Observation of buried water molecules in phospholipid membranes by
surface sum-frequency generation spectroscopy
Maria Sovago,1 Erik Vartiainen,2 and Mischa Bonn1
Institute for Atomic and Molecular Physics, Kruislaan 407, 1098 SJ, Amsterdam, The
Lappeenranta University of Technology (LUT) Box20, Fin-53851 Lappeenranta, Finland.
Supporting information:
1. SFG theory
Conventional SFG yields an intensity spectrum (ISFG) proportional with the modulus squared
of the second-order nonlinear polarization (P(2)):
I SFG  P ( 2 )   ( 2 ) EVIS EIR ,
Here, (2) represents the second-order susceptibility, EVIS and EIR are the VIS and IR electric
fields, respectively.
The second-order polarizability can be enhanced when molecules are aligned at the interface.
This alignment can be due to the presence of a local electrostatic field, E0. This field will
interact with the incident optical fields and can give rise to a third-order effect ((3)): 1-4
I SFG   ( 2 ) EVIS EIR   (3) EVIS EIR E0   NL EVIS EIR ,
With NL given by:
 NL   ( 2)   (3) E0
The magnitude of (3) can have two distinct origins. One is the contribution of the third order
electronic nonlinear polarizability (3) of a water molecules, related to the (3) as:
 (3)  N B (3) , where NB is the water bulk density. The other contribution is due to the
alignment of water molecules by the electric field E0 created at the surface. As such, the  (3)
contribution to the SFG intensity can be written as: 4
 (3)  N B  (3) 
 ( 2) 
bkT 
Where (2) and (3) are, respectively, the second- and the third-order polarizability,  is the
permanent dipole moment of the water and b is a constant determined by the particular
susceptibility element under construction. Note that we (arbitrarily) include the effect of the
charge-induced alignment of the water molecules in the 
contribution (second term in
equation (4)).
The large SFG signal observed here for DPPC and DPPE when compared with neutral
surfactants suggests 1, in fact, that the second term in equation (4) dominates over the first
term. Our findings are in good agreements with the results from SHG experiments on charged
solid-water interfaces, where the second term seems to dominate for liquid water. 4
2. MEM analysis
The application of MEM to VSFG spectra to extract to retrieve the phase and the Im[ ]
spectra, respectively, was described in detail previously.
Briefly, the phase spectrum
obtained from MEM analysis, (), is used to calculate the absolute phase spectrum, (),
and the Im[] spectrum:
 ( )   ( )   ( )
Im[  ( 2) ]  I SFG ( ) sin[ ( )   ( )   NR ]
Here, , is the normalized frequency in the frequency interval 
(with  []) and() represent the error phase.
For the spectra analyzed here, the error phase is negligible. 5 Therefore, only a correction for
the NR phase is necessary. The NR used to calculate the absolute phase for the surfactants
and lipids is listed in Table S1.
Table S1. The values of the NR phase used to correct the MEM phase spectra for the
surfactants and lipids, respectively.
The NR was chosen in the interval [0, 2] such that the following conditions are satisfied.
First, the Im[ ] should be negative in the C-H stretch region, as has been shown
Second, Im[] ≈ 0 in the regions without resonances.
Third, the C-H
resonances must appear as (negative) peaks in the Im[] at frequencies known with an
accuracy of a few cm-1, e.g. for CH3 symmetric stretch (ss) the peak position is around 2875
cm-1. 8
Furthermore, for the VSFG spectra analyzed here we used an additional restriction for NR.
For the surfactants we used the NR phase value close to the values found from the phasesensitive measurements for the cationic and anionic surfactants. 6 There, NR ≈ -2 for cationic
surfactant and NR ≈ 2 for anionic surfactant, respectively. Hence, the NR phase value changes
by a little over , as the local electric field E0 changes sign as going from a positively charged
to a negatively charged interface. The obtained Im[ ] has negative values in the C-H
stretch region, as expected,
while the values in the O-D stretch region are opposite for
OTAB and all lipids. This observation indicates that for these systems the water molecules are
oriented oppositely to the CH3 groups.
To illustrate the sensitivity of the obtained Im[ ] spectrum to the NR phase correction, we
calculated the Im[] for DPTAP monolayers for NR in the interval [-1.1, -3.0], around the
chosen NR phase value NR = -2.3 . The results are displayed in Figure S1. For NR = -1.1, the
peaks in the C-H stretch region have positive amplitudes and have a dispersive shape. On the
contrary, those peaks have negative values for NR = -3.0, and the Im[ ] spectrum is very
similar to the one obtained for NR = -2.3. Therefore we conclude that we can determine NR
with an accuracy of ~ 0.7. Within this error in the NR, there is significant uncertainty
regarding the shape of the spectrum, but we can indisputably determine the sign of the O-D
stretch vibrations and determine the orientation of the water dipoles.
As the shape of the Im[(2)] spectrum depends on the nonresonant phase, direct conclusions
about the change in the water structure near the different lipid headgroups based on changes
in the vibrational response are not fully warranted. In principle, the change of the water
structure can be determined from the change of the central frequencies of the peaks (or the
first moment of the OD intensity distribution) appearing in the Im[(2)] spectrum for the
different monolayers studied here: as the frequency of the O-D stretch increases, the strength
of the H-bonds decreases. Here, we use the first moment of the SFG intensity distribution in
the O-D stretch region of the Im[(2)] spectra to determine the change in the water structure
near the different lipids, as described in the main text.
Figure S1. Top panel: The recalculated Im[] spectra from MEM analyses for DPTAP
monolayer with various NR phase around the chosen NR phase, NR = -2.3. The NR was
chosen in such a way that the C-H modes have negative values and Im[] ≈ 0 in the
regions without resonances. Bottom panel: the same curves in the C-H stretch region. The
vertical dotted line shows the position of the CH3 symmetric stretch (2875 cm-1).
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