Thermodynamics of deformation

A very important problem in the thermodynamics of deformation of condensed systems is the relationship between heat and work. From Eqs. (2) and (4) by integration, the internal energy and enthalpy can be derived. As in other condensed systems, the enthalpy differs from the internal energy at atmospheric pressure only negligibly, since the internal pressure in condensed systems P > P. Therefore, the work against the atmospheric pressure can be neglected in comparison with the term jX.. Hence it follows that... 

The thermodynamics of deformation of solid-oriented polymers in any direction is determined by expressions which may be obtained from Eq. (22)7). The coefficient p may be determined by Eq. (111) and the modulus of elasticity E can be calculated according to the following expression 193)... 

Muller, F. H. Thermodynamics of deformation. Calorimetric investigation of deformation processes, in Rheology, New York Academic Press, Vol. 5, 417 (1969)... 

Staverman, A. J. Thermodynamics of deformation in S, Flugge Hand-buch der Physik Bd. 13, 432 u. 487. Berlin-Gottingen-Heidelberg Springer-Verlag 1962. 

The previous section described the thermodynamics of deformation and fracture in terms of the energy required to elongate and break the sample. This section describes two major experiments to evaluate the deformation and fracture energy stress-strain and impact resistance. In a tensile stress-strain experiment, the sample is elongated until it breaks. The stress is recorded as a function of extension. Stress-strain studies are usually relatively slow, of the order of mm/s. Impact strength measures the material s resistance to a sharp... 

Mueller, F.H., Thermodynamics of Deformation Calorimetric Investigations of Deformations Processes , in Rheology Theory and Applications (F.R. Eirich, Ed.), Vol. 5, Academic Press, NY, 1969, p. 417-489,... 

The full significance of these observations could not be appreciated in advance of the formulation of the second law of thermodynamics by Lord Kelvin and Clausius in the early 1850 s. In a paper published in 1857 that was probably the first to treat the thermodynamics of elastic deformation, Kelvin showed that the quantity of heat Q absorbed during the (reversible) elastic deformation of any body is related in the following manner to the change with temperature in the work — TFei required to produce the deformation ... 

Self-avoiding random walks statistics for intertwining polymeric chains and based on it thermodynamics of their conformational state in m-ball permitted to obtain the theoretical expressions for elasticity modules and main tensions appearing at the equilibrium deformation of /n-ball. Calculations on the basis of these theoretical expressions without empirical adjusting parameters are in good agreement with the experimental data. 

Lipid membranes are quite deformable, allowing water and head groups into their interiors when perturbed. A "water defect" is shown in Figure 1C, where water and lipid head groups enter the hydrophobic interior of only one of the bilayer leaflets. Figure ID shows a "water pore," where both leaflets are perturbed. At the molecular level, pore and defect formation are directly related to specific lipid-lipid interactions. It is important to understand the free energy required for pore formation in membranes and the effect of lipid composition on the process. In Section 3 of this chapter, we review recent MD studies of the thermodynamics of pore formation. 

The thickness of the interphase is a similarly intriguing and contradictory question. It depends on the type and strength of the interaction and values from 10 Ato several microns have been reported in the hterature for the most diverse systems [47,49,52,58-60]. Since interphase thickness is calculated or deduced indirectly from some measured quantities, it depends also on the method of determination. Table 3 presents some data for different particulate filled systems. The data indicate that interphase thicknesses determined from some mechanical properties are usually larger than those deduced from theoretical calculations or from extraction of filled polymers [49,52,59-63]. The data supply further proof for the adsorption of polymer molecules onto the filler surface and for the decreased mobility of the chains. Thermodynamic considerations and extraction experiments yield data which are not influenced by the extent of deformation. In mechanical measurements, however, deformation of the material takes place in all cases. The specimen is deformed even during the determination of modulus. With increasing deformations the role and effect of the immobilized chain ends increase and the determined interphase thickness also increases (see Table 3) [61]. 

Substitution of Equations (36) and (37) into Equation (35) generates a complicated differential equation with a solution that relates the shape of an axially symmetrical interface to y. In principle, then, Equation (35) permits us to understand the shapes assumed by mobile interfaces and suggests that y might be measurable through a study of these shapes. We do not pursue this any further at this point, but return to the question of the shape of deformable surfaces in Section 6.8b. In the next section we examine another consequence of the fact that curved surfaces experience an extra pressure because of the tension in the surface. We know from experience that many thermodynamic phenomena are pressure sensitive. Next we examine the effecl of the increment in pressure small particles experience due to surface curvature on their thermodynamic properties. 

These expressions demonstrate that the change of entropy and internal energy on deformation under these conditions is both intra- and intermolecular in origin. Intramolecular (conformational) changes, which are independent of deformation, are characterized by the temperature coefficient of the unperturbed dimensions of chains d In intermolecular changes are characterized by the thermal expansivity a and are strongly dependent on deformation. The difference between the thermodynamic values under P, T = const, and V, T = const, is vefy important at small deformations since at X - 1 2aT/(/,2 + X — 2) tends to infinity. 

The thermomechanical data accumulated during the last years as a consequence of the improvement of the technique of deformation calorimetry contributed significantly to the understanding of thermodynamics and mechanisms of the reversible deformation of polymers in the glassy, semicrystalline and rubbery state. 

Bianchi, U., and E. Pedemonte Rubber elasticity Thermodynamic properties of deformed networks. J. Polymer Sci. Pt A-2, 5039 (1964). 

---