Number-average molecular weight calculation

Criterion 2. The number average molecular weights of polyisoprenes and poly(a-methylstyrene-l7lock-isoprene-b/ocfc-a-methylstyrene) block copolymers prepared with the initiator, 6, were all within 4% of the number average molecular weights calculated based on the stoichiometry of the reaction (see Eq. 9 note this equation should be modified to Eq. 12 if the moles of dilithium initiator is used in the denominator of Eq. (9)] ... 

The width of molecular weight distribution (MWD) is usually represented by the ratio of the weight—average and the number—average molecular weights, MJM. In iadustry, MWD is often represented by the value of the melt flow ratio (MER), which is calculated as a ratio of two melt indexes measured at two melt pressures that differ by a factor of 10. Most commodity-grade LLDPE resias have a narrow MWD, with the MJM ratios of 2.5—4.5 and MER values in the 20—35 range. However, LLDPE resias produced with chromium oxide-based catalysts have a broad MWD, with M.Jof 10—35 and MER of 80-200. 

The number average molecular weight (M ) is related to the number of particles present in a sample. It is calculated by dividing the sum of the weights of all the species present (monomers, dimers, trimers, and so on) by the number of species present ... 

Proton NMR integrations of methylene and aromatic regions can be used to calculate the number-average molecular weights of novolac resins29 ... 

Functionalization yields have to be checked carefully by comparing the effective number average molecular weight Mn with its value calculated from the functional content of the sample, under the assumption that each macromolecule carries one function (two if a bifunctional initiator is used). Low molecular weight samples are preferred, as the functional analysis would otherwise lack accuracy. In all examples quoted high functionalization yields have been attained. 

Once the primary variables were obtained, numerous secondary variables were also calculated such as overall conversion, monomer A and B conversions, polymer composition from the moles of A and B in the copolymer, and number average molecular weight. The latter was obtained by dividing the mass of monomers A and B in the polymer by the moles of polymer. 

Conventional SEC calculations were performed with the SEC software package GPCl (Chromatix). As described below a universal calibration was carried out to obtain the peak position molecular weight at each V a modified version of GPCl then was used to calculate weight-and number-average molecular weights for the sample fraction at V (Appendix). 

Because of chromatographic dispersion, the sample fraction in the detector cell is polydisperse. The weight-average and number-average molecular weights of the polydisperse fraction are calculated as... 

Having determined b by the above method, the true number average molecular weight and higher moments for the whole polymer can be calculated as follows ... 

The number average molecular weight (Mn) is calculated from Eq. 1.1. 

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. 

Chains per Zn was calculated by using the zinc feed and polymer production rates and the number-average molecular weight of the resulting copolymer corrected for comonomer content. Similarly, chains per Hf was estimated by using the total catalyst metal feed... 

Hence, is the statistics average Molecular weight calculated from the number Molecular weight distribution function, N(M). Mn is the statistical average Molecular weight calculated from the weight... 

Chromatography analysis yields the mass of monomeric species and polymer In the cured resin, from which the moles of monomer are readily calculated. This relationship, coupled with the observed molecular weight, can be utilized to determine the moles of polymer. Hence, the corrected number average molecular weight Is... 

The relationship shown in Equations 4.91 and 4.92 shows that high values of p (0.99) are essential in producing high N and W values. The number-average molecular weight M calculated from Equations 4.89 and 4.90 is as follows ... 

Number-average molecular weights (M ) of the copolymers are often smaller than the theoretical value calculated from the copolymer yield and the total molar amount of initiator. Nevertheless, the polydispersity indexes (PDIs) are small,... 

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