Molecular-Level Surface Structure from Nonlinear Vibrational

Feature Article pubs.acs.org/JPCB

Molecular-Level Surface Structure from Nonlinear Vibrational Spectroscopy Combined with Simulations Shaun A. Hall, Kailash C. Jena, Paul A. Covert, Sandra Roy, Travis G. Trudeau, and Dennis K. Hore* Department of Chemistry, University of Victoria, Victoria, British Columbia, V8W 3V6, Canada ABSTRACT: Vibrational sum-frequency generation spectroscopy is valued for its ability to selectively probe molecules at a variety of interfaces without the use of extrinsic chromophores. The spectra contain valuable information regarding the molecular structure and the interfacial environment through the observation of vibrational resonances associated with specific moieties. Chemical information is obtained by close inspection of the frequencies of these bands and the amplitude of the response under conditions of different beam polarizations. Such sensitivity motivates the development of techniques that can provide structural details. We illustrate several approaches by which various types of calculations and molecular simulations may be used to enhance the sought structural interpretation of experimental data. By applying these techniques to the adsorbate molecules, interfacial water, and the substrate surfaces themselves, we are able to achieve a holistic picture of the adsorption environment. changes.26,27 Keeping with proteins as an example, the solutionphase secondary and tertiary structures are dictated by the balance of residue−residue and residue−solvent interactions.28,29 When the same molecules encounter a solid−liquid interface, those interactions are still important, but additional ones come into play. Now there are specific interactions between residues and the surface, dependent upon the charge and hydrophobicity of the side chains. Furthermore, surface− solvent interactions are responsible for creating an interfacial environment defined by a charge, polarity, hydrogen bonding distribution, and dissolved ion species that may be significantly different from what is found in the adjacent bulk solution phase.30−34 In the case of macromolecular materials such as polymers, the surfaces may also differ in terms of the number and type of chemical functional groups than what is buried in the bulk solid phase. Figure 1 illustrates that understanding the structure of adsorbed molecules therefore has at least three aspects: characterizing the adsorbate itself, the interfacial solvent environment, and the nature of the solid surface. Over the past five years, our group has been seeking to investigate adsorbed molecular structure by targeting each of these three areas. Our approach has been to combine surfaceand structure-sensitive nonlinear vibrational spectroscopy with a suite of modeling tools in order to extract quantitative structural information from the spectral data. The puzzle pieces in Figure 1 represent the six areas that we will touch upon in this article. The complete framework also includes parameters such as ionic strength, pH, temperature, and other environmental considerations that affect the subtle interplay between the three layers.

1. INTRODUCTION The adsorption of molecules onto solid surfaces is a key component of many natural and engineered systems.1−3 For example, the three-dimensional structure that proteins adopt when they land on a hydrophobic polymer may be significantly different from their native conformation, thereby triggering an undesirable biological response, such as aggregation to form plaques.4−6 The molecular basis for the biocompatibility of implant materials is therefore firmly rooted in surface science.7−9 From a more engineering perspective, one of the most critical interactions to control in the design of biosensors is the orientation and conformation of enzymes immobilized on a solid support.10−13 If the surface conditions are not favorable, the protein may denature and catalytic activity would not be possible. However, even if the active conformation was maintained, an unfavorable orientation, such as one where the active site is blocked, would limit the efficiency of such a device.14−16 Over the past decade, there has been significant progress in elucidating the structure of several important proteins in their adsorbed state.14,17−19 Although such knowledge advances scientific and engineering pursuits that rely on understanding these specific protein−surface interactions, it remains difficult to generalize based on such findings. For example, there is a principle that globular proteins stick and are denatured on contact with hydrophobic surfaces but touchand-go on hydrophilic surfaces. As such, one of the methods of rendering a hydrophobic polymer more biocompatible is to modify its surface by exposure to an oxygen plasma,20−22 or by grafting a hydrophilic material such as poly(ethylene glycol).16,23 However, tailored surfaces with water contact angles as low as 48° have been shown to strongly adsorb serum albumin,24,25 illustrating the difficulty in relying on such generalizations. One of the reasons for the complexity of the behavior that eludes simple rules is the multitude of interactions that are responsible for surface-induced structural © 2014 American Chemical Society

Received: December 29, 2013 Revised: March 26, 2014 Published: April 13, 2014 5617

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Figure 1. The structure of molecules at surfaces is a multifaceted phenomenon. In the case of molecules in solution adsorbing at the buried polymer−solution interface, there are three components to the system that are equally important to rationalizing the adsorbed structures: (1) the surface structures of the adsorbates themselves, (2) the interfacial water environment, and (3) the nature of the polymer surfaces. The Hore group applies a combination of experimental and modeling efforts to address each of these areas.

2. BACKGROUND The underlying principles of the experimental and computational approaches we will discuss are the same, as they revolve around the manner in which the molecular response manifests itself in the observed spectra. For a single molecule, the dipole moment p is the sum of the charge q multiplied by the displacement d vectors, but this may also be expressed as the product of the polarizability α(1) and the applied field E. In the case of strong fields, such as those from lasers, one observes that p is no longer proportional to α(1)E, and various nonlinear phenomena are observed that may be accounted for by contributions α(n) that are higher order in the applied field. p=

y, and z lab frame Cartesian unit vectors, with x and y in the plane of the surface and z normal to the surface, we continue our focus on the second-order response. The i component of P(2) is related to the j and k components of the applied field through the 27 elements of χ(2) in Pi(2) = ε0χijk(2) EjEk

In our experiments, one of the input fields is in the infrared at frequency ωIR and one is in the visible at ωvis. When these pulsed fields are overlapped in time and space at the interface of interest, the second-order response χ(2) gives rise to various nonlinear phenomena such as frequency-doubling (2ωvis and 2ωIR), sum-frequency generation (ωvis + ωIR), and differencefrequency generation (ωvis − ωIR). In a noncollinear geometry (Figure 4a), each of these four processes may be isolated by its phase-matching (momentum-conserving) direction. In a collinear experiment (Figure 2), the four outputs are spatially overlapped but may easily be separated according to frequency and detector spectral response. We now focus on sum-frequency generation (SFG) where the visible beam is fixed off-resonance (532 nm in our case), and the IR beam is tunable from 1000−4000 cm−1 to cover a broad range of vibrational resonances targeting specific chemical functional groups, thereby providing a label-free structural probe. There are several general and tutorial reviews on SFG in the literature;35−39 we will provide only the details that are relevant for the type of work that we will describe in this article. SFG achieves its interfacial specificity, since, under the electric dipole approximation, all elements of χ(2) vanish in the presence of an inversion center, as found in the bulk solution phase due to isotropy, or in a bulk solid either due to isotropy or a lack of polarity in the molecular ordering. Figure 2 illustrates that this is a direct result of the phase of the emitted SFG field being tied to the polarity of the functional groups. If the groups are flipped in their orientation, the phase is shifted by 180° with respect to what would be generated in the original orientation. When both orientations are present in equal quantities, these two fields cancel, and no signal at the sumfrequency is detected. As we wish to probe specific portions of surface-bound molecules by targeting the corresponding vibrational resonances, the frequency dependence of the measured quantities is of primary interest. For this, we establish a model for the vibrational hyperpolarizability. In general, α(2)

∑ q·d N

= p(1) + p(2) + p(3) + ... + p(n) 1 1 1 = α(1)E + α(2)EE + α(3)EEE + ... + α(n)En n! 2 6 (1)

In the current discussion, we will be interested in an effect arising from the second-order nonlinearity, the so-called hyperpolarizability α(2). Acknowledging that this is a tensor of rank 3, each of the 27 elements α(2) imn couples m and n components of the applied field to the l component of the induced dipole moment (2) pl(2) = αlmn EmEn

(4)

(2)

where l, m, and n are placeholders for any of the a, b, and c molecule-fixed Cartesian unit vectors. Our interest is not in single molecule response but in experiments that probe macroscopic ensembles. Although eq 2 will be critical in achieving a structural understanding of the spectra, in the experiment, we probe the dipole moment per unit volume, the polarization P. This may be expressed in an analogous manner to eq 1 P = P(1) + P(2) + P(3) + ... + P(n) ⎛ ⎞ 1 1 1 = ε0⎜χ (1) E + χ (2) EE + χ (3) EEE + ... + χ (n) En⎟ ⎝ ⎠ 2 6 n! (3)

where χ is the nth-order susceptibility tensor and ε0 is the vacuum permittivity. Taking i, j, and k as placeholders for the x, (n)

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Figure 2. In visible-IR sum-frequency generation, the visible beam is typically kept at a fixed wavelength off-resonance, while the IR beam is tuned over vibrational resonances. In centrosymmetric structures, either through a random orientation of molecules or due to a surface alignment with no preferred polarity, the second-order response from the individual molecules cancels and no signal at the sum-frequency is observed.

Figure 3. The 27 elements of the microscopic response, the hyperpolarizability tensor for each vibrational mode of interest, are related to the 27 elements of the measured response in the laboratory frame, the second-order nonlinear susceptibility through the molecular orientation. Experimentally determining the nonzero and unique elements of χ(2), and having some way of estimating the local hyperpolarizability α(2), provides a route to describing the ensemble average that relates these quantities.

may be written as the product of three transition dipole moments μ̅ α(2) = ⟨0|μ ̅ |υ⟩⟨υ|μ ̅ |1⟩⟨1|μ ̅ |0⟩

(5)

where |0⟩ is the vibrational ground state, |1⟩ is the first vibrational excited state, and |v⟩ is a virtual state, as illustrated in Figure 2. The anti-Stokes transition from |1⟩ to |0⟩ may be written as ⟨0|α̅ |1⟩, where α̅ is the transition polarizability. In the harmonic approximation, elements of the transition polarizability matrix and IR transition dipole vector may be replaced by elements of the linear polarizability α(1) and dipole moment μ derivatives with respect to the normal mode coordinate Q. This provides a convenient route for calculation of the frequency-dependent α(2) elements from (2) αlmn (ωIR ) =

⎛

⎞⎛ ⎞ ∂α (1) ∂μ 1 ⎟⎟⎜⎜ ⎟⎟ lm n ⎝ 2mQ ωQ ⎠⎝ ωQ − ωIR − i ΓQ ⎠ ∂Q ∂Q 1

∑ ⎜⎜ Q

Alternatively, this may be viewed as an average response of N molecules (eq 7b) where the angular brackets indicate the ensemble that represents the orientation distribution, a statistical description of the sought molecular structure. One way to describe the orientation distribution is with a function, f(θ, ϕ, ψ) as indicated in eq 7c, which we will discuss further in the following sections. The success of the structure elucidation process relies on collecting as much orthogonal experimental information as possible. The ideal scenario is to measure all of the unique and nonzero elements of χ(2). This may be achieved by judicious selection of the polarization state of the incident visible and IR beams, and of the detected SFG beam. Figure 4a has grouped the 27 elements of χ(2) according to which ones would be probed with combinations of s-polarized (electric field perpendicular to the plane of incidence) and p-polarized (electric field in the plane of incidence) states. The convention is to list the beams in decreasing order of energy, so ssp refers to s-polarized SFG detected in an experiment with s-polarized visible and p-polarized IR light. The systems of primary interest to us all have azimuthal symmetry; that is, there is no preference for how the molecules are oriented with respect to the lab x and y directions. Such C∞v symmetry leaves only seven nonzero achiral elements of χ(2), as indicated with the boxes in Figure 4a, necessitating experiments in only the four polarization schemes indicated with arrows. This azimuthal symmetry has also resulted in the equivalence of elements for which x and y are interchanged. Combined with the fact that the off-resonance Raman response is symmetric (∂α(1) ij /∂Q = ∂αij(1)/∂Q), there are only three unique nonzero achiral (2) elements to be determined: χ(2) xxz = χyyz isolated in the ssp (2) (2) (2) (2) configuration, χxzx = χyzy = χzxx = χzyy isolated in either the sps (2) or pss configuration, and χzzz contained as one of the components of the ppp response.

(6)

where mQ and ΓQ are the reduced mass and width of the Qth vibrational mode. The SFG intensity detected in a homodyne experiment, plotted as a function of the infrared beam frequency, is essentially a spectrum of |χ(2)(ωIR)|2. Figure 3 illustrates that experiments probing the macroscopic surface response (eq 4), with some understanding of the molecular hyperpolarzability elements (eq 2), provide a route toward extracting structural information. Calculations provide α(2) imn for each molecule which, when projected into the laboratory frame to yield α(2) ijk , may be summed over N molecules to provide eq 7a. χijk(2) =

1 ε0

∑ αijk(2)

(7a)

N

=

N (2) ⟨αijk ⟩ ε0

=

N ε0

2π

(7b) 2π

∫0 ∫0 ∫0

π

(2) f (θ , ϕ , ψ ) αijk sin θ ∂θ ∂ϕ ∂ψ

(7c) 5619

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example will present the results of a modeling effort to aid in the interpretation of SFG spectral results for a 14-residue peptide adsorbed on a variety of surfaces. 3.1. Extracting Structural Information from Isolated Vibrational Modes. The most straightforward application of the scheme outlined in Figure 3 occurs for systems that are structurally and spectroscopically simple. The structural requirement is that the orientation distribution may be reasonably approximated with a functional form, such as a Gaussian distribution of tilt and twist angles. Such an orientation distribution function (ODF) may take the form ⎡ (θ − θ )2 (ψ − ψ0)2 ⎤ 0 ⎥ f (θ , ψ ) = Nc exp⎢ − − ⎢⎣ 2σθ 2 2σψ 2 ⎥⎦

(8)

where θ0 and ψ0 are the mean tilt and twist angles of a particular chemical moiety of interest, σθ and σψ are the corresponding widths of the distributions, and Nc is a normalization constant defined such that 2π

2π

∫0 ∫0 ∫0

π

f (θ , ψ ) sin θ ∂θ ∂ϕ ∂ψ = 1

(9)

By spectroscopically simple, we are referring to systems for which vibrational modes that serve as markers for the part of the molecule we are interested in studying are clearly identifiable in the vibrational SFG spectrum. Needless to say but surprisingly nontrivial at times, this also implies that one can be confident about the assignment of the mode in the spectrum, as we will need to match up the response with the corresponding αQ(2) . It is not uncommon for Hessian calculations to switch the order of modes that are close in frequency when slightly different basis sets are used.40,41 Comparison with calculations of ∂α(1) ij /∂Q or ∂μk/∂Q alone is therefore not sufficient to confidently assign the modes. It should also be noted that, for a variety of reasons, the frequencies of modes in the SFG spectra are often slightly shifted from those in the bulk IR or Raman spectra.42 Ideally, experimental studies employing techniques such as isotopic dilution are utilized to help in the assignment.43,44 Our first example is the amino acid phenylalanine adsorbed at the D2O−perdeuterated polystyrene interface.45 Figure 4b shows the SFG spectra collected in three polarization schemes over the aliphatic and aromatic C−H stretching region. A global, constrained fit46,47 to all three spectra provided amplitudes for the CH2 symmetric stretch (SS) at 2869 cm−1 and antisymmetric stretch (AS) at 2974 cm−1. All nine (1) /∂Q and three elements ∂μn/∂Q were elements of ∂αlm evaluated considering seven configurations stepping along the normal mode coordinate Q. Values of α(1) lm and μn are shown in Figure 5 for the CH2 SS in blue and CH2 AS in red (open circles). Values at Q = 0 correspond to the equilibrium geometry. Fits to a second-order polynomial are indicated by solid lines. The slopes evaluated at Q = 0 are drawn with broken lines. As the Raman tensor is symmetric far from resonance, only the six lower triangular elements of α(1) are shown. From these derivatives, any element of α(2) is available via eq 6. These hyperpolarizability tensors for the CH2 SS and AS modes have been evaluated in the molecule-fixed frame, α(2) lmn. The final step is to project them into the laboratory frame, (2) 48 thereby obtaining α(2) ijk (θ, ϕ, ψ) that may be related to χijk . This may be accomplished via elements of the rotation matrix D in the transformation

Figure 4. (a) The 27 elements of χ(2) categorized according to which are probed with combinations of s- and p-polarized states. In the case of achiral structures with azimuthal symmetry, only the seven boxed elements are nonzero. These are probed with the four marked polarization combinations. (b) SFG spectra obtained from phenylalanine adsorbed at the D2O−perdeuterated polystyrene interface from different polarization combinations. Adapted with permission from ref 45. Copyright 2010 American Chemical Society.

3. ADSORBED MOLECULAR STRUCTURE Using the formalism described above, we will now demonstrate how quantitative SFG measurements may be combined with various types of simulations in order to obtain structural information on molecules in their surface-adsorbed state. We will divide our examples and discussion into three sections of increasing complexity, starting with the situation in which the vibrational spectra reveal peaks that can be identified as distinct normal modes. (This includes cases where nearby resonances need to be resolved by fitting due to their spectral interference.) We then describe the situation where larger molecules display highly overlapping vibrational modes, and so other approaches are necessary in the analysis. For example, in the case where fitting to identify individual resonances is not possible, we illustrate that insight from molecular dynamics simulations may be used to reconstruct the overlapping peak profiles. Our final 5620

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Figure 5. Values of the linear polarizability α(1) lm (top three rows) and dipole moment μn (bottom) row indicated by the points, evaluated for seven configurations of phenylalanine along the normal mode coordinate Q, with Q = 0 corresponding to the equilibrium geometry. The methylene SS is indicated in blue, and AS, in red. A fit to a second-order polynomial (solid lines) was used to evaluate the derivative (broken line) at Q = 0. Reprinted with permission from ref 45. Copyright 2010 American Chemical Society.

Figure 6. (a) The evaluation of trial orientation distributions in comparison to data obtained under different beam polarizations can be carried out in parallel, dividing the parameter space between all available compute nodes. (b) When CH2 SS and AS modes are considered in multiple polarization schemes, valid θ0, σθ, ψ0, and σψ values were found in all of the shaded (gray and black) regions. If the aromatic C−H modes are also included, only the subset of solutions indicated in black are consistent with the experimental data. (c) Members of the resulting families of structures. Adapted with permission from ref 45. Copyright 2010 American Chemical Society.

abc abc abc (2) αijk (θ , ϕ , ψ ) =

∑ ∑ ∑ Dil(θ , ϕ , ψ )Djm(θ , ϕ , ψ ) l

m

n

(2) × Dkn(θ , ϕ , ψ )αlmn

(10)

The object is now to determine which parameters (θ0, σθ, ψ0, σψ) in the ODF produce χ(2) elements that best describe those in the experimental data set using the comparison outlined in eq 7. One option is to calibrate the experimentally determined χ(2) spectra to remove their arbitrary scaling, and then also scale the computed α(2) elements to proper units. A more common approach is to take ratios of elements obtained using different beam polarizations. Although this gets around many difficult calibration issues (absolute magnitudes of χ(2) and α(2) elements, surface number density, etc.), it does reduce the number of independent experimental observables from three to two. Following this approach, we have taken the ratio of the ssp/ppp elements for the methylene SS and ssp/ppp and sps/ ppp for the AS. These combinations were chosen on the basis of the largest peaks in the corresponding spectra. We then implemented a grid-computing-based method that exhaustively evaluated the ODF obtained with each combination of the parameters in the range 0° < θ < 180°, −180° < ψ < 180°, and widths in the interval 0° < σθ,ψ < 70°, all in 2° increments. As illustrated in Figure 6, a master node kept track of the progress on the four-dimensional parameter space, farmed out the individual ODF, integration in spherical polar coordinates, and scoring based on the experimental data. In the end, the range of these parameters that produced ODFs in agreement with the experimental results are indicated by the shaded (gray and black) regions of Figure 6. To further narrow this solution set,

we note that only small signals were observed in the aromatic C−H stretching region, above 3000 cm−1. Calculation of the α(2) elements for the five aromatic modes expected in this region was then included in the function that was used to score the fit, and only the subset appearing in black in Figure 6 now remains. We emphasize that, in addition to our four-parameter ODF that includes information on the width of the tilt and twist distribution, using our grid-based parallel computing technique we are able to report families of solutionsclusters of all combinations of the parameters that are in agreement with the experimental results. The scheme at the bottom of Figure 6 highlights an important aspect of this method of structure determination: although multiple vibrational modes may be used to narrow down the structural possibilities, combinations that differ only by (θ0, ψ0) and (180° − θ, Ψ + 180°) will remain indistinguishable. That is, we have no spectroscopic means of distinguishing structures in families B and D shown in Figure 6. This is a consequence of the 2 measurement of |χ(2) ijk | . An alternative that is able to overcome this limitation is discussed in section 5. 3.2. Techniques for Determining Structural Information from More Complex Spectra. The above example has 5621

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illustrated the capabilities of combining SFG experiments with various types of computational analyses for isolated vibrational modes. If additional vibrational modes may be analyzed in a similar fashion, they either provide information on additional degrees of freedom in the molecule or may be used as constraints in the parametrization of the ODFs. However, for all but the smallest of molecules, it is difficult to identify specific resonances. For example, the spectrum obtained for 12.5 mg/ mL leucine in D2O adsorbed at the d8-polystyrene surface (ssppolarized data shown in Figure 7a) contains significantly fewer discernible peaks than were expected on the basis of electronic structure calculations. Although some relatively sharp bands are observed at frequencies that correspond to methyl and methylene SS and AS modes, insight from a Hessian calculation tells us that there should be 10 SFG-active normal modes of appreciable intensity in this region, in addition to the Fermi resonances.49 For even larger molecules, such as peptides and proteins, the same is true to an even greater extenthundreds of resonances spaced so closely together that the SFG spectrum appears as if it contains only a few bands. In such cases, even if the spectra appear simple enough to be fit with a small number of Lorentzians, we cannot proceed in the same manner as we have described in the previous cases, as we can no longer assign the amplitudes of the bands to a specific normal mode. However, the methodology we have presented that relates the measured spectra to the molecular nonlinear optical properties of specific chemical function groups still applies. That very formalism may be used in the reverse order, generating model SFG spectra from calculated resonances, even if the constituent modes are highly overlapping. In such cases, we need some additional insight to assist us in formulating the orientation distribution (OD). Using leucine adsorbed onto polystyrene as an example, we will demonstrate how molecular dynamics (MD) simulations can be used to provide this insight. We initially prepared six surfaces of varying hydrophobicity, with water contact angles in the range 84−156° and used MD simulations to determine that leucine adopts a mixture of two orientations on the surfaces: a standing orientation where the isobutyl methyl groups are directed toward the surface, favored as the hydrophobicity of the surface increases, and a laying orientation that becomes increasingly populated for the less hydrophobic surfaces.50 We then analyzed each frame of the MD trajectories for each of the six types of surfaces, isolating those frames for which leucine’s center of geometry was within 0.75 nm of the surface. This cutoff was determined by looking at a histogram of the center of geometry distances. Of all the dihedral molecules in leucine, the two angles ξ1 and ξ2, as defined in Figure 7b, were considered to be the most important, as they lead to structurally distinct conformers. Looking at the subset of surface-bound leucine molecules, we created a map of the (ξ1, ξ2) distribution, as shown in Figure 7b. This revealed five dominant conformers, labeled according to their (ξ1, ξ2) dihedrals. We have considered six different surfaces, as they cover a wide range of leucine−surface interactions, as a single one of these surfaces is not thought to replicate the interactions on polystyrene in the experimental system. Although the dominant surface species have been identified using these simulations, we also keep in mind that the relative proportion of these conformers may be completely different in the experimental system, on account of the differences between polystyrene and model hydrophobic interactions, and also due to the statistical limitations in creating and sampling the MD trajectories. Each of these five

Figure 7. (a) ssp-polarized SFG spectrum of leucine adsorbed at the d8-polystyrene/D2O interface (points), unconstrained search of the best conformers (broken lines), and search constrained to the best four conformers (solid lines). (b) The distribution of leucine conformers on the surface, labeled according to the two dihedrals ξ1 and ξ2; the tilt−twist distribution of the (c) methylene and (d) isobutyl groups. (e) The two isomers, each with two prominent orientations, that best account for the observed spectra on polystyrene. Adapted with permission from ref 49. Copyright 2011 American Chemical Society. 5622

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highly overlapping vibrational modes that cannot be resolved in an experiment. Following this approach, it is intriguing to consider if the same methodology can be applied to larger molecules in the assumption that the high frequency modes are relatively uncoupled. In the case of proteins, structures with hundreds of residues produce relatively simple-looking spectra in the aliphatic stretching region, owing to the localized nature of the vibrational modes from C−H and N−H stretching. In such cases, there are hundreds to thousands of modes but all clustered about narrow frequency distributions. This idea has been pursued extensively in the case of the amide I band,52−55 as analysis of that frequency region reveals the protein backbone structure through the manner in which the carbonyl modes of each residue are coupled. Such efforts are maturing in the case of bulk and surface linear IR absorption, vibrational SFG, and higher order vibrational techniques. The side chains are often ignored as a result of their more random distribution and unclear correlation to the backbone torsional angles. However, in the case of surface-induced orientation and conformation effects, it is the specific interaction of the side chains with the surface that lead to the structural changes. In order to approach this subject, it is useful to start with peptides of well-defined secondary structures and a lower degree of structural heterogeneity. In 1985, DeGrado and Lear synthesized and characterized a series of short leucine- and lysine-containing peptides.56 By adjusting the sequences of these two residues, they were able to obtain a variety of helical and sheet conformations. Among these was a 14-residue α-helical structure, AcLKKLLKLLKKLLK-COO−, termed LKα14, that was amphipathic with the hydrophobic leucine residues on one face and the hydrophilic lysine residues on the opposite face of the molecule. This molecule has served as a model peptide in many adsorption studies, characterized by quartz-crystal microbalance,57,58 mass spectrometry,59 X-ray photoelectron spectroscopy,59 magnetic resonance,60 IR absorption,56 circular dichroism,56,57 SFG,57,58,60−65 and molecular simulations.66−68 Figure 8 illustrates some of the early experimental data with SFG spectra of the LKα14 adsorbed onto (a) a hydrophobic polystyrene surface and (b) a hydrophilic glass surface.58 It is remarkable that, on the hydrophobic surface, only C−H stretching modes have appreciable intensity, while, at the hydrophilic surface, those modes are absent and the side chain N−H modes are observed instead. The authors proposed that, in the case of the hydrophobic substrate, the Leu side chains are directed toward the polystyrene, thereby constraining the terminal methyl groups giving rise to the C−H stretching in the SFG spectra. Likewise, on glass, it was proposed that the hydrophilic NH3+ groups are directed toward the surface. It was further suggested that, in both cases, the residues on the opposite side of the peptide (directed toward the bulk solution phase) have their side chains less ordered, leading to a cancelation of the corresponding SFG response. These ideas have been investigated in more detail in subsequent SFG studies, employing techniques such as isotopic substitution to monitor the response of individual leucine resides along the chain,60 and phase resolution using interference of the side chain SFG response with that of a gold layer buried just below the substrate material of interest.61 From these studies, it was increasingly established that such orientational preferences were clear for the hydrophobic residues on the hydrophobic surface. The Lys chain ends are more difficult to probe, as they do not lend themselves to isotopic substitution.

conformers was then modeled at the B3LYP/6-31G(d,p) level using a polarizable continuum model (PCM) to account for the solvent. Initial energy minimizations constrained the dihedrals to the values indicated with the open circles in Figure 7b. As the Hessian calculations are required to be performed at local minima on the potential energy surface, the final minimizations required lifting the dihedral constraints. This resulted in reasonably close structures, as indicated by the filled black circles in Figure 7b. We have then used the method established in the previous section to model the hyperpolarizability tensor elements in the molecular frame α(2) lmn for each vibrational mode of each of these structures. Projection into the laboratory frame to produce α(2) ijk for a single frame, and hence χ(2) ijk considering many frames in multiple trajectories, was accomplished using the orientation distribution (OD) corresponding to that sampled for the particular conformer. Using this procedure, we have generated model SFG spectra, assuming that the population arrises completely from one of these five structures. As our hyperpolarizability calculations were performed with a harmonic approximation, we do not model any Fermi resonances, and Fermi resonances have been demonstrated to be significant in the SFG spectra of leucine.51 It is important to consider these additional peaks, as they also shift the frequency of the observed fundamental modes. Since the SFG line shape requires the coherent addition of all modes contributing to a given probe frequency before squaring the overall amplitude, interference effects are as prevalent for Fermi resonances as they are for fundamental modes. On the basis of past experimental studies, we therefore include adjustable amplitudes for two Fermi resonances, one at 2889 cm−1 and one at 2930 cm−1. Even with this flexibility, we have not been able to produce anything reasonably close to the experimental spectra acquired with ssp, sps, and ppp polarization combinations. The final step was then to consider that a mixture of the five conformers may be responsible for the experimentally observed spectra. We have developed a search algorithm that consisted of a combination of the global constrained fitting procedure used in the previous phenylalanine study, with the added variables to account for the contribution from these 10 identified adsorbed leucine structures, with an initial Monte Carlo calculation to select the starting points for the optimization to avoid local minima. This allowed us to arrive at the ratio of the species that best accounts for the observed SFG spectra in the three polarization schemes. Results for ssp are shown with the solid dark line in Figure 7a. Although we capture the basic shape of the bands, it is evident that there are significant residuals. We emphasize that this is not a fit to the data in the conventional sense but a description of how the dominant structures (Figure 7e) revealed by MD simulations may account for the experimental SFG spectrum. From this, we have been able to observe the considerable variation in predicted SFG spectra for different proportions of these 10 species and conclude that it was indeed possible to determine a distribution of surface orientations for a molecule with complex SFG spectra. The flexibility of this approach and its ability to extract structural information from experimental spectra containing multiple overlapping bands lends itself to the study of even larger molecules, as will be demonstrated for the case of peptide adsorption in the following section. 3.3. Extension to Larger Molecules. The leucine study described in the previous section provided an example in which the SFG response could be calculated, even for the case of 5623

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use molecular dynamics simulations to study the side chain conformations of LKα14 when adsorbed onto surfaces of different hydrophobicity and charge, and then use the structural data from the MD trajectories to construct model SFG spectra.68 Prior to analyzing the side chain response, gross structural characterization examined the peptide’s end-to-end distance, long axis tilt angle, and backbone torsional angles when adsorbed on the surface, in comparison to the bulk solution state. It was discovered that the backbone was most perturbed from the average solution-state structure when LKα14 was adsorbed onto the charged hydrophilic surface. This is in contrast to conventional wisdom for globular proteins, where the most structural change occurs on hydrophobic surfaces, with minimal perturbation on hydrophilic surfacesthe basis for techniques such as surface PEGylation of hydrophobic polymers to improve their biocompatibility for use as medical implants. Even though LKα14 has an entirely different structure than such proteins, it was interesting to observe that the interactions of the Leu residues with the hydrophobic surface did not result in the most structural change. We now turn our attention to the side chain response. In preparation for generating the SFG spectra, our goal was to first identify the dominant Leu and Lys conformers, for which we will need to determine α(2). Leu has two dihedrals that affect its structure (not counting rotations of methyl groups, etc.); the longer Lys side chains have five relevant dihedrals. Sifting through the trajectories and creating histograms of these torsional angles when LKα14 was adsorbed on the surfaces identified three Leu and three Lys populations for each dihedral. This represents a possible 252 conformers, beyond what we are willing to consider for unique α(2) values. However, subsequent analysis revealed that there are only three Leu and seven Lys conformers to be considered. Scheme 1 outlines the procedure for using these 10 conformers to generate SFG spectra for LKα14 adsorbed on the various surfaces. For the surface of interest, the trajectories are again analyzed frame by frame, searching for snapshots in which the peptide is adsorbed. The 14 residues are then considered in turn. For each residue, a similarity analysis is used to determine the closest matching Leu or Lys conformer from the 10 prototypes we have previously identified. Once the appropriate structure has been identified, the frequency-dependent hyperpolarizability α(2) is calculated for each normal mode. At the end, the SFG spectrum is

Figure 8. SFG spectra of LKα14 adsorbed onto (a) polystyrene and (b) glass. On the hydrophobic substrate, only the Leu C−H modes are visible, while on the hydrophilic surface, only the Lys NH3+ modes appear. The proposed structures illustrate a hypothesis in which residues in contact with the surface are well ordered, resulting in the SFG response, while those directed toward the bulk solvent are disordered, resulting in χ(2) = 0. Adapted with permission from ref 58. Copyright 2006 American Chemical Society.

Our interest in this system stems from two directions. First, LKα14 is an ideal structure for developing a framework for the side chain SFG response of a conformationally complex molecule, as it has been extensively characterized by SFG and other methods as described above. Second, the experimental results as presented in Figure 8 are intriguing, particularly for the residues hypothesized to be at the top of the peptide, directed toward the bulk solution phase. With reference to the structural scenarios outlined in Figure 9, we were interested in what type and degree of orientational averaging is required in order to lose the SFG response of the Lys chain ends on the hydrophobic surface and Leu chain ends on the hydrophilic surface. Furthermore, considering that these chains are tethered to the backbone of a reasonably well-structured α-helix, it is hard to envision such a low level of anisotropy. Our goal was to

Scheme 1. An Algorithm for Generating SFG Spectra for LKα14, That Is Generally Applicable to Modeling the Side Chain Response of Any Peptide or Protein

Figure 9. (left) An isotropic distribution, such as that found in the bulk solution phase, is centrosymmetric and therefore produces no SFG signal. However, one would measure any isotropic average in techniques such as IR absorption or Raman scattering. (middle) If the centrosymmetry is broken, thereby inducing a polarity to the orientation, χ(2) ≠ 0 and SFG is observed. (right) Note that, in cases where molecules are aligned but not in a manner that breaks the inversion symmetry, χ(2) = 0. 5624

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Figure 10. (a) Imaginary component of χ(2) xxz (ssp polarization) for LKα14 adsorbed onto the hydrophobic (blue), neutral hydrophilic (red), and charged hydrophilic (green) surface. The spectra may also be broken down into components arising from exclusively the (a) Leu and (b) Lys residues. The 14 plots to the right illustrate the tilt angle of the Leu isobutyl and Lys NH3+ chain ends. Adapted with permission from ref 68. Copyright 2013 American Chemical Society.

may not only be used to rationalize the spectral features but may also be compared directly with the results of experiments that selectively deuterate the Leu CH3 chain ends, individually for each Leu residue. In summary, we have demonstrated that various types of molecular simulationsranging from electronic structure calculations, evaluations of trial orientation distribution functions, and molecular dynamics simulationscan assist in the interpretation of experimental SFG spectra, especially in the case of overlapping vibrational modes.

obtained by summing the responses over all the modes, over all 14 residues, over all the frames for which the peptide is adsorbed. The resulting imaginary χ(2) spectra (as would be obtained in a phase-resolved experiment) are shown in Figure 10a for the hydrophobic surface in blue, the neutral hydrophilic surface in red, and the charged hydrophilic surface in green. One of the unique opportunities afforded by simulation is that the spectroscopic response may be separated in various ways. For example, we can see the contribution of only the Leu or Lys residues, as plotted in Figure 10b and c, respectively. Examining the spectra, one immediately notices that there is no N−H stretching intensity when LKα14 is adsorbed onto the hydrophobic surface, in agreement with all of the experimental results. Similarly, there are no CH3 stretching bands observed when the peptide is on the charged hydrophilic surface, consistent with experimental observations on silica and hydrophilic self-assembled monolayers. We do observe some CH2 modes, where the experimental spectra are devoid of intensity. We believe this is due to our increased sensitivity to the side chain conformations owing to the finite nature of our simulations. Even though we have more than 500 ns of data for each of the surfaces, we still encounter the sampling limitations typical of molecular dynamics simulations, particularly considering that some structural rearrangements, even for such a small peptide, may occur on the microsecond time scale. Nevertheless, with such good qualitative agreement with the experimental results, it is intriguing to consider the origins of the SFG signatures. The negative Im[χ(2)](ωIR) peaks observed for the CH3 symmetric stretch indicate that the Leu side chains are directed toward the hydrophobic surface. These results may be compared directly to experiments that resolve the phase of the SFG signals using interference from a metal layer below the surface of a hydrophobic polymer.61 From a more direct structural perspective, we have the opportunity to observe the detailed nature of the peptide side chain orientation distribution that gave rise to these spectra. This data is shown on the right side of Figure 10, with plots of population against residue chain end tilt angle for each position along the peptide. An angle of 0° indicates that the chain end is pointing away from the surface, 90° is in the plane of the solid−water interface, and 180° is directed toward the surface. Such data

4. INTERFACIAL WATER STRUCTURE We have illustrated the complementary nature of nonlinear vibrational spectroscopy and modeling in providing detailed, structural information at submolecular scales of adsorbate molecules. A second component of the puzzle described in Figure 1 is interfacial water. Just as water plays a role in dictating the structure of fully solvated molecules, it also affects structure adopted by adsorbed species, albeit in a different manner. This is due to the fact that the nature of the substrate (hydrophobicity, charge, solubility, etc.) influences how the order, density, and coordination of interfacial water differ from those of bulk water. Consider, for example, a charged surface. It has been shown that the direction of interfacial water dipoles is determined according to the polarity of the surface charge.69 In this case, the interface will appear quite different to the adsorbate approaching a positively charged surface versus one approaching a negatively charged surface. Similarly, addition of salt to the bulk solution alters interfacial water structure, influencing the adsorption process. In the following section, we demonstrate some experimental and modeling approaches that provide insight into such phenomena. This is not intended to be a review of interfacial water structure but rather highlights of our work on systems of interest to our group. There are several detailed and comprehensive reviews devoted to interfacial water.34,70−76 4.1. Investigation of Interfacial Water Structure via Perturbation with Salt. As discussed earlier, the specificity of SFG spectroscopy to interfacial environments, in comparison with grazing angle and evanescent wave methods, allows for the 5625

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Figure 11. Two representations of the evolution of SFG spectra as a function of solution NaCl concentration. (a−d) Contours generated from individual spectra, normalized to the strongest overall response, show the evolution of spectral intensity. (e−h) The same data set, but normalized to the strongest response at each ionic strength, illustrates the evolution of spectral shape. Strong spectral response is shown in purple, and weak response is shown in orange. Panels below the contour plots highlight the differences at low (black) and high (gray) salt concentrations, as indicated by the arrows. Reprinted with permission from ref 80. Copyright 2014 American Chemical Society.

where the spectra are nearly insensitive to NaCl addition until the signal dramatically increases at high concentrations. In the bottom row (e−h), the signal is normalized to the maximum intensity at each salt concentration in order to more clearly reveal changes in the shape of the spectra, irrespective of overall intensity variation. Here it is seen that the two dominant bands in nearly all interfacial water spectra, 3200 and 3400 cm−1, respond differently for the different interfaces but, in all cases, the signal shifts to 3400 cm−1 at high salt concentrations. Examining the manner in which the changes occur led us to conclude that the hydrogen bonding environment is sensitive to ionic species near the surface, with a reduction in coordination occurring at high ionic strength. The manner in which this occurs depends strongly on the surface water structure at low ionic strength. It is interesting to see that the surface influences the water structure so strongly, even at concentrations in the 1 M range. Because the shape of the silica−solution spectra remains relatively uniform over the entire range of ionic strength, it was possible to separate the second- and third-order susceptibility contributions to the total signal.79 Even though χ(3) is typically ∼7 orders of magnitude smaller than χ(2),81 its contribution may be significant, as it is weighted by three field factors, as illustrated in eq 3. The first two are the incident visible and infrared electromagnetic fields, common with the second-order contribution. The third field can come from the interfacial charge, which is appreciable at a pH far from the isoelectric point.78,82 Since this electric field extends from the surface (z = 0) into the bulk, the third-order contribution may be written as

selective investigation of the interface in the presence of the bulk phase, without the latter obscuring the interfacial signal. Shortly after the first demonstration of SFG spectroscopy by Y. R. Shen,77 water was studied at the silica surface.78 The use of SFG to study water at solid surfaces continues to be a major focus, with many groups around the world actively working in this field.70 We are specifically interested in the effect of ionic species in solution upon solid−liquid interfacial structure. It has long been known that electrolytes affect the interfacial region. At a macroscopic level, electrolyte addition can lead to an alteration of surface charge, a decrease in interfacial depth, and the establishment or enhancement of interfacial chemical gradients.79 However, less is known about microscopic features of the solid−aqueous interface. The basis of our study of water structure at solid−liquid interfaces has been the observation of changes in spectral response as a result of electrolyte addition. Comparison of neat water spectra from different interfaces can reveal differences between the interfaces; comparison of response at the interface upon salt addition adds a richness to the analysis not otherwise observed. Figure 11 illustrates the evolution of the water SFG response on (a, e) fused silica, (b, f) calcium fluoride, (c, g) polystyrene, and (d, h) poly(methyl methacrylate) surfaces spanning 5 orders of magnitude NaCl concentration up to ∼4 M.80 The top row (a−d) shows the SFG signal, normalized according to the salt concentration that produced the largest peak response in each case. In the case of fused silica and polystyrene, the signal decreases with increasing salt concentration. For CaF2 and PMMA, a very different trend is observed 5626

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E0(z) dz

interfacial processes. The addition of salt increases the surface charge (Figure 12a),82 and in region A (less than 1 mM), this has the effect of inducing polar ordering of water in the interfacial region, thereby increasing ⟨α(2)⟩ (Figure 12b) and χ(2) (Figure 12c). At the same time, the addition of salt increases the screening of the surface potential, thereby decreasing the third-order contribution. These two processes balance each other to yield the constant intensity seen in region A. As the NaCl concentration is further increased (region B, 1− 100 mM), maximum polar ordering of water has been achieved and the decrease in signal is solely a result of decreased thirdorder contribution, driven by increased screening. The transition to constant intensity in region C (0.1−1 M) marks the maximum screening of the interfacial potential. The penetration depth of the field from the surface charge now remains constant as do the second- and third-order contributions to the signal. Finally, in region D, the electrolyte concentration is beginning to disrupt the interfacial hydrogenbonding network, decreasing interfacial order. This study illustrates the importance of the extent of polar ordering of water, gradients in electric potential, and species concentration in describing the surface-bound water molecules. 4.2. Enhanced Understanding through Spectral Modeling. Just as we have acknowledged many groups using SFG to characterize interfacial water structure, there has been and continues to be considerable effort devoted to simulations in this area. From one perspective, experimentalists face challenges in gaining enough specificity to probe interfacial water, especially prior to the advent of SFG experiments, so it is natural to turn to molecular simulations to discriminate surface from bulk behavior. From another perspective, as a vibrational technique, SFG provides a fingerprint of the water structure, but it is difficult to interpret the complex hydrogen bonding environment from this fingerprint alone. In this sense, similar to the cases of adsorbate and substrate structure that we have presented earlier, modeling approaches may be used to gain additional insight into the structural origins of the SFG response.83,84 Finally, even though SFG affords extreme sensitivity to the interfacial region, the depth to which water is ordered is often estimated to be around 10−15 Å, roughly 2− 4 times the size of a single water molecule. Simulations are often used to “peel apart” the response in a depth-profiling study that is difficult to achieve experimentally. We have created surfaces resembling self-assembled monolayers to study the structure and model the SFG response of interfacial water.85 We followed an approach developed by Morita and Hynes to account for the effect of the hydrogen bonding environment on χ(2) and subsequently χ(2) at the air− water interface.86 In this method, the hyperpolarizabilities of individual O−H oscillators were coupled to form the high- and low-energy water modes (akin to the antisymmetric and symmetric stretching modes in the gas phase). The coupling constant was determined by the frequency of the local O−H vibrations, sensitive to the neighboring water molecules. The left column of Figure 13 illustrates the shift in OH oscillator frequency relative to the gas phase value (3707 cm−1), plotted as a difference in the population ΔP relative to that obtained in the bulk of the water phase. Data for the low frequency (red) and high frequency (blue) oscillators are separated; the combination is plotted in black. The right column illustrates the calculated contribution to the imaginary component of χ(2), with xxz (comparable to what is obtained in an ssp experiment) in blue, xzx (sps) in red, and zzz (one of the contributions to

(11)

where E0 is the static field originating from the surface charge. The dependence of total spectral intensity upon ionic strength is shown in Figure 12d. The shape of this curve is a result of a balance between the χ(2) response and an amplification of the χ(3) response by the local field.78 Several interfacial processes contribute to the shape of these curves. In deriving a model of the interface, we have split the curve into four regions, each dependent upon a different subset of

Figure 12. Proposed balance between electrolyte screening and molecular order at the interface. (a) The dashed line shows a function fit to empirical surface charge measurements (points) at the fused silica−water interface.82 The solid line represents the surface potential, calculated from the surface charge data at I ≤ 0.13 M and by the Stern model at I > 0.13 M. (b) Change in the average α(2) (solid lines) and α(3) (dotted lines), each normalized to their maximum values. (c) Contributions of the χ(2) (solid line) and χ(3) terms to the measured signal. (d) The modeled signal (line) alongside the measured data (points). Reprinted with permission from ref 79. Copyright 2011 American Chemical Society. 5627

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in Im[χ(2)], accounting for the experimental observation of very small SFG intensity at energies near 3700 cm−1. As a final example, we illustrate how interfacial water and adsorbate are intimately related. We have created surfaces modeled with a Steele 10−4 potential (essentially a LennardJones 12−6 potential integrated over the surface x and y coordinates so that it is a function of z only).89 Although such surfaces are not as chemically realistic as the explicit ones described above, they allow tuning of the hydrophobicity via the Lennard-Jones σ and ε terms. While experimental studies employ substrates that are relevant to their respective application areas, they are often chemically dissimilar (silica as a hydrophilic surface, polystyrene as a hydrophobic surface). As a result, it is difficult to ascertain how much of the water behavior is due to hydrophobicity, versus the effects of charge, surface roughness, surface hydrogen bonding opportunities, etc. Our approach allows surfaces with varying hydrophobicity but otherwise similar physical properties to be studied. We have tailored our surfaces to obtain water contact angles in the range 84° (semiwetting) to 156° (nonwetting, superhydrophobic). Figure 14 shows the water density variation as a function of distance from the most hydrophilic and hydrophobic surface. Superimposed on the water density profiles (black) are histograms of three coordinates pertaining to the leucine molecule when it is on the surface. The leucine center of geometry is plotted in red, the center of charge in blue, and the average methyl position (between the two isobutyl methyl carbon atoms) in green. On all surfaces, leucine is adsorbed with its methyl group closer than the molecule’s center of geometry, indicating the hydrophobic group preference to be directed toward the surface. As the hydrophobicity of the surface decreases, the water density and the leucine orientation both change. Looking more closely at the features in comparison to our study in the absence of the solute,89 we can notice that in the laying orientation the entire leucine molecule (both hydrophobic and charged hydrophilic ends) prefers to be situated in regions of lower water density. The first change from a local maximum to a minimum in the water (oxygen atom) density is correlated to the position of the hydrophobic end of the leucine molecule. This could indicate an orientation preference of the water hydrogen to be positioned closer to this side of the leucine. Such studies reveal that variations in water density and orientation directly influence the structure of adsorbed molecules.

Figure 13. Results of hydrogen bonding analysis and nonlinear vibrational spectra obtained for water adjacent to solid hydrophilic and hydrophobic surfaces. The first column shows the OH frequency shift with respect to an uncoupled oscillator in the gas phase at 3707 cm−1. This is plotted as a difference in population ΔP with respect to results obtained in the bulk water sample. Data for the low frequency (red) and high frequency (blue) oscillators are separated; the combination is plotted in black. The second column shows the imaginary component (2) of the nonlinear susceptibility tensor elements: χ(2) xxz in blue, χxzx in red, in black. Adapted with permission from ref 85. Copyright and χ(2) zzz 2012 American Chemical Society.

5. SUBSTRATE SURFACE STRUCTURE We now complete our discussion of the molecule−solvent− surface trilogy by providing an example of how SFG data, combined with modeling, can yield information on the substrate surface structure. At the same time, we will illustrate how the phase of the SFG response may be used to access additional information that is unique to this experiment. In Figure 2, we illustrated that, when molecules are arranged in a manner that causes the same number of groups to be pointing toward as away from the surface, the SFG fields cancel, resulting in χ(2) = 0. This accounts for the surface specificity of SFG spectroscopy but also provides a route for the determination of the absolute direction or polarity of the functional groups. If we can measure the phase of the SFG field, we measure a property that is proportional to χ(2), rather than measuring the intensity of the SFG response that is proportional to |χ(2)|2.70,90−93 This requires an interferometric setup, as shown in Figure 15. Here the visible and IR pump

ppp) in black. For all of the results, we have performed a depth analysis where the interface has been divided into regions (rows in Figure 13) defined according to the variation in density and orientation order parameters. From this study, we were able to conclude that, for the hydrophobic surface, the water structure was similar to that which had previously been determined at the vapor−water interface,87,88 despite the more condensed density profile at the solid surface. This provided insight into why the SFG spectra at those two interfaces are also similar. At the hydrophilic surface, we observed strong orientation originating at different depths throughout the interface. However, the water orientations resulted in opposing spectral contributions 5628

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Figure 15) are generated by varying a time delay between the two SFG fields. Spectral fringes over the IR wavelength region of interest (vertical axes) are also evident. By fitting these fringes to an appropriate model accounting for the phase difference, it is possible to determine the magnitude (Figure 15a), phase (Figure 15b), real (Figure 15c), and imaginary (Figure 15d) components of χ(2) yyz for OTS over the aliphatic C− H stretching region between 2800 and 3000 cm−1. Of these four representations, the imaginary χ(2) spectrum is particularly valuable, as it displays the resonances most clearly, enables the most accurate assessment of the peak frequencies, most closely resembles the IR absorption spectrum for comparison and mode assignment, and carries information on the polarity of the chemical functional groups in the sign of the peak. Note that the quantities ∂α(1)/∂Q and ∂μ/∂Q are real; the imaginary component of χ(2) has its origins in the imaginary component of the molecular hyperpolarizability, α(2). As eq 6 reveals, this comes from the line width in the denominator of the Lorentzian form. What is of interest here is the sign of the bands in the imaginary spectrum. This comes from the sign of the product of ∂α(1)/∂Q and ∂μ/∂Q. We provide a demonstration of this polarity resolution in the case of the poly(methyl methacrylate) surface. PMMA is a widely used polymer that is considered hydrophobic, yet its water contact angle is only ≈70°. Adding to the large body of previous work,94−98 we can gain some additional insight into the chemical origins of this behavior by studying the structure of its surface. We target the ester methyl groups at the end of its side chain (see Figure 16), wishing to determine whether they are pointed toward the bulk polymer or away from the surface. Previous studies100,101 have determined that the surface ester methyl group SS is observed at 2956 cm−1. We have measured the phase of χ(2) yyz as ωIR is scanned across this resonance, and compared our results with the phase of the OTS terminal methyl SS response at 2873 cm−1. The data in Figure 16 show that the two methyl groups display the same phase behavior, starting at −180° at probe frequencies below resonance, −90° on resonance, and 0° above the CH3 SS resonance. However, even though we consider the OTS methyl groups to be directed toward the air based on previous studies of OTS and similar molecules,102−106 we must first establish that the relevant hyperpolarizabilities have the same (or different) signs before we can make a conclusion about the direction of the PMMA ester methyl groups. In the case of ester methyl groups versus methyl groups at the end of an aliphatic chain, this is particularly not obvious as the chemical environments are quite different, evidenced by the ∼80 cm−1 difference in SS resonance frequencies. This has been previously discussed, as the permanent dipoles at the methyl positions point in opposite directions,107 as seen in the μc values in Figure 16, positive for OTS and negative for PMMA. However, the slopes, ∂μc/∂Q, are negative in both cases. That is, the dipole moment along the CH3 C3 axis is becoming more negative with a greater internuclear separation for both types of methyl groups. In fact, the signs and magnitudes of all slopes ∂αaa/∂Q, ∂αbb/∂Q, ∂αcc/ ∂Q, ∂μc/∂Q are the same, enabling us to conclude that, for both molecules, a phase of −90° on resonance for the SS indicates the methyl groups are pointed toward the air.99 Such a conformation limits the surface exposure of the ester oxygen atoms that would otherwise lower the water contact angle even further. Through the measurement of this functional group polarity, we therefore have provided a molecular-level rationalization for the mild hydrophobicity of this important polymer.

Figure 14. (top) Water density profiles for a semiwetting and nonwetting surface. (bottom) For each of the six different surfaces of varying hydrophobicity, three leucine coordinates are superimposed on the water density profiles (black solid lines prior to Leu adsorption and dashed lines after Leu adsorption). The leucine center of geometry is plotted in red, center of charge in blue, and average methyl position in green. Solid and dashed lines indicate standing and laying orientations, respectively. Reprinted with permission from refs 89 and 50. Copyright 2009 and 2010 American Chemical Society.

beams are both split, and a fraction is directed toward a reference sample, ideally a material with large χ(2) so that most of the intensity of the beams is passed to the sample (likely with small χ(2)). If the polarity of the reference is known, then the interference between the reference- and sample-generated SFG may be used to determine the phase of the sample SFG field. As a demonstration, we have collected interferometric SFG data for trichloro-octadecyl silane (OTS) at the air−glass interface.93 In order to facilitate analysis of the interference, temporal fringes (horizontal axes of the 2D interferograms presented in 5629

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Figure 15. The phase of the SFG field from the sample of interest may be determined in an interferometry experiment (top), where the visible and IR pump beams are split and a fraction is directed to a material with χ(2) ≠ 0 that generates the local oscillator SFG signal. Two dimensional interferograms (bottom left) are obtained where temporal fringes (horizontal axis) are observed when the time delay between sample and local oscillator is varied, and spectral fringes (vertical axis) occur over the wavelength region of interest. Fitting of these fringes results in spectra (bottom right) of the (a) magnitude, (b) phase, (c) real component, and (d) imaginary component of χ(2). Adapted with permission from ref 93. Copyright 2012 American Institute of Physics.

6. SUMMARY AND PERSPECTIVE Vibrational sum-frequency generation spectroscopy is a powerful probe of adsorbed molecules, interfacial solvent structure, and the surface features of the substrates. One of its key advantages is the ability to differentiate surface species from those in an adjacent bulk phase. While this gives SFG the ability to exclude molecules in solution, it is particularly valuable in the study of adsorbed water and polymer surface structure, as few techniques are able to offer selectivity in such cases. Another advantage over other spectroscopic probes is the ability to resolve the polarity of the surface molecules by measurement and analysis of the phase of the SFG response. In each of these cases, however, the true power of SFG to provide structural information is realized only when the experiments are combined with some degree of modeling effort.55,108−112 In the case of relatively simple molecules, both in a structural and spectroscopic sense, we have demonstrated that isolated normal modes may be used to quantitatively determine the orientation

and conformation of surface species through the use of electronic structure calculations, combined with tools that explore the three-dimensional orientation distribution by scoring model spectra against the experimental results. Extending this approach to include families of orientation distributions enables us to capture the statistical nature of the problem we are addressing by incorporating some of the heterogeneity of the system. This is achieved by the development of grid computing techniques that can explore parameter spaces of high dimension. In the case of larger and more complex molecules, or any molecule displaying a complex vibrational SFG spectrum with many overlapping resonances, we can no longer perform the same kind of analysis on the amplitude of a particular peak/band. However, all of the tools we have developed that relate molecular structures to the experimental observables apply. We are still capable of modeling the SFG response for a candidate structure, and then comparing with the experimental result. However, one of 5630

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Progress in SFG experiments continues to evolve, and some emerging directions generate new data that will in turn provide additional observables with which to compare models. For example, broadband experiments offering spectral resolution better than 1 cm−1 will enable multiple peaks to be resolved from overlapping spectral features, while at the same time offering better time resolution than in scanning experiments.121,122 Time-resolved SFG in particular is another area that is providing insight into surface dynamics.123 Techniques for manipulating the nonresonant background have proven themselves to be another handle that may be applied to the study of vibrationally resonant features.124−126 Finally, since the upconverted SFG signal is in the visible region, SFG microscopy holds the promise for providing spatially resolved information that may provide a better understanding of surface coverage and spatial heterogeneity in the adsorption process.127−130 On the molecular simulation front, advances in developing force fields for describing interfacial environments will enhance the ability of molecular dynamics and Monte Carlo approaches to modeling adsorbate structure.66,131−133 When combined with efforts to model protein amide bands52−55 and more sophisticated models of the solvent response,88,134,135 this will increase our ability understand the interplay between the various components of the adsorbed state. Two significant challenges remain for structural analysis. On the level of a single molecule, the environment at the surface is significantly different from the bulk solvent or substrate phase, and yet it is difficult to step away from the notion that surfacebound molecules differ from their bulk counterparts only in terms of their orientation distribution. For example, the conformation of flexible molecules may be perturbed at the surface and, for large molecules with many conformational degrees of freedom, this remains a challenging feature to capture in the analysis. The second challenge stems from the fact that there is an inevitable focus on the level of a single molecule, with most techniques geared toward providing the best average description of the surface orientation distribution. However, we know that in many cases the surface represents a heterogeneous environment, where a multitude of structures are responsible for the observed spectroscopic response. When candidate structures are scored against experimental data, it is in general not sufficient to consider only the best possibility, or a family of the best possibilities. Structures whose modeled response differs considerably from the measured spectra may be important minor contributors to the ensemble of adsorbed states. We have touched on this in our treatment of the leucine data, but the techniques we have illustrated there have perhaps served only to draw attention to the problem, rather than providing a general solution. Molecular dynamics simulations are able to address both of these areas but necessitate accurate force fields for describing the surface interactions, or ab initio approaches that are currently limited by available computing resources. In the future, we look forward to seeing analysis protocols that are able to interpret experimental data in a manner that increasingly accounts for such intra- and intermolecular heterogeneity.

Figure 16. Determining the absolute orientation of the PMMA side chain ester methyl groups involves first measuring the phase of the SFG response for the symmetric stretch of this methyl group, in comparison to that obtained for the OTS terminal methyl groups, then calculating the relevant hyperpolarizability tensor elements for both types of methyl groups, and finally comparing the tensor elements. Adapted with permission from ref 99. Copyright 2011 American Chemical Society.

the consequences of this route is that we need some way of generating trial structures, and perhaps trial orientation distributions. In the examples we have provided, we sample equilibrium ensembles from molecular dynamics simulations in order to make these connections. Although this article has provided an opportunity to highlight our own work, there are many research efforts around the world devoted to aspects of adsorbed structureadsorbate, solvent, substrateby experiments and simulations.38,73,113−120

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 5631

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Biographies

Paul Covert received a B.A. in Chemistry from Reed College in 1995. In 2001, he completed a M.Sc. in Oceanography at Oregon State University with a focus on transformations of suspended matter in riverine and estuarine systems. Between 2001 and 2010, while working for OSU and the National Oceanic and Atmospheric Administration, he contributed to several research programs investigating coastal nutrient dynamics, air−sea gas-exchange processes, and ocean acidification. Paul joined the Hore group in 2010 to pursue a Ph.D. in Chemistry. His current research interests include the development of sum-frequency generation methods for the study of aqueous−solid interfaces in the environment. Sandra Roy obtained a B.Sc. in Chemistry from Université Laval, Quebec City, in 2010 while working at Defense Research and Development Canada. In 2012, she obtained a M.Sc. in Chemistry in the Hore group. Her thesis entitled “Water and peptide structure at hydrophobic and hydrophilic surfaces” used molecular simulations to probe the interplay between surface charge, hydrophobicity, interfacial water structure, and adsorbed peptide structure. She is now pursuing a Ph.D. in the Hore group. Her current research is focused on biomolecule structure at surfaces by vibrational spectroscopy and molecular modeling. Travis Trudeau obtained his B.Sc. in Chemistry from Thompson Rivers University in Kamloops, BC, in 2006. During his M.Sc. research in the Hore group, he used molecular dynamics simulations to study the structure of water and adsorbed amino acids at aqueous interfaces. He is currently in medical school at Western University in Ontario. Dennis Hore received his Ph.D. from Queen’s University under the mentorship of Profs. Almeria Natansohn (Queen’s, Chemistry) and Paul Rochon (Royal Military College, Physics). His dissertation examined the photoinduced orientation of light-responsive polymers. He was then a postdoc in Prof. Geri Richmond’s group at the University of Oregon, studying surfactant and water structure at the air−water interface. In 2006, he joined the Department of Chemistry at the University of Victoria. His research interests are centered around characterizing the structure of molecules adsorbed at solid surfaces.

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ACKNOWLEDGMENTS This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). Equipment was purchased with support from NSERC, the Canadian Foundation for Innovation, the British Columbia Knowledge Development Fund, and the University of Victoria. Simulations were enabled by a generous resource allocation from WestGrid and Compute Canada. S.A.H. is grateful to NSERC for CGS-M and CGS-D scholarships.

Shaun Hall received his B.Sc. from the University of Ottawa in 2006 and completed his Ph.D in Dennis Hore’s group in Victoria, British Columbia. His dissertation focused on determining the structure of amino acids adsorbed at polymeric surfaces using SFG and computational methods. Following a short postdoc studying drug− metal organic framework interactions using computational methods with Prof. Guillaume Maurin at the Université de Montpellier II, he is currently working in the group of Prof. John Harding at the University of Sheffield, studying biopolymer−mineral interactions. His research interests include surface reactivity of molecules, biomineralization, and high performance computing for scientific applications.

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