Confinement-induced mode simulations

Figure 17. Simulations of confined polymer chains as ideal random walks between two hard impenetrable interfaces. Two populations exist free (nonimmobilized) chains, which contribute to the normal mode, and immobilized chains, which contribute to the confinement-induced mode via fluctuations of their terminal subchains.

In the experiment, the normal mode is related to the fluctuations of the end-to-end vector of free (nonimmobilized) chains, while the novel relaxation process was assigned to the fluctuations of the end-to-end distance of terminal subchains (hence, the confinement-induced mode is by its nature also a normal mode, not of the whole chain but of the terminal subchains only). The dynamics of these two relaxation processes is related to the corresponding end-to-end distances, consequently, their distribution, in dependence on thickness and molecular weight, is simulated in our study. 

Summarizing, two conditions must be fulfilled in order to obtain from the simulations a confinement-induced and thickness-dependent distribution of the end-to-end distance for terminal subchains. First, a chain should be in contact with both interfaces. This happens only when the film thickness becomes comparable to the size of the chains and, obviously, explains why the confinement-induced mode does not exist in the bulk. Second, the interactions at the interfaces should be asymmetric One interface should immobilize the polymer chains, while the second one should only reflect them. This asymmetry could be induced by the nonequivalent preparation of the electrodes in the experiment While one interface is prepared by spin-coating, the other one is prepared by evaporation of aluminium on top of the polymer film (see Section II for details). A similar picture of asymmetry was found in studies on thin PS films, with a preparation procedure identical with ours. For thin PS films capped between two aluminum electrodes a three-layer model was proposed, in which, in addition to a middle-layer having bulk properties, a dead (immobilized) layer and a liquid-like layer were assumed to be present at the interfaces. 

The simulations yield MTsc d11 for the scaling of the molecular weight Mtsc of the terminal subchains with thickness d. Assuming for the terminal subchains Rouse-like dynamics (the confinement-induced mode is faster... 

The main finding of the present study is the discovery of a novel relaxation process in thin films of cis-1,4-polyisoprene, called a confinement-induced mode, attributed to fluctuations of terminal subchains formed by the immobilization of the polymer segments at one of the two confining interfaces. In the context of our molecular model and with the help of the simulations, one can understand most of the features observed in the experiment ... 

From the experiment, the relaxation time of the confinement-induced mode depends on thickness as tcim d6. Assuming Rouse dynamics, one obtains %cim d34 from the simulations. In order to explain this discrepancy, more subtle simulations are required. 

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