Gel phase diffusion

Prediction of Gel Phase Diffusivity and Performance of Responsive Membranes.486... 

The ability of a solute to diffuse within a hydrogel has been described in terms of the probability of a solute of characteristic size (r, defined as the radius of a sphere of equal volume to the solute molecule) passing through an opening equal to the mesh size of the gel (. This probability is taken to be a linear function of the ratio of r/. Therefore, the gel phase diffusivity of a solute can be related to its liquid phase diffusivity, molecular volume, and gel mesh size [70,71]. 

Equation 16.15 shows that, as expected, the gel phase diffusivity approaches zero as the solute radius approaches the mesh size. In a responsive gel, as sweUing increases in response to environmental changes gel phase diffusivity increases with increasing mesh size. Figure 16.16 shows the effect of competitor concentration on predicted gel phase diffusivity assuming a solute radius of 1.5 nm. Using this example and a dextran polymer gel, it is not possible to achieve a cross-link density sufficient to give a predicted mesh size sufficiently small to prevent gel phase diffusivity. However, as Equation 16.12 does not consider the steric effects of the immobilized receptor experimentally determined gel phase diffiisivities are likely to be lower. 

FIGURE 16.16 Effect of competitor concentration on gel phase diffusivity. Arrow denotes increasing covalent cross-hnk density from... 

If supported macroreticular ion exchangers are used as catalysts, the intrapartide transport processes can be decomposed into gel phase diffusion and macropore diffusion [31]. For a combination of the two mechanisms special catalyst models were proposed [32]. 

To summarize, there is a sizable and self-consistent body of data indicating that rotational and translational mobility of molecules inside swollen gel-type CFPs are interrelated and controlled mainly by viscosity. Accordingly, T, self-diffusion and diffusion coefficients bear the same information (at least for comparative purposes) concerning diffusion rates within swollen gel phases. However, the measurement of r is by far the most simple (it requires only the collection of a single spectrum). For this reason, only r values have been used so far in the interpretation of diffusion phenomena in swollen heterogeneous metal catalysts supported on CFPs [81,82]. 

The reptation model for polymer diffusion would predict that the thickness of the gel phase reflects the dynamics of disentanglement. The important factors here are chain length, solvent quality and temperature since they affect the dimensions of the polymer coils in the gel phase. The precursor phase, on the other hand, depends upon solvency and temperature only through the osmotic force it can generate in the system and the viscoelastic response of the system in the region of the front. These factors should be independent of the PMMA molecular weight. 

Tne molar concentration of pure MEK is ca. 11.2 M. One might question why the concentration of MEK does not reach 11.2 M on the SCP. This is mostly due to the slow process of untangling PMMA chains. For the concentration of MEK to reach 11.2 M, the swollen polymer gel phase has to be untangled and removed from the vicinity of the quartz substrate. This is driven by the entropic force which works rather slowly in the absence of high solvent flow. For example, Mills et al. (22) report, for TCE diffusing into PMMA film, that the SCP of TCE stabilizes at a mole fraction of less than 0.2. By comparison, our results of [MEK] = 3.2 M corresponds to a mole fraction of ca. 0.3. This, again, reflects the better solubility of MEK in PMMA relative to TCE (6 = 9.6). 

The vast majority of biological membranes are in the liquid-crystalline phase. There are many experimental studies on model bilayer phase behavior [3]. Briefly, at low temperatures lipid bilayers form a gel phase, characterized by high order and rigidity and slow lateral diffusion. There is a main phase transition, as the temperature is increased, to the liquid-crystalline phase. The liquid-crystalline phase has more fluidity and fast lateral diffusion. 

A detailed study of the structure of the aggregates of the ionic surfactants in polyelectrolyte networks was presented in Refs. [66,68]. The dynamics of the changes in the microenvironment of the fluorescent probe, pyrene, in slightly crosslinked networks of poly(diallyldimethylammonium bromide) (PDADMAB) during diffusion of sodium dodecyl sulfate (SDS) in the gel phase has been investigated by means of fluorescence spectroscopy. In Ref. [66], an analogous investigation was reported for complexes formal by the sodium salt of PMAA with cetyltrimethylammonium bromide (CTAB). 

With ion exchangers as catalysts for olefin hydration, special attention was paid to transport problems within the resin particles and to their effects on the reaction kinetics. In all cases, the rate was found to be of the first order with respect to the olefin. The role of water is more complicated but it is supposed that it is absorbed by the resin maintaining it in a swollen state the olefin must diffuse through the water or gel phase to a catalytic site where it may react. The quantitative interpretation depends on whether the reaction is carried out in a vapour system, liquid-vapour system or two-phase liquid system. In the vapour system [284, 285], the amount of water sorbed by the resin depends on the H20 partial pressure it was found at 125—170°C and 1.1—5.1 bar that 2-methyl-propene hydration rate is directly proportional to the amount of sorbed water... 

In zeolite systems chosen for study diffusion in the liquid phase and crystal growth on the crystal-liquid interface were the two major steps in converting gels to mordenite, zeolites A and X, the former being the rate-determining step for mordenite and the latter for zeolite X crystallization. In the mordenite system the effect of seed crystals, with surface areas per unit mass different by an order of magnitude, demonstrated the mechanism of nucleation on the seed crystal surfaces. The data support the hypothesis that crystal growth of the zeolite occurs from the solution phase rather than in the gel phase. 

When immobilizing biocatalysts within polymer gels using physical entrapment methods, we may take advantage of the great resistance to the diffusion of macromolecular substances due to the gel porosity. However, this limited diffusion within the gel phase also causes a reduced mass transfer rate for low... 

Francois and Varoqui (34) measured diffusion rates of Cs+ in the hexagonal liquid crystalline phases of the water-cesium myristate and water-cesium laurate systems. In each case diffusivity was obtained as a function of temperature for a given liquid crystal composition. Values of 1-2 X 10"5 cm2/sec were reported for 60°-80°C. Diffusivity was about an order of magnitude lower in the gel phase of the cesium myristate system. 

DNA arranges into rectangular superlattice in the low-temperature gel phase of saturated cationic lipids [83, 84]. This is evidenced by two or three diffuse reflections in addition to the set of lamellar reflections these are attributed to DNA ordering both within the layer and across the lipid bilayers, from one DNA layer to another. These reflections index on a centered rectangular lattice. Noteworthy, DNA does not affect the gel-liquid crystalline transition temperatures of the lipoplexes [16, 19, 84]. This transition is associated with loss of the DNA inter-lamellar correlation. 

Hard-sphere or cylinder models (Avena et al., 1999 Benedetti et al., 1996 Carballeira et al., 1999 De Wit et al., 1993), permeable Donnan gel phases (Ephraim et al., 1986 Marinsky and Ephraim, 1986), and branched (Klein Wolterink et al., 1999) or linear (Gosh and Schnitzer, 1980) polyelectrolyte models were proposed for NOM. Here the various models must be differentiated in detail—that is, impermeable hard spheres, semipermeable spherical colloids (Marinsky and Ephraim, 1986 Kinniburgh et al., 1996), or fully permeable electrolytes. The latest new model applied to NOM (Duval et al., 2005) incorporates an electrokinetic component that allows a soft particle to include a hard (impermeable) core and a permeable diffuse polyelectrolyte layer. This model is the most appropriate for humic substances. 

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