Elasticity, of polymers

How does loading affect rubbery elasticity of polymer melts ... 

The elasticity of polymer coils is a well-known phenomenon and is involved in many important mechanical properties of bulk polymers. Stated briefly, it arises from a difference in conformational entropy between stretched and randomly jumbled chains. A statistical theory that counts the number of ways the two conformations can come about can be combined with the Boltzmann entropy equation (Equation (3.45)) to give an expression for the... 

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... 

Inoue T, Okamoto H, Osaki K (1991) Birefringence of amorphous polymers. 1 Dynamic measurements on polystyrene. Macromolecules 24 5670—5675 Isayev AI (1973) Generalised characterisation of relaxation properties and high elasticity of polymer systems. J Polym Sci A-2 116 2123—2133 Ito Y, Shishido S (1972) Critical molecular weight for onset of non-Newtonian flow and upper Newtonian viscosity of polydimethylsiloxane. J Polym Sci Polym Phys Ed 10 2239— 2248... 

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 ... 

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... 

Studies of the mechanical properties of polymer networks have yielded a great deal of important molecular information on the elasticity of polymer chains (1-3). For many systems, however, this approach is being supplemented increasingly by studies of the optical properties of the same... 

FIGURE 85 Elasticity of polymers made with Davison commercial silica grades, varying in structural coalescence and surface area. A loading of 0.4 Cr atoms nm 2 was deposited on each silica, followed by activation at 700 °C and testing at 105 °C. 

TABLE 33 Influence of Reaction Time (or Polymer Yield) on the Elasticity of Polymers Made with Metallocene Supported on Silica-Alumina, Showing that LCB Content Again Drops with Increasing Polymer Yield (Indicated Here by Increasing JC-a and Zero-Shear... 

The already low melt elasticity of polymer made with Cr/alumina was further diminished when sulfate was added. This response is shown in Table 49. The sulfate level on a Cr/alumina catalyst was varied from 0 to 3.0 mmol SO4 g-1 A12C>3, followed by activation at 600 °C. Polymer was then made with each catalyst, and the elastic properties of these polymers are listed in Table 49. H2 was used in all these polymerization runs, although, in the absence of sulfate, less H2 was needed to maintain a similarly high MW. The MW of these polymers was found to increase significantly as sulfate was added. This trend probably reflects a diminished sensitivity to H2 rather than an increase in the natural MW (made without H2). The addition of sulfate to the catalyst also greatly narrowed the MW distribution, as indicated by the Mw/Mn and MyJ Mw moment ratios. Both ratios dropped significantly when sulfate was added. 

It is apparent that a water environment is a limiting case. As this takes place, the ultimate compressive strength and the module of elasticity of polymer concrete samples decreased accordingly, up to 44,000 and 63,000 MPa. 

FIGURE 1.5 Modulus of elasticity of polymer concretes in a water environment. (From Yu. Borisov, Yu. Potapov, O. Figovsky, and D. Beilin, Water Resistance of the Polymer Concretes, /. Scientific Israel AdvancedTechnology 14, no. 3 (2012) 84-91. With permission.)... 

A particularly interesting molecular model for the nonlinear elasticity of polymer networks was proposed by Rubinstein and Panyukov [50], the slip-tube model. In this model the confining potential acting on the network chains depends on the deformation and is modeled by virtual chains attached to the network... 

Method of test for compressive strength and modulus of elasticity of polymer-modified mortar... 

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