Effects of Cross-Link Functionality

The system for making model networks which is most versatile with regard to giving the widest choice for the functionality of the cross-links again involves PDMS chains. These chains, however, have vinyl groups at both ends and yield networks of the desired functionality by reaction with any of variety of silane molecules having j (relatively closely spaced) active hydrogen atoms For example, a hexafunctional network 

Relevant experimental studies have also been carried out on PDMS networks which have a bimodal distribution of chain lengths Such networks are discussed primarily in Parts V and VI, but it should be mentioned here that their values of the important ratio 2 C2/2 Cl show a dependence on f very similar to that shown by the unimodal PDMS networks This is readily evident upon comparison of Fig. 5 with Fig. 

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Junction Functionality. Some results bearing on the possible effect of cross-link functionality on the upturn in modulus are shown in Figure 5(20). The magnitude of the increase in [f ] does not show any obvious correlation with , which again suggests the predominant importance of the intramolecular characteristics of the short chains. At least from the evidence at hand (20), the functionality of the junction points seems relatively unimportant in this regard. 

Vilgis and Erman that the constraint models and slip-link models have much in common, (iv) elucidating the effects of cross-link functionality and degree of cross linking, (v) exploring a variety of elastomeric polymers, particularly those having very different values of the plateau modulus, and (vi) generalizing rubber-elasticity models to include viscoelastic effects as well. 

A more thorough investigation of the effects of cross-link functionality requires use of the more versatile chemical reaction illustrated in Fig. 1.18. Specifically, vinyl-terminated PDMS chains were end linked using a multifunctional silane [78]. This reaction was used to prepare PDMS model networks having functionalities ranging from three to 11, with a relatively unsuccessful attempt to achieve a functionality of 37. The modulus 2C increased with increasing functionality, as expected from the increase in constraints on the cross-links, and as predicted in Eqs. (1.17) and (1.18). Similarly, 2C2 and its value relative to 2C both decreased, for reasons that have already been mentioned. 

Fig. 5. The effect of cross-link functionality on the ratio of elasticity constants ICjZCt for bimodal PDMS networks The open circles, half-filed, and filed circles correspond to values of the mol % of short chains of 90.0, 75.2, and 60,7 and 60.1, respectively...

Model PDMS networks provide an ideal way to determine the effects of cross-link functionality 0 on ultimate properties, particularly in the most important case of the unusually tough bimodal networks. For bimodal networks consisting of mixtures of... 

Effects of Cross-Linking on the Viscoelastic Functions Problem Sets... 

In this curve, the symbol X represents the breaking points as a function of the EPDM domain size (dm)- The smaller EPDM domain size renders the higher tensile strength, which was first observed by Coran et al. (15). They as well as Ellul et al. (30) and Kojina (19) also showed the effect of cross-link densities of the EPDM dispersed phase on the tensile strength and tension set are shown in Fig. 8.18. The higher crosslink density in the EPDM phase was found to result in higher tensile strength and lower permanent set. 

Pandey, R. P. and Shahi, V. K. 2013. Functionalized sUica-chitosan hybrid membrane for dehydration of ethanol/water azeotrope Effect of cross-linking on structure and performance. J. Membr. Sci. 444 116-126. 

The general effect of cross-link density on the elastic modulus of an elastomer is indicated by Eq. 2.3. In their paper Landel and Fedors [189] consider the influence of a time-dependent cross-link density on the shape of the stress-strain curves of silicon, butyl, natural, and fluorinated rubbers. Introducing an additional shift-factor a related to the cross-link density, they were able to represent reduced breaking stresses as a function of reduced time in one common master curve. 

A potentially very useful apphcation of UTDR is to design membranes that offer improved resistance to compaction. Kelley et al. (2002) smdied the effect of cross-linking on the compaction resistance of cellulose-acetate membranes. Figure 33.6 shows the compressive strain as a function of time for pure water permeation through a cellulose-acetate membrane at 4.1 MHz that has been exposed for different periods of time at 23°C to a titanium-isopropoxide cross-hnking agent. Sufficient cross-linking time can reduce the compressive strain by 65% and nearly totally eliminate the elastic compaction. 

Figure 1. The polymer-solvent interaction parameter % in reduced form as a function of cross-link density for poly(isoprene) rubber cross-linked with dicumyl peroxide and showing the effect of cross-link density on x- (After reference 4).

The prime function of the saturated acid is to space out the double bonds and thus reduce the density of cross-linking. Phthalic anhydride is most commonly used for this purpose because it provides an inflexible link and maintains the rigidity in the cured resin. It has been used in increasing proportions during the past decade since its low price enables cheaper resins to be made. The most detrimental effect of this is to reduce the heat resistance of the laminates but this is frequently unimportant. It is usually produced by catalytic oxidation of o-xylene but sometimes naphthalene and is a crystalline solid melting at 131°C. 

The mole fraction of the monomer units that are cross-linked in the polymer is X,., and nt is Ihe number-average number of atoms in the polymer backbone between cross-links. The temperature should be expressed in absolute degrees in this equation. The constant K is predicted to be between 1.0 and 1.2 it is a function of the ratio of segmental mobilities of cross-linked to uncross-linked polymer units and the relative cohesive energy densities of cross-linked and uncross-linked polymer (88). The theoretical equation is probably fairly good, but accurate tests of it are difficult because of the uncertainty in making the correction for the copolymer effect and because of errors in determining nf. 

A unified approach to the glass transition, viscoelastic response and yield behavior of crosslinking systems is presented by extending our statistical mechanical theory of physical aging. We have (1) explained the transition of a WLF dependence to an Arrhenius temperature dependence of the relaxation time in the vicinity of Tg, (2) derived the empirical Nielson equation for Tg, and (3) determined the Chasset and Thirion exponent (m) as a function of cross-link density instead of as a constant reported by others. In addition, the effect of crosslinks on yield stress is analyzed and compared with other kinetic effects — physical aging and strain rate. 

Such reactions may be of considerable significance. This is because, if two pendant p-coumarate linkages (or related molecules) are attached to two adjacent polysaccharide chains, an effective means of cross-linking via photochemical coupling could be achieved. However, there is no evidence at present to indicate that these dimers function as either intermolecular or intramolecular cross-linking reagents. 

The main interest in azacyclobutanes is reserved for azetidin-2-ones ( 3-lactams), as this ring system is found in penicillin and cephalosporin antibiotics (Box 8.2). These compounds are effective because the (3-lactam ring is strained and readily reacts with the enzyme transpepidase, responsible for the development of the bacterial cell wall. The ring of the lactam is cleaved by this enzyme, which becomes 0-acylated in the process (Scheme 8.6). Once this occurs the enzyme s normal cross-linking function is lost and the cell wall is ruptured. 

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