- Email: [email protected]
Effects of hydroxyl groups on binary diffusion coefficients of α-amino acids in dilute aqueous solutions
Available online at www.sciencedirect.com
Fluid Phase Equilibria 264 (2008) 18–22
Effects of hydroxyl groups on binary diffusion coefficients of ␣-amino acids in dilute aqueous solutions Tatsuya Umecky, Shigeyoshi Omori, Tomoyuki Kuga, Toshitaka Funazukuri ∗ Department of Applied Chemistry, Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan Received 10 June 2006; received in revised form 1 October 2007; accepted 19 October 2007
Abstract Binary diffusion coefficients, D12 , of ␣-amino acids with hydroxyl groups, e.g., serine, threonine, allothreonine and homoserine, in dilute aqueous solutions were measured at six different temperatures from 293.2 to 333.2 K by the Taylor dispersion method. The determined D12 values of serine and threonine at 298.2 K were in good agreement with the published data, whereas no data for allothreonine and homoserine is available in the literature. The D12 values for each amino acid were well represented with the Stokes–Einstein equation by adjusting the molecular diameter. The D12 values for amino acids containing hydroxyl groups, except for homoserine, were lower by approximately 5%, on the basis of the same solute molar volume, than those from the corresponding amino acids without hydroxyl groups. © 2007 Elsevier B.V. All rights reserved. Keywords: Amino acid; Binary diffusion coefficient; Hydroxyl group; Molecular diameter; Prediction; Taylor dispersion
1. Introduction Amino acids and their derivatives are important in various fields, e.g., food, pharmaceutical, nutraceutical and cosmetic industries, so that the demand for amino acids is rapidly increasing. To produce amino acids synthetically and to separate them efficiently, it is essential to design chemical reactors and separators that take the transport phenomena of these processes into consideration. The binary diffusion coefficient, D12 , is one of the most important physical properties in estimating mass transfer rates. There are many reports on D12 measurements of ␣-amino acids in aqueous solutions [1–15]. However, few D12 data of ␣-amino acids containing hydroxyl groups are available in the literature [2,4,14,15]. Recently, we measured the D12 values of several ␣-amino acids of the NH2 –CH(COOH)–R form, where R is the alkyl up to a butyl group, in dilute aqueous solutions at temperatures from 293.2 to 333.2 K [16]. In the present study, we focus on ␣-amino acids having a hydroxyl group: serine, Ser (R CH2 –OH), threonine, Thr [R CH(CH3 )–OH], its stereoisomer allothreonine, aThr [R CH(CH3 )–OH] and homoserine,
∗
Corresponding author. E-mail address: [email protected] (T. Funazukuri).
0378-3812/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2007.10.013
Hse (R CH2 –CH2 –OH). The D12 values of these ␣-amino acids in dilute aqueous solutions were measured at temperatures from 293.2 to 333.2 K by the Taylor dispersion method, and the effects of a hydroxyl group on the D12 values were studied and compared to our previous data on ␣-amino acids with no hydroxyl groups. 2. Experimental 2.1. Materials DL-Ser (99%, Acros), DL-Thr (99.5%, Acros), DL-aThr (98%, Acros) and DL-Hse (98%, Tokyo Kasei) were used without further purification. Ultrapure water produced with a Millipore Direct-Q system was used as a solvent. 2.2. Procedures The experimental apparatus and procedure were identical with those employed in the previous study [16], and are briefly described below. The degassed water was supplied at a fixed flow velocity of ≈7.0 × 10−3 m s−1 with a syringe pump (100DM, Isco). The aqueous solution at an ␣-amino acid concentration of 10.0 mol m−3 (corresponding to ≈0.1 wt%) was injected to a diffusion tube (Supelco; inner radius 2.64 × 10−4 m, length
T. Umecky et al. / Fluid Phase Equilibria 264 (2008) 18–22
42.12 m and coil radius ≈0.095 m) through an injector (7725, Rheodyne; sampling loop ≈2.0 × 10−8 m3 ) after the sample solution had been maintained for 30 min or longer in the injector. The ␣-amino acid concentration at the diffusion tube exit was detected with a differential refractometer (L-7490, Hitachi) and the refractive index time change was recorded with an integrator (D-2500, Hitachi). The temperature in the water bath was controlled within ±0.1 K during all measurements. 2.3. Analysis In the Taylor dispersion method [17,18] the cross-sectional average solute concentration Ccal (t) at the exit of a diffusion tube, the distance of L from the inlet, is expressed by Eqs. (1) and (2). m (L − ut)2 Ccal (t) = exp − (1) 4Kt πR2tube (4πKt)1/2 and K = D12 +
R2tube u2 48D12
(2)
where m is the amount of the injected solute, Rtube is the inner radius of the diffusion tube, t is the time and u is the average flow velocity. Two parameters, D12 and u, in Eqs. (1) and (2) were determined so as to minimize the root-mean-square fitting error, ε, defined by Eq. (3), between the response curves of the
19
observed Cexp (t) and calculated Ccal (t) (ε < 1%): 1/2 {Cexp (t) − Ccal (t)}2 t ε= × 100 {Cexp (t)}2 t
(3)
3. Results and discussion The measured D12 value, solvent velocity, rms fitting error ε and DeSc1/2 value are presented in Table 1. They are the mean values obtained from five measurements under each condition, and the figure in parenthesis is the standard deviation. The reproducibility of the D12 values was almost ±1.0% (the maximum ± 2.0%). In this study, densities and viscosities of water were obtained from the literature [19]. The DeSc1/2 values were always lower than 8 under all conditions studied, where De and Sc are the Dean and Schmidt numbers, respectively. Alizadeh et al. estimated the effects of the secondary flow due to tube coiling to be lower than 1.0% in terms of the moment in the Taylor dispersion when DeSc1/2 < 8 [20]. Hence, the effect of the secondary flow in the present study was negligible. The present D12 values of Ser and Thr at 298.2 K are 8.80 × 10−10 and 7.99 × 10−10 m2 s−1 , respectively, and they are consistent with the dilute D12 data reported by Longsworth (8.80 × 10−10 m2 s−1 for Ser and 7.98 × 10−10 m2 s−1 for Thr) [4] and Ma et al. (7.97 × 10−10 m2 s−1 for Thr) [15]. No data for aThr and Hse is available in the literature. It is interesting that the D12 value of Hse is slightly larger than those of Thr and aThr at each temperature, although the molecular weights of the three ␣-amino acids are identical. Differences
Table 1 Values of D12 , u, ε and DeSc1/2 for each ␣-amino acida ␣-Amino acid
T (K)
D12 (10−10 m2 s−1 )
u (10−3 m s−1 )
ε (%)
DeSc1/2
Ser
293.2 298.2 303.2 313.2 323.2 333.2
7.72 (0.08) 8.80 (0.06) 9.91 (0.09) 12.56 (0.14) 15.49 (0.18) 18.76 (0.23)
7.00 (0.01) 6.99 (0.01) 7.02 (0.01) 7.04 (0.01) 7.07 (0.01) 7.11 (0.01)
0.65 (0.14) 0.60 (0.12) 0.49 (0.11) 0.45 (0.07) 0.53 (0.13) 0.57 (0.14)
7.0 (0.1) 6.9 (0.1) 6.9 (0.1) 6.8 (0.1) 6.7 (0.1) 6.6 (0.1)
Thr
293.2 298.2 303.2 313.2 323.2 333.2
6.91 (0.05) 7.99 (0.03) 9.04 (0.04) 11.39 (0.13) 14.26 (0.12) 17.20 (0.03)
7.00 (0.01) 7.02 (0.01) 7.02 (0.01) 7.05 (0.01) 7.08 (0.01) 7.11 (0.01)
0.63 (0.18) 0.65 (0.11) 0.56 (0.13) 0.53 (0.10) 0.62 (0.15) 0.60 (0.14)
7.4 (0.1) 7.3 (0.1) 7.3 (0.1) 7.2 (0.1) 7.0 (0.1) 6.9 (0.1)
aThr
293.2 298.2 303.2 313.2 323.2 333.2
6.97 (0.02) 7.96 (0.05) 9.06 (0.08) 11.44 (0.12) 14.22 (0.09) 17.24 (0.10)
7.00 (0.01) 7.01 (0.01) 7.02 (0.01) 7.05 (0.01) 7.08 (0.01) 7.11 (0.01)
0.59 (0.15) 0.66 (0.11) 0.67 (0.08) 0.64 (0.10) 0.78 (0.09) 0.59 (0.12)
7.4 (0.1) 7.3 (0.1) 7.3 (0.1) 7.1 (0.1) 7.0 (0.1) 6.9 (0.1)
Hse
293.2 298.2 303.2 313.2 323.2 333.2
7.26 (0.08) 8.39 (0.12) 9.39 (0.09) 11.86 (0.11) 14.75 (0.19) 17.83 (0.19)
6.94 (0.01) 6.97 (0.03) 7.01 (0.01) 7.02 (0.01) 7.04 (0.01) 7.07 (0.01)
0.51 (0.12) 0.49 (0.09) 0.50 (0.09) 0.63 (0.09) 0.52 (0.11) 0.46 (0.08)
7.2 (0.1) 7.1 (0.1) 7.1 (0.1) 7.0 (0.1) 6.9 (0.1) 6.8 (0.1)
a
The standard deviation obtained from five measurements is given in parentheses.
20
T. Umecky et al. / Fluid Phase Equilibria 264 (2008) 18–22
Table 2 Determined constants α and β in Eq. (4) together with AAD% and AD%max ␣-Amino acid
1015 α
β
AAD%
AD%max
Ser Thr aThr Hse
2.600 1.990 2.025 2.357
−1.001 −1.025 −1.023 −1.007
0.27 0.33 0.18 0.41
0.57 0.66 0.43 0.91
in the D12 values among ␣-amino acids with the same molecular weights were not observed in our previous study [16]. As discussed later, this could result from the much lower hydrophilicity of Hse compared to Thr [21]. We have already reported that Eq. (4) with two adjustable constants α and β accurately represents the measured D12 data of the ␣-amino acids [16], C5-alcohols [22] and sugars [23] in dilute aqueous solutions, as well as various systems such as organic compounds in supercritical fluids [24], in a mixture of carbon dioxide and hexane [25] and in organic solvents [26] under various pressures: D12 = αηβ T
Table 3 Molecular diameters σ SE obtained from the Stokes–Einstein equation with the D12 data at 293.2–333.2 K, AAD% and AD%max for various ␣-amino acids ␣-Amino acid
1010 σ SE (m)
AAD% (%)
AD%max (%)
With OH Ser Thr aThr Hse
5.585 6.139 6.127 5.892
0.27 0.65 0.52 0.48
0.66 1.14 0.86 0.72
Without OH [16] Gly Ala Abu Nva Val Nle Leu Ile aIle t-Leu
4.640 5.328 5.848 6.282 6.247 6.630 6.626 6.580 6.558 6.621
0.96 0.45 0.37 0.84 0.92 1.01 1.25 1.05 0.82 1.42
1.72 0.96 0.83 1.35 1.56 1.62 2.06 1.61 1.32 2.59
Stokes–Einstein (SE) equation given by Eq. (6): (4)
where T is the absolute temperature and η is the solvent viscosity in units of Pa s. Table 2 lists the constants α and β in Eq. (4) obtained by least-squares fitting, together with average absolute deviations, AAD%, defined by Eq. (5), and maximum absolute deviations, AD%max : 1 D12,exp − D12,prd (5) AAD% = × 100 N D12,exp where N is the number of data points, D12,exp and D12,prd are the values measured experimentally and predicted by correlation, e.g., in Eq. (4) with the α and β values determined, respectively. As seen in Fig. 1, good accuracies were obtained in Eq. (4) by adjusting the two parameters α and β with AAD% and AD%max smaller than 0.5 and 1.0%, respectively. As has been seen in aqueous solutions [16,22,23], β can be assumed to be −1 in this study, corresponding to the
Fig. 1. D12 /T vs. H2 O viscosity for Ser (squares), Thr (circles), aThr (triangles) and Hse (diamonds) at temperatures from 293.2 to 333.2 K.
D12 =
kB T 3πησSE
(6)
where kB is the Boltzmann constant and σ SE is the solute molecular diameter based on the Stokes–Einstein equation. Thus, the molecular diameter σ SE involved in the SE equation was adjusted for each amino acid with a hydroxyl group in the present study, and without a hydroxyl group in the previous study [16], as listed in Table 3, together with AAD% and AD%max . The accuracies are good, as compared with those of the conventional correlations, as listed in Table 4, although it is worse than Eq. (4) with two parameters adjusted. Note that the accuracy of the Wilke–Chang equation [27] is lower, but modifying the equaTable 4 AAD% values for the predictive correlations for various ␣-amino acids measured in the present and previous studies [16] Wilke–Chang [27]
Hayduk–Minhas [29]
ϕ = 2.6
ϕ = 2.26 [28]
With OH Ser Thr aThr Hse
13.7 12.1 11.9 7.6
6.0 4.5 4.3 0.5
6.2 5.0 4.8 1.1
Without OH Gly Ala Abu Nva Val Nle Leu Ile aIle t-Leu
13.5 13.0 10.5 7.8 7.2 4.7 4.6 3.9 4.0 4.5
5.8 5.3 3.0 1.0 0.9 2.4 2.5 3.2 3.0 2.6
5.7 5.5 3.4 1.8 1.7 1.9 2.1 2.5 2.4 2.5
8.5
3.2
3.3
Overall
T. Umecky et al. / Fluid Phase Equilibria 264 (2008) 18–22
21
the Stokes–Einstein equation with one parameter, i.e., molecular diameter σ SE , determined for each solute. The values of σ SE were correlated with solute molar volume with a slope of 0.422. The D12 values of the ␣-amino acids having a hydroxyl group except for Hse were found to be lower by ca. 5% than those of the ␣-amino acids having no hydroxyl group, which distinctively shows low hydrophilicity. Consequently, the D12 values were affected primarily by the solute molecular size, and secondarily by the solute–solvent interaction.
Fig. 2. Molecular diameter σ SE vs. molar volume for various ␣-amino acids with OH (solid triangles) and without OH (blank circles) from 293.2 to 303.2 K.
tion replacing an original association factor ϕ of 2.6 with 2.26, recommended by Hayduk and Laudie [28], improved the accuracy to that of Hayduk and Minhas [29]. Accuracies of these conventional equations are acceptable, but they are lower than Eq. (4) with β = −1. It is known that D12 values are affected by the solute molecular size and the solute–solvent interaction. Fig. 2 shows σ SE (=kB T/3πηD12 ) versus solute molar volume at 293.2–303.2 K predicted with the group contribution method of Yan et al. [30] for ␣-amino acids with a hydroxyl group (solid triangles) and without (blank circles) [16]. Note that the group contribution method is based on their experimental data from 278.15 to 308.15 K [30], and the values for each solute exhibit a slight temperature dependence. As depicted, the σ SE values for the amino acids without a hydroxyl group are correlated with molar volumes with a slope of 0.407 in the logarithmic plot. However, the slope with a hydroxyl group is nearly the same (0.422), but with a different intercept, except for Hse. In other words, the σ SE values for amino acids with a hydroxyl group are higher by approximately 5% (correspondingly, the diffusion coefficients are lower) than those without a hydroxyl group at the same molar volumes. This suggests that the presence of a hydroxyl group retards diffusion rates somewhat, indicating that the solute–solvent interaction for compounds with a hydroxyl group is stronger than those without. It is interesting that the molecular diameter σ SE for Hse is nearly the same as those amino acids without a hydroxyl group. This could be attributed to the significantly lower hydrophilicity of Hse than Ser, Thr or aThr. In fact, Hse shows an exceptionally low hydrophilicity compared to Ser, Thr and aThr as shown by the hydrophilic retention coefficients for various amino acids determined from the retention times measured in liquid chromatography by Yoshida et al. [21]. 4. Conclusion The D12 values of Ser, Thr, aThr and Hse in dilute aqueous solutions were measured at six temperatures from 293.2 to 333.2 K with the Taylor dispersion method. The determined D12 values were in good agreement with the reference data within experimental error. The D12 values were represented by
List of symbols AAD% average absolute deviation defined by Eq. (5) AD%max maximum absolute deviation C(t) cross-sectional average concentration of solute D12 binary diffusion coefficient De Dean number = (2ρuRtube /η)(Rtube /Rcoil )1/2 kB Boltzmann constant L length of diffusion tube m amount of injected solute Rcoil coil radius of diffusion tube inner radius of diffusion tube Rtube Sc Schmidt number = η/(ρD12 ) t time T absolute temperature u average flow velocity Greek symbols α constant in Eq. (4) β constant in Eq. (4) ε root-mean-square fitting error defined by Eq. (3) η water viscosity ϕ solvent association factor ρ water density σ SE molecular diameter based on the Stokes–Einstein equation Subscripts cal calculated exp measured experimentally prd predicted Acknowledgement The authors are grateful to the Ministry of Education, Sports, Culture, Science and Technology of Japan for support through grant-in-aid of #18560725. References [1] [2] [3] [4] [5] [6] [7]
M.S. Lyons, J.V. Thomas, J. Am. Chem. Soc. 72 (1950) 4506–4511. L.G. Longsworth, J. Am. Chem. Soc. 74 (1952) 4155–4159. F.J. Gutter, G. Kegeles, J. Am. Chem. Soc. 75 (1953) 3893–3896. L.G. Longsworth, J. Am. Chem. Soc. 75 (1953) 5705–5709. L.G. Longsworth, J. Phys. Chem. 58 (1954) 770–773. P.J. Dunlop, J. Am. Chem. Soc. 77 (1955) 2994–2996. L.A. Woolf, D.G. Miller, L.J. Gosting, J. Am. Chem. Soc. 84 (1962) 317–331. [8] H.D. Ellerton, G. Reinfelds, D.E. Mulcahy, P.J. Dunlop, J. Phys. Chem. 68 (1964) 403–408.
22
T. Umecky et al. / Fluid Phase Equilibria 264 (2008) 18–22
[9] M. Lemaguer, F.H. Wolfe, T.G. Smyrl, AIChE J. 22 (1976) 389–393. [10] Y.C. Chang, A.S. Myerson, AIChE J. 32 (1986) 1567–1569. [11] L. Paduano, R. Sartorio, V. Vitagliano, L. Costantino, J. Mol. Liq. 47 (1990) 193–202. [12] A.S. Myerson, P.Y. Lo, J. Cryst. Growth 110 (1991) 26–33. [13] R. Lu, D.G. Leaist, J. Solution Chem. 27 (1998) 285–297. [14] Y. Wu, P. Ma, Y. Liu, S. Li, Fluid Phase Equilib. 186 (2001) 27–38. [15] Y. Ma, C. Zhu, P. Ma, K. Yu, J. Chem. Eng. Data 50 (2005) 1192–1196. [16] T. Umecky, T. Kuga, T. Funazukuri, J. Chem. Eng. Data 51 (2006) 1705–1710. [17] G. Taylor, Proc. R. Soc. Lond. A219 (1953) 186–203. [18] R. Aris, Proc. R. Soc. Lond. A235 (1956) 67–77. [19] 1999 JSME Steam Tables, fifth ed., JSME, Tokyo, 1999, p. 167. [20] A. Alizadeh, C.A. Nieto de Castro, W.A. Wakeham, Int. J. Thermophys. 1 (1980) 243–284.
[21] T. Yoshida, T. Okada, T. Hobo, Bunseki Kagaku 48 (1999) 917–926. [22] T. Funazukuri, M. Nishio, J. Chem. Eng. Data 44 (1999) 73– 76. [23] N. Mogi, E. Sugai, Y. Fuse, T. Funazukuri, J. Chem. Eng. Data 52 (2007) 40–43. [24] T. Funazukuri, C.Y. Kong, S. Kagei, J. Chromatogr. A 1037 (2004) 411–429. [25] T. Funazukuri, Y. Ishiwata, Fluid Phase Equilib. 164 (1999) 117–129. [26] T. Funazukuri, N. Nishimoto, N. Wakao, J. Chem. Eng. Data 39 (1994) 911– 914. [27] C.R. Wilke, P. Chang, AIChE J. 1 (1955) 264–270. [28] W. Hayduk, H. Laudie, AIChE J. 20 (1974) 611–615. [29] W. Hayduk, B.S. Minhas, Can. J. Chem. Eng. 60 (1982) 295–299. [30] Z. Yan, J. Wang, W. Liu, J. Lu, Thermochim. Acta 334 (1999) 17–27.
Fluid Phase Equilibria 264 (2008) 18–22
Effects of hydroxyl groups on binary diffusion coefficients of ␣-amino acids in dilute aqueous solutions Tatsuya Umecky, Shigeyoshi Omori, Tomoyuki Kuga, Toshitaka Funazukuri ∗ Department of Applied Chemistry, Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan Received 10 June 2006; received in revised form 1 October 2007; accepted 19 October 2007
Abstract Binary diffusion coefficients, D12 , of ␣-amino acids with hydroxyl groups, e.g., serine, threonine, allothreonine and homoserine, in dilute aqueous solutions were measured at six different temperatures from 293.2 to 333.2 K by the Taylor dispersion method. The determined D12 values of serine and threonine at 298.2 K were in good agreement with the published data, whereas no data for allothreonine and homoserine is available in the literature. The D12 values for each amino acid were well represented with the Stokes–Einstein equation by adjusting the molecular diameter. The D12 values for amino acids containing hydroxyl groups, except for homoserine, were lower by approximately 5%, on the basis of the same solute molar volume, than those from the corresponding amino acids without hydroxyl groups. © 2007 Elsevier B.V. All rights reserved. Keywords: Amino acid; Binary diffusion coefficient; Hydroxyl group; Molecular diameter; Prediction; Taylor dispersion
1. Introduction Amino acids and their derivatives are important in various fields, e.g., food, pharmaceutical, nutraceutical and cosmetic industries, so that the demand for amino acids is rapidly increasing. To produce amino acids synthetically and to separate them efficiently, it is essential to design chemical reactors and separators that take the transport phenomena of these processes into consideration. The binary diffusion coefficient, D12 , is one of the most important physical properties in estimating mass transfer rates. There are many reports on D12 measurements of ␣-amino acids in aqueous solutions [1–15]. However, few D12 data of ␣-amino acids containing hydroxyl groups are available in the literature [2,4,14,15]. Recently, we measured the D12 values of several ␣-amino acids of the NH2 –CH(COOH)–R form, where R is the alkyl up to a butyl group, in dilute aqueous solutions at temperatures from 293.2 to 333.2 K [16]. In the present study, we focus on ␣-amino acids having a hydroxyl group: serine, Ser (R CH2 –OH), threonine, Thr [R CH(CH3 )–OH], its stereoisomer allothreonine, aThr [R CH(CH3 )–OH] and homoserine,
∗
Corresponding author. E-mail address: [email protected] (T. Funazukuri).
0378-3812/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2007.10.013
Hse (R CH2 –CH2 –OH). The D12 values of these ␣-amino acids in dilute aqueous solutions were measured at temperatures from 293.2 to 333.2 K by the Taylor dispersion method, and the effects of a hydroxyl group on the D12 values were studied and compared to our previous data on ␣-amino acids with no hydroxyl groups. 2. Experimental 2.1. Materials DL-Ser (99%, Acros), DL-Thr (99.5%, Acros), DL-aThr (98%, Acros) and DL-Hse (98%, Tokyo Kasei) were used without further purification. Ultrapure water produced with a Millipore Direct-Q system was used as a solvent. 2.2. Procedures The experimental apparatus and procedure were identical with those employed in the previous study [16], and are briefly described below. The degassed water was supplied at a fixed flow velocity of ≈7.0 × 10−3 m s−1 with a syringe pump (100DM, Isco). The aqueous solution at an ␣-amino acid concentration of 10.0 mol m−3 (corresponding to ≈0.1 wt%) was injected to a diffusion tube (Supelco; inner radius 2.64 × 10−4 m, length
T. Umecky et al. / Fluid Phase Equilibria 264 (2008) 18–22
42.12 m and coil radius ≈0.095 m) through an injector (7725, Rheodyne; sampling loop ≈2.0 × 10−8 m3 ) after the sample solution had been maintained for 30 min or longer in the injector. The ␣-amino acid concentration at the diffusion tube exit was detected with a differential refractometer (L-7490, Hitachi) and the refractive index time change was recorded with an integrator (D-2500, Hitachi). The temperature in the water bath was controlled within ±0.1 K during all measurements. 2.3. Analysis In the Taylor dispersion method [17,18] the cross-sectional average solute concentration Ccal (t) at the exit of a diffusion tube, the distance of L from the inlet, is expressed by Eqs. (1) and (2). m (L − ut)2 Ccal (t) = exp − (1) 4Kt πR2tube (4πKt)1/2 and K = D12 +
R2tube u2 48D12
(2)
where m is the amount of the injected solute, Rtube is the inner radius of the diffusion tube, t is the time and u is the average flow velocity. Two parameters, D12 and u, in Eqs. (1) and (2) were determined so as to minimize the root-mean-square fitting error, ε, defined by Eq. (3), between the response curves of the
19
observed Cexp (t) and calculated Ccal (t) (ε < 1%): 1/2 {Cexp (t) − Ccal (t)}2 t ε= × 100 {Cexp (t)}2 t
(3)
3. Results and discussion The measured D12 value, solvent velocity, rms fitting error ε and DeSc1/2 value are presented in Table 1. They are the mean values obtained from five measurements under each condition, and the figure in parenthesis is the standard deviation. The reproducibility of the D12 values was almost ±1.0% (the maximum ± 2.0%). In this study, densities and viscosities of water were obtained from the literature [19]. The DeSc1/2 values were always lower than 8 under all conditions studied, where De and Sc are the Dean and Schmidt numbers, respectively. Alizadeh et al. estimated the effects of the secondary flow due to tube coiling to be lower than 1.0% in terms of the moment in the Taylor dispersion when DeSc1/2 < 8 [20]. Hence, the effect of the secondary flow in the present study was negligible. The present D12 values of Ser and Thr at 298.2 K are 8.80 × 10−10 and 7.99 × 10−10 m2 s−1 , respectively, and they are consistent with the dilute D12 data reported by Longsworth (8.80 × 10−10 m2 s−1 for Ser and 7.98 × 10−10 m2 s−1 for Thr) [4] and Ma et al. (7.97 × 10−10 m2 s−1 for Thr) [15]. No data for aThr and Hse is available in the literature. It is interesting that the D12 value of Hse is slightly larger than those of Thr and aThr at each temperature, although the molecular weights of the three ␣-amino acids are identical. Differences
Table 1 Values of D12 , u, ε and DeSc1/2 for each ␣-amino acida ␣-Amino acid
T (K)
D12 (10−10 m2 s−1 )
u (10−3 m s−1 )
ε (%)
DeSc1/2
Ser
293.2 298.2 303.2 313.2 323.2 333.2
7.72 (0.08) 8.80 (0.06) 9.91 (0.09) 12.56 (0.14) 15.49 (0.18) 18.76 (0.23)
7.00 (0.01) 6.99 (0.01) 7.02 (0.01) 7.04 (0.01) 7.07 (0.01) 7.11 (0.01)
0.65 (0.14) 0.60 (0.12) 0.49 (0.11) 0.45 (0.07) 0.53 (0.13) 0.57 (0.14)
7.0 (0.1) 6.9 (0.1) 6.9 (0.1) 6.8 (0.1) 6.7 (0.1) 6.6 (0.1)
Thr
293.2 298.2 303.2 313.2 323.2 333.2
6.91 (0.05) 7.99 (0.03) 9.04 (0.04) 11.39 (0.13) 14.26 (0.12) 17.20 (0.03)
7.00 (0.01) 7.02 (0.01) 7.02 (0.01) 7.05 (0.01) 7.08 (0.01) 7.11 (0.01)
0.63 (0.18) 0.65 (0.11) 0.56 (0.13) 0.53 (0.10) 0.62 (0.15) 0.60 (0.14)
7.4 (0.1) 7.3 (0.1) 7.3 (0.1) 7.2 (0.1) 7.0 (0.1) 6.9 (0.1)
aThr
293.2 298.2 303.2 313.2 323.2 333.2
6.97 (0.02) 7.96 (0.05) 9.06 (0.08) 11.44 (0.12) 14.22 (0.09) 17.24 (0.10)
7.00 (0.01) 7.01 (0.01) 7.02 (0.01) 7.05 (0.01) 7.08 (0.01) 7.11 (0.01)
0.59 (0.15) 0.66 (0.11) 0.67 (0.08) 0.64 (0.10) 0.78 (0.09) 0.59 (0.12)
7.4 (0.1) 7.3 (0.1) 7.3 (0.1) 7.1 (0.1) 7.0 (0.1) 6.9 (0.1)
Hse
293.2 298.2 303.2 313.2 323.2 333.2
7.26 (0.08) 8.39 (0.12) 9.39 (0.09) 11.86 (0.11) 14.75 (0.19) 17.83 (0.19)
6.94 (0.01) 6.97 (0.03) 7.01 (0.01) 7.02 (0.01) 7.04 (0.01) 7.07 (0.01)
0.51 (0.12) 0.49 (0.09) 0.50 (0.09) 0.63 (0.09) 0.52 (0.11) 0.46 (0.08)
7.2 (0.1) 7.1 (0.1) 7.1 (0.1) 7.0 (0.1) 6.9 (0.1) 6.8 (0.1)
a
The standard deviation obtained from five measurements is given in parentheses.
20
T. Umecky et al. / Fluid Phase Equilibria 264 (2008) 18–22
Table 2 Determined constants α and β in Eq. (4) together with AAD% and AD%max ␣-Amino acid
1015 α
β
AAD%
AD%max
Ser Thr aThr Hse
2.600 1.990 2.025 2.357
−1.001 −1.025 −1.023 −1.007
0.27 0.33 0.18 0.41
0.57 0.66 0.43 0.91
in the D12 values among ␣-amino acids with the same molecular weights were not observed in our previous study [16]. As discussed later, this could result from the much lower hydrophilicity of Hse compared to Thr [21]. We have already reported that Eq. (4) with two adjustable constants α and β accurately represents the measured D12 data of the ␣-amino acids [16], C5-alcohols [22] and sugars [23] in dilute aqueous solutions, as well as various systems such as organic compounds in supercritical fluids [24], in a mixture of carbon dioxide and hexane [25] and in organic solvents [26] under various pressures: D12 = αηβ T
Table 3 Molecular diameters σ SE obtained from the Stokes–Einstein equation with the D12 data at 293.2–333.2 K, AAD% and AD%max for various ␣-amino acids ␣-Amino acid
1010 σ SE (m)
AAD% (%)
AD%max (%)
With OH Ser Thr aThr Hse
5.585 6.139 6.127 5.892
0.27 0.65 0.52 0.48
0.66 1.14 0.86 0.72
Without OH [16] Gly Ala Abu Nva Val Nle Leu Ile aIle t-Leu
4.640 5.328 5.848 6.282 6.247 6.630 6.626 6.580 6.558 6.621
0.96 0.45 0.37 0.84 0.92 1.01 1.25 1.05 0.82 1.42
1.72 0.96 0.83 1.35 1.56 1.62 2.06 1.61 1.32 2.59
Stokes–Einstein (SE) equation given by Eq. (6): (4)
where T is the absolute temperature and η is the solvent viscosity in units of Pa s. Table 2 lists the constants α and β in Eq. (4) obtained by least-squares fitting, together with average absolute deviations, AAD%, defined by Eq. (5), and maximum absolute deviations, AD%max : 1 D12,exp − D12,prd (5) AAD% = × 100 N D12,exp where N is the number of data points, D12,exp and D12,prd are the values measured experimentally and predicted by correlation, e.g., in Eq. (4) with the α and β values determined, respectively. As seen in Fig. 1, good accuracies were obtained in Eq. (4) by adjusting the two parameters α and β with AAD% and AD%max smaller than 0.5 and 1.0%, respectively. As has been seen in aqueous solutions [16,22,23], β can be assumed to be −1 in this study, corresponding to the
Fig. 1. D12 /T vs. H2 O viscosity for Ser (squares), Thr (circles), aThr (triangles) and Hse (diamonds) at temperatures from 293.2 to 333.2 K.
D12 =
kB T 3πησSE
(6)
where kB is the Boltzmann constant and σ SE is the solute molecular diameter based on the Stokes–Einstein equation. Thus, the molecular diameter σ SE involved in the SE equation was adjusted for each amino acid with a hydroxyl group in the present study, and without a hydroxyl group in the previous study [16], as listed in Table 3, together with AAD% and AD%max . The accuracies are good, as compared with those of the conventional correlations, as listed in Table 4, although it is worse than Eq. (4) with two parameters adjusted. Note that the accuracy of the Wilke–Chang equation [27] is lower, but modifying the equaTable 4 AAD% values for the predictive correlations for various ␣-amino acids measured in the present and previous studies [16] Wilke–Chang [27]
Hayduk–Minhas [29]
ϕ = 2.6
ϕ = 2.26 [28]
With OH Ser Thr aThr Hse
13.7 12.1 11.9 7.6
6.0 4.5 4.3 0.5
6.2 5.0 4.8 1.1
Without OH Gly Ala Abu Nva Val Nle Leu Ile aIle t-Leu
13.5 13.0 10.5 7.8 7.2 4.7 4.6 3.9 4.0 4.5
5.8 5.3 3.0 1.0 0.9 2.4 2.5 3.2 3.0 2.6
5.7 5.5 3.4 1.8 1.7 1.9 2.1 2.5 2.4 2.5
8.5
3.2
3.3
Overall
T. Umecky et al. / Fluid Phase Equilibria 264 (2008) 18–22
21
the Stokes–Einstein equation with one parameter, i.e., molecular diameter σ SE , determined for each solute. The values of σ SE were correlated with solute molar volume with a slope of 0.422. The D12 values of the ␣-amino acids having a hydroxyl group except for Hse were found to be lower by ca. 5% than those of the ␣-amino acids having no hydroxyl group, which distinctively shows low hydrophilicity. Consequently, the D12 values were affected primarily by the solute molecular size, and secondarily by the solute–solvent interaction.
Fig. 2. Molecular diameter σ SE vs. molar volume for various ␣-amino acids with OH (solid triangles) and without OH (blank circles) from 293.2 to 303.2 K.
tion replacing an original association factor ϕ of 2.6 with 2.26, recommended by Hayduk and Laudie [28], improved the accuracy to that of Hayduk and Minhas [29]. Accuracies of these conventional equations are acceptable, but they are lower than Eq. (4) with β = −1. It is known that D12 values are affected by the solute molecular size and the solute–solvent interaction. Fig. 2 shows σ SE (=kB T/3πηD12 ) versus solute molar volume at 293.2–303.2 K predicted with the group contribution method of Yan et al. [30] for ␣-amino acids with a hydroxyl group (solid triangles) and without (blank circles) [16]. Note that the group contribution method is based on their experimental data from 278.15 to 308.15 K [30], and the values for each solute exhibit a slight temperature dependence. As depicted, the σ SE values for the amino acids without a hydroxyl group are correlated with molar volumes with a slope of 0.407 in the logarithmic plot. However, the slope with a hydroxyl group is nearly the same (0.422), but with a different intercept, except for Hse. In other words, the σ SE values for amino acids with a hydroxyl group are higher by approximately 5% (correspondingly, the diffusion coefficients are lower) than those without a hydroxyl group at the same molar volumes. This suggests that the presence of a hydroxyl group retards diffusion rates somewhat, indicating that the solute–solvent interaction for compounds with a hydroxyl group is stronger than those without. It is interesting that the molecular diameter σ SE for Hse is nearly the same as those amino acids without a hydroxyl group. This could be attributed to the significantly lower hydrophilicity of Hse than Ser, Thr or aThr. In fact, Hse shows an exceptionally low hydrophilicity compared to Ser, Thr and aThr as shown by the hydrophilic retention coefficients for various amino acids determined from the retention times measured in liquid chromatography by Yoshida et al. [21]. 4. Conclusion The D12 values of Ser, Thr, aThr and Hse in dilute aqueous solutions were measured at six temperatures from 293.2 to 333.2 K with the Taylor dispersion method. The determined D12 values were in good agreement with the reference data within experimental error. The D12 values were represented by
List of symbols AAD% average absolute deviation defined by Eq. (5) AD%max maximum absolute deviation C(t) cross-sectional average concentration of solute D12 binary diffusion coefficient De Dean number = (2ρuRtube /η)(Rtube /Rcoil )1/2 kB Boltzmann constant L length of diffusion tube m amount of injected solute Rcoil coil radius of diffusion tube inner radius of diffusion tube Rtube Sc Schmidt number = η/(ρD12 ) t time T absolute temperature u average flow velocity Greek symbols α constant in Eq. (4) β constant in Eq. (4) ε root-mean-square fitting error defined by Eq. (3) η water viscosity ϕ solvent association factor ρ water density σ SE molecular diameter based on the Stokes–Einstein equation Subscripts cal calculated exp measured experimentally prd predicted Acknowledgement The authors are grateful to the Ministry of Education, Sports, Culture, Science and Technology of Japan for support through grant-in-aid of #18560725. References [1] [2] [3] [4] [5] [6] [7]
M.S. Lyons, J.V. Thomas, J. Am. Chem. Soc. 72 (1950) 4506–4511. L.G. Longsworth, J. Am. Chem. Soc. 74 (1952) 4155–4159. F.J. Gutter, G. Kegeles, J. Am. Chem. Soc. 75 (1953) 3893–3896. L.G. Longsworth, J. Am. Chem. Soc. 75 (1953) 5705–5709. L.G. Longsworth, J. Phys. Chem. 58 (1954) 770–773. P.J. Dunlop, J. Am. Chem. Soc. 77 (1955) 2994–2996. L.A. Woolf, D.G. Miller, L.J. Gosting, J. Am. Chem. Soc. 84 (1962) 317–331. [8] H.D. Ellerton, G. Reinfelds, D.E. Mulcahy, P.J. Dunlop, J. Phys. Chem. 68 (1964) 403–408.
22
T. Umecky et al. / Fluid Phase Equilibria 264 (2008) 18–22
[9] M. Lemaguer, F.H. Wolfe, T.G. Smyrl, AIChE J. 22 (1976) 389–393. [10] Y.C. Chang, A.S. Myerson, AIChE J. 32 (1986) 1567–1569. [11] L. Paduano, R. Sartorio, V. Vitagliano, L. Costantino, J. Mol. Liq. 47 (1990) 193–202. [12] A.S. Myerson, P.Y. Lo, J. Cryst. Growth 110 (1991) 26–33. [13] R. Lu, D.G. Leaist, J. Solution Chem. 27 (1998) 285–297. [14] Y. Wu, P. Ma, Y. Liu, S. Li, Fluid Phase Equilib. 186 (2001) 27–38. [15] Y. Ma, C. Zhu, P. Ma, K. Yu, J. Chem. Eng. Data 50 (2005) 1192–1196. [16] T. Umecky, T. Kuga, T. Funazukuri, J. Chem. Eng. Data 51 (2006) 1705–1710. [17] G. Taylor, Proc. R. Soc. Lond. A219 (1953) 186–203. [18] R. Aris, Proc. R. Soc. Lond. A235 (1956) 67–77. [19] 1999 JSME Steam Tables, fifth ed., JSME, Tokyo, 1999, p. 167. [20] A. Alizadeh, C.A. Nieto de Castro, W.A. Wakeham, Int. J. Thermophys. 1 (1980) 243–284.
[21] T. Yoshida, T. Okada, T. Hobo, Bunseki Kagaku 48 (1999) 917–926. [22] T. Funazukuri, M. Nishio, J. Chem. Eng. Data 44 (1999) 73– 76. [23] N. Mogi, E. Sugai, Y. Fuse, T. Funazukuri, J. Chem. Eng. Data 52 (2007) 40–43. [24] T. Funazukuri, C.Y. Kong, S. Kagei, J. Chromatogr. A 1037 (2004) 411–429. [25] T. Funazukuri, Y. Ishiwata, Fluid Phase Equilib. 164 (1999) 117–129. [26] T. Funazukuri, N. Nishimoto, N. Wakao, J. Chem. Eng. Data 39 (1994) 911– 914. [27] C.R. Wilke, P. Chang, AIChE J. 1 (1955) 264–270. [28] W. Hayduk, H. Laudie, AIChE J. 20 (1974) 611–615. [29] W. Hayduk, B.S. Minhas, Can. J. Chem. Eng. 60 (1982) 295–299. [30] Z. Yan, J. Wang, W. Liu, J. Lu, Thermochim. Acta 334 (1999) 17–27.