Theses Doctoral

From Ensemble to Single Molecule: The Origins of Debye-Stokes-Einstein Breakdown Near Tg

Mandel, Nicole Lorraine

Rotational-translational decoupling, in which translational motion is apparently enhanced overrotational motion in violation of Debye-Stokes-Einstein predictions, has been observed in a wide variety of materials near their glass transition temperatures (Tg). This has been posited to result from ensemble averaging in the context of dynamic heterogeneity. In this thesis, single fluorescent probe molecules are tracked rotationally and translationally to interrogate this explanation. In one study, ensemble and single molecule experiments are performed in parallel on the ideal fluorescent probe N,N’-dipentyl-3,4,9,10-perylenedicarboximide (pPDI) in high molecular weight polystyrene near its Tg. Ensemble results show decoupling onset at approximately 1.15Tg, increasing to over three orders of magnitude at Tg. Single molecule measurements also show a high degree of decoupling, with typical molecules at Tg showing translational diffusion coefficients nearly 400 times higher than expected from Debye-Stokes-Einstein predictions.

The same experiments were performed on a microscope with somewhat lower spatial resolution to investigate the role of localization accuracy in apparent degree of breakdown. Here similar, though slightly larger, degrees of breakdown were found, consistent with the idea that averaging across heterogeneous regions, even within a single molecule’s trajectory, is the primary driver of rotational-translational breakdown, while the lower degree of localization accuracy of the microscope additionally leads to some sub-ensemble selection that further inflates apparent breakdown. Across all single molecule experiments, higher degree of breakdown is associated with particularly mobile molecules and anisotropic trajectories, providing support for anomalous diffusion as a critical driver of rotational-translational decoupling and Debye-Stokes-Einstein breakdown.

In a final study, single molecule translational simulations are performed with varying types (spatial and dynamical) and degrees of heterogeneity to assist in interpreting results of single molecule translation experiments. These reveal that fast portions of translational trajectories inflate diffusion coefficients and that, taken together with experimental results, the majority of rotational- translational decoupling in glassy systems occurs through dynamic exchange consistent with wide underlying distributions of diffusion coefficients and exchange coupled to local spatiotemporal dynamics.


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More About This Work

Academic Units
Thesis Advisors
Kaufman, Laura J.
Ph.D., Columbia University
Published Here
April 13, 2022