Network vulcanizate

Figure 18.17 shows that the characteristics of the stress-strain curve depend mainly on the value of n the smaller the n value, the more rapid the upturn. Anyway, this non-Gaussian treatment indicates that if the rubber has the idealized molecular network strucmre in the system, the stress-strain relation will show the inverse S shape. However, the real mbber vulcanizate (SBR) that does not crystallize under extension at room temperature and other mbbers (NR, IR, and BR at high temperature) do not show the stress upturn at all, and as a result, their tensile strength and strain at break are all 2-3 MPa and 400%-500%. It means that the stress-strain relation of the real (noncrystallizing) rubber vulcanizate obeys the Gaussian rather than the non-Gaussian theory. 

D-TEM gave 3D images of nano-filler dispersion in NR, which clearly indicated aggregates and agglomerates of carbon black leading to a kind of network structure in NR vulcanizates. That is, filled rubbers may have double networks, one of rubber by covalent bonding and the other of nanofiller by physical interaction. The revealed 3D network structure was in conformity with many physical properties, e.g., percolation behavior of electron conductivity. 

The morphology of the agglomerates has been problematic, although some forms of network-like structures have been assumed on the basis of percolation behavior of conductivity and some mechanical properties, e.g., the Payne effect. These network stmctures are assumed to be determining the electrical and mechanical properties of the carbon-black-filled vulcanizates. In tire industries also, it plays an important role for the macroscopic properties of soft nano-composites, e.g., tear. 

Chain scission will have the effect of decreasing the primary chain length, which, of course, is a highly important factor in respect to the vulcanizate network structure. 

The distribution of the thi monomer in molecular chains or in the whole polymer should affect the perfection of the vulcanizate network, free chain ends or the uncross-linked parts in the polymer making no contribution to the tensile strength but acting as a plasticizer of like structure as the polymer. 

Vj g-EPDM and VOCI3-EPDM vulcanizate tensile strength Is not simply explainable by network quality resulting from difference In the third monomer distribution in the terpolymers. 

From a theoretical point of view, the equilibrium modulus very probably gives the best characterization of a cured rubber. This is due to the relationship between this macroscopic quantity and the molecular structure of the network. Therefore, the determination of the equilibrium modulus has been the subject of many investigations (e.g. 1-9). For just a few specific rubbers, the determination of the equilibrium modulus is relatively easy. The best example is provided by polydimethylsiloxane vulcanizates, which exhibit practically no prolonged relaxations (8, 9). However, the networks of most synthetic rubbers, including natural rubber, usually show very persistent relaxations which impede a close approach to the equilibrium condition (1-8). 

The influence of ZnCFO concentration (3,0 5,0 7,0 phr) on formation of properties complex of the unfilled rubber mixes and their vulcanizates on the basis of isoprene rubber of the following recipe, phr isoprene rubber - 100,0 sulfur - 1,0 di - (2-benzothiazolyl) -disulfide - 0,6 N, N -diphenylguanidine - 3,0 stearic acid - 1,0, was carried out in comparison with the known activator - zinc oxide (5,0 phr). The analysis of Rheometer data of sulfur vulcanization process of elastomeric compositions at 155°C (fig. 5) shows, that on crosslink density and cure rate, about what the constants of speed in the main period (k2) testify, they surpass the control composition with 5,0 phr of zinc oxide. Improvement of the complex of elastic - strong parameters of rubbers with ZnCFO as at normal test conditions, and after thermal air aging (tab. 1), probably, is caused by influence of the new activator on vulcanization network character. So, the percent part of polysulfide bonds (C-Sx-C) and amount of sulfur atoms appropriating to one crosslink (S atoms/crosslink) in vulcanizates with ZnCFO are decreased, the percent part of disulfide bonds (C-S2-C) is increased (fig. 62). 

Only when chemical bonds between neighboring molecules are introduced is a raw elastomer converted into a rubber vulcanizate, which is essentially a three-dimensional network structure (see Figure 5.3). The process is referred to as vulcanizahon or curing, or more accurately, as cross-linking. A cross-linked elastomer, or rubber vulcanizate, is capable of large reversible deformations within a broad temperature range and does not dissolve, but only swells in solvents and other liquids. 

A rubber vulcanizate, which is essentially a three-dimensional network structure... 

FIG U RE 5.4 A rubber vulcanizate, which is essentially a three-dimensional network structure (a = uncross-linked b = cross-linked.)... 

From the viewpoint of the mechanics of continua, the stress-strain relationship of a perfectly elastic material is fully described in terms of the strain energy density function W. In fact, this relationship is expressed as a linear combination erf the partial derivatives of W with respect to the three invariants of deformation tensor, /j, /2, and /3. It is the fundamental task for a phenomenologic study of elastic material to determine W as a function of these three independent variables either from molecular theory or by experiment. The present paper has reviewed approaches to this task from biaxial extension experiment and the related data. The results obtained so far demonstrate that the kinetic theory of polymer network does not describe actual behavior of rubber vulcanizates. In particular, contrary to the kinetic theory, the observed derivative bW/bI2 does not vanish. 

In this relation, 2C2 provides a correction for departure of the polymeric network from ideality, which results from chain entanglements and from the restricted extensibility of the elastomer strands. For filled vulcanizates, this equation can still be applied if it can be assumed that the major function of the dispersed phase is to increase the effective strain of the rubber matrix. In other words, because of the rigidity of the filler, the strain locally applied to the matrix may be larger than the measured overall strain. Various strain amplification functions have been proposed. Mullins and Tobin33), among others, suggested the use of the volume concentration factor of the Guth equation to estimate the effective strain U in the rubber matrix ... 

Mil. —, and A. G. Thomas Determination of degree of crosslinking in natural rubber vulcanizates. V. Effect of network flaws due to free chain ends. J. Polymer Sci. 43, 13 (1960). 

An analysis of network formation shows that terminal bifunctionality must be very close to the ideal of two functional groups per molecule to produce a high quality vulcanizate. The quality of a vulcanizate can be related to the required number average molecular weight, MR, of a polymer in an equivalent random network (6). MR values can be determined for an idealized network formed by coupling bi- or monofunctional prepolymers—i.e., no nonfunctional molecules—using the expression ... 

By fitting experimental data for different deformation modes to these functions, the three network parameters of unfilled polymer networks Gc, Ge, and ne/Te can be determined. The validity of the concept can be tested if the estimated fitting parameters for the different deformation modes are compared. A plausibility criterion for the proposed model is formulated by demanding that all deformation modes can be described by a single set of network parameters. The result of this plausibility test is depicted in Fig. 44, where stress-strain data of an unfilled NR-vulcanizate are shown for the three different deformation modes considered above. Obviously, the material parameters found from the fit to the uniaxial data provide a rather good prediction for the two other modes. The observed deviations are within the range of experimental errors. 

Another important point is the question whether static offsets have an influence on strain amplitude sweeps. Shearing data show that this seems not to be the case as detailed studied in [26] where shear rates do not exceed 100 %.However, different tests with low dynamic amplitudes and for different carbon black filled rubbers show pronounced effects of tensile or compressive pre-strain [ 14,28,29]. Unfortunately, no analysis of the presence of harmonics has been performed. The tests indicate that the storage (low dynamic amplitude) modulus E of all filled vulcanizates decreases with increasing static deformation up to a certain value of stretch ratio A, say A, above which E increases rapidly with further increase of A. The amount of filler in the sample has a marked effect on the rate of initial decrease and on the steady increase in E at higher strain. The initial decrease in E with progressive increase in static strain can be attributed to the disruption of the filler network, whereas the steady increase in E at higher extensions (A 1.2. .. 2.0 depending on temperature, frequency, dynamic strain amplitude) has been explained from the limited extensibility of the elastomer chain [30]. 

Swelling tests on the vulcanizates produced are an alternative option. The mean distance between two crosslinks can be applied to determine the concentration of crosslinks [9]. The reaction can only be studied once the gel point has been reached, since only then does a three-dimensional network form. 

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