Double reptation

ENTANGLED POLYDISPEBSE LINEAR CHAINS DOUBLE REPTATION... 

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

For weakly entangled monodisperse and polydisperse polymer melts, J. des Cloizeavuc [26] proposed a theory based on time-dependent diffusion and double reptation. He combines reptation and Rouse modes in an expression of the relaxation modulus where a fraction of the relaxation spectrum is transferred from the Rouse to the reptation modes. Furthermore, he introduces an intermediate time Xj, proportional to M2, which can be considered as the Rouse time of an entangled polymer movii in its tube. But, in the cross-over region, the best fit of the experimental data is obtained by replaced Xj by an empirical combination of... 

For entangled systems, the two first conditions are fulfilled in the framework of reptation theories a comprehensive expression of the monodisperse relaxation modulus G(M,t) is given by expression 3-24 and the double reptation model generalized to a continous molecular weight distribution provides the integral relation between the MWD function P(M) and the polydisperse experimental... 

Problem 3.13(a) (Worked Example) You have a binary blend containing two different molecular weights. Ml and Ms, of the same polymer. Let the weight fraction of Ml be 0, where Ml corresponds to the high molecular weight. Approximate the linear relaxation moduli of the pure melts by Gi t) = Go exp(-t/rt) and Gs t) Go exp(-t/rs). Derive an expression for G(/) for the blend from double reptation theory. 

What value of a corresponds to the double reptation model In Section 9.3, we have presented theoretical arguments and experimental data supporting the value a =4/3 in -solvents (and melts with ideal chain statistics). What is the expression of the stress relaxation modulus of tube dilation models corresponding to a = 4/3 ... 

Consider an isolated long probe P-mer entangled in a melt of shorter Wmers. Tube dilation assumes that as soon as short chains relax, stress in the long P-mer drops to zero. In particular, a version of tube dilation called double reptation imposes an exact symmetry between single chains in a tube and multi-chain processes. As one chain reptates away, stress at a common entanglement (stress point) is relaxed completely. In constraint release models, this stress relaxes only partially due to connectivity of the P-mer. 

Computer) Starting the double reptation relationship equation (3-116) for a bimodal mixture, use an iterative process to estimate the molecular-weight ratio of the two components of the blend with the relaxation data listed in file MW-Blend. TXT in the CD. This data is for a 50 50 blend. Assume exponential forms for the F(t, M,). 

There is growing evidence that t-T superposition is not valid even in miscible blends well above the glass transition temperature. For example, Cavaille et al. [1987] reported lack of superposition for the classical miscible blends — PS/PVME. The deviation was particularly evident in the loss tangent vs. frequency plot. Lack of t-T superposition was also observed in PI/PB systems [Roovers and Toporowski, 1992]. By contrast, mixtures of entangled, nearly mono-dispersed blends of poly(ethylene-a/f-propylene) with head-to-head PP were evaluated at constant distance from the glass transition temperature of each system, homopolymer or blend [Gell et al, 1997]. The viscoelastic properties were best described by the double reptation model , viz. Eq 7.82. The data were found to obey the time-temperature superposition principle. 

We have proposed the use of a quadratic blending law of the double reptation type to express the viscoelastic behavior of [SIS-SI] blends based on the viscoelastic behavior of the diblock and the (Ptribiock copolymers. It may be expressed as Eq. (15), where triblock is the volume fraction of the triblock copolymer in the [SIS-SI] blend. 

We have already shown [23] that the double reptation law can also reasonably be applied to the complex shear modulus, which simpHfies the calculations by avoiding Fourier transforms from the time domain to the frequency domain. 

Haley, J. C., and T. P. Lodge. 2005. Viscosity predictions for model miscible polymer blends Including self-concentration, double reptation, and tube dilation.. Rheol. 49 1277-1302. 

Pathak, J. A., S. K. Kumar, and R. H. Colby. 2004. Miscible polymer blend dynamics Double reptation predictions of linear viscoelasticity in model blends of polyisoprene and polyjvinyl ethylene). Macromolecules 37 6994—7000. 

The double reptation model was used to evaluate viscoelastic behavior of metallocene-catalyzed polyethylene and low-density polyethylene blends by Peon et al. (2003). They compared their results with those obtained for HDPE/BPE blends prepared under similar conditions. Since this model assumes miscibility between the mixed species, the experimental viscosity of HDPE/BPE blends showed only small deviation compared to that expected according to the reputation miscible model. However, the model underestimated the compositional dependence of the zero-shear viscosity for mPE/LDPE blends, especially at intermediate levels. The enhanced zero-shear viscosity in immiscible blends such as PETG/EVA, PP/EVA, or EVA/PE blends was found to be more abrupt than it is for mPE/LDPE blends (Lacroix et al. 1996, 1997 Peon et al. 2003). 

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). 

Yu et al. (2011) studied rheology and phase separation of polymer blends with weak dynamic asymmetry ((poly(Me methacrylate)/poly(styrene-co-maleic anhydride)). They showed that the failure of methods, such as the time-temperature superposition principle in isothermal experiments or the deviation of the storage modulus from the apparent extrapolation of modulus in the miscible regime in non-isothermal tests, to predict the binodal temperature is not always applicable in systems with weak dynamic asymmetry. Therefore, they proposed a rheological model, which is an integration of the double reptation model and the selfconcentration model to describe the linear viscoelasticity of miscible blends. Then, the deviatirMi of experimental data from the model predictions for miscible... 

The rheological properties of miscible blends tmder different temperatures can be obtained from some theoretical models. One such model is the double reptation self-concentration. The DRSC (double reptation self-concentration) model actually includes the temperature dependency and concentration dependency through a complex mixing mle given by the double reptation model and self-concentration model, which helps to exclude the complex contribution from miscible components under different temperatures in the experimental data and only illustrate the effect of the concentration fluctuation and interface formation. This model is applied to study PMMA/SMA (Wei 2011). 

J. Pe6n, C. Dominguez, J.F. Vega, M. Aroca, J. Martinez-Salazar, Viscoelastic behaviour of metallocene-catalysed polyethylene and low density polyethylene blends use of the double reptation and Palieme viscoelastic models. J. Matra-. Sci. 38,4757-4764 (2003)... 

The Doi and Edwards [67] reptation model provides simple mixing rules for miscible systems without the thermodynamic interactions. For athermal systems Tsenoglou [16, 191] proposed the double reptation model ... 

J. des Cloiseaux, Double Reptation vs. Simple Reptation in Pol3maer Melts Ewrop s. Lett. 5, 437-442(1988). 

The second method uses the dynamic moduli data. To describe the behaviour of polydisperse systems different mixing rules have been proposed in the literature that combine the relaxation features of the monodisperse components. The double-reptation mixing rule proposed by Tsenoglou [27] and des Cloiseaux [28] has been used to calculate the relaxation modulus from known MWDs... 

Fig. 3.41. The experimental master curve for a commercial polypropylene and the prediction from its molecular weight distribution obtained by consideration of double reptation [63].

M. Rubinstein (Eastman Kodak Company) In the des Cloizeaux double reptation model which is similar to the Marrucci Viovy model, it is assumed that a release of constraint chain A imposes on chain B when chain A reptates away completely relaxes the stress in that region for both chains. This would imply that for a homopolymer binary blend of long and short chains would be completely relaxed after each of these K entanglements is released only once. But if an entanglement is released, another one is formed nearby. I believe that to completely relax this section one needs disentanglement events and that the Verdier-Stockmayer flip-bond model or the Rouse model is needed to describe the motion and relaxation of the primitive path due to the constraint release process, as was proposed by Prof, de Gennes, J. Klein, Daoud, G. de Bennes and Graessley and used recently by many other scientists. The fact that double reptation is an oversimplification of the constraint release process has been confirmed by experiments. 

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