A new approach is presented to evaluate the molecular strain and
bonding behavior in strained organic molecules
on the basis of the electrostatic theorem of Hellmann−Feynman through
the force concept instead of
energetics.
Taking advantage of the physical simplicity, visuality, and
quantification of this model, chemically meaningful
definitions of equivalent point charge, overlap force angle, strain
force, binding force, tension energy, and
the bond force angle have been proposed to measure the molecular
strain, bent bonds, and bonding behavior
of strained organic molecules at the HF/6-31G* level of theory.
The overlap force angles are consistent with
the experiment and other ab initio molecular orbital
calculations. Results reveal that the overlap force
angle,
strain force, tension energy, and bond force angle can be used to
account for the relative stabilities of small
propellanes. The magnitude of binding force suggests the existence
of central bonds in small propellanes.
The bond force angles in most strained organic molecules seem to
prefer the tetrahedral angle 109.5°, while
those in three-membered rings prefer the angle 120° over the angle
109.5°, though the geometrical angles
can largely range from 60° to 132°. This indicates that, in
most cases, the atomic orbitals have to be overlapped
in the manner of the ideal or nearly ideal tetrahedral hybrid in order
to relax the molecular strain. The
largely shifted overlapping charge outside rings and bond force angles
of nearly 120° for HCH, HCC, and
CCC and the resultant increased s character of C−H bond for
three-membered rings can rationalize the C−C
bond's higher reactivity than the C−C bonds of other rings. In
general, the departure (Δβ) of the bond force
angle from the tetrahedral angle provides a measure of the degree of
relaxation of the charge density from
the geometrical constraints imposed by the nuclear framework and may be
used as a way of assessing the
molecular strain, reactivity, and stability for strained organic
molecules.
The temperature and strain rate significantly affect the ballistic performance of UHMWPE, but the deformation of UHMWPE under thermo-mechanical coupling has been rarely studied. To investigate the influences of the temperature and the strain rate on the mechanical properties of UHMWPE, a Split Hopkinson Pressure Bar (SHPB) apparatus was used to conduct uniaxial compression experiments on UHMWPE. The stress–strain curves of UHMWPE were obtained at temperatures of 20–100 °C and strain rates of 1300–4300 s−1. Based on the experimental results, the UHMWPE belongs to viscoelastic–plastic material, and a hardening effect occurs once UHMWPE enters the plastic zone. By comparing the stress–strain curves at different temperatures and strain rates, it was found that UHMWPE exhibits strain rate strengthening and temperature softening effects. By modifying the Sherwood–Frost model, a constitutive model was established to describe the dynamic mechanical properties of UHMWPE at different temperatures. The results calculated using the constitutive model were in good agreement with the experimental data. This study provides a reference for the design of UHMWPE as a ballistic-resistant material.
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