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Identification and Molecular Understanding of the Odd−Even Effect of Dicarboxylic Acids Aqueous Solubility Hui Zhang, Chuang Xie, Zengkun Liu, Junbo Gong, Ying Bao, Meijing Zhang, Hongxun Hao, Baohong Hou, and Qiu-xiang Yin* School of Chemical Engineering & Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, People’s Republic of China S Supporting Information *

ABSTRACT: The solubilities of the homologous series of dicarboxylic acids, HOOC−(CH2)n−2−COOH (n = 2−10), in water have been measured at temperatures ranging from 288.15 to 323.15 K by a static analytic method at atmospheric pressure. Dicarboxylic acids with even numbers of carbon atoms exhibit lower solubilities than acids with adjacent odd carbon numbers. The odd−even effect of solubility is most likely associated with the twist of the molecules, which influences the molecular packing in the solid state: the molecules stack with some offset in the cases of even (n = even) series, but without offset in the cases of odd (n = odd) series, whereas the carboxyl groups are twisted in even members. The interlayer packing is looser in odd members than that in even ones. The energies of intramolecular torsion were calculated using Materials studio 6.0 (Accelrys Software Inc.). Finally, the molar Gibbs energies were predicted, which also showed odd−even alternation.

1. INTRODUCTION Dicarboxylic acids (HOOC−(CH2)n−2−COOH, n = 2−10) are important raw materials for the chemical and pharmaceutical industry:1 C2 diacid is usually used as a rust and scale remover;2 C2−C7 diacids are intermediates for manufacturing medicine;3 and it is worthy of note that C4 and C9 diacids have pharmacological activities and C7 diacid is always used for biochemical studies; some of them have a variety of uses in synthesis,4 for instance, C5, C6, C9, and C10 diacids are widely used to produce synthetic resin; besides, C6 diacid is an indispensable raw material for many polymers, such as food additives, nylon-66, insecticides, and so on.5 In general, these diacids are manufactured by a synthesis reaction or a microbe ferment process, so byproducts are inevitable. Therefore, a process of separation and purification is necessary. Crystallization from solution is the most common and efficient way to get pure diacids.6 Water is the most popular solvent for the low price. As a result, solubility in water is an significant property that gives essential information for optimization of the operative conditions of crystallization process.7,8 In addition, low molecular weight dicarboxylic acids are the main components of the organic fraction of atmospheric particles.9,10 And they have an influence on the chemical and physical properties of aerosols.11 As the top priority to better understand the physical chemistry of these compounds, study into the solubility of the diacids is also required. Consequently, many people have measured the solubility of some diacids.12−21 Among these reports, Apelblat12 and Rozaini14 had measured solubilities of C2−C6 diacids in water by a synthetic method, respectively. Interestingly enough, the odd−even phenomenon was shown in the solubilities of the homologous series of dicarboxylic acids. However, results obtained from the synthetic method22 are far from equilibrium values (the complete description of the method is given in the Experimental Section of the present work). Furthermore, the © 2013 American Chemical Society

solubilities of C8−C10 diacids in water are scarcely reported in the literature and the reason for the odd−even behavior was not pointed out explicitly. Alternation in solid-state properties such as the melting point, solubility enthalpy, sublimation, etc. is well-known in alkyl derivatives. The earliest work related to the odd−even phenomenon was published in 1877, which dealt with the melting points of dicarboxylic acids and fatty acids. Baeyer23 stated that the melting points of diacids with even numbers of C atoms are relatively higher than those with odd numbers. Since then, the alternation phenomenon was also discovered in n-alkanes and many end-substituted n-alkanes.24 Most of these studies focused on solid-state properties, such as density, molar volume, fusion behavior, enthalpy of sublimation, and solubility. Early theoretical explanations considered that odd−even differences resulted from altering strong and weak bonds along the carbon chain. In 1910, Falk and Nelson25 modified this by raising the idea of alternating positive and negative charges on carbon atoms. These opinions conflicted with views on covalent bonding as pointed out by Burrows.26 In 1966, Larsson27 tried to describe the effect through the packing in the planes: the alternation of the properties is due to differences at the interfaces between the chain ends for even and odd members. However, no one ever carried out comprehensive crystallographic work on diacids before Caspari28 in 1928. Unlike the nalkane derivatives, diacids are solid with remarkable crystallinity, even for the lowest number of the series, oxalic acid. It was observed that the crystal structures were closely related to the chain length. Since then, several researchers began to study the crystalline nature of diacids: Macgillavry et al.29 explained Received: Revised: Accepted: Published: 18458

September 17, 2013 November 5, 2013 November 7, 2013 November 13, 2013 dx.doi.org/10.1021/ie4030837 | Ind. Eng. Chem. Res. 2013, 52, 18458−18465

Industrial & Engineering Chemistry Research

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Figure 1. continued

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Figure 1. Mole fraction solubility (x1) of oxalic acid (1), malonic acid (2), succinic acid (3), glutaric acid (4), adipic acid (5), pimelic acid (6), suberic acid (7), azelaic acid (8), and sebacic acid (9) at different temperatures: ●, experimental data; ▷, data in ref 9; △, data from ref 14; ○, data in ref 16; +, data in ref 18; ◁, data in ref 19; ◇, data in ref 20; ☆, data in ref 21; □, data in ref 22; ▽, data in ref 23.

2. EXPERIMENTAL SECTION 2.1. Materials. C2−C10 dicarboxylic acids with a minimum purity of 99.0% were supplied by Tianjin Xi’ensi Co. Ltd. The corresponding crystallographic data were gathered from the Cambridge Crystallographic data center (CCDC) and listed in the Supporting Information. The distill deionizer water used for the experiments was purified by nanofilteration of Barnstead Nanopure (Beijing Oriental Science & Technology Development Ltd.). 2.2. Solubility Measurement. There are two methods to measure the solubility data: the analytic method35 and the synthetic method.22 With the analytic method, all the materials are stirred together at a given temperature for a certain time, and then the upper solution is analyzed after the stirring stops for some time, and the concentration of solute is considered as the solubility at the temperature. There is no limit to the rate of dissolution to reach the equilibrium so that the method can be used to solid−liquid system for fast and slow dissolution. As long as the two phases achieve equilibrium and can be separated thoroughly, reliable solubility data can be obtained. With the synthetic method, the composition of the suspension is known, and the solubility can be determined by observing the disappearance of the solid phase.35 But the solutions may not reach equilibrium, especially for slow dissolutions.

the phenomenon using crystal structures of diacids. Housty et al.30 performed similar investigations on diacids, but without comparison between odd and even structures. In 1999, Boese et al.31 made a breakthrough to solve this problem by proposing a parallelogram-trapezoid model. This model has explained the melting point alternation in the n-alkanes and diacids successfully.32 Recently, Peter N. Nelson et al.33,34 presented a new chemical model ascribing odd−even alternation to the difference in vertical distances between adjacent molecular layers, within a lamellar. This model has obtained good application in explaining odd−even alternation. In this work, the solubilities of the homologous series of C2− C10 dicarboxylic acids in water have been measured at temperatures ranging from 288.15 to 323.15 K by a static analytic method at atmospheric pressure. The measured solubility data were correlated by the modified Apelblat equation. The main objects of this work are to determine the relationship between the solubilities of the homologous series of dicarboxylic acids and the number of C atoms in their molecules, and to explore the effects of the crystal structures on the solubility behavior of the homologous series of dicarboxylic acids. Furthermore, to understand the solubility behavior, the dissolution enthalpy, dissolution entropy and the molar Gibbs energy of solutions in water were derived. 18460



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In this work, the solubility of dicarboxylic acids was measured by a static analytic method similar to that described in the literature.36 A thermostatic bath (type 501A, Shanghai Laboratory Instrument Works Co., Ltd., China) was used to keep each temperature with an uncertainty of ±0.05 K. An excess amount of drugs and solvent was added in a specially designed sealed dual-wall flask, stirring for 18 h under a stable temperature to reach the equilibrium.37 After that, the suspension was settled down for 2 h. Then, upper clear solution was taken by a syringe, filtered through a 0.2 μm filer and poured into a Petri dish, which was evaporated fully in a vacuum drying oven at 363.15 K. After being dried, each sample was reweighed every 30 min until the values were unaltered. The solubility of dicarboxylic acid in mole fraction (x1) could be obtained as follows: x1 =

m1/M1 m1/M1 + m0 /M 0

Table 1. Parameters of Modified Apelblat Equation for Dicarboxylic Acid in Water dicarboxylic acid

A

B

C

oxalic acid malonic acid succinic acid glutaric acid adipic acid pimelic acid suberic acid azelaic acid sebacic acid

−530.93 −601.69 −322.41 −143.83 −1081.43 −2825.25 −3029.14 −504.40 −3216.36

21155.83 26468.01 11922.47 5476.72 45822.54 124078.30 132719.70 16809.39 138945.55

80.08 89.9 49.01 21.89 162.09 422.08 451.98 77.21 480.83

a

AADa 1.67 1.24 7.89 1.55 1.31 9.54 7.07 8.13 2.21

× × × × × × × × ×

10−2 10−2 10−3 10−2 10−2 10−2 10−2 10−2 10−1

Calculated by eq 3.

(1)

where m1, m0, M1, and M0 stand for the mass of the solute, the mass of the solvent, the molecular weight of the solute, and the molecular weight of the solvent, respectively. Each of the experiments was repeated three times and used the arithmetic average value as the final result. All of the masses were determined by a balance (type AB204, Metler Toledo, Switzerland, ±0.0001 g). The uncertainty of the solubility values was estimated less than 2%.

3. RESULTS AND DISCUSSION 3.1. Experimental Solubility Data of Dicarboxylic Acids in Water. The measured mole fraction solubility data of C2−C10 dicarboxylic acids in water are presented and compared with the literature data in Figure 1. It can be seen that within the temperature range of the measurements, the solubility results of dicarboxylic acids increased with increasing temperature in all cases, indicating that the dissolution process is endothermic. In addition, the results in this work are different from the results reported in literature, indicating that the solutions in synthetic method are far from equilibrium, particularly for slow dissolution. 3.2. Correlation of the Solubility Data. In this study, the experimental solubility data were correlated by the modified Apelblat equation as follows:38 ln x1 = A +

B + C ln T T

Figure 2. Relationship between solubilities of the dicarboxylic acids and carbon chain length at different temperatures: ■, 288.15 K; ●, 293.15 K; ▲, 298.15 K; ▼, 303.15 K; ◆, 308.15 K; ★, 313.15 K; □, 318.15 K; ○, 323.15 K.

obviously that the solubility of dicarboxylic acids is highly dependent on the number of carbon atoms: diacids with odd numbers of carbon atoms being much more soluble than diacids with adjacent even numbers of carbon atoms. The trend was consistent with early literature.12,14 This phenomenon was the so-called odd−even effect,24 which has attracted increasing attention. For reasonable description, the layer structures of C4-diacid and C5-diacid are displayed in Figure 3a,b as representative examples. The molecule structures can be well depicted by the parallelogram-trapezoid model.35 And the crystal packing of diacids has been discussed in detail by Boese et al.32 Obviously, carboxy dimer synthons link lateral molecules in an end-to-end manner to generate infinite hydrogen bonded chains. Adjacent chains aggregate into layers through hydrophobic interactions between methylene groups in even members. It is of note that, in odd series, the carboxyl groups are twisted to avoid O···O repulsion between two neighboring chains. As a result, the carboxy groups turn out-of-plane with respect to the methylene chains, which distorts the molecule and introduces severe torsions into the carbon chains. In even series, the O···O repulsion has been avoided by sliding of the chains, causing offset packing. Thus the carboxy groups locate on the same plane. What is important in the context of solubility alternation is that high torsions in odd members result in energetically unfavorable molecular conformations.

(2)

where x1 is the mole fraction solubility of dicarboxylic acid, T is the absolute temperature (K), and A, B, C are the empirical constants. The experimental and calculated solubility data of dicarboxylic acids are listed in the Supporting Information. The model parameters are given in Table 1, which were obtained by minimizing the average absolute deviation (AAD): 1 AAD = N

N

∑ i=1

cal x1,exp i − x1, i

x1,exp i

(3)

xexp 1,i

where N is the number of experimental points and and xcal 1,i are the experimental solubility and calculated solubility, respectively. 3.3. Odd−Even Effect for Solubility of Dicarboxylic Acids. The solubility of the dicarboxylic acids is presented as a function of carbon chain length up to C10 in Figure 2. It is 18461



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Figure 3. Layer structures in succinic acid (a) and glutaric acid (b) and view down the chain axis illustrating the interlayer packing in succinic acid (c) and glutaric acid (d), respectively.

The energies of the optimized molecules (geometry optimized in water by Dmol3 program) and observed molecular conformations (in single crystal structures) of diacids are calculated using the Materials Studio Dmol3 program from Accelrys. The differences (ΔE) between the molecular energies of optimized and observed conformations for diacids are given in Table 2 and plotted in Figure 4. Calculated energies differ Table 2. Differences in Molecular Energies between Geometry Optimized Molecular Structures and Structures of Molecules in the Crystal dicarboxylic acid oxalic acid malonic acid succinic acid glutaric acid adipic acid pimelic acid suberic acid azelaic acid sebacic acid

ΔE0 (kJ/mol)a

ΔE (kJ/mol)b

2.665 0.978 2.418 0.992 2.235 0.791

1.968 3.431 1.865 3.319 1.762 2.739 1.729 2.315 1.717

Figure 4. Relationship between ΔE (difference in molecular energies between observed and Materials studio DMol3 optimized molecular structures) and carbon chain length.

a

The difference in energies between structures of molecules in the crystal and geometry optimized molecular structures by B3LYP/6-31G (ref 32). bThe difference in energies between structures of molecules in the crystal and geometry optimized molecular structures by Materials Studio 6.0.

even chains, the methyl groups approach each other more closely than is the case for odd chains. In the process of dissolution, water molecules can be expected to reside between the molecular planes. Thus, the odd-chain homologues should have a higher solubility and a lower melting temperature, as is observed. All in all, the twist of molecules and interlayer packing in the solid state are the reason for the odd−even effect. The crystals of even members are more stable than for the odd ones, so the latter are more soluble. It is worth noting that the odd−even behavior of the dicarboxylic acids is reversed compared to the behavior of basic n-alkanes.31,39 The n-alkanes have more stable crystal lattices for the even members due to the closer packing of the even members. However, the acids must twist the molecular backbone, which costs energy that is released when the crystals

from data reported in the literature32 because of the solvent effect and different calculation methods. It is clear from these values that the odd members possess higher energy than even members. This difference in energy is released during the process of dissolution and thereby lowers the heat of solution. Thus, strained torsional conformations are responsible for the higher solubility of odd members. Furthermore, the interlayer packings of C4-diacid and C5diacid are shown in Figure 3c,d: the interlayer separation in the odd diacids are longer than those present in even members. For 18462



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high chain lengths. It can be expected that molecular torsion energies predominate for short chain length compounds, being much stronger than van der Waal interactions, which predominate for long chain lengths.

are dissolved. The inherent energy for the twist of the acids reverses the behavior for the dicarboxylic acids, as we pointed out and found in the lattice energies above. The series of the nalkanes and the dicarboxylic acids are distinguished by the intermolecular interactions at the end of the molecules. nAlkanes interact by weak van der Waals forces of the methyl groups whereas the dicarboxylic acids are linked via the more rigid and stable carboxylic acid supramolecular synthon. It is the rigid synthon which calls for the twist of the chains. 3.4. Odd−Even Alternation in the Molar Gibbs Energy. The dissolution enthalpy ΔsolHo (kJ mol−1), dissolution entropy ΔsolSo (J mol−1 K−1), and molar Gibbs energy ΔsolGo (kJ mol−1) predicted on the basis of the modified Apelblat equation parameters at measured solubility points were calculated by the following equations:40 ⎡ ∂ ln x1 ⎤ Δsol H o = RT ⎢ = R( −B + CT ) ⎣ ∂ ln T ⎥⎦

(4)

⎤ ⎡ ∂ ln x1 Δsol S o = R ⎢ + ln x1⎥ = R[A + C(1 + ln T )] ⎦ ⎣ ∂ ln T

(5)

Δsol Go = Δsol H o − T Δsol S o

(6)

4. CONCLUSION The solubilities of the homologous series of C2−C10 dicarboxylic acids in water were measured by a static analytic method in the temperature range from 288.15 to 323.15 K, at atmospheric pressure. It is indicated that the solubility value exhibits a marked odd−even effect: diacids with odd numbers of carbon atoms being much more soluble than those with adjacent even numbers. This behavior is reversed compared to the behavior of basic n-alkanes due to the different intermolecular interactions and interlayer packings. The measured solubility data were correlated successfully with the modified Apelblat equation. In addition, the crystal structures of diacids were used to describe the differences of structures between the even and odd members, which led to the odd− even effect. And Materials studio 6.0 was used to calculate the energy of intramolecular torsion. Finally, to understand the solubility behavior, the dissolution enthalpy, entropy, and the molar Gibbs energy were predicted on the basis of the modified Apelblat equation parameters. As expected, the molar Gibbs energy also followed the odd−even rule.

The values of ΔsolH , ΔsolS , and the molar Gibbs energy ΔsolGo of dicarboxylic acids within the experimental temperature range are presented in Supporting Information. The result shows that the higher the temperature, the lower the value of ΔsolGo, which corresponds to a more favorable process of dissolution and to a higher solubility. This trend of ΔsolGo versus the solubility is similar to the results for caprolactam and 4,4′-oxydianiline reported in previous literature.41,42 In addition, compared with odd members, diacids with adjacent even numbers of carbon atoms possess higher molar Gibbs energies at the same temperature, as shown in Figure 5 where, o

o

■

ASSOCIATED CONTENT

S Supporting Information *

Crystallographic data, solubility data, and enthalpies, entropies, and Gibbs energies are available for investigated diacids. This material is available free of charge via the Internet at http:// pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Q. Yin: e-mail, [email protected]; phone, 86-22-27405754; fax, 86-22-27314971. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The analysis tools used in this study were supported by the State Key Laboratory of Chemical Engineering (No. SKL-ChE11B02). This work was supported by the National high technology research and development program (863 Program No. 2012AA021202).

■ Figure 5. Relationship between molar Gibbs energies ΔsolGo of the dicarboxylic acids and carbon chain length at 288.15 K.

as an example, the molar Gibbs energies of these diacids at 288.15 K were presented as a function of the carbon chain length. As mentioned above, the differences between the molecular energies of optimized and observed conformations for diacids is released during the process of dissolution. Therefore, the larger the difference is, the lower the value of ΔsolGo is. However, the odd−even alternation is weakened at 18463

ABBREVIATIONS x1 = molar fraction of the solute m1 = the mass of the solute m0 = the mass of the solvent M1 = the respective molecular mass of the solute M0 = the respective molecular mass of the solvent A = empirical constant for the modified Apelblat equation B = empirical constant for the modified Apelblat equation C = empirical constant for the modified Apelblat equation N = number of data points per system ΔE = the difference in energies between observed and Materials studio DMol3 optimized molecular structures R = gas constant T = absolutely temperature ΔsolHo = the dissolution enthalpy dx.doi.org/10.1021/ie4030837 | Ind. Eng. Chem. Res. 2013, 52, 18458−18465


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ΔsolGo = the molar Gibbs energy of solution ΔsolSo = the dissolution entropy AAD = average absolute deviation between experimental and calculated data x1cal = calculated solubility of the solute PXRD = X-ray powder diffraction CCDC = the Cambridge Crystallographic Data Center

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Subscripts

cal = calculated exp = experimental

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