Cooling Rate Dependent Ellipsometry Measurements to Determine the Dynamics of Thin Glassy Films

Summary

Here, we present a protocol for cooling rate dependent ellipsometry experiments, which can determine the glass transition temperature (T_g), average dynamics, fragility and the expansion coefficient of the super-cooled liquid and glass for a variety of glassy materials.

Abstract

This report aims to fully describe the experimental technique of using ellipsometry for cooling rate dependent T_g (CR-T_g) experiments. These measurements are simple high-throughput characterization experiments, which can determine the glass transition temperature (T_g), 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 T_g are particularly challenging. The advantage of cooling rate dependent T_g 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 (τ_α) regimes relevant to the glass transition (τ_α > 100 sec). The limitation to using ellipsometry for cooling rate dependent T_g experiments is that it cannot probe relaxation times relevant to measurements of viscosity (τ_α << 1 sec). Other cooling rate dependent T_g measurement techniques, however, can extend the CR-T_g 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.

Introduction

The seminal work of Keddie Jones and Corey¹ showed that the glass transition temperature (T_g) of ultra-thin polystyrene films decreases with respect to the bulk value at thicknesses lower than 60 nm. Ever since, many experimental studies^2-11 have supported the hypothesis that the observed reductions in T_g 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 debate^12-18 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 (τ_surface). 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 (τ_α) with a much weaker temperature dependence than that of τ_α. Because of its weak temperature dependence, the τ_surface of these films,^19-22 and enhanced dynamics of thin polystyrene films,^23,24 intersects the bulk alpha relaxation (τ_α) at a single point T*, which is a few degrees above T_g, and at a τ_α 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 T_g 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 T_g (CR-T_g) experiments. CR-T_g 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-T_g 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 ≤ T_g, τ_α ≥ 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- T_g experiments can be used for any glassy system so long as the integrity of the film remains throughout the experiment.

Protocol

1. Film Preparation Weigh 0.04 g of polystyrene, and place into a 30 ml vial. Weigh 2 g of toluene into the vial. A 2% by weight solution of polystyrene in toluene yields a film of approximately 100 nm. Let the solution sit O/N to fully dissolve the polystyrene and let the solutions settle. Place a 1 cm x 1 cm Silicon (Si) wafer onto a Spin Coater. Spin the wafer at 8,000 rpm for 45 sec. While it is spinning, drop approximately 1 ml of toluene on the spinning wafer.<br …

Representative Results

Fitting Raw Ellipsometry Data Polystyrene films are transparent in the wavelength range of the ellipsometer (500-1,600 nm). Thus a Cauchy model is a good model for describing the index of refraction of polystyrene films. Figure 1A shows an example of Ψ(λ) and Δ(λ) for a thick (274 nm) film of polystyrene, and the resulting fit to the Cauchy model <img alt="Equation 1" src="/f…

Discussion

Cooling-Rate dependent T_g measurements are high throughput characterization experiments that can determine the T_g, 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-T_g experiments are relatively quick and simple because they do not utilize fluorophores or other com…

Materials

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