Volumetric and Viscometric Studies of Amino Acids in Mannitol

Article pubs.acs.org/jced

Volumetric and Viscometric Studies of Amino Acids in Mannitol Aqueous Solutions at T = (293.15 to 323.15) K Xiaofen Ren, Chunying Zhu,* and Youguang Ma State Key Laboratory of Chemical Engineering, Collaborative Innovation Center of Chemical Science and Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, P. R. China S Supporting Information *

ABSTRACT: Densities and viscosities of glycine, L-alanine, Lvaline, L-threonine, and L-arginine in aqueous solutions of (0.0, 0.2, 0.4, 0.6, 0.8, and 1.0) mol·kg−1 mannitol have been measured in the temperature range of (293.15 to 323.15) K under atmospheric pressure; then the measured densities and viscosities of experimental systems were correlated. These data were further used to calculate the apparent molar volumes (Vφ), the limiting partial molar volumes (Vφ0), the limiting partial molar volumes of transfer (ΔtrVφ0), the viscosity Bcoefficients, and the free energies of activation per mole of solvent (Δμ10≠) and solute (Δμ20≠). The results were interpreted through solute−solute interaction and solute− solvent interaction on the basis of the cosphere overlap model and transition state theory.

1. INTRODUCTION Proteins are of vital significance in the processes and phenomena of life regardless of the lower organisms or higher organisms. As is well-known, the natural surroundings of proteins are usually some complex solutions instead of pure water. In general, the structure of protein is considerably complicated, up to now, it remains still quite far from fully understanding the molecular interactions among proteins. Amino acid, as a basic unit of protein,1,2 is considered to be the most important protein model compound.3−9 The understanding of the structure and property of amino acid is a prerequisite to further realize the structure, property, and biological function of protein. The functional sugar alcohol, as one of the important derivatives of sugar, has been widely used in the food, pharmacy, and chemical industries. Mannitol ((2R,3R,4R,5R)hexane-1,2,3,4,5,6-hexol) is clinically used as osmotic antihypertensive drugs in the treatment of brain trauma; meanwhile, it is also utilized as a diuretic. Moreover, mannitol has been frequently used as an artificial nutritive sweetener owing to its low calorie and small effect on blood sugar level.10 Many studies have shown that sugar alcohol can not only stabilize the natural conformation of spherical protein but also remarkably affect the solubility and denaturalization of protein and their folding/unfolding behavior.11,12 By means of the researches on the volumetric and viscometric properties of amino acids in the sugar alcohols aqueous solutions, we could obtain some necessary information about interactions of the solute−solute and solute−solvent and then clearly understand the mechanism of the protein stability through sugar alcohols. However, the limited data about the volumetric and viscometric properties of © 2015 American Chemical Society

amino acids in the sugar alcohols aqueous solutions could be found in the literature. Jha and Kishore13 presented apparent molar volumes, apparent molar isentropic compressibilities, and enthalpies of dilution of aqueous glycine, alanine, α-amino butyric acid, valine, and leucine in sorbitol aqueous solutions at 298.15 K. Qiu et al.14 reported the transfer enthalpies of amino acids and glycine peptides from water to aqueous solutions of sugar alcohol at 298.15 K. Wang et al.15 studied the densities of solutions of glycine, L-alanine, L-serine and L-threonine in D-mannitol aqueous solutions. In this work, the densities and viscosities of glycine, L-alanine, L-valine, L-threonine, and L-arginine in aqueous mannitol solutions of (0.0, 0.2, 0.4, 0.6, 0.8, and 1.0) mol·kg−1 at T = (293.15, 303.15, 313.15, and 323.15) K were systematically measured. The apparent molar volume (Vφ), transfer partial molar volume (ΔtrVφ0), viscosity B-coefficients, and the free energies of activation per mole of solvent (Δμ10≠) and solute (Δμ20≠) were calculated from the experimental densities and viscosities and discussed based on the cosphere overlap model and transition state theory.

2. EXPERIMENTAL SECTION 2.1. Chemicals. Mannitol, glycine, L-alanine, L-valine, L-threonine, and L-arginine are analytical-grade reagents; more specific details have been given in Table 1. The distilled water with a conductivity 2.45 μS·cm−1 at 293.15 K was used to prepare solutions at room temperature by mass using an electronic balance (FA2204B, Shanghai Jingke, China) with an Received: December 30, 2014 Accepted: May 18, 2015 Published: June 2, 2015 1787

DOI: 10.1021/je501178z J. Chem. Eng. Data 2015, 60, 1787−1802

Journal of Chemical & Engineering Data

Article

Table 1. Specification of Studied Chemicals chemical name mannitol glycine L-alanine L-valine L-threonine L-arginine a

mass fractiona ≥ ≥ ≥ ≥ ≥ ≥

0.99 0.995 0.99 0.99 0.99 0.98

molar mass (g·mol−1)

source

182.17 75.07 89.09 117.15 119.13 174.20

Aladdin Aladdin Aladdin Aladdin Aladdin Aladdin

Chemical Chemical Chemical Chemical Chemical Chemical

Reagent Reagent Reagent Reagent Reagent Reagent

CAS No. Co., Co., Co., Co., Co., Co.,

Ltd. Ltd. Ltd. Ltd. Ltd. Ltd.

69-65-8 56-40-6 56-41-7 72-18-4 72-19-5 74-79-3

Declared by the supplier.

From Table 2, the densities increase monotonously with increasing the molalities of amino acids and mannitol aqueous solutions. The comparisons of densities for glycine, L-alanine, and L-threonine in mannitol aqueous solutions with the literature values15 are depicted in Figure 1. Clearly, the variation tendencies of densities are in accord with the literature values. When the temperature rises, the intermolecular distance increase correspondingly, which leads to the decrease of densities. The densities of ternary solutions were fitted using the following equation:

uncertainty of 0.0001 g, and the uncertainty of the molality is 0.0001 mol·kg−1. 2.2. Density Measurements. The density of all solutions were measured at atmosphere pressure using a vibrating tube densimeter (Anton Paar DMA 4500 M, Austria), and the temperature was automatically controlled within ± 0.03 K by two integrated Pt100 platinum thermometers with built-in Peltier elements. The densimeter was calibrated by the deionized water and dry air, and after each measurement, the distilled-water and anhydrous ethanol were used to clean the vibrating tube automatically. Triplicate measurements of each sample were conducted to obtain the average value of density. The uncertainty in density measurement is 5·10−5 g·cm−3. 2.3. Viscosity Measurements. The viscosity measurements of amino acids in mannitol aqueous solutions at T = (293.15 to 323.15) K with an interval of 10 K were carried out using an iVisc capillary viscometer (LAUDA, Germany), and the Ubbelohde capillary (1834A) with 0.53 mm diameter was supplied by Shanghai Glass Instruments Factory of China. The thoroughly cleaned and perfectly dried Ubbelohde capillary was vertically placed in a Lauda Eco Sliver thermostat with an uncertainty of 0.05 K. The flow time of the measured solutions was detected by the infrared automatically with an uncertainty of 0.01 s. An average of at least four sets of flow time with a deviation of 0.2 s was taken for each sample at the required temperature. Since all flow times were greater than 100 s, the kinetic energy and the end corrections were found to be negligible. The viscosity η of all solutions was calculated by the following equation:16

η ρt = ηw ρw tw

ρ = A1 + A 2 T + A3ma + A4 mb

(2)

where ma is the molality of amino acids, mb (mb > 0) is the molality of mannitol, T is the temperature, and A1, A2, A3, and A4 are the empirical constants. The correlation coefficients of five amino acids in mannitol aqueous solutions by eq 2 are listed in Table 3 along with the values of standard deviation and the absolute average relative deviation. The standard deviation (SD) and the absolute average relative deviation (AARD) were calculated by the following equation, respectively. n

SD = [∑ (yexp, i − ycal, i )2 /(n − k − 1)]1/2 i=1

AARD =

1 n

n

∑ i=1

(3)

yexp, i − ycal, i yexp, i

(4)

where n is the total number of experimental points and k is the number of parameters. yexp,i and ycal,i refer to the experimental values and the calculated values from eq 2, respectively. From Table 3, it could be seen that the maximum values of AARD and SD are 0.06 % and 0.0008 g·cm−3, respectively, which indicates that eq 2 is quite satisfying in correlating densities data of amino acids + mannitol + water solutions. The apparent molar volume, Vφ (cm3·mol−1), could be calculated from ρ using the following relation:19

(1)

where η, ρ, t and ηw, ρw, tw are viscosity, density, and flow time of the solution and water, respectively. The viscosity of water was obtained from the ref 17. The uncertainty in viscosity value is 1 %.

Vφ =

3. RESULTS AND DISCUSSION 3.1. Volumetric Properties. The experimental densities for glycine, L-alanine, L-valine, L-threonine and L-arginine at mb = (0.0, 0.2, 0.4, 0.6, 0.8, and 1.0) mol·kg−1 aqueous mannitol solutions at T = (293.15, 303.15, 313.15, and 323.15) K are given in Table 2. The comparison figures of the experimental densities and viscosities for amino acids and mannitol in water with the literature values3−9,18 are shown in the Supporting Information (Figure S1 to Figure S6). The Figures S1 to S6 show that the experimental densities and viscosities agree well with the literature values.

1000(ρ − ρ0 ) M − ρ mρρ0 −1

(5) −1

where M (g·mol ) and m (mol·kg ) are the molar mass and the molality of amino acids, respectively. ρ and ρ0 (g·cm−1) are the densities of the solution and solvent (mannitol aqueous solution). The values of apparent molar volume (Vφ) are listed in Table 2. From the overall comparison, the values of Vφ of five amino acids increase in the order: glycine < L-alanine < L-threonine < L-valine < L-arginine. From the values of Vφ and ma, we could find that the Vφ displays a good linear function of the molality at all experimental temperatures. The apparent molar volume (Vφ) of L-threonine in 0.2 mol·kg−1 mannitol aqueous solutions 1788


C

mol·L−1

0.0000 0.0996 0.1979 0.2959 0.3926 0.4887 0.5838 0.6780

0.0000 0.1006 0.2001 0.2993 0.3972 0.4947 0.5910 0.6856

0.0000 0.1019 0.2027 0.3026 0.4018 0.5000 0.5973 0.6937

0.0000 0.1030 0.2049 0.3059 0.4060 0.5053 0.6034 0.7009

ma

mol·kg−1

0.0000 0.1002 0.2000 0.3002 0.4001 0.5001 0.6000 0.6998

0.0000 0.1000 0.1998 0.3000 0.4000 0.5003 0.6004 0.6994

0.0000 0.1001 0.2001 0.3000 0.4000 0.5000 0.6000 0.7000

0.0000 0.1001 0.2001 0.3001 0.4001 0.5001 0.5999 0.7001

ρ

1789

1.03343 1.03652 1.03955 1.04252 1.04543 1.04829 1.05109 1.05384

1.02231 1.02544 1.02851 1.03153 1.03451 1.03742 1.04029 1.04313

1.01052 1.01368 1.01679 1.01988 1.02291 1.02590 1.02885 1.03173

0.99819 1.00141 1.00457 1.00770 1.01077 1.01380 1.01678 1.01971

g·cm−3

1.336 1.355 1.376 1.398 1.419 1.441 1.462 1.484

1.221 1.239 1.257 1.275 1.293 1.311 1.329 1.348

1.104 1.119 1.135 1.152 1.169 1.186 1.202 1.218

43.62 43.76 43.90 44.04 44.18 44.32 44.46

43.39 43.50 43.64 43.74 43.87 43.98 44.08

43.20 43.27 43.35 43.43 43.51 43.60 43.68

42.81 42.91 43.01 43.11 43.20 43.30 43.41

1.002017 1.015 1.029 1.042 1.057 1.072 1.086 1.101

Vφ cm3·mol−1

mPa·s

η

T/K = 293.15 ρ

1.03035 1.03338 1.03636 1.03928 1.04216 1.04498 1.04776 1.05049

1.01939 1.02246 1.02549 1.02847 1.03141 1.03431 1.03715 1.03997

1.00782 1.01092 1.01398 1.01700 1.01997 1.02291 1.02581 1.02863

0.99564 0.99880 1.00191 1.00498 1.00800 1.01098 1.01391 1.01680

g·cm−3

Vφ cm3·mol−1

ρ g·cm−3

Glycine in Mannitol Aqueous Solution mb = 0.0 mol·kg−1 0.797517 0.99220 0.809 43.41 0.99532 0.820 43.50 0.99838 0.831 43.60 1.00142 0.842 43.69 1.00440 0.855 43.78 1.00735 0.867 43.88 1.01025 0.878 43.97 1.01311 mb = 0.2 mol·kg−1 0.874 1.00426 0.886 43.83 1.00732 0.899 43.88 1.01033 0.913 43.97 1.01332 0.926 44.05 1.01627 0.939 44.12 1.01918 0.952 44.20 1.02205 0.966 44.28 1.02484 mb = 0.4 mol·kg−1 0.959 1.01574 0.974 43.98 1.01876 0.988 44.06 1.02174 1.003 44.13 1.02467 1.017 44.20 1.02757 1.031 44.29 1.03042 1.045 44.38 1.03322 1.060 44.45 1.03599 mb = 0.6 mol·kg−1 1.044 1.02660 1.060 44.20 1.02959 1.077 44.32 1.03252 1.094 44.43 1.03540 1.110 44.54 1.03824 1.128 44.66 1.04104 1.145 44.77 1.04378 1.162 44.88 1.04649

mPa·s

η

T/K = 303.15

0.841 0.854 0.867 0.881 0.895 0.909 0.923 0.937

0.776 0.788 0.799 0.811 0.823 0.834 0.846 0.858

0.711 0.721 0.732 0.743 0.754 0.765 0.775 0.786

0.653217 0.663 0.672 0.681 0.691 0.701 0.711 0.721

mPa·s

η

T/K = 313.15 Vφ

44.70 44.81 44.90 45.00 45.10 45.19 45.29

44.51 44.56 44.65 44.73 44.80 44.90 44.98

44.30 44.36 44.41 44.46 44.53 44.58 44.66

43.89 43.98 44.06 44.14 44.21 44.30 44.37

cm3·mol−1

ρ

1.02209 1.02503 1.02793 1.03079 1.03362 1.03641 1.03916 1.04187

1.01128 1.01426 1.01721 1.02012 1.02301 1.02586 1.02869 1.03147

0.99996 1.00298 1.00595 1.00891 1.01183 1.01473 1.01759 1.02038

0.98803 0.99111 0.99414 0.99714 1.00009 1.00301 1.00588 1.00872

g·cm−3

0.693 0.704 0.715 0.727 0.738 0.750 0.761 0.773

0.642 0.653 0.662 0.672 0.682 0.692 0.702 0.712

0.592 0.600 0.610 0.619 0.628 0.637 0.647 0.655

0.547117 0.555 0.563 0.571 0.579 0.587 0.596 0.605

mPa·s

η

T/K = 323.15

45.18 45.23 45.30 45.35 45.41 45.46 45.52

44.97 44.99 45.01 45.04 45.07 45.09 45.13

44.76 44.80 44.83 44.86 44.89 44.92 44.95

44.35 44.42 44.49 44.55 44.63 44.69 44.75

cm3·mol−1

Vφ

Table 2. Densities (ρ), Viscosities (η), and Apparent Molar Volumes (Vφ) of Glycine, L-Alanine, L-Valine, L-Threonine, and L-Arginine in Mannitol Aqueous Solutions at Temperature T = (293.15, 303.15, 313.15, and 323.15) K and Pressure p = 101.3 kPaa

Journal of Chemical & Engineering Data Article


0.0000 0.1050 0.2092 0.3120 0.4140 0.5153 0.6151 0.7142

0.0000 0.0992 0.1972 0.2942 0.3901 0.4845 0.5781 0.6702

0.0000 0.1005 0.1997 0.2977 0.3946 0.4903 0.5848 0.6781

0.0000 0.1017

0.0000 0.1001 0.2003 0.3001 0.4001 0.5003 0.6000 0.6999

0.0000 0.1000 0.2000 0.3000 0.4002 0.5001 0.6002 0.6999

0.0000 0.1001 0.2000 0.3001 0.4001 0.5001 0.6000 0.7000

0.0000 0.1001

mol·L

−1

0.0000 0.1041 0.2069 0.3090 0.4101 0.5102 0.6094 0.7078

−1

C

0.0000 0.1001 0.2000 0.3001 0.4001 0.5000 0.6000 0.7000

mol·kg

ma

Table 2. continued

−3

1790

1.02231 1.02505

1.01052 1.01332 1.01608 1.01879 1.02145 1.02408 1.02666 1.02920

0.99819 1.00106 1.00388 1.00666 1.00939 1.01206 1.01469 1.01727

1.05413 1.05715 1.06011 1.06301 1.06586 1.06866 1.07139 1.07407

1.04398 1.04704 1.05004 1.05300 1.05589 1.05874 1.06154 1.06428

g·cm

ρ

1.221 1.250

60.83

60.56 60.62 60.69 60.74 60.80 60.85 60.91

60.24 60.33 60.41 60.49 60.57 60.65 60.73

1.002017 1.027 1.053 1.079 1.107 1.134 1.163 1.191

43.71 43.84 43.96 44.08 44.20 44.31 44.44

43.93 44.07 44.21 44.33 44.46 44.59 44.72

1.104 1.130 1.157 1.184 1.214 1.245 1.277 1.314

−1

cm ·mol 3

Vφ

1.643 1.669 1.695 1.721 1.748 1.774 1.801 1.827

1.494 1.517 1.540 1.565 1.588 1.613 1.637 1.661

mPa·s

η

T/K = 293.15 −3

1.01939 1.02209

1.00782 1.01058 1.01329 1.01597 1.01860 1.02119 1.02374 1.02625

0.99564 0.99848 1.00127 1.00401 1.00671 1.00935 1.01195 1.01450

1.05085 1.05381 1.05672 1.05957 1.06237 1.06513 1.06782 1.07047

1.04088 1.04388 1.04683 1.04973 1.05259 1.05539 1.05814 1.06085

g·cm

ρ −1

−1

cm ·mol 3

Vφ g·cm

ρ −3

mb = 0.8 mol·kg 1.151 1.03692 1.169 44.31 1.03988 1.187 44.41 1.04278 1.206 44.52 1.04565 1.224 44.61 1.04847 1.243 44.71 1.05125 1.263 44.83 1.05400 1.281 44.92 1.05669 mb = 1.0 mol·kg−1 1.262 1.04679 1.283 44.52 1.04970 1.303 44.64 1.05257 1.323 44.76 1.05538 1.344 44.87 1.05815 1.365 44.98 1.06087 1.386 45.09 1.06354 1.407 45.21 1.06617 L-Alanine in Mannitol Aqueous Solution mb = 0.0 mol·kg−1 0.797517 0.99220 0.817 60.66 0.99501 0.837 60.74 0.99776 0.856 60.83 1.00047 0.877 60.91 1.00314 0.897 60.98 1.00576 0.919 61.07 1.00833 0.940 61.14 1.01086 mb = 0.2 mol·kg−1 0.874 1.00426 0.893 61.08 1.00699 0.914 61.12 1.00967 0.934 61.17 1.01232 0.957 61.22 1.01492 0.980 61.27 1.01749 1.006 61.31 1.02002 1.033 61.35 1.02252 mb = 0.4 mol·kg−1 0.959 1.01571 0.981 61.28 1.01837

mPa·s

η

T/K = 303.15

0.775 0.792

0.711 0.726 0.742 0.758 0.775 0.793 0.813 0.833

0.653217 0.668 0.684 0.700 0.715 0.731 0.749 0.765

1.001 1.018 1.034 1.051 1.068 1.084 1.102 1.118

0.917 0.932 0.947 0.961 0.976 0.991 1.007 1.022

mPa·s

η

T/K = 313.15 −1

61.77

61.53 61.58 61.60 61.64 61.67 61.70 61.72

61.11 61.19 61.27 61.34 61.41 61.49 61.55

45.02 45.13 45.23 45.31 45.41 45.51 45.60

44.81 44.88 44.96 45.05 45.11 45.18 45.26

cm ·mol 3

Vφ −3

1.01128 1.01392

0.99996 1.00266 1.00532 1.00795 1.01054 1.01309 1.01561 1.01809

0.98803 0.99081 0.99355 0.99624 0.99890 1.00150 1.00406 1.00658

1.04215 1.04502 1.04785 1.05063 1.05338 1.05610 1.05877 1.06140

1.03228 1.03519 1.03806 1.04089 1.04370 1.04647 1.04920 1.05190

g·cm

ρ

0.642 0.655

0.592 0.603 0.616 0.629 0.642 0.657 0.671 0.686

0.547117 0.559 0.571 0.584 0.596 0.609 0.622 0.635

0.814 0.829 0.842 0.856 0.870 0.883 0.898 0.912

0.752 0.764 0.777 0.789 0.802 0.814 0.827 0.840

mPa·s

η

T/K = 323.15 Vφ

62.15

61.94 61.96 61.98 62.00 62.02 62.04 62.07

61.49 61.55 61.62 61.68 61.73 61.80 61.85

45.53 45.59 45.65 45.71 45.75 45.80 45.86

45.32 45.37 45.41 45.44 45.46 45.51 45.55

cm ·mol−1 3



0.0000 0.1038 0.2062 0.3074 0.4072 0.5058 0.6032 0.6994

0.0000 0.1048 0.2081 0.3103 0.4110 0.5104 0.6087 0.7057

0.0000 0.0990 0.1962 0.2916

0.0000 0.1000 0.2000 0.3001 0.4001 0.5000 0.6000 0.7000

0.0000 0.1000 0.2000 0.3001 0.4000 0.5000 0.6000 0.7000

0.0000 0.1000 0.2001 0.3001

0.0000 0.1028 0.2042 0.3043 0.4033 0.5009 0.5974 0.6927

0.0000 0.1001 0.2001 0.3001 0.4001 0.5001 0.6000 0.7000

mol·L

−1

0.2020 0.3011 0.3991 0.4957 0.5912 0.6857

−1

C

0.2001 0.3000 0.4001 0.5000 0.5999 0.7001

mol·kg

ma

Table 2. continued

−3

1791

0.99819 1.00088 1.00351 1.00608

1.05413 1.05666 1.05915 1.06160 1.06400 1.06636 1.06868 1.07097

1.04398 1.04659 1.04916 1.05168 1.05417 1.05660 1.05901 1.06137

1.03343 1.03611 1.03875 1.04133 1.04387 1.04637 1.04882 1.05124

1.02773 1.03038 1.03298 1.03553 1.03805 1.04052

g·cm

ρ −1

61.58 61.64 61.68 61.74 61.79 61.83 61.88

90.13 90.20 90.26

1.002017 1.044 1.089 1.135

61.24 61.29 61.33 61.38 61.43 61.48 61.51

60.94 61.01 61.08 61.15 61.21 61.27 61.33

60.89 60.94 61.00 61.05 61.11 61.16

cm ·mol 3

Vφ

1.643 1.686 1.730 1.778 1.829 1.881 1.937 1.997

1.494 1.531 1.572 1.614 1.660 1.708 1.756 1.811

1.336 1.368 1.403 1.440 1.481 1.522 1.568 1.612

1.280 1.311 1.343 1.379 1.413 1.453

mPa·s

η

T/K = 293.15 −3

0.99564 0.99829 1.00088 1.00341

1.05085 1.05335 1.05581 1.05824 1.06062 1.06297 1.06529 1.06757

1.04088 1.04345 1.04597 1.04845 1.05090 1.05331 1.05568 1.05801

1.03035 1.03299 1.03558 1.03813 1.04064 1.04311 1.04552 1.04790

1.02474 1.02735 1.02992 1.03245 1.03493 1.03739

g·cm

ρ −1

−1

cm ·mol 3

Vφ g·cm

ρ −3

mb = 0.4 mol·kg 1.004 61.33 1.02099 1.027 61.38 1.02357 1.051 61.43 1.02611 1.078 61.47 1.02861 1.105 61.53 1.03106 1.134 61.57 1.03349 mb = 0.6 mol·kg−1 1.044 1.02660 1.068 61.46 1.02921 1.095 61.51 1.03177 1.123 61.57 1.03429 1.152 61.62 1.03676 1.183 61.67 1.03920 1.215 61.74 1.04161 1.249 61.80 1.04396 mb = 0.8 mol·kg−1 1.151 1.03692 1.178 61.75 1.03945 1.208 61.80 1.04194 1.239 61.85 1.04440 1.272 61.88 1.04682 1.307 61.91 1.04921 1.344 61.94 1.05156 1.381 61.98 1.05388 mb = 1.0 mol·kg−1 1.262 1.04679 1.293 62.00 1.04926 1.326 62.03 1.05169 1.360 62.05 1.05408 1.396 62.08 1.05644 1.435 62.11 1.05877 1.474 62.13 1.06107 1.516 62.16 1.06333 L-Valine in Mannitol Aqueous Solution mb = 0.0 mol·kg−1 0.797517 0.99220 0.829 90.70 0.99481 0.862 90.75 0.99737 0.896 90.82 0.99988

mPa·s

η

T/K = 303.15

0.653217 0.678 0.702 0.728

1.001 1.024 1.049 1.075 1.103 1.130 1.161 1.192

0.917 0.938 0.961 0.984 1.008 1.035 1.062 1.091

0.841 0.859 0.880 0.900 0.922 0.945 0.969 0.994

0.810 0.828 0.847 0.867 0.888 0.909

mPa·s

η

T/K = 313.15 −1

91.29 91.33 91.38

62.46 62.47 62.49 62.51 62.52 62.54 62.55

62.24 62.26 62.28 62.30 62.32 62.35 62.37

61.91 61.97 62.00 62.06 62.11 62.14 62.19

61.81 61.85 61.88 61.92 61.97 62.01

cm ·mol 3

Vφ −3

0.98803 0.99060 0.99311 0.99557

1.04215 1.04459 1.04700 1.04938 1.05172 1.05403 1.05631 1.05855

1.03228 1.03479 1.03726 1.03969 1.04209 1.04446 1.04679 1.04909

1.02209 1.02467 1.02721 1.02971 1.03217 1.03459 1.03698 1.03932

1.01652 1.01908 1.02161 1.02410 1.02655 1.02897

g·cm

ρ

0.547117 0.565 0.585 0.604

0.814 0.833 0.852 0.872 0.893 0.914 0.937 0.960

0.752 0.768 0.786 0.803 0.822 0.842 0.861 0.884

0.693 0.707 0.723 0.739 0.756 0.774 0.792 0.811

0.669 0.684 0.698 0.714 0.730 0.746

mPa·s

η

T/K = 323.15 Vφ

92.05 92.09 92.13

62.85 62.87 62.88 62.89 62.90 62.91 62.92

62.63 62.65 62.67 62.70 62.71 62.72 62.75

62.33 62.37 62.39 62.43 62.47 62.50 62.55

62.17 62.20 62.22 62.24 62.27 62.29

cm ·mol−1 3



1792

0.0000 0.1024 0.2029 0.3015 0.3984 0.4936

0.0000 0.1034 0.2049 0.3045 0.4023 0.4983

0.0000 0.1001 0.2000 0.3000 0.4000 0.5001

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000

0.0000 0.1044 0.2069 0.3074 0.4061 0.5029

0.0000 0.1014 0.2008 0.2984 0.3943 0.4885

0.0000 0.1001 0.2000 0.3000 0.4000 0.5000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000

0.0000 0.1002 0.1986 0.2951 0.3900 0.4831

0.0000 0.1000 0.2001 0.3001 0.4000 0.5000

mol·L

−1

0.3855 0.4775

−1

C

0.4002 0.5000

mol·kg

ma

Table 2. continued

−3

1.05413 1.05636 1.05853 1.06064 1.06270 1.06470

1.04398 1.04630 1.04856 1.05076 1.05291 1.05501

1.03343 1.03583 1.03817 1.04045 1.04267 1.04485

1.02231 1.02482 1.02726 1.02963 1.03195 1.03420

1.01052 1.01313 1.01567 1.01815 1.02057 1.02294

1.00860 1.01105

g·cm

ρ

1.643 1.720 1.801 1.891 1.985 2.087

1.494 1.562 1.633 1.711 1.795 1.883

1.336 1.394 1.457 1.529 1.604 1.682

1.221 1.273 1.327 1.388 1.450 1.516

1.104 1.150 1.199 1.252 1.308 1.369

1.184 1.233

mPa·s

η

T/K = 293.15 −1

90.88 90.96 91.03 91.11 91.19

90.76 90.82 90.89 90.95 91.01

90.69 90.75 90.83 90.91 90.98

90.41 90.51 90.61 90.70 90.79

90.18 90.26 90.34 90.42 90.49

90.31 90.38

cm ·mol 3

Vφ −3

1.05085 1.05304 1.05517 1.05726 1.05930 1.06129

1.04088 1.04316 1.04539 1.04756 1.04970 1.05178

1.03035 1.03271 1.03502 1.03727 1.03946 1.04161

1.01939 1.02186 1.02426 1.02660 1.02889 1.03113

1.00782 1.01039 1.01289 1.01534 1.01773 1.02006

1.00589 1.00831

g·cm

ρ mb 0.929 0.965 mb 0.874 0.909 0.944 0.981 1.022 1.064 mb 0.959 0.997 1.038 1.081 1.125 1.171 mb 1.044 1.089 1.136 1.185 1.236 1.296 mb 1.151 1.201 1.253 1.309 1.367 1.431 mb 1.262 1.318 1.376 1.440 1.507 1.578

mPa·s

η −1

−1

cm ·mol 3

Vφ

91.49 91.55 91.58 91.63 91.67

91.31 91.34 91.40 91.42 91.47 = 1.0 mol·kg−1

91.27 91.31 91.37 91.44 91.49 = 0.8 mol·kg−1

90.98 91.06 91.14 91.21 91.28 = 0.6 mol·kg−1

90.75 90.82 90.89 90.96 91.03 = 0.4 mol·kg−1

= 0.0 mol·kg 90.89 90.94 = 0.2 mol·kg−1

T/K = 303.15 −3

1.04679 1.04894 1.05104 1.05310 1.05512 1.05709

1.03692 1.03916 1.04135 1.04350 1.04560 1.04765

1.02660 1.02892 1.03118 1.03339 1.03555 1.03766

1.01574 1.01816 1.02053 1.02284 1.02510 1.02732

1.00426 1.00678 1.00925 1.01165 1.01400 1.01629

1.00233 1.00472

g·cm

ρ

1.001 1.044 1.087 1.132 1.180 1.231

0.917 0.956 0.994 1.035 1.079 1.125

0.841 0.875 0.909 0.946 0.983 1.024

0.775 0.805 0.836 0.868 0.901 0.934

0.711 0.739 0.765 0.792 0.823 0.854

0.753 0.779

mPa·s

η

T/K = 313.15 −1

92.11 92.13 92.15 92.18 92.21

91.95 91.97 92.00 92.04 92.07

91.90 91.98 92.03 92.07 92.14

91.65 91.71 91.76 91.80 91.84

91.41 91.49 91.55 91.61 91.70

91.42 91.48

cm ·mol 3

Vφ −3

1.04215 1.04425 1.04631 1.04832 1.05029 1.05222

1.03228 1.03447 1.03662 1.03872 1.04078 1.04279

1.02209 1.02436 1.02659 1.02877 1.03090 1.03299

1.01128 1.01366 1.01598 1.01826 1.02049 1.02268

0.99996 1.00244 1.00486 1.00724 1.00957 1.01185

0.99798 1.00034

g·cm

ρ

0.814 0.848 0.879 0.914 0.948 0.984

0.752 0.781 0.811 0.842 0.874 0.907

0.693 0.719 0.744 0.772 0.799 0.826

0.642 0.665 0.689 0.713 0.738 0.763

0.592 0.612 0.633 0.655 0.678 0.701

0.624 0.644

mPa·s

η

T/K = 323.15 Vφ

92.89 92.91 92.93 92.95 92.98

92.71 92.74 92.76 92.78 92.81

92.66 92.69 92.71 92.73 92.76

92.41 92.44 92.47 92.49 92.51

92.16 92.19 92.22 92.24 92.27

92.17 92.20

cm ·mol−1 3



0.0000 0.1003 0.1993 0.2963 0.3921 0.4863 0.5789 0.6705

0.0000 0.1014 0.2014 0.2996 0.3962 0.4916 0.5855 0.6779

0.0000 0.1025 0.2033 0.3027 0.4005 0.4968 0.5915 0.6848

0.0000 0.1036

0.0000 0.1000 0.2003 0.3000 0.4002 0.5000 0.5997 0.6998

0.0000 0.0999 0.2001 0.3000 0.3998 0.5000 0.6000 0.7000

0.0000 0.1000 0.1998 0.3000 0.3999 0.5000 0.6000 0.7000

0.0000 0.1000

mol·L

−1

0.0000 0.0989 0.1966 0.2926 0.3876 0.4806 0.5725 0.6629

−1

C

0.0000 0.0999 0.1999 0.2999 0.4002 0.5000 0.6000 0.6998

mol·kg

ma

Table 2. continued

−3

1793

1.04398 1.04799

1.03343 1.03749 1.04144 1.04531 1.04908 1.05276 1.05635 1.05985

1.02231 1.02642 1.03043 1.03436 1.03818 1.04193 1.04559 1.04916

1.01052 1.01470 1.01878 1.02277 1.02669 1.03052 1.03425 1.03793

0.99819 1.00241 1.00656 1.01063 1.01464 1.01855 1.02240 1.02616

g·cm

ρ

1.494 1.552

1.336 1.387 1.438 1.491 1.545 1.605 1.662 1.723

1.221 1.266 1.311 1.359 1.409 1.462 1.513 1.566

1.104 1.143 1.184 1.227 1.269 1.313 1.360 1.412

77.07

76.98 77.15 77.30 77.47 77.63 77.79 77.94

76.90 77.07 77.20 77.34 77.49 77.64 77.78

76.72 76.87 76.98 77.08 77.21 77.34 77.44

76.62 76.69 76.76 76.84 76.91 76.99 77.07

1.002017 1.035 1.072 1.107 1.145 1.184 1.225 1.269

−1

cm ·mol 3

Vφ

mPa·s

η

T/K = 293.15 −3

1.04088 1.04482

1.03035 1.03434 1.03824 1.04206 1.04579 1.04943 1.05298 1.05646

1.01939 1.02345 1.02741 1.03128 1.03506 1.03878 1.04239 1.04593

1.00782 1.01193 1.01597 1.01990 1.02376 1.02754 1.03123 1.03486

0.99564 0.99981 1.00390 1.00792 1.01187 1.01573 1.01952 1.02324

g·cm

ρ −1

cm ·mol 3

Vφ g·cm

ρ −3

in Mannitol Aqueous Solution mb = 0.0 mol·kg−1 0.797517 0.99220 0.823 77.24 0.99632 0.849 77.32 1.00037 0.876 77.40 1.00434 0.905 77.47 1.00825 0.934 77.56 1.01207 0.965 77.64 1.01583 0.996 77.71 1.01952 mb = 0.2 mol·kg−1 0.874 1.00426 0.902 77.44 1.00832 0.933 77.53 1.01231 0.965 77.64 1.01620 0.996 77.76 1.02003 1.029 77.85 1.02377 1.063 77.97 1.02741 1.100 78.08 1.03100 mb = 0.4 mol·kg−1 0.959 1.01574 0.992 77.53 1.01973 1.025 77.69 1.02365 1.061 77.81 1.02748 1.098 77.95 1.03123 1.137 78.07 1.03491 1.175 78.21 1.03851 1.215 78.34 1.04203 mb = 0.6 mol·kg−1 1.044 1.02660 1.082 77.69 1.03053 1.120 77.80 1.03438 1.161 77.95 1.03816 1.198 78.08 1.04184 1.242 78.23 1.04544 1.285 78.37 1.04899 1.332 78.49 1.05243 mb = 0.8 mol·kg−1 1.151 1.03692 1.192 77.84 1.04080

L-Threonine

mPa·s

η

T/K = 303.15

0.917 0.950

0.841 0.868 0.897 0.929 0.959 0.991 1.023 1.058

0.775 0.801 0.826 0.853 0.881 0.911 0.939 0.970

0.711 0.733 0.757 0.781 0.805 0.830 0.856 0.886

0.653217 0.673 0.693 0.714 0.736 0.759 0.782 0.806

mPa·s

η

T/K = 313.15 −1

78.52

78.38 78.48 78.59 78.72 78.83 78.91 79.04

78.22 78.34 78.43 78.54 78.63 78.73 78.84

78.07 78.14 78.22 78.32 78.41 78.54 78.65

77.84 77.92 77.99 78.06 78.13 78.19 78.26

cm ·mol 3

Vφ −3

1.03228 1.03611

1.02209 1.02598 1.02979 1.03354 1.03721 1.04082 1.04434 1.04779

1.01128 1.01524 1.01912 1.02293 1.02666 1.03034 1.03395 1.03748

0.99996 1.00398 1.00793 1.01179 1.01559 1.01930 1.02293 1.02651

0.98803 0.99211 0.99612 1.00005 1.00393 1.00771 1.01144 1.01510

g·cm

ρ

0.752 0.777

0.693 0.714 0.736 0.760 0.784 0.810 0.835 0.860

0.642 0.661 0.681 0.702 0.725 0.747 0.769 0.793

0.592 0.610 0.628 0.646 0.666 0.686 0.707 0.730

0.547117 0.562 0.579 0.595 0.613 0.630 0.649 0.667

mPa·s

η

T/K = 323.15 Vφ

79.18

79.01 79.06 79.13 79.19 79.25 79.34 79.41

78.81 78.87 78.93 78.99 79.04 79.09 79.15

78.66 78.71 78.78 78.85 78.92 79.02 79.09

78.44 78.50 78.56 78.62 78.68 78.74 78.80

cm ·mol−1 3



1794

0.0000 0.0986 0.1948 0.2888 0.3804 0.4699 0.5573 0.6426

0.0000 0.0998 0.1972 0.2921 0.3848 0.4753 0.5637 0.6499

0.0000 0.1010 0.1994 0.2953

0.0000 0.1000 0.2000 0.3001 0.4000 0.5000 0.6000 0.7000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6001 0.7000

0.0000 0.1000 0.2000 0.3000

0.0000 0.1048 0.2076 0.3087 0.4083 0.5064 0.6025 0.6973

0.0000 0.1002 0.2002 0.3000 0.4001 0.5002 0.6000 0.7000

mol·L

−1

0.2056 0.3058 0.4044 0.5015 0.5973 0.6911

−1

C

0.2001 0.3000 0.4000 0.4999 0.6001 0.6998

mol·kg

ma

Table 2. continued

−3

1.02231 1.02700 1.03156 1.03598

1.01052 1.01535 1.02005 1.02461 1.02904 1.03335 1.03753 1.04161

0.99819 1.00317 1.00800 1.01268 1.01721 1.02160 1.02586 1.03000

1.05413 1.05809 1.06191 1.06560 1.06919 1.07267 1.07604 1.07929

1.05188 1.05568 1.05937 1.06296 1.06647 1.06986

g·cm

ρ

1.221 1.289 1.363 1.441

1.104 1.164 1.230 1.298 1.374 1.449 1.534 1.623

1.002017 1.054 1.108 1.167 1.230 1.298 1.362 1.435

1.643 1.708 1.776 1.846 1.923 1.998 2.074 2.159

1.613 1.676 1.744 1.814 1.885 1.960

mPa·s

η

T/K = 293.15 −1

124.97 125.04 125.12

124.49 124.57 124.67 124.76 124.85 124.96 125.04

123.89 124.08 124.25 124.44 124.60 124.77 124.93

77.23 77.50 77.77 78.04 78.29 78.53 78.79

77.29 77.47 77.66 77.86 78.04 78.24

cm ·mol 3

Vφ −3

1.01939 1.02403 1.02853 1.03290

1.00782 1.01258 1.01721 1.02170 1.02607 1.03031 1.03444 1.03846

0.99564 1.00055 1.00530 1.00991 1.01438 1.01871 1.02290 1.02697

1.05085 1.05474 1.05850 1.06216 1.06572 1.06917 1.07253 1.07579

1.04865 1.05238 1.05601 1.05954 1.06299 1.06634

g·cm

ρ −1

−1

cm ·mol 3

Vφ g·cm

ρ −3

mb = 0.8 mol·kg 1.237 78.03 1.04460 1.283 78.22 1.04829 1.331 78.40 1.05190 1.380 78.59 1.05543 1.432 78.77 1.05889 1.485 78.95 1.06224 mb = 1.0 mol·kg−1 1.262 1.04679 1.309 78.00 1.05062 1.358 78.19 1.05434 1.411 78.40 1.05795 1.466 78.61 1.06147 1.519 78.83 1.06490 1.574 79.02 1.06825 1.638 79.23 1.07149 L-Arginine in Mannitol Aqueous Solution mb = 0.0 mol·kg−1 0.797517 0.99220 0.838 124.82 0.99705 0.879 125.00 1.00175 0.923 125.18 1.00631 0.970 125.35 1.01073 1.021 125.52 1.01501 1.069 125.69 1.01915 1.124 125.85 1.02318 mb = 0.2 mol·kg−1 0.874 1.00426 0.919 125.39 1.00897 0.968 125.48 1.01355 1.019 125.58 1.01799 1.075 125.67 1.02231 1.132 125.76 1.02650 1.194 125.85 1.03059 1.260 125.93 1.03456 mb = 0.4 mol·kg−1 0.959 1.01574 1.010 125.74 1.02033 1.065 125.79 1.02478 1.124 125.89 1.02911

mPa·s

η

T/K = 303.15

0.776 0.815 0.857 0.903

0.711 0.746 0.784 0.824 0.866 0.911 0.958 1.009

0.653217 0.685 0.717 0.751 0.788 0.826 0.864 0.905

1.000 1.036 1.074 1.112 1.152 1.192 1.235 1.281

0.982 1.016 1.053 1.090 1.129 1.169

mPa·s

η

T/K = 313.15 −1

126.49 126.56 126.63

126.20 126.26 126.35 126.45 126.55 126.63 126.72

125.66 125.83 126.00 126.17 126.33 126.50 126.65

78.65 78.83 79.02 79.21 79.39 79.54 79.72

78.63 78.78 78.91 79.04 79.17 79.31

cm ·mol 3

Vφ −3

1.01128 1.01584 1.02027 1.02457

0.99996 1.00463 1.00917 1.01358 1.01787 1.02203 1.02609 1.03003

0.98803 0.99284 0.99750 1.00203 1.00641 1.01067 1.01480 1.01882

1.04215 1.04592 1.04960 1.05319 1.05670 1.06014 1.06350 1.06678

1.03987 1.04355 1.04715 1.05069 1.05417 1.05755

g·cm

ρ

0.642 0.673 0.707 0.743

0.592 0.619 0.650 0.682 0.715 0.751 0.787 0.826

0.547117 0.572 0.598 0.625 0.654 0.684 0.714 0.747

0.814 0.842 0.870 0.900 0.931 0.961 0.994 1.030

0.802 0.828 0.856 0.884 0.914 0.945

mPa·s

η

T/K = 323.15 Vφ

127.14 127.20 127.26

126.91 126.99 127.07 127.16 127.26 127.34 127.42

126.43 126.59 126.73 126.88 127.02 127.16 127.29

79.40 79.48 79.59 79.71 79.81 79.91 80.02

79.25 79.31 79.38 79.44 79.50 79.57

cm ·mol−1 3



1795

0.0000 0.1031 0.2035 0.3014 0.3968 0.4899 0.5806 0.6692

0.0000 0.1041 0.2054 0.3041 0.4004 0.4943 0.5857 0.6750

0.0000 0.1001 0.2000 0.3000 0.4000 0.5000 0.5999 0.7000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.5999 0.7000

−3

1.05413 1.05850 1.06273 1.06683 1.07080 1.07464 1.07835 1.08196

1.04398 1.04845 1.05279 1.05700 1.06107 1.06504 1.06888 1.07261

1.03343 1.03802 1.04248 1.04679 1.05098 1.05505 1.05900 1.06283

1.04028 1.04447 1.04854 1.05250

g·cm

ρ

1.643 1.740 1.857 1.977 2.099 2.243 2.398 2.555

1.494 1.582 1.680 1.783 1.897 2.018 2.146 2.284

1.336 1.413 1.499 1.591 1.691 1.801 1.916 2.039

1.529 1.618 1.714 1.814

mPa·s

η

T/K = 293.15 −1

125.42 125.52 125.63 125.77 125.89 126.03 126.15

125.31 125.41 125.49 125.60 125.69 125.78 125.88

125.05 125.12 125.23 125.35 125.44 125.56 125.66

125.20 125.28 125.35 125.43

cm ·mol 3

Vφ −3

1.05085 1.05516 1.05934 1.06338 1.06730 1.07109 1.07477 1.07834

1.04088 1.04529 1.04956 1.05371 1.05774 1.06165 1.06544 1.06913

1.03035 1.03488 1.03928 1.04355 1.04771 1.05175 1.05566 1.05946

1.03716 1.04129 1.04531 1.04922

g·cm

ρ mb 1.188 1.254 1.324 1.398 mb 1.044 1.102 1.167 1.233 1.306 1.385 1.466 1.559 mb 1.151 1.216 1.288 1.363 1.447 1.536 1.629 1.732 mb 1.262 1.333 1.415 1.505 1.593 1.698 1.807 1.919

mPa·s

η −1

−1

cm ·mol 3

Vφ

126.23 126.32 126.44 126.55 126.67 126.78 126.89

126.15 126.24 126.32 126.41 126.50 126.59 126.67 = 1.0 mol·kg−1

125.86 125.93 125.99 126.06 126.13 126.24 126.32 = 0.8 mol·kg−1

= 0.4 mol·kg 125.95 126.03 126.11 126.19 = 0.6 mol·kg−1

T/K = 303.15 −3

1.04679 1.05105 1.05518 1.05919 1.06308 1.06684 1.07051 1.07404

1.03692 1.04128 1.04550 1.04959 1.05357 1.05744 1.06119 1.06483

1.02660 1.03108 1.03544 1.03966 1.04378 1.04777 1.05166 1.05543

1.03332 1.03741 1.04140 1.04527

g·cm

ρ

1.001 1.055 1.118 1.183 1.252 1.328 1.408 1.493

0.917 0.967 1.022 1.079 1.142 1.210 1.280 1.356

0.841 0.885 0.934 0.986 1.042 1.099 1.164 1.230

0.952 1.002 1.056 1.112

mPa·s

η

T/K = 313.15 −1

127.03 127.11 127.17 127.27 127.37 127.44 127.56

126.97 127.05 127.16 127.24 127.31 127.40 127.49

126.61 126.68 126.75 126.82 126.89 126.96 127.04

126.71 126.79 126.85 126.93

cm ·mol 3

Vφ −3

1.04215 1.04638 1.05048 1.05446 1.05833 1.06208 1.06573 1.06927

1.03228 1.03660 1.04080 1.04488 1.04884 1.05270 1.05644 1.06009

1.02209 1.02655 1.03088 1.03509 1.03918 1.04316 1.04703 1.05079

1.02876 1.03283 1.03681 1.04066

g·cm

ρ

0.814 0.857 0.906 0.956 1.010 1.067 1.128 1.192

0.752 0.790 0.834 0.879 0.927 0.979 1.032 1.091

0.693 0.727 0.767 0.807 0.850 0.897 0.944 0.997

0.781 0.820 0.862 0.906

mPa·s

η

T/K = 323.15 Vφ

127.76 127.81 127.87 127.93 128.02 128.07 128.15

127.70 127.74 127.78 127.84 127.90 127.97 128.02

127.23 127.29 127.34 127.41 127.46 127.53 127.61

127.32 127.40 127.43 127.51

cm ·mol−1 3

ma stands for the molality of glycine/L-alanine/L-threonine/L-valine/L-arginine in pure water or the (mannitol + water) mixture solvents. mb stands for the molality of mannitol aqueous solution. C stands for the molar concentration of amino acids in the mannitol aqueous solutions. Standard uncertainty: in molality u(m) = 1·10−4 mol·kg−1; in density u(ρ) = 5·10−5 g·cm−3, u(T) = 0.03 K; in viscosities u(η) = 1 %, u(T) = 0.05 K.

a

0.0000 0.1021 0.2015 0.2984 0.3930 0.4852 0.5753 0.6631

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.6999

mol·L

−1

0.3890 0.4804 0.5696 0.6567

−1

C

0.4000 0.5000 0.6000 0.7000

mol·kg

ma

Table 2. continued




Article

Figure 1. Comparisons of the densities (ρ) of glycine, L-alanine and L-threonine in mannitol aqueous solutions between the experimental data and literature values: solid symbols for experimental data; hollow symbols for literature values in ref 15; ■, ma = 0.1 mol·kg−1; ●, ma = 0.2 mol·kg−1; ▲, ma = 0.3 mol·kg−1; black, mb = 0.0 mol·kg−1; blue, mb = 0.2 mol·kg−1; red, mb = 0.4 mol·kg−1.

Table 3. Correlated Coefficients A1, A2, A3, A4, the Standard Deviation (SD), and the Absolute Average Relative Deviation (AARD) for Amino Acids in Mannitol Aqueous Solutions 104 A2

A1 −3

g·cm glycine L-alanine L-valine L-threonine L-arginine

1.117 1.116 1.115 1.117 1.118

−3

g·cm ·K

A3 −1

−3

−3.910 −3.874 −3.869 −3.915 −3.923

28.79 24.99 22.43 37.07 41.36

−3

−1

g ·cm ·mol 2

52.80 52.41 52.37 52.30 51.55

100AARD

g·cm−3

0.06 0.05 0.07 0.05 0.06

8 7 8 7 8

solute−solute interactions. In Figure 2, for a given concentration of mannitol in all ternary solutions, the values of Sv decrease with increasing temperature. It is noteworthy that the all values of Vφ0, which reflects the solute−solvent interactions, are positive and increase with an increase in temperature, this is probably due to the reduction of electrostriction of water. Additionally, the observed order of Vφ0 of amino acids is the same as the apparent molar volumes Vφ. The limiting transfer properties can provide qualitative information regarding the interactions of a cosolvent and a solute without considering the effects of solute−solute interactions.23 To further study the interactions of amino acids in the solvent of mannitol aqueous solution, we calculated

versus the molality of L-threonine are plotted in Figure 2. The Vφ0 was obtained by least-squares fitting as follows:20

Vφ = V φ0 + Svma

104SD

A4 −1

g ·cm ·mol 2

(6)

where the Sv is the experimental slope, which depends on solute−solute interactions,21 and the results are given in Table 4. The comparison of the limiting partial molar volumes (Vφ0) between the experimental data and literature value7−9,22 is shown in Figure 3. It could be found that the limiting partial molar volumes in this work were good agreement with the literature values. It is evident that the values of Sv for all amino acids in different molalities of mannitol from (293.15 to 323.15) K are positive, indicating the existence of stronger 1796



Article

Figure 3. Comparison of limiting partial molar volumes (Vφ0) between the experimental data and literature values: □ and ■, glycine; △ and ▲, L-alanine; ○ and ●, L-threonine; ▽ and ▼, L-valine; ◇ and ◆, L-arginine; hollow symbols for experimental data; solid symbols for literature values, glycine and L-valine in ref 22, L-alanine in ref 8, L-threonine in ref 9, and L-arginine in ref 7.

Figure 2. Apparent molar volume of L-threonine in 0.2 mol·kg−1 mannitol aqueous solutions: ■, 293.15 K; ●, 303.15 K; ▲, 313.15 K; ▼, 323.15 K.

the values of the limiting partial molar volume of transfer (ΔtrVφ0) by the following equation:24 Δtr V φ0 = V φ0[mannitol + water] − V φ0[water]

(7)

From Table 4, it could be clearly observed that the values of ΔtrVφ0 are positive and increase with the molality of mannitol. The ΔtrVφ0 also increases with rising temperature except L-arginine. Based on the cosphere overlap model,25,26 the main types of interactions occurring between amino acids and mannitol could be classified as (1) ion−hydrophilic interactions between the zwitterionic groups (NH3+, COO−) of amino acids and the hydrophilic −OH groups of mannitol; (2) hydrophilic− hydrophilic interactions between the hydrophilic groups of amino acids and the −OH groups of mannitol; (3) ion− hydrophobic interactions between the zwitterionic groups (NH3+, COO−) of amino acids and the alkyl chain of mannitol; (4) hydrophobic−hydrophobic interactions between the alkyl chain of amino acids and the alkyl chain of mannitol; (5) hydrophobic−hydrophilic interactions between the alkyl chain of amino acids and the −OH groups of mannitol. Analyzing information above, in the type (1) and type (2), the interaction makes positive contribution to the limiting partial molar volume of transfer, since the overlap of the hydration cosphere of charged ions (NH3+, COO−), hydrophilic groups (NH2, OH) and −OH groups could lead to the reduction of electrostriction of water molecules lying in the proximity of these amino acids. The interactions of type (3), (4), and (5) contribute negatively to the ΔtrVφ0. In the system studied, the values of ΔtrVφ0 of L-valine and L-threonine are smaller than glycine and L-alanine due to the longer alkyl chain. Because of the presence of the longer alkyl chain, hydrophobic−hydrophobic interactions lead to the decrease of ΔtrVφ0. For glycine, L-alanine and L-valine, there only exist types (1), (3), (4), and (5). Therefore, type (1) predominates over the latter three interactions owing to the positive values of ΔtrVφ0 in the three amino acids. The positive ΔtrVφ0 of L-threonine could be related to the predominance of type (1) and type (2), as well as L-arginine. In the case of 0 L-arginine, the values of ΔtrVφ are the largest among the five amino acids, thereby there exist the strongest solute−solvent interactions. L-arginine is an alkaline amino acid, and the mannitol aqueous solution presents acidic. It may be inferred

Figure 4. Viscosities of amino acids in 0.2 mol·kg−1 mannitol aqueous solutions at T = 293.15 K: ■, glycine; ●, L-alanine; ▼, L-threonine; ▲, L-valine; ◀, L-arginine; , the calculated values of η by eq 8

that mannitol gives H+ to alkaline L-arginine, causing L-arginine charge redistribution, which leads to a negative contribution to ΔtrVφ0. However, mannitol is a natural six-hydroxyl sugar alcohol; the −OH groups and the hydrophilic groups (NH2), the zwitterionic groups (NH3+, COO−) of L-arginine have stronger interactions, and which results in a net increase in volume. 3.2. Viscometric Properties. Table 2 shows that the viscosities vary nonlinearly with the solute molar concentration and the measured temperature. It could be easily found from Figure 4 that the values of viscosities increase with the molar concentration of amino acids for a given temperature, and at a certain molar concentration of amino acids, the viscosities of five amino acids decrease in the order: L-arginine > L-valine > L-threonine > L-alanine > glycine. In general, the variation of relative viscosity ηγ could be correlated by the extended Jones−Dole equation.27 η = 1 + BC + DC 2 ηr = η0 (8) where C is the molar concentration of amino acids in mannitol aqueous solutions at 293.15 K, η and η0 are the viscosities of 1797


a

−1

1798

90.07 90.10 90.32 90.61 90.70 90.80

76.54 76.62 76.77 76.82 76.89 76.98

123.73 124.39 124.89 124.92 125.21 125.28

0.0000 0.2000 0.4000 0.6000 0.8000 1.0000

0.0000 0.2000 0.4000 0.6000 0.8000 1.0000

0.0000 0.2000 0.4000 0.6000 0.8000 1.0000

0.66 1.16 1.19 1.48 1.55

0.08 0.23 0.28 0.35 0.44

0.03 0.25 0.54 0.63 0.73

0.34 0.61 0.71 1.02 1.37

0.40 0.57 0.77 0.89 1.09

−1

cm ·mol

3

ΔtrVφ0

T/K = 293.15 Sv −2

0.9317 0.7780 1.0483 0.9537 1.2424

1.1843 1.4515 1.6079 1.9341 2.5926

0.7843 0.9540 0.7331 0.6292 0.7716

0.5779 0.5531 0.6538 0.4639 0.4965

0.8061 1.1585 1.4084 1.1992 1.3147

cm ·kg·mol 3

mb stands for the molality of mannitol in water.

60.17 60.51 60.78 60.88 61.19 61.54

0.0000 0.2000 0.4000 0.6000 0.8000 1.0000

cm ·mol

3

42.71 43.11 43.28 43.48 43.60 43.80

−1

0.0000 0.2000 0.4000 0.6000 0.8000 1.0000

mol·kg

mb

Vφ0 −1

124.66 125.30 125.65 125.77 126.06 126.11

77.16 77.33 77.41 77.55 77.66 77.78

90.63 90.68 90.91 91.21 91.27 91.45

60.58 61.03 61.23 61.40 61.72 61.98

43.31 43.74 43.90 44.09 44.21 44.41

cm ·mol 3

Vφ0

0.64 0.99 1.11 1.40 1.45

0.17 0.25 0.39 0.50 0.62

0.05 0.28 0.58 0.64 0.82

0.45 0.65 0.82 1.14 1.40

0.43 0.59 0.78 0.90 1.10

cm ·mol 3

−1

ΔtrVφ0

T/K = 303.15 Sv −2

0.9034 0.7641 0.7639 0.8689 1.1149

1.0705 1.3334 1.3587 1.8504 2.0693 L-Arginine

0.7099 0.7475 0.5644 0.4071 0.4363 L-Threonine

0.4610 0.4892 0.5619 0.3732 0.2605 L-Valine

0.7654 0.7954 1.1392 1.0195 1.1435 L-Alanine

Glycine

cm ·kg·mol 3

−1

125.50 126.10 126.42 126.54 126.89 126.93

77.78 77.95 78.12 78.26 78.38 78.48

91.24 91.34 91.61 91.86 91.91 92.08

61.04 61.50 61.73 61.87 62.22 62.45

43.82 44.24 44.42 44.61 44.73 44.94

cm ·mol 3

Vφ0

0.60 0.92 1.04 1.39 1.43

0.17 0.34 0.48 0.60 0.70

0.10 0.37 0.62 0.67 0.84

0.46 0.69 0.83 1.18 1.41

0.42 0.60 0.79 0.91 1.12

−1

cm ·mol 3

ΔtrVφ 0

T/K = 313.15 Sv

0.8905 0.7266 0.7149 0.8552 0.8809

0.9713 1.0182 1.1058 1.3158 1.7817

0.7020 0.4774 0.5577 0.3124 0.2425

0.3246 0.3961 0.4657 0.2174 0.1520

0.5794 0.7901 0.9782 0.7546 0.9543

cm ·kg·mol 3

−2

−1

126.29 126.82 127.08 127.17 127.63 127.68

78.38 78.57 78.76 78.93 79.12 79.28

92.01 92.14 92.38 92.64 92.69 92.87

61.43 61.92 62.12 62.29 62.61 62.84

44.29 44.74 44.94 45.12 45.29 45.48

cm ·mol 3

Vφ0

0.53 0.79 0.88 1.34 1.39

0.19 0.38 0.55 0.74 0.90

0.13 0.37 0.63 0.68 0.86

0.49 0.69 0.86 1.18 1.41

0.45 0.65 0.83 1.00 1.19

cm3·mol−1

ΔtrVφ0

T/K = 323.15

0.8531 0.6116 0.6120 0.5411 0.6584

0.7306 0.5582 0.6788 0.6412 1.0559

0.2702 0.2635 0.2270 0.2478 0.2098

0.1997 0.2391 0.3577 0.1935 0.1092

0.3081 0.2618 0.5600 0.3612 0.5458

cm3·kg·mol−2

Sv

Table 4. Limiting Partial Molar Volumes (Vφ0), Limiting Partial Molar Volumes of Transfer (ΔtrVφ0), and the Experimental Slope (Sv) of Amino Acids in Mannitol Aqueous Solutions at T = (293.15 to 323.15) Ka




Article

Table 5. B and D Coefficients of the Jones−Dole Equation, the Free Energies of Activation Per Mole for Solvent (Δμ10≠) and Solute (Δμ20≠) at T = (293.15, 303.15, 313.15, and 323.15) K T

B

D

Δμ10≠

Δμ20≠

K

dm3·mol−1

dm6·mol−2

kJ·mol−1

kJ·mol−1

Table 5. continued

0.2 mol·kg−1 Aqueous Mannitol Solution 293.15

0.139 (±0.002)

0.017 (±0.003)

9.58

31.27

0.144 (±0.002)

0.014 (±0.003)

9.32

32.45

313.15

0.148 (±0.001)

0.010 (±0.002)

9.10

33.54

323.15

0.152 (±0.001)

0.009 (±0.002)

8.91

34.66

0.141 (±0.001)

0.012 (±0.001)

9.87

31.39

303.15

0.146 (±0.001)

0.008 (±0.002)

9.60

32.54

313.15

0.150 (±0.001)

0.006 (±0.002)

9.38

33.60

323.15

0.154 (±0.001)

0.005 (±0.002)

9.18

34.70

0.146 (±0.001)

0.020 (±0.002)

10.14

31.86

303.15

0.150 (±0.001)

0.017 (±0.001)

9.87

32.87

313.15

0.153 (±0.001)

0.015 (±0.001)

9.64

33.78

323.15

0.156 (±0.001)

0.013 (±0.002)

9.44

34.71

0.148 (±0.001)

0.015 (±0.002)

10.45

32.00

303.15

0.151 (±0.001)

0.013 (±0.001)

10.16

32.83

313.15

0.154 (±0.001)

0.012 (±0.002)

9.91

33.69

323.15

0.158 (±0.001)

0.010 (±0.002)

9.71

34.75

293.15

0.150 (±0.001)

0.011 (±0.001)

10.73

32.11

0.155 (±0.001)

0.009 (±0.001)

10.44

33.19

313.15

0.158 (±0.001)

0.009 (±0.002)

10.19

34.04

323.15

0.162 (±0.002)

0.008 (±0.004)

9.97

35.07

0.094 (±0.005)

9.58

43.64

303.15

0.206 (±0.003)

0.091 (±0.005)

9.32

43.28

313.15

0.199 (±0.002)

0.080 (±0.004)

9.10

43.14

323.15

0.192 (±0.001)

0.065 (±0.001)

8.91

42.92

0.218 (±0.003)

0.084 (±0.004)

9.87

43.67

303.15

0.210 (±0.002)

0.081 (±0.004)

9.60

43.44

313.15

0.204 (±0.001)

0.069 (±0.002)

9.38

43.44

323.15

0.197 (±0.001)

0.058 (±0.002)

9.18

43.23

0.226 (±0.002)

0.106 (±0.003)

10.14

44.27

303.15

0.218 (±0.001)

0.094 (±0.002)

9.87

44.08

313.15

0.209 (±0.001)

0.078 (±0.002)

9.64

43.69

323.15

0.200 (±0.001)

0.066 (±0.002)

9.44

43.21

0.230 (±0.002)

0.104 (±0.003)

10.45

44.46

303.15

0.222 (±0.001)

0.092 (±0.001)

10.16

44.25

313.15

0.212 (±0.001)

0.085 (±0.002)

9.91

43.71

323.15

0.203 (±0.002)

0.067 (±0.004)

9.71

43.25

293.15

0.234 (±0.002)

0.100 (±0.003)

10.73

44.62

303.15

0.226 (±0.001)

0.084 (±0.001)

10.44

44.41

313.15

0.216 (±0.001)

0.077 (±0.002)

10.19

43.89

323.15

0.207 (±0.001)

0.066 (±0.002)

9.97

43.42

293.15

0.386 (±0.002)

0.226 (±0.005)

9.58

70.21

303.15

0.372 (±0.006)

0.163 (±0.014)

9.32

70.00

313.15

0.358 (±0.007)

0.121 (±0.017)

9.10

69.70

323.15

0.341 (±0.003)

0.087 (±0.007)

8.91

68.82

293.15

0.393 (±0.002)

0.206 (±0.004)

9.87

70.26

303.15

0.379 (±0.002)

0.150 (±0.006)

9.60

70.08

313.15

0.365 (±0.003)

0.111 (±0.007)

9.38

69.78

323.15

0.349 (±0.002)

0.076 (±0.004)

9.18

69.07

293.15

0.401 (±0.004)

0.253 (±0.009)

10.14

70.37

303.15

0.386 (±0.007)

0.201 (±0.017)

9.87

70.09

313.15

0.373 (±0.005)

0.136 (±0.012)

9.64

69.94

323.15

0.356 (±0.003)

0.072 (±0.006)

9.44

69.11

293.15

0.410 (±0.004)

0.227 (±0.009)

10.45

303.15

0.394 (±0.005)

0.188 (±0.012)

10.16

70.26

313.15

0.380 (±0.006)

0.150 (±0.013)

9.91

69.96

323.15

0.363 (±0.002)

0.102 (±0.005)

9.71

69.17

−1

70.69

Aqueous Mannitol Solution

293.15

0.419 (±0.004)

0.235 (±0.009)

10.73

70.95

303.15

0.403 (±0.003)

0.189 (±0.007)

10.44

70.57

313.15

0.388 (±0.006)

0.137 (±0.015)

10.19

70.18

323.15

0.370 (±0.005)

0.089 (±0.012)

9.97

69.28

293.15

0.335 (±0.005)

0.116 (±0.008)

9.58

61.67

303.15

0.318 (±0.003)

0.101 (±0.005)

9.32

60.80

313.15

0.300 (±0.004)

0.097 (±0.007)

9.10

59.66

323.15

0.283 (±0.004)

0.095 (±0.007)

8.91

58.48


0.346 (±0.003)

0.105 (±0.006)

9.87

62.39

303.15

0.325 (±0.002)

0.103 (±0.004)

9.60

61.03

313.15

0.307 (±0.002)

0.094 (±0.004)

9.38

59.91

323.15

0.289 (±0.002)

0.084 (±0.004)

9.18

58.63

0.6 mol·kg−1 Aqueous Mannitol Solution


kJ·mol−1

L-Threonine


kJ·mol−1



dm6·mol−2

1.0 mol·kg

0.2 mol·kg−1 Aqueous Mannitol Solution 0.215 (±0.003)

dm3·mol−1


L-Alanine

293.15

K



Δμ20≠



Δμ10≠

L-Valine


D



B


Glycine

303.15

T

293.15

0.354 (±0.002)

0.101 (±0.004)

10.14

62.62

303.15

0.334 (±0.005)

0.095 (±0.008)

9.87

61.46

313.15

0.314 (±0.003)

0.092 (±0.005)

9.64

60.12

323.15

0.296 (±0.003)

0.085 (±0.004)

9.44

58.86


1799

293.15

0.361 (±0.001)

0.1305 (±0.002)

10.45

62.83

303.15

0.340 (±0.001)

0.1157 (±0.002)

10.16

61.54



Article

Table 5. continued T

B

D

Δμ10≠

Δμ20≠

K

dm3·mol−1

dm6·mol−2

kJ·mol−1

kJ·mol−1

behaves as structure-breaker, another four amino acids are structure-makers. By considering the structures of the five amino acids, the charged end groups (NH3+, COO−) of all amino acids influence the electrostatic interactions of water molecules. Compared with glycine, L-alanine, L -valine, L-threonine, and L-arginine have long alkyl chains, the interaction of hydrophobic hydration between the alkyl chain and water molecules is stronger than the electrostatic interaction, which leads to the negative values of dB/dT for the four amino acids in mannitol aqueous solutions, and all of them act as structure-makers. The viscosity data have also been analyzed in the light of transition state theory for relative viscosity by Feakins et al.31,32 According to the theory, the B-coefficient could be given as follows:


0.321 (±0.003)

0.1116 (±0.005)

9.91

60.33

323.15

0.302 (±0.002)

0.1000 (±0.004)

9.71

59.00


0.368 (±0.003)

0.117 (±0.005)

10.73

62.98

303.15

0.347 (±0.005)

0.112 (±0.008)

10.44

61.75

313.15

0.327 (±0.003)

0.106 (±0.005)

10.19

60.45

323.15

0.309 (±0.003)

0.099 (±0.006)

9.97

59.29

L-Arginine


0.503 (±0.005)

0.334 (±0.009)

9.58

90.25

303.15

0.483 (±0.004)

0.300 (±0.008)

9.32

89.90

313.15

0.464 (±0.004)

0.275 (±0.007)

9.10

89.50

323.15

0.449 (±0.004)

0.248 (±0.007)

8.91

89.44

B = (V1̅ 0 − V2̅ 0)/1000 + V1̅ 0(Δμ20 ≠ − μ10 ≠ )/1000RT (9)

where ∑xiMi/ρ0) and are the molar volume of the solvents (mannitol + water) and the standard partial molar volume of the solute at infinite dilution, respectively. The xi and Mi denote the mole fraction and molar weight of water and mannitol in mixed solvent, respectively. ρ0 is the density of the solvent mixture. The free energy of activation per mole of solvent Δμ10≠ and the free energy of activation per mole of solute Δμ20≠ could be calculated by the following equations:33 V̅ 01(=


0.508 (±0.002)

0.352 (±0.004)

9.87

89.70

303.15

0.489 (±0.001)

0.316 (±0.002)

9.60

89.48

313.15

0.472 (±0.002)

0.287 (±0.003)

9.38

89.34

323.15

0.456 (±0.002)

0.257 (±0.003)

9.18

89.16


0.516 (±0.003)

0.417 (±0.006)

10.14

89.40

303.15

0.496 (±0.008)

0.367 (±0.014)

9.87

89.10

313.15

0.479 (±0.004)

0.328 (±0.007)

9.64

88.98

323.15

0.464 (±0.005)

0.295 (±0.009)

9.44

88.92

0.524 (±0.003)

0.395 (±0.006)

10.45

89.28

303.15

0.502 (±0.004)

0.374 (±0.008)

10.16

88.69

313.15

0.484 (±0.003)

0.345 (±0.006)

9.91

88.41

323.15

0.469 (±0.005)

0.304 (±0.009)

9.71

88.39


0.530 (±0.009)

0.432 (±0.016)

10.73

88.83

303.15

0.508 (±0.006)

0.390 (±0.011)

10.44

88.27

313.15

0.492 (±0.004)

0.349 (±0.007)

10.19

88.28

323.15

0.475 (±0.004)

0.313 (±0.006)

9.97

88.00

Vφ0)

Δμ10 ≠ = RT ln(η0V1̅ 0/hNA )

(10)

Δμ20 ≠ = Δμ10 ≠ + RT[1000B − (V1̅ 0 − V2̅ 0)]/V1̅ 0

(11)

where R is gas constant, h is Planck’s constant, NA is Avogadro’s number, and η0 is the viscosity of the solvent. The values of Δμ10≠ and Δμ20≠ at all measured temperatures are included in Table 5. The magnitude of Δμ20≠ reflects the ability to form the transition state, the higher the value of Δμ20≠ is, the more difficult it is to form the transition state because of the stronger solute−solvent interactions. A perusal of Table 5 would find that Δμ10≠ and Δμ20≠ are positive, and the values of Δμ20≠ are larger than Δμ 1 0≠ , which suggests the solute−solvent interactions between amino acids and mannitol aqueous solution in the ground state are stronger than in the transition state. That is, the formation of the transition state is less favored by the solvation of the solute molecules. It is interesting to note that the values of Δμ20≠ of L-alanine, L-valine, L-threonine, and L-arginine decrease with rising temperature, indicating that the high temperature is favorable in the formation of the transition state. While glycine is reverse, implying the low temperature is favorable in the formation of the transition state for glycine in mannitol aqueous solution. Besides, for five amino acids, the values of Δμ20≠ of glycine in aqueous mannitol solution are smallest. According to the Feakins’s model, the smaller Δμ20≠ has high trend to act as structure-breaker, this feature shows an agreement with the results of the dB/dT trend. The Δμ20≠ of L-arginine is the largest, indicating the existence of the stronger solute−solvent interactions in mannitol aqueous solution caused by acid and alkali neutralization.


V̅ 02(=

solutions (amino acids + mannitol + water) and the mixed solvents (mannitol + water), respectively. The fitting parameters B and D are the constants at a given temperature, and B-coefficient stands for the solute−solvent interaction which reflects the effect of solute size and structure. The D-coefficient seems to account for solute−solute interactions.28 B and D-coefficients are calculated by least-squares fitting method, and the deviations are also shown in Table 5. The values of B-coefficient are positive for all amino acids, indicating the strong solute−solvent interactions, and decrease with the rise of temperature except glycine. In the other words, only the B-coefficients of glycine increase with temperature. As we know, dB/dT values could provide useful information about the solute ability to be structure-maker or breaker in the solvent media.29,30 The positive dB/dT indicates that the solute prefer to act as a structure-breaker, whereas the negative dB/dT predicts the structure-maker characteristics. Thus, the presently observed positive values of dB/dT for glycine imply that glycine

4. CONCLUSIONS In this study, the densities and viscosities of glycine, L-alanine, L-valine, L-threonine, and L-arginine in aqueous mannitol 1800



Article

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solutions were measured at T = (293.15 to 323.15) K under atmospheric pressure. The experimental densities were applied to obtain the apparent molar volumes (Vφ), the limiting partial molar volumes (Vφ0), the limiting partial molar volumes of transfer (ΔtrVφ0). Both the values of Vφ and Vφ0 for five amino acids increase in the order: glycine < L-alanine < L-threonine < 0 0 L-valine < L-arginine, and all Vφ, Vφ and ΔtrVφ are positive, implying strong solute−solvent interactions. The experimental viscosities were correlated using the extended Jones-Dole equation in order to obtain the viscosity B-coefficient. Successively, the free energies of activation per mole of solvent Δμ10≠ and solute Δμ20≠ were calculated. The values of B-coefficient are positive for all amino acids, and decrease with the rise of temperature except glycine, indicating that glycine tends to act as a structure breaker, whereas L-alanine, L-valine, L-threonine, and L-arginine are likely to be a structure maker.

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ASSOCIATED CONTENT

S Supporting Information *

Comparison between experimental densities and viscosities of amino acids + water and mannitol + water solutions and the literature values. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ je501178z.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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Volumetric and Viscometric Studies of Amino Acids in Mannitol

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