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{{Language_sel|LANG=ger|ARTIKEL=Zeit-Temperatur-Verschiebungsgesetz}}
{{PSM_Infobox}}
Time–temperature shift law or time–temperature superposition principle
__FORCETOC__

==General==

The time–temperature shift law is also referred to in the literature [1] as the time–temperature superposition principle. In addition to their pronounced time dependence, [[Viscoelastic Material Behaviour|viscoelastic]] materials also exhibit strong temperature dependence in their properties. The reason for this lies in the molecular motion and rearrangement processes that determine the [[Relaxation Plastics|relaxation]] and [[Creep Plastics|retardation spectrum]] of the [[Material & Werkstoff|material]].

==The time-temperature equivalence==

As thermally activated processes, these molecular processes occur at increasing [[Velocity|velocity]] as the temperature rises. This shifts the relaxation and retardation time spectrum to shorter times. If only the speed of the molecular processes changes with temperature, but not their type and number, the shape of the relaxation or retardation spectrum and thus also the shape of the viscoelastic characteristic functions along the logarithmic time axis remain unchanged. However, their temporal position changes according to the temperature. One consequence of this behaviour, referred to as ‘thermorheologically simple’, is time-temperature equivalence, the application of which in the form of the time-temperature superposition principle has become very important in practice for predicting long-term behaviour (see: [[Tensile Creep Test|tensile creep test]]). If the curve of a viscoelastic [[Material Parameter|parameter]], for example the [[Elastic Modulus|modulus ''E'']] (log ''t''), is known for a specific time interval at different temperatures, the individual curves can be aligned by horizontal displacement with the curve ''E''0 (log ''t'') determined at the reference temperature ''T''0, as shown schematically in '''Fig. 1'''.

[[File:Time-Temperature Fig-1.jpg|500px]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px" |Schematic diagram of master curve construction using time–temperature superposition
|}

This produces a master curve that depicts the material behaviour over a wide time range. The displacement function log ''a''T = log ''t'' – log ''t''0 is temperature-dependent. In many cases, it can be described on the basis of an ARRHENIUS approach:

{|
|-
|width="20px"|
|width="500px" | <math> log \ a_{T}=log \left(\frac{t}{t_{0}}\right)=\frac{\Delta H}{2.3k}\left(\frac{1}{T}-\frac{1}{T_{0}} \right)</math>
|(1)
|}

In the glass transition range (see also: [[Glass Transition Temperature|glass transition temperature]]), however, it often follows the WILLIAMS, LANDEL and FERRY (WLF) equation:

{|
|-
|width="20px"|
|width="500px" | <math> log \ a_{T}=log \left(\frac{t}{t_{0}}\right)=\frac{C_{1}(T-T_{0})}{C_{2}+T-T_{0}}</math>
|(2)
|}

with the universal constants ''C''1 and ''C''2 [2].

==See also==

* [[BOLTZMANN's Superposition Principle|BOLTZMANN's superposition principle]]
* [[Correspondence Principle|Correspondence principle]]
* [[Thermostability PVC]]
* [[Stepped Isothermal Method, Tensile Stress|Stepped isothermal method, tensile stress]]
* [[Relaxation Behaviour Determination|Relaxation behaviour determination]]

==References==

{|
|-valign="top"
|[1]
|Lüpke, T.: Fundamental Principles of Mechanical Behavior. In: [[Grellmann,_Wolfgang|Grellmann, W.]], [[Seidler,_Sabine|Seidler, S.]] (Eds.): Polymer Testing. Carl Hanser, Munich (2022), 3rd Edition, pp. 83/84 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-807-5; see [[AMK-Library]] under A 22)
|-valign="top"
|[2]
|Williams, M. L., Landel, R. F., Ferry, J. D.: The Temperature Dependence of Relaxation Mechanism in Amorphous Polymers and other Glass-forming Liquids. J. Amer. Chem. Soc. 77 (1955) 3701−3707; https://doi.org/10.1021/ja01619a008
|}

[[Category:Thermoanalytical Methods]]

Time–Temperature Shift Law - Revision history