Chemical crosslinking points

Much effort has been dedicated to the development of better molecularly based models, which have been discussed in an excellent recent review [50]. Since our block copolymer blends are not strictly speaking rubbers (PS spheres occupy some volume and have a high functionahty relative to chemical crosslink points), any quantitative comparison between our data and a molecularly based model should be taken with a bit of caution. We feel however that the insight provided by the molecularly based model is essential for the understanding of the mechanical properties of our systems. 

Figure 11.7 Fractal dimension (D) of a macromolecule section between chemical crosslinking points versus crosslinking density vf) for epoxy polymers based on epoxy oligomers and amino-containing curing agents. The D values were found from Equation (11.31) for a=A (1), A (2) and 0.25 nm (3).

Let us discuss in more detail the physical meaning of the fractal dimension (D) of a chain section between chemical crosslinking points (or between entanglement points). Snbstitution of L = Lj, R = Rj, and a = m Equation (11.31) gives the relationship [104,109] ... 

Relationship (11.45) actually holds (with a deviation of 20%) for epoxy polymers based on bisphenol A and cured by diamine (EP-1) or anhydride (EP-2) (Figure 11.9) [48]. This indicates that the fractality of the macromolecule section between chemical crosslinking points (entanglements) in a vitreous polymer is due to known mechanisms of the change in the statistical rigidity. 

Figure 11.9 Relationships between the conformational length (1, 3) and primitive path Lpj (2, 4) of the chain section between chemical crosslinking points and its fractal length Lf for EP-1 (1, 2) and EP-2 (3, 4).

Figure 11.10 Fractal dimension of the macromolecule section between chemical crosslinking point (D) versus scale of measurement a for EP-1 with v of 1 0.2 X 2 0.6 x lO m 3 1.7 x lO m ...

Figure 11.11 Fractal dimension of a section of macromolecule between chemical crosslinking points (D) versus cross-sectional area of the macromolecule S with of...

Below we consider practical aspects of the estimation of the fractal dimension D of a macromolecule section between chemical crosslinking points with allowance for these statements as well as for those considered in the preceding Sections. This approach differs fundamentally from that of the Cates [56] and Vilgis models [61, 62]. All the foregoing is valid not only for a network of chemical bonds but also for a network of macromolecular entanglements in linear polymers. 

Figure 11.12 Correlation between fractal dimensions of the structure df and the chain section between chemical crosslinking points D(df) dependence (a)and the D vf) dependence b) for EP-1 (1) and EP-2 (2) [109]. The straight line was drawn through the points D = df= 2.5 and D = 2.0, df = 3.0.

Thus, the fractal dimension of a section of the macromolecule between chemical crosslinking points in network polymers varies over limits close to those predicted for a fractal broken line, i.e., 1molecular mobility and is related to the fractal dimension of the cluster structure of epoxy polymers... 

With the assumption that = const and K = 1.0, = 0.85 was obtained with L = const and K > 1.0, the calculations gave % = (0.85) = 0.926. The calculation of the dimension D from Equation (11.55) gave 1.17. Thus, when the condition mentioned above is fulfilled, the section of a macromolecule between chemical crosslinking points can be represented as a fractal. Variation of K changes the crosslinking density and, hence, L. As a consequence, the chain ceases to be a self-similar fractal. Nevertheless, it can still be modelled by a non-homogeneous fractal with the same fragmentation step but with a variable D value, determined from relationship (11.39). The D values calculated in this way are listed in Table 11.6. 

Recall that the parameter D characterises the degree of deformability (mobility) of a macromolecule fragment between chemical crosslinking points. Indeed, an increase in the chain flexibility brings about an increase in C , i.e., an increase in D. It should be... 

Figure 11.14 Distance between chemical crosslinking points Rfj versus characteristic...

Thus, the density of chemical crosslinking points cannot serve as an index for the cormectivity of the macromolecular skeleton of network polymers. This makes it impossible to use to characterise the structure of network polymers in a computer simulation, which follows from the results presented previously. The d value, which provides determination of elastic properties, may serve as a suitable parameter. However, to estimate other properties, one more parameter is required, which would characterise the degree of thermodynamic nonequilibrium of the structures of vitreous polymers. This role can be played by dfOr the density of the cluster network of physical entanglements [48], or by the proportion of clusters (p [140] For instance, the necessity to take into account d, V i or [Pg.334]

Figure 4.8 shows a plot of double tan6 versus curing time during the multifrequency shear testing of a PES-modified bismaleimide resin. The second gd point -the chemical crosslinking point - was fitted by the gel time versus temperatures, as in Eq. (4.3), to calculate the activation energy. All had values of about 95 kj mol [71], which is typical for a bismaleimide resin. 

From the point of view of technology, it is convenient to classify polymers as thermosetting and thermoplastic. The former set by chemical crosslinks introduced during fabrication and hence do not change appreciably in their deformability with changes in temperature. Thermoplastics, on the other hand, soften and/or melt on heating and can therefore be altered in shape by heating... 

When a thermoplastic polyurethane elastomer is heated above the melting point of its hard blocks, the chains can flow and the polymer can be molded to a new shape. When the polymer cools, new hard blocks form, recreating the physical crosslinks. We take advantage of these properties to mold elastomeric items that do not need to be cured like conventional rubbers. Scrap moldings, sprues, etc. can be recycled directly back to the extruder, which increases the efficiency of this process. In contrast, chemically crosslinked elastomers, which are thermosetting polymers, cannot be reprocessed after they have been cured. 

The chemical gel point defines the instant of LST of chemically crosslinking polymers. Before the crosslinking polymer has reached its gel point it consists of a distribution of finite clusters. It is called a sol since it is soluble in good solvents. Beyond the gel point, it is called a gel . The gel is an infinitely large... 

The terminal groups of a dendrimer are large in number and can have functionalities capable of chemical reactions. If the terminal reactive terminal groups were near the periphery, they would be readily accessible for attachment to surfaces or to reagents. Block copolymers or networks with dendrimers as crosslink points would benefit from having them on the outside. 

An example for the polymer network characterization by the 13C CP MAS NMR is shown in Fig. 35. The chemical structure of the cured polystyrylpyridine resins (PSP), synthesized from terephthalic aldehyde and collidine (2,4,6-trimethylpyridine), is determined from CP-MAS spectra by comparison with the solution state spectra of the model compounds and supported by selective DD observations. The CH and CH2 of the crosslinking points, as deduced from the model BP2, give rise to a composite line at about 45 ppm the assignment of other signals is indicated in the figure 239). 

Gels usually consist of small amount of polymer as a network and a lai amount of solvent. Therefore when we discuss the dynamics erf polymer gels, we are tempted to deal with these Is from the stand point of the dynamics of polymer solutions. However, since the polymer chains in a gel are connected to each other via chemical bonds and/or some kinds of sj cific interaction, sudi as, hydrogen bonding or hydrophobic interaction, the gel has to be treated as a continuum. In addition, gels behave as an assembly of springs due to the entropy elasticity of polymer chains between the crosslink points. Therdbre, the dynamics of polymer gels is well described in terms of the theory of elasticity... 

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