Re-orientation of water molecules in response to surface charge at surfactant interfaces

Water at charged interfaces is the medium in which many important chemical and biological processes take place, from biological self-assembly and molecular recognition at biomembranes to environmental chemistry and electrochemistry.^1–7 A molecular-level understanding of how the water hydrogen bonding network is affected by the vicinity of charged interfaces, i.e., surface charge density, surface electrostatics, and spatial distribution of ions, is crucial for our ability to theoretically describe and model these processes.

Bulk water owes its unique properties due to its ability to form extensive hydrogen bond networks, where most of the water molecules are tetrahedrally coordinated giving rise to the maximum number of hydrogen bonds possible around a single water molecule. This three dimensional network of hydrogen bonds is sharply terminated at the interface making it more heterogeneous than the bulk.^8,9 Theoretical studies of the air/water interface^10,11 show that this thin region (about 3 Å) is comprised of several different types of water molecules with various degrees of hydrogen bonding.^10,17,20

This inherently inhomogeneous network of hydrogen bonds is likely to undergo structural changes when the surface becomes electrically charged. Charge-dipole interactions can be thought of as the major factor that competes with H-bonding in determining the water structure at the charged interface. For example, in the simplest case of a uniformly charged plane, the water dipoles would tend to align “up” or “down” depending on the sign of the charge, which is clearly incompatible with the nearly tetrahedral H-bond coordination. For a negatively charged interface, the hydrogen of the water molecules should orient up toward the negative charge, whereas at a positively charged interface, the oxygen atom of a water molecule should orient toward the positive charge. Nihonyanagi et al.⁴ provided direct spectroscopic evidence for this orientational flip-flop of water molecules at charged interfaces by phase sensitive vibrational sum frequency generation (SFG) spectroscopy in the OH-stretch region. Their conclusion of water orientation at charged interfaces was based on the sign of the Im χ⁽²⁾ SFG spectra at charged aqueous interfaces. It must be pointed out however, that although the vibrational spectroscopy in the OH-stretch region is a powerful tool for studying the H-bond structures and ultrafast dynamics of both bulk^12–14 and interfacial water,^8,15–19 the OH-stretch region spectra of pure H₂O can only provide qualitative (up/down) orientational information because of spectral broadening, non-Condon effects, and intramolecular and intermolecular coupling (also known as vibrational excitonic effects) that complicate interpretation of the spectra.^13,20 The only exception is the “free OH” feature,¹⁵ which has been shown to be largely unaffected by intermolecular coupling.⁸ However, a free OH peak is not present in the SFG spectra of water at most charged interfaces. Recently, Drier et al. reported charge induced water alignment at biologically relevant interfaces.²¹ They concluded that water alignment at the Stern layer and the diffuse layer scales with increasing charge density for the low surface charge and saturates for charge densities exceeding ±0.1 C/m².

Water bend spectroscopy is believed to be less affected by the aforementioned complications.^22–24 The weaker transition dipole of the water bend (about 5 times less than the OH-stretch) results in reduced intermolecular coupling; additionally, there is no intramolecular coupling since there is only one bend mode per water molecule (in contrast with two local OH-stretch modes). Thus, quantitative orientational information can be obtained from the analysis of the water bend SFG spectra. The direction of the transition dipole for the bend mode is the same as that of the permanent dipole of water. Thus, at least qualitatively, the orientation obtained from the water bend spectra can be interpreted in terms of the permanent dipole being oriented by the external E-field. As shown in our previous publications on the water bend SFG spectra^22,23 and theoretical analysis by other groups,^24,25 the spectral line shape of the water bend shows two distinct features, a negative peak at 1630 cm⁻¹ which is mostly (although not exclusively) associated with the free OH species and a positive peak at 1662 cm⁻¹ that is attributable mostly to the fully hydrogen-bonded species. Thus, water bend SFG spectra offer a hope of independently measuring orientation of different H-bonded species of water molecules and how they respond to changes of the surface charge.

In principle, water bend and OH-stretch spectroscopy should provide complementary information about the molecular orientation. The aforementioned complications of the OH-stretch spectra can be circumvented by performing isotopic dilution measurements on HOD/H₂O or HOD/D₂O mixtures, which removes excitonic coupling effects. The OH-stretch spectroscopy then would yield orientation of the OH-bond, while the water bend spectra yield orientation of the C_2v symmetry axis, which together define the three-dimensional molecular orientation.^26,27 We also note that a significant quadrupole contribution to the SFG spectra of the water bend has recently been suggested,²⁸ although other previous theoretical calculations have successfully reproduced the spectra within the electric dipole approximation.^24,25,29 The orientational analysis presented here is within the limits of the electric dipole approximation for the water bend.

In this article, we present the water bend SFG spectra at a positively charged surfactant cetyltrimethylammonium bromide (CTAB)/water interface in SSP, PPP, and SPS (SFG, visible, and IR) polarization combinations and provide average orientation of water molecules belonging to two (fairly broad) hydrogen-bonding classes according to their bend frequencies: (1) the ones with free-OH bonds and (2) fully hydrogen bonded water molecules. Our comparative line shape analysis and orientation analysis of the water bend spectra from a negatively charged surfactant (sodium dodecyl sulfate, SDS) and positively charged surfactant (CTAB) interface show structural and orientational dissimilarity between these two interfaces. Orientational changes as a function of surface charge density (at charge densities lower than ±0.1 C/m²) are also presented, providing a quantitative estimation of the surface charge density required for a molecular re-orientation at the interface.

A detailed description of our VSFG (vibrational sum frequency generation) setup has been described previously.¹⁹ We have used similar experimental procedures in the water bending vibrational region (a center frequency of IR ∼1600 cm⁻¹). The narrow bandwidth (∼20 cm⁻¹) visible (800 nm) pulses generated using a 4f-stretcher and broadband IR pulses (∼300 cm⁻¹) generated using an optical parametric amplifier (OPA) were focused on the sample surface to a spot size of ∼150 µm. The laser powers at the sample surface were 2 and 10 µJ per pulse for the IR and visible pulses, respectively. The angle of incidence from the surface normal was 67° for the visible and 62° for the IR beams. All of the spectra were collected for SSP, PPP, and SPS polarizations (SFG, visible, and IR) and recorded with a 500 nm monochromator (Princeton Instruments, 1800 g/mm grating) and a liquid nitrogen-cooled charge-coupled device (CCD) detector (Roper Scientific). The SFG spectra were corrected for the scattering of the 800 nm light (recorded by blocking IR light only and subtracted from the raw SFG data).

We used doubly distilled water, starting with 18 MΩ water from a Millipore system, which was then distilled again through a sealed all-glass distillation apparatus cleaned with Piranha solution to prepare water free of ions and organic contamination. SFG experiments at the air/water interface are extremely sensitive to organic contaminants which, if present, are readily observed in the spectra. All solutions were made from the freshly distilled water before every measurement.

Curve fitting of the actual measured spectra with the resonant and nonresonant parts is necessary to get the actual frequencies and amplitudes of different transitions. The second-order nonlinear susceptibility χ⁽²⁾ is expressed as a sum of Lorentzians, and the nonresonant part is fitted as a constant term with a phase factor

where A_NR is the nonresonant contribution to the overall spectra with a phase difference, φ, from the resonant parts and B_j is the resonant amplitude with center frequency ω_j and linewidth Γ_j. We adopted a two Lorentzian fitting scheme with varying amplitude and width. The frequencies of the resonant Lorentzian were kept constant as there is no spectral contamination present due to the surfactant molecule. Fitting parameters for all the CTAB spectra are presented in Table S1 of the supplementary material.

Previously, we reported the SFG spectra of the water bend vibrational mode at the air/water interface.^22,23 The observed line shape for SSP and PPP polarizations consists of a lower frequency negative feature (1630 cm⁻¹) and a higher frequency positive feature (1662 cm⁻¹) on top of a broad background which is presumably due to librational overtones in this spectral region. Theoretical studies carried out within the electric dipole approximation for this transition^24,25 have attributed the negative red-shifted peak to the water molecules from 1_N, 2_S, 3_S H-bond classes (which we collectively refer to as “free OH” species) as defined by Ni and Skinner,²⁴ and the blue-shifted positive peak is attributed to molecules from 3_D, 4_D H-bonded classes (which we refer to as “fully hydrogen-bonded”) at the air/water interface. Here, 2, 3, and 4 represents the total number of hydrogen bonds around a water molecule and N, S, and D subscript signifies “nondonor,” “single-donor,” and “double-donor” hydrogen bond, respectively. For example, 2_S represents water molecules having 2 hydrogen bonds with single donor hydrogen, 1_N - water with only one acceptor hydrogen bond, etc. We provided experimental support for this assignment by comparing SFG spectra of the air/water interface with the SDS/water interface and also explained that the apparent frequency shift in the SSP vs PPP spectra occurs due to the interference of the two peaks with opposite signs and different amplitudes.²³ At the SDS/water interface, the “free-OH” hydrogen bonded species are suppressed, and the corresponding suppression of the negative 1630 cm⁻¹ feature was observed in the spectra.

Figure 1 shows SFG spectra of the water bend at the positively charged surfactant interface (0.4 mM solution of CTAB) compared to the negatively charged surfactant interface (1.0 mM solution of SDS) for SSP and PPP polarization combination for SFG, visible, and IR pulses, where S is perpendicular polarization of light with respect to the plane of incidence and P is polarization parallel to the plane of incidence. At the negatively charged SDS surfactant interface, the overall spectral line shape of the water bend resembles that of an air/water interface with a negative peak and a positive peak in both SSP and PPP polarization combinations. However, the SFG spectra form a positively charged CTAB surfactant interface in the water bend region are different, as shown in Fig. 1. It is quite clear that the SSP spectrum has a similar line shape as the air/water interface, having a negative peak at 1630 cm⁻¹ and a positive peak at 1662.5 cm⁻¹, whereas in the PPP spectrum, the two peaks have opposite sign with respect to the SSP spectrum. Curve fitting of the SDS and CTAB spectra was performed with the two Lorentzian fitting model adopted for the air/water interface,²³ keeping the resonant frequencies fixed but allowing the amplitudes to flip sign. In SSP, the 1630 cm⁻¹ peak is negative and the 1662.5 cm⁻¹ peak has positive amplitude which is similar to SSP spectra of the air/water interface. For the PPP spectrum, the 1630 cm⁻¹ peak has positive amplitude and the 1662.5 cm⁻¹ peak is negative. The complete table of the fitting parameters is presented in the supplementary material.

Since the PPP spectrum from the water/CTAB interface has a flipped spectral line shape as compared to the air/water interface, we should expect to observe a gradual change in the water bend spectra with a gradual increase in the positive surface charge density. In Fig. 2, SFG spectra from CTAB solutions in SSP, SPS, and PPP polarization combinations have been plotted for increasing the CTAB concentration from 0.01 mM to 0.07 mM. Surface density of a CTAB surfactant can be calculated from the bulk concentrations using the Gibbs adsorption isotherm and is presented in Table I. All spectra were fitted using the same two Lorentzians, keeping the resonant frequencies constant at 1630 cm⁻¹ and 1662.5 cm⁻¹. For SSP and SPS polarization combinations, the amplitudes of the two peaks increase with the surfactant concentration while their signs remain the same. SSP spectra have negative amplitude of the 1630 cm⁻¹ peak and positive amplitude of the 1662.5 cm⁻¹ peak, irrespective of the surface coverage. SPS spectra have a positive feature on the low frequency side and a negative peak on the high frequency side of the spectrum at all concentration. By contrast, the PPP spectra show different concentration dependent behavior. At the lowest concentration (0.01 mM), PPP spectral fitting gives a negative red-side and a positive blue-side resonant feature. However, with the increasing concentration, the amplitude of the negative Lorentzian at 1630 cm⁻¹ becomes less negative and eventually turns positive at 0.07 mM bulk concentration, whereas the amplitude of the Lorentzian at 1662.5 cm⁻¹ is initially positive at 0.01 mM and becomes negative at 0.07 mM bulk CTAB concentration.

Figure 3 shows this variation of the amplitudes at 1630 cm⁻¹ (B₁ in the left panel) and at 1662.5 cm⁻¹ (B₂ in the right panel) with the change of bulk CTAB concentration. As the surface charge density increases, the B₁ amplitude decreases while the B₂ amplitude increases in SSP. In SPS, both B₁ and B₂ remain nearly constant, i.e., B₁ remains positive and B₂ remains negative. However, the signs of B₁ and B₂ amplitudes change as the surface charge density grows gradually from lower to the higher value for the PPP spectra. The extracted amplitudes allow us to calculate the average molecular orientation for the two H-bonded species, as detailed in the next section. The average angles between the C_2v axis of water and the surface normal are indicated in Fig. 3 for each surfactant concentration. Fitting results of all the spectra also provided the nonresonant background (A_NR) for each concentration of the CTAB solution (Fig. S1 of the supplementary material). A_NR shows the linear change as a function of the bulk CTAB concentration, and there is no indication of change in sign of the background signal.

Using mixed quantum/classical calculations, Ni and Skinner²⁴ decomposed the overall water bend spectral line shape at the air/water interface into separate spectral contributions of different hydrogen bonding classes. Their model shows significant spectral overlap of these components, whose interference results in the distinct negative feature in the red side of the spectrum and the positive feature on the blue side of the spectrum. In light of their analysis, we would like to point out that the positive and negative amplitudes in the fitting of our experimentally measured SFG spectra could contain contributions from various hydrogen bonded species, both strongly and weakly hydrogen bonded. Hence, we cannot obtain orientational information separately for each of the hydrogen-bonded classes directly from the experimental SFG spectra. Instead, we aim to understand the average orientation of the species that contribute to the negative vs positive feature,³⁷ which we collectively label “free OH” and “hydrogen bonded,” in agreement with the theoretical assignments.^24,25

Orientation of the C_2v axis of the water molecules at the interface (Fig. 4) in the presence of surfactant molecules has been determined by orientational analysis of the polarization depended SFG spectra of the water bend mode. The second-order nonlinear susceptibility tensor $χijk(2)$ in the lab-frame is connected to the molecular hyperpolarizability tensor (⁠$βi′j′k′(2)$⁠) by rotational transformation (Euler) matrices $R(θ,ϕ,φ),$³⁰ 

where “$⟨⟩$” represent orientational average of the corresponding property over the orientational distribution function. N_s is the number density of molecules at the interface. Molecular hyperpolarizability $βi′j′k′(2)$ is a frequency-dependent quantity and can be written as a sum of resonant and nonresonant terms. The resonant part contains the vibrational information of the molecules at the interface [described by the Lorentzian functions in our model, Eq. (1)], and the nonresonant part generally provides a broad background over the entire spectral region. The molecular symmetry group of the vibrational mode determines the nonzero tensor elements of the molecular hyperpolarizability tensor $βi′j′k′2$⁠. Water bend is a totally symmetric mode in the C_2v point group, and there are three nonzero tensor elements which contribute to the symmetric bending mode, β_aac, β_bbc, and β_ccc.

Rao et al.³¹ showed that the experimentally measured susceptibility $χeff2$ (which includes Fresnel factors and accounts for the incidence angles of all laser beams) can be simplified in the form of the following expression:

where θ is the tilt angle of the C_2v axis of the water molecule with respect to the surface normal; parameters c and d for the three polarization combinations (SSP, SPS, and PPP) can be calculated after transforming the molecular frame hyperpolarizability tensor into the laboratory frame. A plot of $χeff2$ vs the average tilt angle $θ$ can be used to determine the average orientation of different hydrogen bonded species provided the SFG amplitudes of the respective species in different polarizations are determined from the experimentally measured spectra. Figure 5 shows the calculated variation of $χeff2$ as a function of $θ$ for SSP, PPP, and SPS polarizations. For this calculation, a Gaussian distribution of θ was assumed with the width of 15° (the calculated curves are not very sensitive to the Gaussian width in the range between 10° and 30°; this uncertainty is included into the estimated error bar for the tilt angles discussed below). Because the water bend mode is not subject to intramolecular coupling (there is only one bend mode per water molecule) and is only weakly affected by intermolecular coupling (due to its weak transition dipole), the SFG orientational analysis provides the direction of the C_2v axis for the water molecules. We note that the analysis presented here relies on the electric dipole approximation for the water bend spectroscopy. Recently, an alternative model has been proposed which attributes the spectrum to the dominant quadrupole contribution.²⁸ However, the quadrupole model does not (at least in its current form) allow one to obtain orientational information directly from the SFG spectra. Here, we restrict our analysis to the electric dipole model which seems to satisfactorily explain our experimental results.

A comparison of the calculated SFG amplitudes $χeff2$ for the SSP, PPP, and SPS spectra (Fig. 5) with the experimentally determined amplitudes B₁ and B₂ (Fig. 3) allows us to follow the changing orientation of the water molecules as a function of the positive surfactant coverage. Our results are consistent with the “free OH” molecules (the red-side spectral feature) changing their orientation “up” (their C_2v axis tilting closer to the surface normal with hydrogen pointing up) for the higher concentration of the positive CTAB surfactant. The extracted average tilt angle $θ$ is 52°, 47°, and 38° for CTAB surface density of 3 × 10¹² cm⁻², 6 × 10¹² cm⁻², and 2 × 10¹³ cm⁻², respectively. On the contrary, the hydrogen-bonded species (the blue-side spectral feature) tilt their hydrogen down toward bulk water with $θ$ = 131°, 134°, and 155°. The estimated uncertainty of the average tilt angle is ±5°.

One way to rationalize these findings is schematically depicted in the bottom panel of Fig. 5. A charged surfactant headgroup (either positive or negative) may be expected to be fully solvated. This implies that there are some water molecules that, on average, are located above the head groups. We hypothesize that these are the molecules that contribute to the red-side spectral feature at 1630 cm⁻¹ of the water bend spectrum at the CTAB/water interface. While no MD simulations of the SFG spectra at the surfactant/water interfaces are presently available, this assignment is consistent with simulations of the air/water interface, where the free OH species are only found in the top monolayer.^8,10,24 With the increasing positive charge, the C_2v axis of these water molecules above the CTAB head group (the bottom left panel of Fig. 5) reorients away from the positive charge which leads to a decrease in the tilt angle of the C_2v axis with respect to the surface normal.

The fully hydrogen-bonded molecules, contributing to the blue-side feature at 1662 cm⁻¹, are likely to be located deeper than the “free OH” species on average below the CTAB headgroups. Thus, they reorient in the opposite direction when the surface charge density increases (the bottom right panel of Fig. 5), with their hydrogen pointing away from the CTAB headgroups and into bulk water.

Our results for the negatively charged SDS surfactant interfaces can also be understood within this simple model. The negative SDS head groups would pull the hydrogen of the “free OH” water molecules down, toward $θ$ = 90°, and those of the hydrogen-bonded water molecules “up.” As can be seen from Fig. 5, such reorientation does not lead to the change in sign of any spectral amplitudes for either SSP, PPP, or SPS polarization.

We also note that the hydrogen-bonded (blue-side) spectral feature at charged interfaces likely contains a χ⁽³⁾ contribution due to alignment/polarization of deeper water layers by the surface E-field.^32,33 This may affect the interpretation of the extracted molecular orientation from this feature and is one of the directions for future studies. The analysis presented above yields an average orientation for all fully H-bonded molecules (both near the surface and deeper layers) that contribute to the 1662 cm⁻¹ feature.

The orientational flip-flop of water molecules at SDS vs CTAB interfaces was previously reported by Nihonyanagi et al.⁴ using phase sensitive vibrational SFG spectroscopy in the OH-stretch region. In that case, the whole OH-stretch band (3050–3550 cm⁻¹) was observed to change sign from positive at the SDS interface to negative at the CTAB interface (in our study, spectra in Fig. 1, we used the same SDS and CTAB concentrations). The result was interpreted simply as the negative head groups (SDS) pulling hydrogen of the underlying water molecules up vs positive head groups (CTAB) pushing them down. A comparison of the two experiments shows that the water OH-stretch spectroscopy and the water bend spectroscopy sample the hydrogen bonding species differently and thus provide complementary information. For example, the “free-OH” species are not well represented in the OH-stretch spectra at surfactant interfaces, while they feature prominently in the bend spectra for the positively charged CTAB surfactant.

The surfactant concentration of the CTAB in our work corresponds to the surface charge density of the order of 0.03 C/m². MD simulations by Dreier et al.²¹ of the water dipole moment density profiles in the Stern layer and the diffuse layer show that water alignment is almost independent of the surface charge density beyond ±0.05 C/m², although it is yet unclear whether this behavior is general for all surfactant systems. Previous studies^34–36 of electrokinetic measurements and measurements of the diffuse electric double layer in aqueous solutions with the increasing concentration of a cationic surfactant also show charge reversal at these relatively low charge densities. The diffuse electric layer potential changes from a negative value at the air/water interface to a positive value with the increasing cationic surfactant concentration. Our quantitative measurement of the surface positive charge concentration at which the surface orientation of water molecules changes provides comparable charge density at which charge reversal occurs as predicted previously by electrokinetic measurements.

We have presented SFG spectra of the water bend at positively (CTAB) and negatively (SDS) charged surfactant interfaces. Spectral line shapes for three different polarization combinations (SSP, PPP, and SPS) were analyzed in terms of the hydrogen bonding classes and orientation of water molecules. We observed and quantified the change of the molecular orientation as a function of the surface coverage of a positively charged surfactant. Different hydrogen-bonded species of water were found to re-orient in opposite directions, likely reflecting their different positions relative to the depth of the charged head groups. Orientational changes of the order of 10–20° are affected by surface coverage of the order of 1 elementary charge per 500 Ų, or an average charge density of 0.03 C/m², comparable to those found in biomembranes at mineral surfaces or in electrochemical systems. We hope that these results will promote further mechanistic studies of how the interfacial water and its properties are affected by the surface electrostatics.

See supplementary material for curve fitting parameters and nonresonant background.

This research was supported by NSF Grant No. CHE-1153059, AFOSR Grant No. FA9550-15-1-0184, and ARO Grant No. W911NF-14-1-0228.