On the Symmetry of a Zig-Zag and an Armchair Polyhex Carbon Nanotorus
Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan, I. R. Iran * Author to whom correspondence should be addressed: E-mail: Ashrafi@kashanu.ac.ir Received: 17 July 2009; in revised form: 13 September 2009 / Accepted: 14 September 2009 / Published: 8 October 2009 Abstract: A Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [d
Symmetry classification of stereoregular polymers
The symmetry of stereoregular polymers enables classification of elementary polymers according to the line groups. Their schemes are presented and the notation, extracting the data relevant for the symmetry considerations of the polymer, is proposed. The advantages of the concept (efficient and precise description of the structure, easy prediction of properties of the polymer, reductions of numerical calculations) are discussed and illustrated by several examples.
O2 constraints from Paleoproterozoic detrital pyrite and uraninite
Redox-sensitive detrital grains such as pyrite and uraninite in sedimentary successions provide one of the most conspicuous geological clues to a different composition of the Archean and early Paleoproterozoic atmosphere. Today, these minerals are rapidly chemically weathered within short transport distances. Prior to the rise of oxygen, low O2 concentrations allowed their survival in siliciclastic deposits with grain erosion tied only to physical transport processes. After the rise of oxygen, redox-sensitive detrital grains effectively vanish from the sedimentary record. To get a better understanding of the timing of this transition, we examined sandstones recorded in a scientifi c drill core from the South African 2.415 Ga Koegas Subgroup, a mixed siliciclastic and iron formation–bearing unit deposited on the western deltaic margin of the Kaapvaal craton in early Paleoproterozoic time. We observed detrital pyrite and uraninite grains throughout all investigated sandstone beds in the section, indicating the rise of oxygen is younger than 2.415 Ga. To better understand how observations of detrital pyrite and uraninite in sedimentary rocks can quantitatively constrain Earth surface redox conditions, we constructed a model of grain erosion from chemical weathering and physical abrasion to place an upper limit on ancient environmental O2 concentrations. Even conservative model calculations for deltaic depositional systems with suffi cient transport distances (approximately hundreds of kilometers) show that redox-sensitive detrital grains are remarkably sensitive to environmental O2 concentrations, and they constrain the Archean and early Paleoproterozoic atmosphere to have <3.2 × 10 –5 atm of molecular O2. These levels are lower than previously hypothesized for redox-sensitive detrital grains, but they are consistent with estimates made from other redox proxy data, including the anomalous fractionation of sulfur isotopes. The binary loss of detrital pyrite and uraninite from the sedimentary record coincident with the rise of oxygen indicates that atmospheric O2 concentrations rose substantially at this time and were never again suffi ciently low (<0.01 atm) to enable survival and preservation of these grains in short transport systems.