Glass and Gel Effects

According to equation (20-59), there must be a linear relationship between the overall rate v,ot and the yield u = ([M]o - [M])/[M]o of the monomer. The higher the yield, the smaller will be the monomer concentra- 

In experimental work, however, it is frequently noticed that after a linear decrease in with u the rate of polymerization again increases and goes through a maximum, only to fall again to zero (at u = 1). This effect is seen at 60°C with methyl methacrylate for yields as low as 20% with styrene, by contrast, it does not occur until 65%. The effect is also observed when reactions are carried out isothermally. Therefore, it cannot primarily be caused by liberation of heat. The effect is accentuated when the medium is more viscous (addition of otherwise inert polymer, low initiator concentrations, poor solvent). Therefore, it must originate from some kind of diffusion control, and is called the gel effect or Trommsdorf-Norrish effect. 

Quantitative analysis of the kinetic measurements shows that the propagation constant kp remains constant, while the termination constant Kipp) decreases. In allyl acetate, on the other hand, the termination constant Kipm) remains constant even at high yields. Therefore the termination by mutual deactivation of two polymer free radicals must be prevented by the high viscosity, causing the free radical concentration, and hence the rate of polymerization, to increase. Since the termination constants Kipp) are diffusion controlled (Section 20.2.4.2) even at low viscosities, however, the effect cannot be due to the beginning of diffusion control. It must rather develop from the fact that diffusion-controlled effects are altered. The interpretation of the gel effect is assumed to be diffusion control caused by the whole polymer molecule. On the other hand, mobility of segments governs the rate constants for termination. 

At even higher yields, because of the very high viscosities, there is an additional diffusion control of addition of monomer to the polymer free radicals. Consequently, the rate of polymerization again decreases (glass effect). 

Kinetics, degree of polymerization, and constitution can be changed, however, by a series of other reactions (see Section 20.3). Under certain conditions, for example, the appearance of cauliflower-shaped forms, frequently representing cross-linked polymers, is observed (popcorn polymerization).  

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The situation becomes more complicated in the polymer-rich phase, where diffusion limitations must be accounted for. In this model, the following expressions for cage, glass, and gel effect in the dispersed phase (subscript 2) have... 

In all considered reactions, some kind of auto-acceleration in the reaction rate is quite evident In order to elucidate the relevance of this phenomenon, the same simulation shown in Fig. 6.1 has been repeated neglecting cage, glass, and gel effects (i.e. using Eqs. 17-19 with cop = 0). Fig. 6.5 shows the result it can be seen that diffusion limitations play a major role in the system, and they need to be properly accounted for. 

The main process control challenges in solution and bulk polymerizations are the control of molecular weight averages [103], molecular weight distribution (MWD) [104], monomer conversion [105], and copolymer composition and copolymer composition distribution (CCD) [106, 107]. The development of mathematical models for solution and bulk processes is relatively easy, as it is not necessary to take into account mass transfer between different phases. The main challenge in this field is the proper description of the glass and gel effects, which is usually performed with the help of anpirical models [108]. Therefore, reliable process models are usually available for solution and bulk processes. 

Diffusion-controlled phenomena affecting the termination and propagation reactions, as well as the initiator efficiency (gel-, glass- and cage effect, respectively) are expressed in terms of a reaction-limited term and a diffusion-limited one (Keramopoulos and Kiparissides, 2(X)2). The latter depends on the diffusion coefficients of the corresponding species (i.e., polymer and monomer) and an effective reaction radius. 

Shape-memory materials are those materials that return to a specific shape after being exposed to specific temperatures. In other words, these materials are able to remember their initial shape. This process of changing the shape of the material can be repeated several times. The shape-memory effect has been observed in different materials, such as metallic alloys, ceramics, glasses, polymers and gels. 

Third, assays need to describe methods used for obtaining minimal detection limits (e.g., mean plus 3 SD of 20 replicates of a zero calibrator) and total imprecision, describing at what concentration a 10% CV is attained. Preanalytical factors that should be described include the effects of storage time and temperature, glass versus plastic tubes and gel separator tubes, and the influence of anticoagulants and whole blood measurements. As more assay systems are devised for POCT, the same rigors applied to the central laboratory methodologies need to be adhered to by the POCT systems. 

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