Entanglement coupling theory

In the entanglement coupling theory, (8) the self-diffusion constant is related to N as... 

Each of the viscoelastic parameters G°, rj0, and Je° has associated with it a characteristic molecular weight which either measures an equivalent spacing of entanglement couples along the chain (Me, deduced from G with the kinetic theory of rubber elasticity), or marks the onset of behavior attributed to the presence of entanglements (Mc and AT, deduced from r/0 and Je° as functions of molecular weight). Table 5.2 lists Me, Mc, and M c for several polymers. Aside from certain difficulties in their evaluation, each is a rather direct and independent reflection of experimental fact. 

Kokorin YuK, Pokrovskii VN (1993) New approach to the relaxation phenomena theory of the amorphous linear entangled polymers. Int J Polym Mater 20(3-4) 223-237 Kostov KS, Freed KF (1997) Mode coupling theory for calculating the memory functions of flexible chain molecules influence on the long time dynamics of oligoglycines. J Chem Phys 106(2) 771-783... 

The self-difhision of polymers ) in concentrated and undiluted solutions has been described by at least three theories entanglement coupling, reptation, and cooperative. 

Friction coefficients which vary with position and elastic coupling have also been introduced by Hansen, Williams, and Shen, as well as intramolecular entanglement coupling Hayashi treats an entafigled molecule as moving in a viscoelastic medium. A detailed discussion of some of these theories has been presented by Graessley. °... 

The terminal relaxation time t can be roughly estimated from equation 7 of Chapter 10, derived from the Rouse theory it may be expected to be nearly correct since the molecular weight is only moderately greater than that for onset of entanglement coupling effects. The result is ti = 1.2 X 10 sec, which happens to be very close to the observed value of 1.3 X 10 sec. 

Figure 2.13 Model of several orders of coupling through entanglements according to Bueche theory.

As we conjectured in the introduction, the fundamental role of topology in this approach to entangled polymer dynamics would indicate that changes to the topology of the molecules themselves would radically affect the dynamic response of the melts. In fact rheological data on monodisperse star-branched polymers, in which a number of anionically-polymerised arms are coupled by a multifunctional core molecule, pre-dated the first application of tube theory in the presence of branching [22]. Just the addition of one branch point per molecule has a remarkable effect, as may be seen by comparing the dissipative moduli of comparable linear and star polymer melts in Fig. 5. 

In a mode coupling approach, a microscopic theory describing the polymer motion in entangled melts has recently been developed. While these theories describe well the different time regimes for segmental motion, unfortunately as a consequence of the necessary approximations a dynamic structure factor has not yet been derived [67,68]. 

The manifestation of the dipole-dipole approximation can be seen explicitly in Equation (3.134) as the R 6 dependence of the energy transfer rate. In Equation (3.134) the electronic and nuclear factors are entangled because the dipole-dipole electronic coupling is partitioned between k24>d/(td R6) and the Forster spectral overlap integral, which contains the acceptor dipole strength. Therefore, for the purposes of examining the theory it is useful to write the Fermi Golden Rule expression explicitly,... 

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... 

We presented our most recent NCS results of short lived protonic quantum entanglement in different materials. Quantum entanglement manifests itself by a strong shortfall of the protonic SCS density. The emphasis of the present work is on the different electronic environments the protons are coupled to. As pointed out in the introduction, within the framework of modern quantum theory, the environment may be responsible both for the creation and destruction of QE. The present experimental results on II O / D2O, LiH and LaH-2 and Lai 1-2 indicate that the electronic environment surrounding the hydrogen atom in the material is responsible for the different features of the cross section anomalies of the proton and thus for different decoherence mechanisms. 

Decoherence theory states that the entanglement in a system is broken only when the environment vectors, to which it is coupled, form an orthogonal set. This can be expressed as a condition on the reduced density operator ps> corresponding to the product wavefunction J>) = afc) E, i)(Sk, particle system (with orthonormal basis vectors ) ) coupled to an environment E (basis vectors E,i) ),... 

For the restricted case of low molecular weights and no coupling entanglements, the viscoelastic properties of star-branched undiluted polymers can be described by a special case of the Zimm-Kilb theory o in which there is no hydrodynamic interaction. Calculations were made by Ham i by use of a method which is somewhat different from that of Rouse but yields the same results for unbranched molecules. Stars with arms of unequal length were included. For such a branched molecule, the terminal relaxation time ti, the viscosity r/o, and the steady-state compliance are always smaller than for an unbranched molecule of the same molecular weight the more branches and the more nearly equal their lengths, the... 

The new elements are required to describe new interaction phenomena that involve, in an entangled way, the molecular system, the medium (i.e. the solvent) and the external time-dependent perturbing fields. The couplings has two main effects. The first effect is to add a non-linearity in the time-dependent QM problem. More specifically, the time-dependent QM problem requires a proper extension of the time-dependent variation principle. The second effect is to induce a time-dependence in the solute-solvent responsive interaction, which must be described in a non-equilibrium solvation scheme. The PCM response theory face also the complex problem of the connection of the response functions of the molecular solutes... 

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