Network junction functionality

The 6-function makes sure that if two segments and 2 meet on the huge network chain they can form a permanent constraint R( i) = R( 2)- Hence, this process will produce a network junction of functionality/n = 4, usually realized as sulfur bridges in technical elastomers like, for example, tire treads. 

The structure of a perfect network may be defined by two variables, the cycle rank and the average junction functionality (f>. Cycle rank is defined as the number of chains that must be cut to reduce the network to a tree. The three other parameters used often in defining a network are (i) the number of network chains (chains between junctions) v, (ii) the number of junctions p, and (iii) the molecular weight Mc of chains between two junctions. They may be obtained from and using the relations... 

Equation (40) shows that the small deformation shear modulus of an affine network increases indefinitely over the phantom network modulus as junction functionality approaches 2. 

Equilibrium Tensile Behavior of Model Silicone Networks of High Junction Functionality... 

Elastomeric networks with junction functionalities ranging from 4 to 70 were prepared by endlinking a,u)-divinyl poly(dimethylsiloxane) chains having number average molecular weights ranging from 8,800 to 55,300 with polyfunctional junctions provided by linear and branched poly(methylhydrogensiloxanes). 

As already described, the upper three portions of Figure 2 summarize the differences in the way the constraints are applied in the constrained-junction theory, constrained-chain theory, and the diffused-constraints theory, respectively [4], Additional comparisons between theory and experiment for a variety of elastomeric properties should be very helpful [20], Also, neutron-scattering measurements conducted on series of networks having different values of the junction functionality , which is the number of chains emanating from a junction (cross-link), would be extremely useful in suggesting how to position the constraints along a chain in refining such models, since should have a pronounced effect on the... 

Figure 10.8 The density of network junctions as a function of the volume fraction of paraffinic oil in EPDM/oil vulcanisates [74], The solid line represents the result of a linear regression analysis of the dependence (intercept = 453 5 mmol/kg slope = -6.2 0.0.3 mmol/kg the correlation coefficient = 0.996). Maximum torque in the rheometer curve for the vulcanisates is shown on the right ordinate...

Figure 10.9 A simplified graphic representation of EPDM chains at the carbon black surface [62], Monomer units with low mobility in the interface and mobile chain units outside of interface are represented by solid and open points, respectively. The rotational and translational mobilities of a few chain units next to the adsorption layer along the chain (dashed points) are hindered somewhat more than those of the chain units in the matrix. The chain fragments with low mobility in the interface provide adsorption network junctions for the rubber matrix. At the bottom of the figure, the spatial profile of the correlation time Tc of the chain motion is schematically represented as a function of the distance, r, from the carbon black surface. The xc is the average time of a single reorientation of a chain unit...

The apparent number of monomer units between different types of network junctions in bound rubber is shown as a function of the volume fraction of Aerosil in Fig. 11 [14]. 

Fig. 11. The apparent number of elementary chain units ( ) between network junctions (line) and contribution in it from chemical (a) and adsorption (b) Junctions, and topological hindrances near the filler surface (c) as a function of the volume fraction of Aerosil (300 m g" ) in bound PDMS rubber [14] the apparent number of elementary chain units between transient entanglements is shown by an arrow the absolute error for the determination of the n value is shown by the dashed area...

The transient net work model is an adaptation of the network theory of rubber elasticity. In concentrated polymer solutions and polymer melts, the network junctions are temporary and not permanent as in chemically crosslinked rubber, so that existing junctions can be destroyed to form new junctions. It can predict many of the linear viscoelastic phenomena and to predict shear-thinning behavior, the rates of creation and loss of segments can be considered to be functions of shear rate. 

The functionality of alkoxy groups at the silicon allows us to localize the probe in the polymer. Trifunctional compounds are located at the network junction of a crosslinked poly-dimethylsiloxane while bifunctional probe molecules are placed on the main chain during polymer formation. 

The concentration of effective network junctions or cross-link density is just the initial concentration of the appropriate Af. species, [Ay.]o, times the probability P (Xmji) summed over /i = m to the highest functionality... 

Figure 11.14. Empirical master curve for ultimate stress Gmax of a crosslinked elastomer (normalized by crosslink density and by absolute temperature) as a function of maximum draw ratio Amax-Vn", where n is the average number of Kuhn segments between network junctions.

Figure 11.15. Effects of input material parameters on stress-strain curves of elastomers under uniaxial tension, as calculated by the theory of rubber elasticity with finite chain extensibility. G denotes the shear modulus, while n denotes the average number of statistical chain segments (Kuhn segments) between elastically active network junctions, (a) Engineering stress a as a function of draw ratio X, as calculated by using Equation 11.41. (b) True stress (simply equal to aX for an elastomer) as a function of true strain [In (A,)].

In a real network of functionality four or less, the smallest loops apparently lead to elastically ineffective junction points. In addition, larger loops can also contribute to such defects. 

The density of cluster network junctions V,] is a function of temperature, which decreases as temperature increases. This network decay, is complete at T = T. The increasing of V i (the density of the entanglement of the cluster network) caused by decreasing of temperature, is slowed down drastically for T < T = - 223 °C. 

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