Confinement-induced mode

III. Confinement-Induced Mode in Thin Films of cis-1,4-Polyisoprene... 

In thin PIP films, for thicknesses comparable to the size of the polymer chains, a novel relaxation process—a confinement-induced mode [5]—shows up (Fig. 10). 

Figure 10. Dielectric loss s" versus temperature at 970 Hz for a thin PIP film of 61 nm (Mw = 35,000 g/mol), showing the segmental, the normal, and the confinement-induced mode. Inset Dielectric loss e" versus temperature at 970 Hz for a PIP film of 677 nm (Mw = 35,000 g/mol), showing the segmental and the normal mode.

Figure 11. Dielectric loss e" versus temperature at 30 Hz showing the segmental, the normal and the confinement-induced mode for thin PIP films I /V/, — 52,000g/mol) of different thicknesses, as indicated.

The overall dynamics of PIP in the context of dependence on the confinement size is illustrated in Fig. 11, showing the temperature dependence of the dielectric loss of PIP (Mw = 52 kg/mol) down to a him thickness smaller than the end-to-end distance of the polymer chains. The confinement-induced mode becomes faster with decreasing him thickness and approaches the segmental mode, while its relaxation strength increases at the expense of the normal mode, which decreases (Figs. 11 and 12). 

The scaling for the relaxation rate of the confinement-induced mode as a function of film thickness is given in Fig. 15, in a double logarithmic plot. The... 

Figure 14. Relaxation rate of segmental, normal, and confinement-induced mode versus inverse temperature for a thin PIP film of 45 nm and different molecular weights, as indicated. Inset The corresponding raw data, i.e. dielectric loss s" vs. temperature at 96 Hz for the same thickness and same molecular weights.

Figure 16. Scheme illustrating the molecular configuration of the confinement-induced mode. R jf represents the end-to-end distance of the terminal subchains formed by the immobilization of the polymer segments at the interface, while d is the film thickness. 

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. 

Taking into account the existing indications for asymmetric interactions at the interfaces (e.g., three-layer model in Ref. 4), two distinct cases must be analyzed (i) Both interfaces immobilize the chains or (ii) the chains are immobilized only at one interface while at the other one they are reflected (hard-wall behavior). In Fig. 18 the distribution of the end-to-end distance of terminal subchains is shown when both interfaces immobilize the chain segments. No shifts of the maximum position of the distribution are observed with decreasing film thickness. This result would imply that the confinement-induced mode does not exhibit thickness dependence, in contrast to the experiment. 

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 confinement-induced mode does not exist in the bulk because it arises from chains in contact with both interfaces. Thus it appears only when the films thickness become comparable to the size of the PIP chains. 

The confinement-induced mode becomes faster with decreasing film thickness because the terminal subchains become on average shorter. 

The confinement-induced mode exhibits no molecular weight dependence because increasing chain length increases also its probability to touch the... 

The relaxation strength of the confinement-induced mode increases because the relative number of immobilized chains increases with decreasing film thickness. 

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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