Polymer average molar masses

How does average molar mass affect each of the following polymer characteristics (a) softening point ... 

Why do polymers not have definite molar masses How does the fact that polymers have average molar masses affect their melting points ... 

Acrylic resins are polymeric materials used to make warm yet lightweight garments. The osmotic pressure of a solution prepared by dissolving 47.7 g of an acrylic resin in enough water to make 500. mL of solution is 0.325 atm at 25°C. (a) What is the average molar mass of the polymer ... 

Polymers generally do not have definite molecular masses because there is no fixed point at which the chainlengthening process will cease. There is no fixed molar mass, only an average molar mass. Because there is no one unique compound, there is no one unique melting point, rather a range of melting points. 

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... 

SEC-GC-FID, according to Figure 7.40, has been used to carry out the simultaneous determination of the polymer average molecular masses and molar mass distribution and the concentration of additives [984]. The effluent was split and adsorbed on PTV packing material before GC analysis. The choice of PTV... 

Reaction mechanisms and molar mass distributions The molar mass distribution of a synthetic polymer strongly depends on the polymerization mechanism, and sole knowledge of some average molar mass may be of little help if the distribution function, or at least its second moment, is not known. To illustrate this, we will discuss two prominent distribution functions, as examples the Poisson distribution and the Schulz-Flory distribution, and refer the reader to the literature [7] for a more detailed discussion. 

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. 

SEC or gel permeation chromatography (GPC) is one of the widely used chromatographic techniques [56,57]. In contrast to the already discussed colligative and scattering methods it is not an absolute method and requires proper calibration with some known polymer standards. One obtains not only the average molar masses (M , Mw, Mz) but the complete molar mass distributions. 

The term "degradation of macromolecules" concerns the processes that are accompanied by deterioration in polymer properties. Chemical processes related to the worsening polymer properties may lead to both a reduction of average molar mass due to the scission of bonds in the macromolecular chain, or to an increase of the molar mass due to the crosslinking causing the polymer to become insoluble. 

The quality of the polymer, its photo-oxidation and thermo-oxidation history expressed in concentration of hydroperoxides, carbonyl groups or of other oxidized structures and terminal groups. The rate of an oxidative attack may then be related to the average molar mass and to its distribution, and to the ratio of amorphous/crystalline structures. Polymers cannot be simply ordered according to the intensity of light emission at a given temperature. The chemiluminescence-time patterns are related with the rate of sample oxidation, but they may differ from one to the next polymer. 

On well characterised non-stabilized PP samples [48] having molar mass within 45-180 kg/mol with differing tacticity and crystallinity, we can see that the increasing molar mass leads to an increase of induction time and reduction of the maximum chemiluminescence intensity (Figure 14). The polymer with higher average molar mass appears to be more stable than that with lower molar mass. This may be ascribed to the effect of increased concentration of more reactive terminal groups, which promote initiation of thermal oxidation. 

Figure 15 Chemiluminescence oxidation runs for polypropylene powder at different temperatures the average molar mass of the polymer is 180 kg/mol. 

Fig. 10a Average hydrodynamic radii ((Rh)agg) and b weight-average molar mass ((Mw)agg) of the aggregates in aqueous block copolymer solutions at different polymer concentrations (c given in moles of PNIPAM blocks) at 45 °C a NE-A, b NE-B, c NE-C, d NE-1, e NE-2, and/ NE-3. (Reprinted with permission from Ref. [169] copyright 2002 American Chemical Society)... 

In order to facilitate the reader, the chapter is split into various sections. Section 15.2 deals with instrumentation, sample preparation, and matrices, remaining sections deal with the analysis of ultrapure polymers, polymer mixtures in which backbones are identical, and polymer mixtures in which backbones are different, respectively. The final section deals with the determination of average molar masses. 

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 ... 

An example can best explain the procedure. A poly(bisphenolA carbonate) sample characterized by a broad-MMD was injected in an SEC apparatus, about 100 fractions were collected, and 24 of them were analyzed by MALDI [7]. Figure 15.2 reports the SEC trace of the PC sample. The trace covers a quite broad range of elution volumes and it is centered at about 30 ml. The polymer starts eluting at about 26 ml and ends at about 38 ml. The MALDI spectra yielded MP values (see above). Using this information, the SEC trace in Fig. 15.2 is calibrated and the average molar masses turn out to be Mw = 55,800, Mn = 23,600. 

The dissolved polymer molecules are separated on the basis of their size relative to the pores of a packing material contained in a column. The chromatograms can be converted to molar mass distributions, average molar masses, Mn, M, and M, long-chain branching and its distribution. 

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...

Although average molar masses are convenient for evaluation of G(S) and G(X), we have shown that the molar mass distribution should be considered (5). In particular, the formation of a high molar mass tail can result in serious underestimation of the correct average molar masses, especially after high doses of radiation. Cross-linking causes changes in the hydrodynamic volume of the polymer molecules relative to linear molecules and this affects viscosity and GPC estimates of molar mass, which should be taken into consideration. 

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. 

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