Schematic diagram (not to scale) of the epi-fluorescence microscope. BS = beam splitter, F = filter, M = mirror, PEB = piezoelectric buzzer, L = lens.
Rotational relaxation times vs. temperature for tbPDI (blue triangles), dpPDI (red circles), and egPDI (black squares) together with each dye's molecular structure outlined in the same color. Each point represents the heat corrected τc,med value for a single movie. Lines represent the best-fit DSE fit for each PDI dye. Extracted hydrodynamic radii are Vh = 1.87 nm3 (tbPDI), Vh = 1.17 nm3 (dpPDI), and Vh = 0.80 nm3 (egPDI). The structural relaxation of OTP as measured by dielectric spectroscopy 30 is plot as a function of temperature (green line).
(Left) Distribution of SM τc values for (a) tbPDI, (b) dpPDI, and (c) egPDI in OTP at 258 K (black), 257 K (red), 256 K (green), 255 K (blue), 254 K (magenta), 253 K (wine), 252 K (olive), 251 K (orange), and 250 K (cyan). All histograms are normalized to the maximum number of occurrences. Each histogram is taken from two data sets for each dye, with the histograms across data sets normalized to the median τc value of one of the data sets for that particular PDI dye. This alleviates any potential widening of the distribution arising from differing thermal contact of the sample and stage between data sets. (Right) SM data from all temperatures normalized by τc,med and combined to form a single histogram for (d) tbPDI, (e) dpPDI, and (f) egPDI. Each histogram is fit with a Gaussian function (black line). Histogram of τc distribution of simulations of homogeneous rotational diffusion with trajectory length for each simulation tuned to match average experimental trajectory length as described in the text is shown by the red lines.
Distributions of β values from individual SM ACF fits for (a) tbPDI, (b) dpPDI, and (c) egPDI. The solid black lines indicate the median value, βmed, of these distributions. The red curve represents distributions from simulations of homogeneous rotational diffusion with trajectory length set to match average experimental trajectory length. For all experimental and simulated data, β is allowed to float from 0.3 to 2.0 when each ACF is fit with a stretched exponential as described in the text. (d) βQE values for each probe for each movie collected as a function of true temperature for tbPDI (black squares), dpPDI (red circles), and egPDI (blue triangles). The dashed lines of corresponding color represent the mean βQE value for each probe for all temperatures studied. The solid lines of corresponding color represent the βQE values from the corresponding simulations.
SM data from all temperatures normalized and combined to form a single histogram for (a) each PDI in OTP: tbPDI (blue), dpPDI (red), and egPDI (black) and (b) each PDI in glycerol: dpPDI (red), dapPDI (green), and tbPDI (blue). All histograms are normalized to their maximum number of occurrences. Each PDI in OTP histogram is fit with a fixed height Gaussian and each PDI in glycerol histogram is fit with a fixed-height Lorentzian (lines of solid colors corresponding to histogram colors). The histogram for egPDI in OTP is additionally fit with a fixed-height Lorentzian (black dashed line in a) and tbPDI in glycerol is fit with a fixed-height Gaussian (blue dashed line in b). (c) τc,med from each movie plot with respect to Tg/T for egPDI (black squares), dpPDI (red circles), and tbPDI (blue triangles) in OTP and tbPDI (open blue triangles), dapPDI (open green sideways triangle), and dpPDI (open red circles) in glycerol. Structural relaxation data for OTP (dashed blue line) 30 and glycerol (dashed black line) 29 are plot with respect to Tg/T. (d) FWHM from Gaussian (squares) and Lorentzian (circles) fits to each of the OTP (blue) and glycerol (black) histograms pictured in (a) and (b) plot as a function log(τc/τα). FWHM from Gaussian fits of OTP (blue squares) and from Lorentzian fits of glycerol (black circles) τc distributions vs. log(τc/τα) are fit to lines. y-intercepts correspond to FWHM for τc/τα = 1.
(a) βQE with respect to median trajectory length in terms of τc,med for each measurement for egPDI (black squares), dpPDI (red circles), and tbPDI (blue triangles) in OTP and tbPDI (open blue triangles), dapPDI (open green sideways triangles), and dpPDI (open red circles) in glycerol. Inset shows the same data with trajectory length plot on a log scale. (b) Average βQE for each PDI studied in OTP (blue) or glycerol (black) with respect to FWHM from Gaussian (OTP) or Lorentzian (glycerol) fits to each histogram pictured in Figs. 5(a) and 5(b) as well as best-fit lines to the data.
Number of molecules and FWHM values of best-fit Gaussian distributions of log(τc) values for all SM data shown in Fig. 3 , left panel. Average FWHM over all temperatures as a function of probe as well as the FWHM values for the combined histograms shown in the right panel of Fig. 3 are also given.
Various quantities for experiments and simulations for the three employed probes in OTP. Lifetime/τc is determined for each movie as the average time each SM is “on” (typically the time until photobleaching) divided by the average τc value for that movie. These quantities are then averaged. FWHM, βmed, and βQE are experimental quantities as described in the text and shown in Figs. 3 and 4 . FWHMsim, βmed,sim, and βQE,sim are quantities obtained from simulation as described in the text and shown in Figs. 3 and 4 .
Molecular weight (MW), extracted hydrodynamic volumes (Vh), van der Waals volume (Vv), Vh/Vv ratios, and τc/τα values as described in the text for the three probes investigated in OTP and in glycerol. 14
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