Number of ring structures per

Previous studies( ) have shown how the number fraction of ring structures formed during irreversible linear random polymerisations leading to polyurethanes may be measured. The work has been extended(7,8) to non-linear polyurethane formation using hexa-methylene diisocyanate(HDI) and POP triols. For non-linear polymerisations, it is found that the number of ring structures per molecule(Nr) is always significant, even in bulk reactions. 

Figure 1. Number of ring structure per molecule (Np) as a function of extent of reaction(p) for linear and non-linear polyurethane forming reactions in bulk with approximately equimolar concentrations of reactive groups, r =[NC0no/[pHlo = 1) (6.7).

Figure 1. Number fraction of ring structures per molecule (Nr) as a function of extent of reaction (p) for bulk, linear, and nonlinear polyurethane-forming reactions with approximately equimolar concentrations of reactive groups (r = [NCO]J [OH]0 ss 1) (2,3). Conditions O-linear polymerization, HDI + poly(ethyleneglycol) at 70°, [NCOfo — 5.111 mol/kg, [OH], = 5.188 mol/kg number-average number of bonds in chain forming smallest ring structure (v) = 25.2, and nonlinear polymerization, HDI and POP triol at 70°C, [NCO] — 0.9073 mol/kg, [OH]0 = 0.9173 mol/kg v = 115. Reproduced with permission from Ref. 5.

NMR is independent of the number of unit structures per molecule, the MS value for Z number is very sensitive to this parameter. L = 1, that is two unit structures per molecule, would be compatible only with an average Z value of 46, and this is definitively excluded by MS data on the volatile portion of the sample. We must conclude that L is equal to zero and assume 2.6 naphthenic rings per molecule (Table X). This conclusion could not be arrived at from MS or NMR alone, only the combination of the two techniques. 

From the profile of the molecular weights obtained by the use of GPC data on the acetylated derivatives, the average molecular weight was calculated. From x, y, z, and N the average molecular weight of the basic structural unit was determined, and finally the number of benzene rings per molecule was realized, and hence the number of reactive sites per molecule. 

The most stable of the boron modifications is j -rhombohedral boron (Figure 4.8), which has a unit cell made out of boron icosahedra with each atom being connected to the top of a pentagonal pyramid. This part of the structure is similar to a buckyball (Buckminster-Fullerene or C q), but this boron ball is filled with a boron icosahedron. The unit cell is finished with a single boron atom and two B q units that are draped as three fivefold rings around a central boron atom. The total number of boron atoms per unit cell in this modification is 105. 

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