Critical point gelation

Material properties at a critical point were believed to be independent of the structural details of the materials. Such universality has yet to be confirmed for gelation. In fact, experiments show that the dynamic mechanical properties of a polymer are intimately related to its structural characteristics and forming conditions. A direct relation between structure and relaxation behavior of critical gels is still unknown since their structure has yet evaded detailed investigation. Most structural information relies on extrapolation onto the LST. 

Most remarkable is the immense increase of the polydispersity index x x and of the ratio x/x which both increase with x This distribution follows asymptotically a power law of wfx)°cx with r 2.5, when the critical point of gelation is approached. Figure 20 shows some of these distributions for various a, or different x ... 

Another development underway is to try to locate on the above mentioned sigmoid curves the critical point (t. ). where gelation occurs. Rheological experiments and structural determinations will be used to calculate some critical quantities as a critical fiber density to gelify the system. 

In general, the critical point of gelation is defined by Pw —> oo7), which yields with Eq. (C.45) the very compact relationship105-10 ... 

Phase diagram asymmetry can be evaluated by (i) the ratio of the biopolymer concentrations at a critical point, (ii) the angle made by the tie-lines with the concentration axis of one of the biopolymers and (iii) the length of the segment of a binodal curve between the critical point and the phase separation threshold. Association of macromolecules usually changes both their excluded volume and the affinity for the solvent water. This results in nonparallel tie-lines on the phase diagram. Normally, the tie-lines can be nonparallel since an increase in concentration of biopolymers is usually accompanied by their self-association. Equilibrium between the phases is not achievable when phase separation is accompanied by gelation. 

Whereas the calculation of the time to gelation is relatively simple, the calculation of the time to vitrification (tyu) is not so elementary. The critical point is to obtain a relationship between T, and the extent of conversion at T, (Pvu)- Once the conversion at Tg is known, then the time to vitrification can be calculated from the kinetics of the reaction. Two approaches have been examined one calculates tyu based on a relationship between T, and Pyj, in conjunction with experimental values of Pvit the other approach formulates the Tg vs. pyj, relationship from equations in the literature relating Tg to molecular weight and molecular weight to extent of reaction... 

Theoretical and experimental treatments of gels go hand-in-hand. The former are covered first because they will help us understand gel point and other concepts. Two main theories have been used to interpret results of experimental studies on gels the classical theory based on branching models developed developed by Floiy and Stockmayer, and the percolation model credited to de Gennes. Gelation theories predict a critical point at which an infinite cluster first appears. As with other critical points, the sol-gel transition can be in general characterized in terms of a set of generally applicable (universal) critical exponents. 

The most characteristic aspect of the critical point problem is that the three phenomena, cyclization, excluded volume effects, and dimension, intimately interacting with each other, spontaneously appear at the critical point. At the beginning, it was thought that cyclization would make little contribution to such an important question that has remained unsolved for so long in physical science. The author s early conjecture was wrong. As we have seen in the text, cyclization plays a central role in the location of the critical point. For the percolation model, dimension is almost equivalent to cyclization (Sects. 4 and 5) even excluded volume effects seem to manifest themselves as an element of cyclization (Sects. 6 and 7), while dimensionality is in close conjunction with excluded volume effects (Sect. 7). In real gelations, the three effects are deeply connected with one another. 

E. M. Flanigen 1) We can only attribute differences in the results of Barrer and Marshall and those reported here to variation in the method of preparing the gel network, and in some cases perhaps to different crystallization temperatures. We believe the critical point in achieving framework substitution is incorporation of all of the phosphate in the insoluble gel network, rather than in a soluble phosphate form. This is controlled by the exact method of coprecipitation and gelation. 

The gelation plane of the polyurethane is illustrated in Fig. 6.4 see G2-MMA-PMMA. For completeness, the gelation plane Gj of the PMMA from Fig. 6.3 is also shown. The gelation plane G2 occurred after about 67 % conversion of the PU. The intersection of the two planes, G1-G2, illustrates the line of simultaneous gelation of the two polymers. Reactions passing to one side or the other of this line will have one polymer or the other gelling first. It must be noted that the line G1-G2 also intersects the line A-B of Fig. 6.3, not shown. The intersection of these two curves expresses the presence of a triple critical point, where both polymers simultaneously gel and phase separate. While this triple critical point represents the ideal SIN synthesis condition, it would not, in general, produce the best physical or mechanical properties. 

Gelation links macromolecular chains to result in the formation of a branched polymer structure with a solubility that depends on the chemical nature of the starting materials (Lan et al., 2015 Wu and Morbidelli, 2014). The mixture containing water and the soluble branched polymer is called a sol. The solubility of the polymer decreases with increasing dimension of the structure. This infinite polymer is called the gel or network, and it is composed of several finite branched polymers (Li et al., 2012 Cravotto and Cintas, 2009). The transition from a system with finite branched polymer to inhnite molecules is called sol—gel transition or gelation, and the critical point where gel first appears is called the gel point. The gelation process is depicted in Fig. 10.6. 

For the ease of demonstration how the branching reaction in a step-growth polymerization reaction of A-A-I-B-B-I-Ay molecules proceeds, Flory has used a simple picture to sketch the branching procedure which at some critical point finally leads to gelation [13]... 

A pluronic gel was prepared by dissolving solid Pluronic F127 (Sigma-Aldrich, Germany) in cooled (4°C) water in concentration 20 wt. %. If necessary, the solid-phase modifier was added (silica gel or hydrophobized silica gel) in the required concentration. The resulting solution undergoes a transition at a critical point when heated to 30°C, accompanied by gelation. 

As discussed briefly in the previous section, gelation can generally be discussed within the framework of critical phenomena [7] by having the gel point and critical point correspond. Stauffer applied the percolation theory often used for the general theory of critical phenomena to the crosslinking reaction of polymers [8, 9],... 

Critical angle method for refractive index, 395-6 Critical chain length, 176 determination, 177-9 Critical index, 127, 128 Critical point, 76 drying method, 229 Critical relaxation, 90-2 Crosslink density and relaxation time, 373 Crosslink formation, 5-7 Crosslink points, schematic diagram, 8 Crosslink points per pritnaiy polymer at gelation, 34... 

Gelation is an important phenomenon. During polymerization, there exists a critical point called gd point or gdation point or onset of gelation. In production of gd materials, it is important to cross this point, otherwise the produced materials are still soluble. However, if only branching is wanted, the polymerization system should be stopped bdore the gel point. Knowledge of the gel point is therdore critical. 

Figure 14. Scanning electron micrographs of critical-point dried gels of UHMW PE, obtained from 2 % solutions in decalin. A) quiescent conditions B) agitated solutions (lOOOX). Note the lamellar nature of the polyethylene crystals in A, and the fibrillar crystals reminiscent of the flow that occurred during agitation prior to gelation, in B.

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