The enthalpic interaction coefficients of N,N′-hexamethylenebisacetamide and N-methylformamide with four types of amino acids in aqueous sucrose solutions at 298.15 K

J. Chem. Thermodynamics 48 (2012) 160–174

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The enthalpic interaction coefficients of N,N0 -hexamethylenebisacetamide and N-methylformamide with four types of amino acids in aqueous sucrose solutions at 298.15 K Guangqian Li, Min Liu ⇑, Lina Dong, Lili Wang, Dezhi Sun, Xilian Wei, Youying Di College of Chemistry and Chemical Engineering, Liaocheng University, Liaocheng 252059, Shandong Province, China

a r t i c l e

i n f o

Article history: Received 14 May 2011 Received in revised form 2 October 2011 Accepted 8 December 2011 Available online 14 December 2011 Keywords: HMBA NMF Amino acid Heterotactic enthalpic interaction coefficients

a b s t r a c t The mixing enthalpies of N,N0 -hexamethylenebisacetamide (HMBA) and N-methylformamide (NMF) with glycine, L-alanine, L-serine, and L-valine in aqueous sucrose solutions have been determined by using mixing-flow isothermal microcalorimetry at the temperature of 298.15 K along with their dilution enthalpies, respectively. Based on the obtained results, the heterotactic enthalpic interaction coefficients (hxy, hxxy, and hxyy) have been obtained according to McMillan–Mayer’s theory with the sucrose molality from 0 to 1.5 mol  kg1. The fitted results indicate that the values of hxy between HMBA or NMF and the four investigated amino acids in aqueous sucrose solutions are all positive. Meanwhile, the values of hxy reach the corresponding maximum at different sucrose molalities except that the values of hxy between NMF and glycine decrease monotonically with the increasing molality of sucrose. Furthermore, the order for the value of hxy of the four amino acids with HMBA or NMF are hxy (L-valine) > hxy (L-alanine) > hxy (L-serine) > hxy (glycine) in pure water or in aqueous solution with the same molality of sucrose. The values of hxy between HMBA and the four amino acids are much larger than that between NMF and the same amino acids with the same molality of sucrose. All the variations of the heterotactic enthalpic pairwise interaction coefficients in the quaternary systems can be interpreted with the help of the solute–solute and solute–solvent interactions theory. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction While health problem is an eternal topic of human attracting more and more people’s attention, cancer, the uncontrolled growth of cells, is the second largest cause of death all over the world, only after the cardiovascular disease. Though a large number of researches on cancer and antitumor drugs have been conducted and also great improvements have been made over the past generations [1–4], it remains one of the most important and difficult fields. Among numerous antitumor drugs, a small polar molecule compound, N,N0 -hexamethylenebisacetamide (HMBA), has attracted great attention. In the past decades, a lot of researches on the property of HMBA [5–7], especially its revulsive function on cells [8–11], have been made. However, the differentiation mechanism induced by HMBA has not been clearly demonstrated. The studies on the interactions among drug and protein molecules are necessary because the drug–protein interactions may affect the distribution, free concentration, metabolism, and effects of various drugs in the blood system. However, the protein molecules ⇑ Corresponding author. Fax: +86 635 8239196. E-mail address: [email protected] (M. Liu). 0021-9614/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2011.12.014

are much larger than the drug molecules, and the conformational and configurational three-dimensional structures of protein molecules are very complicated, which make the direct study of the drug–protein interactions difficult. Therefore, such studies are usually carried out on low-molecular model compounds such as the amino acids, oligopeptides, and acylamides [12–15]. Being the simplest amino acid in nature, glycine is one of the most attractive models for protein study. Compared with glycine, L-alanine, L-serine, and L-valine have an apolar side-chain of –CH3, a polar side chain of –CH2OH and two apolar side-chains of –CH3 on the a-carbon, respectively. Study of these three amino acids can help us to understand the effect of hydroxyl and alkyl groups on the interactions of protein’s interior. What is more, all the four kinds of amino acids mentioned foregoing are the components of proteins, such as bovine serum albumin (BSA), human serum albumin (HSA). So the drug-amino acid interactions could reflect the drug– protein interaction in a certain extent. For example, we may deduce which interaction types play dominant role in the drug– protein interaction, such as hydrophobic interaction or hydrogen bond interaction. The structure of NMF molecule is similar to that of HMBA molecule, both containing acylamino and alkyl groups. The only difference between them is the number of acylamino

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group and the length of alkyl group. Comparative study on HMBA and NMF may elucidate the different contribution of different groups to drug–protein interactions. In addition, sucrose is one of the most important biological substances in organisms, which can not only provide energy for the cellular metabolism but also can change the thermal stability of proteins [16,17]. While there have been many reports about the enthalpy and entropy properties of saccharide solutions [18–20], amino acids [21–23], and NMF [24–26], there are still few reports about the thermodynamic properties of HMBA or NMF with amino acids in the aqueous sucrose solutions. In order to understand the differentiation mechanism induced by HMBA in the human body, we have studied the enthalpies of dilution of HMBA and the mixing enthalpies of HMBA with glycine in the aqueous glucose and sucrose solutions [27,28]. The present work, as one important part of our series of studies, aimed at measuring the mixing enthalpies of HMBA with L-alanine, L-serine, and L-valine as well as the mixing enthalpies of NMF with glycine, L-alanine, L-serine, and L-valine in aqueous sucrose solutions by means of flow microcalorimetry. Using the McMillan–Mayer’s theory, we obtained the heterotactic enthalpic pairwise interaction coefficients among HMBA or NMF molecules and glycine, L-alanine, L-serine, or L-valine molecules. And these important thermodynamic parameters reflected the sum of the enthalpic effects of the interactions among these investigated species. 2. Experimental 2.1. Reagents and preparation of solutions The reagents of HMBA, NMF, glycine, L-alanine, L-serine, and were all purchased from Acros, with the purities of 98%, 99%, 99%, 99%, 99%, and 99%, respectively. The molecular structures of them are provided in schemes 1 to 3. Sucrose was analytical reagent (mass fraction > 99%) obtained from Tianjin Damao Reagent Co., Ltd. All the reagents were stored over P2O5 in a vacuum desiccator for 72 h at room temperature prior to use. The water was deionized and distilled three times by passing through a quartz sub-boiling purifier before using. And the solutions were prepared by mass using an analytical balance (Mettler Toledo AG 135) with the precision of ±0.00001 g. The molality ranges of the aqueous sucrose solution was 0 mol  kg1 to 1.5 mol  kg1 and the molality range of the aqueous HMBA, NMF, and amino acids solutions were 0.05 to 0.32 or 0.30 mol  kg1. All the solutions were degassed with ultrasonic waves and used within 12 h after preparation to minimize possible bacterial contamination. L-valine

R

O

H 2N

OH

SCHEME 3. Molecular structure of amino acid: the structures are glycine, L-alanine, L-serine, and L-valine when R = –H, –CH3, –CH2OH, –(CH3)2, respectively.

2.2. Calorimetric measurements The mixing enthalpies of HMBA or NMF with the four amino acids as well as their respective enthalpies of dilution in aqueous sucrose solutions at 298.15 K were determined with a 2277-204 measuring cylinder by a TAM 2277 thermal activity monitor (Thermometric, Sweden). Using the VS2-10R MIDI dual-channel pumps, all the solutions were pumped through the mixing-flow vessel of the calorimeter with the flow rates determined by the mass of the solutions delivered in 6 min. The uncertainties of thermal power, the initial molalities of solutes and the flow rates were ±0.2 lW, ±0.0001 mol  kg1, and ±0.002 mg  s1, respectively. Thermal effects of the diluting or mixing process were obtained with the following method. The liquids passing through channels A and B of the dual-channel pumps were changed in the following sequence: (1) A (aqueous sucrose solution) + B (aqueous sucrose solution)—baseline determination. (2) A (aqueous sucrose solution) + B (aqueous amino acid or HMBA, NMF solution)—dilution thermal power determination. (3) A (aqueous HMBA or NMF solution) + B (aqueous amino acid solution)—mixing thermal power determination. (4) A (aqueous sucrose solution) + B (aqueous sucrose solution)—baseline re-established. Steps (1), (2), and (4) were taken in the dilution process and steps (1), (3), and (4) were taken in the mixing process. The thermal-effects caused by friction of the two channels were same and neglected. Details about this apparatus, associated equipment, and the experimental procedure can also be seen from other articles [29,30]. The excess enthalpy concept is the foundation of the thermodynamic formula of the enthalpies of dilution or mixing. In the following equation, the excess enthalpy of a solution is written as a virial expansion of pair and triplet interaction coefficients which accounts for all variations of the solute–solute and solute–solvent interactions according to the McMillian–Mayer theory [31]

HE ðmx ; my Þ ¼ Hðmx ; my Þ  Hw  mx Hx  my Hy ¼ hxx m2x þ 2hxy mx my þ hyy m2y þ hxxx m3x

O H N N H

SCHEME 1. Molecular structure of HMBA.

O

N H

SCHEME 2. Molecular structure of NMF.

þ 3hxxy m2x my þ 3hxyy mx m2y þ hyyy m3y þ    ; O

ð1Þ

where HE(mx, my) and H(mx, my) are the excess and the absolute enthalpy of a solution containing 1 kg solvent, mx mol of solute x, and my mol of solute y, respectively. Hw ; Hx and Hy represent the standard enthalpy of 1 kg of pure solvent, the limiting partial molar enthalpies of species x and y at infinite dilution, respectively. mx and my are respectively the final molality of the solute x or y after dilution or mixing. And the hij and hijk terms are the enthalpic virial coefficients representing the pairwise and triplet interactions between the subscripted species. An auxiliary function DH⁄ can simplify the above calculations [31]:

DH ¼ DHmix  DHdilðxÞ  DdilðyÞ ¼ HE ðmx ; my Þ  HE ðmx Þ  HE ðmy Þ:

ð2Þ

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TABLE 1 The mixing enthalpies of HMBA (x) and L-alanine (y) along with their corresponding dilution enthalpies in water and aqueous sucrose solutions at 298.15 K (msucrose – molality of sucrose, mx,i, my,i, and mx, my are the initial molalities of HMBA and L-alanine, the final molalities of HMBA and L-alanine, respectively. DHdil(x), DHdil(y), DH (mix) are the dilution enthalpy of HMBA, the dilution enthalpy of L-alanine and the mixing enthalpy of HMBA with L-alanine, respectively. DH⁄ = DH(mix)  DHdil(x)  DHdil(y)). msucrose/ (mol  kg1)

mx,i/ (mol  kg1)

my,i/ (mol  kg1)

mx / (mol  kg1)

my/ (mol  kg1)

DHdil(x)/ (J  kg1)

DHdil(y)/ (J  kg1)

DH(mix)/ (J  kg1)

D H⁄ / (J  kg1)

0.0000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0263 0.0422 0.0525 0.0631 0.0784 0.0941 0.1048 0.1148 0.1300 0.1454 0.1554 0.1650

0.0249 0.0398 0.0498 0.0595 0.0746 0.0899 0.0994 0.1094 0.1244 0.1390 0.1483 0.1583

1.09 3.08 5.04 7.45 11.92 17.26 21.43 26.17 34.10 42.90 49.53 56.29

0.16 0.39 0.59 0.84 1.28 1.82 2.24 2.70 3.46 4.32 4.94 5.60

0.01 0.09 0.01 0.11 0.34 0.42 0.65 1.07 1.65 2.33 3.20 3.68

1.27 3.55 5.64 8.18 12.86 18.67 23.02 27.80 35.91 44.89 51.27 58.21

0.1000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0242 0.0388 0.0485 0.0580 0.0720 0.0863 0.0966 0.1053 0.1194 0.1341 0.1426 0.1515

0.0242 0.0386 0.0482 0.0578 0.0720 0.0864 0.0961 0.1057 0.1199 0.1339 0.1437 0.1530

1.12 3.15 5.08 7.47 11.91 17.40 21.62 26.33 34.25 43.06 49.75 56.72

0.18 0.42 0.63 0.88 1.36 1.93 2.36 2.84 3.64 4.56 5.23 5.94

0.15 0.22 0.26 0.23 0.11 0.09 0.06 0.08 0.32 0.44 0.70 0.96

1.45 3.79 5.97 8.59 13.38 19.42 24.04 29.09 37.58 47.18 54.28 61.71

0.3000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0267 0.0430 0.0530 0.0635 0.0792 0.0947 0.1052 0.1154 0.1306 0.1459 0.1561 0.1670

0.0243 0.0387 0.0483 0.0580 0.0724 0.0868 0.0962 0.1060 0.1203 0.1343 0.1439 0.1538

0.84 2.53 4.25 6.38 10.45 15.58 19.59 24.12 31.87 40.76 47.30 54.02

0.16 0.40 0.63 0.91 1.43 2.06 2.54 3.07 3.96 4.96 5.68 6.45

0.25 0.52 0.82 1.32 1.94 2.39 2.65 3.02 3.06 2.80 2.65 2.59

0.75 3.45 5.71 8.62 13.81 20.03 24.77 30.21 38.89 48.52 55.64 63.06

0.6000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0237 0.0378 0.0470 0.0566 0.0698 0.0845 0.0935 0.1028 0.1155 0.1299 0.1416 0.1476

0.0241 0.0387 0.0484 0.0581 0.0723 0.0868 0.0963 0.1057 0.1197 0.1345 0.1441 0.1535

0.59 1.94 3.30 5.07 8.47 12.85 16.32 20.20 26.93 34.70 39.42 46.57

0.22 0.52 0.78 1.10 1.69 2.41 2.95 3.55 4.54 5.65 6.43 7.30

0.64 1.55 2.22 3.00 4.07 5.32 6.04 6.77 7.47 8.77 11.10 9.87

1.45 4.01 6.31 9.17 14.23 20.58 25.31 30.51 38.94 49.12 56.94 63.73

0.9000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0235 0.0375 0.0469 0.0562 0.0699 0.0839 0.0923 0.1016 0.1148 0.1270 0.1370 0.1463

0.0240 0.0383 0.0478 0.0573 0.0715 0.0859 0.0950 0.1045 0.1185 0.1328 0.1422 0.1513

0.44 1.49 2.59 4.06 6.90 10.58 13.49 16.74 22.40 28.80 33.55 38.59

0.17 0.46 0.73 1.06 1.67 2.43 3.01 3.65 4.72 5.92 6.80 7.72

0.80 1.80 2.57 3.40 4.65 5.95 6.64 7.60 8.74 9.67 10.78 11.73

1.41 3.75 5.89 8.52 13.23 18.96 23.14 27.99 35.85 44.39 51.13 58.04

1.2000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500

0.0239 0.0384 0.0476 0.0567 0.0707 0.0846 0.0938 0.1032 0.1165

0.0251 0.0402 0.0501 0.0602 0.0750 0.0899 0.0999 0.1098 0.1246

0.28 1.11 2.01 3.19 5.56 8.66 11.15 14.00 18.87

0.24 0.56 0.83 1.17 1.76 2.47 3.01 3.60 4.59

0.79 1.89 2.77 3.73 5.16 6.65 7.65 8.56 9.90

1.31 3.56 5.61 8.09 12.48 17.78 21.81 26.16 33.36

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G. Li et al. / J. Chem. Thermodynamics 48 (2012) 160–174 TABLE 1 (continued) msucrose/ (mol  kg1)

1.5000

mx,i/ (mol  kg1)

my,i/ (mol  kg1)

mx / (mol  kg1)

my/ (mol  kg1)

DHdil(x)/ (J  kg1)

DHdil(y)/ (J  kg1)

DH(mix)/ (J  kg1)

D H⁄ / (J  kg1)

0.2800 0.3000 0.3200

0.2800 0.3000 0.3200

0.1300 0.1386 0.1475

0.1395 0.1497 0.1594

24.44 28.53 32.91

5.73 6.56 7.46

11.32 12.55 13.32

41.49 47.64 53.69

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0239 0.0384 0.0476 0.0567 0.0707 0.0846 0.0938 0.1032 0.1165 0.1300 0.1386 0.1475

0.0234 0.0375 0.0471 0.0566 0.0703 0.0843 0.0936 0.1028 0.1165 0.1306 0.1400 0.1489

0.12 0.76 1.49 2.47 4.46 7.08 9.18 11.56 15.65 20.30 23.67 27.16

0.27 0.65 0.99 1.40 2.16 3.07 3.77 4.54 5.82 7.27 8.32 9.43

1.28 2.32 3.11 3.99 5.21 6.57 7.44 8.30 9.51 10.95 12.16 13.07

1.68 3.73 5.59 7.86 11.83 16.72 20.39 24.41 30.99 38.52 44.15 49.66

TABLE 2 The mixing enthalpies of HMBA (x) and l-serine (y) along with their corresponding dilution enthalpies in water and aqueous sucrose solutions at 298.15 K (msucrose – molality of sucrose, mx,i, my,i, and mx, my are the initial molalities of HMBA and L-serine, the final molalities of HMBA and L-serine, respectively. DHdil(x), DHdil(y), and DH(mix) are the dilution enthalpy of HMBA, the dilution enthalpy of L-serine and the mixing enthalpy of HMBA with L-serine, respectively. DH⁄ = DH(mix)  DHdil(x)  DHdil(y)). msucrose/ (mol  kg1)

mx,i/ (mol  kg1)

my,i/ (mol  kg1)

mx / (mol  kg1)

my/ (mol  kg1)

DHdil(x)/ (J  kg1)

DHdil(y)/ (J  kg1)

DH(mix)/ (J  kg1)

D H⁄ / (J  kg1)

0.0000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0263 0.0422 0.0525 0.0631 0.0784 0.0941 0.1048 0.1148 0.1300 0.1454 0.1554 0.1650

0.0256 0.0409 0.0510 0.0612 0.0762 0.0917 0.1015 0.1116 0.1268 0.1419 0.1521 0.1617

1.09 3.08 5.04 7.45 11.92 17.26 21.43 26.17 34.10 42.90 49.53 56.29

0.51 1.21 1.84 2.58 3.92 5.52 6.73 8.05 10.29 12.68 14.64 16.63

0.13 0.85 1.31 1.85 2.74 4.02 4.82 5.54 6.80 8.19 9.28 10.24

0.71 2.71 4.51 6.72 10.74 15.76 19.52 23.66 30.61 38.41 44.17 49.91

0.1000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0242 0.0388 0.0485 0.0580 0.0720 0.0863 0.0966 0.1053 0.1194 0.1341 0.1426 0.1515

0.0257 0.0411 0.0513 0.0615 0.0768 0.0923 0.1024 0.1124 0.1279 0.1430 0.1533 0.1632

1.12 3.15 5.08 7.47 11.91 17.40 21.62 26.33 34.25 43.06 49.75 56.72

0.60 1.30 1.91 2.64 3.95 5.53 6.72 8.02 10.16 12.59 14.27 16.14

0.66 1.32 1.85 2.41 3.37 4.68 5.85 6.71 8.43 10.88 11.87 13.27

1.19 3.17 5.02 7.24 11.33 16.55 20.75 25.02 32.52 41.35 47.35 53.85

0.3000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0267 0.0430 0.0530 0.0635 0.0792 0.0947 0.1052 0.1154 0.1306 0.1459 0.1561 0.1670

0.0253 0.0404 0.0505 0.0607 0.0759 0.0909 0.1010 0.1110 0.1258 0.1409 0.1508 0.1608

0.84 2.53 4.25 6.38 10.45 15.58 19.59 24.12 31.87 40.76 47.30 54.02

0.57 1.24 1.82 2.51 3.74 5.21 6.33 7.53 9.55 11.77 13.39 15.08

0.28 1.37 2.14 3.05 4.58 6.17 7.32 8.36 9.92 11.60 12.71 14.18

0.55 2.66 4.58 6.93 11.29 16.54 20.58 24.95 32.24 40.59 46.62 53.12

0.6000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800

0.0237 0.0378 0.0470 0.0566 0.0698 0.0845 0.0935 0.1028 0.1155 0.1299

0.0256 0.0410 0.0513 0.0613 0.0767 0.0919 0.1020 0.1121 0.1273 0.1423

0.59 1.94 3.30 5.07 8.47 12.85 16.32 20.20 26.93 34.70

0.55 1.18 1.72 2.34 3.46 4.79 5.80 6.90 8.72 10.77

0.82 2.09 3.09 4.21 5.96 8.03 9.38 10.86 12.97 15.31

0.86 2.85 4.68 6.93 10.97 16.09 19.91 24.16 31.18 39.25 (continued on next page)

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G. Li et al. / J. Chem. Thermodynamics 48 (2012) 160–174

TABLE 2 (continued) mx,i/ (mol  kg1)

my,i/ (mol  kg1)

mx / (mol  kg1)

my/ (mol  kg1)

DHdil(x)/ (J  kg1)

DHdil(y)/ (J  kg1)

DH(mix)/ (J  kg1)

D H⁄ / (J  kg1)

0.3000 0.3200

0.3000 0.3200

0.1416 0.1476

0.1525 0.1626

39.42 46.57

12.27 13.82

18.20 18.72

45.35 51.47

0.9000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0235 0.0375 0.0469 0.0562 0.0699 0.0839 0.0923 0.1016 0.1148 0.1270 0.1370 0.1463

0.0254 0.0407 0.0509 0.0610 0.0761 0.0913 0.1011 0.1113 0.1263 0.1412 0.1514 0.1610

0.44 1.49 2.59 4.06 6.90 10.58 13.49 16.74 22.40 28.80 33.55 38.59

0.52 1.10 1.58 2.15 3.16 4.35 5.25 6.23 7.84 9.65 10.99 12.38

1.85 3.21 4.31 5.46 7.30 9.40 10.79 12.41 14.72 17.21 19.24 21.04

1.77 3.61 5.31 7.36 11.04 15.63 19.03 22.92 29.27 36.36 41.81 47.25

1.2000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0239 0.0384 0.0476 0.0567 0.0707 0.0846 0.0938 0.1032 0.1165 0.1300 0.1386 0.1475

0.0253 0.0404 0.0506 0.0606 0.0756 0.0909 0.1008 0.1108 0.1258 0.1403 0.1507 0.1606

0.28 1.11 2.01 3.19 5.56 8.66 11.15 14.00 18.87 24.44 28.53 32.91

0.57 1.12 1.57 2.09 2.99 4.04 4.82 5.66 7.05 8.58 9.69 10.86

1.59 3.07 4.21 5.42 7.47 9.69 11.25 12.89 15.25 17.72 19.53 21.37

1.30 3.06 4.64 6.52 10.04 14.32 17.58 21.22 27.07 33.59 38.37 43.42

1.5000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0241 0.0380 0.0476 0.0569 0.0712 0.0850 0.0938 0.1030 0.1160 0.1301 0.1395 0.1479

0.0254 0.0407 0.0508 0.0608 0.0760 0.0910 0.1012 0.1113 0.1262 0.1411 0.1513 0.1613

0.12 0.76 1.49 2.47 4.46 7.08 9.18 11.56 15.65 20.30 23.67 27.16

0.63 1.17 1.60 2.08 2.92 3.87 4.58 5.34 6.57 7.92 8.90 9.90

2.21 3.65 4.83 6.06 8.13 10.26 11.77 13.36 15.71 18.31 20.39 22.49

1.70 3.24 4.71 6.44 9.67 13.47 16.38 19.59 24.79 30.69 35.17 39.74

msucrose/ (mol  kg1)

TABLE 3 The mixing enthalpies of HMBA (x) and L-valine (y) along with their corresponding dilution enthalpies in water and aqueous sucrose solutions at 298.15 K (msucrose – molality of sucrose, mx,i, my,i, and mx, my are the initial molalities of HMBA and L-valine, the final molalities of HMBA and L-valine, respectively. DHdil(x), DHdil(y), and DH (mix) are the dilution enthalpy of HMBA, the dilution enthalpy of L-valine and the mixing enthalpy of HMBA with L-valine, respectively. DH⁄ = DH(mix)  DHdil(x)  DHdil(y)). msucrose/(mol  kg1)

mx,i/(mol  kg1)

my,i/(mol  kg1)

mx/(mol  kg1)

my/(mol  kg1)

DHdil(x)/(J  kg1)

DHdil(y)/(J  kg1)

DHmix/(J  kg1)

DH⁄/(J  kg1)

0.0000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0263 0.0422 0.0525 0.0631 0.0784 0.0941 0.1048 0.1148 0.1300 0.1454 0.1554 0.1650

0.0270 0.0434 0.0538 0.0646 0.0807 0.0966 0.1075 0.1181 0.1341 0.1503 0.1604 0.1713

1.09 3.08 5.04 7.45 11.92 17.26 21.43 26.17 34.10 42.90 49.53 56.29

0.54 1.35 2.10 3.00 4.66 6.65 8.20 9.88 12.70 15.87 18.21 20.67

0.02 0.79 1.14 1.79 2.74 3.89 5.00 5.62 6.96 8.75 9.18 10.75

1.65 5.22 8.28 12.25 19.32 27.81 34.64 41.68 53.76 67.53 76.92 87.72

0.1000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0242 0.0388 0.0485 0.0580 0.0720 0.0863 0.0966 0.1053 0.1194 0.1341 0.1426 0.1515

0.0270 0.0430 0.0537 0.0645 0.0804 0.0964 0.1067 0.1177 0.1333 0.1494 0.1590 0.1696

1.12 3.15 5.08 7.47 11.91 17.40 21.62 26.33 34.25 43.06 49.75 56.72

0.43 1.23 2.00 2.95 4.71 6.89 8.60 10.46 13.60 17.15 19.75 22.48

0.90 1.57 2.17 2.81 3.82 5.26 6.21 7.53 9.23 11.87 12.42 14.33

2.45 5.95 9.25 13.23 20.44 29.56 36.42 44.32 57.09 72.08 81.92 93.53

165

G. Li et al. / J. Chem. Thermodynamics 48 (2012) 160–174 TABLE 3 (continued) msucrose/(mol  kg1)

mx,i/(mol  kg1)

my,i/(mol  kg1)

mx/(mol  kg1)

my/(mol  kg1)

DHdil(x)/(J  kg1)

DHdil(y)/(J  kg1)

DHmix/(J  kg1)

DH⁄/(J  kg1)

0.3000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0267 0.0430 0.0530 0.0635 0.0792 0.0947 0.1052 0.1154 0.1306 0.1459 0.1561 0.1670

0.0268 0.0428 0.0535 0.0640 0.0803 0.0957 0.1061 0.1168 0.1323 0.1485 0.1585 0.1690

0.84 2.53 4.25 6.38 10.45 15.58 19.59 24.12 31.87 40.76 47.30 54.02

0.68 1.62 2.48 3.52 5.41 7.70 9.45 11.39 14.61 18.23 20.88 23.70

0.21 1.04 1.88 2.94 4.87 6.60 7.91 9.18 10.97 13.06 14.03 15.83

1.31 5.19 8.61 12.84 20.73 29.88 36.94 44.69 57.45 72.05 82.21 93.55

0.6000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0237 0.0378 0.0470 0.0566 0.0698 0.0845 0.0935 0.1028 0.1155 0.1299 0.1416 0.1476

0.0267 0.0428 0.0532 0.0638 0.0797 0.0954 0.1057 0.1162 0.1320 0.1476 0.1577 0.1681

0.59 1.94 3.30 5.07 8.47 12.85 16.32 20.20 26.93 34.70 39.42 46.57

0.68 1.66 2.55 3.62 5.58 7.96 9.81 11.82 15.22 19.02 21.81 24.80

0.77 2.07 3.17 4.48 6.47 8.97 10.43 12.22 14.28 17.31 21.63 20.60

2.04 5.67 9.02 13.16 20.52 29.78 36.56 44.24 56.43 71.04 82.85 91.96

0.9000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0235 0.0375 0.0469 0.0562 0.0699 0.0839 0.0923 0.1016 0.1148 0.1270 0.1370 0.1463

0.0270 0.0432 0.0540 0.0646 0.0807 0.0965 0.1071 0.1179 0.1337 0.1495 0.1601 0.1709

0.44 1.49 2.59 4.06 6.90 10.58 13.49 16.74 22.40 28.80 33.55 38.59

0.65 1.61 2.45 3.52 5.41 7.71 9.46 11.38 14.63 18.29 20.98 23.86

0.70 2.30 3.65 5.06 7.48 9.96 11.48 13.35 15.75 17.99 19.65 21.54

1.79 5.40 8.69 12.64 19.80 28.25 34.43 41.47 52.77 65.08 74.19 84.00

1.2000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0239 0.0384 0.0476 0.0567 0.0707 0.0846 0.0938 0.1032 0.1165 0.1300 0.1386 0.1475

0.0271 0.0433 0.0540 0.0647 0.0809 0.0968 0.1076 0.1180 0.1341 0.1499 0.1604 0.1708

0.28 1.11 2.01 3.19 5.56 8.66 11.15 14.00 18.87 24.44 28.53 32.91

0.83 1.93 2.92 4.11 6.28 8.91 10.89 13.10 16.78 20.93 23.96 27.17

1.62 3.18 4.44 5.80 8.18 10.65 12.54 14.07 17.00 19.78 21.97 23.84

2.73 6.22 9.37 13.11 20.01 28.22 34.58 41.17 52.65 65.16 74.46 83.92

1.5000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000

0.0241 0.0380 0.0476 0.0569 0.0712 0.0850 0.0938 0.1030 0.1160 0.1301 0.1395

0.0268 0.0442 0.0552 0.0662 0.0827 0.0990 0.1099 0.1208 0.1372 0.1535 0.1642

0.12 0.76 1.49 2.47 4.46 7.08 9.18 11.56 15.65 20.30 23.67

0.90 2.07 3.10 4.33 6.58 9.27 11.31 13.57 17.36 21.58 24.68

2.43 3.90 5.19 6.58 9.01 11.73 13.50 15.53 18.44 22.19 24.85

3.45 6.73 9.78 13.38 20.04 28.08 34.00 40.66 51.45 64.07 73.20

DHmix ¼ Pmix =ðfx þ fs  mx;i M x fx  my;i M y fy Þ;

Then, equation (1) can be rewritten as [31]:

DH ¼ 2hxy mx my þ 3hxxy m2x my þ 3hxyy mx m2y þ   

ð3Þ

ð5Þ

In the above equations, DHmix, DHdil(x), and DHdil(y) mean the mixing enthalpy, the dilution enthalpy of x and y, respectively.The dilution enthalpy DHdil(x) of x and the mixing enthalpy DHmix of aqueous x solution with aqueous y solution can be gained from the two following equations [32]:

where Px or Pmix is the dilution thermal power of solute x or the mixing thermal power; mx, my are the initial molality of the solution x and y before dilution or mixing; Mx, My represent the molar mass of the solute x and y; and fx, fy, and fs are the flow rates of solution x, y, and the solvent, respectively. The final molality mx can be obtained from the equation [32]:

DHdilðxÞ ¼ Px =ðfx þ fs  mx;i Mx fx Þ;

mx ¼ mx;i fx =½fs ð1 þ mx;i M x Þ þ fx :

ð4Þ

ð6Þ

166

G. Li et al. / J. Chem. Thermodynamics 48 (2012) 160–174

TABLE 4 The mixing enthalpies of NMF (x) and glycine (y) along with their corresponding dilution enthalpies in water and aqueous sucrose solutions at 298.15 K (msucrose – molality of sucrose, mx,i, my,i, and mx, my are the initial molalities of NMF and glycine, the final molalities of NMF and glycine, respectively. DHdil(x), DHdil(y), DH(mix) are the dilution enthalpy of NMF, the dilution enthalpy of glycine and the mixing enthalpy of NMF with glycine, respectively. DH⁄ = DH(mix)  DHdil(x)  DHdil(y)).

D H⁄ / (J  kg1)

msucrose/ (mol  kg1)

mx,i/ (mol  kg1)

my,i/ (mol  kg1)

mx / (mol  kg1)

my/ (mol  kg1)

DHdil(x)/ (J  kg1)

DHdil(y)/ (J  kg1)

DH(mix)/ (J  kg1)

0.0000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0244 0.0391 0.0489 0.0586 0.0730 0.0877 0.0974 0.1071 0.1217 0.1360 0.1458 0.1553

0.0237 0.0378 0.0472 0.0566 0.0705 0.0842 0.0934 0.1028 0.1177 0.1311 0.1407 0.1506

0.11 0.36 0.61 0.92 1.49 2.20 2.74 3.35 4.36 5.51 6.36 7.28

0.25 0.67 1.05 1.52 2.39 3.43 4.24 5.11 6.57 8.25 9.45 10.72

0.60 1.11 1.56 2.12 3.10 4.35 5.28 6.29 8.05 9.98 11.44 12.85

0.46 0.81 1.12 1.52 2.21 3.11 3.79 4.52 5.83 7.25 8.35 9.41

0.1000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0247 0.0394 0.0494 0.0592 0.0737 0.0884 0.0982 0.1080 0.1230 0.1371 0.1470 0.1569

0.0380 0.0463 0.0568 0.0707 0.0855 0.0942 0.1033 0.1219 0.1318 0.1409 0.1501 0.1646

0.13 0.40 0.64 0.95 1.52 2.24 2.79 3.39 4.42 5.59 6.46 7.36

0.69 1.05 1.51 2.30 3.25 4.01 4.85 6.03 7.71 8.83 10.02 12.00

0.25 0.66 1.19 2.17 3.25 3.98 4.88 6.47 8.13 9.10 10.32 12.66

0.31 0.00 0.33 0.82 1.52 2.21 2.82 3.84 4.84 5.86 6.76 8.01

0.3000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0247 0.0395 0.0493 0.0593 0.0736 0.0886 0.0984 0.1084 0.1230 0.1373 0.1471 0.1571

0.0248 0.0397 0.0496 0.0594 0.0741 0.0890 0.0989 0.1086 0.1236 0.1384 0.1481 0.1578

0.16 0.42 0.67 0.98 1.54 2.23 2.76 3.35 4.34 5.44 6.26 7.12

0.49 0.99 1.42 1.90 2.75 3.75 4.47 5.30 6.64 8.17 9.24 10.46

0.24 0.79 1.28 1.83 2.73 3.87 4.72 5.63 7.15 8.82 10.02 11.41

0.09 0.22 0.54 0.91 1.52 2.35 3.01 3.68 4.85 6.09 7.04 8.07

0.6000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0248 0.0398 0.0498 0.0597 0.0745 0.0892 0.0992 0.1089 0.1236 0.1386 0.1482 0.1583

0.0247 0.0396 0.0494 0.0592 0.0741 0.0890 0.0988 0.1085 0.1232 0.1379 0.1476 0.1575

0.13 0.37 0.60 0.89 1.43 2.10 2.62 3.18 4.14 5.21 6.02 6.85

0.47 0.93 1.31 1.75 2.51 3.39 4.03 4.75 5.93 7.26 8.22 9.28

0.26 0.78 1.21 1.72 2.59 3.61 4.33 5.14 6.50 7.99 9.11 10.31

0.08 0.22 0.50 0.86 1.51 2.32 2.92 3.57 4.71 5.95 6.91 7.88

0.9000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0257 0.0409 0.0513 0.0612 0.0763 0.0919 0.1021 0.1121 0.1276 0.1424 0.1522 0.1630

0.0250 0.0400 0.0500 0.0599 0.0749 0.0899 0.0998 0.1097 0.1245 0.1394 0.1490 0.1588

0.10 0.33 0.54 0.82 1.34 1.99 2.49 3.03 3.96 5.01 5.76 6.59

0.32 0.68 0.98 1.33 1.95 2.69 3.23 3.84 4.84 5.97 6.79 7.70

0.29 0.71 1.11 1.52 2.29 3.18 3.85 4.62 5.86 7.28 8.28 9.37

0.07 0.36 0.67 1.01 1.68 2.48 3.11 3.81 4.98 6.31 7.25 8.27

1.2000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500

0.0251 0.0403 0.0503 0.0602 0.0755 0.0905 0.1004 0.1105 0.1253

0.0250 0.0400 0.0499 0.0599 0.0749 0.0896 0.0996 0.1096 0.1245

0.12 0.35 0.58 0.85 1.37 2.00 2.51 3.04 3.97

0.22 0.50 0.75 1.05 1.59 2.23 2.72 3.26 4.15

0.25 0.58 0.90 1.25 1.93 2.71 3.28 3.97 5.04

0.15 0.43 0.72 1.05 1.71 2.48 3.07 3.75 4.86

167

G. Li et al. / J. Chem. Thermodynamics 48 (2012) 160–174 TABLE 4 (continued) msucrose/ (mol  kg1)

1.5000

DHdil(y)/ (J  kg1)

DH(mix)/ (J  kg1)

D H⁄ / (J  kg1)

mx,i/ (mol  kg1)

my,i/ (mol  kg1)

mx / (mol  kg1)

my/ (mol  kg1)

DHdil(x)/ (J  kg1)

0.2800 0.3000 0.3200

0.2800 0.3000 0.3200

0.1402 0.1501 0.1597

0.1392 0.1490 0.1587

4.98 5.74 6.52

5.16 5.89 6.69

6.34 7.29 8.29

6.17 7.14 8.11

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0248 0.0399 0.0500 0.0598 0.0747 0.0895 0.0994 0.1092 0.1245 0.1389 0.1490 0.1588

0.0246 0.0395 0.0492 0.0590 0.0746 0.0885 0.0983 0.1079 0.1229 0.1373 0.1470 0.1566

0.12 0.34 0.55 0.81 1.29 1.91 2.37 2.90 3.76 4.73 5.46 6.21

0.17 0.40 0.61 0.87 1.32 1.88 2.31 2.78 3.55 4.42 5.06 5.74

0.52 0.82 1.07 1.41 2.01 2.66 3.23 3.80 4.86 6.05 6.87 7.79

0.47 0.76 1.01 1.35 1.99 2.69 3.29 3.93 5.07 6.35 7.27 8.26

TABLE 5 The mixing enthalpies of NMF (x) and L-alanine (y) along with their corresponding dilution enthalpies in water and aqueous sucrose solutions at 298.15 K (msucrose – molality of sucrose, mx,i, my,i, and mx, my are the initial molalities of NMF and L-alanine, the final molalities of NMF and L-alanine, respectively. DHdil(x), DHdil(y), DH (mix) are the dilution enthalpy of NMF, the dilution enthalpy of L-alanine and the mixing enthalpy of NMF with L-alanine, respectively. DH⁄ = DH(mix)  DHdil(x)  DHdil(y)).

DH(mix)/ (J  kg1)

D H⁄ / (J  kg1)

msucrose/ (mol  kg1)

mx,i/ (mol  kg1)

my,i/ (mol  kg1)

mx / (mol  kg1)

my/ (mol  kg1)

DHdil(x)/ (J  kg1)

DHdil(y)/ (J  kg1)

0.0000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0244 0.0391 0.0489 0.0586 0.0730 0.0877 0.0974 0.1071 0.1217 0.1360 0.1458 0.1553

0.0249 0.0398 0.0498 0.0595 0.0746 0.0899 0.0994 0.1094 0.1244 0.1390 0.1483 0.1583

0.11 0.36 0.61 0.92 1.49 2.20 2.74 3.35 4.36 5.51 6.36 7.28

0.16 0.39 0.59 0.84 1.28 1.82 2.24 2.70 3.46 4.32 4.94 5.60

0.18 0.36 0.53 0.71 1.07 1.51 1.84 2.15 2.76 3.33 3.86 4.33

0.46 1.11 1.73 2.47 3.84 5.53 6.82 8.19 10.58 13.16 15.17 17.21

0.1000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0247 0.0394 0.0494 0.0592 0.0737 0.0884 0.0982 0.1080 0.1230 0.1371 0.1470 0.1569

0.0242 0.0386 0.0482 0.0578 0.0720 0.0864 0.0961 0.1057 0.1199 0.1339 0.1437 0.1530

0.13 0.40 0.64 0.95 1.52 2.24 2.79 3.39 4.42 5.59 6.46 7.36

0.18 0.42 0.63 0.88 1.36 1.93 2.36 2.84 3.64 4.56 5.23 5.94

0.23 0.38 0.55 0.73 1.09 1.45 1.78 2.14 2.70 3.30 3.74 4.22

0.54 1.19 1.83 2.56 3.97 5.62 6.93 8.38 10.76 13.45 15.43 17.52

0.3000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0247 0.0395 0.0493 0.0593 0.0736 0.0886 0.0984 0.1084 0.1230 0.1373 0.1471 0.1571

0.0243 0.0387 0.0483 0.0580 0.0724 0.0868 0.0962 0.1060 0.1203 0.1343 0.1439 0.1538

0.16 0.42 0.67 0.98 1.54 2.23 2.76 3.35 4.34 5.44 6.26 7.12

0.16 0.40 0.63 0.91 1.43 2.06 2.54 3.07 3.96 4.96 5.68 6.45

0.14 0.33 0.48 0.69 1.00 1.44 1.73 2.11 2.63 3.15 3.57 4.08

0.46 1.16 1.79 2.58 3.97 5.72 7.03 8.53 10.94 13.55 15.52 17.65

0.6000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000

0.0248 0.0398 0.0498 0.0597 0.0745 0.0892 0.0992 0.1089 0.1236 0.1386 0.1482

0.0241 0.0387 0.0484 0.0581 0.0723 0.0868 0.0963 0.1057 0.1197 0.1345 0.1441

0.13 0.37 0.60 0.89 1.43 2.10 2.62 3.18 4.14 5.21 6.02

0.22 0.52 0.78 1.10 1.69 2.41 2.95 3.55 4.54 5.65 6.43

0.20 0.31 0.46 0.63 0.87 1.20 1.48 1.75 2.18 2.80 3.21

0.54 1.20 1.84 2.63 3.99 5.71 7.05 8.48 10.86 13.66 15.66 (continued on next page)

168

G. Li et al. / J. Chem. Thermodynamics 48 (2012) 160–174

TABLE 5 (continued) msucrose/ (mol  kg1)

mx,i/ (mol  kg1)

my,i/ (mol  kg1)

mx / (mol  kg1)

my/ (mol  kg1)

DHdil(x)/ (J  kg1)

DHdil(y)/ (J  kg1)

DH(mix)/ (J  kg1)

D H⁄ / (J  kg1)

0.3200

0.3200

0.1583

0.1535

6.85

7.30

3.59

17.74

0.9000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0257 0.0409 0.0513 0.0612 0.0763 0.0919 0.1021 0.1121 0.1276 0.1424 0.1522 0.1630

0.0240 0.0383 0.0478 0.0573 0.0715 0.0859 0.0950 0.1045 0.1185 0.1328 0.1422 0.1513

0.10 0.33 0.54 0.82 1.34 1.99 2.49 3.03 3.96 5.01 5.76 6.59

0.17 0.46 0.73 1.06 1.67 2.43 3.01 3.65 4.72 5.92 6.80 7.72

0.04 0.10 0.24 0.36 0.56 0.88 1.03 1.26 1.61 1.91 2.12 2.45

0.23 0.89 1.51 2.24 3.58 5.30 6.52 7.94 10.29 12.83 14.68 16.76

1.2000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0251 0.0403 0.0503 0.0602 0.0755 0.0905 0.1004 0.1105 0.1253 0.1402 0.1501 0.1597

0.0251 0.0402 0.0501 0.0602 0.0750 0.0899 0.0999 0.1098 0.1246 0.1395 0.1497 0.1594

0.12 0.35 0.58 0.85 1.37 2.00 2.51 3.04 3.97 4.98 5.74 6.52

0.24 0.56 0.83 1.17 1.76 2.47 3.01 3.60 4.59 5.73 6.56 7.46

0.13 0.24 0.35 0.47 0.73 1.02 1.19 1.45 1.71 2.13 2.41 2.67

0.49 1.15 1.76 2.49 3.86 5.49 6.71 8.09 10.27 12.84 14.71 16.65

1.5000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0248 0.0399 0.0500 0.0598 0.0747 0.0895 0.0994 0.1092 0.1245 0.1389 0.1490 0.1588

0.0234 0.0375 0.0471 0.0566 0.0703 0.0843 0.0936 0.1028 0.1165 0.1306 0.1400 0.1489

0.12 0.34 0.55 0.81 1.29 1.91 2.37 2.90 3.76 4.73 5.46 6.21

0.27 0.65 0.99 1.40 2.16 3.07 3.77 4.54 5.82 7.27 8.32 9.43

0.29 0.35 0.40 0.49 0.59 0.75 0.94 1.07 1.49 1.90 2.28 2.67

0.69 1.34 1.94 2.71 4.04 5.73 7.08 8.52 11.08 13.90 16.06 18.31

TABLE 6 The mixing enthalpies of NMF (x) and L-serine (y) along with their corresponding dilution enthalpies in water and aqueous sucrose solutions at 298.15 K (msucrose – molality of sucrose, mx,i, my,i, and mx, my are the initial molalities of NMF and L-serine, the final molalities of NMF and L-serine, respectively. DHdil(x), DHdil(y), DH(mix) are the dilution enthalpy of NMF, the dilution enthalpy of L-serine and the mixing enthalpy of NMF with L-serine, respectively. DH⁄ = DH(mix)  DHdil(x)  DHdil(y)). msucrose/ (mol  kg1)

mx,i/ (mol  kg1)

my,i/ (mol  kg1)

mx / (mol  kg1)

my/ (mol  kg1)

DHdil(x)/ (J  kg1)

DHdil(y)/ (J  kg1)

DH(mix)/ (J  kg1)

D H⁄ / (J  kg1)

0.0000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0244 0.0391 0.0489 0.0586 0.0730 0.0877 0.0974 0.1071 0.1217 0.1360 0.1458 0.1553

0.0256 0.0409 0.0510 0.0612 0.0762 0.0917 0.1015 0.1116 0.1268 0.1419 0.1521 0.1617

0.11 0.36 0.61 0.92 1.49 2.20 2.74 3.35 4.36 5.51 6.36 7.28

0.51 1.21 1.84 2.58 3.92 5.52 6.73 8.05 10.29 12.68 14.64 16.63

0.66 1.51 2.22 3.07 4.63 6.48 7.89 9.41 12.01 14.79 17.03 19.30

0.26 0.66 0.99 1.41 2.20 3.15 3.90 4.70 6.08 7.63 8.76 9.95

0.1000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0247 0.0394 0.0494 0.0592 0.0737 0.0884 0.0982 0.1080 0.1230 0.1371 0.1470 0.1569

0.0257 0.0411 0.0513 0.0615 0.0768 0.0923 0.1024 0.1124 0.1279 0.1430 0.1533 0.1632

0.13 0.40 0.64 0.95 1.52 2.24 2.79 3.39 4.42 5.59 6.46 7.36

0.60 1.30 1.91 2.64 3.95 5.53 6.72 8.02 10.16 12.59 14.27 16.14

0.64 1.44 2.17 3.01 4.53 6.36 7.72 9.24 11.73 14.47 16.40 18.58

0.17 0.54 0.90 1.32 2.10 3.07 3.79 4.61 5.99 7.47 8.59 9.79

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G. Li et al. / J. Chem. Thermodynamics 48 (2012) 160–174 TABLE 6 (continued) msucrose/ (mol  kg1)

mx,i/ (mol  kg1)

my,i/ (mol  kg1)

mx / (mol  kg1)

my/ (mol  kg1)

DHdil(x)/ (J  kg1)

DHdil(y)/ (J  kg1)

DH(mix)/ (J  kg1)

D H⁄ / (J  kg1)

0.3000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0247 0.0395 0.0493 0.0593 0.0736 0.0886 0.0984 0.1084 0.1230 0.1373 0.1471 0.1571

0.0253 0.0404 0.0505 0.0607 0.0759 0.0909 0.1010 0.1110 0.1258 0.1409 0.1508 0.1608

0.16 0.42 0.67 0.98 1.54 2.23 2.76 3.35 4.34 5.44 6.26 7.12

0.57 1.24 1.82 2.51 3.74 5.21 6.33 7.53 9.55 11.77 13.39 15.08

0.59 1.37 2.05 2.87 4.33 6.10 7.41 8.87 11.27 13.84 15.75 17.85

0.18 0.56 0.91 1.34 2.13 3.12 3.85 4.69 6.06 7.51 8.62 9.89

0.6000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0248 0.0398 0.0498 0.0597 0.0745 0.0892 0.0992 0.1089 0.1236 0.1386 0.1482 0.1583

0.0256 0.0410 0.0513 0.0613 0.0767 0.0919 0.1020 0.1121 0.1273 0.1423 0.1525 0.1626

0.13 0.37 0.60 0.89 1.43 2.10 2.62 3.18 4.14 5.21 6.02 6.85

0.55 1.18 1.72 2.34 3.46 4.79 5.80 6.90 8.72 10.77 12.27 13.82

0.56 1.29 1.94 2.67 3.97 5.54 6.69 7.95 10.03 12.40 14.03 15.83

0.13 0.48 0.83 1.22 1.94 2.85 3.52 4.24 5.45 6.84 7.79 8.87

0.9000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0257 0.0409 0.0513 0.0612 0.0763 0.0919 0.1021 0.1121 0.1276 0.1424 0.1522 0.1630

0.0254 0.0407 0.0509 0.0610 0.0761 0.0913 0.1011 0.1113 0.1263 0.1412 0.1514 0.1610

0.10 0.33 0.54 0.82 1.34 1.99 2.49 3.03 3.96 5.01 5.76 6.59

0.52 1.10 1.58 2.15 3.16 4.35 5.25 6.23 7.84 9.65 10.99 12.38

0.61 1.32 1.90 2.58 3.77 5.21 6.29 7.45 9.39 11.53 13.13 14.81

0.19 0.55 0.86 1.25 1.95 2.85 3.53 4.25 5.51 6.88 7.90 9.02

1.2000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0251 0.0403 0.0503 0.0602 0.0755 0.0905 0.1004 0.1105 0.1253 0.1402 0.1501 0.1597

0.0253 0.0404 0.0506 0.0606 0.0756 0.0909 0.1008 0.1108 0.1258 0.1403 0.1507 0.1606

0.12 0.35 0.58 0.85 1.37 2.00 2.51 3.04 3.97 4.98 5.74 6.52

0.57 1.12 1.57 2.09 2.99 4.04 4.82 5.66 7.05 8.58 9.69 10.86

0.55 1.22 1.75 2.35 3.42 4.72 5.65 6.73 8.44 10.38 11.80 13.29

0.10 0.45 0.75 1.11 1.80 2.68 3.34 4.11 5.35 6.79 7.85 8.94

1.5000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0248 0.0399 0.0500 0.0598 0.0747 0.0895 0.0994 0.1092 0.1245 0.1389 0.1490 0.1588

0.0254 0.0407 0.0508 0.0608 0.0760 0.0910 0.1012 0.1113 0.1262 0.1411 0.1513 0.1613

0.12 0.34 0.55 0.81 1.29 1.91 2.37 2.90 3.76 4.73 5.46 6.21

0.63 1.17 1.60 2.08 2.92 3.87 4.58 5.34 6.57 7.92 8.90 9.90

0.57 1.19 1.72 2.30 3.33 4.48 5.38 6.30 7.93 9.66 10.95 12.31

0.06 0.36 0.67 1.03 1.71 2.52 3.17 3.87 5.12 6.47 7.52 8.62

The enthalpies of dilution DHdilðyÞ of solution y and the final molality my can also be calculated from equations (5) and (6) by replacing the subscript of x with y. According to the law of propagation of uncertainty and the above uncertainties of measured variables, the combined standard uncertainties of the final molalities mx, the enthalpy changes (DHdil(x) or DHmix) and the auxiliary functions DH⁄ were estimated to be within ±0.0001 mol  kg1, ±0.03 J  mol1, and ±0.05 J  mol1 at a confidence level of 0.95 (k = 2), respectively.

3. Results and discussion In aqueous solutions, the interactions between two molecules are dominated over the interactions among three or more solute molecules. It is difficult to discover the regularities of the interactions among three or more solute molecules in a series of aqueous solutions with different sucrose molalities because the interactions among them are very complex. Therefore, we only discussed the heterotactic enthalpic pairwise interaction coefficient of hxy in this paper.

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TABLE 7 The mixing enthalpies of NMF (x) and L-valine (y) along with their corresponding dilution enthalpies in water and aqueous sucrose solutions at 298.15 K (msucrose – molality of sucrose, mx,i, my,i, and mx, my are the initial molalities of NMF and L-valine, the final molalities of NMF and L-valine, respectively. DHdil(x), DHdil(y), and DH (mix) are the dilution enthalpy of NMF, the dilution enthalpy of L-valine and the mixing enthalpy of NMF with L-valine, respectively. DH⁄ = DH(mix)  DHdil(x)  DHdil(y)). msucrose/(mol  kg1)

mx,i/(mol  kg1)

my,i/(mol  kg1)

mx/(mol  kg1)

my/(mol  kg1)

DHdil(x)/(J  kg1)

DHdil(y)/(J  kg1)

DHmix/(J  kg1)

DH⁄/(J  kg1)

0.0000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0244 0.0391 0.0489 0.0586 0.0730 0.0877 0.0974 0.1071 0.1217 0.1360 0.1458 0.1553

0.0270 0.0434 0.0538 0.0646 0.0807 0.0966 0.1075 0.1181 0.1341 0.1503 0.1604 0.1713

0.11 0.36 0.61 0.92 1.49 2.20 2.74 3.35 4.36 5.51 6.36 7.28

0.54 1.35 2.10 3.00 4.66 6.65 8.20 9.88 12.70 15.87 18.21 20.67

0.11 0.14 0.12 0.11 0.10 0.11 0.13 0.15 0.23 0.25 0.27 0.29

0.76 1.86 2.83 4.04 6.25 8.96 11.08 13.38 17.29 21.64 24.84 28.24

0.1000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0247 0.0394 0.0494 0.0592 0.0737 0.0884 0.0982 0.1080 0.1230 0.1371 0.1470 0.1569

0.0270 0.0430 0.0537 0.0645 0.0804 0.0964 0.1067 0.1177 0.1333 0.1494 0.1590 0.1696

0.13 0.40 0.64 0.95 1.52 2.24 2.79 3.39 4.42 5.59 6.46 7.36

0.43 1.23 2.00 2.95 4.71 6.89 8.60 10.46 13.60 17.15 19.75 22.48

0.05 0.01 0.02 0.04 0.00 0.01 0.03 0.05 0.07 0.09 0.31 0.32

0.51 1.62 2.66 3.93 6.23 9.12 11.35 13.80 17.95 22.65 25.89 29.52

0.3000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0247 0.0395 0.0493 0.0593 0.0736 0.0886 0.0984 0.1084 0.1230 0.1373 0.1471 0.1571

0.0268 0.0428 0.0535 0.0640 0.0803 0.0957 0.1061 0.1168 0.1323 0.1485 0.1585 0.1690

0.16 0.42 0.67 0.98 1.54 2.23 2.76 3.35 4.34 5.44 6.26 7.12

0.68 1.62 2.48 3.52 5.41 7.70 9.45 11.39 14.61 18.23 20.88 23.70

0.31 0.38 0.47 0.52 0.67 0.83 0.96 1.03 1.29 1.45 1.73 1.82

0.53 1.67 2.68 3.98 6.28 9.10 11.25 13.71 17.66 22.22 25.41 29.00

0.6000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0248 0.0398 0.0498 0.0597 0.0745 0.0892 0.0992 0.1089 0.1236 0.1386 0.1482 0.1583

0.0267 0.0428 0.0532 0.0638 0.0797 0.0954 0.1057 0.1162 0.1320 0.1476 0.1577 0.1681

0.13 0.37 0.60 0.89 1.43 2.10 2.62 3.18 4.14 5.21 6.02 6.85

0.68 1.66 2.55 3.62 5.58 7.96 9.81 11.82 15.22 19.02 21.81 24.80

0.21 0.25 0.28 0.33 0.37 0.48 0.58 0.66 0.76 0.86 1.10 1.20

0.60 1.78 2.87 4.18 6.64 9.58 11.85 14.34 18.60 23.38 26.73 30.45

0.9000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200

0.0257 0.0409 0.0513 0.0612 0.0763 0.0919 0.1021 0.1121 0.1276 0.1424 0.1522 0.1630

0.0270 0.0432 0.0540 0.0646 0.0807 0.0965 0.1071 0.1179 0.1337 0.1495 0.1601 0.1709

0.10 0.33 0.54 0.82 1.34 1.99 2.49 3.03 3.96 5.01 5.76 6.59

0.65 1.61 2.45 3.52 5.41 7.71 9.46 11.38 14.63 18.29 20.98 23.86

0.28 0.29 0.30 0.34 0.43 0.47 0.58 0.67 0.84 1.23 1.56 1.71

0.48 1.64 2.70 4.00 6.33 9.23 11.37 13.74 17.75 22.06 25.18 28.75

1.2000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800

0.0251 0.0403 0.0503 0.0602 0.0755 0.0905 0.1004 0.1105 0.1253 0.1402

0.0271 0.0433 0.0540 0.0647 0.0809 0.0968 0.1076 0.1180 0.1341 0.1499

0.12 0.35 0.58 0.85 1.37 2.00 2.51 3.04 3.97 4.98

0.83 1.93 2.92 4.11 6.28 8.91 10.89 13.10 16.78 20.93

0.22 0.38 0.52 0.65 0.87 1.18 1.32 1.49 1.78 2.14

0.73 1.90 2.98 4.32 6.77 9.73 12.08 14.65 18.97 23.78

171

G. Li et al. / J. Chem. Thermodynamics 48 (2012) 160–174 TABLE 7 (continued) msucrose/(mol  kg1)

1.5000

mx,i/(mol  kg1)

my,i/(mol  kg1)

mx/(mol  kg1)

my/(mol  kg1)

DHdil(x)/(J  kg1)

DHdil(y)/(J  kg1)

DHmix/(J  kg1)

DH⁄/(J  kg1)

0.3000 0.3200

0.3000 0.3200

0.1501 0.1597

0.1604 0.1708

5.74 6.52

23.96 27.17

2.40 2.60

27.30 31.08

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000

0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.2000 0.2200 0.2500 0.2800 0.3000

0.0248 0.0399 0.0500 0.0598 0.0747 0.0895 0.0994 0.1092 0.1245 0.1389 0.1490

0.0268 0.0442 0.0552 0.0662 0.0827 0.0990 0.1099 0.1208 0.1372 0.1535 0.1642

0.12 0.34 0.55 0.81 1.29 1.91 2.37 2.90 3.76 4.73 5.46

0.90 2.07 3.10 4.33 6.58 9.27 11.31 13.57 17.36 21.58 24.68

0.03 0.15 0.31 0.48 0.77 1.08 1.30 1.55 1.78 2.14 2.35

1.05 2.26 3.34 4.66 7.10 10.10 12.38 14.92 19.34 24.17 27.79

TABLE 8 Enthalpic interaction coefficients (hxy, hxxy, and hxyy) of HMBA with L-alanine, L-serine, and L-valine in water and aqueous sucrose solutions at 298.15 K (msucrose – molality of sucrose, S.D. – standard deviation). msucrose/(mol  kg1)

hxxy/(J  kg2  mol3)

hxy/(J  kg  mol2)

hxyy/(J  kg2  mol3)

S.D.

1077 ± 396 5038 ±511 16821 ±6985 2581 ± 174 854 ± 467 8227 ± 412 8025 ± 300

0.02 0.03 0.10 0.03 0.03 0.01 0.01

0.0000 0.1000 0.3000 0.6000 0.9000 1.2000 1.5000

1112 ± 2 1275 ± 5 1355 ± 17 1434 ± 4 1344 ± 5 1272 ± 4 1213 ± 2

HMBA—L-alanine 1011 ± 384 4836 ± 527 15920 ± 6485 2795 ± 181 1028 ± 488 9466 ± 460 8514 ± 312

0.0000 0.1000 0.3000 0.6000 0.9000 1.2000 1.5000

948 ± 3 975 ± 3 1012 ± 3 1054 ± 2 983 ± 3 926 ± 2 854 ± 5

HMBA—L-serine 1332 ± 546 1773 ± 339 2927 ± 671 4172 ±110 3768 ± 287 1174 ± 283 3279 ± 715

1352 ± 548 1176 ± 307 3009 ± 695 3900 ± 101 3453 ± 258 1136 ± 253 2861 ± 644

0.01 0.02 0.02 0.02 0.02 0.01 0.03

0.0000 0.1000 0.3000 0.6000 0.9000 1.2000 1.5000

1587 ± 7 1700 ± 4 1760 ± 2 1879 ± 4 1927 ± 4 1808 ± 6 1607 ± 3

HMBA—L-valine 5969 ± 915 9708 ± 826 1586 ± 406 346 ± 185 6442 ± 477 17665 ± 1052 933 ± 531

5649 ± 866 9130 ± 732 1246 ± 401 382 ± 165 4596 ± 402 14671 ± 889 954 ± 446

0.04 0.03 0.02 0.03 0.03 0.02 0.02

Tables 1 to 3 show the experimental values of DHmix and DHdil for HMBA with L-alanine, L-serine, and L-valine in water and different aqueous sucrose solutions, respectively, together with those of DH⁄. The experimental values of DHmix, DHdil, and DH⁄ for NMF with glycine, L-alanine, L-serine, and L-valine in water and different aqueous sucrose solutions are listed in tables 4 to 7, respectively. By analyzing the results with the least-square method, we obtained the heterotactic enthalpic interaction coefficients according to equation (3) which are showed in tables 8 and 9, respectively. The heterotactic enthalpic pairwise interaction coefficients hxy of HMBA and NMF with glycine, L-alanine, L-serine, and L-valine versus the molality of sucrose in aqueous solutions are also showed in figure 1. The data for glycine in figure 1 were obtained from reference [27]. From tables 8 and 9 and figure 1, we can obtain the following five conclusions: (1) the heterotatic pairwise enthalpic coefficients hxy for HMBA and NMF with glycine, L-alanine, L-serine, and L-valine are all positive in water and aqueous sucrose solutions; (2) the values of hxy for HMBA and the four amino acids are much larger than that for NMF with the same amino acids; (3) the values of hxy between HMBA or NMF with one of the four investigated amino acids in the same molality of aqueous sucrose solution, from high to low,

are hxy (L-valine) > hxy (L-alanine) > hxy (L-serine) > hxy (glycine); (4) the values of hxy reach the corresponding maximum at about 0.6 mol  kg1of the sucrose molality for HMBA with amino acids, except that the values of hxy for HMBA with L-valine get to the maximum at about 0.9 mol  kg1of the sucrose molality; and (5) the values of hxy for NMF with L-alanine, L-serine, and L-valine reach the corresponding maximum at about 0.3 mol  kg1, 0.3 mol  kg1, and 0.6 mol  kg1, respectively, while the values of hxy between NMF and glycine decrease monotonically with the increasing molalities of sucrose. All the phenomena can be explained with the theory of the solute–solute and solute–solvent interactions. There are mainly two types of interactions in the aqueous solutions: the solute–solute and solute–solvent interactions. The direct solute–solute interactions between HMBA or NMF and the studied amino acid contain: (a) hydrophobic–hydrophilic interactions between the alkyl groups of the HMBA or NMF molecules and the zwitterionic groups of the amino acid molecules (positive contribution to hxy); (b) hydrophobic–hydrophobic interactions between the alkyl groups of the HMBA or NMF molecules and the apolar parts of the amino acid molecules (positive contribution to hxy); (c) hydrogen-bond interactions between the acylamino groups of HMBA or NMF molecules and the zwitterionic groups of the amino

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TABLE 9 Enthalpic interaction coefficients of NMF with glycine, L-alanine, L-serine, and L-valine in water and aqueous sucrose solutions at 298.15 K (msucrose – molality of sucrose, S.D. – standard deviation). msucrose/(mol  kg1)

hxxy/(J  kg2  mol3)

hxy/(J  kg  mol2)

hxyy/(J  kg2  mol3)

S.D.

1600 ± 333 17 ± 15 975 ± 525 2745 ± 467 935 ± 211 2958 ± 956 2207 ± 595

0.01 0.01 0.02 0.01 0.01 0.01 0.01

0.0000 0.1000 0.3000 0.6000 0.9000 1.2000 1.5000

185 ± 2 175 ± 1 169 ± 2 161 ± 1 153 ± 1 145 ± 1 139 ± 1

NMF—glycine 1600 ± 328 50 ± 14 977 ± 529 2720 ± 463 873 ± 204 3005 ± 952 2086 ± 583

0.0000 0.1000 0.3000 0.6000 0.9000 1.2000 1.5000

352 ± 2 359 ± 2 381 ± 1 365 ± 2 356 ± 2 347 ± 3 337 ± 2

NMF—L-alanine 2548 ± 596 1258 ± 798 2388 ± 834 1154 ± 693 681 ± 262 2899 ± 1049 1251 ± 538

2511 ± 590 1305 ± 821 2510 ± 851 1184 ± 714 783 ± 284 2815 ± 1041 1137 ± 576

0.02 0.02 0.01 0.02 0.01 0.02 0.01

0.0000 0.1000 0.3000 0.6000 0.9000 1.2000 1.5000

192 ± 2 194 ± 1 202 ± 2 188 ± 1 170 ± 1 158 ± 1 154 ± 1

NMF—L-serine 647 ± 556 484 ± 215 2720 ± 524 854 ± 418 218 ± 158 1176 ± 340 715 ± 481

597 ± 536 469 ± 206 2676 ± 514 886 ± 409 212 ± 161 1098 ± 337 634 ± 475

0.01 0.01 0.01 0.01 0.01 0.01 0.01

0.0000 0.1000 0.3000 0.6000 0.9000 1.2000 1.5000

518 ± 1 531 ± 3 545 ± 2 564 ± 1 554 ± 1 542 ± 3 534 ± 2

NMF—L-valine 1287 ± 208 1062 ± 459 389 ± 340 1895 ± 357 976 ± 411 3153 ± 1678 869 ± 599

1124 ± 189 1093 ± 432 379 ± 318 1827 ± 341 1058 ± 392 3057 ± 1574 681 ± 547

0.01 0.02 0.01 0.01 0.01 0.02 0.01

2000 1800 1600

1200 1000 800

hxy/(J

kg

-2

mol )

1400

300

0.0

0.2

0.4

0.6

0.8

msucrose/(mol

1.0

1.2

1.4

1.6

-1

kg )

FIGURE 1. Enthalpic pair interaction coefficients (hxy) of HMBA and NMF with amino acids versus the molality m of sucrose in aqueous solutions at 298.15 K. j, hxy(glycine– NMF); d, hxy(L-alanine–NMF); N, hxy (L-serine–NMF); ., hxy(L-valine–NMF); h, hxy (glycine–HMBA); s, hxy (L-alanine–HMBA); 4, hxy(L-serine–HMBA); and 5, hxy(L-valine– HMBA).

acid molecules (negative contribution to hxy); (d) hydrophilic– hydrophobic interactions between the acylamino groups of HMBA or NMF molecules and the apolar parts of the amino acid molecules (positive contribution to hxy). The solute–solvent interactions can also be divided into five types: (i) formation of intermolecular

hydrogen bonds caused by the interaction of the carbonyl oxygen in the solute (HMBA, NMF, or amino acids) molecules with the hydroxyl groups in the sucrose molecules (negative contribution to hxy); (ii) hydrophilic–hydrophobic interactions between the acylamino or zwitterionic groups of the solute molecules and the alkyl

G. Li et al. / J. Chem. Thermodynamics 48 (2012) 160–174

173

FIGURE 2. Structural hydration interaction model. Hb, hydrophobic ion and Hl, hydrophilic ion. (I) Hb–Hb; (II) Hl–Hl (same charge); (III) Hl–Hl (opposite charge); and (IV) Hb–Hl.

groups of the solvent molecules (positive contribution to hxy); (iii) hydrophobic–hydrophilic interactions between the alkyl groups of the solute molecules and the hydroxyl groups of the solvent molecules (positive contribution to hxy); (iv) hydrophobic–hydrophobic interactions between the alkyl groups of the solute molecules and the alkyl groups of the solvent molecules (positive contribution to hxy). (v) the partial dehydration of the hydration shell of the solute molecules (positive contribution to hxy). The competitive equilibrium of all the aforementioned interactions affected the hxy values. Positive hxy values indicate that the cooperative effects of solute–solute interactions of (a), (b), and (d) and solute–solvent interactions of (ii) to (v) are dominant over the interactions of (c) and (i). That is, the hydrophobic–hydrophilic interactions, hydrophobic–hydrophobic interactions, and the partial desolvation are stronger than the hydrogen-bond interactions. All the interactions in the solution can be illustrated in figure 2. The reason that the heterotatic pairwise enthalpic coefficient between HMBA and one of the four amino acids is much larger than that between NMF and the same amino acid could be: each NMF molecule contains one acylamino group and one methyl group while each HMBA molecule contains two acylamino groups, two methyl groups, and another alkyl group containing six carbons. We can compare the heterotatic pairwise enthalpic coefficients qualitatively according to the additivity groups approach by Savage and Wood [33]. This approach assumes that a functional group of one molecule will interact with each functional group of another molecule, and the contribution of every interaction to the overall pairwise coefficient is independent of the position of the interacting groups in molecule [34,35]. What is more, the alkyl group is a hydrophobic group and contributes positively to the pairwise coefficient. So the coefficient of HMBA with amino acid is more than double that of NMF. The discrepancy that the heterotactic enthalpic pairwise interaction coefficients hxy (L-valine) > hxy (L-alanine) > hxy (L-serine) > hxy (glycine) with the same molality of sucrose, may be attributed to the different side chains of the four amino acids. Compared with glycine, there are one or two hydrophobic apolar-CH3 groups on the a-carbon of L-alanine or L-valine, which cause the increasing of hydrophobic–hydrophilic interactions and the hydrophobic–hydrophobic interactions. So the side chain will give more positive contribution to hxy, and lead to the result of hxy (L-valine) > hxy (L-alanine) > hxy (glycine). The regularity agrees with the change of the transfer volumes DV 0/ of them in aqueous sucrose solution [36]. In addition, the change trend of hydration number nH for the three amino acids is nH(L-valine) > nH(L-alanine) > nH(glycine) [37], which is similar to our results. On the other side, a hydrophilicCH2OH group substitutes the place of one hydrogen atom on the a-carbon of L-serine molecule, which will cause the increasing of the hydrophilic–hydrophobic interaction of the –CH2OH group of L-serine molecule with the alkyl groups of solute and solvent molecules and the hydrogen-bond interaction of the –CH2OH group of L-serine molecule with the acylamino group of HMBA and NMF molecules or the hydroxyl group of sucrose molecule. Because hxy (L-serine) is larger than hxy (glycine), we can conclude that the

increasing degree of the hydrophilic–hydrophobic interaction is bigger than that of the hydrogen-bond interaction. Also, compared with L-alanine, –OH group of L-serine leads to the increasing positive contribution of L-erine is less than that of L-alanine. So we can obtain the conclusion that hxy (L-valine) > hxy (L-alanine) > hxy (serine) > hxy (glycine). From figure 1, we can also see that the value of hxy for HMBA with amino acid reaches the maximum at about 0.6 mol  kg1or 0.9 mol  kg1 of the sucrose molality in the range of the sucrose solution investigated. This result can be explained as follows. With the increase of the sucrose molality, the solute–solvent interactions (ii) to (v) described above will increase and make more positive contribution to hxy. What is more, the polyhydroxy compounds have a structure-breaking effect in water [38] and a special hydrogen bonding between sugar and surrounding water molecules, which is stronger than the hydrogen bonding within the water molecule itself [39]. So the partial dehydration of solute molecules will be more difficult in sucrose solution than in water, and the more energy the partial dehydration process absorbs, the more positive contribution to hxy it makes. But at the same time, the hydrogen-bond effect between the HMBA and sucrose molecules will increase, which will give more negative effects and cancel part of the positive effects. The competition of the two types of increasing interactions leads to the maximum value of hxy at 0.6 or 0.9 mol  kg1 of sucrose molality in the quaternary systems. In contrast, the values of hxy for NMF with L-alanine, L-serine, and 1 L-valine reach the corresponding maximum at about 0.3 mol  kg , 1 1 0.3 mol  kg , and 0.6 mol  kg , respectively, while the value of hxy between NMF and glycine decrease monotonically in the range of investigated sucrose solutions. This difference is caused by the different structure of NMF molecule. The apolar group of NMF molecule is much shorter than that of HMBA molecule, so the increasing of the hydrophobic–hydrophobic and hydrophobic– hydrophilic interactions is much smaller. And the values of hxy for NMF with L-alanine, L-serine, and L-valine are also the competition of the two types of increasing interactions as discussed above in the interactions of HMBA and the amino acid molecules. Therefore, the maximum value of NMF with L-alanine, L-serine, and L-valine will reach at a lower concentration of sucrose. Since glycine has only one zwitterionic group, the increase of the negative contribution is always larger than the positive contribution. But the dominant thermal effect is still the positive effects contribution in the investigated molality ranges. As a result, the value of hxy between NMF and glycine decrease monotonically in the range of investigated sucrose solutions. 4. Conclusion By means of a mixing-flow microcalorimeter, we gained the mixing thermal effect of HMBA and NMF with four typical amino acids in different molality sucrose solutions at 298.15 K. The heterotactic enthalpic interaction coefficients (hxy, hxxy, and hxyy) obtained from virial expansion are discussed in virtue of the solute–solute and solute–solvent interactions.

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(1) The heterotactic enthalpic pairwise interaction coefficients hxy between HMBA or NMF and the four investigated amino acids in water or aqueous sucrose solutions of different molalities are all positive, which is the result of the leading position of the hydrophobic–hydrophilic interaction, hydrophobic– hydrophobic interaction, and partial desolvation over the hydrogen-bond interactions. (2) The heterotactic enthalpic pairwise interaction coefficients hxy between HMBA and one of the four amino acids is much larger than that between NMF and the same amino acid. This is due to that the apolar group of HMBA molecule is much longer than that of NMF molecule, causing the more positive contribution to hxy. (3) The order of the value of hxy is hxy (L-valine) > hxy (L-alanine) > hxy (L-serine) > hxy (glycine) in aqueous solution with the same molalities of sucrose. This discrepancy is mainly attributed to the different side chains of the four amino acids, which lead to the different increasing degree of the hydrophobic–hydrophilic, hydrophobic–hydrophobic, and hydrogen-bond interactions as well as the partial dehydration. (4) The values of hxy reach the maximum at different molalities of the sucrose molality for NMF or HMBA with amino acids, except that the values of hxy between NMF and glycine decrease monotonically with the increasing molalities of sucrose. This is because of the competition between the positive contributions and the negative contributions to hxy.

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JCT-11-173