Density of cross-linking

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. 

Many mechanical properties are dependent on the density of cross-links and on the rigidity of the molecules between cross-links. It has already been shown that cross-link intensity may be controlled by varying the ratio of unsaturated to saturated acids whereas rigidity is to a large extent determined by the structure of the saturated acid employed. 

Degree, or density, of cross-linking (or branching), i.e., fraction of units cross-linked in the entire system (Chaps. IX and XI). 

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. 

The degree of cross-linking can be expressed in terms of cross-links per gram or per unit volume. If C is the moles of cross-links per unit volume, n the number of network chains per unit volume, d the density of cross-linked polymer, and Me the number-average molecular weight of the polymer segments between cross-links, then... 

The number of possible conformations n for each mobile molecular segment is reciprocal to the density of cross-links AT (defined for 100 C-C groups in the polymer chain). 

With the advent of the structosets, relationship between the density of cross linking, the average molecular weight between cross links, and the character of the segments becomes more controllable so the following classification is proposed (Figure 2). 

They have been able to show that these two effects may be separated and that the change in the glass transition temperature is equal to a constant times the density of cross linking p, at moderate degrees of cross linking. 

The density of cross-linking can be adjusted by co-condensation of multialkoxy-silane monomers, such as [Me(EtO)2(CH2)2SiMe2]0 or [Me(Et0)2(CH2)2SiMc20]4. DSC and TGA analyses did not show much difference in the amount of unreacted sSiOH or reduction of thermal resistance. 

Effect of Through Pores on Selectivity of Plasma-Treated Polymer Membranes Applied for Gas Separation. Using relation (9-109), find ouf the maximum value of selectivity of the plasma-treated polymer membranes considered as a function of the factor y, which characterizes the specific energy input and density of cross-links. 

The principal feature that distinguishes thermosets and conventional elastomers from thermoplastics is the presence of a cross-linked network structure. As we have seen from the above discussion, in the case of elastomers the network structure may be formed by a limited number of covalent bonds (cross-linked rubbers) or may be due to physical links resulting in a domain structure (thermoplastic elastomers). For elastomers, the presence of these cross-links prevents gross mobility of molecules, but local molecular mobility is still possible. Thermosets, on the other hand, have a network structure formed exclusively by covalent bonds. Thermosets have a high density of cross-links and are consequently infusible, insoluble, thermally stable, and dimensionally stable under load. The major commercial thermosets include epoxies, polyesters, and polymers based on formaldehyde. Formaldehyde-based resins, which are the most widely used thermosets, consist essentially of two classes of thermosets. These are the condensation products of formaldehyde with phenol (or resorcinol) (phenoplasts or phenolic resins) or with urea or melamine (aminoplastics or amino resins). 

Because of their more compact structure, cycloaliphatic resins produce greater density of cross-links in the cured products than bisphenol A-based glycidyl resins. This generally leads to higher heat-distortion temperatures and to increased brittleness. 

A network of effective cross-links behaves as a normal elastic network for t T. We discussed the classical theory of high elasticity in Chapter 7. The Young s modulus of a network, as you remember, is of the order of ksT multiplied by the density of cross-links. (As usual, ks is Boltzmann s constant, and T is the temperature.)... 

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