Crosslinking density of polymer

When plasticized polymers are in contact with the mother polymers, plasticizers are likely to migrate to mother polymers and the extent of their migration depends on a number of factors such as polymer-plasticizer system, polarity of polymer and plasticizer, crosslink density of polymer, molecular weight of plasticizer etc. 

Eq. [4.2.9] has different forms depending on the form of elasticity potential but for practical purposes (evaluation of crosslinking density of polymer networks) it is more eon-venient to use the above form. The equation can be used in a modified form if the concentration dependence of the parameter %i is known. 

Where, is volume fraction of the polymer, is molar volume of solvent, X is the polymer solvent interaction parameter. Me is the crosslink density of polymer, pi is solvent density, P2 is polymer density, / is functionality of crosslink, Fequ is equilibrium volume of the hydrogel. 

SBR/PS (see Figure 2.3), where the crosslink density of polymer I was the principal variable. The results are shown in Table 6.2. ... 

The crosslink density of a polymer network determines the number of elastically effective chains. Some of the chains are tied to a network and... 

If we accept the model proposed for these mixed monofunctional/ difunctional systems, we can draw some conclusions about the network structure in polymers based on I alone. For example, Fig. 7 shows how the Tg varied with the relative crosslink density in the mixed systems. The abcissa represents the probability that a monomer chosen at random is linked to the network at both ends. At moderate degrees of crosslinking, the expected relationship between Tg and crosslink density is linear, so the data were approximated by a straight line (10). From the extrapolation in Fig. 7, one concludes that a typical bis-phthalonitrile cured to a Tg of 280 0 has a relative crosslink density of 0.5, or about 70% reaction of nitrile groups. 

The diffusion and the permeability are inversely related to the density, degree of crystallinity, orientation, filler concentration, and crosslink density of a polymeric film. As a general rule, the presence of plasticisers or residual solvents increases the rate of diffusion in polymers. Films cast from poor solvents have high permeability. The rate of diffusion or permeability is independent of the molecular weight of the polymer, providing the polymer has a moderately high molecular weight. 

Figure 2 illustrates the temperature dependence of the swelling degree as a function of precursor polymer type. Methylcellulose (MC), hydroxypropyl-methylcellulose, type E (HPMC-E) and hydroxypropylmethylcellulose, type K (HPMC-K) gels have comparable effective crosslink densities of about 2 x 10 5 mol/cm3 (as determined from uniaxial compression testing), while the crosslink density of the hydroxypropylcellulose (HPC) gel is about half this [52]. The transition temperature for each gel is within several degrees of the precursor polymer lower critical solution temperature (LCST), except for the MC gel, which has a transition temperature 9 °C higher than the LCST. The sharpness of the transition was about 3%/°C, except for the HPC gel transition, which was much sharper - about 8%/°C. 

It is obvious that the polymer created by the addition of the commercial size exhibits a monotonic decrease in Tg. This indicates that the silanes and other ingredients in the sizing are acting to reduce the crosslink density of mixtures. This is not surprising since the silanes present in commercial size usually contain a chemical group which is reactive with the matrix constituents. 

One of the most characteristic properties of crosslinked rubbers is the ability to swell in appropriate solvents to a constant volume. Not only is this property exploited for estimation of parameters such as crosslink densities and polymer-solvent interaction parameters, but the resultant change in nuclear magnetic resonance (NMR) parameters allows a large number of new and interesting NMR experiments. It is the aim of this chapter to introduce some simple concepts of polymer swelling and to examine the information obtainable for the range of NMR experiments possible on swollen gels. 

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