Binary Self-assembled Monolayers for Surface Control of Liquid-Crystal Orientation: An X-ray Study
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Mat. Res. Soc. Symp. Proc. Vol. 501 ©1998 Materials Research Society
Aqz = 7x 10-' A-` where the z-axis is normal to the film surface and the x-axis is perpendicular to this normal and in the scattering plane. Specular x-ray scattering was measured for each of the films and one bare substrate. Before quantitative analysis the specular diffuse scattering was subtracted from the measured specular intensity. This subtraction is necessary for meaningful data analysis [2]. In addition, an intensity correction to the measured specular intensity was included at scattering angles below which the projected area of the incident beam exceeded the sample area [3]. X-ray Reflectivity Modeling: X-ray reflectivity has been previously used to determine the electron density profile relative to the substrate [2, 4-5]. I d(p(Z))e R(qz) = RF(qz) I9_o
dz
iqzdz
(1)
RF is the Fresnel reflectivity [2]. p is the average electron density of the material. The angle brackets in the integral denote an in-plane average over the probing area of the x-ray beam (determined by the beam coherence length and resolution). p-,. is the electron density of the substrate far from the surface. For the self-assembled monolayers the density profile (p(z)) is modeled as a series of two-dimensional strata of varying thickness Li and density pi. The interfaces between successive strata, the strata and the substrate and the strata and air are approximated by gaussian smeared steps (error function profiles) of varying width or. The derivative of this density model (utilized in Eq. 2) is 2 d(p(z)) d 2 1 Ip i-p /'Aep i,1 "_P (z-D (2 2cy+,) 0 dz i= ri+l p where D,
i j=0
Quantitative analysis of the measured x-ray reflectivity data employs Eq. 1 for standard forward modeling using a nonlinear least-squares fitting algorithm. Optimization and convergence of this algorithm provides the strata thickness, density, and interfacial gaussian widths to reconstruct the electron density profile of the monolayer [4]. The number of strata used to described the density profile of each particular monolayer is discussed in more detail below. RESULTS Silica Substrate: To provide a correct baseline for the analysis of the monolayer x-ray measurements, x-ray reflectivity was measured from a bare float-glass (fused silica) substrate. The measured specular intensity is shown in Fig. 1. The qz dependence of this scattering is not consistent with a simple gaussian roughness of the silica surface which would result in a parabolic curve on the semilog plot of Fig. 1. Instead, it was modeled using a density profile which possessed a surface region 10 ± 1.5 A thick with a relative density (p/psilica)of 0.85 ± 0.03, and substrate and air interfacial widths of 6.7 ± 0.6 A and 5.3 ± 0.2 A, respectively. The fit using these parameters is shown as a solid line on the silica reflectivity data in Fig. 1. The
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electron density profile itself is plotted in Fig. 2 and shows a smooth rolloff from the bulk silica density to that of air (essentially zero). At such a surface x-ray reflec
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