Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (II)

This is the second of a series of papers which give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in a 2-bridge link complement to be homotopic in the link complement. The first paper of the series treated the case of the \(2\) -bridge torus links. In this paper, we treat the case of \(2\) -bridge links of slope \(n/(2n+1)\) and \((n+1)/(3n+2)\) , where \(n \ge 2\) is an arbitrary integer.     

Effective synthesis of diiodinated picene and dibenzo[a,h]anthracene by AuCl-catalyzed double cyclization

6,13-Diiododibenzo[a,h]anthracene and 5,8-diiodopicene were synthesized by AuCl-catalyzed double cyclization. The highly selective reaction yielded a new class of peri-halogenated fused aromatics.     

Synthesis and properties of high‐molecular‐weight stereo di‐block polylactides with nonequivalent D/L ratios

Di‐stereoblock polylactides (di‐sb‐PLA: PLLA‐b‐PDLA) having high molecular weight (M_n > 100 kDa) were successfully synthesized by two‐step ring‐opening polymerization (ROP) of L ‐ and D ‐lactides using tin(2‐ethylhexanoate) as a catalyst. By optimizing the polymerization conditions, the block sequences were well regulated at non‐equivalent feed ratios of PLLA and PDLA. This synthetic method consisted of three stages: (1) polymerization of either L ‐ or D ‐lactide to obtain a PLLA or PDLA prepolymer with a molecular weight less than 50 kDa, (2) purification of the obtained prepolymer to remove residual lactide, and (3) polymerization of the enantiomeric lactide in the presence of the purified prepolymer. Their ¹³C and ³¹P NMR spectra of the resultant di‐sb‐PLAs strongly supported their di‐stereo block structure. These di‐sb‐PLAs, having weight‐average molecular weights higher than 150 kDa, were fabricated into polymer films by solution casting and showed exclusive stereocomplexation. The thermomechanical analysis of the films revealed that their heat deformation temperature was limited probably because of their low crystallinity owing to the non‐equivalent PLLA/PDLA ratio. The blend systems of the di‐sb‐PLAs having complementary stereo‐sequences (the one with a long PLLA block and the other with long PDLA block) were also prepared and characterized to enhance the sc crystallinity. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 794–801, 2010     

Fracture theory based on the concept of characteristic fracture length of materials

Fracture theory is a classic, but not a well-dealt with, difficulty in solid mechanics. This paper has proposed the concept of characteristic fracture length of materials from the fact that fracture happens with area failure rather than point failure in materials. A unified theory is then proposed, which can be applied both to smooth and defected materials (whether with micro or macro defects). Brittle fracture tests with specimens of different sizes of holes are carried out to examine the fracture theory. It is found that the fracture stresses obtained by experiments agree well with those predicated by the presented fracture theory. Though the brittle fracture is the focus of the paper, the concept of characteristic length can be easily extended to fatigue or other failure problems.     

Angioarchitecture of tumors induced by two different cloned cell lines established from a transplantable rat malignant fibrous histiocytoma.

Angiogenesis, a biologic process whereby endothelial cells divide and migrate to form new blood vessels, is a key step in tumor growth, invasion, and metastasis. In the present study, we investigated the differences in angioarchitecture between two different tumors induced by cloned cell lines (MT-8 and MT-9), derived from a transplantable rat malignant fibrous histiocytoma, by scanning electron microscopy of vascular corrosion casts. During a 3-week observation period after implantation, the growth of MT-8 tumors appeared to be faster than that of MT-9 tumors. Histologically, MT-8 tumors were of the uniformly undifferentiated sarcoma type arranged in characteristic organoid structures, and MT-9 tumors showed a storiform growth pattern. In MT-8 tumors, neovascularization occurred by sprouting at postimplantation (PI) week 1, and the newly formed capillaries gradually became more tortuous. In MT-9 tumors, at PI week 1, the corrosion casts of newly formed capillaries mainly showed a wavy course but no finger-like outgrowths of capillaries were seen. At PI weeks 2 and 3, the sprouting was seen specifically in MT-9 tumors, forming basket-like structures and glomeruloid structures of capillaries. These results indicate that angiogenesis or angioarchitecture of MT-8 tumors is different from that of MT-9 tumors, depending on the differences in their tumor histology and by the features like absence or presence of basket-like structures and glomeruloid structures of capillaries.     

Structure and morphology of the aliphatic polyester poly(δ‐valerolactone) in solution‐grown,chain‐folded lamellar crystals

Poly(δ‐valerolactone) (PVL) crystals in the form of chain‐folded lamellae were prepared by isothermal crystallization from a 2‐methylbutane‐2‐ol solution. Wide‐angle and small‐angle X‐ray diffraction data, obtained from PVL lamellae sedimented to form oriented mats, were supplemented with morphological and structural data from electron microscopy, both imaging and diffraction. The diffraction signals index on an orthorhombic unit cell with the parameters a = 0.747 ± 0.002 nm, b = 0.502 ± 0.002 nm, and c (chain axis) = 0.742 ± 0.002 nm. Similar unit cell parameters were obtained from crystals grown from 1‐octanol and also from drawn melt‐pressed films. The evidence supports a model containing two antiparallel chain segments in the unit cell. The c value of 0.742 nm is appropriate for an all‐trans or onefold helical backbone conformation for the straight stems. Possible slight perturbations at the ester units from the all‐trans backbone conformation are discussed. Computerized modeling was used to optimize the adjacent‐reentry folded structure. The setting angles, with respect to the a axis, are ±58° for the corner and center chains. The lamellae are 7.26 ± 0.05 nm thick, and the chains run orthogonal to the lamellar surface. The chains fold in the diagonal (110) and (11¯0) planes in an alternating fashion. The X‐ray diffraction data suggest that a proportion of adjacent paired antiparallel entities, or hairpin units, are c‐axis‐sheared, and a relationship to the results obtained from drawn films is discussed. A brief comparison is also made with related polymer structures. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2622–2634, 2001     

A Normal Force on the Free Surface of a Coated Material

The three-dimensional theoretical solution of a concentrated normal force acting on the free surface of a coated material has been deduced by applying the reflection method. It is found that all stress functions defined in the local coordinate systems with their origins placed at each mirror point can be deduced from the fundamental solution of a concentrated normal force acting on the free surface of a semi-infinite homogeneous medium. The structure of the elastic solution has been illustrated by numerical analysis. It is found that only the stress functions corresponding to the first few mirror points are influential. It is also found that the effect of material combination on the stress field shall be described by three parameters, the two Dundurs' parameters and one additional parameter.     

Fast and Robust Nanocellulose Width Estimation Using Turbidimetry

The dimensions of nanocelluloses are important factors in controlling their material properties. The present study reports a fast and robust method for estimating the widths of individual nanocellulose particles based on the turbidities of their water dispersions. Seven types of nanocellulose, including short and rigid cellulose nanocrystals and long and flexible cellulose nanofibers, are prepared via different processes. Their widths are calculated from the respective turbidity plots of their water dispersions, based on the theory of light scattering by thin and long particles. The turbidity‐derived widths of the seven nanocelluloses range from 2 to 10 nm, and show good correlations with the thicknesses of nanocellulose particles spread on flat mica surfaces determined using atomic force microscopy.

     

Neutron crystallographic and molecular dynamics studies of the structure of ammonia-cellulose I: rearrangement of hydrogen bonding during the treatment of cellulose with ammonia

The hydrogen bond arrangement in a complex of cellulose with ammonia has been studied using neutron crystallography in combination with molecular dynamics simulations. The O6 atom of the hydroxymethyl group is donor in a highly occupied hydrogen bond to an ammonia molecule. This rotating ammonia molecule is donor in partially occupied and transient hydrogen bonds to the O2, O3 and O6 atoms of the hydroxyl groups of other chains. The hydrogen atom bound to the O3 atom is disordered but it is almost always involved in some type of hydrogen bonding. It is donated in a hydrogen bond most of the time to the O5 atom on the same chain. However, it also rotates away from this O5 atom to be donated to an ammonia molecule part of the time. On the other hand the hydrogen atom bound to the O2 atom is free from hydrogen bonding most of the time. It is donated in a hydrogen bond to the O6 atom on a neighboring chain only with a relatively small probability. These results provide new insights into how hydrogen bonds are rearranged during the conversion of cellulose I to cellulose III_I by ammonia treatment.