Link molar mass

Expression of density (8) and values of elementary links molar masses substitute to Equation (7)... 

FIGURE 22.2 Flocculation behavior of the smaU-strain modulus at 160°C of uncross-linked solution-based styrene-butadiene rubber (S-SBR) composites of various molar mass with 50 phr N234, as indicated (left) and strain dependence of the annealed samples after 60 min (right). (From Kliippel, M. and Heinrich, G., Kautschuk, Gummi, Kunststoffe, 58, 217, 2005. With permission.)... 

As emphasized in Section 2-, many of the calculations in chemistry involve converting back and forth among the mass of a substance, the number of moles, and the number of atoms and/or molecules. These calculations are all centered on the mole. The connections shown in Figure apply to chemical compounds as well as to atoms of pure elements. Molar mass and Avogadro s number provide links between mass of a sample, the number of moles, and the number of molecules. 

Electricity is normally measured in units of charge, the coulomb (C), or as rate of electrical current flow, the ampere (A 1 A — 1 C/. ). The total amount of charge is the product of the current flow, symbolized by I, and the time for which this current flows Charge = It Just as molar mass provides the link between mass and moles, the Faraday constant provides the link between charge and moles. The number of moles of electrons transferred in a specific amount of time is the charge in coulombs divided by the charge per mole, F ... 

For polymerization reactors, the main concern is the characteristics of the product that relate to the mechanical properties. The distribution of molar masses in the polymer product, orientation of groups along the chain, cross-linking of the polymer chains, copolymerization with a mixture of monomers, and so on, are the main considerations. Ultimately, the main concern is the mechanical properties of the polymer product. 

The properties of a polymer network depend not only on the molar masses, functionalities, chain structures, and proportions of reactants used to prepare the network but also on the conditions (concentration and temperature) of preparation. In the Gaussian sense, the perfect network can never be obtained in practice, but, through random or condensation polymerisations(T) of polyfunctional monomers and prepolymers, networks with imperfections which are to some extent quantifiable can be prepared, and the importance of such imperfections on network properties can be ascertained. In this context, the use of well-characterised random polymerisations for network preparation may be contrasted with the more traditional method of cross-linking polymer chains. With the latter, uncertainties can exist with regard to the... 

As is clear from the earlier discussions of pre-gel intramolecular reaction, such reaction in principle always occurs in random polymerisations, although its amount may be reduced by using reactants of higher molar mass, lower functionalities, and stiffer chain structures. Thus, the use of end-linking reactions to produce model networks (for example(35) and references quoted... 

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). 

These observations require a detailed explanation. After several unsuccessful attempts a satisfying answer was finally found. A first step was made by the ingenious derivation of the molar mass distributions of randomly branched or randomly cross-linked materials [14]. The equation, that was later rederived by Elory [13], will be given in the next section. Here it suffices to point out that the width of the distribution, or the polydispersity index MJM , increases asymptotically with the weight average degree of polymerization... 

Fig. 16. Molar mass dependencies of the intrinsic viscosity [rf] for the same samples as shown in Fig. 15 (end-linked PS-stars [94] and randomly crosslinked polyesters [92,93,95]...

Fig. 22. KMHS relationships for the fractions of end-linked 3-arm star-branched polystyrene molecules and of linear polystyrene fractions. The data refer to three samples of different in the pregel state and one from the sol fraction of a gel. The curves for the branched macromolecules coincide within experimental error in the high molar mass region. The deviations at lowM result from a different amount of non-reacted end-functionalized stars. The exponents of the end-linked and linear PS chains are a =0.42 0.02 while that of linear chains is 0.70 0.01 [95,120,123,124]. Reprinted with permission from [95]. Copyright [1997] American Society...

Fig. 23. The intrinsic viscosity of several end-linked PS star molecules as a function ofM [95]. In the limit of low and high molar masses asymptotic power law behavior may be derived. That at low molar masses is widely controlled by the presence of non-reacted star molecules, that at high molar masses is expected from theory for randomly branched macromolecules. The exponents of the two asymptotic lines are a =0.49 0.08 for M <0.8x10 g/mol and a =0.18 0.05 for M >2.0xl0 g/mol. Reprinted with permission from [95]. Copyright [1997] American Society...

Fig. 26. Molar mass dependence of the g factor for three pregel and one postgel fraction of end linked PS stars. A good fit was obtained with the Zimm Stockmayer equation (Eq. 69) and an exponent in Eq. (70) of fi 0.63 [95] which agrees well with Kurata s estimation with b-0.6 [129]. Reprinted with permission from [129]. Copyright [1972] American Society...

It is shown that model, end-linked networks cannot be perfect networks. Simply from the mechanism of formation, post-gel intramolecular reaction must occur and some of this leads to the formation of inelastic loops. Data on the small-strain, shear moduli of trifunctional and tetrafunctional polyurethane networks from polyols of various molar masses, and the extents of reaction at gelation occurring during their formation are considered in more detail than hitherto. The networks, prepared in bulk and at various dilutions in solvent, show extents of reaction at gelation which indicate pre-gel intramolecular reaction and small-strain moduli which are lower than those expected for perfect network structures. From the systematic variations of moduli and gel points with dilution of preparation, it is deduced that the networks follow affine behaviour at small strains and that even in the limit of no pre-gel intramolecular reaction, the occurrence of post-gel intramolecular reaction means that network defects still occur. In addition, from the variation of defects with polyol molar mass it is demonstrated that defects will still persist in the limit of infinite molar mass. In this limit, theoretical arguments are used to define the minimal significant structures which must be considered for the definition of the properties and structures of real networks. 

Note 1 In most cases (e.g., in vinyl polymers, polyamides) degradation is accompanied by a decrease in molar mass. In some cases (e.g., in polymers with aromatic rings in the main chain), degradation means changes in chemical structure. It can also be accompanied by cross-linking. 

As already shown, conventional macromolecules (or polymers) consist of a minimum of a several hundred covalently linked atoms and have molar masses clearly above 10 g/mol. The degree of polymerization, P, and the molecular weight, M, are the most important characteristics of macromolecular substances because nearly all properties in solution and in bulk depend on them. The degree of polymerization indicates how many monomer units are linked to form the polymer chain. The molecular weight of a homopolymer is given by Eq. 1.1. 

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. 

Changes in molar mass of irradiated polymers were measured by viscosity, gel permeation chromatography, osmometry and light scattering. G (scission) and G (cross-link) values can be derived from gel contents if cross-linking predominates (3) and a GPC technique requiring only 50 mg of polymer, which could be in the form of powder, was developed for this purpose (4). 

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. 

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