Electrolyte and Temperature Effects on Third-Order Susceptibility in

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Electrolyte and Temperature Effects on Third-Order Susceptibility in Sum Frequency Generation Spectroscopy of Aqueous Salt Solutions Tatsuya Joutsuka, and Akihiro Morita J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02445 • Publication Date (Web): 02 May 2018 Downloaded from http://pubs.acs.org on May 5, 2018

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The Journal of Physical Chemistry

Electrolyte and Temperature Effects on Third-Order Susceptibility in Sum Frequency Generation Spectroscopy of Aqueous Salt Solutions Tatsuya Joutsuka∗,† and Akihiro Morita∗,‡,¶ †Department of Biomolecular Functional Engineering, College of Engineering, Ibaraki University, Hitachi 316-8511, Japan ‡Department of Chemistry, Graduate School of Science, Tohoku University, Aoba-ku, Sendai 980-8578, Japan ¶Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-8520, Japan E-mail: T.J.:[email protected]; A.M.:[email protected]

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Sum-frequency generation (SFG) spectra from charged solid-liquid interfaces include significant contribution from third-order susceptibility χ(3) , which mainly originates from induced water orientation in the electric double layer. We quantitatively evaluate the χ(3) susceptibility by molecular dynamics simulation in aqueous electrolyte solutions with varying concentration and temperature. We found that the value of χ(3) decreases with increasing concentration or temperature, and that the perturbation on χ(3) is quite well correlated with that on the dielectric constant ϵ of the solution. This correlation is understood as both quantities are commonly governed by the response of molecular orientation to the electric field. Accurate evaluation of χ(3) in various conditions is important in quantitative estimate of the third-order effect on the SFG spectroscopy, particularly in conditions of high surface charge and ion concentration.

1 Introduction Understanding liquid structure and dynamics at interfaces in contact with charged substrates is relevant to various phenomena, including biological membranes, electrochemical reactions, corrosion, weathering of minerals, etc. 1,2 Selective investigation of the molecules at these buried interfaces is a challenging issue, and surface-sensitive nonlinear spectroscopies, such as sum frequency generation (SFG) 3,4 and second harmonic generation (SHG), 5,6 are quite powerful for the purpose. However, the SFG and SHG spectra of charged interfaces involve third-order contribution, called the χ(3) effect, in addition to the usual second-order χ(2) contribution. The χ(3) effect stems from the electric field of the charges, which penetrates into the diffuse electric double layer (EDL) of liquid region formed by the charged interfaces and counter ions. 5–18 We have recently developed a theoretical method to calculate the χ(3) spectra by molecular dynamics (MD) simulation at the same accuracy as the usual χ(2) spectra. 19 The present work reports the calculated results of χ(3) spectra in various aqueous solutions 2


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with varying electrolyte and temperature. A number of previous SFG/SHG measurements have been conducted at interfaces between electrolyte solutions and charged substrates, such as aqueous interfaces of silica, 7,8,11,13,20 surfactant, 21,22 acid, 23 lipid, 12 and alcohol. 10,24 Accurate evaluation of the χ(3) effect in such conditions is crucial to analyze the SFG and SHG spectra of these charged interfaces. The remainder of this paper is constructed as follows. Section 2 summarizes the theoretical formulation of the χ(3) spectra and Section 3 describes the computational details. In Section 4, the computed χ(3) spectra under various conditions are discussed. Concluding remarks follow in Section 5.

2 Theory We here briefly summarize the computational procedure of the χ(3) spectra. 19 In the vibrational SFG spectroscopy at charged interfaces, the sum-frequency polarization P SFG is represented by

PpSFG

=

∑

vis IR χ(2) pqr Eq Er

+

∑

∫ vis IR χ(3) pqrz Eq Er

q,r

q,r

0

−∞

Ez dz,

(1)

where Eqvis and ErIR are the visible and infrared electric fields, respectively, and Es is the electric field generated by the charged interfaces. The suffixes p, q, r, s denote the x ∼ z (2)

(3)

tensor elements in the space-fixed coordinates. χpqr and χpqrs are the second-order and thirdorder susceptibilities. χ(3) is a fourth-rank tensor and accordingly non-zero in isotropic bulk media, whereas χ(2) vanishes in isotropic environment. χ(2) is comprised of the vibrationally resonant (χ(2),res ) and non-resonant (χ(2),nonres ) terms, χ(2) = χ(2),res + χ(2),nonres , and the resonant term can be calculated using the time correlation function of the dipole moment M and polarizability A as 4,25

χ(2),res pqr (ω2 )

iω2 = kB T

∫

∞

dt exp(iω2 t)⟨Apq (t)Mr (0)⟩, 0

3


(2)


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where ω2 represents the IR frequency, kB is the Boltzmann constant, and T is the temperature. The MD calculation of χ(3) spectra is performed with eq 2 as well, using a bulk liquid under a small constant electric field, EzBulk . Since χ(2) is zero in an isotropic bulk liquid, the calculated finite amplitude of eq 2 under the field, χ(2),Bulk , corresponds to the χ(3) effect, the SFG signal induced by the electric field. The χ(3) susceptibility is defined per unit volume, and it is calculated by (2),Bulk

χ(3) pqrz =

χpqr , Lz EzBulk

(3)

where Lz is the cell length of MD simulation. Eq 3 indicates the perturbation on χ(2) by the electric field through the change in orientational structure. The purely electronic contribution to χ(3) is neglected hereafter, because it has been estimated to be negligibly small in the OH stretching band of water. 19

3 Computational Details The MD calculations of χ(3) are carried out for liquid water with varying temperature and electrolyte aqueous solutions. The temperature T is set to 25, 50 and 75◦ C for liquid water, and electrolyte solutions of NaCl and CsI are examined with various concentrations at 25◦ C. A total of 2000 molecules are placed in a cubic cell with the three-dimensional periodic boundary conditions. The cell size is determined from the experimental densities of bulk solutions. 26,27 First, MD simulations of pure water are conducted and the initial configurations of salt solutions are generated by replacing water molecules with ions from the MD trajectories of pure water. The box lengths are summarized in Table 1. Flexible and polarizable molecular models by charge response kernel (CRK) 28,29 are employed for water and ions, since the CRK model can reproduce experimental IR, Raman and SFG spectra including the temperature change. 28,30 In the CRK formalism, the partial charge Qai of the site a in molecule i is determined self-consistently with the electrostatic 4


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Table 1: Box lengths L in MD simulations. They were determined from experimental densities. 26,27 (a) temperature change temp. /◦ C 25 50 75 L/Å 39.150 39.27 39.45 (b) concentration change conc. / M L/Å

NaCl CsCl 0.00 0.11 0.33 0.56 1.1 0.54 39.150 39.108 39.055 39.006 38.890 39.366

potential V as

Qai =

Q0ai

+

sites ∑

sites ∑∑ Qbj Vai = fai,bj , rai,bj b

Kab,i Vbi ,

b

(4)

j(̸=i)

where fai,bj is the damping function. 28 The CRK models of the monoatomic ions are constructed after ref 29. Four auxiliary sites are placed for each ion at the tetrahedral vertices around the ion center by 31   1  l  √  , 1  3   1



 −1  l  √  , −1  3   1





1  l  √  , −1  3   −1

  −1  l  √  , 1  3   −1

where the ion center is set to the origin, l = σ/8 and σ is the Lennard-Jones (LJ) size parameter of the ion described below. The four auxiliary sites carry the partial charges. The equilibrium partial charges Q0 and the CRK K are expressed in the matrix form as

Q0 =

Qtotal 4

  1   1    , 1     1

  3 −1 −1 −1    3 −1 −1 −1 3α    K= ,  16l2 −1 −1 3 −1     −1 −1 −1 3 

(5)

where Qtotal is the total charge of each ion and α is the isotropic polarizability of the ion. 5



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The form of eq 5 has been determined to reproduce Qtotal and α. The LJ parameters σ and ϵ are adopted from ref 32. α is taken from ref 33 for anions, from ref 34 for Na+ , and from ref 35 for Cs+ . In addition, the width of Gaussian charge distribution ξ is adopted from ref 29. The force field parameters are summarized in Table 2. Table 2: Force field parameters of ions by the CRK model: Lennard-Jones parameters σ and ϵ, polarizability α, and width of Gaussian charge distribution ξ. ion Na+ Cl− Cs+ I−

σ/Å 2.583 4.401 3.883 5.167

ϵ / kJ/mol 418.4 418.4 418.4 418.4

α / Å3 0.250 3.250 2.360 6.900

ξ/Å 0.5 0.7 0.5 0.7

In MD simulations, the LJ interaction is cut off at 15.0 Å. The long-range electrostatic interaction is evaluated by the Ewald summation with the surface term 19,36 unless otherwise noted. The time evolution is carried out with the reversible reference system propagator algorithms (RESPAs) 37 with the time steps of 1.83 and 0.1 fs for the inter and intramolecular interactions, respectively. The MD trajectories were generated from independent 2000 initial conditions. Each trajectory is equilibrated for 18.3 ps, and the production run follows for 9.15 ps, resulting in a total of 9.15 ps × 2000 = 18.3 ns sampling. In the calculations of radial distribution functions (RDFs) in 0.11 and 0.33 M NaCl solutions, the simulations time was increased by 10 and 3 times, respectively. All the calculations were performed by our in-house code. The dielectric constant ϵ of aqueous solutions is calculated by the linear-response formula 19,36,38 ϵ=1+

4π|Mw |2 V kB T

(6)

under zero field without the surface term. 19,36 Here, V is the volume of the simulation cell and Mw denotes the total dipole moment of water molecules. We neglected the effect of ions in eq 6, since their contributions are shown to be negligible. 39

6


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The calculation of χ(3) spectra is performed by applying a constant external field E0 = 0.3 V/Å along the z axis to the bulk solutions, where EzBulk in eq 3 is evaluated to be E0 /ϵ using the computed value of ϵ by eq 6. We note that the Ewald boundary condition with the surface term 19,36 is important in the calculation of eq 3. Supporting Information (SI) provides other calculated properties than χ(3) and ϵ to validate the present MD calculations using the CRK model in comparison with the SPC/E model 40 and the details on the SFG spectral calculation.

4 Results In this section, we discuss the results of χ(3) spectral calculations and the dielectric constant. The temperature and ion effects are discussed in Sections 4.1 and 4.2, respectively. The two effects are further examined in Section 4.3 to explore the effects of perturbation on the χ( 3) effect in general.

4.1 Temperature Effect 1.2

Neat water 25 °C 50 °C 75 °C

1 Im χ(3)yyzz

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.8 0.6 0.4 0.2 0 3000 3100 3200 3300 3400 3500 3600 3700 Frequency / cm −1

(3)

Figure 1: Temperature effect of Im[χyyzz ] spectra in neat water. (3)

(3)

The temperature dependence of the imaginary part of χyyzz spectrum, Im[χyyzz ], is dis(3)

played in Figure 1. The amplitude of Im[χyyzz ] decreases as the temperature T rises. This tendency is in parallel with the temperature dependence of the dielectric constant ϵ. The 7



computed ϵ also decreases; ϵ = 88.6 at T = 25◦ C, 82.7 at 50 ◦ C, and 74.6 at 75 ◦ C. This tendency is consistent to the experiment, 26 ϵ = 78.4 at T = 25◦ C, 69.9 at 50 ◦ C and 62.3 at 75 ◦ C. We also find the change in spectral lineshapes with increasing temperature in Figure 1. As the temperature rises, the low-frequency component at about 3300 cm−1 is blue shifted and decreases its amplitude, while the high-frequency shoulder at about 3500 cm−1 grows slightly. Qualitatively similar change has been observed in experimental IR and Raman spectra of liquid water in the O-H stretching band with increasing temperature. 41,42

4.2 Ion Effect 4.2.1 Dielectric Constant 90

Exp CRK SPC

85 Dielectric constant

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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80 75 70 65 60 55

0

0.2

0.4

0.6

0.8

1

1.2

Concentration / M

Figure 2: Dielectric constants ϵ in NaCl aqueous solutions at 25◦ C. Black circles stand for experiment, 43 red triangles for the MD simulation with CRK, and blue squared for MD simulation with SPC/E.

Then we discuss aqueous electrolyte solutions with varying concentrations. We first examine the dielectric constant ϵ in the aqueous NaCl solutions from 0.11 M to 1.1 M. Figure 2 presents the calculated values of ϵ by the CRK model (red triangles) in comparison with the experimental values 43 (black circles) and calculated values by the SPC/E water model (blue squares). The three sets of data commonly show decreasing values of ϵ with increasing concentrations, though the CRK model systematically overestimates the experimental values while SPC/E underestimates. With increasing the ion concentration, water molecules be-

8


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come immobilized by strong hydrogen (H)-bonds with ions, which hinders their orientational response to the applied field and thus reduces the dielectric constant. 44 4.2.2

χ(3) Spectra in SFG Spectroscopy

1

Neat water NaCl 0.11 M 0.33 M 0.56 M 1.1 M

(a)

Im χ(3)yyzz

0.8

1

0.6

0.4

0.4

0.2

0.2

1 0.8

1

0.6

0.4

0.4

0.2

0.2

3100

3200

3300

3400

3500

3600

(d)

Neat water NaCl 0.56 M CsI 0.54 M

0.8

0.6

0 3000

Neat water Na+ 0.11 M 0.33 M 0.56 M 1.1 M

0

Neat water Cl− 0.11 M 0.33 M 0.56 M 1.1 M

(c)

(b)

0.8

0.6

0

Im χ(3)yyzz

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3700

0 3000

3100

3200

Frequency / cm −1

3300

3400

3500

3600

3700

Frequency / cm −1

(3)

Figure 3: (a) Im[χyyzz ] spectra in aqueous NaCl solutions with varying concentration. (3) Im[χyyzz ] of (b) Na and (c) Cl solutions without counter ions and (d) 0.56 M CsI solution. In (3) panels (a)–(d), Im[χyyzz ] spectrum of neat water is also plotted in black for reference. The amplitudes are normalized so that the peak amplitude of neat water is unity.

Concentration dependence of χ(3) :

(3)

Figure 3a shows Im[χyyzz ] spectra of neat water and

aqueous NaCl solutions with various concentrations. The spectrum of neat water (black) has a main band around 3200–3300 cm−1 and a minor shoulder around 3500 cm−1 , consistent to the experimental estimate. 9 In the dilute NaCl solution such as 0.11 M (red), the (3)

Im[χyyzz ] spectrum remains quite similar to that in neat water though slightly red-shifted. (3)

However, with increasing concentration above 0.11 M, the Im[χyyzz ] spectrum decreases the peak amplitude and augments the low-frequency tail. This behavior of Im[χ(3) ] may appear in contrast to the IR and Raman spectra of the aqueous solutions, which are rather insensitive to the change in concentration. 45,46 The 9



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present MD simulation also confirmed that the IR and Raman spectra are not sensitive to the concentration in this range (0.11 – 1.1M, see SI). However, we also notice that the IR and Raman intensities reduce more strongly with increasing concentration under the external field E0 , as shown in SI, which indicates that the ions suppress the fluctuations of molecular orientation more under the external field. Further elucidation of the reduction mechanism should be pursued. Solution of one-component cation/anion:

In addition, we examine the perturbation

of Na+ or Cl− alone on the Im[χ(3) ] spectra without the counter ions. In the actual electric double layer at charged interfaces, either cation or anion can surpass the counter ion in (3)

local concentration. To mimic such situations, we calculated the Im[χyyzz ] spectra of Na+ or Cl− solutions with varying concentrations including no counter ions. The MD conditions of these systems are the same as those in the NaCl solutions, except that the counter ions are replaced by the same number of water molecules. The calculated Im[χyyzz ] spectra including Na+ or Cl− alone in Figure 3b and Figure 3c (3)

also decrease their amplitudes with increasing concentration of either ion, in a similar manner as in Figure 3a. The analogy indicates that the reduction of χ(3) amplitudes generally occurs with ions present in solutions, and is not attributed to the ion pair formation in solution. The reduction of χ(3) is understood from the fact that the strong hydrogen bonds between ions and water molecules pin the hydrogen-bonding network of water and thereby hinder its response to the external field. Comparing Figure 3b and Figure 3c, we notice that Cl− reduces the χ(3) amplitude slightly larger than Na+ , arguably because Cl− can form stronger hydrogen bonds with water molecules. Other electrolytes (NaCl vs CsI):

We further examine the effect of other ion species

(3)

(3)

on the Im[χyyzz ] spectra. Figure 3d displays the Im[χyyzz ] spectrum of 0.56 M CsI solution in comparison with 0.56 M NaCl solution. CsI is chosen as a typical example of soft ions. The spectrum in the CsI solution is quite similar to that in the NaCl solution, indicating 10


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that the perturbation of electrolyte on the decreasing χ(3) amplitudes is general in aqueous salt solutions.

4.3 Discussion 4.3.1 Correlation between χ(3) Spectra and Dielectric Constant So far we have investigated the perturbed χ(3) spectra with varying temperature and ion concentrations, and the reduction of χ(3) amplitude is in accord with that of the dielectric (3)

constant ϵ. Therefore, the correlation between the peak amplitude of Im[χyyzz ] and the dielectric constant ϵ is plotted in Figure 4. The clear linear relation suggests that the dielectric constant ϵ can be a good indicator of the χ(3) amplitude. Noting that the dielectric constant ϵ can be rewritten as the linear response of the induced dipole moment (eq 7 of ref 19), both quantities reflect the orientational response of water molecules to the external field. We note in passing that there are some recent evidences that the dielectric constant at the interface is different from that in the bulk. 47,48 The plot of Figure 4 is performed using the dielectric constant ϵ in the bulk liquids to be compared with χ(3) , since χ(3) is an intrinsic bulk property. 1.2 Imχ (3)yyzz peak amplitude

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Neat water Ion Temperature

1.1 1 0.9 0.8 0.7 0.6 0.5 0.4

70

75

80

85

90

95

Dielectric constant

Figure 4: Correlation plot between the dielectric constants ϵ and the peak amplitudes of (3) Im[χyyzz ] with varying temperatures (blue squares) and ion concentrations (red triangles). The solid line shows the linear regression.

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4.3.2 Significance of Ion Effects on χ(3) Spectra These results have significant influence on quantitative evaluation of the χ(3) effect in SFG or SHG spectra at charged interfaces. The SFG or SHG signals from the charged interfaces are determined by both the χ(2) and χ(3) contributions as

(3) χ(2),eff = χ(2) pqr pqr − χpqrz Φ(0),

(7)

where the second term χ(3) Φ(0) denotes the contribution of EDL, 49 usually called the χ(3) effect. The contribution of EDL consists of the χ(3) susceptibility and the surface potential Φ(0). Φ(0) is determined with the charge density of the interface σ and the electrolyte concentration of the solution C. Accordingly, we evaluate Φ(0) at an arbitrary set of given σ and C in the case of 1:1 electrolyte solutions by the modified Gouy-Chapman theory, as detailed in Section S4 of SI. (3)

The peak amplitude of −Im[χyyzz Φ(0)] is plotted in Figure 5a in a wide range of σ and C, where Φ(0) is calculated by the modified Gouy-Chapman and χ(3) is assumed to be that of neat water.

(3)

In this two-dimensional plot, the amplitude of −Im[χyyzz Φ(0)] is (2)

normalized with the peak amplitude of Im[χyyz ] of the air/water interface to indicate the relative importance of the EDL contribution. This plot shows that the relative amplitude of |χ(3) Φ(0)| to |χ(2) | becomes significant in the lower right corner, i.e. high charge density σ and low electrolyte concentration C. This behavior reflects the variation of |Φ(0)| from the EDL. The present paper has revealed that the χ(3) susceptibility varies with the electrolyte concentration C when C exceeds ∼ 100 mM. Accordingly, Figure 5b displays the two(3)

dimensional plot of Im[χyyzz Φ(0)] in a similar manner with Panel a, though the Panel b takes account of the varying χ(3) susceptibility in the electrolyte solutions. The difference of the two panels is also displayed in Panel c, which indicates the effect of the perturbed χ(3) on the EDL contribution −Im[χ(3) Φ(0)]. This effect manifests itself in the upper right

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corner, i.e. high charge density σ and high electrolyte concentration C. Such situation is seen, for example, in the interfaces of silica and aqueous solutions. 11,20 Actually this effect of perturbed χ(3) susceptibility is largely masked by high C in many cases, where |Φ(0)| is reduced by the strong ion screening. (a) −Im[Φ(0)χ(3)water]

0.0

10.0

(b) −Im[Φ(0)χ(3)electrolyte]

20.0

0.0

10.0

(c) Difference

20.0

0.0

1.0

2.0

Surface charge density / nm −2 0.2

0.4

0.6

0

0.2

0.4

0.6

0

0.2

0.4

0.6 3

1 1 5

0.1

1.5

1 5 10

1.0 10

15

0.5 15

10

Debye length / Å

0 Ionic concentration / M

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(3)

Figure 5: EDL contribution (peak amplitude of −Im[χyyzz Φ(0)]) as a function of surface charge density and ionic concentration. Panel (a) uses χ(3) for that of neat water, (b) for the (3) electrolyte solution of each concentration, and (c) shows the difference, −Im[Φ(0)χwater ] + (3) (2) Im[Φ(0)χelectrolyte ]. All these plots are normalized by the peak amplitude of Im[χyyz ] at the air/neat water interface. 19 The contour lines are drawn at 1, 5, 10, 15 in Panel (a–b), and every 0.5 in Panel (c). The above findings are consistent with the preceding experiment by Tian and co-workers 9 who assumed the χ(3) spectrum independent of concentration, since the investigated range of concentration was sufficiently low below 1 mM. However, in many other experiments that treated electrolyte solutions above 100 mM, 7,8,10,13,20–24 the perturbation of χ(3) can be relevant to the interpretation to some extent. We finally note that the electrolyte and temperature effects have been extracted by MD simulation without resorting to phenomenological model of the electric potential.

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5 Conclusions In summary, we examined the effects of temperature and electrolytes on the χ(3) spectra in aqueous salt solutions by MD simulation. The spectral amplitudes are reduced with increasing temperature or electrolyte concentration above 100 mM. The reduction of the χ(3) susceptibility is well correlated with the decrease of the dielectric constant, implying that these phenomena commonly reflect the reduced response of molecular orientation to external electric field. The perturbed χ(3) susceptibility in aqueous salt solutions is relevant to the quantitative estimate of the EDL contribution, called χ(3) effect, in the SFG or SHG spectroscopy when the electrolyte concentration exceeds ∼100 mM. The perturbed χ(3) susceptibility has been omitted so far, partially because the EDL contribution itself is reduced in electrolyte solutions of such high concentrations.

Supporting Information Available The Supporting Information is available free of charge. • si.pdf: Radial distribution functions and coordination numbers, total SFG spectra, bulk spectra, and computational conditions of interface potential

Acknowledgement The authors thank Prof. Michiel Sprik, Dr. Shuhei Urashima, and Dr. Tahei Tahara for stimulating discussions. The computations were performed using the supercomputers at Research Center for Computational Science, Okazaki, Japan. This work was supported by the Grants-in-Aid for Scientific Research (No. JP25104003, JP26288003) by the Japan Society for the Promotion of Science (JSPS) and Ministry of Education, Culture, Sports and Technology (MEXT), Japan.

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Electrolyte and Temperature Effects on Third-Order Susceptibility in

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