Critical crosslink

Our interest from the outset has been in the possibility of crosslinking which accompanies inclusion of multifunctional monomers in a polymerizing system. Note that this does not occur when the groups enclosed in boxes in Table 5.6 react however, any reaction beyond this for the terminal A groups will result in a cascade of branches being formed. Therefore a critical (subscript c) value for the branching coefficient occurs at... 

The mechanical properties of ionomers are generally superior to those of the homopolymer or copolymer from which the ionomer has been synthesized. This is particularly so when the ion content is near to or above the critical value at which the ionic cluster phase becomes dominant over the multiplet-containing matrix phase. The greater strength and stability of such ionomers is a result of efficient ionic-type crosslinking and an enhanced entanglement strand density. 

The formation mechanism of structure of the crosslinked copolymer in the presence of solvents described on the basis of the Flory-Huggins theory of polymer solutions has been considered by Dusek [1,2]. In accordance with the proposed thermodynamic model [3], the main factors affecting phase separation in the course of heterophase crosslinking polymerization are the thermodynamic quality of the solvent determined by Huggins constant x for the polymer-solvent system and the quantity of the crosslinking agent introduced (polyvinyl comonomers). The theory makes it possible to determine the critical degree of copolymerization at which phase separation takes place. The study of this phenomenon is complex also because the comonomers act as diluents. 

Tubular reactors are used for some polycondensations. Para-blocked phenols can be reacted with formalin to form linear oligomers. When the same reactor is used with ordinary phenol, plugging will occur if the tube diameter is above a critical size, even though the reaction stoichiometry is outside the region that causes gelation in a batch reactor. Polymer chains at the wall continue to receive formaldehyde by diffusion from the center of the tube and can crosslink. Local stoichiometry is not preserved when the reactants have different diffusion coefficients. See Section 2.8. 

The first elastomeric protein is elastin, this structural protein is one of the main components of the extracellular matrix, which provides stmctural integrity to the tissues and organs of the body. This highly crosslinked and therefore insoluble protein is the essential element of elastic fibers, which induce elasticity to tissue of lung, skin, and arteries. In these fibers, elastin forms the internal core, which is interspersed with microfibrils [1,2]. Not only this biopolymer but also its precursor material, tropoelastin, have inspired materials scientists for many years. The most interesting characteristic of the precursor is its ability to self-assemble under physiological conditions, thereby demonstrating a lower critical solution temperature (LCST) behavior. This specific property has led to the development of a new class of synthetic polypeptides that mimic elastin in its composition and are therefore also known as elastin-like polypeptides (ELPs). 

While the critical role of intrastrand 1,2-crosslinks in the mechanism of action of the anti-tumor drug cis- [PtCl2(NH3)2] is well established, much less is known about the few frans-analogs that exhibit similar efficacy. A series of 1,3-adducts has been characterized with 3-mers generally involving purine N7 coordination (32-34), and either monofunctional or interstrand adducts are formed with duplex DNA (35). However, one of the most active compounds, frans-[PtCl2 ( )-HN = C(OMe)Me 2], (2), has been shown to form a 1,2-adduct with 2-mer ribonucleotide sequence r(AG) (36). Though the formation of the... 

None of the Cr(III) products from Equations 6 or 7 are effective crosslinkers since a chromic aqua ion must be hydrolyzed first to form olated Cr to become reactive. Colloidal and solid chromium hydroxides react very slowly with ligands. In many gelation studies, this critical condition was not controlled. Therefore, both slow gelation times and low Cr(VI) Cr(III) conversion at high chromate and reductant concentrations were reported (9,10). 

In samples with early stages of crosslinking (lower curves in Fig. 2), stress can relax quickly. As more and more chemical bonds are added, the relaxation process lasts longer and longer, i.e. G(t) stretches out further and further. The downward curvature becomes less and less pronounced until a straight line ( power law ) is reached at the critical point. 

Fig. 11. Schematic of relaxation time spectrum of the critical gel of PBD 44 (Mw = 44 000). The entanglement and glass transition is governed by the precursor s BSW-spectrum, while the CW spectrum describes the longer modes due to the crosslinking [60]. denotes the longest relaxation time of PBD44 before crosslinking...

Fig. 12. Dynamic moduli master curves of PBD 44 precursor (p = 0) and PBD 44 critical gel [60]. The entanglement and glass transition regime is hardly affected by the crosslinking. Open symbols correspond to G, filled ones to G"...

The critical gel equation is expected to predict material functions in any small-strain viscoelastic experiment. The definition of small varies from material to material. Venkataraman and Winter [71] explored the strain limit for crosslinking polydimethylsiloxanes and found an upper shear strain of about 2, beyond which the gel started to rupture. For percolating suspensions and physical gels which form a stiff skeleton structure, this strain limit would be orders of magnitude smaller. 

The damping material does not have to be a critical gel. Many applications do not require extra low damping frequencies. The lowest vibration damping frequency comin determines the longest relaxation time, Amax. A suitable damping material would be crosslinked beyond the gel point, with a 2max of about... 

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