Conformational Relaxation Times

C.J. Farrell, A. Keller, M.J. Miles, and D.P. Pope, Conformational relaxation time in polymer solutions by elongational flow experiments 1. Determination of exten-sional relaxation time and its molecular weight dependence, Polymer, 21,1292 (1980). 

It is instructive to compare the system of equations (3.46) and (3.47) with the system (3.37). One can see that both the radius of the tube and the positions of the particles in the Doi-Edwards model are, in fact, mean quantities from the point of view of a model of underlying stochastic motion described by equations (3.37). The intermediate length emerges at analysis of system (3.37) and can be expressed through the other parameters of the theory (see details in Chapter 5). The mean value of position of the particles can be also calculated to get a complete justification of the above model. The direct introduction of the mean quantities to describe dynamics of macromolecule led to an oversimplified, mechanistic model, which, nevertheless, allows one to make correct estimates of conformational relaxation times and coefficient of diffusion of a macromolecule in strongly entangled systems (see Sections 4.2.2 and 5.1.2). However, attempts to use this model to formulate the theory of viscoelasticity of entangled systems encounted some difficulties (for details, see Section 6.4, especially the footnote on p. 133) and were unsuccessful. 

Derived from linear approximation of the equations (3.37), the equilibrium correlation function (4.29), defines two conformation relaxation times r+ and r for every mode. The largest relaxation times have appeared to be unrealistically large for strongly entangled systems, which is connected with absence of effect of local anisotropy of mobility. To improve the situation, one can use the complete set of equations (3.37) with local anisotropy of mobility. It is convenient, first, to obtain asymptotic (for the systems of long macromolecules) estimates of relaxation times, using the reptation-tube model. 

This is exactly the molecular-weight dependence of conformational relaxation times of polymer in non-entangled state and for the region of diffusive mobility (see equation (4.41), weakly-entangled system). 

McKechnie et al. also provide a detailed comparison of methods for both initial amorphous growth and relaxation procedures in fluid and glassy samples.2 At temperatures resulting in conformational relaxation times that are short in comparison with the simulation time, the dynamic pseudorotational isomeric state method followed by dynamic evaluation is extremely efficient for ascertaining conformational distributions. In the case of glassy samples, no... 

As already mentioned (pp. Ill and 112) the deformational mechanism is characteristic of kinetically flexible molecules for which the orientation time to is greater than the deformation time Tj, i.e. the time during which the molecule in solution retains a random conformation (relaxation time of the conformation). 

On the other hand is comparable to solvent structural relaxation times and is shorter than solvent reorientation and conformational relaxation times. In this case the effective friction for motion in the vicinity of Rj will be less than the zero frequency friction which describes diffusion for R > R. ... 

Figure 18 illustrates the pronounced effect of the presence of counterions in HPAA. In pure water as a solvent, the flow resistance enhancement occurs at a very low flow rate. As the ionic strength is increased, the strain rate at which the dramatic enhancement in flow resistance occurs is markedly increased until beyond about 0.5 M, where no further effect occurs. The magnitude of the effect, however, remains approximately constant. The shear viscosity is greatly reduced by the increase in ionic strength. This effect is attributed to a progressive collapse of the HPAA coils because of counterion screening and results in a reduction in the conformational relaxation time and a consequent increase in the strain rate required to produce a coil-stretch transition. 

HPAA in Pore Flow. The preceding findings lead us to reinterpret results from porous media and capillary entrance flow. Strong non-Newtonian effects have previously been attributed to the increase in extensional viscosity associated with the coil-stretch transition, occurring when the strain rate exceeds the reciprocal of the lowest order conformational relaxation time (47-49),... 

Here R and R are the rms (root mean square) end-to-end distances of the polymer chain parallel and perpendicular to the director, respectively, xr is the conformational relaxation time of the polymer, c the polymer concentration, N is the degree of polymerization, and T the temperature (K). These results are interesting, because they predict that if the dissolved polymer stretches along the director, because of an interaction with the nematic field, the increment in r]c will be much larger than that in T]b. Specifically, from Eqs. (1.82) and (1.83), the ratio of the two scales as... 

Moreover, we point out that when one has determined the ratio 7 /Rx viaEq. (1.87), it becomes possible to determine the conformational relaxation time xr via the following equation, obtained by subtracting Eq. (1.86) from Eq. (1.85) ... 

TABLE 1.2 Conformational Relaxation Time (tk(/u.s)) of TPBIO Samples in Nematic E48... 

Narh KA, Odell JA, Keller A (1992) Temperature-dependence of the conformational relaxation-time of polymer-molecules in elongational flow-invariance of the molecular-weight exponent. J Polym Sci Polym Phys 30 335-340... 

Fig. 7.15 Conformational relaxation time as a function of position of the dihedral in comb-branch polymer electrolytes from MD simulation...

Analysis of the MD simulations of the PEPE5 reveal that Li" occurs primarily by hopping of the cation from one side chain to another [60]. The six oxygen atoms of the side chains facilitated coordination of Li", as anticipated. However, a fraction of Li" cations are partially coordinated by the polyether backbone. These cations have very slow dynamics and do not contribute appreciably to Li" motion. The slow dynamics of cations partially coordinated by the chain backbone can be understood by considering conformational dynamics in the comb-branch polymer. Figure 7.15 shows conformational relaxation time, based on... 

The conformational relaxation times in Table I suggest that a correlation exists between macrocycle rigidity and the speed at which the ring undergoes the conformational change. 

Table 3 summarizes the conformational relaxation times of the polyamide in several solvents. In solvents such as A -dimethylacetamide (DMA) and A -dimethylformamide (DMF), the unfolding process proceeds rather quickly, whereas in poor solvents, the unfolding is retarded. The response time was in the range 10 to 10 s. 

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