Roughness of free surfaces of bulk amorphous polymers as studied by x-ray surface scattering and atomic force microscopy

Abstract

The morphology of free surfaces of polyetherimide (PEI) samples has been characterized using atomic force microscopy in noncontact mode (NC-AFM), x-ray reflectivity (XRR), and x-ray diffuse scattering (XDS). PEI slabs have been prepared by molding pellets onto float glass. In order to characterize the roughness and morphology mathematically, we considered the surfaces as being self-affine with a rms roughness σ and Hurst coefficient H up to a finite correlation length ξ. NC-AFM topographs with $\sigma =61\mathrm{}\pm 6.3\AA$ showed the presence of blobs on the surface having a slight tendency to form clusters. These features are reflected in the height-height correlation function which shows the presence of “strong” short-range $({\xi }_1=1064\mathrm{}\AA ,$ $H_1=0.46)$ and “weak” long-range $({\xi }_2=14537\mathrm{}\AA ,$ $H_2=0.99)$ correlations. The detection of the specularly reflected contribution in XRR scans only gives access to σ, the lateral fluctuations being averaged out over the coherence area. Scans in XDS include the detection of the diffuse (off-specular) scattering arising from lateral correlations in the surface fluctuations profile and are hence sensitive to σ, ξ, and H. The XDS data have been analyzed by simultaneous fits using the distorted-wave Born approximation up to the first order. Calculations were performed using previously published approximations. Best fits to the experimental data provided strongly different correlations length values $(7570\mathrm{}\AA <~\xi <~1245\AA )$ indicating that the estimation of the latter by XDS is somewhat ambiguous. This is in agreement with the strong discrepancy between the correlation lengths determined with x rays and NC-AFM, which can be accounted for by the limits of the perturbation theory for interfaces with high rms roughnesses.