THE PHYSICS. OF. RUBBER. ELASTICITY. BY. L. R. G. TRELOAR kinetic theory of rubber elasticity and discussed in general ther- modynamic terms some of. Download Citation on ResearchGate | The Physics of Rubber ELasticity | 1. The probability distribution function (PDF) of a perfectly flexible chain with fixed. PDF | Rubbers are highly elastic solids formed by the random permanent linkages Their elasticity is largely entropic in origin, so that the molecular theory is largely a Article (PDF Available) in Reports on Progress in Physics 51 (2)
|Language:||English, Spanish, Portuguese|
|Genre:||Children & Youth|
|Distribution:||Free* [*Registration needed]|
Chemical constitution of rubbers. 3. Early theories of rubber elasticity. 6. The kinetic theory of elasticity. 7. Cross-linking and vulcanization: network. The physics of rubber elasticity (third edition). Letters/Book Reviews From (3) and (4) the values Pcv = and Pvc = are obtained. These values indicate. The Physics of Rubber Elasticity (Third Edition). L. R. G. Treloar, Clarendon Press , Oxford. pp. xii + Price: £ M. Gordon · Search for more papers.
Network properties I n order to apply this result for the entropy of the single chain to the problem of the elasticity of rubber it is necessary to introduce certain assumptions concerning the structure of the rubber and the relation between the deformation of the molecules and the strain in the bulk material.
The first of such assump- tions is that the forces between the chains are negligibly small. This means that on deformation of the material no work is done against inter-molecular forces, the only change being a change in the entropy of the individual chains.
However, if there were no forces between molecules the system would behave as a liquid; there would be no restriction on the slippage of one molecule past another. To overcome this difficulty the further assumption is made that a small number of permanent connections or cross-linkages are introduced between the chains. Since the molecules are very long the number of such cross-linkages required may be quite small, and these will therefore not seriously interfere with the freedom of motion of the chains the micro-Brownian motion except in the immediate vicinity of the cross-linkages.
Trebar This concept of cross-linking is basic t o the theory of rubber elasticity. I n practice these cross-linkages are introduced in the process of vulcanization, originally discovered by Charles Goodyear in This process, which consists essentially of a chemical reaction with sulphur, greatly enhances the elastic properties of the original raw rubber, and reduces irreversible creep and flow effects.
By cross-linking, the original assembly of individually separate chains fig.
Model of rubber a before cross-linking, b after cross-linking, c on subsequently straining. Afine deformation of chains Let us now consider a network, such as that represented in fig. We define the ' chain ' in the network structure as the segment of the molecule between successive points of cross-linkage.
When the structure is deformed, the individual chains are likewise deformed in the sense that their end-to-end distances defined by the points of cross-linkage are changed. The problem is to calculate the changes in the entropy of the individual chains, and hence by summation the change in the total entropy of the system, corresponding to a specified deformation applied to the boundaries of the network. We thus have the problem of relating the molecular deforma- tion to the deformation of the material in bulk.
The mathematical examination of this problem James and Guth leads to a very simple result, namely that the junction points in the network move as if embedded in an elastic continuum.
The deformation of the chain end-to-end vectors is thus identical t o the deformation of lines drawn in corresponding directions on the bulk material. This is called an afine i. Application of the affine deformation principle enables the change in the entropy of the system for any given state of strain t o be derived.
Preface to the Third Edition. These values indicate that the distribution of structural units does not follow Bernoullian chain statistics but statistics with a tendency towards alternation of structural units. This can also be seen qualitatively by comparing the relatively strong intensity of the signal cv3c 12 of triads with alternating structure with the intensity of the signal w3v I0 of block triads.
By means of the statistical parameters determined from the spectrum the relative intensities of all signals were evaluated assuming first order Markov statistics as well as Bernoullian chain statistics. Table 2 shows that for all signal groups, the intensity of which can be measured with sufficient accuracy, the best agreement between predicted and experimental intensities is found for the Markov model.
To explain these results further investigations are being carried out on this system. The first nine chapters deal with general phenomena, statistics of a single chain, network statistics and the experimental examination of the predictions of theory which includes the thermodynamics of dry and swollen rubbers and photoelasticity.
Extraneous information has been carefully pruned from the earlier texts and the main arguments are clarified and amplified. The author is at pains to point out where opinions differ and where he stands with respect to these opinions.
The remainder of the book deals with recent developments in the phenomenology of general strain, the theory of large deformations and thermoelastic studies. These chapters are new and two at least - 'alternative forms of the strain-energy function' and 'thermoelastic analysis of the Gaussian network' - are gems.
Treloar's personal qualities include a clear mind and a facility for designing simple pertinent experiments. These qualities shine through the book.
It will be enjoyed by research workers, teachers and students whether or not they are familiar with the subject. One sad comment: The elasticity of caoutchouc is exceeded only by the elasticity shown by the publishers in stretching the price of the third edition. Allen W. Gronski, N. Murayama and H. Polymer , 16, 3 Elgert, K.
Macromolecules , 3, 5 Tanaka, Y. MakromoL Chem. It deservedly won respect from physicists and chemists of the time for its lucid exposition of a subject which was widely regarded until then as being unamenable to scientific discipline. The second edition appeared in In maintained the same high standard but in order to allow an adequate updating of the major themes some peripheral topics were curtailed.
This process is continued in the third edition to the point where the chapters on the dynamic mechanical properties and on crystallization have been dropped completely. The book is still about the same length as of previous editions, but it is now devoted entirely to the equilibrium properties of rubbers and to the rubbery state of matter.
The treatment of this narrower field is refined and very much up-to-date. It sets a standard of presentation rarely equalled in monographs of this kind. It may also be useful to researchers requiring information on aspects of polymer mechanics related to their work. Chapter 1 provides a good general introduction to polymers and plastics. Viscoelasticity is outlined in some detail in Chapter 3.