Correlation function for the logarithm of the intensity ratio (orientational correlation function) in the ensemble average as a function of temperature (thick lines) with fits to a stretched exponential function (thin blue lines). The temperature is given relative to the glass transition temperature, T g = 43 ○C.
Temperature dependence of the correlation time, τ c , for the autocorrelation of the logarithm of the intensity ratio for the two fluorescence polarization directions (orientational correlation) for single Rhodamine B molecules in poly(vinyl acetate) (M w = 100 kg/mol) at various temperatures around the glass transition temperature. Also shown are results from dielectric experiments on the same glass former, 21–23 albeit with differing molecular weights, as indicated.
(a) Intensity of the two polarization components, I ∥ and I ⊥, of the fluorescence emitted by a single Rhodamine B molecule embedded in poly(vinyl acetate) at the glass transition temperature. (b) Ratio of the intensity of the two polarization components, ρ = I ∥/I ⊥ (green), and sequence of single molecule angular jumps (black), reconstructed using a model-free statistical analysis method.
Logarithm of the intensity ratio in the two polarization directions, log (ρ), with ρ = I ∥/I ⊥, for single molecule trajectories recorded with Rhodamine B in poly(vinyl acetate) at various temperatures above and below T g , as indicated on the vertical axis relative to the glass transition temperature. (Top) All trajectories plotted on same time scale and (bottom) time axis scaled with experimental orientational correlation time, τ c .
Probability distribution for waiting times between single molecule reorientation events in poly(vinyl acetate) at various temperatures above and below T g , as indicated.
Ensemble-averaged experimental orientational correlation function at T = T g − 2 K (red) compared to hypothetical correlation functions constructed from experimental waiting times, selectively eliminating correlations between jump sizes (green) and between waiting times (blue), leading to similar correlation functions. (Black line) Hypothetical correlation constructed from the experimental results after removing the longest 10% of the waiting times.
Long-time decay of the scattering function F s (q, t) for the CH 2 group of the model polymer at a temperature of T = 400 K, 350 K, 325 K, 300 K, 275 K, 250 K, 240 K, 230 K, 220 K, 210 K, 200 K, 190 K, 180 K, 170 K, and 160 K (top), and for the majority component, A, in the binary Lennard-Jones system for a reduced temperature of T = 1.0, 0.83, 0.75, 0.67, 0.58, 0.54, 0.50, 0.46, 0.43, 0.42, 0.40, 0.39, 0.38, 0.37, and 0.36 (bottom).
Schematic representation of the event markers investigated in this work: dihedral transitions for polymeric glass former, atom displacements, and neighbor exchanges.
(Top) Time evolution of a dihedral angle in the center of a model polymer chain at T = 250 K. (Bottom) Coordinates of an atom in the binary Lennard-Jones fluid as a function of time at a reduced temperature of T = 0.43 with reconstructed trajectory.
Comparison of the time evolution of a dihedral angle in the center of a model polymer chain at various temperatures as indicated by the axis on the left. (Top) Plotted on an absolute time scale and (bottom) time axis scaled with time-weighted average waiting time (persistence time, τ pers ).
Probability density for the waiting time between structural relaxation events of a given atom in the model polymer system using dihedral transitions (top), neighbor exchanges (center), and atom displacements (bottom) as event markers for temperatures ranging from 250 K to 160 K.
Probability density for the waiting time between structural relaxation events of a given atom in the binary Lennard-Jones system using atom displacements (top), and neighbor exchanges (bottom) as indicators for these events for temperatures ranging from T = 0.5 to 0.37.
Temperature dependence of the structural relaxation time, τ c , of the majority component, A, in the binary Lennard-Jones system (line). Persistence times, τ pers , counting all displacement events exceeding Δr min = 0.15σ AA (open blue circles), and counting only successful displacements (full red circles).
Number of trajectories recorded, N traj , and average trajectory lengths, t avg , in the single molecule experiment at each temperature.
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