Vulcanization theories

The fact that mbber shows mbber elasticity was discovered more than 100 years earlier than professor H. Staudinger s proposal. The memory effect acquired by vulcanization, so-called Gough-Joule effect, and its thermodynamic explanation were the great achievements in the nineteenth century. As seen in many textbooks, this thermodynamic approach was the easiest one to gain consistency between ever-performed experiments and theory. In fact, thermodynamics of mbbery material can be treated in parallel with thermodynamics of gas. One could show experimentally that... 

The results of Cohan on the force of retraction r at a = 1.5 for GR-S synthetic rubbers vulcanized with various proportions of a calcium carbonate filler are shown in Fig. 104. The agreement with the theoretical curve drawn according to Eq. (52) is good. In further confirmation of the theory, variations in average particle diameter... 

De Gennes [41] predicted that percolation theory should hold for crosslink-ing of small molecule precursors. However, he argued that for vulcanizing polymers (high Mw), only a very narrow regime near the gel point exists for which percolation is valid, i.e. these polymers should exhibit more mean fieldlike behavior. 

The conventional four-element theory claimed that all four of Aristotle s elements are present in all substances. But Boyle observes that some materials cannot be reduced to the classical elementary components, however they are manipulated by Vulcan , the heat of a furnace ... 

The degree of crosslink density in vulcanized elastomeric gum compounds can be estimated by applying the Flory-Rehner network theory [226]. But, their... 

Attempts were made to remove the third assumption above, and it was shown that correct considerations of the limited extensibility of the chain adequately explain the S-shaped feature of stress-strain curves observed in uniaxial extension of vulcanized rubbers. However, the improved theory still gave zero for bW/bI2. Up to now there is no molecular theory available which predicts bW/bI2 that varies with//. 

The deformation y or A decreases with increasing density of the cross-links (e.g.) an increase of the sulphur bridges in vulcanized caoutchouc). Moreover the saturation stress omax increases with the temperature. A better reproduction of the experimental values can be obtained by using. <4 = const a2 in the molecular exchange theory or with the empirical Mooney-Rivling equation... 

T 4. Treloar, L. R. G. Network theory of vulcanized rubber in H. A. Stuart Die Physik der Hochpolymeren, Bd. IV, 311. Berlin-GOttingen-Heidelberg Springer-Verlag 1956. 

Finally, the applicability of the cascade theory to rather complicated systems with unequal functional groups, substitution effect, vulcanization of chains and long rang correlation as a result of directed chain reactions is shown. The limitation of the theory to essentially tree-like molecules and their unperturbed dimensions is outlined and the consequence of this error for the prediction of reed systems is discussed. 

In Chap. C we have discussed in some detail the application of the cascade theory to polycondensates in their unperturbed state. In Chap. D some experimental results were already given for cross-linked or vulcanisated linear chains. In this chapter we shall now outline in brief how cross-linking chain reactions or the vulcanization of preformed chains of an arbitrary length distribution can be treated by cascade theory. Second, we shall discuss how heterogeneities in branching or a rigidity of a certain domain can be taken into account. 

At temperatures well below Tg, when entropic motions are frozen and only elastic bond deformations are possible, polymers exhibit a relatively high modulus, called the glassy modulus (Eg) which is on the order of 3 Gpa. As the temperature is increased through Tg the stiffness drops dramatically, by perhaps two orders of magnitude, to a value called rubbery modulus Er. In elastomers that have been permanently crosslinked by sulphur vulcanization or other means, the values of Er, is determined primarily by the crosslink density the kinetics theory of rubber elasticity gives the relation as... 

This brings us to the elastic behavior of rubber networks. There are a number of problems involved in developing a good theory, not the least of which is the fact chat real networks are not perfect. If natural rubber is vulcanized there are all sorts of defects in the resulting network dangling ends and... 

Weakly crosslinked epoxy-amine networks above their Tg exhibit rubbery behaviour like vulcanized rubbers and the theory of rubber elasticity can be applied to their mechanical behaviour. The equilibrium stress-strain data can be correlated with the concentration of elastically active network chains (EANC) and other statistical characteristics of the gel. This correlation is important not only for verification of the theory but also for application of crosslinked epoxies above their Tg. 

Network polymers can also be made by chemically linking linear or branched polymers. The process whereby such a preformed polymer is converted to a network structure is called cross-linking. Vulcanization is an equivalent term that is used mainly for rubbers. The rubber in a tire is cross-linked to form a network. The molecular weight of the polymer is not really infinite even if all the rubber in the tire is part of a single molecule (this is possible, at least in theory), since the size of the tire is finite. Its molecular weight is infinite, however, on the scale applied in polymer measurements, which require the sample to be soluble in a solvent. 

An important difference between randomly branched and linear polymers is that the fractal dimension of branched polymers is larger than the dimension of space (d—3). This severely limits the applicability of the mean-field theory to the crosslinking of long linear chains, called vulcanization. Long chains in the melt have a fractal dimension of P = 2, which leaves lots of room inside the pervaded volume of the chain (i.e., filled by other chains in a polymer melt). The extra room created by the linear sections between crosslinks allows the fractal dimension of P = 4 to exist in three-dimensional space on a certain range of length scales (see Section 6.5.4). 

The correlation length and the number of monomers in a characteristic branched polymer N have simple predictions for vulcanization. These predictions can be easily obtained from the mean-field percolation theory [Eqs (6.105) and (6.125) with exponents a=v = jl] by replacing the monomer in the previous treatment by the precursor linear chain of size bN J containing Nq monomers. 

Figure 7.5 (a) A comparison of experimental data for nitrogen adsorbed at 77 K on Vulcan 3-G(2700) (points) with the fit given by the modified nonlocal density functional theory (MNLDFT) models (line), (b) The adsorptive potential distribution for the Vulcan 3 graphite. 

It has been shown that the life time in the creep process of rubbery polymers scatters largeley but obeys the specified statistical distribution which are introduced theoretically based on some assumptions. Two assumptions are made here that "one crack leads the body to failure" and "the v th crack leads the body to failure". The former assumption leads the exponential distribution of tg, and the latter the unimodal distribution when v>2. It has been explained from experiments that the distribution of tg for pure rubbers of vulcanized SBR and NR are the exponential, type and for filled systems the unimodal type. Theory introduced here can be applied not only to the creep failiire but also to the failure process varing stress level such as uniaxial extension with constant strain rate. It has been demonstrated that the distribution of Xg, the stretch ratio at breedc in the constant rate of extension, is well estimated by the theory substituting the parameters n and c which are obtained from creep failure experiment to eq(l9). 

Ozone attack on the oxidatively violated rubber surface is thus prevented (21, 27, 29, 30). Creation of the surface layer was confirmed using microscopy. The theory is in agreement with the observation that the initial rapid ozone consumption is stabilized rubber drops and may be renewed after mechanical break of the formed film 21). There is a chemical proof of the theory. Ozonation products of N,N -bis(l-methylheptyl)-l,4-PD (DOPPD) form a surface film on ozonized and DOPPD doped vulcanized NR (31) and carbon-black loaded NR (24, 32). In addition to unreacted DOPPD, many of the low-molecular weight compounds observed in the film were found also in the ozonation of pure DOPPD (24) the only difference was a... 

An interesting, indirect application of the statistical theory to filled rubbers has been published by Wolff (/33). In recent years increasing use has been made of oscillating disc rheometers to follow the course of vulcanization. These instruments operate at low frequencies and at vulcanization temperatures, so that torque recorded at full cure is a good measure of an equilibrium shear modulus and hence proportional to v. Wolff finds for polymers filled with furnace blacks and cross-linked with dieumyl peroxide ... 

S-B-S and S-I-S. Much of our discussion will refer directly to data for S-B-S and S-I-S block polymers. We justify this on several counts. These block polymers can be clearly defined as to structures, molecular weights, and compositions. They have served as model systems for much of the recent work in block polymers. They also comprise the largest volume of commercial block polymers. Finally, we believe that the discovery (20) of the S-B-S and S-I-S thermoplastic rubbers which are strong, resilient rubbers without vulcanization, and the concomitant, readily understood theory (21). provided a paradigm (terminology of T. S. Kuhn (2 2)) that significantly accelerated the scientific work on these polymers in recent years. 

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 Eerraro JR, Nakamoto K (1994) Introductory Raman spectroscopy. Academic Press, San Diego Flory PJ (1942) Thermodynamics of high-polymer solutions. J Chem Phys 10 51-61 Flory PJ (1944) Network stmcture and the elastic properties of vulcanized mbber. Chem Rev 35 51-75... 

Miscellaneous Couplins Asents Examples in Table 5.48 show use of coupling agents that can, in theory, react at sites along the main chain of each of two immiscible polyolefins. Both examples involve concomitant dynamic vulcanization of an elastomeric, dispersed phase with the added crosslinking agent. 

John Cremer, a fourteenth-century abbot who lived in Westminster, was reputed to have joined Raymond Lully in alchemical works in Westminster Abbey and the Tower of London. Thomas Norton, author of the Ordinall of Akhimy, began writing this famous work in 1477. The reputed Basil Valentine is mentioned later in our Chemical History Tour and also by Read. Vulcan is the god of fire. Arms of Vulcan refers to fire as an instrument of chemical change. The picture depicts an immediate proximity between a chemical laboratory and a chemical library—the duality of practice and theory. Although the American Chemical Society recommends location of a university chemical research library in the chemistry laboratory building, it is unlikely that they have quite this closeness in mind. 

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