Molecular network elasticity

From the foregoing it is clear that indentation anisotropy is a consequence of high molecular orientation within highly oriented fibrils and microfibrils coupled with a preferential local elastic recovery of these rigid structures. We wish to show next that the influence of crystal thickness on AMH is negligible. The latter quantity is independent on 1 and is only correlated to the number of tie molecules and inter-crystalline bridges of the oriented molecular network. 

In a recent series of papers, Kilian 9,50 52) proposed a new phenomenological approach to rubber elasticity and suggested a molecular network might be considered as a formelastic fluid the conformational abilities of which were adequately characterized by the model of a van der Waals conformational gas with weak interaction. The ideal network is treated as an ideal conformational gas. According to... 

According to the theory of rubber elasticity, the elastic response of molecular networks is characterized by two mechanisms. The first one is connected with the deformation of the network, and the free energy change is determined by the conformational changes of the elastically active network chains. In the early theories, the free energy change on deformation of polymeric networks has been completely identified with the change of conformational entropy of chains. The molecular structure of the chains... 

Smith, K. J., A. Ciferri, and J. J. Hermans Anisotropic elasticity of composite molecular networks formed from non-Gaussian chains. J. Polymer Sci., Pt. A, 2, 1025 (1964). 

In today s world, quality rubber products are defined not only by their strength, durability, and elasticity, but also by their recyclability. During the curing of rubber, an irreversible reaction takes place leading to the creation of a new three-dimensional molecular network where the plastic and viscous material is converted into an elastic one. Ultimately, it is the effectiveness of the curing process that determines the quality of that material. 

With regard to the mechanical reactirai of a polymer network to a stress applied, it is important that loose ends of macromolecules in a network structure are as shmrt as possible and/or their concentration is low. As these ends mostly extend out of the lamellas of crystallites then, while crossUnking is taking place in an amorphous phase and with the simultaneous presence of crystallites, a network with small loose ends should be formed. The crosslink junctions stabilize the natural molecular network (entanglements and crystallites), and every chain in the system is potentially elastically operative and can contribute to the stress in a tensile experiment [33]. The stabilization effect of chemical crosslinks on entanglements and crystallites may be the direct cause of observed differences in the determination of the amount of chemical crosslinks from mechanical property measurements and sol-gel analysis of the cross-linked polymer. 

The elastic properties of such a molecular network are treated later. We consider first another type of interaction between molecules. 

For random crosslinking rf may be assumed to be equal to r, the corresponding mean square end-to-end distance for unconnected chains of the same molecular length. Because A is inversely proportional to (Eq. (1.2)), the only molecular parameter that remains in Eq. (1.8) is the number N of elastically effective chains per unit volume. Thus, the elastic behavior of a molecular network under moderate deformations is predicted to depend only on the number of molecular chains and not on their flexibility, provided that they are long enough to obey Gaussian statistics. 

As normally prepared, molecular networks comprise chains of a wide distribution of molecular lengths. Numerically, small chain lengths tend to predominate. The effect of this diversity on the elastic behavior of networks, particularly under large deformations, is not known. A related problem concerns the elasticity of short chains. They are inevitably non-Gaussian in character and the analysis of their conformational statistics is likely to be difficult. Nevertheless, it seems necessary to carry out this analysis to be able to treat real networks in an appropriate way. 

Vulcanization is a process generally applied to rubbery or elastomeric materials. These materials forcibly retract to their approximately original shape after a rather large mechanically imposed deformation. Vulcanization can be defined as a process that increases the retractile force and reduces the amount of permanent deformation remaining after removal of the deforming force. Thus, vulcanization increases elasticity while it decreases plasticity. It is generally accomplished by the formation of a crosslinked molecular network (Figure 7.1). 

The width of the molecular network mesh sequence length) plays a central role in copolymerization (thermoplastics and elastomers/duroplastics) and determines material properties during elastic deformation. 

Composites are three dimensional working materials consisting of a continuous matrix with matrial of higher modulus of elasticity embedded in it. Examples include molecular networks, fibers, weaves or honeycombs. 

The spheres represent the positions of tie points of the molecular network the network is not shown. The elastic properties of the network are represented by Nnearly elastic springs which act along the lines which interconnect the tie points. The mactomolecules may be dismissed from further consideration. 

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