Boyer-Simha rule

Some deviations from the Simha-Boyer rule with increasing side chain length were discovered by Simha59. In so an attempt was made on the basis of a good deal of literature data to establish the range of applicability of the SB equation. 

This relationship can be simplified assuming the validity of the Simha-Boyer rule, Tg = constant, which leads to... 

The Simha-Boyer rule may be derived if it is assumed that the fractional excess volume universal constant for all polymers. In this case we have... 

Sherwood number, 56, 59 Shielding constant, 368 Shift factor, 443 Shish kebab structure, 705, 731 Shore D hardness, 831 Shore hardness testers, 838 Short-range order, 25 Short shots, 804 line region, 807 Short-term behaviour, 820 Short-time stiffness, 25 Side chain effects, 184 Significance of the shift factor, 450 Silky lustre, 876 Simha/Boyer rule, 100... 

According to the Simha-Boyer rule (Simha and Boyer, 1962), the product of the Tg times the change in thermal expansivity at Tg is a material-independent... 

FIGURE 6.32 (Top) Product of the glass transition temperature and the thermal expansion coefficient of the rubber at Tg for 51 polymers. (Bottom) Product of Tg and the difference in thermal expansivity of the rubber and glassy states for the same materials. The data fall close to the respective predictions of the Boyer-Spencer and Simha-Boyer rules (Section (v)) (Krause et al., 1965). 

According to Simha-Boyer rule AaTg = constant and thus the Gordon-Taylor parameter can be expressed as ... 

A different equation results if one assumes that the product of the change in expansivity with the glass transition temperature, AaT, is a constant, known as the empirical Simha-Boyer rule AaT = 0.113. The well-known and simple Fox expression for the glass transition temperature results on insertion of the Simha-Boyer rule into the Gordon-Taylor equation. The Gibbs-Di Marzio and the Fox equations are easily generalized to SVT or pVT equations of state when assuming that the solution can be based on simple additivity of the homopolymer properties. 

For water uptake, the Simha-Boyer rule (i.e., Aa T -constant) is often applied to... 

The free-volume fraction /exp calculated from Equation (10-51) agrees very well with the values given in Table 5-7 (Table 10-6). According to the empirical Boyer-Simha rule, the product (a/ - aam) Tg generally has a value of about 0.11 for a large number of polymers. Partially crystalline polymers and polymers with relaxation mechanisms lying below the glass transition temperature are exceptions to this rule. 

An additional, important empirical rule was discovered by Simha and Boyer (33-35), who found regularity in thermal expansion discontinuities, which can be written as follows ... 

---