Fine Structure Evaluation of the Pair Distribution Function with Molecular Models of the Argonne Premium Coals

Abstract

The pair distribution function (PDF) is one means of evaluating the atomic spatial arrangements of coals. Analysis of PDF based on X-ray diffraction data provides structural information on turbostratic crystalline parameters that can be utilized to further characterize coal structure. With coalification, expectations are of limited growth in aromatic stacking and a slight growth in the aromatic cluster size over the lignite to medium-volatile bituminous range. The PDF can be also used to construct and validate atomistic representations for carbonaceous materials including coal. Here, the PDF was evaluated with molecular slice models of several Argonne Premium coals (Beulah-Zap, Illinois No. 6, Upper Freeport, Pocahontas No. 3), also a non-Argonne Hon Gai anthracite, and compared to experimental observations. Atomistic representations were generated directly from high-resolution transmission electron microscope (HRTEM) lattice fringe images. The Fringe3D approach populates aromatic moieties matching the distributions of fringe: length, layers per stack, interlayer spacing, and orientations to produce an aromatic slice model of limited depth. Perl scripts incorporated appropriate aliphatic and heteroatom components. This approach creates atomistic representations with greater ease, improved accuracy, and reduced computational expense than other construction approaches. The constructed coal models were partially geometry-optimized to achieve realistic bond lengths but without displacement of coal molecules enabling the distribution of fringe length, stacking, and orientations to be duplicated in 3D modeling space. The resulting coal slice models, devoid of cross-links, captured a distribution of turbostratic crystalline dimensions with an average cluster size of about 1 nm, an average interlayer spacing ranging between 0.37 and 0.39 nm, and an average stacking number of ∼2–3 in accordance with HRTEM and XRD data for Argonne coals. These structural models were used to predict PDFs and to evaluate the fine detail of the frequency spectra via examination of intermolecular and intramolecular contributions. There was good agreement between predicted and experimental observations. Analysis of the simulated intermolecular PDF contribution showed strong intensities with increasing coal rank in agreement with the growth in the stacking number and stack height observed from low- to high-rank coals. The simulated intramolecular PDF contribution showed shorter peak amplitudes for low-rank coals in comparison to high-rank coals in agreement with the increase in stack width as coal rank increases. To further examine these contributions, lattice models composed of pyrene molecules were also constructed via Fringe 3D and manipulated to directly investigate the effect of aromatic orientation distributions and stacking on the simulated PDF. Peak intensities of simulated intermolecular PDFs at the average interlayer spacing increased with the degree of alignment (ϕ) according to g(r)interd002 = 0.0014ϕ2 + 0.0107ϕ + 4.2784. This result was consistent with the slight increase in the stacking number observed from low- to high-rank coals with a more dramatic transition for anthracite.