Angle deformation

Glassy state In amorphous plastics, below the Tg, cooperative molecular chain motions are frozen , so that only limited local motions are possible. Material behaves mainly elastically since stress causes only limited bond angle deformations and stretching. Thus, it is hard, rigid, and often brittle. 

Chain scission is the ultimate fate of a stressed bond. At some value below the critical stress for chain rupture, bond angle deformation may result in an increase in reactivity. As stated in Sect. 3.1, mechanically activated hydrolysis of polymers containing ester groups can lead to the scission of the bond this concurrent reaction should be differentiated from homolytic chain scission, for example by looking at any pH-dependence as was found to be the case during shear degradation of DNA [84]. 

The summations in Eq. (8) and (9) usually extend over all internal parameters, independent and dependent, i.e. the potential constants in these expressions are also not all independent. For example, the nonsymmetric tetrasubstituted methane CRXR2R3R4 possesses five independent force constants for angle deformations at the central carbon atom, whereas in our calculations we sum over the potential energy contributions of the six different angles (only five are independent ) at this atom using six different potential constants for angle deformations. The calculation of the independent force constants, which is necessary for the evaluation of the vibrational frequencies, will be dealt with in Section 2.3. 

Terms representing these interactions essentially make up the difference between the traditional force fields of vibrational spectroscopy and those described here. They are therefore responsible for the fact that in many cases spectroscopic force constants cannot be transferred to the calculation of geometries and enthalpies (Section 2.3.). As an example, angle deformation potential constants derived for force fields which involve nonbonded interactions often deviate considerably from the respective spectroscopic constants (7, 7 9, 21, 22). Nonbonded interactions strongly influence molecular geometries, vibrational frequencies, and enthalpies. They are a decisive factor for the transferability of force fields between systems of different strain (Section 2.3.). 

The simple cycloalkanes (CH2)n with n = 5 to 12 are the compounds most frequently studied by force field calculations (8, 9, 11, 12,17, 21). This preference results from their simple structure, from the abundant available experimental material (structural (46), thermo-chemical (47) and vibrational spectroscopic (27, 48, 49) data), and from the fact that, apart from bond length deformations, all other strain factors (angle deformations, unfavourable torsion angles, strongly repulsive nonbonded interactions) are important for the calculation of their properties. The cycloalkanes are thus good candidates for testing force fields. For a more detailed discussion we choose cyclodecane, a so-called medium-ring compound. 

A regular PI proceeds without breaking and making of bonds, by bond angle deformations or internal rotations. 

Buttressing effects are known to raise the barrier to rotation in the biphenyl series by preventing bond angle deformations of a substituent involved in direct interaction in the transition state. Similar effects were found in the 9-arylfluorene series (108). The barrier to rotation of 9-(3-bromo-6-methoxy-2,4-dimethyl-phenyl)fluorene (67, X = H) in chloroform-d at 56.3°C is 25.7 kcal/mol for... 

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