Monomeric friction coefficient

Fig. 8. Self-diffusion coefficients of polyethylene chains as a function of molecular mass. The measurements were carried out at the same value of the monomeric friction coefficient. (Reprinted with permission from [48]. Copyright 1987 American Chemical Society, Washington)...

In addition to the Rouse model, the Hess theory contains two further parameters the critical monomer number Nc and the relative strength of the entanglement friction A (0)/ . Furthermore, the change in the monomeric friction coefficient with molecular mass has to be taken into account. Using results for (M) from viscosity data [47], Fig. 16 displays the results of the data fitting, varying only the two model parameters Nc and A (0)/ for the samples with the molecular masses Mw = 3600 and Mw = 6500 g/mol. 

Table 4 Monomeric Friction Coefficients of Selected Polymers...

Setting the time scale, the monomeric friction coefficient is a basic quantity in all rheological measurements. This quantity is inferred indirectly in two ways ... 

Table 3.1 Monomeric friction coefficients from NSE experiments compared to rheological data from the compilation of Ferry [34] ...

Fig. 3.8 Temperature dependence of the monomeric friction coefficients for PEP and PE. The symbols present the NSE results (filled triangle PEP, filled circle PE). The solid lines display the respective rheological predictions extrapolations are shown as dashed lines (solid lines prediction [51],point dashed line prediction [34] for PEP)...

Fig. 4.35 Right-hand side Monomeric friction coefficients derived from the viscosity measurements on PB [205]. The open and solid symbols denote results obtained from different molecular weights. Solid line is the result of a power-law fit. Dashed line is the Vogel-Fulcher parametrization following [205]. Left hand side Temperature dependence of the non-ergodicity parameter. The three symbols display results from three different independent experimental runs. Solid line is the result of a fit with (Eq. 4.37) (Reprinted with permission from [204]. Copyright 1990 The American Physical Society)...

Under the simplifying assumption that hydrodynamic interactions may be neglected, the only new parameter that controls the dynamics is a monomeric friction coefficient (Rouse model). Then the prediction for the rate Pj is given by ... 

W. G. Miller, University of Minnesota, Minnesota In vlsco elastic studies the monomeric friction coefficient is used to describe motion. The same parameter Is used to look at translational diffusion of solvent and Its concentration dependence. Is there any relationship between this parameter and your three bond motion or Is the correlation length way too long ... 

In any circumstance where the whole displacement of a polymer chain is involved, it is important to characterise friction arising from the surroundings. This is achieved through the monomeric friction coefficient, , which can be determined from melt viscoelasticity measurement of the Newtonian viscosity, corresponding to the low frequency plateau in rj (co). f is calculated... 

At much higher temperatures, where CDCs are able to develop, one has a temperature dependence of ocdc> which involves both oy2 and the monomeric friction coefficient, f. In systems where the activation energy of f is high enough, its temperature dependence can lead to a steeper decrease of ctcdc with increasing temperature than for ay. For such polymers, at temperatures not much lower than Ta, CDCs can be the favoured micromechanism and a SDZ-CDC transition will take place. 

It is not clear why this transition should occur at such a higher level of arm entanglement for polystyrene stars than for other star polymers. This observation is in direct conflict with the standard assumption that through a proper scaling of plateau modulus (Go) and monomeric friction coefficient (0 that rheological behavior should be dependent only on molecular topology and be independent of molecular chemical structure. This standard assumption was demonstrated to hold fairly well for the linear viscoelastic response of well-entangled monodisperse linear polyisoprene, polybutadiene, and polystyrene melts by McLeish and Milner [24]. 

The first relaxation process (designated A hereafter) corresponds to a Rouse-like relaxation of chain segments between entanglement points. It is assumed that the entanglement points remain fixed during the time-scale of this relaxation and that no diffusion of monomers through the slip-links is allowed in such short times. The associated relaxation time,, is related to a monomeric friction coefficient, to thie number of monomers between... 

Due to difficulties in measuring the zero-shear viscosity of such high molecular weight polymers, and thus deducing the monomeric friction coefficient from Graessley s uncorrelated drag model [43], the following equation adapted from the modified Rouse theory has been applied [8]. 

The results have indicated that the monomeric friction coefficient is sensitive to the presence of the short chains, and is smaller, at a given temperature, than the homopolymer. This observed reduction in has been shown to be only attributed to an increase in the fractional free volume. Indeed, the temperature dependence of the monomeric friction coefficient is described by a WLF-type equation ... 

Figure 21. Logarithmic plot of the monomeric friction coefficient as a function of 1/(T-Tc ,) for PS2000 ( ) and PS2000/PS10(30 wt.-%) ( ).

All viscoelastic functions may be expressed in terms of a single reptation parameter (for example the plateau modulus or tube diameter) and the monomeric friction coefficient (or mobility factor in our terminology), in agreement with the above phenomenological presentation. 

Weibull scale parameter monomeric friction coefficient craze fibril extension ratio (=l/vj) average extension ratio in stretch zone... 

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