Liquids Near the Glass Transition are Supercooled! Investigating the ...
Liquids Near the Glass Transition are Supercooled! Investigating the Dynamic Heterogeneities of Supercooled Glycerol using Single Molecule Microscopy Lindsay M. Leone, Stephan A. Mackowiak, and Laura J. Kaufman Department of Chemistry, Columbia University, 3000 Broadway, New York, NY 10027
Introduction
Analysis
Schematic diagram of probes (red) embedded in a supercooled liquid host. The probe mimics the slow (white ovals) or fast (green ovals) dynamics of the molecules that surround it.
Glass former host
The intensities of both polarizations of fluorescence emission of each molecule are recorded over time. From these trajectories, the linear dichroism (LD) is calculated. Subsequently, an autocorrelation function (ACF) is calculated and fit with the non exponential decay function. From this fit, the rotational relaxation time, τc, is extracted: t β
C(t) = Ke ( ) τ
Linear Dichroism
Bulk Dynamics Before considering the information contained in the SM results (left), first, the average results for the probes studied must be considered. For each PDI probe in glycerol for temperatures ranging from 198 K (1.04Tg) – 212 K (1.12Tg), all SM τc values are averaged as shown on the graph below. Based on the DebyeStokesEinstein (DSE) equation for typical liquids,
τc = Vη(T) kBT
dapPDI
dapPDI, MW = 561 g/mol
a hydrodynamic volume for each probe is assigned based on the probe's average τc values across temperatures. Unexpectedly, the probe with the largest molecular weight and space filling volume, tbPDI rotated the fastest (corresponding to the smallest hydrodynamic volume). This suggests hydrogenbonding ability of dpPDI and dapPDI (which is sterically hindered by the bulky tbutyl groups in tbPDI) slows their rotation. V = 2.02nm3
tbPDI, MW = 767 g/mol V = 1.27nm3
tbPDI
V = 0.40nm
3
Alternates plane polarized light between s to p polarization
Each molecule's s and ppolarized emission fluorescence intensity is tracked.
AOM = acoustooptical modulator EOM = electrooptical modulator L = lens F = filter BS = beamsplitter
An ACF for each movie for each molecule is calculated and fit with the nonexponential decay function. All τc's for each molecule are normalized to the smallest τc recorded for that particular
Ip
τc= τ Γ (1 ) β β
Breadth of Relaxation Times
dpPDI, MW = 599 g/mol
τ
(103τα 106τα) between each movie, and subsequently the linear dichroism is calculated.
Heterogeneous Dynamics
Fluorescent Probes
Experimental Setup
exchange on very long times compared to τα. Several movies are collected consecutively on the same dpPDI molecules embedded in a glycerol sample at a given temperature with specific wait times
t β ( )
Autocorrelation Function
Above are the normalized distributions of τc values for each SM probe across eight temperatures: . Each histogram for a given temperature contains at least 150 molecules and as many as 1319! The histograms have a log normal distribution, and the shape and width of the distributions for a given probe remain constant as a function of temperature, suggesting the degree of heterogeneity is constant over the temperature range probed. The broader distribution of tbPDI relaxation times relative to those of dpPDI and dapPDI suggests that the more quickly rotating probes can report a more significant breadth of heterogeneity than the more slowly rotating probes. Therefore, the time averaging resulting from relatively slow probe rotation can be considered responsible for narrowing the rotational relaxation time distribution. This suggests that dynamic exchanges occur on time scales similar to or shorter than probe rotation. Explicit investigation of the time scale of dynamic exchange is discussed at right.
Dynamic Exchange
molecule. These values are plotted. Changing values of τc (as indicated by crossing lines in the figure at left) indicate changes in dynamics. Investigation of such changes in τc as a function of waiting
The time scale on which regions of molecules alter their dynamics is investigated explicitly using two complementary techniques that probe different time scales.
times from 103τα 106τα
indicates no more exchanges occur
Window Shifting Technique A window shifting approach can detect changes in dynamics during the collected trajectories. The LD trajectory for each molecule is split up into segments by a window slid along the trajectory. An ACF is calculated and fit for each segment, and the relaxation times from each fit are plotted a function of starting window position time. This is called trajectory. Each molecule can now be assessed for heterogeneity, and exchange times can be determined. At 204K, 15 30% of individual probe molecules are found to be heterogeneous by this approach. A distribution of exchange times (τex) with respect to τc is τtrajectory plot presented for all heterogeneous dpPDI molecules (out of 243 molecules assessed) at 204K (below). τex/τc can be translated into values relative to τα , the structural relaxation time of glycerol. As such, τex/τα ∼3600 for dpPDI and τex/τα ∼600 for tbPDI in glycerol at 204K. This large shows probe size difference sensitively influences the time scale on which exchange times can be assessed. We assess exchange on longer time scales relative to τα in a complementary technique presented at right.
106τα
105τα
Results and Discussion
Glycerol, MW = 92 g/mol Tg=190K (83°C) Fluorescent probes are uniformly mixed in spectrophotometric grade glycerol to make a 109 M solution. The probe/glycerol solution is spin coated onto a clean silicon wafer. After the sample is placed in the cryostat, the sample is held under vacuum and cooled to the desired temperature near glycerol's Tg. The fluorophores in the sample are excited by alternating s and p polarized light from a 514 nm Ar+ ion laser. The emitted fluorescence is split into 2 orthogonal polarizations by a Wollaston prism and collected on an EMCCD camera. As the orientation of the induced dipole of the probe changes due to the relaxation of the surrounding host molecules, the emitted fluorescence will change, and therefore its rate of rotation can be monitored.
Ke
Is
dpPDI
Experimental
A second technique is performed to directly observe dynamic
ppolarization
τc / τminimum
Amorphous systems lacking long range order in the temperature range between the melting temperature, Tm, and the glass transition temperature, Tg, are known as supercooled liquids. They remain one of the least understood types of condensed matter; therefore, their fundamental properties as well as applications are of interest. Supercooled liquids exhibit nonexponential relaxations and are believed to have submicron sized regions of molecules exhibiting relaxation times that can differ by orders of magnitude from those in neighboring regions. To observe the length scales over which these heterogeneous regions exist and the time scales on which they persist while avoiding ensemble averaging over multiple regions, a single molecule (SM) approach becomes crucial. SM fluorophores embedded in the glass former host are believed to mimic the dynamics of their surrounding molecules. By observing many individual probes' rotational relaxation rates simultaneously using wide field single molecule microscopy across temperatures near Tg, the dynamics of the supercooled liquid can be monitored. The breadth of rotational relaxation times reports on the spatial heterogeneity of the system while the changes in a particular probe's dynamics over time reports on temporal heterogeneity, i.e. whether the dynamics are changing from fast to slow or vice versa.
spolarization
Long Time Heterogeneity Assessment
10 τ α 5
10 τ α 6
between 105τα
and
106τα than at shorter
times.
Conclusions Heterogeneous Dynamics ●
Temperature dependence of the median relaxation time for each probe mirrors that of glycerol. ●
●
The calculated hydrodynamic volume is the smallest for the largest probe, tbPDI, due to its lack of hydrogenbonding with glycerol.
On the SM level ●
●
●
The distribution of relaxation times of probes ● appears lognormal. ● is relatively constant as a function of temperature. The breadth of spatially heterogeneous dynamics reported is not proportional to probe molecular weight but is proportional to average probe rotational relaxation time. Temporal not spatial averaging by the probe is the determining factor for reported breadth of heterogeneity.
Dynamic Exchange ●
The window shifting technique reports heterogeneity is present at the time scales probed for all SM probes. ●
●
Long time sensitivity length is ~103τα105τα (depending on the probe).
The long time heterogeneity assessment of exchange is consistent with results attained from the window shifting analysis. ●
An upper bound on exchange time dynamics in supercooled glycerol is attained. Future Research
● ●
Investigating probe dependent behavior in a nonpolar glass former Measuring translation and rotation of probe molecules in a glassy host
Acknowledgements This research was supported by the National Science Foundation under grant numbers CHE 0744322 and DGE 0801530 and NSF GRFP. Contributors to the work shown here are Stephan Mackowiak, Tobias Herman, Lindsay Leone and Professor Laura Kaufman. Also, a special thanks to all of the Kaufman lab members for their help and support.
Introduction
Analysis
Schematic diagram of probes (red) embedded in a supercooled liquid host. The probe mimics the slow (white ovals) or fast (green ovals) dynamics of the molecules that surround it.
Glass former host
The intensities of both polarizations of fluorescence emission of each molecule are recorded over time. From these trajectories, the linear dichroism (LD) is calculated. Subsequently, an autocorrelation function (ACF) is calculated and fit with the non exponential decay function. From this fit, the rotational relaxation time, τc, is extracted: t β
C(t) = Ke ( ) τ
Linear Dichroism
Bulk Dynamics Before considering the information contained in the SM results (left), first, the average results for the probes studied must be considered. For each PDI probe in glycerol for temperatures ranging from 198 K (1.04Tg) – 212 K (1.12Tg), all SM τc values are averaged as shown on the graph below. Based on the DebyeStokesEinstein (DSE) equation for typical liquids,
τc = Vη(T) kBT
dapPDI
dapPDI, MW = 561 g/mol
a hydrodynamic volume for each probe is assigned based on the probe's average τc values across temperatures. Unexpectedly, the probe with the largest molecular weight and space filling volume, tbPDI rotated the fastest (corresponding to the smallest hydrodynamic volume). This suggests hydrogenbonding ability of dpPDI and dapPDI (which is sterically hindered by the bulky tbutyl groups in tbPDI) slows their rotation. V = 2.02nm3
tbPDI, MW = 767 g/mol V = 1.27nm3
tbPDI
V = 0.40nm
3
Alternates plane polarized light between s to p polarization
Each molecule's s and ppolarized emission fluorescence intensity is tracked.
AOM = acoustooptical modulator EOM = electrooptical modulator L = lens F = filter BS = beamsplitter
An ACF for each movie for each molecule is calculated and fit with the nonexponential decay function. All τc's for each molecule are normalized to the smallest τc recorded for that particular
Ip
τc= τ Γ (1 ) β β
Breadth of Relaxation Times
dpPDI, MW = 599 g/mol
τ
(103τα 106τα) between each movie, and subsequently the linear dichroism is calculated.
Heterogeneous Dynamics
Fluorescent Probes
Experimental Setup
exchange on very long times compared to τα. Several movies are collected consecutively on the same dpPDI molecules embedded in a glycerol sample at a given temperature with specific wait times
t β ( )
Autocorrelation Function
Above are the normalized distributions of τc values for each SM probe across eight temperatures: . Each histogram for a given temperature contains at least 150 molecules and as many as 1319! The histograms have a log normal distribution, and the shape and width of the distributions for a given probe remain constant as a function of temperature, suggesting the degree of heterogeneity is constant over the temperature range probed. The broader distribution of tbPDI relaxation times relative to those of dpPDI and dapPDI suggests that the more quickly rotating probes can report a more significant breadth of heterogeneity than the more slowly rotating probes. Therefore, the time averaging resulting from relatively slow probe rotation can be considered responsible for narrowing the rotational relaxation time distribution. This suggests that dynamic exchanges occur on time scales similar to or shorter than probe rotation. Explicit investigation of the time scale of dynamic exchange is discussed at right.
Dynamic Exchange
molecule. These values are plotted. Changing values of τc (as indicated by crossing lines in the figure at left) indicate changes in dynamics. Investigation of such changes in τc as a function of waiting
The time scale on which regions of molecules alter their dynamics is investigated explicitly using two complementary techniques that probe different time scales.
times from 103τα 106τα
indicates no more exchanges occur
Window Shifting Technique A window shifting approach can detect changes in dynamics during the collected trajectories. The LD trajectory for each molecule is split up into segments by a window slid along the trajectory. An ACF is calculated and fit for each segment, and the relaxation times from each fit are plotted a function of starting window position time. This is called trajectory. Each molecule can now be assessed for heterogeneity, and exchange times can be determined. At 204K, 15 30% of individual probe molecules are found to be heterogeneous by this approach. A distribution of exchange times (τex) with respect to τc is τtrajectory plot presented for all heterogeneous dpPDI molecules (out of 243 molecules assessed) at 204K (below). τex/τc can be translated into values relative to τα , the structural relaxation time of glycerol. As such, τex/τα ∼3600 for dpPDI and τex/τα ∼600 for tbPDI in glycerol at 204K. This large shows probe size difference sensitively influences the time scale on which exchange times can be assessed. We assess exchange on longer time scales relative to τα in a complementary technique presented at right.
106τα
105τα
Results and Discussion
Glycerol, MW = 92 g/mol Tg=190K (83°C) Fluorescent probes are uniformly mixed in spectrophotometric grade glycerol to make a 109 M solution. The probe/glycerol solution is spin coated onto a clean silicon wafer. After the sample is placed in the cryostat, the sample is held under vacuum and cooled to the desired temperature near glycerol's Tg. The fluorophores in the sample are excited by alternating s and p polarized light from a 514 nm Ar+ ion laser. The emitted fluorescence is split into 2 orthogonal polarizations by a Wollaston prism and collected on an EMCCD camera. As the orientation of the induced dipole of the probe changes due to the relaxation of the surrounding host molecules, the emitted fluorescence will change, and therefore its rate of rotation can be monitored.
Ke
Is
dpPDI
Experimental
A second technique is performed to directly observe dynamic
ppolarization
τc / τminimum
Amorphous systems lacking long range order in the temperature range between the melting temperature, Tm, and the glass transition temperature, Tg, are known as supercooled liquids. They remain one of the least understood types of condensed matter; therefore, their fundamental properties as well as applications are of interest. Supercooled liquids exhibit nonexponential relaxations and are believed to have submicron sized regions of molecules exhibiting relaxation times that can differ by orders of magnitude from those in neighboring regions. To observe the length scales over which these heterogeneous regions exist and the time scales on which they persist while avoiding ensemble averaging over multiple regions, a single molecule (SM) approach becomes crucial. SM fluorophores embedded in the glass former host are believed to mimic the dynamics of their surrounding molecules. By observing many individual probes' rotational relaxation rates simultaneously using wide field single molecule microscopy across temperatures near Tg, the dynamics of the supercooled liquid can be monitored. The breadth of rotational relaxation times reports on the spatial heterogeneity of the system while the changes in a particular probe's dynamics over time reports on temporal heterogeneity, i.e. whether the dynamics are changing from fast to slow or vice versa.
spolarization
Long Time Heterogeneity Assessment
10 τ α 5
10 τ α 6
between 105τα
and
106τα than at shorter
times.
Conclusions Heterogeneous Dynamics ●
Temperature dependence of the median relaxation time for each probe mirrors that of glycerol. ●
●
The calculated hydrodynamic volume is the smallest for the largest probe, tbPDI, due to its lack of hydrogenbonding with glycerol.
On the SM level ●
●
●
The distribution of relaxation times of probes ● appears lognormal. ● is relatively constant as a function of temperature. The breadth of spatially heterogeneous dynamics reported is not proportional to probe molecular weight but is proportional to average probe rotational relaxation time. Temporal not spatial averaging by the probe is the determining factor for reported breadth of heterogeneity.
Dynamic Exchange ●
The window shifting technique reports heterogeneity is present at the time scales probed for all SM probes. ●
●
Long time sensitivity length is ~103τα105τα (depending on the probe).
The long time heterogeneity assessment of exchange is consistent with results attained from the window shifting analysis. ●
An upper bound on exchange time dynamics in supercooled glycerol is attained. Future Research
● ●
Investigating probe dependent behavior in a nonpolar glass former Measuring translation and rotation of probe molecules in a glassy host
Acknowledgements This research was supported by the National Science Foundation under grant numbers CHE 0744322 and DGE 0801530 and NSF GRFP. Contributors to the work shown here are Stephan Mackowiak, Tobias Herman, Lindsay Leone and Professor Laura Kaufman. Also, a special thanks to all of the Kaufman lab members for their help and support.
