Filler-chain links

a distinction is made regarding the permanence of filler chain bonds. This subject has evolved throughout this chapter and it is an important factor in understanding the mechanism of reinforcement. 

This equation gives a quantitative description of the storage modulus of a filled material  

Equation 7.20 shows that the changes in mechanical properties are first affected by temperature and then by the network of unstable links. Only after the unstable links are consumed stable links take the impact of changes occurring in the material. A similar logic can be applied to show that filler concentration also plays an essential role, considering that with small addition of filler most chains will form weak bonds because of very high competition for free surfaces on filler particles and the effect of reinforcement will be diminished. This is expressed by a simple equation  

When filler concentration is low, g 1. Each filler is bound only once. Carbon black filled rubber does not form gel if only small amounts of carbon black are used. The molecular weight of polymer in the matrix affects the fraction of bound polymer according to the equation  

As molecular weight increases, (])b increases as does the probability of multiple connections. 

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However, when a fumed silica is added to the RTV silicone, it provides excellent tensile strength and elongation compared to the unfilled material with the same formulations. The chain-linked spherical SIO2 particles which interact with themselves (filler-filler interaction) and/or the silicone-resin... 

Commercially produced elastic materials have a number of additives. Fillers, such as carbon black, increase tensile strength and elasticity by forming weak cross links between chains. This also makes a material stilfer and increases toughness. Plasticizers may be added to soften the material. Determining the effect of additives is generally done experimentally, although mesoscale methods have the potential to simulate this. 

The Hquid polymer is then compounded with metal oxides or peroxides, as weU as fillers (carbon black) and can undergo cold vulcanization, ie, chain extension and cross-linking iato a soHd matrix. It is largely used as a sealant and gasket material for wiadows, automobile wiadshields, etc. 

S-B-S Triblocks are block copolymers consisting of a block of butadiene units flanked by blocks of styrene. Below the T, of polystyrene blocks from different chains congregate into domains which act both as cross-links and reinforcing fillers. The jDolymers will dissolve in hydrocarbon solvents. Hydrogenated S-B-S materials have better resistance to ageing. 

So far, we have not introduced a specific model of the polymer network chains. This problem can be rigorously solved for cross-linked polymer networks consisting of phantom chains [13], or even in the more general case of filled networks where the chains interact, additionally, with spherical hard filler particles [15]. 

Here, b denotes the Kuhn s statistical segment length. The network is represented by a huge chain internally cross-linked at cross-linking points where it touches and at the surfaces of Mf filler particles. The point-like local cross-hnk constraints are easy to handle and can be represented by the term... 

Equations 22.3-22.14 represent the simplest formulation of filled phantom polymer networks. Clearly, specific features of the fractal filler structures of carbon black, etc., are totally neglected. However, the model uses chain variables R(i) directly. It assumes the chains are Gaussian the cross-links and filler particles are placed in position randomly and instantaneously and are thereafter permanent. Additionally, constraints arising from entanglements and packing effects can be introduced using the mean field approach of harmonic tube constraints [15]. 

As already mentioned, a network can be obtained by linking polymer chains together, and this linkage may be either physical or chemical. Physical linking can be obtained by (i) absorption of chains onto the surface of finely divided particulate fillers, (ii) formation of small crystallites, (iii) coalescence of ionic groups, or (iv) coalescence of glassy sequences in block copolymers. 

To illustrate how the effect of the adsorption on the modulus of the filled gel may be modelled we consider the interaction of the same HEUR polymer as described above but in this case filled with poly(ethylmetha-crylate) latex particles. In this case the particle surface is not so hydrophobic but adsorption of the poly (ethylene oxide) backbone is possible. Note that if a terminal hydrophobe of a chain is detached from a micellar cluster and is adsorbed onto the surface, there is no net change in the number of network links and hence the only change in modulus would be due to the volume fraction of the filler. It is only if the backbone is adsorbed that an increase in the number density of network links is produced. As the particles are relatively large compared to the chain dimensions, each adsorption site leads to one additional link. The situation is shown schematically in Figure 2.13. If the number density of additional network links is JVL, we may now write the relative modulus Gr — G/Gf as... 

Diffusion and permeability are inversely related to the density, degree of crystallinity, orientation, filler concentration, and cross-link density of a polymeric film. Generally, the presence of smaller molecules, such as plasticizers, increases the rate of diffusion in polymers since they are more mobile and can create holes or vacancies within the polymer. The rate of diffusion or permeability is fairly independent of polymer chain length just as long as the polymer has a moderately high chain length. 

The cell wall of the yeast Saccharomyces is rich in mannoproteins that contain 50-90% mannose.264 The 250-residue mannan chains consist of an a-1,6-linked backbone with mono-, di-, and tri-mannosyl branches. These are attached to the same core structure as that of mammalian oligosaccharides. All of the core structures are formed in a similar way.258 265 The mannoproteins may serve as a "filler" to occupy spaces in a cell wall constructed from P-1,3- and P-l,6-linked gly-cans and chitin. All of the four components, including the mannoproteins, are covalently linked together.266 As was emphasized in Chapter 4 (pp. 186-188)... 

The desirability of segregation in block copolymers can be demonstrated by considering the behaviour of SBS, which is one of the oldest types. It has about the same chain composition as SBR, but, rather than SBR, it shows two glass-rubber transitions, namely that of polybutadiene and that of polystyrene. Between these two temperatures it behaves as a rubber, in which the PS domains act as cross-links it is, therefore, a self-vulcanizing rubber (see also Figure 3.8 see Qu. 9.14). Moreover, the hard domains play the role of a reinforcing filler. 

From a fit of Equation (10) to spatially resolved relaxation curves, images of the parameters A, B, T2, q M2 have been obtained [3- - 32]. Here A/(A + B) can be interpreted as the concentration of cross-links and B/(A + B) as the concentration of dangling chains. In addition to A/(A + B) also q M2 is related to the cross-link density in this model. In practice also T2 has been found to depend on cross-link density and subsequently strain, an effect which has been exploited in calibration of the image in Figure 7.6. Interestingly, carbon-black as an active filler has little effect on the relaxation times, but silicate filler has. Consequently the chemical cross-link density of carbon-black filled elastomers can be determined by NMR. The apparent insensitivity of NMR to the interaction of the network chains with carbon black filler particles is explained with paramagnetic impurities of carbon black, which lead to rapid relaxation of the NMR signal in the vicinity of the filler particles. 

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