Chain internal viscosity

From the weak dependence of ef on the surrounding medium viscosity, it was proposed that the activation energy for bond scission proceeds from the intramolecular friction between polymer segments rather than from the polymer-solvent interactions. Instead of the bulk viscosity, the rate of chain scission is now related to the internal viscosity of the molecular coil which is strain rate dependent and could reach a much higher value than r s during a fast transient deformation (Eqs. 17 and 18). This representation is similar to the large loops internal viscosity model proposed by de Gennes [38]. It fails, however, to predict the independence of the scission yield on solvent quality (if this proves to be correct). 

It is expected, however, that the Gaussian representation is inadequate in transient elongational flow, even if the chain is only weakly deformed. During a fast deformation, the presence of non-equilibrium effects, like internal viscosity , noncrossability and self-entanglements will stiffen the molecular coil which is now capable of storing a much larger amount of elastic energy than that predicted from Eq. (113). 

The description of the chain dynamics in terms of the Rouse model is not only limited by local stiffness effects but also by local dissipative relaxation processes like jumps over the barrier in the rotational potential. Thus, in order to extend the range of description, a combination of the modified Rouse model with a simple description of the rotational jump processes is asked for. Allegra et al. [213,214] introduced an internal viscosity as a force which arises due to a transient departure from configurational equilibrium, that relaxes by reorientational jumps. Thereby, the rotational relaxation processes are described by one single relaxation rate Tj. From an expression for the difference in free energy due to small excursions from equilibrium an explicit expression for the internal viscosity force in terms of a memory function is derived. The internal viscosity force acting on the k-th backbone atom becomes ... 

Parameter characterizing the internal viscosity of chain molecules (Part 8). 

Thurston, G.B., Peterlin,A, Influence of finite numbers of chain segments, hydro-dynamic interaction, and internal viscosity on intrinsic birefringence and viscosity of polymer solutions in an oscillating laminar flow field. J. Chem. Phys. 46, 4881-4885 (1967). 

It may be surprising that the effect of the nearest-neighbor bond correlations on the one-dimensional chain depends on the sign of P i.e., that the spectrum broadens when extended conformations are favored and narrows when compact conformations are favored. No simple qualitative explanation of this result has occurred to us. The usual internal viscosity always produces a narrowing of the spectrum. This effect is easily introduced into a one-dimensional Rouse model an internal viscous force is... 

One arives at the conclusion that the internal viscosity of chain molecules in solution must not necessarily be so important that it can be detected with the aid of flow birefringence measurements at low shear rates. 

On the deformation of the macromolecule, i.e. when the particles constituting the chain are involved in relative motion, an additional dissipation of energy takes place and intramolecular friction forces appear. In the simplest case of a chain with two particles (a dumbbell), the force associated with the internal viscosity depends on the relative velocity of the ends of the dumbbell u1 — u° and is proportional, according to Kuhn and Kuhn (1945) to... 

The internal viscosity force is defined phenomenologically by equations (2.26) formulated above. Various internal-friction mechanisms, discussed in a number of studies (Adelman and Freed 1977 Dasbach et al. 1992 Gennes 1977 Kuhn and Kuhn 1945 Maclnnes 1977a, 1977b Peterlin 1972 Rabin and Ottinger 1990) are possible. Investigation of various models should lead to the determination of matrices Ca/3 and Ga and the dependence of the internal friction coefficients on the chain length and on the parameters of the macromolecule. 

In other words, it is assumed here that the particles are surrounded by a isotropic viscous (not viscoelastic) liquid, and is a friction coefficient of the particle in viscous liquid. The second term represents the elastic force due to the nearest Brownian particles along the chain, and the third term is the direct short-ranged interaction (excluded volume effects, see Section 1.5) between all the Brownian particles. The last term represents the random thermal force defined through multiple interparticle interactions. The hydrodynamic interaction and intramolecular friction forces (internal viscosity or kinetic stiffness), which arise when the macromolecular coil is deformed (see Sections 2.2 and 2.4), are omitted here. 

In this case the theory, apart from the characteristic Rouse relaxation time r, contains three more parameters, namely the relaxation time r of the medium, the measure B of the increase in the resistance of the particle when it moves among the chains, and the measure of internal viscosity E associated with resistance to the deformation of the coil due to the present of ambient macromolecules. 

Note that the internal viscosity is a residual of internal relaxation process in the case, when the slow deformation is considered. In a more general case, the elastic and internal viscosity forces acting on the chain, according to equations (2.2) and (2.28), can be written as... 

To calculate the characteristics of viscoelasticity in the framework of mesoscopic approach, one can start with the system of entangled macromolecules, considered as a dilute suspension of chains with internal viscoelasticity moving in viscoelastic medium, while the elastic and internal viscosity forces, according to equations (3.4)-(3.6) and (3.8), have the form... 

It follows from equations (9.9) that the viscosity (or, what amounts to the same thing, the characteristic viscosity) is independent of the velocity gradient for flexible chains (p = 0). For chains with an internal viscosity, the viscosity... 

The rotational correlation times of a benzene solution of a nitroxide imbibed in polystyrene of varied crosslinking density and the analogous compound covalently attached to the chains of the crosslinked polystyrene were measured. In the latter case the modified polystyrene matrix was also equilibrated with benzene. An estimate of the influence of crosslinking density on the internal viscosity can be obtained... 

In a laminar flow or in an external potential field a polymer molecule is subjected to forces that can both make it rotate as a whole and cause a relative shift of its parts leading to a deformation, i.e. changing its conformation. Which of these two mechanisms of motion predominates depends on the ratio of times required for the deformation and rotation of the molecule. If the time of the rotation of the molecule as a whole, tq, is shorter than the time required for its deformation, tkinetically rigid. In the opposite case, when tq > r<, the deformation mechanism of motion will predominate and the molecule will be kinetically flexible. To characterize quantitatively the kinetic rigidity of chain molecules Kuhn has introduced the concept of internal viscosity - a quantity describing the resistance of the molecule to a rapid charge in its shape. Later, the theory of internal viscosity has been developed by Cerf ... 

In contrast, the parameters of local motions are very sensitive to the local conformational microstructure of the polymer chain and to the interactions of units located at a large distance apart along the chain contour but close to each other in space (kinetic volume effects). The parameters of local motions also depend on the external viscosity of the solvent and internal viscosity of the polymer chain... 

We stress that the present approach is essentially self-contained. In addition to the self-consistent derivation of the average chain configuration at equilibrium, with the only exception of the internal viscosity, chain dynamics will be derived from the equilibrium results under classical assumptions (e.g., the preaveraged approximation, the linear Langevin equation). In particular, no a priori use will generally be made of scaling considerations. 

Figure 11. Dynamic correlation function B k, t) [from Eqn. (41) of ref 12] as function of t/to for three values of k as indicated on curves in presence of internal viscosity. Result with Tq = 0 (i.e., with no internal viscosity) are given by dashed lines. [Model assumptions and parameters periodic chain same as in Figure 10, N P 100.]...

The preceding conclusions may be suitably checked upon comparison with PDMS. We send the interested reader to ref. 15 for the choice of the parameters. Unlike the case of PS, a molten polymer sample was also considered, in which case the hydrodynamic interaction was assumed to vanish [i.e., v(q) = 1] because of the hydrodynamic screening exerted by the polymer chains. In view of the apparently low energy barriers to the rotation around SUO chain bonds, we assumed the internal viscosity to be absent, that is. To = O Incidentally, we remark the difference from the case of polystyrene where, in addition to the intrinsic rotation barrier around C-C bonds adjoining tetrahedral-coordinated atoms ( 3 kcal/mol), the side phenyl rings contribute significantly to the rotational hindrance. In Figure 13 the characteristic times ti/2 [13/4 for the melts [115]] are plotted versus Q. 

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