Deformation mechanisms of constrained polymer chains. II. Deformation energetics of tie molecules

Abstract

Energy‐deformation characteristics for the primary T, S, and U conformational units of tie molecules were obtained from the analysis of data generated from a constrained minimization algorithm. Energy‐deformation profiles (covering the range from compact equilibrium defect structures to the fully extended chain) are reported for the S0 and S1 members of the Sλ family and for the U00 member of the Umn family. Estimates of the energy content V0 and the elastic modulus E were obtained from the computed energy‐deformation data in the vicinity of the equilibrium Structure—S0 → {60°, 180°, −60°}, V 0italicS 0 = 1.7 kcal/mole, E italicS 0 = 60 kcal/cm3 [250 × 1010 dyn/cm2];S1 → {60°, 180°, 180°, 180°, −60°}: V 0italicS 0 = 1.7 kcal/mole, E italicS 1 = 25 kcal/cm3 [100 × 1010 dyn/cm2]; and U00 → {60°, 180°, 60°, 180°, 60°}: V 0italicU 00 = 2.7 kcal/mole, E italicU 00 = 80 kcal/cm3 [340 × 1010 dyn/cm2]. Although the elastic modulus of the U00 unit is comparable to the elastic modulus of the fully extended chain, the highenergy content of this unit (V0 = 2.7 Kcal/mole) prohibits a significant population and thereby mitigates an appreciable reinforcing effect from this rigid unit. A model for a surrogate force constant is introduced to generalize the results from this study to any member of the Sλ or Umn family as well as any combination of Sλ and Umn units. This generalization provides a basis for estimating the deformation characteristics of tie molecules comprised of various populations of these primary conformational building blocks.

The chemistry, manufacture and tensile behaviour of polyester fibers

“…This approach is generally referred to as micromechanical. There are a number of models that describe the mechanical behavior of typical structural elements such as tie chains [198,199] and various other elements (folded chains, parallel chain bundles, meanders, etc.). Many models are based on the formal idea of a fiber as a composite structure.…”

Molecular Vibrations of Polymers

“…Knowledge of chain confor mations in noncrystall ine regions is sketchy and there is considerable current interest in this area (119). Various models have been proposed (120)(121)(122)(123)(124)(125)(126)(127)(128)(129) for conformations that are thought to account for certain physical properties such as dielectric and mechanical relaxation processes (130,131), mechanical deformation (129,132), annealing, etc.…”

Deformation energetics of chain defects of polyethylene

“…Theoretical values from molecular mechanics calculations have been reported ranging from 186 GPa27 to 267 GPa7 to 380 GPa. 15 Experimental estimates have been reported by means of X-ray diffraction (240 GPa28), neutron scattering (329 GPa29), Raman scattering (358 GPa30), and stress-strain measurements (288 GPa31). In a recent evaluation of these results by Fanconi and Rabolt,32 it was concluded that data from neutron and Raman scattering give the better estimates of the ultimate values of the Young's modulus.…”

“…Á2, the elastic modulus of the all-trans chain from Figure 3 would be 177 GPa.There is considerable ambiguity about the ultimate value of the Young's modulus of polyethylene. Theoretical values from molecular mechanics calculations have been reported ranging from 186 GPa27 to 267 GPa7 to 380 GPa 15.…”