Number average functionality

In all calculations the molar masses given in the top of Table I were used. First of all, the effects of variations in the concentration of trifunctional monomers were determined, as exemplified by the nine formulations of Table I and the resulting prepolymer characteristics after full conversion given in Table II. Formulations FIO to F40 result in branched prepolymers, which are cured in the third stage by difunctional monomers. On the other hand, formulations FOO to F04 result in the same linear prepolymer, which is subsequently cured with various mixtures of di- and trifunctional monomers. The number average functionalities of PI (and P2) and of the mixtures of E and F monomers are varied systematically between 2.0 and 2.4. Therefore, the only difference between formulations FjO and FOj is the stage in which the branching units are added. 

One system studied by the authors(3) used LG56 triol which had been characterised by molar-mass as well as end-group determinations. The data for the samples used are given in Table III, indicating a true number-average functionality (fn) of between 2.95 and 2.99. The triol was reacted with HDI in bulk (see Figure 1) and at various dilutions in benzene, and values of Nr and ac determined. To estimate functionality from ac, equations... 

Polyurethane networks were prepared from polyoxypropylene (POP) triols(Union Carbide Niax Polyols) after removal of water by azeotropic distillation with benzene. For Niax LHT 240, the number-average molecular weight determined by VPO was 710 and the number-average functionality fn, calculated from Mjj and the content of OH groupSj determined by using excess phenyl isocyanate and titration of unreacted phenyl isocyanate with dibutylamine, was 2.78 the content of residual water was 0.02 wt.-%. For the Niax LG-56, 1 =2630, fn=2.78, and the content of H2O was 0.02wt.-%. The triols were reacted with recrystallized 4,4"-diphenylmethane diisocyanate in the presence of 0.002 wt.-% dibutyltin dilaurate under exclusion of moisture at 80 C for 7 days. The molar ratio r0H = [OH]/ [NCO] varied between 1.0 and 1.8. For dry samples, the stress-strain dependences were measured at 60 C in nitrogen atmosphere. The relaxation was sufficiently fast and no extrapolation to infinite time was necessary. 

After prolonged degassing of a large batch of PPG, analyses showed that its hydroxyl, unsaturation, and water contents were 0.97 meq/g, 0.033 meq/g, and 0.0035%, respectively. The hydroxyl content was determined by an acetylation method, carried out with acetic anhydride (10). The amounts of unsaturation and water were determined by the mecuric acetate and Karl Fischer methods (10), respectively. The obtained analytical results indicate that the number-average molecular weight of the dihydroxy material is 2062, provided its molecular weight is arbitrarily assumed to be twice that of the monohydroxy material, and that the mole fraction of the monohydroxy poly (propylene oxide) is 0.066. This value corresponds to a number-average functionality of 1.93 for the PPG. 

Triols. One triol used was the propylene oxide adduct of 1,2,6-hexanetriol, designated LHT-240 and supplied by Union Carbide Chemicals Company. After degassing, its hydroxyl, unsaturation, and water contents were 4.31 meq/g, <0.01 meq/g, and 0.004%, respectively. Thus, the material was essentially trifunctional, and its number average molecular weight was 696. If the unsaturation was exactly 0.01 meq/g, then the number-average functionality was 2.99. 

For the application of hyperbranched polymers as precursors in network formation, the functionality averages are important. The number-average functionality is given by the equation... 

In the case of oligomers, the concept of number-average functionality, fn, is usually applied, which is the ratio between the total number of functional groups and the total number of molecules in the system, or, in other words, the average number of RFG per initial oligomer molecule. 

The number-average functionality is obtained from the molar concentration of OH groups and number-average molecular weight of the polymer Mn... 

Flory Rgel — l/(J5pwO 1) — Z)p o is the initial weight-average functionality of starting polymer chains Df o is the initial number-average functionality of starting polymer chains (Miller et al, 1979). 

In regard to Step 3, the telechelic diolefin II can be quantitatively converted to the diol V by hy-droboration/alkaline oxidation. Specifically, hydro-boration of II by BH 3 THF (or 9-BBN) yields an intermediate III which without isolation can be converted in situ by alkaline oxidation (NaOH/H2C>2) to the diol IV, the starting material for polyurethane synthesis. The number average functionality of IV was found to be 2.0 within experimental error. The analytical methods used were 1H NMR and UV spectroscopy [4]. The latter method involved the reacting of the diol with phenyl isocyanate, PhNCO, removing the excess PhNCO, filtration, Mn determination and differential UV spectroscopy. Table I shows representative data. 

Figure 9.29 Number average functionality versus number average molecular weight for HTPB fractions.

This is defined not by the number of monomers but by the functional groups. The number average functionality of the monomers is... 

The number-average functionality / of the /u.-molecules is then given by... 

F = number average functionality TMPD = 2,2,4-trimethyl-1,3-pentanediol CHDM = cyclohexane dimethanol BEPD = 2-butyl-2-ethyl-1,3-propanediol HBPA = hydrogenated bisphenol A TMP = trimethylol propane TME = trimethybl ethane... 

A simple theory for prediction of gel-points can be derived using the principles employed in the linear step polymerization theory of Carothers. When there is a stoichiometric balance in the numbers of mutually-reactive functional groups, the number-average functionality, is used and is defined by... 

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