Networks defects

The structure of the network is closely related to the network formation process, of which the general picture is well-known In the first stages the molecular weight increases through branching and its weight average reaches an infinite value at the gel point. 

When the reaction proceeds beyond the gel point finite species (sol fraction) still coexist with the infinite network and are gradually attached to it as the crosslinking reaction proceeds. At sufficiently high degrees 

Even if completely homogeneous and disordered in the relaxed state, a real network differs from the ideal network, defined in Chapter I. Three types of network defects are commonly considered to be present in polymer networks unreacted functionalities, closed loops, and permanent chain entanglements. Within each group there are several possibilities dependent on the arrangement of chains the effect of defects on the elastic properties of the network is thus by no means simple, as has been stressed e.g. by Case (28). Several possible arrangements are shown in Fig. 1, where only nearest neighbour defect structures have been drawn. 

Branching and crosslinking processes can be treated as a combinatorial problem which is not too complicated when the functionalities are equally reactive and unreacted functionalities are considered as the only kind of defects. If loop formation (intra-molecular cyclization) is involved, the complexity increases considerably. The same holds if the monomers contain groups of unequal reactivity or if the reactivity is influenced by substitution effects. 

The statistical treatment of random stepwise crosslinking reactions (e.g. polycondensation) neglecting ring formation originates from Stock-mayer and Flory and is explained in Flory s book (55) on a number of examples. Using simple probability statistics, it is possible to calculate the molecular size distribution in the sol and in the gel, fractions of sol and gel, the crosslinking density and the fraction of free functionalities in 

It follows from the above discussion that a junction is elastically active if at least three paths leading away from it are independently attached to the network., A polymer chain segment, also called a strand, is elastically active if it is bound at each end by elastically active junctions. Loops in the network structure [Fig. 2.32(b)] do not contribute to the elasticity of the network as they have the two ends of a chain segment connected to the network at the same point. 

---

The ultraviolet cutoff or the absorption edge for pure vitreous siUca is 8.1 eV or 153 nm (171). This uv cutoff is influenced by the impurity level and stoichiometry of the material. Several impurities, such as the transition metals (Fe, Cu, Ti, etc) and alkaU metal ions (Na, Li, K), degrade the ultraviolet performance, shifting the uv cutoff to longer wavelengths. Ferric ions (Fe " ) cause absorption or result in network defects under reducing conditions. This contaminant at only a few ppm can be detected as an absorption at 230 nm and below (176). 

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. 

In the present paper, theoretical arguments and modulus measurements are used to deduce the significant gel structures which lead to inelastic loop formation and to quantify the network defects and reductions in modulus which may be expected, even in the limit of no pre-gel intramolecular reaction. In this limit all the existing theories and computer simulations of polymerisations including intramolecular reactlon(8,10,ll) predict that perfect networks are formed. 

Extrapolation of pj. g to the limit of zero pre-gel intramolecular reaction for given reaction systems shows that post-gel intramolecular reaction always results in network defects, with significant increases in Mg above Mg. Such post-gel intramolecular reaction is characterised as pg g. The variation of pg g with intramolecular-reaction parameters shows that even in the limit of infinite molar mass, i.e. no spatial correlation between reacting groups, inelastic loops will be formed. The formation may be considered as a law-of-mass-action effect, essentially the random reaction of functional groups. Intramolecular reaction under such conditions (p2 ) must be post-gel and may be treated using classical polymerisation theory. 

Note A network defect is caused by a loose end or a cyclic structure. 

In 1944, Flory (3) noted that the moduli of cross-linked butyl rubbers generally differ somewhat from values calculated from the crosslink density according to the kinetic theory of rubber elasticity. In many cases, the modulus also depends on the primary (uncross-linked) molecular weight distribution of the polymer. He attributed both observations to three kinds of network defects chain ends, loops, and chain entanglements. The latter are latent in the system prior to cross-linking and become permanent features of the network when cross-links are added. 

Chapter II describes the various kinds of network structures which may exist before or arise during its formation. Of these, the various network defects resulting from the crosslinking statistics, have received far more attention in the literature than the effects of inhomogeneous network formation and syneresis (separation in a gel + diluent phase). This is reflected in this review (Chapter II, section 2) although a special emphasis is also laid on the latter aspect (Chapter II, section 3 and 4). 

Other imperfections are developed in the process of crosslinking network defects (unreacted functionalities, intramolecular loops, chain entanglements), inhomogeneity in crosslink distribution, or heterogeneity of the network due to phase separation. These four types of network imperfections are interdependent and a sharp borderline between them does not exist. 

It is the opinion of the present authors that frequently too much emphasis is placed in network studies on the influence of network defects (Chapter II, Section 2), while in reality pre-existing order, inhomogeneous crosslinking, composite network formation, or microsyneresis may play an important role in the mechanical behaviour, as well as in most other network properties. Examples of this will be given in Chapter IV. 

In this Chapter we will consider the elasticity and swelling of networks which deviate from our definition of ideal networks only because of a certain number of network defects (see Chapter II, Section 2). We will designate by v the number of elastically effective network chains, which in an ideal network equals the number of chains because of the absence of defects. 

Without any proof it has often been assumed that C equals C so that an estimate of rcl could be obtained which could be compared with the number of chemically crosslinked units, vc. Any differences were subsequently interpreted in terms of various network defects, as e.g. entanglements, closed loops, or unreacted functionalities. 

The network parameters that can affect the mechanical response of a crosslinked epoxy are the network defects and topography. 

Network defects in the form of unreacted groups serve as sites for crack initiation and propagation. When such defects are non-randomly distributed within the network a nodular morphology will be observed upon fracture or chemical etching of the bulk network. 

Impure starting materials will also cause network defects. We have found epoxies prepared from purified monomers with Tg s > 130 °C can exhibit excellent mechanical properties at 23 °C with tensile strengths of 140 MPa and ultimate elongations of 5-8% 5>. 

Macromolecular 10-100 nm Network chains/strands, crosslinks network defects (dangling chains) Macro- molecular science Rubber elasticity, solvent swelling... 

Figure 10.3 Mean molecular mass between chemical crosslinks and trapped chain entanglements Mc+e in a cured mixture of a poly(ethylene glycol) diacrylate (PEGDA) and 2-ethylhexyl acrylate (EHA) as a function of the EHA content [52]. Mc+e values were determined from (1/T2s)max and the plateau modulus (see Figure 10.2). A substantial difference in Mc+e value, as determined by these two methods at low crosslink density, is caused by the effect of network defects which decrease volume average network density determined by DMA (see Section 10.3). The molecular mass of PEGDA (Mn = 700 g/mol) is indicated by an arrow. The molecular mass of network chains in cured PEGDA is about three times smaller than that of the initial monomer. The molecular origin of this difference is discussed in Section 10.3...

A significant difference between the large spatial-scale mobility of network chains and that of network defects allows us to determine the degree of network heterogeneity. The most reliable data are obtained for swollen samples, because an increasing solvent content results in the disentanglement of network defects from network chains [52, 61, 62], The molecular mobility of network chains is consequently decoupled from that of network defects, resulting in a major distinction in the relaxation behaviour. 

---