Raman Scattering from Confined Liquid Films in the Sub-Nanometre Regime

Abstract

Raman spectroscopy has been used to study the confinement of octamethylcyclotetrasiloxane (OMCTS) and n-hexadecane between a prism and a lens at contact pressures of 40 MPa. Both lens and prism surfaces were optically smooth but not atomically flat. A total internal reflection geometry was employed to provide the sensitivity needed to detect liquid films of sub-nanometre thickness. For both liquids, the thickness of the residual film under load corresponded to less than a monolayer of liquid. The Raman spectra of the confined liquids were identical or very similar to that of the bulk liquid. Similar results were obtained for hexadecane confined between two surfaces coated with a Langmuir-Blodgett monolayer of a fatty acid. We infer that the liquids do not form a boundary layer under these conditions but rather they are squeezed out of the contact under the modest pressure applied. We ascribe the residual signal to liquid trapped in scratches or other defects on the surfaces.

Appendix

The evanescent wave of a totally internally reflected laser can be used to determine the thickness of a confined liquid, using the relative strengths of the Raman spectrum of a thick film and that of the confined film (see Fig. 1b). The electric field intensity of the evanescent wave can be expressed as a function of the interfacial electric field, E ₀, and the distance from the interface, z:

$$ \hbox{E}=\hbox{E}_0\exp\left({-z/d_p}\right) $$

(A1)

where d _p is the penetration depth of the evanescent wave, given by

$$ d_p=\frac{\lambda}{2\pi n_i \left({\sin^2\theta_i-n_{ti}^2}\right)^{1/2}} $$

(A2)

where λ is the wavelength of the light, θ _i is the incident angle, and n _ti is the ratio of the refractive indices of the transmitted and incident media, respectively (n _t /n _i ).

Raman scattering intensity is proportional to the square of the electric field. The intensity (I _thick ) of the Raman scattering from a thick film of liquid (thickness >> d _p ) is proportional to the integral of the electric field strength over the depth of the evanescent wave:

$$ \begin{array}{l} I_{thick}\propto\int_0^\infty{\hbox{E}^2dz} \\ \propto\frac{1}{2}\hbox{E}_0^2 d_p \\ \end{array} $$

(A3)

In the case of a thin film of liquid at the solid–solid interface, the intensity of the Raman scattering is proportional to the interfacial electric field multiplied by the thickness of the film:

$$ I_{thin}\propto\hbox{E}_0^2 d_t $$

(A4)

The interfacial electric field is not the same at the solid–liquid (E_0,s-l ) and solid–solid interfaces (E_0,s-s ). Dividing Eq. A3 by Eq. A4 yields an expression for the thickness of the thin film:

$$ d_t=\frac{\hbox{E}_{0,s-l}^2}{\hbox{E}_{0,s-s}^2}\frac{I_{thin} d_p}{2I_{thick}} $$

(A5)

If the incident electric field is the same in both cases, the ratio E ²_0,s-l /E ²_0,s-s can be replaced by the corresponding ratio of the Fresnel coefficients, K, that express the interfacial electric field in terms the incident field.

$$ d_t=\frac{\left|{K_{s,y}^{sol-liq}}\right|^2}{\left|{K_{s,y}^{sol-sol}} \right|^2}\frac{I_{thin}d_p}{2I_{thick}} $$

(A6)

For s-polarised light, the real and imaginary parts of the Fresnel coefficients are

$$ \hbox{Re}(K_{s,y})=\frac{2\cos^2\theta_i}{1-n_{ti}^2} $$

(A7)

$$ \hbox{Im}(K_{s,y})=\frac{-2\cos\theta_i(\sin^2\theta_i-n_{ti}^2) ^{1/2}}{1-n_{ti}^2} $$

(A8)