Temperature-dependent mechanical relaxation

The WLF approach is a general extension of the VTF treatment to characterize relaxation processes in amorphous systems. Any temperature-dependent mechanical relaxation process, R, can be expressed in terms of a universal scaling law ... 

M.L. Williams, R.E. Landel, and J.D. Ferry, The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming Uquids, J. Am. Chem. Soc., 77, 3701-3707, 1955. 

Temperature dependence proton relaxivity 188 relaxation rate 144-5 Temperature-sensitive contrast agents 218-19 Th -" 368 Ti "" 347 Tilt angle 242 Time constant 14 Time correlation functions 76 Time-dependent mechanism 14 Time-dependent perturbation methods 23 Time-dependent perturbation theory 45-8 Titanium(III) 115,134-5,161 TPEN 224 TPPS 219... 

M. L. Williams, R.R Landel, and J.D. Ferry The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids. ... 

The dynamic characteristics of adsorbed molecules can be determined in terms of temperature dependences of relaxation times [14-16] and by measurements of self-diffusion coefficients applying the pulsed-gradient spin-echo method [ 17-20]. Both methods enable one to estimate the mobility of molecules in adsorbent pores and the rotational mobility of separate molecular groups. The methods are based on the fact that the nuclear spin relaxation time of a molecule depends on the feasibility for adsorbed molecules to move in adsorbent pores. The lower the molecule s mobility, the more effective is the interaction between nuclear magnetic dipoles of adsorbed molecules and the shorter is the nuclear spin relaxation time. The results of measuring relaxation times at various temperatures may form the basis for calculations of activation characteristics of molecular motions of adsorbed molecules in an adsorption layer. These characteristics are of utmost importance for application of adsorbents as catalyst carriers. They determine the diffusion of reagent molecules towards the active sites of a catalyst and the rate of removal of reaction products. Sometimes the data on the temperature dependence of a diffusion coefficient allow one to ascertain subtle mechanisms of filling of micropores in activated carbons [17]. 

Although the supramolecular polymers based on bifunctional ureidopyrimidinone derivatives in many ways behave like conventional polymers, the strong temperature dependence of their mechanical properties really sets them apart from macromolecular polymers. At room temperature, the supramolecular polymers show polymer-like viscoelastic behavior in bulk and solution, whereas at elevated temperatures liquid-like properties are observed. These changes are due to a 3-fold effect of temperature on the reversible polymer chain. Because of the temperature dependence of the Ka value of UPy association, the average DP of the chains is drastically reduced at elevated temperatures. Simultaneously, faster dynamics of the scission—recombination process leads to faster stress relaxation in an entangled system. These two effects occur in addition to the temperature-dependent stress relaxation processes that are also operative in melts... 

The deformation behaviour of semi-crystalline materials is mainly determined by the behaviour of the two components - the crystalline and the amorphous phase with their characteristic temperature-dependent mechanical behaviour and sometimes their anisotropy. So the crystalline phase is elastically with a rather high modulus. Above a certain stress the crystallites break down into smaller fragments. Aligned chains enable recrystallisation. The mobility in the amorphous phase depends on the difference between the ambient temperature and the temperature characteristic of the glass transition, which is the dominant relaxation process in the temperature range under investigation. On the other side the amorphous phase is constrained within the crystalline one. So it shows to some extent stress relaxation or frozen stress. Both phases are connected via anchor molecules, bridging the phase boundaries. Those molecules are mainly responsible for stress transfer between the phases. 

In 2004, Gibson et al. [10] then presented an upgraded version by adding a new mechanical model. A function that assumes the relaxation intensity is normally distributed over the transition temperature was used to fit the temperature-dependent Young s modulus. Furthermore, in order to consider the resin decomposition, each mechanical property was modified by a power law factor. Predictions of mechanical responses based on the thermomechanical models were also performed by Bausano et al. [11] and Halverson et al. [12]. Mechanical properties were correlated to temperatures through dynamic mechanical analysis (DMA) but no special temperature-dependent mechanical property models were developed. 

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