Troutons Rule

The rule of Trouton states that the entropy of vaporization at the boiling point is for all substances approximately 

Trouton s rule was published in 1883 and after the 100 years anniversary, several papers with historical remarks appeared [1-3], 

Guggenheim has collected data and expressed phase equilibria in terms of corresponding states [4], The modeling of the coexistence equations with regard to the liquid - gas equilibrium is still an object of research [5], 

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As in PP-based nanocomposite systems, the extended Trouton rule, 3r 0 (y t) = r E (so t), also does not hold for PLANC melts, in contrast to the melt of pure polymers. These results indicate that in the case of P LANC, the flow induced internal structural changes also occur in elongation flow [48], but the changes are quite different in shear flow. The strong rheopexy observed in the shear measurements for the PLA-based nanocomposite at very slow shear rate reflects the fact that the shear-induced structural change involved a process with an extremely long relaxation time. 

Strain hardening is an abrupt, positive deviation of from the Trouton rule as e increases with time. In the view of Hwang and Kokini (1991), with reference to polysaccharides, this phenomenon is due to branch points acting as hooks, thereby increasing the resistance to flow. 

As a conclusion from the Hildebrand/Trouton Rule, the definition of a standard vapor phase in a standard state with a well known amount of disorder can be made. This definition can be used as a starting point for modeling diffusion coefficients of gases and liquids. 

JK mol-1 the value V°L = 0.91 cm3mol is obtained. An interpretation of the Hildebrand/Trouton Rule is that this free volume, V°L, allows for the freedom of movement of molecules (particles) necessary for the liquid state at the temperature Th. The explanation of the constant entropy of evaporation is that it takes into account only the translational entropy of the vapor and the liquid. It has to be pointed out that V°L does not represent the real molar volume of a liquid, but designates only a fraction of the corresponding molar volume of an ideal gas Vy derived from the entropy of evaporation. The real molar volume VL of the liquid contains in addition the molar volume occupied by the molecules V0. As a result the following relations are valid VL -V°L + V0 and Vc=Vq + V0. However, while V] < V0 and VL is practically independent of the pressure, V0 VaG in the gaseous phase. Only in the critical phase does VCIVL = 1 and the entropy difference between the two phases vanishes. 

Thomas presented an interesting paper (2021) relating H bonding and viscosity, and he was quick to point out the approximate nature of his treatment. He combined a modification of Andrade s viscosity equation with a relation between vapor pressure and latent heat of vaporization and still another function relating the heat of H bonding with the degree of association. From these he calculated an approximate heat of vaporization and compared it to a nonassociated value from a modified Trouton rule equation. The difference is called... 

This 70 J K 1 mol-1 value is close to the 87 J I< mob1 which is given by the original Trouton rule. The (AHV/TB) ratio may be replaced by (ATPub/TSB) for solids which can sublime, where AJTsub is the enthalpy of sublimation and TSB is the sublimation temperature. (We... 

In the extensional, irrotational field, under steady state conditions, the particles remain oriented in the direction of stress. In uniaxial flow, they align with the main axis in the flow direction, while in biaxial they lie on the stretch plane [Batchelor, 1970, 1971]. For dilute spherical suspensions in Newtonian liquid the extensional viscosity follows the Trouton rule, i.e., = 3q. 

Even for substances that do not obey the Trouton rule, the proportionality between Af/ ap and the boiling point is roughly correct. In view of Eq. (26.1) we may take the boiling point of a liquid as a convenient measure of the cohesive energy, which in turn depends on the strength of the intermolecular forces. 

A simple rule of thumb (to within 15%) for A//vb th classical Trouton rule A/fvb... 

Pressure ratio (in the validation range of the Trouton rule) (Fig. 2-40)... 

Keywords blends, alloys, compatibilizer, rheology, flow, viscosity, extru-date swell, shear modulus, shear flow, elongational flow, orientation in flow, sizing, yield stress, fillers, talc, mica, glass fibers, reinforced system, interlayer slip, log-additivity rule, concentration dependence, Trouton rule. 

The rheological responses measured at low values of strain better reflect the effects of the blend structure. For multiphase systems, there are serious disagreements between the predictions of continuum-based theories and experiments, that is, between the small and large deformation behavior. For example, the identity of zero-deformation rate dynamic and steady state viscosity is seldom found, and so is the Trouton rule. Similarly, the derived by Cogswell, relationship between the extensional viscosity and the capillary entrance pressure drop, and derived by Tanner equation for calculating the first normal stress difference from the extrudate swell, are rarely valid. 

Similar to the Pictet-Trouton rule we can derive a corresponding relation here,... 

Clear evidence for a crystalline transition at about 90"C is presented in a series of papers by Araki, Refs. 3-5. He also presents evidence for doublets in the transitions Ref 4, and points out that the alpha and gamma transitions follow the so called 2/3 (Trouton) rule when compared with the first order crystalline transitions at 19 and 327°C, Ref. 3. See also evidence for a doublet in the freezing-point plot shown in Ref 65. 

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