Chain Modulus Research Articles

Mechanical properties of thermotropic liquid crystalline polyesters and polyamides

The dynamic mechanical behaviour of highly oriented tapes and monofilaments of thermotropic liquid crystalline polymers based on hydroxynaphthoic acid, terephthalic acid and either aminophenol (designated HNATA) or hydroquinone (designated HNATH) have been studied in tension and torsion. It was found that the mechanical properties of these two polymers were very similar. In the case of HNATA both the tensile modulus and the chain modulus determined from X-ray diffraction measurements were studied as a function of applied stress. The aggregate model, when extended to include non-linearity, modelled the macroscopic tensile and shear behaviour with some success. The X-ray measurements could not be reconciled with the macroscopic measurements, which is tentatively attributed to the fact that these materials possess a complex hierarchical morphology.

Energetics of strain-induced conformational transitions in polymethylene chains

Deformation potentials have been calculated for highly extended polymethylene chains containing simple torsional defects. The calculations were performed by using molecular mechanics techniques. The deformation potentials show abrupt discontinuities, which have been identified as gauche-trans transitions of chains containing strained defects into chains in the fully extended zigzag form. The reverse trans- gauche transition was observed during compression of all-trans chains. The observed discontinuity in the conformational transition is a direct consequence of the input of mechanical energy into the torsional angles and also into the bond lengths and bond angles in the chain. The transition point imposes a limit on the amount of energy stored in chains containing defects; the energy is fully recovered at the transition. It is suggested that abrupt conformational transitions may occur upon drawing crystalline and glassy polymers as a mechanism of avoiding large translational movements of atoms under the conditions of strong constraints from neighboring chains. The Hookean behavior of single chains containing a conformational defect was tested and the effect of this defect on the chain modulus was estimated.

Elastic modulus of poly(ethylene oxide) determined from the Raman longitudinal acoustic mode

AbstractThe chain modulus of poly(ethylene oxide) is determined by the Raman longitudinal acoustic mode method with the aid of a normal coordinate analysis and found to be 1.3 × 1011 dyn/cm2. Our normal mode calculations provide a clear basis for explaining the discrepancy between chain moduli determined from Raman and x‐ray experiments. They show that the uncorrected Raman modulus of helical polymers reflects the presence of interchain interactions and therefore should not be taken as the correct elastic modulus of a single chain.

Morphology of High-Performance Rigid-Rod Polymer Fibers and Molecular Composites

Rigid-rod polymers such as PBO, poly(paraphenylene benzobisoxazole), Figure 1a, are now in commercial development for use as high-performance fibers and for reinforcement at the molecular level in molecular composites. Spinning of liquid crystalline polyphosphoric acid solutions of PBO, followed by washing, drying, and tension heat treatment produces fibers which have the following properties: density of 1.59 g/cm3; tensile strength of 820 kpsi; tensile modulus of 52 Mpsi; compressive strength of 50 kpsi; they are electrically insulating; they do not absorb moisture; and they are insensitive to radiation, including ultraviolet. Since the chain modulus of PBO is estimated to be 730 GPa, the high stiffness also affords the opportunity to reinforce a flexible coil polymer at the molecular level, in analogy to a chopped fiber reinforced composite. The objectives of the molecular composite concept are to eliminate the thermal expansion coefficient mismatch between the fiber and the matrix, as occurs in conventional composites, to eliminate the interface between the fiber and the matrix, and, hopefully, to obtain synergistic effects from the exceptional stiffness of the rigid-rod molecule. These expectations have been confirmed in the case of blending rigid-rod PBZT, poly(paraphenylene benzobisthiazole), Figure 1b, with stiff-chain ABPBI, poly 2,5(6) benzimidazole, Fig. 1c A film with 30% PBZT/70% ABPBI had tensile strength 190 kpsi and tensile modulus of 13 Mpsi when solution spun from a 3% methane sulfonic acid solution into a film. The modulus, as predicted by rule of mixtures, for a film with this composition and with planar isotropic orientation, should be 16 Mpsi. The experimental value is 80% of the theoretical value indicating that the concept of a molecular composite is valid.

Dynamic mechanical properties of random copolyesters of 4-hydroxybenzoic acid and 2-hydroxy 6-naphthoic acid

The dynamic mechanical moduli have been determined in tension and torsion for oriented thermotropic liquid crystalline polymers formed by copolymerization of 4-hydroxybenzoic acid and 2-hydroxy 6-naphthoic acid. The behaviour has been interpreted in terms of an aggregate model of units of structure. On this basis the fall in tensile modulus with increasing temperature can be quantitatively related to two factors, a decrease in the intrinsic chain modulus and a reduction in the shear modulus.

Harnack-type mass bounds and bernstein theorems for area-minimizing flat chains modulo v.

For an area-minimizing flat chain modulo v with no boundary inside the unit ball, an absolute upper bound is given for the amount of area inside a shrunken ball. Such Harnack-type estimates lead to generalizations of area inside a shrunken ball. Such Harnack-type estimates lead to generalizations of Bernstein's Theorem. For example, for n⪇5, a 2-dimensional, area-minimizing locally flat chain modulo 2 without boundary in IRn which has at least 1 singularity must consist of 2 orthogonal planes.

Examples of Unoriented Area-Minimizing Surfaces

A comprehensive study is made of constructions of area-minimizing flat chains modulo two. Many have singularities. For instance, any bounded, area-minimizing submanifold of ${{\mathbf {R}}^n}$ occurs as the singular set of some area-minimizing flat chain modulo two in some ${{\mathbf {R}}^N}$.

Examples of unoriented area-minimizing surfaces

A comprehensive study is made of constructions of area-minimizing flat chains modulo two. Many have singularities. For instance, any bounded, area-minimizing submanifold of R n {{\mathbf {R}}^n} occurs as the singular set of some area-minimizing flat chain modulo two in some R N {{\mathbf {R}}^N} .

Molecular deformation of polypropylene

Molecular deformation of polypropylene (PP) was investigated by stress infrared experiments on ultraoriented isotactic PP samples, and the results were compared with single chain deformation calculations. A nonlinear stress-strain curve of PP was determined in a strain range of 8% which resulted in an average chain modulus, Ec ?40 GPa, and an initial Ec ?30 GPa. PP chain stretching was accompanied by considerable C-C bond stretching and valence angle bending in addition to torsional angle changes. Vibrational frequency shifts Δν with stress were calculated using both harmonic and anharmonic potential energy functions for C-C stretching. The harmonic results incorrectly predicted a considerable number of Δν’s to higher frequencies in addition to lower frequencies. Experimentally, only one band shifted to higher frequencies, and shifts to lower frequencies generally increased with increasing temperature. These results are in agreement with the anharmonic calculation in which the majority of vibrations shifted to lower frequencies. Detailed valence coordinate changes and vibrational frequency shifts with stress and temperature are presented and discussed.

Oriented chain-extended polyethylene

Abstract Simple observations have been made of the fracture behaviour and Young's modulus parallel to c, for drawn polyethylene after annealing at 5·34 kbar between 220 and 260°C. The modulus shows three regions of behaviour, corresponding to the textural changes described in the preceding paper. At first the polymer has extra stiffness associated with drawing, but this has disappeared by 236°C when the average crystal thickness is only of order 500 A. There follows a region of series behaviour, to 1000 A thickness, in which the modulus increases according to the proportion of crystalline and interlamellar regions, both of which have constant properties. Beyond this the polymer softens abruptly as chain-extended lamellae replace chainfolded and then stiffens again with further increase of crystal thickness. The maximum overall chain modulus produced is about 40 kbar, essentially determined by the proportion of interlamellar regions, which have a modulus of 3 kbar. Attainment of the theoretical modulus req...

Regularity of the singular sets of two-dimensional area-minimizing flat chains modulo 3 inR 3

Regularity of the singular sets of two-dimensional area-minimizing flat chains modulo 3 inR 3