Disentanglement rate

Anomalous Transport and Reptation Anomalous transport, disentanglement rate, scaling laws, experiments [57]... 

Fig. 8. Effect of the disentanglement rate on the dissolution time for different particle dimensions. Theoretical predictions have been obtained from the work of Devotta et al. [46]...

The boundary condition on the solvent side of the gel-solvent interface was written by considering that a polymer chain requires a minimum time to disentangle and move out of the gel. This minimum time is the reptation time [58]. Hence, the disentanglement rate is zero till a time equal to the reptation time elapses ... 

It was postulated that for a dissolving polymer, the disentanglement rate, kd, can be given as the ratio of the radius of gyration, tg, to the reptation time, t p ... 

Exact expressions for rg and t p were derived [61]. The final expression for the disentanglement rate was obtained as... 

The objectives of the present research were (i) to develop a solvent transport model accounting for diffusional and relaxational mechanisms, in addition to effects of the viscoelastic properties of the polymer on the dissolution behavior (ii) to perform a molecular analysis of the polymer chain disentanglement mechanism, and study the influence of various molecular parameters like the reptation diffusion coefficient, the disentanglement rate and die gel layer thickness on the phenomenon and (iii) to experimentally characterize the dissolution phenomenon by measuring the temporal evolution of the various fronts in the problem. 

Molecular Analysis of the Diflhision Coefficient. The next step was to obtain expressions for the diffusion coefficients and the disentanglement rate of the polymer. It has been shown by us that the mode of diffiision of the polymer undergoes a change (20) from a reptation-type to a classical Zimm t as the polymer dissolves. Thus, expressions were needed for the "reptation" diffusion coefficient and the Zimm (U sion coefficient. 

Having developed an expression for the tube diameter as a function of time, we now define the disentanglement rate, as... 

The justification for the above definition comes from the argument that the disentanglement rate represents a characteristic length for a disentangling chain divided by a characteristic time. We have chosen this length to be the primitive path and the time to be the reptation time. Using the scaling laws developed in the previous section, we can write... 

This completes the prediction of all the parameters in the system. In the above expression, k. o is the value of the disentanglement rate at t = 0 and this can be approximated oy using the definition given in (27), which is given by... 

A maximum of draw ratio as a function of deformation temperature is also observed for many samples [117,122]. Initially, increased temperature facilitates the relief of excessive strain on individual chain segments by molecular slippage, but above a critical temperature the disentanglement rate overtakes the deformation rate. The temperature at which this occurs in linear samples increases as a function of molecular weight [123]. In ultrahigh molecular weight polyethylene samples, the maximum draw ratio is not obtained until the deformation temperature exceeds the melting temperature of the sample. 

It has already been mentioned that polymer melts are non-Newtonian and are in fact under normal circumstances pseudoplastic. This appears to arise from the elastic nature of the melt which will be touched on only briefly here. In essence, under shear, polymers tend to be oriented. At low shear rates Brownian motion of the segments occurs so polymers can coil up at a faster rate than they are oriented and to some extent disentangled. At high shear rates such re-entangling rates are slower than the orientation rates and the polymer is hence apparently less viscous. 

Viscoelastic polymers essentially dominate the multi-billion dollar adhesives market, therefore an understanding of their adhesion behavior is very important. Adhesion of these materials involves quite a few chemical and physical phenomena. As with elastic materials, the chemical interactions and affinities in the interface provide the fundamental link for transmission of stress between the contacting bodies. This intrinsic resistance to detachment is usually augmented several folds by dissipation processes available to the viscoelastic media. The dissipation processes can have either a thermodynamic origin such as recoiling of the stretched polymeric chains upon detachment, or a dynamic and rate-sensitive nature as in chain pull-out, chain disentanglement and deformation-related rheological losses in the bulk of materials and in the vicinity of interface. 

CR 3nd tp are the contributions from chain recoiling and interfacial dynamics (i.e. drag forces and disentanglement), respectively, and / ve is the viscoelastic loss function which has interfacial and bulk parts. / is a characteristic length of the viscoelastic medium, t is the contact time and n is the chain architecture factor. Fig. 21 illustrates the proposed rate dependency of adhesion energy. 

At high rates of strain, or when complete disentanglement cannot occur when M > M, bond rupture occurs randomly in the network and the percolation parameter p becomes dominated by chain ends such that... 

The melt index (MI) or melt flow index (MFT) is an inverse measure of viscosity. High MI implies low viscosity and low MI means high viscosity. Plastics are shear thinning, which means that their resistance to flow decreases as the shear rate increases. This is due to molecular alignments in the direction of flow and disentanglements. 

The empirical frictional factor (T fric) is independent of shear rate but increases in poor solvent this permits to account for the dependence of the scission rate constant on solvent quality. The entanglement part (r enl), as given by Graessley s theory which considers the effect of entanglement and disentanglement processes, is a complex function of shear rate ... 

This process tends to occur when substituents (R) on the a-carbon atom are bulky enough to reduce markedly the rate of direct SN2 displacement at Ca. Allylic rearrangements are of quite common occurrence, but disentangling the detailed pathway by which they proceed is a matter of considerable difficulty. 

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