Thermal constraint release

The molecular theory of extensional viscosity of polymer melts is again based oti the standard tube model. It considers the linear viscoelastic factors such as reptation, tube length fluctuations, and thermal constraint release, as well as the nonlinear viscoelastic factors such as segment orientations, elastic contractimi along the tube, and convective constraint release (Marrucci and lannirubertok 2004). Thus, it predicts the extensional stress-strain curve of monodispersed linear polymers, as illustrated in Fig. 7.12. At the first stage, the extensional viscosity of polymer melts exhibits the Newtonian-fluid behavior, following Trouton s ratio... 

Tube models have been used to predict this material function for linear, monodisperse polymers, and a so-called standard molecular theory [159] gives the prediction shovm in Fig. 10.17. This theory takes into account reptation, chain-end fluctuations, and thermal constraint release, which contribute to linear viscoelasticity, as well as the three sources of nonlinearity, namely orientation, retraction after chain stretch and convective constraint release, which is not very important in extensional flows. At strain rates less than the reciprocal of the disengagement (or reptation) time, molecules have time to maintain their equilibrium state, and the Trouton ratio is one, i.e., % = 3 7o (zone I in Fig. 10.17). For rates larger than this, but smaller than the reciprocal of the Rouse time, the tubes reach their maximum orientation, but there is no stretch, and CCR has little effect, with the result that the stress is predicted to be constant so that the viscosity decreases with the inverse of the strain rate, as shown in zone II of Fig. 10.17. When the strain rate becomes comparable to the inverse of the Rouse time, chain stretch occurs, leading to an increase in the viscosity until maximum stretch is obtained, and the viscosity becomes constant again. Deviations from this prediction are described in Section 10.10.1, and possible reasons for them are presented in Chapter 11. 

Leygue, A., BaUly, C., Keunings, R. A differential formulation of thermal constraint release for entangled linear polymers. /. Non-Newt. Fluid Mech., (2005) 128, pp. 23-28... 

In interpreting the relaxation behavior of polydisperse systems by means of the tube model, one must consider that renewal of the tube occurs because the chain inside it moves thermally, either by reptation mode, by fluctuation of the tube length in time (breathing motion), or in both ways (13,14). Moreover, the tube wall can be renewed independently of the motion of the chain inside the tube because the segments of the chains of the wall are themselves moving. The relaxation mechanism associated with the renewal of the tube is called constraint release. 

Phase changes are typically associated with the evaporation of any suspended liquid phase in an aerosol release. As air is mixed with an aerosol, equilibrium constraints cause additional evaporation of the liquid phase which reduces the temperature of the liquid phase (and the vapor phase if thermal equilibrium is maintained). 

This is the most common mode of addition. For safety or selectivity critical reactions, it is important to guarantee the feed rate by a control system. Here instruments such as orifice, volumetric pumps, control valves, and more sophisticated systems based on weight (of the reactor and/or of the feed tank) are commonly used. The feed rate is an essential parameter in the design of a semi-batch reactor. It may affect the chemical selectivity, and certainly affects the temperature control, the safety, and of course the economy of the process. The effect of feed rate on heat release rate and accumulation is shown in the example of an irreversible second-order reaction in Figure 7.8. The measurements made in a reaction calorimeter show the effect of three different feed rates on the heat release rate and on the accumulation of non-converted reactant computed on the basis of the thermal conversion. For such a case, the feed rate may be adapted to both safety constraints the maximum heat release rate must be lower than the cooling capacity of the industrial reactor and the maximum accumulation should remain below the maximum allowed accumulation with respect to MTSR. Thus, reaction calorimetry is a powerful tool for optimizing the feed rate for scale-up purposes [3, 11]. 

Two systems ( ) and ("), not necessarily reservoirs, but big systems, can be thermally coupled by a Carnot cycle. This is in practice a heat pump, or if it runs in the reverse direction, a heat engine. In this case, we have S + S" = 0, thus if the systems are big, for one revolution of the Carnot cycle d5 -I- d5" = 0. This constraint does not imply that T = T". Namely, the Carnot engine is an active device that releases or donates energy. In the Carnot engine, the change of entropy S is not directly connected with the change of entropy S", even when the cross balance d5 -F d5" = 0 over a full turn holds. 

Shape-memory cycle of a thermo-responsive SMP. The typical shape-memory cycle of a thermo-responsive SMP consists of the following steps 1) start with a SMP in its original shape (permanent shape) 2) heat the SMP above its thermal transition temperature (Ttrans) and deform the SMP by applying an external force, cool well below 3 rans and remove the constraint to obtain the temporary shape with energy stored and 3) heat the pre-deformed SMP above Ttrans at which point the SMP releases the stored energy and recovers the permanent shape (shape recovery). Reprinted and adapted by permission from Cambridge University Press." ... 

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