Characterization of the potential energy landscape of an antiplasticized polymer

The nature of the individual transitions on the potential energy landscape (PEL) associated with particle motion are directly examined for model fragile glass-forming polymer melts, and the results are compared to those of an antiplasticized polymer system. In previous work, we established that the addition of antiplasticizer reduces the fragility of glass formation so that the antiplasticized material is a stronger glass former. In the present work, we find that the antiplasticizing molecules reduce the energy barriers for relaxation compared to the pure polymer, implying that the antiplasticized system has smaller barriers to overcome in order to explore its configuration space. We examine the cooperativity of segmental motion in these bulk fluids and find that more extensive stringlike collective motion enables the system to overcome larger potential energy barriers, in qualitative agreement with both the Stillinger-Weber and Adam-Gibbs views of glass formation. Notably, the stringlike collective motion identified by our PEL analysis corresponds to incremental displacements that occur within larger-scale stringlike particle displacement processes associated with PEL metabasin transitions that mediate structural relaxation. These “substrings” nonetheless seem to exhibit changes in relative size with antiplasticization similar to those observed in “superstrings” that arise at elevated temperatures. We also study the effects of confinement on the energy barriers in each system. Film confinement makes the energy barriers substantially smaller in the pure polymer, while it has little effect on the energy barriers in the antiplasticized system. This observation is qualitatively consistent with our previous studies of stringlike motion in these fluids at higher temperatures and with recent experimental measurements by Torkelson and co-workers.

Figure 1

Vibrational density of states for the pure polymer (solid line) and antiplasticized polymer (dashed line).

Figure 2

(Color online) Excess vibrational density of states for the pure polymer (◇) and the antiplasticized systems (엯) in both the bulk (solid lines) and thin film (dashed lines) geometries.

Figure 3

Composition (mole fraction) of the largest displacement vectors as a function of frequency for the antiplasticized polymer. The overall mole fraction of the system is indicated by the horizontal dashed line.

Figure 4

(Color online) Cumulative probability of finding an energy barrier less than $\Delta U_{\mathit{bar}}$ for the pure polymer (◇) and the antiplasticized polymer (엯). Solid lines indicate the barrier to escape the initial minimum while dotted lines are for the energy barrier into the second minimum.

Figure 5

(Color online) Mean-square displacement $⟨r^2⟩$ against the height of the energy barrier as the system moves from a minimum to the saddle point on the PEL. Results for the pure polymer (◇) and the antiplasticized polymer are shown (엯).

Figure 6

(Color online) Probability of finding a substring of length $L_{s}s$ for the pure polymer (◇) and the antiplasticized polymer (엯) as the system moves from either $M_1$ to SP (solid lines) or from $M_2$ to SP (dashed lines).

Figure 7

(Color online) Extent of cooperativity for the pure polymer (◇) and antiplasticized polymer (엯) plotted against $\Delta U_{\mathit{bar}}$.

Figure 8

(Color online) Cumulative probability of finding an energy barrier less than $\Delta U_{\mathit{bar}}$ for the pure polymer in the bulk (lines) and thin film geometries (엯). Barriers for the $M_1$-to-SP transition are shown with solid lines; $M_2$-to-SP transitions are shown with dashed lines.

Figure 9

(Color online) Cumulative probability of finding an energy barrier less than $\Delta U_{\mathit{bar}}$ for the antiplasticized polymer in the bulk (lines) and thin-film geometries (엯). Barriers for the $M_1$-to-SP transition are shown with solid lines; $M_2$-to-SP transitions are shown with dashed lines.