Fibril spacing

D0 fibril spacing (long period in scattering experiment)... 

The miCTOstructure, in particular the mean fibril spacing D, of the growing craze is a consequence of the geometry of the surface drawing process and the surface energy of the fibrils being created. It is useful to model the polymer in the active zone as a strain-softened non-Newtonian fluid with the following flow law,... 

Suppose now that there is a wide spectrum of craze microstructures with different values of the fibril spacing D,. For the crazes with very small and very large Dq the craze interface velocity from Eq. (9) is miniscule, since for these crazes Vctq is small. Clearly there will be a value of D which maximizes Wq, and hence v, and this value is given by... 

Fig. 12. Mean fibril spacing D versus temperature for crazes grown in a 1,800,000 molecular weight PS deformed at a rate of 4.1 x 10 s (From Ref. courtesy J. Polymer Sci.-Polymer Phys. (Wiley))...

Figure 4 are about 750 ms apart, corresponding to a spacing of 1.2 mm. This agrees well with the distance between fibrils in Figure 6b. At lower normal forces, the slip events are spaced more closely. The average distance between slip events inferred from the current signals at a normal load of 2 N is 0.8 mm, in good agreement with the fibril spacing observed by SEM (about 0.7 mm).

USE OF INTER-FIBRIL SPACES AMONG ELECTROSPUN FIBRILS AS ION-FIXATION AND NANO-CRYSTALLIZATION... 

When solution of a polymer with some inoiganic ions is electrospun, the polymer fibrils will be elongated within the spinning direction and those ions are held in the inter-fibril spaces. When those electrospun fibers are calcined, ceramic fibers wiH be obtained. The present study has attempted to employ such spaces formed in poIy(vinyl alcohol) (PVA) as nano- or micro-reactor spaces for precipitation of nano-crystaUine particles. Exposing the spun PVA mats to ammonia vapor fixed metal ions in the form of hydroxide and, induced apatitic calcium phosphate crystallites when the precursor solution involved calcium and hydrogen orthophosphate ions. 

Use of Inter-Fibril Spaces among Electrospun Fibrils... 

Figure 2.2 Polytetrafluoroethylene graft consisting of nodes and connecting fibrils. Space between the nodes can be controlled.

In Fig. 24.1 we show a part of a craze. The parameter/) is the (mean) craze fibril diameter while Do is the craze fibril spacing. Both D and Do increase somewhat with increasing He. Berger [42] traced the craze fibril breakdowns to the formation of small pear-shaped voids at the craze/bulk interface. The results in [42] confirm the microscopic model of Kramer and Berger [38] which we see in Fig. 24.1. 

T < Tg (T Tg) Intense thermally induced disentanglement (lower disentanglement stress than yield stress) results in coarsening of craze structure with increasing fibril thickness and fibril spacing. 

Porod analysis of the SAXS and SAEX measurements provided a quantitative estimate of the mean craze fibril spacing. Brown [40] subsequently made the key observation that the presence of the cross-tie fibrils has a profound effect on the failure mechanism of a craze because they enable stress transfer between broken and unbroken fibrils. Brown [40], and then Kramer [41], followed this idea through to produce a quantitative theory of craze failure of the molecular chains at the mid-rib of the craze. Brown s theory is a very ingenious mixture of the macroscopic and the microscopic. Starting at the macroscopic level the craze can be modelled as a continuous anisotropic elastic sheet. The stress on the craze plane in front of the crack is then... 

The highest stress in the craze is assumed to be in the fibril closest to the crack tip, and can be approximated by putting r = dll, where d is the fibril spacing, to calculate... 

WLF constant WLF constant [K] characteristic ratio tensile compliance [Pa ] craze fibril spacing [m]... 

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