Gel-point data

Fig. 2. Relaxation modulus G(t) of a set of polydimethylsiloxane samples with increasing extent of crosslinking plotted against time of crosslinking. The linear PDMS chains (Mn 10 000, polydis-persity index 2) were endlinked with a four-functional silane crosslinker catalyzed by a platinum compound. Samples with different extent of reaction were prepared by poisoning the reaction at different times. The actual extent of reaction was not determined. Two of the samples are clearly before the gel point (LST) and two beyond. The third sample is very close to the gel point. Data of Chambon and Winter [5] evaluated by Baumgartel and Winter [8]...

The paper first considers the factors affecting intramolecular reaction, the importance of intramolecular reaction in non-linear random polymerisations, and the effects of intramolecular reaction on the gel point. The correlation of gel points through approximate theories of gelation is discussed, and reference is made to the determination of effective functionalities from gel-point data. Results are then presented showing that a close correlation exists between the amount of pre-gel intramolecular reaction that has occurred and the shear modulus of the network formed at complete reaction. Similarly, the Tg of a network is shown to be related to amount of pre-gel intramolecular reaction. In addition, materials formed from bulk reaction systems are compared to illustrate the inherent influences of molar masses, functionalities and chain structures of reactants on network properties. Finally, the non-Gaussian behaviour of networks in compression is discussed. 

Figure 5. Analysis (21) according to Eq. 7 of gel-point data (22) from reactions of diacid chlorides (adipoyl and sebacoyl chlorides) and POP triols (LHT240, LHT112 (oxypropylated 1,2,6-hexane triols), and LG56 (oxypropylated glycerol)) in bulk and in diglyme solution at 60°C, with cext = cao...

Figure 6. Analysis (29) according to Eq. 7 of gel-point data (25, 26, 28) from reactions of HDI and diphenylmethane diisocyanate (MDl) with POP trilos (LHT-240, LHTII2) and tetrols (OPPE-NHI, OPPE-NH2-oxypropylated pentaerythri-tols) in bulk and in nitrobenzene solution at 80°C, with cMt = cao + ecosystems 1 and 2, HDI and POP triols 3, MDl and POP triol 4 and 5, HDI and POP tetrols. Key 1, HDI and LHT240, is 33 2, HDI and LHTII2, v is 61 3, MDl and LHT240, v is 30 4, HDI and OPPE-NHI, v is 29 S, HDI and OPPE-NH2, v is 33.

Methyl methacrylate has been polymerized with small amounts of ethylene glycol dimethacrylate (0.5, 1.0, and 2.0 volume Z) via a radical chain addition mechanism. Conversion, viscosity, and gel point data are presented. Branching theory based on the recursive nature of the branching process is developed to calculate M, the weight average molecular weight of the polymer, and the... 

This paper has presented the first gel-point data from PDMS-forming polymerisations. It is shown that A-R-S theory holds reasonably satisfactorily over wide ranges of r, dilution and molar masses of reactants. 

A recent series of papers [18, 24, 32-34] substantially clears up the three-dimensional polymerization mechanism in the AAm-MBAA system. Direct observation of the various types of acrylamide group consumption using NMR technique, analysis of conversion at the gel-point, and correlation of the elastic modulus with swelling indicate a considerable deviation of the system from the ideal model and a low efficiency of MBAA as a crosslinker. Most of these experimental data, however, refer to the range of heterogeneous hydrogels where swelling is not more than 80 ml ml-1 [24]. 

With increasing distance from the gel point, the simplicity of the critical state will be lost gradually. However, there is a region near the gel point in which the spectrum still is very closely related to the spectrum at the gel point itself, H(A,pc). The most important difference is the finite longest relaxation time which cuts off the spectrum. Specific cut-off functions have been proposed by Martin et al. [13] for the spectrum and by Martin et al. [13], Friedrich et al. [14], and Adolf and Martin [15] for the relaxation function G(t,pc). Sufficiently close to the gel point, p — pc <4 1, the specific cut-off function of the spectrum is of minor importance. The problem becomes interesting further away from the gel point. More experimental data are needed for testing these relations. 

Fig. 14. Loss tangent of several stopped samples of vulcanizing polybutadiene (Mw = 18000) [31]. At the gel point, tan 3 is frequency independent (flat curve in the middle). The relaxation exponent n can be easily evaluated from the data (tan 3 = 1 yields n = 0.5)...

Fig. 20. Dynamic moduli, G (open symbols) and G" (filled symbols), for five partially crosslinked PDMS samples at different extents of reactions (same data as Fig. 2). Gr curves downward for the liquid and curves to the left for the solid. The straight lines belong to the sample which is very close to the gel point, t — tc is given in minutes...

The relaxation modulus evolves gradually during gelation. A set of data along the lines of Fig. 2 gives a good estimate of where the gel point occurs. The problem with it is that one cannot decide very well when exactly G(t) has straightened out into a power law. 

Dynamic mechanical data near the gel point allow easy determination of the parameters of the critical gel, Eq. 1-1. Tan 8, as shown in Fig. 26, gives the relaxation exponent n... 

Recently, Ahmad and Stepto(21) compared existing gel-point expressions(6,19,20) and illustrated shortcomings in them and in the way they were applied to gelation data. A new expression for the gel-point in RA2 + RBf random polymerisations was derived, namely,... 

Gel Point and Shear Modulus. Trifunctional and tetrafunc-tional polyurethane(25,26,28) and trifunctional polyester net-works (32) have been studied. The gelation data for the reaction systems forming the polyurethane networks were those discussed with reference to Figure 6 and Table II. 

Gel Point and Tg. The variation of Tg with ac was investigated (18, 2J5,29) for dry networks formed from system 3 of Figure 9 at different initial dilutions of reaction mixtures. Measurements were carried out at 1Hz using a torsion pendulum(26). The results were shown in Figure 10. The two limiting values of Tg for this system correspond to networks with Me = > and Mc = Me-Thus, the horizontal broken line gives the minimum Tg, that of a linear MDI/POP polymer having a repeat unit of molar mass equal to Mq, and the maximum value of Tg at ac = 0.5 was obtained by extrapolation of (1/MC, Tg) data to 1/M . 

We also correlated the elastic modulus (G ) with the extent of reaction by combining data obtained from rheology and FTIR. We found that the elastic modulus did not show an appreciable increase until a short time before the gel point of the sample had been reached. However, in the vicinity of the gel point and beyond, the elastic modulus increased significantly with conversion. Information relating modulus to extent of reaction, which plays a critical role in the application of these systems, can therefore be readily obtained using our approach. 

An example of the possibility that network scission experiments may be subject to topological interpretation is suggested by the results reported by Hookway and Shelton (2). Of particular interest is the degelation point where the network dissolves. (Degelation implies transition through a gel point that may or may not be related structurally to the usual non-gel to gel transition observed in the corresponding network synthesis. The data (ref. 2, Fig. 3) show that hydrogen peroxide causes the release of about 0.5 mole... 

It is shown that model, end-linked networks cannot be perfect networks. Simply from the mechanism of formation, post-gel intramolecular reaction must occur and some of this leads to the formation of inelastic loops. Data on the small-strain, shear moduli of trifunctional and tetrafunctional polyurethane networks from polyols of various molar masses, and the extents of reaction at gelation occurring during their formation are considered in more detail than hitherto. The networks, prepared in bulk and at various dilutions in solvent, show extents of reaction at gelation which indicate pre-gel intramolecular reaction and small-strain moduli which are lower than those expected for perfect network structures. From the systematic variations of moduli and gel points with dilution of preparation, it is deduced that the networks follow affine behaviour at small strains and that even in the limit of no pre-gel intramolecular reaction, the occurrence of post-gel intramolecular reaction means that network defects still occur. In addition, from the variation of defects with polyol molar mass it is demonstrated that defects will still persist in the limit of infinite molar mass. In this limit, theoretical arguments are used to define the minimal significant structures which must be considered for the definition of the properties and structures of real networks. 

From Equation 1.4, the complex viscosity at 57 percent conversion of the caprolactam monomer, which may be defined as solidification or gel point, is 100Pas (1000 Poise). Combining the information on conversion at the gel point with the data presented in Figures 1.20 and 1.21, the time to gel formation during pultrusion can be estimated. 

Figure 4.2 is a plot of log(cr) versus log(viscosity) constructed from dielectric data of Figure 4.1 and measurements on a dynamic rheometer. The figure shows that at a viscosity less than 1 Pas (10P), a is proportioned to l/tj because the slope of log(n) versus log( j) is approximately — 1. The gel point of the polymerization reaction occurs at 90 min based on the crossover of G and G" measured at 40rad/s. This is very close to the time at which rj achieves 100 Pas, which is also often associated with gel. The region of gel marks the onset of a much more rapid change in viscosity than with a. This is undoubtedly due to the fact that as gel occurs the viscoelastic properties of the resin involve the cooperative motion of many chains, whereas the translational diffusion of the ions continues to involve motions over much smaller molecular dimensions. 

The above data suggest that a crosslinked bilayer vesicle is essentially a single polymer molecule (really two, one in each half of the bilayer). In other words the polymerization of the lipid monomers exceeded a gel-point. This concept raises the question of what mole fraction of bis-substituted lipid is necessary to achieve a gel-point for a bilayer composed of a crosslinker lipid, i.e. bis-lipid, and a mono-substituted lipid. Approximately 30% of the lipids in a bilayer vesicle of SorbPCs must be bis-SorbPC (4) in order to produce a polymerized vesicle that could not be dissolved by detergent or organic solvent [29], A complementary study of Kolchens et al. found that the lateral diffusion coefficient, D, of a small nonreactive lipid probe in a polymerized bilayer of mono- and bis-AcrylPC was dramatically reduced when the mole fraction of the bis-AcrylPC, was increased from 0.3 to 0.4 [24]. The decreased freedom of motion of the probe molecule indicates the onset of a crosslinked bilayer in a manner consistent with a 2-dimensional gel-point. 

The ideal behavior after 0.57 extent of reaction may indicate the gel point. Dusek s theory 76 78) of cascade processes provides the changes in structural parameters with conversion. This along with C-13 NMR data in Fig. 20 shows the functionality of the epoxide as 2.6. 

Figure 3. Gel permeation data for linear randomly coiled polypeptides on various agarose resins, plotted according to the method of Ackers (9). M0 555 is plotted vs. the inverse error function complement of Kd (erfc 1 Kd). Lines drawn through the data points represent best fits obtained from linear least-squares analysis of the data. Numerical designation of each curve represents the percent agarose composition for the resin used. Filled triangles on the curve for the 6% resin, and the filled squares on the curve for the 10% resin are points determined using fluorescent proteins. Data for the labeled polypeptides were not included in the least-squares analysis.

Using an exponential equation to describe the time dependence of the viscosity clearly represents this process adequately, and in many cases the fit to the experimental data is quite satisfactory. However, this approach does not allow us to determine the gel-point directly. The gel-point is defined as the time when the viscosity increases without limit but according to Eq. (2.39), the viscosity is always limited (although it can be very high) at any specified time. Therefore, if order to use Eq. (2.39), in practice, it is necessary to characterize the properties of a material either by the time to or by the time required to reach a certain viscosity level, for example 1000 Pa s. 

Therefore, Eq. (2.67) clearly reflects the existence of the gel-point, and the form of the function q(P,T) can be found. This last problem was solved elsewhere. It was shown that the whole range of experimental data on the viscous properties of polyurethane-based compounds used for reactive processing can be described by the following equation ... 

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