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

1. Weigh 0.04 g of polystyrene, and place into a 30 ml vial.
2. Weigh 2 g of toluene into the vial. A 2% by weight solution of polystyrene in toluene yields a film of approximately 100 nm.
3. Let the solution sit O/N to fully dissolve the polystyrene and let the solutions settle.
4. Place a 1 cm x 1 cm Silicon (Si) wafer onto a Spin Coater.
5. Spin the wafer at 8,000 rpm for 45 sec. While it is spinning, drop approximately 1 ml of toluene on the spinning wafer.
   Note: All steps involving spin coating are performed in a fume hood.
6. On the now stationary Si wafer, add the solution from step 1.3 drop-wise onto the Si wafer until the entire surface of the Si wafer is covered.
7. Before the solution dries on the wafer, spin the Si wafer at 4,000 rpm for 20 sec.
8. Determine the thickness of the film using ellipsometry (see step 2).
9. If the film is the desired thickness, anneal the film in a vacuum oven at 393 K for 15 hr.

2. Determining Film Thickness

1. Place the spun cast film onto the ellipsometer stage and measure the ellipsometric angles Ψ(λ) and Δ(λ) at an incident light angle of 70° with a 1 sec acquisition time and the zone averaging setting turned on.
2. Using the ellipsometer software, fit the resulting Ψ (λ) and Δ (λ) data to a three-layer model according to manufacturer's protocol. There are no additional user inputs. The first layer is a substrate layer of Si, the second layer is a native oxide layer with a thickness of 1.5 nm, and the third layer is a Cauchy model (n=A+B/λ² , k=0), which corresponds to the optical properties of the polystyrene film. In this model, A and B are fit parameters, and n and k are the real and imaginary components of the index of the refraction, respectively.
3. For the Cauchy layer, fit the thickness and A and B parameters if the film is above 10 nm. If the film is below 10 nm, only fit A.
   Note: This will be discussed further in the Representative results section.

3. Cooling Rate Dependent T_g Measurements

1. Coat the surface of the heating element of the variable temperature ellipsometer stage with thermal paste.
2. Place the annealed polystyrene film onto the heating element.
3. Clamp the film tightly onto the heating element.
4. Flow 100% dry Nitrogen gas through the temperature stage at a pressure of <69 KPa.
5. Using the temperature stage software, create a temperature profile. This temperature profile begins with a heating ramp to 393 K at 150 K/min. Hold the film at 393K for 20 min.
   1. Then, alternate cooling ramps to 293 K at rates of 150, 120, 90, 60, 30, 10, 7, 3, and 1 K/min with heating ramps to 393 K at 150 K/min. Place a 5 min temperature hold after each ramp.
6. In the ellipsometer software, make a temperature dependent ellipsometry model similar to that in section 2. All three layers are the same, except that the substrate is changed to a temperature dependent Si model.
7. In the layer for the temperature dependent Si model, turn on the "Use Ext Temp from Parm Log" Parameter.
8. Using laboratory equipment controlling software, have the ellipsometer software read the temperature values from temperature stage.
9. Align the ellipsometer such that the signal reaches maximum intensity.
10. Under "Edit Hardware Configurations", set the fast acquisition time to 1 sec with high-accuracy zone averaging. Set the normal acquisition time to 3 sec with high-accuracy zone averaging.
11. Under the "in situ" tab in the ellipsometer software check the "fast acquisition time mode" box, and press "Start Acquisition". Then, start the temperature profile. Before the 3 K/min cooling ramp, uncheck the fast acquisition time box.

4. Determining Values of T_g

1. Export the temperature and thickness profiles into the preferred graphing and analysis software, and separate the temperature and thickness data for all 9 cooling rates.
2. In order to account for the effect of zone averaging during acquisition on the temperature, take every temperature value, and average it with the temperature value preceding it, such that T=(T_i + T_i-1)/2, where T_i is a temperature value at a given time, and T_i-1 is the temperature of the preceding time point.
3. Plot Thickness vs. Temperature for each cooling rate.
4. Perform a linear fit on a portion of the Super Cooled Liquid regime (the high temperature regime with the larger expansion coefficient). This regime will be approximately from 393 K to 380 K.
5. Perform a linear fit on a portion of the glassy regime of that same set of data. This regime has a lower expansion coefficient, and will be approximately from 293 K to 340 K.
6. Find the intersection point of these two lines. The temperature where these lines intersect is the glass transition temperature.
7. Do this for all nine ramps.

5. Analyzing Average Thin Film Dynamics

1. For a given film thickness plot Log(Cooling Rate (K/min)) vs. 1/T_g (K^-1).
2. Compare this indirectly to direct measurements of bulk and surface dynamics by the empirical relation: Cooling Rate * τ_α = 1000.^23,24

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

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

List of materials used in this article

Name	Company	Catalog Number	Comments
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