Article pubs.acs.org/EF
Determination of the Solubility Parameters of Biodiesel from Vegetable Oils Matheus M. Batista, Reginaldo Guirardello, and Maria A. Kraḧ enbühl* School of Chemical Engineering−UNICAMP, 13083-970 Campinas, SP, Brazil ABSTRACT: The fatty acid methyl esters of vegetable oils and animal fats, more commonly known as biodiesel, represent a renewable, biodegradable, noninflammable, and low toxicity alternative to diesel. In this study, the Hansen solubility parameters (HSPs) and the interaction radius of the solute sphere (R0) were determined for the biodiesel derived from soybean oil, coconut oil, palm oil, and castor oil, using 45 solvents and solvent mixtures. The values for the HSPs and R0 obtained for the different biodiesels were soybean (15.03, 3.69, 8.92, and 11.33; MPa(1/2)); coconut (15.12, 3.99, 9.25, and 10.92; MPa(1/2)); palm (15.43, 5.28, 6.61, and 10.54; MPa(1/2)); and castor (16.10, 6.72, 9.11, and 11.78; MPa(1/2)). The HSPs of four biofuels were also determined using the average values of the fatty esters of each oil, calculated using group contribution. Subsequently, the solubilities of the biofuels were predicted using the van Krevelen−Hoftyzer, Greenhalgh, and Bagley approaches.
1. INTRODUCTION Biodiesel is a renewable fuel for diesel engines produced from biological oils and fats and considered as a potential source of fuel. The use of biodiesel as a fuel is growing rapidly worldwide since its production chain has promising potential in various sectors, such as the social, environmental, and technological sectors. From the environmental aspect, the emission of pollutants such as SOx, CO, CO2, and hydrocarbons in exhaust gas can be reduced.1,2 Many types of vegetable oil have been investigated for the production of biodiesel, among which soybean, sunflower, castor, coconut, palm, canola, cottonseed, and others stand out, with diversified fatty acid compositions. Methanol and ethanol are the alcohols most frequently used in the transesterification reactions. Therefore, biodiesel can be obtained by the transesterification of triacylglycerol with an excess of alcohol. These triacylglycerols are converted to the corresponding alkyl esters of straight chain fatty acids, with glycerol and water as the byproducts.3−5 The biodiesel production reaction can be carried out in the presence of homogeneous (alkaline and acid), heterogeneous (zeolites, sulfonic resins), or enzymatic (lipases) catalysts or with no catalyst using supercritical conditions. The differences between the chemical structures of biodiesel (mixture of monoalkyl esters of saturated and unsaturated long-chain fatty acids) and diesel fuel (mixture of paraffinic, naphthenic, aromatics, and olefins from approximately C9 to C20) generate different results in their basic properties, such as the cetane number, heat of combustion, cold flow, oxidative stability, viscosity, and lubricity.6−8 Biodiesel is also considered a biosolvent due to its properties (such as being renewable, biodegradable, noninflammable, nontoxic, ecofriendly, and having good solubility) and could be an integral part of green chemistry, not only as an environmentally friendly fuel alternative but also as an effective diluent for liquid−liquid extraction.9,10 The term “solubility parameters” (δT) was first used by Hildebrand and Scott,11,12 who postulated that interactions such as solvation should be stronger when the δT’s of the solvent and solute are equal. The Hildebrand solubility parameters are determined in the absence of any specific interactions, especially © XXXX American Chemical Society
hydrogen-bonding. Hansen has extended the theory developed by Hildebrand to polar and associated compounds by dividing the δT parameters into three-dimensional solubility parameters, consisting of dispersive interactions, polar interactions, and hydrogen-bonding interactions.13 These three components are not arithmetically additive, but they appear as a vector, thus representing Hildebrand’s solubility parameters (δT) in the three-dimensional space.14 Material with similar Hansen solubility parameters (HSPs) will show physical affinities. The theorical classical and group contribution methods are also commom. The classical method13,15 consists of testing the solute solubility in different solvents and plotting these solvents in three-dimensional space. The location of the center of the sphere determines the value of the HSPs for the solute. The greatest distance between any two solvents is taken as the diameter of the sphere and three HSP values as the midpoint. Group contribution or additive methods have a long tradition of successful use in predicting properties that only require knowledge of the compounds’ chemical structures to calculate the HSPs.16 The cohesive energy or HSPs of solvents and solutes can be determined using the methods of Barton,17 van Krevelen,18 Hoy,19 Breitkreutz,20 Askadskii,21 and Stefanis and Panayiotou.22,23 HSPs have been widely used to estimate the solubility or miscibility of polymer blends; determine chemical resistance; and analyze pharmaceuticals, mineral oils,13 carbon nanotubes,24 bitumens, 25 and asphaltenes.26 Medina Ganzales et al. determined HSPs to fatty acid methyl esters (C8−C18:2) for use with biosolvent epoxy resins.27 Srinivas et al. characterized the physicochemical properties (including HSPs) of methyl soyate (soybean biodiesel methyl esters) as a renewable solvent in liquid−liquid separation.28 The present work estimated the HSPs and radius of interaction sphere R0 of biodiesel derived from four different vegetable oils, soybean, coconut, palm, and Received: August 23, 2013 Revised: October 21, 2013
A
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importance of cohesive energy density, rather than the strength of a single type of physical bond. Skaarup and Hansen have developed an equation for the solubility parameter “distance,” Ra, between two materials, based on their respective partial solubility parameter components:13
castor, using an optimization technique. In the optimization technique, mixtures of good and bad solvents were used to improve the accuracy of R0 and hence of the HSPs. The optimization method minimizes the radius of the sphere subject to the constraints that good solvents are found within the sphere while bad solvents are found outside the sphere. In the second part of this work, the group contribution method was used to predict the HSPs in order to investigate the theoretical solubility of these biofuels. The group contribution method can be used as a tool for the selection of possible solvents to be used by the Hansen method, thus avoiding possible anomalies in the data fit. The extended use of biodiesel from different vegetable oils for various applications is important, not only as an alternative fuel but also as a sustainable and renewable solvent. 1.1. Solubility Parameter (Cohesive Energy Density). The solubility parameters are sometimes also called the cohesion energy parameter. Cohesive energy is a measure of all the intermolecular forces responsible for the material cohesion and can be defined as the square root of the cohesive energy density. The relationship between the solubility parameter and cohesive energy density is shown in the following expression: δ = c1/2 =
1/2 ⎛ E ⎞1/2 ⎛ ΔHV − RT ⎞ ⎜ ⎟ ⎟ =⎜ ⎝V ⎠ ⎝ ⎠ V
(Ra)2 = x(δ D1 − δ D2)2 + y(δ P1 − δ P2)2 + z(δ H1 − δ H2)2 (5)
The subscripts are 1 for the solute and 2 for the solvent. Hansen has suggested, on the basis of empirical test settings of x = 4 and y = z = 1 that a doubling of the dispersive force converts the otherwise elliptical shaped volume of the solubility body to an almost spherical volume.13 However, the use of fixed variables for complex mixtures has been questioned.31 Other experiments have shown that, in general, solubility regions are unsymmetrical.32 However, the overpowering practical evidence is that the value of the constant “4” is the most usable value and has been used in this paper.13,33 The HSPs of the solute at issue are at the center of the spheroid body, and the solubility radius (R0) defines a sphere that contains the good solvents, the bad ones being outside. The Relative Energy Difference (RED) term in eq 6 is useful for a quick evaluation of whether a solvent is likely to appear inside the solubility sphere.
(1)
where δ is the solubility parameter, c the cohesive parameter, E the latent heat of evaporation, V the molar volume, ΔHV the enthalpy of evaporation, R the gas constant, and T the temperature. δ is measured in units of MPa1/2 or cal1/2 cm−3/2 where one MPa1/2 is 2.0455 times larger than those in the cal1/2cm−3/2. This theory was developed for nonpolar, nonassociating systems, but the concept has been extended to polar systems. Gharagheizi et al. divided the solubility parameter into two portions, one nonpolar contribution and one polar contribution.29,30 Hansen expanded this concept in an effort to account for both polar and hydrogen bonding interactions in solvent−polymer systems via the use of a three-dimensional solubility parameter (HSPs) such that the total solubility parameter is separated into three independent parameters and takes into account the (atomic) dispersion forces, (molecular) polarity, and (molecular) hydrogen bonding (electron exchange). The basic equation that governs Hansen’s theory is that which relates the total cohesion energy (E) of a system with the three parameters discussed above. E = ED + EP + EH
RED =
f (δ Dbio , δ Pbio , δ Hbio , R 0) = 1 − data fit
δ T2
(4)
=
δ D2
+
δ P2
+
δ H2
(7)
where
where ED, EP, and EH are dispersion, permanent-dipole/ permanent-dipole, and hydrogen bonding forces, respectively. Dividing this by the molar volume gives the square of the total (or Hildebrand) solubility parameter as the sum of the squares of the Hansen D, P, and H components: (3)
(6)
Either Ra or the RED number can be used to rank solvents and solvent blends. A solvent with identical solubility parameters as the solute will have a RED equal to 0. The bad solvents will have RED values greater than 1, and good solvents will have RED values less than or equal to 1. Solvents with RED ≈ 1 are very important for finding the correct R0. Numbers less than 0.5 indicate that good affinity is expected.14,34 1.2. Data Fitting Procedure. The HSPs and values for the radius of interaction of the biodiesel from soybean oil, coconut oil, palm oil, and castor oil were calculated using a program created in GAMS (The General Algebraic Modeling System), version 23.2.1. The procedure for data fitting is based on the algorithm described by Ma and Zhou35 and by Gharagheizi,36 which seeks to minimize the objective function given by eq 7:
(2)
E E E E = D + P + H V V V V
Ra R0
data fit = (A1·A 2...A n)1/ n
(8)
Ai = e−(error_distance)
(9)
where Ai is the data fit for the ith solvent, given in eqs 10 and 11. For good solvents (sol(i) = 1): ⎧ Rai − Ro if Rai > Ro error distance = ⎨ 0 if Rai ≤ Ro ⎩ ⎪
⎪
(10)
For bad solvents (sol(i) = 0): ⎧ 0 if Rai > Ro error distance = ⎨ ⎩ Ro − Rai if Rai ≤ Ro
where δD, δP, and δH are the dispersion, polar, and hydrogenbond parts of HSPs, respectively, which can be represented in a three-dimensional coordinate system. The HSP coordinates of the solute are determined by analyzing the solubility of this solute in a series of solvents with known HSPs. The total solubility parameter, δT, is customarily related to room temperature (25 °C). The solubility parameter concept demonstrates the
⎪
⎪
(11)
where Rai2 = 4·(δ Di − δ Dbio)2 + (δ Pi − δ Pbio)2 + (δ Hi − δ Hbio)2 (12) B
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A good fit is given by a data fit value close to 1. However, errors may occur in the fitting called “outliers.” Outliers are solvents that do not dissolve the solute but are inside the sphere (wrong in) or solvents that do dissolve the solute but are outside the sphere (wrong out). When the number of such an outlier decreases to zero, the fit accuracy increases to 1. The quantities that are fitted are the values for the biodiesel (δDbio, δPbio, and δHbio) and R0. The data that must be given for the fitting are the solvent values (δDi, δPi, δHi) and the list of good and bad solvents (sol(i)). 1.3. Nonlinear Programming Model. In this work, the previously described procedure was transformed into an equivalent nonlinear programming model to minimize the multivariable objective function given by
δH =
(13)
i=1
such that
δ=
ei ≥ Rai − Ro
i∈ {i = 1, ..., n: sol(i) = 1}
(14)
ei ≥ Ro − Rai
i ∈ {i = 1, ..., n: sol(i) = 0}
(15)
Rai ≥
ei ≥ 0
4·(δ Di − δ Dbio)2 + (δ Pi − δ Pbio)2 + (δ Hi − δ Hbio)2
Rai ≥ 0
δ Dbio ≥ 0
(16)
In this optimization model, the decision variables are ei, Rai, δDi, δPi, δHi, sol(i) and the parameters are δDbio, δPbio, δHbio, and R0. The average value of δD, δP, and δH of the good solvent and the radius of 0 were chosen as the starting point. The value of the data fit can be calculated by
∑ FDi V
(20)
∑ NA i i + W ∑ MjBj (21)
j
0.4126 δ D = (∑ NA i i + W ∑ MjBj + 959.11) i
j
(22)
δ P = (∑ NA i i + W ∑ MjBj + 7.6134) i
j
(23)
δ H = (∑ NA i i + W ∑ MjBj + 7.7003)
(17)
i
The problem has been defined as finding a sphere with the minimum radius containing the maximum number of good solvents and the minimum number of bad solvents and outliers. The advantage of this method is that it could be used to determine more accurate HSPs, a smaller R0, and a better data fit as compared to Hansen’s. 1.4. Group Contribution Methods for the Estimation of Solubility Parameters. This kind of method has been used to estimate the solubility parameter: van Krevelen18 and Stefanis and Panayiotou22,23 have reviewed these techniques and given tables of group values. The sets of group constants given by van Krevelen and Stefanis and Panayiotou seem to be most comprehensive. The group contribution values of van Krevelen are based on the cohesive energy data of polymers. The Stefanis values are based on two kinds of characteristic group: first-order groups that describe the basic molecular structure of the compounds and second-order groups, which are based on the conjugation theory and improve the accuracy of the predictions. These theoretical methods are useful in the case of compounds for which experimental HSPs are not available. 1.4.1. The van Krevelen18 Method. The solubility parameter components, δD, δP, and δH may be calculated from the group contributions using the following equations: δD =
∑ E Hi V
where Ci is the contribution of the type i first-order group that appears Ni times in the compound and Dj is the contribution of the type j second-order group that appears Mj times in the compound. The constant W is equal to 0 for compounds without second-order groups and equal to 1 for compounds with secondorder groups.22 The HSPs components may be predicted using the following equations:23
δ Hbio ≥ 0
⎡ 1 n ⎤ data fit = exp⎢ − ·∑ ei ⎥ ⎢⎣ n i = 1 ⎥⎦
(19)
i
Ro ≥ 0
δ Pbio ≥ 0
V
where FDi is the type i group contribution of to the dispersion forces, FPi is the group contribution to the polar forces, EHi is the group contribution to the hydrogen-bonding energy, and V is the molar volume of the substance. 1.4.2. The Stefanis−Panayiotou22 Method. The Stefanis− Panayiotou method can be described using two kinds of functional group: first-order groups (UNIFAC groups), which describe the basic molecular structure of the compounds, and second-order groups, which use the first-order groups as building blocks.22,23 The basic equation that gives the value of the solubility parameters from the molecular structure is
n
min ∑ ei
∑ FP2i
δP =
j
(24)
However, eqs 23 and 24 are only valid for HSPs values greater than 3 MPa(1/2). In the case of low δP or low δH values (less than 3 MPa(1/2)), the equations for the estimation and for δP and δH are the following:22 δ P = (∑ NA i i + W ∑ MjBj + 2.6560) i
j
(25)
δ H = (∑ NA i i + W ∑ MjBj + 1.3720) i
j
(26)
The advantage of this method for estimating HSPs is that it can be used for a broad series of organic compounds, including those having complex multiring, heterocyclic, and aromatic molecular structures. This predictive method is not only important for the selection of solvents for a particular material but also for the synthesis of new solvents with desired properties.22,23
2. EXPERIMENTAL SECTION 2.1. Materials. Commercial coconut and castor oils were purchased from Campestre (São Paulo, Brazil). Refined soybean oil was purchased from Cargill (Mairinque/SP, Brazil), and palm oil was obtained from Agropalma (Para, Brazil). Potassium hydroxide (Synth-Brazil) was used as the catalyst. All the other solvents used in this study were common, high purity laboratory solvents obtained from commercial chemical suppliers.
(18) C
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Table 1. HSPs, Radius of Interaction, R0, and Correlation Coefficients for Biofuels biodiesel
δD MPa(1/2)
δP MPa(1/2)
δH MPa(1/2)
δT MPa(1/2
R0 MPa(1/2)
G/Ba
wrong inb
wrong outc
data fitd
soybean coconut palm castor
15.03 15.12 15.43 16.10
3.69 3.99 5.28 6.72
8.92 9.25 6.61 9.11
17.86 18.17 17.60 19.68
11.33 10.92 10.54 11.78
35/25 35/25 35/25 40/20
0 0 0 0
1 1 1 1
0.993 0.993 0.955 0.956
a
Good and bad solvents. bSolvents that do not dissolve the biodiesel but are inside the sphere. cSolvents that do dissolve the biodiesel but are outside the sphere. dFit accuracy. 2.2. Biodiesel Production. Biodiesel was produced from soybean, coconut, and palm oils according to the following procedure: The methyl esters were synthesized using 300 g of oil, 60 g of methanol, and about 3 g of KOH. The mixture was stirred at a temperature of 60 °C for a period of 2 h. After 30 min, two different phases were observed: one containing the methyl esters (less dense and clearer) and the other containing glycerin (denser and darker). After resting for 24 h, the glycerin was removed. The lighter phase (methyl esters) was purified by washing with a solution containing 0.5% v/v of HCl, which neutralized the remaining catalyst (KOH), confirmed by analyzing the wash water with a 1% v/v phenolphthalein indicator. The washing was followed by an evaporation step at 110 °C. After purification, the biodiesel was characterized. The castor oil transesterification process was based on an earlier work,7 using hexane as the cosolvent. The use of hexane increases the reaction rate and facilitates phase separation (methyl esters and glycerin). The separation and washing processes were carried out as detailed above. The conversion of the esters (Y; eq 27) was determined by highperformace size-exclusion chromatography (HPSEC; Waters, USA). The Schoenfelder methodology is specific for the analyses of triacylglycerols (TG), diacylglycerols (DG), monoacylglycerols (MG), and glycerol (GL) and was adapted for the analysis of esters (EE) because the ester peak appeared between the monacyglycerol and glycerol peaks. The mobile phase was tetrahydrofuran (THF). C0 was the raw material concentration (wt %) at t = 0 min and was Ci at the end of the reaction. TG, DG, MG, EE, and GL were identified on the basis of standard references (Sigma-Aldrich). The free fatty acids were determined according to the American Oil Chemists’ Society (AOCS official method Ca 5a-40).
Y=
C0 − Ci C0
3. RESULTS AND DISCUSSION 3.1. Calculation of the Hansen Solubility Parameters for Biodiesel. The conversions of the biodiesels (fatty acid methyl esters) were greater than 90.84% with acid numbers of 0.080 to 0.094 mg KOH/g and densities (20 °C) between 0.857 and 0.915 g/cm3. Table 1 presents the HSPs for the four different biodiesels calculated from the experimental data given in Table 2. The values of the data fits were below 1 due to the presence of outliers. In this case, ethanol was the solvent that dissolved the soybean biodiesel (RED =1.038), coconut biodiesel (RED =1.036), and palm biodiesel (RED = 1.260) but was outside the sphere of solubility (wrong out), and methanol was wrong out for the castor biodiesel. According to Redelius,25 the existence of outliers located away from the interface of the spherical region indicates that there are some solubility aspects of the solute that are not completely covered by the Hansen approach. A comparison of the RED biofuels is shown in Figure 1 for the 45 pure solvents listed in Table 2. The solvents (ethylene glycol monobutyl ether acetate, ethyl acetate, n-butyl acetate, tetrahydrofuran, and diethyl malonate) lower the RED values. Consequently, these solvents are ideal for biofuels. The values obtained for the HSPs of soybean biodiesel (δD, δP, δH = 15.03, 3.69, 8.92) and coconut biodiesel (δD, δP, δH = 15.12, 3.99, 9.25) were very similar, due to the small differences in solubility between the experimental mixtures of the solvents. For example, soybean biodiesel was insoluble in 70/30% dimethyl sulfoxide/1-methyl-2-pyrrolidone, 70/30% diethylene glycol/mcresol, and 60/40% ethanolamine/ethanol, while for coconut biodiesel, these values for insolubility were 80/20%, 80/20%, and 70/30%, values sufficient to generate the small difference between the values of the HSPs. According to Table 1, the HSPs of soybean biodiesel showed slightly different values from those reported by Thiebaud-Roux and de Caro (δD, δP, δH = 16.6, 5.2, 8.2) in 60 solvents38 and by Srinivas et al. (δD, δP, δH = 15.40, 5.81, 4.99) in 41 solvents.28 Although both have created a program using the MATLAB environment with a similar algorithm to that one proposed by that work, these values differed (HSPs) due to the use of different solvents in each study. For the palm biodiesel (δD, δP, δH = 15.43, 5.28, 6.61), the value of δD was also very similar to that of coconut biodiesel and soybean biodiesel, although that for δP was higher and that for δH lower. The smallest values for δH were found for the solubility in mixtures of 40/60% ethanolamine/aniline, 40/60% ethanolamine/dimetilformamide, 80/20% dimethyl sulfoxide/ethanol, 40/60% ethanolamine/ethanol, and 50/50% diethylene glycol/ 1-methyl-2-pyrrolidone, proportions in which soybean biodiesel and coconut biodiesel are soluble. Castor biodiesel showed higher values for the solubility parameters (δD, δP, δH = 16.1, 6.72, 9.11), since methyl ricinoleate contains a hydroxyl group, which increases its solubility in solvents which exhibit strong hydrogen bonds, such as the alcohols methanol and ethanol. Furthermore, the presence of a hydroxyl group in the castor biodiesel increases its lubricating power, and it is therefore an excellent candidate for
(27)
2.3. Solubility Test. The solubility tests were initially carried out in 45 organic solvents in order classify them as good (one-phase systems) or bad (two-phase systems) solvents. According to the results obtained for solubility in the 45 solvents, several solvent mixtures (bad/good solvents) were prepared to improve the data and construct the solubility sphere in three-dimensional space. The series consisted of volume ratios (bad solvent/good solvent) of 90/10, 80/20, 70/30, 60/40, 50/50, 40/ 60, 30/70, 20/80, and 10/90. The solubility parameters of the mixtures were calculated using eq 28. δDmix ,P ,H =
∑ φδi Di , P , H i
i = 1, 2, ..., N components (28)
where ϕi is the volume fraction i of the components in the solvent mixture, and D, P, and H are the solubility parameters of dispersion, polar, and hydrogen bonding, respectively. The procedure used to determine solubility was as follows: 0.5 mL of biodiesel was placed in a test tube with 4.5 mL of the test solvent or solvent mixture. The tube was sealed with a suitable stopper to prevent solvent evaporation and stirred vigorously for 24 h at room temperature. After shaking, the tube was allowed to stand at room temperature for 6 days. The behavior of the biodiesel was observed by a visual inspection. The solubility parameters of the 45 solvents and 15 solvent mixtures were used to determine the solubility profile of the biodiesel produced from the vegetable oils studied here. The solubility behavior of the test substance was judged as soluble (1) or insoluble (0). D
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Table 2. Good and Bad Solvents for the Biofuels to Determine the Hansen Solubility Parameters units of MPa(1/2) solvents 1. n-hexane 2. n-heptane 3. cyclohexane 4. benzene 5. o-xylene 6. toluene 7. ethylbenzene 8. cumene 9. α- methylstyrene 10. methanol 11. ethanol 12. propan-2-ol 13. octan-1-ol 14. hexan-1-ol 15. 2-methyl propan-1-ol 16. n-butanol 17. EGa 18. diethylene glycol 19. triethylene glycol 20. glycerol 21. EGMEAb 22. acetone 23. cyclohexanone 24. butanone 25. 4-methylpentan-2-one 26. ethyl acetate 27. n-butyl acetate 28. m-cresol 29. pyridine 30. DMFc 31. 1MPd 32. acetonitrile 33. nitrobenzene 34. diethyl ether 35. anisole 36. tetrahydrofuran 37. 1,4- dioxane 38. DMSOe 39. aniline 40. ethanolamine 41. diethyl malonate 42. carbon tetrachloride 43. 1,2-dichloroethane 44. formic acid 45. water solvents mixture (vol %) 46. diethylene glycol/ethanol 90/10 47. diethylene glycol/ethanol 70/30 48. diethylene glycol/ethanol 60/40 49. diethylene glycol/ethanol 50/50 50. DMSO/1MP 80/20 51. DMSO/1MP 70/30 52. glycerol/ethanol 60/40 53. glycerol/ethanol 40/60 54. glycerol/ethanol 30/70 55. ethanolamine/aniline 90/10 56. ethanolamine/aniline 50/50 57. ethanolamine/aniline 40/60 58. EG/acetone 80/20
soybean
coconut
palm
castor
δD
δP
δH
RED
RED
RED
RED
14.9 15.3 16.8 18.4 17.6 18.0 17.8 18.1 18.6 15.1 15.8 15.8 17.0 15.9 15.1 16.0 17.0 16.6 16.0 17.4 16.0 15.5 17.8 16.0 15.3 15.8 15.8 18.0 19.0 17.4 18.0 15.3 15.8 14.5 17.8 16.8 19.0 18.4 19.4 17.0 16.1 17.8 16.5 14.3 15.5
0.0 0.0 0.0 0.0 1.0 1.4 0.6 1.2 1.0 12.3 8.8 6.1 3.3 5.8 5.7 5.7 11.0 12.0 12.5 12.1 4.1 10.4 6.3 9.0 6.1 5.3 3.7 5.1 8.8 13.7 12.3 18.0 8.6 2.9 4.1 5.7 1.8 16.4 5.1 15.5 7.7 0.0 7.8 11.9 16.0
0.0 0.0 0.2 2.0 3.1 2.0 1.4 1.2 4.1 22.3 19.4 16.4 11.9 12.5 15.9 15.8 26.0 20.7 18.6 29.3 8.2 7.0 5.1 5.1 4.1 7.2 6.3 12.9 5.9 11.3 7.2 6.1 5.1 5.1 6.7 8.0 7.4 10.2 10.2 21.2 8.3 0.6 3.0 16.6 42.3
0.853 0.854 0.893 0.913 0.726 0.830 0.869 0.898 0.797 1.404 1.038* 0.707 0.438 0.398 0.641 0.655 1.676 1.302 1.168 1.990 0.187 0.622 0.637 0.602 0.478 0.249 0.269 0.643 0.875 1.000 0.936 1.288 0.623 0.357 0.528 0.369 0.733 1.275 0.790 1.543 0.450 0.941 0.687 1.000 3.141
0.923 0.922 0.956 0.966 0.773 0.880 0.923 0.951 0.838 1.416 1.036* 0.694 0.426 0.369 0.629 0.640 1.698 1.308 1.169 2.023 0.187 0.626 0.655 0.617 0510 0.255 0.298 0.632 0.890 1.000 0.944 1.315 0.644 0.409 0.543 0.363 0.757 1.288 0.794 1.256 0.394 1.000 0.716 1.000 3.220
0.809 0.803 0.830 0.872 0.667 0.751 0.802 0.819 0.764 1.632 1.260* 0.935 0.613 0.568 0.884 0.879 1.941 1.497 1.332 2.279 0.216 0.487 0.482 0.396 0.252 0.089 0.168 0.771 0.758 0.988 0.827 1.208 0.401 0.321 0.463 0.294 0.757 1.244 0.827 1.716 0.307 0.882 0.465 1.157 3.536
0.982 0.971 0.955 0.918 0.749 0.820 0.884 0.887 0.773 1.277* 0.892 0.623 0.405 0.300 0.607 0.575 1.487 1.084 0.943 1.787 0.236 0.374 0.448 0.392 0.450 0.208 0.354 0.476 0.590 0.659 0.595 1.000 0.457 0.543 0.418 0.175 0.662 0.914 0.584 1.277 0.108 0.965 0.531 0.831 2.927
16.5 16.4 16.3 16.2 18.3 18.3 16.8 16.4 16.3 17.2 18.2 18.4 16.7
11.7 11.0 10.7 10.4 15.6 15.2 10.8 10.1 9.8 14.5 10.3 9.3 10.9
20.6 20.3 20.2 20.1 9.6 9.3 25.3 23.4 22.4 20.1 15.7 14.6 22.2
E
1.065 1.193 1.169
1.221 1.195
1.398 1.377
1.212 1.169
1.117 1.422 1.430
1.325
1.567 1.158
1.006
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Table 2. continued units of MPa(1/2)
a
solvents
δD
δP
δH
59. EG/acetone 70/30 60. EG/acetone 60/40 61. EG/acetone 50/50 62. diethylene glycol/m-cresol 90/10 63. diethylene glycol/m-cresol 80/20 64. diethylene glycol/m-cresol 70/30 65. EG/propan-2-ol 80/20 66. EG/propan-2-ol 70/30 67. EG/propan-2-ol 60/40 68. EG/propan-2-ol 50/50 69. ethanolamine/DMF 60/40 70. ethanolamine/DMF 40/60 71. DMSO/ethanol 90/10 72. DMSO/ethanol 80/20 73. ethanolamine/ethanol 70/30 74. ethanolamine/ethanol 60/40 75. ethanolamine/ethanol 40/60 76. diethylene glycol/1MP 90/10 77. diethylene glycol/1MP 60/40 78. diethylene glycol/1MP 50/50 79 EG/aniline 70/30 80. EG/aniline 50/50 81. EG/aniline 40/60 82. EG/methanol/octan-1-ol 50/40/10 83. EG/methanol/octan-1-ol 50/20/30 84. EG/methanol/DMF 50/30/20 85. EG/methanol/DMF 50/10/40
16.6 16.4 16.3 16.7 16.9 17.0 16.8 16.6 16.5 16.4 17.2 17.2 18.1 17.9 16.6 16.5 16.3 16.7 17.2 17.3 17.7 18.2 18.4 16.2 16.6 16.5 17.0
10.8 10.8 10.7 11.3 10.6 9.9 10.0 9.5 9.0 8.6 14.8 14.4 15.6 14.9 13.5 12.8 11.5 12.1 12.1 12.2 9.2 8.1 7.5 10.8 9.0 11.9 12.2
20.3 18.4 16.5 19.9 19.1 18.4 24.1 23.1 22.2 21.2 17.2 15.3 11.1 12.0 20.7 20.5 20.1 19.6 15.3 14.0 21.3 18.1 16.5 23.1 21.0 22.0 19.8
soybean
coconut
palm
RED
RED
RED
castor RED 1.014
1.071
1.070 1.082 1.000 1.135
1.059
1.238 1.308 1.214
1.287
1.296
1.282
1.286
1.198
1.206
1.431 1.241 1.146 1.389 1.326 1.419 1.002 1.007
1.001 1.024 1.090
1.197
1.056 1.114 1.237
1.197
1.200
1.427
1.268
1.271
1.444
1.181
Ethylene glycol. bEthylene glycol monobutyl ether acetate. cDimethylformamide. d1-Methyl-2-pyrrolidone. eDimethyl sulfoxide.
biofuels in the 45 pure solvents shown in Table 2. Figure 4d represents a dimensional graph of δa = δP + δH versus δD, which accentuates the combined effect of the polar and hydrogenbonding interactions on the four biofuels. It can be seen in Figure 4a−d that using only the 45 pure solvents would not be sufficient to generate different HSPs for soybean biodiesel, coconut biodiesel, and palm biodiesel, and therefore the use of solvent mixtures (bad/good solvents) is a good technique for differentiating the solubility of materials with similar chemical structures. 3.2. Solubility Parameter Calculated for Biodiesel by the Van Krevelen and Stefanis−Panayiotou Methods. The general equation for the calculation of the three solubility components of the biodiesel is as follows:
Figure 1. Comparison of RED values for biofuels.
use as an additive in products based on a mineral oil lubricant.39 Figure 2a−d show the Hansen spheres plotted using threedimensional axes for the biofuels in 45 solvents + 15 solvent mixtures. The blue symbols represent the solvents that dissolved the biodiesels (good solvents) while the symbols in red represent the solvents and solvent mixtures in which the biodiesels were insoluble (bad solvents). It is evident that there were three bad solvents with RED ≫ 1, due to high values for polar and hydrogen-bonding interactions for ethylene glycol, glycerol, and water, in the range from 11.0 to 16.0 and 26.0−42.3 MPa1/2. Figure 3a−d show the importance of using solvent mixtures such as ethanolamine/aniline, ethylene glycol/acetone, and diethylene glycol/1-methyl-2-pyrrolidone, which have RED values close to 1. This is an important factor in defining the region of solubility. Figure 4 shows the three-dimensional (Figure 4a) and twodimensional (Figures 4b−d) contour plots of the HSPs for the
δX̅ = (∑ xiδxm) i
(29)
where xi is the weight of the fatty acid methyl ester fractions present in the soybean biodiesel, coconut biodiesel, palm biodiesel, and castor biodiesel, the fractions being provided by Gustone et al.40 For example, the approximate composition of soybean biodiesel is 11.9% methyl palmitate, 4.3% methyl stearate, 22.5% methyl oleate, 54.4% methyl linoleate, and 6.9% methyl linolenate; the factor mδx is the average of the solubility parameters of the methyl esters obtained by the van Krevelen and Stefanis−Panayiotou methods (see Table 3). The results of such calculations are reported in Table 4. As in the optimization method, the values for the HSPs predicted by group contribution methods for soybean biodiesel (δD, δP, δH = 16.1, 1.6, 3.8), coconut biodiesel (δD, δP, δH = 16.0, F
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Figure 2. HSPs of biofuels in solvents + mixtures of solvents (a) soybean biodiesel, (b) coconut biodiesel, (c) palm biodisel, (d) castor biodiesel.
Figure 3. Solvent mixtures with RED values close to 1.000 for solvents (a) soybean biodiesel, (b) coconut biodiesel, (c) palm biodisel, (d) castor biodiesel.
1.8, 4.2), and palm biodiesel (δD, δP, δH = 16.1, 1.6, 3.6) were similar, whereas those for castor biodiesel (δD, δP, δH = 16.4, 3.3, 8.7) were higher. The fatty acid methyl esters present in these biofuels represent a range of hydrocarbon chain lengths from C8 to C18, with 0 to 3 double bonds per ester and one C18−OH (hydroxyl). The CCOO group is a small portion of the molecule
that has a small dipole moment and poor ability to participate in forming hydrogen bonds. For this reason, there was little variation in the values for δP and δH of the methyl caprylate and methyl linoleate. The only exception was the ricinoleate, which has a functional hydroxyl group at C-12, which explains the higher values obtained for the δP and δH of this ester as compared G
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Figure 4. (a) Spherical region characterizing four biofuels in 45 pure solvents, (b) two-dimensional plot of δP versus δD, (c) two-dimensional plot of δH versus δD, (d) two-dimensional plot of δa versus δD.
did not obey the approach of 5 ≤ Δδ̅ MPa1/2. The variation in Δδ̅ of 13.5−14.3 MPa1/2 for soluble and 14.0−16.0 MPa1/2 for insoluble, as in the optimization method, ethanol and methanol (wrong out) did not fit as soluble solvents, exhibiting the same solubility error. Comparative solubility methodologies can be used, such as those of Greenhalgh et al.41 (eq 31) and Bagley et al.42 (eq 32)
to the others. Other studies27,28 have shown similar results for the fatty acid methyl esters, where the results for the δP and δH parameters were characterized by the presence of two oxygen atoms from the functional group (CCOO) and the absence of the electropositive hydrogen atom. As can be seen in Table 3, by increasing the number of CH2 groups in one molecule of the ester, the dispersion solubility parameter (δD) increases, due to the intermolecular forces (van der Waals forces). The structural characteristics of the various fatty acid esters making up the biodiesel, such as chain length, degree of unsaturation, and chain branching, determine the overall properties of the biodiesel. 3.2.1. Theoretical Solubility of the Biofuels. The values of the solubility parameters calculated by the group contribution methods were then used to study the theorical solubility of the four biofuels and the pure solvents listed in Table 2, using the methodology developed by van Krevelen,18 Greenhalgh et al.,41 and Bagley et al.42 The difference between the solubility parameter of the solvent (s) and the biodiesel (bio) could then be determined using the Δδ̅ factor. Δδ ̅ =
Δδt = |δts − δtbio| Rv =
4(δvs − δvbio)2 + (δ Hs − δ Hbio)2
(31)
(32)
Greenhalgh et al. demonstrated that, in general, materials with Δδt < 7 MPa1/2 are soluble and Δδt > 7 MPa1/2 are insoluble.16,41 The parameter δv = (δD + δP)1/2 is the volume-dependent solubility parameter. Bagley et al. concluded that the effects of δD and δP were thermodynamically similar, while the effect of δH was quite different in nature.42 For the Greenhalgh solubility model (see Table 6), the solvents cyclohexane, 4-methylpentan-2-one, and n-butyl acetate were the best solvents for soybean biodiesel, coconut biodiesel, and palm biodiesel. For castor biodiesel (with Δδt > 7 MPa1/2), α-methylstyrene, butanone, and nitrobenzene were the best solvents. This approach also introduced errors in the classification solubility of the solvents (ethanol, methanol, dimethyl sulfoxide) with the variation of Δδt of 6.9−8.7 MPa1/2 being soluble and 7.8−10.3 MPa1/2 being insoluble. According to the predictions for solubility by the Bagley approach (Table 7), 4-methylpentan-2-one, n-butyl acetate, and o-xylene were the best solvents for soybean biodiesel and palm biodiesel, and 4-methylpentan-2-one, n-butyl acetate, and diethyl ether were the best solvents for the coconut biodiesel. For castor biodiesel, ethylene glycol monobutyl ether acetate, n-butyl acetate, and tetrahydrofuran were the best solvents. The variation
(δ Ds − δ Dbio)2 + (δ Ps − δ Pbio)2 + (δ Hs − δ Hbio)2 (30)
For good solubility between the solvent and biodiesel, the difference between the solubility parameters should be ≤ 5 MPa1/2.14,18 However, some studies16,43 showed variable experimental systems that were miscible and were therefore not provided for by this condition. According to eq 30, the sequence of solubility of the biofuels in the solvents can be calculated and is shown in Table 5. The solvents o-xylene, diethyl ether, and toluene are the best solvents for the soybean and palm biodiesels, whereas o-xylene, diethyl ether and α-methylstyrene were best for the coconut biodiesel and ethylene glycol monobutyl ether acetate n-butyl acetate and tetrahydrofuran for the castor biodiesel. However, these biofuels H
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5.9 5.7 5.2 4.2 3.6 3.2 3.5 3.9 4.2 9.3
16.7 17.0 16.9 16.7 16.4 16.3 16.6 16.7 16.8 19.2
Table 4. HSPs Calculated for the Biofuels According to eq 29
2.7 2.4 2.1 1.9 1.6 1.4 1.5 1.6 1.7 3.5 15.4 15.9 16.0 16.0 16.0 15.9 16.1 16.2 16.2 16.4 17.1 17.0 16.8 16.5 16.3 16.2 16.4 16.8 17.1 19.9 5.7 5.6 5.1 3.3 2.6 1.8 2.4 3.1 3.7 9.7 2.8 2.5 2.2 2.0 1.7 1.4 1.5 1.7 1.8 4.9
δD MPa(1/2)
δP MPa(1/2)
δH MPa(1/2)
δT MPa(1/2)
soybean coconut palm castor
16.1 16.0 16.1 16.4
1.6 1.8 1.6 3.3
3.8 4.7 3.6 8.7
16.6 16.8 16.6 18.8
4. CONCLUSION The HSPs and solubility spheres for four different biofuels were determined by a solubility test in 45 solvents (with known solubility parameters) and mixtures of solvents (with calculated solubility parameters). The results of the solubility test were then used to determine more accurate values for the HSPs and a smaller R0 by the optimization method. The solubilities of the soybean and coconut biodiesels were very similar, leading to small differences in the solubility parameters. The δD value of the palm biodiesel was also very similar to those of the coconut and soybean biodiesels, but the value for δP was higher and that for δH lower. The castor biodiesel was soluble in strongly polar solvents such as methanol, acetonitrile, and dimethyl sulfoxide, resulting in higher δP and δH values. The HSP values of the biofuels, derived using group contribution methods, were empirically investigated for their solubility in 45 solvents, using the van Krevelen, Grenhalgh, and Bagley approaches. o-Xylene and ethylene glycol monobutyl ether acetate were the best solvents according to the van Krevelen approach, cyclohexane and α-methylstyrene by the Greenhalgh approach, and diethyl ether and 4-methylpentan-2one by the Bagley approach. Group contribution methods to calculate the HSPs of the biofuels are based on the knowledge of structural fragments of fatty acid methyl esters. There is still a difference between the estimated and experimental methods, as errors exist for the carboxyl functional group. The polar solubility parameter (coming from the carboxyl functional group (CCOO)) provided by the group contribution methods (Table 4) was substantially lower than expected, especially if compared with the experimental values shown in Table 1. The optimization method is superior to other methods because it considers the bad solvents’ data also as a part of the procedure for obtaining the HSPs. These methods are based on the “like dissolves like” principle and are useful approaches for the solubility problem.
6.0 5.7 5.3 5.0 4.5 4.5 4.6 4.6 4.6 8.9
Units are MPa1/2 for the δD, δP and δH parameters.
2.6 2.3 2.0 1.8 1.5 1.4 1.5 1.5 1.5 2.1
■
AUTHOR INFORMATION
Corresponding Author
*Tel.: 55 19 3521 3964. Fax: 55 19 3521 3965. E-mail: mak@feq. unicamp.br. Notes
The authors declare no competing financial interest.
a
14.9 15.9 16.0 16.0 15.9 15.8 16.0 15.9 15.7 16.1 CH3−(CH2)5−COOCH3 CH3−(CH2)7−COOCH3 CH3−(CH2)9−COOCH3 CH3−(CH2)11−COOCH3 CH3−(CH2)13−COOCH3 CH3−(CH2)15−COOCH3 CH3−(CH2)7−CHCH−(CH2)7−COOCH3 CH3−(CH2)4−CHCH−CH2−CHCH−(CH2)7−COOCH3 CH3−CH2−CHCH−CH2−CHCH−CH2−CHCH−(CH2)7COOCH3 CH3−(CH2)5−CH(OH)−CH2−CHCH−(CH2)7COOCH3 methyl caprylate methyl caprate methyl laurate methyl myristate methyl palmitate methyl stearate methyl oleate methyl linoleate methyl linolenate methyl ricinoleate
biodiesel
in Rv was from 12.3 to 13.9 MPa1/2 for soluble and from 13.4− 14.2 MPa1/2 for insoluble. The acetonitrile, dimethylformamide, and dimethyl sulfoxide solvents were not classified as “soluble” because the polar parameter (δP) predicted by eq 29 was substantially lower than expected, especially if compared with the experimental values shown in Table 2. A simple explanation was not found for the behavior of the ethanol and methanol solvents. One explanation may be that there are some aspects of solubility of such solvents that are not fully covered by these theoretical methods.
16.3 17.0 17.0 16.9 16.6 16.5 16.7 16.6 16.4 18.5
15.9 15.9 15.9 16.0 16.0 16.0 16.2 16.4 16.6 16.7
δH δP δD δH δP δD chemical formula fatty acid methyl esters
Table 3. Calculated values for the HSPs of the Fatty Acid Methyl Estersa
van Krevelen−Hoftyzer
δT
Stefanis−Panayiotou
δT
m
δD
m
δP
mean
m
δH
m
δT
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>14.0
16.0
16.0
