Terahertz Spectroscopy Applied for Investigation of Water Structure

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Terahertz Spectroscopy Applied For Investigation of Water Structure Nikita Penkov, Nikolay Shvirst, Valery Alexandrovich Yashin, Eugeny Eugenievich Fesenko (Jr.), and Eugeny Eugenievich Fesenko J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b06622 • Publication Date (Web): 03 Sep 2015 Downloaded from http://pubs.acs.org on September 16, 2015

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The Journal of Physical Chemistry

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Terahertz Spectroscopy Applied For Investigation of Water Structure

Nikita Penkova,*, Nikolay Shvirsta, Valery Yashina, Eugeny Fesenko (Jr.)a, Eugeny Fesenkoa

a

Institute of Cell Biophysics RAS, Institutskaya str., 3, Pushchino, Moscow region 142290, Russia * Corresponding author. Tel.: +7 4967 73 05 19; fax: +7 4967 33 05 09 E-mail address: [email protected] (N.V. Penkov)

ACS Paragon Plus Environment


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Abstract The absorption spectra of liquid water and various aqueous solutions were analyzed in a terahertz frequency domain (from 6 to 200 cm–1) which characterize the collective dynamics of water molecules. The particular attention was paid to the relaxation process in the range of ~6–80 cm-1. The physical essence of this process on the molecular level is still unclear. We found that the amplitude of this relaxation process correlates with the degree of destruction of water structure. The obtained data allowed us to interpret this process as a monomolecular relaxation of free water molecules. Based on a consideration of the water polarization in the electric field we proposed a method of calculation of the amount of free water molecules in solution.


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1. Introduction The liquid state of water has a very complex structure. The reason for this is the specific structure of water molecules that allow them to form up to 4 hydrogen bonds with surrounding molecules1 (even more if we take into account the bifurcated bonds). It results in a formation of branched three dimensional structure of water molecules interconnected with hydrogen bonds. Various methods were applied to study the properties of water structure such as thermodynamic2, viscometric3, conductometric4 ones as well as X-ray structural analysis5, neutron diffraction6, NMR7, dielectric spectroscopy8, Raman spectroscopy9, IR-spectroscopy10, et cetera. Among these methods the absorption spectroscopy plays an important role in deriving valuable information on the molecular structure and dynamics. In addition, the frequency range of absorption spectra reflects the time responses and energetic characteristics of molecular processes. When studying the structural characteristics of water the most informative parts of spectra are those, which reflect the dynamics of intermolecular interaction. Several ranges of the absorption spectrum of water are related to the specific types of intermolecular dynamics (Figure 1): 1. R1 around 0.6 cm-1 (at 25°C) – Debye relaxation; 2. T1 around 50 cm-1 – the bending mode between two water molecules connected by the H-bond; 3. T2 around 180 cm-1 – stretching mode between two water molecules connected by the Hbond.

Figure 1. Dielectric losses in aqueous solutions: R1 and R2 are the relaxation bands; T1 and T2 are the bands related to bending and stretching modes, respectively.



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Recently, it was found that the relaxation process in water and aqueous solutions cannot be described by the relaxation function containing only one relaxation time11-16. It turned out that in the right wing of the R1 band there is one more band – R2 (Figure 1). To separate the smallamplitude R2 relaxation process it is necessary to perform difficult decomposition of spectral contour. For the water spectrum this technique was applied by several authors. However, the obtained parameters for the R2 band varied significantly. For example, the maximum of this band was determined in 5 - 30 cm-1 range.11,12,16 It should be noted that main goal of the most studies was to confirm the presence of R2 band in water spectrum, and only a few of them dealt with the investigation of the nature of this band. Buchner et al.11 suggested that the R2 band caused by the relaxation of water molecules connected by one hydrogen bond. The findings of Lyashchenko and colleagues support the idea that the R2 band is the resonance band caused by the rotation of dimers of water molecules14. Yada et al. assumed that this band is caused by the relaxation of water molecules free of hydrogen bonds15. Thus, in spite of the strong evidence of the presence of R2 band in the water spectrum its nature is still unclear. It is obvious that an understanding of the molecular dynamics underlying this type of relaxation could gain the knowledge of the structural-dynamic organization of water and its solutions. The goals of this study were to carry out an accurate analysis of the absorption spectra of water and water solutions in the spectral range corresponding to R2 band and to give the molecular-dynamic interpretation of this band. A new method to calculate the quantity of free water molecules in solution was suggested.

2. Experimental Section We studied the transmission spectra of pure water, various aqueous solutions of electrolytes (CaCl2, NaCl, KCl, CsCl, KBr, KI) and water solution of tetrahydrofuran (THF). The concentrations of all electrolytes except the solution of CaCl2 were 1 M. The concentration of CaCl2 solution was reduced to 0.5 M to balance the anion concentrations. The concentration of THF was 5.6 mol%. Water solutions were prepared by using deionized water obtained with Millipor system (conductivity 0.055 µS/cm). Temperature of all samples was stabilized at 25±0.1oC. All spectra were measured in the range of 6 – 80 cm-1 with THz spectrometer TPS Spectra 3000 (Teraview Ltd, UK) and in the range of the maximum of T2 band 150 – 200 cm-1 with IR Fourier spectrometer Vertex 80 (Bruker, Germany). All spectra of water samples were measured in a cuvette with windows made of monocrystalline quartz (thickness 2.04 mm). In the range of 6-80 cm-1, we actually measured the transmission spectra of three layer media: quartz – water solution – quartz. To obtain the spectral


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parameters of solutions we took into account the influence of the quartz windows as described in Appendix 1. The absorption of monocrystalline quartz in the range of 6-80 cm-1 is negligible. Spectral losses related to the cuvette windows are entirely caused by reflections from the window boundaries. The thickness of liquid samples was 104 µm. In the range of 150 – 200 cm-1, the quartz windows are not transparent anymore for radiation, and the transmittance of water drops significantly. Therefore, to eliminate the influence of the cuvette windows on the spectra the measurements were performed as follows. First, we measured the transmission spectrum of solution in a cuvette with the thickness of 12.5 µm which was used as a background spectrum. Then we measured the transmission spectrum of the same solution in a cuvette with the thickness of 19.8 µm (sample spectrum). On the base of Beer's law the pure spectrum of solution of the thickness equal to the difference between thicknesses of two cuvettes (7.3 µm) was obtained dividing the sample spectrum to the background one. This approach allowed us to exclude the influence of the most processes of reflections on the spectrum. The thicknesses of the layers were determined by using the distances between the neighboring interference lines ∆λ appearing in the near IR-transmission spectra of empty cuvettes measured with the spectrometer Nicolet 6700 (Thermo, USA). The air gap thickness (l) between the cuvette windows was calculated as follows: l [cm] = 1/(2∆λ [cm-1]). The viscosity of THF solution was determined with vibro-viscometer SV-10 (A&D Company, Japan).

Evaluation of the parameters of spectral bands Along with measuring the experimental spectra, we developed a modelling of spectra based on four bands R1, R2, T1 and T2 shown in Figure 1. Analysis of the spectral data was performed by using the complex permittivity of water solution. The permittivity of liquid consisting of the four bands was expressed as follows:

ε (ω ) = ε ∞ +

∆ε1 ∆ε 2 A1 A2 σ + + 2 + 2 + 0 2 2 1 − iωτ1 1 − iωτ 2 ω1 − ω − iωγ 1 ω2 − ω − iωγ 2 ε 0ω

(1)

In Eqn. (1) contribution of the relaxation processes to the permittivity was described by the Debye function and the contribution of the vibration processes was described by the Lorenz function; ε∞ is the high frequency permittivity; τ1,2 are the relaxation times of R1 and R2 processes; ∆ε1 is the amplitude of the R1 band, ∆ε 2 is the amplitude of the R2 band; A1,2 are the amplitudes of T1 and T2 bands, respectively; ω1,2 are the resonance frequencies of the T1 and T2 modes, respectively; γ1,2 are the damping rates of the T1 and T2 modes, respectively; ω=2, is a frequency. The term

σ0 describes the losses due to the ionic conductivity σo, where εo is ε 0ω



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the permittivity of vacuum. The function (1) is used further to determine the model transmission spectrum (A.6) (see Appendix). To describe the spectra more accurately in the model (A.6) we took into account the interference of two rays: the ray transmitted without reflection (A, Figure 2) and the ray reflected twice from the internal surfaces of the cuvette (B, Figure 2). The mentioned interference plays a notable role at lower frequencies where water is more transparent for radiation.

Figure 2. The diagram of the transmission of radiation through the cuvette. The lines A and B are conditionally separated to illustrate the ongoing processes. Actually, A and B are the plane waves interfering to one another. Analysis of the spectral data was performed based on the fitting of the model spectrum (A.6) to the experimental spectrum. The aim of the analysis was to find the parameters of model spectrum providing the best fitting to the experimental data. To evaluate the quality of the fitting we used the value s2 determined as follows:

1 s = N 2

 Ti exp − Ti mod    ∑ Ti exp i =1   N

2

(2)

where Ti exp and Ti mod are the experimental and model values of transmission, respectively, at the frequencies ωi . We used 80 equidistant points ωi . Value s2 did not exceed 2⋅10-4 for all fitted spectra. The transmission spectrum of each sample was measured 10 times. Each spectrum was used in the fitting procedure to determine the parameters of the spectral bands. Thus, for every studied substance the data sample consisted of 10 sets of parameters. Results are presented as the mean of 10 measurements with 95% confidence interval. The model spectra were fitted to the experimental spectra in the range of 6-80 cm-1. We used 80 equidistant points in this interval for the fitting. The maxima of R1 and T2 bands used in the modeling were not within this frequency range, but both bands significantly affected the


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spectra in the range under study. Therefore, for the spectral parameters of the R1 band (and σo values) we used the literature data (Table A1 in Appendix). For the T2 band we used our own data obtained by measuring the spectra in the range of 150-200 cm-1 (see Appendix). The final aim of the modeling was to find the parameters of all bands and primarily the parameters Δε and τ2 of the R2 band. 3. Results and discussions Transmission spectra of the investigated aqueous solutions measured in the range of 6 – 80 cm-1 are presented in Figure 3. The values of Δε and τ2 calculated using the spectral data are given in Table 1. The corresponding values for pure water obtained in the present study were within the order-of-magnitude agreement with literature data.11-16



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Figure 3. Transmission spectra of the aqueous solutions measured in the range of 6 – 80 cm-1.

Table 1. Parameters of the R2 band of different solutions at 25oC resulted from the fitting procedure. B is The Jones-Dole coefficient17 and S is molar entropy of hydration of ions18 H2O

CaCl2

NaCl

KCl

CsCl

KCl

Cations

KBr

KI

THF

Anions

τ2 , ps

0.31±0.06

0.33±0.06

0.34±0.06

0.36±0.07

0.35±0.07

0.36±0.07

0.31±0.03

0.31±0.02

0.30±0.03

1.4±0.1

1.2±0.1

1.3±0.2

1.5±0.1

1.8±0.2

1.5±0.1

1.8±0.1

2.1±0.1

1.2±0.1

-

- 136

- 79

14

52

14

39

75

-

-

-41

-26

11

26

11

27

46

-

1.57±0.05

1.67±0.06

1.74±0.05

1.67±0.02

1.52±0.04

1.67±0.02

1.56±0.03

1.45±0.03

1.72±0.02

3

- В*10 , l M-1 S, JK-1M-1 A ⁄ω

It can be noticed that the τ2 values for all studied solutions are indistinguishable from each other within the measurement accuracy, i.e. they do not vary notably. Another important parameter (additional to τ2) characterizing R2 band is the ∆ε amplitude which determines the contribution of the relaxation process R2 to the permittivity. According to Table 1 there is an increase of the ∆ε value in the series of cations Ca2+, Na+, K+, Cs+ and in the series of anions Cl-


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, Br-, I-. It is interesting to note that these series correspond to the Hofmeister series extended from kosmotropes to chaotropes. It is well known that the Hofmeister series reflects the ability of ions to structure water around them. The same series may be formed in sequence with the decrease of the solution viscosity or the increase of entropy of ion formation in solution depending on the ion composition. The coefficients of the Jones-Dole equation for the viscosity and the entropy of the ion formation in solutions are given in Table 1. The Jones-Dole coefficient B determines the dependence of the relative change of the volume viscosity of electrolyte solution on its concentration С: 0

= 1 + А√С + ВС,

(3)

η and η0 – viscosity of solution and solvent, A and B – coefficients. Coefficient B characterizes the ion-dipole interactions and hence reflects the structuredness of water solution. The S value determines the changes of entropy at the transfer of 1 mole of the corresponding cations and anions from gaseous phase to water at 25oC.18 It should be noted that in our case the S values were calculated in the conditional energetic scale playing a comparative role, i.e. they have the physical meaning only if compared with one another in different solutions. According to the data presented in Table 1 the coefficient B decreases in the series of cations and anions in the following sequence: Ca2+, Na+, K+, Cs+ and Cl-, Br-, I-. The values of S increase in the same sequence. Both parameters (the viscosity and the entropy) are directly resulted from the water structuredness. Thus, based on the obtained results we can conclude that the ∆ε 2 amplitude is directly correlated with the extent of water structuredness. It may be stated that in electrolytic solutions the greater the value of 2 , the less the structuredness of water and vice versa. Since the THF solution is not electrolyte, we cannot determine the Jones-Dole coefficient for the solution of this substance in water. Instead, we measured the dynamic viscosity of THF solution at 25oC. The obtained value of viscosity was 1.43 cP which is about 1.5 times greater than that of water (0.89 cP). As was mentioned above, the viscosity may be used as a criterion reflecting the solution structuredness since the viscosity reflects the translational mobility of molecules. Hence, the structuredness of THF solution is higher than that of pure water. As is shown in Table 1, the value of ∆ε 2 for THF solution is somewhat lower than that for pure water. This result is in a good agreement with the relationship between the ∆ε 2 amplitude and structuredness of solution. This relationship is valid not only for the electrolytic solutions, but also for the non-electrolytic ones. Considering the R2 relaxation process in the relation to the extent of structuredness of water, it is important to suggest an interpretation of this process on a molecular level. We



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identified several types of molecular dynamics, which in our opinion could account for the occurrence of the R2 band. 1. This may be a vibrational process of collective character, which includes a large number of water molecules (analog of phonon). In this case, the contribution of this process to spectrum should diminish following disruption of the intermolecular bonds. However, we observed the opposite effect: the greater the disruption of the water structure, the stronger the manifestation of the R2 band. 2. The R2 band may appear because of the relaxation of water molecules connected by one hydrogen bond. For the first time this hypothesis was put forward by Buchner et al.11 According to this work, the ∆ε 2 amplitude should increase with increasing the number of water molecules, having only one hydrogen bond, in solution. It is known that molecules with one hydrogen bond contribute to the translational absorption bands.19,20 The number of such molecules directly related to the amplitude of translational absorption bands. The values of A2 ⁄ω22 calculated for all studied solutions are presented in Table 1. The A2 value is the amplitude of the T2 band, ω22 is the squared frequency of absorption maximum of the T2 band. This dimensionless value corresponds to the contribution of the indicated band into the permittivity. As shown in Table 1 the contribution of the T2 band into the spectrum in the series of cations Na , K+, Cs+ and anions Cl-, Br-, I- diminishes, that indicates the decrease of water molecules with one hydrogen bond in the presence of these ions. At the same time, the contribution of the R2 band into the spectrum (value 2 ) in the same series of ions increases. The obtained data indicate that the contribution of the R2 band into the spectrum can increase at decreasing the number of water molecules, having one hydrogen bond. Hence, the assumption that the R2 band occurred due to relaxation of water molecules with one hydrogen bond contradicts to the presented data. +

3. One of the possible types of molecular dynamics may be the rotation of free water molecules or some molecular complexes. An example of such interpretation is the hypothesis suggested by Lyashchenko et al.14 which explains the occurrence of this band by the excitation of rotational resonance in the water dimers. This hypothesis associates the occurrence of this band with the resonance process rather than with the relaxation one. If we assume that R2 band associates with dimers then there should be the second band coupled with monomers in the higher frequency region of water spectra with the amplitude much greater than that of the suggested rotational excitation band of dimer. To our current knowledge such a band in IR-spectra was not found. Also, Fucasawa et al.21 have conducted a detailed study of R2 band approximating it by the resonance and relaxation functions. It was found that the relaxation function gives the best approximation of the experimental data. 4. Yada et al. analyzed the data on the isotopic shift of the R2 band caused by the replacement of H2O by D2O15. On the basis of these data authors suggested hypothesis that the R2 band is a spectral manifestation of the relaxation of single water molecules, free of hydrogen bonds.


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Based on our analysis of the conceivable models, we can conclude that the most creditable interpretation of the R2 band on a molecular level is the rotational relaxation of free water molecules. Water molecules are considered to be free if they do not have any hydrogen bond and do not undergo the influence of the strong polarizing Coulomb field of ions. This is the only approach that does not contradict to all our experimental data. First, the greater the distractions of water structure by different dissolved substances, the larger the number of free molecules that contributes into the relaxation band (Table 1). Second, the relaxation time does not depend on the type of solution (Table 1). Therefore, it reflects relaxation of the solvent i.e. water molecules.

Calculation of the number of free water molecules based on spectral data If the R2 band is really caused by the relaxation of free water molecules then the ∆ε 2 amplitude should be directly related to the number of free molecules in the liquid phase. The fraction of free water molecules can be calculated in the framework of the model of polarization of water as a dielectric in the electric field. After applying the electric field water molecules become polarized. Conditionally, the polarization processes can be divided into several groups: orientational polarization of molecular skeleton interconnected with hydrogen bonds, orientational polarization of free molecules, and number of faster polarization processes including the displacement of nuclei and polarization of electron shells of molecules (Figure 4). Each process has its own characteristic time and contribution into the static permittivity. All polarization processes contribute to total polarization in additive manner. Therefore, the process of orientation polarization of free water molecules in the electric field can be treated separately from other polarization processes. However, it should be taken into account that other polarization processes can induce the screening effect with respect to the electric field. The notable screening is induced by the fast (high frequency) processes while screening by slow (low frequency) processes in the first approximation can be neglected as they are too slow to cause the screening effect on the relatively faster R2 process.



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Figure 4. Polarization of water molecules in the electric field. Contribution of the orientation polarization of free water molecules into the permittivity is determined by the ∆ε 2 amplitude. The only slow process is the Debye relaxation. The contribution of all more rapid processes appearing at frequencies exceeding those of the R2 band can be described by the high frequency permittivity ′∞ . For the orientational polarization of free water molecules we can write the following relationship: 1 +2

=

4 ∞ 3

+

1 !2 $ 40 3"#

(4)

where = Δε2 + ε′∞ , N is a number of molecules in unit volume, ∞ is the polarizability at high frequency, n is a fraction of free water molecules, εo is the permittivity of vacuum, p is a dipole moment of water molecule, k is the Boltzmann constant, T is absolute temperature. This relationship is similar to the Debye-Langevin formula written in SI system connecting the permittivity of substance with the polarizability of its molecules with one exception: it contains the coefficient n. This coefficient indicates that only free water molecules, composing a small fraction of a total number N of molecules, undergo the orientation polarization while all N molecules undergo faster polarization. The ∞ value can be calculated using the following equation: &'( )* &'( +

=

,.

/ ,


(5)

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This equation is similar to the Lorentz-Lorentz formula written not for the optical range of frequencies but for THz frequencies. It should be noted that ′∞ is different from ∞ in Eq. (1). Both parameters are the high frequency permittivities though they are determined in a different way. It is supposed that the high frequency range in Eq. (1) takes an origin beyond the T2 band (Figure 1) while ′∞ characterizes the permittivity beyond the R2 band. Hence, the relationship between these two parameters can be expressed as follows: 0

0

′∞ = ∞ + 213 + 233. 1

(6)

3

After simple mathematical transformation of equations (4), (5) the fraction of free water molecules can be calculated using the following equation:

= 4∆&

.∆&3

3 +&′(

567&8

+)4&′( +) 9:3

.

(7)

Substituting in (7) the known constants k=1.38×10-23 J/К, р=6.17×10-30 C*m, N=NA×55.56×103 m-3, NA=6.02×1023 mol-1 the fraction of free water molecules has the form:

= 4∆&

.;×*=>? ∆&3 7

3 +&′(

+)4&′( +)

.

(8)

The equation (8) allows us to calculate the fraction of the free water molecules provided that the values of Δε , ′∞ , and T are known. As temperature is set in experiment, and only two parameters are required to determine n: Δε and ′∞ . These parameters are determined using the described method of the spectrum analysis, i.e. the fitting procedure. The results of calculation of the number of free water molecules in solutions with the use of equation (8) are presented in Figure 5.



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Figure 5. The fraction of the free water molecules n (%) in different solutions at 25oC. Taking into account the data given in Figure 5, our suggestion on the relation of the Δε amplitude to the extent of structuredness of water acquires a specific meaning. The Δε amplitude is the parameter, which is directly connected to the quantity of free water molecules, i.e. the greater the distraction of water structure, the larger the number of free water molecules, and vice versa, the larger the number of free water molecules, the greater the distraction of water structure. Thus, in this paper we suggest a new approach for analyzing the structuredness of water solutions based on the determination of the quantity of free water molecules.

4. Conclusions We concluded that the amplitude ∆ε2 of the high-frequency relaxation band R2 directly correlates with extent of water structuredness. It may be stated that in water solutions the greater the value of 2 , the less the structuredness of water and vice versa. Based on the obtained data, the most creditable interpretation of the R2 band on a molecular level is the rotational relaxation of free water molecules. Water molecules are considered to be free if they do not have any hydrogen bond and do not undergo the influence of the strong polarizing Coulomb field of ions. Based on a consideration of the water polarization in the electric field we proposed a method of calculation of the amount of free water molecules in solution using the ∆ε 2 value.


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APPENDIX. DEVELOPMENT OF THE MODEL TRANSMISSION SPECTRUM In our model, permittivity of water is described by the following equations:

 A1 (ω12 − ω 2 ) A2 (ω22 − ω 2 ) ∆ε 1 ∆ε 2 ,  + + + 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 + ω τ 1 1 + ω τ 2 (ω1 − ω ) + ω γ 1 (ω2 − ω ) + ω γ 2   A1ωγ 1 A2ωγ 2 ∆ε 1ωτ 1 ∆ε 2ωτ 2 σ0  + + + + . ε ′′(ω ) = 1 + ω 2τ 12 1 + ω 2τ 22 (ω12 − ω 2 )2 + ω 2γ 12 (ω22 − ω 2 )2 + ω 2γ 22 ε 0ω 

ε ′(ω ) = ε ∞ +

(A.1)

where ε ′(ω) и ε ′′(ω ) are the real and imaginary parts of permittivity, respectively, other designations are the same as in eq. (1). This model contains 12 parameters: ε ∞ , ∆ε1 , ∆ε 2 , τ 1 ,

τ 2 , ω1 , A1 , γ 1 , ω 2 , A2 , γ 2 , σ 0 . However, they are dependent on each other. By definition, we can write the following relationship:

∆ε1 + ∆ε 2 +

A1

ω

2 1

+

A2

ω22

+ ε∞ = εS

(A.2)

Parameters εs, τ1, and σo are determined from Table A1. The ε ∞ value is equal to 2.5. It is varied a little from sample to sample, and the result is slightly dependent on this parameter.

Table A1. The values of @1, s and σ0 for different substances used in modeling

τ 1 , ps

εS

σ0, S/m

H2O

8.2522

78.422

0

CaCl 2

7.523

64.323

824

NaCl

7.222

64.322

8.625

KCl

7.3526

6726

11.224

CsCl

7.8727

68.627

1127

KBr

7.7423

69.323

11.524

KI

6.928

65.328

11.2628

THF

12.7729

72.629

0

Thus, the formulae for real and imaginary parts of permittivity can be derived in the following form:



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16   ∆ε 2 A1 ω − ω A2 ω − ω ω ω  , + + + + ε ′(ω ) = ε ∞ 1 + ω τ 12 1 + ω 2τ 22 ω12 − ω 2 2 + ω 2γ 12 ω22 − ω 2 2 + ω 2γ 22       A1 A2   ε S − ∆ε 2 − 2 − 2 − ε ∞ ωτ 1  ω1 ω2 ∆ε 2ωτ 2 A1ωγ 1 A2ωγ 2   + + + ε ′′(ω ) =  1 + ω 2τ 12 1 + ω 2τ 22 ω12 − ω 2 2 + ω 2γ 12 ω22 − ω 2 2 + ω 2γ 22   σ0  + .  ε 0ω 

ε S − ∆ε 2 −

A1

2 1 2

−

A2

2 2

−ε∞

(

(

2 1

)

2

)

(

(

(

)

(

2 2

)

2

)

(A.3)

)

Parameter ω2 is determined from the transmission spectrum as the location of minimum in the T2 band. The amplitude of the stretching bend A2 is also excluded from the number of variable parameters. It is calculated separately for each set of variable parameters using the absorption coefficient α at frequency ω2 in the following way. According to (A.3) ε ′(ω) and ε ′′(ω ) are the linear functions of A2. The relationship between the absorption coefficient α and ε ′ , ε ′′ can be expressed as follows:

α=

2 kω , c

    2 2 ε ′ + ε ′′ − ε ′  . 2 

k=

(A.4)

Based on the relationships (A.4) we can write the following equation: 2

 α 2 c 2  α 2c 2  2  + 2 ε ′ − ε ′′2 = 0 ω  2ω 

(A.5)

After substitution the values of ′ and ′′ from equations (A.3), Eq. (A.5) is transformed into the quadratic equation for A2. Solving this equation, we obtain the numerical values of A2 for every set of variable parameters. Consequently, the number of variable parameters used for the fitting is reduced to 6: , @ , A*, B* , C*,C. The final equations describing the spectral model of studied solutions can be written as follows:


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17

      2 2 2    ( n − nsi ) + k 2nk 2 kω (1 − nsi )  , ϕ = Arc tan  2 ,α = ,r = R=  2 2 2 2  (n + nsi ) + k c (1 + nsi )2   n + k − nsi   ε ′2 + ε ′′2 + ε ′ ε ′2 + ε ′′2 − ε ′  n= ,k = ,  2 2   

2 2 2  k  1 − * 1 − * 1 + r R ( ) ( )     * exp( −α d )   n   T (ω ) =   nd ω  1 − 2 R * exp( −α d ) * 1 − 2sin 2  + φ   + R 2 exp( −2α d )  c  

(A.6)

where the dependence of the ε ′ and ε ′′ functions on the parameters of the model is determined from Eq. (A.3), n and k are the real and imaginary parts of the refractive index, ϕ is the phase jump at reflection from the quartz – water interface, r is the reflection coefficient for the air – quartz interface, R is the reflection coefficient for the water – quartz interface, nsi is the refractive index of a monocrystalline quartz equal to 2.1177, d is the thickness of the solution layer (in our case 104 µm), c is the velocity of light in vacuum, T(ω) is the transmission spectrum of three layer structure: quartz window- water solution- quartz window. In the model spectrum T(ω) the following factors were taken into account: absorption in solution; reflection of radiation from two surfaces of the quartz-air interface; reflection of radiation from two surfaces of the quartz-solution interface with accounting for the frequency dependence of the refractive index of solution. The formula also takes into account the contribution of the interference of two waves shown in Figure 2 to the spectrum. Since the model spectrum (A.6) was not used previously for calculations of the parameters of spectral bands we compared our results with literature data obtained by other methods. We compared our ε ′ and ε ′′ spectra of 1M NaCl solution at 25oC with similar data obtained by Tielrooij et al.30 The difference between these two results does not exceed several percents.

ACKNOWLEDGMENTS We are grateful to M. Goltyaev for helpful discussions. We are especially grateful to Prof. S. Alekseev for his assistance in preparation of this paper. The work was supported in part by the RAS Presidium program No. 28 “Problems of Origin of Life and Biosphere Formation” (direction “Physics, Chemistry and Biology of Water”).



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18

REFERENCES (1) Marechal, Y. The hydrogen bond and the water molecule. The physics and chemistry of water, aqueous and bio media. Oxford, U.K.: Elsevier, 2007. (2) Bandura, A. V.; Lvov, S. N. The ionization constant of water over wide ranges of temperature and density. J. Phys. Chem. 2006, 35, 15-30. (3) Zhu, Y.; Granick, S. Viscosity of interfacial water. Phys. Rev. Lett. 2001, 87, 096104. (4) Ivanov, A. A. Electrical conductivity of aqueous acids in binary and ternary waterelectrolyte systems. Russian Journal of Inorganic Chemistry 2008, 53, 1948-1963. (5) Narten, A. H.; Danford, M. D.; Levy, H. A. X-ray diffraction study of liquid water in the temperature range 4–200°C. Discuss. Faraday Soc. 1967, 43, 97-107. (6) Narten, A. H.; Thiessen, W. E.; Blum, L. Atom pair distribution functions of liquid water at 25° C from neutron diffraction. Science 1982, 217, 1033-1034. (7) Simpson, J. H.; Carr, H. Y. Diffusion and nuclear spin relaxation in water. Phys. Rev. 1958, 111, 1201-1202. (8) Jansson, H.; Swenson, J. Dynamics of water in molecular sieves by dielectric spectroscopy. EPJE 2003, 12, S51-S54. (9) Walrafen, G. E.; Chu, Y. C.; Piermarini, G. J. Low-frequency Raman scattering from water at high pressures and high temperatures. J. Phys. Chem. 1996, 100, 10363-10372. (10) Riemenschneider, J. Spectroscopic investigations on pure water and aqueous salt solutions in the mid infrared region. Thesis for the degree Dr. rer. nat. : 0000000812 / Riemenschneider Julian. - Rostock, 2011. (11) Buchner, R.; Barthel, J.; Stauber, J. The dielectric relaxation of water between 0° C and 35° C. Chem. Phys. Lett. 1999, 306, 57-63. (12) Kaatze, U.; Behrends, R.; Pottel, R. Hydrogen network fluctuations and dielectric spectrometry of liquids. J. Non-Cryst. Solids 2002, 305, 19-28. (13) Meissner, T.; Wentz, F. J. The complex dielectric constant of pure and sea water from microwave satellite observations. IEEE Transactions on Geoscience and Remote Sensing 2004, 42, 1836-1849. (14) Lyashchenko, A. K.; Novskova, T. A. Structural dynamics of water and its dielectric and absorption spectra in the range 0–800 cm-1. J. Mol. Liquids 2006, 125, 130-138. (15) Yada, H.; Nagai, M.; Tanakа, K. Origin of the fast relaxation component of water and heavy water revealed by terahertz time-domain attenuated total reflection spectroscopy. Chem. Phys. Lett. 2008, 464, 166-170. (16) Moeller, U.; Cooke, D. G.; Tanaka, K.; Jepsen, P. U. Terahertz reflection spectroscopy of Debye relaxation in polar liquids. J. Opt. Soc. Am. B 2009, 26, A113-A125.


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(17) Kwak, H.T.; Zhang, G.; Chen, S. The effects of salt type and salinity on formation water viscosity and NMR responses. Proceedings of the International Symposium of the Society of Core Analysts, Toronto, Canada. 2005, 21–25. (18) Barrett, J. Inorganic Chemistry in Aqueous Solutions. Cambridge, U.K.: The Royal Society of Chemistry, 2003. (19) Yuhnevich, G. V. Infrared spectroscopy of water. Nauka, Moscow, 1973. [in Russian] (20) Walrafen, G. E.; Hokmabadi, M. S.; Yang, W.-H. Raman isosbestic points from liquid water. J. Chem. Phys. 1986, 85, 6970-6982. (21) Fukasawa, T.; Sato, T.; Watanabe, J.; Hama, Y.; Kunz, W.; Buchner, R. Relation between dielectric and low-frequency Raman spectra of hydrogen-bond liquids. Phys. Rev. Lett. 2005, 95, 197802. (22) Lileev, A. S. Dielectric relaxation and molecular-kinetic state of water in solutions. Doctor of Chemistry thesis: 02.00.04, Moscow, 2004. [in Russian] (23) Ahadov, Ya. Yu. Dielectric properties of binary solutions. Nauka, Moscow, 1977. [in Russian] (24) Rabinovich, V. А. Short chemical guide, edited by Rabinovich V.А., Havin Z.Ya. Himiya, Leningrad, 1978. [in Russian] (25) Bordi, F.; Cametti, C., Colby, R. H. Dielectric spectroscopy and conductivity of polyelectrolyte solutions. J. Phys.: Condens. Matter 2004, 16, R1423-R1463. (26) Lyashchenko, A.; Lileev, A. Dielectric relaxation of water in hydration shells of ions. J. Chem. Eng. Data 2010, 55, 2008-2016. (27) Wei, Y. Z.; Chiang, P., Sridhar, S. Ion size effects on the dynamic and static dielectric properties of aqueous alkali solutions. J. Chem. Phys. 1992, 96, 4569-4573. (28) Kobelev, A. V.; Lileev, A. S.; Lyashchenko, A. K. Microwave dielectric properties of aqueous potassium iodide solutions as a function of temperature. Russian Journal of Inorganic Chemistry 2011, 56, 652-659. (29) Kumbharkhane, A. C.; Helambe, S. N.; Lokhande, M. P.; Doraiswamy, S.; Mehrotra, S. C. Structural study of aqueous solutions of tetrahydrofuran and acetone mixtures using dielectric relaxation technique. Paramana – J. Phys. 1996, 46, 91-98. (30) Tielrooij, K. J.; Timmer, R. L. A.; Bakker, H. J.; Bonn, M. Structure dynamics of the proton in liquid water probed with terahertz time-domain spectroscopy. Phys. Rev. Lett. 2009, 102, 198303.



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20

TOC Graphic


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Figure 1. Dielectric losses in aqueous solutions: R1 and R2 are the relaxation bands; T1 and T2 are the bands related to bending and stretching modes, respectively. 82x64mm (600 x 600 DPI)



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Figure 2. The diagram of the transmission of radiation through the cuvette. The lines A and B are conditionally separated to illustrate the ongoing processes. Actually, A and B are the plane waves interfering to one another. 54x35mm (300 x 300 DPI)


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Figure 3. Transmission spectra of the aqueous solutions measured in the range of 6 – 80 cm-1. 84x68mm (600 x 600 DPI)



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Figure 3. Transmission spectra of the aqueous solutions measured in the range of 6 – 80 cm-1. 84x68mm (600 x 600 DPI)


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Figure 4. Polarization of water molecules in the electric field. 83x66mm (600 x 600 DPI)



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Figure 5. The fraction of the free water molecules n (%) in different solutions at 25oC. 57x31mm (600 x 600 DPI)


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TOC Graphic 38x28mm (300 x 300 DPI)


Terahertz Spectroscopy Applied for Investigation of Water Structure

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