Diffusion reptation and

A comparison of different theories is given under Theories of adhesion. Further considerations of interdiffusion are discussed under Solvent welding, Polymer diffusion reptation and interdigitation and Polymer-poiymer adhesion weid strength. 

In the article on Polymer diffusion reptation and interdigitation, the mechanisms of interdiffusion that may occur when two polymers are brought into good contact were considered. Here, we consider how those mechanisms, and the structure they produce, may be related to the adhesion between the polymers and the strength of the interface formed. 

The self-adhesion (autohesion) of polymers is of considerable practical importance as many moulding operations involve the need for streams of merging polymer melt to self-adhere to form a strong bond necessary to the integrity of the moulded article. Mechanisms of polymer diffusion are discussed in Polymer diffusion reptation and interdigitation and theories that relate interfacial structure to strength in Polymer-polymer adhesion models. In the latter article, the vector percolation (VP) model was described, which is here applied to welding, and the practical consequences of its predictions are drawn out. - ... 

Some rubber-based adhesives need vulcanization to produce adequate ultimate strength, and the adhesion is mainly due to chemical interactions at the interface. Other rubber-based adhesives (see Contact adhesives) do not necessarily need vulcanization but need adequate compounding to produce the adhesive joints, mainly with porous substrates. In this case, the mechanism of diffusion dominates their adhesion properties. See Diffusion theory of adhesion and Polymer diffusion reptation and interdigitation. 

When a polymeric and rubbery substrate is put on contact with silicones, interdiffusion of polymer chains may occur (see Polymer diffusion reptation and interdigitation and Compatibility). The original interface becomes an interphase composed of mixtures of the two polymeric materials. Such a macromolecular interdiffusion process is limited... 

Polymer diffusion reptation and interdigitation R P WOOL Mechanisms for polymer chain diffusion... 

The rod is visualised as being constrained to a tube in a similar fashion to entanglements constraining a polymer in reptation theory. So for a finite concentration our diffusion coefficient and rotary Peclet number changes ... 

The realisation of a certain mode of motion of a macromolecule among other macromolecules depends on the lengths of both diffusing macromolecule and macromolecules of the environment. The solid line M divides the dilute blends into those, in which macromolecules of the additive can reptate, and those, where no reptation occurs. The dashed line marks the systems with macromolecules of equal lengths. 

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... 

It is not possible to estimate the value of k in this case, but it will remain proportional to T//7. In concentrated polymer solutions and in solid polymers, diffusion will almost certainly involve movement by reptation and will be very slow. This explains the results reported earlier for low quantum yields for photolysis of backbone carbonyls. 

One can try to locate a critical polymerisation index above which the data are no longer compatible with a Rouse-like dynamics, Ng = 500, lager than the Ng= 100 value determined from the diffusion measurements in a frozen matrix. This is an illustration of the fact that the two processes. Rouse motion and entangled motion are in competition the slowest process is the one which is indeed observed.When the matrix chains are mobile, the entangled dynamics becomes more rapid than pure reptation, and the Rouse motion can dominate the dynamics for larger molecular weights than when the matrix chains are immobile. 

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... 

A value of c equal to 0.3, previously used to describe FT selectivity data on Ru catalysts (4), was also chosen here to describe the behavior of cobalt catalysts. This equation for hydrocarbon diffusion in melts reflects the strong influence of molecular size in reptation and entanglement models of transport in such systems (IJ6). Our model also requires the input of intrinsic values for jSn (given by the asymptotic j8r), jSo, j8r, and j8s, measured independently. After such parameters are specified, the model yields a non-Flory carbon number distribution of increasingly paraffinic hydrocarbons that agrees well with our experimental observations (Fig. 16). 

The center of gravity of a linear chain now moves by two uncorrelated processes, reptation and constraint release, so the diffusion coefficient is just the sum of the individual contributions. Equation 21 gives the reptation contribution. Equation 18 gives the constraint release contribution with

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The above butyl-branched alkane was studied by solid-state 13C NMR, alongside its linear analogue C198H398, to establish the solid-state diffusion coefficient.150 Both alkanes were in the once-folded form. The progressive saturation experiments have shown that the longitudinal relaxation of magnetization is consistent with a solid state chain diffusion process. Reptation and one-dimensional diffusion models were demonstrated to satisfactorily represent the data. The addition of the branch to the alkane chain was shown to result in a decrease in the diffusion coefficient, which ranged from 0.0918 nm2 s 1 for the linear chain to 0.016 nm2 s 1 for the branched chain. These diffusion coefficients are consistent with those of polyethylene. 

The simple reptation model does not properly account for all the relaxation modes of a chain confined in a tube. This manifests itself in all measures of terminal dynamics, as the longest relaxation time, diffusion coefficient and viscosity all have stronger molar mass dependences than the reptation model predicts. Tn Sections 9.4.5 and 9.6.2, more accurate ana-... 

Recall that Fig. 9.3 showed the linear viscoelastic response of a polybutadiene melt with MjM = 68. The squared term in brackets in Eq. (9.82) is the tube length fluctuation correction to the reptation time. With /i = 1.0 and NjN = 68, this correction is is 0.77. Hence, the Doi fluctuation model makes a very subtle correction to the terminal relaxation time of a typical linear polymer melt. However, this subtle correction imparts stronger molar mass dependences for relaxation time, diffusion coefficient, and viscosity. 

Both diffusion coefficient and relaxation time obey stronger power laws in chain length than predicted by the simple reptation model [Eqs (9.8) and (9.12)]. 

To understand this viscosity enhancement, it is easier to start with the theory for linear polymers. The behavior of linear polymers can be described by the reptation model.For a linear polymer of high molecular weight in the melt, chains can be modeled as a confined tube where the diffusion of the chain is restricted along the tube contour. Entanglements are formed between chains where the reptation of a chain along its contour becomes the dominant mode of movement. The addition of a branch point prevents reptation and other forms of movement must occur for the chain to change its configuration. In the case... 

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