Density of crosslinks

Crosslinking can be introduced into an assembly of polymer molecules either as the polymerisation takes place or as a separate step after the initial macromolecule has been formed. Typical of the first category are polymers made by step processes, often condensations, in which monomers of functionality greater than 2 are present. The relative concentration of such higher functionality monomers then determines the density of crosslinks in the final material. 

Solvent Swelling and Extraction, The residue samples were extracted with pyridine at the boiling point to obtain the amount and composition of the extract. A portion of the dried, extracted solids was swelled in pyridine in order to estimate the density of crosslinks introduced by the preliquefaction process. The solvent swelling measurements were carried out according to the method of Green et al. (30,31). 

Various relationships have been derived to describe the crosslinking density of a system past pc [Argyropoulos et al., 1987 Durand and Bruneau, 1982a,b Dusek, 1979a,b Dusek et al., 1987 Flory, 1953 Miller and Macosko, 1976] (see also Sec. 2-11). The density of crosslinks in a reaction system increases with conversion and with increasing functionality of reactants. For a system such as... 

Fumaric and itaconic acids are also used as the diacid component. Most reaction formulations involve a mixture of a saturated diacid (iso- and terephthalic, adipic) with the unsaturated diacid or anhydride in appropriate proportions to control the density of crosslinking (which depends on the carbon-carbon double-bond content of the prepolymer) for specific applications [Parker and Peffer, 1977 Selley, 1988], Propylene glycol, 1,4-butanediol, neopentyl glycol, diethylene glycol, and bisphenol A are also used in place of ethylene glycol as the diol component. Aromatic reactants are used in the formulation to improve the hardness, rigidity, and heat resistance of the crosslinked product. Halogenated reactants are used to impart flame resistance. 

Low concentrations of radical scavengers can greatly reduce the density of crosslinking of liquid polymers although most radicals will be formed some distance from a scavenger. For a solid polymer much higher concentrations are needed, but crosslink densities can still be approximately halved. 

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... 

Number of functional groups in resins and hardeners density of crosslinking. 

Molar ratio of resin and hardener density of crosslinking. 

Through use of classical network theories of macromolecules, G has been shown to be proportional to crosslink density by G = nKT -i- Gen, where n is the nnmber density of crosslinkers, K is the Boltzmann s constant, T is the absolnte temperature, and Gen is the contribution to the modulus because of polymer chain entanglement (Knoll and Prud Homme, 1987). The loss modulus (G") gives information abont the viscous properties of the fluid. The stress response for a viscous Newtonian fluid would be 90 degrees out-of-phase with the displacement but in-phase with the shear rate. So, for an elastic material, all the information is in the storage modulus, G, and for a viscous material, aU the information is in the loss modulus, G". Refer to Eigure 6.2, the dynamic viscosities p and iT are defined as... 

Problem 3.20 The structure of a three-dimensional random network may be described quantitatively by two quantities the density of crosslinking designated by the fraction e of the total structural units engaged in crosslinkages and the fraction 6f of the total units which occurs as terminal units or free chain ends (i.e., which are connected to the structure by only one bond). Alternative quantities, such as the number (mole) N of primary molecules and the number (mole) v of crosslinked units, in addition to M and Me, defined above, are also used to characterize a random network stmeture. Relate N and v to these other quantities. 

Therefore, the presence of crosslinks in the interdiffused depth is clear after long contact times but no crosslinks, or only a few, are formed at shorter times. Because the density of crosslinks inside the elastomer sheets is the same in all cases (the same dose is received), only the effect of diffusion depth on this number of crosslinks in the interfacial domain can explain the observed behavior. Moreover, Eq. (2) tells us that the thickness of the interdigitated zone in-... 

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