Temperature-dependent mechanical relaxation process

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 ... 

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... 

For transport in amorphous systems, the temperature dependence of a number of relaxation and transport processes in the vicinity of the glass transition temperature can be described by the Williams-Landel-Ferry (WLF) equation (Williams, Landel and Ferry, 1955). This relationship was originally derived by fitting observed data for a number of different liquid systems. It expresses a characteristic property, e.g. reciprocal dielectric relaxation time, magnetic resonance relaxation rate, in terms of shift factors, aj, which are the ratios of any mechanical relaxation process at temperature T, to its value at a reference temperature 7, and is defined by... 

The temperature dependency of the apparent energy of activation of the bleeching process as exhibited by the curvature in the Arrhenius plot (Fig. 3) is typically found for, e. g., dynamic mechanical relaxation processes (17), which leads to the connection whith the free volume theory. The latter processes are best described by the WLF-equation (18), log a =Cj(T-Tg)/(C +T-Tg), i. e., a master plot is obtained when plotting the logarithm of... 

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. 

The non-linear dependence of the relaxation process on the DNA concentration was also observed in stopped-flow experiments and the same mechanism, i.e. fast pre-equilibrium followed by a slow intercalation step, was proposed." This latter study did not report values for the individual rate constants. The mechanism proposed in Scheme 4 was employed in subsequent studies despite the criticism on the accuracy for the data related to the fast kinetic component (see below). The original temperature jump study also showed that the relaxation kinetics depend on the structure of the DNA.117 The slower intercalation rate for 5 with T2 Bacteriophage DNA when compared to ct-DNA was ascribed to the glucosylation of the former DNA (Table 3). 

In Fig. 1, various elements involved with the development of detailed chemical kinetic mechanisms are illustrated. Generally, the objective of this effort is to predict macroscopic phenomena, e.g., species concentration profiles and heat release in a chemical reactor, from the knowledge of fundamental chemical and physical parameters, together with a mathematical model of the process. Some of the fundamental chemical parameters of interest are the thermochemistry of species, i.e., standard state heats of formation (A//f(To)), and absolute entropies (S(Tq)), and temperature-dependent specific heats (Cp(7)), and the rate parameter constants A, n, and E, for the associated elementary reactions (see Eq. (1)). As noted above, evaluated compilations exist for the determination of these parameters. Fundamental physical parameters of interest may be the Lennard-Jones parameters (e/ic, c), dipole moments (fi), polarizabilities (a), and rotational relaxation numbers (z ,) that are necessary for the calculation of transport parameters such as the viscosity (fx) and the thermal conductivity (k) of the mixture and species diffusion coefficients (Dij). These data, together with their associated uncertainties, are then used in modeling the macroscopic behavior of the chemically reacting system. The model is then subjected to sensitivity analysis to identify its elements that are most important in influencing predictions. 

The dynamic mechanical thermal analyzer (DMTA) is an important tool for studying the structure-property relationships in polymer nanocomposites. DMTA essentially probes the relaxations in polymers, thereby providing a method to understand the mechanical behavior and the molecular structure of these materials under various conditions of stress and temperature. The dynamics of polymer chain relaxation or molecular mobility of polymer main chains and side chains is one of the factors that determine the viscoelastic properties of polymeric macromolecules. The temperature dependence of molecular mobility is characterized by different transitions in which a certain mode of chain motion occurs. A reduction of the tan 8 peak height, a shift of the peak position to higher temperatures, an extra hump or peak in the tan 8 curve above the glass transition temperature (Tg), and a relatively high value of the storage modulus often are reported in support of the dispersion process of the layered silicate. 

In all the above three polymers only a single process is apparently observed in the time window for PCS (10-6 to 100 s). The shape of the relaxation function is independent of temperature. The temperature dependence of (r) follows the characteristic parameters observed for mechanical or dielectric studies of the primary (a) glass-rubber relaxation. Relaxation data obtained by many techniques is collected together in the classic monograph of McCrum, Read and Williams41. The data is presented in the form of transition maps where the frequencies of maximum loss are plotted logarithmically... 

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