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Studies on the interactions between some α -amino acids with a non-polar side chain and two saturated cyclic ethers at 298.15 K: enthalpic measurement and computer simulation
Chemical Engineering Science 61 (2006) 794 – 801 www.elsevier.com/locate/ces
Studies on the interactions between some -amino acids with a non-polar side chain and two saturated cyclic ethers at 298.15 K: enthalpic measurement and computer simulation Li Yua, b,∗ , Shi-Ling Yuana , Xin-Gen Huc , Rui-Sen Linb a Key Lab for Colloid and Interface Chemistry, Shandong University, Ministry of Education, Jinan 250100, PR China b Department of Chemistry, Zhejiang University, Hangzhou 310027, PR China c Department of Chemistry, Wenzhou Normal College, Wenzhou 325000, PR China
Received 11 April 2005; received in revised form 4 August 2005; accepted 8 August 2005 Available online 19 September 2005
Abstract Mixing enthalpies of heterocyclic compounds (THF and 1, 4-dioxane) and -amino acids with a non-polar side chain (glycine, L-alanine, acid and L-valine), and dilution enthalpies of each compound have been determined in aqueous solutions at 298.15 K by a flow-mixing microcalorimeter. The heterotactic enthalpic pairwise interaction coefficients, hxy , of each amino acid with THF and 1, 4-dioxane have been calculated by the McMillan–Mayer formalism, and discussed in terms of intermolecular interactions between the hydrated solute species. Using the additivity groups concept by Savage and Wood (SWAG), contributions of each functional group of studied solutes have been estimated. In addition, the mixing energies and Huggins parameters of amino acid-heterocyclic compound systems have been obtained by computer simulation. The results of computer simulation are consistent with enthalpic measurements. 䉷 2005 Elsevier Ltd. All rights reserved. L-aminobutyric
Keywords: Enthalpy; Computer simulation; SWAG approach; Interaction coefficient
1. Introduction The stability of the native structure of proteins in aqueous solutions can be ascribed to the weak non-bonding interactions between the groups of amino acids as well as amino acids and the other components in solutions (Castronuovo et al., 1996). The majority of proteins exist in aqueous mixed solvents containing many organic substances. Studies on various thermodynamic properties of amino acids and simple peptides in aqueous solutions of organic substances are of current interest due to their importance in the better understanding of the nature and mechanisms taking place in biological cells (Fernandez and Lilley, 1992). ∗ Corresponding author. Key Lab for Colloid and Interface Chemistry, Shandong University, Ministry of Education, Jinan 250100, PR China. Tel.: +86 0531 8366145; fax: +86 531 856 4750. E-mail address: [email protected] (Li Yu).
0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.08.008
Scarcely any report has been found about calorimetric studies of simple heterocyclic compounds. However, these compounds, for example, the simple heterocyclic compounds in pesticides, are very important to the living organisms and the environment. 1, 4-dioxane and tetrahydrofuran (THF) are both two kinds of heterocyclic compounds containing an oxygen atom, familiar to all of us. Of the thermodynamic functions describing solvation or solution processes, entropy is significantly connected to the solvent structure perturbations brought about by the introduction of a solute. Unfortunately, only limited entropy data in mixed solvents are available. Enthalpy values are more widely available and are more frequently used. It is effective to investigate the interaction between amino acids and organic substances using an enthalpic measurement method. As an extension to our previous study (Yu et al., 2003a,b; Shao et al., 2001), we address the non-covalent bonding interactions that occur between amino acids and
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heterocyclic compounds. The present work reports the calorimetric results of the mixing enthalpies of some typical -amino acids with a non-polar side chain (glycine, L-alanine, L-aminobutyric acid and L-valine) and THF and 1, 4-dioxane, together with their respective dilution enthalpies in aqueous solutions. The data served as a basis for calculations of the heterotactic enthalpic coefficients of interactions between the amino acids studied and THF and 1, 4-dioxane in an aqueous solution. The results are interpreted from the point of view of solute–solute interactions and discussed by the Savage and Wood (SWAG) approach. In addition, the computer simulation provides useful information on the interactions between the two mixed systems. The results of computer simulation are in agreement with those of the experiment.
2. Materials and methods 2.1. Materials
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The excess enthalpy of a solution is defined as H E (mx , my )/w1 ∞ ∞ = H (mx , my )/w1 − h∗w − mx Hx,m − my Hy,m = hxx m2x + 2hxy mx my + hyy m2y + hxxx m3x + 3hxxy m2x my + 3hxyy mx m2y + hyyy m3y + · · · ,
(1)
where H E (mx , my )/w1 and H (mx , my )/w1 represent the excess and the absolute enthalpy, respectively, of a solution containing 1 kg of water, mx mol of x and my mol of y, h∗w ∞ and is the standard enthalpy of 1 kg of pure water, and Hx,m ∞ Hy,m are the limiting partial molar enthalpies of species x and y, respectively. hij and hiij are the enthalpic virial coefficients characterizing the pairwise and triplet interactions of the solvated species and mx and my are the molalities of the solutes x and y, respectively. Since Hdil (x), Hdil (y) and Hmix have been determined, an auxiliary function H ∗ is introduced, defined as
H ∗ = Hmix − Hdil (x) − Hdil (y) = H E (mx , my ) − H E (mx ) − H E (my ).
(2)
Thus, Eq. (1) can be rewritten as Glycine, L-alanine, L-aminobutyric acid and L-valine (BR, from Shanghai Chem. Co.) were recrystallized from methanol–water mixtures. The materials were used after drying at 100 ◦ C for 6 h and then in vacuo over silica gel at room temperature for a minimum of 24 h. THF and 1, 4-dioxane (AR, from Shanghai Chem. Co.) were used without any pre-treatment. Deionized water was distilled using a quartz sub-boiling purifier and stored in a CO2 free atmosphere before use. Both the aqueous amino acid solutions and the aqueous THF and 1, 4-dioxane solutions were prepared by weight by a Mettler AE 200 balance with a precision of ±0.0001 g. All the solutions were degassed and used within 12 h after preparation to minimize decomposition due to bacterial contamination. 2.2. Calorimetric measurement The enthalpies of dilution and mixing were carried out at (298.15 ± 0.01) K by an LKB flow microcalorimeter. Details of the apparatus and procedures used have been given elsewhere (Yu et al., 2003a,b). Experimental errors in the determination of the molar enthalpies of dilution and mixing were estimated to be < 1%. Every dilution and mixing experiment was repeated three times, and the average of the three measured values was calculated. An excess thermodynamic property can be expressed as a virial expansion of pair and triplet interaction coefficients, which account for all the variations of the solute–solute and solute–solvent interactions according to McMillan–Mayer’s model (McMillan and Mayer, 1945) as modified by Franks (Franks et al., 1976). The thermodynamic procedures used have been described previously (Yu et al., 2003a,b) and only a summary will be given here.
H ∗ /w1 = 2hxy mx my + 3hxxy m2x my + 3hxyy mx m2y + · · · .
(3)
2.3. Blend computer simulation The interaction between the solute and the solvent molecules plays a crucial role in understanding the various molecular processes involved in chemistry and biochemistry. The solvent–solvent, solute–solvent and solute–solute interaction can be best illustrated by calculating the free energy of mixing as a function of composition at different temperatures. Although several methods are available to predict the free energy of binary mixtures (Tomasi and Persico, 1994), Flory–Huggins interaction parameters (Huh and Bae, 2002; Lee et al., 2004; Petri et al., 1996; Fuller et al., 2001) have been used to understand the mixing of two molecular systems qualitatively. When the molecules of amino acids, THF and 1, 4dioxane are considered as the simulated objects, the mixing energies and interaction parameters, i.e., the Flory–Huggins -parameters, between two simulated objects can be obtained. The interaction energies of mixing between different monomers (Emix ) were calculated using the following equation: 1 Zij Eij (T ) − Zij Eij (T ) , (4) Emix (T ) = 2 i =j
i=j
where Eij is the molecular pair interaction energy, i.e., the energy of the complex being composed of one molecule i and one molecule j, and Zij is the coordinated number, i.e., the number of molecules j which can surround one molecule
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i in space. These values of Eij and Zij can be calculated using the program Blend. Here the temperature dependence is introduced as a result of the Metropolis Monte Carlo method. After the interaction energy of mixing between two molecules was calculated, the interaction parameter was obtained via the following equation:
= Z ∗ Vseg
Emix (T ) , RT
(5)
where Z ∗ denotes the average coordination number and Vseg represents the volume of one molecule (Blanco, 1991). Using the Flory–Huggins -parameters, we can understand the intensity of interaction between different molecules. The values of parameters are lower; the intensities of interaction are stronger.
3. Results and discussions 3.1. Enthalpic interactions The experimental results of enthalpies of mixing at 298.15 K of aqueous amino acid (x) solutions and aqueous solutions of THF and 1, 4-dioxane (y) and their respective enthalpies of dilution have been measured by the flowmixing method using an LKB microcalorimeter. A molality range of 0.1–0.5 mol kg−1 was used for these measurements. The heterotactic enthalpic interaction coefficients, which have been calculated according to Eq. (3), are reported in Table 1 . As there are some difficulties in the interpretation of higher h coefficients, only the pairwise coefficients hxy are considered here. The hxy coefficients are considered as enthalpic contributions to the coefficients of the excess Gibbs free energy and a measure of the global effect constituting a sum of the following processes (Palecz, 1995): the partial dehydration of the solutes and the further direct interaction caused by the short-range molecular forces. By and large, the interactions of amino acids with THF and 1, 4-dioxane in the aqueous solutions can be characterized as: the partial dehydration of hydration shell of the amino acid zwitterions, the oxygen atom of THF and 1, 4-dioxane molecule (an endothermic process), and the direct interaction of amino acid with THF and 1, 4-dioxane, which plays a dominant role in the processes of interaction between amino acids and THF and 1, 4-dioxane. The oxygen atom of THF and 1, 4-dioxane has a pair of lone pair electrons and displays hydrophilicity to a certain extent. The direct interactions between -amino acids with the non-polar side chain and THF and 1, 4-dioxane compromise the following four kinds of interactions: (i) the hydrophilic–hydrophilic interaction between the zwitterions part of an amino acid molecule and the oxygen atom of THF and 1, 4-dioxane;
(ii) the hydrophobic–hydrophilic interaction between the non-polar side-group of an amino acid and the oxygen atom of THF and 1, 4-dioxane; (iii) the hydrophilic–hydrophobic interaction between the zwitterions part of an amino acid and the non-polar ring of THF and 1, 4-dioxane; and (iv) the hydrophobic–hydrophobic interaction between the non-polar side-group of an amino acid and the non-polar ring of THF and 1, 4-dioxane. The hxy coefficients for the interactions between amino acids and THF and 1, 4-dioxane molecules in aqueous solutions are a result of competition of the above complex interactions between the two kinds of solute molecules. The experimentally observed positive values of hxy indicate that endothermic processes are dominant during the interaction processes of amino acids with THF and 1, 4-dioxane. The magnitude tendency of the hxy coefficients of amino acids with THF and 1, 4-dioxane has been analyzed concretely as follows: (1) Heterotactic enthalpic pairwise interactions of different -amino acids with THF and 1,4-dioxane. The differences of hxy coefficients between amino acids and THF and 1, 4-dioxane are dramatically contingent on the discrepancies of the structure of amino acids. Glycine, which has no side-chain, is the simplest amino acid in nature. L-alanine, L-aminobutyric acid and L-valine have alkyl side-chains of increasing length. The enthalpic pairwise interaction coefficients between the -amino acids and THF and 1, 4-dioxane have positive values which increase with the increase in the size of the alkyl radicals. The dependence of hxy coefficients on the number of CH2 groups in the amino acid molecule has a linear course (Fig. 1). For the above four amino acids, there are marked discriminations in the interaction (ii) and (iv) concerning the non-polar groups of -amino acid, which make positive contributions to hxy . As the alkyl side-chain of amino acid is lengthened, the positive contributions made to the hxy coefficients of the interaction between amino acids and THF and 1, 4-dioxane in aqueous solutions become larger. Thus, these have rendered the hxy coefficients to increase in the following sequence: hxy (glycine)< hxy (L-alanine)< hxy (Laminobutyric acid)< hxy (L-valine). (2) Enthalpic pairwise interactions between the same amino acid and THF and 1, 4-dioxane. From Table 1, it can be clearly seen that the rule of the hxy coefficients between amino acids and 1, 4-dioxane is similar to that of the hxy coefficients between amino acids and THF. In the meantime, there exist some distinctions in their interaction behaviors. These can be attributed primarily to the similarities and discrepancies in the structures of 1, 4dioxane and THF. Both of them have four methylene groups (–CH2 ). 1, 4-dioxane has two ether oxygen atoms (–O–) but THF only has one. Considering the interactions of the same amino acid molecule studied in this work with 1, 4-dioxane and THF, interactions (iii) and (iv) concerning the non-polar
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Table 1 Heterotactic enthalpic interaction coefficients of amino acids with THF and 1, 4-dioxane in aqueous solutions at 298.15 K Solutes x/y
hxy (J kg mol−2 )
hxxy × 10−3 (J kg2 mol−3 )
hxyy × 10−3 (J kg2 mol−3 )
SD
cr (mol kg−1 )
Glycine/THF L-Alanine/THF L-Aminobutyric acid/THF L-Valine/THF Glycine/1, 4-dioxane L-Alanine/1, 4-dioxane L-Aminobutyric acid/1, 4-dioxane L-Valine/1, 4-dioxane
568.0 578.6 701.5 741.8 254.3 465.4 538.1 716.3
−8.6 82.6 −14.2 58.1 18.5 126.8 −71.2 76.7
8.9 −84.0 14.7 −58.1 −19.1 −129.6 72.5 −77.3
0.57 0.70 0.66 1.57 0.24 0.28 0.27 1.22
0.1–0.5 0.1–0.5 0.1–0.5 0.1–0.5 0.1–0.5 0.1–0.5 0.1–0.5 0.1–0.5
(123.5) (153.5) (146.3) (347.3) (51.80) (61.70) (59.22) (271.15)
(1536.7) (134.0) (152.1) (108.3) (45.0) (810.0) (60.5) (134.3)
(1576.7) (136.5) (155.1) (108.3) (46.4) (826.7) (61.6) (135.8)
most useful application is for a series of compounds related in structure. According to the SWAG approach, the enthalpic pairwise coefficients can be separated into several contributions due to the interactions among the functional groups of two molecules. This approach assumes that when two solute molecules interact, every functional group on molecule x interacts with every functional group on molecule y and that each interaction has a characteristic enthalpy, which is independent of the position of each group within their respective molecules. The total pairwise interaction is then the sum of all of the various functional group interactions. The resulting equation is y nxi nj Hij , (6) hxy = i,j
y
Fig. 1. The dependence of the heterotactic enthalpic pairwise interaction coefficients of amino acids/THF(A) and amino acids/1, 4-dioxane (B) systems calculated by the enthalpic determination method with the number of methylene groups in the side chains of amino acid molecules at 298.15 K.
groups of heterocyclic compounds are basically similar and interactions (i) and (ii) relational to the ether oxygen atoms of 1, 4-dioxane are all stronger than those of THF. Therefore, the relative magnitude of hxy coefficients between the same amino acid and THF and 1, 4-dioxane is a result of the balance between the interactions (i) (making negative contributions to hxy ) and (ii) (making positive contributions to hxy ). For the same amino acid molecule the experimental result is hxy (THF) > hxy (1, 4-dioxane) (Table 1), which suggests that the interaction (i) plays a dominant role in the process. 3.2. SWAG analysis In recent years, a clear, although qualitative, understanding of non-bonding interactions in aqueous solutions has been attained through the analysis of the excess thermodynamic properties using the Savage and Wood groupadditivity approach (SWAG) (Savage and Wood, 1976). Its
where nxi is the number of type i groups on molecule x, nj is the number of type j groups on molecule y, and Hij is the enthalpic contribution of an i–j interaction. Although the approach has limitations (Franks and Pedley, 1983; Barone et al., 1983), it has been used with varying degrees of success in a considerable number of investigations including amides (Savage and Wood, 1976), alcohols (Okamoto et al., 1978), amines (Tasker and Wood, 1982a,b), N-acetyl amino acid amides (Blackburn et al., 1980), and even charged solute species like amino acids (Wegrzyn et al., 1984). But so far many reports on unbranched chain molecules have been made and scarcely any report has been found about heterocyclic compounds. There is some interest to see whether the approach can extend to heterocyclic compounds containing oxygen atoms. The experimental results of the amino acid-1, 4-dioxane and amino acid/THF systems have been analyzed using the SWAG approach. To apply this additivity approach it is necessary to divide each molecule in the set into a number of functional groups. The way this is carried out, of course, is somewhat arbitrary. For amino acid molecules, the following division method − has been used: the NH+ 3 and COO functional groups are treated as one unit, which have been denoted E. The hydrocarbon function is based on the methylene unit. Following the literature (Savage and Wood, 1976), a CH3 group is equivalent to 1.5 CH2 groups, a CH group is equivalent to 0.5 CH2 groups, and H is also counted as 0.5 CH2 group.
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Table 2 Experimental and calculated values of hxy for amino acids with THF and 1, 4-dioxane in aqueous solutions at 298.15 K Solutes x/y
hxy (expt.)/J kg mol−2
hxy (calc.)/J kg mol−2
Glycine/THF L-Alanine/THF L-Aminobutyric acid/THF L-Valine/THF Glycine/1, 4-dioxane L-Alanine/1, 4-dioxane L-Aminobutyric acid/1, 4-dioxane L-Valine/1, 4-dioxane
568.0 578.6 701.5 741.8 254.3 465.4 538.1 716.3
557 617 677 737 274 418 562 706
−1.9 6.6 −3.5 −0.65 7.7 −10.2 4.4 −1.4
For 1, 4-dioxane and THF molecules, the division method is employed as follows: –O– and –CH2 are considered as two independent groups. Using this scheme multiple linear regression analysis applied to Eq. (6) for the data of Table 1 yields the following Hij values: HE.O = −345(7),
HE.CH2 = 213(10),
HCH2 .O = 84(12),
HCH2 .CH2 = −6(5),
to SWAG, this approach is of great value to the amino acids/THF and amino acids/1, 4-dioxane systems in the aqueous solutions. It is a valuable discovery that the SWAG approach can be applied to study and predict the interaction parameters of these classes of compounds. But to obtain satisfactory results, it is necessary to ameliorate the SWAG model in further studies.
(7)
where the unit of Hij is J kg mol−2 , the correlation coefficient is 0.9956 and the data in the parenthesis are the estimative deviation. Table 2 gives a comparison of the experimental enthalpies of interaction and the calculated ones on the basis of the above-mentioned contributions of the interactions from the different selected groups. As can be seen from Table 2, in spite of the simplicity of the model of interactions in most cases the two sets of data are in satisfactory agreement. The results obtained from the SWAG approach make the interactions of amino acids with THF and 1, 4-dioxane quantitative and can basically reflect the rules of the interaction processes. The results show: the ion–dipolar interaction between the zwitterions of amino acids and the ether oxygen atoms of THF and 1, 4-dioxane makes larger negative contributions to hxy (HE.O = −345 J kg mol−2 ); the hydrophilic–hydrophobic interaction between the zwitterions of amino acids and the non-polar ring of the heterocyclic compounds makes larger positive contributions to hxy (HE.CH2 = 213 J kg mol−2 ); and the hydrophobic–hydrophilic interaction between the hydrophobic groups of amino acids and the ether oxygen atoms of the heterocyclic compounds can make positive contributions to hxy to some extent (HCH2 .O = 84 J kg mol−2 ). The above three values for HE.O , HE.CH2 and HCH2 .O seem reasonable; however, the value for HCH2 .CH2 is clearly of the wrong sign. The main reason for this is that the assumptions of the SWAG approach are very simple. It assumes that each functional group interacts with every other functional group independent of its position. And some effects such as steric effects and configurational effects are ignored. In other words, although in the present work there are some errors arising from the results obtained according
3.3. Florry–Huggins interaction parameters In order to further testify our experimental results of amino acids/THF and amino acids/1, 4-dioxane systems, the mixing energy Emix (namely, the free energy of the mixing process) and Florry–Huggins interaction parameter x are obtained using the Blend simulation from the point of view of theory. The interaction between two different molecules in the vacuum is defined as an interaction parameter. The information on the mixing process can be obtained from the mixing energy and the interaction parameter. As discussed above, the lower the parameters, the stronger the interaction between different molecules. We found that the complex composed of amino acids and THF has a lower mixing energy, it means that the interaction between them is stronger, and the complex is more stable than that composed of amino acids and 1, 4-dioxane. The parameters x for amino acids/THF and amino acids/1, 4-dioxane systems can be calculated via Eq. (5). Because the parameters x are calculated from the mixing energies, their physical meaning is in agreement with that of the energy. This Huggins parameter x implies the interaction intensity between two different molecules. The value of x between two water molecules is considered as zero and other x values are compared with zero. The negative x value shows that the attractive interaction in the studied system is stronger than that between two water molecules. Fig. 2 shows a plot of the interaction parameters of amino acids/THF and amino acids/1, 4-dioxanesystems versus the number of methylene groups in the side chains of amino acid molecules at 298 K. As can be seen from Fig. 2, for amino acids/THF and amino acids/1, 4-dioxanesystems, the interaction parameters x increase with the increase of the number of carbon atoms. We found that the system of glycine and
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ber of methylene groups in the side-chain of amino acid molecules; the hxy coefficient of amino acids/1, 4-dioxane is more negative than that of amino acids/THF for the same amino acid. The experimentally observed results have been interpreted in terms of a solute–solute interaction. The SWAG approach applied to unbranched chain molecules has been applied to heterocyclic compounds. The theoretical calculated values of hxy coefficients using the SWAG approach are in satisfactory agreement. In addition, the SWAG approach has been appraised according to the results obtained. Mixing energy and interaction coefficient for -amino acids and THF and 1,4-dioxane have been obtained using the Flory–Huggins interaction parameters employing Monte Carlo Simulation techniques. The tendency displayed by the computer simulation results is in accordance with that of the experimental results. Fig. 2. The dependence of interaction parameters of amino acids/THF(A) and amino acids/1, 4-dioxane (B) systems calculated by the computer simulation method with the number of methylene groups in the side chains of amino acid molecules at 298 K.
THF has the lowest parameter; it means that the interaction between them is the strongest, and the mixing of glycine and THF is the most stable. For amino acids and 1, 4-dioxane system, a similar conclusion can be obtained. From Fig. 2, we noticed at the same number of carbon atoms, that the interaction parameter x of amino acids/1, 4-dioxane system is smaller than that of the amino acids/THF system. This means that the interaction intensity of the former is stronger than that of the latter. As can be seen from Fig. 1, in the amino acids/THF (or amino acids/1, 4-dioxane) series, the glycine/THF (or glycine/1, 4-dioxane) system has the lowest hxy value. The hxy coefficient of any amino acid studied with 1, 4-dioxane is more negative than that of the amino acid with THF. The more negative the hxy value, the less the endothermic effect during the process of interaction between amino acids and THF and the more stable the mixing process, the stronger the interaction between them. There is also a very good linear relationship between the Huggins parameters of the studied systems and the number of CH2 groups in the -amino acid molecule (Fig. 2). The information obtained from Fig. 2 in terms of theoretical calculation is consistent with that of Fig. 1 on the basis of experimental results. 4. Conclusions The interactions for amino acids/THF and amino acids/1, 4-dioxane systems are studied by experiments, theoretical calculation and computer simulation. The experimental results are as follows: for amino acids/THF and amino acids/1, 4-dioxanesystems, the values of hxy coefficients increase linearly with the increase of the num-
Notation cr Emix Eij
hxy hxxy hxyy hxy (calc.)
hxy (expt.) h∗w Hij H (mx , my )/w1 H E (mx , my )/w1 ∞ Hx,m
concentration range (mol kg−1 ) interaction energies of mixing between different monomers molecular pair interaction energy, i.e., the energy of the complex being composed of one molecule i and one molecule j pairwise heterotactic enthalpic interaction coefficient between x and y solutes (J kg mol−2 ) triplet heterotactic enthalpic interaction coefficient between x, x and y solutes (J kg2 mol−3 ) triplet heterotactic enthalpic interaction coefficient between x, y and y solutes (J kg2 mol−3 ) calculated pairwise heterotactic enthalpic interaction coefficient between x and y solutes by the SWAG approach (J kg mol−2 ) experimental pairwise heterotactic enthalpic interaction coefficient between x and y solutes (J kg mol−2 ) standard enthalpy of 1 kg of pure water enthalpic contribution of an i–j interaction absolute enthalpy of a solution containing 1 kg of water, mx mol of x and my mol of y (J kg−1 ) excess enthalpy of a solution containing 1 kg of water, mx mol of x and my mol of y (J kg−1 ) limiting partial molar enthalpies of solute x (J mol−1 )
800 ∞ Hy,m
Hdil(x) /w1 Hdil(y) /w1 Hmix /w1 H ∗ /w1 mx my nxi y nj SD Vseg Zij Z∗
Li Yu et al. / Chemical Engineering Science 61 (2006) 794 – 801
limiting partial molar enthalpies of solute y (J mol−1 ) dilution enthalpy of solute x in 1 kg of water (J kg−1 ) dilution enthalpy of solute y in 1 kg of water (J kg−1 ) mixing enthalpy of aqueous x and y solutions in 1 kg of water (J kg−1 ) auxiliary function in 1 kg of water (J kg−1 ) final molality of solute x final molality of solute y number of type i groups on molecule x number of type j groups on molecule y standard derivation volume of one molecule coordinated number, i.e., the number of molecules j which can surround one molecule i in space average coordination number
Greek letter
Relative deviation between the experimental and calculated pairwise heterotactic enthalpic interaction coefficients
Acknowledgements The authors are grateful for financial assistance from the Natural Science Foundation of Shandong Province of China (No. Q2003B01) and the Key Technologies R & D Programme of China (No. 2004BA313B09). References Barone, G., Castronuovo, G., Doucas, D., Elia, V., Mattia, C.A., 1983. Excess enthalpies of aqueous solutions of monosaccharides at 298.15 K: pentoses and 2-deoxy sugars. Journal of Physical Chemistry 87, 1931–1937. Blackburn, G.M., Lilley, T.H., Walmsley, E., 1980. Aqueous solutions containing amino acids and peptides part 11-enthalpy of dilution of single and binary solute solutions of N-acetyl-glycine amide, N-acetylL-alanine amide, N-acetyl-L-valine amide and N-acetyl-L-leucine amide at 298.15 K. Journal of Chemical Science Faraday Transaction I 76, 915–922. Blanco, M., 1991. Molecular silverware I. General solutions to excluded volume constrained problems. Journal of Computational Chemistry 12, 237–247. Castronuovo, G., Elia, V., Velleca, F., 1996. On the role of the functional group in determining the strength of hydrophobic interactions in aqueous solutions of -amino acid derivatives. Journal of Solution Chemistry 25, 971–982. Fernandez, J., Lilley, T.H., 1992. Aqueous solution containing amino acids and peptides part 28—Enthalpy of interaction of some amides with glycine and -alanine: interactions of the zwitterionic group of -amino acids with hydrophobic groups and peptide groups. Journal of Chemical Science Faraday Transaction 88, 2503–2509.
Franks, F., Pedley, M.D., 1983. Solute interactions in dilute aqueous solutions Part 5—microcalorimetric study of polyols and their mixtures with alkanols. Journal of Chemical Science Faraday Transaction I 79, 2249–2260. Franks, F., Pedley, M., Reid, D.S., 1976. Solute interactions in dilute aqueous solutions part 1: —microcalorimetric study of the hydrophobic interaction. Journal of Chemical Science Faraday Transaction I 72, 359–367. Fuller, C.S., Macrae, R.J., Walther, M., Cameron, R.E., 2001. Interaction in poly(ethylene oxide)-hydroxypropyl methylcellulose blends. Polymer 42, 9583–9592. Huh, J.Y., Bae, Y.C., 2002. Water activities of florinated solid polymer electrolyte/water systems using group-contribution method. Chemical Engineering Science 57, 2747–2752. Lee, K.W.D., Chan, P.K., Feng, X.Sh., 2004. Morphology development and characterization of the phase-separated structure resulting from the thermal-induced phase separation phenomenon in polymer solutions under a temperature gradient. Chemical Engineering Science 59, 1491–1504. McMillan, W.G., Mayer, J.E., 1945. The statistical thermodynamics of multicomponents systems. Journal of Chemical Physics 13, 276–305. Okamoto, B.Y., Wood, R.H., Thompson, P.T., 1978. Freezing points of aqueous alcohols. Free energy of interaction of the CHOC, CH2 , CONH and C&C functional groups in dilute aqueous solutions. Journal of Chemical Science Faraday Transaction I 74, 1990–2007. Palecz, B., 1995. The enthalpies of interaction of glycine with some amides and ureas in water at 25 ◦ C. Journal of Solution Chemistry 24 (6), 537–550. Petri, H.M., Horst, R., Wolf, B.A., 1996. Determination of interaction parameters for highly incompatible polymers. Polymer 37 (13), 2709–2713. Savage, J.J., Wood, R.H., 1976. Enthalpy of dilution of aqueous mixtures of amides, sugars, urea, ethylene glycol and pentaerythritol at 25 ◦ C: enthalpy of interaction of the hydrocarbon, amide, and hydroxyl functional groups in dilute aqueous solutions. Journal of Solution Chemistry 5, 731–750. Shao, S., Lin, R.S., Hu, X.G., 2001. Enthalpic interactions between amino acids and monomethylurea. Acta Physical Chimica Sinica 17 (7), 645–650. Tasker, I.R., Wood, R.H., 1982a. Enthalpies of dilution of aqueous systems containing hexamethylenetetramine and other nonelectrolytes. Journal of Solution Chemistry 11, 729–747. Tasker, I.R., Wood, R.H., 1982b. Enthalpies of dilution of aqueous solutions of cyclohexanol, inositol and mannitol. Journal of Physical Chemistry 86, 4040–4045. Tomasi, J., Persico, M., 1994. An overview of different approaches to studying chemistry in solution. Chemical Reviews 94, 2027–2094. Wegrzyn, T.F., Watson, I.D., Hedwig, G.R., 1984. Enthalpies of mixing of aqueous solutions of the amino acids glycine, L-alanine and L-serine. Journal of Solution Chemistry 13 (4), 233–244. Yu, L., Lin, R.S., Hu, X.G., Xu, G.Y., 2003a. Enthalpic interaction of amino acids with ethanol in aqueous solutions at 25 ◦ C. Journal of Solution Chemistry 32 (3), 273–281. Yu, L., Hu, X.G., Lin, R.S., Zh, H.L., Xu, G.Y., 2003b. Enthalpies of interaction of L-valine and L-threonine with pyridine and methylpyridine in aqueous solutions at 298.15 K. Journal of Chemical Engineering Data 48, 1591–1596.
Further reading Abbate, M., Barone, G., Castronuovo, G., et al., 1990. Thermodynamic behavior of some uncharged organic molecules in concentrated aqueous urea solutions and other polar solvents. Thermochimica Acta 173, 261–272.
Li Yu et al. / Chemical Engineering Science 61 (2006) 794 – 801 Abbate, M., Barone, G., Borghesani, G., 1993. Dilution enthalpies alkanols in concentrated aqueous solutions of urea at 25 ◦ C. Journal of Solution Chemistry 22, 695–706. Blackburn, G.M., Lilly, T.H., Milburn, P.J., 1984. Aqueous solutions containing amino acids and peptides. Part 19: the enthalpic coefficients for the interactions of N-acetylsarcosinamide with 2-(Nacetylamino)acyl amides at 25 ◦ C. Journal of Solution Chemistry 13, 789–803. Cascella, C., Catronuovo, G., Elia, V., Sartorio, R., Wurzburger, S., 1990. Hydrophobic interactions of alkanols—a calorimetric study in water at 298.15 K. Journal of Chemical Science Faraday Transaction 86 (1), 85–88. DeVisser, C., Heuvelsland, W.J.M., Somsen, G., 1978. The pairwise interaction concept of Savage and Wood applied to electrolytes. Journal of Solution Chemistry 7 (3), 193–196.
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Krishnan, C.V., Friedman, H.L., 1971. The solvent–isotope effect in the enthalpy of some solutes in methanol. Journal of Physical Chemistry 75, 388–391. Lilley, T.H., 1993. The interplay between solute solvation and solute–solute interactions in solutions containing amino acids, peptides and related species. Pure and Applied Chemistry 65, 2551–2560. Shao, S., Hu, X.G., Lin, R.S., 2000. Enthalpic interactions of L-alanine and L-serine in aqueous urea solutions. Thermochimica Acta 360, 93–100. Soldi, L.G., Marcus, Y., Blandamer, M.J., Cullis, P.M., 1995. Titration calorimetric determination of the pairwise interaction parameters of glycerol, D-threitol, mannitol, and D-glucitol in dilute aqueous solutions. Journal of Solution Chemistry 24 (3), 201–209.
Studies on the interactions between some -amino acids with a non-polar side chain and two saturated cyclic ethers at 298.15 K: enthalpic measurement and computer simulation Li Yua, b,∗ , Shi-Ling Yuana , Xin-Gen Huc , Rui-Sen Linb a Key Lab for Colloid and Interface Chemistry, Shandong University, Ministry of Education, Jinan 250100, PR China b Department of Chemistry, Zhejiang University, Hangzhou 310027, PR China c Department of Chemistry, Wenzhou Normal College, Wenzhou 325000, PR China
Received 11 April 2005; received in revised form 4 August 2005; accepted 8 August 2005 Available online 19 September 2005
Abstract Mixing enthalpies of heterocyclic compounds (THF and 1, 4-dioxane) and -amino acids with a non-polar side chain (glycine, L-alanine, acid and L-valine), and dilution enthalpies of each compound have been determined in aqueous solutions at 298.15 K by a flow-mixing microcalorimeter. The heterotactic enthalpic pairwise interaction coefficients, hxy , of each amino acid with THF and 1, 4-dioxane have been calculated by the McMillan–Mayer formalism, and discussed in terms of intermolecular interactions between the hydrated solute species. Using the additivity groups concept by Savage and Wood (SWAG), contributions of each functional group of studied solutes have been estimated. In addition, the mixing energies and Huggins parameters of amino acid-heterocyclic compound systems have been obtained by computer simulation. The results of computer simulation are consistent with enthalpic measurements. 䉷 2005 Elsevier Ltd. All rights reserved. L-aminobutyric
Keywords: Enthalpy; Computer simulation; SWAG approach; Interaction coefficient
1. Introduction The stability of the native structure of proteins in aqueous solutions can be ascribed to the weak non-bonding interactions between the groups of amino acids as well as amino acids and the other components in solutions (Castronuovo et al., 1996). The majority of proteins exist in aqueous mixed solvents containing many organic substances. Studies on various thermodynamic properties of amino acids and simple peptides in aqueous solutions of organic substances are of current interest due to their importance in the better understanding of the nature and mechanisms taking place in biological cells (Fernandez and Lilley, 1992). ∗ Corresponding author. Key Lab for Colloid and Interface Chemistry, Shandong University, Ministry of Education, Jinan 250100, PR China. Tel.: +86 0531 8366145; fax: +86 531 856 4750. E-mail address: [email protected] (Li Yu).
0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.08.008
Scarcely any report has been found about calorimetric studies of simple heterocyclic compounds. However, these compounds, for example, the simple heterocyclic compounds in pesticides, are very important to the living organisms and the environment. 1, 4-dioxane and tetrahydrofuran (THF) are both two kinds of heterocyclic compounds containing an oxygen atom, familiar to all of us. Of the thermodynamic functions describing solvation or solution processes, entropy is significantly connected to the solvent structure perturbations brought about by the introduction of a solute. Unfortunately, only limited entropy data in mixed solvents are available. Enthalpy values are more widely available and are more frequently used. It is effective to investigate the interaction between amino acids and organic substances using an enthalpic measurement method. As an extension to our previous study (Yu et al., 2003a,b; Shao et al., 2001), we address the non-covalent bonding interactions that occur between amino acids and
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heterocyclic compounds. The present work reports the calorimetric results of the mixing enthalpies of some typical -amino acids with a non-polar side chain (glycine, L-alanine, L-aminobutyric acid and L-valine) and THF and 1, 4-dioxane, together with their respective dilution enthalpies in aqueous solutions. The data served as a basis for calculations of the heterotactic enthalpic coefficients of interactions between the amino acids studied and THF and 1, 4-dioxane in an aqueous solution. The results are interpreted from the point of view of solute–solute interactions and discussed by the Savage and Wood (SWAG) approach. In addition, the computer simulation provides useful information on the interactions between the two mixed systems. The results of computer simulation are in agreement with those of the experiment.
2. Materials and methods 2.1. Materials
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The excess enthalpy of a solution is defined as H E (mx , my )/w1 ∞ ∞ = H (mx , my )/w1 − h∗w − mx Hx,m − my Hy,m = hxx m2x + 2hxy mx my + hyy m2y + hxxx m3x + 3hxxy m2x my + 3hxyy mx m2y + hyyy m3y + · · · ,
(1)
where H E (mx , my )/w1 and H (mx , my )/w1 represent the excess and the absolute enthalpy, respectively, of a solution containing 1 kg of water, mx mol of x and my mol of y, h∗w ∞ and is the standard enthalpy of 1 kg of pure water, and Hx,m ∞ Hy,m are the limiting partial molar enthalpies of species x and y, respectively. hij and hiij are the enthalpic virial coefficients characterizing the pairwise and triplet interactions of the solvated species and mx and my are the molalities of the solutes x and y, respectively. Since Hdil (x), Hdil (y) and Hmix have been determined, an auxiliary function H ∗ is introduced, defined as
H ∗ = Hmix − Hdil (x) − Hdil (y) = H E (mx , my ) − H E (mx ) − H E (my ).
(2)
Thus, Eq. (1) can be rewritten as Glycine, L-alanine, L-aminobutyric acid and L-valine (BR, from Shanghai Chem. Co.) were recrystallized from methanol–water mixtures. The materials were used after drying at 100 ◦ C for 6 h and then in vacuo over silica gel at room temperature for a minimum of 24 h. THF and 1, 4-dioxane (AR, from Shanghai Chem. Co.) were used without any pre-treatment. Deionized water was distilled using a quartz sub-boiling purifier and stored in a CO2 free atmosphere before use. Both the aqueous amino acid solutions and the aqueous THF and 1, 4-dioxane solutions were prepared by weight by a Mettler AE 200 balance with a precision of ±0.0001 g. All the solutions were degassed and used within 12 h after preparation to minimize decomposition due to bacterial contamination. 2.2. Calorimetric measurement The enthalpies of dilution and mixing were carried out at (298.15 ± 0.01) K by an LKB flow microcalorimeter. Details of the apparatus and procedures used have been given elsewhere (Yu et al., 2003a,b). Experimental errors in the determination of the molar enthalpies of dilution and mixing were estimated to be < 1%. Every dilution and mixing experiment was repeated three times, and the average of the three measured values was calculated. An excess thermodynamic property can be expressed as a virial expansion of pair and triplet interaction coefficients, which account for all the variations of the solute–solute and solute–solvent interactions according to McMillan–Mayer’s model (McMillan and Mayer, 1945) as modified by Franks (Franks et al., 1976). The thermodynamic procedures used have been described previously (Yu et al., 2003a,b) and only a summary will be given here.
H ∗ /w1 = 2hxy mx my + 3hxxy m2x my + 3hxyy mx m2y + · · · .
(3)
2.3. Blend computer simulation The interaction between the solute and the solvent molecules plays a crucial role in understanding the various molecular processes involved in chemistry and biochemistry. The solvent–solvent, solute–solvent and solute–solute interaction can be best illustrated by calculating the free energy of mixing as a function of composition at different temperatures. Although several methods are available to predict the free energy of binary mixtures (Tomasi and Persico, 1994), Flory–Huggins interaction parameters (Huh and Bae, 2002; Lee et al., 2004; Petri et al., 1996; Fuller et al., 2001) have been used to understand the mixing of two molecular systems qualitatively. When the molecules of amino acids, THF and 1, 4dioxane are considered as the simulated objects, the mixing energies and interaction parameters, i.e., the Flory–Huggins -parameters, between two simulated objects can be obtained. The interaction energies of mixing between different monomers (Emix ) were calculated using the following equation: 1 Zij Eij (T ) − Zij Eij (T ) , (4) Emix (T ) = 2 i =j
i=j
where Eij is the molecular pair interaction energy, i.e., the energy of the complex being composed of one molecule i and one molecule j, and Zij is the coordinated number, i.e., the number of molecules j which can surround one molecule
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i in space. These values of Eij and Zij can be calculated using the program Blend. Here the temperature dependence is introduced as a result of the Metropolis Monte Carlo method. After the interaction energy of mixing between two molecules was calculated, the interaction parameter was obtained via the following equation:
= Z ∗ Vseg
Emix (T ) , RT
(5)
where Z ∗ denotes the average coordination number and Vseg represents the volume of one molecule (Blanco, 1991). Using the Flory–Huggins -parameters, we can understand the intensity of interaction between different molecules. The values of parameters are lower; the intensities of interaction are stronger.
3. Results and discussions 3.1. Enthalpic interactions The experimental results of enthalpies of mixing at 298.15 K of aqueous amino acid (x) solutions and aqueous solutions of THF and 1, 4-dioxane (y) and their respective enthalpies of dilution have been measured by the flowmixing method using an LKB microcalorimeter. A molality range of 0.1–0.5 mol kg−1 was used for these measurements. The heterotactic enthalpic interaction coefficients, which have been calculated according to Eq. (3), are reported in Table 1 . As there are some difficulties in the interpretation of higher h coefficients, only the pairwise coefficients hxy are considered here. The hxy coefficients are considered as enthalpic contributions to the coefficients of the excess Gibbs free energy and a measure of the global effect constituting a sum of the following processes (Palecz, 1995): the partial dehydration of the solutes and the further direct interaction caused by the short-range molecular forces. By and large, the interactions of amino acids with THF and 1, 4-dioxane in the aqueous solutions can be characterized as: the partial dehydration of hydration shell of the amino acid zwitterions, the oxygen atom of THF and 1, 4-dioxane molecule (an endothermic process), and the direct interaction of amino acid with THF and 1, 4-dioxane, which plays a dominant role in the processes of interaction between amino acids and THF and 1, 4-dioxane. The oxygen atom of THF and 1, 4-dioxane has a pair of lone pair electrons and displays hydrophilicity to a certain extent. The direct interactions between -amino acids with the non-polar side chain and THF and 1, 4-dioxane compromise the following four kinds of interactions: (i) the hydrophilic–hydrophilic interaction between the zwitterions part of an amino acid molecule and the oxygen atom of THF and 1, 4-dioxane;
(ii) the hydrophobic–hydrophilic interaction between the non-polar side-group of an amino acid and the oxygen atom of THF and 1, 4-dioxane; (iii) the hydrophilic–hydrophobic interaction between the zwitterions part of an amino acid and the non-polar ring of THF and 1, 4-dioxane; and (iv) the hydrophobic–hydrophobic interaction between the non-polar side-group of an amino acid and the non-polar ring of THF and 1, 4-dioxane. The hxy coefficients for the interactions between amino acids and THF and 1, 4-dioxane molecules in aqueous solutions are a result of competition of the above complex interactions between the two kinds of solute molecules. The experimentally observed positive values of hxy indicate that endothermic processes are dominant during the interaction processes of amino acids with THF and 1, 4-dioxane. The magnitude tendency of the hxy coefficients of amino acids with THF and 1, 4-dioxane has been analyzed concretely as follows: (1) Heterotactic enthalpic pairwise interactions of different -amino acids with THF and 1,4-dioxane. The differences of hxy coefficients between amino acids and THF and 1, 4-dioxane are dramatically contingent on the discrepancies of the structure of amino acids. Glycine, which has no side-chain, is the simplest amino acid in nature. L-alanine, L-aminobutyric acid and L-valine have alkyl side-chains of increasing length. The enthalpic pairwise interaction coefficients between the -amino acids and THF and 1, 4-dioxane have positive values which increase with the increase in the size of the alkyl radicals. The dependence of hxy coefficients on the number of CH2 groups in the amino acid molecule has a linear course (Fig. 1). For the above four amino acids, there are marked discriminations in the interaction (ii) and (iv) concerning the non-polar groups of -amino acid, which make positive contributions to hxy . As the alkyl side-chain of amino acid is lengthened, the positive contributions made to the hxy coefficients of the interaction between amino acids and THF and 1, 4-dioxane in aqueous solutions become larger. Thus, these have rendered the hxy coefficients to increase in the following sequence: hxy (glycine)< hxy (L-alanine)< hxy (Laminobutyric acid)< hxy (L-valine). (2) Enthalpic pairwise interactions between the same amino acid and THF and 1, 4-dioxane. From Table 1, it can be clearly seen that the rule of the hxy coefficients between amino acids and 1, 4-dioxane is similar to that of the hxy coefficients between amino acids and THF. In the meantime, there exist some distinctions in their interaction behaviors. These can be attributed primarily to the similarities and discrepancies in the structures of 1, 4dioxane and THF. Both of them have four methylene groups (–CH2 ). 1, 4-dioxane has two ether oxygen atoms (–O–) but THF only has one. Considering the interactions of the same amino acid molecule studied in this work with 1, 4-dioxane and THF, interactions (iii) and (iv) concerning the non-polar
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Table 1 Heterotactic enthalpic interaction coefficients of amino acids with THF and 1, 4-dioxane in aqueous solutions at 298.15 K Solutes x/y
hxy (J kg mol−2 )
hxxy × 10−3 (J kg2 mol−3 )
hxyy × 10−3 (J kg2 mol−3 )
SD
cr (mol kg−1 )
Glycine/THF L-Alanine/THF L-Aminobutyric acid/THF L-Valine/THF Glycine/1, 4-dioxane L-Alanine/1, 4-dioxane L-Aminobutyric acid/1, 4-dioxane L-Valine/1, 4-dioxane
568.0 578.6 701.5 741.8 254.3 465.4 538.1 716.3
−8.6 82.6 −14.2 58.1 18.5 126.8 −71.2 76.7
8.9 −84.0 14.7 −58.1 −19.1 −129.6 72.5 −77.3
0.57 0.70 0.66 1.57 0.24 0.28 0.27 1.22
0.1–0.5 0.1–0.5 0.1–0.5 0.1–0.5 0.1–0.5 0.1–0.5 0.1–0.5 0.1–0.5
(123.5) (153.5) (146.3) (347.3) (51.80) (61.70) (59.22) (271.15)
(1536.7) (134.0) (152.1) (108.3) (45.0) (810.0) (60.5) (134.3)
(1576.7) (136.5) (155.1) (108.3) (46.4) (826.7) (61.6) (135.8)
most useful application is for a series of compounds related in structure. According to the SWAG approach, the enthalpic pairwise coefficients can be separated into several contributions due to the interactions among the functional groups of two molecules. This approach assumes that when two solute molecules interact, every functional group on molecule x interacts with every functional group on molecule y and that each interaction has a characteristic enthalpy, which is independent of the position of each group within their respective molecules. The total pairwise interaction is then the sum of all of the various functional group interactions. The resulting equation is y nxi nj Hij , (6) hxy = i,j
y
Fig. 1. The dependence of the heterotactic enthalpic pairwise interaction coefficients of amino acids/THF(A) and amino acids/1, 4-dioxane (B) systems calculated by the enthalpic determination method with the number of methylene groups in the side chains of amino acid molecules at 298.15 K.
groups of heterocyclic compounds are basically similar and interactions (i) and (ii) relational to the ether oxygen atoms of 1, 4-dioxane are all stronger than those of THF. Therefore, the relative magnitude of hxy coefficients between the same amino acid and THF and 1, 4-dioxane is a result of the balance between the interactions (i) (making negative contributions to hxy ) and (ii) (making positive contributions to hxy ). For the same amino acid molecule the experimental result is hxy (THF) > hxy (1, 4-dioxane) (Table 1), which suggests that the interaction (i) plays a dominant role in the process. 3.2. SWAG analysis In recent years, a clear, although qualitative, understanding of non-bonding interactions in aqueous solutions has been attained through the analysis of the excess thermodynamic properties using the Savage and Wood groupadditivity approach (SWAG) (Savage and Wood, 1976). Its
where nxi is the number of type i groups on molecule x, nj is the number of type j groups on molecule y, and Hij is the enthalpic contribution of an i–j interaction. Although the approach has limitations (Franks and Pedley, 1983; Barone et al., 1983), it has been used with varying degrees of success in a considerable number of investigations including amides (Savage and Wood, 1976), alcohols (Okamoto et al., 1978), amines (Tasker and Wood, 1982a,b), N-acetyl amino acid amides (Blackburn et al., 1980), and even charged solute species like amino acids (Wegrzyn et al., 1984). But so far many reports on unbranched chain molecules have been made and scarcely any report has been found about heterocyclic compounds. There is some interest to see whether the approach can extend to heterocyclic compounds containing oxygen atoms. The experimental results of the amino acid-1, 4-dioxane and amino acid/THF systems have been analyzed using the SWAG approach. To apply this additivity approach it is necessary to divide each molecule in the set into a number of functional groups. The way this is carried out, of course, is somewhat arbitrary. For amino acid molecules, the following division method − has been used: the NH+ 3 and COO functional groups are treated as one unit, which have been denoted E. The hydrocarbon function is based on the methylene unit. Following the literature (Savage and Wood, 1976), a CH3 group is equivalent to 1.5 CH2 groups, a CH group is equivalent to 0.5 CH2 groups, and H is also counted as 0.5 CH2 group.
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Table 2 Experimental and calculated values of hxy for amino acids with THF and 1, 4-dioxane in aqueous solutions at 298.15 K Solutes x/y
hxy (expt.)/J kg mol−2
hxy (calc.)/J kg mol−2
Glycine/THF L-Alanine/THF L-Aminobutyric acid/THF L-Valine/THF Glycine/1, 4-dioxane L-Alanine/1, 4-dioxane L-Aminobutyric acid/1, 4-dioxane L-Valine/1, 4-dioxane
568.0 578.6 701.5 741.8 254.3 465.4 538.1 716.3
557 617 677 737 274 418 562 706
−1.9 6.6 −3.5 −0.65 7.7 −10.2 4.4 −1.4
For 1, 4-dioxane and THF molecules, the division method is employed as follows: –O– and –CH2 are considered as two independent groups. Using this scheme multiple linear regression analysis applied to Eq. (6) for the data of Table 1 yields the following Hij values: HE.O = −345(7),
HE.CH2 = 213(10),
HCH2 .O = 84(12),
HCH2 .CH2 = −6(5),
to SWAG, this approach is of great value to the amino acids/THF and amino acids/1, 4-dioxane systems in the aqueous solutions. It is a valuable discovery that the SWAG approach can be applied to study and predict the interaction parameters of these classes of compounds. But to obtain satisfactory results, it is necessary to ameliorate the SWAG model in further studies.
(7)
where the unit of Hij is J kg mol−2 , the correlation coefficient is 0.9956 and the data in the parenthesis are the estimative deviation. Table 2 gives a comparison of the experimental enthalpies of interaction and the calculated ones on the basis of the above-mentioned contributions of the interactions from the different selected groups. As can be seen from Table 2, in spite of the simplicity of the model of interactions in most cases the two sets of data are in satisfactory agreement. The results obtained from the SWAG approach make the interactions of amino acids with THF and 1, 4-dioxane quantitative and can basically reflect the rules of the interaction processes. The results show: the ion–dipolar interaction between the zwitterions of amino acids and the ether oxygen atoms of THF and 1, 4-dioxane makes larger negative contributions to hxy (HE.O = −345 J kg mol−2 ); the hydrophilic–hydrophobic interaction between the zwitterions of amino acids and the non-polar ring of the heterocyclic compounds makes larger positive contributions to hxy (HE.CH2 = 213 J kg mol−2 ); and the hydrophobic–hydrophilic interaction between the hydrophobic groups of amino acids and the ether oxygen atoms of the heterocyclic compounds can make positive contributions to hxy to some extent (HCH2 .O = 84 J kg mol−2 ). The above three values for HE.O , HE.CH2 and HCH2 .O seem reasonable; however, the value for HCH2 .CH2 is clearly of the wrong sign. The main reason for this is that the assumptions of the SWAG approach are very simple. It assumes that each functional group interacts with every other functional group independent of its position. And some effects such as steric effects and configurational effects are ignored. In other words, although in the present work there are some errors arising from the results obtained according
3.3. Florry–Huggins interaction parameters In order to further testify our experimental results of amino acids/THF and amino acids/1, 4-dioxane systems, the mixing energy Emix (namely, the free energy of the mixing process) and Florry–Huggins interaction parameter x are obtained using the Blend simulation from the point of view of theory. The interaction between two different molecules in the vacuum is defined as an interaction parameter. The information on the mixing process can be obtained from the mixing energy and the interaction parameter. As discussed above, the lower the parameters, the stronger the interaction between different molecules. We found that the complex composed of amino acids and THF has a lower mixing energy, it means that the interaction between them is stronger, and the complex is more stable than that composed of amino acids and 1, 4-dioxane. The parameters x for amino acids/THF and amino acids/1, 4-dioxane systems can be calculated via Eq. (5). Because the parameters x are calculated from the mixing energies, their physical meaning is in agreement with that of the energy. This Huggins parameter x implies the interaction intensity between two different molecules. The value of x between two water molecules is considered as zero and other x values are compared with zero. The negative x value shows that the attractive interaction in the studied system is stronger than that between two water molecules. Fig. 2 shows a plot of the interaction parameters of amino acids/THF and amino acids/1, 4-dioxanesystems versus the number of methylene groups in the side chains of amino acid molecules at 298 K. As can be seen from Fig. 2, for amino acids/THF and amino acids/1, 4-dioxanesystems, the interaction parameters x increase with the increase of the number of carbon atoms. We found that the system of glycine and
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ber of methylene groups in the side-chain of amino acid molecules; the hxy coefficient of amino acids/1, 4-dioxane is more negative than that of amino acids/THF for the same amino acid. The experimentally observed results have been interpreted in terms of a solute–solute interaction. The SWAG approach applied to unbranched chain molecules has been applied to heterocyclic compounds. The theoretical calculated values of hxy coefficients using the SWAG approach are in satisfactory agreement. In addition, the SWAG approach has been appraised according to the results obtained. Mixing energy and interaction coefficient for -amino acids and THF and 1,4-dioxane have been obtained using the Flory–Huggins interaction parameters employing Monte Carlo Simulation techniques. The tendency displayed by the computer simulation results is in accordance with that of the experimental results. Fig. 2. The dependence of interaction parameters of amino acids/THF(A) and amino acids/1, 4-dioxane (B) systems calculated by the computer simulation method with the number of methylene groups in the side chains of amino acid molecules at 298 K.
THF has the lowest parameter; it means that the interaction between them is the strongest, and the mixing of glycine and THF is the most stable. For amino acids and 1, 4-dioxane system, a similar conclusion can be obtained. From Fig. 2, we noticed at the same number of carbon atoms, that the interaction parameter x of amino acids/1, 4-dioxane system is smaller than that of the amino acids/THF system. This means that the interaction intensity of the former is stronger than that of the latter. As can be seen from Fig. 1, in the amino acids/THF (or amino acids/1, 4-dioxane) series, the glycine/THF (or glycine/1, 4-dioxane) system has the lowest hxy value. The hxy coefficient of any amino acid studied with 1, 4-dioxane is more negative than that of the amino acid with THF. The more negative the hxy value, the less the endothermic effect during the process of interaction between amino acids and THF and the more stable the mixing process, the stronger the interaction between them. There is also a very good linear relationship between the Huggins parameters of the studied systems and the number of CH2 groups in the -amino acid molecule (Fig. 2). The information obtained from Fig. 2 in terms of theoretical calculation is consistent with that of Fig. 1 on the basis of experimental results. 4. Conclusions The interactions for amino acids/THF and amino acids/1, 4-dioxane systems are studied by experiments, theoretical calculation and computer simulation. The experimental results are as follows: for amino acids/THF and amino acids/1, 4-dioxanesystems, the values of hxy coefficients increase linearly with the increase of the num-
Notation cr Emix Eij
hxy hxxy hxyy hxy (calc.)
hxy (expt.) h∗w Hij H (mx , my )/w1 H E (mx , my )/w1 ∞ Hx,m
concentration range (mol kg−1 ) interaction energies of mixing between different monomers molecular pair interaction energy, i.e., the energy of the complex being composed of one molecule i and one molecule j pairwise heterotactic enthalpic interaction coefficient between x and y solutes (J kg mol−2 ) triplet heterotactic enthalpic interaction coefficient between x, x and y solutes (J kg2 mol−3 ) triplet heterotactic enthalpic interaction coefficient between x, y and y solutes (J kg2 mol−3 ) calculated pairwise heterotactic enthalpic interaction coefficient between x and y solutes by the SWAG approach (J kg mol−2 ) experimental pairwise heterotactic enthalpic interaction coefficient between x and y solutes (J kg mol−2 ) standard enthalpy of 1 kg of pure water enthalpic contribution of an i–j interaction absolute enthalpy of a solution containing 1 kg of water, mx mol of x and my mol of y (J kg−1 ) excess enthalpy of a solution containing 1 kg of water, mx mol of x and my mol of y (J kg−1 ) limiting partial molar enthalpies of solute x (J mol−1 )
800 ∞ Hy,m
Hdil(x) /w1 Hdil(y) /w1 Hmix /w1 H ∗ /w1 mx my nxi y nj SD Vseg Zij Z∗
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limiting partial molar enthalpies of solute y (J mol−1 ) dilution enthalpy of solute x in 1 kg of water (J kg−1 ) dilution enthalpy of solute y in 1 kg of water (J kg−1 ) mixing enthalpy of aqueous x and y solutions in 1 kg of water (J kg−1 ) auxiliary function in 1 kg of water (J kg−1 ) final molality of solute x final molality of solute y number of type i groups on molecule x number of type j groups on molecule y standard derivation volume of one molecule coordinated number, i.e., the number of molecules j which can surround one molecule i in space average coordination number
Greek letter
Relative deviation between the experimental and calculated pairwise heterotactic enthalpic interaction coefficients
Acknowledgements The authors are grateful for financial assistance from the Natural Science Foundation of Shandong Province of China (No. Q2003B01) and the Key Technologies R & D Programme of China (No. 2004BA313B09). References Barone, G., Castronuovo, G., Doucas, D., Elia, V., Mattia, C.A., 1983. Excess enthalpies of aqueous solutions of monosaccharides at 298.15 K: pentoses and 2-deoxy sugars. Journal of Physical Chemistry 87, 1931–1937. Blackburn, G.M., Lilley, T.H., Walmsley, E., 1980. Aqueous solutions containing amino acids and peptides part 11-enthalpy of dilution of single and binary solute solutions of N-acetyl-glycine amide, N-acetylL-alanine amide, N-acetyl-L-valine amide and N-acetyl-L-leucine amide at 298.15 K. Journal of Chemical Science Faraday Transaction I 76, 915–922. Blanco, M., 1991. Molecular silverware I. General solutions to excluded volume constrained problems. Journal of Computational Chemistry 12, 237–247. Castronuovo, G., Elia, V., Velleca, F., 1996. On the role of the functional group in determining the strength of hydrophobic interactions in aqueous solutions of -amino acid derivatives. Journal of Solution Chemistry 25, 971–982. Fernandez, J., Lilley, T.H., 1992. Aqueous solution containing amino acids and peptides part 28—Enthalpy of interaction of some amides with glycine and -alanine: interactions of the zwitterionic group of -amino acids with hydrophobic groups and peptide groups. Journal of Chemical Science Faraday Transaction 88, 2503–2509.
Franks, F., Pedley, M.D., 1983. Solute interactions in dilute aqueous solutions Part 5—microcalorimetric study of polyols and their mixtures with alkanols. Journal of Chemical Science Faraday Transaction I 79, 2249–2260. Franks, F., Pedley, M., Reid, D.S., 1976. Solute interactions in dilute aqueous solutions part 1: —microcalorimetric study of the hydrophobic interaction. Journal of Chemical Science Faraday Transaction I 72, 359–367. Fuller, C.S., Macrae, R.J., Walther, M., Cameron, R.E., 2001. Interaction in poly(ethylene oxide)-hydroxypropyl methylcellulose blends. Polymer 42, 9583–9592. Huh, J.Y., Bae, Y.C., 2002. Water activities of florinated solid polymer electrolyte/water systems using group-contribution method. Chemical Engineering Science 57, 2747–2752. Lee, K.W.D., Chan, P.K., Feng, X.Sh., 2004. Morphology development and characterization of the phase-separated structure resulting from the thermal-induced phase separation phenomenon in polymer solutions under a temperature gradient. Chemical Engineering Science 59, 1491–1504. McMillan, W.G., Mayer, J.E., 1945. The statistical thermodynamics of multicomponents systems. Journal of Chemical Physics 13, 276–305. Okamoto, B.Y., Wood, R.H., Thompson, P.T., 1978. Freezing points of aqueous alcohols. Free energy of interaction of the CHOC, CH2 , CONH and C&C functional groups in dilute aqueous solutions. Journal of Chemical Science Faraday Transaction I 74, 1990–2007. Palecz, B., 1995. The enthalpies of interaction of glycine with some amides and ureas in water at 25 ◦ C. Journal of Solution Chemistry 24 (6), 537–550. Petri, H.M., Horst, R., Wolf, B.A., 1996. Determination of interaction parameters for highly incompatible polymers. Polymer 37 (13), 2709–2713. Savage, J.J., Wood, R.H., 1976. Enthalpy of dilution of aqueous mixtures of amides, sugars, urea, ethylene glycol and pentaerythritol at 25 ◦ C: enthalpy of interaction of the hydrocarbon, amide, and hydroxyl functional groups in dilute aqueous solutions. Journal of Solution Chemistry 5, 731–750. Shao, S., Lin, R.S., Hu, X.G., 2001. Enthalpic interactions between amino acids and monomethylurea. Acta Physical Chimica Sinica 17 (7), 645–650. Tasker, I.R., Wood, R.H., 1982a. Enthalpies of dilution of aqueous systems containing hexamethylenetetramine and other nonelectrolytes. Journal of Solution Chemistry 11, 729–747. Tasker, I.R., Wood, R.H., 1982b. Enthalpies of dilution of aqueous solutions of cyclohexanol, inositol and mannitol. Journal of Physical Chemistry 86, 4040–4045. Tomasi, J., Persico, M., 1994. An overview of different approaches to studying chemistry in solution. Chemical Reviews 94, 2027–2094. Wegrzyn, T.F., Watson, I.D., Hedwig, G.R., 1984. Enthalpies of mixing of aqueous solutions of the amino acids glycine, L-alanine and L-serine. Journal of Solution Chemistry 13 (4), 233–244. Yu, L., Lin, R.S., Hu, X.G., Xu, G.Y., 2003a. Enthalpic interaction of amino acids with ethanol in aqueous solutions at 25 ◦ C. Journal of Solution Chemistry 32 (3), 273–281. Yu, L., Hu, X.G., Lin, R.S., Zh, H.L., Xu, G.Y., 2003b. Enthalpies of interaction of L-valine and L-threonine with pyridine and methylpyridine in aqueous solutions at 298.15 K. Journal of Chemical Engineering Data 48, 1591–1596.
Further reading Abbate, M., Barone, G., Castronuovo, G., et al., 1990. Thermodynamic behavior of some uncharged organic molecules in concentrated aqueous urea solutions and other polar solvents. Thermochimica Acta 173, 261–272.
Li Yu et al. / Chemical Engineering Science 61 (2006) 794 – 801 Abbate, M., Barone, G., Borghesani, G., 1993. Dilution enthalpies alkanols in concentrated aqueous solutions of urea at 25 ◦ C. Journal of Solution Chemistry 22, 695–706. Blackburn, G.M., Lilly, T.H., Milburn, P.J., 1984. Aqueous solutions containing amino acids and peptides. Part 19: the enthalpic coefficients for the interactions of N-acetylsarcosinamide with 2-(Nacetylamino)acyl amides at 25 ◦ C. Journal of Solution Chemistry 13, 789–803. Cascella, C., Catronuovo, G., Elia, V., Sartorio, R., Wurzburger, S., 1990. Hydrophobic interactions of alkanols—a calorimetric study in water at 298.15 K. Journal of Chemical Science Faraday Transaction 86 (1), 85–88. DeVisser, C., Heuvelsland, W.J.M., Somsen, G., 1978. The pairwise interaction concept of Savage and Wood applied to electrolytes. Journal of Solution Chemistry 7 (3), 193–196.
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Krishnan, C.V., Friedman, H.L., 1971. The solvent–isotope effect in the enthalpy of some solutes in methanol. Journal of Physical Chemistry 75, 388–391. Lilley, T.H., 1993. The interplay between solute solvation and solute–solute interactions in solutions containing amino acids, peptides and related species. Pure and Applied Chemistry 65, 2551–2560. Shao, S., Hu, X.G., Lin, R.S., 2000. Enthalpic interactions of L-alanine and L-serine in aqueous urea solutions. Thermochimica Acta 360, 93–100. Soldi, L.G., Marcus, Y., Blandamer, M.J., Cullis, P.M., 1995. Titration calorimetric determination of the pairwise interaction parameters of glycerol, D-threitol, mannitol, and D-glucitol in dilute aqueous solutions. Journal of Solution Chemistry 24 (3), 201–209.