Strain additivity rule

Bicyclobutane is unique in that it does not obey the strain additivity rule of small-ring bicyclo[n.m.O]alkanes. For example, the strain energy of bicyclo[2.1.0]pentane, using the Franklin group increment is 53.6 kcal mol" This should be compared to the sum of the strain energies in cyclobutane (26.4) and cyclopropane (27.6 kcal mol" ). Yet, the sum of two cyclopropanes (55.2 kcal mol" is ca. 9 kcal mol" lower than that of bicyclobutane. 

Therefore, although it is generally accepted that electrophilic mercuration of di- and polycyclic systems containing a double bond takes place in accordance with the exo-syn addition rule, at least a part of the reported results shows that the strain of the unsaturated system is insufficient to be the only determining factor for syn addition of mercury salts. 

It should be noted that the Doi and Ohta theory predicts oifly an enhancement of viscosity, the so called emulsion-hke behavior that results in positive deviation from the log-additivity rule, PDB. However, the theory does not have a mechanism that may generate an opposite behavior that may result in a negative deviation from the log-additivity rule, NDB. The latter deviation has been reported for the viscosity vs. concentration dependencies of PET/PA-66 blends [Utracki et ah, 1982]. The NDB deviation was introduced into the viscosity-concentration dependence of immiscible polymer blends in the form of interlayer slip caused by steady-state shearing at large strains that modify the morphology [Utracki, 1991]. 

Owing to the emulsion-like character of polymer blends, the system viscosity increases faster with (]) than predicted by the log additivity rule In = 2 <1), In Ti,. The maximum deviation from the additivity occurs at positive deviation, or PDB. At higher stresses and strains, a negative deviation (NDB) has often been observed. Its origin is in interlayer slip [7] l/ri = -I- where... 

An alternative approach [24] assumes an additivity rule based on a plane strain K c, which pertains to fracture in the central part of the specimen and is designated ic, and a plane stress K c, which is effective for the two surface skins of depth w/2 and is designated K ic- For the overall specimen it is then proposed that... 

For compliance constants the substitution is based on the above conversion for stiffness constants, but additional rules apply because of the factor 2 difference between the definition of engineering and tensor shear strains ... 

This difficulty has been circumvented by the introduction of a modified concept [100]. Here, flexible alkyl chains are used as tethers that are incorporated in macrocyclic cyclo-[n]-malonates. In this way, the regioselectivity is not based on steric preorganization but on the avoidance of unequal strain in the alkyl chains. This has very important consequences for the symmetry of the product addition pattern and dictates selection rules (1) Cyclo-[n]-malonates containing alkyl chains... 

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