Nonspecular X-Ray Scattering from a Planar Phospholipid Multilayer

Abstract

Reflectometry and nonspecular (diffuse) X-ray scattering data are used to refine the structure parameters of planar multilayer films of saturated DPPC and DSPC phospholipids with thickness of about 400 Å formed on the surface of an aqueous suspension of silica nanoparticles about 27 nm in diameter. A consistent analysis of the scattering data shows that the hydrosol–lipid film–air structure consists of a monolayer of nanoparticles, a lamellar lipid layer, and an approximately half-filled (loose) phospholipid monolayer at the air interface. Model electron concentration profiles indicate the hydration of the lamellar structure at a level of about 6 H₂O molecules per lipid. In this case, water and Na⁺ cations are localized in the region of phosphocholine groups, which is in agreement with the results of molecular dynamics calculations of other authors. The observed roughness of the interfaces between lipid layers is at least 5 Å and is indicative of the presence of a 3–6-Å-wide noncapillary-wave structure. In our opinion, one of the possible applications of the described technology is coating the concave surface of a rotating hydrosol liquid with a lipid multilayer in an X-ray deflecting device with a whispering gallery mode.

APPENDIX

The profile ρ(z) corresponding to the multilayer structure shown in Fig. 7 can be parameterized as follows:

$$\rho (z) \approx {{P}_{1}} + {{P}_{2}} + {{P}_{3}} + \frac{1}{2}{{\rho }_{b}},$$

(A.1)

where the boundary with air is taken at z₀ = 0.

The unfilled (loose) monolayer of lipid tails of thickness l_t and density ρ_t at the interface with air is described by the first term

$${{P}_{1}} \approx \frac{1}{2}{{\rho }_{t}}{\text{erf}}\left( {\frac{z}{{\sigma \sqrt 2 }}} \right) + \frac{1}{2}({{\rho }_{2}} - {{\rho }_{t}}){\text{erf}}\left( {\frac{{z + {{l}_{t}}}}{{\sigma \sqrt 2 }}} \right),$$

(A.2)

where σ is the standard deviation of the position of the boundaries in the lipid structure from their nominal values.

A multilayer of N phospholipid bilayers is described by the periodic structure

$$\begin{gathered} {{P}_{2}} \approx \sum\limits_{j = 1}^{k = N} {\frac{1}{2}({{\rho }_{2}} - {{\rho }_{1}}){\text{erf}}\left( {\frac{{z + {{z}_{j}} - 2{{l}_{1}}}}{{\sigma \sqrt 2 }}} \right)} \\ + \frac{1}{2}({{\rho }_{p}} - {{\rho }_{2}}){\text{erf}}\left( {\frac{{z + L}}{{\sigma \sqrt 2 }}} \right), \\ \end{gathered} $$

(A.3)

where l₁ is the thickness of the layer with density ρ₁ consisting of hydrocarbon chains, l₂ is the thickness of the layer with density ρ₂ formed by polar groups, z_j = l_t + jl is the period, l = 2(l₁ + l₂) is the thickness of the bilayer, L = z_N + l₂ is the total thickness of the lipid film, and ρ_p is the electron concentration in the nanoparticle monolayer. The boundaries of the lamellar structure in Fig. 7 are formed by layers of polar groups of lipid molecules and lie in the interval (–l_t, ‒L).

The electron concentration in the monolayer of SiO₂ nanoparticles adjacent to a lipid film is described by the third term

$$\begin{gathered} {{P}_{3}} \approx \frac{1}{2}({{\rho }_{p}} - {{\rho }_{2}}){\text{erf}}\left( {\frac{{z + L}}{{{{\sigma }_{p}}\sqrt 2 }}} \right) \\ + \frac{1}{2}({{\rho }_{b}} - {{\rho }_{p}}){\text{erf}}\left( {\frac{{z + L + D}}{{{{\sigma }_{p}}\sqrt 2 }}} \right), \\ \end{gathered} $$

(A.4)

where D is the thickness of the monolayer of nanoparticles with ρ_p and σ_p is the standard deviation of the position of its boundaries from their nominal values ‒L and –(L + D).

Since σ_p ≫ σ, in a consistent analysis of data, the contribution of the inhomogeneities P₃ can be neglected. In this case, the structure factor Φ(q) of the film has the following form:

$$\Phi \approx {{\Phi }_{1}} + {{\Phi }_{2}}.$$

(A.5)

The loose monolayer of lipid tails corresponds to

$${{\Phi }_{1}}(q) \approx \frac{{\exp ( - {{\sigma }^{2}}{{q}^{2}}{\text{/}}2)}}{{{{\rho }_{b}}}}[{{\rho }_{t}} + ({{\rho }_{2}} - {{\rho }_{t}})\exp ( - iq{{l}_{t}})].$$

(A.6)

The structure factor of a multilayer of N bilayers is

$$\begin{gathered} {{\Phi }_{2}}(q) \approx \frac{{\exp ( - {{\sigma }^{2}}{{q}^{2}}{\text{/}}2)}}{{{{\rho }_{b}}}} \\ \times \sum\limits_{j = 1}^N {({{\rho }_{1}} - {{\rho }_{2}})[1 - \exp (2iq{{l}_{1}})]\exp ( - iq{{z}_{j}})} \\ + \frac{{\exp ( - {{\sigma }^{2}}{{q}^{2}}{\text{/}}2)}}{{{{\rho }_{b}}}}({{\rho }_{p}} - {{\rho }_{2}})\exp ( - iqL). \\ \end{gathered} $$

(A.7)

Note that the model of the lamellar structure is in good agreement with the spatial resolution of the available experimental data (2π/$q_{z}^{{{\text{max}}}}$ ≈ 10 Å). The use of more complex models leads to a significant increase in ambiguity in determining the values of their parameters.