Epoxy polymers microvoids

The fluctuation free volume in crosslinking epoxy polymers has a fractal structure and the microvoids formed in the matrix are simulated by Df dimensional spheres. The size of a microvoid is considered as the volume that is necessary for its formation and is a consequence of the accumulation of thermal fluctuations. 

As can be seen in Figure 15.2, the dependence (15.3) is correct for the epoxy polymers investigated and confirms the self-similarity of a cluster of microvoids of fluctuation free volume. The interval of the scale of the self-similarity, with allowance for correlations between Df and fractal dimension of the structure of the polymer df may be assumed. This interval coincides with a similar interval for the structure of an amorphous polymer which is distributed from several units up to several tens of Angstrom (5-50 A) [1, 4]. 

Figure 15.1 The dependence of a number of microvoids on their size in logarithmic coordinates for epoxy polymers 1 EP-1, 2 EP-2 and 3 EP-3.

Thns, the flnctnation free volume in a crosslinking epoxy polymer has a fractal structure and the microvoids, forming are simulated by Df dimensional sphere. The volume that is necessary for accnmulation of the thermal fluctuation energy, sufficient for its formation controls the size of a microvoid. 

Bag Bagheri, R., Pearson, R. A. Role of particle cavitation in rubber-toughened epoxies 1. Microvoid toughening. Polymer 37 (1996) 4529-4538. 

Huang Y and Kinloch A J (1992) The toughness of epoxy polymers containing microvoids, Polymer 92 1330-1332. 

Figure 5.40 The dependences of microvoids of fluctuation free volume number on their characteristic size in double logarithmic coordinates for epoxy polymers EP-1 (1), EP-2 (2) and EP-3 (3) [155]...

Hence, the results stated above have shown that fluctuation free volume in epoxy polymers possesses fractal structure. Therefor a microvoid forming it should be simulated by D -dimensional sphere. The size of the microvoids is controlled by the volume which is necessary for accumulation of the thermal fluctuations enei y required for their formation. The absolute values of can serve as characteristic of polymer structure thermodynamic non-equilibrium and for quasi-equilibrium structures the value of coincides with the data obtained according to the William-Landel-Ferry equation. Microvoids of fluctuation free volume form fractal structure, which is a mirror of polymer structure [152-158]. 

Figure 8.14 The dependences of free volume microvoid diameter on epoxy polymer contents c p for HDPE/EP nanocomposites. The calculation of d according to Equation 8.13 for oxygen (1) and nitrogen (2) and d according to Equation 8.15 (3). The horizontal dashed lines indicate experimental values of for polyethylenes of high (4) and low (5) density [40]...

Therefore, the quantitative analysis fulfilled above has confirmed that reduction in the permeability to gas coefficient for HDPE/EP nanocomposites is due to filling by epoxy polymer the largest free volume microvoids that excludes them from the gas transport process. The multifractal treatment of this effect is offered and the combined diagram in coordinates f-a is constructed, which is multifractal for < 4.4 A and monofractal for d, > 4.4 A. 

Lazzeri and Bucknall [131] have proposed that the pressure dependence of yield behaviour caused by the presence of microvoids can explain the observation of dilatation bands in rubber-toughened epoxy resins [132], rubber-toughened polycarbonate [133] and styrene butadiene diblock copolymers [134]. These dilatation bands combine in-plane shear with dilatation normal to the shear plane. Whereas true crazes contain interconnecting strands, as described in Section 12.5.1 above, dilatation bands contain discrete voids that, for rubber-toughened polymers, are confined to the rubber phase. 

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