Molecular weight between crosslinks

A cross-linked polymer has a density of 0.94 g cm" at 25°C and a molecular weight between crosslinks of 28,000. The conformation of one bond in the middle of the molecule changes from trans to gauche, and the molecule opens up by 120°. In w-butane, the trans to gauche transformation requires about 3.3 kJ mol". Estimate a value for AH of stretching based on this model, and use the law of cosines to estimate the magnitude of the opening up that results. 

For thermosets with molecular weight between crosslinks M, the crosslink density Px, is described by Px N /Mx- As Px increases, the nets become tighter and stiffer, and thus require more stress to break via... 

To determine the crosslinking density from the equilibrium elastic modulus, Eq. (3.5) or some of its modifications are used. For example, this analysis has been performed for the PA Am-based hydrogels, both neutral [18] and polyelectrolyte [19,22,42,120,121]. For gels obtained by free-radical copolymerization, the network densities determined experimentally have been correlated with values calculated from the initial concentration of crosslinker. Figure 1 shows that the experimental molecular weight between crosslinks considerably exceeds the expected value in a wide range of monomer and crosslinker concentrations. These results as well as other data [19, 22, 42] point to various imperfections of the PAAm network structure. 

Analysis of data pertaining to the modulus of PEO gels obtained by the polyaddition reaction [90] shows that even in this simplified case the network structure substantially deviates from the ideal one. For all samples studied, the molecular weight between crosslinks (M p) exceeds the molecular weight of the precursor (MJ. With decreasing precursor concentration the M xp/Mn ratio increases. Thus, at Mn = 5650 a decrease in precursor concentration from 50 to 20% increases the ratio from 2.3 to 12 most probably due to intramolecular cycle formation. 

Figure 9. SANS measurements of R /Rt° and RL/R ° for stretched radiation cross-linked polystyrene. is determined by measurements in which the neutron is parallel (iso) and perpendicular (aniso) to the stretching direction. Mc is molecular weight between crosslinks. Theoretical curves 2 and 3 are drawn for tetrafunctional networks. Data from Ref. 21.

C. C. Han, H. Yu and their colleagues (23) have presented some new SANS data on end-linked trifunctional isoprene networks. These are shown in Figure 10. Those materials of low molecular weight between crosslinks exhibit greater chain deformation consistent with the thesis that the junction points are fixed. This is the reverse of that found by Beltzung et al. for siloxane networks. 

Inhomogeneities in a real network may occur either because of a continuous distribution of molecular weight between crosslinks or due to the regions of different average molecular weights (as may be the case in randomly crosslinked networks). 

Peppas and Merrill (1977) modified the original Flory-Rehner theory for hydrogels prepared in the presence of water. The presence of water effectively modifies the change of chemical potential due to the elastic forces. This term must now account for the volume fraction density of the chains during crosslinking. Equation (4) predicts the molecular weight between crosslinks in a neutral hydrogel prepared in the presence of water. 

Here, r is the stress applied to the polymer sample, p is the density of the polymer, R is the universal gas constant, T is the absolute experimental temperature, and Mc is the desired molecular weight between crosslinks. 

Fig. 9. The effect of interpolymer complexation on the correlation length, , and the effective molecular weight between crosslinks, Mc, in P(MAA-g-EG) graft copolymer networks with permanent, chemical crosslinks ( ).

Gupta et al. (3) reported that elcistically effective molecular weight between crosslinks. Me, was lowest at the stoichicnetric ratio of MPD and epoxy, and post curing resulted in a considerable decrease in Me only in epoxy rich sanples (3). 

The molecular weight between crosslinks (Me) was determined for each epoxy/amine ratio of the neat resin from the rubbery plateau region of the modulus curve following the Tg region. This can be seen in Figure 13 for several epoxy/amine ratios. The Me values were calculated from the following equation ... 

Figure lA. Glass transition temperature (Tg) and molecular weight between crosslinks (Me) as a function of epoxy/amine ratio for C-stage cured neat resin. 

Table V. Molecular Weight Between Crosslinks, Me, for Several Epoxy/Amine Ratios ...

Polymer Effect of Molecular Weight Between Crosslinks", J. Appl. Polym. Scl., 14, 1901-1906 (1970). 

The thermoset included here is derived from bisphenol-A dicya-nate. It can be thermally trimerized yielding a triazine or cyanurate network (8,9,10) as seen in the reaction scheme (Table 1). The critical molecular weight between crosslinks is relatively low, resulting in an extremely tight, brittle network. The material is usually used as a prepeg because a total cure produces a hard, infusible, and insoluble matrix. It possesses excellent adhesive properties and is currently used as a metal coupling agent. It offers many superior properties relative to conventional epoxies derived from bisphenol-A. 

These data are consistent with the observation O) that increased crosslinking (i.e., epoxy resins with lower EEW s) will result in a decreased propensity for the cured polymer to absorb solvents. Thus, the solvent resistence of an organic coating can be controlled by the formulator via variations in the molecular weight between crosslinks. 

Mc number average molecular weight between crosslinks... 

Several theories have been proposed to calculate the molecular weight between crosslinks in a hydrogel membrane. Probably the most widely used of these theories is that of Flory and Rehner [5]. This theory deals with neutral polymer networks and assumes a Gaussian distribution of polymer chains and tetrafunctional crosslinking within the polymer network. 

Models which also describe the molecular weight between crosslinks for neutral polymer networks but use a non-Gaussian chain distribution have also been derived. These models would be useful in cases of highly crosslinked polymer networks. Examples of these types of models include those of Peppas and Lucht [7], Kovac [8], and Galli and Brummage [9]. 

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