Fibril stability

Additional factors may influence fibril stability in vivo. The glycan molecules and amyloid P component found in amyloid deposits may stabilize amyloid fibrils (Pepys, 2006, and references therein). Also, monomer concentration is important to amyloid formation and stability in vivo several amyloidoses are associated with elevated levels of the fibril precursor protein, and deposits regress when the levels of the precursor protein are sufficiently reduced (Pepys, 2006, and references therein). 

As mentioned, the molecular weight between entanglements, Me, or equivalently the entanglement density, ve, is involved in crazing, in craze fibril stability and, thus, in crack formation and propagation. 

Owing to the important role played by fibril stability in the behaviour at high temperatures, it is more suitable to consider the toughness as a function of (Ta - T). Thus, Kic and G c are plotted versus (Ta-T) in Fig. 64. 

As regards the temperature range above - 40 °C, the effect of chemical structure is limited to the results of toughness of MI and MT0.5I0.5 copolyamides, due to the meaningless data obtained for MT0.7I0.3 copolyamide (as explained above). Furthermore, the temperature dependence is expressed in terms of (T - Ta), since the chain mobility plays an important role in fibril stability in this temperature range. The corresponding data for K c and Gic are plotted as a function of (T - Ta) in Fig. 110. Furthermore, the yield stress, cry, for the two copolyamides is shown as a function of (T- Ta) in Fig. 111. 

Nyrkova, I.A., Semenov, A.N., Aggeli, A., and Boden, N. "Fibril stability in solutions of twisted beta-sheet peptides a new kind of micellization in chiral systems". Eur. Phys.. B 17(3), 481-497 (2000b). 

The loss of entanglements (and the decrease in molecular weight due to chain scission) adversely impacts fibril stability. Fibril breakdown by localized creep should occur more rapidly in polymer crazes with low entanglement densities and small diameter fibrils. 

Fig. 36. Craze fibril stability — 8, in the PS blends (2,000 + 1,800,000) for ultraclean specimens (strain rate = 3x10 s ) as a function of %, the weight fraction of the high molecular component in the blend The solid curve is a prediction from the model of fibril breakdown, Eq. (41)...

The results in Fig. 37 reinforce how important the entanglements are for fibril stability It shows the results for measured for blends with x = 0.3 as a... 

Fig. 37. Effect of the diluent molecular weight in blends with 1,800,000 molecular weight PS (X = 0.3) on craze fibril stability (e — ej. The samples were unfiltered and the strain rate used was 5 X 10 s Mc(as2Me) is the critical molecular weight for entanglement effects on the zero-shear-rate viscosity (From Ref. courtesy Macromolecules (ACS))...

While one might suppose that one could correlate the fibril stability for the mono-disperse PS s and the PS blends by using the number-average, viscosity-average or... 

Fig. 38. Craze fibril stability (s - ej versus the number-average molecular weight M , weight-average molecular weight M, and viscosity-average molecular weight for ultraclean specimens...

It is possible to make models which give microscopic meaning to the Weibull parameter 8 of the statistical description of fibril breakdown given in Eq. (31), or the related fibril stability — e. The necessary inputs are values for Pg CSi) which is defined as the P at a craze stress corresponding to a plastic strain e = 1. Modi-... 

With the exception of all the parameters in Eqs. (40) and (41) are known so we can compute values of the fibril stability for various values of and compare these with experiment. (Actually the entire quantity which appears in the exponent... 

Fig. 39. Craze fibril stability (e — e, ) versus molecular weight for the ultraclean nearly mono-disperse PS films The solid lines are computed using the model for craze fibril stability and three different i , 150 s, 195 s and 250 s...

Figure 39 shows the results of this fitting procedure for the data of Yang et al, for different molecular weight monodisperse polystyrenes. Computed fibril stability curves for residence times of 150 sec and 250 sec, as well as 195 sec which produces the best fit, are shown as solid lines. Note that varying the residence time simply appears to scale the fibril stability curve up or down by nearly a constant factor without... 

Fig. 40a. Craze fibril stability (e — e ) versus n, the mean number of effectively entangled strands per fibril for monodisperse PS (circles) PS molecular weight blends (squares) monodisperse PMMA (diamonds) and monodisperse PotMS (stars) The solid lines are the predictions of the model using the parameters given in the text, b Craze fibril stability (e — e ) vereus 1 / where is the mean force per effectively entangled strand in the fibrils. Same symbols and lines as in a...

The same residence time of 195 seconds which fits the fibril stabihty versus M data for PS also can be used to predict the fibril stability in the blends of high and low molecular weight PS. The computed fibril stability for these blends is shown as the solid curve in Fig. 36. The general decrease in fibril stability predicted as the volume fraction of high molecular weight PS in the blend is decreased is in reasonable agreement with the data. 

It has been previously suggested that fibril stability can be correlated uniquely with n, the mean number of entangled strands within each fibril which survive fibril formation. The present analysis does not quantitatively bear out this claim as demonstrated by the plot of fibril stability versus n shown in Fig. 40a. While the fibril stability certainly increases with n, not even the data for the monodisperse PS s and the PS blends fall on the same curve. In particular the use of the incorrect formula for the entanglement density of the diluted blends (v = [v] % instead of the correct v = [v] x ) caused a fortuitous superposition of the data in the paper by Yang et al. 

Plotting the data as fibril stability versus l/ where is the mean force per surviving strand (1 / = nJF) narrows the range between the curves on the abscissa as shown in Fig. 40 b but just as clearly l/ does not produce a much better single parameter description of the fibril stability than does n alone. 

Since even relatively small stress concentrations can increase P by orders of magnitude even small volume fractions of a stress concentrating particle will lead to serious decreases in the measured fibril stability. To demonstrate this in a concrete manner we have computed the effect of a volume fraction =0.01 of a stress concentrator with a stress concentration factor of 4 for PS films of various molecular weights using the same 195 sec) we used for comparison with the dust free... 

Fig. 41. Craze fibril stability (e — versus molecular weight for monodisperse PS. Dust free ultraclean films (circles), dust-containing unfiltered films (squares). Dashed line is the same curve as in Fig. 39 with = 195 solid line is computed using Eq. (42) assuming a volume fraction of 0.01 of dust particles with a stress concentration factor of 4...

Wilkins DK, Dobson CM, Gross M (2000) Biophysical studies of the development of amyloid fibrils from a peptide fragment of cold shock protein B. Eur J Biochem 267 2609-2616 Williams AD, Shivaprasad S, Wetzel R (2006) Alanine scanning mutagenesis of Abeta(1 0) amyloid fibril stability. J Mol Biol 357 1283-1294... 

---