Ideal elastomers

Figure 8.4 The use of bis(3-trimethoxysilyl)tetrasulfane) modified silica in the vulcanization of elastomers (idealized a+b=4, l3Ax3A8) taken from ref (55).

Ideal elastomer (ideal rubber) n. An elastomer, which on deformation at constant,... 

For large deformations or for networks with strong interactions—say, hydrogen bonds instead of London forces—the condition for an ideal elastomer may not be satisfied. There is certainly a heat effect associated with crystallization, so (3H/9L) t. would not apply if stretching induced crystal formation. The compounds and conditions we described in the last section correspond to the kind of system for which ideality is a reasonable approximation. 

Since entropy plays the determining role in the elasticity of an ideal elastomer, let us review a couple of ideas about this important thermodynamic variable ... 

Comparing this result with Eq. (3.1) shows that the quantity in brackets equals Young s modulus for an ideal elastomer in a perfect network. Since the number of subchains per unit volume, i /V, is also equal to pN /Mj, where M, is the molecular weight of the subchain, the modulus may be written as... 

The shear modulus for an ideal elastomer in a perfect network is not difficult to derive ... 

A constant force is applied to an ideal elastomer, assumed to be a perfect network. At an initial temperature Tj the length of the sample is Ij. The temperature is raised to Tf and the final length is If. Which is larger Ij or If (remember F is a constant and Tf > Tj) Suppose a wheel were constructed with spokes of this same elastomer. From the viewpoint of an observer, the spokes are heated near the 3 o clock position-say, by exposure to sunlight-while other spokes are shaded. Assuming the torque produced can overcome any friction at the axle, would the observer see the wheel turn clockwise or counterclockwise How would this experiment contrast, in magnitude and direction, with an experiment using metal spokes ... 

Applications. Polymers with small alkyl substituents, particularly (13), are ideal candidates for elastomer formulation because of quite low temperature flexibiUty, hydrolytic and chemical stabiUty, and high temperature stabiUty. The abiUty to readily incorporate other substituents (ia addition to methyl), particularly vinyl groups, should provide for conventional cure sites. In light of the biocompatibiUty of polysdoxanes and P—O- and P—N-substituted polyphosphazenes, poly(alkyl/arylphosphazenes) are also likely to be biocompatible polymers. Therefore, biomedical appHcations can also be envisaged for (3). A third potential appHcation is ia the area of soHd-state batteries. The first steps toward ionic conductivity have been observed with polymers (13) and (15) using lithium and silver salts (78). 

Another class of water-based materials that has recently (ca 1997) begun to see use ia masoary water repeUeacy treatmeats is sUicoae elastomer latex (89), which can deHver a water-permeable sUicone mbber film. These latex elastomers are ideal as water repeUents for substrates that contain very large pores, such as concrete block. In addition, the elastomer can bridge minor cracks, and wUl expand and contract with the substrate. 

The ability to bond natural rubber to itself and to steel makes it ideal for lining tanks. Many of the synthetic elastomers, while more chemically resistant than natural rubber, have veiy poor bonding characteristics and hence are not well suited for hning tanks. 

The main models are described in a review by Vrhovski and Weiss [8]. For ideal elastomers in the extended mode, all the energy resides on the backbone and can therefore be recovered upon relaxation [18]. Generally, it is believed that the mechanism of elasticity is entropy-driven, thus the stretching decreases the entropy of the system and the recoil is then induced by a spontaneous return to the maximal level of entropy [8]. 

Let us now assume momentarily that the elastomers are perfect, in the sense that all functional groups (originally present in equivalent amounts) have reacted in such a manner that no sol exists. Under such idealized conditions, each molecule of monohydroxy PPO will in effect produce one inactive junction. (Strictly speaking, i molecules of monohydroxy PPO can produce somewhat more than i inactive junctions.) Thus, the concentration of junctions in the network becomes about 0.073 mole/kg instead of 0.100 mole/kg (Table II). As each junction gives 3/2 chains, the modulus, after equating h to zero in eq 1, is given by... 

Butyl diphenyl phosphate, 11 494 Butyl elastomers, 4 409 Butylene(s), 4 402-433 10 486 alkylation, 2 175-176 analysis, 4 421-422 chemical reactions, 4 404-410 economic aspects, 4 421 equilibrium distribution of ideal gas at selected temperatures, 4 409t feedstock for higher aliphatic alcohols, 2 211... 

A solid electrolyte is an ionic conductor and an electronic insulator. Ideally, it conducts only one ionic species. Aside from a few specialty applications in the electronics industry, solid electrolytes are used almost exclusively in electrochemical cells. They are particularly useful where the reactants of the electrochemical cell are either gaseous or liquid however, they may be used as separators where one or both of the reactants are solids. Used as a separator, a solid electrolyte permits selection of two liquid or elastomer electrolytes each of which is matched to only the solid reactant with which it makes contact. 

Atomic force microscopy and attenuated total reflection infrared spectroscopy were used to study the changes occurring in the micromorphology of a single strut of flexible polyurethane foam. A mathematical model of the deformation and orientation in the rubbery phase, but which takes account of the harder domains, is presented which may be successfully used to predict the shapes of the stress-strain curves for solid polyurethane elastomers with different hard phase contents. It may also be used for low density polyethylene at different temperatures. Yield and rubber crosslink density are given as explanations of departure from ideal elastic behaviour. 17 refs. 

This most widely used black pigment is also in the top 50 chemicals. About 4.0 billion lb of carbon black were made in 2001. Commercial value was 1.4 billion at 35C/lb, but 93% of this is used for reinforcement of elastomers. Only 7% is used in paints and inks. Carbon black is made by the partial oxidation of residual hydrocarbons from crude oil. See Chapter 6, Section 7.2. The hydrocarbons are usually the heavy by-product residues from petroleum cracking, ideally high in aromatic content and low in sulfur and ash, bp around 260°C. 

PIB and various copolymers are called butyl rubber. Butyl rubbers have lower permeability and higher damping than other elastomers making them ideal materials for tire inner liners and engine mounts. 

While polymer melts and non-cross-linked elastomers flow readily when stress is applied, structural plastics must resist irreversible deformation and behave as elastic solids when relatively small stresses are applied. These plastics are called ideal or Bingham plastics with their behavior described mathematically by... 

In shear yielding, oriented regions are formed at 45° angles to the stress. No void space is produced in shear yielding. Crazing often occurs prior to and in front of a crack tip. As noted earlier, the craze portion contains both fibrils and small voids that can be exploited after the stress is released or if the stress is maintained. Since many materials are somewhat elastic, most plastics are not ideal elastomers and additional microscopic voids occur each time a material is stressed. 

Figure 5.77 Comparison of idealized stress-strain diagrams for metals, amorphous polymers, and elastomers.

In summaiy, theie aie a lange of vulcanizing systems which can be used for natural rubber, and the choice is dependent on the combination of properties required. No single one offers ideal, all-around properties combined with good heat resistance. The end user has to be selective, according to the properties required foi the final application. Certain properties such as oil resistance and gas permeability have been omitted from Table 3, because in legaid to these properties natural mbbei is substantially inferior to synthetic mbbers such as acrylonitrile rubber and halobutyl rubber (see Elastomers,... 

Since there is no change in internal energy when an ideal elastomer is stretched, the entire contribution to the retraction or restoring force is entropy. Unstretched elastomers are amorphous, but the random chains become more ordered when the elastomer is stretched. The modulus of an elastomer changes slightly as the temperature is reduced, but there is an abrupt change in modulus as the elastomer becomes a glassy polymer at the Tr... 

Most thermoplastics, such as PVC, have relatively high moduli at their useful temperatures, which are below the Tr The intermolecular forces of plastics are much stronger than those of elastomers and are usually weaker than the intermolecular hydrogen bonds characteristic of most fibers. Figure 5.2 describes the idealized behavior of a thermoplastic as a function of chain length and temperature. 

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