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Structure of DPPC Monolayers at the Air/Buffer Interface: A Neutron Reflectometry and Ellipsometry Study

Authors:
  • The University of Manchester / Institut Laue Langevin

Abstract and Figures

Langmuir monolayers of 1,2-dipalmitoyl-sn-glycerol-3-phosphocholine, known as DPPC, at the air/water interface are extensively used as model systems of biomembranes and pulmonary surfactant. The properties of these monolayers have been mainly investigated by surface pressure–area isotherms coupled with different complementary techniques such as Brewster angle microscopy, for example. Several attempts using neutron reflectometry (NR) or ellipsometry have also appeared in the literature. Here, we report structural information obtained by using NR and ellipsometry on DPPC monolayers in the liquid condensed phase. On one side, NR can resolve the thickness of the aliphatic tails and the degree of hydration of the polar headgroups. On the other side, ellipsometry gives information on the refractive index and, therefore, on the physical state of the monolayer. The thickness and surface excess obtained by multiple-angle-of-incidence ellipsometry (MAIE) is compared with the results from NR measurements yielding a good agreement. Besides, a novel approach is reported to calculate the optical anisotropy of the DPPC monolayer that depends on the orientation of the aliphatic chains. The results from both NR and ellipsometry are also discussed in the context of the existing results for DPPC monolayers at the air/water interface. The differences observed are rationalized by the presence of buffer molecules interacting with phospholipids.
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Coatings 2020, 10, 507; doi:10.3390/coatings10060507 www.mdpi.com/journal/coatings
Article
Structure of DPPC Monolayers at the Air/Buffer
Interface: A Neutron Reflectometry and Ellipsometry
Study
Javier Carrascosa-Tejedor
1,2,†
, Andreas Santamaria
1,3,†
, Daniel Pereira
1
and Armando Maestro
1,
*
1
Large Scale Structures Group, Institut Laue-Langevin, 71 Avenue des Martyrs, 38042 Grenoble, Cedex 9,
France; carrascosa-tejedor@ill.fr (J.C.-T.); santamariaa@ill.fr (A.S.); pereirad@ill.fr (D.P.)
2
Division of Pharmacy and Optometry, University of Manchester, Manchester M13 9PT, UK
3
Departamento de Química - Física I, Facultad de Ciencias Químicas, Universidad Complutense de Madrid,
Ciudad Universitaria s/n, 28040 Madrid, Spain
* Correspondence: maestro@ill.fr
† These authors contributed equally to this work.
Received: 1 April 2020; Accepted: 21 May 2020; Published: 26 May 2020
Abstract: Langmuir monolayers of 1,2-dipalmitoyl-sn-glycerol-3-phosphocholine, known as DPPC,
at the air/water interface are extensively used as model systems of biomembranes and pulmonary
surfactant. The properties of these monolayers have been mainly investigated by surface pressure–
area isotherms coupled with different complementary techniques such as Brewster angle
microscopy, for example. Several attempts using neutron reflectometry (NR) or ellipsometry have
also appeared in the literature. Here, we report structural information obtained by using NR and
ellipsometry on DPPC monolayers in the liquid condensed phase. On one side, NR can resolve the
thickness of the aliphatic tails and the degree of hydration of the polar headgroups. On the other
side, ellipsometry gives information on the refractive index and, therefore, on the physical state of
the monolayer. The thickness and surface excess obtained by multiple-angle-of-incidence
ellipsometry (MAIE) is compared with the results from NR measurements yielding a good
agreement. Besides, a novel approach is reported to calculate the optical anisotropy of the DPPC
monolayer that depends on the orientation of the aliphatic chains. The results from both NR and
ellipsometry are also discussed in the context of the existing results for DPPC monolayers at the
air/water interface. The differences observed are rationalized by the presence of buffer molecules
interacting with phospholipids.
Keywords: neutron reflectometry; ellipsometry; DPPC; lipid monolayers; air/water interface
1. Introduction
Synthetic in vitro lipid mono- and bilayers, as well as uni- and multi-lamellar vesicles, can be
considered as simple biomembrane models. For more than 20 years, 1,2-dipalmitoyl-sn-glycerol-3-
phosphocholine (DPPC) has been widely exploited to mimic plasma membranes or lung surfactant,
mostly in the form of monolayers at the air/water interface. Indeed, phospholipids with 16- and 18-
carbon fatty acids chains are the most abundant in plasma membranes [1,2]. DPPC is, therefore, a
well-studied lipid. Besides, DPPC has being used alone or in combination with other lipids, to study
the interaction of biomembrane with proteins [3,4], anticancer [5–8] and antifungal [9] compounds,
and small molecules of biological relevance, such as cholesterol [10], hormones [11], and antibiotics
[12]. Its handling simplicity, relatively low price, and stability at room temperature as well as when
exposed to air, make DPPC a versatile model system for biomedical research.
In general, phospholipid monolayers at the air/water interface can be characterized by different
techniques such as microscopy (e.g., atomic force microscopy, AFM, and Brewster angle microscopy,
Coatings 2020, 10, 507 2 of 15
BAM), scattering (e.g., neutron reflectometry, NR, and X-ray reflectometry, XRR), and ellipsometric
and spectroscopic (e.g., polarization modulation infrared reflection–absorption spectroscopy)
techniques, together with surface pressure-area (Π-A) isotherms. Currently, there are many
outstanding examples of the usefulness of this combinatorial approach, exploited to study DPPC
monolayers structure and properties [13,14] as well as their interaction with different cations [15],
nanoparticles [16], graphite-based compounds [17], and molecules of biological relevance, such as
proteins [4,18], small peptides [19], and antibiotics [12].
Different techniques have been used to study the structure and optical properties of lipid
monolayers. Indeed, the refractive index of the film (nF) in combination with the reflectivity allows
obtaining the thickness (dF) of the monolayers. Kienle et al. successfully used multiple beam
interferometry to determine simultaneously nF and dF of DPPC and DPPE (1,2-dipalmitoyl-sn-
glycero-3-phosphoethanolamine) supported monolayers at high surface pressures [20]. The results
obtained by this technique were in good agreement with those obtained by XRR and AFM. Another
approach to determine nF of monolayers at the air/water interface is looking at the minimum of the
reflectivity as a function of the refractive index of the subphase. Pusterla et al. used this approach
varying the concentration of glycerol or sucrose in the subphase, with known refractive indices [21];
the refractive index of the monolayer is equal to the one of the subphase when the reflectivity is
minimum. Besides, knowing the refractive index and the reflectivity they calculated dF. The
determination of the increment of the refractive index with concentration (dn/dc) constitutes another
alternative to obtain nF. The subsequent application of the lipid density to the dn/dc provides nF [22].
However, nF can slightly vary with the surface pressure, especially from one phase to another, so it is
necessary to take into account the physical state of the monolayer to know its nF [23]. NR has also been
widely exploited to perform studies at the air/water interface to investigate the structure and
properties of lipid monolayers [24–26]. This technique enables complete structural characterization
of the monolayers, giving information about the chemical composition along the axis normal to the
interface, the thickness of both polar headgroups layer and hydrophobic tails layer when a two-layer
model is used to interpret the data. Through NR it is also possible to determine the hydration degree
of the lipids, as well as the surface excess and the area per molecule at a certain value of surface
pressure [27]. Hence, NR is a very powerful tool to study lipid monolayers at the air/water interface.
Traditionally, ellipsometry has been one of the most exploited techniques to study surfactant
and lipid monolayers at the air/water interface [28,29]. It gives access to the determination of the
thickness and the refractive index of films, and it is useful to investigate the interaction of monolayers
with different molecules such as proteins [30,31] or nanoparticles [32,33] through time/spatial
resolved experiments. Nevertheless, the simultaneous determination of the nF and the dF for
Langmuir films at the air/water interface with dF << λ by the measurement of the phase shift at a fixed
angle of incidence, can give inaccurate results due to the strong coupling of the parameters [29,34].
The combination of ellipsometry with other techniques that give access to the determination of one
of the parameters allows the accurate determination of the other one by ellipsometry [35,36].
Benjamins et al. developed a method for the study of films at liquid interfaces by ellipsometry without
assumptions of the thickness or the refractive index [37]. They demonstrated that the combination of
measurements performed for the same system using D2O and H2O as the subphase, i.e., different
refractive indices of the subphase, give enough additional information to determine the amount of
material adsorbed.
In this work, we use the combination of two reflection techniques, NR and ellipsometry, and
surface pressure measurements to determine the interfacial structure and the optical properties,
including the refractive index anisotropy, of a condensed DPPC monolayer at the air/buffer interface
(see Figure 1). Besides, we show how HKM buffer molecules (see composition below), widely
exploited in biological assays, are responsible for the differences observed in the structure and
density of DPPC monolayers.
This work reports complementary measurements from two different methods. On one hand,
NR, which has been demonstrated to be a suitable technique for the investigation of the structure at
the sub-nm scale of thin films, allowed us to determine the thickness of the aliphatic chains and the
Coatings 2020, 10, 507 3 of 15
level of hydration of the polar headgroups of the DPPC monolayer. On the other hand, we propose
a novel ellipsometric method to determine both the surface excess and the optical anisotropy shown
by the DPPC monolayer in the condensed phase that depends on the orientation of the aliphatic chains.
(a) (b)
(c) (d)
Figure 1. (a) Structure formula of DPPC. The polar headgroup is depicted in green and the
hydrophobic tails in violet following a two-layer model proposed in the main text. A green sphere
and a violet cylinder are drawn to better show V
m_heads
and V
m_tails
, respectively. (b) The scheme
representing the main electrostatic interactions between the phospholipids molecules with the ions
composing the buffer: the magnesium cation is depicted as a red sphere, while the acetate anion is
depicted as a green sphere. We deduce that these interactions have an influence on DPPC monolayer
structure. Bottom panel compares neutron reflectometry (c) and ellipsometry (d) principles of
measurement. In the case of NR, a two-layer model can be exploited in order to get both the thickness
of the headgroups (t
heads
) and the one of the tails (t
tails
); indeed, the two-layer model is shown, depicting
the heads in green and the tails in violet. Moreover, NR also gives information about the fraction of
water per polar headgroup (f
w_heads
) and the roughness of the interfaces (r), whose value depends on
the water capillary waves. The angle of incidence of the neutron beam (θ) and the scattering vector,
or momentum transfer, (Q
Z
) are shown. On the other hand, ellipsometry does not disentangle the
contribution of the headgroup and the aliphatic chains to the thickness as NR. In addition, the
roughness is considered to be equal to zero (as an ideal interface). The incoming and the reflected
light beams, whose electric field is divided in parallel (E
p
) and perpendicular (E
s
) components, are
shown. Besides, the angle of incidence (AOI) and the ellipsometric angle Ψ are shown.
2. Materials and Methods
2.1. Materials
Hydrogenous DPPC (h-DPPC) and chain-deuterated DPPC (d62-DPPC) were purchased as
powder from Avanti Polar Lipids (>99%, Alabaster, AL, USA). Solutions of 1 mg·mL
1
of h-DPPC,
d62-DPPC, and h-DPPC/d62-DPPC (95:5 mol %) mixture, from now on contrast matched DPPC (cm-
DPPC), were prepared in chloroform stabilized with ethanol (99.8%; Sigma Aldrich, St. Louis, MO,
USA). Ultra-pure water was generated by passing deionized water through a Milli-Q unit (total
Coatings 2020, 10, 507 4 of 15
organic content = 4 ppb; resistivity = 18 mΩ·cm, Millipore, Burlington, MA, USA). D2O (99.9%) was
purchased from Sigma Aldrich and used as received.
The experiments were performed in HKM buffer pH = 7.2, whose composition is the following:
25 mM HEPES (4-(2-hydroxyethyl)piperazine-1-ethanesulfonic acid and N-(2-hydroxyethyl)piperazine-
N’-(2-ethanesulfonic acid)), 125 mM potassium acetate, 5 mM magnesium acetate, and 1 mM DTT
(threo-1,4-dimercapto-2,3-butanediol, DL-dithiothreitol, Cleland’s reagent, and DTT). HEPES (in
solution, 1 M in H2O, and powder 99.5%), potassium acetate (99.0%), magnesium acetate (99.0%),
and DTT (99.0%) were purchased from Sigma Aldrich.
2.2. Surface Pressure-Area Isotherm
The surface pressure (Π)-Area (A) isotherm of h-DPPC was measured using a Langmuir trough
(Kibron, Finland) with a maximum area of 166.4 cm2. The trough was carefully cleaned with ethanol
and Milli-Q water before filling it with 120 mL of HKM buffer. Subsequently, the solution of h-DPPC
with a concentration of 0.1 mg·mL1 was spread over the subphase using a Hamilton microsyringe
(Hamilton Co., Reno, NV, USA) with a precision of 1 μL. After the chloroform was evaporated for
about 20 min, the variation of surface pressure during three different compression/expansion cycles
was recorded using a Wilhelmy plate made of filter paper and applying a barrier speed of 5 cm2·min1.
The same cleaning and experiment preparation methods were followed for the NR and ellipsometry
measurements. In all the experiments performed in this work, the temperature of the subphase was
maintained at 21.0 ± 0.5 °C. Finally, it should be noted here that parameters such as the compression
rate, the spreading solvent, the geometry and the dimensions of the trough, the temperature, or the
composition of the subphase can affect the resulting isotherm [38]. In view of this, we compare our
data with other isotherms performed in a similar way, including a similar compression ratio and
spreading solvent.
2.3. Neutron Reflectometry Data Acquisition
Neutron reflectometry (NR) experiments were performed on FIGARO, a time-of-flight
reflectometer [27,39,40] at the Institut Laue-Langevin, Grenoble (France). Two different angles of
incidence (θ1 = 0.6° and θ2 = 3.7°) and a wavelength resolution of 7% dλ/λ were used, yielding a
momentum transfer of 7 × 103 Å1 < QZ < 0.25 Å1, normal to the interface, and defined as follows:
𝑄=
λ
sin(ϑ) (1)
where λ is the wavelength of the neutron beam. Usually, reflectivity (R) is defined as the ratio of the
intensity of the neutrons scattered from the air/water interface over the incident intensity of the
neutron beam. The measured R(QZ) profile is linked to an in plane-averaged scattering length density
(SLD) profile perpendicular to the interface, which is a measure of the coherent scattering cross-
section of the molecular species that constitutes each interfacial layer. The data were reduced using
COSMOS [41]. Data of the samples were normalized to a measurement of pure D2O.
NR experiments were performed using HKM buffer prepared with a mixture 8:92 V/V % of
D2O:H2O as a solvent, generally known as air contrast matched water (ACMW) since its scattering
length density is equal to the one of air, i.e., equals to zero. h-DPPC, cm-DPPC (with an SLD of the
aliphatic tails equals to zero), and d62-DPPC monolayers were prepared using a Langmuir trough
(NIMA, Coventry, UK) with a total area of 354 cm2. The volume of HKM buffer used to fill the trough
was 200 mL. We compressed the monolayer with a barrier speed of 10 cm2·min1 until Π = 30 mN·m1
and we used the pressure control to keep the pressure constant along the reflectivity measurements.
2.4. NR Data Modeling
The data analysis was performed using AuroreNR software (v5.0) [42]. A two-layer model was
used to fit the data, dividing surface-active molecules between polar heads and aliphatic tails (Figure
1). It has been recently demonstrated that using this model results in a better fit of the experimental
curves [27]. The fixed parameters used in the fitting procedure (Table 1) are molecular volumes of
Coatings 2020, 10, 507 5 of 15
DPPC heads (Vm_heads) and tails (Vm_tails) [43,44] and the total scattering length of DPPC heads (Σbheads)
and tails (Σbtails). Heads-layer thickness (theads) was calculated from the Vm_heads, and finally, the
roughness (r) of the three interfaces (i.e., air/tails-layer, tails-layer/heads-layer, and heads-
layer/subphase) was assumed identical following the approach reported by Campbell et al. [27].
Besides, its value was consistent with the presence of capillary waves [45]. A real interface is
characterized by a finite roughness, whose minimum value depends on the capillary waves of the
subphase [45,46]. Therefore, the change in SLD along the z-axis of a real interface is described here
by the SLD profile of the ideal interface modulated by an error function, ERF [47]:
ERF𝑧−𝑧
σ/
2=2
πe
d𝑡

/
(2)
where z0 and σ indicate the position and the roughness (respectively) of the interface between the layers.
Table 1. Fixed parameters used for data modeling. The molecular volumes of h-DPPC, cm-DPPC, and
d62-DPPC are equal; the only difference between the sample parameters is the value of the total
scattering length of the tails Σbtail. One can calculate the scattering length density (SLD) values shown
considering b and Vm (SLD = Σb/Vm).
Fixed Parameters h-DPPC cm-DPPC d62-DPPC
Vm_heads3) 319 319 319
Σbhead (105 Å) 60.06 60.06 60.06
SLDhead (106 Å2) 1.88 1.88 1.88
Vm_tails3) 825 825 825
Σbtail (105 Å) 32.50 0 612.98
SLDtails (106 Å2) 0.39 0 7.43
ftails (%) 100 100 100
Experimental data of h-DPPC, cm-DPPC and d62-DPPC were fitted together. Thus, the
ambiguity in the interpretation of the sample structure, which may arise from the different sensitivity
that the curves exhibit with respect to the different sample components, is significantly reduced.
Using this approach, the variables determined through the fitting procedure were solely the surface
roughness (r), the thickness of the tails-layer (ttails), and the heads volume fraction (fheads), whose value
was constrained to ensure the same surface excess (Γ) of tails Γtails and heads Γhead, calculated as
follows: Γ=SLD𝑡
𝑓
Σ𝑏N (3)
where Σbi and fi are the total scattering length and the volume fraction of the i-th component (tails or
heads), respectively, and NA is the Avogadro’s number. While the tails volume fraction ftails was fixed
to unity (i.e., 100%), for the determination of fheads the solvation of the polar headgroups was taken
into account. This yields the following equation:
𝑓
=𝑡𝑉
_

𝑡𝑉
_
 (4)
2.5. Ellipsometry
Ellipsometry experiments were performed on a Picometer Light ellipsometer (Beaglehole
Instruments, Kelburn, New Zealand) using a He-Ne laser with λ = 632 nm. The Langmuir trough
used to record the isotherm was coupled with the ellipsometer to measure and control the surface
pressure of the lipid monolayer during the measurements of the ellipsometric angles. We studied a
DPPC monolayer at the air/buffer interface by measuring the ellipsometric angles as a function of the
angle of incidence, AOI, at Π = 30 mN·m1. The range of AOI was 45°–70° with a step of 0.5°.
Ellipsometry is a non-destructive optical technique widely used for the study of surfaces and
thin films [28,48]. It is based on the determination of the polarization changes that light undergoes
Coatings 2020, 10, 507 6 of 15
when it is reflected at an interface. The reflection coefficients parallel and perpendicular to the plane
of incidence, rp and rs respectively, are related to the ellipsometric angles Δ, and Ψ. This relationship
is known as ellipticity, ρ, and is defined by the following equation:
ρ=𝑟
𝑟=tanΨe∆ (5)
where ρ is the ellipticity that depends on the AOI, the wavelength of the light and both the thickness
and the dielectrical properties of the material on which the reflection of the light beam occurs.
Although the ellipsometric angles are experimentally easily accessible, they do not provide direct
access to the refractive index and the thickness of the lipid monolayer. Thus, it is necessary to model
the experimental sets of Δ and Ψ vs. AOI to determine dF and nF. For the data analysis, we constructed
a slab model considering the profile of refractive indices perpendicular to the surface. In contrast to NR,
ellipsometry cannot distinguish between heads and tails of lipid molecules, and the different layers are
considered as one homogenous layer with negligible roughness (see Figure 1). Therefore, the model
used in this work consisted of one slab formed by the lipid monolayer characterized by nF and dF.
Once constructed the model, we fitted the data of Δ and Ψ vs. AOI using a numeric nonlinear
minimization procedure, specifically, a trust-region reflective algorithm [49]. This method is based on
the determination of the ellipsometric angles of the model that minimizes the differences with those
experimentally obtained (a more detailed explanation can be found in references [49–51]). For the
calculation of Δ and Ψ of the model, we used a power series expansion to the first order of the relative
film thickness (2πdF/λ) that allows us to relate ρ, i.e., Δ and Ψ, with nF and dF as follows:
ρ≈ρ+𝑖ρ2π𝑑
λ
(6)
where ρ0 is the ellipsometric ratio of the ambient/substrate interface and ρ’ (Equation (7)) is a linear
coefficient defined by the refractive indices of the air and the subphase, n1 and n2, respectively, and
the incident and transmission angles, αinc and αtra, respectively.
ρ=−2 𝑛
𝑛−𝑛sin)cos )
cos−α)(𝑛−𝑛)(𝑛−𝑛)
𝑛 (7)
Drude reported this approximation for the first time based on the fact that the terms of a higher
order than the first are negligible when the thickness of the film is very small [34,52]. Therefore, the
Equations (5)–(7) provide the values of Δ and Ψ for given values of nF and dF. Finally, the variation of
nF and dF allows one to obtain the real parameters of the film as those that minimizes the differences
between the calculated ellipsometric angles and those experimentally obtained. The function
minimized and used to determine the quality of a given solution is the squared deviation (χ2) between
measured and calculated ellipsometric angles and it is defined by:
χ=1
𝑁−𝑀Δ()−Δ()
δ() +Ψ()−Ψ()
δ()
 (8)
where N is the number of points, M is the number of parameters determined (i.e., two parameters, dF
and nF), Δexp and Δmodel correspond to the ellipsometric angle Δ experimentally obtained and the
calculated for the model, respectively, and δΔ the uncertainty of the i-th experimental Δ or Ψ value.
3. Results
3.1. Π-A Isotherm
Figure 2a shows the Π-A isotherm for DPPC in the HKM buffer. DPPC shows a liquid expanded
(LE) phase at a very low surface pressure, followed by a minor liquid expanded–liquid condensed
(LE–LC) coexistence region at Π 5 mN·m1. Further compression yields a LC phase, characterized
by a long range molecular order, until it reaches the collapse at Π 54 mN·m1. The Π-A isotherm
does not show a well-defined LE–LC coexistence region as DPPC on water, characterized by a well-
Coatings 2020, 10, 507 7 of 15
defined plateau of coexistence [27,38]. In Figure 2b, we report the corresponding compressional
elastic modulus Cs1, calculated from the surface pressure isotherm following
𝐶=−
𝐴
∂Π
𝐴
(9)
where Π represents the surface pressure and A the surface area. The Π-A isotherm shown in Figure
2a is quite similar to those previously reported in the literature for DPPC in water, consequently, we
interpret them in a similar way [27]. At increasing Π, DPPC molecules are pushed closer and the
compressional elastic modulus increases until it reaches a maximum. The low Π region is commonly
assigned to a 2D liquid expanded state (LE). A minimum in the compression modulus at Π 5
mN·m1, is commonly attributed to the existence of a LE–LC phase transition, which can be more
clearly observed than the slight pseudo plateau in the isotherm (Figure 2a). The global maximum
value of Cs1 is 130 mN·m1, which corresponds to the LC phase. The values of Cs1 in this LC phase
are smaller than the ones observed for DPPC at the air/water interface, which present a maximum at
Cs1 230 mN·m1 [27], indicating a less condensed monolayer. Importantly, Figure 2 shows that a
DPPC monolayer in the presence of buffer containing divalent salts exhibits more lateral
compressibility due to a less acyl chain compaction, and, therefore, is more permeable [53].
(a) (b)
Figure 2. (a) Π-A isotherm of a DPPC monolayer at the air/buffer interface and (b) corresponding Cs1
as a function of Π.
3.2. NR Results
Neutron reflectometry measurements were performed to study the structure of DPPC
monolayers in the LC phase. In particular, we selected a sample with a surface pressure value of 30
mN·m1 corresponding to an area per molecule of 53.8 Å2, well above the LE–LC coexistence phase.
This guarantees a laterally homogeneous interface on the length scale of the in-plane neutron
coherence length, on the order of several microns, and implies that the measured NR can be
correlated with the SLD depth profile averaged across the interfacial area delimited by this coherence
length. The reflectivity profiles were recorded over the whole Q-range accessible in three isotopic
contrasts: h-DPPC, cm-DPPC, and d62-DPPC in ACMW as shown in Figure 3a. As a reference, the
measurement of the bare air/D2O interface is shown also in Figure 3a, including a fit to the data that
corresponds to a roughness, r0, of 2.8 ± 0.1 Å in agreement with the theoretical value expected for
thermally excited capillary waves (~𝑘𝑇γ
), with γ0 being the interfacial tension of the bare D2O
interface [45,46].
The neutron reflectivity profiles were fitted according to a two-layer model, based on the model
recently reported by Campbell et al. [27]. In detail, the model consists of a first layer containing the
lipid aliphatic tails in contact with air and, a second one, containing the polar headgroups submerged
in the aqueous subphase (see Figure 1a). All parameters used to describe both layers (such as the
values of Σb and molecular volumes) are included in Table 1. The best fit of the reflectivity profiles
measured is also included in Figure 3a as solid lines. The resulting SLD profiles across the interface
are plotted in Figure 3b.
Coatings 2020, 10, 507 8 of 15
(a) (b)
(c) (d)
Figure 3. (a) Neutron reflectivity data of pure D2O interface (black circle), h-DPPC (red squares), cm-
DPPC (blue triangles), and d62-DPPC (magenta diamonds) monolayers at Π = 30 mN·m1 in HKM-
ACMW. The fitting curves of the bare D2O interface (orange curve), h-DPPC (red), cm-DPPC (blue),
and d62-DPPC (magenta) monolayers are shown. The χ2 value is 2. The figure is displayed on an
R(Qz)Qz4 scale to highlight the quality of the fits at high Qz values. (b) SLD profiles normal to the
interface of monolayers of h-DPPC (red), cm-DPPC (blue), and d62-DPPC (magenta) monolayers at
Π = 30 mN·m1. (c) Volume fraction profiles normal to the interface of monolayers to highlight the
distribution of tails (violet) and heads (green). (d) Cross-sectional area profiles normal to the interface
of monolayers to highlight the distribution of tails (violet) and heads (green). Note that the area of the
head-groups here does not consider the hydration.
The structural parameters obtained from the fits are summarized in Table 2. The roughness of
the three interfaces (air/tails-layer, tails-layer/heads-layer, and heads-layer/subphase) was
constrained to be equal. The value obtained from the fitting is 3.0 ± 0.5 Å, which is perfectly consistent
with the presence of capillary waves due to thermal fluctuations (usually estimated through the
relation: 𝑟 ≈ 𝑟γ(γ−Π) [54,55]). The value of the thickness of DPPC monolayer is 23.5 Å, with
15.0 Å corresponding to the aliphatic tails in contact with air. Using the parameters from Tables 1 and
2, the variation of the volume fraction, fDPPC(z), with the distance to the interface, was calculated using
the difference of two error functions as follows
𝑓(𝑧)=
1
2
𝑓
ERF𝑧
𝑟2
−ERF 𝑧−𝑡
𝑟2
,0≤𝑧≤𝑡
1
2
𝑓
ERF𝑧
𝑟
2
−ERF 𝑧−𝑡
𝑟
2
,𝑡≤𝑧≤𝑡+𝑡
(10)
The structural information elucidated by NR on DPPC monolayers can be better interpreted,
therefore, by the volume fraction profiles and the corresponding cross-sectional area profiles as a
function of the distance from the interface, which are shown in Figure 3c,d, respectively. Such as the
volume fraction, the cross-sectional area profile is modulated by the same error function and it is
calculated as follows:
0.00 0.05 0.10 0.15 0.20 0.25 0.30
10
-14
10
-13
10
-12
10
-11
10
-10
10
-9
10
-8
10
-7
R(Q
z
) Q
4
-4
)
Q
z
-1
)
-10-5 0 5 101520253035
-1
0
1
2
3
4
5
6
7
8
SLD (10
-6
Å
-2
)
z (Å)
-10-5 0 5 101520253035
0
10
20
30
40
50
60
Cross-sectional Area (Å
2
)
z
(
Å
)
-10-5 0 5 101520253035
0.0
0.2
0.4
0.6
0.8
1.0
Volume fraction, f
z (Å)
Coatings 2020, 10, 507 9 of 15
𝐴(𝑧)=
𝑉_
2 𝑡𝑓ERF𝑧
𝑟2
−ERF 𝑧−𝑡
𝑟2
,0𝑧𝑡
𝑉_
2 𝑡
𝑓
ERF𝑧
𝑟
2
−ERF 𝑧−𝑡
𝑟
2
,𝑡≤𝑧≤𝑡+𝑡
(11)
The values used to calculate the cross-sectional area from Equation (11) are collected from Tables
1 and 2.
Table 2. Parameters resulting from the data modeling. *The hydration degree of the headgroups are
considered here.
Fitting Parameters h-DPPC, cm-DPPC, Π = 30 mN·m1
theads (Å) 8.5
ttails (Å) 15.0 ± 0.5
fheads (%) 68 ± 1
Atails2) 55.2 ± 0.3
Aheads*2) 55.2 ± 0.3
Γtails (µmol·m2) 3.0 ± 0.1
Γheads (µmol·m2) 3.0 ± 0.1
r (Å) 3.0 ± 0.5
3.3. Ellipsometry
We performed ellipsometry measurements by exploring the variation of the ellipsometric angles
Δ and Ψ as a function of the AOI. In Figure 4a,b, we show the variation of Δ and Ψ for the air/water
interface, as a reference measurement, the air/buffer interface, and the h-DPPC monolayer (Π = 30
mN·m1) spread on the HKM buffer. Firstly, both interfaces air/water and air/buffer yield similar results,
which allows us to consider that the refractive index of the buffer does not change to that of water.
Nevertheless, the DPPC monolayer at the air/buffer interface shows different values of Δ with respect
to the ones obtained for the HKM buffer and water, particularly at values of the angle of incidence close
to the Brewster angle. This is the consequence of the change in the state of polarization of the light beam
when it interacts with the lipid molecules instead of the bare air/buffer interface. To explain the
experimental data, we consider a one-layer optically anisotropic model for the DPPC monolayer (as
described in the methods section) with an average refractive index 𝑛=
𝑛+
𝑛. Considering the
DPPC monolayer in LC as an optically uniaxial system (uniaxially birefringent), the anisotropy can be
defined as Δn = nz nx, being nx and nz the refractive indexes of the layer parallel and perpendicular to
the interface, respectively [35]. In our first approach, we simultaneously get the values of nF and dF that
better fit the experimental data thus yielding the lowest χ2 value. In detail, we simultaneously fit the
variation of Δ and Ψ with AOI shown in Figure 4a,b with different nF dF initial values covering a wide
range of nF (from 1.33, corresponding to the bulk phase, to 1.60) and dF (from 0 to 30 Å). Concretely, the
combination of 300 values of both parameters resulted in 9 × 105 nF dF pairs of solutions with a given
χ2. This approach allowed us to build a matrix shown as a color-map in Figure 4c. This map presents a
clear dark blue area in the region defined by nF [1.44,1.60] and dF [10Å,30Å] that correspond to
values of χ2 1. A priori, it is difficult to select a single pair of values in this area with the minimum χ2.
In the following, we show how we can extract the surface excess and the optical anisotropy of the DPPC
monolayer from further analysis of the results shown in Figure 4c and compare with the ones obtained
by neutron reflectometry.
Coatings 2020, 10, 507 10 of 15
(a) (b)
(c) (d)
Figure 4. (a) Δ and (b) Ψ vs. AOI of H2O (blue diamonds), HKM buffer (red circles), and DPPC (green
circles). The green line corresponds to the ellipsometric angles values obtained from the fit that
minimizes the χ2. (c) Colormap of the squared deviation χ2 between measured and calculated Δ and
Ψ of a DPPC monolayer at the air/buffer interface at Π = 30 mN·m1. Each pixel of the figure represents
a value of χ2 obtained from the fit of Δ and Ψ vs. AOI using the correspondent values of dF and nF. (d)
Normal distribution of Γ values correspondent to the region of lowest χ2.
Approach 1: Calculation of the surface excess of DPPC monolayer using de Feitjer’s equation.
We first used the sets of values (nF, dF) that yields χ2 1 in Figure 4c to calculate the surface excess of
DPPC monolayers (Γ) by using de Feitjer’s equation [56]:
Γ=𝑑(𝑛−𝑛)
d𝑛 d𝑐
(12)
Here dn/dc is the refractive index increment. In detail, we used a value of 0.138 mL·g1 obtained
from reference [22]. nbulk is the refractive index of the bulk phase, here we used a value of 1.335 that
corresponds to water taking into account that the presence of buffer does not change the ellipsometry
angles as shown in Figure 4a,b. Figure 4d reports the distribution of Γ calculated for the different
pairs of (nF, dF) values yielding the lowest χ2. Concretely, we have used all the values that satisfies χ2
1.5χ2min, where χ2min accounts for the best value. The tendency shown by Γ can be modelled by a normal
distribution (red line in Figure 4d) obtaining Γ = 3.0 ± 0.2 µmol·m2. This result is in further agreement
with the values of Γtails, and Γheads obtained by NR.
Approach 2: A new method to calculate the anisotropy of the refractive index nF. We present
here for the first time a novel approach to calculate the anisotropy parameter Δn as well as nx and nz,
which are the refractive indices corresponding to the aliphatic tails parallel and normal to the surface,
respectively. Let us first consider here that the hydrophilic heads-layer has a refractive index close to
that of the bulk due to the high level of head group hydration, 32% according to the NR data (see
Table 2) and previously demonstrated in references [23,35]. We, therefore, assumed that only the
hydrophobic aliphatic chains can be precisely detected by ellipsometry. In this context, using the
values of nF = 1.547 ± 0.005 and dF = 13.7 ± 0.3 Å that yields the best χ2 (=1.71, according to data plotted
in Figure 4c) together with a value of dΔ = Δ Δbulk for a single angle of incidence close to the Brewster
conditions, we could calculate the values of nx and nz using
Coatings 2020, 10, 507 11 of 15
d∆(AOI)=−4π𝑑
λ
𝑛sin(AOI)tan(AOI)
1− 𝑛
𝑛tan(AOI)
1
𝑛−𝑛𝑛−𝑛−𝑛+𝑛𝑛
𝑛
(13)
which comes from the separation of the real and imaginary parts in Equation (5) according to the
Drude approximation [52], and the definition of the average refractive index
𝑛=1
3(2𝑛+𝑛) (14)
In particular, we used a value of dΔ = 0.1375 rad that comes from the difference between the
value of Δ of the lipid monolayer (188.48°) and the one correspondent to the buffer (180.60°) at an
angle of incidence of 52°, for which we had the highest sensitivity as it was close to the Brewster angle
(see Figure 4a). Using the values of nF, dF and dΔ in Equations (13) and (14), we obtained nx = 1.537
and nz = 1.566 yielding an anisotropy value, Δn, of 0.029.
4. Discussion
4.1. Effect of HKM Buffer on the DPPC Monolayer Π-A Isotherm
In this work, we studied the optical and structural properties of a DPPC monolayer in the fluid
condensed phase (Π = 30 mN·m1). Looking at the Π-A isotherm and the corresponding Cs1 as a
function of the surface pressure (Figure 2), we obtained information about the different phases of the
lipid monolayer and its molecular packaging. The behavior of DPPC at the air/buffer interface is
different from the one observed using pure water. Although this is an aspect that merits future work,
there are different studies in the literature on the influence of mono and divalent cations on the
behavior of DPPC at the air/water interface that agree with our findings: the formation of a liquid-
condensed phase with higher lateral compressibility and shifted towards larger molecular areas than
the same monolayer at the air/water interface. Complexation effects of mono-, but especially, divalent
ions to amphiphilic molecules, such as phospholipids, are known to modify their orientation,
morphology and packing. These aspects have been recently evaluated by Adams et al. by studying
the influence of highly concentrated salt solutions on the behavior of DPPC monolayers at the
air/water interface [15]. The Π-A isotherms reported, together with the Brewster angle microscopy
images, showed that the presence of K+, Na+, or Mg2+ causes an expansion of the isotherm towards
higher values of area per molecule and a decrease in the compressibility modulus, especially in the
latter case. This is in full agreement with what we observed here. These authors also demonstrated
that the presence of high salt concentration disrupts lipid packing, resulting in an extension of the
liquid-expanded phase. Since we observed a slight LE–LC coexistence phase, we thought that we
were not in this situation. It is important to mention that the salt concentrations used in that study
are higher than the ones that we used. However, the general trend of the expansion of the isotherm
and the decrease of the compressibility modulus are indicators that the behavior of DPPC at the
air/water interface is affected by the constituents of the HKM buffer. Besides, in this work, there were
up to five different species that could affect the organization of DPPC at the interface. Indeed,
Bringenzu et al. studied the interaction of a protein with DPPC monolayers using a very similar buffer
and they also observed an expansion of the isotherm [57].
4.2. Influence of HKM Buffer on the Structural Parameters of DPPC Monolayers at the LC Phase
By means of NR, we reported a total thickness of the DPPC monolayer of 23.5 Å, in agreement
with literature values of DPPC in the condensed phase [20,58]. The thickness of the aliphatic chains
was found to be 15 Å by NR. This was close enough to the thickness obtained from ellipsometry (ca.
14 Å) corresponding to the best fit. Assuming a length of 19 Å of an aliphatic chain of 16-CH2 groups
in trans configuration [59], we obtained a tilting angle of 37°, a value that is higher than the value
Coatings 2020, 10, 507 12 of 15
expected for DPPC at the LC phase (27° at Π 30 mN·m1). This agrees with a decrease in the packing
density of DPPC monolayers in the presence of divalent salts from the HKM buffer (see Figure 1b).
The average refractive index nF = 1.547, found here agrees with previous values reported by Ducharme
et al. [23] and Thoma et al. [35] on the DPPC monolayer at the air/water interface. Ducharme et al.
rationalized this increase of the refractive index of lipid monolayers to the existence of condensed
phases. In addition, the value reported here for the anisotropy was slightly smaller to the one reported
by Thoma et al. (Δn = 0.05). It is well known that an increase in anisotropy is observed for DPPC
monolayers going from LE to LC. It is rationalized by the increase of all-trans configurations for the
alkyl chains. In our case, the reduced anisotropy found can also be explained by the effect of the buffer
on the packing density of the alkyl chains.
The values obtained from the fitting of both NR (Table 2) and ellipsometry yields a surface
excess, Γ, or molecular area (𝐴=1/(N×Γ)) [60], which is consistent with the one extrapolated from
the isotherm (see Figure 2a) at Π = 30 mN·m1. The value found of 55.2 Å2 is slightly larger in
comparison with the value for DPPC in water at a similar surface pressure [27]. This has been
previously attributed to the effect of the buffer molecules on the monolayer. The calculation of both
volume fraction and cross-sectional area profiles with the distance to the interface, (Figure 3c,d,
respectively) allows us to rationalize the structure of the DPPC monolayer in real-space, even
unraveling the contribution from the aliphatic chains facing the air and the solvated polar
headgroups in contact with the buffer. We observed that the solvation of the polar heads by water
molecules was about 30% of the volume fraction of the layer (see, cyan curve in Figure 3c) in
agreement with previous studies on DPPC/water interfaces [27].
4.3. Combining Neutron Reflectometry and Ellipsometry Experiments
Here, we considered that performing NR and ellipsometry experiments to study lipid
monolayers at the air/water interface is convenient due to their complementarity. On one side, the
thickness of aliphatic chains as well as the degree of hydration of the polar headgroups can be
obtained by NR whilst ellipsometry is more sensitive to the orientation of the aliphatic chains and,
therefore, to the physical state of the monolayer. Despite ellipsometry being a very versatile
technique, overcoming its limitations in obtaining the refractive index and thickness of monolayers
at the air/water interface has required to date complex mathematical calculations (see, for example
[34,61]), and/or the parallel use of another technique such as NR. However, we show here an
alternative approach to overcome those limitations and the possibility to study optically anisotropic
interfacial systems such as phospholipid monolayers in the LC phase (e.g., DPPC). Besides, we report
a method to derive the surface excess of the monolayer by the simultaneous modeling of Δ and Ψ as
a function of the angle of incidence (Figure 4) that yields a similar value than the one obtained by NR.
5. Conclusions
We firstly reported the Π-A isotherm of DPPC at the air/buffer interface. The Π-A isotherm
presented in this work shows an expansion towards higher molecular areas and a less pronounced
phase transition than that using pure water as the subphase. We attributed these differences to the
presence of cations (especially Mg2+) and HEPES in the subphase, interacting with the lipid molecules
at the interface. We have also shown how, combining NR and ellipsometry, we could get a complete
characterization of DPPC monolayers. All of the results obtained in this work are consistent with each
other, and can be rationalized due to the presence of the HKM buffer when comparing with the
literature data on DPPC thickness, molecular area, and refractive index. Therefore, the use of NR in
combination with ellipsometry is proposed as an effective and accurate method for studying the
optical properties including the anisotropy in the refractive index and the structure of lipid
monolayers in the liquid condensed phase at the air/water interface.
Author Contributions: Conceptualization, methodology, data curation and writing the manuscript by all the
authors: J.C.-T., A.S., D.P., and A.M. All authors have read and agreed to the published version of the
manuscript.
Coatings 2020, 10, 507 13 of 15
Funding: This research received no external funding.
Acknowledgments: We thank the ILL for the provision of neutron beam time on FIGARO instrument
(10.5291/ILL-DATA.TEST-3104), and the Partnership for Soft and Condensed Matter, PSCM, for the use of the
ellipsometer and the Langmuir trough. AS and JC acknowledge a PhD contract from the ILL. The authors are
grateful to Richard Campbell for a critical review of this manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
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... Here, the LE-LC coexistence region, whose identification a priori was not straightforward from the visualization of the P-A isotherm of both monolayers, was evident from the appearance of a minimum in the C s À1 profile. This minimum has been already reported for DPPC monolayers spread onto both pure water [33] and buffer (rich in Mg 2+ ) [36] subphases. Further compression yielded a LC phase for both DPPC and DPPC:PIP 2 monolayers. ...
... This low impact of PIPs on model membranes has been also observed in bilayers [11,21]. Secondly, in buffer with Mg 2+ ions, the values of C s À1 corresponding to the LC phase for DPPC:PIP 2 mixed monolayers are much lower in comparison with the DPPC monolayer [36]. However, in both systems, the values of C s À1 are remarkably smaller in comparison to those measured for DPPC monolayers in water [33]. ...
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... DPPC fulfills the first requirement, which has pushed the use of DPPC monolayers as minimal models for understanding some physico-chemical aspects related to the impact of particles in LS films. Furthermore, the interfacial behavior of this lipid has been extensively studied by many researchers [59,66,175,[183][184][185][186][187]. However, the use of DPPC as a model for understanding the performance of LS is rather limited because its inefficiency in the reservoir formation and its slow respreading at the interface during expansion. ...
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... Neutron reflectometry (NR) has been extensively used for studying structural organisation of soft matter [33][34][35][36][37][38]. This technique is advantageous when studying soft matter as it is possible to conduct experiments at atmospheric pressure and has a vertical resolution (∼0.5 nm, limited by the beam collimation and the size of the silicon blocks used) capable of resolving structure changes on the molecular scale. ...
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Specular neutron reflectometry is a powerful technique to resolve interfacial compositions and structures in soft matter. Surprisingly however, even after several decades, a universal modeling approach for the treatment of data of surfactant and phospholipid monolayers at the air/water interface has not yet been established. To address this shortcoming, first a systematic evaluation of the suitability of different models is presented. The result is a comprehensive validation of an optimum model, which is evidently much needed in the field, and which we recommend as a starting point for future data treatment. While its limitations are openly discussed, consequences of failing to take into account various key aspects are critically examined and the systematic errors quantified. On the basis of this physical framework, we go on to show for the first time that neutron reflectometry can be used to quantify directly in situ at the air/water interface the extent of acyl chain compaction of phospholipid monolayers with respect to their phase. The achieved precision of this novel quantification is ∼10%. These advances together enhance significantly the potential for exploitation in future studies data from a broad range of systems including those involving synthetic polymers, proteins, DNA, nanoparticles and drugs.
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The Refl1d program is used for modeling and fitting data from neutron and X-ray reflectometry experiments. The model of the (thin-film) samples is typically constructed of discrete layers of different scattering-length densities (SLD). Interlayer roughness is represented as an error-function transition from one layer to the next. Previous versions of the software truncated this error-function at the next interface. This strategy has the advantage of preventing layers with unbounded effective extent, but it can also result in SLD depth profiles that do not conform to the physical expectations of the users (such as introducing sharp transitions) whenever the layer roughness approaches the thickness of the layer. In this article we introduce a new version of the software in which the option is provided to extend the roughness of each layer over the entire structure; the resulting SLD profiles often more closely resemble the physical models intended by the user. Most importantly no sharp transitions are introduced by truncating the roughness, when a smooth transition is often desired when adding rough layers together.