Article pubs.acs.org/IECR
Experimental and Modeling Studies on the Solubility of D‑Arabinose, D‑Fructose, D‑Glucose, D‑Mannose, Sucrose and D‑Xylose in Methanol and Methanol−Water Mixtures Robert-Jan van Putten,†,‡ Jozef G. M. Winkelman,‡ Farhad Keihan,† Jan C. van der Waal,† Ed de Jong,*,† and Hero J. Heeres*,‡ †
Avantium Chemicals, Zekeringstraat 29, 1014 BV Amsterdam, The Netherlands Department of Chemical Engineering, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
‡
S Supporting Information *
ABSTRACT: The solubilities of D-glucose, D-arabinose, D-xylose, D-fructose, D-mannose, and sucrose in methanol and methanol−water mixtures (99% purity. Methanol was obtained from Fisher and was HPLC gradient grade. Milli-Q grade water was used for all experiments. Solubility Measurements. All experiments were performed using the Avantium Pharmatech Crystal16 equipment. This equipment has been specifically designed for determining clear points and cloud points for crystallization studies. It consists of four heating blocks with magnetic stirring, with four slots each for standard 1.6 mL HPLC vials. Validation of the equipment showed that the temperature of the liquid in the vial was always within 1 K of the set point temperature for the complete temperature range of the experiments. Each reactor has a light source and a sensor. The equipment determines the percentage of light passing through the vials allowing for automatic turbidity measurements and thus for the determination of the clear points and cloud points of the solutions under investigation. The software provided with the Crystal16 equipment allows for automatic and regulated temperature increases and cooling
ln(γixi) =
ΔC pi ⎛ ΔHf, i ⎛ 1 Tf, i Tf, i ⎞ 1⎞ ⎜⎜ − ⎟⎟ − + ln ⎟ ⎜1 − R ⎝ Tf, i T⎠ R ⎝ T T ⎠ (1)
where γi and xi denote the activity coefficient and the molar fraction of the solute in the liquid phase. ΔCpi denotes the difference of the solute’s specific heat in the solid and liquid phases, T is the actual temperature and Tf,i the fusion point temperature. Equation 1 is obtained with the assumptions that the solid phase that is in equilibrium with the solution consists of the pure solute and that ΔCpi is independent of the temperature in the range of T to Tf,i Equation 1 can be used to evaluate the experimental results if a model for the activity of the solute is implemented. Here the UNIQUAC model formulation26 was chosen to model the activity coefficients because of its suitability for the systems under investigation, i.e. a highly polar, non-electrolyte, lowpressure mixture that contains both large and small molecules.27 From eq 2 ln γi is calculated: 8286
dx.doi.org/10.1021/ie500576q | Ind. Eng. Chem. Res. 2014, 53, 8285−8290
Industrial & Engineering Chemistry Research
Article
⎛ ϕ ϕ⎞ ln γi = 1 − ϕi + ln ϕi − 5qi⎜1 − i + ln i ⎟ θi θi ⎠ ⎝ ⎛ + qi⎜⎜1 − ln Si − ⎝
∑ j
⎞ xjθτ j i,j ⎟ Sj ⎟⎠
(2)
where ϕ and θ depend on the volume and surface area parameters ri and qi, and S also on the binary parameters τij (see list of symbols).The values of the parameters ri and qi were taken from Poling et al.27 (Table 2). Table 2. UNIQUAC Parameters ri and qi27 methanol water arabinose fructose glucose mannose sucrose xylose
M [g/mol]
ri
qi
32.04 18.015 28 150.13 180.16 180.16 180.16 342.30 150.13
1.9011 0.92 6.7089 8.1589 8.1558 8.1558 14.5586 6.7089
2.048 1.40 6.492 8.004 7.92 7.92 13.764 6.492
Figure 1. The solubility of glucose in pure methanol and methanol/ water mixtures containing up to 25 wt % water. Symbols: measured results of this work. Lines: calculated according to the model of this work.
The adjustable binary parameters are defined in terms of binary energy interaction parameters Aij: τij = exp( −Aij /T )
(3)
where in general Aii = Ajj = 0 and Aij ≠ Aji. The values of the parameters Aij were obtained by fitting the calculated solubilities of eqs 1−2 to the measured ones using a standard Newton routine for nonlinear optimization. The physical properties of the carbohydrates mentioned in eq 1, i.e. the heat of fusion, the temperature of fusion, and the solid−liquid specific heat difference, were taken from the literature when available, or estimated following the literature (Table 3).
Figure 2. The solubility of arabinose in pure methanol and methanol/ water mixtures containing up to 25 wt % water. Symbols: measured results of this work. Lines: calculated according to the model of this work.
Table 3. Physical Properties of the Sugars Used in This Study
a
sugar
ΔHf [kJ/mol]
Tf [K]
ΔCp [J/mol.K]
arabinose fructose glucose mannose sucrose xylose
35.7828 33.030 3228,30,32 24.728 46.228 31.728
43529 37830,31 42029−32 40428,29 45229,31 42028,29,31
120b 120a 120a 120a 25433 120a
Figure 3. The solubility of xylose in pure methanol and methanol/ water mixtures containing up to 25 wt % water. Symbols: measured results of this work. Lines: calculated according to the model of this work.
Estimated by Ferreira et al.15 bEstimated following Ferreira et al.15
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RESULTS AND DISCUSSION Experimental Studies. The solubility of the six sugars in methanol and methanol/water mixtures (0−25 wt % water) was studied at temperatures in the range of 298−353 K. Determination of the solubility of fructose at a water content higher than 10 wt % proved not possible due to stirring issues as a result of the high solid loading required by the high solubility under those conditions. The experimental results, combined with the modeled solubilities (vide inf ra) are shown in Figures 1−6. As expected the solubility of the sugars increased with temperature and water content. Of the sugars tested fructose shows clearly the highest solubility in methanol,
followed in order of decreasing solubility by mannose, xylose, glucose, arabinose and sucrose. Notably arabinose and glucose showed almost equal solubility in pure methanol. The order was the same in methanol containing 10 wt % water, with the exception that glucose now possessed significantly better solubility than arabinose. Modeling studies. The UNIQUAC binary energy interaction parameters were obtained by matching the calculated to the measured solubilities, and the results are given in Table 4. The data were modeled on a mass basis to avoid possible complications due to density changes. 8287
dx.doi.org/10.1021/ie500576q | Ind. Eng. Chem. Res. 2014, 53, 8285−8290
Industrial & Engineering Chemistry Research
Article
A parity plot of experimental versus calculated values for 323 data points is shown in Figure 7. This figure clearly shows that the model fits the experimental results very well.
Figure 4. The solubility of fructose in pure methanol and methanol/ water mixtures containing up to 10 wt % water. Symbols: measured results of this work. Lines: calculated according to the model of this work.
Figure 7. Parity plot of the solubilities of six carbohydrates (323 points).
The modeling results for all sugars are given in Figures 1−6. The measured solubilities show consistent trends, and the data points are all very close to the model lines, again indicating that the model fits the data very well. Deviations between the model and experimental data in the figures are mainly due to small differences in the actual water concentration in the solutions and not due to modeling inaccuracies. For instance, in the specific case of Figure 1 at 15 wt % water, the experimental points above the line were actually obtained at 16.1 wt % water in methanol and those below that at 15.6 wt % water, whereas the line represents the model prediction at a 15 wt % water content. The actual water contents were used in estimating the parameters for the model. The average absolute error between the calculated model and the experimental data was 3.7%, which shows that the obtained models are accurate representations of the solubilities of these sugars in methanolic mixtures. As such, the high-throughput technology is very well suited for this type of solubility research. Literature comparison. The solubility of fructose, glucose, and sucrose in methanol and methanol−water mixtures has been reported (Table 1). Figures 8−10 show a comparison of the experimental solubility data obtained in this study with those previously reported. In addition, the model lines are provided. For fructose (Figure 8), agreement between our and the literature data is, in general, good in the range 310−325 K. In addition, the combined data are predicted well using the model provided in this paper. However, at both the high and low end of the temperature range, some deviations between our
Figure 5. The solubility of mannose in pure methanol and methanol/ water mixtures containing up to 25 wt % water. Symbols: measured results of this work. Lines: calculated according to the model of this work.
Figure 6. The solubility of sucrose in pure methanol and methanol/ water mixtures containing up to 25 wt % water. Symbols: measured results of this work. Lines: calculated according to the model of this work.
Table 4. Modelled UNIQUAC Binary Energy Interaction Parameters Aij methanol water arabinose fructose glucose mannose sucrose xylose
methanol
water
arabinose
fructose
glucose
mannose
sucrose
xylose
0 167.19 112.39 171.59 122.22 226.14 187.87 152.50
−13.88 0 −1.34 48.58 380.87 −225.16 410.38 −164.80
79.48 57.73 0 − − − − −
−6.64 65.91 − 0 − − − −
92.31 −124.81 − − 0 − − −
13.72 6558.79 − − − 0 − −
43.73 −127.48 − − − − 0 −
37.67 306.31 − − − − − 0
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dx.doi.org/10.1021/ie500576q | Ind. Eng. Chem. Res. 2014, 53, 8285−8290
Industrial & Engineering Chemistry Research
Article
In Figure 9 the experimental glucose data and the model developed in this work are compared with the results from literature. In pure methanol, our experimental data and those obtained by Montañes et al.22 and Macedo and Peres20 are in agreement, although the literature results are consistently slightly higher. The glucose solubilities in methanol with 10 wt % water at 313 and 333 K reported by Macedo and Peres20 are only slightly above the model line obtained in this work. At 20 wt % water content the results reported by Macedo and Peres20 are significantly higher than the model line obtained in this work. In Figure 10 the sucrose solubility data and model from this work are compared to results from the literature. At all three water concentrations given, the data reported by Macedo and Peres20 are exactly in line with the model and data obtained in this work.
Figure 8. Comparison of fructose solubility vs temperature in pure methanol (0%) and methanol with 10% by weight water (10%). Symbols: closed symbols: 0% water; open symbols: 10% water; ▲: Montañes et al.;22 ◇, ◆: Macedo and Peres;17 □, ■: this work. Lines: calculated according to the model of this work.
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CONCLUSIONS The solubilities of six sugars in methanol and methanol−water mixtures (
