Number-Average Molecular Weight M

Molecular weights of polymers are determined by the weight—average molecular weight, and the number—average molecular weight, M. The... 

Na" > > Cs". The amount of unsaturation also iacreases with number-average molecular weight (M ) suggesting that the rate of polymerisation... 

An antioxidant such as phenyl-(3-naphth larnine, was then added to the latex (1.25 parts) prior to coagulation by salt—acid mixtures and drying of the mbber cmmb, which was compressed into 34-kg bales. The SBR produced by this recipe had a Mooney viscosity of about 50 and a number-average molecular weight M of 100,000—200,000. 

These values are given for polymers of narrow molecular-weight distribution, with number-average molecular weights (M ) of about 20,000 prior to chlorination. Chlorination reactions are carried out under homogeneous conditions in CCl solutions at temperatures between 90 and 110°C with viscosities at about 5 Pa (50 P). 

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 ... 

The synthesis of a PPV derivative, 94, with donor (di-n-hexylamino) and acceptor (nitro) substituents attached regioselectively to the PPV backbone, was published by Yu et al. following the Heck-type cross coupling approach [118] starting from an AB-type monomer (95). The red-orange polymer (94), which is soluble in THE, chloroform and 1,2-dichloroethane, displays a number-average molecular weight M of about 12,000. 

The glass transition increases wilh number-average molecular weight M, to a limiting asymptotic value of Tg for infinite molecular weight, in the... 

Gel permeation chromatography is an attractive technique for determination of the number-average molecular weight (M ) distribution of petroleum fractions, especially the heavier constituents, and penoleum products (Altgelt, 1968 1970 ... 

The most important parameters that can be determined by MALDI are number-average molecular weight (M ), weight-average molecular weight (M ), and the molecular weight distribution expressed as polydispersity (PD) [106,124]... 

Matrix-Assisted Laser Desorption/lonization Time-of-liight Mass Spectrometry (MALDI-TOF MS, PerSeptive Biosystems Voyager-DE STR) was used to characterize the molecular weight distribution and the number average molecular weight (M ) of the poly(methacrylic acid) (PMAA) degradation products as described elsewhere [25]. 

It is possible to uniquely determine both the scission efficiency Gis) and the crosslinking efficiency G(x) via Equations 9 and 10 providing both the number average molecular weight (M ) and the weight average molecular weight (Af ) can be measured. 

The apparent difference between viscosity average (M ) and number average molecular weight (M ) for unfractionated triacetate samples and high molecular weight fractions may be attributed to the presence of hemicellulose and polydispersity effect in these materials as shown in the table in question and in Figure 3. 

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,... 

The number-average molecular weight M , defined as the total weight of a polymer sample divided by the total number of moles in it (Eqs. 1-15 and 1-16), is given by... 

Table4.1. Degree of polymerization P and number-average molecular weight M (assuming a structural element of molecular weight 100) as a function of conversion in condensation and stepwise addition polymerizations...

Now we compare the above osmotic pressure data with the scaled particle theory. The relevant equation is Eq. (27) for polydisperse polymers. In the isotropic state, it can be shown that Eq. (27) takes the same form as Eq. (20) for the monodisperse system though the parameters (B, C, v, and c ) have to be calculated from the number-average molecular weight M and the total polymer mass concentration c of a polydisperse system pSI in the parameters B and C is unity in the isotropic state. No information is needed for the molecular weight distribution of the sample. On the other hand, in the liquid crystal state2, Eq. (27) does not necessarily take the same form as Eq. (20), because p5I depends on the molecular weight distribution. 

In this way, cyclic polymers with number-average molecular weights M up to 1200 k Dalton can be prepared by varying the ration of catalyst to monomer or the initial monomer concentration. 

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