Molar mass between

Overall, as is apparent from this description, light scattering is a difficult, time-consuming technique, despite its great importance. Despite this, the technique has been used to measure relative molar masses as low as that of sucrose and as high as those of proteins, and has been found to have a useful range for polymers of relative molar masses between ten thousand and ten million. 

A typical polyester molecule has 50 to 100 repeat units and a molar mass between 10,000 and 20,000 g/mol. PET can be formed into fibers (such as Dacron) or films (such as Mylar). Mylar films, which can be rolled into sheets 30 times thinner than a human hair, are used to make magnetic recording tape and packaging for frozen food. Dacron is best known for its use in clothing, but it has many other applications. For example, tubes of Dacron are used as synthetic blood vessels in heart bypass operations because Dacron is inert, nonallergenic, and noninflammatory. 

Practically, polymers with molar masses between 2 x 104 and 2 x 106 g/mol can be characterized by membrane osmometry, but measurements of Mn <104 g/mol have also been reported with fast instruments and suitable membranes [16]. The lower limit is set by insufficient retention of short polymer chains. Above M 2 x 106 g/mol, the osmotic pressure, which is proportional to Mr1, is too low for a reasonable signal-to-noise ratio. An advantage of the low molar mass cut-off is that impurities with a very low molar mass can permeate through the membrane and, hence, do not contribute to the measured osmotic pressure. Their equilibration time may, however, be different from that of the solute, leading to complex time-dependent signals. 

Figure 8 illustrates(29) the close relationship between the chain defining the molar mass between junction points of the perfect network (M ) and the chain of v bonds of the preceding sections. The illustrations in (b) and (c) are for the RA2 +... 

The networks studied were prepared from reactions carried out at different initial dilutions. Aliquots of reaction mixtures were transferred to moulds, which were maintained at the reaction temperature under anhydrous conditions, and were allowed to proceed to complete reaction(32). Sol fractions were removed and shear moduli were determined in the dry and equilibrium-swollen states at known temperatures using uniaxial compression or a torsion pendulum at 1Hz. The procedures used have been described in detail elsewhere(26,32). The shear moduli(G) obtained were interpreted according to Gaussian theory(33 34 35) to give values of Mc, the effective molar mass between junction points, consistent with the affine behaviour expected at the small strains used(34,35). 

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-...

Figure 9. Molar mass between elastically effective junction points (Mc) relative to that for the perfect network (Mc°) versus extent of intramolecular reaction at gelatin (pr,c) for polyurethane networks (29).

Time-crosslink density superposition. Work of Plazek (6) and Chasset and Thirion (3, 4) on cured rubbers suggests that there is one universal relaxation function in the terminal region, independent of the crosslink density. Their results indicate that the molar mass between crosslinks might be considered as a reducing variable. However, these findings were obtained from compliance measurements on natural rubber vulcanizates,... 

Figure 1, Ratio of molar mass between elastically effective junctions to front factor (M(-/A) relative to molar mass between junctions of the perfect network (M ) versus extent of intramolecular reaction at gelation (pj- (.) Polyurethane networks from hexamethylene diisocyanate (HDI) reacted with polyoxpropylene (POP) triols at 80°C in bulk and in nitrobenzene solution(5-7,12). Systems 1 and 2 HDI/POP triols >i= 33, V2= 61. Systems 3-6 ...

When a chain with M= 200,000 g/mole is linked to other chains at four points, the average molar mass between cross-links, M., amounts to 40,000. The mass of one unit is 4x12 + 6x1 =54 g/mole so the number of units between cross-links is about 740. At the glass-rubber transition no whole chains obtain free mobility, as a result of the entanglements, but chain parts of 30 to 100 monomer units. The chemical cross-links, therefore, hardly contribute to the restriction in chain mobility the increase in Tg will, therefore, be negligible. 

Figure 13.10 Toughness (K C) and toughening mechanisms of epoxy networks modified with 10 phr CSR versus molar mass between crosslinks, Me (O) neat systems ( ) with 10 phr CSR. (Adapted from Lu, 1995.)...

Klc = critical stress intensity factor in mode I, MPam1/2 Km = stress concentration factor Me = average molar mass between crosslinks, kg mol 1 Mn = number-average molar mass, kg mol 1 p = hydrostatic pressure, Pa Tg = glass transition temperature, K... 

It is important to point out that several different superstructures are formed in polyethylene depending on the molar mass of the polymer and the crystallisation temperature (Fig. 16). Linear polyethylenes (narrow molar mass distribution Mw/Mn 1.1) of molar mass between 18,000 and... 

Crystallisation at higher temperatures (degree of super-cooling <17.5 °C) of linear polyethylene fractions of molar masses between 18,000 and... 

Mc = molar mass between cross-links (here 5 x 50 = 250)... 

In each of the studies quoted in Table 23 increasing nAi/ Nd-ratios result in decreases of molar mass. Between these studies there is unanimous agreement that molar mass reduction is caused by chain transfer with the cocatalyst. Most of the studies quoted in Table 23 consider the transfer reaction as irreversible. Only Friebe et al. explain their results on the basis of a reversible transfer of living polybutadienyl chains between Nd and Al [178,179]. A comparison of chain transfer efficiencies between DIBAH and TIBA reveals that chain transfer is much less pronounced for TIBA (Sect. 4.5). For DIBAH chain transfer efficiency is 8-fold over that of TIBA and the substitution probability... 

Determine the molecular formula of a compound with molar mass between 105 and 115 g/mol which contains 88.8% C and 11.2% H. 

A rubber band with molar mass between crosslinks Afs = 3000 g mop is uniaxially stretched to three times its original length. After achieving equilibrium at 21 °C it is allowed to contract adiabatically back to the unstretched state. 

In this experiment we follow a procedure adapted from Pfau, Schrepp and Horn [26]. Commercial PEI with a molar mass between 30 and 1,000 kD is dissolved in water (buffer with pH 4, 1 mM KC1) to yield a solution of 1 to 10 ppm concentration. The latex spheres are separated from the solution and precipitated by centrifugation onto a mica surface fixed at the bottom of the centrifugation tube. Finally, the water is decanted and the samples are dried in air. Alternatively, drops of the solution are placed onto freshly cleaved mica substrates which are rinsed with pure Milli-Q water after several minutes. Subsequently the samples are dried in air. 

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