Frozen system

I hi5 expression can be tidied up by introducing three operators that represent the contribu-tio.is to the energy of the spin orbital Xi in the frozen system ... 

R. A. Marcus From the peak related to the inhomogeneous contribution, how large was the range of inhomogeneity in the AG changes, in absolute amount, in the system treated by Prof. Fleming Did this result refer to a highly viscous (e.g., frozen ) system ... 

That the above sugar epoxidea undergo cleavago in opposite directions is consistent with the principle of diaxisl product control in conform tion Uy frozen systems.1801... 

In addition to these technical problems, the complexity inherent to physical properties of gels is, as exemplified above, that they depend very sensitively on the preparation condition. This is because, in a formal language, a gel is a frozen system and we need two sets of statistical information, the preparative ensemble and the final ensemble , to understand its equilibrium properties [29]. Hence, a gel is by nature more complex than the usual equilibrium systems. We should clarify the dependence of the properties of gels on preparation conditions, and also on structural defects of the network before going into precise investigations such as critical phenomena associated with the phase transition. 

However, unlike Davy s experiments, Priestley s temperature (17°F) of the gas mixture was below the ice point, so there is no unequivocal evidence that the frozen system was hydrate. There is also no record of validation experiments by Priestley consequently, Davy s independent discovery of chlorine hydrate is generally credited as the first observance. 

Nail, S. L., Schwegmani, J. J., Kamp, V. analytical tools for characterization of frozen systems in the development of freeze-dried pharmaceuticals. Amer Pharm... 

The best explanation of the good results for peptide syntheses in ice-water mixtures are based on the freeze-concentration-model, which just provides for a volume-reducing function for the ice while the liquid aqueous part is still the only relevant phase for the reaction. All observed enhancements of reaction rate would then have to be attributed to an increase in effective concentration. H-NMR relaxation time measurements have been used to determine the amount of unfrozen water in partially frozen systems, thus quantifying the extent of the freeze-concentration effect (Ullmann, 1997). Comparative studies in ice and at room temperature verify the importance of freeze-concentration which, however, is not sufficient for a complete understanding of the observed effects. 

As ice crystals grow in the freezing system, the solutes are concentrated. In addition to increased ionic strength effects, the rates of some chemical reactions—particularly second order reactions—may be accelerated by freezing through this freeze-concentration effect. Examples include reduction of potassium ferricyanide by potassium cyanide (2), oxidation of ascorbic acid (3), and polypeptide synthesis (4). Kinetics of reactions in frozen systems has been reviewed by Pincock and Kiovsky (5). 

In addition to characterizing frozen systems intended to be freeze dried, it is important to characterize the freeze-dried product. This includes determination of the physical state of the dried product that is, crystalline, partially crystalline, or amorphous. It may also include identification of the polymorph of a crystallizing component which exhibits polymorphism and determination of whether the crystal form observed is affected by changes in formulation and processing conditions. For amorphous systems, the glass transition temperature of the amorphous solid, as well as the extent to which Ts changes with residual moisture, may be a critical attribute of the product with regard to both physical and chemical stability. 

Thermal transitions which are commonly observed in frozen systems are illustrated in Figure 7 where, for the sake of this discussion, a deflection upward indicates an endothermic transition. The glass transition is a shift in the baseline toward higher heat capacity. Crystallization during the DSC experiment is observed as an exothermic event, and eutectic melting is an endothermic transition which preceeds the melting of ice. 

Glass transitions, both in frozen systems and in freeze-dried solids, can be difficult to detect. This may be caused by the small heat capacity change associated with the glass transition, a broad glass transition region, or both. Interpretation is made more uncertain by baseline drift or other noise. In addition, other thermal events at temperatures close to the glass transition, such as enthalpy recovery or crystallization, may disguise the heat capacity... 

Larsen SS. Studies on stability of drugs in frozen systems. VI. The effect of freezing upon pH for buffered aqueous solutions. Arch Pharm Chem Sci Ed 1973 1 433-445. 

If we allow the molecules to rotate during the lifetime of excitation r the emission axis no longer bears the fixed relation with the electric vector of the incident beam and the degree of polarization is diminished. The extent of diminution, i.e., the depolarization, is therefore determined by tJq, where q is the rotational relaxation time of the whole fluorescing molecule. The degree of polarization p compared with that for the frozen system p0 can then be represented in the form... 

Cause of denaturation. Many hypotheses have been proposed to explain the denaturation of muscle proteins (9-17). These hypotheses include 1) the effects of inorganic salts concentrated into the liquid phase of the frozen system 2) water-activity relations 3) reactions with lipids 4) reaction with formaldehyde derived from trimethyl amine (in fish) 5) auto-oxidation ... 

For both linear and star polymers, the above-described theories assume the motion of a single molecule in a frozen system. In polymers melts, it has been shown, essentially from the study of binary blends, that a self-consistent treatment of the relaxation is required. This leads to the concepts of "constraint release" whereby a loss of segmental orientation is permitted by the motion of surrounding species. Retraction (for linear and star polymers) as well as reptation may induce constraint release [16,17,18]. In the homopol5mier case, the main effect is to decrease the relaxation times by roughly a factor of 1.5 (xb) or 2 (xq). In the case of star polymers, the factor v is also decreased [15]. These effects are extensively discussed in other chapters of this book especially for binary mixtures. In our work, we have assumed that their influence would be of second order compared to the relaxation processes themselves. However, they may contribute to an unexpected relaxation of parts of macromolecules which are assumed not to be reached by relaxation motions (central parts of linear chains or branch point in star polymers). 

Figure 14 In pure glycerol submitted to a strong gamma irradiation (30 kGy) in the frozen state (-196°C) we can see that, during rewarming, the electric rigidity (impedance) starts to drop almost at the same time as the system undergoes vitreous transformation (Tg = -81 °C). The subsequent rapid fall in Z sin tp also coincides with the thermoluminescence peak (-64°C), which is a clear indication that a major transition is taking place within the frozen system.

When the formulated solution contains essentially saline or organic solutes that crystallize easily, the interstitial phase will crystallize out abruptly as an eutectic or a mixture of eutectics. The crystallization results in an immediate hardening of the frozen system, which becomes fully rigid. At this point, the system has reached its maximum temperature for complete... 

When the formulated solution predominantly contains polyols, sugars, or polymers, the interstitial phase does not usually crystallize out upon cooling but increases progressively in viscosity as a glass-like system. In the case where the interstitial phase has effectively the structure of a glass, the frozen system becomes fully rigid once the glass transition temperature (Fg) is reached. In contrast, some amorphous systems may show no such definite transition, but they eventually become very stiff at low temperature, as shown by electrical resistance studies. 

Although the thermodynamic requirement of freezing below the solidification temperature is compulsory, this condition is not always sufficient to guarantee an easy and satisfactory lyophilization of the product. This is because the structure of the frozen system is affected not only by thermodynamic factors but by kinetic ones. 

Most of the frozen systems demonstrate an intermediate behavior, that is, moderately complicated intradiffusion. A decrease in solution... 

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