Novel Melt-Spun Polymer-Optical Poly(methyl methacrylate) Fibers Studied by Small-Angle X-ray Scattering

Abstract

The structural properties of novel melt-spun polymer optical fibers (POFs) are investigated by small-angle X-ray scattering. The amorphous PMMA POFs were subjected to a rapid cooling in a water quench right after extrusion in order to obtain a radial refractive index profile. Four fiber samples were investigated with small-angle X-ray scattering (SAXS). The resulting distance-distribution functions obtained from the respective equatorial and meridional SAXS data exhibit a real-space correlation peak indicative of periodic cross-sectional and axial variations in the scattering density contrast. Simple model calculations demonstrate how the structural information contained particularly in the equatorial distance distribution function can be interpreted. The respective results are qualitatively verified for one of the fiber samples by comparison of the model curve with the measured SAXS data. Eventually, the study confirms that the cross-sectional variation of the (scattering-) density is the main reason for the formation of radial refractive-index profiles in the POFs.

Keywords: fiber fabrication; graded-index profile; material characterization; measurement technique; melt-spinning; nanostructure; polymer optical fiber; scattering.

Figure 1

Example of a continuous POF fabrication process based on extrusion [5]. With this approach, only step-index fibers can be produced.

Figure 2

Schematic of the melt-spinning process based with subsequent rapid cooling in a water quench [16]. The still hot polymer filament is subjected to a rapid cooling in a water quench right below the spinning nozzle. The rapid cooling results in an inhomogeneous cooling speed over the fiber cross-section.

Figure 3

(Left) 2D-SAXS intensity distribution of the empty beam displaying an isotropic scattering. (Right) 2D-SAXS intensity distribution of the sample POF 4. The strong anisotropic equatorial and meridional scattering indicates that at least parts of the PMMA chains are highly oriented. Note that the color codes of empty beam and sample scattering are not to scale. The empty beam scattering intensity is on average about two orders of magnitude smaller than the small-angle scattering arising from the fiber sample.

Figure 4

2D SAXS intensity distributions of the four PMMA POF samples. The anisotropic equatorial and meridional scattering is present in all samples, but clearly different, which indicates a high sensitivity of the fiber nanostructure to changes in the production processes.

Figure 5

Extracted 1D SAXS intensity curves of the four POF samples. (Top row): equatorial intensities corresponding to the scattering from the fiber cross-section. (Bottom row): meridional intensities corresponding to the scattering contribution along the fiber axis.

Figure 6

Analysis of the equatorial (Top row), and meridional (Bottom row) scattering contributions using the Guinier fit and the Patterson function exemplarily shown for the sample POF 4. Note that r corresponds to a distance, i.e., for the analysis of the equatorial SAXS intensities, D_MAX = 2Δ_min, and for the meridional SAXS, D_MAX = L_SC. The correlation peaks in the meridional and equatorial Patterson functions correspond to periodically occurring density variations along the fiber axis and the fiber cross-section, respectively.

Figure 7

(Left) simple structure model for the description of radially decaying periodical density variations over the fiber cross-section. (Top right) equatorial SAXS intensity patterns of a model GI-POF and a two-step MSI-POF calculated with the structure model sketched on the left. The respective model parameters are displayed in the insets. For better visibility, high frequency oscillations in the SAXS curves were suppressed by a seven-point moving average. (Bottom right) equatorial distance-distribution functions for GI- and MSI-POF. The information content is essentially the same. In both cases, the smaller dimension Δ₂ and the parameter D_tot can be extracted from the functions.

Figure 8

Simulated SAXS intensities (blue solid lines) in comparison with the observed data (symbols and green solid lines) for the sample POF1 using the structure parameters displayed in the inset on the left for different numbers N of repeat units. For better visibility, high-frequency oscillations in the model SAXS curves were suppressed by a seven-point moving average. The model curve with N = 6 repeat units reproduces the positions of the maxima and minima in the measured data quite well. A POF1 sample consisting of only one single repeat unit (N = 1) is not very likely.

Figure 9

Dependence of the integral equatorial and meridional parameters R_tot (Left) and L_tot (Right) on the overall process-parameter f_tot. Although the major differences in the structure parameters are induced by the mechanical draw ratio, the impact of small changes in the spin-draw ratio between POF1 and POF2 is also noticeable.