Factors affecting energy decrease

Nucleation kinetics are experimentally determined from measurements of the nucleation rates, induction times, and metastability zone widths (the supersaturation or undercooling necessary for spontaneous nucleation) as a function of initial supersaturation. The nucleation rate will increase by increasing the supersaturation, while all other variables are constant. However, at constant supersaturation the nucleation rate will increase with increasing solubility. Solubility affects the preexponential factor and the probability of intermolecular collisions. Furthermore, when changes in solvent or solution composition lead to increases in solubility, the interfacial energy decreases as the affinity between crystallizing medium and crystal increases. Consequently, the supersaturation required for spontaneous nucleation decreases with increasing solubility, ° as shown in Fig. 7. 

One of the most important factors affecting the wavelength of UV absorp tion by a molecule is the extent of conjugation. Molecular orbital calculation show that the energy difference between HOMO and LUMO decreases as th ... 

There exist additional factors that can influence the v(OH) of isolated (non-H-bonded) hydroxyls. One of them is the anharmonicity of the O—H bond, which is related to the shape of the Morse potential that is overlaid with the harmonic potential. The harmonic frequencies are higher than the measured ones in general, an increase of the anharmonicity of a particular vibration lowers the O—H stretching frequency. For Morse potentials of equal shape, the anharmonicity decreases with decreasing wavenumber, because the zero-point energy of O—H bonds characterized by low frequencies hes closer to the bottom of the Morse potential curve, where the deviations from the harmonic oscillator model are smaller. However, the factors affecting the anharmonicity are far from being completely... 

The mechanism of irreversible shrinkage is not clear there are presumably all the factors affecting shrinkage involved. The decreasing distance between the gel particles may be considered as irreversible, because it leads to the reduction of free energy of the system. The effect of different factors on irreversible shrinkage is shown in Fig. 5.57. 

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