Solubility, crystallization and oiling-out behavior of PEGDME: 1. Pure-solvent systems

Fluid Phase Equilibria 298 (2010) 253–261

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Solubility, crystallization and oiling-out behavior of PEGDME: 1. Pure-solvent systems Kai Kiesow, Feelly Ruether ∗ , Gabriele Sadowski Laboratory of Thermodynamics, Department of Biochemical and Chemical Engineering, Technische Universitaet Dortmund, Emil-Figge-Str. 70, 44227 Dortmund, Germany

a r t i c l e

i n f o

Article history: Received 28 January 2010 Received in revised form 30 July 2010 Accepted 9 August 2010 Available online 14 August 2010 Keywords: Oiling out Solid–liquid equilibria Crystallization PC-SAFT

a b s t r a c t Oiling out denotes a (metastable) liquid–liquid demixing during cooling crystallization prior to formation of the first crystals. This in most cases unwanted effect deteriorates the properties of the desired solid product. On the basis of the crystallization of the model substance polyethylenglycoldimethylether (PEGDME) from pure solvents, the influence of the molecular size of the solute and the type of solvent on the oiling-out behavior was systematically investigated. In this study the solubility data were determined gravimetrically as well as by using differential scanning calorimetry. The crystallization and oiling-out temperatures were detected visually in batch crystallization experiments. Oiling out was observed during the crystallization of PEGDME with a molar mass of 2000 g/mol (PEGDME2000) from diethylketone, ethyl acetate and 2-propanol, whereas no oiling out was detected during the cooling process of PEGDME with a molar mass of 1000 g/mol (PEGDME1000) from all solvents considered. Furthermore the oilingout temperature for PEGDME2000 was not significantly influenced by the chosen solvents diethylketone, ethyl acetate and 2-propanol. In the second part of this study, it is shown that the appearance and absence of oiling out in all considered solvents can be qualitatively predicted by the pertubed chain statistical association theory (PC-SAFT) only using solubility data. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Oiling out has initially been observed during the crystallization of complex molecules like proteins from aqueous solutions. The experimental investigation of the liquid–liquid phase separation is reported, e.g., for the crystallization of the bovine lens protein ␥II -crystals [1] and bovine pancreatic trypsin inhibitor (BPTI) [2]. The influence of additives on the liquid–liquid demixing during the crystallization of lysozyme solutions is presented in [3,4]. Therein Muschol and Rosenberger [3] determined the effect of NaCl on the binodal curve, whereas Galkin and Vekilov [4] found, that the addition of glycol and polyethylenglycol shift the phase boundary and even can suppress or enhance the nucleation rate of lysozyme. Similarly, Vivares and Bonnete report in [5], that a liquid–liquid phase separation delays the crystallization of urate oxidase in presence of polyethylenglycol. Furthermore oiling out was observed for the crystallization of several pharmaceutical compounds from water/alcohol solutions. In case of the crystallization of Osanetant (being researched for the treatment of schizophrenia) from ethanol/water mixtures it is reported, that liquid–liquid demixing prevented the drug from crystallizing [6–8].

∗ Corresponding author. Tel.: +49 231 755 3199; fax: +49 231 755 2572. E-mail address: [email protected] (F. Ruether). 0378-3812/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2010.08.005

It has also been reported that to obtain the desired product, on the one hand seeding [9,10] and on the other hand varying the solvent composition [11] were found to be appropriate to avoid oiling out during the cooling process. Nevertheless, the literature references so far only present experimental and phenomenological observations. No systematical investigation regarding the influence factors of oiling out (such as molecule size and solvent type, respectively) has been reported yet. To our best knowledge the feasibility of modeling or even predicting oiling out has only been investigated in our previous work considering the crystallization of 4,4 -dihydroxydiphenylsulfone (DHDPS) [12]. Therein, PC-SAFT has already been successfully applied to predict qualitatively the oiling-out behavior of DHDPS in solvent mixtures water/acetone [12]. Moreover, it was already used to describe the phase behavior of, e.g., polymers [13] and copolymers [14–16]. Since the use of a polymer allows for investigation of the size effect without chemical modification of the molecule, the crystallization of polyethylenglycoldimethylether (PEGDME) of different molecular weights is now investigated in this work. Furthermore, the influence of the solvent type on the oiling-out behavior is determined for the crystallization of PEGDME from diethylketone, 2-propanol and ethyl acetate, respectively. This paper is organized as follows: first, the solubility, crystallization and – when existing – the oiling-out temperature of PEGDME2000 and PEGDME1000 in diethylketone, ethyl acetate

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Table 1 Solubility data of PEGDME2000 in diethylketone, 2-propanol, and ethyl acetate. Grey-shaded data are determined by DSC, unshaded data are determined gravimetrically. Diethylketone L wPEGDME2000

[g/g]

0.0034 0.0043 0.0099 0.0159 0.0159 0.0509 0.1011 0.1499 0.3121 0.701 0.798

2-Propanol Solubility

T

[K]

281.06 289.66 295.71 300.41 300.55 302.44 305.38 305.56 308.07 316.32 319.41

L wPEGDME2000

Ethyl acetate [g/g]

0.0011 0.0032 0.0491 0.2026 0.2993 0.3991 0.4988

Solubility

T

[K]

289.65 295.71 307.12 309.08 310.97 311.83 313.58

L wPEGDME2000 [g/g]

TSolubility [K]

0.0102 0.0940 0.3767 0.5011 0.6943

296.13 299.55 305.19 308.70 315.01

Table 2 Solubility data of PEGDME1000 in diethylketone, 2-propanol and ethyl acetate. Grey-shaded data are determined by DSC, unshaded data are determined gravimatrically. Diethylketone L wPEGDME1000

0.0491 0.0997 0.1999 0.2990 0.5012 0.6968

[g/g]

2-Propanol Solubility

T

287.33 291.61 294.98 295.58 299.51 304.52

[K]

L wPEGDME1000

0.0035 0.0164 0.0248 0.0529 0.1026 0.1993 0.3004 0.4992 0.6936

Ethyl acetate [g/g]

Solubility

T

274.34 287.32 292.71 296.80 297.25 299.93 300.02 301.45 305.17

[K]

L wPEGDME1000 [g/g]

TSolubility [K]

0.0100 0.0484 0.1994 0.2933 0.3937 0.4983

287.34 288.55 290.44 292.81 295.20 297.54

L Fig. 1. Determination of the solubility temperature from the offset temperature of the heat-flow curve for the system PEGDME2000/2-propanol at mass fractions of wPEGDME = L = 0.5: (a) heat-flow curve and (b) T, w-diagram. 0.2 and wPEGDME

Fig. 2. Crystallization of PEGDME2000 from 2-propanol: (a) crystallization without oiling out at a weight fraction wPEGDME = 0.3 and (b) oiling out prior to crystallization at a weight fraction wPEGDME = 0.15.

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Table 3 Pure-component parameters of the PC-SAFT equation of state for PEGDME, diethylketone, ethyl acetate, and 2-propanol. Component

M [g/mol]

m/M [mol/g]

 [Å]

ε/k [K]

Ref.

PEGDME Diethylketone Ethyl acetate 2-Propanol

– 86.134 88.110 60.096

0.020352 0.03906 0.040149 0.06

4.0261 3.4877 3.3079 3.7000

250.00 252.70 230.80 240.00

This work [19] [18] This work

and 2-propanol is determined and discussed. In a second step, PCSAFT is applied to model the solubility of PEGDME2000 in pure solvents and subsequently to predict the presence or absence of oiling out for the systems considered. 2. Experiments 2.1. Materials PEGDME with a molar mass of 2000 g/mol (PEGDME2000) and 1000 g/mol (PEGDME1000) were used at synthetical-grade purity without any further purification and were supplied by Merck Schuchardt (Hohenbrunn, Germany) and Fluka (Buchs, Switzerland), respectively. Diethylketone supplied by Merck Schuchardt (Hohenbrunn, Germany), and ethyl acetate supplied by Merck (Darmstadt, Germany) were used at synthetical-grade purity, whereas 2-propanol supplied by Merck (Darmstadt, Germany) was used at analytical-grade purity. 2.2. Measurement of solubility of PEGDME in pure solvents The solubility of PEGDME in diethylketone, ethyl acetate, and 2-propanol was measured gravimetrically as well as by differential scanning calorimetry (DSC). For the gravimetric method a supersaturated solution was tempered while stirring in a 200-mL glass vessel with jacket heating and cooling until the solid–liquid equilibrium was reached. The stirrers were turned off to allow the solute for settling. Three samples of 2 mL each were taken from the liquid phase of each vial, weight and dried until the solvent was vaporized. To determine the solubility Table 4 Binary interaction parameter for the binary system PEGDME–diethylketone, –ethyl acetate and –2-propanol (pure-component parameters from Table 3). Binary system

kij

PEGDME–diethylketone PEGDME–ethyl acetate PEGDME–2-propanol

0.0196 0.02435 0.021

of PEGDME in the solvent gravimetrically, the remaining amount of the solid was weighted again. To obtain reproducible results, the solubility was measured three times at each temperature. The equilibrium temperature was measured using a PT100 resistance thermometer. This experimental setup allowed for detecting the solubility temperature with an accuracy of ±1 K. The experimental solubility data obtained from averaging three measurements at each temperature was determined with a deviation of less than 5% from the average value, as will be shown in Section 4. It turned out, that the solubility of PEGDME strongly depends on temperature for concentrations higher than 5 wt.% of PEGDME, as it can bee seen from Tables 1 and 2. In this range of concentration, the gravimetric method was hardly applicable and was therefore only used to determine the solubility of PEGDME for concentrations less than 5 wt.%. For higher concentrations the solubility was determined by DSC. The applicability of DSC for solubility measurements was already reported in [17]. For this purpose a known amount of PEGDME was dissolved in a certain amount of the solvent. The homogeneous solution was then with the help of a micropipette filled into a closable aluminium crucible with a volume of 110 ␮L. The mass of the sample varied between 60 and 100 mg depending on the concentration of PEGDME. The crucible was sealed by the use of a collet chuck and weighed with an accuracy of 0.01 mg before and after the DSC measurement to guarantee the leak tightness. The heat-flow curve between the sample and an empty reference crucible was determined by the use of the DSC Q100 from TA Instruments (Eschborn, Germany). For illustration, the heat-flow curves of the systems PEGDME2000 in 2-propanol with weight fractions L L of wPEGDME = 0.2 and wPEGDME = 0.5 are shown in Fig. 1a. The sample was first equilibrated at 280 K. After that the temperature was raised at a constant heating rate of 1 K/min. This led to dissolution of the solute accompanied by a change of enthalpy. The result is a deviation of the heat-flow curve from the baseline. In case of the illustrated dissolution process, the heat-flow decreases, reaches a minimum and increases again, due to the decrease of the remaining amount of solute in the sample crucible. After the solute is complete dissolved, the heat-flow curve flattens out and reaches again a constant level (final baseline).

Fig. 3. Microscopic observation of crystallization and oiling out: (a) microscopic view cell with Leica optical microscope DM4000M and (b) behaviour of the system PEGDME2000/diethylketone where droplets of a second liquid phase were observed prior to the formation of particles.

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Fig. 4. Heat-flow curves of PEGDME2000 (a, c and d) and PEGDME1000 (b, d and f) from diethylketone, ethyl acetate and 2-propanol determined by DSC at various PEGDME concentrations.

The solubility temperature according to the respective PEGDME concentration is determined as the offset temperature of the heatflow curve, which is the intersection of the tangents on the heatflow curve as illustrated in Fig. 1a. One tangent is drawn manually

at the final baseline, the second tangent is drawn manually through the inflection point of the increasing slope of the heat-flow curve. It can be seen from Fig. 1a, that the deviation of the heat-flow curve from the baseline strongly depends on the solubility of the

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257

Fig. 5. Phase diagrams of PEGDME1000 and PEGDME2000 in diethylketone (a and b), ethyl acetate (c and d) and 2-propanol (e and f). Symbols mean experimental solubility determined gravimetrically or by DSC (triangles), crystallization (circles) and – in case of PEGDME2000 – oiling-out temperatures (squares).

solute. Hence, the solubility curves of PEGDME in the considered solvents can be obtained by plotting the offset temperature of the heat-flow curve versus the respective weight fraction of PEGDME in a temperature-concentration diagram as shown in Fig. 1b.

To ensure the reproducibility of the results, the heat-flow curves were measured three times for each sample, and the average heat-flow curves out of three runs are presented in Section 4.

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Fig. 6. Solubility and oiling-out temperatures for the systems PEGDME/diethylketone: (a) PEGDME2000 and (b) PEGDME1000. Lines are calculation results using PC-SAFT. Symbols represent experimental solubility (triangles), crystallization (circles) and – in case of PEGDME2000 – oiling-out temperatures (squares).

The DSC method was capable to determine the solubility of PEGDME in the considered solvents for concentration higher than 5 wt.% of PEGDME. For smaller concentrations, the enthalpy of fusion was too small and did not result in a measureable deviation of the heat-flow curve from the baseline.

2.3. Measurement of crystallization temperatures and oiling out Crystallization and oiling out were observed visually. Therefore, a solution of known feed concentration was heated up to a temperature of about 5 K above the solubility curve. The 60 mL glass crystallizer used was equipped with jacket heating/cooling and a PT100 with an accuracy of ±0.2 K. Subsequently, the homogeneous solution was cooled down with a constant cooling rate of 0.5 K/min under stirring. The stirrer speed was set to 240 rpm. The crystallization temperature was then determined when the first crystals could be identified visually (Fig. 2a). As it can be seen from Fig. 2b, in case of oiling out, the solution became cloudy during cooling before any particles could be detected. Additionally, crystallization and oiling-out experiments were performed in a microscopic view cell (Fig. 3a) in order to prove

that the cloudiness was caused by the formation of a second liquid phase. The cell has a sample volume of 9 mL and is connected to a thermostat at the bottom side, which allows for heating and cooling of the sample. The temperature can be measured inside of the sample with a PT100. A Leica optical microscope DM4000M with a micro publisher 3.3 RTV digital camera from QImaging was used to observe crystallization processes inside the view cell. The view-cell experiments have been conducted as follows. A known amount of PEGDME was dissolved in a certain amount of solvent. Then the homogenous solution was filled into the view cell with the help of an injection device. Afterwards, the sample was cooled down with a cooling rate of 0.5 K/min without stirring. As an example, Fig. 3b shows the behaviour of the system PEGDME2000/diethylketone where droplets of a second liquid phase were observed prior to the formation of particles. 3. Modeling 3.1. Calculation of solid–liquid and liquid–liquid equilibria The solubility of PEGDME was calculated under the assumption that the solid phase consists only of pure PEGDME. Furthermore the

Fig. 7. Solubility and oiling-out temperature for the system PEGDME/ethyl acetate: (a) PEGDME2000 and (b) PEGDME1000. Symbols are experimental solubility (triangles), crystallization (circles) and oiling-out temperatures (squares). Lines are calculation results using PC-SAFT.

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259

Fig. 8. Solubility and oiling-out temperature for the system PEGDME/2-propanol: (a) PEGDME2000 and (b) PEGDME1000. Symbols represent experimental solubility (triangles), crystallization (circles) and oiling-out data (squares). Lines are calculation results using PC-SAFT.

influence of the difference in heat capacity of liquids and solids was neglected. Hence the solubility of PEGDME at atmospheric pressure can be calculated as follows: L xPEGDME =

1 L PEGDME



exp −

hSL PEGDME RT



1−

T SL TPEGDME



(1)

Therein, the solubility is represented by the mole fraction L L ), whereas PEGDME of PEGDME in the liquid phase (xPEGDME is the activity coefficient of PEGDME in the liquid phase. SL TPEGDME and hSL are the melting temperature and the PEGDME enthalpy of melting of PEGDME, respectively, both of which were determined using DSC. For the calculation of the (metastable) liquid–liquid equilibrium the phase-equilibrium conditions for all components i (PEGDME and solvent, respectively) have been used: xiL1 · iL1 = xiL2 · iL2

(2) 4. Results and discussion

3.2. PC-SAFT model In this work, the following contributions to PC-SAFT [18] were considered to calculate the residual Helmholtz energy (Ares ): Ares = Ahc + Adisp

(3)

The hard-chain contribution (hc) represents the repulsion between the molecules. For the attraction of the molecules in this work only dispersive interactions (disp) are taken into account. Hence, to model the phase behavior of the considered compounds with PCSAFT, three pure-component parameters have to be known, namely segment number (m), segment diameter (), and dispersion-energy parameter (ε/k). For mixtures, the conventional Berthelot–Lorentz combining rules are applied to calculate the segment diameter ( ij ), whereas one adjustable binary interaction parameter (kij ) is introduced to correct the dispersion-energy parameter in the mixture: ij = εij =

1 ( + j ) 2 i



εi εj (1 − kij )

PEGDME as well as the binary interaction parameter for the system PEGDME/diethylketone were fitted to the experimental solubility data of PEGDME2000 in diethylketone. In this work, only dispersive interactions have been taken into account. Hence, the three pure-component parameters for 2-propanol were fitted to density and vapor pressure data [20]. Afterwards, only the binary interaction parameters of the systems PEGDME/ethyl acetate and PEGDME/2-propanol were fitted to experimental solubility data of PEGDME2000 in ethyl acetate and 2-propanol, respectively. These parameters are presented in Tables 3 and 4. Subsequently, the solubility of PEGDME1000 in diethylketone, ethyl acetate and 2-propanol as well as the presence or absence of oiling out in the considered systems was calculated without readjusting any parameter. Hence these calculations are purely predictive.

(4) (5)

3.3. Estimation of the PC-SAFT parameters The PC-SAFT parameters of diethylketone and ethyl acetate can be found in [18,19] whereas the pure-component parameters of

4.1. Experimental results: solubility, oiling out and crystallization of PEGDME As an example, Fig. 4 shows the heat-flow curves of PEGDME2000 and PEGDME1000 in diethylketone (Fig. 4a and b), ethyl acetate (Fig. 4c and d) and 2-propanol (Fig. 4e and f) at three concentrations of PEGDME, each of them being between L L wPEGDME = 0.1 and wPEGDME = 0.7. In all diagrams the heat-flow is plotted versus temperature. It can be seen from the position of the heat-flow curve, that for all systems considered, the offset temperature – determined as explained in chapter 2 – and hence the solubility temperature increases with an increase of the PEGDME concentration. Although the peak of the heat-flow curves of PEGDME1000 in all solvents (Fig. 4b, d and f) is not as sharp as the heat-flow curves of the systems containing PEGDME2000 (Fig. 4a, c and e), the steep increase of the heat-flow curves at the end of the dissolution process allows for the determination of the offset temperature. All results of the solubility temperatures of PEGDME2000 and PEGDME1000 in diethylketone, ethyl acetate and 2-propanol are presented together with the solubility data measured gravimetrically in Tables 1 and 2. For the sake of clarity Tables 1 and 2 only contain the average values of three solubility measurements at each temperature. The experimental solubility data measured gravimetrically for the three samples deviate less than 5% from the

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Table 5 Crystallization and oiling-out data of PEGDME2000 in diethylketone, 2-propanol and ethyl acetate. Diethylketone L wPEGDME2000

[g/g]

0.0099 0.0503 0.1516 0.1992 0.3004 0.4981 0.6999 0.8033

2-Propanol Oiling out

T

[K]

Crystallization

T

284.56 287.56 289.98 298.40 301.45 304.99 305.37 310.01

[K]

L wPEGDME2000

Ethyl acetate [g/g]

0.0101 0.0499 0.0751 0.0999 0.1499 0.1751 0.1991 0.3001

Oiling out

T

Crystallization

[K]

T

296.85 301.89

L wPEGDME2000 [g/g]

0.0105 0.1020 0.1499 0.1997 0.2999 0.3499 0.4000 0.4990

303.01 303.82 304.70 303.77 301.70 302.70

average value (w < 5%), which is shown exemplarily for the solubility of PEGDME2000 in diethylketone at 295.71 K: the average average solubility of wPEGDME (295.71 K) = 0.0099 (see Table 1) was deter1 mined from the three experimental values wPEGDME (295.71 K) = 2 0.01033, w = 4.34%, wPEGDME (295.71 K) = 0.00969, w = 3 (295.71 K) = 0.00968, w = 2.22 %. 2.12%, and wPEGDME Additionally, since the melting temperature and enthalpy of melting of pure PEGDME2000 and PEGDME1000 are required for the solubility calculation in Section 4.2, these properties SL = 326.32 K were also determined by DSC resulting in: TPEGDME2000 SL = 252.20 kJ/mol, T = 315.16 K and and hSL PEGDME2000 PEGDME1000 = 127.69 kJ/mol. hSL PEGDME2000 The crystallization and oiling-out temperatures (when existing) are listed in Tables 5 and 6 and presented with the respective solubility data in the complete phase diagrams of PEGDME2000 and PEGDME1000 systems in Fig. 5. It can be seen from the form of the solubility curves, that the solubility data measured gravimetrically as well as by DSC correspond and overlap very well in the concentration range between 5 and 10 wt.% of PEGDME. To demonstrate the applicability of both techniques, the result of the gravimetric solubility measurement of L PEGDME2000 in diethylketone at 300.41 K (wPEGDME2000 = 0.0159, see Table 1, first column) was compared to the result of the solubility measurement obtained by DSC at the same concentration. It can be seen, that the solubility temperatures determined by the two methods deviate only by about 0.14 K. Hence, this confirms that both of them can be utilized for the solubility measurement. Furthermore, Fig. 5 shows that an oiling out has only been detected during the crystallization of PEGDME2000 (Fig. 5a, c and d) whereas no oiling out has been observed during the cooling process of PEGMDE1000 in all solvents considered (Fig. 5b, d and f). It can thus be concluded that the oiling-out behavior for the model substance PEGDME depends on the molecular size of the polymer. This result is in good agreement with the well-known liquid–liquid phase behavior of polymer/solvent systems as function of the polymer molar mass: a decrease of the molar mass of a polymer in general leads to an increase in miscibility; hence the miscibility gap becomes smaller for lower molar masses or even disappears.

[K]

TOiling out [K]

TCrystallization [K] 278.04 282.08 285.01

291.07 294.93 295.84 292.04 294.18

The phase diagrams of PEGDME2000 show that the oilingout temperature does not differ significantly for the solvents diethylketone, ethyl acetate, and 2-propanol. The approximated experimental critical temperature of the liquid–liquid miscibility gap ranges between 305 K in case of diethylketone and 2-propanol and 295 K in case of ethyl acetate. None of the solvents chosen led to a remarkable decrease of the oiling-out temperature or even prevention of oiling out. Only the concentration range of the miscibility gap differs between wPEGDME = 0.2 and wPEGDME = 0.6 for diethylketone and wPEGDME = 0.075 and wPEGDME = 0.175 for 2propanol. Additionally the determined crystallization points are more or less in the same temperature range between 280 and 310 K for all three solvents. Apparently, the crystallization and oiling-out behavior of PEGDME2000 do not depend strongly on the considered type of solvents.

4.2. Modeling and prediction results Fig. 6a shows the comparison of the experimental solubility, crystallization and oiling-out temperatures of PEGDME2000 in diethylketone to the modeling results using PC-SAFT. For this figure L and all the following figures the molefraction xPEGDME as calculated L using Eq. (1) was converted into massfraction wPEGDME . It can be seen from Fig. 6a that PC-SAFT is able to satisfactorily describe the experimental solubility data of PEGDME with a molar mass of 2000 g/mol in diethylketone. Even the strong temperature dependence of the solubility can be captured over the whole range of concentration without using a temperature-depending binary interaction parameter. Furthermore, Fig. 6a shows that PC-SAFT predicts a liquid–liquid miscibility gap for the system PEGDME2000/diethylketone in the L considered range of concentration between wPEGDME = 0.2 and L wPEGDME = 0.6. Even though the predicted critical temperature of the miscibility gap deviates about 10 K from the experimental oiling-out temperature at the same weight fraction of PEGDME, it can be concluded, that PC-SAFT is able to predict the appearance of oiling out qualitatively for the considered system only based on binary solubility data.

Table 6 Crystallization data of PEGDME1000 in diethylketone, 2-propanol and ethyl acetate. Diethylketone L wPEGDME1000

0.0500 0.0964 0.1496 0.1992 0.2446 0.3001 0.3537 0.3994 0.4999 0.6993

[g/g]

2-Propanol Crystallization

T

278.41 281.66 283.73 285.77 287.72 289.32 290.68 291.89 294.22 299.60

[K]

L wPEGDME1000

0.0501 0.1002 0.1433 0.1996 0.2978 0.4000 0.5002 0.6997

Ethyl acetate [g/g]

Crystallization

T

290.79 292.60 293.85 294.47 295.80 296.80 297.44 300.33

[K]

L wPEGDME1000 [g/g]

TCrystallization [K]

0.1000 0.1410 0.2000 0.2998 0.3998 0.5000 0.5995

277.69 279.89 282.42 286.04 289.43 292.60 295.91

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Without readjusting any parameter PC-SAFT also satisfactorily predicts the solubility of PEGDME1000 in diethylketone (Fig. 6b). The absence of a calculated miscibility gap in the same range of temperature compared to Fig. 6a (270–330 K) shows that PC-SAFT is able to capture the difference in molecular size of the PEGDME1000 and the PEGDME2000 and is able to predict the absence of oiling out for PEGDME1000/diethylketone in the mentioned temperature range. To describe the oiling-out behavior of PEGDME in ethyl acetate and 2-propanol, only the binary interaction parameters of the systems PEGDME/ethyl acetate and PEGDME/2-propanol, respectively, had to be fitted to binary solubility data of PEGDME2000 in the respective solvents. The modeling results are presented in Figs. 7 and 8. It can be seen from Fig. 7a that PC-SAFT is able to model satisfactorily the solubility of PEGDME2000 in ethyl acetate. Additionally, PC-SAFT qualitatively predicts a liquid–liquid miscibility gap within the concentration range of the experimentally observed oiling-out region. The prediction of the solubility and the oiling-out behavior of PEGDME1000 in ethyl acetate compared to the respective experimental data are shown in Fig. 7b. Again, PC-SAFT is able to predict satisfactorily the experimental solubility data. The absence of a calculated miscibility gap indicates that PC-SAFT is also able to predict the absence of oiling out for this system within the same temperature range. Fig. 8a shows, that PC-SAFT also predicts a liquid–liquid miscibility gap for the system PEGDME2000/2-propanol, although the concentration range of the calculation results deviates slightly from the experimentally observed oiling-out region. Nevertheless, it can be seen from Fig. 8b that PC-SAFT is able to predict the absence of oiling out in case of PEGDME1000/2-propanol within the same range of temperature. Finally it can be concluded, that only based on binary solubility data, PC-SAFT successfully predicts the presence or absence of the oiling-out region as function of the molecular weight of the solute. Furthermore, PC-SAFT was able to predict qualitatively the oilingout region of PEGDME samples in diethylketone, ethyl acetate, and 2-propanol. 5. Conclusions In this work the solubility, crystallization and – when existing – the oiling-out temperatures of PEGDME2000 and PEGDME1000 in the solvents diethylketone, ethyl acetate and 2-propanol, respectively, were presented. The solubility was determined gravimetrically as well as by using DSC measurements whereas crystallization and oiling out were observed visually. The experimental results proved a dependence of the oiling-out behavior on the molecular size of the solute whereas it does not significantly depend on the considered type of solvent. Moreover, this work demonstrated the feasibility of predicting the molecular-weight dependence of the solubility of the PEGDME-systems as well as that of their oiling-out behavior by applying the PC-SAFT equation of state. On the basis of binary solubility data of PEGDME2000 in diethylketone, ethyl acetate, and 2-propanol, PC-SAFT was able to predict satisfactorily the solubility of PEGDME1000 in the respective solvents. Beyond that, PC-SAFT was capable of predicting the presence or absence of an oiling out depending on the molar mass of PEGDME in all solvents considered.

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