Activation Parameters of Self-Diffusion of Aromatic Chiral Molecules in

Novosibirsk State University, 2, Pirogova st., 630090, Russian Federation. Abstract. The mobility of aromatic chiral molecules 1-phenylethanol and 1-p...
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Activation Parameters of Self-Diffusion of Aromatic Chiral Molecules in External Magnetic Fields Svetlana G. Kozlova,*,†,‡ Nikolay B. Kompankov,† and Marina S. Zavakhina†,‡ †

Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, 3, Akad. Lavrentiev Avenue, Novosibirsk 630090, Russian Federation ‡ Novosibirsk State University, 2, Pirogova Street, 630090 Novosibirsk, Russian Federation S Supporting Information *

ABSTRACT: The mobility of aromatic chiral molecules 1-phenylethanol and 1-phenyl-1-propanol in liquids was studied by 1H NMR spectroscopy depending on the strength of the external magnetic field, temperature, and concentration ratio of enantiomers. The data obtained were analyzed using Arrhenius law. The activation parameters were found to depend on the applied field. This effect is caused by the induced magnetic moments in aromatic molecules. The use of strong magnetic fields seems to be promising for investigation of intermolecular interactions of chiral molecules.

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INTRODUCTION The action of external magnetic fields on matter is a topical problem in various fields of physics, chemistry, biology, and medicine.1−7 The mechanisms underlying the observed responses to such action remain unclear and debatable. In particular, many human diseases are known to be caused by blood hyperviscosity, which can be reduced by the applied external magnetic field.8 The reduction of viscosity is related to the increased mobility of individual particles arranged along magnetic field lines. However, in some cases, a magnetic field can, on the contrary, retard the mobility because the induced magnetic moments increase the scattering cross section of a diffusing particle.9 Earlier, it was shown that self-diffusion of aromatic chiral molecules (1-phenylethanol and 1-phenyl-1-propanol) in liquids depends on the magnetic field strength and concentration ratio of enantiomers.10,11 In mixtures consisting of enantiomers, enantiomers may be surrounded by enantiomers of other chirality. The dynamic distribution of molecules must be different and depend on the concentration ratio of enantiomers in a liquid. In addition, the instantaneous distribution of induction magnetic moments in molecules with aromatic bonds can also be different and lead to different dispersion interactions.12 This set of factors can lead to different diffusion of enantiomers in mixtures. The present work deals with the temperature dependence of selfdiffusion coefficients of the indicated systems in various external magnetic fields.

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purchased from Aldrich and Fluka. The racemate densities of 1-phenylethanol and 1-phenyl-1-propanol were 1.012 and 0.994 g/mL (25 °C),13 and the viscosities were 8.49 and 13.49 mPa s (25 °C),14 respectively. Mixtures were prepared by the addition of corresponding enantiomers to their racemates, as was done in refs 10 and 11. These mixtures were described with the enantiomeric excess parameter ee = (xR − xS)/(xR + xS), where xR and xS are the concentration ratios of R and S molecules in the mixture (chiral polarized medium). Parameter ee had values of 1, 0.6, 0.2, and 0. The 1H NMR studies were done using Bruker Avance NMR 500 and 600 spectrometers with magnetic fields (H0) of 11.7 and 14.1 T, respectively. A pulse method of NMR diffusion ordered spectroscopy (DOSY) was used with a bipolar longitudinal eddy current delay sequence to determine diffusion coefficients.15−17 The temperature was adjusted and maintained by purging through the radio frequency coil with a sample of heated air. Prior to each measurement, the temperature of the sample was maintained for 20 min and determined with an accuracy of ±0.1 K. Despite the fact that chiral mixtures of 1-phenylethanol and 1-phenyl-1-propanol were used in the experiments, the separate spectral lines of 1H NMR of the enantiomers were not observed. This is due to the weak effect of the chiral polarized mediums in the chemical shifts for 1H nuclei.18,10,11

EXPERIMENTAL SECTION

Received: June 15, 2017 Revised: June 17, 2017 Published: June 19, 2017

For the experiment, R- and S-(+/−)-1-phenylethanol, R- and S-(+/−)-1-phenyl-1-propanol, and their racemic mixtures were © 2017 American Chemical Society

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DOI: 10.1021/acs.jpcb.7b05847 J. Phys. Chem. B 2017, 121, 6655−6658

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Figure 1. Dependence of the self-diffusion coefficients (D) on temperature (a) and their Arrhenius plot (b) in the 1-phenylethanol racemic mixture (ee = 0.0). H0 = 11.7 (●) and 14.1 T (○).

Figure 2. Dependence of the self-diffusion coefficients (D) on temperature (a) and their Arrhenius plot (b) in the 1-phenyl-1-propanol racemic mixture (ee = 0.0). H0 = 11.7 (●) and 14.1 T (○).

Figure 3. Dependences of activation energy (E) on ee in liquids: (a) 1-phenylethanol and (b) 1-phenyl-1-propanol. Horizontal discontinuous lines are to the average values of E (in parentheses) for the corresponding experiments in different magnetic fields of H0 = 11.7 (●) and 14.1 T (○).

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RESULTS AND DISCUSSION Figures 1a and 2a display the dependences of self-diffusion coefficients (D) on temperature in racemic liquids of 1-phenylethanol and 1-phenyl-1-propanol, which were obtained in external magnetic fields of H0 = 11.7 and 14.1 T. For both the 1-phenylethanol and 1-phenyl-1-propanol mixtures, an increase in D values with raising the temperature is more pronounced in the field H0 = 14.1 T. A similar behavior of D was observed for all of the tested liquids having different ee values (Figures S1−S6). In the simplest case, the dependences of molecular selfdiffusion coefficients in liquids for the limited temperature range are determined by the Arrhenius law18−20 D = D0 ·exp( −E /RT )

where D0 is the entropy-related pre-exponential factor, E is the activation energy, R is the universal gas constant, and T is the temperature. Experimental dependences of D on temperature in all of the tested mixtures (Figures 1b, 2b, and S1−S6) obey the Arrhenius law. The obtained E and D0 values are presented in Figure 3 and in Tables 1 and 2. In a magnetic field of 11.7 T, the E values are comparable values of activation barriers for diffusion processes in liquids obtained not by NMR methods.21 In a magnetic field of 14.1 T, the E values are several fold higher as compared to similar values in a magnetic field of 11.7 T. In the magnetic field of 11.7 T, the D0 values are close to typical diffusion coefficients of molecules in gases,22 whereas in the magnetic field of 14.1 T,

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DOI: 10.1021/acs.jpcb.7b05847 J. Phys. Chem. B 2017, 121, 6655−6658

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The Journal of Physical Chemistry B

Table 1. Activation Energy (E) and Pre-exponential Factor (D0) for Liquid Mixtures of 1-Phenylethanol and 1-Phenyl-1-Propanol with Different ee Values in an External Magnetic Field of H0 = 11.7 T with W as the Level of Confidence for Arrhenius Plots 1-phenylethanol ee 0 0.2 0.6 1.0

E, kcal/mol 6.8 ± 0.5 6.5 ± 0.6 6.7 ± 0.3 6.1 ± 0.4

1-phenyl-1-propanol

D0, m2/s −5

(1.0 ± 2.0) × 10 (1.0 ± 1.0) × 10−5 (1.0 ± 1.0) × 10−5 (0.4 ± 0.4) × 10−5

W

E, kcal/mol

D0, m2/s

W

0.980 0.966 0.987 0.979

8.3 ± 0.4 8.1 ± 0.3 8.4 ± 0.4 8.3 ± 0.5

(1.0 ± 1.0) × 10−4 (1.0 ± 1.0) × 10−4 (1.0 ± 1.0) × 10−4 (1.0 ± 1.0) × 10−4

0.992 0.996 0.992 0.985

Table 2. Activation Energy (E) and Pre-exponential Factor (D0) for Liquid Mixtures of 1-Phenylethanol and 1-Phenyl-1-Propanol with Different Chiral Polarization Values (ee) in an External Magnetic Field of H0 = 14.1 T with W as the Level of Confidence for Arrhenius Plots 1-phenylethanol

1-phenyl-1-propanol

ee

E, kcal/mol

D0, m2/s

W

E, kcal/mol

D0, m2/s

W

0 0.2 0.6 1.0

17.1 ± 0.6 22.0 ± 1.5 16.4 ± 0.8 21.4 ± 2.0

(1 ± 1) × 103 (1 ± 5) × 106 (1 ± 2) × 102 (0.4 ± 4) × 106

0.995 0.982 0.988 0.961

24.0 ± 1.0 23.0 ± 1.0 22.1 ± 0.8 13.8 ± 0.7

(2 ± 1) × 107 (1 ± 3) × 107 (1 ± 2) × 106 (1 ± 2) × 100

0.990 0.990 0.995 0.991

Figure 4. Dependences of the self-diffusion coefficients (D) on ee in 1-phenylethanol (a) and 1-phenyl-1-propanol (b) mixtures. H0 = 11.7 (●) and 14.1 T (○). T = 318.15 K.

the D0 values are high, which also testifies to their dependence on H0. It is known that D0 may depend on E20 D0 ≈ k1 E ·exp(k 2·E)

Various approaches are used to investigate self-diffusion coefficients of each component in a binary mixture with an arbitrary composition;23 in the ideal case, the Darken equation can be employed,24,25 which postulates that

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D = x R DR + xSDS

where k1 and k2 are the phenomenological parameters depending on the type of diffusion process. The increase of E values with increasing H0 cannot be responsible for the ∼1010 increment in D0 if assuming that k1 and k2 remain constant with changes in magnetic field (Tables 1 and 2). Hence, it follows that variation of H0 changes the type of mobility, which implicitly enters into parameters k1 and k2, if using for analysis of the Arrhenius equation.18−20 Such changes in self-diffusion of aromatic molecules can be related to the induced magnetic moments in aromatic molecules and their interactions with the external magnetic field.10,11 The indicated interactions affect the orientation of the molecules, their hydrodynamic status, and the overall self-diffusion process, as was shown earlier.3 The earlier measurements of diffusion coefficients at room temperature (298−303 K) revealed that an increase in magnetic field strength produces differences in the mobility of enantiomers relative to each other.10,11 In the present work, activation barriers of self-diffusion E in the fields H0 = 11.7 and 14.1 T were estimated with errors of ±0.4 and ±2.0 kcal/mol (Tables 1 and 2). Thus, in the field H0 = 14.1 T, the observed difference between E values for the tested mixtures with different ee values can be considered as a significant difference (Figure 3).

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where DR and DS are the self-diffusivities of enantiomers in the mixture. If the studied enantiomers have virtually indistinguishable viscosity and diffusion parameters, then DR, DS, and D should be identical and independent of ee. Figure 4 displays the dependences of D on ee. At H0 = 11.7 T, the coefficients D are virtually independent of ee, whereas at H0 = 14.1 T, a different pattern is observed. Moreover, at H0 = 14.1 T, the form of D − ee dependences changes with temperature (Figures S8−S11).

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CONCLUSIONS In external magnetic fields of 11.7 and 14.1 T, the 1H NMR spectra do not show differences in chemical shifts between 1phenylethanol and 1-phenyl-1-propanol enantiomers in liquid mixtures.10,11 However, as was demonstrated in our study, parameters of self-diffusion mobility of the enantiomers depend on the strength of the external magnetic field. The observed dependence of these parameters may be related to the induced magnetic moments, their interaction with each other and the magnetic field, and the overall changes in correlated motion of 6657

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(12) Zarycz, N.; Provasi, P. F.; Pagola, G. I.; Ferraro, M. B.; Pelloni, S.; Lazzeretti, P. Computational Study of Basis Set and Electron Correlation Effects on Anapole Magnetizabilities of Chiral Molecules. J. Comput. Chem. 2016, 37, 1552−1558. (13) Yaws, C. L. The Yaws Handbook of Physical Properties for Hydrocarbons and Chemicals; 2nd ed., Gulf Professional Publishing, 2015. (14) Wohlfarth, C.; Wohlfarth, B. In Pure Organic Liquids; Lechner, M. D., Ed.; Springer-Verlag: Berlin, Heidelberg, Germany, 2002. (15) Morris, K. F.; Johnson, C. S. The Resolution of Discrete and Continuous Molecular Size Distributions by Means of Diffusion Ordered 2D-NMR Spectroscopy. J. Am. Chem. Soc. 1993, 115, 4291− 4299. (16) Wu, D.; Chen, A.; Johnson, C. S. An Improved Diffusion-Ordered Spectroscopy Experiment Incorporating Bipolar-Gradient Pulses. J. Magn. Reson., Ser. A 1995, 115, 260−264. (17) Johnson, C. S. Diffusion Ordered Nuclear Magnetic Resonance Spectroscopy: Principles and Applications. Prog. Nucl. Magn. Reson. Spectrosc. 1999, 34, 203−256. (18) Preissing, G.; Noack, F.; Kosfeld, R.; Gross, B. Zur Deutung der Protonenspinrelaxation in Glycerin. Z. Phys. A: Hadrons Nucl. 1971, 246, 84−90. (19) Tomlinson, D. J. Temperature Dependent Self-Diffusion Coefficient Measurements of Glycerol by the Pulsed NMR Technique. Mol. Phys. 1973, 25, 735−738. (20) Slotfeldt-Ellingsen, D.; Pedersen, B. The Bonded Water Molecule = III. 180 Flip and Diffusion. J. Phys. Chem. Solids 1977, 38, 65−72. (21) Messaâdi, A.; Dhouibi, N.; Hamda, H.; Belgacem, F. B. M.; Adbelkader, Y. H.; Ouerfelli, N.; Hamzaoui, A. H. A New Equation Relating the Viscosity Arrhenius Temperature and the Activation Energy for Some Newtonian Classical Solvents. J. Chem. 2015, 2015, 1− 12 , and references therein.. (22) Cussler, E. L. Diffusion: Mass Transfer in Fluid Systems, 3rd ed.; Cambridge University Press, 2009. (23) Arkhipov, V. P. A Method for Calculating the Self-Diffusion Coefficients of Molecules in Multicomponent Mixtures of Liquids. Russ. J. Phys. Chem. A 2011, 85, 423−426. (24) Darken, L. S. Diffusion, Mobility and Their Interrelation Through Free Energy in Binary Metallic Systems. Trans. Inst. Min. Metall. Engrs. 1948, 175, 184−202. (25) Krishna, R.; Van Baten, J. Validating the Darken Relation for Diffusivities in Fluid Mixtures of Varying Densities by Use of MD Simulations. Chem. Eng. Technol. 2006, 29, 761−765. (26) Chen, C.; Li, W. Z.; Song, Y. C.; Weng, L. D.; Zhang, N. Concentration Dependence of Water Self-Diffusion Coefficients in Dilute Glycerol−Water Binary and Glycerol−Water−Sodium Chloride Ternary Solutions and the Insights from Hydrogen Bonds. Mol. Phys. 2012, 110, 283−291. (27) Gabuda, S. P.; Kozlova, S. G. Correlation and Relativistic Effects on Coordinate Bonding in Hexafluorides and Hexafluoro Complexes. Russ. J. Inorg. Chem. 2001, 46, S171−S186.

electrons in molecules with increasing external magnetic field.12,26,27 We think that studies on molecular mobility in ultrahigh fields could make it possible not only to separate 1H NMR signals but also to estimate self-diffusion coefficients of individual enantiomers. This will give new insight into intermolecular interactions, particularly of chiral molecules.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b05847. Dependences of the self-diffusion coefficients on temperature and their Arrhenius plots (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Svetlana G. Kozlova: 0000-0001-7114-8676 Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by RFBR Grant N 15-03-04905. The authors thank the Institute of Organic Chemistry SB RAS for the measurements with the Avance 600 spectrometer.

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REFERENCES

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DOI: 10.1021/acs.jpcb.7b05847 J. Phys. Chem. B 2017, 121, 6655−6658