2.6 Mechanical Properties
65
MO calculation software is applicable to enumeration of the H f values (see, e.g.,
Sect. 2.1). There are two ways of experimental estimations of the strain energy with
the use of the observed H f data (Cox and Pilcher 1970) as follows: (i) utilization
of the homodesmotic reactions as employed in the above (George et al. 1976) and
(ii) comparison of the observed H f value of the concerning molecule with that
of assembly of the strain-free standard molecule fragments separately considered
(Wiberg 1986). In the process (ii), for instance, the strain energy of cyclopropane is
obtained as the difference of H f values of that and the strain-free three methylene
fragments derived from H f of cyclohexane selected as the standard, although there
can be a certain arbitrariness in selection of the standard molecule as a matter of
course. These experimental-based strain energies are also listed in Table 2.16.
It is seen that the strain energies theoretically obtained are in reasonable agreement
with those based on the experimental estimations. The more distorted bond angles
duly cause the more strain energies, which is more remarkable in the molecules
with the unsaturated bonds. It is noted that substitution of all the carbon to silicon
atoms decreases strain energies as a whole except for silacyclopropane. Moreover,
introduction of unsaturated bond in Si-substituted molecules has been shown to bring
about less strain energies, which has been explained by the strain-energy relaxation
associated with the presence of high π-orbital energy and low σ*-orbital energy of the
Si–H bonds through the orbital interaction from the theoretical viewpoints (Naruse
et al. 2006).
It is noted that the experimental H f is generally derived from the observed heat
of combustion of each molecule but this quantity is sometimes difficult to be obtained
when the molecule can only exist under special conditions such as impregnation in
the matrix of other materials and so on. Hence in such case or for yet unsynthesized
molecules only the theoretical calculation of H f would become accessible.
2.6.2 Elastic Constant of Polymers
One of the conspicuous and crucial mechanical properties manifesting in the linear
oligomeric or polymeric chains would be the elastic constant. This property is generally represented by Young’s modulus which decides the strain replying to compression or tensile strength along the main chain of the polymer. The strain generally
appears as response of the system to the external force causing stress to the material.
Although these quantities are rather macroscopic variables in macromolecules or
their oligomeric model structures, analysis of those from microscopic viewpoints
using theoretical chemistry is also possible as described in this subsection.
There are several experimental ways for measurement of elastic constant of pure
crystal regions of polymers such as X-ray diffraction method, inelastic neutron scattering, and Raman scattering as well as macroscopic measurement of strain curve
(Tashiro 1993). Various theoretical estimations of elastic constant of polymers have
also been performed with the use of conventional molecular mechanics (Špitalský
and Bleha 2001), force field method derived from HF/6-31G**/MP2 calculation
65
MO calculation software is applicable to enumeration of the H f values (see, e.g.,
Sect. 2.1). There are two ways of experimental estimations of the strain energy with
the use of the observed H f data (Cox and Pilcher 1970) as follows: (i) utilization
of the homodesmotic reactions as employed in the above (George et al. 1976) and
(ii) comparison of the observed H f value of the concerning molecule with that
of assembly of the strain-free standard molecule fragments separately considered
(Wiberg 1986). In the process (ii), for instance, the strain energy of cyclopropane is
obtained as the difference of H f values of that and the strain-free three methylene
fragments derived from H f of cyclohexane selected as the standard, although there
can be a certain arbitrariness in selection of the standard molecule as a matter of
course. These experimental-based strain energies are also listed in Table 2.16.
It is seen that the strain energies theoretically obtained are in reasonable agreement
with those based on the experimental estimations. The more distorted bond angles
duly cause the more strain energies, which is more remarkable in the molecules
with the unsaturated bonds. It is noted that substitution of all the carbon to silicon
atoms decreases strain energies as a whole except for silacyclopropane. Moreover,
introduction of unsaturated bond in Si-substituted molecules has been shown to bring
about less strain energies, which has been explained by the strain-energy relaxation
associated with the presence of high π-orbital energy and low σ*-orbital energy of the
Si–H bonds through the orbital interaction from the theoretical viewpoints (Naruse
et al. 2006).
It is noted that the experimental H f is generally derived from the observed heat
of combustion of each molecule but this quantity is sometimes difficult to be obtained
when the molecule can only exist under special conditions such as impregnation in
the matrix of other materials and so on. Hence in such case or for yet unsynthesized
molecules only the theoretical calculation of H f would become accessible.
2.6.2 Elastic Constant of Polymers
One of the conspicuous and crucial mechanical properties manifesting in the linear
oligomeric or polymeric chains would be the elastic constant. This property is generally represented by Young’s modulus which decides the strain replying to compression or tensile strength along the main chain of the polymer. The strain generally
appears as response of the system to the external force causing stress to the material.
Although these quantities are rather macroscopic variables in macromolecules or
their oligomeric model structures, analysis of those from microscopic viewpoints
using theoretical chemistry is also possible as described in this subsection.
There are several experimental ways for measurement of elastic constant of pure
crystal regions of polymers such as X-ray diffraction method, inelastic neutron scattering, and Raman scattering as well as macroscopic measurement of strain curve
(Tashiro 1993). Various theoretical estimations of elastic constant of polymers have
also been performed with the use of conventional molecular mechanics (Špitalský
and Bleha 2001), force field method derived from HF/6-31G**/MP2 calculation