Long model network

One of the most interesting types of model networks is the bimodal. These networks consist of very short chains intimately end-linked with the much longer chains that are representative of elastomeric materials.237,251,253,268-278 Such a network is shown in Figure 4.11,269 where the short chains are arbitrarily drawn thicker than the long ones. 

Figure 15.2 2H NMR relaxation function obtained in a PDMS model network in the relaxed state, showing the two components the fast relaxing component (the curve with alternatively long and short dashes) is pseudo-solid and belongs to elastic chains (which have restricted motions), the slowly relaxing, exponential component (dashed line), is liquid-like and belongs to dangling chains. The total signal (black points) is a superposition of both contributions, which gives the fraction of dangling chains...

The interactions between long overlapping network strands suppress fluctuations not only of the network junctions, but of all monomers in every network strand. In an attempt to capture this effect, Kloczkowski, Mark, and Erman proposed a diffused-constraints model. Instead of the... 

Undoubtedly, in the preparation of model networks from rather long polymeric precurson by the end-hnking reactions, the strands between the junction points wid maintain the conformation of coils. In accordance with classical ideas, the cods in the dry model network should acquire unperturbed dimensions, simdar to cods in a -solvent. However, on contacting a model polystyrene network with cyclohexane at room temperature, which is far below the -point for linear polystyrene (34.5°C), its volume increases by a factor of 3. Thus, the solvent breaks some polymer-polymer interactions, stimulates swelling of the network, and may result in an increase of chain dimensions. Hence, even at room temperature, the polystyrene chains prefer replacing the alien chain segments by cyclohexane molecides. 

The second restriction results from the time of calculation of these models. It is not at all exceptional, that one-dimensional models with many parameters and for long modelling-times will need hours or even days - despite of fast computers - for one run of the programme. Skilful handling of the model might possibly avoid absurd calculations, and computer networks may speed up the time of calculation, however these models will always be restricted due to their time of calculation. 

To have greater control of the chain topology, it was decided to use model networks. PDMS networks were chosen because of the extensive work by Mark and his coworkers on these systems. The-networks were prepared by crosslinking divinyl terminated PDMS chains with a tetra silane in the presence of a platinum catalyst. All networks were prepared in bulk. By choosing the appropriate prepolymers, it was possible to prepare unimodal and bimodal networks. For the bimodal networks, the short chains had M = 770 and the long chains had M = 22,500. In both cases M /M 1.8. 

In the case of such noncrystalUzable, unfilled elastomers, the mechanism for network rupture has been elucidated to a great extent by studies of model networks similar to those already described. For example, values of the modulus of bimodal networks formed by end-linking mixtures of very short and relatively long chains as illustrated in Fig. 6.4 were used to test the weakest-link theory [7] in which rupture was thought to be initiated by the shortest chains (because of their very limited extensibility). It was observed that increasing the number of very short chains did not significantly decrease the ultimate properties. The reason [85] is the very nonaffine... 

Figure 18(a) presents normalized proton DQ buildup functions of end-linked polydimethylsiloxane model networks prepared by mixing and subsequent cross-linking of very short and rather long chains. Such bimodal networks are known to consist of clusters of highly cross-linked regions embedded in a long-chain elastomer matrix. The buildup curves as well as the cross-link density distributions (i.e., the distributions of D s) derived from these show clear bimodal... 

When a model is based on a picture of an interconnected network of pores of finite size, the question arises whether it may be assumed that the composition of the gas in the pores can be represented adequately by a smooth function of position in the medium. This is always true in the dusty gas model, where the solid material is regarded as dispersed on a molecular scale in the gas, but Is by no means necessarily so when the pores are pictured more realistically, and may be long compared with gaseous mean free paths. To see this, consider a reactive catalyst pellet with Long non-branching pores. The composition at a point within a given pore is... 

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