1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Single molecule probing of the glass transition phenomenon: Simulations of several types of probes
Rent:
Rent this article for
USD
10.1063/1.2794334
/content/aip/journal/jcp/127/15/10.1063/1.2794334
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/15/10.1063/1.2794334

Figures

Image of FIG. 1.
FIG. 1.

Self-incoherent scattering functions of the dumbbell (dash), the polymer chains surrounding it (solid), and of the model system simulated in the absence of the probe (open circles). The probe is either a dimer of the surrounding mers (, , top) or a larger probe (, , bottom). , 0.55, 0.55, 0.6, 0.7, 1.0, and 2.0 from right to left, respectively.

Image of FIG. 2.
FIG. 2.

(Color online) Reduced radiative lifetime (full curves, left ordinate scale) and translational average square displacement (broken curve, right ordinate scale), trajectories of a probe (, ) in a polymer matrix for .

Image of FIG. 3.
FIG. 3.

(Color) Distance matrix for translational DM (top) and rotational RDM (bottom) diffusion of a single probe (, , cf. Fig. 2) in the considered system at temperature . The gray scale indicates the values of (color online).

Image of FIG. 4.
FIG. 4.

(Color) Legendre polynomials (solid) and (dashed) trajectories of a probe (, ) in a polymer matrix for (top) and (bottom). Corresponding translational (solid) and rotational (dashed) average square displacement trajectories ( in the case of the probe in the system at and for ).

Image of FIG. 5.
FIG. 5.

(Color online) Fluorescence lifetime time correlation functions for the dumbbell (, ) in the considered system at temperatures (squares), (circles), (diamonds) and (stars). The error bars are estimated by the Jackknife approach (Refs. 63 and 64).

Image of FIG. 6.
FIG. 6.

(Color) Fluorescence lifetime time correlation functions for the small (, , squares; , , circles) or large (, , diamonds; , , stars) dumbbell in the considered system for two temperatures: and . The error bars are estimated by the Jackknife approach (Refs. 63 and 64).

Image of FIG. 7.
FIG. 7.

(Color online) Orientational time correlation functions of order (solid), 2 (dash), and 4 (dot) and (open diamonds) for the dumbbell (, ) in the considered system at temperatures (top), (middle) and (bottom). The error bars are estimated by the Jackknife approach (Refs. 63 and 64). Black lines are the best stretched exponential fits performed in the relaxation zone of the decays , with and values given in Table I.

Image of FIG. 8.
FIG. 8.

(Color online) (a) Angell plot of the relaxation times of (stars), (large full diamonds), (large filled circles), (small open diamonds), (small open circles), and (small balls) for the dumbbell (, ) in the considered system. (b) Angell plot of the relaxation times of (full symbols) and (open symbols) for a small (, , square; , , circle) or large (, , diamond; , , star) dumbbell in the considered system. Note that, in the standard Angell plot, is normalized by the glass transition temperature , while we normalize here by the critical temperature of mode coupling theory.

Image of FIG. 9.
FIG. 9.

(Color online) Vogel-Fulcher plots of the relaxation times [ (stars), (full diamonds), (full circles)] (open diamonds) and (open circles) for the dumbbell (, ) in the considered system. The values of the Vogel temperature and of the “fragility parameter” are presented in Table II.

Image of FIG. 10.
FIG. 10.

(Color online) Vogel-Fulcher plots of the relaxation times for a small (, , squares; , , circles) or large (, , diamonds; , , stars) dumbbell in the considered system. The values of the Vogel temperature and of the “fragility parameter” are presented in Table III.

Image of FIG. 11.
FIG. 11.

(Color online) Log-log plot of the relaxation times for the small (, , squares; , , diamonds) or large (, , circles; , , stars) dumbbell in the considered system. The parameters and obtained from the fits to a power law (see text) are given in Table IV.

Image of FIG. 12.
FIG. 12.

(Color) Translational (top) and rotational (bottom) mean square displacement curves for the small (, , squares; , , circles) or large (, , diamonds; , , stars) dumbbell in the considered system for two temperatures: and .

Image of FIG. 13.
FIG. 13.

Log-log plot of the relaxation times obtained from the incoherent scattering functions at (a) and translational (b) and rotational (c) mean square displacement curves for the small (, , squares; , , diamonds) or large (, , circles; , , stars) dumbbell in the considered system. The parameters and obtained from the fits to a power law (see text) are given in Table V.

Image of FIG. 14.
FIG. 14.

Power law fits of translational (a) and rotational (b) diffusivities and as functions of (, upper part) and (lower part); and for the small (, , squares; , , diamonds) or large (, , circles; , , stars) dumbbell in the considered system. Results for the exponents are collected in Table VI.

Tables

Generic image for table
Table I.

Amplitudes, relaxation times , and stretching parameters of the OTCFs for , 2, and 4 at various temperatures for the large and heavy dumbbell , , determined by fitting the KWW function to the curves in the relaxation zone. Three values are indicated in most columns for each line, which concern fits starting at , (0.5), and [0.4], respectively. In each case, the amplitude has only been given for the best fit (shown on Fig. 7). The errors determined by the fitting procedure, using a Levenberg-Marquadt algorithm with a least square minimization method, are also indicated for and . The quality of the fits has been judged on the base on the usual criterion.

Generic image for table
Table II.

Parameters obtained by fitting the Vogel Fulcher law to the various relaxation times of the small and light dumbbell. Results of fits obtained by fixing the Vogel temperature to the known value for this polymer model are given in column 3 (Data and fits are shown in Fig. 9). Results of the “best” fits obtained by varying both Vogel temperature and the parameter are given in columns 4 and 5.

Generic image for table
Table III.

Parameters obtained by fitting the Vogal Fulcher law to the fluorescence lifetime relaxation time for the four types of dumbbell. Results of fits obtained by fixing the Vogel temperature to the known value for this polymer model are given in column 3 (Data and fits are shown in Fig. 10). Results of the “best” fits obtained by varying both the Vogel temperature and the parameter are given in column 4 and 5.

Generic image for table
Table IV.

Parameters obtained by fitting the MCT law to the fluorescence lifetime relaxation time for the four types of dumbbell. Results of fits obtained by fixing the critical temperature to the known value for this polymer model are given in column 3 (Data and fits are shown in Fig. 11). Results of the “best” fits obtained by varying both the critical temperature and the parameter are given in column 4 and 5.

Generic image for table
Table V.

Parameters obtained by fitting the MCT law to the fluorescence lifetime relaxation time and the translational. and rotational diffusion constants for the four types of dumbbell. Results of fits obtained by fixing the critical temperature to the known value for this polymer model are given in column 4 (Data and fits are shown in Fig. 13). Results of the “best” fits obtained by varying both the critical temperature and the parameter are given in column 4 and 5.

Generic image for table
Table VI.

Parameters obtained by fitting the fractional functional forms [Eq. (16)] to the relaxation times and for the four types of dumbbell (data and fits are shown in Fig. 14).

Loading

Article metrics loading...

/content/aip/journal/jcp/127/15/10.1063/1.2794334
2007-10-16
2014-04-17
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Single molecule probing of the glass transition phenomenon: Simulations of several types of probes
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/15/10.1063/1.2794334
10.1063/1.2794334
SEARCH_EXPAND_ITEM