Article pubs.acs.org/JPCA
Mobility of Supercooled Liquid Toluene, Ethylbenzene, and Benzene near Their Glass Transition Temperatures Investigated Using Inert Gas Permeation R. Alan May, R. Scott Smith,* and Bruce D. Kay* Fundamental and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States ABSTRACT: We investigate the mobility of supercooled liquid toluene, ethylbenzene, and benzene near their respective glass transition temperatures (Tg). The permeation rate of Ar, Kr, and Xe through the supercooled liquid created when initially amorphous overlayers are heated above their glass transition temperature is used to determine the diffusivity. Amorphous benzene crystallizes at temperatures well below its Tg, and as a result, the inert gas underlayer remains trapped until the onset of benzene desorption. In contrast, for toluene and ethylbenzene the onset of inert gas permeation is observed at temperatues near Tg. The inert gas desorption peak temperature as a function of the heating rate and overlayer thickness is used to quantify the diffusivity of supercooled liquid toluene and ethylbenzene from 115 to 135 K. In this temperature range, diffusivities are found to vary across 5 orders of magnitude (∼10−14 to 10−9 cm2/s). The diffusivity data are compared to viscosity measurements and reveal a breakdown in the Stokes−Einstein relationship at low temperatures. However, the data are well fit by the fractional Stokes− Einstein equation with an exponent of 0.66. Efforts to determine the diffusivity of a mixture of benzene and ethylbenzene are detailed, and the effect of mixing these materials on benzene crystallization is explored using infrared spectroscopy.
I. INTRODUCTION Glasses and other noncrystalline solids are utilized in a variety of scientific and applied fields and are important in diverse disciplines ranging from art and architecture to catalysis and drug delivery.1 Given that glasses and amorphous solids hold such a ubiquitous place in our lives, it is reasonable to assume that they are well studied. Indeed, there are several review articles that describe the properties of and discuss the scientific issues related to our understanding glasses and amorphous solids.2−8 However, the relative importance of kinetic processes to the properties of glasses makes it difficult to clearly define and measure these properties. For example, the glass transition temperature, Tg, is not an intrinsic property but varies based on the chosen definition and experimental factors such as the cooling rate. Difficulties caused by this ambiguity are compounded by the constant threat that the supercooled liquid will fall back into its thermodynamically stable crystalline state. Obtaining high quality measurements in this temperature range is difficult but necessary to understand the rapid change in properties observed when materials approach Tg. We have worked to overcome the measurement limitations imposed by crystallization by using nanoscale amorphous films created by vapor depositing materials at temperatures well below Tg. The idea is that when heated above its Tg, an amorphous solid will transform into a supercooled liquid, and at temperatures near Tg, extremely slow diffusivity will delay crystallization. We have previously shown that the lifetime of the supercooled liquid at these low temperatures is long enough to observe the intermixing of distinct layers over nanometer distances.9−12 More recently, we have extended this basic approach to develop a technique in which the permeation rate © 2013 American Chemical Society
of inert gases is used to determine the diffusivity of the supercooled liquid.13−19 In this technique, a layer of an inert gas (e.g., Ar, Kr, and Xe) is deposited beneath the amorphous solid overlayer. When the amorphous solid transforms into a supercooled liquid, the gas begins to permeate through the supercooled liquid. Desorption of the gas can be measured and is related to the diffusivity of the supercooled liquid itself. We have previously shown that the gas permeation rates and the diffusivity of the supercooled liquid have the same temperature dependence and are within a factor of 5 for methanol.14 In other systems, the absolute difference between the gas permeation rate and the supercooled liquid diffusivity may vary, but we expect it to be relatively small compared to the orders of magnitude change in the liquid diffusivity that occurs when going from the melting point to temperatures near Tg. In this article, we use the inert gas permeation technique to investigate the mobility of toluene, ethylbenzene, and benzene by monitoring the permeation of Ar, Kr, and Xe through the hydrocarbon overlayer. In pure benzene, crystallization occurs well below Tg and therefore the inert gas permeation technique could not be used to determine the diffusivity of its supercooled liquid. For toluene and ethylbenzene, crystallization occurs above Tg and inert gas permeation is used to extract diffusivities. These values compare favorably with viscosity and self-diffusivity values determined at higher temperatures. Special Issue: Curt Wittig Festschrift Received: March 28, 2013 Revised: June 4, 2013 Published: June 12, 2013 11881
dx.doi.org/10.1021/jp403093e | J. Phys. Chem. A 2013, 117, 11881−11889
The Journal of Physical Chemistry A
Article
the UHV chamber, the infrared signal was focused onto a liquid nitrogen cooled mercury cadmium telluride (MCT) detector.
However, the measured diffusivities are found to diverge significantly from viscosity measurements taken over the same temperature range. This is not unexpected because as the temperature approaches Tg, the diffusivity is known to decouple from viscosity. In other words, the Stokes−Einstein equation, frequently utilized to connect diffusivity and viscosity, becomes invalid. These low temperature deviations are modeled using the empirical fractional Stokes−Einstein formalism to determine an exponential parameter relating diffusivity and viscosity. Finally, in the last section, the effect of increasing amounts of ethylbenzene on the crystallization of benzene is explored using infrared spectroscopy. Efforts to use the observed ethylbenzene induced delay in benzene crystallization to determine the diffusivity of benzene are discussed.
III. RESULTS AND DISCUSSION A. Inert Gas Permeation Through Toluene, Ethylbenzene, and Benzene. One monolayer (ML) of Kr deposited on graphene and heated at a rate of β = 1 K/s has a desorption peak at 62.5 K (not shown). Figure 1 displays the
II. EXPERIMENTAL SECTION Temperature programmed desorption (TPD) and infrared measurements (IR) were acquired simultaneously utilizing an ultra high vacuum system (UHV) with a base pressure of
