Crystallinity
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Crystallinity
Fundamentals
Crystallinity Xc (in %), also referred to as degree of crystallinity or degree of crystallisation, is a material property that is particularly important in thermoplastic polymer materials (thermoplastics) and, to a much lesser extent, in selected elastomers, such as in the strain-induced crystallisation of natural rubber (NR). In most cases, it is defined as the mass fraction of the crystalline regions in the total polymer phase, which in turn also comprises amorphous regions. Technically applied thermoplastics, if they are crystalline at all, always have amorphous regions between the crystalline regions (e.g. the crystal lamellae) in the nano range or the superstructures (e.g. the spherulitics) in the micro range, i.e. their crystallinity is always less than 100 %. Exceptions are technically irrelevant polymer single crystals. The number of amorphous thermoplastics with a crystallinity of or very close to 0 % is manageable and includes atactic thermoplastics ((such as atactic polymethyl methacrylate (abbreviation: PMMA) and polystyrene (abbreviation: PS)) and thermoplastics that cannot crystallise under the selected processing conditions due to their complex molecular structure (such as polycarbonate (abbreviation: PC). All other thermoplastics are classified as semi-crystalline thermoplastics with a crystallinity typically in the range of 10 % to 80 % [1, 2, 4].
Methods for determining crystallinity
A number of very different methods have now been established for determining crystallinity. However, comparisons of crystallinities determined using different methods for one and the same thermoplastic material show considerable deviations in some cases. This means that a comparative evaluation of the crystallinity of different thermoplastics only makes sense if one and the same method and identical evaluation routines are used. For this reason, dynamic differential calorimetry (see: Differential Scanning Calorimetry (DSC)) has become the most important of the methods briefly outlined below [1–3].
The following methods can be used to determine crystallinity, among other things:
Differential scanning calorimetry (DSC) [3] exploits the fact that phase transitions that occur when the temperature rises, such as the melting of crystalline structures at their melting temperature, require additional energy, i.e., an endothermic enthalpy change occurs. Since polymeric semi-crystalline materials are composed of a large number of crystals of different sizes, mostly in the form of lamellar crystals of varying thickness, the smaller, less perfect crystals melt at lower temperatures than the larger crystals, in accordance with the ADAM-GIBBS relation. This results in the formation of a melting range until all crystals have melted when the temperature is further increased.
The energy required to melt the crystals, the melting enthalpy ΔH, can be measured using DSC and correlates linearly with the crystallinity Xc according to
| (1) |
Δ H0 is the approximate melting enthalpy of 100 % crystalline material. The organic and inorganic phases that do not contribute to determining the crystalline content of the polymer phase under investigation in heterogeneous polymer materials, such as rubber, fillers and reinforcing materials, can be easily taken into account.
X-ray diffraction
X-ray diffraction exploits qualitative and quantitative differences in the diffractograms of the amorphous and crystalline regions, which add up to the diffractogram of the semi-crystalline polymer. While the diffractogram of the amorphous regions appears as an amorphous halo in the form of a very broad bell curve due to the lack of long-range order in these regions, the regular arrangements of polymer chains or parts thereof in the crystalline regions produce a diffractogram with much narrower distributions in the form of peaks, in accordance with the BRAGG equation. The intensity of these peaks and the underlying halo can be analysed using mathematical methods and used to calculate the crystallinity.
Density measurement
Density measurements assume that the crystalline areas are more densely packed and therefore have a higher density compared to the amorphous areas. The density increases linearly with crystallinity according to
| (2) |
where ρa and ρc represent the approximate density of the amorphous and crystalline areas and ρ represents the average density of the polymer phase. However, this method only works reliably with homopolymers and single-phase copolymers.
Plasticising agents (e.g. water in polyamides (abbreviation: PA)), which increase molecular mobility in the amorphous regions due to the lower packing density and thus lower density, must be taken into account when determining crystallinity. It should also be noted that the density of the amorphous regions is slightly dependent on the cooling conditions and increases slightly over time in the glass state. Further significant complications arise with heterogeneous polymer materials, such as rubber-modified, filled or reinforced materials, to the point where the method is no longer applicable.
Other indirect methods
Infrared spectroscopy (see: FTIR spectroscopy) exploits the fact that specific absorption bands occur in the infrared spectra of (at least some) semi-crystalline polymers, which are attributable to deformation vibrations that are only made possible by the regular arrangement of the polymer chains or parts thereof. The crystallinity can be calculated by evaluating these bands.
Nuclear magnetic resonance (NMR) spectroscopy exploits the line shape in the NMR spectrum, which is influenced by the different proton mobility in crystalline and amorphous regions. Taking into account a suitable structural model, this can be used to make statements about crystallinity.
Furthermore, crystallinity can be estimated by means of polarization microscopy from measurements of birefringence.
See also
References
| [1] | Ehrenstein, G. W.: Polymer-Werkstoffe – Struktur Eigenschaften Anwendung. 2nd, completely revised Edition, Carl Hanser, Munich Vienna (1999) (ISBN 3-446-21161-6; AMK-Library under G 91) |
| [2] | Menges, G., Haberstroh, E., Michaeli, W., Schmachtenberg, E.: Werkstoffkunde Kunststoffe. 5th, completely revised Edition, Carl Hanser, Munich (2002) (ISBN 3-446-21257-4; see AMK-Library under L 38), 7th Edition (2021) (ISBN 978-3-446-45801-7) |
| [3] | Ehrenstein, G. W., Riedel, G., Trawiel, P.: Praxis der thermischen Analyse von Kunststoffen. 2nd Edition, Carl Hanser, Munich Vienna (2003) (ISBN 3-446-22340-1; see AMK-Library under C 10-2) |
| [4] | Kaiser, W.: Kunststoffchemie für Ingenieure. Carl Hanser, Munich Vienna (2006) p. 80 (ISBN 3-446-22069-0; see AMK-Library under N 12) |