Molar mass between elastically

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).

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 ...

Fig 2 Molar mass between elastically effective junction points(M ) relative... 

From the value taken by the elastic modulus at the mbbery plateau, the molar mass between entanglements (Me) can be indeed deduced using the relation E=4p RT/5Me, where p is the density. Plotting the variation of the Newtonian viscosity (rio) as a function of the molar mass also gives a critical value (Me) above which entanglements occur (see Figure 13.7), where Me is roughly equal to 10/4 of Mg (see Table 13.1). 

Table 13.1. Critical molar masses between entanglements (Me) determined from viscosity measurements and molar mass between entanglements (Me) drawn from the value of the elastic modulus at the rubbery plateau...

The experimental data to be considered are shown in Figure 1. They refer to previously published data on hexamethylene diisocyanate(HDI) reacting with polyoxypropylene(POP) triols and tetrols in bulk and in nitrobenzene(5-7,12) that is, to RA2 + RBj polymerisations. is the molar mass of chains between elastically effective junction points. A/Mj. has been determined directly from small-strain compression measurements on swollen and dry networks using the equations... 

Chain entanglements are the cause of rubber-elastic properties in the liquid. Below the "critical" molecular mass (Mc) there are no indications of a rubbery plateau. The length of the latter is strongly dependent on the length of the molecular chains, i.e. on the molar mass of the polymer. From the shear modulus of the pseudo rubber plateau the molecular weight between entanglements may be calculated ... 

The number average molar mass of a chain section between two junction points in the network is an important factor controlling elastomeric behavior when is small, the network is rigid and exhibits limited swelling, but when is large, the network is more elastic and swells rapidly when in contact with a compatible liquid. Values of can be estimated from the extent of swelling of a network, which is considered to be ideal but rarely is, and interpretation of the data is complicated by the presence of network imperfections. A real elastomer is never composed of chains linked solely at tetrafunctional junction points but will inevitably contain defects such as (1) loose chain ends, (2) intramolecular chain loops, and (3) entangled chain loops. 

The temperature range between the glass transition range and the flow or fusion (melt) range, in which the shear modulus remains nearly constant, becomes wider as the molar mass grows. The plastic is then described as entropy or mbber elastic, or even thermoelastic (as opposed to thermoplastic). 

Here, elastoviscous is defined as rheological behavior with predominantly viscous and little elastic character, whereas viscoelastic is behavior with mainly elastic and little viscous character. Materials that behave elastoplastically show a marked flow limit. Naturally, all kinds of intermediate patterns of behavior are found between these two. Spinning into fibers can be considered a special case in the processing of plastics. In general, the processibility improves with increasing width of the molar mass distribution. 

In homopolymers, physical properties are to some extent dependent on molar mass. Class transition temperature and various mechanical properties will increase with molar mass and eventually reach some sort of plateau value. The same is of course tme for a (statistical) copolymer, but in the case of a copolymer there is an additional degree of freedom. The copolymer composition may have a significant influence on maaoscopic properties. If the homopolymers of the two monomers in a copolymer have different Tg values, the Tg value of a statistical copolymer will fie in between the two homopolymer values. More or less, the same holds tme for other properties, such as hardness and elasticity modulus. All of this is tme if the copolymer has a narrow CCD. If the CCD is broader or even bimodal, phase separation may occur. This will lead to a much more complex situation, where the properties are a function not just of the overall chemical composition, but also of the phase morphology as was indicated in Section 6.12.3.1. An additional complication can be introduced if the copolymer chains contain a gradient as explained in Section 6.12.7. 

To determine N it is assnmed that there are no free chain ends or loops in the network. Even if these exist, they do not contribute to its elastic energy. Assuming that all network chains are fixed at two crosslinks, the density of the polymer is p = NMc/Na, where iWc is the number average molar mass of the segments between crosslinks and Na is Avogadro s number. Then Eq. (2.43) can be rewritten as... 

Hence, the effect of the entanglements is two-fold, since both the elastic and the viscous properties are concerned. The observations all indicate the existence of a critical molar mass, introduced earlier as the critical molar mass at the entanglement limit, denoted by Me. Polymers with low molar masses, M < Me, exhibit no entanglement effects, but for M > Me they show up and become dominant. All properties that are founded on motions on length scales corresponding to a molar mass above Me are affected. This holds, in particular, for the viscosity and the dielectric normal mode since these include the whole polymer chain. On the other hand. Rouse dynamics is maintained within the sequences between the entanglement points, as has already been mentioned. 

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