ ⎝ ⎠ x1γ1 RTm T

(5)

From the literature,4−6 the melting points of PAPBE, PNBE, and PEPA are 463.02 K, 383.11 K, and 485.29 K, respectively. The melting enthalpy of PAPBE, PNBE, and PEPA are 60.21 kJ·mol−1, 41.66 kJ·mol−1, and 29.5 kJ·mol−1, respectively. Using the experimental data, x1, Tm, ΔfusH, and T, the activity coefficients of PAPBE, PNBE, and PEPA in the selected solvents can be calculated, and are listed in Table 2. At the room temperature, the activity coefficients of PAPBE, PNBE, and PEPA have the lowest values in MPP, MPA, and MP at the same time show the largest values in MPA, PP, and MPA, respectively. The activity coefficients of solute can estimate the intermolecular interactions between solute and solvent. For the activity coefficient, a larger value shows a greater deviation compared with the ideal behavior. Under the circumstances, the intermolecular interactions of solute and solvent are weak, and specific chemical forces or polar between the solute particles are strong.

(3)

Here, N refers to the experimental points of each system. xexp and xcalc are the measurement values and calculated value of solubilities, respectively. The relative standard deviations (RSD) of PAPBE, PNBE, and PEPA are listed in Table 3. 3.2. Activity Coefficient Model. According to the rigorous thermodynamics equation, the solid−liquid phase equilibrium for nonelectrolyte solute can be described by the following equation23 F



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Table 4. UNIQUAC Volume Parameter, r, and Surface Parameter, q, Values for Selected Solvents and PAPBE, PNBE, and PEPA solvent or solute ethyl acetate acetonitrile i-propanol ethanol n-propanol acetone methanol chloroform

r

q 31

3.4786 1.870131 3.249131 2.105531 3.249931 2.573531 1.431131 2.870031

solvent or solute 31

3.116 1.72431 3.12431 1.97231 3.12831 2.33631 1.43231 2.41031

r

q 31

MP PP MPA MPP PAPBE PNBE PEPA

4.1674 5.516231 5.070531 6.435331 19.2174 21.2195 6.190932−34

3.90431 4.98431 4.43231 5.76831 14.3484 15.7205 5.40332−34

β21

RSD %

Table 5. Regressed Parameters and RSDs for the Wilson Equation solvent

α12

β12

α21 PAPBE

MP PP MPA MPP overall

−4392.0 5365.8 −13785 −52024

12.702 981.58 53.711 201.26


16617 −7008.1 −15746 74561

594.17 13334 30026 89.801

MP PP MPA MPP ethyl acetate acetonitrile i-propanol ethanol n-propanol aectone methanol chloroform overall

−7903.6 −4197.3 −1432.7 −90043 −2225.9 23748 −2277.4 2887.8 −3033.1 −20128 −6087.2 −533.23

1936.9 −22265 −15463 −28481

8.8964 49.419 37.073 64.392

1.32 2.21 1.20 0.77 1.38

−11086 −10522 −23095 −14208

44.973 46.923 74.681 46.792

1.27 1.63 1.40 2.09 1.60

−3.1700 −38.342 −19.386 10.733 −71.888 50.296 −40.239 −13.517 −44.431 4.2629 3.5310 38.646

0.82 0.79 1.34 0.64 0.72 0.27 0.43 0.53 0.38 0.14 0.28 0.23 0.55

PNBE

PEPA −2922.6 20660 15440 −5571.9 29879 −14721 17699 5506.5 20222 −145.82 −2719.2 −4268.3

34.673 3.7502 −3.0460 330.66 13.244 214.95 15.208 251.77 14.772 335.46 1111.1 3553.5

3.3. Correlation with Wilson, NRTL and UNIQUAC Models. The three activity coefficient models of the Wilson,25 NRTL,26 and UNIQUAC27 are usually useful for many practical calculations to associate the solid−liquid equilibrium properties of the nonideal solutions over a wide range of temperature.28−30 In previous studies, the binary interaction parameters of the Wilson equation (Δλ12 andΔλ21), the NRTL equation (Δg12 andΔg21), and the UNIQUAC equation (Δu12 andΔu21) are presumed have a linear relationship with the temperature17 kij = αij + βijT

Here, N refers to the number of data points in each measurement system. The optimization algorithm of minimizing eq 7 refers to the Levenberg−Marquardt method. The volume parameters (r) and the surface parameters (q) of the solutes and solvents are needed in the UNIQUAC model calculation. According to the Bondi group contribution method, the parameters of the selected solvents are calculated by the sum of the group volume and area parameters.31 The parameters of the solute can be calculated according to the bond distances and the van der Waals radii,32,33 by way of the geometric method from Bondi.34 In addition, the parameters r and q for PAPBE and PNBE has been listed in literature.4,5 The solubilities of PEPA in ethyl acetate, acetonitrile, i-propanol, ethanol, n-propanol, acetone, methanol, and chloroform had been measured in the literature,6 and the values of r and q of these solvents are also calculated by the literature.31 All the values of r and q of aforementioned materials are presented in Table 4. Tables 5, 6, and 7 show the optimized parameter values of three models and the correlation results of different models comparing with the overall relative standard deviation.

(6)

where k refers to the binary interaction parameter. The parameters of α and β can be fitted from the solubility data. The parameters of these three models can be achieved by correlating the solubility data with minimizing of the following objective function: N

f=

∑ (xiexp − xicalc)2 i=1

(7) G



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Table 6. Regressed Parameters and RSDs for the UNIQUAC Model solvent

α12

β12

α21

β21

RSD %

PAPBE MP PP MPA MPP overall

−4148.1 527.14 −4619.8 −3958.4

11.364 −6.4559 11.893 7.5461


−226.88 −484.72 −1283.8 −730.75

−5.4251 −4.8335 −2.7090 −5.0394

1741.8 4822.4 2555.1 −859.57 5857.5 −2616.2 3447.3 −6422.4 4146.4 73.093 −29831 −2377.9

3.6858 −4.7253 4.5671 −5.7998 −19.825 4.9848 −10.776 13.418 −11.088 −2.8835 37.491 19.432

3586.5 −4506.0 4106.9 3557.2

−9.6825 20.677 −9.4348 −5.6459

1.25 0.38 1.24 0.97 0.96

PNBE −17201 −12445 −1531.7 −4081.4

87.458 473.57 2329.5 276.31

1.19 1.17 1.24 0.94 1.14

−1325.3 −1454.8 −43.846 −72872 −1444.6 4500.2 −556.24 1793.4 −981.24 −276.82 2348.9 19.602

−2.4621 −1.3558 −6.0690 285.266 17.487 246.50 7.5341 −21.015 6.1381 12.831 −28.041 −14.722

0.83 0.88 1.37 0.63 0.78 0.17 0.46 0.42 0.43 0.14 0.04 0.14 0.52

β21

RSD %

−51.520 −47.064 97.447 −40.828

1.33 0.41 1.20 0.97 0.98

24.415 62.531 27.094 32.217

1.18 1.27 0.99 1.44 1.22

PEPA MP PP MPA MPP ethyl acetate acetonitrile i-propanol ethanol n-propanol aectone methanol chloroform overall

Table 7. Regressed Parameters and RSDs for the NRTL Modela solvent

α12

β12

α21 PAPBE


−35604 −37347 −20779 −41910


−1056.9 −8419.7 −21867 −13177

35.866 48.530 78.757 50.653

4678.8 20955 13969 −14879 29019 −14847 18071 5928.9 21090 117.01 −2387.9 −3438.6

5.7439 −35.543 −6.2654 38.127 −64.619 65.914 −38.985 −10.594 −43.136 6.0731 9.6936 36.950

110.95 114.98 55.079 120.35

15511 14865 −25939 13792 PNBE −8184.1 −11774 −131.33 −118.87 PEPA

MP PP MPA MPP ethyl acetate acetonitrile i-propanol ethanol n-propanol aectone methanol chloroform overall a

−4020.9 −4796.7 −365.44 −72266 78686 −20405 −1637.8 354.34 −2675.6 −428.09 −86.727 −4.8573

−2.4981 2.2276 −11.304 281.29 −2162.7 2286.7 10.011 37.233 8.7005 18.683 37.629 29.515

0.83 0.86 1.36 0.59 0.72 0.21 0.45 0.50 0.42 0.14 0.25 0.15 0.54

The value of the parameter a12 in NRTL equation is a12 = 0.3.

From these parameter values, it can be seen that these models can well reproduce these experimental results. On the basis of

the values of the overall relative standard deviation, the correlated results of different models are as follows. PAPBE: H



Article

volume. The computed result can be expressed by the following formula43

Wilson, 1.38 %; NRTL, 0.98 %; UNIQUAC, 0.96 %. PNBE: Wilson, 1.60 %; NRTL, 1.22 %; UNIQUAC, 1.14 %. PEPA: Wilson, 0.55 %; NRTL, 0.54 %; UNIQUAC, 0.52 %. The UNIQUAC model obtains the best correlation results according to the overall relative standard deviation. 3.4. Calculation of the Solubility Parameters. The solubility parameters can be used to select the solvents in the coatings industry. As well, they can be used in other industries to predict compatibility of polymers, permeation rates, and chemical resistance. They can also be used to characterize the surfaces of fibers, pigments, fillers, and so forth.35,36 The research on the solubility parameters of flame retardants are very important for their solubility in the solvents and matching with polymer dissolved. According to the experiment values, the solubility parameters of the solute can be obtained at a certain temperature based on the Scatchard−Hildebrand model.17 In previous studies of our research group, the solubility parameters of a lot of phosphorus flame retardants had been calculated by the determination of solubility. The calculated values (δS−H/(J cm−3)1/2) are listed in Table 8.4−6,37−41 However, the solubility parameters for a lot of

δ = (∑ Δei /∑ Δvi)0.5

Here, Δvi and Δei refer to the molar volume and energy of vaporization of the additived atomic and group contribution, respectively. These contributions applicable of group contribution method are listed in Table 9 at 298.15 K.43 The calculated Table 9. Atomic and Group Contributions to the Energy of Vaporization and the Molar Volume at 298.15 K

Ta

−3 1/2

K PPA MPPA HCCP HPCCP DDP THPPO PNBTE PAPBE PNBE BPEA DPDMO PEPA TCEP HPO HMPPA CEPPA TMOPP MDPPO TPPPO ODOPB

δS−H (J·cm )

303.15 303.15 303.15 303.15 293.15 313.15 293.15 b

293.15 293.15 c

313.15 313.15 308.15 303.15 303.15 303.15 303.15 303.15 303.15

25.437 24.137 23.237 22.737 23.9517 27.4938 23.3539 23.294 23.495 19.9140 23.2841 25.366 25.9837 32.9137 33.1637 33.0237 21.9337 16.537 17.9337 33.7737

δFd

Δvi −1

cal mol CH3 CH2 CH C phenyl phenylene (o, m, p) phenyl (trisubstituted) phenyl (tetrasubstituted) COOH NH N N CN O OH OH (disubstituted or on adjacent C atoms) PO4 PO3 Cl Cl (disubstituted) Cl (trisubstituted) Br Br (disubstituted) Br (trisubstituted) P

absolute error

(J·cm−3)1/2 29.73 25.93 26.84 24.35 27.26 28.71 22.89 22.09 22.48 19.78 23.77 27.23 26.25 27.76 31.46 27.79 21.95 21.30 22.35 32.25

Δei

atom or group

Table 8. Solubility Parameters Calculated by Scatchard− Hildebrand Model and Group Contribution Method and the Absolute Error of Two Calculation Methods compound

(8)

4.33 1.83 3.64 1.65 3.31 1.22 0.46 1.20 1.01 0.13 0.49 1.87 0.27 5.15 1.70 5.23 0.02 4.80 4.42 1.52

1125 1180 820 350 7630 7630 7630 7630 6600 2000 1000 2800 6100 800 7120 5220 5000 3400 2760 2300 1800 3700 2950 2550 2250

cm mol−1 3

33.5 16.1 −1.0 −19.2 71.4 52.4 33.4 14.4 28.5 4.5 −9.0 5.0 24.0 3.8 10.0 13.0 28.0 22.7 24.0 26.0 27.3 30.0 31.0 32.4 −1.0

results of the solubility parameters by group contribution method (δF/(J cm−3)1/2) are listed in Table 8. In addition, the absolute errors of two kinds of calculation methods of the Scatchard−Hildebrand model and the group contribution method have been calculated. The calculation results are shown in Table 8. From Table 8, it can be seen that part of the calculated values by group contribution method and Scatchard−Hildebrand model method approximately equal.

a Temperature correspond the values of δS−H/(J·cm−3)1/2. bTemperature in calculation process did not list in the literature, and the experiment temperature ranged from 293.15 K to 343.15 K. cThe result is an average value of the solute solubility parameters, and the measurement temperature ranged from 293.15 K to 333.15 K. d Temperature is 298.15 K.

4. CONCLUSIONS The solubility data of PAPBE, PNBE, and PEPA were measured by a static analytical method in four single organic solvents at different temperatures. The solubilities of PAPBE, PNBE, and PEPA in four organic solvents increase with the increasing temperature. At ambient temperature, the solubilities of three solutes were arranged in the following orders. PAPBE: MPP > MP > PP > MPA. PNBE: MPA> MPP > MP > PP. PEPA: MP > MPP > PP > MPA. Comparing the solubilities of the three flame retardants in the four solvents with the solubilities in acetone and toluene, the result shows that most of solubilities in four solvents are larger than the values in acetone and toluene. The experimental data were correlated by

materials still have not been obtained on the base of experimental measurements. The group contribution method is based on the hypothesis that the thermodynamic properties of the molecules can be estimated as the sum of each corresponding group they are composed of.42 The solubility parameters of materials can be calculated by the atomic and group contribution to the energy of vaporization and the molar I



Article

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the Scatchard−Hildebrand, UNIQUAC, Wilson, and NRTL model. The results showed that all the models are able to give satisfying correlations with optimized parameters. The UNIQUAC model shows the best overall correlation results. Using the group contribution methods, the solubility parameters of PAPBE, PNBE, and PEPA were predicted, which were in good match with the values from the Scatchard− Hildebrand model.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +86-10-68912660. Fax: +86-10-68911040. Notes

The authors declare no competing financial interest.

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REFERENCES

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K


Solubilities of Three Phosphorus Flame Retardants in Selected

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