Polymer number average molar mass

Gelation occurs at relatively low conversions of monomer to polymer hence the number-average molar mass at the gel point is low. By contrast, however, the weight-average molar mass becomes infinite at the gel point. 

The methods by which polymers are prepared result in a mixture of molecular sizes whose properties depend on the average size of the molecules present. In principle there are a number of ways in which such an average can be calculated. The most straightforward is the simple arithmetic mean, usually called the number average molar mass, M. This is defined by the expression... 

In the case of a polydisperse polymer it is still the total number n of solute molecules that is measured and the total mass m of solute molecules that is known from sample preparation, resulting in the number average molar mass M = ... 

M) is the number average molar mass of the solute (polymer), R — 8.315 J/K mol the gas constant, and c the polymer concentration in polymer mass per volume solution. 

Mass spectrometry can be used to measure the molar mass distribution (MMD) of a polymer sample by simply measuring the intensity, Nt, of each mass spectral peak with mass m . This is due to the fact that mass spectrometers are equipped with a detector that gives the same response if an ion with mass 1 kDa or 100 Da (actually any mass) strikes against it. In other words, the detector measures the number fraction and this implies that Nt also represents the number of chains with mass m,. Thus, the number-average molar mass, Mn, is given by ... 

Polymers are therefore mainly characterised in terms of two molar masses. These are the Number Average Molar Mass, M, (Eq. 5.6) and the Mass Average Molar Mass, M, (Eq.5.7)... 

Interestingly, our own studies have revealed that both the shape of the macromolecule and the glass transition temperature, Tg, change with irradiation time. For example, the irradiation of a bimodal commercial sample of polyvinylcarbazole (PNVK) (Fig. 5.31a) in dichloromethane occurred with an initial increase in (the number average) molar mass (M ) and an apparent loss in the bimodal nature of the polymer (Tab. 5.16, Fig. 5.31b). A similar initial increase in has been observed by Price [39] during a sonically induced polymerisation. 

Number-average molar mass of polymer chains between two adjacent crosslinks or junction points in a polymer network. 

A reactor block consisting of 16 reactors was divided into 4 zones with 4 different CTA to initiator ratios, and 4 different acrylates or methacrylates were used in each set of experiments. The polymerization of tert-buiyl methacrylate was repeated four times to demonstrate the reproducibility of the polymerization in an automated parallel synthesizer. Structural analysis of the polymers revealed that there was less than 10% deviation in the number average molar mass (Mn) and the PDI values. 

Table 13 Number of incorporated monomer units into the 30 triblock copoly(2-oxazoline)s resulting from combined H NMR spectroscopy analyses (top) of the model [A and AB (block co) polymers] and final polymers as well as the measured number average molar masses (Mn,SEC/PDI bottom). H NMR spectra were recorded in CDCI3 or CD2CI2 (PhOx containing polymers) and GPC analyses were performed using DMF (with 5 mM NH4PF6) as eluent. Mn,GPC was calculated utilizing poly(methyl methacrylate) (PMMA) standards...

Here, /u ° and ju are, respectively, the chemical potentials of pure solvent and solvent at a certain concentration of biopolymer V is the molar volume of the solvent Mn=2 y/M/ is the number-averaged molar mass of the biopolymer (sum of products of mole fractions, x, and molar masses, M, over all the polymer constituent chains (/) as determined by the polymer polydispersity) (Tanford, 1961) A2, A3 and A4 are the second, third and fourth virial coefficients, respectively (in weight-scale units of cm mol g ), characterizing the two-body, three-body and four-body interactions amongst the biopolymer molecules/particles, respectively and C is the weight concentration (g ml-1) of the biopolymer. 

For conversions lower than xgei the average molar mass of the polymer exhibits a continuous increase. The first two moments of the molar mass distribution are the number-average molar mass, Mn, and the mass-average molar mass, Mw, respectively. Mn is defined in terms of the number contribution of every species to the whole population. The weight factor used to define this average is the molar fraction. Mw is defined in terms of the mass contribution of every species to the whole mass, so that the mass fraction is the weight factor used in its definition. 

The number-average molar mass of polymer chains is defined as Mn = (mass of reacted monomers)/[(l/2) of chain ends] (3.161)... 

The number-average molar mass of the polymer fraction may be obtained by dividing the polymer mass by the number of moles in the polymer fraction. This leads to (Williams and Vallo, 1988) ... 

This is called the number-average molar mass (M ) and is the average molar mass of each chain. The chains have a chemical group attached at each end, the nature of which depends upon how the polymer was synthesized. For high polymers the mass of these end groups is negligible, however and is ignored. 

Several experiments were also carried out using similar recipe (runs 8-10). Reproducibility was difficult to achieve in terms of molar masses and cycle contents, surely because reactants were used as received, i.e. neither distilled not dried, and also due to the difficulty to control the addition of L H thoroughly. This fact is particularly striking while looking at the evolution of the number average molar mass and polymer content for different L H period of time as reported in Fig. 3. Polymers of high molar masses were obtained only for low conversion, i.e. large contents of small cycles. There are no clear trend of the effect of addition time on final conversion and molar masses except for slow addition times, where hnal molar masses were systematically low. 

The number-average is the common average used, for example, to determine the average denomination of the coins in your pocket. The number traction of each type of coin (n ) is multiplied by its denomination Mm)-Substituting Eq. (1.27) into Eq. (1.23) shows that the ratio of the molar mass of a polymer with AT monomers and the number-average molar mass Mn relates the number fraction and weight fraction of molecules ... 

In order to obtain the number-average molar mass of a particular sample, osmotic coefficient (II/c) data, measured at various low concentrations, must be extrapolated to the zero concentration limit. In addition to the ideal gas contribution [Eq. (1.73)] that arises from individual polymers, the osmotic pressure also has a contribution from polymer-polymer interactions. The contribution to osmotic pressure from interaction... 

Determine the number-average molar mass of the polymer and the second virial coefficient of the solution Aj. 

The number of network strands per unit volume (number density of strands) is p = njV. In the last equality, p is the network density (mass per unit volume), Mg is the number-average molar mass of a network strand, and IZ is the gas constant. The network modulus increases with temperat-iire hpnaiisp its origin is entropic, analogous to the pressure of an ideal gas p = nkTjV. The modulus also increases linearly with the number density of network strands u = n/V = pJ fEquation (7.31) states that the modulus of any network polymer is kT per strand. 

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