A Monte Carlo method, namely, the ‘‘statistical counting method’’ (SCM) has been proposed for simulating the conformational entropy of a single free or confined linear self-avoiding random walk chains on the simple cubic lattice. For a free linear chain with length 1081, it is found from the calculated results of 100 groups of 104 samplings that the maximum and the minimum values of the conformational entropy are 1670.2 and 1660.3, respectively, the deviations from the average value 1663.8 are only +0.39% and −0.2%. In the range of chain length 8–20 the calculated entropy data are found to be in agreement with their precise values obtained by M. F. Sykes, et al. [J. Phys. A 5, 653 (1972)] with deviation less than 0.05%. In the range of chain lengths up to 27 confined in a cube of side length 2, the entropy data are also consistent with their precise values obtained from the direct counting of conformation number with the deviations less than 0.6%. For a long chain with lengths up to 2101, the calculated entropy data have confirmed the prediction by the renormalization group theory very well and the deviation is less than 0.8%.
A concise
and stereoselective total synthesis of (±)-cephanolide
B was achieved in 15 steps. The key steps in the synthesis were as
follows: (i) an intermolecular Diels–Alder reaction followed
by lactonization to form the oxabicyclo[2.2.2]octane DE ring; (ii)
a tandem reaction, featuring an intramolecular Pauson–Khand
reaction, a 6π-electrocyclization, and an oxidative aromatization
by O2, to construct the ABC-tricyclic rings (6-5-6); and
(iii) a phthaloyl peroxide-mediated arene oxygenation to install the
C-13 phenol group.
The optically active and crystalline poly(R-methyl-R-ethyl--propiolactone) (PMEPL) shows conformational changes and polymorphic behavior depending on the preparation method of the sample. The melt-crystallized isotactic PMEPL exhibits a monoclinic lattice and an extended planar zigzag conformation. Using computational modeling, we have solved and refined its crystal structure. Both the two-step and single-step procedures were used to evaluate packing energies. The results indicate that two chains with the same chirality and opposite directions pass through a monoclinic unit cell having lattice dimensions a ) 9.10, b ) 7.44, c(fiber period) ) 4.84 Å and ) 83.1°. The space group is P21 with unique axis b. The final crystal structure was confirmed by comparison with electron diffraction data and X-ray powder diffraction spectra. Both procedures result in crystal structures in good agreement with the experiments. The final discrepancy R factors are 0.16 for the flexible model and 0.20 for the rigid model when compared to X-ray data and 0.20 for the flexible model and 0.23 for the rigid model when compared to electron diffraction data.
Optically active poly(α-methyl-α-n-propyl-β-propiolactone) (PMPPL) crystallizes in a 21
helical conformation, but its conformational structure and packing symmetry have not been solved and
refined yet. On the basis of the rotational isomeric state approximation and the conformational algorithm
for polymer helices, optimum conformational models derived from single helices were used as a starting
point in building crystal structures. Both intra- and intermolecular interactions were simultaneously
optimized. Semiempirical molecular mechanics calculations of an isotactic single chain having fixed
experimental helical parameters revealed that the preferred conformation for PMPPL entails the ttg-g-
backbone chain conformation with a g-t side-chain orientation. Crystal models compatible with the
observed orthorhombic lattice dimensions (a = 10.6, b = 11.1 Å) were built and refined against electron
diffraction data, X-ray powder diffraction spectra, and structure factor calculations. The favored structure
contains two 2-fold screw helices packed antiparallel in an orthorhombic lattice with space group P212121−D2
4. With the ttg-g- main chain conformation, both the g-t and tt conformations are possible for the side
chain according to the refinement of X-ray structure factors. However, the g-t side-chain conformation
shows a better fit than that of the tt conformation with the electron diffraction patterns. The flexible
procedure of energy minimization yields distinct values of fiber period for the g-t and tt conformations,
e.g., 6.31 and 6.14 Å, respectively. The final discrepancy R factors are 0.20 for the g-t and 0.17 for the tt
side-chain models when compared to X-ray data and 0.17 for the g-t and 0.27 for the tt side-chain models
when compared to electron diffraction data.
SUMMARYThe unperturbed chain dimensions of poly(3-ethylthiophene)~ have been calculated using the full-relaxation optimization of con formational energies and the chain statistical mechanics with a rotational isomeric state model of two states. The computation indicates that the conjugated polymer with side groups is more flexible than without, and that the orientation of the ethyl group and the regioirregular sequences perturb the chain conformation to a certain extent. Specially, the calculated chain conformations under &conditions are more rigid than those observed in good solvent. This supports experiments showing that the chain dimensions of conjugated polymers are very sensitive to variations of intermolecular interactions.
SUMMARY:The purpose of this paper is to construct a unified theoretical framework to link microto macro-mechanical properties of glassy polymers. Starting from a model of microcrack propagation in craze on a mesoscale, the kinetic process of microcrack propagation resulting from fibril breakdown in the crack tip zone is mathematically formulated by a combination of fracture mechanics and fracture kinetics. A microcrack evolution equation involving both the geometric structure parameters of craze and the meso-mechanical quantities is obtained. After solving this evolution equation, a statistical distribution function of microcrack size which evolves with time and the moment generating function of microcrack size are derived. Any-order averaged damage functions can be therefore deduced. Specifically, the analytical expressions of the first-order averaged damage function and its damage rate are presented, which correspond to a similar definition of damage mechanics.
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