Equations Ostwald-Freundlich

Solubility is also affected by particle size, small crystals (<1 pm say) exhibiting a greater solubility than large ones. This relationship is quantified in the Gibbs-Thomson, Ostwald-Freundlich equation (see Mullin, 2001)... 

The principles of particle stabilization are even more critical to the stabilization of very small solid particles, less than one micron in diameter (e.g., nanosuspensions), which have much greater surface area. The Ostwald-Freundlich equation,... 

Over-saturation is necessary to breakthrough the thermodynamic barrier of nucleation. According to the Ostwald-Freundlich equation, the concentration in a confined space CiCn = exp(2 aVm RTr). Figure 2 shows the dependence of... 

Changes in crystal dispersion due to surface effects are typically based on the Gibbs-Thomson equation (sometimes called the Ostwald-Freundlich equation), which describes the effects of particle size on equilibrium conditions (Hartel 2001). For solution systems, the equation is given as... 

As early as 1878, Gibbs concluded that the breakdown or growth of a crystal was not a continuous transformation, as the gas-liquid transition was considered to be. Thomson derived what has come to be known as the Gibbs-Thomson equation, relating the vapor pressure of liquid droplets to the size of the droplets. Ostwald extended the concept to the problem of solubility, but made a numerical error later corrected by Freundlich. Similar to the Gibbs-Thomson equation, the Ostwald-Freundlich equation was expressed by... 

Compared with solutions, suspensions afford superior loading. As with emulsions, suspended particles must be kinetically stabilized with surfactants to prevent aggregation. The Ostwald-Freundlich equation. 

The solubility of any solid substance in a liquid phase is well known to be dependent on the size of its particles (crystals) which are in contact with the saturated solution. For substances existing in solutions in the molecular form, the dependence of their solubility against the particle size is expressed by the Ostwald-Freundlich equation (3.6.57). From this equation it follows, in particular, that an increase in the crystal (particle) dimensions results in a decrease in solubility. The oxide particles precipitated from concentrated solutions should be larger than those formed from more dilute solutions. The increase in the particle sizes in concentrated solutions of cations and oxide ions may be explained by ageing oxide, i.e. by the re-crystallization processes, whose rate increases with the concentration of the dissolved substance. 

As mentioned in Section 3.7.1.2, there is a considerable scatter of solubility product values obtained in the molten KCl-NaCl eutectic using different methods of solubility determination. This disagreement in the solubility parameters may be explained by differences in the sizes of oxide particles whose solubility is to be determined. The difference in size causes the scatter of the solubility data according to the Ostwald-Freundlich equation and the employment of the isothermal saturation method, which implies the use of commercial powders (often pressed and sintered), leads to values which are considerably lower than those obtained by the potentiometric titration technique where the metal-oxides are formed in situ. Owing to this fact, the regularities connected with the effect of physico-chemical parameters of the oxides or the oxide cations should be derived only from solubility data obtained under the same or similar experimental conditions. However, this does not concern the dissociation constants of the oxides, since homogeneous acid-base equilibria are not sensitive to the properties of the solid phase of... 

The difference in thermodynamic equilibrium between crystals of different size is defined by the Gibbs-Thomson or Ostwald-Freundlich equation (Mullin 1993). The original Kelvin equation was written to describe droplets of liquid in a vapor in terms of vapor pressures around droplets of different size. However, in crystallization studies, the vapor pressure may be related, through the solution activity, to the equilibrium concentration in solution for crystals of different size, faking the assumption that concentration can be used directly fpr vapor pressure gives... 

A known effect contributing to an increased saturation solubility is the formation of highly energetic surfaces by the milling process. The breaking of crystals lead to the exposure of inner parts of the crystal to the outer dispersion medium, implying that energetically less favorable surfaces are now in contact with water. The Ostwald-Freundlich equation also describes saturation solubility as a function of the tnterfacial tension between solid—liquid interphase. An increase in the interfacial tension y leads to an increase in the saturation solubility. 

The Ostwald-Freundlich equation (1-3) (III), derived from straight thermodynamics, describes in a quantitative way the relation between solubility and particle size of a solute. 

The Ostwald-Freundlich equation assumes that the surface energy, a , and the density of the solute, p, are independent of particle size, which is not strictly valid. Later on, several equations have been advanced, trying to overcome these shortcomings (8,9). Experimentally, however, in many cases a maximum of... 

At the basis of this ripening (14) is the Ostwald-Freundlich equation (III), which gives the solubility of a nucleus in terms of its particle size. It is in fact easily demonstrated as illustrated in Fig. 4 that based on such free energy diagram, the critical size for a viable nucleus increases with decreasing degree of sursaturation. 

Ostwald ripening is happening because the solubility of a substance in the near vicinity of small particles is greater than in the near vicinity of large particles. The relationship between the solubility and the size of the particles is given by the Ostwald-Freundlich equation ... 

The Ostwald-Freundlich equation, applied to solubility (known as the Thompson-Gibbs effect), is as follows ... 

Briefly, the increase in saturation solubility is due to an increase in the dissolution pressure when going below a size of approx. 1 iim. The relevant physical equations are the Kelvin equation and the Ostwald-Freundlich equation. The increase... 

High-energy input can lead to the complete iran.sformation of the crystalline drug to an amorphous state (22). ll is known that amorphous compounds possess a higher. solubility than crystalline compounds. This can be explained by the Ostwald-Freundlich equation, which describes the saturation solubility as a function of particle size. An amorphous powder can be considered as particles with an indefinite small particle size, thus the saturation solubility is increased. This effect is broadly described in the literature, e.g.. for griseofulvin modifications 1 and II compared to amorphous griseofulvin (23). 

The preparation of dense primary particles (1-5 nm in diameter) was discussed at length in the preceding chapters. As explained by Her [13] the fate of these particles depends on their size, as well as on the temperature and pH of the solution. The solubility, S, of a particle is related to its radius, r, by the Ostwald-Freundlich equation ... 

The Ostwald-Freundlich equation (Equation 13.1) is frequently used to discuss the relationship between the particle size and the solubility in liquids [70],... 

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