Randomly Crosslinked Polymers

Crosslinking a linear polymer in absence of a solvent or in presence of a good solvent will result in a uniform distribution of crosslinking density. 

The predominant method used to prepare a crosslinked polymer support is to polymerize a monovinylcompound with a small amount of a divinylcompound by radical initiators. This enables the use of suspension techniques and spherical particles are therefore available. 

When polymerizing a monovinyl compound with a small amount of a divinyl compound, the amount of crosslinking agent determines the pore size. The pore size will increase with decreasing amounts of crosslinking agent (Fig. 3). 

EPR rotational correlation time of nitroxides in polystyrene crosslinked with different amounts of divinyl benzene (DVB) 

The rotational correlation times of a benzene solution of a nitroxide imbibed in polystyrene of varied crosslinking density and the analogous compound covalently attached to the chains of the crosslinked polystyrene were measured. In the latter case the modified polystyrene matrix was also equilibrated with benzene. An estimate of the influence of crosslinking density on the internal viscosity can be obtained 

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Returning focus to the more traditional use of the term "polymer", Fox [18] examines what, in common parlance, is referred to as "regularly crosslinked" vs. randomly crosslinked polymers. As an example of a general two dimensional regularly crosslinked polymer, consider the polymer depicted in Figure 12. Although this polymer has fourteen... 

Note that the class which Fox designates as "randomly crosslinked polymers" (see Figure 15) belong to what has been designated in [1] as "multimers". For multimers, there is no generalizable combination that is amenable to a standardized nomenclature. 

A linear high polymer can also be represented by the spaghetti-like strand shown in V and, in these terms, we can recognize branched polymers (VI) and random crosslinked polymers (VII). Ladder polymers (VIII) are also known ... 

In terms of polymer type, flexibility, size and chemistry, the pendent polymers seem to be excellent candidates for drug delivery vectors. Control of molecular mass and the distribution hydrophobicity, solubility, charge, binding of drug and so on are necessary for use in systemic drug delivery applications. The abihty to time the properties of pendent polymers should facilitate their use in drug delivery applications. As with randomly crosslinked polymers, pendent polymers bind drug molecules via inclusion... 

Fig. 1. Diagrams of polymer gel microstructures a) ideal end-linked pwlymer gel b) end-linked gel with dangling ends (in green) and loop defects (in orange) c) randomly crosslinked polymer gel.

In tree radical polymerization, unlike for the random crosslink polymers discussed in the previous section, primary polymer chains are formed during polymerization. The crosslink points are also formed as the polymers propagate. Furthermore, flee radical polymerization is a typical example of classic kinetically controlled systems. It is impossible to disconnect the formed bonds even by accident. Therefore, it can be easily seen that the resultant structure will not necessarily conform to the maximum probability given the primary polymer chains and crosslink density. 

To our knowledge there are only two sets of simulations on completely mobile randomly crosslinked polymer melts, the MD simulation of Duering et and the bond fluctuation MC simulation of Schulz and... 

The bond fluctuation lattice simulations investigate the relaxational properties of randomly crosslinked polymer melts, starting out from an equih-brated melt and then add additional bonds between monomers. Besides studying the gelation threshold they are concerned with two cases. One is the shp link problem, the other the collective relaxation of the whole network. 

More recently Schulz and Sonuner studied randomly crosslinked polymer networks by the bond fluctuation method and compared their... 

The most investigated examples are to be formd in the precipitation of polyelectrolytes by metal ions. Here, networks are formed by the random crosslinking of linear polymer chains, and the theory requires some modification. The condition for the formation of an infinite network is that, on average, there must be more than two crosslinks per chain. Thus, the greater the length of a polymer chain the fewer crossUnks in the system as a whole are required. 

The theory of gelation (Flory, 1953,1974) has been summarized in Section 2.2.3. This theory regards gelation as the consequence of the random crosslinking of linear polymer chains to form an infinite three-dimensional network. The phenomenon is, of course, well illustrated by examples drawn from the gelation of polycarboxylic acids by metal ions. 

Randomly - Crosslinked PDMS. The polydimethylsiloxane (PDMS) used to make random networks was obtained from General Electric. Membrane osmometry showed to be 430,000 g/g-mole. The polymer was mixed with various amounts of a free-radical crosslinking agent, dicumylperoxide (Di-Cup R, Hercules Chemical Co.). Samples were then pressed into sheets and crosslinking was effected by heating for 2 h at 150°C in a heated press. Mc values were calculated using equation 2, and are included in Table I. 

High functionality precursors of/ > 10-20 are primary chains if they participate in crosslinking by vulcanization each monomer unit of primary chain is a potential site for crosslinking. Also, dendrimers and random hyperbranched polymers of higher molecular weight, rank among high-functionality precursors. 

Perhaps the most viable short-term use for dendritic macromolecules lies in their use as novel catalytic systems since it offers the possibility to combine the activity of small molecule catalysts with the isolation benefits of crosslinked polymeric systems. These potential advantages are intimately connected with the ability to control the number and nature of the surface functional groups. Unlike linear or crosslinked polymers where catalytic sites may be buried within the random coil structure, all the catalytic sites can be precisely located at the chain ends, or periphery, of the dendrimer. This maximizes the activity of each individual catalytic site and leads to activities approaching small molecule systems. However the well defined and monodisperse size of dendrimers permits their easy separation by ultrafiltration and leads to the recovery of catalyst-free products. The first examples of such dendrimer catalysts have recently been reported... 

A hydrocarbon prepolymer containing terminal carboxyl groups (28) is available to the propellant chemist. These polymers were synthesized to eliminate some of the variables found in the copolymers. The carboxyl groups can be made of the same types with like reactivity. These linear non-branched polymers impart greater extensibility to elastomeric formulations. The chemistry in propellants is similar to the random functionality polymer. As 20 years of the chemistry of crosslinked propellant binders is reviewed, one familiar with the art cannot fail to predict solid propellant formulations using these polymers tailored to the specific requirements of the solid rocket design with the confidence that any discipline of science can be practiced. 

In ideal random crosslinking polymerization or crosslinking of existing chains, the reactivity of a group is not influenced by the state of other groups all free functionalities, whether attached or unattached to the tree, are assumed to be of the same reactivity. For example, the molecular weight distribution in a branched polymer does not depend on the ratio of rate constants for formation and scission of bonds, but only on the extent of reaction. Combinatorial statistics can be applied in this case, but use of the p.g.f. simplifies the mathematics considerably. 

In a plastic the polymer chains can be either intertwined simply at random to form a three-dimensional pattern, or they can be linked together by chemical bonds. This latter type is called a crosslinked polymer, and it... 

Figure 6.7 Schematic diagrams of different polymer types a homopolymer (a), a sequential (ordered) heteropolymer (b), and random heteropolymers (bf with two monomeric units and c with several monomeric units), (d) is a crosslinked polymer...

Consider the case of polymer chains with an arbitrary distribution of chain lengths and with a number of potentially reactive sites equal to the degree of polymerization (every monomeric unit of the polymer chain constitutes one potentially reactive site). The random crosslinking (vulcanization) of these linear primary chains may be considered a stepwise homopolymerization of Afl species, where the functionality of every species is directly proportional to its molar mass,... 

More precisely, the magnetic relaxation depends on the variable of gelation, i.e., the density of crosslinks, and is closely related to the modulus of elasticity, E, on the one hand and to the swelling ratio, Qm, on the other hand. Long polybutadiene chains are currently randomly crosslinked, using sulfur they can serve to illustrate the NMR approach to the characterisation of vulcanised polymers. It has been shown that the... 

Thermosetting phenolic resins include a number of polymers, the most common being obtained from the condensation of phenol with formaldehyde. The OH group on the benzene ring increases the reactivity in the o- and p- positions leading to three reactive centers for the phenolic component, while formaldehyde acts as having two active centers that can lead to a fully crosslinked polymer. The process may take place in neutral or alkaline conditions when in the first stage of the reaction, compounds known as methylol derivatives are formed. The condensation of phenol with formaldehyde occurs randomly at ortho- or para- position of the phenol, as shown below ... 

Another important feature controlling the properties of polymeric systems is polymer architecture. Types of polymer architectures include linear, ring, star-branched, H-branched, comb, ladder, dendrimer, or randomly branched as sketched in Fig. 1.5. Random branching that leads to structures like Fig. 1.5(h) has particular industrial importance, for example in bottles and film for packaging. A high degree of crosslinking can lead to a macroscopic molecule, called a polymer network, sketched in Fig. 1.6. Randomly branched polymers and th formation of network polymers will be discussed in Chapter 6. The properties of networks that make them useful as soft solids (erasers, tires) will be discussed in Chapter 7. 

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