Elastomers volume fraction

Unlike the case of toughening binary blends, where the primary variables controlling the fracture resistance are elastomer volume fraction and the size and distribution of elastomer inclusions (26-28), the toughness of composites with EILs is extremely sensitive to the thickness and elastic moduli of the interphase (6,7,31). A lower limit of strain energy release rate, Gc (or fracture toughness. 

Ep/E = modulus of filler/modulus of unfilled elastomer

volume fraction of filler... 

Therefore, at room temperature Fluoro-PSB-II a thermoplastic elastomer with a soft polymer phase (fluorinated block) and a hard phase (PS-block), similar to the parental polystyrene-6-polybutadiene block copolymer. Depending on the relative volume fraction of both components and the continuity of the phases, the resulting bulk material is rubbery or a high-impact solid. 

Predictions of the mechanical response of filled elastomers are further aggravated by the phenomenon of strain dilatation. As soon as dilatation commences, the tensile stress lag behind elongation, the degree of dilatation for a given composite being roughly a measure for the deviation from the expected mechanical response. Dilatation increases with particle size and volume fraction of filler—it decreases somewhat if the filler is bonded to the matrix. Farris (16,17) showed that dilatation can account well for the mechanical behavior of solid propellants and his equation ... 

The description of the physical properties of fluoroelastomers is necessarily less precise than that of fluoroplastics because of the major effect of adding curatives and fillers to achieve useful cross-linked materials of a given hardness and specific mechanical properties Generally, two parameters are varied increasing cross-link density increases modulus and decreases elongation, and raising filler levels increases hardness and decreases solvent swell because of the decreased volume fraction of the elastomer In addition to these two major vanables, the major determinants of vulcanizate behavior are the chemical and thermal stabilities of its cross-links The selection of elastomer, of course, places limits on the overall resistance to fluids and chemicals and on its service temperature range... 

The degree of toughness is determined by the crosslink density of the matrix, the elastomer particle size and size distribution, the volume fraction of the elastomeric phase, and the degree of adhesion between the epoxy matrix and the particle. The formulating procedure was found to have as strong an effect on the fracture toughness as the materials themselves.16... 

We can now go back to the evaluation of the adhesion energy between the grafted surface and the elastomer. In all what follows we assume that the elastomer was cross-linked in the dry state. As long as olocal volume fraction of grafted chains, , is much smaller than unity. More precisely, Nc/N for o Nc/N312 (see [105]) and we expect Eq.(8) to hold. For o>Nc /Nil2, Eq. (8) should be replaced by [ 107]... 

Kevlar pulp can be used in thermosets, thermoplastics and elastomers. Injection-moldable pellets consisting of short Kevlar fibers in a thermoplastic resin can be made These can be blended with unreinforced resins to obtain a composite with the desired volume fraction of reinforcement. 

The rabber modulus increases with an increasing volume fraction of Aerosil. The modulus increase can be caused by the elastomer-filler and filler-filler interactions and by an increase of effective filler content. A very sharp peak for the tanZ is observed at 163 K for an unfilled crosslinked sample. This maximum corresponds to the glass transition of the rubber. Furthermore, it is observed that the Tg of the rubber does not change in the presence of filler. However, the second maximum of to 5 can be seen in the vicinity of 200 K for filled samples. The intensity of this maximum becomes more pronounced with increasing Aerosil content. This observation is in agreement with the results of the h and Ty relaxation study, as demonstrated in Fig. 4a and 6, respectively. Therefore, it seems reasonable to assign the maximum for at 200 K to the motion of adsorbed chain units. This maximum is observed at a lower temperature than the H and T, minimum for the adsorbed chain units (at about 280 K) due to difference in frequency of these methods 1.6 Hz and 46-90 MHz, respectively. 

Three factors associated with particle packing are common use critical volume fraction (or loading), effective volume fraction, and critical pigment volume concentration. The effective volume fraction of a filler includes the filler and the elastomer immobilized within the aggregates. This is given by the equation ... 

For most elastomers the ultimate tensile and elongation values were found to be quantitatively related by simple linear equations to the volume fraction of the rubber swelled In mixtures of gasoline and ethanol or MTBE. They were also found to be related to each other by simple logarithmic relatlonshlps. 

Davies model (see Equation 20.3 [20,21]) can be used for materials with co-continuous interpenetrating phases (as in interpenetrating networks), such as certain types of reaction injection molded elastomers [22], at all volume fractions. Equation 11.7 can then be used if (as is usually the case) one is interested in Young s modulus E rather than the shear modulus G. 

If the elastomer is swollen to below the equilibrium swelling so that no deswelling will occur upon deformation, the statistical expression for the shear modulus [equation (6-59)] can be readily modified. We define Vr as the ratio of the unswollen volume to the swollen one, which is identical to the volume fraction of polymer in the mixture. The number of network chains per unit volume then becomes NQVr and the mean square end-to-end distance of the network chain is now r02 / Vr2/3. Equation (6-59) then reads... 

Figure 6-8. Effect of swelling on the Mooney-Rivlin plot of natural rubber where Vr is the volume fraction of elastomer in the swollen sample, (swelling liquid, n-decane). [After Mullins, J. Appl. Polym. Sci., 2, 257 (1959), by the permission of John Wiley Sons, Inc.]...

In these equations, fa is the volume fraction of filler, and subscripts / and 0 refer to the filled and unfilled elastomers respectively. Note that equations (6-95) and (6-96) introduce a parameter m that accounts for the maximum packing fraction of the filler. For randomly placed spherical filler particles, m = 0.637. 

In many cases, toughening of a brittle polymer can be achieved by introduction of stiffness heterogeneity, viz. incorporation of an elastomer, immiscible polymer, sohd particles, gas bubbles (i.e., foaming or micro-foaming), etc. However, the size and concentration of these heterogeneities should be optimized. For most thermoplastic s the optimum diameter of the dispersed elastomeric particle is d < 3 jj.m and its volume fraction ... 

Commercially important elastomeric thermoplastic alloys are dynamically vulcanized blends of polypropylene with high volume fractions of EPDM, polybutadiene rubber, nitrile rubber, and butyl rubber (Santoprene , Vyram , Geolast and Trefsin ) all currently sold by Advanced Elastomer Systems, a joint venture of Monsanto and Exxon. Another recent member of the commercial dynamically cured elastomeric thermoplastic alloys is the blend of PVC and a crosslinked ethylene copolymer (Alcryn , DuPont). The current consumption of all the elastomeric thermoplastic alloys in the USA is over 23 kton/y, with the EPDM/PP blend (Santoprene ) assuming about 90% of the market share. 

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