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Structure, Transport Properties, and Dielectric Properties of Lactic Acid/Pyruvic Acid Aqueous Solution in a Biofuel Cell: A Molecular Simulation Study.

INTRODUCTION

In recent years, natural polymers attract considerable attention, because they are made from waste natural materials. Some natural polymers such as poly lactic acid (L-acid) are suitable for biomedical applications, e.g., organic implants or safe drug delivery system, because they are easily hydrolyzed and resolved to L-acid, in a human body [1], Furthermore, according to the recent report, the wearable skin based biofuel cell has been achieved. It works using L-acid in human sweat as energy resource [2], These facts prompt us to investigate structure, transport properties, and dynamic properties of L-acid in a physiological salt solution by molecular dynamics (MD) simulations. As a matter of fact, in our preliminary study, we have obtained anomalous large dielectric constant in lactic acid and pyruvic acid (P-acid) in physiological salt solution [3], The main purpose of this study is to discuss the anomalous behavior of dielectric constant in relation with other physical properties, structure, vibrational motion, rotational motion, and diffusion of ions by MD.

SIMULATION PROCEDURE

The reaction processes of L-acid in a solution for biofuel cell mentioned in the previous section are summarized as follows,

Cathode: HO - CHC[H.sub.3] - COOH [right arrow] COC[H.sub.3] - COOH + 2[H.sup.+] +2[e.sup.-] (1)

Anode: (1 /2)[O.sub.2] + 2[H.sup.+] + 2[e.sup.-] [right arrow] [H.sub.2]O (2)

Total: HO - CHC[H.sub.3] - COOH + (1 /2) [O.sub.2] [right arrow] COC[H.sub.3] - COOH + [H.sub.2]O, (3)

where HO-CHC[H.sub.3]-COOH is a L-acid, and COC[H.sub.3]-COOH is a Pacid molecule, respectively. They are expected to be anions in a physiological salt solution, as, HO-CHC[H.sub.3]-CO[O.sup.-] and COC[H.sub.3]-CO[O.sup.-].

The molecules and their ions used in MD are optimized in advance to determine the configurations and charges of atoms by Gaussian09 using the density functional theory at the B3LYP/6-311++G(d,p) level of the theory in a cavity within the IEF-PCM solvent field. The IR-spectra of L-acid, L-acid anions, P-acid, and P-acid anions obtained by Gaussian09 are shown in Ref. [3]. In the region around 3,000-4,000 per cm, the modes corresponding to O-H stretching can be seen. The large peaks attributed to C=O stretching appears around 1,700 per cm. In the region 600-1,500 per cm, C-O stretching mods can be seen. In addition, in 500-1,000 per cm region, H-C-H bending mods can be observed. These modes reflect the difference of the structures of molecules and ions. The peaks in the higher region for L-acid anion and P-acid anion have tendency to shift to the lower frequency region comparing to L-acid and P-acid.

The essential procedure of MD simulation is same as our previous works [4-6], which is briefly described below. The water molecule is treated as the rigid body model, TIP4P. The pair potential function for water molecules are expressed in the charged Lennard-Jones (L-J) type potentials as [7, 8],

[[phi].sub.ij](r) = [z.sub.i][z.sub.j][e.sup.2]/r + 4[epsilon] {[([sigma]/r).sup.12] - [([sigma]/r).sup.6]}. (4)

In the equations, i and j stand for the constituent atoms; [z.sub.i] is the charge for the constituent species i; e is the elementary charge. The interactions [Na.sup.+]-[Na.sup.+], [Na.sup.+]-[Cl.sup.-], [Cl.sup.-] -[Cl.sup.-], TIP4P-[Na.sup.+], and TIP4P--[Cl.sup.-] are expressed as [9],

[[sigma].sub.ij](r) = [z.sub.i][z.sub.j][e.sup.2]/r + C/[r.sup.9] - D/[r.sup.6]. (5)

MD is performed in the NPT constant condition, at 1 atm, 310 K. The one time step is 0.1 fs. Ewald method is used for the calculation of charge interactions. The number of molecules used in MD is about 5,000 to 10,000 for calculation of structure and dielectric properties etc. The total concentrations of L-acid and P-acid anions are assumed from 0.10 to 2.5 mol/L in a physiological salt solution, where L-acid anions and P-acid anions are of the same number. SEIGRESS package (Fujitsu) is used for the main MD calculation [10]. One MD calculation is performed during 300,000 or 500,000 time steps.

SIMULATION RESULTS AND DISCUSSION

The obtained pair distribution functions, [g.sub.ij](r)'s, are shown in Fig. la-h. In these figures, no large peaks can be seen. This result suggests that the hydrogen bonds between L-acid and P-acid anions are quite weak in the solution, although some discrepancies can be seen in [g.sub.ij](r)'s between the lower concentrations and the higher concentrations. As seen in Fig. la and b for O(L-acid)--H(water), the slight differences between the lower concentration (a) and the higher concentration (b) can be seen around the first sharp peaks at 2.5 [Angstrom] and the second peaks at 3.9 [Angstrom]. In Fig. 1c and d H(L-acid)-O(water), the whole shapes of the lower concentrations and higher concentrations are similar, i.e., there are no high first peaks at 3.5 [Angstrom], and the second low peaks can be seen around 5.8 [Angstrom], although the increasing tendency of the first and second peaks as the concentration increases can be seen in Fig. Id. As seen in Fig. le and f for O(P-acid)--H(water), the first sharp peaks and the second peaks can be seen at 2.5 and 6.2 [Angstrom], respectively, although there are slight discrepancies between the lower concentrations (e) and the higher concentrations (f) at the plateaus around 4.0 [Angstrom]. Although there remain noises in Fig. 1g and f for H(P-acid)--O(water), the peak shapes are different around 5.9 [Angstrom]. These difference of water distributions around L-acid anion and P-acid anion suggests the difference of interactions between L-acid anion and P-acid anion and water molecule in the lower concentrations and the higher concentrations.

The dynamic properties of L-acid anion and P-acid anion are examined by the frequency dependent diffusion coefficient [D.sub.i](v), which is expressed using the velocity auto-correlation function (VAF) for the ith atom species, <[v.sub.i](t) x [v.sub.i](0) > as [11],

[D.sub.i](v) = 1/3 [[integral].sup.[infinity].sub.0] <[v.sub.i](t) x [v.sub.i] (0)>cos(2[pi]vt) dt. (6)

The obtained [D.sub.i](v)'s are shown in Fig. 2a and b. In Fig. 2a and b, the concentration dependence of the frequency distributions of L-acid and P-acid are shown from bottom to top, respectively. The discrepancies of frequency distributions between Fig. 2a and b may be attributed to the difference of the molecular structure of L-acid and P-acid. The large frequencies in the lower frequency regions in both Fig. 2a and b may be yielded by the larger interaction of L-acid and P-acid anions with surrounding water molecules. The extreme vibrations can be observed in 700-1,000 per cm region, which may be caused by C-H vending. Although, the bond length of L-acid anion and P-acid anion are fixed, and only bond angles can be altered in MD, the higher frequencies larger than 1,600 per cm are also obtained. These higher frequencies may be attributed to the "inter"-molecular interaction, i.e., the atomic interactions between "adjacent" L-acid/P-acid anions and/or water molecules may yield the higher frequencies like the stretching modes. It is noteworthy that the extreme frequency distributions in the low frequency region decrease as the concentration of L-acid anion and P-acid anion increases. In other words, the interaction between ions is more significant in the dilute region. We will discuss this point later in relation with the concentration dependence of dielectric constant and other physical properties.

The static dielectric constant of the solution, [epsilon], is important for the biofuel cell construction, which is defined as [11],

([epsilon]-1)(2[epsilon]'+1)/([epsilon] + 2[epsilon]') = 3[k.sub.B] [[epsilon].sub.0] TV/[M.sub.2], (7)

where [k.sub.B] is the Boltzmann constant, [[epsilon].sub.0] is the static dielectric constant in a vacuum, [epsilon]' is the static dielectric constant on the outside of the cell, T is the temperature, V is the volume of the cell. The term [M.sup.2] is expressed as,

[M.sup.2] = <[[absolute value of [[SIGMA].sup.N.sub.i=1] [[??].sub.i]].sup.2]>, (8)

where [[??].sub.i] represents the dipole moment of the i-th molecule. Under the periodic boundary condition, [epsilon]'[right arrow][infinity] is assumed, then [epsilon] is expressed as,

[epsilon] = [M.sup.2]/3[k.sub.B] [[epsilon].sub.0]TV + 1. (9)

The estimated [epsilon] values for various concentration of L-acid anion and P-acid anion are shown in Fig. 3. The characteristic peak is observed around 0.20 mol/L. These quite large e values in the dilute side may be explained by the interactions of ions in the solution, and the increasing dielectric constant in the large concentration region is proportional to the square of x as in Eq. 9[ 12].

To support above simulation results, we calculate the rotational correlational function (RCF), and estimate the lifetime of the complex in the solution, which may affect the dielectric constant. RCF is defined as [11].

[C.sub.l](t) = <[P.sub.l][[u.sub.i](t) x [u.sub.i]]>, (10)

where [u.sub.i](t) is an unit vector parallel to the principal axis of an ion or a molecule; [P.sub.l](x) is the l-th degree Legendre polynomial. The rotational correlation function is the case of l = 2, which is expressed as

[C.sub.2](t)= 1/2 <3[{[u.sub.i](t)x [u.sub.i]}.sup.2] -1>. (11)

The natural logarithm of RCFs, i.e., ln[C.sub.2](t) for L-acid and P-acid anions in the lower concentrations and higher concentrations are shown in Fig. 4a and b. The RCFs for water molecules are also shown in Fig. 4a and b for comparison. In Fig. 4a and b, the small oscillations of RCFs for P-acid are still observed, the linear region of ln[C.sub.2](0 for RCFs for L-acid can be seen until 3 ps. In the case that the decay in polarization anisotropy [C.sub.2] (t) is expressed in the exponential form [C.sub.2](f) = Aexp(-t/[tau]), the relaxation time can be obtained from the inclination of the logarithm plot of [C.sub.2](t). Therefore, the relaxation time is estimated from the inclination of ln[C.sub.2](t) from 1 to 3 ps. In Fig. 4a for the lower concentration region, the largest life time are estimated 3.3 ps at the concentration 0.10 mol/L. The linear part of ln[C.sub.2](t) also can be seen in RCFs for L-acid in the larger concentration region in Fig. 4b. The relaxation times are also estimated from the inclination of ln[C.sub.2](t) from 1 to 3 ps. The obtained lifetime in the concentration from 0.75 to 2.5 mol/L is about 1.7 to 2.9 ps. These values are comparable to that of HC[O.sub.3.sup.-] ions in seawater 1.6 ps [5]. These results may suggest that L-acid anions and surrounding water molecules affect the dielectric constant also in the large concentration region.

Finally we examine the diffusion coefficient in various concentrations of the solution. The diffusion coefficient of ions are obtainable from the slope of the mean square displacement (MSD), as,

[mathematical expression not reproducible] (12)

where i stands for the ith [alpha]-type ion, and [N.sub.[alpha]] represents its number, respectively. The angular brackets mean the average over all atomic position [r.sub.i](f) and the time average, i.e., the ensemble average. The calculated results for L-acid, P-acid and water molecules are shown in Fig. 5. The obtained [D.sub.[alpha]]'s are comparable to 1.13 x[10.sup.-5][cm.sup.2]/s for L-acid by the experiment at 303 K [13], 3.46 x[10.sup.-5][cm.sup.2]/s for water within a poly glycolic acid by MD at 300 K [14], Although the margin of errors are comparatively large, the minimum for L-acid and P-acid can be seen at 0.25 and 0.375 mol/L, respectively. This result suggests the relation between the relaxation time and the diffusion coefficient, as, [[tau].sub.[alpha]] [varies] 1/[D.sub.[alpha]], to some extent [15]. However, the detailed analysis are left for future study.

CONCLUSIONS

The pair distribution functions [g.sub.ij](r), the frequency dependent diffusion coefficients [D.sub.i](v), the dielectric constants [epsilon], the rotational correlation functions RCF, the diffusion coefficient of ions have been obtained for various concentration of L-acid and P-acid in a physiological salt solution by MD. The anomalous behavior of [epsilon] has been obtained in the lower concentration of the solution. The results are expected to be attributed to the difference of the interactions between anions of L-acid and P-acid and water molecules in the lower concentration and the higher concentration of the solution.

Shigeki Matsunaga [iD]

National Institute of Technology, Nagaoka College, Nagaoka, Japan

Correspondence to: S. Matsunaga; e-mail: matsu@nagaoka-ct.ac.jp DOI 10.1002/pen.25244

Published online in Wiley Online Library (wileyonlinelibrary.com).

ACKNOWLEDGMENTS

I would like to express my thanks to Professor S. Tamaki for his helpful comments and encouragement on this study. Part of the results in this study was obtained using the supercomputing facilities at Research Institute for Information Technology, Kyushu University. This study received financial support from the Nippon Sheet Glass Foundation for Materials Science and Engineering.

REFERENCES

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[3.] S. Matsunaga, AIP Conference Proceedings, 1981, 020115(1-4) (2018).

[4.] S. Matsunaga and S. Tamaki, J. Sol. Chem., 43, 1771 (2014).

[5.] S. Matsunaga, Int. J. Mol. Sci., 17(45), 18 (2016).

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[7.] W.L. Jorgensen, J. Chandrasekhar, J.D. Madura, R.W. Impey, and M.L. Klein, J. Chem. Phys., 79, 926 (1983).

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[10.] FUJITSU Technical Computing Solution SCIGRESS. http://www. fujit.su.com/global/solutions/business-technology/tc/sol/scigress/index. html Accessed November 20, 2018.

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[13.] A.C.F. Ribeiro, V.M.M. Lobo, D.G. Leaist, J.J.S. Natividade, L.P. Verissimo, M.C.F. Barros, and A.M.T.D.P.V. Cabral, J. Sol. Chem., 34, 1009 (2005).

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Caption: FIG. 1. (a) [g.sub.ij](r)'s for O(L-acid)--H(water) in the lower concentrations, (b) [g.sub.ij](r)'s for O (L-acid)--H(water) in the higher concentrations, (c) [g.sub.ij](r)'s for H(L-acid)--O(water) in the lower concentrations, (d) [g.sub.ij](x)'s for H(L-acid)--O (water) in the higher concentrations, (e) [g.sub.ij](r)'s for O(P-acid)--H(water) in the lower concentrations, (f) [g.sub.ij](r)'s for O(Pacid)--H(water) in the higher concentrations, (g) [g.sub.ij] (r)'s for H(P-acid)--O(water) in the lower concentrations, (h) [g.sub.ij](r)'s for H(P-acid)--O(water) in the higher concentrations. [Color figure can be viewed at wileyonlinelibrary.com]

Caption: FIG. 2. (a) Concentration dependence of [D.sub.i](v) for L-acid. (b) Concentration dependence of [D.sub.i](v) for P-acid. [Color figure can be viewed at wileyonlinelibrary.com]

Caption: FIG. 3. Concentration dependence of [epsilon]. [Color figure can be viewed at wileyonlinelibrary.com]

Caption: FIG. 4. (a) RCFs in the lower concentrations, (b) RCFs in the higher concentrations. [Color figure can be viewed at wileyonlinelibrary.com]

Caption: FIG. 5. Concentration dependence of [D.sub.a]'s. [Color figure can be viewed at wileyonlinelibrary.com]
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Author:Matsunaga, Shigeki
Publication:Polymer Engineering and Science
Geographic Code:7IRAN
Date:Dec 1, 2019
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