Physicochemical study of solute–solute and solute–solvent interactions of glycine, l -alanine, l -valine and l -isoleucine in aqueous-d -mannose solutions at temperatures from 293.15 K to 318.15 K

J. Chem. Thermodynamics 98 (2016) 338–352

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Physicochemical study of solute–solute and solute–solvent interactions of glycine, L-alanine, L-valine and L-isoleucine in aqueous-D-mannose solutions at temperatures from 293.15 K to 318.15 K Anil Kumar Nain Department of Chemistry, Dyal Singh College, University of Delhi, New Delhi 110 003, India

a r t i c l e

i n f o

Article history: Received 28 December 2015 Received in revised form 4 March 2016 Accepted 5 March 2016 Available online 19 March 2016 Keywords: Density Ultrasonic speed Viscosity a-Amino acids D-Mannose Molecular interactions

a b s t r a c t Densities, q, ultrasonic speeds, u, and viscosities, g of aqueous-D-mannose (2.5% and 5% of D-mannose, w/w in water) and of solutions of glycine, L-alanine, L-valine and L-isoleucine in aqueous-D-mannose solvents were measured at temperatures (293.15, 298.15, 303.15, 308.15, 313.15 and 318.15) K and at atmospheric pressure. These experimental values have been used to calculate the apparent molar volume, V / , limiting apparent molar volume, V
/ and the slope, Sv, apparent molar compressibility, K s;/ , limiting apparent molar compressibility, K
s;/ and the slope, Sk, transfer limiting apparent molar volume, V
/;tr , transfer limiting apparent molar compressibility, K
s;/;tr , hydration number, nH , Falkenhagen coefficient, A, Jones–Dole coefficient, B, and temperature derivative of B-coefficient, dB/dT. The Gibbs free energies
# of activation of viscous flow per mole of solvent, Dl
# 1 and per mole of solute, Dl2 were also calculated. The results are interpreted in terms of solute–solvent and solute–solute interactions in these systems. The structure-making/breaking ability of the amino acids has also been discussed in terms of the sign of dB/dT. Furthermore, the values of V
/ , K
s;/ , V
/;tr , K
s;/;tr , B and Dl
# 2 have been split into groups’ contributions of the amino acids using linear correlation with number of carbon atoms in the alkyl chain of the amino acids. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Studies in the stability of proteins have generated a great interest for a long time, but because of complications due to their complex structures and large molar mass, their low molar mass model compounds are generally taken for investigations [1,2]. Physicochemical properties of amino acids in mixed aqueous media are important in investigating the solute–solvent and solute–solute interactions, which help in understanding the complex mechanism of molecular interactions occurring in various biochemical processes in the human body [3–7]. But due to complicated structure of proteins the study of their interactions are somewhat difficult, therefore, the physicochemical properties of amino acids, peptides and their derivatives in aqueous solutions have been extensively studied to gain a better understanding of solute–solvent interactions and their role in the conformational stability of proteins [8–12]. It is well known [13,14] that various substances cause changes in the conformation of proteins when present in aqueous-protein solutions. The additives, like sugars, alcohols, polyhydroxy E-mail address: [email protected] http://dx.doi.org/10.1016/j.jct.2016.03.012 0021-9614/Ó 2016 Elsevier Ltd. All rights reserved.

alcohols, etc. decrease the denaturation of proteins [13], in particular, sugars help in stabilizing the native conformation of globular proteins [14]. This stabilizing ability of different sugars depends on the number of hydroxyl groups present in them. Back et al. [15] and Fujita et al. [16] studied the effect of a variety of sugars on the thermal transition of lysozyme and other proteins and enzymes and tried to correlate the stabilizing effect of sugars and polyols to the number and configuration of the OH groups present in them. Several physicochemical properties of constituent amino acids in aqueous and mixed aqueous solutions have been used by various researchers to investigate solute–solute and solute–solvent interactions [3–12,17,18]. In continuation to our earlier studies [19–25] on amino acids in aqueous-carbohydrate solutions, we report here the densities, q, ultrasonic speeds, u, and viscosities, g of aqueous-D-mannose (2.5% and 5% of D-mannose, w/w in water) and of solutions of glycine, L-alanine, L-valine and L-isoleucine in aqueous-D-mannose solvents were measured at 293.15, 298.15, 303.15, 308.15, 313.15, and 318.15 K and at atmospheric pressure. These experimental data have been used to calculate the values of various parameters, viz., V / , V
/ , Sv, K s;/ , K
s;/ , Sk, V
/;tr , K
s;/;tr , nH , Coefficient A, Coefficient B and dB/dT. These parameters have been used to discuss the

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solute–solute and solute–solvent interactions in these systems. The Gibbs free energies of activation of viscous flow per mole of solvent, Dl
# and per mole of solute, Dl
# were also calculated 1 2 are discussed in terms of transition state theory. Furthermore, the values of V
/ , K
s;/ , V
/;tr , K
s;/;tr , B and Dl
# 2 have been split into groups’ contributions of the amino acids using linear correlation with number of carbon atoms in the alkyl chain of the amino acids. 2. Experimental Glycine, L-alanine and L-valine (SRL, India, purity > 99%) and Lisoleucine (Thomas Baker, India, mass fraction purity > 0.99) were used after recrystallization from ethanol–water mixture and dried in vacuum over P2O5 at room temperature for 72 h. The purity of the purified amino acids was checked by performing gas chromatography analysis using Shimadzu Gas Chromatograph (Model: GC-2010 Plus). The D-mannose (SRL, India, mass fraction purity > 0.99) was used as received without further purification, except drying in oven for 24 h. The final purities and other specifications of the chemicals used are given in Table 1. The aqueous-Dmannose solvents (2.5% and 5% of D-mannose, w/w in water) were prepared using triple distilled water (conductivity less than 1  106 Scm1) and these were used as solvents to prepare amino acid solutions of six different molal concentrations (ranging from 0 to 0.15) m. The weighing was done on an electronic balance (Model: GR-202R, AND, Japan) with a precision of ±0.01 mg. The solutions were prepared with care and stored in special airtight bottles to avoid contamination and evaporation. The uncertainty in the molality of the solutions was estimated within ±1  104 molkg1. The densities of the solutions were measured by using a singlecapillary pycnometer (made of Borosil glass) having a bulb capacity of 10 mL. The capillary, with graduated marks, had a uniform bore and could be closed by a well-fitting glass cap. The marks on the capillary were calibrated by using triply distilled water. The densities of pure water used in the calibration at required temperatures were taken from the literature [26]. The uncertainty in density measurements was within ±0.60 kgm3. The ultrasonic speeds in the solutions were measured using a single-crystal variable-path multifrequency ultrasonic interferometer (Model: M-81DS, Mittal Enterprises, India) having stainless steel sample cell (with digital micrometer) operating at 3 MHz. The uncertainty in ultrasonic speed measurements was within ±1.5 ms1. The viscosities of the solutions were measured by using Ubbelohde type suspended level viscometer. The viscometer was calibrated by using triple distilled water. The viscosities of pure water for calculations of viscosity at required temperatures were taken from the literature [27]. The viscometer containing the test liquid was allowed to stand for about 30 min in a thermostatic water bath so that the thermal fluctuations in viscometer were minimized. The times of flow were recorded in triplicate with a digital stopwatch with an accuracy of ±0.01 s and the results were averaged. The uncertainty in viscosity measurements was within ±11%. The temperature of the test

solutions during the measurements was maintained to an accuracy of ±0.01 K in an electronically controlled thermostatic water bath (JULABO, Model: ME-31A, Germany). 3. Results The experimental values of density, q, ultrasonic speed, u, and viscosity, g of aqueous-D-mannose solvents and of solutions of amino acids in aqueous-D-mannose as functions of amino acid/Dmannose concentration and temperature are listed in Tables 2–4. The experimental data of q and g have been compared with the available values in the literature at (298.15, 308.15 and 318.15) K. The comparison has been given graphically as Figs. S1 and S2 in the Supplementary Material along with the citations. The comparison is found good in general, except few data points. However, the deviations were found within the stated uncertainty limits. 3.1. Apparent molar volume and compressibility The ultrasonic speed may be considered as a thermodynamic property, provided that a negligible amount of ultrasonic absorption of the acoustic waves of low frequency and of low amplitude is observed; in which case, the ultrasonic absorption of the acoustic waves is negligible [28]. The apparent molar volume, V / and apparent molar compressibility, K s;/ of these solutions were calculated by using the relations

V/ ¼

1000ðqo  qÞ M þ mqqo q

K s;/ ¼

ð1Þ

1000ðjs qo  jos qÞ js M þ mqqo q

ð2Þ

where m is the molal concentration of the amino acid (glycine/Lalanine/L-valine/L-isoleucine), q and qo are the densities of the solution and the solvent (aqueous-D-mannose), respectively; M is the molar mass of the amino acid, and js and j
s are the isentropic compressibility of the solution and the solvent (aqueous-D-mannose), respectively, calculated using the relation

js ¼ 1=u2 q

ð3Þ

The values of V / and K s;/ , as functions of amino acid concentration and temperature, are shown graphically as Figs. S4S7 in the Supplementary Material. It is observed that, for these amino acids in aqueous-D-mannose solvents, the curves of V / and K s;/ vs. m (Figs. S4S7) are found to be almost linear in the studied concentration range and at each investigated temperature. 3.2. Limiting apparent molar volume and compressibility The values of limiting apparent molar volume, V
/ and the slope, Sv, limiting apparent molar compressibility, K
s;/ and the slope, Sk have been obtained using method of linear regression of V / and K s;/ vs. m from the following relations [29]

Table 1 Specification of chemical samples. Chemical name (CAS number)

Provenance

Purification method

Final mass fraction purity

Analysis method

Glycine (50-40-6)

SRL, India SRL, India

Re-crystallization Re-crystallization

>0.998 >0.996

GCa GC

SRL, India

Re-crystallization

>0.996

GC

Thomas Baker, India

Re-crystallization

>0.994

GC

SRL, India

Used as received

>0.99

–

L-Alanine L-Valine

(56-41-7)

(72-18-4)

L-Isoleucine D-Mannose a

(72-32-5) (3458-28-4)

GC = Gas chromatography.

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Table 2 Densities, q/kgm3 of solutions of glycine/L-alanine/L-valine/L-isoleucine in mannose + water (2.5% and 5% mannose, w/w in water) solvents as functions of molality, m of glycine/ a L-alanine/L-valine/L-isoleucine at temperatures (293.15–318.15) K and at pressure p = 101 kPa. m/molkg1

q/kgm–3 298.15 K

303.15 K

308.15 K

313.15 K

318.15 K

Glycine in 2.5% aqueous-mannose 0.0000 1007.81 0.0249 1008.38 0.0499 1008.93 0.0749 1009.46 0.0999 1009.96 0.1249 1010.44 0.1499 1010.89

293.15 K

1006.66 1007.23 1007.79 1008.31 1008.81 1009.29 1009.74

1005.29 1005.87 1006.42 1006.94 1007.44 1007.92 1008.37

1003.71 1004.29 1004.84 1005.37 1005.87 1006.34 1006.79

1001.93 1002.51 1003.07 1003.60 1004.10 1004.57 1005.02

999.95 1000.54 1001.09 1001.63 1002.13 1002.61 1003.06

Glycine in 5% aqueous-mannose 0.0000 1017.15 0.0249 1017.84 0.0499 1018.51 0.0749 1019.17 0.0999 1019.81 0.1249 1020.42 0.1499 1021.02

1016.04 1016.73 1017.41 1018.06 1018.70 1019.31 1019.91

1014.73 1015.42 1016.10 1016.75 1017.39 1018.01 1018.61

1013.21 1013.90 1014.58 1015.23 1015.87 1016.49 1017.09

1011.50 1012.19 1012.87 1013.53 1014.17 1014.79 1015.39

1009.58 1010.28 1010.96 1011.62 1012.26 1012.88 1013.49

in 2.5% aqueous-mannose 1007.81 1008.47 1009.11 1009.72 1010.30 1010.85 1011.38

1006.66 1007.32 1007.96 1008.57 1009.15 1009.70 1010.22

1005.29 1005.95 1006.59 1007.19 1007.77 1008.32 1008.84

1003.71 1004.37 1005.01 1005.61 1006.19 1006.74 1007.26

1001.93 1002.60 1003.23 1003.84 1004.41 1004.96 1005.48

999.95 1000.62 1001.26 1001.86 1002.44 1002.99 1003.50

in 5% aqueous-mannose 1017.15 1017.77 1018.37 1018.97 1019.54 1020.10 1020.65

1016.04 1016.66 1017.26 1017.85 1018.43 1018.99 1019.54

1014.73 1015.35 1015.95 1016.54 1017.12 1017.68 1018.23

1013.21 1013.83 1014.43 1015.02 1015.60 1016.16 1016.71

1011.50 1012.12 1012.73 1013.32 1013.90 1014.46 1015.01

1009.58 1010.20 1010.81 1011.41 1011.99 1012.55 1013.10

in 2.5% aqueous-mannose 1007.81 1008.41 1008.99 1009.55 1010.08 1010.59 1011.08

1006.66 1007.26 1007.85 1008.40 1008.93 1009.44 1009.93

1005.29 1005.89 1006.48 1007.03 1007.56 1008.07 1008.55

1003.71 1004.32 1004.90 1005.45 1005.98 1006.49 1006.97

1001.93 1002.54 1003.13 1003.68 1004.22 1004.72 1005.20

999.95 1000.56 1001.15 1001.71 1002.24 1002.75 1003.23

in 5% aqueous-mannose 1017.15 1017.70 1018.25 1018.78 1019.31 1019.83 1020.33

1016.04 1016.59 1017.14 1017.68 1018.20 1018.72 1019.23

1014.73 1015.28 1015.83 1016.37 1016.90 1017.42 1017.93

1013.21 1013.77 1014.32 1014.86 1015.39 1015.91 1016.43

1011.50 1012.06 1012.61 1013.16 1013.69 1014.22 1014.73

1009.58 1010.14 1010.70 1011.25 1011.78 1012.31 1012.83

in 2.5% aqueous-mannose 1007.81 1008.38 1008.93 1009.46 1009.96 1010.44 1010.89

1006.66 1007.23 1007.79 1008.31 1008.81 1009.29 1009.74

1005.29 1005.87 1006.42 1006.94 1007.44 1007.92 1008.37

1003.71 1004.29 1004.84 1005.37 1005.87 1006.34 1006.79

1001.93 1002.51 1003.07 1003.60 1004.10 1004.57 1005.02

999.95 1000.54 1001.09 1001.63 1002.13 1002.61 1003.06

in 5% aqueous-mannose 1017.15 1017.67 1018.18 1018.67 1019.16 1019.63 1020.08

1016.04 1016.56 1017.07 1017.57 1018.05 1018.52 1018.98

1014.73 1015.25 1015.76 1016.26 1016.75 1017.22 1017.68

1013.21 1013.73 1014.25 1014.75 1015.24 1015.72 1016.18

1011.50 1012.03 1012.54 1013.05 1013.54 1014.02 1014.49

1009.58 1010.11 1010.63 1011.14 1011.64 1012.12 1012.59

L-Alanine

0.0000 0.0249 0.0499 0.0749 0.0999 0.1249 0.1499 L-Alanine

0.0000 0.0249 0.0499 0.0749 0.0999 0.1249 0.1499 L-Valine

0.0000 0.0249 0.0499 0.0749 0.0999 0.1249 0.1499 L-Valine

0.0000 0.0249 0.0499 0.0749 0.0999 0.1249 0.1499

L-Isoleucine

0.0000 0.0249 0.0499 0.0749 0.0999 0.1249 0.1499 L-Isoleucine

0.0000 0.0249 0.0499 0.0749 0.0999 0.1249 0.1499

a m is the molality of amino acid in aqueous-D-mannose solvents. Uncertainty in composition of D-mannose + water solvent s(%) = ±0.05%. Standard uncertainties s are s(T) = ±0.01 K, s(m) = ±1.0  104 molkg1, and s(q) = ±0.6 kgm3, s(p) = ±1.0 kPa.

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Table 3 Ultrasonic speeds, u/ms1 of solutions of glycine/L-alanine/L-valine/L-isoleucine in mannose + water (2.5% and 5% mannose, w/w in water) solvents as functions of molality, m of glycine/L-alanine/L-valine/L-isoleucine at temperatures (293.15–318.15) K and at pressure p = 101 kPa.a m/molkg1

u/ms1 298.15 K

303.15 K

308.15 K

313.15 K

318.15 K

Glycine in 2.5% aqueous-mannose 0.0000 1495.7 0.0249 1496.5 0.0499 1497.6 0.0749 1499.1 0.0999 1501.0 0.1249 1503.3 0.1499 1506.0

293.15 K

1506.6 1507.3 1508.4 1510.0 1511.9 1514.2 1516.9

1516.9 1517.6 1518.7 1520.2 1522.1 1524.4 1527.1

1526.9 1527.6 1528.6 1530.1 1531.9 1534.2 1536.9

1535.2 1535.8 1536.8 1538.2 1540.0 1542.3 1545.0

1543.0 1543.6 1544.5 1545.9 1547.7 1549.9 1552.5

Glycine in 5% aqueous-mannose 0.0000 1508.3 0.0249 1509.1 0.0499 1510.3 0.0749 1511.9 0.0999 1513.9 0.1249 1516.4 0.1499 1519.3

1516.6 1517.4 1518.5 1520.1 1522.1 1524.5 1527.3

1525.2 1525.9 1527.0 1528.6 1530.5 1532.9 1535.7

1534.1 1534.8 1535.8 1537.3 1539.2 1541.6 1544.3

1542.6 1543.2 1544.2 1545.7 1547.5 1549.8 1552.5

1551.0 1551.6 1552.5 1553.9 1555.7 1557.9 1560.5

L-Alanine in 2.5% aqueous-mannose 0.0000 1495.7 0.0249 1496.4 0.0499 1497.4 0.0749 1498.9 0.0999 1500.7 0.1249 1502.9 0.1499 1505.4

1506.6 1507.3 1508.3 1509.7 1511.5 1513.7 1516.3

1516.9 1517.5 1518.5 1519.9 1521.7 1523.9 1526.5

1526.9 1527.5 1528.5 1529.8 1531.6 1533.8 1536.3

1535.2 1535.7 1536.7 1538.0 1539.7 1541.9 1544.4

1543.0 1543.5 1544.4 1545.7 1547.4 1549.5 1552.0

L-Alanine in 5% aqueous-mannose 0.0000 1508.3 0.0249 1509.0 0.0499 1510.0 0.0749 1511.4 0.0999 1513.1 0.1249 1515.2 0.1499 1517.5

1516.6 1517.2 1518.2 1519.6 1521.3 1523.3 1525.7

1525.2 1525.8 1526.8 1528.1 1529.7 1531.7 1534.0

1534.1 1534.7 1535.6 1536.8 1538.4 1540.4 1542.7

1542.6 1543.1 1544.0 1545.2 1546.8 1548.7 1550.9

1551.0 1551.5 1552.3 1553.5 1555.0 1556.9 1559.1

L-Valine in 2.5% aqueous-mannose 0.0000 1495.7 0.0249 1496.1 0.0499 1497.0 0.0749 1498.2 0.0999 1499.9 0.1249 1502.0 0.1499 1504.5 0.0000 1508.3 0.0249 1508.8 0.0499 1509.8 0.0749 1511.2 0.0999 1513.2 0.1249 1515.6 0.1499 1518.6

1506.6 1507.0 1507.8 1509.0 1510.7 1512.8 1515.3 1516.6 1517.0 1518.0 1519.4 1521.3 1523.7 1526.6

1516.9 1517.3 1518.0 1519.2 1520.8 1522.9 1525.4 1525.2 1525.6 1526.5 1527.8 1529.7 1532.1 1534.9

1526.9 1527.2 1528.0 1529.1 1530.7 1532.8 1535.2 1534.1 1534.5 1535.3 1536.6 1538.4 1540.7 1543.5

1535.2 1535.5 1536.2 1537.3 1538.9 1540.9 1543.3 1542.6 1542.9 1543.7 1545.0 1546.7 1549.0 1551.6

1543.0 1543.2 1543.9 1545.0 1546.5 1548.5 1550.9 1551.0 1551.3 1552.0 1553.2 1554.9 1557.1 1559.8

L-Isoleucine in 2.5% aqueous-mannose 0.0000 1495.7 0.0249 1496.0 0.0499 1496.8 0.0749 1497.9 0.0999 1499.5 0.1249 1501.5 0.1499 1504.0

1506.6 1506.9 1507.6 1508.7 1510.3 1512.3 1514.7

1516.9 1517.1 1517.8 1518.9 1520.4 1522.4 1524.8

1526.9 1527.1 1527.7 1528.8 1530.3 1532.2 1534.6

1535.2 1535.4 1535.9 1537.0 1538.4 1540.3 1542.6

1543.0 1543.1 1543.6 1544.6 1546.0 1547.8 1550.1

L-Isoleucine in 5% aqueous-mannose 0.0000 1508.3 0.0249 1508.6 0.0499 1509.5 0.0749 1510.7 0.0999 1512.5 0.1249 1514.7 0.1499 1517.4

1516.6 1516.9 1517.7 1518.9 1520.6 1522.8 1525.5

1525.2 1525.5 1526.2 1527.4 1529.1 1531.2 1533.8

1534.1 1534.3 1535.0 1536.2 1537.8 1539.9 1542.5

1542.6 1542.8 1543.4 1544.5 1546.1 1548.2 1550.7

1551.0 1551.1 1551.7 1552.8 1554.3 1556.3 1558.8

a m is the molality of amino acid in aqueous-D-mannose solvents. Uncertainty in composition of D-mannose + water solvent s(%) = ±0.05%. Standard uncertainties s are s(T) = ±0.01 K, s(m) = ±1.0  104 molkg1 and s(u) = ±1.5 ms1, s(p) = ±1.0 kPa.

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Table 4 Viscosities, 103  g/Nsm2 of solutions of glycine/L-alanine/L-valine/L-isoleucine in mannose + water (2.5% and 5% mannose, w/w in water) solvents as functions of molality, m of glycine/L-alanine/L-valine/L-isoleucine at temperatures (293.15–318.15) K and at pressure p = 101 kPa.a m/molkg1

103  g /Nsm2 298.15 K

303.15 K

308.15 K

313.15 K

318.15

Glycine in 2.5% aqueous-mannose9 0.0000 1.0737 0.0249 1.0841 0.0499 1.0916 0.0749 1.0983 0.0999 1.1047 0.1249 1.1112 0.1499 1.1173

293.15 K

0.9514 0.9608 0.9677 0.9742 0.9804 0.9866 0.9925

0.8479 0.8564 0.8629 0.8690 0.8750 0.8811 0.8868

0.7636 0.7714 0.7776 0.7834 0.7894 0.7951 0.8006

0.6922 0.6994 0.7053 0.7112 0.7166 0.7222 0.7276

0.6347 0.6414 0.6471 0.6527 0.6581 0.6634 0.6688

Glycine in 5% aqueous-mannose 0.0000 1.1457 0.0249 1.1582 0.0499 1.1677 0.0749 1.1766 0.0999 1.1852 0.1249 1.1938 0.1499 1.2022

1.0067 1.0179 1.0267 1.0351 1.0435 1.0516 1.0594

0.8925 0.9027 0.9110 0.9192 0.9270 0.9347 0.9425

0.8017 0.8111 0.8190 0.8268 0.8345 0.8419 0.8495

0.7265 0.7352 0.7428 0.7503 0.7577 0.7651 0.7724

0.6654 0.6735 0.6808 0.6882 0.6953 0.7024 0.7095

in 2.5% aqueous-mannose 1.0737 1.0846 1.0936 1.1024 1.1110 1.1195 1.1280

0.9514 0.9612 0.9698 0.9780 0.9861 0.9942 1.0022

0.8479 0.8568 0.8649 0.8727 0.8804 0.8881 0.8956

0.7636 0.7718 0.7794 0.7868 0.7942 0.8015 0.8088

0.6922 0.6998 0.7070 0.7141 0.7212 0.7281 0.7352

0.6347 0.6418 0.6486 0.6555 0.6623 0.6690 0.6758

in 5% aqueous-mannose 1.1457 1.1586 1.1696 1.1803 1.1908 1.2013 1.2117

1.0067 1.0183 1.0284 1.0384 1.0484 1.0583 1.0680

0.8925 0.9031 0.9126 0.9222 0.9317 0.9410 0.9503

0.8017 0.8115 0.8206 0.8297 0.8388 0.8478 0.8569

0.7265 0.7356 0.7443 0.7529 0.7616 0.7703 0.7790

0.6654 0.6739 0.6823 0.6906 0.6990 0.7075 0.7158

in 2.5% aqueous-mannose 1.0737 1.0850 1.0974 1.1100 1.1228 1.1356 1.1484

0.9514 0.9616 0.9730 0.9846 0.9965 1.0084 1.0204

0.8479 0.8572 0.8680 0.8789 0.8899 0.9010 0.9121

0.7636 0.7722 0.7824 0.7925 0.8029 0.8134 0.8239

0.6922 0.7002 0.7097 0.7194 0.7292 0.7391 0.7489

0.6347 0.6422 0.6512 0.6605 0.6697 0.6792 0.6886

in 5% aqueous-mannose 1.1457 1.1591 1.1734 1.1880 1.2024 1.2170 1.2319

1.0067 1.0187 1.0318 1.0454 1.0588 1.0721 1.0856

0.8925 0.9033 0.9156 0.9282 0.9407 0.9530 0.9654

0.8017 0.8116 0.8232 0.8349 0.8467 0.8583 0.8701

0.7265 0.7357 0.7465 0.7576 0.7687 0.7798 0.7910

0.6654 0.6740 0.6842 0.6947 0.7054 0.7159 0.7267

in 2.5% aqueous-mannose 1.0737 1.0855 1.0995 1.1142 1.1293 1.1437 1.1590

0.9514 0.9621 0.9751 0.9888 1.0021 1.0162 1.0300

0.8479 0.8577 0.8699 0.8824 0.8952 0.9079 0.9208

0.7636 0.7726 0.7843 0.7960 0.8078 0.8197 0.8318

0.6922 0.7006 0.7117 0.7226 0.7337 0.7450 0.7564

0.6347 0.6426 0.6529 0.6633 0.6740 0.6846 0.6954

in 5% aqueous-mannose 1.1457 1.1593 1.1750 1.1915 1.2080 1.2247 1.2415

1.0067 1.0189 1.0334 1.0485 1.0636 1.0792 1.0945

0.8925 0.9036 0.9170 0.9310 0.9452 0.9594 0.9735

0.8017 0.8119 0.8246 0.8377 0.8508 0.8641 0.8775

0.7265 0.7359 0.7479 0.7601 0.7725 0.7849 0.7975

0.6654 0.6742 0.6856 0.6972 0.7088 0.7208 0.7327

L-Alanine

0.0000 0.0249 0.0499 0.0749 0.0999 0.1249 0.1499 L-Alanine

0.0000 0.0249 0.0499 .0749 0.0999 0.1249 0.1499 L-Valine

0.0000 0.0249 0.0499 0.0749 0.0999 0.1249 0.1499 L-Valine

0.0000 0.0249 0.0499 0.0749 0.0999 0.1249 0.1499

L-Isoleucine

0.0000 0.0249 0.0499 0.0749 0.0999 0.1249 0.1499 L-Isoleucine

0.0000 0.0249 0.0499 0.0749 0.0999 0.1249 0.1499

a m is the molality of amino acid in aqueous-D-mannose solvents. Uncertainty in composition of D-mannose + water solvent s(%) = ± 0.05%. Standard uncertainties s are s(T) = ± 0.01 K, s(m) = ±1.0  104 molkg1 and s(g) = ±1.1%, s(p) = ±1.0 kPa.

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A.K. Nain / J. Chem. Thermodynamics 98 (2016) 338–352

Table 5 Limiting apparent molar volume, V
/ , slope, Sv, transfer volume, V
/;tr , and standard deviations of linear regression, r for glycine/L-alanine/L-valine/L-isoleucine in mannose + water (2.5% and 5% mannose, w/w in water) solvents at temperatures (293.15–318.15) K.a Property

T(K) 293.15 K

Glycine in water [32] 105 V
/ /(m3mol–1)

10  r for Eq. (4) 106  Sv/(m3mol1kg1) Glycine in 2.5% aqueous-mannose 105  V
/ /(m3mol1)

10  r for Eq. (4) 105  Sv/(m3mol1kg1) 106  V
/;tr /(m3mol1)

Glycine in 5% aqueous-mannose 105  V
/ /(m3mol1)

10  r for Eq. (4) 105  Sv/(m3mol1kg1) 106  V
/;tr /(m3mol1) L-Alanine in water [32] 105  V
/ /(m3mol1)

10  r for Eq. (4) 105  Sv/(m3mol1kg1) L-Alanine in 2.5% aqueous-mannose 105  V
/ /(m3mol1)

10  r for Eq. (4) 105  Sv/(m3mol1kg1) 106  V
/;tr /(m3mol1)

L-Alanine in 5% aqueous-mannose 105  V
/ /(m3mol1)

10  r for Eq. (4) 105  Sv/(m3mol1kg1) 106  V
/;tr /(m3mol1) L-Valine in water [32] 105  V
/ /(m3mol1)

10  r for Eq. (4) 106  Sv/(m3mol1kg1) L-Valine in 2.5% aqueous-mannose 105  V
/ /(m3mol1)

10  r for Eq. (4) 105  Sv/(m3mol1kg1) 106  V
/;tr /(m3mol1)

L-Valine in 5% aqueous-mannose 105  V
/ /(m3mol1)

10  r for Eq. (4) 105  Sv/(m3mol1kg1) 106  V
/;tr /(m3mol1)

L-Isoleucine in water [32] 105  V
/ /(m3mol1)

10  r for Eq. (4) 105  Sv/(m3mol1kg1)

L-Isoleucine in 2.5% aqueous-mannose 105  V
/ /(m3mol1)

10  r for Eq. (4) 105  Sv/(m3mol1kg1) 106  V
/;tr /(m3mol1)

L-Isoleucine in 5% aqueous-mannose 105 V
/ /(m3mol1)

10  r for Eq. (4) 105 Sv /(m3mol1kg1) 106 V
/;tr /(m3mol1) a

298.15 K

303.15 K

308.15 K

313.15 K

318.15 K

4.325

4.341

4.361

4.378

4.392

4.409

0.006 1.311

0.011 1.327

0.008 1.289

0.010 1.295

0.010 1.310

0.009 1.302

4.3919

4.4037

4.4207

4.4337

4.4452

4.4589

0.004 1.401 0.664

0.010 1.426 0.628

0.006 1.411 0.593

0.004 1.427 0.559

0.009 1.459 0.529

0.013 1.461 0.501

4.4731

4.4854

4.5026

4.5158

4.5273

4.5411

0.005 1.318 1.476

0.009 1.326 1.445

0.005 1.300 1.411

0.005 1.318 1.380

0.009 1.335 1.350

0.009 1.322 1.323

6.008

6.032

6.052

6.076

6.094

6.111

0.010 1.320

0.008 1.260

0.008 1.269

0.008 1.264

0.010 1.293

0.009 1.356

6.0770

6.0971

6.1142

6.1350

6.1507

6.1643

0.090 2.052 0.686

0.015 2.039 0.653

0.003 2.100 0.623

0.014 2.111 0.593

0.016 2.172 0.564

0.007 2.250 0.535

6.1590

6.1794

6.1961

6.2168

6.2325

6.2462

0.006 0.979 1.506

0.010 0.928 1.475

0.010 0.943 1.442

0.016 0.931 1.411

0.012 0.938 1.382

0.008 0.970 1.354

9.043

9.063

9.083

9.098

9.117

9.136

0.008 1.106

0.007 1.144

0.007 1.121

0.004 1.154

0.005 1.161

0.005 1.129

9.1169

9.1331

9.1508

9.1625

9.1789

9.1962

0.018 1.667 0.740

0.023 1.677 0.705

0.013 1.733 0.677

0.022 1.835 0.647

0.009 1.860 0.622

0.016 1.909 0.597

9.1992

9.2161

9.2334

9.2451

9.2608

9.2772

0.005 0.526 1.564

0.002 0.495 1.534

0.009 0.468 1.503

0.007 0.473 1.472

0.003 0.482 1.441

0.005 0.481 1.408

10.548

10.569

10.589

10.607

10.630

10.650

0.009 1.126

0.005 1.235

0.009 1.258

0.010 1.271

0.008 1.268

0.008 1.276

10.6251

10.6421

10.6601

10.6751

10.6953

10.7126

0.011 1.725 0.768

0.011 1.725 0.731

0.011 1.771 0.707

0.024 1.846 0.679

0.026 1.863 0.653

0.007 1.890 0.626

10.7082

10.7257

10.7431

10.7573

10.7770

10.7939

0.009 0.813 1.598

0.008 0.792 1.567

0.008 0.760 1.536

0.006 0.743 1.501

0.008 0.709 1.470

0.007 0.707 1.440

The standard uncertainties s are s(V
/ ) = ±2.0  108 m3mol1, s(Sv) = ±2.0  108 m3mol1kg1 and s(V
/;tr ) = ±2.0  108 m3mol1.

V / ¼ V
/ þ Sv m

ð4Þ

K s;/ ¼ K
s;/ þ Sk m

ð5Þ

where the intercepts, V
/ or K
s;/ , by definition are free from solute– solute interactions and therefore provide a measure of solute–solvent interactions, whereas the slope, Sv or Sk provides information

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A.K. Nain / J. Chem. Thermodynamics 98 (2016) 338–352

Table 6 Limiting apparent molar compressibility, K
s;/ , slope, Sk, transfer compressibility, K
s;/;tr and standard deviations of linear regression, r for glycine/L-alanine/L-valine/L-isoleucine in mannose + water (2.5% and 5% mannose, w/w in water) solvents at temperatures (293.15–318.15) K.a Property

T(K) 293.15 K

Glycine in water [32] 1011  K
s;/ /(m5N1mol1)

4.172

r for Eq. (5)

1011  Sk/(m5N1mol1kg1)

303.15 K

308.15 K

313.15 K

318.15 K

4.046

3.936

3.818

3.722

3.627

0.113 12.735

0.133 12.720

0.139 12.690

0.152 12.561

0.157 12.534

Glycine in 2.5% aqueous-mannose 1011  K
s;/ /(m5N1mol1)

3.964

3.825

3.701

3.570

3.461

3.352

1011  Sk/(m5N1mol1kg1) 1011  K
s;/;tr /(m5N1mol1)

0.087 15.995 0.208

0.060 16.217 0.221

0.048 16.147 0.235

0.062 16.101 0.248

0.126 15.922 0.261

0.045 15.807 0.275

r for Eq. (5)

Glycine in 5% aqueous-mannose 1011  K
s;/ /(m5N1mol1)

3.697

3.553

3.418

3.279

3.165

3.047

1011  Sk/(m5N1mol1kg1) 1011  K
s;/;tr /(m5N1mol1)

0.064 16.666 0.475

0.127 16.533 0.493

0.068 16.407 0.518

0.135 16.241 0.539

0.049 15.899 0.557

0.149 15.564 0.580

L-Alanine in water [32] 1011  K
s;/ /(m5N1mol1)

3.775

r for Eq. (5)

r for Eq. (5)

1011  Sk/(m5N1mol1kg1)

3.678

3.587

3.486

3.386

3.294

0.057 15.053

0.135 14.835

0.113 14.660

0.126 14.568

0.147 14.497

L-Alanine in 2.5% aqueous-mannose 1011  K
s;/ /(m5N1mol1)

3.520

3.404

3.292

3.173

3.055

2.944

1011  Sk/(m5N1mol1kg1) 1011  K
s;/;tr /(m5N1mol1)

0.090 15.338 0.255

0.084 15.345 0.274

0.073 15.193 0.295

0.066 15.137 0.313

0.079 15.090 0.331

0.073 15.049 0.349

r for Eq. (5)

L-Alanine in 5% aqueous-mannose 1011  K
s;/ /(m5N1mol1)

3.251

3.130

3.014

2.894

2.773

2.661

1011  Sk/(m5N1mol1kg1) 1011  K
s;/;tr /(m5N1mol1)

0.091 14.072 0.525

0.077 14.181 0.547

0.091 13.809 0.572

0.063 13.609 0.592

0.065 13.566 0.613

0.096 13.577 0.633

L-Valine in water [32] 1011  K
s;/ /(m5N1mol1)

3.038

r for Eq. (5)

r for Eq. (5)

1011  Sk/(m5N1mol1kg1)

2.944

2.866

2.773

2.710

2.639

0.129 17.109

0.105 16.944

0.150 16.856

0.146 16.549

0.058 16.382

L-Valine in 2.5% aqueous-mannose 1011  K
s;/ /(m5N1mol1)

2.672

2.554

2.454

2.338

2.253

2.159

1011  Sk/(m5N1mol1kg1) 1011  K
s;/;tr /(m5N1mol1)

0.078 17.497 0.366

0.034 17.476 0.390

0.071 17.038 0.412

0.062 16.951 0.435

0.072 16.717 0.457

0.081 16.652 0.480

r for Eq. (5)

L-Valine in 5% aqueous-mannose 1011  K
s;/ /(m5N1mol1)

2.412

2.294

2.194

2.079

1.992

1.899

1011  Sk/(m5N1mol1kg1) 1011  K
s;/;tr /(m5N1mol1)

0.054 21.066 0.626

0.079 20.749 0.649

0.053 20.264 0.673

0.050 19.975 0.694

0.082 19.441 0.717

0.067 19.180 0.741

L-Isoleucine in water [32] 1011  K
s;/ /(m5N1mol1)

2.693

r for Eq. (5)

r for Eq. (5)

1011  Sk/(m5N1mol1kg1)

2.603

2.537

2.455

2.388

2.339

0.066 17.204

0.091 17.012

0.117 16.716

0.104 16.456

0.148 16.005

L-Isoleucine in 2.5% aqueous-mannose 1011  K
s;/ /(m5N1mol1)

2.275

2.162

2.068

1.960

1.866

1.792

1011  Sk /(m5N1mol1kg1) 1011  K
s;/;tr /(m5N1mol1)

0.128 18.163 0.417

0.093 17.893 0.442

0.125 17.506 0.469

0.141 17.342 0.494

0.081 17.017 0.522

0.054 16.526 0.547

r for Eq. (5)

L-Isoleucine in 5% aqueous-mannose 1011  K
s;/ /(m5N1mol1)

2.013

1.902

1.809

1.705

1.611

1.534

1011  Sk/(m5N1mol1kg1) 1011  K
s;/;tr /(m5N1mol1)

0.081 19.904 0.679

0.038 19.718 0.701

0.045 19.341 0.728

0.046 19.245 0.749

0.069 18.944 0.777

0.059 18.524 0.805

r for Eq. (5)

a

298.15 K

The standard uncertainties are s(K
s;/ ) = ±2.0  1014 m5N1mol1, s(Sk) = ±2.0  1014 m5N1mol1kg1 and s(K
s;/;tr ) = ±2.0  1014 m5N1mol1.

regarding solute–solute interaction. The values of V
/ , Sv, K
s;/ , and Sk along with the standard deviations of linear regression, r for glycine/L-alanine/L-valine/L-isoleucine in aqueous-D-mannose solutions at each temperature are listed in Tables 5 and 6.

3.3. Transfer limiting apparent molar volume/compressibility Limiting apparent molar properties of transfer provide qualitative as well as quantitative information regarding solute–solvent

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A.K. Nain / J. Chem. Thermodynamics 98 (2016) 338–352 Table 7 Hydration number, nH , glycine/L-alanine/L-valine/L-isoleucine in D-mannose + water (2.5% and 5% D-mannose, w/w in water) solutions at temperature, T/K = 298.15 Ka Hydration number, nH . Property

Volumetric method

Compressibility method

Glycine + water [32] Glycine + 2.5% D-mannose Glycine + 5% D-mannose

2.563 2.373 2.125 3.463

4.995 4.722 4.386 4.540

L-Alanine

+ water [32]

L-Alanine

+ 2.5% D-mannose

3.265

4.202

L-Alanine

+ 5% D-mannose

3.016

3.865 3.634

L-Valine

+ water [32]

3.473

L-Valine

+ 2.5% D-mannose

3.260

3.153

L-Valine

+ 5% D-mannose

3.008

2.833

L-Isoleucine

+ water [32]

4.514

3.214

L-Isoleucine

+ 2.5% D-

4.293

2.669

+ 5% D-mannose

4.039

2.349

¼

K
s;/;aqstreptomycin sulfate



K
s;/;water

ð6Þ ð7Þ

where V
/;water and K
s;/;water are the limiting apparent molar volume and limiting apparent molar compressibility of amino acids in water and their values have been taken from our earlier work [30]. The transfer values V
/;tr and K
s;/;tr for amino acids from water to aqueous-D-mannose solutions are included in Tables 5 and 6, respectively. 3.4. Hydration number The partial molar volume of the amino acids can be studied by a simple model given by following equation [7]

V
/ ðamino acidÞ ¼ V
/ ðint:Þ þ V
/ ðelect:Þ

ð8Þ

where V
/ (elect) is the electrostriction partial molar volume due to the hydration of amino acid and can be calculated from experimentally measured values of V
/ (amino acid), and V
/ (int.) is the intrinsic partial molar volume of the amino acid and has been calculated from equation

V
/ ðint:Þ

¼

ð0:7=0:634ÞV
/ ðcryst:Þ

ð9Þ

where V
/ (cryst.) (=M/dcryst.) is the crystal molar volume, 0.7 is the packing density for molecules in organic crystals and 0.634 is the packing density for random packing spheres. The value of V
/ (int.) for the amino acid can be estimated from above Eq. (9) using values of dcryst. for the amino acids taken from the work of [33]. V
/ (elect) can be calculated from experimentally measured values of V
/ (amino acid),

V
/ ðelect:Þ ¼ V
/  V
/ ðint:Þ

is

ð12Þ

K
s;/ ðelect:Þ ¼ K
s;/  K
s;/ ðint:Þ

interactions without taking into account the effects of solute–solute interactions [30,31]. The transfer limiting apparent molar volumes, V
/;tr and transfer limiting apparent molar compressibility, K
s;/;tr of amino acids from water to aqueous-D-mannose solutions were calculated by using the relation [30,31]

K
s;/;tr

is the molar volume of electrostricted water and

the molar volume of bulk water. The reported value of ðV
/;e  V
/;b Þ ¼ 3.3  106 m3mol1 at 298.15 K determined using the value of ðV
/;e  V
/;b Þ and the values of V
/ (elect). The nH values estimated from Eq. (11) are included in Table 7. Further, the number of water molecules hydrated to the amino acids was calculated by using the method given by [7]

lowing equation

The standard uncertainties are s(nH) using volumetric method = ±0.003 and s (nH) using compressibility method = ±0.005.


sulfate  V /;water

ð11Þ V
/;b

where, K
s;/;b is the isothermal compressibility of bulk water. Value of ðV
/;b :K
s;/;b Þ is 0.81  106 m3mol1 GPa1. The electrostriction partial molar compressibility, K
s;/ ðelect:Þ can be calculated from the K
s;/ values (obtained from experimental data) by using the fol-

a

V
/;tr ¼ V
/;aqstreptomycin

where,

V
/ e

nH ¼ K
/ ðelect:Þ=ðV
/;b :K
s;/;b Þ

mannose L-Isoleucine

nH ¼ V
/ ðelect:Þ=ðV
/;e  V
/;b Þ

ð10Þ

The change in volume due to elecrostriction can be related to the number of water molecules, nH , hydrated to the amino acids by following equation

K
s;/

K
s;/

ð13Þ K
s;/

where (int) is (isomer) for amino acids. Since (int) is expected to be less than 5  106 m3mol1 GPa1 for ionic crystals and many organic solutes in water. So, we can assume K
s;/ (int) = 0. Therefore, for K
s;/ (int) = 0, Eq. (13) becomes

K
s;/ ðelect:Þ ¼ K
s;/

ð14Þ

The nH values estimated from Eq. (12) are included in Table 7. 3.5. Analysis of viscosity values The viscosity values were analysed by using the Jones–Dole [34] equation of the form

gr ¼

g ¼ 1 þ Am1=2 þ Bm g


ð15Þ

where gr is the relative viscosity of the solution, g and go are the viscosities of solution and the solvent (aqueous-D-mannose), respectively, A and B are the Falkenhagen [35,36] and Jones–Dole [34] coefficients, respectively. Coefficient A accounts for the solute–solute interactions and B is a measure of structural modifications induced by the solute–solvent interactions [34]. The ½ðgr  1Þ=m1=2  vs. m1/2 curves from Eq. (15) are shown graphically as Figs. S8 and S9 in the Supplementary Material. The values of A and B have been obtained as the intercept and slope from linear regression of ½ðgr  1Þ=m1=2  vs. m1/2 curves, which were found almost linear for these systems (Figs. S8 and S9). The values of A and B along with the standard deviations of linear regression, r are listed in Table 8. 3.6. Thermodynamics of viscous flow The viscosity data have also been used for calculating the Gibbs energies of activation per mole of solute and Gibbs energies of activation per mole of solvent according to transition state theory of the relative viscosity [37,38]. According to this theory, the B-coefficient is given by the relation




B¼


 
# V
1  V
2 þ V
1 Dl
# RT 2  Dl 1 1000

ð16Þ

where V
1 is the apparent (partial) molar volume of the solvent (aqueous-D-mannose) and V
2 (=V
/ ) is the limiting apparent (partial) molar volume of the solute, respectively. The free energy of activation per mole of solvent (Dl
# 1 ) has been calculated by using the Eyring viscosity relation [39]



Dl
# 1 ¼ RT ln go V 1 =hN

ð17Þ

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A.K. Nain / J. Chem. Thermodynamics 98 (2016) 338–352

Table 8 Falkenhagen coefficient, A, Jones–Dole coefficient, B, standard deviations of linear regression, r, free energies of activation of viscous flow per mole of solvent, Dl
# 1 and per mole a of solute, Dl
# 2 for glycine/L-alanine/L-valine/L-isoleucine in D-mannose + water (2.5% and 5% D-mannose, w/w in water) solutions at temperatures (293.15–318.15) K. Property

T(K) 293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

318.15 K

0.1234 0.1434 9.16

0.1336 0.1543 9.04

0.1315 0.1620 8.93

0.1296 0.1688 8.83

0.1247 0.1745 8.74

205.92

224.03

237.89

250.83

262.49

0.2892 0.2139 0.001 9.36

0.2547 0.2403 0.003 9.23

0.2287 0.2647 0.004 9.12

0.2046 0.2889 0.004 9.01

0.1765 0.3129 0.002 8.93

261.20

299.13

339.76

378.70

418.12

458.18

0.2921 0.2534 0.005 9.68

0.2569 0.2837 0.003 9.53

0.2271 0.3150 0.003 9.39

0.1925 0.3477 0.003 9.27

0.1551 0.3812 0.002 9.17

0.1230 0.4106 0.003 9.09

343.39

389.09

437.38

488.85

542.48

591.71

0.0226 0.2584 9.16

0.0329 0.2733 9.04

0.0334 0.2866 8.93

0.0399 0.2995 8.83

0.0413 0.3107 8.74

363.73

389.69

414.06

438.31

460.43

0.1568 0.3158 0.003 9.36

0.1273 0.3433 0.003 9.23

0.0990 0.3695 0.001 9.12

0.0730 0.3955 0.002 9.01

0.0442 0.4206 0.002 8.93

395.07

437.22

481.41

524.99

569.10

612.94

0.1802 0.3375 0.001 9.68

0.1447 0.3688 0.003 9.53

0.1141 0.4027 0.003 9.39

0.0801 0.4379 0.003 9.27

0.0528 0.4676 0.003 9.17

0.0182 0.5005 0.003 9.09

454.18

502.97

556.58

613.22

663.40

719.14

0.3992 0.4855 9.16

0.4124 0.5096 9.04

0.4075 0.5292 8.93

0.4163 0.5502 8.83

0.4241 0.5728 8.74

675.30

718.98

757.05

797.81

841.53

0.1126 0.4932 0.001 9.49

0.1456 0.5207 0.003 9.36

0.1683 0.5490 0.002 9.23

0.1907 0.5766 0.004 9.12

0.2177 0.6036 0.003 9.01

0.2431 0.6298 0.003 8.93

667.18

714.82

764.45

814.13

863.81

913.24

0.0849 0.5231 0.003 9.68

0.1175 0.5540 0.005 9.53

0.1510 0.5860 0.008 9.39

0.1863 0.6188 0.007 9.27

0.2197 0.6499 0.004 9.17

0.2539 0.6804 0.003 9.09

698.61

750.81

805.66

862.75

918.55

974.45

0.5168 0.5811 9.16

0.5144 0.5981 9.04

0.5008 0.6132 8.93

0.5081 0.6336 8.83

0.4970 0.6489 8.74

806.37

842.25

875.76

917.37

952.21

0.2716 0.6212 0.005 9.36

0.2945 0.6500 0.003 9.23

0.3156 0.6784 0.009 9.12

0.3357 0.7063 0.011 9.01

0.3640 0.7330 0.007 8.93

Glycine in water [32] 10  A/kg1/2mol1/2 B/kgmol1 1 Dl
# 1 /kJmol ) 1 Dl
# 2 /kJmol )

Glycine in 2.5% aqueous-mannose d-mannose 0.3196 10  A/kg1/2mol1/2 B/kgmol1 0.1888 10  r for Eq. (15) 0.004 9.49 Dl
# /kJmol1) 1

1 Dl
# 2 /kJmol )

Glycine in 5% aqueous-mannose 10  A/kg1/2mol1/2 B/kgmol1 10  r for Eq. (15) 1 Dl
# 1 /kJmol ) 1 Dl
# 2 /kJmol )

L-Alanine in 1/2

water [32] 10  A/kg mol1/2 B/kgmol1

1 Dl
# 1 /kJmol ) 1 Dl
# 2 /kJmol )

L-Alanine in 1/2

2.5% aqueous mannose 0.1856 10  A/kg mol1/2 B/kgmol1 0.2891 10  r for Eq. (15) 0.001
# 9.49 Dl /kJmol1) 1

1 Dl
# 2 /kJmol )

L-Alanine in 1/2

5% aqueous mannose mol1/2

10  A/kg B/kgmol1 10  r for Eq. (15)

1 Dl
# 1 /kJmol ) 1 Dl
# 2 /kJmol )

L-Valine

in water [32] 10  A/kg1/2mol1/2 B/kgmol1

1 Dl
# 1 /kJmol ) 1 Dl
# 2 /kJmol )

L-Valine

in 2.5% aqueous-mannose 10  A/kg1/2mol1/2 B/kgmol1 10  r for Eq. (15)

1 Dl
# 1 /kJmol ) 1 Dl
# 2 /kJmol )

L-Valine

in 5% aqueous-mannose 10  A/kg1/2mol1/2 B/kgmol1 10  r for Eq. (15)

1 Dl
# 1 /kJmol ) 1 Dl
# 2 /kJmol )

L-Isoleucine 1/2

in water [32] 10  A/kg mol1/2 B/kgmol1

1 Dl
# 1 /kJmol ) 1 Dl
# 2 /kJmol )

L-Isoleucine 1/2

in 2.5% aqueous-mannose 0.2449 10  A/kg mol1/2 B/kgmol1 0.5928 10  r for Eq. (15) 0.006 9.49 Dl
# /kJmol1) 1

347

A.K. Nain / J. Chem. Thermodynamics 98 (2016) 338–352 Table 8 (continued) Property

T(K)

1 Dl
# 2 /kJmol )

293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

318.15 K

800.01

850.88

903.42

956.22

1009.33

1061.52

0.2635 0.6499 0.003 9.53

0.2929 0.6820 0.005 9.39

0.3204 0.7140 0.004 9.27

0.3498 0.7431 0.006 9.17

0.3787 0.7733 0.007 9.09

L-Isoleucine in 5% aqueous-mannose 0.2276 10  A /kg1/2mol1/2 B /kgmol1 0.6161 10  r for Eq. (15) 0.004 9.68 Dl
# /kJmol1) 1

1 Dl
# 2 /kJmol )

821.20

879.12 3

The standard uncertainties are s(A) = ±2.0  10

1/2

kg

1/2

mol

936.15

, s(B) = ±2.0  10

2

993.94 , s(Dl

1

kgmol


# 1 )

11

0.80

10

0.75

7 6

3

8

0.65 0.60 0.55

(a)

5

= ± 0.2 kJmol

1

1048.90 and s(Dl


# 2 )

0.45

0

1

2

3

4

0

5

1

2

4

5

1.65

11

1.60

7 6

(b)

3

8

1.55 1.50

o

9

1.45

6

10 .V φ,tr /m mol−1

10

105.V φo /m3 mol−1

3

nc

nc

1.40

(d)

1.35

5

1.30

4 0

1

2

3

4

5

0

1

Fig. 1. Variations of limiting apparent molar volume, V
/ vs. number of carbon atoms in the alkyl side chain, nc for glycine/L-alanine/L-valine/L-isoleucine, in (a) 2.5% mannose + water and (b) 5% D-mannose + water at temperatures, T/K = 293.15, r; T/K = 298.15, j; T/K = 303.15, ▲; T/K = 308.15, h; T/K = 313.15, D; T/K = 318.15, s.

where h and N are Planck’s constant and Avogadro number, respectively. Eq. (16) rearranges to give free energy of activation per mole of the solute, Dl
# 2

¼ Dl


# 1

!
 RT  1000B  V
1  V
2 þ V
1

ð18Þ


# The values of Dl
# 1 and Dl2 are included in Table 8.

3.7. Analysis of group contribution of amino acids

# The variation of values of V
/ , V
/;tr , K

of s;/ , K s;/;tr , B and Dl2 amino acids vs. the number of carbon atoms in alkyl chain, nc for

2

3

4

5

nc

nc

Dl

.

(c)

0.50

4


# 2

= ±0.2 kJmol

1106.31 1

0.70

o

9

6

10 .V φ,tr /m mol−1

105.V φo /m3 mol−1

a

Fig. 2. Variations of transfer limiting apparent molar volume, V
/;tr vs. number of carbon atoms in the alkyl side chain, nc for glycine/L-alanine/L-valine/L-isoleucine, in (a) 2.5% mannose + water and (b) 5% D-mannose + water at temperatures, T/ K = 293.15, r; T/K = 298.15, j; T/K = 303.15, ▲; T/K = 308.15, h; T/K = 313.15, D; T/K = 318.15, s.

glycine/L-alanine/L-valine/L-isoleucine in aqueous-D-mannose solutions are shown graphically in Figs. 1–6. These plots were found to vary linearly with nc at a given temperature. The linear relation is represented by the following equation

D ¼ DðNHþ3 ; COO Þ þ nc DðCH2 Þ

ð19Þ

where D is V
/ or V
/;tr or K
s;/ or K
s;/;tr or B or Dl
# 2 ; and  DðNHþ 3 ; COO Þ and DðCH2 Þ are zwitterionic end groups and methylene group contributions to D, respectively. The number of carbon atoms in the alkyl side chains of homologous series of a-amino acids investigated in the present study are 0 (Gly), 1 (Ala), 3 (Val) and 4 (Ile). The values of DðCH2 Þ obtained by this procedure

348

A.K. Nain / J. Chem. Thermodynamics 98 (2016) 338–352

0.60

o

5

-3.0

(a)

-3.5

0.30

(c)

11

11

o

0.45

5

10 .K s,φ,tr /m N−1 mol−1

1

-2.5

10 .K s,φ /m N− mol−

-2.0

1

-1.5

0.15

-4.0

0

1

2

3

4

5

0

1

2

nc

5

0.45

5

5

o

-3.0

11

(b)

-3.5

0.30

(d)

11

o

4

0.60

10 .K s,φ,tr /m N−1 mol−1

1

-2.5

10 .K s,φ /m N− mol−

1

-1.5 -2.0

3 nc

-4.0

0.15

0

1

2

3

4

5

nc

1

2

3

4

5

nc

Fig. 3. Variations of limiting apparent molar compressibility, K
s;/ vs. number of carbon atoms in the alkyl side chain, nc for glycine/L-alanine/L-valine/L-isoleucine, in (a) 2.5% mannose + water and (b) 5% D-mannose + water at temperatures, T/ K = 293.15, r; T/K = 298.15, j; T/K = 303.15, ▲; T/K = 308.15, h; T/K = 313.15, D; T/K = 318.15, s.

characterize the mean contribution of CH and CH3 groups to D of the a-amino acids. The contributions of the other alkyl chain of these a-amino acids are calculated by the method given in the literature [40,41]

DðCH3 Þ ¼ 1:5DðCH2 Þ

ð20Þ

DðCHÞ ¼ 0:5DðCH2 Þ

ð21Þ

The values of group contributions of glycine/L-alanine/L-valine/ L-isoleucine

0

in aqueous-D-mannose solutions are given in Table 9.

4. Discussion A perusal of Table 5 reveals that the V
/ values are positive and Sv values are also positive but the Sv values is smaller in magnitude than the values of V
/ for glycine/L-alanine/L-valine/L-isoleucine in aqueous-D-mannose solutions indicating the presence of strong solute–solvent interactions and weak solute–solute interactions in these systems. The V
/ values increase with increase in concentration of D-mannose. The trends observed in V
/ values may be due to their hydration behavior [42–45], which mainly comprises of three type of interactions in these systems: (a) The terminal groups of zwitterions of amino acids, NH+3 and COO are hydrated in an electrostatic manner whereas, hydration of R group depends on its nature, which may be hydrophilic, hydrophobic or amphiphilic; (b) electrostriction of NH+3 group is 10 times greater than

Fig. 4. Variations of transfer limiting apparent molar compressibility, K
s;/;tr vs. number of carbon atoms in the alkyl side chain, nc for glycine/L-alanine/L-valine/Lisoleucine, in (a) 2.5% mannose + water and (b) 5% D-mannose + water at temperatures, T/K = 293.15, r; T/K = 298.15, j; T/K = 303.15, ▲; T/K = 308.15, h; T/ K = 313.15, D; T/K = 318.15, s.

COO group; and (c) the overlap of hydration co-spheres of terminal NH+3 and COO groups and of adjacent groups results in volume change. The V
/ values increase due to reduction in the electrostriction at terminals, whereas it decreases due to disruption of side group hydration by that of the charged end. The V
/ values (Table 5) increase with increase in temperature for these amino acids in aqueous-D-mannose solutions, which can be explained by considering the size of primary and secondary solvation layers around the zwitterions. At higher temperatures the solvent molecules from the secondary solvation layer of amino acid zwitterions are released into the bulk of the solvent, resulting in the expansion of the solution, as inferred from larger V
/ values at higher temperatures [46,31,47]. The V
/ values increase with the increase in the molar mass of the amino acids, from glycine to L-isoleucine, due to increase in hydrophobic character of the side chain. Thus, the order of increase of V
/ values is gly < ala < val < ile. The values of K
s;/ are negative (Table 6) for glycine/L-alanine/Lvaline/L-isoleucine in aqueous-D-mannose solutions, indicating that the water molecules around ionic charged groups of amino acids are less compressible than the water molecules in the bulk solution [48,49]. This shows that there exist strong solute–solvent interactions in these systems. The values of K
s;/ increase with increase in temperature indicating release of more water molecules from the secondary solvation layer of amino acid zwitterions into the bulk, thereby making the solution more compressible.

349

A.K. Nain / J. Chem. Thermodynamics 98 (2016) 338–352

0.75

1100 1000

1

900

0.55

Δμ 2 /kJ.mol−

0.45

o#

B /kg∙mol−1

0.65

0.35

(a)

800 700 600 500

(a)

400

0.25

300 200

0.15 0

1

2

nc

3

4

0

5

1

2

3

4

5

nc 1150

0.80

1050 950 1

Δμ 2 /kJ.mol−

0.50

o#

B /kg∙mol−1

0.65

(b)

850 750 650 550

(b)

450

0.35

350 250 0

0.20 0

1

2

nc

3

4

5

Fig. 5. Variations of Jones–Dole coefficient, B vs. number of carbon atoms in the alkyl side chain, nc for glycine/L-alanine/L-valine/L-isoleucine, in (a) 2.5% mannose + water and (b) 5% D-mannose + water at temperatures, T/K = 293.15, r; T/ K = 298.15, j; T/K = 303.15, ▲; T/K = 308.15, h; T/K = 313.15, D; T/K = 318.15, s.

Table 5 indicates that V
/ of glycine/L-alanine/L-valine/Lisoleucine in aqueous-D-mannose are more than those in pure water [32], i.e., V
/;tr values are positive. Moreover, these V
/;tr values increase with increase in D-mannose concentration. In general, the interactions occurring between amino acid (glycine/L-alanine/Lvaline/L-isoleucine) and D-mannose can be categorized into following three types [44,45] (a) The hydrophilic–ionic interaction between OH groups of Dmannose and zwitterions of amino acid. (b) Hydrophilic–hydrophobic group interaction between the OH groups of D-mannose molecule and non-polar (–CH2) in side chain of amino acid molecules. (c) Hydrophobic–hydrophobic group interactions between the non-polar groups of D-mannose and non-polar (–CH2) in side chain of amino acid molecules. The V
/ values increase due to reduction in the electrostriction at terminals by positive contribution from the interactions of type (a), whereas it decreases due to disruption of side group hydration by that of the charged end by negative contribution from the interactions of type (b) and (c) mentioned above. The observed positive V
/;tr values suggest that the hydrophilic–ionic group interactions dominate over hydrophilic–hydrophobic group and hydrophobic– hydrophobic group interactions in these systems. The K
s;/;tr values for glycine/L-alanine/L-valine/L-isoleucine from water to aqueous-D-mannose solutions are included in Table 6.

1

2

3

4

5

nc Fig. 6. Variations of free energies of activation of viscous flow per mole of solute, Dl
# 2 vs. number of carbon atoms in the alkyl side chain, nc for glycine/L-alanine/Lvaline/L-isoleucine, in (a) 2.5% mannose + water and (b) 5% D-mannose + water at temperatures, T/K = 293.15, r; T/K = 298.15, j; T/K = 303.15, ▲; T/K = 308.15, h; T/ K = 313.15, D; T/K = 318.15, s.

Table 6 indicates that K
s;/ values of glycine/L-alanine/L-valine/Lisoleucine in aqueous-D-mannose are more than that in pure water [32], i.e., K
s;/;tr values are positive and increase with increase in the concentration of D-mannose. The observed positive K
s;/;tr values suggest that the hydrophilic–ionic groups interactions dominate in these systems. The observed trends in K s;/ and K
s;/;tr further support the conclusions drawn from V
/ and V
/;tr . The decrease in V
/;tr and increase in K
s;/;tr values with increase in temperature, indicate that release of water molecules from the secondary solvation layer of amino acid zwitterions into the bulk, becomes difficult with addition of D-mannose in the solution due to greater hydrophilic–ionic groups interactions as compared to those in water. A close perusal of Table 7 reveals that nH values [50] for glycine/ L-alanine/L-valine/L-isoleucine in aqueous-D-mannose solutions calculated from Eqs. (13) and (14) are less than that in water [32] and these nH values further decrease with increase in D-mannose concentration, which indicates an increase in soluteco-solute (amino acid–D-mannose) interaction with the increase in D-mannose concentration. These trends in nH values further support our earlier conclusions regarding the behavior of these systems from values of V
/ , V
/;tr , K
s;/ and K
s;/;tr . The values of A- and B-coefficients (Table 8) are positive, however, the A-coefficients are much smaller in magnitude as compared to B-coefficients, suggesting weak solute–solute and strong solute–solvent interactions in these solutions. However, the B-coefficients values are larger in 5% aqueous-D-mannose than

350

A.K. Nain / J. Chem. Thermodynamics 98 (2016) 338–352

Table 9 Contributions of (NH+3, COO) and (CH2) groups to the limiting apparent molar volume, V
/ , transfer limiting apparent molar volume, V
/;tr , limiting apparent molar compressibility, K
s;/ , transfer limiting apparent molar compressibility, K
s;/;tr , Jones–Dole coefficient, B, and free energies of activation of viscous flow per mole of solute, Dl
# 2 for for glycine/Lalanine/L-valine/L-isoleucine in D-mannose + water (2.5% and 5% D-mannose, w/w in water) solutions at temperatures (293.15–318.15) K.a Property

T(K) 293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

318.15 K

105  V
/ /(m3mol1) water [32] (NH+3, COO) (CH2)

4.385 1.548

4.404 1.549

4.424 1.549

4.443 1.548

4.459 1.550

4.475 1.551

2.5% D-mannose (NH+3, COO) (CH2)

4.452 1.551

4.467 1.551

4.483 1.552

4.500 1.551

4.512 1.553

4.525 1.554

5% D-mannose (NH+3, COO) (CH2)

4.533 1.551

4.548 1.552

4.565 1.552

4.582 1.551

4.594 1.553

4.607 1.554

106  V
/;tr /(m3mol1) 2.5% d-mannose (NH+3, COO) (CH2)

0.662 0.026

0.628 0.026

0.593 0.028

0.561 0.029

0.531 0.031

0.502 0.031

5% D-mannose (NH+3, COO) (CH2)

1.476 0.030

1.445 0.030

1.411 0.031

1.380 0.031

1.351 0.030

1.324 0.029

4.041 0.362

3.935 0.352

3.821 0.344

3.720 0.345

3.621 0.323

1011  K
s;/ /(m5N1mol1) water [32] (NH+3, COO) (CH2) 2.5% D-mannose (NH+3, COO) (CH2)

3.953 0.423

3.821 0.418

3.700 0.410

3.511 0.406

3.547 0.399

3.343 0.391

5% D-mannose (NH+3, COO) (CH2)

3.685 0.421

3.547 0.414

3.416 0.404

3.282 0.396

3.163 0.389

3.043 0.379

1011  K
s;/;tr /(m5N1mol1) 2.5% d-mannose (NH+3, COO) (CH2)

0.206 0.025

0.220 0.026

0.236 0.028

0.250 0.029

0.263 0.031

0.278 0.031

5% D-mannose (NH+3, COO) (CH2)

0.474 0.051

0.494 0.052

0.519 0.052

0.539 0.052

0.557 0.055

0.578 0.056

0.1466 0.1102

0.1590 0.1124

0.1687 0.1145

0.1769 0.1180

0.1845 0.1211

B/(kgmol1) water [32] (NH+3, COO) (CH2) 2.5% D-mannose (NH+3, COO) (CH2)

0.1885 0.1012

0.2140 0.1019

0.2406 0.1025

0.2564 0.1034

0.2900 0.1043

0.3142 0.1049

5% d-mannose (NH+3, COO) (CH2)

0.2503 0.0911

0.2805 0.0918

0.3129 0.0918

0.3469 0.0913

0.3792 0.0906

0.4101 0.0905

210.33 151.25

230.59 156.57

247.44 161.87

262.56 169.26

277.06 176.05

1 Dl
# 2 /(kJmol ) water [32] (NH+3, COO) (CH2)

2.5% D-mannose (NH+3, COO) (CH2)

260.92 134.97

299.29 138.11

340.19 141.03

379.68 144.42

419.67 147.71

460.07 150.70

5% d-mannose (NH+3, COO) (CH2)

339.34 120.00

384.92 122.79

434.62 124.66

487.75 125.97

539.74 126.80

591.00 128.45

a The standard uncertainties are s(V
/ ) = ±2.0  108 m3mol1, s(V
/;tr ) = ±2.0  108 m3mol1, s(K
s;/ ) = ±2.0  1014 m5N1mol1, s(K
s;/;tr ) = ±2.01014 m5N1mol1, s(B) 1 = ±2.0  102 kgmol1 and s(Dl
# 2 ) = ±0.2 kJmol .

those in the 2.5% aqueous-D-mannose solvents due to increased greater hydrophilic–ionic group interactions. B-coefficients values increase with increasing concentration of D-mannose, indicate a solution structure which allow the co-solute (D-mannose) to act on solvent [5]. B-coefficients increase (Table 8) when the water is replaced by D-mannose, i.e., D-mannose act as water structuremaker by hydrogen bonding. The increase in B-coefficients (Table 8) with increasing concentration of D-mannose may be due to the fact that the friction increases to prevent water flow at increased Dmannose concentration. Thus, the values of coefficients A and B

support the behaviors of V
/ , K
s;/ , Sv, Sk, V
/;tr and K
s;/;tr , which suggested stronger solute–solvent interactions as compared to solute– solute interactions in these solutions. The temperature derivatives of B-coefficient, (dB/dT) have also been calculated. The sign of dB/ dT values is found to provide important information regarding structure-making or structure-breaking ability of the solute in solvent media [37,38,51]. In general, the dB/dT is negative for structure-maker and positive for structure-breaker solutes in solution. The positive dB/dT values for glycine/L-alanine/L-valine/Lisoleucine in aqueous-D-mannose solvents indicate that these

A.K. Nain / J. Chem. Thermodynamics 98 (2016) 338–352

amino acids act as structure-breaker in aqueous-D-mannose solvents under study. A close perusal of Table 8 reveals that the Dl
# 2 values for glycine/L-alanine/L-valine/L-isoleucine in water and in aqueous-Dmannose solutions, are positive and much larger than those of Dl
# 1 . This suggests that the interactions between amino acid and solvent (aqueous-D-mannose) molecules in the ground state are stronger than in the transition state [35,36]. Hence in the transition state, the solvation of the solute molecules is less favored in Gibbs
# energy terms. Also, the values of Dl
# 1 and Dl2 for these amino acids in aqueous-D-mannose solvents are larger than those in water [32] and these values increase with increase in concentration of D-mannose in solution (Table 8). This further supports the existence of strong solute–solvent (hydrophilic–ionic group) interactions in these systems, which increase with increase in D-mannose

concentration leading to an increase in the friction pre-

venting water flow. The Dl
# 2 values increase with increase in temperature, indicating that solute–solvent interaction increase making the flow of solute molecules difficult. It has been reported
# [35,36], Dl
# for solutes with positive viscosity B2 > Dl 1 coefficients indicates stronger solute–solvent interactions in the ground state than in the transition state, i.e., the formation of transition state is accompanied by the rupture/ distortion of intermolecular forces in the solvent structure. Thus, the conclusions drawn from Dl
# are in agreement with those drawn from V
/ , 2


V /;tr , K s;/ , K s;/;tr and B values. Figs. 1–6 indicate that the values of V
/ , V
/;tr , K
s;/ , K
s;/;tr , B and

Dl
# 2 increases almost linearly with increase in number of carbon atoms, nc in the alkyl chain of the amino acids [52]. It is observed from Table 9 that the contributions of (NH+3,COO) to V
/ are more than that of (CH2) in side chain of amino acids. The contribution V
/ (NH+3,COO) increase on addition of D-mannose to water [32] and further increase with increase in concentration of D-mannose. The V
/ (NH+3,COO) increase with increase in temperature. In contrast, V
/ (CH2) is almost insensitive to changes in the temperature. The contribution V
/;tr (NH+3,COO) increase on addition of D-mannose to water and further increase with increase in concentration of D-mannose. The V
/;tr (NH+3,COO) decrease with increase in temperature, whereas V
/;tr (CH2) do not vary much with temperature. The variations of V
/ (NH+3,COO) and V
/;tr (NH+3,COO) with concentration of D-mannose indicate that the interactions between  + D-mannose molecule and charged end groups (NH3,COO ) of amino acids, i.e., the hydrophilic–ionic interaction between OH groups of D-mannose and zwitterions of amino acid are stronger than hydrophilic–hydrophobic interactions between the OH groups of D-mannose molecule and non-polar alkyl side chain of amino acids and these interactions are stronger in 5% aqueous-D-mannose than in 2.5% aqueous-D-mannose. It is seen from Table 9 that the contributions of (NH+3,COO) to K
s;/ and K
s;/;tr are less than that of (CH2) in side chain of amino acids. The K
s;/ (NH+3,COO) and K
s;/;tr (NH+3,COO) increase with increase in temperature; however, K
s;/ (CH2) and K
s;/;tr (CH2) is almost insensitive to increase in the temperature. It is observed from Table 9 that the contribution K
s;/ (NH+3,COO) and K
s;/;tr (NH+3,COO) increase on addition of D-mannose to water [32] and further increase with increase in concentration of D-mannose. This indicates that the interactions between D-mannose and charged end groups (NH+3,COO) of amino acids are much stronger than those between the D-mannose and alkyl chain of amino acids. A similar conclusion was obtained for amino acids in aqueous magnesium chloride [52], in aqueous calcium chloride [53] and in aqueous cetyltrimethylammonium bromide [54] solutions.

351

It is seen from Table 9 that the contributions of (NH+3,COO) to B and Dl
# 2 are more than those due to (CH2) in side chain of amino acids. The contributions of (NH+3,COO) and (CH2) groups to B and Dl
# increase on addition of D-mannose to water and further 2 increase with increase in concentration of D-mannose. It is observed that the contribution B(NH+3,COO) and Dl
# (CH2) 2 increase with increase in temperature, however, the increase in B (CH2) with temperature is much less as compared to those of Dl
# 2 (CH2). This indicates that the hydrophilic–ionic interactions between D-mannose molecule and charged end groups (NH+3,COO) of the amino acids are stronger than hydrophilic–hydrophobic interactions between the D-mannose molecule and alkyl chain of amino acids. Thus, the conclusions drawn from group contribution to values of B and Dl
# 2 are in agreement with those drawn from the group contributions to V
/ , V
/;tr , K
s;/ and K
s;/;tr values. 5. Conclusions The densities, q, ultrasonic speeds, u, and viscosities, g of solutions of glycine/L-alanine/L-valine/L-isoleucine in aqueous-Dmannose solvents (2.5% and 5% D-mannose, w/w in water) were measured at different temperatures. From the experimental values, various parameters, viz., V / , V
/ , K s;/ , K
s;/ , V
/;tr , K
s;/;tr , nH , Falken
# hagen coefficient A, Jones–Dole coefficient B, Dl
# 1 , Dl2 and dB/ dT were calculated. The results indicate that there exist strong solute–solvent (hydrophilic–ionic group) interactions in these systems which increase with increase in D-mannose concentration. It is also observed that these amino acids act as structure-breaker in these aqueous-D-mannose solvents. The groups’ contributions of amino acids to V
/ , V
/;tr , K
s;/ , K
s;/;tr , B and Dl
# 2 also indicates that the hydrophilic–ionic interactions between OH groups of Dmannose and charged end groups (NH+3,COO) of the amino acids are stronger than hydrophilic–hydrophobic interactions between OH groups of d-mannose and non-polar alkyl chain of amino acids.

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JCT 15-897