Platelet formation, thermodynamics

The formation of mixed Mo — P —S compounds is thermodynamically restricted at temperatures lower than 1000°C (70). This restriction implies that the sulfur atoms in M0S2 are not directly replaced by phosphorus atoms. In the same way, phosphorus does not regularly occupy the edges of the M0S2 platelets through bonds with sulfur atoms as in the case of the promoted CoMoS or NiMoS phases. The presence of P(white), P(red), and P(black) on catalysts can also be excluded because they have extremely high vapor pressures under hydrotreating conditions. 

Because the free energy of formation of a surface is always positive, a particle that consists only of surfaces (that is, platelets or droplets of atomic dimensions) would be thermodynamically unstable. This is also apparent from the Kelvin equation [Eq. 3.70], which states that a particle that falls below a certain size will have an increased vapor pressure and will therefore evaporate. There must be a stabilizing influence, however, that allows small particles of atomic dimensions to form and grow a common occurrence in nature. This influence is given by the free energy of formation of the bulk condensed phase. In this process, n moles of vapor are transferred to the liquid phase under isothermal conditions. This work of isothermal compression is given by... 

The spherical shape is thermodynamically more stable than other shapes of particles which depend on the nature of materials used and the mode of preparation, such as inorganic colloids to yield ellipsoidal, rod-like, cubic, platelet, or needle-like shapes. In the case of organic particles, it is also feasible to make colloids with organic particles having a nonspherical shape, which leads to the formation of metastable thermodynamic state with their diffusion capability. 

In this technique water-polymer emulsion is formed which is thermodynamically unstable. At low gelation temperature, nanoscale fibers network is formed, whereas high gelation temperature leads to the formation of platelet-like structure. Uniform nanofiber can be produced as the cooling rate is increased. Polymer concentration has a significant effect on the nanofiber properties, as polymer concentration is increased porosity of fiber decreased and mechanical properties of fiber are increased. The final product obtained is mainly porous in nature but due to controlling the key parameters we can obtain a fibrous structure (Figure 9.29). The key parameters involved are as follows [36]. 

From a thermodynamic viewpoint, both the entropic and enthalpic factors are important in controlling the dispersion of clay layers in a polymer matrix [19-21]. It was reported that the confinement of the polymer chains inside the silicate galleries results in a decrease in the overall entropy of the macromolec-ular chains [10,20] this is, however, compensated by the increase in conformational freedom of the tethered alkyl surfactant chains as the inorganic layers separate due to the less confined environment (Figure 11.2). It was also shown that apolar interactions are generally unfavorable and so in the case of nonpolar polymers, there is no favorable excess enthalpy to promote the dispersion of clay platelets and it is hence necessary to improve the interactions between the polymer and clay so as to become more favorable than the alkylammonium-clay interactions. This can be achieved by functionalization of the polymer matrix or addition of compatibilizers [3,18,22-29]. For polar polymers, an alkyl-ammonium surfactant is adequate to offer sufficient excess enthalpy and promote the formation of exfoliated nanocomposites. 

Kinetics is another important factor in determining if a mixture of nanoparticles and polymer can form a nanocomposite. The extent of nanoparticle dispersion (e.g., exfoliation of the stacks of clay platelets, debonding of nanotube bundles, and deagglomeration of nanosphere agglomerates) in a polymer matrix is affected critically by the kinetic barriers. Such kinetic barriers often inhibit the formation of thermodynamically favorable structure. 

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