Transition concentration

Figure 6. Comparison of volume change for potassium in liquid ammonia (

The amount of silane deposited from water on a mineral surface, increases rapidly with increasing concentration, up to certain transition concentrations. Above this concentration deposition increases more slowly. These type of transitions are attributed to the onset of micelle formation between the aqueous silanetriols, causing enhanced stability of the hydrolyzed molecules.2 The detailed hydrolysis and condensation behaviour of silane molecules in solution has been studied repeatedly, those were brought together in the festschrift in honour of Prof. Plueddemann.66... 

For the case of film thickness measurements in the presence of CaCl2 (po and diffuse electric layer planes due to Ca2+ ion binding. The calculation in the electrolyte concentration range 10 3 - 5-10 2 mol dm3 indicates an increase in films from ionic surfactant solutions [e.g. 171,186,189] (see also Section 3.4.1.3). So, the formation of CBF through initial formation of common black spots can be interpreted as due to the specific interaction of Ca2+ ions with lyso PC. 

The dimensionless constant turns out to be large (around 1350) for perfectly rigid rods (Teraoka and Hayakawa 1989 Bitsanis et al. 1990). The transitional concentration Vo from dilute to semidilute occurs when Dr departs from its dilute solution value D o according to Eq. (6-44), this occurs when 30, or so, as noted above. 

The transition concentration of cocrystal component can be predicted by substituting the single component crystal solubility, Sa, for the cocrystal solubility, S, in Eq. (7) and rearranging to give... 

A priori knowledge of the solubility of cocrystal in pure solvent is useful to predict the ligand transition concentration and to determine conditions under which cocrystals dissolve or cocrystallize. Fig. 20 shows... 

A whole range of cations and anions in different combinations have been explored. The results are surprising. Measurements of coalescence rates for a range of typical electrolytes as a function of electrolyte concentration are shown in Fig. (3.5). There is a correlation between valency of the salt and transition concentration, defined as 50% bubble coalescence, with more highly charged salt effective at lower concentration. The effect is independent of gas flow rate. All the results scale with Debye length (ionic strength). Some salts and acids have no effect at all on bubble coalescence, a situation summarised in Table 3.1. 

There is no known mechanism that can account for these effects. Water structure has to be implicated. But there is clearly a remarkable correlation between the ions present in a salt and their effect on the coalescence phenomenon. A property a or P can be assigned to each anion or cation. The combination aa or PP results in inhibition of bubble coalescence at a critical salt concentration, whereas the combinations aP or Pa produces no effect at all. Different gases of widely different molecular size, from helium to sulphur hexafluoride, affect the transition concentration a little, but do not change the phenomenon. 

Measurements of the hydrophobic attraction between solid surfaces using an atomic force microscope have also been performed in solutions of NaCl and NaClOa. The attraction was found to be equivalent to that in water in 0.2M NaClOs, whilst in 0.2M NaCl the attractive force was much reduced, supporting expectations. (NaClOa, has no effect on bubble coalescence, NaCl does, cf. Table 3.1.) It has also been observed previously that the range of the attractive force acting between bubbles is substantially reduced from about lOOnm to 40nm on addition of KCl above the transition concentration. 

The observations discussed above may have implications for any system where water, dissolved salts and hydrophobic entities are present and there must be many. Currently the separation of hydrophobic proteins can be achieved using a hydrophobic chromatography column, by elution with salt solutions. There is no adequate theory for this process and present understanding is purely empirical. Suppose then, that while all salts reduce electrostatic forces, only those salts that reduce bubble coalescence also reduce the hydrophobic attraction. Further, these salts have a significant effect on the hydrophobic attraction only above their transition concentration. With this notion in mind the experimental results are explained. This then enables separations to be simplified, as the salt type and concentration gradient required are easily determined. 

The second point of interest is that the linewidth in the equilibrated state does reflect the transition concentration c. This is seen in Figure 15 where the plot of Av against c shows a break at around 7,5 mM. This shows that the mobility of tfie aggregates which determines the correlation time is further reduced above c. ... 

The self-diffusion of water itself provided proof of the above hypothesis, because ions due to hydration retarded it, but structure breakers could accelerate it. The plot of the self-diffusion parameter as a function of transition concentration fully confirmed the above-mentioned assumption. The transition concentration thus corresponded with that at which the maximum hydration occured. 

These components of are transition concentration diffusion reaction crystallization and resistance. 

Transition° Concentration of Sodium Palmitate Transition Temperature, °< NMR Lit. (23) ... 

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