57th Annual Report on Research 2012 Under Sponsorship of the ACS Petroleum Research Fund

Hydrocarbons from petroleum reservoirs provide an inexpensive source of monomers that are used to synthesize polymers for numerous applications. The effect of pressure on polymers is an important factor in extrusion and molding processes, as well as failure mechanisms. Deriving accurate equations of state for polymers is essential to model the response to extreme pressures and temperatures. To date, however, there are few reliable methods for obtaining pressure-volume relations for polymers.

In this work, we are developing confocal microscopy to investigate polymers and alkanes under large hydrostatic pressures. Unlike conventional optical microscopy, confocal microscopes collect data point-by-point, enabling three-dimensional image reconstruction. Using this method, we are producing three-dimensional images of materials under large hydrostatic pressures. By combining these images with Fabry-Perot interference measurements, we determine the volume and refractive index, as a function of pressure, in the same experiment. This novel approach enables us to determine accurate equations of state and probe phase transitions with unprecedented accuracy.

The response of condensed matter to extreme pressures is of fundamental and technological interest. Diamond anvil cells (DACs), which combine high strength with optical transparency, have been used successfully in a broad range of high-pressure studies. However, it is difficult to measure the volume of a sample in a DAC. While the area of the sample can be observed with standard microscopy, the metal gasket that contains the sample is not transparent to visible light, making thickness measurements challenging. X-ray and neutron diffraction experiments can measure the lattice constants of crystals to good accuracy, but they are of limited use in measuring the density of fluids or amorphous solids. These experimental limitations have prevented researchers from obtaining accurate EOS data for a range of non-crystalline materials.

To overcome these difficulties, my research group has adapted confocal microscopy to measure the density of fluids under pressure. In the past year, we have developed a home-built confocal microscope to accurately determine thickness. In this system, a microscope objective focuses laser light onto the sample. The reflected light is focused by a second lens onto a detector. The intensity of collected light is maximized when the laser spot is focused on a diamond/sample interface. This effect results in peaks in the reflected intensity, corresponding to each interface. From the peak positions, we obtain the sample thickness divided by the refractive index. Fabry-Perot interference measurements are then performed to determine the product of thickness and index, and the area of the sample is measured from the scanned 2D image. In this way, we are able to measure the volume and refractive index in the same experiment. 

Along with accurate EOS and refractive-index data, confocal microscopy also provides 3D images with a high level of detail. The image created by this process is a planar slice through the sample, called an optical section. By obtaining a series of optical sections, a 3D image is constructed. Such an image can be analyzed to determine the properties of a solid sample immersed in a hydrostatic fluid.

We are currently measuring the compressibility of n-heptane by confocal microscopy. After collecting the data, we aim to model these polymers with a molecular-based EOS such as that of Simha and Somcynsky. Pressure-volume-temperature relations will be obtained by heating the diamonds from room temperature up to ~200°C. We have also performed x-ray diffraction at the Advanced Light Source. Combining these measurements, we will obtain a complete continuum picture of how heptane responds to extreme conditions of stress and temperature.

Along with EOS data, our experiments also yield the refractive index as a function of pressure, in the same experiment. In general, as the density of a condensed-matter system increases, the index increases as well. At extremely high densities, the electron orbitals overlap and metallization occurs. For polymers, the overlap would occur between orbitals on neighboring chains. The onset of metallization and inter-chain interactions are important phenomena for electronic devices based on organic polymers. By measuring the index as a function of pressure, we will predict the critical density for the insulator-to-metallic transition, via the Herzfeld criterion. Accurate determination of the index versus pressure will also enable researchers to measure sound velocities under pressure with Brillouin spectroscopy.

This New Directions grant has enabled my group to begin a long-term study of polymers, an important class of materials that my group has not investigated previously. Because we have no experience with polymers, the New Directions program has been extremely important to get us started. The work has provided graduate students with a challenging, hands-on, interdisciplinary research experience. The striking visual aspect of this research will be used in outreach to inspire high school and college students to enter scientific careers.