Lab 9 X-ray Diffraction
Small Angle X-ray Scattering
Objective: To become familiar with small-angle x-ray scattering and its application for nano-phase characterization in ceramics and polymers.
Background: Cullity and Stock Chapter 18 Polymers, Chapter 19 SAXS. Web notes on polymer crystalline structure (Polymer Morphology) and SAXS (XRD Class).
This lab will involve measurement of the SAXS pattern for a series of polyethylene ptherathalate samples (water bottle) crystallized at several temperatures to demonstrate the behavior of lamellar thickness with under cooling. The functionality for this dependence is based on the Hoffman-Lauritzen equation, t = 2s T°/(DHf DT) where t is the lamellar thickness, s, is the fold surface energy, T°, is the melting point for lamellae of infinite thickness, DHf, is the enthalpy of melting and DT is the quench depth below the equilibrium (infinite thickness) melting point. "t" can be obtained from azimuthally averaged SAXS pattern after a Lorentzian correction, Iq2 versus q. The peak position in this plot, q*, is related to the long period which is given by L = t + a, where a is the amorphous thickness. The degree of crystallinity is generally related to t and a by DOC = t/L. We will either measure the DOC using XRD or DSC measurments or assume a value for DOC to obtain t from the peak in scattered intensity at q* using L = 2p/q*.
We will also measure several samples of silica that display mass-fractal scaling. These samples show a weak power-law decay in log I versus log q that reflects the dimensionality of mass-fractal aggregates in the samples. The knees in this plot reflect mean sizes for the primary particles and aggregates in these ramified nano-particles. You will determine the mass-fractal dimension, primary particle size and aggregate size for these samples using a power-law fit, I(q) = B q-P, and a fit using Guinier's law, I(q) = G exp(-q2Rg2/3). You will also identify Porod regimes where surface scattering is observed, I(q) = BPorod q-4, where BPorod is proportional to the surface to volume ratio (specific surface area) for the material.
Procedure:
1) Prepare isothermally crystallized PET samples by annealing water bottle pieces at 240°C for 10 minutes followed by a quench to temperatures in the 140 to 190°C range. Allow crystallization to proceed for 10 to 15 minutes prior to quenching in water.
2) Slice the PET samples to 1 to 2 mm thickness and 5mm x 1 cm.
3) Prepare Silica samples by sprinkling a small amount of silica powder on scotch tape and sealing the tape with a second piece of tape so that no silica can escape. The thinnest possible layer is needed.
4) Mount samples on the SAXS sample holder sheets.
5) Run the SAXS measurement
6) Reduce data to I versus q data and save as text files.
Required Analysis:
1) Make Iq2 versus q plots for the PET SAXS data and determined the value for q*.
2) From the data plot 1/t versus T and find T° from the t=>0 intercept. Either use a fixed value for the degree of crystallinity or measure using DSC or XRD (see previous lab).
3) Find a value for 2s T°/(DHf) using this value for T°.
4) From the Polymer Handbook find a value for DHf and calculate s.
5) Plot log(I) versus log(q) for the silica samples and the PET samples.
6) Note in these plots the Porod Regimes, I = B q-4.
7) For the silica plots note where the Guinier regimes for the primary particle and aggregate occur (these will appear as knees in the plots).
8) From a power-law fit determine the mass fractal dimension, df for the silica samples.
9) From local Guinier fits determine the primary particle Rg and the aggregate Rg for the silica samples.
Questions:
1) Explain the relationship between SAXS and XRD both in scattering angle and in terms of calculation of intensity (Cullity and Stock section 19-3).
2) In a paragraph and with sketches show the structure of polymer crystalline aggregates and explain what parts of this structure are observed in SAXS.
3) Explain the basis of the Hoffman-Lauritzen equation (see web notes for this if necessary).
4) Explain why Iq2 is used to determine q* rather than I.
5) Sketch the structure of the silica aggregates and correlate this sketch with the observed scattering pattern.
6) Why would a material display such a mass-fractal structure rather than a solid structure? (you answer should involve a discussion of how these mass-fractal aggregates grow).
7) Qualitatively compare the SAXS and XRD 2d patterns in the web file for LDPE blown films and briefly discuss the relationship between XRD and SAXS orientation from a morphological perspective.