Effects of Molecular Structure and Solvent Polarity on Adsorption of

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Effects of Molecular Structure and Solvent Polarity on Adsorption of Carboxylic Anchoring Dyes onto TiO2 Particles in Aprotic Solvents Hui Fang, Bolei Xu, Xia Li, Danielle L. Kuhn, Zachary Zander, Guocai Tian, Victoria Chen, Rosa Chu, Brendan G. DeLacy, Yi Rao, and Hai-Lung Dai Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b01442 • Publication Date (Web): 24 Jun 2017 Downloaded from http://pubs.acs.org on June 27, 2017

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Effects of Molecular Structure and Solvent Polarity on Adsorption of Carboxylic Anchoring Dyes onto TiO2 Particles in Aprotic Solvents

Hui Fang,1 Bolei Xu,1 Xia Li,1 Danielle L. Kuhn,2 Zander Zachary,2 Guocai Tian,3 Victoria Chen,4 Rosa Chu,4 Brendan G. DeLacy,2 Yi Rao,1* and Hai-Lung Dai1 1

Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122

2

U.S. Army Edgewood Chemical Biological Center, Research & Technology Directorate,

Aberdeen Proving Ground, Maryland 21010 3

State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization,

Kunming University of Science and Technology, Kunming 650093, China 4

Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104

* Corresponding author: [email protected]

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Abstract Interactions of molecules with the surface of TiO2 particles are of fundamental and technological importance. One example is that the adsorption density and energy of the dye molecules on TiO2 particles affect the efficiency of dye sensitized solar cells (DSSC). In this work, we present measurements characterizing the adsorption of the two isomers, para-ethyl red (p-ER) and ortho-ethyl red (o-ER), of a dye molecule potentially applicable for DSSC onto TiO2 particles by Second Harmonic Scattering (SHS). It is found that while at the wavelengths used here o-ER has a much bigger molecular hyperpolarizability, p-ER exhibits strong SHS responses but o-ER gives no detectable SHS when the dyes are added to the TiO2 colloids respectively. This observation indicates that o-ER does not adsorb onto TiO2, likely due to steric hindrance. Furthermore, we investigate how solvents affect the surface adsorption strength and density of p-ER onto TiO2 in four aprotic solvents with varying polarity. The absolute magnitude of the adsorption free energy was found to increase with the specific solvation energy that represents the ability of accepting electrons and solvent polarity. It is likely that re-solvation of the solvent molecules displaced by the adsorption of the dye molecule at the surface in stronger electron-accepting and more polar solvents results in a larger adsorption free energy for the dye adsorption.

Keywords Second Harmonic Scattering, Adsorption, Aprotic Solvents, TiO2 Particles, Dye Sensitized Solar Cells

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Introduction Interaction of molecules with the surface of semiconductor particles is a topic of fundamental interests that affects many technological applications.1-3 One such technological application is the dye sensitized solar cell (DSSC) in which TiO2 particle surfaces are adsorbed with organic dyes in order to absorb solar radiation for the generation of photoexcited carriers.4 The efficiency of sun-light absorption depends on the density of the surface adsorbed dyes and the efficiency of injection of photo-excited charge carriers into the semiconductor should depend on the strength of adsorption of the dyes onto the particles. TiO2 is one of the well-documented semiconductors for DSSC because it is photo-corrosion resistant, non-toxic, cheap, and easy-to manufacture.2, 4-6 While the selection of the dyes and semiconductor particles is critical for the DSSC efficiency, it is important to recognize that both the adsorption strength and density of the dye molecules onto TiO2 are mediated by solvents chosen for the DSSC operation.7-8 Understanding solvent effects on molecular adsorption at the particle surface not only is important for the optimization of the DSSC efficiency,9-10 but also has fundamental interest in interface and colloidal sciences. Solvent properties such as the polarity, dipole moment, polarizability, exclusive volume of the solvent molecule, dielectric constant, and hydrogen bonding could modulate the interactions among the dye molecules and also between the dyes and the surface.11-13 Previous theoretical studies focused primarily on how the adsorption geometry of organic dyes is configured on TiO2 surface in the presence of solvents.14-17 Although the surface density of some organic dyes at TiO2 surfaces has been experimentally examined,18 the adsorption energy has not

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been measured and the effect of different solvents on surface adsorption has not been explored. Furthermore, for dyes with different isomers, this effect that the structure plays on adsorption is also expected to happen. The quantitative determination of adsorption characteristics for dye/TiO2 in solution is challenging. The chosen experimental probe should have the surface sensitivity to be able to discern the contribution from the sub-monolayer signal on the surface from that of the overwhelming quantity of molecules in the solution. Many surface-sensitive techniques require vacuum conditions,19-21 which render most of these techniques not amenable to the characterization of particle surfaces in solution. As second order optical processes, second harmonic generation (SHG) and sum frequency generation (SFG) have been proven to be valuable surface/interface tools.22-33 A prominent feature of SHG and SFG is that they can characterize buried interfaces within solids and liquids. Previously, SHG and SFG have been used to characterize planar buried interfaces.24-25, 32, 34-36 In recent years, these techniques, second harmonic scattering (SHS) and sum frequency scattering (SFS),22-23,

37-44

have been

extended to forms of curved particle surfaces in colloidal solutions. Although SHG and SFG are forbidden in centrosymmetric and isotropic bulk media as coherent nonlinear optical processes, they can be facilitated at the surface of a centrosymmetric structure, e.g., a sphere. 41-42, 45 There is no SHG and SFG from the randomly oriented molecules in the bulk liquid, but their signals can be generated coherently by the much smaller population of aligned molecules on the surface of a particle.42 SHS has been demonstrated as a means for accurate measurement of adsorption characteristics of

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molecules on colloidal particle surfaces42, 45 and can be applied to the dye on the TiO2 system. In this study, we employ SHS to 1) examine surface adsorptions of the para- and ortho-isomers of a carboxylic anchoring dye, ethyl red, onto TiO2 particles, 2) investigate the adsorption free energy and density of the dyes at the surface of TiO2 particles, and 3) determine the effect of different solvents on the surface adsorption of the dyes. ParaEthyl Red (p-ER) and ortho-Ethyl Red (o-ER) were chosen as the case study dyes in our experiments since their uses in sensitized TiO2 photovoltaic applications have been documented.46-51 We first focus on how interactions between aprotic solvents and p-ER affect the surface binding properties at TiO2 particles. The effect of protic solvents in which hydrogen-bonding interactions occur between solvent molecules and the carboxylic acid group of p-ER, will be discussed in a separate study.

Experimental Second Harmonic Scattering The experimental setup used in this work has been described previously.23, 37-38, 41 Briefly, a Ti:Sapphire oscillator (Coherent, Micra-5, average power 350 mW) with 80 MHz repetition rate and 50 fs pulse duration centered at 800 nm was used for our experiments. The laser was focused at the center of a glass cuvette (inner diameter 0.8 cm, outer diameter 1.0 cm) in which a magnetic stirrer was positioned to ensure homogeneous mixing of the dye molecules and TiO2 particles. A forward geometry was adopted to implement our experiments. A photomultiplier tube (R1527, Hamamatsu) operated at 1000 V and coupled with a single photon counting system (Stanford Research

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System SR400) was used to detect the SHS signal. A long pass filter was placed before the glass cuvette to remove second harmonic signal generated along the propagation path of the fundamental beam. A short pass filter was used to filter out the fundamental light before the monochromator (Acton 300, Grating 300 groves/mm, blazed at 500 nm) which was set at the SHS wavelength of 400 nm. Materials The average size of commercially available titanium oxide powders (Rutile TiO2, 99.9%, US Research Nanomaterials Inc.) was characterized by SEM and dynamic light scattering (DLS) to be ~160 nm in diameter. We have used XRD to confirm that the rutile crystalline phase dominates the TiO2 nanoparticle powder. Four solvents were used without further purification for this study: Tetrahydrofuran (THF, 99.7%, Alfa Aesar), Acetonitrile (ACN, ≥99.93%, SigmaAldrich), Acetone (Ace, ≥99.9%, Sigma-Aldrich), and Ethyl Acetate (AcOEt, 99.5%, Sigma-Aldrich). The chemical structures of the two dyes used in this study, para-Ethyl Red (p-ER) and ortho-Ethyl Red (o-ER) are shown in Scheme 1. o-ER (Alfa Aesar) was used as received commercially and the purity of

≥ 98% was checked by NMR

measurements. The dye p-ER was synthesized according to the procedure reported in the literature:52 2.0 g 4-amino benzoic acid (Alfa Aesar) and 30 ml 6 M HCl aqueous solution in a 100 ml flask were cooled in an ice-bath. Ice-cold NaNO2 (1.0 g in 5 ml H2O) solution was added slowly into the flask. The solution was stirred for 30 min to produce diazonium. Subsequently, an ice-cold solution with 2.3 ml diethylaniline (Alfa Aesar) and 10 ml 12 M HCl was added into the mixture and left to stir for 1 hour at 0 °C. The resultant product was neutralized with saturated NaHCO3 solution. The precipitated

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orange solid was collected and washed with water three times, followed by recrystallization with methanol. The final powder was dried at 50 °C under vacuum. The purity of p-ER was ≥ 98% checked by NMR measurements as well. The density of TiO2 particles was set to 3.8×109 per ml in the solution for the SHS experiments. Different concentrations of the dyes were added into the TiO2 colloids by diluting from the 500 µM stock solution. All experiments were performed at room temperature (22 ± 1 °C).

Results and Discussion Effect of Molecular Structure on adsorption To illustrate the influence of molecular structure on adsorption onto TiO2 particle surfaces, the two isomers of a dye, o-ER and p-ER, were chosen. Their adsorption can be detected through the SHS experiments. The SHS intensity in principle depends on the density of surface adsorbed molecules and the surface nonlinear susceptibility which is a coherent sum of the molecular hyperpolarizability according to the ensemble orientation average. Figure 1 shows SHS measurements of the two dyes in the TiO2-in-ACN solution. Upon adding p-ER into the TiO2 colloidal solution to make a 20 µM concentration, discernable SHS signal was detected. In contrast, with 20 µM o-ER in the TiO2-in-ACN solution the SHS signal was too weak to be detected within our experimental sensitivity. This observation is related to adsorption density and the surface nonlinear susceptibility. We first consider adsorption on the surface. The TiO2 particle surfaces were found to be neutral in these four aprotic solvents from zeta potential measurements. The Ti atoms on the surface of TiO2 are the sites for –COOH to bind to.53 The ER dyes adsorb onto the

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TiO2 surface with the –COOH group anchored at the surface. For the para isomer the hydrophobic part of the molecule stretches away from the surface. In contrast, the part of the ortho isomer beyond the N=N group presents steric hindrance upon adsorption. In addition, the interaction of –COOH and the adjacent nitrogen of the azo- moiety of o-ER could attenuate the interaction of the –COOH and TiO2 surface. This possibility was previously proposed with the computational predictions in the literature.46 Consequently, the formation of intramolecular hydrogen bond for the ortho-isomer could lead to the weak binding of the dye with TiO2 surface. These results imply that o-ER unlikely binds to the TiO2 surface so there is no detectable SHS signal. One of other possibilities is that although o-ER adsorbs onto the surface, the molecules tend to lie down, and orient tangentially on the TiO2 particles. Such a geometric configuration might lead to weak SHS responses from o-ER on TiO2 surfaces. To assess which is the most likely causing the near-zero SHS from o-ER, we first determine the relative strength of the molecular hyperpolarizability (with 800 nm fundamental for generating 400 nm second harmonic) of o-ER vs p-ER. The same experimental setup described above was used for measuring the hyper-Rayleigh scattering intensity. The scattered light intensity at 400 nm was recorded for 2 mM dye in either THF or ACN and for the solvents only. It was found that the hyper-Rayleigh intensities from the two dye isomers, with the solvent background subtracted, show the following ratio: In THF, I(o-ER)/I(p-ER) = 2.21/1.0 and in ACN, I(o-ER)/I(p-ER) = 10.7/1.0. The difference in the ratios presumably is from the solvent induced shift of the electronic transition strength at 400 nm. The hyper-Rayleigh measurements clearly indicate that the molecular hyerpolarizability of o-ER is much larger than p-ER. The fact

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that there is zero SHS intensity while p-ER gives strong SHS intensity can only result from the fact that o-ER does not adsorb onto TiO2 surface due to steric hindrance. If oER does adsorb onto the surface tangentially, there still should be a component of hyperpolarizability that is perpendicular to the surface for generating detectable, low SHS intensity. This comparative study clearly shows the effect of molecular structure on adsorption and explains why the o-ER derivative-sensitized solar cells exhibit a very low solar energy conversion.46 Effect of solvents on adsorption The solvent-dye interactions can be examined from the electronic spectra which are shown in Figure 2: absorption spectra in the visible region of p-ER in four aprotic solvents, ACN, Ace, AcOEt, and THF. Each of the four spectra show two peaks and was analyzed through non-linear least squares fit with each of the peaks assuming a Gaussian band shape with band center and full-width-half-maximum as fitting parameters. The fitting results show that both peaks shift to the red approximately in the order of solvent polarity of THF, AcOEt, Ace and ACN. The high-energy band centers are 372 nm (THF), 371 nm (AcOEt), 378 nm (Ace), and 390 nm (ACN) while the low-energy band centers are 447 nm (THF), 444 nm (AcOEt), 450 nm (Ace), and 454 nm (ACN). A consequence of this shift is that as the polarity of the solvent increases, the high-energy peak comes closer to be in resonance with the second harmonic frequency. According to the classical solvation theory,11 the solvent-induced energy shift is given by,

∆E = −

µg (µe − µg ) a

3

 f (ε ) − f (n2 )

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where µg is dipole moment of solute in the ground state, µe is dipole moment of solute in an excited state, a is the spherical solute molecule radius with the units of Å, f(ε)= (2(ε 1))/(2 ε +1), ε is the dielectric constant of solvents at low frequency, f(n2)=(2(n21))/(2n2+1), n is the refraction index of solvents. The spectral shifts with solvent polarity are in accord with the equation 1 described above for both the high-energy peak and the low-energy peak. The low-energy peak is attributed to π-π* transition, whereas the highenergy peak is due to an intramolecular charge transfer transition. The red shifts in UV spectra suggest that the solvachromism of the two transitions for p-ER is of positive character. To check if the SHS signal comes from molecules adsorbed at the surface of TiO2 particles, SHS intensities taken from three samples with the solvent ACN: TiO2 with 20 µM p-ER, TiO2 alone, and 20 µM p-ER alone are compared in Figure 3. The p-ER/TiO2 sample produces much larger SHS signal than p-ER and TiO2 alone, confirming that the SHS signal is from surface bound p-ER molecules on TiO2. From the Langmuir adsorption isotherm measured as the SHS intensity as a function of the p-ER concentration, the surface density and adsorption free energy of p-ER on TiO2 can be quantitatively determined.45 Figure 4 displays the SHS intensity measured as a function of the p-ER concentration added into the TiO2 colloidal solution prepared with the four different aprotic solvents. The SHS intensity at each data point was collected after it reached a plateau following the addition of the dye, indicating that equilibrium has been reached at that particular p-ER concentration. The adsorption isotherms for the four aprotic solvents show different rising slopes, indicating that the adsorption free energy of p-ER onto TiO2

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varies with the solvent. In addition, the maximum SHS intensity level varies with the solvent – it increases with increasing solvent polarity, in the order from THF, AcOEt, Ace, to ACN. The maximum SHS intensity depends on the following factors: the maximum adsorption density on the surface, the individual molecular hyperpolarizability α(2) in the specific solvent, as well as the molecular orientation on the surface which affects the overall surface nonlinear susceptibility. The transition energy for the highenergy peak shifts towards 400 nm from less polar THF to polar ACN as shown in Figure 2. The electronic transition shifts closer to be resonant with 2ω (400 nm) from THF to ACN, leading to a larger hyperpolarizability α(2) in the more polar ACN. As a consequence, the hyperpolarizability α(2) of the p-ER may increase in the same direction.54 To quantitatively determine the adsorption free energy of p-ER on the TiO2 surface, the Modified Langmuir model was used to fit the SHS-measured adsorption isotherms. In the analysis the SHS intensity is proportional to the square of the surface coverage of p-ER which is related to the total concentration C0 of dye molecules including the ones in the solvent and on TiO2 and the adsorption equilibrium constant Kb (L. mol-1). The surface population N relative to the maximum density of molecules on the surface (Nmax), namely, surface coverage, is given by:23, 39, 44, 55 ே ே೘ೌೣ

=

ሺே೘ೌೣ ା஼బ ାଵ/௄್ ሻିඥሺே೘ೌೣ ା஼బ ାଵ/௄್ ሻమ ିସ.ே೘ೌೣ .஼బ ଶ.ே೘ೌೣ

(2)

A nonlinear least squares fit of the SHS intensity measured as a function of C0 yields Nmax and Kb from which the adsorption free energy △G can be deduced. The fitting results for the adsorption of p-ER onto TiO2 in the four solvents are listed in Table 1.

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The maximum surface density Nmax of p-ER obtained from the fitting reported in Table 1 is close to or smaller than that of the maximum surface coverage, 5.0×106 µm-2, estimated under the assumption that the TiO2 particle is spherical and the area of the anchoring -COOH group56 is on the order of ca. 20 Å2 for a diameter of 160 nm TiO2 particle. The comparison, together with the saturation behavior of the SHG intensity at increasing p-ER concentrations, indicates that p-ER adsorption onto TiO2 particles is characterized by a saturated monolayer. To get insights into the solvent-dependent adsorption of p-ER onto TiO2 particles, we analyzed the correlation of the adsorption free energies measured in our experiments with several solvent scales, including Kamlet-Taft parameters (hydrogen bond donation ability α, hydrogen bond acceptance ability β, and pority/polaribility parameters π),57-58 acidity and basicity,59 donor numbers and acceptor numbers,60 polarity Z,61 and ET(30).57, 62 These scales are categorized into two: the first three are microscopic and the last two are macroscopic. It was found that the β value in Kamlet-Taft parameters, acidity, and donor numbers give consistent tendency of the correlations with abilities of accepting electrons for the solvents or donating protons with the adsorption free energies of the dye onto TiO2. In other words, either of them could be used to describe the correlation with the adsorption free energies measured in our experiments. Furthermore, the more macroscopic scales such as ET(30) and polarity Z are also consistent with each other. The bigger the solvent ET(30) and polarity Z are, the larger the surface adsorption free energy △G. As such, we plotted the △G obtained above with the β value in Kamlet-Taft parameters and the ET(30) solvent scales,57, 62 as shown in Figure

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5. Such correlations suggest that interactions between p-ER and the solvents determine the adsorption of the dye onto TiO2 particle surfaces. As the solvated p-ER adsorbs onto the surface, the free energy change encompasses the energies associated with the following contributions: 1) taking the solvated p-ER to the surface, 2) surface binding of p-ER, 3) partial solvation of the surface-bound p-ER, 4) desorption of the surface-bound solvent molecule(s) replaced by p-ER, and 5) re-solvation of the displaced solvent molecule(s); as well as entropy induced energy change. Now we consider the possible effects of solvent polarity in each of the contributions. It is reasonable to assume that the energies associated with entropy change and Item 2 remain unchanged with the increase of solvent polarity. Item 1 – de-solvation of p-ER in fact would contribute to the opposite direction to the adsorption free energy change with increasing solvent polarity; i.e. it would take more energy to de-solvate p-ER from solvents with larger polarity and actually cause the adsorption free energy to be smaller. This particular effect in Item 1 will be offset by Item 3 – partial solvation of the surface-bound p-ER. It is most likely that the difference in energy caused by Items 1 and 3 is small so that the combined influence is not consequential. This leaves the energies associated with desorption and re-solvation of the surface-bound solvent molecules displaced by the adsorption of p-ER as the major cause of the free energy change as a function of solvent polarity. The re-solvation of the displaced solvent molecules in a more polar solvent will contribute more to the free energy change, consistent with the trend observed experimentally. The above discussion illustrate that the effect of solvent polarity is due primarily to the re-solvation of the displaced solvent molecules from the surface by the dye molecule. These hypothetical processes require support from

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calculations and are under investigation. Our experimental findings also explain that treatment of dyes in ACN improves sensitized solar cells efficiency in the literature.63-64 The most likely interpretation, based on our measurements, is that the difference of 1.4 kcal/mole in adsorption free energies from the least polar solvent THF to the most polar ACN depicts the most efficient adsorption of p-ER onto TiO2 in the most polar solvent. With this amount of difference in free energy at room temperature, it takes approximately one order of magnitude less dye concentration to achieve monolayer coverage in ACN than in THF.

Conclusions The effects of molecular structure and solvent polarity on the adsorption of carboxylic anchoring dyes p-ethyl red and ortho-ethyl red, two isomers, onto TiO2 particles in aprotic solvents have been investigated. The interface-sensitive Second Harmonic Scattering technique has been used to directly detect adsorption of the dye molecules on the surface of the TiO2 particles in the colloidal solution. Through hyper-Rayleigh scattering measurements, we have determined that o-ER has a much larger molecular hyperpolarizability than p-ER. It was found, however, that upon adding the dyes into the TiO2 colloids, the SHS signal from p-ER was strong but there was no detectable signal from o-ER. This observation can only be explained by concluding that o-ER does not adsorb onto the particle surface because of steric hindrance presented by the o-ER structure. This observation also provides the explanation about why o-ER has a much lower DCCS efficiency. The Langmuir adsorption isotherm of p-ER in four aprotic dyes Acetonitrile,

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Acetone, Ethyl Acetate and Tetrahydrofuran have been measured as the SHS intensity detected as a function of the dye concentration in the colloids. Analyses of the isotherms afford the determination of the maximum adsorption density and the adsorption free energy of p-ER in each of the four solvents. It was found that the maximum density varies slightly, less than 50% from each other, among the four solvents. On the other hand, there is a 1.4 kcal/mole difference in the adsorption free energy with the magnitude being smallest from the least polar solvent THF to the most polar solvent ACN. This observation provides the explanation why ACN is the most efficient among commonly used electrolytes for DSSC. The adsorption free energy measured for p-ER onto TiO2 linearly correlates with the β value in Kamlet-Taft parameters, acidity, and donor numbers, polarity Z and ET (30). It appears that the higher the ability of accepting electrons and solvent polarity are, the larger the adsorption free energy. After examining the various contributions to the adsorption free energy, this trend is best understood from the difference in re-solvation of the solvent molecules displaced by the adsorption of the dye from the TiO2 surface.

Acknowledgments This research was funded by Reactive Chemical Systems Program, U.S. Army Research Office (W911NF-15-2-0052).

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Scheme 1. Chemical structures of p-ER (left) and o-ER (right).

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Table 1. Comparison of the experimentally determined maximum number density Nmax and the binding constant Kb of p-ER adsorption onto TiO2 in four aprotic solvents (ACN, Ace, AcOEt, and THF). △G is calculated from Kb. Nmax

Kb

△G

(number of p-ER /µm2)

(L/mol)

(kcal/mol)

ACN

3.09 (± 0.08) × 106

13.84 (± 1.78) × 106

-9.73 ± 0.07

Ace

2.83 (± 0.35) × 106

6.97 (± 2.85) × 106

-9.09 ± 0.14

AcOEt

4.69 (± 0.42) × 106

2.69 (± 1.30) × 106

-8.74 ± 0.10

THF

4.68 (± 0.38) × 106

1.47 (± 0.39) × 106

-8.32 ± 0.06

Solvents

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Figure 1. SHS intensity profiles from 20 µM p-ER (red solid circles) and 20 µM o-ER (black solid circles) in TiO2-in-ACN colloids.

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Figure 2. UV spectra (solid lines) of p-ER in four different aprotic solvents including acetonitrile (ACN), acetone (Ace), ethyl acetate (AcOEt), and tetrahydrofuran (THF). The UV envelops were fitted with two Gaussian peaks (broken lines), both of which show red-shift with shift magnitude increasing approximately with solvent polarity. The center of the high-energy peaks: 372 nm (THF), 371 nm (AcOEt), 378 nm (Ace), and 390 nm (ACN). The low-energy peaks: 447 nm (THF), 444 nm (AcOEt), 450 nm (Ace), and 454 nm (ACN).

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Figure 3. SHG intensity profiles from 20 µM p-ER in TiO2-in-ACN solution (red), 20 µM p-ER in ACN alone (green), and TiO2 in ACN alone (black), respectively.

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Figure 4. SHS measured adsorption isotherms of p-ER onto TiO2 in the four aprotic solvents (ACN, Ace, AcOEt, and THF). The red solid circles refer to the SH intensity in ACN, the green Ace, the orange AcOEt, and the blue THF. The solid lines are the fittings to the Modified Langmuir model (Equation 2). The inset displays the normalized SHS isotherms of the four solvents.

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Figure 5. The adsorption free energy of p-ER onto TiO2 as a function the ET(30) energy representing the solvent polarity and the hydrogen bond acceptance (HBA) ability β for the four aprotic solvents.

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TOC

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