Chains random networks

Electron microscopy and X-ray diffraction experiments conducted on resilin-containing insect cuticle provided further support for resilin existing in the rubbery state as a crosslinked random network of protein chains. No fine structure was revealed by the electron microscopy experiments and zero crystallinity could be detected from the X-ray diffraction experiments. Furthermore, the diffraction... 

The Chompff-Duiser procedure of symmetry-preserved decoupling does not appear to be applicable in an easy way to random networks in three dimensions. Junctions which anchor strands of unequal length can be decoupled, but with a considerable increase in difficulty (234). On the other hand, Chompff and Prins (235) have introduced a degree of randomness in the decoupling procedure (the distribution of slow points within each uncoupled chain of the equivalent system was taken to be random) without altering the results appreciably. Random decoupling is much easier to implement, as shown below. 

The tenet of classical rubber theory has been that the chains are in random networks and the networks comprise a Gaussian distribution of end-to-end chain lengths. However, the mechanisms and molecular bases for the elasticity of proteins are more complex than that of natural rubber. In biological systems elastomeric proteins consist of domains with blocks of repeated sequences that imply the formation of regular stmctures and domains where covalent or noncovalent cross-linking occurs. Although characterised elastomeric proteins differ considerably in their precise amino acid sequences they all contain elastomeric domains comprised of repeated sequences. It has also been suggested that several of these proteins contain p-tums as a structural motif (Tatham and Shewry 2000). 

Another possibility is to measure the stress relaxation (chemorheology) [Refs. 69, 167, 612, 691]. The chain number of random network chain scissions per cm3 (Q) is given by... 

Problem 3.20 The structure of a three-dimensional random network may be described quantitatively by two quantities the density of crosslinking designated by the fraction e of the total structural units engaged in crosslinkages and the fraction 6f of the total units which occurs as terminal units or free chain ends (i.e., which are connected to the structure by only one bond). Alternative quantities, such as the number (mole) N of primary molecules and the number (mole) v of crosslinked units, in addition to M and Me, defined above, are also used to characterize a random network stmeture. Relate N and v to these other quantities. 

A form of addition polymerization is that of copolymerization in which two or more different monomers are linked together, either at random or alternating, to form one single copolymer chain or network ... 

For a random network of such chains under a general deformation characterized by extension ratios Xi,X2,X3 (deformed dimensionAindeformed dimension) in the three principal directions (Figure 1.7), Wis given by (Treloar, 1975)... 

Preparing glasses for glass-ionomer cements was guided by the Random Network concept of Zacheriasen [30]. This concept models glasses as random assemblies of SiO tetrahedra linked at their comers to form chains. The main mles of the Random Network concept are as follows ... 

Recently, Prigodin and Efetov have developed a theoretical model for interchain interaction at the M-I transition in a random network of coupled metallic chains [94]. In this model, the interchain disorder due to intrinsic defects and the randomness in the distribution of interchain contacts induce localisation. The M-I transition in such a system is determined by the critical concentration of interchain crosslinks, which in turn depends on the localisation lengths and interchain coupling. Moreover, a metallic state can exist in such a random network of coupled metallic chains only if the concentration of interfibril contacts is large enough to overcome the percolation threshold. 

We consider a typical covalent polymer network in the rubbery state at room conditions, consisting of V hnear chains whose ends are joined to multifunctional junctions of any functionality higher than 2 (i.e., more than two chains are attached at each junction). The chains that join pairs of junctions are long, very flexible, and of equal size, all of which can be easily related to real situations described in previous section (e.g., for chains of size equal to average size for many real systems of 400 bonds where, with high flexibility of random network, some differences in size... 

It is likely that in many red phosphorus samples polymer growth is terminated by occluded impurity atoms such as halogen, oxygen or hydroxyl. The existence of simple structure (4.26a) has not been substantiated. Amorphous samples may consist of random networks of atoms (4.26c), or randomly arranged P rings linked by short chains of P atoms. 

Falender, J. R. Yeh, G. S. Y. Mark, J. E., The Effect of Chain Length Distribution on Elastomeric Properties. 1. Comparisons Between Random Networks and Highly Nonrandom Networks. J. Am. Chem. Soc. 1979,101, 7353-7356. 

It is also probable that the matrix surface is more densely arranged in some localities due to the necessity for non-random packing. Thus, calculations of the mean centre-to-centre distance of the dextran chains revealed the impossibility of a purely random network in the most highly cross-linked gels, since in this case the mean inter-chain distance would be less than their Van der Waals diameter (in Sephadex G-25 and the more highly cross linked members G-15 and G-10). 

Theoretically the polymerisation (cross-linking) process should not result in a random network of dextran chains but in a heterogeneous gel with crosslink-dense, matrix-rich, water-poor domains intermingled with cross-link-sparse, matrix-poor, water-rich regions (2,20). 

Size of the chains between cross-links The randomly coiled chains exhibit self-similar behavior and the transition from the self-similar critical gel to the self-similar chain (between network junctions) is difficult to detect experimentally. 

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