Polymer internal viscosity

Adachi K, Kotaka T (1993) Dielectric normal mode relaxation. Prog Polym Sci 18 585—622 Adelman SA, Freed KF (1977) Microscopic theory of polymer internal viscosity Mode coupling approximation for the Rouse model. J Chem Phys 67(4) 1380-1393 Aharoni SM (1983) On entanglements of flexible and rodlike polymers. Macromolecules 16(11) 1722-1728... 

The use of internal viscosity forces permit us to take into account kinetic effects associated with deformation rates which were beyond the scope of most polymer... 

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). 

A final piece of evidence against both finite extensibility and internal viscosity is provided by flow birefringence studies. One would expect each to produce variations in the stress optical coefficient with shear rate, beginning near the onset of shear rate dependence in the viscosity (307). Experimentally, the stress-optical coefficient remains constant well beyond the onset of shear rate dependence in r for all ranges of polymer concentration (18,340). 

Bazua,E.R., Williams, M.C. A molecular formulation of the internal viscosity in polymer dynamics, and stress symmetry. J. Chem. Phys. 59,2858-2868 (1973). 

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). 

G. G. Fuller and L. G. Leal, The effects of conformation-dependent friction and internal viscosity on the dynamics of the nonlinear dumbbell model for a dilute polymer solution, J. Non-Newt. Fluid Mech. 8, 271 (1981). 

Here the linear terms in respect to the coefficient of internal viscosity ipa have taken into account only. Averaging with respect to the velocity distribution has been assumed here. One ought to add the stresses (6.13) of carrier viscous liquid to stresses (6.14) to determine the stress tensor for the entire system, that is for the dilute solution of the polymer. 

Comparison with experimental data demonstrates that the bead-spring model allows one to describe correctly linear viscoelastic behaviour of dilute polymer solutions in wide range of frequencies (see Section 6.2.2), if the effects of excluded volume, hydrodynamic interaction, and internal viscosity are taken into account. The validity of the theory for non-linear region is restricted by the terms of the second power with respect to velocity gradient for non-steady-state flow and by the terms of the third order for steady-state flow due to approximations taken in Chapter 2, when relaxation modes of macromolecule were being determined. 

The stress-optical coefficient C is defined by equation (10.27) and the relaxation times t,1 and t][ are defined by relations (2.30). One can see that the dynamo-optical coefficient of dilute polymer solutions depends on the non-dimensional frequency t w, the measure of internal viscosity ip and indices zv and 6... 

In the simplest case, at N = 1, the considered subchain model of a macromolecule reduces to the dumbbell model consisting of two Brownian particles connected with an elastic force. It can be called relaxator as well. The re-laxator is the simplest model of a macromolecule. Moreover, the dynamics of a macromolecule in normal co-ordinates is equivalent to the dynamics of a set of independent relaxators with various coefficients of elasticity and internal viscosity. In this way, one can consider a dilute solution of polymer as a suspension of independent relaxators which can be considered here to be identical for simplicity. The latter model is especially convenient for the qualitative analysis of the effects in polymer solutions under motion. 

Daoud M, Cotton JP, Farnoux B, et al (1975) Solution of flexible polymers. Neutron experiments and interpretation. Macromolecules 8(6) 804—818 Dasbach TP, Manke CW, Williams MC (1992) Complex viscosity for the rigorous formulation of the multibead internal viscosity model with hydrodynamic interaction. J Phys Chem 96(10) 4118—4125 (McMahon)... 

De Gennes PG (1977) Origin of internal viscosity in dilute polymer solution. J Chem Phys 66(12) 5825—5826... 

Maclnnes DA (1977a) Internal viscosity in the dynamics of polymer molecules. J Polym Sci Polym Phys Ed 15(3) 465-476... 

Paul W, Smith GD (2004) Structure and dynamics of amorphous polymers computer simulations compared to experiment and theory. Rep Prog Phys 67 1117-1185 Peterlin A (1967) Frequency dependence of intrinsic viscosity of macromolecules with finite internal viscosity. J Polym Sci A - 2 5(1) 179-193 Peterlin A (1972) Origin of internal viscosity in linear macromolecules. Polym Lett 10 101— 105... 

Pokrovskii VN, Chuprinka VI (1973) The effect of internal viscosity of macromolecules on the viscoelastic behaviour of polymer solutions. Fluid Dyn 8(1) 13-19 Pokrovskii VN, Kokorin YuK (1984) Theory of viscoelasticity of dilute blends of linear polymers. Vysokomolek Soedin B 26 573-577 (in Russian)... 

Rabin Y, Ottinger HCh (1990) Dilute polymer solutions internal viscosity, dynamic scaling, shear thinning, and frequency-dependent viscosity. Europhys Lett 13(5) 423—428 Rallison JM, Hinch EJ (1988) Do we understand the physics in the constitutive equation J Non-Newton Fluid Mech 29(l) 37-55... 

If an amorphoiis polymer is cooled it will usually attempt to crystallize, but because of the high internal viscosity of the medium it is often precluded from packing into its lowest energy conformation. At 0 K, the lack of thermal excitation prevents the occurrence of most photochemical reactions. As the temperature is increased, the specific volume of the polymer will also increase as a result of forming "free volume", that is, space vdiich is not occupied by hard-shell dimensions of the atoms comprising the polymeric structure. The amount of free volume will depend to a certain extent on the previous thermal history. As free volume increases along with thermal excitation, various kinds of molecular motions will be observed in the polymer vdiich can be detected by I ysical measurements. 

Any treatment of diffusion processes in polymers must include estimates of the "internal viscosity", of the solid polymer... 

When considering the rates of chemical processes in polymers which require diffusion of reagents and products, it is necessary to estimate the internal viscosity q. to substitute in expressions such as Equations 6 and 7. We ave made estimates for q in solid polyethylene from luminescence quenching of naphthalene fluorescence in ethylene -OO copolymers [24]. (Table VII)... 

Smets and Evens assumed that the pre-exponential term of the Arrhenius equation of the rate constant is proportional to the jump frequency of a molecular segment from one position to another, i.e. proportional to the reciprocal of the internal viscosity of the bulk polymer at a given temperature. 

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