Solubility Measurement Study on a Metastable Polymorph of Î²-2,4,6,8

Subscriber access provided by Lancaster University Library

Article

Solubility measurement study on a metastable polymorph of #-2,4,6,8,10,12-hexanitro-2,4,6,8,10,12hexaazaisowurtzitane by Raman spectroscopy In-Ho Park, Hee-Og Yang, Jun-Hyung Kim, and Kwang-Joo Kim Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.9b00245 • Publication Date (Web): 25 Jul 2019 Downloaded from pubs.acs.org on August 5, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Crystal Growth & Design

Solubility measurement study on a metastable polymorph of β-2,4,6,8,10,12hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane by Raman spectroscopy In-Ho Park1, Hee-Og Yang1, Jun-Hyung Kim2, Kwang-Joo Kim1, * Department of Biological and Chemical Engineering, Hanbat National University, 125 Dongseodaero, Yuseonggu, Daejeon 305-718, Korea 1

2

Agency for Defense Development, 462 Jochiwon-gil, Yuseong-gu, Daejeon 305-150, Republic of Korea

*Correspondence: Kwang-Joo Kim (E-mail: [email protected]), Department of Biological and Chemical Engineering, Hanbat National University, Daejeon, Korea

ABSTRACT Raman spectroscopy was used to measure the solubility of the metastable form of 2,4,6,8,10,12-hexanitro2,4,6,8,10,12-hexaazaisowurtzitane (HNIW) in organic binary solvent mixtures. The distinct Raman spectra peaks of the solid, solute, solution, and solvent were investigated. Peaks that weren’t overlapping each other were used to develop a calibration curve. Then, linear relationships between solution concentration and Raman intensity were used to measure the solubility of HNIW in binary solvent mixtures during the dissolving process. The solubility of HNIW in binary solvent mixtures (ethyl acetate + n-hetpane, ethyl acetate + 1,1,2-trichloroethane, ethyl acetate + cyclohexane, ethyl acetate + toluene, ethyl acetate + diethyl ether, and ethyl acetate + petroleum ether) were investigated. The temperature ranged from 283.15K to 333.15K at atmospheric pressure. The solubility of HNIW in binary solvent mixtures decreases with increasing temperature. In order to correlate the solubility of -HNIW, the combined nearly ideal binary solvent/Redlich-Kister (CNIBS/R-K) model and Jouyban-Acree model were employed. The Jouyban-Acree model is in better agreement with experimental solubility for all of the binary solvent mixtures. The average relative error is less than 0.05. Dissolution enthalpy and entropy were determined using the van’t Hoff equation.

 INTRODUCTION 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (HNIW) is a high-density, high-energy, ecofriendly, less-sensitive material used in propellants and non-nuclear explosives.1 The chemical structures of its  and  forms are shown in Fig. 1.2 It meets the stringent munitions sensitivity requirements and has a higher energy content than cyclotetramethylenetetranitramine (HMX) and cyclotrimethylenetrinitramine (RDX), which are commonly used. Raman spectroscopy is a widely used technique for quantitative analysis and qualitative monitoring of chemical reactions in solution, and has also been applied extensively to the characterization of polymorphic systems. Almost every molecular species other than metals and simple salts produces Raman spectra.3,4 Therefore, it’s suitable for analysis in order to measure in situ the solubility of metastable –HNIW in organic binary solvent mixtures. Supersaturation is a parameter that effects nucleation rate, as well as crystal growth and polymorphic transformation kinetics.5 The supersaturation state, which is calculated from the solubility and solution concentration, is an essential requirement for all crystallization operations.6 Therefore, it is important to be able to measure the solubility that determines supersaturation in order to understand the crystallization process. HNIW in ethyl acetate exists in   and  forms, where the  form is stable above 353.15K and the  form is stable below 353.15K. HNIW obeys Ostwald’s rule of stages, so HNIW in ethyl acetate, which has a high supersaturation, precipitates initially as the  form, and is then transformed to the  form through a solution-mediated process. 7 Solubility data for metastable polymorphs of energetic materials are rarely reported. When the metastable form is suspended in saturated solution, the transformation to the stable form can occur. Thus it is difficult to measure solubility data for metastable polymorphs. In order to measure solubility of the metastable form, the experiment requires sufficient time for equilibration to be reached and ensure that the solid form is still is the metastable form.

ACS Paragon Plus Environment

Crystal Growth & Design 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Thus, to measure solubility of metastable forms, it is necessary to measure in line both the solution phase and solid phase at the same time. The solubility of the metastable form is measured to reach equilibrium at a temperature. There are many methods for measuring solute concentration, such as gravimetric analysis,8 titration,9 UV−vis spectroscopy,10 HPLC11 or solution density. Alternatively, methods for measuring equilibrium temperature at a component concentration, include the synthetic method,12 differential scanning calorimetry (DSC),13 in-situ infrared spectroscopy,14 and microscopic methods.15 Raman spectroscopy is a light scattering technique whereby a monochromatic source (laser) illuminates the sample and the resulting scattered light is collected and analyzed. Photon interaction with the molecular vibrations of a sample causes the light to be shifted to a wavelength away from the wavelength of the incident laser. Thus the Raman technique can be used to determine the chemical structure (polymorph) by the detection of molecular vibrations of characteristic frequency. Therefore, the solubility of the metastable form of -HNIW in binary solvent mixtures has to been measured by Raman spectroscopy using a calibration curve. The solubility of HNIW in ethyl acetate is rarely affected by temperature, so polymorphic control is carried out through anti-solvent crystallization, which lowers the solubility of the solution by adding a rarely soluble solvent.16 In this study, solubility in binary solvent mixtures containing ethyl acetate as the solvent was measured. In this study, both of these approaches for measuring polymorph solubility are presented. The gravimetric method was used as a comparative method to measure solubility. Due to transformation of the  form polymorph to the  form in bulk experiments, where the  form nucleated immediately with no induction time, it was decided to measure the  form solubility using in-situ Raman spectroscopy. Solubility data for -HNIW in six binary solvent mixtures (ethyl acetate + n-heptane, ethyl acetate + 1,1,2-trichloroethane, ethyl acetate + cyclohexane, ethyl acetate + toluene ethyl acetate + diethyl ether, and ethyl acetate + petroleum ether) were measured by Raman spectroscopy at temperatures ranging between 283.15K and 333.15K at atmospheric pressure. Experimental data were correlated to the CNIBS/R-K model and Jouyban-Acree model for binary solvent mixtures. Experimental data were correlated using the modified Apelblat equation, and the dissolution enthalpy and entropy of -HNIW were estimated using the van't Hoff equation.

 EXPERIMENTAL SECTION Materials. HNIW was supplied by the Agency for Defense Development, with a mole fraction purity of 99.9 wt%. In this study, HNIW used in experiments was prepared by anti-solvent crystallization, which involved crystallization by injecting IPA into acetone-dissolved HNIW at a certain mass ratio.16 All organic solvents, including ethyl acetate, n-heptane 1,1,2-trichloroethane, cyclohexane, toluene, diethyl ether, petroleum ether, isopropyl alcohol, and acetone were analytic grade and purchased from Aldrich. All HNIW samples were used without further purification. Metastable -HNIW Preparation. As metastable -HNIW formation was reported in a previous study16, preparation was performed through anti-solvent crystallization using isopropanol and acetone. The experiment was carried out by a reverse anti-solvent crystallization method. After the  form crystals (25g) were dissolved in 50g of acetone at 35oC, the HNIW solution was then cooled to 20oC. The operating temperature was set to 20oC by adjusting the temperature of IPA in the vessel using a thermostat, before adding the HNIW solution. The HNIW solution was then fed into 250g of agitated IPA in less than 1 s. During experiments, Raman peaks and temperature were recorded at 5-s intervals. Crystals were separated after one minute using a solid-liquid separator with a glass filter, and dried at 50oC for 24 h under full vacuum. XRD and Raman spectroscopy were used to confirm the polymorphic form of the product. The purity of the prepared  form was shown to be above 0.998 in mass fraction using HPLC (Prominence UFLC XR, Shimadzu Corp.). Solubility measurements method. The gravimetric method was used as a comparative method to measure solubility. Solubilities of the β form were measured by adding excess β form to approximately 50mL of solvent in a sealed test tube. Isothermal temperature was adjusted at each temperature using a thermostatic bath. The test tube was placed in the bath and stirred using a magnetic stirrer bar. After 24 h at a specific temperature agitation was stopped and undissolved solids were allowed to settle for 30 min. A 5-mL sample of the solution was taken, carefully filtered (0.22-μm filter) into a pre-weighed vial and then weighed to determine the solution mass. After drying in a fume hood, the vials were transferred to a vacuum oven set at 40°C for 24 h. The last hour of drying was carried out under vacuum at below 10kPa. This removed the solvent completely, achieving perfect dryness.16 The remaining solute was weighed, and the concentration was expressed as g of solute/g of solvent. Each solution was sampled in triplicate. Weighing was carried out using a balance (Mettler-Toledo) with a readability of 0.1 mg. A solid sample was also vacuum-filtered at the time of solution sampling and analyzed by Raman spectroscopy to identify the solid phase that was present in suspension in the solution. The solubility of the


Page 2 of 49

Page 3 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


metastable β form of HNIW was measured at 10, 20, 30, 40 and 50°C, respectively. The mass of the β form added in excess at each temperature was equal to the amount of HNIW already dissolved to make the solution saturated with respective. Each solution was tested in triplicate. At the same time of solution sampling a small sample of excess solid was vacuum-filtered and analyzed by PXRD. The Kaiser Raman spectra were recorded on the Raman RXN Systems (Kaiser Optical Systems, Ann Arbor MI, USA) equipped with a light-emitting diode laser (785nm, 450mW) as an excitation source. A one-fold objective lens with probe was used to collect the spectra. The spectra of this system were in the range of 100−1 to 1890cm−1, and spectra were acquired using a spectral width of 4 cm−1 and 5-s exposure. The iCRaman software (MettlerToledo) was used in combination with this system. Analysis of Raman data to determine concentration was performed by searching for the absence and occurrence of peaks originally found in spectra of the individual components. To predict the concentration of the solid and solution, the multivariate PLS (partial least square) model supplied in the iCRaman software was used. A Raman spectrometer (Kaiser Optical systems, Ann, Mi, USA) equipped with a light-emitting diode laser (785nm, 450mW) was used in order to measure the solubility of β-HNIW in binary solvent mixtures. The powder X-ray diffraction (XRD) pattern of the solid was calculated using a SmartLab X-ray diffractometer (Rigaku) with Cu Kα radiation generated at 200mA and 45kV. The sample was placed on a silicone plate at room temperature. Data were collected from 3° to 45° (2θ) at a step size of 0.02° and scan rate of 5°/min. -HNIW solids and solution, as well as the solvent have characteristic Raman spectra, where Raman spectra of the solution that weren’t overlapped by others are selected to develop the calibration curve as a function of solution concentration. 100mL of the binary solvent mixtures were placed in a double-jacket glass with a Raman probe. The double-jacket glass was kept at a constant temperature using a thermostat (RAUDA, K-4/R) with an accuracy of 0.1K. Then, the binary solvent mixtures that were measured through in-situ monitoring with a Raman spectrometer had excess -HNIW added to them and were then stirred by a mechanical stirrer. Linear relationships between the concentration of solution and Raman intensity were then used to measure the solubility of HNIW in binary solvent mixtures during the dissolving process. All experiments were conducted three times and the mean value was taken as the solubility. Solubility measurements using Raman spectroscopy. In order to measure the solubility of the β form, an experimental setup previously developed to investigate solution-mediated phase transitions of HNIW poymorphs was used.16,17 The setup consists of a Raman spectrometer (Kaiser Optical Systems, Ann Arbor MI, USA) used in conjunction with a temperature controller (±0.1°C) in a jacketed vessel. The vessel was used to hold and seal a quiescent solution sample in which a single crystal of the β form could be observed. In situ measurement of solid and solution was used to obtain the solubility measurements.17 The in situ Raman method typically involves producing a solution of known concentration/ composition and varying the temperature until the point of equilibrium is reached, where crystals neither dissolve nor grow.18 The in situ Raman method requires examining for the point of equilibrium under isothermal conditions, where the solution concentration is varied for each experiment. For this method, a temperature was chosen at which to measure the solubility of the β form. A solution of known concentration was prepared in the vessel by accurately weighing HNIW and solvent to an approximate volume of 100mL.

 RESULTS AND DISCUSSION Characterization of materials. The powder X-ray diffraction (PXRD; D/MAX 2500H, Rigaku) pattern of HNIW used in this study is shown in Fig. 2. A comparison of the PXRD pattern of HNIW used in this study with that from the literature showed that the PXRD pattern of HNIW has the same characteristic peaks at 2θ of 12.6°, 12.8°, 13.8°, 15.7°, 19.9°, 22.0°, 25.8°, 27.8°, 29.9°, and 30.3°. Furthermore, a comparison of the PXRD pattern of -HNIW used in this study with that from the literature showed that the PXRD pattern of HNIW has the same characteristic peaks at 2θ of 12.1°, 13.8°, 15.1°, 20.2°, and 28.0°.19 The Raman spectra of β,-HNIW measured by a Raman spectrometer (Kaiser Optical Systems, Ann, MI, USA) equipped with a light-emitting diode laser (785nm, 450mW) are shown in Fig. 3. Compared with the Raman spectra of -HNIW from the literature, the Raman spectra of -HNIW show the same Raman feature at 219cm-1, 264cm-1, 318cm-1, 344cm-1, 369cm-1, 446cm-1, 465cm-1, 527cm-1, 580cm-1, 591cm-1, 912cm-1, 940cm-1, 1608cm1, and 1625cm-1. Furthermore, the Raman spectra of β–HNIW show the same Raman feature at 282cm-1 , 805cm-1, 1076cm-1, 1130cm-1, and 1188cm-1.20 Therefore, that characteristic peaks of β,-HNIW were chosen as 282cm-1,



and 344cm-1, respectively. Calibration and analysis of Raman spectroscopic data. The Raman spectra of the solvent, solution and β,HNIW measured by Raman spectroscopy are shown in Figs. 3-5. These show that Raman spectra of HNIW dissolved in solvent have distinct peaks at 216cm-1, 310cm-1, and 1612cm-1. Raman spectra of ethyl acetate were found to be at 373cm-1, 418cm-1, 1742cm-1. Therefore, in order to obtain the calibration curve, multiple distinct peaks (216cm-1, 310cm-1, and 1612cm-1) for HNIW dissolved in solution were chosen. This PLS technique was used in order to calculate the solubility of HNIW. The Raman spectra of the solution were measured in solutions in which 0-50g of HNIW was completely dissolved in 100g of solvent ethyl acetate. Raman spectra were collected at various fractions of solute/solvent for the HNIW concentration range of 0-0.5mg/mg. Measurements were taken at a set temperature using a jacketed glass vessel controlled by a thermostatic circulation bath. Peaks at approximately 216cm-1, 310cm-1, and 1612cm-1 were used to measure solution concentration. Spectra were normalized to the intensity difference of the solvent peak and valley at 418cm-1. Fig. 6 shows that the predicted HNIW concentration in solution was calculated using the linear relationship of the concentration of HNIW dissolved in solution with the Raman intensity of the peak of HNIW dissolved in solution per solvent (ethyl acetate) peak that had a distinct peak at 418cm-1. The PLS technique is useful for ignoring the weak effect of temperature, crystal size, solution density, or unpredictable variables. The calibration curve of HNIW in solution shows a correlation coefficient of 0.9997 and root mean square error calibration (RMSEC) of 0.0049. A calibration line using Raman spectra from slurries dispersed under stirring in the saturated solution was developed. However, transformations in Raman spectra were found while measuring the  form. Before the transformation occurs, the solid fraction was determined using Raman spectra of the slurries. The validity of the calibration line for in-situ measurements was confirmed by comparing the results of in-situ and off-line Raman measurements. Spectra were normalized to the intensity difference of the solvent peak and valley at 418cm-1. The Raman spectra of HNIW have distinct peaks at 344cm-1 and 282cm-1, respectively. The calibration curve of HNIW concentration shows a correlation coefficient of 0.9941 and 0.9978 and RMSEC of 0.0154 and 0.0160, respectively. Figs. 7-8 show the calibration curve results for solid -HNIW and -HNIW, respectively, and show good agreement between predicted concentration and actual concentration. The solubility of HNIW in binary solvent mixtures measured by the gravimetric method was compared with the solubility of HNIW in binary solvent mixtures measured by Raman spectroscopy. The solubility of HNIW measured by the gravimetric method in binary solvent mixtures (ethyl acetate + n-heptane) as a function of ethyl acetate in the absence of a solute is in good agreement with the solubility of HNIW measured by Raman spectroscopy in binary solvent mixtures (ethyl acetate + n-heptane), as shown in Fig. 9, so it’s suitable for use in determining the solubility of βHNIW in binary solvent mixtures. Solubility is the concentration at which no change in the HNIW polymorphs was observed, before nucleation of the  form. This method was then repeated to measure the solubility of the β form at other temperatures. The nucleation and growth of the  form was easily detected in Raman peaks. The in-situ concentrations of HNIW, HNIW and solubility of HNIW in binary solvent mixtures (ethyl acetate:n-heptane, 1:3 w/w) were measured at 298.15K using Raman spectroscopy, and are shown in Fig. 10. 5 g of -HNIW solids are injected into 100 g of solvent. After the injection, -HNIW solid starts to dissolve. 0.0204g of -HNIW solid dissolve and 0.0296g of -HNIW solid does not dissolve (see red curve) in equilibrium. At about 3890 seconds, the -HNIW solid starts to decrease sharply (see red curve) and is transformed into -HNIW solid (see blue curve). As -HNIW crystals increase in the transformation process, the solute concentration decreases to 0.0131 g / g. As a result, the solubility of -HNIW is 0.0204 g / g and the solubility of -HNIW is 0.0131 g / g. This is due to the fact that HNIW is more thermodynamically stable than HNIW in organic solvents so HNIW is less soluble than HNIW. It has a good correlation with the solubility of HNIW calculated through regression analysis using the CNIBS/R-K model. The Raman waterfall plot under the same conditions as Fig. 10 is shown in Fig. 11. It shows that the Raman shift peak at 282cm-1 disappeared and the peak at 344cm-1 appeared at 1hr 20min. This indicates that β-HNIW in binary solvent mixtures (ethyl acetate + n-heptane) was transformed to -HNIW from 3360 s to 5460 s. The mole fraction solubility of -HNIW in binary solvent mixtures was calculated by,


Page 4 of 49

Page 5 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


𝑚1/𝑀1

(1)

𝑥1 = 𝑚1/𝑀1 + 𝑚2/𝑀2 + 𝑚3/𝑚3

where 𝑥1 is the mole fraction solubility of the solute, 𝑚1, 𝑚2, and 𝑚3 are the mass of the solute, solvent A and solvent B, respectively, and 𝑀1, 𝑀2, and 𝑀3 are the molar mass of the solute, solvent A and solvent B, respectively. Solubility correlation of -HNIW in binary solvent mixtures. The experimental solubility data for -HNIW in six binary solvent mixtures (ethyl acetate + n-heptane, ethyl acetate + 1,1,2-trichloroethane, ethyl acetate + cyclohexane, ethyl acetate + toluene, ethyl acetate + diethyl ether, and ethyl acetate + petroleum ether) were measured at a temperature range of 283.15K to 333.15K. The solubility of -HNIW in the binary solvent mixtures at temperatures ranging from 283.15K to 323.15K at atmospheric pressure is listed in Tables 1−6 and shown in Figs. 12−17. Considering the limitation of the boiling points of petroleum ether and diethyl ether, their temperature range for measurement was controlled from 283.15K to 303.15K. The relative average deviation (RAD) in order to compare the experimental solubility data to calculated solubility data, is calculated using Eq. (2): 1

𝑁

|𝑥𝑒𝑥𝑝 ― 𝑥𝑐𝑎𝑙|

%RAD = 100 ∙ 𝑁∑𝑖 = 1

(2)

𝑥𝑒𝑥𝑝

where 𝑥𝑒𝑥𝑝 is the experimental mole fraction solubility, and 𝑥𝑐𝑎𝑙 is the calculated mole fraction solubility of each model. The root mean square deviation (RMSD) is used to evaluate the accuracy and predictability of the calculated data by models and is calculated using Eq. (3): RMSD =

[∑ 1 𝑁

(𝑥𝑒𝑥𝑝 ― 𝑥𝑐𝑎𝑙)2]

𝑁 𝑖=1

1/2

(3)

where 𝑥𝑒𝑥𝑝 is the experimental mole fraction solubility, 𝑥𝑐𝑎𝑙 is the calculated mole fraction solubility of each mode, and N is the number of experimental data points. Based on these data, it can be seen that the experimental solubility of -HNIW in binary solvent mixtures (ethyl acetate + n-heptane, ethyl acetate + 1,1,2-trichloroethane, ethyl acetate + toluene, ethyl acetate + cyclohexane, ethyl acetate + toluene, ethyl acetate + diethyl ether, and ethyl acetate + petroleum ether) decreases with increasing temperature in the temperature range of 283.15K to 333.15K. This also shows that solubility in binary solvent mixtures increases with increasing mole fraction of ethyl acetate.  is defined as the ratio of polarity to dipolarity of the solvent (dimensionless).The order of the π value for each antisolvent is: toluene > 1,1,1-trichloroethane > diethyl ether > cyclohexane > petroleum ether > n-heptane.21 When the initial mole fraction of ethyl acetate is 0.275 at 293.15K, the order of solubility of -HNIW is: toluene > diethyl ether > cyclohexane > petroleum ether ≈ 1,1,2-trichloroethane ≈ n-heptane. It was found that solubility of -HNIW in ethyl acetate is correlated with positive polarity of the other solvents. The solubility of -HNIW in the binary solvent mixtures by mole fraction of solvent composition is shown in Fig. 18. Solubility data in solvent mixtures were correlated by the CNIBS/R-K equation and Jouyban−Acree model. The CNIBS/R-K model is an empirical equation that correlates the solubility of materials as a function of composition. The equation is represented as follows:22,23 N

ln𝑥1 = 𝑥2ln (𝑥1)2 + 𝑥3ln (𝑥1)3 + 𝑥2𝑥3∑i = 0𝑆𝑖(𝑥2 ― 𝑥3)i

(4)

where x1 is the mole fraction solubility of the solute, x2 and x3 refer to the mole fraction of the binary solvents in the absence of solute, and represent the solubility of the solute in pure solvents 2 and 3, respectively., Si is a model parameter, N stands for the number of solvents, and T represents the absolute temperature. In this study, N equals 2, so substituting (1 − 𝑥3) for 𝑥2 in Eq. (4), allows it to be rewritten as Eq (5): ln𝑥1 = 𝐵0 + 𝐵1𝑥3+𝐵2𝑥23+𝐵3𝑥33+𝐵4𝑥43

(5)

where x1 is the mole fraction solubility of the solute, and 𝐵0, 𝐵1, 𝐵2, 𝐵3 and 𝐵4 are parameters of this model that can predict and correlate solubility as a function of composition. These parameters are listed in Tables 8-13.



Page 6 of 49

Taking both temperature and composition of the binary solvent mixtures into consideration, the Jouyban–Acree model is widely used to correlate solubility data in binary solvent mixtures. The equation is as follows:24 ln𝑥1 = 𝐴0 + 𝐴1/(𝑇/K) + 𝐴2ln (𝑇/𝐾) + 𝐴3𝑥3 + 𝐴4𝑥3/(𝑇/K) + 𝐴5𝑥23/(𝑇/K) + 𝐴6𝑥33/(𝑇/K) + 𝐴7𝑥43/(𝑇/K) + 𝐴8𝑥3ln(T/K) (6) where 𝑥1 is the saturated mole fraction solubility of the solute, 𝐴0-𝐴8 are empirical parameters of the Jouyban-Acree model, x2 and x3 refer to the mole fraction composition of the binary solvents in the absence of solute, and T represents the absolute temperature. The parameters are listed in Table 14. The CNIBS/R-K equation and Jouyban−Acree model were found to provide a satisfactory correlation. The Jouyban−Acree model equation was found to be better. The relative deviation on comparing experimental solubility data to calculated solubility data shows a good agreement for both models. Dissolution enthalpy and entropy of -HNIW in binary solvent mixtures. The van’t Hoff equation relates the logarithm of the mole fraction of a solute as a linear function of the reciprocal of the absolute temperature, as shown in Eq. (7); ∆𝑑𝑖𝑠𝐻 and ∆𝑑𝑖𝑠𝑆 represent the dissolution enthalpy and entropy, respectively. The van’t Hoff equation relates the logarithm of a solute as a function of 1/(T/K) by the real solution, and the equation is as follows:25 ln𝑥1 = ―

∆𝑑𝑖𝑠𝐻 𝑅𝑇

+

∆𝑑𝑖𝑠𝑆

(7)

𝑅

where R is the gas constant, ∆𝑑𝑖𝑠𝐻, ∆𝑑𝑖𝑠𝑆 are the dissolution enthalpy and entropy, respectively, and T is the absolute temperature. The value of dissolution enthalpy and dissolution entropy calculated from the slope and intercept in Eq. (7) are listed in Tables 15-20. These data show that the ∆𝑑𝑖𝑠𝐻 of -HNIW in each binary solvent mixture is exothermic. This means that the solubility of -HNIW decreases with increasing temperature. The dissolution process is exothermic because interactions between -HNIW molecules and binary solvent mixture molecules are less powerful than those between binary solvent mixture molecules. The course of -HNIW dissolving in binary solvent mixtures used in our studies has no driving force in the temperature range of 283.15K to 333.15K. (∆𝑑𝑖𝑠𝐻, ∆𝑑𝑖𝑠𝑆 < 0) The negative dissolution entropy value in seven binary solvent mixtures may be due to the hydrogen bond between solute and solvent molecules, which may give a more ordered structure in solution.26,27

 CONCLUSIONS Raman spectra were used to develop a calibration curve of the solubility of -HNIW in binary solvent mixtures. Linear relationships between solubility of -HNIW and Raman intensity were used to measure the solubility of HNIW in binary solvent mixtures. Polymorphs were also monitored in situ by Raman spectroscopy. The results show that the experimental solubility of -HNIW in the binary solvent mixtures (ethyl acetate + n-heptane, ethyl acetate + 1,1,2-trichloroethane, ethyl acetate + cyclohexane, ethyl acetate + toluene, ethyl acetate + diethyl ether, and ethyl acetate + petroleum ether) decreases with increasing temperature in the range of 283.15K to 333.15K. The data also show that solubility increases with increasing mole fraction of ethyl acetate in the binary solvent mixtures. The results indicate that solubility of -HNIW in ethyl acetate is correlated with positive polarity of the other solvent. This may be explained by the polarity and molecular size of the solvent. The CNIBS/R-K model is in better agreement with experimental solubility for all of the binary solvent mixtures. Dissolution enthalpy and entropy were calculated using the van’t Hoff equation. Dissolution enthalpy of the -HNIW in the binary solvent mixtures is exothermic. Dissolution entropy of the -HNIW in the binary solvent mixtures has a negative value.


Page 7 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


REFERENCES (1) Viswanath, J. V.; Venugopal, K. J.; Rao, N. V. S.; Venkataraman, A. An overview on importance, synthetic strategies and studies of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (HNIW). Defence Technology. 2016, 12, 401–4183. (2) Liu, Y.; Li, S.; Wang, Z.; Xu, J.; Sun, J.; Huang, H.; Thermally Induced Polymorphic Transformation of Hexanitrohexaazaisowurtzitane (HNIW) Investigated by in-situ X-ray Powder Diffraction. Central European Journal of Energetic Materials. 2016, 13, 1023-1037. (3) Shackman, J. G.; Giles, J. H.; Denton, M. D.; Pharmaceutical Reaction Monitoring by Raman Spectroscopy. The royal society of chemistry. 2000, 254, 186-201. (4) Failloux, N.; Bonnet, I.; Baron, M.; Perrier, E. Quantitative Analysis of Vitamin A Degradation by Raman Spectroscopy. Appllied Spectroscopy, 2003, 57, 1117-1122. (5) Kim, D. Y.; Kim, K. J.; Solubility of Cyclotrimethylenetrinitramine (RDX) in Binary Solvent Mixtures. Journal of Chemical Engineering Data. 2007, 52, 1946-1949. (6) Mullin, J. W.; Crystallization. 4th ed.; Butterworth-Heinemann: Boston, 2001. (7) Xu, J.; Tian, Y.; Liu, Yu.; Zhang, H.; Shu, Y.; Sun, J.; Polymorphism in hexanitrohexaazaisowurtzitane crystallized from solution. Journal of Crystal Growth. 2012, 354, 13-19. (8) Pinho, S. P.; Macedo, E. A.; Solubility of NaCl, NaBr, and KCl in Water, Methanol, Ethanol, and Their Mixed Solvents. Journal of Chemical Engineering Data. 2005, 05, 29-32. (9) Buchauer, K.; A comparison of two simple titration procedures to determine volatile fatty acids in influents to waste-water and sludge treatment processes. Water SA-PRETORIA. 1998, 24, 49-56. (10) Haruki, M.; Kobayashi, F.; Kishimoto, K.; Kihara, S.; Measurement of the solubility of metal complexes in supercritical carbon dioxide using a UV–vis spectrometer. Fluid Phase Equilibria. 2009, 280, 49-55. (11) Wolfff, S. D.; Yancey, P. H.; Santon, T. S.; A simple HPLC method for quantitating major organic solutes of renal medulla. American Journal of Physiology-Renal Physiology. 1989, 256, 954-956. (12) Grant, D. J. W.; Abougela, I. K. A.; A synthetic method for determining the solubility of solids in viscous liquids. International Journal of Pharmaceutics. 1983, 16, 11-21. (13) Costa, M. C.; Rolemberg, M. P.; Boros, L. A. D.; Solid-Liquid Equilibrium of Binary Fatty Acid Mixture. Journal of Chemical Engineering Data. 2007, 52, 30-36. (14) Liu, R.; Qi, S.; Lu, J.; Han, D.; in situ infrared spectroscopy, Measurement of Soluble Solids Content of Three Fruit Species Using Universal near Infrared Spectroscopy Models. Journal of Near Infrared Spectroscopy. 2015, 23, 301-309. (15) O'Mahony, M. A.; Croker, D. M.; Rasmuson, Å. C.; Veesler, S.; Hodnett, B. K.; Measuring the Solubility of a Quickly Transforming Metastable Polymorph of Carbamazepine. Org. Process Res. Dev. 2013, 17, 512-518. (16) Lim, C. H.; Kim, H. S.; Kim, K. J.; Control of Polymorphism and Particle Size of Hexanitrohexaazaisowurtzitane in Drowning‐Out Crystallization. Industrial crystallization. 2017, 40, 1309-1317. (17) Pan, B.; Wei, H.; Jiang, J.; Zong, S.; Lv, P.; Dang, L.; Solution-mediated polymorphic transformation of CL20: An approach to prepare purified form ε particles. Journal of Molecular Liquids. 2018, 265, 216-225. (18) Nguyen, D. L. T.; Kim, K. J.; Inline Monitoring of Taltirelin Crystallization in Batch Cooling Mode Using Raman Spectroscopy. Chemical engineering technology. 2015, 38, 1059-1067. (19) Chen, H.; Jin, S.; Li, L.; Jin, S.; Quantitative Determination of ε-phase in polymorphic HNIW using X-ray Diffraction Patterns. Propellants, Explosion, Pyrotechnics. 2008, 33, 467–471.



(20) Ghosh, M.; Venkatesan, V.; Sikder, A. K.; Sikder, N.; Preparation and Characterisation of ε-CL-20 by Solvent Evaporation and Precipitation Methods. Defense Science Journal. 2012, 62, 390-398. (21) Abraham, M. H.; Scales of solute hydrogen bonding: Their construction and application to physicochemical and biochemical process. Chemical Society Reviews. 1993, 22, 72-83. (22) Acree, Jr. W. E.; Mathematical representation of thermodynamic properties: Part 2. Derivation of the combined nearly ideal binary solvent (NIBS)/Redlich-Kister mathematical representation from a two-body and three-body interactional mixing model. Thermochimica Acta. 1992, 198, 71-79. (23) Jouyban, A.; Hanaee, J.; novel method for improvement of predictability of the CNIBS/R − K equation, International Journal of Pharmaceutical. 1997, 154, 245-247. (24) Jouyban, A.; Acree, Jr. W. E.; Solubility correlation of structurally related drugs in binary solvent mixtures, International Journal of Pharmaceutics. 1998, 166, 205-209. (25) Wilson, G.M.; Vapor−liquid equilibrium. XI. A new expression for the excess free energy of mixing, Journal of American Chemical Society. 1964, 86, 127-130. (26)Wang, P; Wang, J.; Gong, J.; Zhang, M.; Determination of the solubility, dissolution enthalpy and entropy of deflazacort in different solvents, Fluid Phase Equilibria. 2012. 324, 41-43. (27)Wang, N.; Fu, Q.; Yang, G.; Determination of the solubility, dissolution enthalpy and entropy of icariin in water, ethanol, and methano. Fluid Phase Equilibria. 2011, 306, 171-174.


Page 8 of 49

Page 9 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1. Experimental mole fraction solubility of β-HNIW in ethyl acetate + n-heptane solvent mixtures in the temperature range of 283.15K to 333.15K. a 𝒙𝟑b

𝒙𝒆𝒙𝒑,𝒄

𝒙𝑪,𝒅

𝒙𝑱 ― 𝑨,𝒆

T=283.15K 0.8198

0.0893

0.0900

0.0891

0.7707

0.0799

0.0789

0.0790

0.6959

0.0653

0.0651

0.0648

0.6304

0.0526

0.0532

0.0509

0.5346

0.0353

0.0356

0.0346

0.4312

0.0194

0.0190

0.0185

0.3266

0.0080

0.0082

0.0080

0.2214

0.0030

0.0030

0.0029

T=288.15K 0.8198

0.0885

0.0890

0.0880

0.7707

0.0782

0.0774

0.0776

0.6959

0.0630

0.0628

0.0632

0.6304

0.0502

0.0507

0.0505

0.5346

0.0332

0.0335

0.0333

0.4312

0.0182

0.0178

0.0178

0.3266

0.0076

0.0077

0.0077

0.2214

0.0028

0.0028

0.0028

T=293.15K 0.8198

0.0876

0.0883

0.0869

0.7707

0.0765

0.0755

0.0763

0.6959

0.0604

0.0602

0.0617

0.6304

0.0474

0.0480

0.0493

0.5346

0.0307

0.0309

0.0321

0.4312

0.0164

0.0160

0.0170

0.3266

0.0067

0.0068

0.0074

0.2214

0.0026

0.0025

0.0026

T=298.15K 0.8198

0.0862

0.0864

0.0859

0.7707

0.0751

0.0748

0.0750



Page 10 of 49

0.6959

0.0593

0.0592

0.0602

0.6304

0.0467

0.0469

0.0478

0.5346

0.0307

0.0308

0.0309

0.4312

0.0170

0.0169

0.0163

0.3266

0.0074

0.0074

0.0071

0.2214

0.0025

0.0025

0.0025

T=303.15K 0.8198

0.0852

0.0858

0.0849

0.7707

0.0743

0.0734

0.0737

0.6959

0.0586

0.0584

0.0587

0.6304

0.0460

0.0465

0.0464

0.5346

0.0298

0.0300

0.0298

0.4312

0.0159

0.0156

0.0156

0.3266

0.0064

0.0065

0.0067

0.2214

0.0023

0.0023

0.0024

T=308.15K 0.8198

0.0838

0.0840

0.0839

0.7707

0.0724

0.0721

0.0725

0.6959

0.0565

0.0564

0.0573

0.6304

0.0441

0.0443

0.0450

0.5346

0.0286

0.0287

0.0286

0.4312

0.0156

0.0155

0.0150

0.3266

0.0067

0.0067

0.0064

0.2214

0.0022

0.0022

0.0023

T=313.15K 0.8198

0.0825

0.0825

0.0829

0.7707

0.0710

0.0711

0.0712

0.6959

0.0552

0.0552

0.0558

0.6304

0.0430

0.0430

0.0436

0.5346

0.0280

0.0280

0.0275

0.4312

0.0156

0.0156

0.0143

0.3266

0.0070

0.0070

0.0061

0.2214

0.0022

0.0022

0.0022


Page 11 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


T=318.15K 0.8198

0.0813

0.0820

0.0819

0.7707

0.0702

0.0692

0.0700

0.6959

0.0545

0.0543

0.0545

0.6304

0.0422

0.0428

0.0422

0.5346

0.0267

0.0270

0.0265

0.4312

0.0139

0.0135

0.0137

0.3266

0.0055

0.0056

0.0058

0.2214

0.0021

0.0021

0.0021

T=323.15K 0.8198

0.0796

0.0802

0.0810

0.7707

0.0688

0.0680

0.0688

0.6959

0.0536

0.0534

0.0531

0.6304

0.0416

0.0421

0.0409

0.5346

0.0265

0.0267

0.0254

0.4312

0.0139

0.0136

0.0130

0.3266

0.0055

0.0056

0.0056

0.2214

0.0020

0.0020

0.0020

T=328.15K 0.8198

0.0787

0.0786

0.0801

0.7707

0.0694

0.0695

0.0677

0.6959

0.0537

0.0540

0.0524

0.6304

0.0409

0.0406

0.0396

0.5346

0.0242

0.0242

0.0244

0.4312

0.0120

0.0121

0.0124

0.3266

0.0052

0.0052

0.0053

0.2214

0.0020

0.0020

0.0019

T=333.15K 0.8198

0.0776

0.0768

0.0792

0.7707

0.0680

0.0686

0.0666

0.6959

0.0506

0.0525

0.0518

0.6304

0.0403

0.0383

0.0383

0.5346

0.0218

0.0217

0.0234



Page 12 of 49

0.4312

0.0101

0.0105

0.0119

0.3266

0.0048

0.0047

0.0050

0.2214

0.0019

0.0019

0.0018

Table 2. Experimental mole fraction solubility of β-HNIW in ethyl acetate + 1,1,2-trichloroethane solvent mixtures in the temperature range of 283.15K to 333.15K. a 𝒙𝟑b


𝒙𝑪,𝒅


T=283.15K 0.8583

0.1007

0.1011

0.0969

0.7762

0.0807

0.0798

0.0786

0.6943

0.0622

0.0626

0.0633

0.6052

0.0442

0.0447

0.0461

0.5023

0.0269

0.0267

0.0276

0.4319

0.0177

0.0175

0.0179

0.3476

0.0100

0.0102

0.0100

0.2746

0.0066

0.0066

0.0062

T=288.15K 0.8583

0.0988

0.0991

0.0958

0.7762

0.0791

0.0783

0.0775

0.6943

0.0609

0.0612

0.0622

0.6052

0.0433

0.0437

0.0452

0.5023

0.0265

0.0263

0.0271

0.4319

0.0175

0.0173

0.0175

0.3476

0.0099

0.0100

0.0099

0.2746

0.0063

0.0063

0.0061

T=293.15K 0.8583

0.0965

0.0968

0.0950

0.7762

0.0773

0.0766

0.0765

0.6943

0.0596

0.0598

0.0612

0.6052

0.0425

0.0429

0.0444

0.5023

0.0261

0.0259

0.0266

0.4319

0.0173

0.0171

0.0172


Page 13 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.3476

0.0097

0.0098

0.0097

0.2746

0.0060

0.0060

0.0060

T=298.15K 0.8583

0.0958

0.0961

0.0943

0.7762

0.0768

0.0761

0.0757

0.6943

0.0593

0.0596

0.0603

0.6052

0.0423

0.0427

0.0436

0.5023

0.0259

0.0257

0.0261

0.4319

0.0171

0.0169

0.0169

0.3476

0.0096

0.0097

0.0096

0.2746

0.0060

0.0059

0.0059

T=303.15K 0.8583

0.0946

0.0949

0.0938

0.7762

0.0761

0.0753

0.0749

0.6943

0.0588

0.0591

0.0595

0.6052

0.0419

0.0423

0.0429

0.5023

0.0256

0.0254

0.0256

0.4319

0.0168

0.0166

0.0166

0.3476

0.0093

0.0094

0.0094

0.2746

0.0057

0.0057

0.0058

T=308.15K 0.8583

0.0932

0.0935

0.0934

0.7762

0.0751

0.0743

0.0743

0.6943

0.0582

0.0585

0.0587

0.6052

0.0416

0.0420

0.0422

0.5023

0.0254

0.0252

0.0252

0.4319

0.0167

0.0165

0.0163

0.3476

0.0092

0.0094

0.0093

0.2746

0.0057

0.0057

0.0057

T=313.15K 0.8583

0.0931

0.0935

0.0932

0.7762

0.0751

0.0742

0.0738

0.6943

0.0581

0.0584

0.0581



Page 14 of 49

0.6052

0.0414

0.0419

0.0416

0.5023

0.0252

0.0250

0.0248

0.4319

0.0165

0.0163

0.0161

0.3476

0.0091

0.0092

0.0091

0.2746

0.0057

0.0057

0.0056

T=318.15K 0.8583

0.0910

0.0914

0.0931

0.7762

0.0740

0.0731

0.0734

0.6943

0.0576

0.0580

0.0575

0.6052

0.0412

0.0417

0.0410

0.5023

0.0250

0.0248

0.0244

0.4319

0.0162

0.0160

0.0158

0.3476

0.0088

0.0089

0.0090

0.2746

0.0055

0.0054

0.0056

T=323.15K 0.8583

0.0888

0.0893

0.0931

0.7762

0.0730

0.0719

0.0731

0.6943

0.0573

0.0577

0.0570

0.6052

0.0411

0.0418

0.0405

0.5023

0.0249

0.0246

0.0240

0.4319

0.0160

0.0157

0.0155

0.3476

0.0086

0.0088

0.0088

0.2746

0.0055

0.0055

0.0055

T=328.15K 0.8583

0.0891

0.0896

0.0933

0.7762

0.0733

0.0720

0.0729

0.6943

0.0574

0.0579

0.0565

0.6052

0.0410

0.0418

0.0400

0.5023

0.0246

0.0243

0.0236

0.4319

0.0157

0.0153

0.0153

0.3476

0.0082

0.0085

0.0087

0.2746

0.0053

0.0053

0.0054

T=333.15K


Page 15 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.8583

0.0886

0.0892

0.0935

0.7762

0.0731

0.0717

0.0727

0.6943

0.0574

0.0579

0.0561

0.6052

0.0410

0.0418

0.0395

0.5023

0.0244

0.0241

0.0233

0.4319

0.0154

0.0150

0.0151

0.3476

0.0079

0.0082

0.0086

0.2746

0.0051

0.0051

0.0053

Table 3. Experimental mole fraction solubility of β-HNIW in ethyl acetate + cyclohexane solvent mixtures in the temperature range of 283.15K to 333.15K. a 𝒙𝟑b


𝒙𝑪,𝒅


T=283.15K 0.7926

0.0972

0.0967

0.0923

0.7241

0.0839

0.0850

0.0837

0.6574

0.0714

0.0713

0.0725

0.5889

0.0589

0.0582

0.0606

0.4880

0.0418

0.0417

0.0441

0.3890

0.0268

0.0273

0.0284

0.2909

0.0142

0.0140

0.0139

0.1928

0.0044

0.0044

0.0041

T=288.15K 0.7926

0.0957

0.0952

0.0918

0.7241

0.0825

0.0835

0.0823

0.6574

0.0699

0.0699

0.0705

0.5889

0.0575

0.0568

0.0584

0.4880

0.0404

0.0404

0.0419

0.3890

0.0256

0.0260

0.0267

0.2909

0.0133

0.0131

0.0130

0.1928

0.0040

0.0040

0.0039

T=293.15K 0.7926

0.0952

0.0947

0.0912

0.7241

0.0816

0.0827

0.0809



Page 16 of 49

0.6574

0.0688

0.0688

0.0687

0.5889

0.0563

0.0555

0.0564

0.4880

0.0392

0.0392

0.0399

0.3890

0.0246

0.0251

0.0252

0.2909

0.0126

0.0124

0.0122

0.1928

0.0037

0.0037

0.0037

T=298.15K 0.7926

0.0918

0.0915

0.0905

0.7241

0.0792

0.0799

0.0796

0.6574

0.0670

0.0670

0.0670

0.5889

0.0548

0.0543

0.0545

0.4880

0.0379

0.0379

0.0382

0.3890

0.0233

0.0236

0.0238

0.2909

0.0116

0.0115

0.0115

0.1928

0.0035

0.0035 T=303.15K

0.7926

0.0898

0.0895

0.0899

0.7241

0.0774

0.0781

0.0783

0.6574

0.0653

0.0652

0.0654

0.5889

0.0531

0.0527

0.0528

0.4880

0.0363

0.0363

0.0366

0.3890

0.0220

0.0222

0.0227

0.2909

0.0107

0.0106

0.0109

0.1928

0.0032

0.0032

0.0033

T=308.15K 0.7926

0.0886

0.0884

0.0892

0.7241

0.0763

0.0768

0.0771

0.6574

0.0643

0.0642

0.0639

0.5889

0.0522

0.0519

0.0513

0.4880

0.0356

0.0356

0.0352

0.3890

0.0214

0.0216

0.0217

0.2909

0.0103

0.0102

0.0104

0.1928

0.0031

0.0031

0.0031


Page 17 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


T=313.15K 0.7926

0.0868

0.0867

0.0885

0.7241

0.0751

0.0754

0.0759

0.6574

0.0635

0.0634

0.0625

0.5889

0.0516

0.0514

0.0498

0.4880

0.0351

0.0351

0.0340

0.3890

0.0209

0.0210

0.0207

0.2909

0.0100

0.0100

0.0099

0.1928

0.0032

0.0032

0.0030

T=318.15K 0.7926

0.0860

0.0857

0.0877

0.7241

0.0735

0.0741

0.0748

0.6574

0.0616

0.0615

0.0612

0.5889

0.0497

0.0494

0.0485

0.4880

0.0336

0.0336

0.0328

0.3890

0.0200

0.0202

0.0199

0.2909

0.0095

0.0095

0.0095

0.1928

0.0028

0.0028

0.0029

T=323.15K 0.7926

0.0844

0.0841

0.0870

0.7241

0.0716

0.0723

0.0737

0.6574

0.0596

0.0596

0.0600

0.5889

0.0479

0.0475

0.0473

0.4880

0.0322

0.0322

0.0318

0.3890

0.0192

0.0194

0.0192

0.2909

0.0092

0.0091

0.0092

0.1928

0.0027

0.0027

0.0028

T=328.15K 0.7926

0.0840

0.0837

0.0862

0.7241

0.0711

0.0718

0.0726

0.6574

0.0591

0.0590

0.0588

0.5889

0.0474

0.0470

0.0462

0.4880

0.0318

0.0318

0.0308



Page 18 of 49

0.3890

0.0189

0.0191

0.0186

0.2909

0.0090

0.0089

0.0089

0.1928

0.0026

0.0026

0.0027

T=333.15K 0.7926

0.0837

0.0833

0.0854

0.7241

0.0704

0.0711

0.0716

0.6574

0.0582

0.0582

0.0577

0.5889

0.0465

0.0460

0.0452

0.4880

0.0311

0.0311

0.0300

0.3890

0.0185

0.0188

0.0180

0.2909

0.0089

0.0088

0.0086

0.1928

0.0025

0.0025

0.0027

Table 4. Experimental mole fraction solubility of β-HNIW in ethyl acetate + toluene solvent mixtures in the temperature range of 283.15K to 333.15K. a 𝒙𝟑b


𝒙𝑪,𝒅


T=283.15K 0.8071

0.1009

0.1006

0.0995

0.7509

0.0904

0.0910

0.0906

0.6853

0.0786

0.0787

0.0786

0.6107

0.0657

0.0653

0.0654

0.5095

0.0492

0.0491

0.0498

0.4108

0.0345

0.0348

0.0357

0.3010

0.0198

0.0197

0.0200

0.2073

0.0090

0.0090

0.0086

T=288.15K 0.8071

0.1003

0.0999

0.0991

0.7509

0.0895

0.0902

0.0898

0.6853

0.0774

0.0775

0.0775

0.6107

0.0645

0.0640

0.0642

0.5095

0.0482

0.0481

0.0485

0.4108

0.0338

0.0342

0.0346

0.3010

0.0194

0.0192

0.0193


Page 19 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.2073

0.0085

0.0085

0.0084

T=293.15K 0.8071

0.1007

0.1001

0.0986

0.7509

0.0888

0.0898

0.0890

0.6853

0.0761

0.0762

0.0764

0.6107

0.0630

0.0623

0.0630

0.5095

0.0471

0.0470

0.0473

0.4108

0.0333

0.0339

0.0335

0.3010

0.0193

0.0191

0.0187

0.2073

0.0079

0.0079

0.0081

T=298.15K 0.8071

0.0980

0.0977

0.0980

0.7509

0.0874

0.0880

0.0881

0.6853

0.0754

0.0755

0.0753

0.6107

0.0626

0.0621

0.0618

0.5095

0.0464

0.0463

0.0462

0.4108

0.0322

0.0325

0.0326

0.3010

0.0182

0.0181

0.0182

0.2073

0.0080

0.0080

0.0079

T=303.15K 0.8071

0.0963

0.0959

0.0973

0.7509

0.0857

0.0864

0.0872

0.6853

0.0740

0.0741

0.0743

0.6107

0.0613

0.0608

0.0607

0.5095

0.0454

0.0453

0.0452

0.4108

0.0315

0.0319

0.0318

0.3010

0.0179

0.0177

0.0177

0.2073

0.0078

0.0079

0.0078

T=308.15K 0.8071

0.0961

0.0958

0.0966

0.7509

0.0853

0.0859

0.0862

0.6853

0.0734

0.0734

0.0733

0.6107

0.0606

0.0602

0.0597



Page 20 of 49

0.5095

0.0447

0.0446

0.0442

0.4108

0.0308

0.0311

0.0310

0.3010

0.0173

0.0172

0.0173

0.2073

0.0076

0.0076

0.0076

T=313.15K 0.8071

0.0949

0.0947

0.0957

0.7509

0.0845

0.0849

0.0853

0.6853

0.0727

0.0727

0.0723

0.6107

0.0599

0.0596

0.0587

0.5095

0.0438

0.0438

0.0434

0.4108

0.0298

0.0300

0.0304

0.3010

0.0165

0.0164

0.0169

0.2073

0.0075

0.0075

0.0075

T=318.15K 0.8071

0.0946

0.0942

0.0948

0.7509

0.0834

0.0840

0.0843

0.6853

0.0712

0.0713

0.0713

0.6107

0.0585

0.0581

0.0578

0.5095

0.0430

0.0429

0.0426

0.4108

0.0297

0.0300

0.0298

0.3010

0.0168

0.0167

0.0166

0.2073

0.0073

0.0073

0.0074

T=323.15K 0.8071

0.0939

0.0935

0.0939

0.7509

0.0828

0.0834

0.0833

0.6853

0.0707

0.0708

0.0703

0.6107

0.0580

0.0576

0.0570

0.5095

0.0425

0.0424

0.0419

0.4108

0.0293

0.0296

0.0293

0.3010

0.0166

0.0165

0.0164

0.2073

0.0073

0.0073

0.0074

0.0931

0.0929

T=328.15K 0.8071

0.0935


Page 21 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.7509

0.0816

0.0823

0.0823

0.6853

0.0690

0.0691

0.0694

0.6107

0.0563

0.0558

0.0561

0.5095

0.0413

0.0412

0.0412

0.4108

0.0287

0.0291

0.0288

0.3010

0.0165

0.0163

0.0161

0.2073

0.0072

0.0072

0.0073

T=333.15K 0.8071

0.0933

0.0928

0.0918

0.7509

0.0806

0.0814

0.0812

0.6853

0.0675

0.0676

0.0684

0.6107

0.0547

0.0541

0.0553

0.5095

0.0402

0.0401

0.0406

0.4108

0.0283

0.0288

0.0284

0.3010

0.0166

0.0164

0.0159

0.2073

0.0071

0.0071

0.0073

Table 5. Experimental mole fraction solubility of β-HNIW in ethyl acetate + diethyl ether solvent mixtures in the temperature range of 283.15K to 303.15K. a 𝒙𝟑b


𝒙𝑪,𝒅


T=283.15K 0.7709

0.0956

0.0949

0.0928

0.7052

0.0816

0.0830

0.0824

0.6342

0.0677

0.0676

0.0676

0.5579

0.0542

0.0533

0.0536

0.4582

0.0387

0.0387

0.0395

0.3593

0.0254

0.0260

0.0271

0.2561

0.0133

0.0130

0.0133

0.1738

0.0048

0.0049

0.0046

T=288.15K 0.7709

0.0919

0.0912

0.0896

0.7052

0.0787

0.0801

0.0795

0.6342

0.0655

0.0654

0.0652



Page 22 of 49

0.5579

0.0525

0.0516

0.0517

0.4582

0.0375

0.0375

0.0382

0.3593

0.0246

0.0252

0.0262

0.2561

0.0129

0.0126

0.0129

0.1738

0.0047

0.0047

0.0045

T=293.15K 0.7709

0.0894

0.0886

0.0881

0.7052

0.0764

0.0779

0.0777

0.6342

0.0635

0.0635

0.0634

0.5579

0.0510

0.0500

0.0499

0.4582

0.0364

0.0363

0.0366

0.3593

0.0238

0.0245

0.0249

0.2561

0.0125

0.0122

0.0123

0.1738

0.0044

0.0044

0.0043

T=298.15K 0.7709

0.0879

0.0870

0.0881

0.7052

0.0747

0.0764

0.0768

0.6342

0.0619

0.0618

0.0619

0.5579

0.0495

0.0484

0.0482

0.4582

0.0353

0.0352

0.0347

0.3593

0.0230

0.0238

0.0233

0.2561

0.0119

0.0115

0.0114

0.1738

0.0039

0.0039

0.0040

T=303.15K 0.7709

0.0874

0.0862

0.0895

0.7052

0.0737

0.0759

0.0767

0.6342

0.0606

0.0605

0.0608

0.5579

0.0481

0.0467

0.0465

0.4582

0.0341

0.0340

0.0328

0.3593

0.0222

0.0233

0.0215

0.2561

0.0113

0.0108

0.0103

0.1738

0.0032

0.0032

0.0036


Page 23 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 6. Experimental mole fraction solubility of β-HNIW in ethyl acetate + petroleum ether solvent mixtures in the temperature range of 283.15K to 303.15K. a 𝒙𝟑b


𝒙𝑪,𝒅


T=283.15K 0.7887

0.0913

0.0913

0.0874

0.7152

0.0749

0.0749

0.0735

0.6532

0.0617

0.0616

0.0623

0.5832

0.0477

0.0477

0.0496

0.4835

0.0301

0.0302

0.0317

0.3835

0.0159

0.0158

0.0162

0.2867

0.0063

0.0063

0.0062

0.1891

0.0016

0.0016

0.0015

T=288.15K 0.7887

0.0869

0.0870

0.0856

0.7152

0.0725

0.0722

0.0716

0.6532

0.0603

0.0603

0.0605

0.5832

0.0471

0.0473

0.0480

0.4835

0.0299

0.0300

0.0306

0.3835

0.0157

0.0155

0.0156

0.2867

0.0060

0.0061

0.0060

0.1891

0.0015

0.0015

0.0015

T=293.15K 0.7887

0.0836

0.0838

0.0844

0.7152

0.0704

0.0699

0.0701

0.6532

0.0590

0.0589

0.0588

0.5832

0.0463

0.0466

0.0464

0.4835

0.0294

0.0296

0.0294

0.3835

0.0153

0.0150

0.0150

0.2867

0.0057

0.0058

0.0058

0.1891

0.0015

0.0015

0.0015

T=298.15K 0.7887

0.0814

0.0818

0.0837

0.7152

0.0688

0.0681

0.0688



Page 24 of 49

0.6532

0.0578

0.0577

0.0573

0.5832

0.0453

0.0459

0.0449

0.4835

0.0287

0.0289

0.0281

0.3835

0.0147

0.0143

0.0142

0.2867

0.0053

0.0054

0.0055

0.1891

0.0014

0.0014

0.0014

T=303.15K 0.7887

0.0803

0.0807

0.0836

0.7152

0.0676

0.0667

0.0679

0.6532

0.0565

0.0564

0.0559

0.5832

0.0441

0.0447

0.0433

0.4835

0.0277

0.0279

0.0268

0.3835

0.0140

0.0136

0.0134

0.2867

0.0049

0.0050

0.0051

0.1891

0.0013

0.0013

0.0013

a standard uncertainties are u(T) = 0.05K, u(xexp) = 0.05 × 10 ―3. b x3b is the mole fraction of ethyl acetate in binary solvents in the absence of solute. c xexp,c is the mole fraction solubility of solute in binary solvent mixtures. d x3C,d is the mole fraction solubility calculated using the CNIBS/R-K model. e x3J-A,e is the mole fraction solubility calculated using the Jouyban-Acree model. f standard uncertainties are u(T) = 0.05K, u(xexp) = 0.03.

Table 7. Parameters of solvents used

Ethyl acetate

𝛑𝒂 0.55

𝐃𝐢𝐩𝐨𝐥𝐞 𝐦𝐨𝐦𝐞𝐧𝐭𝒃 1.78

𝐒𝐮𝐫𝐟𝐚𝐜𝐞 𝐭𝐞𝐧𝐬𝐢𝐨𝐧𝒄 33.67

n-heptane

-0.08

0.00

28.28

1,1,1-trichloroehtnae

0.49

1.76

36.24

Cyclohexane

0.00

0.00

35.48

Toluene

0.54

0.38

40.20

Diethyl ether

0.27

1.13

24.86

Petroleum ether

-0.06

0.00

24.03

Solvent


Page 25 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


a 𝜋𝑎 is the polarity/dipolarity of the solvent (dimensionless). b Dipole moment in the unit debye. c Surface tension of the solvent at 298K in the unit cal ∙ mol ―1 ∙ Å ―2.

Table 8. Parameters of the CNIBS/R-K model for binary solvent mixtures of ethyl acetate + n-heptane at different temperatures. T/K

𝐁𝟎

𝐁𝟏

𝐁𝟐

𝐁𝟑

𝐁𝟒

%RAD

𝟏𝟎𝟓RMSD

283.15

-7.7973

6.4918

19.2376

-41.0480

21.5947

1.0700

5.1997

288.15

-8.1394

8.9383

11.6869

-31.3347

17.2754

0.9377

4.1691

293.15

-7.6950

4.2489

25.1824

-47.2418

24.1072

1.1173

5.1051

298.15

-9.4829

19.8938

-20.8275

8.7630

-0.2331

0.3673

1.5199

303.15

-8.2452

7.9843

15.4200

-36.2233

19.5673

0.9876

4.3869

308.15

-9.4701

18.8260

-17.4941

4.7900

1.5010

0.3873

1.5786

313.15

-10.3140

26.4930

-40.8626

33.9081

-11.3352

0.0588

0.3381

318.15

-7.6895

2.0553

32.5672

-56.5454

28.2739

1.2718

5.1962

323.15

-8.2100

6.2746

20.6300

-42.3992

22.2242

1.0786

4.2979

328.15

-8.7193

12.5756

-6.0710

0.3329

-0.5247

0.3299

1.5091

333.15

-8.2677

9.6382

-2.7029

2.3794

-3.7511

2.3553

10.3710

Table 9. Parameters of the CNIBS/R-K model for binary solvent mixtures of ethyl acetate + 1,1,2trichloroethane at different temperatures. T/K

𝐁𝟎

𝐁𝟏

𝐁𝟐

𝐁𝟑

𝐁𝟒

%RAD

𝟏𝟎𝟓RMSD

283.15

-4.9671

-9.7092

50.3811

-65.2334

27.8991

0.9844

4.4551

288.15

-5.6554

-4.8041

37.6231

-51.1176

22.2455

0.8429

3.7640

293.15

-6.2258

-0.9297

27.9168

-40.7134

18.1787

0.7441

3.1787

298.15

-6.0446

-2.4814

32.2634

-45.7567

20.2613

0.7741

3.3167

303.15

-6.2012

-1.8848

31.4599

-45.3580

20.2099

0.8480

3.5888

308.15

-6.0830

-2.8473

34.1284

-48.5076

21.5343

0.8667

3.5610

313.15

-5.8107

-4.9508

39.6208

-54.5174

23.9045

0.9881

4.0789

318.15

-5.6760

-6.6268

45.1207

-61.4590

26.8875

1.0745

4.4393

323.15

-4.9543

-12.2390

60.3286

-78.7675

33.9124

1.3187

5.3607

328.15

-4.7615

-14.3747

66.9385

-86.7858

37.3122

1.5554

6.1753



333.15

-4.4282

-17.5741

76.5112

-98.3111

Page 26 of 49

42.1825

1.7158

6.7705

Table 10. Parameters of the CNIBS/R-K model for binary solvent mixtures of ethyl acetate + cyclohexane at different temperatures. T/K

𝐁𝟎

𝐁𝟏

𝐁𝟐

𝐁𝟑

𝐁𝟒

%RAD

𝟏𝟎𝟓RMSD

283.15

-10.4606

40.0183

-89.3319

97.5135

-40.6146

0.8645

5.2277

288.15

-10.5947

40.2576

-89.1883

96.9054

-40.2556

0.8143

4.9207

293.15

-10.9056

42.1214

-94.0288

102.6244

-42.7358

0.8806

5.2572

298.15

-10.4311

37.0000

-77.5553

81.2467

-32.9913

0.6015

3.4841

303.15

-10.5319

36.8057

-76.0794

79.0403

-31.9666

0.5302

3.1001

308.15

-10.3588

34.8610

-69.7972

70.8102

-28.1480

0.4202

2.3744

313.15

-9.8952

30.6683

-57.1841

55.0261

-21.1154

0.2638

1.4629

318.15

-10.5856

35.9425

-72.6158

74.2246

-29.6432

0.5003

2.6665

323.15

-10.8838

38.1962

-79.5739

83.2197

-33.7361

0.6065

3.1894

328.15

-10.8633

37.8341

-78.4068

81.7261

-33.0460

0.6003

3.1042

333.15

-11.1169

39.8810

-84.7284

89.8790

-36.7484

0.7129

3.5694

Table 11. Parameters of the CNIBS/R-K model for binary solvent mixtures of ethyl acetate + toluene at different temperatures. T/K

𝐁𝟎

𝐁𝟏

𝐁𝟐

𝐁𝟑

𝐁𝟒

%RAD

𝟏𝟎𝟓RMSD

283.15

-8.3492

26.6888

-55.0203

57.1874

-22.8924

0.4539

3.1189

288.15

-8.6977

29.3208

-62.5585

66.3387

-26.8590

0.5727

3.6906

293.15

-9.4204

35.2264

-79.7984

87.3168

-35.9100

0.8330

5.2996

298.15

-8.6772

28.4207

-59.4612

62.4092

-25.1350

0.5076

3.2001

303.15

-8.6990

28.5539

-60.1324

63.4975

-25.6976

0.5578

3.5412

308.15

-8.6692

27.8482

-57.5981

60.0752

-24.0793

0.4889

3.0511

313.15

-8.2794

24.1578

-46.6626

46.8332

-18.3860

0.3201

2.0034

318.15

-8.8060

28.8701

-60.9639

64.4742

-26.0217

0.5452

3.2323

323.15

-8.6960

27.9573

-58.5914

61.9092

-25.0262

0.5239

3.1535

328.15

-8.9558

30.2478

-65.7711

70.8763

-28.8707

0.6328

3.5807

333.15

-9.3393

33.7738

-76.8818

84.9353

-35.0434

0.7692

4.2900


Page 27 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 12. Parameters of the CNIBS/R-K model for binary solvent mixtures of ethyl acetate + diethyl ether at different temperatures. T/K

𝐁𝟎

𝐁𝟏

𝐁𝟐

𝐁𝟑

𝐁𝟒

%RAD

𝟏𝟎𝟓RMSD

283.15

-9.8414

39.6430

-96.9486

114.4882

-50.7122

1.2219

6.8727

288.15

-9.8315

39.3007

-95.9599

113.3197

-50.2528

1.2295

6.6730

293.15

-10.1229

41.5224

-102.7002

122.0017

-54.2790

1.4535

7.5088

298.15

-10.7079

46.0224

-115.9415

138.7051

-61.8830

1.6780

8.4091

303.15

-11.9293

56.1559

-146.9169

179.0049

-80.7235

2.2331

11.0241

Table 13. Parameters of the CNIBS/R-K model for binary solvent mixtures of ethyl acetate + petroleum ether at different temperatures. T/K

𝐁𝟎

𝐁𝟏

𝐁𝟐

𝐁𝟑

𝐁𝟒

%RAD

𝟏𝟎𝟓RMSD

283.15

-11.1783

34.7407

-60.7227

54.1873

-19.1957

0.1275

0.4447

288.15

-10.9776

32.1122

-51.0703

40.4431

-12.5709

0.4085

1.3972

293.15

-10.7614

29.2467

-40.7972

26.0823

-5.6928

0.7081

2.4372

298.15

-10.5040

25.8645

-28.9295

9.7516

2.0986

1.0289

3.7387

303.15

-10.3991

23.9253

-21.9219

0.0627

6.7673

1.2371

4.5516

Table 14. Parameters of the Jouyban-Acree model for binary solvent mixtures at different temperatures and composition. Parameter

Valuea

Valueb

Valuec

Valued

Valuee

Valuef

𝑨𝟎

102.7905

38.5302

-121.3892

-98.9052

1097.1121

583.3314

𝑨𝟏

-4416.5132

-1432.9375

4945.1941

3643.9733

-48518.4891

-26090.0669

𝑨𝟐

-16.9249

-6.8799

16.5297

13.6628

-165.8297

-88.9113

𝑨𝟑

-121.1566

-89.4574

169.3031

152.7562

-1920.1196

-922.4466

𝑨𝟒

6450.0982

374.0556

1418.6967

631.5813

94699.2307

46653.9949

𝑨𝟓

1092.3115

13832.2108

-24265.2934

-19024.4172

-32585.2141

-12012.2016

𝑨𝟔

-5837.6814

-18650.1021

25509.3730

20197.8261

38937.4650

7780.9420

𝑨𝟕

3387.4225

8121.5677

-10380.5024

-8177.4798

-17371.5382

-1740.1898

𝑨𝟖

19.4357

14.1935

-23.7987

-21.9411

288.9350

139.5091

%RAD

2.4489

1.9738

2.0291

1.0015

2.6855

1.8685

𝟏𝟎𝟓RMSD

7.6723

12.6309

11.8973

5.9408

11.7177

10.9979

a valuea is the value of the parameters of the Jouyban-Acree model for binary solvent mixtures of ethyl acetate +



Page 28 of 49

n-heptane in the temperature range of 283.15K to 333.15K b valueb is the value of the parameters of the Jouyban-Acree model for binary solvent mixtures of ethyl acetate + 1,1,2-trichloroethane in the temperature range of 283.15K to 333.15K c valuec is the value of the parameters of the Jouyban-Acree model for binary solvent mixtures of ethyl acetate + cyclohexane in the temperature range of 283.15K to 333.15K d valued is the value of the parameters of the Jouyban-Acree model for binary solvent mixtures of ethyl acetate + toluene in the temperature range of 283.15K to 333.15K e valuee is the value of the parameters of the Jouyban-Acree model for binary solvent mixtures of ethyl acetate + diethyl ether in the temperature range of 283.15K to 333.15K f valuef is the value of the parameters of the Jouyban-Acree model for binary solvent mixtures of ethyl acetate + petroleum ether in the temperature range of 283.15K to 333.15K

Table 15. Dissolution enthalpy and entropy of β-HNIW in ethyl acetate + n-heptane solvent mixtures in the temperature range of 283.15K to 333.15K. 𝒙𝟑a

∆𝒅𝒊𝒔𝑯(𝒌𝑱 ∙ 𝒎𝒐𝒍 ―𝟏)

∆𝒅𝒊𝒔𝑺(𝑱 ∙ 𝒎𝒐𝒍 ―𝟏 ∙ 𝑲 ―𝟏)

0.8198

-28.0739

-2.2861

0.7707

-30.0709

-2.5534

0.6959

-35.4201

-3.5744

0.6304

-38.9669

-4.0434

0.5346

-50.2648

-6.3509

0.4312

-61.7439

-8.2521

0.3266

-65.6848

-7.2602

0.2214

-72.7866

-6.8478

Table 16. Dissolution enthalpy and entropy of β-HNIW in ethyl acetate + 1,1,2-trichloroethane solvent mixtures in the temperature range of 283.15K to 333.15K. 𝒙𝟑a


∆𝒅𝒊𝒔𝑺(𝑱 ∙ 𝒎𝒐𝒍 ―𝟏 ∙ 𝑲 ―𝟏)

0.8583

-26.3171

-2.0349

0.7762

-26.4144

-1.5246

0.6943

-27.4603

-1.1984

0.6052

-29.9487

-1.1005

0.5023

-35.2322

-1.4518

0.4319

-40.9581

-2.1176

0.3476

-50.4277

-3.4867

0.2746

-53.9096

-3.3914


Page 29 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 17. Dissolution enthalpy and entropy of β-HNIW in ethyl acetate + cyclohexane solvent mixtures in the temperature range of 283.15K to 333.15K. 𝒙𝟑a


∆𝒅𝒊𝒔𝑺(𝑱 ∙ 𝒎𝒐𝒍 ―𝟏 ∙ 𝑲 ―𝟏)

0.7926

-28.4646

-2.5743

0.7241

-30.8774

-2.9205

0.6574

-33.5819

-3.3084

0.5889

-36.9042

-3.7974

0.4880

-43.0349

-4.7141

0.3890

-51.2508

-5.9716

0.2909

-62.5071

-7.6206

0.1928

-75.4487

-8.5131

Table 18. Dissolution enthalpy and entropy of β-HNIW in ethyl acetate + toluene solvent mixtures in the temperature range of 283.15K to 333.15K. 𝒙𝟑a


∆𝒅𝒊𝒔𝑺(𝑱 ∙ 𝒎𝒐𝒍 ―𝟏 ∙ 𝑲 ―𝟏)

0.8071

-23.9535

-1.3886

0.7509

-26.3105

-1.7994

0.6853

-29.0192

-2.2379

0.6107

-31.9715

-2.6531

0.5095

-35.6987

-3.0263

0.4108

-39.3385

-3.2153

0.3010

-43.9902

-3.2083

0.2073

-51.2284

-3.3156

Table 19. Dissolution enthalpy and entropy of β-HNIW in ethyl acetate + diethyl ether solvent mixtures in the temperature range of 283.15K to 303.15K. 𝒙𝟑a


∆𝒅𝒊𝒔𝑺(𝑱 ∙ 𝒎𝒐𝒍 ―𝟏 ∙ 𝑲 ―𝟏)

0.7709

-30.9539

-3.2140

0.7052

-33.8322

-3.6658

0.6342

-36.4502

-3.9754

0.5579

-39.2437

-4.2494

0.4582

-42.8271

-4.4747

0.3593

-47.4804

-4.8027

0.2561

-56.2849

-5.7888



0.1738

-95.6941

Page 30 of 49

-14.6785

Table 20. Dissolution enthalpy and entropy of β-HNIW in ethyl acetate + petroleum ether solvent mixtures in the temperature range of 283.15K to 303.15K. 𝒙𝟑a


∆𝒅𝒊𝒔𝑺(𝑱 ∙ 𝒎𝒐𝒍 ―𝟏 ∙ 𝑲 ―𝟏)

0.7887

-36.2956

-4.6180

0.7152

-34.5829

-3.6819

0.6532

-34.1647

-3.1169

0.5832

-35.0984

-2.7874

0.4835

-39.4316

-2.9409

0.3835

-50.3920

-4.5509

0.2867

-74.0328

-9.0746

0.1891

-79.2840

-7.3245

a x3a is the the mole fraction of ethyl acetate in binary solvent mixtures when absence of solute.


Page 31 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 1. Chemical structure of HNIW and molecular structure of β,ε-HNIW.



-HNIW -HNIW

Relative Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 49

10

20

30

40

50

2 theta () Fig. 2. Powder X-ray diffraction pattern of HNIW.


Page 33 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 3. Raman spectra of β,Ɛ-HNIW in the Raman shift range of 150cm-1 to 1800cm-1.



Fig. 4. Raman spectra of -HNIW, solution and solvent in the Raman shift range of 200cm-1 to 600cm-1.


Page 34 of 49

Page 35 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 5. Raman spectra of -HNIW, solution and solvent in the Raman shift range of 1500cm-1 to 1700cm1.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Predicted HNIW concentration in solution (g/g)


Page 36 of 49

0.6

Rsqr=0.9994 0.5

0.4

0.3

0.2

0.1

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Actual HNIW concentration in solution (g/g) Fig. 6. Calibration curve showing the predicted solute concentration measured by Raman spectroscopy as a function of actual solute concentration, with distinct peaks at 216cm-1, 310cm-1, and 1612cm-1. The calibration curve of HNIW concentration in solution is developed using relative Raman intensity, which is HNIW solute peaks (216cm-1, 310cm-1, and 1612cm-1)/solvent peak (418cm-1).


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Predicted -HNIW concentration(g/g)

Page 37 of 49

0.8

Rsqr=0.9956

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

Actual -HNIW concentration (g/g) Fig. 7. Calibration curve showing the predicted -HNIW concentration measured by Raman spectroscopy as a function of actual -HNIW concentration, with a distinct peak at 282cm-1.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Predicted -HNIW concentration (g/g)


Page 38 of 49

0.5

Rsqr=0.9883 0.4

0.3

0.2

0.1

0.0 0.0

0.1

0.2

0.3

0.4

0.5

Actual -HNIW concentration (g/g)

Fig. 8. Calibration curve showing the predicted -HNIW concentration measured by Raman spectroscopy as a function of actual -HNIW concentration, with a distinct peak at 344cm-1.


Page 39 of 49

0.07 Gravimetric method Raman spectrometer

0.06

0.05

0.04

x1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.03

0.02

0.01

0.00 0.2

0.3

0.4

0.5

0.6

0.7

0.8

x3 Fig. 9. Comparison of mole fraction solubility of -HNIW by each measurement method in binary solvent mixtures (ethyl acetate + n-heptane) as a function of initial mole fraction of ethyl acetate. The calibration curve of HNIW concentration in solution is developed using relative Raman intensity, which is HNIW solute peaks (216cm-1, 310cm-1, and 1612cm-1)/solvent peak (418cm-1).



Fig. 10. Concentration of HNIW and solubility of HNIW in binary solvent mixtures (ethyl acetate + n-heptane) measured by Raman spectroscopy.


Page 40 of 49

Page 41 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 11. Raman waterfall plot of dissolved HNIW solution in binary solvent mixtures (ethyl acetate + nheptane) at 298.15K, measured by Raman spectroscopy.



0.10

0.08

0.06

x1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 49

0.04

0.02

0.00 280

290

300

310

320

330

T/K Fig. 12. Mole fraction solubility of 𝛃-HNIW in binary solvent mixtures (ethyl acetate + n-heptane) as a function of temperature. ◊, 𝒙𝟑 = 0.8198; ◆, 𝒙𝟑 = 0.7707; □, 𝒙𝟑 = 0.6959; ∎, 𝒙𝟑 = 0.6304; ∆, 𝒙𝟑 = 0.5346; ▼, 𝒙𝟑 = 0.4312; ○, 𝒙𝟑 = 0.3266; ●, 𝒙𝟑 = 0.2214. The solid lines are calculated using the van’t Hoff equation.


Page 43 of 49

0.12

0.10

0.08

x1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.06

0.04

0.02

0.00 280

290

300

310

320

330

T/K Fig. 13. Mole fraction solubility of 𝛃-HNIW in binary solvent mixtures (ethyl acetate + 1,1,2trichloroethane) as a function of temperature. ◊, 𝒙𝟑 = 0.8583; ◆, 𝒙𝟑 = 0.7762; □, 𝒙𝟑 = 0.6943; ∎, 𝒙𝟑 = 0.6052; ∆, 𝒙𝟑 = 0.5023; ▼, 𝒙𝟑 = 0.4319; ○, 𝒙𝟑 = 0.3476; ●, 𝒙𝟑 = 0.2746. The solid lines are calculated using the van’t Hoff equation.



0.10

0.08

0.06

x1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 44 of 49

0.04

0.02

0.00 280

290

300

310

320

330

T/K Fig. 14. Mole fraction solubility of 𝛃-HNIW in binary solvent mixtures (ethyl acetate + cyclohexane) as a function of temperature. ◊, 𝒙𝟑 = 0.7926; ◆, 𝒙𝟑 = 0.7241; □, 𝒙𝟑 = 0.6574; ∎, 𝒙𝟑 = 0.5889; ∆, 𝒙𝟑 = 0.4880; ▼, 𝒙𝟑 = 0.3810; ○, 𝒙𝟑 = 0.2909; ●, 𝒙𝟑 = 0.1928. The solid lines are calculated using the van’t Hoff equation.


Page 45 of 49

0.12

0.10

0.08

x1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.06

0.04

0.02

0.00 280

290

300

310

320

330

T/K Fig. 15. Mole fraction solubility of 𝛃-HNIW in binary solvent mixtures (ethyl acetate + toluene) as a function of temperature. ◊, 𝒙𝟑 = 0.8071; ◆, 𝒙𝟑 = 0.7509; □, 𝒙𝟑 = 0.6853; ∎, 𝒙𝟑 = 0.6107; ∆, 𝒙𝟑 = 0.5095; ▼, 𝒙𝟑 = 0.4108; ○, 𝒙𝟑 = 0.3010; ●, 𝒙𝟑 = 0.2073. The solid lines are calculated using the van’t Hoff equation.



0.10

0.08

0.06

x1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 46 of 49

0.04

0.02

0.00 280

285

290

295

300

305

T/K Fig. 16. Mole fraction solubility of 𝛃-HNIW in binary solvent mixtures (ethyl acetate + diethyl ether) as a function of temperature. ◊, 𝒙𝟑 = 0.7709; ◆, 𝒙𝟑 = 0.7052; □, 𝒙𝟑 = 0.6342; ∎, 𝒙𝟑 = 0.5579; ∆, 𝒙𝟑 = 0.4582; ▼, 𝒙𝟑 = 0.3593; ○, 𝒙𝟑 = 0.2561; ●, 𝒙𝟑 = 0.1738. The solid lines are calculated using the van’t Hoff equation.


Page 47 of 49

0.10

0.08

0.06

x1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.04

0.02

0.00 280

285

290

295

300

305

T/K Fig. 17. Mole fraction solubility of 𝛃-HNIW in binary solvent mixtures (ethyl acetate + petroleum ether) as a function of temperature. ◊, 𝒙𝟑 = 0.7887; ◆, 𝒙𝟑 = 0.7152; □, 𝒙𝟑 = 0.6532; ∎, 𝒙𝟑 = 0.5832; ∆, 𝒙𝟑 = 0.4835; ▼, 𝒙𝟑 = 0.3835; ○, 𝒙𝟑 = 0.2867; ●, 𝒙𝟑 = 0.1891. The solid lines are calculated using the van’t Hoff equation.



0.12

0.10

0.08

0.06

x1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 48 of 49

0.04

0.02

0.00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

x3 Fig. 18. Mole fraction solubility of -HNIW as a function of mole fraction of ethyl acetate at 293.15K. ■, petroleum ether; △, n-heptane; ○, cyclohexane; ●, 1,1,2-trichloroethane; ▼, diethyl ether; □, toluene. The lines are calculated using the CNIBS/R-K equation.


Page 49 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


For Table of Contents Use Only

Solubility measurement study on a metastable polymorph of β-2,4,6,8,10,12-hexanitro2,4,6,8,10,12-hexaazaisowurtzitane by Raman spectroscopy In-Ho Park1, Hee-Og Yang1, Jun-Hyung Kim2, Kwang-Joo Kim1,*

TOC graphic

Synopsis Raman spectroscopy was used to measure the solubility of the metastable form of 2,4,6,8,10,12hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (HNIW) as well as stable form(-HNIW) in organic binary solvent mixtures. The distinct Raman spectra peaks of the solid, solute, solution, and solvent were used for measurement of their concentrations. Relationships between their concentrations and Raman intensity measured successfully the solubility of HNIW in binary solvent mixtures during the dissolving process.


Solubility Measurement Study on a Metastable Polymorph of Î²-2,4,6,8

Recommend Documents