Isothermal-adiabatic transition

The isothermal/adiabatic transition argument was originally applied to poly(me-thyl methacrylate) in which crack propagation was observed to become unstable above a certain fast crack velocity . This instability was attributed to the transition of the crack tip deformation from an isothermal process to an adiabatic one, resulting in substantial softening at the crack tip. The applicability of this process to epoxies is questionable based on the observation that it is slow, not fast, rates at which the epoxy stable to unstable transition occurs. 

Relaxation processes control most polymer properties. Some mechanical properties are controlled by isothermal-adiabatic transitions at high deformation rates. 

If more heat is generated locally than is diffused, isothermal-adiabatic transition occurs. This happens when the deformation time M is less than the temperature relaxation time rrlD. 

Jortner and Ulstrup have demonstrated that for isothermic atom transfers and for sufficiently high temperatimes, the non-adiabatic transition rate takes the form 49)... 

Two basically different models have been developed to explain this crack transition behavior, the already discussed (see Sect. 3.2.2) isothermal-adiabatic effect and the P-relaxation Both models have been discussed controversely and profound... 

FIG. 16-23 Transition paths in isotherm plane for adiabatic adsorption and thermal regeneration. 

The experiments result in an explicit measure of the change in the shock-wave compressibility which occurs at 2.5 GPa. For the small compressions involved (2% at 2.5 GPa), the shock-wave compression is adiabatic to a very close approximation. Thus, the isothermal compressibility Akj- can be computed from the thermodynamic relation between adiabatic and isothermal compressibilities. Furthermore, from the pressure and temperature of the transition, the coefficient dO/dP can be computed. The evaluation of both Akj-and dO/dP allow the change in thermal expansion and specific heat to be computed from Eq. (5.8) and (5.9), and a complete description of the properties of the transition is then obtained. 

If the curing reaction occurs at adiabatic or isothermal conditions above the glass transition temperature of the ultimately cured polymer, the reaction kinetics is adequately described by the adopted mechanism 5> 16,l7 69 7i However, at temperatures substantially below the final glass transition temperature, the reaction rate at a certain... 

The changes in crack propagation types (from stable to stick-slip) are associated with the crack blunting mechanism, which is favored by high temperatures and low strain rates, conditions that decrease general trends cannot be extended to very high strain rates because a transition from isothermal to adiabatic conditions may... 

For a system with n components (including nonad-sorbable inert species) there are n — 1 differential mass balance equations of type (17) and n — 1 rate equations [Eq. (18)]. The solution to this set of equations is a set of n — 1 concentration fronts or mass transfer zones separated by plateau regions and with each mass transfer zone propagating through the column at its characteristic velocity as determined by the equilibrium relationship. In addition, if the system is nonisothermal, there will be the differential column heat balance and the particle heat balance equations, which are coupled to the adsorption rate equation through the temperature dependence of the rate and equilibrium constants. The solution for a nonisothermal system will therefore contain an additional mass transfer zone traveling with the characteristic velocity of the temperature front, which is determined by the heat capacities of adsorbent and fluid and the heat of adsorption. A nonisothermal or adiabatic system with n components will therefore have n transitions or mass transfer zones and as such can be considered formally similar to an (n + 1)-component isothermal system. 

Fig-1 Mechanical response of SAN to simple shear at an applied strain rate of 10 2/s and 10 4/s for isothermal or adiabatic conditions (solid and dashed lines, respectively). The temperature increase delays the hardening for a strain rate of 10 4/s which vanishes for 10 2/s. In this case, the material reaches the glass transition temperature and enters the rubbery state resulting in a small load-bearing capacity... 

Transition, isothermal to adiabatic 138f. Trapped entanglement 36, 42 Trapping factor 36 Triads 36... 

In a car ully designed high quality resonator, the dissipation processes 2), 3), and 4) can be kept negligibly small. It is important to minimize the perturbations caused by these effects, because a theoretical treatment is difficult. It was shown in Ref. and that such an optimization of the cell is in fact possible and then only viscous and thermal boundary layer losses ne be taken into account. Throughout the principal portion of the volume of the resonator, the expansion and contraction of the gas occurs adiabatically. Near the walls, however, this process becomes isothermal. This leads to heat conduction, which is responsible for the thermal dissipation process. The viscous dissipation can be explained by the boundary conditions imposed by the wails. At the surface, the tangential component of the acoustic velocity is 2 0, whereas in the interior of the cavity, it is proportional to the gradient of the acoustic pressure. Thus, viscoelastic dissipation occurs in the transition region. 

In this section experimental results are discussed, concerned with analyses of melting and crystallization kinetics, as well as reversibility of the phase transition. The frame of the discussion is set by Fig. 3.76, which will be supported by experimental data on poly(oxyethylene). The thermal analysis tools involved are TMDSC, optical and atomic-force microscopy, DSC, adiabatic calorimetry, and dilatometry. Most of these techniques are described in more detail in Chap. 4. Results from isothermal crystallization, and reorganization are attempted to be fitted to the Avrami equation. This is followed by a short remark on crystallization regimes and finally some data are presented on the polymerization and crystallization of trioxane crystals. 

Figure 4.49 shows the results of adiabatic calorimetry, standard DSC and quasi-isothermal MTDSC for poly-/ -dioxanone (—CH2—CH2— O—CH2—COO—)x, (PPDX). The ordinate is labelled as apparent heat capacity since in the transition region, latent heat contributions may increase the heat capacity. Up to 250 K, the heat capacity is practically fiilly vibrational as is typical for glassy and crystalline solids. The skeletal and group vibrational contributions are then extrapolated to higher temperature, as is discussed with Figure 4.1 for polyethylene. The sample analysed with... 

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