Solubility of 1,3,2-dioxaphosphorinane-5,5-dimethyl-2-(2,4,6-tribromophenoxy)-2-oxide in selected solvents

Fluid Phase Equilibria 360 (2013) 97–105

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Solubility of 1,3,2-dioxaphosphorinane-5, 5-dimethyl-2-(2,4,6-tribromophenoxy)-2-oxide in selected solvents Gui-Qin Sun, Li-Sheng Wang ∗ , Jun-Chao Du, Chun-Mei Qi School of Chemical Engineering and Environment, Beijing Institute of Technology, Beijing 100081, PR China

a r t i c l e

i n f o

Article history: Received 18 May 2013 Received in revised form 3 August 2013 Accepted 11 September 2013 Available online 19 September 2013 Keywords: Phosphorus-containing flame retardant Synthesis Solubility Activity coefficient

a b s t r a c t A phosphorus-containing flame retardant, 5,5-dimethyl-1,3,2-dioxaphosphorinane-2-(2,4,6tribromophenoxy)-2-oxide(DPDMO), was synthesized successfully and characterized by elemental analysis (EA), mass spectra (MS), infrared spectroscopy (FT-IR) and nuclear magnetic resonance (1 H NMR and 13 C NMR). The melting point and the enthalpy of fusion of DPDMO were measured by differential scanning calorimeter (DSC), and the thermal stability of DPDMO was obtained by thermogravimetric analysis (TGA). The solubility of DPDMO in selected solvents could be achieved by a gravimetric method. The experimental data were correlated with some thermodynamic models, such as the empirical equation and the Scatchard–Hildebrand, Wilson, nonrandom two liquid (NRTL), universal quasi chemical (UNIQUAC), and Buchowski–Ksiazaczak (h) equation. The results show that the calculated values indicated good agreement with the experimental data. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Polymeric materials have been widely used in aerospace, electronic, mechanical, chemical and other fields because of their good heat endurance, chemical corrosion resistance, mechanical properties etc. However, polymeric materials are organic and thus combustible or flammable in air. Hence, the flame ability of the materials limits their applications. In order to prepare good thermal stability materials, the most common method is to add flame retardant additives into the materials, in which halogenated compounds, particularly brominated aromatic compounds, are the most widely used as flame retardant additives for polymeric materials [1,2]. In general, these additives with low cost are very effective. These properties have extremely attracted the attention of plastics formulators. However, some of these compounds such as pentabromodiphenyl ether and octabromodiphenyl ether have the potential negative environmental impaction. The environmentally friendly flame retardants are urgently demanded for the concerns about the use of some organobromine compounds. High effective FRs with lower levels of bromine are demanded to meet this concern. Organohalogen compounds working in gas phase can liberate hydrogen halide and halogen atoms which effectively scavenge oxygen and hydroxyl radicals when the polymer undergoes degradation [3]. While organophosphorus compounds working in the solid phase facilitate the formation of a protective layer at the

surface of the degrading polymer which inhibits heat feedback from the flame and limits the production of fuel fragments by thermal degradation of the polymers. Most flame retardants acting in solid phase can promote cross-linking and char formation by creating a carbon-carbon net work whereby chain cleavage, which produce s volatile components and thus retards the polymer materials [4,5]. Epoxy resin has been widely used in adhesive compositions and electric insulating sheets. The flame retardant epoxy resin can be prepared with the FRs dissolved in a solvent. Moreover, the purity of the FRs has great effect on its thermal stability. Knowledge of the solubilities of these compounds in different solvents is very important for their purification. However, to the best of our knowledge, no solubility data about DPDMO are found in the literature. In order to obtain more systematic and complete thermodynamic information on the crystallization of DPDMO from some organic solvents, the solubilities of DPDMO in the ten selected organic solvents were measured in this work. The well known models of Scatchard–Hildebrand, Wilson, non-random two-liquid (NRTL), UNIQUAC and h were adopted to correlate the experimental data. Comparison and discussion of the solubilities and the capabilities of the models were then carried out.

2. Experimental 2.1. Materials

∗ Corresponding author. Tel.: +86 1068912660; fax: +86 1068912660. E-mail address: [email protected] (L.-S. Wang). 0378-3812/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2013.09.023

In this work, all the raw materials used in the synthesis of DPDMO (its formula is shown in Fig. 1) included phosphorus

98

G.-Q. Sun et al. / Fluid Phase Equilibria 360 (2013) 97–105

Br O O

O P O

Br

Br

Fig. 1. Structure of 5,5-dimethyl-1,3,2-dioxaphosphorinane-2-(2,4,6tribromophenoxy)-2-oxide (DPDMO).

oxychloride, neopentyl glycol 2,4,6-tribromophenol and triethylamine. Phosphorus oxychloride was purchased from the Beijing Xingjin Chemical Reagent Factory (Beijing, China); neopentyl glycol was provided by the Sinopharm Chemical Reagent limited Factory (Shanghai, China); 2,4,6-tribromophenol was obtained from the Sinopharm Chemical Reagent limited Factory (Shanghai, China); triethylamine was supplied by Tianjin Bodi Chemical Reagent Company and sodium bicorbonate was got from Beijing Chemical Factory. Phosphorus oxychloride, neopentyl glycol, 2,4,6tribromophenol and triethylamine were analytical grade reagents. Their mass fraction purities were found to be more than 0.99. All of the solvents were analytical grade reagents, which were purchased from Beijing Chemical Factory. They were used without further purification. The water was double distilled before use. The sample descriptions are summarized in Table 1. The properties of organic solvents were reported in Table 1, including density, refractive index. The literature values of these properties should be listed in Table 1, and calculated the average error from the experimental values. 2.2. Apparatus and procedure The elemental analysis was carried out with a Vario EL III element analyzer. The mass spectrometer of the DPDMO was measured with A Bruker APEX IV mass spectrometer. The FT-IR spectrum was obtained from a Nicolet Magna-IR 750 infrared spectrophotometer using KBr pellets. The transmission mode was used, and the wavenumber range was set from 4000 to 400 cm−1 . 1 H NMR and 13 C NMR spectra were determined with a Bruker ARX-400

and JEOL ECA-600, respectively. The melting points and enthalpy of fusion were performed on a DSC Q100 (TA Instruments) differential scanning calorimeter under nitrogen atmosphere at a heating rate of 10 K min−1 . The uncertainty of DSC measurement was the same as that described in the literature13 . Thermogravimetric analysis (TGA) was recorded with a TGA SDT Q600 (TA Instruments) thermogravimetric analyzer with 3–5 mg samples from (294.22 to 866.35) K in flowing nitrogen at a heating rate of 10 K min−1 . The apparatus for the solubility measurement was the same as that described in the literature [6]. The schematic diagram of the experimental setup was shown in Fig. 5. A jacketed equilibrium cell with a working volume of 120 mL, a magnetic stirrer and a circulating water bath were used for the solubility measurement. The circulating water bath was used with a thermostat (type 50L, made from Shanghai Laboratory Instrument Works Co., Ltd.), which was able to maintain the temperature with an uncertainty of ±0.05 K. The mass measurements in the experiment were measured by an analytical balance (type TG328B, Shanghai Balance Instrument Works Co.) with an uncertainty of ±0.1 mg.

2.3. Synthesis and characterization 2.3.1. Synthesis of DOPC Scheme 1 shows the synthetic route of 5,5-dimethyl1,3,2-dioxaphosphorinane-2-(2,4,6-tribromophenoxy)-2-oxide (DPDMO). The intermediate 2-chloro-2-oxo-5,5-dimethyl1,3,2-dioxaphosphorinane (DOPC) was first synthesized as follows. Neopentyl glycol (28.2004 g, 0.271 mol) dissolved in trichloromethane (150 mL) and triethylamine (41.1577 g, 0.467 mol) was added in a dry, four-necked 500 mL flask equipped with a reflux condenser, a mechanical stirrer, a thermometer and a dropping funnel which was immersed in an ice water bath. Phosphorus oxychloride (43.7483 g, 0.285 mol) dispersed in trichloromethane (50 mL) was added dropwise to the reaction flask within about 2 h, and the temperature was maintained at 0–5 ◦ C. After the addition was completed, the reaction mixture was then rose to room temperature and refluxed for 4 h until no HCl gas could release. The solvent was evaporated under the vacuum state and the crude product was obtained. The residual of reactant (POCl3 ) was removed by washing several times with

Table 1 Sample properties and description. Chemical Name

Source

Density

Refractive index

Phosphorus oxychloride

Beijing Xingjin Chemical Reagent Factory Sinopharm Chemical Reagent limited Factory Sinopharm Chemical Reagent limited Factory Tianjin Bodi Chemical Reagent Company Beijing Chemical Factory Beijing Chemical Factory Beijing Chemical Factory Beijing Chemical Factory Beijing Chemical Factory Beijing Chemical Factory Beijing Chemical Factory Beijing Chemical Factory Beijing Chemical Factory Beijing Chemical Factory Beijing Chemical Factory Synthesis

—

—

—

Neopentyl glycol 2,4,6-Tribromophenol Triethylamine Sodium bicorbonate Methanol Acetone Tetrahydrofuran Acetonitrile Ethanol Toluene Ethyl acetate Dichloromethane Trichloromethane Methyl acetate DPDMO

The relative standard uncertainty u is ur (x) = 0.02.

Mole fraction purity

Purification method

Final mole fraction purity

Analysis method

99.0%

—

—

—

—

96.0%

Recrystallization

99.0%

Melting range

—

—

98.0%

Recrystallization

99.0%

Melting range

—

—

99.0%

—

—

—

— 0.7913 0.7908 0.8892 0.7875 0.7894 0.8660 0.9033 1.3265 1.4832 0.9185 —

— 1.3284 1.3591 1.4050 1.3460 1.3611 1.4960 1.3723 1.4246 1.4459 1.3614 —

99.8% 99.0% 99.0% 99.0% 99.0% 99.0% 99.0% 99.0% 99.0% 99.0% 99.0% —

— — — — — — — — — — — Recrystallization

— — — — — — — — — — — 99.0%

— — — — — — — — — — — Melting range

G.-Q. Sun et al. / Fluid Phase Equilibria 360 (2013) 97–105

99

Scheme 1. Synthesis scheme of DPDMO.

2.3.2. Synthesis of DPDMO DPDMO was synthesized by the reaction of 2,4,6tribromophenol with DOPC in the presence of trichloromethane. A mixture of DOPC (36.7235 g, 0.199 mol) dissolved in trichloromethane (150 mL) and triethylamine (25.1972 g, 0.249 mol) was added into a dry, four-necked 500 mL flask equipped with a reflux condenser, a mechanical stirrer, a thermometer and a dropping funnel. 2,4,6-tribromophenol (54.9120 g, 0.166 mol) dissolved in 30 mL trichloromethane was added into the reaction flask dropwise at 0–5 ◦ C within about 2 h. The solution was white, and the reaction flask had a large number of white smokes. After the addition was finished, the reaction was kept about 4 h. The ice bath was removed, and the reaction temperature then went up slowly to 60 ◦ C, then the reaction was stopped after refluxing for 8 h. After the solvent was dried under the vacuum state, the crude product was given. It could be purified further by repeatedly washing with aqueous solution of sodium bicarbonate and then washing with distilled water. Thus, the residual reactants and the salt (Et3 NHCl) were removed. After filtration, evaporation of filtrate, dried for overnight, the white power (DPDMO) with purity 98% was obtained [8] (yield: 85%).

was placed into an appropriate mass (about 1/3 of a jacketed equilibrium cell) of solvent. Then the jacketed equilibrium cell was heated to a constant temperature with continuously stirring. After at least 2 h (the solute fully dissolved and solid–liquid equilibrium 100

80

60

T/ %

aqueous solution of sodium carbonate. The intermediate (DOPC) precipitated in distilled water, filtered, and dried for overnight and a white powder was given [7] (yield: 94%).

40

20

0 4000

3500

The solubility of DPDMO was tested by a gravimetric method [9] as follows. For each measurement, an excess mass of the solute

2500

2000

1500

1000

500

-1

v / cm

2.3.3. Characterization of DPDMO The results of FT-IR, 1 H NMR and 13 C NMR of DPDMO were shown in Figs. 2–4. The elemental analysis (%, calcd): C, 27.55(27.59); H, 2.50(2.53); Br, 50.07(50.06); O, 13.39(13.36); P, 6.49(6.47). MS (EI) m/z: 479.90 (M + 1). FTIR (KBr, cm−1 ): 3061, 2968, 2941, 2893, 1317, 1072, 1054, 1028, 1009 990, 895. 1 H NMR (CDCl3 -d6 ), ı (ppm): 7.68 (s, 2H), 4.47 to 4.50(m, 2H), 4.02 to 4.10 (m, 2H), 1.35(s, 3H), 0.95(s, 3H); 13 C NMR (CDCl3 -d6 ): 115–150 (Ar C); 19.9, 21.6, 31.8 ( CH3 , CH2 and C ). Figs. 6 and 7 listed the results of DSC and TGA measurements of DPDMO. The melting point and the enthalpy of fusion of DPDMO were 460.41 K and 65.35 kJ g−1 , respectively. The uncertainty of the melting point measurement is 0.26 K and the relative uncertainty of the enthalpy of fusion of DPDMO is 0.30%. TGA results show that there was single step decomposition. The temperature of 5% decomposition was about 541.2 K; the temperature of 10% decomposition was about 549.8 K; the temperature of 50% decomposition was about 553.7 K; and about 14% char residue remains for DPDMO at 460.41 K. 2.4. Solubility measurement

3000

Fig. 2. FT-IR spectra of DPDMO.

16

14

12

10

8

6

4

2

0

δ / ppm Fig. 3.

1

H NMR spectra of DPDMO in CDCl3 .

-2

-4

100

G.-Q. Sun et al. / Fluid Phase Equilibria 360 (2013) 97–105

100

100W / %

80

60

40

20

250

200

150

100

50

0

-50

0 200

δ / ppm Fig. 4.

13

300

400

500

600

700

800

900

T/K

C NMR spectra of DPDMO in CDCl3 . Fig. 7. TGA thermograms of DPDMO under N2 .

injector was placed into a previously weighed vial (m0 ). The vial was quickly and tightly closed and weighed (m1 ) to determine the mass of the extracting solution (m1 − m0 ). Then the vial was lifted up the cap with a piece of filter paper covering to prevent dust contamination. After the solvent in the vial had completely evaporated, the vial was reweighed (m2 ) to determine the mass of the solute in the extracting solution (m2 − m0 ). So the mass of the solvent in the extracting solution was (m1 − m2 ). Thus, the mole fraction of the solute in the sample solution, x, could be determined from Eq. (1) [10]. x=

Fig. 5. Schematic diagram of the experimental apparatus.

was reached at this time), the stirring was stopped, and the solution was kept still until the solution was clear about 2 h. After the solute reached equilibrium with the solvent in the system, 2 mL of the clear upper portion of the solution with a preheated disposable 0

-65.35J/g

-2 -4

(m2 − m0 )/M1 (m2 − m0 )/M1 + (m1 − m2 )/M2

(1)

In which M1 an M2 represent the molar mass of the solute and the solvent, respectively. Different dissolution times were tested in order to determine an appropriate equilibrium time. The results show that 2 h was sufficient to reach equilibrium for DPDMO in all selected solvents. After three parallel measurements were carried out at the same solvent for each experiment temperature, an average value was taken. The minimum standard deviation of each triplicate data was 0.06%, and the maximum was 0.26%. Based on repeated observations and error analysis, the estimated relative uncertainty of the solubility values was within 0.16%. 3. Solubility of DPDMO

-6

3.1. Results and analysis

Q / mW

-8

The measured solubility data (the mole fraction x) of DPDMO in selected ten solvents were listed in Table 2 and the relation between ln x and 1/T is presented in Fig. 8. From this figure, it was found that the solubility increased with the increasing temperature. Under the condition of weak solution concentration, a frequently used empirical equation which correlated the natural logarithm of molar fraction solubility x against the reciprocal of the absolute temperature T was expressed as followed:

-10 -12 -14 -16 -18

460.41K

-20 250

300

350

400

450

500

550

600

T/K Fig. 6. Experimental heat Q flow from DSC measurement of DPDMO.

650

ln x =

A+B (T/K)

(2)

Parameters A and B in above equation for selected solvents based on Eq. (2) were summarized in Table 3. The calculated data from Eq. (2) are compared with the data listed in Table 2. The relative

G.-Q. Sun et al. / Fluid Phase Equilibria 360 (2013) 97–105

-2.0

Table 2 Molar fraction solubility (x) and activity coefficients () of DPDMO in selected solvents. T/K

x

␥

(x–xcal )/x

Methanol

293.15 298.15 303.15 308.15 313.15 323.15 333.15

0.00195 0.00240 0.00296 0.00354 0.00424 0.00614 0.00810

4.9903 5.0115 4.9916 5.0988 5.1728 5.1705 5.5466

−0.0137 −0.0046 0.0122 0.0035 0.0011 0.0242 −0.0244

293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.01306 0.01529 0.01709 0.01936 0.02264 0.02539 0.02951

0.7433 0.7863 0.8655 0.9331 0.9688 1.0420 1.0755

0.0041 0.0170 −0.0120 −0.0226 0.0028 −0.0093 0.0178

293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.02396 0.02583 0.03027 0.03291 0.03738 0.04090 0.04476

0.4052 0.4656 0.4887 0.5490 0.5867 0.6468 0.7091

0.0016 −0.0380 0.0107 0.0124 0.0118 0.0018 −0.0051

293.15 298.15 308.15 313.15 323.15 333.15 343.15

0.00399 0.00504 0.00755 0.00936 0.01283 0.01842 0.02645

2.4348 2.3853 2.3935 2.3430 2.4733 2.4380 2.3551

−0.0115 0.0086 0.0044 0.0250 −0.0299 −0.0159 0.0180

293.15 298.15 303.15 308.15 313.15 318.15 323.15 333.15

0.00250 0.00298 0.00358 0.00414 0.00465 0.00556 0.00643 0.00795

3.8817 4.0415 4.1287 4.3630 4.7205 4.7549 4.9392 5.6537

−0.0185 −0.0077 0.0201 0.0128 −0.0199 0.0177 0.0229 −0.0295

Toluene

293.15 298.15 303.15 313.15 323.15 333.15 343.15

0.00784 0.00900 0.01033 0.01446 0.01951 0.02680 0.03493

1.2389 1.3368 1.4322 1.5170 1.6269 1.6764 1.7836

0.0362 0.0000 −0.0315 −0.0164 −0.0187 0.0151 0.0131

Ethyl acetate

293.15 298.15 308.15 313.15 318.15 323.15 328.15 333.15

0.00497 0.00564 0.00748 0.00853 0.00951 0.01108 0.01266 0.01425

1.9553 2.1322 2.4161 2.5708 2.7829 2.8637 2.9914 3.1512

0.0163 −0.0041 −0.0034 −0.0056 −0.0273 0.0007 0.0114 0.0122

Dichloromethane

288.15 293.15 298.15 303.15 308.15

0.04918 0.05464 0.05940 0.06527 0.07119

0.1582 0.1777 0.2024 0.2266 0.2538

−0.0027 0.0061 −0.0035 0.0005 0.0001

Trichloromethane

288.15 293.15 298.15 303.15 308.15 313.15 318.15 328.15

0.08013 0.08442 0.08815 0.09467 0.10043 0.10642 0.11274 0.12367

0.0971 0.1150 0.1364 0.1562 0.1799 0.2061 0.2347 0.3061

0.0110 0.0008 −0.0165 −0.0033 −0.0007 0.0026 0.0073 −0.0012

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.00530 0.00649 0.00765 0.00867 0.01072 0.01186 0.01385 0.01632

1.4682 1.4951 1.5721 1.7068 1.6858 1.8486 1.9105 1.9449

−0.0143 0.0158 0.0121 −0.0254 0.0304 −0.0193 −0.0113 0.0104

Acetone

Tetrahydrofuran

Acetonitrile

Ethanol

Methyl acetate

Standard uncertainty: (T) = 0.1 K; (P) = 5%; (x) = 1%

-2.5 -3.0 -3.5 -4.0

lnX

Solvent

101

-4.5 -5.0 -5.5 -6.0 -6.5

0.0029

0.0030

0.0031

0.0032

0.0033

0.0034

0.0035

-1

K /T Fig. 8. Mole fraction solubility of DPDMO in selected solvents. Experimental data.

standard deviations (RSDs) of the measured solubilities, also listed in Table 3, were defined by Eq. (3).

⎡

1 RSD = ⎣ N N



1

xi − xical

2

xi

⎤1/2 ⎦

(3)

where the superscript “cal” stands for the calculated values and N is the number of experimental points. The RSDs of the measured solubility data of DPDMO were 1.58%. It can be seen from the results that Eq. (2) can be used to correlate the solubility data. As for the temperature effect for the solubility of DPDMO, within the temperature range of the measurements, it can be seen that the solubility of DPDMO in all of the selected solvents increased with an increasing temperature. It can be seen from the Fig. 8 that the solubility order of DPDMO in the select solvents at most temperatures is ranked as trichloromethane > dichloromethane > tetrahydrofuran > acetone > toluene > methyl acetate > acetonitrile > ethyl acetate > ethanol > methanol. Likewise, from the Fig. 8, as can be seen that trichloromethane displays the highest solubility for DPDMO and the solubility of DPDMO in methanol shows the lowest value, which was probably related to the rule of “Like dissolves like”[11–13]. DPDMO has a large solubility in low polar solvents because of its small polarity. The results that the mass of DPDMO dissolved in 100 g selected solvents are presented in Table 4. It can be seen from Table 4 that large solubilities of DPDMO were obtained in most selected solvents, especially in trichloromethane, dichloromethane, acetonitrile, tetrahydrofuran and acetone. DPDMO may be a good compatibility with polymer materials.

Table 3 Parameters of Eq. (2) and RSDs of DPDMO in selected solvents. Solvent

A

B

RSD/%

Methanol Acetone Tetrahydrofuran Acetonitrile Ethanol Toluene Ethyl acetate Dichloromethane Trichloromethane Methyl acetate

5.7360 4.2856 3.0704 7.2698 3.7429 5.5335 3.4957 2.6458 1.1251 4.9299

−3507.4 −2529.2 −1994.4 −3747.3 −2848.1 −3054.4 −2584.8 −1629.6 −1054.7 −2926.4

1.61 1.51 1.77 1.97 2.10 2.35 1.39 0.38 0.82 1.86

102

G.-Q. Sun et al. / Fluid Phase Equilibria 360 (2013) 97–105

Table 4 The mass of the solute DPDMO dissolved in 100 g each solvent at 298.15 K. Solvent

Table 5 Solubility parameter (ı), molar volume (V), UNIQUAC volume parameter (r), and surface parameter (q) values for selected solvents and DPDMO.

The mass of the solute DPDMO dissolved in 100 g each solvent/g

Methanol Acetone Tetrahydrofuran Acetonitrile Ethanol Toluene Ethyl acetate Dichloromethane Trichloromethane Methyl acetate

12.2035 25.0702 31.1179 31.7006 8.3251 18.8123 7.8602 43.2160 56.6082 10.7239

Solvent

ıi /(J cm−3 )1/2

106 Vi /m3 mol−1

r

q

Methanol Acetone Tetrahydrofuran Acetonitrile Ethanol Toluene Ethyl acetate Dichloromethane Trichloromethane Methyl acetate DPDMO

29.52 19.77 19.13 24.09 26.42 18.35 18.35 20.38 19.03 19.435 2.377

40.70 73.93 81.94 52.68 58.52 106.6 98.59 64.43 80.66 81.50 237.20

1.4311 2.5735 2.9415 1.8701 2.1055 3.9228 3.4786 2.2564 2.8700 2.8042 10.8179

1.432 2.336 2.720 1.724 1.972 2.968 3.116 1.988 2.410 2.576 8.513

3.2. Correlation with the empirical equation

3.4. Correlation with the Wilson, NRTL and UNIQUAC models

According to fluid phase equilibrium of molecular thermodynamics, the activity coefficients of DPDMO in the different solvent composition from the experimental data can be obtained. It was described by the following equilibrium equation [14].

The Wilson [17,18], NRTL [17–20], and UNIQUAC [21,22] activity coefficient models are applied in order to correlate the experimental solubility data through Eq. (4) in this study. These models have been successfully used to correlate the solid–liquid equilibrium properties for many nonideal solutions in wide temperature ranges [23–25].

fus H 1 = RTm x2 2

T

m

T



−1

(4)

In which Tm is the melting temperature; R is the gas constant; fus H refers to the enthalpy of fusion; and x2 and  2 are the mole fraction and activity coefficient of solute in the solution, respectively. With the experimental values of x2 , T, fus H, and Tm known, the activity coefficients  2 of DPDMO in different selected solvents were obtained. The results are listed in Table 2. It can be seen from the experimental data that the higher the temperature was, the greater the solubility was, and the larger activity coefficient was in all selected solvents. 3.3. Correlation with the Scatchard–Hildebrand model The Scatchard–Hildebrand model for the regular solution [15] (Eq. (4)) will be used to correlate the activity coefficients presented in Table 2. According to this model and a further simplification, the form of the equation in the study can be expressed as the following equation: ln 2 =

V2 2 2  (ı2 − ı1 ) RT 1

RT ln 2 V2 12

− ı21 = −2ı1 ı2 + ı22

gE = −x1 ln(x1 + ∧12 x2 ) − x2 ln(x2 + ∧21 x1 ) RT

(7)

The solubility of DPDMO changing with the solvent composition can be correlated by the Wilson equation [17,18]. The equation was expressed as follows. ln 2 = − ln(x2 + ∧21 x1 ) − x1



∧12 x1 + ∧12 x2



−

∧21 ∧21 x2 + x2

In the Eq. (7), 12 and 21 are given by ∧12 ≡



2 12 − 11 exp − 1 RT



=



2 12 exp − 1 RT

(8)



(5)

where V2 is the molar volume of the subcooled liquid at the temperature lower than melting point of pure solid solute;  2 is the activity coefficient of solute; ı1 and ı2 refer to the solubility parameters of the solvent and solute; T is the temperature in Kelvin; R is the gas constant; and 1 refers to the volume fraction of the solvent. The value V2 for DPDMO was calculated using advanced chemistry development (ACD/Laboratories) Software V11.02, which is listed in Table 5. The solubility parameter ı1 of the selected solvents was got from the literature [16]. A residual function Y can be rearranged from Eq. (5): Y=

3.4.1. Wilson model Based on the consideration of molecules, Wilson put forward an equation of excessive free energy for a binary system. The equation was given by

(6)

From the Eq. (5), it can be seen that there is a linear dependence between Y and ı1 in a given solvent at the temperature T. The value of ı2 can be got from the slope and intercept of this line, respectively. The linear relation between Y and ı1 at 298.15 K was shown in Fig. 9. The values of solubility parameter of DPDMO from (293.15 to 333.15) K indicate that ı2 tends to reach a constant within the range of measuring temperature. The average value of the solute solubility parameter ı2 is 23.277(J cm−3 )1/2 , which is also presented in Table 5.

-300

-400

-500

Y / J⋅cm-3

ln

-600

-700

-800

-900 18

20

22

24

26

28

30

-3 1/2

δsolvent / (Jcm ⋅ )

Fig. 9. Residual function Y for DPDMO versus solvent solubility parameter ısolvent .

G.-Q. Sun et al. / Fluid Phase Equilibria 360 (2013) 97–105

∧21



1 21 − 22 ≡ exp − 2 RT





1 21 = exp − 2 RT

(9)

where ij is the parameter in the Wilson model; x1 and x2 are the mole fraction of a solvent and a solute, respectively; 1 and 2 are the molar volume of a solvent and a solute, respectively. ij is solute and solvent interaction parameters. 3.4.2. NRTL model According to the concept of local composition, Renon and Prausnitz adopting the two-fluid theory of the equation came up with NRTL model [17–20]. The NRTL equation of excessive free energy was expressed as



GE

21 G21

12 G12 = x1 x2 + RT x1 + x2 G21 x2 + x1 G12

Table 6 Regression results of Wilson equations: parameter values of Eq. (22) and RSDs of DPDMO in selected solvents. Solvents

˛12

ˇ12

˛21

ˇ21

RSD/%

Methanol Acetone Tetrahydrofuran Acetonitrile Ethanol Toluene Ethyl acetate Dichloromethane Trichloromethane Methyl acetate Overall

−27,134 −6354.6 −810.69 −132.82 −7167.6 11,010 2734.4 1975.5 15,257 −13,633

407.93 18.601 37.282 14.517 12,073 −23.540 8790.8 −2.8131 −35.578 316.35

−2305.1 12,528 −14,019 −723.37 −7789.5 −12,779 −9947.1 −18,718 −28,665 −6915.9

−1.8241 −18.795 22.459 −4.1284 17.768 33.992 24.030 47.253 65.137 9.8724

1.5780 0.90550 1.4009 1.7360 2.0287 1.4259 1.1667 0.33115 0.49436 1.8651 1.29

(10) ϕ1 =

In the Eq. (10), Gij and ij are given by G12 = exp(−a12 ) 12 ,

12

G21 = exp(−a12 ) 21

g12 − g22 g12 = =− , RT RT

21

(11)

g21 − g11 g21 = =− RT RT



G12 x2 + x1 G12

2

+

G

2 21 21

(13)

x1 + x2 G21

where ij are the interaction parameters between the solvent and the solute in the NRTL model; gij similar to ij is a solute–solvent interaction parameter. x1 and x2 refer to the mole fraction of a solvent and a solute, respectively. In the experiment, a12 was taken as an adjustable parameter, which ranges between 0.20 and 0.47. 3.4.3. UNIQUAC model According to the concept of local composition, Abrams and Prausnitz [22] put forward the UNIQUAC model [20–22] in order to calculate the activity coefficient. The UNIQUAC equation was divided into a combinatorial part and a residual part.

r1 x1 , r1 x1 + r2 x2

ϕ2 =

u

12

12 = exp −

(12)

In the NRTL model [17–20], the following equation is used to correlate the activity coefficient of a solute in a pure solvent (the binary system including a solute and a solvent). ln 2 = x12 12

103

l1 =

RT

,

r2 x2 r1 x1 + r2 x2

u

21

21 = exp −

z (r1 − q1 ) − (r1 − 1), 2

(19)

l2 =

(20)

RT

z (r2 − q2 ) − (r2 − 1) 2

(21)

where ij is an adjustable parameter in the binary system; uij refers to a characteristic energy, which always only weakly depends on temperature; z is the coordination number which is usually taken as 10;  and ˚ refer to the molecular surface fraction and volume fraction of each component in the binary system, respectively; r and q refer to the volume and surface parameters for each component in the UNIQUAC models, respectively, which depend on the sizes of molecules and the external surface area molecular structure constant of the pure component. They can be calculated from the sum of the group volume and area parameters through the Bondi group contribution method [26]. The calculated values of r and q for all compounds are listed in Table 5. It was worthwhile to O

The activity coefficient in the UNIQUAC model by Eq. (14) can be expressed as

O P mention that structure parameters of a new group, , were calculated based on bond distances and the van der Waals radii got from the literature [27]. The results are summarized in Table 7. The cross-interaction parameters for a binary system are assumed to have a linear relation with the temperature in the Wilson equation (ij ), the NRTL equation (gij ) and the UNIQUAC equation (uij ), that is:

ln 2 = ln 2C + ln 2R

kij = ˛ij + ˇij T

GE = RT



GE RT

C

 +

GE RT

R (14)

(15) ln 2C

The combinatorial part of the activity coefficient attempts to describe the contributions of the dominating entropies for  2 , which are related to the compositions and sizes of the molecules. The combinatorial part can be expressed as ln 2C = ln

˚

2

x2

z + q2 ln 2



2 ˚2



+ ˚1



r2 l2 − l1 r1

(16)





12

21 − 2 + 1 12 1 + 2 21



(17)

In the Eq. (16) and (17) 1 =

q1 x1 , q1 x1 + q2 x2

2 =

q2 x2 q1 x1 + q2 x2

where k is any interaction parameter mentioned above. The parameters ˛ and ˇ are fitted from solubility data by minimizing the following objective function:

min f =

Np 

2 exp (ln i

− ln ical )

(23)

i=1

The residual part of the activity coefficient ln 2R is mainly due to the intermolecular forces of the mixing enthalpies, which are determined by the sizes of the molecules and the interactions between the solvent molecules and the solute molecules. ln 2R = q2 ln 2 + 1 12 + 1 q2

(22)

(18)

In which the superscripts “exp” and “cal” stand for the experimental and calculated values, respectively; Np is the number of data points for each solid–liquid equilibrium system. The natural logarithm of exp the experimental activity coefficient ln i was determined from Eq. (4) with the experimental solubility and melting properties of the solute. The optimization algorithm for minimizing Eq. (19) was used the Levenberg–Marquardt method. The optimized parameter values and the calculation results are listed in Table 6, Tables 8 and 9 for the Wilson model, NRTL model and UNIQUAC model, respectively.

104

G.-Q. Sun et al. / Fluid Phase Equilibria 360 (2013) 97–105

Table 7 Van der Waals group volume (r) and surface area (q) parameters for the UNIQUAC model. mol vol/Å3

Group CH2 O CH3 AC ACH

Surf. area/Å2

– – – –

– – – –

r

q

Solvents



0.9183a1 0.9011a2 0.3652a3 0.5313a4

0.780b1 0.848b2 0.120b3 0.400b4

1.5886

1.481

Methanol Acetone Tetrahydrofuran Acetonitrile Ethanol Toluene Ethyl acetate Dichloromethane Trichloromethane Methyl acetate

0.06 0.12 0.10 0.16 0.03 0.13 0.05 0.18 0.14 0.09

O O 1

1

2

P 2

3

40.019 3

4

61.491

4

a , b , a , b , a , b , a , b parameters are taken from the model of UNIFAC.

Table 8 Regression results of the NRTL equations: parameter values of Eq. (22) and RSDs of DPDMO in selected solvents. Solvents

˛12

ˇ12

˛21

ˇ21

RSD/%

Methanol Acetone Tetrahydrofuran Acetonitrile Ethanol Toluene Ethyl acetate Dichloromethane Trichloromethane Methyl acetate

−2155.5 6663.4 30,985 −705.36 −7260.0 −14,406 −3790.3 −14,825 −18,980 −6850.4

10.818 12.150 −45.654 10.586 36.048 43.855 41.112 34.011 36.724 32.113

−24.049 −6902.1 −11,491 −130.36 9,441,319 43.855 −3681.7 38,728 −12,612 −459.84

36.271 5.0020 15.891 −0.37794 −28,181 −37.113 −1.0283 −3.6505 59.581 −2.8650

1.5432 0.89393 1.2735 1.7354 1.3196 1.3801 0.72599 0.33175 0.78590 1.8558

Overall

1.19

3.5. Correlation with h model Buchowski et al. [28] studied the relationship between activity, solubility and temperature and then derived the solubility equation of solid–liquid equilibrium in a binary system. The solubility of DPDMO can also be correlated by the h model. The h equation is given as



ln 1 + 

1 − xA xA



sat

= h

1 T

−

1 Tm



(24)

In which x is the molar fraction at temperature T; Tm is the melting point of the solute;  and h are two adjustable parameters. Table 10 listed the optimized parameter values  and h. It can be seen that all the models can reproduce the experimental results well with the optimized parameters. The correlated results by different models were compared on the basis of the overall relative standard deviation. The results are as follows: Wilson, 1.29%; NRTL, 1.19%; UNIQUAC, 1.42%. The correlation deviation order based on the RSDs is NRTL < Wilson < UNIQUAC. The NRTL model gives the best correlation results because the RSD of the NRTL model is smallest in all equations. Table 9 Regression results of UNIQUAC equations: parameter values of Eq. (22) and RSDs of DPDMO in selected solvents. Solvents

˛12

ˇ12

˛21

ˇ21

RSD/%

Methanol Acetone Tetrahydrofuran Acetonitrile Ethanol Toluene Ethyl acetate Dichloromethane Trichloromethane Methyl acetate

−82.066 −601.78 −1126.8 17.620 −796.70 −2766.5 −1046.8 −1421.9 −1426.3 −745.53

−3.0985 6.1992 −4.5990 −2.0325 5.7326 −7.3834 −3.3615 −2.4848 −2.7507 1.6738

−1316.0 −913.99 −447.33 −268.98 3410.8 −63,319 743.82 966.50 −3013.1 −283.86

267.86 0.55403 493.83 9.2599 −6.0078 246.41 1139.4 9.9826 19.611 3.8469

1.3226 0.93115 1.9318 1.7294 1.9486 1.3917 1.4532 0.32741 1.2953 1.8584

Overall

Table 10 Regression results of h equations: parameter values of Eq. (24) and RSDs of DPDMO in selected solvents.

1.42

Overall

h 61,719.13 21,784.13 19,306.55 23,299.39 88,009.63 23,631.38 57,120.18 9576.01 8098.47 32,088.35

RSD/% 1.46 1.44 3.78 1.87 1.94 2.31 1.33 0.33 0.81 1.86 1.71

4. Conclusions The phosphorus-containing flame retardant (DPDMO) was synthesized successfully in high purity and its chemical structure was confirmed by EA, MS, FT-IR, 1 H NMR, and 13 C NMR. The measured solubility data of DPDMO in ten organic solvents measured by a gravimetric method have been correlated with the Scatchard–Hildebrand, Wilson, NRTL, UNIQUAC and h models. All the models are able of giving good agreements with optimized parameters. The experimental results were compared. The solubility order of DPDMO in the select solvents at most temperatures is ranked as trichloromethane > dichloromethane > tetrahydrofuran > acetone > toluene > methyl acetate > acetonitrile > ethyl acetate > ethanol > methanol. The results show that DPDMO in trichloromethane has the highest solubility while in methanol has the lowest value. The solubility of DPDMO in all solvents increases with the increasing temperature. The NRTL equation gives the best overall correlation results with an overall relative standard deviation of 1.19%. List of symbols

x1 x2 xcal A, B RSD T Tm R fus H 2 ı1 ı2 1 V2

the mole fraction of selected solvents the mole fraction of the solute DPDMO the calculated mole fraction the parameters of the empirical equation the relative standard deviation the experimental temperature the melting temperature the gas constant the enthalpy of fusion the activity coefficient of the solute DPDMO the solubility parameters of the solute DPDMO the solubility parameters of the selected solvents the volume fraction of selected solvents the molar volume of the subcooled liquid of pure solid solute 12 , 21 two adjustable parameters in the Wilson model the molar volume of the selected solvents 1 2 the molar volume of the solute DPDMO 12 , 21 the solute and solvent interaction parameters in the Wilson model

12 , 21 the interaction parameters between the solvent and the solute in the NRTL models a12 an adjustable parameter, g12 , g21 : the solute and solvent interaction parameters in the NRTL model ln 2C the combinatorial part of the activity coefficient the residual part of the activity coefficient ln 2R

G.-Q. Sun et al. / Fluid Phase Equilibria 360 (2013) 97–105

12 , 21 the interaction parameters between the solvent and the solute in the UNIQUAC models z the coordination number ˚ the volume fraction of each component in the UNIQUAC models the molecular surface fraction of each component in the  UNIQUAC models r the volume parameters for each component in the UNIQUAC models the surface parameters for each component in the UNIq QUAC models u12 , u21 two adjustable energy parameters ˛12 , ˇ12 , ˛21 , ˇ21 the optimized parameter of for the Wilson model, NRTL model and UNIQUAC model , h two adjustable parameters for the h equation References [1] L.S. Wang, H.B. Kang, S.B. Wang, Y. Liu, R. Wang, Fluid Phase Equilib. 258 (2007) 99–107. [2] A. Siriviriyanun, E.A. O’Rear, N.J. Yanumet, Appl. Polym. Sci. 109 (2008) 3859–3866. [3] A. Tewarson, J. Fire Flammability 8 (1997) 115–119. [4] E.D. Weil, S. Levchik, J. Fire Sci 22 (2004) 339–342. [5] B.A. Howell, Y. Cui, D.B. Priddy, J. Therm. Anal. Cal. 17 (2004) 313–317.

105

[6] N.N. Tian, L.S. Wang, M.Y. Li, Y. Li, R.Y. Jiang, J. Chem. Eng. Data 56 (2011) 661–670. [7] S. Zhang, B. Li, M. Lin, Q. Li, S. Gao, W. Yi, J. Appl. Polym. Sci. 122 (2011) 3430–3439. [8] Y. Tang, D. Wang, X. Jing, X. Ge, B. Yang, Y. Wang, J. Appl. Polym. Sci. 108 (2008) 1216–1222. [9] Z.W. Wang, Q.X. Sun, J.S. Wu, L.S. Wang, J. Chem. Eng. Data 48 (2003) 1073–1075. [10] M.J. Zhu, Chem. Eng. Data 46 (2001) 175–176. [11] W.L. Smith, C.J. Colby, Chem. Educ. 54 (1977) 228–229. [12] R. Schmid, Monatsh. Chem. 132 (2001) 1295–1326. [13] I. Montes, C. Lai, D. Sanabria, J. Chem. Educ. 80 (2003) 447–449. [14] J.M. Prausnitz, R.N. Lichtenthaler, E.G. Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, third ed., Prentice Hall, New York, 1999. [15] P.B. Chol, E. Mclaughlln, Ind. Eng. Chem. Fundam. 22 (1983) 46–51. [16] C.L. Yaws, Chemical Properties Handbook, McGraw-Hill, USA, 1999. [17] B.W. Long, J. Li, R.R. Zhang, L. Wan, Fluid Phase Equilib. 297 (2010) 113–120. [18] S.H. Ali, O.A. Al-Rashed, Fluid Phase Equilib. 281 (2009) 133–143. [19] S. Jang, S. Hyeong, M.S. Shin, Fluid Phase Equilib. 298 (2010) 270–275. [20] Y.H. Ji, W.J. Huang, X.H. Lu, Fluid Phase Equilib. 297 (2010) 210–214. [21] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144. [22] D.S. Abrams, J.M. Prausnitz, AIChE J. 21 (1975) 116–128. [23] D.W. Wei, Y.H. Pei, Ind. Eng. Chem. Res. 47 (2008) 8953–8956. [24] D.W. Wei, H. Li, C. Liu, B. Wang, Ind. Eng. Chem. Res. 50 (2011) 2473–2477. [25] S.N. Chen, Q. Xia, L.F. Liu, M.S. Zhang, Y.S. Chen, F.Z. Zhang, G.L. Zhang, J. Chem. Eng. Data 55 (2010) 1411–1415. [26] B.E. Poling, J.M. Prausnitz, J.P. O’Connell, The Properties of Gases and Liquids, fifth ed., McGraw-Hill, New York, 2001. [27] X.Z. Shao, L.S. Wang, M.Y. Li, Ind. Eng. Chem. Res. 51 (2012) 5082–5089. [28] H. Buchowski, A. Kslazcak, S.J. Pletrzyk, Phys. Chem. 84 (1980) 975–979.