Reptation approach

A comparison with the tube diameter derived from plateau moduli measurements on PEB-7 underlines this assertion. The coincidence of tube diameters determined macroscopically by application of the reptation model and direct microscopic results is far better than what could have been expected and strongly underlines the basic validity of the reptation approach. 

From the theoretical point of view, the first refinement of the reptation approach has been to introduce the collective dynamics of the chains in terms of the constraint release process[7, 8, 13]. Due to the motions of the surrounding chains, some constraints which constitute the tube may disappear during one reptation lime, and thus give more freedom to the test chain. Quantitative attempts have been made to take into account these additional... 

The double reptation approach allows us to visualize the blend of n different... 

However, experiments (25) have indicated that the molecular weight exponent is close to 3.4. From the mc els that have been proposed to improve the reptation approach, it appears that in concentrated polymer solutions in good solvents, the solution viscosity is given as... 

The enhanced viscoelastic functions are attributable to additional relaxation processes that occur at low frequencies associated with deformation of the dispersed phase. Therefore, for cases such as mPE/LDPE, where partial miscibility at high LDPE content and the extremely different relaxatimi times of the phases in the blends rich in mPE are observed, a hybrid model including the double reptation approach for the matrix and the linear Palieme approach for the whole system could successfully explain the viscoelastic response of these blends (Peon et al. 2003). 

MC simulations and semianalytical theories for diffusion of flexible polymers in random porous media, which have been summarized [35], indicate that the diffusion coefficient in random three-dimensional media follows the Rouse behavior (D N dependence) at short times, and approaches the reptation limit (D dependence) for long times. By contrast, the diffusion coefficient follows the reptation limit for a highly ordered media made from infinitely long rectangular rods connected at right angles in three-dimensional space (Uke a 3D grid). 

The earliest and simplest approach in this direction starts from Langevin equations with solutions comprising a spectrum of relaxation modes [1-4], Special features are the incorporation of entropic forces (Rouse model, [6]) which relax fluctuations of reduced entropy, and of hydrodynamic interactions (Zimm model, [7]) which couple segmental motions via long-range backflow fields in polymer solutions, and the inclusion of topological constraints or entanglements (reptation or tube model, [8-10]) which are mutually imposed within a dense ensemble of chains. 

A quantitative analysis of scattering data, originating from the crossover regime between short-time Rouse motion and local reptation, needs explicit consideration of the initial Rouse motion neglected by de Gennes. Ronca [50] proposed an effective medium approach, where he describes the time-dependent... 

Polydispersity of the molecular weight is not so well described by the DE approach, even qualitatively. In reptation theory the blend of two compatible homopolymers A and B of different molecular weights is given by... 

Rubinstein has constructed on a reptation-fluctuation approach a detailed self-consistent theory of constraint release, allowing each loss of entanglement in one chain to permit a random jump in the tube of another [37]. When this is done the form of predicted relaxation functions are in good accord with experiments. However, in monodisperse linear melts it appears that the fluctuation contribution is more important than constraint release. 

There are a number of QMC approaches being pursued that are variously labeled as variational MC (VMC), diffusion MC (DMC), auxiliary field QMC [18], and reptation QMC [19]. The methods that have found the most application to molecules are the leading two listed and these will be the focus of further comments. 

Pokrovskii VN (2006) A justification of the reptation-tube dynamics of a linear macromolecule in the mesoscopic approach. Physica A 366 88-106 Pokrovskii VN (2008) The reptation and diffusive modes of motion of linear macromolecules. J Exper Theor Phys 106(3) 604-607... 

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