Chain Entanglement in Thin Freestanding Polymer Films

When a thin glassy film is strained uniaxially, a shear deformation zone (SDZ) can be observed. The ratio of the thickness of the SDZ to that of the undeformed film is related to the maximum extension ratio, $\lambda$, which depends on the entanglement molecular weight, $M_e$. We have measured $\lambda$ as a function of film thickness in strained freestanding films of polystyrene as a probe of $M_e$ in confinement. It is found that thin films stretch further than thick films before failure, consistent with the interpretation that polymers in thin films are less entangled than bulk polymers, thus the effective value of $M_e$ in thin films is significantly larger than that of the bulk. Our results are well described by a conceptually simple model based on the probability of finding intermolecular entanglements near an interface.

Figure 1

(a) A freestanding membrane that has been strained is transferred to a Si substrate. (b) AFM is used to scan the sample in order to measure the thickness of the film and the deformed neck. The image is $25\mu \mathrm{m}\times 25\mu \mathrm{m}$ wide; $z$ range is 140 nm. The scan lines are averaged in a region (white bar) that simultaneously shows the substrate, film, and neck.

Figure 2

Plot of the ratio of the neck thickness to the film thickness, $h_c/h$, as a function of $h$ for three molecular weights. In the inset the data are replotted as the normalized value of the effective entanglement molecular weight, $M_{\mathrm{eff}}/M_e(\mathrm{\text{bulk}})$.

Figure 3

Diagram of the Gaussian chain between two entanglement points before and after an applied strain.

Figure 4

(a) Diagram of a polymer chain in a film. The pervaded volume of a chain is reduced near an interface. (b) Plot of the normalized film-averaged effective entanglement density vs the inverse film thickness (the plot is for $P=0.05$; similar results are obtained for other values of $P$).

Figure 5

Plot of the experimentally obtained value of $(h_c/h{)}^2$ as a function of the dimensionless ratio $R_{ee}/h$ for three molecular weights. According to the model $(h_c/h{)}^2\sim ⟨{\nu }_{\mathrm{eff}}⟩$ [see Fig. 4b].