Supersaturated State

Crystallization of a novel protein using any method is unpredictable as a rule. Every macromolecule is unique in its physical and chemical properties because every amino acid or nucleotide sequence produces a unique three-dimensional structure having distinctive surface characteristics. Thus lessons learned by investigation of one protein are only marginally applicable to others. This is compounded by the behavior of macromolecules, which is complex owing to the variety of molecular masses and shapes, aggregate states, and polyvalent surface features that change with pH and temperature, and to their dynamic properties. 

Because of the intricacy of the interactions between solute and solvent, and the shifting character of the protein, the methods of crystallization must usually be applied over a broad 

FIGURE 2.6 A small amount of protein solution is confined by dialysis membrane within a 5 to 50 jjlI cavity bored into a dome-shaped plastic button. The button is then submerged into a larger volume of external fluid. By exchange of ions and small molecules across the membrane, the protein solution is brought to a state of supersaturation. 

FIGURE 2.7 With the free interface diffusion method illustrated schematically here, the protein sample, in buffer, is simply layered, with care, atop the precipitant solution, which may be either salt or polyethylene glycol. Salt ions diffuse rapidly into the protein solution aided by convective transport, and local concentration gradients are created in the region of the interface. With polymeric precipitants, both the polymer and the protein diffuse into one another, but at a greatly reduced rate. 

Through the vapor phase, then, water is removed slowly from the droplet of mother liquor, its pH may be changed, or volatile solvents such as ethanol may be gradually introduced. As with the liquid-liquid dialysis and free-interface diffusion methods, the procedure may be carried out at a number of different temperatures to gain advantage of that parameter as well. 

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All these results support our kinetic interpretations of these supersaturated gelling solutions. We assume that the network growth is described by the growth of individual domains, each one ruled by the autocatalytic model (S). This system behaves like an assembly of microdomains. Sach steroid in a supersaturation state is a potential germ of microdo.main. According to distribution curves of induction times for each microdomain, the typical kinetic curves for each part A and B of the phase diagram are obtained. 

Clear drops indicates that the RNA supersaturation state has not been reached, the RNA concentration is outside the nucleation zone (Fig. 14.2). These experiments must be repeated with higher sample and/or salt concentrations. The temperature could also be lowered. 

The dipping technique is used (13), and because of the great stability of the solutions in the supersaturated state, large numbers of substrates, up to 30 at a time (19), can be dipped simultaneously under nearly isothermal conditions. 

If supersaturated NaCl (or KCl) aqueous solution is kept in a wineskin or cellophane bag in the shade, numerous NaCl (or KCl) whiskers grow on the surface of the wineskin after a few days. The explanation is that a supersaturated solution is transported by capillary action to the surface of the wineskin, which rapidly attains a highly supersaturated state, and crystallization starts. As a result, hollow tube whiskers are formed, and the supersaturated solution is transported to the tip of the whisker until the point at which the tube is closed, resulting in the formation of whiskers. There is only one growth site, and so this whisker grows at the tip [16]. 

The extrusion temperatures of the polymer far below the melting point of the drug. Upon cooling of the extruded fibers, dissolved drugs may either recrystallize or remain soluble, which results in a supersaturated state. The amount of the dissolved drug can be correlated to the release properties. The state in which the drugs are left after extrusion determine their properties of permeation. 

When fine powders of vitreous silica, quartz, tridymite, cristobalite, coesite, and stishovite of known particle-size distribution and specific surface area are investigated for their solubility in aqueous suspensions, final concentrations at and below the level of the saturated concentration of molybdate-active silicic acid are established. Experimental evidence indicates that all final concentrations are influenced by surface adsorption of silicic acid. Thus, the true solubility, in the sense of a saturated concentration of silicic acid in dynamic equilibrium with the suspended silica modification, is obscured. Regarding this solubility, the experimental final concentration represents a more or less supersaturated state. Through adsorption, the normally slow dissolution rates of silica decrease further with increasing silicic acid concentrations. Great differences exist between the dissolution rates of the individual samples. 

Figure 1 gives results obtained by Alexander et al. (I) and Baumann (2) by dissolving fine particles of commercially available vitreous silica powders in aqueous solutions. Similar data obtained in polymerization and depolymerization experiments by Scheel et al. (15) and Friedberg (10) indicate that the curve shown in Figure 1 represents an equilibrium concentration for oligomeric acid. It can be approached from the supersaturated state of monomeric silicic acid as well as from a solution of pure polymeric silicic acid. 

With regard to a solubility equilibrium, the fact that vitreous silica behaves like a precipitate of polymeric silicic acid must be caused by the similarity between polymeric silicic acid and the hydrated surface of vitreous silica. Both forms can release silicic acid by hydrolysis and desorption, and likewise both forms are able to adsorb and condense silicic acid by means of silanol groups randomly distributed on their surfaces. Thus, in order to explain equal final states, the only assumption necessary is that the condensates will not attain the degree of dehydration of the bulk of the vitreous silica. The resulting equilibrium then relates to the two-phase system silicic acid—polymeric precipitate, and strictly speaking, this system is in a supersaturated state with respect to vitreous silica, which can be considered as an aged form of silica gel. 

Care has to be taken when considering simple concentrations of the permeant since the driving force for diffusion is really the chemical potential gradient. As stated above the maximum flux should occur for a saturated solution of the permeant. However, if supersaturated solutions are applied to the skin, it is possible to obtain enhanced fluxes [27]. This can only be true if the outer skin lipids are capable of sustaining a supersaturated state of the diffusant. Figure 4.4 shows the linear increase in skin permeation with degree of supersaturation, and Fig. 4.5 demonstrates... 

Polymers that can interact with drug molecules especially adsorbed onto crystal surfaces have been widely used to inhibit drug crystallization to maintain supersaturated states for drug delivery systems. Raghavan et observed that methylcellulose... 

The problem of instability of the supersaturated state upon dissolution, which results in a stable form, has been dealt with by addition of a retarding agent. Methyl cellulose was used as a retarding agent in dispersions of indomenhacin and flufenamic acid in... 

A solid phase is precipitated from solution if the chemical potential of the solid phase is less than that of the dissolved component. A solution in which the chemical potential of the solute is the same as that of the corresponding solid phase and is in equilibrium with the solid phase under the given conditions (temperature, pH, and concentration) is called a saturated solution. For crystallization to occur, however, this equilibrium concentration or solubility must be exceeded. This excess concentration or chemical potential is called supersaturation. Supersaturated states may be created by increasing the solute concentration or decreasing the solute solubility using a variety of methods including the following ... 

The concentration threshold above which crystallization is observed at times shorter than the processing time or desired product shelf-life or GI transit time, is determined by the kinetic stability of supersaturated states and is regulated by the nucleation mechanisms and kinetics. Nucleation phenomena are equally important in the control of micrometric properties and in the selective crystallization of a particular polymorph. 

While nucleation phenomena have their origin at the molecular level, they are often described in terms of macroscopic properties owing to the scarcity of experimental techniques that allow for monitoring events at the molecular level. Nucleation rates can be determined by measuring the induction time, rjnd, for nucleation. The induction time represents the time elapsed between the creation of a supersaturated state to the appearance of a solid phase and is represented by... 

Fig. 9 Schematic of SEDS process showing coaxial nozzles. Solvent containing drug is introduced into a stream of SC fluid, using a two or three fluid coaxial nozzle design with mixing chamber. The high velocity and turbulence of the SC fluid stream causes the solvent solution to break up into small droplets. The SC fluid extracts the solvent, acting as the antisolvent for the compound, leading to a supersaturated state and precipitation of drug particles. Control over the size of the particles is achieved by controlling the flow rates of the input streams to the nozzle, and the pressure drop across the nozzle. Typical mean particle sizes are 1-20 pm in a narrow particle size distribution. (From Palakodaty, S., Walker, S., Townend, G., York, P., Humphreys, G. Eur. Pharm. Contractor 2000, (Aug), 60-63.)...

Analogously to 3D nucleation processes, a supersaturated state of an expanded structure is formed first which is characterized by actual Fep () and 9ep(0 values kinetically controlled by Me oiy bulk diffusion and charge transfer. 2D nucleation and growth start from a supersaturated expanded 2D Meads phase and lead to a condensed 2D Meads phase which is characterized, in a first approximation, by time-independent equilibrium values of Tcd(AEf) and cdfAEf). 

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