Electronic Supplementary Information for
Single Molecule Probe Reports of Dynamic Heterogeneity in Supercooled ortho-Terphenyl
Lindsay M. Leone and Laura J. Kaufman*
Department of Chemistry, Columbia University, New York, NY 10027
*
corresponding author
Heating of the sample by the incident laser light can occur in our experimental set up, and
degree of heating differs not only with incident light power but also with thermal contact
between the sample and the cryostat, which varies with the thickness of vacuum grease used to
affix the sample to the cryostat stage. To test for heating and potentially correct for it in the
samples measured, movies are collected at several powers at temperatures in the interrogated
range for each sample. Median probe rotational correlation time as a function of set temperature
and laser power is used to extrapolate an actual temperature for each sample, as described in the
Supplementary Information of Reference 1 and briefly in Section II.D of this manuscript. The
temperature dependent viscosity data for OTP used to perform the heating correction is given in
Reference 2.
In this manuscript a second, nearly identical heating correction is performed to obtain
relative time scales of probe and host relaxation dynamics as characterized by probe rotational
correlation time and host structural relaxation time, c/. If the published temperature
dependence of viscosity2 and structural relaxation3,4 of OTP were identical, a single c/ for
each probe could be extracted from the heating correction procedure based on viscosity.
However, because these curves are not identical using this approach results in somewhat
temperature-dependent c/values. To avoid this, we perform a second heating correction that
yields c/. As for the viscosity-based heating correction, the set temperature is first corrected to
1
an actual temperature for each movie collected. Here, it is assumed the temperature dependence
of probe c follows the temperature dependence of the structural relaxation of OTP as given by,
2
 J  T


log( )     0  1
0

 T0   T
2
(1)
where τ is the structural relaxation time, T is temperature in Kelvin, and τ0, J and T0 are fit
parameters. The parabolic fit parameters for OTP in the temperature range investigated here as
determined by dielectric spectroscopy are log(τ0) = -9.8 s, J = 2898.5 K and T0 = 341 K4,5.
Using probe rotational correlation times, c, and set temperatures as  and T in Equation
1, respectively, the data is plot and a best-fit line to the data is chosen using the three lowest
temperature data points, where low laser powers are used and little heating is expected. This
initial guess line is used to calculate corrected temperatures for the sample. The difference in the
corrected temperature value and the set recorded temperature is calculated for individual c,med
values and from this data, an average heating in terms of K/mW is obtained. This average value
is then used to correct the set temperature to a new corrected temperature for each τc,med point.
Using the new temperatures and the original τc values, a new best-fit line is found. The slope of
this line is then artificially increased by 2% and the procedure is repeated. This procedure
continues until the calculated best-fit line slope is 1 ± 0.01. At that point, the value of the line at
T = Tg relative to the value of the host structural relaxation at Tg yields τc/τ. Maximum
difference between a set temperature and corrected temperature is 1.9K for the data presented in
this manuscript.
To attain sufficient data at a given temperature, correcting the values for the relaxation
times of the probes to the set temperature rather than correcting the set temperature to an actual
temperature is helpful. Doing this assumes that time-temperature superposition holds over the
2
temperature range between the set and actual temperatures of the combined data. With this
assumption and known actual temperature, heat-corrected τc values can be corrected to the
sample stage temperature via:
 1   2 *10
2
2
 J    T0   T0  
  
 

 T    T 1   T 1  
 0   1   2  
2
(2)
where J and T0 are the parabolic fit parameters, τ2 is the measured rotational relaxation time, T2 is
the actual temperature, T1 is the set temperature of the sample stage, and τ1 is the corrected
relaxation time for the sample stage set temperature.
This process allows determination of c/however, this value depends sensitively on the
structural relaxation data, and in cases where multiple sets of data and fits are available, the
newest published data has been used4. A second procedure to determine c/does not depend on
any particular data set but instead relies on probe measurements, a defined Tg, and a definition of
as 100s at Tg. Using heat-corrected SM data and extrapolating probe c to Tg = 243K yields
very similar c/values to those obtained via the procedure described above for all probe:host
pairs interrogated.
References
1
S. A. Mackowiak, L. M. Leone, and L. J. Kaufman, Probe dependence of spatially
heterogeneous dynamics in supercooled glycerol as revealed by single molecule
microscopy, Phys. Chem. Chem. Phys. 13, 1786-1799 (2011).
2
W. T. Laughlin and D. R. Uhlmann, Viscous flow in simple organic liquids, J. Phys.
Chem. 76, 2317-2325 (1972).
3
R. Richert and C. A. Angell, Dynamics of glass-forming liquids. V. On the link between
molecular dynamics and configurational entropy, J. Chem. Phys. 108, 9016-9026 (1998).
4
R. Richert, On the dielectric susceptibility spectra of supercooled o-terphenyl, J. Chem.
Phys. 123, 154502 (2005).
3
5
Y. S. Elmatad, D. Chandler, and J. P. Garrahan, Corresponding states of structural glass
formers, J. Phys. Chem. B 113, 5563-5567 (2009).
4