Chain dynamics diffusion constant

Fig. 5.3. Log-log plot of the self-diffusion constant D of polymer melts vs. chain length N. D is normalized by the diffusion constant of the Rouse limit, DRoUse> which is reached for short chain lengths. N is normalized by Ne, which is estimated from the kink in the log-log plot of the mean-square displacement of inner monomers vs. time [gi (t) vs. t]. Molecular dynamics results [177] and experimental data on PE [178] are compared with the MC results [40] for the athermal bond fluctuation model. From [40]...

Within the Rouse model for polymer dynamics the viscosity of a melt can be calculated from the diffusion constant of the chains using the relation [22,29,30] ... 

The other important physical assumption is that the friction is local (hydro-dynamic interactions are screened in the melt [2]) so that D -(N /N)D with the diffusion constant in the melt of an unentangled chain of segments. Now the characteristic relaxation (Rouse) time of an entanglement segment % is just a /D. so that... 

Two atomistic approaches have been presented briefly above molecular dynamics and the transition-state approach. They are still not ideal tools for the prediction of diffusion constants because (i) in order to obtain a reliable chain packing with a MD simulation one still needs the experimental density of the polymer and (ii) though TSA does not require classical dynamics it involves a number of simplifying assumptions, i.e. duration of jump mechanism, elastic polymer matrix, size of smearing factor, that impair to a certain degree the ab initio character of the method. However MD and TSA are valuable achievements, they are complementary in several... 

There could be two possible reasons for this apparently contradictory situation,. First, in the above discussion, we adopted a diffusion constant that was evaluated from the diffusion constant of polymer chains at the interface between two bulk polymeric layers [72]. Recent measurements have revealed the existence of heterogeneous dynamics in confined geometries such as thin films and nanopores [73,74]. For stacked thin films of polymers, the dynamics vary with an essential dependence on the distance of the layer of interest from the free surface or from the substrate [75]. If such dynamical heterogeneity is taken into account, the diffusion of polymer chains could be restricted by the existence of an immobile region. 

It was discussed in Sect. 4.2 that there is a very slow change in the a-dynamics in stacked thin films of P2CS. There may be several possibilities for this slow change. If heterogeneous diffusion in thin polymer layers is an essential process, then direct measurement of diffusion constant of a tracer polymer chain in a thin layer of the... 

As indicated by Eqs. (3.41) and (3.55), the molecular translational motion and the internal modes of motion of a Rouse chain ultimately depend on the diffusion constant of each individual Rouse bead, D = kT/ The diffusion of a Brownian particle (Eq. (3.3)) can be simulated by the random walk model as shown in Appendix 3.D, which in turn can be used to introduce the diffusion process into different discrete-time models of polymer dynamics (Chapters 8 and 16-18). 

Although an isolated polymer chain with excluded volume interactions is a good model for a macromolecule in dilute solution under good solvent conditions, as far as its conformation is concerned, it is not a correct description of the chain dynamics in this case, of course, due to the neglect of hydro-dynamic interactions. The latter give rise to a scaling of the diffusion constant Djqo=l/Rg rather than D oc i/N, and... 

The first two quantities allow determination of relaxation times of corresponding objects in the model (bonds and chains) and the last two allow determination of diffusion constants. Chain length dependencies of the self-diffusion constant and of the relaxation times of bonds and chains are presented in Fig. 3. These results show that the dynamic behavior of... 

Diffusion constant or any other related properties such as viscosity always differ from original value because of the fast dynamic of the CG beads. Therefore, absolute number for dynamical quantities from CG MD is not comparable with the experimental or atomistic simulation results. However, relative numbers are meaningful for different system of interest. It is a normal practice to scale the dynamical quantities by a scaling factor obtained from known values from atomistic details calculations or experimental observation. In case of PS the diffusion constant calculated from the Einstein s relation (ref equation 14) and CG MD for = 9 chain was 4.8 x 10 enrols and for N = 350 chain the value was 4.6 x 10 cm /s at 500 K. 

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