Tube-renewal process

Moreover, as far as relaxation times are concerned, the reptation mechanism in an enlarged tube should lead us to favour the tube renewal process. The expression of... 

Fig. 5. (a) Two molecules, A and B, are shown as represented by their primitive paths, (b) An end of B has reptated past A destroying a portion of B s tube. When that end moves back it can do so in any direction, loosing all memory of its original orientation. B was also part of the tube of A so that the illustrated motion represents a tube renewal process. A segment of A can make a limited step of distance Og until the next entanglement is encountered. The attachment of the released segment of A at both ends to the rest of the molecule allows only limited randomization of the orientation of this segment. 

Although reptation and tube renewal contribute equal magnitudes to viscoelastic relaxation and viscosity, reptation dominates diffusion. Consider a time when reptation moves the molecule s center of mass a distance of order of the radius of gyration, i.e., a squared distance agN. In there have also been about N tube renewal processes, each of which moves the center of mass Og/N. These add incoherently to produce a squared displacement NiuglN) a IN. The contribution of tube renewal to the diffusion constant is thus only 1/AT that of reptation. 

So far, we have considered only the reptative motion of the test chains, assuming that their environment is frozen.This pure reptation model should, therefore, be applied either to the motion of a linear chain in a gel or to the motions of a short chain in a matrix of infinite chains. If the test chain is embedded in a matrix of chains of the same length, then during the reptation motion the neighboring chains which build the tube also move and the tube is partially renewed. This tube renewal process, also called constraint release, should thus increase the self-diffusion... 

The two situations are displayed in Fig.3.13b and c. The first process, where the chain performs Rouse motion along the tube, is called local reptation the creeplike diffusion along the tube which eventually leads to a complete tube renewal is also termed pure reptation. 

Removing the hypothesis of fixed obstacles the models In the context of the reptation model, the finite lifetime of the tube constraints leads to an extra relaxation process called tube-renewal or constraint-release. 

The first attempts to model the process consisted of assuming the tube itself to be a Gaussian flexible chain made of N/Ne subunits of size d (the tube diameter), and thus obeying Rouse-type dynamics. The characteristic time for tube-renewal can then be identified with the longest relaxation time of this chain ... 

In any case, whatever the model, since tube-renewal is more important (compared to reptation) and accelerates the motion more efficiently for short chains than for long chains, it introduces additional molecular weight dependences of the dynamical quantities, and certainly contributes to the experimental deviation of the viscosity/molecular weight exponent from the reptation value 3. All treatments, including tube renewal, exhibit such deviations which vanish for asymptotically long chains. Detailed quantitative tests are, however, very difficult to perform when tube-renewal is taken into account, polydispersity becomes an essential parameter (the shortest mechanism, reptation and tube-renewal, dominates the relaxation process). No complete set of experiments, either for diffusion or for viscoelasticity, with constant polydispersity at all molecular weights, are presently available. 

Relaxation of Single and of Entangled Macromolecules. In the absence of hydrodynamic interactions (HI) the normal modes of a polymer are Rouse modes, which act as overdamped harmonic oscillators. With HI the Rouse modes are still nearly normal modes, but the relaxation spectrum is modified. The HI are screened in semidilute solutions. At higher concentrations and in bulk disentanglement by reptation and tube renewal dominate slow viscoelastic processes. 

Each of the processes for moving ends past entanglements - reptation as a whole, primitive path length fluctuations, contraction in stretched tubes - contributes to tube renewal. The different time scales for each, as well as the distribution of time scales arising in a polydispersed sample, introduce new features in the relaxation modulus. 

In recent years there has been renewed interest in treating coal at high temperatures both by rapid processing in the more conventional type of carbonization apparatus (I) and by using such devices as flash tubes (5, 12, 13), lasers (13), arc image furnaces (9, 11), and plasma jets (3). All these methods produce conditions whereby the coal can be heated rapidly to a temperature well in excess of 1000°C. followed by quenching of the products. The work described here is an investigation into the reactions of coal in a plasma jet and has been reported briefly elsewhere (3). 

Wall-coated flow tube reactors have been used to study the uptake coefficients onto liquid and solid surfaces. This method is sensitive over a wide range of y (10" to 10 1). For liquids this method has the advantage that the liquid surface is constantly renewed, however if the uptake rate is fast, the liquid phase becomes saturated with the species and the process is limited by diffusion within the liquid, so that corrections must be applied [70,72,74]. Many experiments were designed to investigate the interaction of atmospheric species on solid surfaces. In this case the walls of the flow tube were cooled and thin films of substrate material were frozen on the wall. Most of the reaction probabilities were obtained from studies on flow tubes coated with water-ice, NAT or frozen sulfate. Droplet train flow tube reactors have used where liquid droplets are generated by means of a vibrating orifice [75]. The uptake of gaseous species in contact with these droplets has been measured by tunable diode laser spectroscopy [41]. 

Among the renewable energy processes, it is the wind turbines that benefit the most from the measurement of wind direction and velocity. Doppler-type sensors are used to determine the wind velocity and to obtain three-dimensional air motion profiles and also in the balancing of HVAC systems and measuring of the velocity of wet and dirty gases in industry. For a more detailed discussion of Pitot tubes and thermal flowmeters, also refer to the Sections 3.9.7.2 and 3.9.10. Here, the focus is on mechanical- and Doppler-type anemometers. 

At the end of the first relaxation process, the chain is still inside the old tube that existed right after the deformation, in the sense that the orientations of its parts are those produced by the deformation. The chain renews the tube by reptation, thus relaxing those orientations. This process requires a time that is much greater than the Rouse relaxation time Xr. The two processes merge into a single one for unentangled chains. In this case the chains relax according to the Rouse time Xr. 

The Roll Technologies Company s (U.S.) STT reactor (see Fig. 6.34) consists of a tube inside another tube, where the inner tube spins inside the annular tube, whereby only a very small gap is maintained. The reactants All the slightly eccentric gap. Immediately upon entry the reactants encounter a very large interfacial contact area leading to extreme rates of surface renewal. Typical shear-rate values are in the range of 30,000/s to 70,000/s. Process rates in reactors are influenced by the minimum length of turbulent eddies and the molecular diffusive mixing time. This reactor... 

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