Here, we present a protocol for cooling rate dependent ellipsometry experiments, which can determine the glass transition temperature (Tg), average dynamics, fragility and the expansion coefficient of the super-cooled liquid and glass for a variety of glassy materials.
This report aims to fully describe the experimental technique of using ellipsometry for cooling rate dependent Tg (CR-Tg) experiments. These measurements are simple high-throughput characterization experiments, which can determine the glass transition temperature (Tg), average dynamics, fragility and the expansion coefficient of the super-cooled liquid and glassy states for a variety of glassy materials. This technique allows for these parameters to be measured in a single experiment, while other methods must combine a variety of different techniques to investigate all of these properties. Measurements of dynamics close to Tg are particularly challenging. The advantage of cooling rate dependent Tg measurements over other methods which directly probe bulk and surface relaxation dynamics is that they are relatively quick and simple experiments, which do not utilize fluorophores or other complicated experimental techniques. Furthermore, this technique probes the average dynamics of technologically relevant thin films in temperature and relaxation time (τα) regimes relevant to the glass transition (τα > 100 sec). The limitation to using ellipsometry for cooling rate dependent Tg experiments is that it cannot probe relaxation times relevant to measurements of viscosity (τα << 1 sec). Other cooling rate dependent Tg measurement techniques, however, can extend the CR-Tg method to faster relaxation times. Furthermore, this technique can be used for any glassy system so long as the integrity of the film remains throughout the experiment.
The seminal work of Keddie Jones and Corey1 showed that the glass transition temperature (Tg) of ultra-thin polystyrene films decreases with respect to the bulk value at thicknesses lower than 60 nm. Ever since, many experimental studies2-11 have supported the hypothesis that the observed reductions in Tg are caused by a layer of enhanced mobility near the free surface of these films. However, these experiments are indirect measures of a single relaxation time, and thus there is a debate12-18 centered on a direct correlation between average thin film dynamics and the dynamics at the air/polymer interface.
To answer this debate, many studies have directly measured the dynamics of the free surface (τsurface). Nanoparticle embedding,19,20 nanohole relaxation,21 and fluorescence22 studies show that the air/polymer interface has dynamics orders of magnitude faster than the bulk alpha relaxation time (τα) with a much weaker temperature dependence than that of τα. Because of its weak temperature dependence, the τsurface of these films,19-22 and enhanced dynamics of thin polystyrene films,23,24 intersects the bulk alpha relaxation (τα) at a single point T*, which is a few degrees above Tg, and at a τα of ≈ 1 sec. The presence of T* could explain why experiments which probe relaxation times faster than * fail to see any thickness dependence on the Tg of ultra-thin Polystyrene films.13-18 Lastly, while direct measurements of the enhanced mobile layer show that it has a thickness of 4-8 nm,20-22 there is evidence that the propagation length of the dynamics at the air/polymer interface is much larger than the thickness of the mobile surface layer.5,25,26
This report aims to fully describe a protocol for using ellipsometry for cooling rate dependent Tg (CR-Tg) experiments. CR-Tg have been previously used to describe the average dynamics of ultra-thin films of polystyrene.23,24,27,28 Furthermore, This technique was recently used to show a direct correlation between the average dynamics in ultra-thin polystyrene films, and the dynamics at the free surface.23 The advantage of CR-Tg measurements over other types of measurements such as fluorescence, nanoparticle embedding, nanohole relaxation, nanocalorimetry, dielectric spectroscopy, and Brillouin light scattering, studies is that they are relatively quick and simple experiments that do not utilize fluorophores or other complicated experimental techniques. Recent advances in spectroscopic ellipsometry allow this technique to be used to efficiently determine the optical properties of ultra-thin films of polymers and other types of hybrid materials with exceptional accuracy. As such, this technique probes the average dynamics of technologically applicable thin films in temperature and time regimes relevant to the glass transition (T ≤ Tg, τα ≥ 100 sec). Furthermore, this technique will provide information on the expansion coefficients of the glassy and supper cooled liquid states as well as the fragility of the system, which can then be compared with data for bulk films. Lastly, CR- Tg experiments can be used for any glassy system so long as the integrity of the film remains throughout the experiment.
Cooling-Rate dependent Tg measurements are high throughput characterization experiments that can determine the Tg, the expansion coefficient of the glass and the super-cooled liquid, the temperature dependence of the average dynamics, and the fragility of a particular glassy material in a single experiment. Furthermore, unlike fluorescence, embedding, or nanohole relaxation experiments, CR-Tg experiments are relatively quick and simple because they do not utilize fluorophores or other com…
The authors have nothing to disclose.
The Authors would like to acknowledge James A. Forrest for help in the initial idea for this technique.26 This work was supported by funding from the University of Pennsylvania and was partially supported by the MRSEC program of the National Science Foundation under award no. DMR-11- 20901 at the University of Pennsylvania.
Toluene | Sigma Aldrich | 179418-1L | This can be purchased from any chemical company. |
Atactic Polystyrene | Polymer Source Inc. | P-4092-S | This can be purchased from any chemical company. |
THMS 600 temperature stage | Linkam | THMS 600 | any temperature stage that can be fit to an ellipsometer could be used. |
M2000V Spectroscopic Ellipsometer | J.A. Woollam | M200V | This procedure should be applicable for any spectroscopic ellipsometer. |
Spin Coater | Laurell Technologies | WS-650-23B | This Procedure is possible with any spin coater |
Sample vials | Fisher Scientific | 02-912-379 | Any sample vials will do |
Silicon wafers | Virginia semi conductors | 325S1410694D |