Network collapse

In this section, we will consider the swelling of the network in the solution which is a mixture of two components. We will limit our consideration to the case of purely polyelectrolyte networks (ct = CTj) because in this case, the phenomenon of network collapse is most pronounced and it is this case that is usually studied experimentally. 

When Co grows, the network volume slightly decreases and the concentration of surfactant q within the network increases. When cjj, exceeds a critical concentration of micelle formation (at this point cq = c, see Figs.14,15), the network collapses because the surfactant molecules aggregated in micelles cease to impose osmotic pressure which causes additional expansion of the network. At relatively small values of the ratio Vf/V, the collapse is continuous (Figs. 14, 15), so that the number of surfactant molecules in micelles increases from zero starting at the concentration c. However, when the ratio Vf/V is sufficiently large, a discrete first-order phase transition takes place. 

If bulk recombination is important in the depletion layer, then we cannot separate hole and electron flows in the above manner and the Zr, / scp network collapses to a frequency-independent resistor I D, as shown in Fig. 100. In this figure IFis a Warburg impedance for the hole current. This is too complex, as it stands, for analysis and a simpler case can be derived if Css is dominant and the frequency range is such that W can also be neglected. Under these circumstances, I D, Raan and 7 ssp further collapse to a simple resistor Rr, leading to the equivalent circuit shown in Fig. 101, which has been applied to p-GaAs under illumination and n-GaAs under hole injection. 

These concepts have been routinely employed to determine psds of genuine porous media [88]. A difficulty arises when they are applied to PEMs, since these membranes do not possess an intrinsic porosity. Instead, pores in them are created by the water of hydration, whereas in the dry state the pore network collapses. Gas permeability of PEM is very small. Thus, only with a certain degree of tolerance can one speak about three-phase capillary equilibria, implied in the Laplace equation. It is rather a semiempirical phenomenology, that allows one to relate the liquid pressure (the driving force of the hydraulic permeation)... 

As a consequence, there is a network collapse and better volume utilization. Therefore, rapid reversals occur in the variation of molar volume, refractive indices, Tg, thermal expansivity etc., as a function of alkali composition. All of these variations are directly or indirectly related to energy density and the observed variations are often referred as borate anomaly. An example of the variation of some of these properties is shown in Figure 12.12. 

Figure 7. Partially emptied pores during drying cause uneven capillary pressures and uneven stresses which result in fracture and network collapse.

Fig. 5 (a) Temperature-dependent CW EPR spectra of TEMPO in an aqueous solution with PNIPAAM-based hydrogels and (b) comparison of the fraction of spin probes in hydrophihc enviromnent a. as found from combining spectral simulations of both species (according to Scombined = a Sa + (1 Wa)>Sb) and a macroscopic (APM-based) observation of hydrogel collapse. (c) Model of network collapse as seen by EPR spin probes individual pockets continuously collapse before the macroscopic collapse happens... 

These findings have led to the conclusion that the polymer network collapse is a continuous, nano-inhomogeneous process, in which individual polymeric pockets are in a collapsed state even at temperatures significantly below the LCST and that the macroscopic collapse takes place only when a certain number and/or volume of collapsed pockets is reached. 

This is exactly the phenomenon called the collapse of polymer networks. It was discovered by T. Tanaka (1946-2000) and his colleagues at the Massachusetts Institute of Technology (MIT) in 1978. They used networks of polyacrylamide diluted in a mixture of acetone and water. In these experiments, the temperature was not varied. To make the solvent worse, they just poured some extra acetone into the solution. (This worked because acetone, in contrast to water, is a bad solvent for polyacrylamide.) Figure C9.7 gives an idea of what was found. It sketches how the size of the network depends on the acetone concentration. You can see that if you dump 42% of acetone, the network collapses suddenly. Its volume drops by a factor of nearly 20. 

The collapse of polymer networks has recently attracted a lot of attention. This boom is partially due to some important applications, which all stem from the fact that you need only slightly change the quality of the solvent to make the network collapse rapidly. It is especially useful that the collapse is very sensitive to the presence of charged monomers and counterions in the solution. Thus collapsing networks can be adapt to detect small ion impurities in a solution, as well as to clear the impurities away. Besides all this, the collapse of networks can also serve as a good model for some other processes in biology (e.g., in the vitreous body in the eye). 

The active micro-reactors described above cannot be recycled because the SiH moieties cannot be renewed. Recyelable micro-networks may be realized in the form of passive miero-reactors which do not actively take part in the reaction but merely provide the confined reaction space. For this purpose hollow micro-networks are synthesized first, a micro-emulsion of linear poly(dimethyl-siloxane) (PDMS) of low molar mass (M = 2000-3000 g/mol) is prepared and the endgroups are deactivated by reaction with methoxytrimethylsilane. Subsequent addition of trimethoxymethyl-silane leads to core-shell particles with the core formed by linear PDMS surrounded by a crosslinked network shell. Due to the extremely small mesh size of the outer network shell the PDMS ehains become topologically trapped and do not diffuse out of the micro-network over periods of several months (Fig. 3). However, if the mesh size of the outer shell is increased by condensation of trimethoxymethylsilane and dimethoxydimethylsilane the linear PDMS chains readily diffuse out of the network core and are removed by ultrafiltration. The remaining empty or hollow micro-network collapses upon drying (Fig. 4). So far, shape-persistent, hollow particles are prepared of approximately 20 nm radius, which may be viewed as structures similar to crosslinked vesicles. At this stage the reactants cannot be concentrated within the micro-network in respect to the continuous phase. 

The sol-gel transition can be induced by various physicochemical parameters, such as the temperature, the concentration in salt in the solution and the pH. Poly(N-isopropylacrylamide) (PNIPAm) exhibits a thermosensitive transition. Below 31 °C, the polymer is hydrophilic and swollen by water. Above this temperature, the polymer is hydrophobic and the network collapses, as shown in Figure 2.12. Such temperature-dependent behaviour can be of great interest. 

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