Thermodynamics elastomer deformation

In equation (6-1) the increment of work, dW, refers to all of the work (i.e., electrical, mechanical, pressure-volume, chemical, etc.) performed by the system (the sample) on its surroundings. The development of thermodynamics given in most physical chemistry texts is confined to gases where d W becomes simply pressure-volume work, PdV, where P is the external environment. In the case of an elastomer deformed by an amount dL in tension and exerting a restoring force f the mechanical work performed on the system to accomplish the deformation, namely fdL, must also be included in dW. Thus, for an elastomer strained uni axially in tension,... 

The properties of elastomeric materials are controlled by their molecular structure which has been discussed earlier (Section 4.5). They are basically all amorphous polymers above their glass transition and normally crosslinked. Their unique deformation behaviour has fascinated scientists for many years and there are even reports of investigations into the deformation of natural rubber from the beginning of the nineteeth century. Elastomer deformation is particularly amenable to analysis using thermodynamics, as an elastomer behaves essentially as an entropy spring . It is even possible to derive the form of the basic stress-strain relationship from first principles by considering the statistical thermodynamic behaviour of the molecular network. 

Although traditionally the thermodynamic treatment of the deformation of elastomers has been centered on the force, the alternative condition of keeping the force (or tension) constant and recording the sample length as a function of temperature at constant pressure is even simpler 23,271. 

The aim of the thermodynamic treatment is to relate the elastic force opposing the deformation of the elastomer to changes in energy and entropy occurring during the process. 

Recently Zhao and Suo developed a thermodynamic model of electrostriction for elastomers capable of large deformation that helps elucidate the roles that... 

It has been found that a non-stationary boundary regime initiated by deformations arising in elastomer duiing swelling and increasing a thermodynamical compatibility of elastomer with a liquid is the main reason for swelling anomalies observed in the experiments. Anomalies of sorption kinetics turn out to be a typical phenomenon observable to one or another extent in elastic swelling materials. 

Under deformation, sections of chains between the network points are stretched. In a good approximation, elastomers do not change their volume under strain (Av = 0). Hence, the work of deformation (stretching) of a specimen is due only to the action of the applied force,/ According to 1st and 2nd Law of Thermodynamics, it might be separated in an energetic and entropic contribution ... 

When an amorphous cross-linked polymer above Tg is deformed and released, it snaps back with rubbery characteristics. The dependence of the stress necessary to deform the elastomer depends on the cross-link density, elongation, and temperature in a way defined by statistical thermodynamics. 

The deformation of elastomers can be considered as a reversible process and so d 0 can be evaluated from the second law of thermodynamics which states that for a reversible process... 

Most of the experimental investigations on elastomers have been done under conditions of constant pressure. The thermodynamic function which can be used to describe equilibrium under these conditions is the Gibbs free energy (Equation 4.1), but since elastomers tend to deform at constant volume it is possible to use the Helmholtz free energy, A in the consideration of equilibrium. It is defined as... 

Thermodynamic equation of state Boltzmann constant Affine deformation Gaussian distribution Phantom chain approximation Phantom model Constrained fluctuation model Slip-link model Nonaffine slip tube model Mooney-Rivlin equation Visoelasticity of elastomers Alpha transition Beta transition Gamma transition Storage modulus... 

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