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Cartesian Decomposition of Infrared Spectra Reveals the Structure of Solution-Deposited, Self-Assembled Benzoate and Alkanoate Monolayers on Rutile (110) William J. I. DeBenedetti, Erik S. Skibinski, Joshua A. Hinckley, Sara B. Nedessa, and Melissa A. Hines* Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, United States S Supporting Information *

ABSTRACT: Cartesian polarization analysis transforms a set of surface infrared spectra obtained in different geometries into their Cartesian components using a mathematical transform, providing direct insight into the bonding geometry of adsorbed molecules. This technique was extended to uniaxial substrates and used to analyze solution-deposited, self-assembled benzoate and alkanoate monolayers on rutile (110). This analysis resolved a long-standing controversy regarding the existence of paired molecules in benzoate monolayers, showing that two distinct isomers exist within the monolayer: a tilted tetramer, which is paired, and a twisted monomer, which is not. The two isomers are nearly isoenergetic, as shown by analysis of STM images and complementary DFT simulations. Infrared and XPS spectra as well as STM images of heptanoate and octanoate monolayers showed the formation of complete monolayers (as opposed to sparse layers or multilayers); however, the alkyl chains in the monolayer are disordered and loosely packed with a significant density of conformational defectsa stark contrast to the near-crystalline, all-trans alkyl monolayers typically formed on Au and Si surfaces. The high disorder in the alkanoate monolayers was attributed to geometry, as the density of alkanoate binding sites on rutile (110) is 30% less than the density of alkyl monolayers on Si. The high density of gauche defects in alkanoate monolayers was attributed to the small energy difference between the all-trans and single-gauche-defect conformers in isolated alkyl chains. In contrast, strong intermolecular interactions in tight-packed alkyl monolayers on Au and Si surfaces suppress gauche defect formation.

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INTRODUCTION Self-assembled monolayers of organic molecules find application in numerous contexts. In their simplest incarnation, they can be used to displace unwanted molecules and act as a surface passivating layer. For example, self-assembled monolayers can protect silicon surfaces from oxidation,1−3 prevent stiction,4,5 and improve mechanical performance6,7 in microelectromechanical devices. Self-assembled monolayers can also be used to impart functionality, such as improving electrical performance,8 controlling charge density in electrically active layers,9 tuning metal work functions,10 or controlling crystal nucleation.11,12 To date, most studies of self-assembled monolayers have focused on silicon13 and gold14 surfaces, primarily due to their technological importance and chemical stability, respectively. We are interested in self-assembled monolayers on metal oxide surfaces, including the prototypical metal oxide rutile, in part because they play an important role in the shape-controlled growth of metal oxide nanoparticles.15−17 The high density of self-assembled monolayers often induces an ordered molecular structure  a structure that may not be the same as that of an isolated molecule on the surface. Indeed, the term “self-assembling monolayer” was originally coined to describe the spontaneous near-vertical alignment of fatty acid monolayers on a solid surface.18 Spectroscopies that use polarized light, such as infrared absorption spectroscopy, are particularly © 2016 American Chemical Society

valuable in monolayer structural analysis, as the anisotropy of the absorption bands provides direct information on molecular alignment. Cartesian decomposition,19 which uses knowledge of the surface electric field to transform spectra from the experimental reference frame defined by s- and p-polarized light to the high-symmetry axes of the substrate, aids in this structural assignment. As an example, Cartesian decomposition of the Si−H vibrational spectrum on etched Si(100) wafers20 disproved a long-standing and much-cited spectral assignment21 that postulated the production of a rough, disordered surface, revealing instead the production of a near-atomically flat surface. Similarly, the technique was used to uncover the mechanism of pH-induced surface roughening during Si(100) etching, revealing the production of faceted nanohillocks at low pH.22 The multiple-internal-reflection geometry is particularly valuable in surface infrared spectroscopy due to its enhanced detection sensitivity as well as it improved polarization sensitivity over external reflection.23 This geometry enables the detection of relatively weak or broad absorbances; however, multiphonon absorption by the substrate limits its spectral range. Received: August 21, 2016 Revised: September 29, 2016 Published: October 4, 2016 24866

DOI: 10.1021/acs.jpcc.6b08450 J. Phys. Chem. C 2016, 120, 24866−24876

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The Journal of Physical Chemistry C On rutile, only transitions with energies greater than ∼2000 cm−1 are detectable. One of the challenges in applying infrared spectroscopy to the study of rutile is that the crystal is uniaxial and highly birefringent. As a result, the dielectric response of the substrate is dependent on both the propagation direction and the polarization of the infrared radiation. In addition, the intense Ti−O absorption bands of the substrate (∼900−1000 cm−1) affect the substrate dielectric response throughout the infrared via the Kramers−Kronig relations. As a result, the dielectric response of the substrate is highly wavelength dependent in the mid-infrared. In this manuscript, we first derive the mathematical transformation for Cartesian decomposition of spectra taken in the multiple-internal reflection geometry on uniaxial substrates. We then apply this technique, in combination with scanning tunneling microscopy (STM) and X-ray photoemission spectroscopy (XPS) experiments and density functional theory (DFT) calculations, to the analysis of two types of solutiondeposited monolayers on rutile (110): benzoate and alkanoate monolayers. In the first, we resolve a controversy regarding the structure of benzoate monolayers, showing that the monolayers form domains with two distinct structures, one paired and one unpaired. In the second, we show that alkanoate monolayers on rutile are very different than similar monolayers on gold and silicon, as the large distance between binding sites prevents the crystallization of the alkane chains, leading to a highly rotationally and conformationally disordered structure.

aqueous solution; these spectra are reported. Whether these spectral differences are intrinsic to the solvent system or simply a matter of incomplete process optimization is a subject of ongoing research. Rutile (110) samples for scanning tunneling microscopy (STM) or X-ray photoemission spectroscopy (XPS) were thermally reduced at 700 °C for 5 min in UHV before use to provide sufficient conductivity. Samples were then cleaned by sequential immersion a basic peroxide bath of 1:1:2 NH4OH:H2O2:H2O at 80 °C for 10 min, then an acidic peroxide bath of 1:1:2 HCl:H2O2:H2O at 80 °C for 10 min, followed by a second basic peroxide clean. Self-assembled monolayers were then prepared with the previously described procedure, then transferred to UHV through an oil-free load lock. STM images were collected using electrochemically etched, recrystallized tungsten26 tips that had been prepared by field-directed sputter sharpening.27 X-ray photoelectron spectroscopy was performed using an unmonochromated MgKα source with photoelectrons collected 70° from the surface normal. A Tougaard baseline was subtracted from each XPS spectrum, and small energy corrections (∼0.05 eV) were applied using reference binding energies28 to offset small band bending effects.29 Computational Methods. Density functional theory (DFT) was used to model the structure of benzoate monolayers on periodically repeating slabs consisting of 5 TiO2 trilayers separated by a 12.5 Å vacuum spacing with autocompensated surfaces (Supporting Information).30 During optimization, the positions of the bottommost TiO2 layer and its terminating bridging O rows were held fixed. Calculations were performed using DFT within the generalized gradient approximation31 (GGA) with the Perdew, Burke, and Ernzerhof (PBE) exchangecorrelation functional,32 as implemented in the Vienna ab initio simulation package (VASP).33−36 The functional was corrected for long-range dispersion interactions using the zero damping DFT-D3 method.37 Electron−ion interactions were described using the projector augmented wave (PAW) method.38,39 Electronic states were expanded in plane waves with a kinetic energy cutoff of 400 eV. Brillouin-zone integration was performed using Gaussian smearing. STM images were modeled within the Tersoff− Hamann approximation40 as isosurfaces of constant local density of states in an energy band from 0.66 eV below the highest occupied band to the Fermi energy. A rolling ball filter was used to simulate the effects of tip convolution.

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EXPERIMENTAL AND COMPUTATIONAL Experimental Methods. These experiments used ultrapure H2O (Milli-Q) exclusively. Prior to use, all glassware for sample preparation was cleaned in a basic peroxide bath of 1:1:5 28% NH4OH (aq, BDH, ACS grade):30% H2O2 (aq, J.T. Baker, CMOS grade):H2O for 10 min at 80 °C then H2O rinsed. Glassware for samples used in ultrahigh vacuum (UHV) was additionally cleaned in an acidic peroxide bath of 1:1:5 37% HCl (aq, BDH, ACS grade):H2O2 (aq, J.T. Baker, CMOS grade):H2O then H2O rinsed. Rutile (110) samples (MTI or Crystek) for infrared spectroscopy were beveled on parallel faces at 45° from 10 mm × 10 mm × 0.5 mm die for use in the multiple-internal-reflection geometry. Instead of using one crystal that had been beveled on all four faces, we used two crystals, each beveled on a single pair of faces. Before each use, rutile samples were immersed in a basic peroxide bath of 1:1:2 NH4OH:H2O2:H2O at 80 °C for 10 min to create an atomically smooth,24 clean, bicarbonate-terminated25 surface. This surface was used as a reference for all infrared spectra. Samples were then immersed in boiling aqueous solutions of 16 mM benzoic acid (Sigma, > 99%), 6 mM heptanoic acid (Sigma, > 99%), or 6 mM octanoic acid (Sigma, > 99%) for 10 min to yield self-assembled monolayers of benzoate, heptanoate, or octanoate. Alternatively, samples were immersed in 6 mM heptanoic acid or 6 mM octanoic acid in hexadecane for ∼16 h at room temperature. After synthesis, surfaces terminated with alkanoate monolayers were rinsed in mixed pentanes to remove excess alkanoic acid. Samples were then transferred to a dry-airpurged infrared spectrometer (Nicolet 670) for analysis. Polarized infrared spectra were collected with a mercury−cadmium− telluride detector and ZnSe wire grid polarizer (Molectron), and computationally transformed to a Cartesian reference frame (vide inf ra). Alkanoate monolayers synthesized in organic solvent were of higher quality and reproducibility than those synthesized in

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RESULTS AND DISCUSSION Cartesian Polarization Analysis on Birefringent Substrates. Cartesian polarization analysis transforms a set of infrared spectra obtained in different geometries into their Cartesian components using a mathematical transform. Cartesian polarization analysis was originally developed for optically isotropic substrates analyzed in the multiple internal reflection geometry. The transformation was derived and experimentally verified in ref 19. In the following, we focus solely on the additional complications caused by substrate birefringence, referring the interested reader to ref 19 for a complete discussion and verification of the technique. The defining characteristic of birefringent materials is double refraction, the spontaneous separation of unpolarized refracted light into two rays of opposite polarization, the ordinary and extraordinary rays. In general, these rays propagate in different directions and with different velocities; their interaction with the birefringent material is therefore described by different dielectric constants. The ordinary ray is always polarized perpendicular to 24867


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The Journal of Physical Chemistry C

of this displacement, the p-polarized ray makes ∼15% fewer internal reflections than the s-polarized ray. To correct for this change in path length, the absorbance of the p-polarized spectrum in geometry 1 must be multiplied by a factor of η where

the optic axis of the crystal, and its interaction is determined by the dielectric constant ε⊥, which is wavelength dependent. The propagation of the extraordinary ray is determined by εe, which is given by sin 2 γ cos2 γ 1 = + εe ε ε⊥

η = ε /ε⊥

(3)

In geometry 2, the plane of incidence is perpendicular to the optic axis. In this geometry, both rays traverse the same path, and there is no double refraction. Incident s-polarized light generates a pure extraordinary ray, and incident p-polarized light generates a pure ordinary ray. These geometries are summarized in Table 1.

(1)

where ε∥ is a second wavelength-dependent dielectric constant, and γ is angle between the wave vector of the radiation and the optic axis.41 For the specific case where γ = 45°, eq 1 reduces to 2ε ε⊥ εe = ε + ε⊥ (2)

Table 1. Dielectric Constants Relevant to the Geometries in Figure 1, Assuming a Bevel Angle of 45° from the Surface Normal on All Four Faces

Rutile is an intensely birefringent material with an optic axis along [001]. In the visible regime, the absolute birefringence of rutile, |Δn| = |n⊥ − n∥| where n is the index of refraction, is significantly larger than that of calcite, the first discovered and most well-known birefringent material. In the mid-infrared regime, the dielectric response of rutile varies significantly, with ε∥varying between 5.9 and 6.7, and ε⊥ varying between 5.0 and 5.76 over the range 1800−4000 cm−1.42 To make this discussion more concrete, consider the two multiple-internal-reflection geometries sketched in Figure 1.

geometry

incident polarization

ray

γ

1

p

e

45°

dielectric constant 2ε ε⊥ ε + ε⊥

s p s

2

o o e

45° 90° 90°

ε⊥ ε⊥ ε∥

The extraction of geometrical information from a surface vibrational spectrum requires a knowledge of the magnitude and orientation of the electric field in the molecular overlayer, the so-called surface electric field.23,43 In both reflection and transmission geometries, this field differs substantially from the incident electric field and is influenced by the dielectric response of both the adsorbate layer and the substrate. The surface electric field can be calculated from classical electrodynamics using the three-layer model,23,43 as sketched in Figure 2. In this model, the substrate, adsorbate layer, and

Figure 2. Three-layer model used to calculate the surface electric fields in the multiple-internal-reflection geometry. The surface electric field is dependent on the z component of the surface dielectric constant, εz, as well as the substrate dielectric constant, εsub.

Figure 1. Two experimental geometries used for the Cartesian decomposition of surface infrared spectra on a uniaxial substrate. The optic axis is parallel to x, and the surface normal is parallel to z. In geometry 1, the extraordinary ray is displaced toward the optic axis by ∼4.1° (wavelength dependent) as shown by the dashed line in the inset, which results in a somewhat shorter effective path length for the p-polarized ray. In geometry 2, the two rays traverse identical paths. For the specific case of rutile (110), the optic axis is parallel to the Ti rows, which are indicated by parallel lines on the top face of the crystal.

vacuum are modeled as homogeneous dielectric media separated by abrupt planar interfaces. The dielectric constant of the substrate and the gas phase/vacuum are εsub and 1, respectively. The dielectric response of the adsorbate may be anisotropic, but one of the principal axes of the dielectric tensor is assumed to be aligned with the surface normal. When the incident light is p-polarized, the surface electric field has components that are parallel to the surface, E∥, and perpendicular to the surface, E⊥. For reference, the squared magnitude of these fields are

In both geometries, the light is incident at a 45° incident angle θ onto a 45° bevel. In geometry 1, the plane of incidence is parallel to the optic axis. In this geometry, p-polarized incident radiation generates a pure extraordinary ray, and s-polarized radiation generates a pure ordinary ray. The two rays propagate along slightly different paths, with the extraordinary ray being displaced toward the optic axis by ∼4.1° as sketched in Figure 1. As a result

I⊥ ≡ |E⊥|2 =

εz2(1

4 cos2 θ sin 2 θ |E inc|2 − 1/εsub)[(1 + 1/ εsub) sin 2 θ − 1/εsub]

(p polarization) 24868

(4) DOI: 10.1021/acs.jpcc.6b08450 J. Phys. Chem. C 2016, 120, 24866−24876

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εz with the Lorentz oscillator model have yielded poor matches to experiment.19 For the specific case of H/Si, εz2 has been experimentally measured to be 3.24−4.0,19,44−46 which implies significant screening. In contrast, the Lorentz oscillator model predicts εz2 = 1.8 for this system.19 As a result, infrared spectroscopy cannot be used to reliably calculate tilt angles unless εz is independently measured. Third, the surface electric field induced by p-polarized radiation has a significant out-ofplane component; this field is not perpendicular to the surface. Indeed, if εz ≳ 1.3, the in-plane component of the field will dominate on rutile. The absorbance A of a surface layer is defined by47

and I ≡ |E |2 =

4 cos2 θ(sin 2 θ − 1/εsub) (1 − 1/εsub)[(1 + 1/ εsub)sin 2 θ − 1/εsub]

|Einc|2

(p polarization)

(5)

where |Einc| is the magnitude of the incident electric field. Importantly, the perpendicular component of the surface field is screened by the z-component of the adsorbate dielectric constant, εz. In general, εz is an unknown constant. When the incident light is s-polarized, the surface electric field Es is parallel to the surface, and its squared magnitude is Is ≡ |Es|2 =

4cos2 θ |E inc|2 1 − 1/εsub

(s polarization)

⎛I ⎞ A ≡ log10⎜ 0 ⎟ ⎝I⎠

(6)

For the case of a pure ordinary or a pure extraordinary ray propagating in a birefringent substrate, these equations can be used unchanged by substituting the appropriate dielectric constant for εsub. Although the form of eqs 4−6, particularly their dependence on 1/εsub, might suggest that the substrate dielectric constant has little impact on the surface electric field, Table 2 shows this is far

where I0 is the intensity of the radiation passing through the sample in the absence of the surface layer, and I is the intensity in the presence of the surface layer. The absorbance follows the Beer−Lambert law and is proportional to the concentration of molecules in the surface layer. On a molecular scale, the absorbance is given by A = a(E ⃗ • μ ⃗ )2

Table 2. Relative Squared Magnitudes of the Three Principle Components of the Surface Electric Field in the Mid-infrared Assuming Four Different Substrate Dielectric Constants: The Minimum and Maximum Dielectric Constants for TiO2 (5.0 and 6.7, respectively), the Dielectric Constant of Si (11.7), and the Infinite Limita

I∥ (p-pol) Is (s-pol) I⊥ (p-pol)

εmax

Si

εsub → ∞

0.61 0.80 1/εz2

0.70 0.85 1/εz2

0.83 0.92 1/εz2

1.00 1.00 1/εz2

⎛ η A p1 ⎞ ⎛I e ⎜ ⎟ ⎜ ⎜ As1 ⎟ ⎜0 ⎜ ⎟ = c⎜ ⎜ A p2 ⎟ ⎜0 ⎜ ⎟ ⎜ ⎝ Is ⊥ ⎝ As2 ⎠

a

These squared magnitudes have been normalized to the unscreened z component of the field.

or

0 Iso I 0

o

I⊥ e ⎞ ⎟⎛ mx ⎞ 0 ⎟⎜ ⎟ ⎟ my , I⊥ o ⎟⎜⎜ ⎟⎟ m ⎟⎝ z ⎠ 0 ⎠

or

A = c Im (9)

where η corrects for double refraction in geometry 1, mk = μ2k, c is a constant, and the squared surface electric fields I are described by eqs 4−6 and the appropriate dielectric constants. In this notation, the second subscript on I denotes the appropriate substrate dielectric constant, where e, o, and ⊥ denote εe, ε∥ (the dielectric constant of the ordinary ray), and ε⊥, respectively. Equation 8 is overdetermined. The best-fit dipole matrix m can be extracted from the absorption spectra using the MoorePenrose inverse,48 or “pseudoinverse,” of I, which is denoted I+. This yields

from the truth. In this table, the relative squared magnitudes of the three principle components of the surface electric field calculated using the maximum and minimum substrate dielectric constants for TiO2 are compared to those of Si and the infinite dielectric constant limit. Three important conclusions can be drawn from this table. First, the relative magnitudes of these fields vary significantly and are typically far from their limiting values. Second, the z-component of the surface electric field is screened by an unknown constant, εz. Attempts to approximate

m = c −1I+A,

(8)

where E⃗ is the local electric field at the absorber, μ⃗ is the transition dipole moment of the absorber, and a is a constant. If four spectra are obtained on a square crystal in the geometries described in Figure 1, ref 19. shows that the absorbances in each spectrum can be expressed as

TiO2 εmin

(7)

⎛ I I I ( A I I + ( η A I − A I ) I ) + A (I 2 I 2 + (I 2 + I 2 )I 2 )I ⎞ ⊥e ⊥ o so s ⊥ e ⊥ o so s1 o ⊥ e p1 ⊥ o p2 ⊥ e so s2 o ⊥e ⎜ ⎟ 2 2 2 2 2 2 2 2 2 ⎜ ⎟ + + + I I I I I I I I I ( ( ) ) ⊥ ⊥ ⊥ ⊥ ⊥ e o so o e e o so s 2 ⎛ μ ⎞ ⎜ ⎟ x ⎜ ⎟ ⎜ I I I (A I I + (A I − ηA I )I ) + A I (I 2 I 2 + (I 2 + I 2 )I 2 ) ⎟ 2 2 1 1 ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ o e s s e o p e p o s s so e o e o s ⎜ μ2 ⎟ −1⎜ ⎟ ⎜ y ⎟=c ⎜ ⎟ I 2eI⊥2 oIso2 + (I 2oI⊥2 e + (I⊥2 e + I⊥2 o)Iso2 )Is2⊥ ⎜⎜ 2 2 ⎟⎟ ⎜ ⎟ μ ε / ⎝ z z⎠ ⎜ I⊥ e(I 2o + Iso2 )Is ⊥(ηA p1Is ⊥ − As2 I e) − As1I oI⊥ oIso(I 2e + Is2⊥) + A p2I⊥ oIso2 (I 2e + Is2⊥) ⎟ ⎜⎜ ⎟⎟ I 2eI⊥2 oIso2 + (I 2oI⊥2 e + (I⊥2 e + I⊥2 o)Iso2 )Is2⊥ ⎝ ⎠ (10)

If the incident intensity is constant in all four experiments, the right-hand side of eq 10 depends only on the measured spectra (i.e., Ap1, As1, Ap2, and As2), the experimental geometry

(i.e., θ and γ), the principal dielectric constants of the substrate (i.e., ε∥ and ε⊥), and a constant. If different crystals are used for 24869


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The Journal of Physical Chemistry C data collection, the absorbances in eq 10 must also be adjusted for their relative lengths. To aid in the implementation of this analysis, sample code in a C-like language is provided in the Supporting Information. This code also uses linear interpolation to correct the dielectric response for dispersion. Special Case: Rotational Averaging or Other Symmetry. In special cases, all in-plane components of the infrared spectrum may be equivalent or approximately equivalent. For example, molecules that rotate about the surface normal or that form a number of rotationally inequivalent domains may have spectra in which μx2 = μy2 ≡ μ 2

(11)

Once this isotropy has been experimentally confirmed, it is more convenient to obtain data in a single experimental geometry, either geometry 1 or 2, incorporating the symmetry into the decomposition analysis. For the case where the incident radiation is in the plane of the optic axis (i.e., geometry 1), eq 9 reduces to ⎛ η A p1 ⎞ ⎛ I e I⊥ e ⎞⎛ μ 2 ⎞ ⎜⎜ ⎟⎟ = c ⎜⎜ ⎟⎟⎜ ⎟ ⎝ Iso 0 ⎠⎜⎝ μz2 ⎟⎠ ⎝ As1 ⎠

(12)

Figure 3. STM images of paired and unpaired regions of a benzoate monolayer. (a) Paired domain, (b) unpaired domain, and (c) mixed domain.

This equation is not overdetermined and can be directly inverted to yield ⎛ As1 ⎜ ⎛ μ2 ⎞ Iso ⎜ ⎟ = c −1⎜ ⎜ ηA I − A I ⎜ 2 2⎟ s1 ⎜⎜ p1 so ⎝ μz /εz ⎠ I⊥ eIso ⎝

⎞ ⎟ ⎟ ⎟ e⎟ ⎟ ⎠

some have shown paired molecules,50,51,54 and some have shown regions of both.55 Consistent with the latter, Figure 3 shows STM images of unpaired and paired molecules on identically prepared benzoate/rutile (110) monolayers. Using a combination of experimental and computational techniques, Skibinski et al.55 recently showed that a tilted tetramer stabilized by π−π interactions between adjacent molecules, as shown in Figure 4, is both consistent with the paired domains and significantly more stable than any of the previously proposed, high-symmetry dimers. The unit cell of this structure consists of four molecules arranged in T configurations with their neighbors. This geometry can be rationalized in terms of the quadrupolar and dispersion forces acting between adjacent phenyl rings, so-called π−π interactions. This structure is further stabilized by a ∼ 7° tilt across the Ti rows, which brings the phenyl rings on the two cross-row pairs into closer proximity. This tilting explained the apparent pairing observed experimentally, as shown by the simulated STM images in Figure 4. Monte Carlo simulations55 of a simplified version of this structure also reproduced the characteristic defects seen in paired regions of the monolayer. Nevertheless, neither the DFT calculations or the Monte Carlo simulations explain the existence of unpaired regions of the monolayerregions that were stable for periods of hours with no interconversion to the paired structure.55 Cartesian analysis of aromatic C−H stretch modes in infrared spectra of the benzoate monolayer, shown in Figure 5, provided significant insight into the structure of the unpaired domains. Aromatic C−H stretch vibrations were observed in all four of the raw spectra. (Interestingly, these modes appear to have been undetectable in the reflection geometry.49) After Cartesian transformation, two types of spectral features were observed. First, all three Cartesian orientations displayed prominent C−H stretch modes centered at ∼3062 cm−1. Importantly, these modes showed only small differences between the x- and y-polarized spectra.

(13)

For the case where the incident radiation is perpendicular to the optic axis (i.e., geometry 2), eq 9 reduces to ⎛ A p2 ⎞ ⎛ I o I⊥ o ⎞⎛ μ 2 ⎞ ⎜⎜ ⎟⎟ = c ⎜⎜ ⎟⎟⎜ ⎟ I 0 A ⎝ ⎠⎜⎝ μz2 ⎟⎠ ⎝ s2 ⎠ s⊥

(14)

which can be inverted to yield ⎛ As2 ⎜ ⎛ μ2 ⎞ Is ⊥ ⎜ ⎟ = c −1⎜ ⎜ ⎜ 2 2⎟ A I − As2 I ⎜⎜ p2 s ⊥ ⎝ μz /εz ⎠ I⊥ oIs ⊥ ⎝

⎞ ⎟ ⎟ ⎟ o⎟ ⎟ ⎠

(15)

We caution that eqs 13 and 15 are rarely appropriate for rutile (110) surfaces and can only be used on systems in which eq 11 has been experimentally verified. Simply put, one must first show that spectra obtained in geometries (1) and (2) with s-polarized light are equivalent. If this criterion is not met, the four spectra defined by Figure 1 and eq 10 must be used for Cartesian decomposition; there is no shortcut. Sample code in a C-like language for these analyses is provided in the Supporting Information. Application to Benzoate Monolayers. Benzoic acid binds to rutile (110) dissociatively, resulting in a benzoate molecule bound to two Ti atoms and a protonated bridging O atom.49−55 STM investigations of the structure of benzoate monolayers prepared by vapor50−53 or solution deposition54,55 have come to conflicting conclusions: some have shown unpaired molecules52,53 24870


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Figure 5. (Left) The C−H stretch region of four infrared spectra of benzoate monolayers obtained in the geometries defined in Figure 1. (Right) Cartesian transform of the four experimental spectra revealed the transition dipole moment projected along the x (Ti row or [001] direction), y ([110̅ ] direction), and z axes. The dotted lines denote observed peak transitions at 3033.5, 3056.5, 3062.5, 3070, and 3091.5 cm−1.

Both experiment and theory found the two structures to be nearly isoenergetic. As a check on the DFT simulations, STM images of benzoate monolayers were used to estimate the relative energies of the two isomers. Although domains of twisted monomers and domains of tilted tetramers could be found, as shown in Figure 3, the relative densities of tilted tetramers and twisted monomers were measured to be ∼2:1. If the surface structure was in thermal equilibrium with the deposition solution, then

Figure 4. Filled state simulated STM images and orthographic views of the (left) tilted tetramer and (right) twisted monomer isomers of benzoate/rutile (110) determined from DFT simulations. The view along the Ti rows corresponds to the x or [001] direction, whereas the view across the Ti rows corresponds to the y or [11̅0] direction. The red, white, and blue balls represent O, H, and Ti atoms, respectively.

These small differences are consistent with the near-4-fold rotational symmetry of the tilted tetramera symmetry that is broken only by the 7° tilt of the molecules and the small rectangular distortion of the underlying lattice. Second, two modes were observed only in the x-polarized spectrum: one ∼30 cm−1 above the central transition and one ∼30 cm−1 below the central transition. Their strong x-polarization suggested the existence of a second isomer that had the phenyl rings roughly parallel to the Ti rows. With the infrared spectra as a structural clue, additional DFT simulations identified a second low energy isomer, a twisted monomer, as shown in Figure 4. In this isomer, the phenyl rings were twisted by 20° about the surface normal to relieve steric interactions between H atoms on adjacent rings. In contrast to the tilted tetramer geometry, this isomer was only slightly stabilized by tilting (i.e., the stabilization was less than thermal energy), which can be understood by comparing the distances between adjacent molecules in the “Along Ti Rows” view. The T orientation of adjacent molecules in the tilted tetramer geometry leads to a much smaller distance of closest approach than found in the twisted monomer geometry. As a result, tiltinga motion that brings adjacent molecules closer together, strengthening quadrupolar and dispersion interactionshas a much stronger effect on the twisted tetramer isomer.

Tilted Tetramer (ads) ⇋ Twisted Monomer (ads)

(16)

The relative densities of the two domains should then be given by the equilibrium constant K = e−ΔGrxn / kBT ≈ e−ΔErxn / kBT

(17)

where Grxn and Erxn are the Gibbs free energy and energy of reaction 15, respectively, kB is Boltzmann’s constant, and T is the deposition temperature. The approximation in eq 17 neglects entropic effects, which are expected to slightly favor the twisted monomer phase, and the grain boundary energy. From eqn 17, we estimated ΔErxn = +22 meV/molecule, which is in reasonable agreement with our DFT simulations, which estimated ΔErxn = −60 meV/molecule. In other words, experiment suggested the tilted monomer is 22 meV/molecule more stable than the twisted monomer, whereas DFT simulations suggested the twisted monomer is 60 meV/molecule more stable than the tilted monomer. Overall, the disagreement between experiment and simulation is ∼3 kBT. Application to Alkanoate Monolayers. Fatty acids are commonly used as capping agents in colloidal nanocrystal synthesis. Although their primary role is to solubilize the crystals and prevent agglomeration,56 fatty acids can also be used to control the shape of the growing crystal, presumably through selective attachment to specific facets.17 One open question is the 24871


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The absolute C coverage was calculated from the integrated areas of the C 1s and Ti 2p spectra as described in the Supporting Information. This analysis yielded an absolute heptanoate coverage of 1.1 monolayers, consistent with the formation of a complete monolayer. The infrared spectra of octanoate monolayers taken in all four geometries were strikingly similar, although not identical, and displayed four resolved C−H stretch transitions, as shown in Figure 7. In analogy with previous spectral assignments of

nature of these organic monolayers. Are they close packed? Crystalline? Anisotropic? And how do their properties change from facet to facet? As a first step in answering these questions, we investigated the structure of heptanoate (C6H13COO) and octanoate (C7H15COO) monolayers on rutile (110), while noting that most syntheses use somewhat longer-chain fatty acids. To confirm that the deposition process produced monolayersnot multilayers or sparse layersthe heptanoate monolayers were first characterized using XPS, as shown in Figure 6.

Figure 7. (Left) The C−H stretch region of four infrared spectra of octanoate (C7H15COO/TiO2) monolayers obtained in the geometries defined in Figure 1. (Right) Cartesian transform of the four experimental spectra revealed the transition dipole moment projected along the x (Ti row or [001] direction), y ([11̅0] direction), and z axes. The dotted lines represent the transitions in Table 3.

n-alkanes,57−59 partially deuterated n-alkyl carboxylic acids,60 and alkyl SAMs on Au,61,62 Al2O3,63 Si(111),6,64 and Si(100),65 we assigned these modes to the symmetric and asymmetric C−H stretch vibrations of the CH2 and CH3 groups as shown in Table 3. To choose the most appropriate Cartesian decomposition, we tested for rotational degeneracy by comparing the s-polarized spectra obtained in geometries 1 and 2, as shown in Figure 8. Although the two orientations produced very similar spectra, spectra obtained in geometry 1 (i.e., with the electric field perpendicular to the Ti rows) were consistently more intense than those obtained in geometry 2. This intensity difference was not uniform across the spectrum, as shown by the spectral ratio in Figure 8, with the symmetric CH3 stretch at 2877.3 cm−1 and the antisymmetric CH2 stretch at 2927.8 cm−1 being selectively enhanced in geometry 1. As a result of this anisotropy, the full Cartesian decomposition was necessary, the results of which are shown in Figure 7. The infrared spectra of octanoate monolayers on rutile provided overwhelming evidence that the alkyl chains are disordered and loosely packed with a significant density of conformational defectsa stark contrast to the near-crystalline, all-trans alkyl monolayers typically formed on Au61,62 and Si6,64,65 surfaces. First, the energies of the symmetric and antisymmetric CH2 stretch vibrations in octanoate/TiO2 monolayers were consistent with a loosely packed geometry, being nearly identical to those of liquid

Figure 6. High-resolution XPS spectra of heptanoate monolayers on rutile (110) detected at 70° from the surface normal showing the (top) C 1s, (middle) O 1s, and (bottom) Ti 2p regions. The relative areas of the C and Ti spectra are consistent with an absolute heptanoate coverage of 1.1 monolayers.

High-resolution scans of the Ti 2p region showed two Ti4+ transitions, Ti 2p3/2 at 459.3 eV and Ti 2p1/2 at 465.0 eV, which were attributed to bulk TiO2 with no evidence of Ti3+ defects (e.g., O vacancies) at ∼457.3 eV. High-resolution scans of the O 1s region showed a dominant transition at 530.4 eV which was attributed to bulk TiO2 and a prominent shoulder at 531.9 eV, which was attributed to O in carboxylate. High-resolution scans of the C 1s region showed two transitions that were assigned to carboxylate C at 289.3 eV and aliphatic C at 285.8 eV. 24872


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Table 3. Comparison of the Energies of C−H Stretch Vibrations of Alkanoate/TiO2 Monolayers with Those Obtained on Similar Monolayers on Al2O362 and Si(100)64 As Well As Those Obtained in Liquid and Crystalline Neat n-Alkanes58a mode d+(0) r+ d−(0) rb−

liquid n-alkaneb (cm−1)

C6H13COO/TiO2 (cm−1)

C7H15COO/TiO2 (cm−1)

C15H31COO/Al2O3c (cm−1)

C12H25/ Si(100)d (cm−1)

crystal. n-alkaneb (cm−1)

2856

2858.6 2875.6 2927.8 2960.8

2858.9 2877.3 2927.8 2960.7

2857 2880 2926 2966

2851.6 2879.3 2921.0 2960.4

2850

2928

2920

assignment CH2 sym. stretch CH3 sym. stretch CH2 antisym. stretch CH3 asym. stretch

a c

The energies of the CH2 vibrations are correlated with molecular packing, with lower energies being associated with tighter packing. bReference 58. Reference 62. dReference 64.

Figure 8. Direct comparison of the s-polarized spectra of octanoate (C7H15COO/TiO2) monolayers disproved complete rotational degeneracy. (Top) Overlaid spectra, and (bottom) ratioed spectra. (The ratio of regions without significant absorbance was suppressed for clarity.) If the spectra were identical, the bottom trace would be unity. The dotted lines represent the transitions in Table 3. Figure 9. Molecular models of a (left) single-gauche conformer and (right) the all-trans conformer of octanoate on rutile (110). The black arrows indicate the orientation of the transition dipole moment of the CH3 symmetric stretch, r+. The all-trans conformer was determined from DFT simulations, whereas the gauche conformer was not. The red, white, blue, and black balls represent O, H, Ti, and C atoms, respectively.

n-alkanes as shown in Table 3. The CH2 stretch energies are known to be very sensitive to packing, and the crystalline-to-liquid phase transition in neat n-alkanes is associated with a ∼ 8 cm−1 increase in energy.59 Consistent with this, the energies of the two CH2 vibrations in the octanoate/TiO2 monolayers were ∼7 cm−1 higher in energy than the analogous transitions in dodecyl/Si(100) monolayers, as shown in Table 3. Second, the weak polarization of the symmetric CH3 stretch vibration provided evidence for a significant density of gauche conformers. As shown in Figure 9, the symmetric CH3 stretch vibration of the all-trans conformer would be vertically polarized. In contrast, the symmetric stretch vibration was observed in all three Cartesian orientations, indicating a substantial density of gauche defects. Finally, the nearly identical intensities of the symmetric and antisymmetric CH2 stretch vibrations in the x- and y-polarized spectra suggested near-complete rotational disorder in the monolayer, at least when averaged over the surface. (Although these nearly equivalent intensities are also consistent with alkyl chains perfectly aligned in a plane that is 45° from the x−z and y−z planes, the loose packing and disorder in the CH3 stretch is inconsistent with such perfect ordering.) Importantly, we note that a high degree of reproducibility in both geometries was only obtained when the surfaces were thoroughly rinsed in organic solvent after synthesis. Significantly higher C−H stretch absorbances were obtained on unrinsed or incompletely rinsed surfaces. The energies of the CH2 stretch absorbances were also shifted ∼4 cm−1 to lower energy on these surfaces. Both observations are consistent with the formation of condensed alkanoic acids on top of the alkanoate monolayer. Spectroscopic analysis of heptanoate monolayers on rutile (Supporting Information) showed similarly disordered monolayers.

The formation of a complete but conformationally disordered monolayer was also consistent with STM images of heptanoate, as shown in Figure 10. The images displayed bright protrusions

Figure 10. STM image of heptanoate monolayer on rutile (110) displaying near-complete monolayer of molecules separated by 0.60 nm along the [001] direction. The “tall” protrusions are interpreted as the all-trans conformer, whereas the “shorter” molecules are interpreted as disordered, likely gauche, conformers.

separated by 0.60 nm along the [001] direction, consistent with the expected bidentate bonding of heptanoate. Interestingly, the protrusions had multiple heights. Neglecting the low density 24873


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stretch vibrations along the [001] and [110̅ ] directions. The two isomers are nearly isoenergetic, as shown by experiment and DFT simulations. STM images of the benzoate monolayer showed the tilted tetramer isomer was twice as prevalent as the twisted monomer isomer, implying the tilted tetramer isomer was 22 meV/molecule more stable than the twisted monomer isomer. In comparison, DFT simulations estimated the tilted tetramer isomer to be 60 meV/molecule less stable than the twisted monomer. Infrared and XPS spectra as well as STM images of heptanoate and octanoate monolayers on rutile (110) showed that the alkyl chains were disordered and loosely packed with a significant density of conformational defectsa stark contrast to the nearcrystalline, all-trans alkyl monolayers typically formed on Au and Si surfaces. The high disorder in the alkanoate monolayers was attributed to simple geometry, as the density of alkanoate binding sites on rutile (110) is 30% smaller than the density of alkyl monolayers on Si. Similarly, the apparent high density of gauche defects in alkanoate monolayers was attributed to the small energy difference between the all-trans and single-gauchedefect conformers in isolated alkyl chains. In contrast, the nearcrystalline nature of tight-packed alkyl monolayers on Au and Si surfaces suppresses gauche defect formation.

of physisorbed molecules (i.e., the white protrusions), Figure 10 shows both “tall” molecules and “shorter” molecules. In agreement with the infrared spectra, we interpret the tall molecules as the all-trans conformer and the shorter molecules as disordered, likely gauche, conformers. The high disorder in the alkanoate monolayers is likely attributable to simple geometry. Because of the large distance between adjacent Ti rows and the bidentate nature of alkanoate bonding, a perfect alkanoate monolayer on rutile (110) would have 2.6 × 1014 molecs/cm2. In contrast, the density of alkyl monolayers on Si66−69 is ∼3.9 × 1014 molecs/cm2  50% greater than the density of available binding sites on rutile (110). Interestingly, we note that a similar degree of disorder was found in hexadecanoate monolayers on amorphous Al2O3,63 as evidenced by the energies of the methylene stretch vibrations shown in Table 3. Because of this low density of binding sites, increasing chain length alone is unlikely to lead to close-packed monolayers. The apparent high density of gauche defects in the alkanoate monolayers is likely attributable to simple thermodynamics. The energies of the all-trans and single-gauche-defect conformers of an isolated heptane molecule70 differ by only 23 meV. As a result, a specific single-gauche-defect conformer (e.g., a defect at C6) has a density 42% of that of the all-trans conformer at room temperature. In the absence of significant chain−chain interactions within the monolayer, the density of gauche defects in alkanoate monolayers would likely be similar. We expect this approximation to be valid for gauche defects near the chain terminus; however, gauche defects near the carboxylate will likely be disfavored by chain−chain interactions. From STM images, we estimate ∼40% of the molecules are in the all-trans configuration, which is roughly consistent with the generation of single-gauche defects at multiple sites along the chain. In contrast, the near-crystalline nature of tight-packed alkyl monolayers on Au and Si surfaces suppresses gauche defect formation, leading to a high preference for the all-trans conformer. Interestingly, our results are quite different from those recently reported for hexadecanoate adsorbed on supported anatase TiO2 nanocrystals.71 In those studies, symmetric and antisymmetric CH2 stretch modes consistent with crystalline packing were observed for layers synthesized at high hexadecanoic acid concentrations. Of course, the geometry of supported nanocrystals is more complicated than the planar interfaces studied here. Interdigitation of alkyl chains on adjacent nanoparticles, which has been observed in other systems,14 could lead to higher chain densities and improved packing. Additionally, the complex morphology of the nanoparticles may hinder complete rinsing. Finally, nanocrystals express many facets, and some facets likely have a different geometry than that of rutile (110).

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b08450. Spectra of heptanoate/TiO2 monolayers, XPS quantification of heptanoate/TiO2 coverage, structures used in DFT calculations, sample analysis code (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; phone: +1-607-255-3040. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation (NSF) under Award CHE-1303998. ESS was supported by the NSF IGERT program (DGE-0903653). This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy (DE-AC0205CH11231) as well as the Cornell Center for Materials Research Shared Facilities supported through the NSF MRSEC program (DMR-1120296).

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CONCLUSIONS Cartesian decomposition of infrared spectra obtained in multiple geometries provided direct insight into the bonding geometry of adsorbed molecules. Infrared spectroscopy resolved a long-standing controversy regarding the existence of paired molecules in benzoate monolayers, showing that two distinct isomers exist within the monolayer: a tilted tetramer and a twisted monomer. The phenyl rings of the twisted monomer isomer are nominally aligned with the Ti rows on rutile (110), as evidenced by C−H stretch vibrations preferentially aligned with the [001] direction. In contrast, the tilted tetramer isomer has near-4-fold rotational symmetry within the surface plane, leading to nearly equivalent C−H

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