Deformation molecular

Ehrenson S 1974 Analysis of least motion paths for molecular deformations J. Am. Chem. Soc. 96 3778... 

As the most notable contribution of ab initio studies, it was revealed that the different modes of molecular deformation (i.e. bond stretching, valence angle bending and internal rotation) are excited simultaneously and not sequentially at different levels of stress. Intuitive arguments, implied by molecular mechanics and other semi-empirical procedures, lead to the erroneous assumption that the relative extent of deformation under stress of covalent bonds, valence angles and internal rotation angles (Ar A0 AO) should be inversely proportional to the relative stiffness of the deformation modes which, for a typical polyolefin, are 100 10 1 [15]. A completly different picture emerged from the Hartree-Fock calculations where the determined values of Ar A0 AO actually vary in the ratio of 1 2.4 9 [91]. 

We will focus on molecular deformations that most strongly modulate the anion s HOMO, so... 

The elastic free energy given by the elementary and the more advanced theories are symmetric functions of the three extension ratios Xx, Xy, and Xz. One may also express the dependence of the elastic free energy on strain in terms of three other variables, which are in turn functions of Xx, Xy, and Xz. In phenomenological theories of continuum mechanics, where only the observed behavior of the material is of concern rather than the associated molecular deformation mechanisms, these three functions are chosen as... 

Figure 6. A plot of S(x)/SD(x) versus f for a network in which junction fluctuations are partially inhibited (k 0) and where molecular deformations are less than...

The requirements for Raman resonance that must be fulfilled are the following (120,121) (a) total symmetry of the vibrations with respect to the absorbing center, and (b) same molecular deformation induced by the electronic and vibrational excitations. Quantum chemical calculations (41) of the vibrational frequencies and the electronic structure of shell-3 cluster models allowed the assignment of the main vibrational features, as shown in Fig. 7. The 1125 cm-1 band is unequivocally assigned to the symmetric stretching of the Ti04 tetrahedron. 

The motion of the absorption and emission dipoles in the molecular frame R is now assumed to be statistically independent of the motion of the R frame in the laboratory frame L. In a deformable molecule, the R frame may be attached to some small part of the molecule, which can be regarded as locally rigid. In this case, motion of the R frame occurs as a consequence of molecular deformation, as well as overall (uniform) rotation of the molecule. In such a case, statistical independence of the motion of a dipole in the R frame and the motion of the R frame itself is not guaranteed. However, with this assumption, Eq. (4.15) becomes... 

Attempts have been made in the past to explain the plasticity of glassy polymers based on different theories (a review of which can be found in (1)). Most of the earlier approaches are based on models non-specific about the molecular deformation process. The theory by Argon... 

The original mathematical derivations of the yield stress in relation to the molecular deformation are somewhat involved (1,2). However, a rather simple linear relationship can be obtained as follow ... 

The plastic deformation in several amine and anhydride cured epoxy resins has been studied. The experimental results have been reasonably interpreted by the Argon theory. The molecular parameters determined from the data based on the theory reflect the different molecular structures of the resins studied. However, these parameters are in similar enough range to also show the structural similarity in these DGEBA based systems. In general, the mechanisms of plastic deformation in epoxy resins below T are essentially identical to those in amorphouE thermoplastics. The yield stress level being related to the modulus that controls the intermolecular energy due to molecular deformation will, however, be affected by the crosslinks in the thermosets. 

Another important point deals with selectivity in the abstraction of -protons on equally substituted carbons. In a iyw-periplanar transition state as described above, the minimization of energy concept implies proton abstraction with a maximum of orbital overlap and a minimum of molecular deformation. Consequently, conformations possessing the more acute dihedral angles for bonds H —C—C—O wiU be favored (Scheme 2l/. 

Note 1 In the equation for g, the term go is usually equal to zero because the undistorted state of nematics is the state of uniform alignment. However, for chiral nematics, a nonzero value of go allows for the intrinsic twist in the structure. In order to describe g for smectic phases, an additional term must be added, due to the partially solid-like character of the smectic state and arising from positional molecular deformations. 

Response time which can be controlled by taking into account the origin of the transition (1) fs for pure electronic transition, (2) addition of molecular deformation leads to ps response time, (3) further addition of lattice deformation leads to a slower response time > ps. 

Response temperature (operating temperature) may decrease in the foUowing order bond formation and cleavage —> molecular deformation lattice deformation —> electronic deformation such as SDW and charge-order melting. 

The phase transition consists of a cooperative mechanism with charge-ordering, anion order-disorder, Peierls-like lattice distortion, which induces a doubled lattice periodicity giving rise to 2 p nesting, and molecular deformation (Fig. 11c). The high temperature metallic phase is composed of flat EDO molecules with +0.5 charge, while the low temperature insulating phase is composed of both flat monocations... 

Fig. 12 Probe photon energy dependence of the time profile for the refiectance change AR/R observed at 180 K and 260 K. The pump photon energy (E//h) was 1.55 eV and the probe photon energy (E//b) was 1.72 and 1.38 eV for the upper and lower panels, respectively. The oscillations in AR/R relate molecular deformation modes [162]...

Another hmitation is inherent to the harmonic approximation on which standard quantum mechanical force-field calculations are invariably based. Due to a fortui-tious (but surpisingly systematic) cancellation of errors, the harmonic frequencies calculated by modem density functional methods often match very well with the experimental ones, in spite of the fact that the latter involve necessarily more or less anharmonic potentials. Thus one is tempted to forget that the harmonic approx-imaton can become perilous when strong anharmonicity prevails along one or another molecular deformation coordinate. 

Infrared spectroscopy has been used to study molecular deformation processes in polymers as a function of stress, strain, time and temperature. Wool has summarized... 

We subject a sample of solid polymer material to a sudden deformation process y0, with an elastical stress o0 = Gy0 (G shear modules). The original strain gives rise to an increase of the molecular valency angles and the intermolecular distances. From these molecular deformations an elastic molecular potential A0 arises which in turn causes molecular displacements. These prevail in the direction of the original strain, decreasing the elastic potential A in that neighborhood. We can calculate... 

Keywords Crazing Creep Molecular deformation mechanisms Disentanglement Time-dependent strength Toughness... 

In the simplest molecular theory now available, there are two major assumptions. The first is that m/mnolccular interactions are unimportant, that is, they do not change with deformation. The second is that the deformation is affine, which means that the molecular deformation is the same as the macroscopic deformation. More precisely, the assumption is that the cross-link positions vary in a simple linear manner with the macroscopic dimensions. 

The presence of overcrowding in triphenylene has been demonstrated by Clar (1950) from an examination of the absorption spectra at 18°C and — 170°C. At — 170°C the / -band spectra of such aromatic hydrocarbons as benzene, naphthalene, anthracene, and pyrene become more distinct, showing much more fine structure than at 18°C. This is explained by the cessation at low temperature of thermal collisions which produce molecular deformations, thereby improving the definition of the molecular electronic orbitals. Where this change in spectra does not occur, permanent deformation at both low and high temperatures... 

In a dynamic real case, the situation is very different. This analysis may be extended to formally achiral molecules that are composed of four or more atoms. The motions in such polyatomic molecules are restricted by the restoring forces imposed by bonding, and here, stochastic achirality is the result of internal vibrations. Thus, for example, molecular deformations in some vibrational states impart... 

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