Molar number average

Besides aliphatic diisocyanates, an aromatic isocyanate was also used to prepare polyurethanes. A new renewable copolymer (Scheme 17) was synthesized from reactive bis-hydroxylated poly(3-hydroxybutyrate-co-3-hydroxyvalerate) oligomers (PHBHV-diol), isosorbide, and 1,4-phenylene diisocyanate. The molar number-average molecular weights (M of most of the copolyesters were about... 

Figure I 6.34 Degree of polymerization distribution molar distribution ( ) with number average degree of polymerization (dp = 140 glucose unimers) mass distribution ( ) with weight average degree of polymerization dp = 1242 glucose unimers.

The number-average molar mass of thermoplastic polyesters varies from about 20,000 for film and fiber applications to 40,000 for injection-molding or blowmolding resins. Relationships between intrinsic or molten viscosity and molar mass have been published for PET,131-136 PBT,135,137 and PEN.138... 

The rigid and soft blocks used in polyesteredier diermoplastic elastomers (polyesteretlier TPEs) are typically PBT and poly(oxyteti amethylene) (PTMO), respectively, witii block number-average molar mass varying between 1000 and 3000. They are obtained by the melt reaction between dimethyl terephthalate, butanediol, and dihydroxy-terminated PTMO in the conditions typical of a PBT syndiesis. 

Thermoplastic linear polyesters, 18 Thermoplastic polyesters, 20-29, 31 commercial (table), 21-22 number-average molar mass of, 45... 

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... 

If it is possible to analyse end groups of a particular specimen of polymer, it may be possible to use the data to determine number average relative molar mass. If the molecules are branched the degree of branching can be measured from a combination of end group analysis and relative molar mass determination (determined by an alternative method). 

In all calculations the molar masses given in the top of Table I were used. First of all, the effects of variations in the concentration of trifunctional monomers were determined, as exemplified by the nine formulations of Table I and the resulting prepolymer characteristics after full conversion given in Table II. Formulations FIO to F40 result in branched prepolymers, which are cured in the third stage by difunctional monomers. On the other hand, formulations FOO to F04 result in the same linear prepolymer, which is subsequently cured with various mixtures of di- and trifunctional monomers. The number average functionalities of PI (and P2) and of the mixtures of E and F monomers are varied systematically between 2.0 and 2.4. Therefore, the only difference between formulations FjO and FOj is the stage in which the branching units are added. 

The number average molecular weight at equilibrium is governed by the initial molar ratio of the cyclic tetramer to the disiloxane. In general, the DSX incorporates more readily using the quaternary ammonium catalyst. 

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. 

One system studied by the authors(3) used LG56 triol which had been characterised by molar-mass as well as end-group determinations. The data for the samples used are given in Table III, indicating a true number-average functionality (fn) of between 2.95 and 2.99. The triol was reacted with HDI in bulk (see Figure 1) and at various dilutions in benzene, and values of Nr and ac determined. To estimate functionality from ac, equations... 

Figure 8. Part of a tetrafunctional network formed from an RA t and RBi polymerization corresponding to Mc°, the molar mass between junction points of the perfect network (a). Detail of the chain structure defining Mc° for HDl reacting with an OPPE, n is the number-average degree of polymerization of each arm with respect to oxypropylene units, (b). Part of the chain structure defining v, the number of bonds in the chain forming the smallest ring structure (C), for the reaction system in (b) (29). Reproduced, with permission, from Ref. 21. Copyright 1980, Stein-...

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. 

In this section, we review the properties of a series of PNIPAM-b-PEO copolymers with PEO blocks of varying length, with respect to the PNIPAM block. Key features of their solutions will be compared with those of PNIPAM-g-PEO solutions. PNIPAM-b-PEO copolymers were prepared by free-radical polymerisation of NIPAM initiated by macroazoinitiators having PEO chains linked symmetrically at each end of a 2,2/-azobis(isobutyronitrile) derivative [169,170]. The polydispersities of PEOs were low, enabling calculations of the number-average molar mass for each PNIPAM block from analysis of their H-NMR spectra (Table 2). 

Furthermore, polymeric samples are usually a mixture of macromolecular chains terminated by different end-groups and thus, an interesting quantity to be determined (in order to characterize the mixture) is the relative abundance of end-groups [1—3]. Other two important quantities are Mn and Mw, the number-average and the weight-average molar masses [1—3]. 

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 ... 

Number-average molar masses were determined using a vapor pressure osmometer (VPO) (Hitachi 117 Molecular Weight Apparatus) at 54.8 0.1°C in toluene (Fisher Scientific, certified A.C.S.) which was distilled from freshly crushed CaH2. The VPO apparatus was calibrated with pentaerythritol tetrastearate (Pressure Chemical). Gel permeation chromatographic (GPC) analyses were performed in tetrahydrofuran by HPLC (Perkin-Elmer 601 HPLC) using six y-Styragel columns (106, 105, 10l, 103, 500, and 100 A) after calibration with standard polystyrene samples. 

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)... 

Eq. 5.17 when written in terms of number average molar mass yields ... 

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. 

Thus, the result of an osmotic pressure experiment with a mixture of solute macromolecules yields the number-average molar mass M . 

Table 15.1 contains osmotic pressure data calculated from the work of Browning and Ferry [3] for solutions of polyvinyl acetate in methyl ethyl ketone at 10°C. Plot H/vv against w, fit the data to a quadratic polynomial, and calculate the number-average molar mass from the intercept with the n/w axis. 

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