Rouse number

The effectiveness of turbulence at maintaining the suspension is quantified by the ratio of the fall velocity to the turbulent velocity. This dimensionless parameter is called the Rouse number ... 

Recoverable shear compliance for several polymers. Lines represent experimental data (Graessley, 1974). Asymptote of 0.4 is the Rouse number. 

Since PY ) x V, we have x V It is important to note that Xj should be independent of the length of the Rouse unit given by <3j. Since rj is proportional to the number of monomer units between two beads, should scale... 

Lay-up proceeds by laying down the veneer which is to be the back surface of the panel. Then a sufficient number of pieces of core veneer are passed through the glue spreader to form the next layer of cross-oriented veneer. The glue spreader commonly used in hardwood plywood manufacture is a roU coater in which a pair of opposing mbber roUs are coated with a thin layer of adhesive. As the veneer is passed between the roUs, the adhesive is transferred to the surfaces of the veneer. Adhesive is appHed only to the cross-pfles and in sufficient quantity to provide a continuous layer on both opposing faces of veneer. Thus, in the case of a three-ply panel, only the core layer is spread with adhesive and in that of a five-ply panel, the second and fourth layers both of which are cross-pfles, are spread with adhesive. Then the top surface veneer, which is normally the decorative surface, is placed on the assembly. 

At high speeds, the pond of the flooded nip size press becomes turbulent. RoU maintenance is a problem with the gate-roU size press. To avoid these problems, the blade/rod metering size press was developed. Short-dweU coater heads are used to apply a precisely controUed quantity of chemicals to the size press roUs. This quantity is controUed with either a metering blade or a metering rod. Blade or rod metering eliminates the pond, and does not increase the number of roUs required for surface chemical appHcation. 

The main predictions of the scaling theory [40], concerning the dynamics behavior of polymer chains in tubes, deal with a number of characteristic times the smallest time rtube measures the interval of essentially Rouse relaxation before the monomers feel the tube constraints significantly, 1 < Wt < Wrtube = and diffusion of an inner monomer is... 

First approaches to approximating the relaxation time on the basis of molecular parameters can be traced back to Rouse [33]. The model is based on a number of boundary assumptions (1) the solution is ideally dilute, i.e. intermolecular interactions are negligible (2) hydrodynamic interactions due to disturbance of the medium velocity by segments of the same chain are negligible and (3) the connector tension F(r) obeys an ideal Hookean force law. 

In addition to the Rouse model, the Hess theory contains two further parameters the critical monomer number Nc and the relative strength of the entanglement friction A (0)/ . Furthermore, the change in the monomeric friction coefficient with molecular mass has to be taken into account. Using results for (M) from viscosity data [47], Fig. 16 displays the results of the data fitting, varying only the two model parameters Nc and A (0)/ for the samples with the molecular masses Mw = 3600 and Mw = 6500 g/mol. 

Fig. 17. Time-dependent correlators for different Rouse modes in the Hess model. The calculations where performed for PE of Mw = 6500 g/mol. The mode numbers increase from the top commencing with p = 1. (Reprinted with permission from [36]. Copyright 1994 American Chemical Society, Washington)...

In fact, the diffusion constant in solutions has the form of an Einstein diffusion of hard spheres with radius Re. For a diffusing chain the solvent within the coil is apparently also set in motion and does not contribute to the friction. Thus, the long-range hydrodynamic interactions lead, in comparison to the Rouse model, to qualitatively different results for both the center-of-mass diffusion—which is not proportional to the number of monomers exerting friction - as well as for the segment diffusion - which is considerably accelerated and follows a modified time law t2/3 instead of t1/2. 

To guarantee the transformational invariance of DG = kBT/(NQ (see Table 4) in the case of Rouse relaxation, the replacement of N by N/A, requires the simultaneous replacement of the segmental friction coefficient by X which is natural, since friction is proportional to the number of segments involved. 

In contrast to -conditions a large number of NSE results have been published for polymers in dilute good solvents [16,110,115-120]. For this case the theoretical coherent dynamic structure factor of the Zimm model is not available. However, the experimental spectra are quite well described by that derived for -conditions. For example, see Fig. 42a and 42b, where the spectra S(Q, t)/S(Q,0) for the system PS/d-toluene at 373 K are shown as a function of time t and of the scaling variable (Oz(Q)t)2/3. As in Fig. 40a, the solid lines in Fig. 42a result from a common fit with a single adjustable parameter. No contribution of Rouse dynamics, leading to a dynamic structure factor of combined Rouse-Zimm relaxation (see Table 1), can be detected in the spectra. Obviously, the line shape of the spectra is not influenced by the quality of the solvent. As before, the characteristic frequencies 2(Q) follow the Q3-power law, which is... 

The movement from the tube is restricted to odd-numbered Rouse modes, and this is determined by the nature of the motion required for a defect ... 

Fig. 3.5 Single chain structure factor from a PEE melt at 473 K. The numbers along the curves represent the experimental Q-values in [A ]. The solid lines are a joint fit with the Rouse model (Eq. 3.19). (Reprinted with permission from [44]. Copyright 1999 American Institute of Physics)...

Having obtained a very good agreement between experiment and simulation, the simulations containing the complete information about the atomic trajectories may be further exploited in order to rationalize the origin of the discrepancies with the Rouse model. A number of deviations from Rouse behaviour evolve. 

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