Monomer friction coefficient

Table 7 Relaxation time (t), self-diffusion coefficient (D), and monomer friction coefficient (Co) of unfilled (B) and nanoclay-filled (BCLNA8) BIMS rubber...

Various factors govern autohesive tack, such as relaxation times (x) and monomer friction coefficient (Co) and have been estimated from the different crossover frequencies in the DMA frequency sweep master curves (as shown in Fig. 22a, b). The self-diffusion coefficient (D) of the samples has been calculated from the terminal relaxation time, xte, which is also called as the reptation time, xrep The D value has been calculated using the following equation ... 

The dependence of the characteristic quantities (6.58) on temperature is mainly determined by the monomer friction coefficient Co, which depends on temperature, concentration, and (for small M) of molecule length (Berry and Fox 1968). The dependencies were recently discussed by Tsenoglou (2001). The monomer friction coefficient Co is a material characteristic of the system, its value is strongly determined by chemical structure of macromolecule as was shown for polybutadiene by Allal et al. (2002). 

We present here the results of such a systematic investigation on the dependence of the self-diffusion coefficient of flexible polymer chains as a function of P and N, conducted on polydimethylsiloxane (PDMS). This model polymer is well above its glass temperature at room temperature (Ta = - 120°C), so that one can expect that spurious effects associated with the variation of the free volume and of the local monomer-monomer friction coefficient with the molecular weights of the chains are minimised. 

An important question is to decide how far one can believe that a self-diffusion coefficient varying like N is characteristic of reptation. It has been argued that additional molecular weight dependences could exist and compensate for departures from the N 2 law [48 to 52]. Such an effect can come from the local monomer-monomer friction coefficient w hich appears as a prefactor in equation 8, hidden in the diffusion coefficient D. Several processes can combine and lead to a local friction which is molecular weight dependent, and W hich decreases when the polymer molecular weight is decreased. This is, for example, the... 

The chain pullout model developed by Xu et al. [42] is described schematically in Fig. 8. A chain, embedded in the polymer, is pulled at one end with a force /which is larger than the critical value/ = Nfmono below which chain pullout cannot occur fmono is a monomer friction coefficient. 

The Rouse model is the simplest molecular model of polymer dynamics. The chain is mapped onto a system of beads connected by springs. There are no hydrodynamic interactions between beads. The surrounding medium only affects the motion of the chain through the friction coefficient of the beads. In polymer melts, hydrodynamic interactions are screened by the presence of other chains. Unentangled chains in a polymer melt relax by Rouse motion, with monomer friction coefficient C- The friction coefficient of the whole chain is NQ, making tha diffusion coefficient inversely proportional to chain length ... 

The purpose of our study was a rheological evaluation of the effect of composition on the properties of ABS resins in the molten state. Steady-state viscosity was determined over a wide range of temperatures and shear rates. The shear modulus in the molten state was determined by measurement of the diameter of the extrudate. ABS resins in the molten state behaved as an amorphous homophase polymer. The effect of the elastomer phase on the viscoelastic properties which characterize the behavior of the continuous matrix, i.e. monomer friction coefficient and molecular weight between entanglements (Me), was calculated by the application of the molecular theories. The significance of these properties in heterophase systems is discussed. 

For imentangled chains the monomer friction coefficient, can be calculated from the self-diffusion coefficient. For C44H90 the self-diffusion coefficient is reported to be 2.4 x 10 cm s and 4.9 X 10 cm s at 400 and 450 K, respectively. Calculate and comment on its temperature dependence. 

At large concentrations of polymer the zero-shear viscosity of the mixture can be written as the product of two parameters a monomer friction coefficient and a structure factor F (1). The friction factor is controlled by local features such as the free volume and depends on the temperature. The structure factor is controlled by the large-scale structure and the configuration of the polymer chain. This factor depends on the dimensions and the molecular weight of the polymer chains and the polymer concentration. If the friction factor is properly evaluated for concentration dependence, the structure factor F depends for concentrated solutions on the polymer concentration to the power 3.4 (1-3). Therefore the rheological properties of a polymer-monomer mixture are mainly determined by the amount and the molecular weight of the polymer in the mixture. These different concepts can be combined to a semiempirical model for the viscosity (4) ... 

Monomer friction coefficient Rheokinetic parameter for molecular weight... 

FIG. 5 Monomer friction coefficient f vs. chain length N, obtained from mapping the atomistic MD data onto the Rouse model (squares) or the reptation model (circles). 

The dependence of the characteristic quantities (138) on temperature is mainly determined by the monomer friction coefficient < o which is a function of temperature, concentration, and (for small M) of molecule length [103]. 

Bulk viscosity, also monomer-monomer friction coefficient... 

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