Polymers number average

Therefore by combining equations (9) and (10) and assuming some appropriate value for e, the number average number of LCB points per molecule can be calculated as a function of elution volume. The corresponding whole polymer number average number of LCB points per molecule is given by... 

In order to determine the branching structure factor e, Foster ( ) studied a large qroup of high pressure low density polyethylene resins (HP-LDPE). Using the MWBD method, he calculated the whole polymer number average number of branch points per JOOO carbon atoms from SEC data as a function of e. Then the Xfj values were compared with those obtained by nMR. 

While there are several statistically described averages, we will concentrate on the two that are most germane to polymers—number average and weight average. These are averages based on statistical approaches that can be described mathematically and that correspond to measurements of specific values. 

On the other hand the kinetic methods suffer from experimental error connected with the evaluation of the polymer number average molecular weight. Moreover, if the kinetics are not steady from the initial moments of polymerization, the latter... 

Polymer Number-Average Molecular Weight, M (x KF3) Styrene-to-Rubber Ratio (wt/wt) Yield Stress, Vy (MPa) Engineering Fracture Stress, Vf,e,mrg (MPa) Fracture Stress, (Tf(MPa) Fracture Strain, f(%)... 

One final area for discussion is the use of NMR for the determination of polymer number average molecular weights. End group resonances were clearly visible in the 13c NMR spectrum of the ethylene-l-hexene copolymer in Figure 3. An opportunity to determine polymer degrees of polymerization or number average molecular weights should not be overlooked. 

The activity of CALB immobilized on resins 1 to 4 (see Table 1) was assessed by s-CL ring-opening polymerizations. All immobilized resins have similar CALB loading (5.1 to 5.7 %-by-wt) and water content (1.4 to 1.9%). As shown previously , different chemical shifts are observed for methylene protons (-OC//2-) of e-CL monomer, PCL internal repeat units and chain terminal -012-OH moities. Hence, by in situ NMR monitoring, monomer conversion and polymer number average molecular weight (A/ ) were determined. 

Figure 4. Adnesion energy (erg/cm ) for SUPC biiayers in 0.1 M salt (PBS) plus dextran polymers. Number average polymer indices - Np (number of glucose monomers). Solid and dasned curves - predictions from mean field theory with first and second virial coefficients from osmotic pressure measurements (14).

Molecular sieve type and size Re- action time (days) Stirring Unreacted iso- butylene Yield of polymer % Number average molecular weight Mn We t average molecular weight Mw... 

Exp. No. Re- action time (days) Temp. (K) Ratio of catalyst to monomer (g/ml) Stirring Un- icacted iso- butylene (%) Yield of polymer Number average mol. Wright Mg Weight average mol. weight Mw... 

In the absence of an externally added strong acid, the diacid monomer acts as its own catalyst for the esterification reaction. For this case, [HA] is replaced by [-COOH] in Equation 4.1. Assuming that the two functional groups are nearly stoichiometric, and setting [-COOH] = N, the final equations expressing the variation of reaction extent,/ and polymer number average degree of polymerization (NADP), DP,j with time can be written as [34, 35]... 

Differentiation of A/x with respect to w at the same MWl) (Equation 40), summation and comparison with Equation 41 at = 0 lead to a differential equation for the polymer number average chemical potential (Scholte, 1970ab)... 

These values were used to calibrate GPC colunms for the polymer. Number-average molecular weights determined with modified calibration curves agreed well with those determined by embulliometry. The value of 0.96 for a was consistent with the idea that poly(3-alkylthiophene)s formed relatively stiff polymer chains in solutions. 

M = polymer number-average [Mvftv], [17VW] = indices for a crystallographic... 

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