Polymerization - curves

Figure 8.5 illustrates the sort of separation this approach predicts. Curve A in Fig. 8.5 shows the weight fraction of various n-mers plotted as a function of n. Comparison with Fig. 6.7 shows that the distribution is typical of those obtained in random polymerization. Curve B shows the distribution of molecular weights in the more dilute phase-the coacervate extract-calculated for the volumes of the two phases in the proportion 100 1. The distribution in the concentrated phase is shown as curve C it is given by the difference between curves A and B. 

The primary cation CH20H is created in the cage reaction under photolysis of an impurity or y-radiolysis. The rate constant of a one link growth, found from the kinetic post-polymerization curves, is constant in the interval 4.2-12 K where = 1.6 x 10 s . Above 20K the apparent activation energy goes up to 2.3 kcal/mol at 140K, where k 10 s L... 

The situation is quite different when actin is polymerized under sonication in the presence of ATP. In this case, the polymerization curve cannot be described by equation (4). At a high actin concentration, overshoot polymerization kinetics are observed, with a maximum and subsequent decrease to a lower stable plateau (Carlier et al., 1985). The final amount of polymer is the same as that obtained when sonication is applied to F-actin that had polymerized spontaneously without sonication. Conversely, when sonication is stopped, repolymerization accompanies the spontaneous length redistribution to a population of less numerous, but longer filaments. 

Note that the reaction rate in the presence of the mixture of amines (Curve 4) considerably exceeds the rate of monomer consumption if the same amines are reacted separately and are involved in polycondensation (Curve 1) and polymerization (Curve 6) therefore, an obvious synergetic effect is operative. Considering the fact that the initial rate of aniline consumption (Fig. 15 b, Curve 4) is practically the... 

Fig. 4. Another case of slow initiation (curve l) and another of slow termination (curve 2). Curve / differs from Figure 2 because here termination is faster than polymerization. Curve 2 differs from Figure 3 because here initiation is faster than polymerization.

Hydrogenation experiments with the triglycerides are given by the curve D-C-B-A theoretical polymerization curves of the esters (assuming removal of the double bonds without any change in the elementary composition) can be represented by D-D, C-C and B-B. ... 

Shape of the Polymerization Curves. Since polymerization takes place within the polymer particle, the rate depends on monomer concentration in the particles this concentration remains relatively constant as long as free monomer phase is present. At some point during the polymerization, the amount of polymer present is sufficient to absorb essentially all of the unreacted monomer. After this point in the polymerization, the monomer consumed by the radicals cannot be replaced and monomer concentration in the particle must decrease. It then follows that the rate must also decrease. 

A range is given for vinyl hexanoate since the low percentage of monomer used makes determination of the point more difficult. From these observations and the shape of the polymerization curves, it seems that vinyl hexanoate behaves similarly to styrene in showing first-order dependence on monomer concentration during polymerization. 

Figure 25 shows typical GPC chromatogram patterns of the polymers obtained at each stage of the polymerization. Curves a, b and c correspond to homopolypropylene at the first stage (180 min), P—R diblock copolymer at the second stage (180 min... 

Figure 1. Conversion representation of MMA semicontinuous emulsion polymerization. Curve A results from neglecting lag in sampling while curve B is corrected for 2.7 min of lag.

Modification of Solids. Our next step was to investigate the behavior of washed solids when recombined with various alkylaluminum compounds. A 0.9 1-BU3AI solid with relatively little residual activity was chosen for this purpose. Figure 9 illustrates a typical polymerization curve for the solid upon activation with triethylaluminum. The addition of only minute amounts, in the range of 0.025-0.075 mole per mole Ti in the solid, was needed to regain or surpass the original activity of the unseparated catalyst. The same procedures were used to study the activation of the above brown TiCh solid with other organo-... 

As to be seen from Figure 3 productivity (curve a) and rate of polymerization (curve b) increased both with increasing pressure. At the highest pressure of 1500 bar a very high productivity of 4400 kg polymer/g Zr resulted. Also the rate of polymerization at this pressure was high and was in the range of 0.4 kg polymer/s/m3. 

Figure 3 Influence of the pressure on productivity and rate of polymerization Curve a productivity curve b rate of polymerization...

Figure 11. Solutions of the Smith-Ewart recursion equation for the case of no aqueom propagation or termination. Dotted line m = 0 (Smith-Ewart Case II). Curve 1 (m = 10 ) depicts typical styrene-like polymerization. Curve 2(m = 0.01) depicts radiation initiated emulsion polymerization of vinyl chloride. Curve 3 (m > 1.0) depicts chemically initiated emulsion polymerization of vinyl chloride.

Figure 6.12 Comparison of conversion-time plots for normal, inhibited, and retarded free-radical polymerization. Curve 1 normal polymerization curve 2 inhibition curve 3 retardation curve 4 inhibition followed by retardation.

Figure 6.11 Comparison of conversion-time plots for normal, inhibited, and retarded free-radical polymerization. Curve 1 normal polymerization in the absence of inhibitor/retarder. Curve 2 inhibition polymerization is completely stopped by inhibitor during the initial induction period, but at the end of this period with the inhibitor having been completely consumed, polymerization proceeds at the same rate as in normal polymerization (curve 1). Curve 3 retardation a retarder reduces the polymerization rate without showing an induction period. Curve 4 inhibition followed by retardation (After Ghosh, 1990).

The major point of Interest in the polymerization curve, Figure 2, is the onset of the Trommsdorff effect, sometimes called autoacceleration. As is well known, the molecular weight increases rapidly after the onset of the Trommsdorff effect. 

FIGURE 2.4 (a) Number fraction distribution curves for linear step-growth polymerizations curve 1, p = 0.9600 curve 2, p = 0.9875 curve 3, p = 0.9950. (b) Corresponding weight fraction distribution for the same system. 

All the data shown in Fig. 11-31 fall on a definite curve regardless of extrusion rate. Again, the curve shapes match polymethyl methacrylate polymerization curves. And, again, this would seem to indicate that chemical reaction was the prevailing rate process. 

Figure 4 Universal polymerization curves of EPs, TAEPs, and CAEPs. Plotted is the fraction of polymerized material, ri, as a function of the ratio X/Xp. The quantity X is the strength of the mass action as defined in the main text, proportional to the overall concentration of dissolved material. Xp denotes its value at the polymerization transition, which for EPs is defined as the point where half the material is absorbed into polymers. The curve for CAEPs and TAEPs is the limiting one for conditions where the polymerization transition becomes a true phase transition.

Figure 5 Universal polymerization curve of EPs. Plotted is the fraction polymerized material r/ as function of the concentration ratio / p, where is the concentration at the half-way or polymerization point. The line... 

Figures Universal polymerization curve of EPs. Plotted is the fraction polymerized material as a function of the dimensionless ratio hp T - Tp)/kBT with hp the net enthalpy gain of the formation of a single link, Tp the concentration-dependent polymerization temperature, and kg Boltzmann s constant. The line gives the theoretical prediction of the isodesmic model. The symbols Indicate experimental data on five chemically different ollgo(phenylene vlnyl)s In the solvent methyl cyclohexane at a concentration of 1M [38], By fitting to the data, values of hp are obtained from 24 to 70 kg T equivalent to 60 to 170 kJ mol". ...

Figure 7 Polymerization curves of EPs as a function of the temperature T relative to the reference temperature Tp at the crossover from the monomer to the polymer-dominated regimes. Different curves give the fraction polymerized material rj for different values of the dimensionless link enthalpy hp/k Tp = 15, 30, 60, 90 (from bottom to top).

In line with the results for EPs, we find that the steepness of the growth of the amount of polymerized material depends on the ratio hp/k Tp, which is thus amenable to experimental determination (see Figure 8). The quantity hp/ksTp can be extracted from the polymerization curve without a full curve-fitting procedure, for at the polymerization transition (drj/dT)T=Tp = -hp/k Tp. 

Both defect absorption and electroabsorption grow during the thermal polymerization process though differently. The absorption band saturates after about 6 h at 80°C. The electroabsorption peak increases rapidly when the autocatalytic range is reached, together with a red shift by about 70 meV similar as the excitons (Fig. 2, PTS-7). As shown in Fig. 3 the growth of Aa follows closely the polymerization curve (14). When most of the material is polymerized, however, Aa decreases again to about half its peak value quite in contrast to the absorption spectrum. 

Kinetic polymerization curves show that autoacceleration takes place essentially from the beginning of the process. 

A different form of retardation occurs when a radical species formed from transfer (S in Scheme 4.3) reinitiates at a slow rate. In addition to the slower reaction rate with monomer to form a polymer radical, the termination of S with other radicals in the system may also need to be considered (Scheme 4.8). Explicit balances must be written for S, and the extra mechanisms must be included when deriving expressions for [Ptot], Rpoi, and DP . As solvent/transfer agent is generally not completely consumed, the retardation effect will last the duration of the polymerization (curve b in Figure 4.2). The degree of retardation depends on the value of which can vary with monomer type many carbon-centered radicals show much lower reactivity toward vinyl esters (for example, vinyl acetate) than (meth)acrylates [3]. 

Figure 6.5 Temperature dependence of the lateral diffusion coefficient of the fluorescence probe di018 (see Reference 49) in large vesicles of pure DMPC (curve 1), of a 1/1 mixture of DMPC and of a butadiene lipid before polymerization (curve 2), of the same mixture after polymerization of the butadiene lipid (curve 3), of the butadiene lipid before polymerization (curve 4) and of this lipid after polymerization (curve 5). T, Tg, Tg and Tg correspond to the transition temperatures of the lipids or lipid mixture. Polymerization is seen to reduce the lateral diffusion coefficient. Reproduced from Reference 49 with permission of American Physical Society.

Figure 2.34. Kinetic polymerization curves of tetramethylene-dimetacrylate in a matrix of cis-polyisoprene at various values of Xex (I-IV) and ti 8 (1), 24 (2), 48 (3) and 240 (5) hour. Blackened markings show samples after secondary swelling. Explanation is provided in the text, see table 2.5.

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