Elasticity network polymer

The parameters which characterize the thermodynamic equilibrium of the gel, viz. the swelling degree, swelling pressure, as well as other characteristics of the gel like the elastic modulus, can be substantially changed due to changes in external conditions, i.e., temperature, composition of the solution, pressure and some other factors. The changes in the state of the gel which are visually observed as volume changes can be both continuous and discontinuous [96], In principle, the latter is a transition between the phases of different concentration of the network polymer one of which corresponds to the swollen gel and the other to the collapsed one. 

Elastin-mimetic protein polymers have been fabricated into elastic networks primarily via y-radiation-induced, radical crosslinking of the material in the coacervate state [10]. Although effective, this method cannot produce polymers gels of defined molecular architecture, i.e., specific crosslink position and density, due to the lack of chemoselectivity in radical reactions. In addition, the ionizing radiation employed in this technique can cause material damage, and the reproducibility of specimen preparations may vary between different batches of material. In contrast, the e-amino groups of the lysine residues in polymers based on Lys-25 can be chemically crosslinked under controllable conditions into synthetic protein networks (vide infra). Elastic networks based on Lys-25 should contain crosslinks at well-defined position and density, determined by the sequence of the repeat, in the limit of complete substitution of the amino groups. 

Rubber elasticity, which is a unique characteristic of polymers, is due to the presence of long chains existing in a temperature range between the Tg and the Tm. The requirements for rubbery elasticity are (1) a network polymer with low cross-link density, (2) flexible segments which can rotate freely in the polymer chain, and (3) no volume or internal energy change during reversible deformation. 

The structure and properties of a network polymer are determined by the relation between the inter- and intramolecular reactions of functional groups. The latter gives rise to ineffective cycles, and has been studied fairly well3-5 7°.71-8i-85.i°8 u2 Their occurrence in the system results in the gelation point being shifted towards higher conversions, higher sol fraction, fewer elastically active chains, and smaller equilibrium modulus of the network. 

The procedure used for testing the ideal Donnan theory is applicable to any model that decouples ionic effects from network elasticity and polymer/solvent interactions. Thus we require that nnet depend only on EWF and not C. While this assumption may seem natural, several models which include ionic effects do not make this assumption. For example, the state of ionization of a polymer chain in the gel and the ionic environment may affect the chain s persistence length, which in turn alters the network elasticity [26]. Similarly, a multivalent counterion can alter network elasticity by creating transient crosslinks. 

Flory.P.J. Elasticity of polymer networks cross-linked in state of strain. Trans. Faraday Soc. 56,722-743 (1960). 

Erman B, Flory PJ (1978) Theory of elasticity of polymer networks. II The effect of geometric constraints on junctions. J Chem Phys 68 5363—5369 Erukhimovich IYa, Irzhak VI, Rostiashvili VG (1976) On concentration dependence of swelling coefficient of weakly non-Gaussian macromolecules. Polym Sci USSR 18 1682-1689... 

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

It is possible to classify polymers by their structure as linear, branched, cross-linked, and network polymers. In some polymers, called homopolymers, merely one monomer (a) is used for the formation of the chains, while in others two or more diverse monomers (a,p,y,...) can be combined to get different structures forming copolymers of linear, branched, cross-linked, and network polymeric molecular structures. Besides, on the basis of their properties, polymers are categorized as thermoplastics, elastomers, and thermosets. Thermoplastics are the majority of the polymers in use. They are linear or branched polymers characterized by the fact that they soften or melt, reversibly, when heated. Elastomers are cross-linked polymers that are highly elastic, that is, they can be lengthened or compressed to a considerable extent reversibly. Finally, thermosets are network polymers that are normally rigid and when heated do not soften or melt reversibly. 

Heinrich, G., Straube, E. and Helmis, G. Ruber Elasticity of Polymer Networks Theories. Vol. 84, pp. 33-87. 

Therefore, the principal difficulty connected with the application of Eq. (12) is due to the incompleteness of the Gauss invariant. So, the use of the Gauss invariant for adequate classification of topologically different states in many-chain systems is very problematic. Nevertheless, that approach was used repeatedly for consideration of such physically important question as the high-elasticity of polymer networks with topological constraints [15]. Unfortunately,... 

The problem of determination of the partition function Z(k, N) for the iV-link chain having the fc-step primitive path was at first solved in Ref. [17] for the case a = c by application of rather complicated combinatorial methods. The generalization of the method proposed in Ref. [17] for the case c> a was performed in Refs. [19,23] by means of matrix methods which allow one to determine the value Z(k,N) numerically for the isotropic lattice of obstacles. The basic ideas of the paper [17] were used in Ref. [19] for investigation of the influence of topological effects in the problem of rubber elasticity of polymer networks. The dependence of the strain x on the relative deformation A for the uniaxial tension Ax = Xy = 1/Va, kz = A calculated in this paper is presented in Fig. 6 in Moon-ey-Rivlin coordinates (t/t0, A ), where r0 = vT/V0(k — 1/A2) represents the classical elasticity law [13]. (The direct Edwards approach to this problem was used in Ref. [26].) Within the framework of the theory proposed, the swelling properties of polymer networks were investigated in Refs. [19, 23] and the t(A)-dependence for the partially swollen gels was obtained [23]. In these papers, it was shown that the theory presented can be applied to a quantitative description of the experimental data. 

The polymer chain in a tube model and its modifications are widely used for investigation of the rubber elasticity of polymer networks with topological constraints. The detailed review on that problem one can find in the monograph... 

It is well known that the elasticity of polymer networks with constrained chains in the rubbery state is proportional to the number of elastically active chains. The statistical (topological) model of epoxy-aromatic amine networks (see Sect. 2) allows to calculate the number of elastically active chains1 and finally the equilibrium modulus of elasticity Eca,c for a network of given topological structure 9 10). The following Equation 9) was used for the calculations of E, c ... 

Kurkcuoglu O, Jernigan RL, Doruker P (2004) Mixed levels of coarse-graining of large proteins using elastic network model succeeds in extracting the slowest motions. Polymer 45 649-657... 

Gels usually consist of small amount of polymer as a network and a lai amount of solvent. Therefore when we discuss the dynamics erf polymer gels, we are tempted to deal with these Is from the stand point of the dynamics of polymer solutions. However, since the polymer chains in a gel are connected to each other via chemical bonds and/or some kinds of sj cific interaction, sudi as, hydrogen bonding or hydrophobic interaction, the gel has to be treated as a continuum. In addition, gels behave as an assembly of springs due to the entropy elasticity of polymer chains between the crosslink points. Therdbre, the dynamics of polymer gels is well described in terms of the theory of elasticity... 

Dusek K. (1984) Formation, structure and elastic properties polymer network. Preprints of the International Rubber Conference, Moscow... 

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