Rubbers retracting force

Anthony, Caston, and Guth obtained considerably better agreement between the experimental stress-strain curve for natural rubber similarly vulcanized and the theoretical equation over the range a = 1 to 4. KinelP found that the retractive force for vulcanized poly-chloroprene increased linearly with a — l/a up to a = 3.5. 

Equilibrium retractive force, referred to unit undeformed cross section, for elongated rubber (Chap. XI). Same quantity specifically for the elongation a. 

The change of chemical potential due to the elastic retractive forces of the polymer chains can be determined from the theory of rubber elasticity (Flory, 1953 Treloar, 1958). Upon equaling these two contributions an expression for determining the molecular weight between two adjacent crosslinks of a neutral hydrogel prepared in the absence of... 

From the dynamic mechanical investigations we have derived a discontinuous jump of G and G" at the phase transformation isotropic to l.c. Additional information about the mechanical properties of the elastomers can be obtained by measurements of the retractive force of a strained sample. In Fig. 40 the retractive force divided by the cross-sectional area of the unstrained sample at the corresponding temperature, a° is measured at constant length of the sample as function of temperature. In the upper temperature range, T > T0 (Tc is indicated by the dashed line), the typical behavior of rubbers is observed, where the (nominal) stress depends linearly on temperature. Because of the small elongation of the sample, however, a decrease of ct° with increasing temperature is observed for X < 1.1. This indicates that the thermal expansion of the material predominates the retractive force due to entropy elasticity. Fork = 1.1 the nominal stress o° is independent on T, which is the so-called thermoelastic inversion point. In contrast to this normal behavior of the l.c. elastomer... 

Unvulcanized rubber consists of a large number of flexible long molecules with a structure that permits free rotation about single bonds in the primary chain. On deformation the molecules are straightened, with a decrease in entropy. This results in a retractive force on the ends of the polymer molecules. The molecular structure of the flexible rubber molecules makes it relatively easy for them to take up statistieally random conformations under thermal motion. This property is a result of the weak intermolecular attractive forces in elastomers and distinguishes them chemically from other polymers which are more suitable for use as plastics or fibers. 

The osmotic pressure of the polystyrene solution is balanced by the elastic retractive forces of the more or less densely crosslinked rubber lamellae osmotic pressures in the swollen rubber particles are rather high because of the high positive virial coefficient of polystyrene in toluene (A2 = 5 X 10"4 mole cm3 g"2) (14). For SI = 10 (corresponding to c = 0.1 g X cm3) and M = 5 X 104, one... 

Structurally, most polymers that are rubbers near room temperature are composed of long linear chains with a) freely rotating links and b) weak interactions between chains. This combination results in flexible chains that can readily extend in response to an applied stress. Crosslinks introduced in the rubber during processing generate retractive forces required for elasticity. As shown in Chapter 2, Section 7, the length of the polymer chain limits the total extension. The molecular weight of... 

The Flory model also leads to a prediction of the effect of crystallization on the retractive force (oq) exerted by a stretched rubber... 

Rubber networks will imbibe solvent liquids until the elastic retractive force of the network crosslinks counterbalances the swelling force exerted by the liquid. If no crosslinks are present, the rubber dissolves completely on immersion in an excess of solvent. The degree of swelling is thus a function of crosslink density. As crosslink density increases, the degree of swelling decreases and vice versa. The average crosslink between junction points can be related to swelling measurements from potential considerations, as shown below. 

At the end of the cross-hnking process, the topology of the mesh is composed of the different entities represented in Figure 6 (16,57-59). An elastically active junction is one joined by at least three paths to the gel network (60,61). An active chain is one terminated by an active jimction at both its ends. Rubber-like elasticity is due to elastically active chains and jimctions. Specifically, upon deformation the number of configurations available to a chain decreases and the resulting decrease in entropy gives rise to the retractive force. 

EXAMPLE 2.4 Why is robber elastic When you stretch a rubber band, it pulls back. This retractive force is due to the tendency of polymers to adopt conformations that maximize their multiplicities. Polymers have fewer conformational states when fully stretched (see Chapters 31-33). Figure 2.9 illustrates the idea. Fix the first monomer of a chain to a wall. The degree of freedom is... 

Equation (9.15) implies that you can get the entropic component of the force, dSld )T, from a very simple experiment. Hold the rubber band at a fixed stretched length T (and constant pressure) and measure how the retractive force depends on the temperature (see Figure 9.1). The slope of that line, (df jdT)(, will give - (dSld )r. The positive slope in Figure 9.1 indicates that the entropy decreases upon stretching. 

Rubber bands are entropic springs. Experiments show that the retractive force / of polymeric elastomers as a function of temperature T and expansion H is approximately given by f(T,C) = aT ( - tn) where a and l ) are constants. 

Rubber and other pol>nneric materials are elastic. Polymeric elastomers are covalently cross-linked networks of pol>Tner chains. Here w e describe one of the simplest and earliest models for the retractive forces of polymeric materials, the affine network model. 

The retractiv e stress in elastomers depends not only on the deformation but also on the cross-link density, through m/V, the density of chains. In a unit volume there are 2m total chain ends. If each junction is an intersection of j chain ends, then there will be (1 junction/ / chain ends) x (2m chain ends) = 2ml j) junctions, so the number of junctions is proportional to m. Therefore the retractive force increases linearly with the cross-link density of the network. Bowling balls are made of a type of rubber that has a much higher cross-link density than rubber bands. 

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