Polymers rubber matrix

Fillers are defined as additives in solid form that differ from the polymer/rubber matrix with respect to their composition and structure. A mineral filler is defined as a finely pulverized inert mineral or rock that is included in a manufactured product (e.g. paper, rubber, and plastics) to impart certain useful properties, such as hardness, smoothness, or strength etc (http //www.mindat.org/glossary/ mineral filler). Mineral particulate fillers are used in rubber/polymer composites to reduce the cost of the final product and to add some mineral property with the host (rubber/polymer) matrix, that is, to improve the properties of the matrix [19-22]. Common mineral fillers include asbestos, kaolin, talc, mica, wollastonite, and calcium carbonate etc (http //www.mmdat.org/glossary/mmeral filler) [19]. 

It is well known that the lower the AGM value, the better is the rubber-filler interaction. As for the Ch/MEK solvent combination x is zero, hence the A CN, cp2X term of (27) is zero for such a solvent combination. In all other solvent combinations, where x 0. the A l N r tp2X term of (27) is positive. Thus, AGM of the system for the Ch/MEK solvent combination is the least, and dispersion (if clay is in the rubber matrix) is also best in this solvent combination, giving rise to the highest polymer-filler interaction. 

It is observed from this figure that there are a lot of small dark lines preferably oriented in a north-south direction. Here, the organoclay is distributed evenly in the whole rubber matrix. Some small dark clusters are shown enlarged in Fig. 29b. These structures are formed due to the separation of the polar XNBR phase from the nonpolar S-SBR matrix. Furthermore, exfoliated layers of organoclay are visible in the interface between the two polymer phases, which obviously promotes a better compatibility between XNBR and S-SBR phases. Figure 29c displays the ... 

Furthermore, another advantage of nanofillers is not only to reinforce the rubber matrix but also to impart a number of other properties such as barrier properties, flammability resistance, electrical/electronic and membrane properties, and polymer blend compatibility. In spite of tremendous research activities in the field of polymer nanocomposites during the last two decades, elastomeric nanocomposites... 

Graftcopolymerization onto silicone rubber is rather difficult to achieve and is often accompanied by unwanted changes in physico-mechanical properties of the polymer caused by initiating agents. To overcome the problem, silica was introduced into the rubber matrix as an active filler capable of binding cationic compounds such a cationic compound being y-aminopropyltriethoxysilane. Schematically the pathway for heparinization of the latter may be presented as follows ... 

The necessity to label (deuterate) the systems under study may appear as a practical drawback. It often prevents working with real (industrially designed) materials. A way to circumvent this problem is to use labelled molecules as 2H NMR probes whose behaviour reflects that of the rubber matrix. These molecules may be solvent molecules or even polymer chains chemically identical to the rubber matrix itself. This approach is described in Section 15.4 and is illustrated by a few examples. 

So far the micro-mechanical origin of the Mullins effect is not totally understood [26, 36, 61]. Beside the action of the entropy elastic polymer network that is quite well understood on a molecular-statistical basis [24, 62], the impact of filler particles on stress-strain properties is of high importance. On the one hand the addition of hard filler particles leads to a stiffening of the rubber matrix that can be described by a hydrodynamic strain amplification factor [22, 63-65]. On the other, the constraints introduced into the system by filler-polymer bonds result in a decreased network entropy. Accordingly, the free energy that equals the negative entropy times the temperature increases linear with the effective number of network junctions [64-67]. A further effect is obtained from the formation of filler clusters or a... 

An important role in the present model is played by the strongly non-linear elastic response of the rubber matrix that transmits the stress between the filler clusters. We refer here to an extended tube model of rubber elasticity, which is based on the following fundamental assumptions. The network chains in a highly entangled polymer network are heavily restricted in their fluctuations due to packing effects. This restriction is described by virtual tubes around the network chains that hinder the fluctuation. When the network elongates, these tubes deform non-affinely with a deformation exponent v=l/2. The tube radius in spatial direction p of the main axis system depends on the deformation ratio as follows ... 

Figure 45a-c shows an adaptation of the developed model to uniaxial stress-strain data of a pre-conditioned S-SBR-sample filled with 40 phr N220. The fits are obtained for the third stretching cycles at various prestrains by referring to Eqs. (38), (44), and (47) with different but constant strain amplification factors X=Xmax for every pre-strain. For illustrating the fitting procedure, the adaptation is performed in three steps. Since the evaluation of the nominal stress contribution of the strained filler clusters by the integral in Eq. (47) requires the nominal stress aR>1 of the rubber matrix, this quantity is developed in the first step shown in Fig. 45a. It is obtained by demanding an intersection of the simulated curves according to Eqs. (38) and (44) with the measured ones at maximum strain of each strain cycle, where all fragile filler clusters are broken and hence the stress contribution of the strained filler clusters vanishes. The adapted polymer parameters are Gc=0.176 MPa and neITe= 100, independent of pre-strain. According to the considerations at the end of Sect. 5.2.2, the tube constraint modulus is kept fixed at the value Ge=0.2 MPa, which is determined by the plateau modulus Gn° 0.4 MPa [174, 175] of the uncross-linked S-SBR-melt (Ge=l/2GN°). The adapted amplification factors Xmax for the different pre-strains ( max=l> 1-5, 2, 2.5, 3) are listed in the insert of Fig. 45a.

The discussion in the Introduction led to the convincing assumption that the strain-dependent behavior of filled rubbers is due to the break-down of filler networks within the rubber matrix. This conviction will be enhanced in the following sections. However, in contrast to this mechanism, sometimes alternative models have been proposed. Gui et al. theorized that the strain amplitude effect was due to deformation, flow and alignment of the rubber molecules attached to the filler particle [41 ]. Another concept has been developed by Smith [42]. He has indicated that a shell of hard rubber (bound rubber) of definite thickness surrounds the filler and the non-linearity in dynamic mechanical behavior is related to the desorption and reabsorption of the hard absorbed shell around the carbon black. In a similar way, recently Maier and Goritz suggested a Langmuir-type polymer chain adsorption on the filler surface to explain the Payne-effect [43]. 

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