Sol phase

For comparison, a telechelic sulfonated polystyrene with a functionality f = 1.95 was prepared. In cyclohexane the material forms a gel independent of the concentration. At high concentrations the sample swells. When lower concentrations were prepared, separation to a gel and sol phase was observed. Thus, dilution in cyclohexane does not result in dissolution of the gel even at elevated temperatures. Given the high equilibrium constant determined for the association of the mono functional sample, the amount of polymer in the sol phase can be neglected. Hence, the volume fraction of polymer in the gel phase can be calculated from the volume ratio of the sol and gel phases and the total polymer concentration. The plot in Figure 9 shows that the polymer volume fraction in the gel is constant over a wide range of concentrations. 

Al fundamental question about the interpretation of acidic aerosol data is whether researchers can characterize past and current atmospheric concentrations and distributions (spatial and temporal) with sufficient accuracy for studies of their effects on ecosystems and human health. Part of the answer to this question can be provided by a review of the methods that have been used to measure the strong acid content of aerosol particles collected from the atmosphere. This chapter serves as such a review, and, in evaluating analytical procedures, it specifically assesses the ability of each procedure to overcome sampling artifacts, to distinguish between strong and weak acids, to properly partition strong acidity between gas-phase and aero-sol-phase species, and to quantitate strong acidity at the levels at which it is found in the ambient atmosphere. 

Fig. 16. Scheme for the calculation of the rate constant ks of polymer transfer from the sol into the gel, according to two models for the gel surface (full line model (a) dashed model (b) with a transition zone between the actual gel and sol phases)... 

Cross-linked hydrogels can be formed which contain affinity cross-links between polymer-supported hgands and receptors [46]. Such gels can be based only on these biophysical interactions as described by Taylor et al. [28,29]. In these systems, displacement of affinity cross-links by soluble competitors ultimately leads to a gel/sol transition (Figure 16.4) requiring that the responsive phase be constrained between two diffusive membranes to prevent leakage while in the sol phase (Figure 16.5). 

In return for introducing the basic assumptions (i) to (iii), the classical theory thus furnished the beautiful mathematical formalisms for (1) the gel point, (2) the molecular weight distribution in sol phase, (3) the gel fraction, and (4) the molecular profile as mentioned above. At first sight, the classical theory may ap-... 

In this section, we derive ring distribution functions in the sol phase of real branching reactions to show how this result can be applied to the estimation of gel points in real systems. Although we push forward our argument taking a polycondensation as an example, the basic concept is, of course, applicable to all types of polymerizations as well. 

Second, the failure of the D ring) term should arise from the high dimension expansion based on the premise of Eq. (110). The result of Fig. 24 shows that the expansion works well for d>8. It has been well established that lattice branched clusters have the marginal dimensionality, dc = 8, in the sol phase (bond animals) above which the ideal behavior applies [33]. Now, the critical point shift results from ring formation which is a phenomenon in the sol phase up to the gel point, and the cyclization frequency is influenced by the excluded volume effects. The gel point, therefore, must shift in response to the behavior of the sol clusters. This leads us to a conjecture that a mathematical singularity may arise at dc = 8 on the Dc vs. d curve, in parallel with the phase transition from the excluded volume clusters to the ideal ones. If this is the case, it follows that the high dimension expansion must fail below eight dimensions. To date, there is no experimental evidence that shows the existence of the discontinuity on the Dc vs. d curve, but it is likely that Dc is not a monotonous function of d the result of Fig. 

Obaidat, A.A. Park, K. Characterization of glucose dependent gel-sol phase transition of the polymeric glucose-concanavalin A hydrogel system. Pharm. Res. 1996, 13, 989-995. 

Many important chemical reactions take place in the aqueous component of the atmospheric aerosol or in fog droplets. An example is the solution-phase oxidation of SO2 to SO. Such reactions may drive the dilTusioiial transport of reactants from the gas to the particles followed by absorption and chemical reaction. If the chemical reactions are slow compared with the gas- and aero.sol-phase transport rates, the dissolved reactive species will be nearly in equilibrium between the gas and particles. 

Gas-phase molecules in the atmosphere can be converted to the aero.sol phase by homogeneous (gas phase) or heterogeneous aerojtol phase) reactions. Both mechanisms may be operative over different particle size ranges. Information on the dominant growth mechanisms can be inferred by an analysis of aerosol dynamics in power plant plumes (McMurry et al., 1981 Wilson and McMurry. 1981). When homogeneous gas-phase reactions are controlling, there are two possible pathways for the reaction products to enter the size distribution function ... 

Finally, the so called Sol-gel processes should be mentioned in which porosity, pore size, and polarity of products manufactured by this method can be controlled. Processing begins with a solution (= sol) which becomes a gel. The solution can be prepared from either inorganic salts or organic compounds. It is then hydrolized to a sol or condensed to form a gel. The process can be terminated in the sol-phase, where a dispersion of colloidal particles in a liquid exists, or continued to the gel-phase, the development of a three-dimensional, linked solid structure in which the pores are filled with a liquid. In the wet gel-phase, the pores are interconnected. 

SnOa doped with Tb " was prepared by the sol-gel technique [7]. In the synthesis of undoped and doped Sn02 sol-phases SnCl2 2H20 and TbCh were used as precursors and absolute ethanol as a solvent. The concentration of Tb " is estimated to be 3% in relation with the Sn content in the sol. 

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