X-Ray Diffraction Lab
Lab 8. Diffractometer: Polymer Degree of Crystallinity
PET Crystallization series for DOC versus Crystallization TemperatureObjective: To become familiar with use of the diffractometer for quantitative analysis of phases in semi-crystalline polymers.
Background: Cullity and Stock Chapter 18 p. 539, Chapter 11,
Chapter 12 (Phase Analysis), Chapter 6 (Diffractometer), and Alexander XRD Book,
R. J. Roe X-ray Scattering Book, Vonk Book
(Old Cullity: Chapter 14 (Phase Analysis), Chapter 7 (Diffractometer), pp. 139 section 4-12 and equation 4-21 for Diffractometer.)
The integrated intensity from a diffraction peak is proportional to the volume fraction of that material in a sample. This means that for a material with multiple phases, crystalline/amorphous or several crystalline phases, XRD can be used to determine the volume fraction of these phases. For a semicrystalline polymer such as polyethylene this results in a determination of the degree of crystallinity of the sample which is a critical measurement for determination of the properties of the polymer. There are alternative approaches to determination of phase composition including density measurements, thermal analysis and spectroscopy, but XRD remains the most robust and simplest technique so it is of dominant importance.
The intensity from a diffractometer in reflection geometry must be corrected for the angular dependence of absorption/beam profile and for the Lorentz Polarization factor which is also angularly dependent. In addition, account must be made for the multiplicity of planes in a crystal, variation in thermal broadening with angle and some other factors, see equation 12-1.
Degree of Crystallinity for a series of PET samples Annealed at Different Temperatures:
The crystallization rate changes with quench depth below the crystallization temperature. If a series of sample are annealed for similar times the final degree of crystallinity will change with quench depth. Such data can be used to determine a processing window for polymer samples. For example, PET is often used as water and soda bottle materials. For this application an amorphous sample is desired for toughness and clarity. It is possible to quench a processed sample to a temperature where the rate of crystallization is extremely slow and to produce an amorphous sample. To determine this temperature a series of samples quenched at different temperatures can be examined.
1) Determine the DOC for a series of PET samples.
2) Plot DOC versus crystallization temperature.
3) What shape curve is expected in this plot and why does the curve take this shape? Polymer Crystalline Morphology
4) Does your curve follow this shape? Why?
5) What temperature would you hold the die in a blow-molding operation making PET water bottles?
Degree of Crystallinity for Polyethylene:
A similar approach for determination of the degree of crystallinity of a semi-crystalline polymer is a common technique in the plastics industry. The degree of crystallinity governs the properties of these materials. For instance, PE can vary from an elastomeric material (Metallocene PE) with a degree of crystallinity of about 10%, to a flexible film material (LLDPE) with a degree of crystallinity of about 40% (Baggies), to a rigid structural material (HDPE) with a degree of crystallinity of about 80% (Milk Jug). We will examine several PE's to demonstrate the determination of the degree of crystallinity measurement.
This measurement involves estimation of the area under the amorphous halo which is a broad hump in the XRD pattern, as well as the estimation of the area under the crystalline peaks. Organic materials also display a strong Compton background which must be subtracted from the data. It is not possible to use the raw data to perform a phase analysis on polymer samples since the amorphous halo and Compton scattering are broad features.
The intensity in numerical form is multiplied by the inverse of the angular dependent terms involved in R above and the diffraction angle is converted to q = 4
p/l sinq. The Compton background is estimated from the raw data as the high-q value for intensity and this value is multiplied by q2 and is included in all plots which follow. Two copies of the corrected intensity versus q are plotted with the Compton background included. On one a sketch is made to estimate the amorphous halo and the region between the Compton background and this amorphous halo is cut out to simulate the integrated amorphous scattering. On the second plot the crystalline peaks are sketched from the Compton curve to the observed peaks and are cut out. The integrated intensity from the crystalline peaks is estimated from the weight of these cuttings. The degree of crystallinity is estimated from the weight of these crystalline peaks divided by the sum of the weights of the amorphous background and the crystalline peaks.You can use the azimuthally averaged image plate data for PE from Lab 2 for the DOC determination if it is better than your diffractometer scan.