Quantitative Measurements of Polymer Chain-End Edge Dislocation Strain Fields by High Resolution Electron Microscopy

Abstract

The strain fields around chain-end edge dislocations in poly(diacetylene) crystals were analyzed by high resolution electron microscopy (HREM). Experimental measurements of the tilt of the polymer chain axis as a function of azimuthal angle φ at a constant radius r from the dislocation core were compared to theoretical predictions. The shear deformation was localized in parabolic regions parallel to the Burger's vector b near the chain end. For an edge dislocation in the poly(diacetylene) 1,6-di(N-carbazolyl)-2,4-hexadiyne (DCHD) with a Burger's vector of b = 3a/2 [100] (2.4 nm), we found a tilt distortion of ±6° at 12 nm from the core. A parameter W was introduced to describe the anisotropy of the compliance matrix with respect to the chain direction. A parameter of W = 3.5 was needed to fit the measured tilt deformation with anisotropic linear elastic dislocation theory. We also found that the theory of distortions near dislocations in columnar liquid crystals could closely predict our experimental observations. A value of 0.8 nm (the interchain spacing) for the characteristic length, λ3, was the best fit for the columnar liquid crystal solution. This analysis reveals similarities between the elasticity of anisotropic crystals and liquid crystals.

High-Temperature Behavior of Cellulose I

“…If cellulose chains are fully extended along the length of a microfibril, any twist in the microfibril requires some amount of slip between or within hydrogen-bonded layers. Point defects such as broken chains, which can be characterized with a Burger’s vector, are also likely to exist. A layer slip defect is termed a stack fault, and these types of faults can shift peak locations in diffraction patterns. ,, Stack faults explain the observation of cellulose Iα and Iβ coexistence along the length of single microfibrils, as this difference in layer packing is the essential difference between cellulose Iα and Iβ .…”

Orbital Influence on Earth's Magnetic Field: 100,000-Year Periodicity in Inclination

“…Furthermore, the observation that in inclination the 100-kyr periodicity dominates even in the Matuyama Chron, when lithological changes that appeared in the variations of k were governed by 40-kyr periodicity (Fig. 3C) (25), excludes the possibility of lithological control on the inclination. Coarse sampling of directional secular variations with 10 2 -to 10 3year periods could produce apparent long periods by an aliasing effect (26).…”

“…The dominance of the 100-kyr signal even when paleoclimate changes were governed by the 40kyr obliquity period (25) suggests that the long-term secular variations did not result from ice-volume changes. Another important implication of the paleomagnetism is that a time period of longer than 100 kyrs is re-quired for averaging out secular variations, which is much longer than usually assumed, on obtaining, for example, mean virtual geomagnetic pole (VGP) positions for tectonic applications and angular dispersions of VGPs for modeling paleosecular variation.…”

Analysis of Displacement Fields near Dislocation Cores in Ordered Polymers

“…θ is then defined as Our previous analysis directly related the tilt of the polymer chain to the local shear strain. 24 As we will demonstrate, in certain cases (such as highly rigid chains) this proves to be a good approximation. For an edge dislocation line along z with Burgers vector b in the x direction, the shear strain is defined as 37 where λ and µ are the Lame ´constants and ν, Poisson's ratio, is equal to λ/2(λ + µ).…”

“…We have studied direct images of dislocation cores in crystalline polymers and compared them with the deformation fields predicted by anisotropic dislocation theory. Wilson and Martin 24 previously focused on chain-end edge dislocations in DCHD. The analysis was based on the correlation between θ, the tilt of the polymer chains near a dislocation, and xy , the local shear strain.…”