Network theory 136, effects

Flory ( 9) has treated the interesting case of subsequent removal of the first stage cross-links without chain scission. Even after complete removal, i.e. =0, there is still a certain memory of the structure of the first network since the composite network strands were physically part of both networks. According to Flory s theory, the resulting network may be treated as if a certain fraction, 0, of the strands of the second network were effectively converted into strands of the first network, >ie. 

Figure 1. Effective first network modulus, Gle, after complete removal of first network cross-links plotted against second network modulus, Gi. Calculated from the composite network theory of Flory (19J for G, — 0.75 MPa.

At the same time as attributing human capacities to non-human objects, the accounts of actor-network theory strip human actors of important aspects of their agency. What counts as an actant is an effect generated by a network of heterogeneous, interacting materials (Law, 1992, p383, emphasis in original) and... 

The simplest way to consider the formation of ion pairs was discussed in Ref. [29]. It was shown that the concentration of ion pairs exponentially increases with the decrease of the dielectric constant of the solvent . This effect should be taken into account in the theory of collapse of polyelectrolyte networks, because effective values of in the collapsed state are usually much less than in the swollen state (e depends mainly on the water content which is much larger in swollen networks). This effect has not been taken into account in the theories developed so far. 

In general, it appears that the fraction of configurations in the various topological classes can be determined for models in which one of the elements is a fixed curve and the other is a random coil. The detailed calculations are intricate and difficult, however, and some simple generalizations are needed which could be used as a step towards building classification effects into the network theories. Classification for the case of two random coils and for self-entanglement are unsolved problems at the present time. 

A review by Bird and Wiest [6] gives a more complete list of existing viscoelastic models. The upper convective model and the White-Metzner model are very similar with the exception that the White-Metzner model incorporates the strain rate effects of the relaxation time and the viscosity. Both models provide a first order approximation to flows, in which shear rate dependence and memory effects are important. However, both models predict zero second normal stress coefficients. The Giesekus model is molecular-based, non-linear in nature and describes thepower law region for viscosity andboth normal stress coefficients. The Phan-Thien Tanner models are based on network theory and give non-linear stresses. Both the Giesekus and Phan-Thien Tanner models have been successfully used to model complex flows. 

It is rarely addressed in the literature that for molecular versions of circuit elements to be useful, there has to be the possibility to connect them together in a way where their electrical characteristics — measured individually between electrodes — would be preserved in the assembled circuit. However, it has been recently shown that such a downscaling of electrical circuits within classical network theory cannot be realized due to quantum effects, which introduce additional terms into Kirchhoff s laws and let the classical concept of circuit design collapse [16]. Circuit simulations on the basis of a topological scattering matrix approach have corroborated these results [34]. 

Flory PJ (1977) Theory of elasticity of polymer networks. The effect of local constraints on junctions. J Chem Phys 66(12) 5720-5729... 

Both these models find their basis in network theories. The stress, as a response to flow, is assiimed to find its origin in the existence of a temporary network of junctions that may be destroyed by both time and strain effects. Though the physics of time effects might be complex, it is supposed to be correctly described by a generalized Maxwell model. This enables the recovery of a representative discrete time spectrum which can be easily calculated from experiments in linear viscoelasticity. 

Gordon [30] has pointed out that even Simpson s treatment considerably underestimates the importance of the effect and has extended the network theory to include a formal allowance for cyclization. He predicted that the conversion at gelation for a polymerizing monomer which undergoes cyclization is given by... 

The resistance distance is based on electrical network theory and is defined as the effective electrical resistance between two vertices (nodes) when a battery is connected across them and each graph edge is considered as a resistor taking a value of 1 ohm. 

Jeyaseelan and Giacomin (1995) examine the use of large-amplitude oscillatory-shear (LAOS) rheology of filled polymer melts (HDPE filled with carbon black) and use transient-network theory (which separates filler and polymer entanglement effects) to describe the non-linear flow behaviour. 

Disagreement between classical network theory and experimental data occurs. The entanglement effect was thought to be responsible for the deviation. According to the classical network theory, the stress-strain relationship should follow Equation 2.139. The plot of the reduced force, ct /(A2 — 1/A), against the reciprocal strain, 1/A, should be constant, i.e., unity. But experiments show that the reduced force is a function of the extension ratio A. Figure 2.33 shows the typical experimental data of PDMS... 

Due to the dual filler and crosslinking nature of the hard domains in TPEs, the molecular deformation process is entirely different than the Gaussian network theories used in the description of conventional rubbers. Chain entanglements, which serve as effective crosslinks, play an important role in governing TPE behavior. The stress-strain results of most TPEs have been described by the empirical Mooney-Rivlin equation ... 

A network of effective cross-links behaves as a normal elastic network for t T. We discussed the classical theory of high elasticity in Chapter 7. The Young s modulus of a network, as you remember, is of the order of ksT multiplied by the density of cross-links. (As usual, ks is Boltzmann s constant, and T is the temperature.)... 

Chemical genomics represents a holistic approach since in principle the small molecules could interact with the whole proteome either through direct binding interaction or indirectly as a downstream effect through the signaling network. Since the cell response is the overall consequence of the interactions initiated by the small molecules, chemical genomics is closely associated with systems biology and network theory (Yildirim et al., 2007). 

Because of the special swelling and mutual dilution effects encountered in sequential IPN s, special equations were derived for their rubbery modulus and equilibrium swelling. The new equations were used to analyze polystyrene/polystyrene homo-IPN swelling and rubbery modulus data obtained by four different laboratories. In the fully swollen state, there was no evidence for IPN related physical crosslinks, but some data supported the concept of network I domination. In the bulk state, network I clearly dominates network II because of its greater continuity in space. The analysis of the data concerning the possible presence of added physical crosslinks in the bulk state yielded inconclusive results, but this latter is of special interest for modern network theories. 

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