Rouse segment motional time

Fig. 15. Relaxation times of the first Rouse mode of confined pentamers (h=10) as a function of the number of contacts for all the simulated wall affinities, from Bitsanis I, Pan C (1993) J Chem Phys 99 5520. The data indicate clearly a dramatic increase of the relaxation time inside the solid-oligomer interface with increasing 8 The origin of these glassy dynamics is attributed to the slowdown of segmental motions inside the adsorbed layer.

In Chapter 3, we used the Rouse model for a polymer chain to study the diffusion motion and the time-correlation function of the end-to-end vector. The Rouse model was first developed to describe polymer viscoelastic behavior in a dilute solution. In spite of its original intention, the theory successfully interprets the viscoelastic behavior of the entanglement-free poljuner melt or blend-solution system. The Rouse theory, developed on the Gaussian chain model, effectively simplifies the complexity associated with the large number of intra-molecular degrees of freedom and describes the slow dynamic viscoelastic behavior — slower than the motion of a single Rouse segment. 

For chemically uniform homopolymer systems, it is well known that the thermally activated motion of the monomeric segments is intimately related to the glass transition, whereas the motion of the Rouse segments is the basic process for the rubbery/terminal relaxation (see Section 3.3). The temperature dependence of the relaxation time is not identical for these two types of segments at low T, as noted from a difference of the shift factors in the glassy and rubbery relaxation regimes. 

Note that v is the number density of Rouse segments in chains of N segments in length and that are monodisperse. The indexp is the eigenmode from the solution to the equation of motion. Furthermore, equation 65 is the equation for a special form of the generalized Maxwell model having constant coefficients Gj = vkBT (see eq. 18). The relaxation times are given by Xr g/ p. ... 

The segmental motion of a polymer chain was successfully described by a bead-spring model, discussed by Rouse [17] in the so-called free-draining limit and by Zimm [18] in the hydrodynamic limit, de Gennes [19,20] calculated the coherent and incoherent intermediate scattering functions for both the Rouse and Zimm models. In the low Q and long time limit, the time decay of the intermediate scattering function depends on and and the Q dependence of the... 

Figure 5.7 Evolution of the ordering field, XN, in the course of the expanded ensemble simulation along both branches. The system parameters are identical to Figure 5.5. Smart Monte Carlo moves are used to update the molecular conformations. The local segment motion gives rise to Rouse-like dynamics for all but the very first Monte Carlo steps. Time is measured in units of the Rouse-time of the...

Two other possible segmental motions not depicted in Fig. 6 are in distinctly different time realms. At the slow end of the time scale (greater than milliseconds for reasonable amplitudes) are the Rouse-Zimm normal coordinate modes that result from the collective behavior of units of atoms (beads) along the chain pulling one another and acted on by Brownian forces, solvent frictional resistance, and other parts of the chain (Berne and Pecora, 1976). Librational motions, generally accorded to be of the order of 10 s , may also result from the thermally induced displacements of groups of atoms such wobbling motions have been proposed as important factors in the NMR relaxation of proteins (Howarth, 1979). 

The velocity gradient leads to an altered distribution of configuration. This distortion is in opposition to the thermal motions of the segments, which cause the configuration of the coil to drift towards the most probable distribution, i.e. the equilibrium s configurational distribution. Rouse derivations confirm that the motions of the macromolecule can be divided into (N-l) different modes, each associated with a characteristic relaxation time, iR p. In this case, a generalised Maxwell model is obtained with a discrete relaxation time distribution. 

Local reptation regime For times t > xe we have to consider curvilinear Rouse motion along the spatially fixed tube. The segment displacement described by Eq. (18) (n = m) must now take the curvilinear coordinates s along the tube into consideration. We have to distinguish two different time regimes. For (t < xR), the second part of Eq. (19) dominates - when the Rouse modes... 

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. 

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