Spider Silk: Structure, Engineering, and Applications - Soft Fibrillar Materials: Fabrication and Applications - page 193

800
700

2.5 mms -1

(120) 25 mms -1

1000 (120)

800

600

500

600

400
300
200
100
0
-100

400

200

0

-50 0 50 100 150 200 250 300 350 400 -50 0 50 100 150 200 250 300 350 400

(a) (b) Azimuth (degree) Azimuth (degree)

Figure 6.8 Intensity as a function of az-
imuth angle at the radial position of the
equatorial (120) peak: (a) at 2.5mms − 1 and
(b) at 25mms − 1 . The peaks are fitted as
sums of two Gaussians, corresponding to

crystalline (narrow) and amorphous (broad)
distributions. (Reprinted with permission
from Ref. [17]. Copyright (2006) Biophysical
Society.)

Since (120) is 65 ◦ from the (200), A = 0.8 and B = 1.2. Orientation function f
can be obtained from FWHM . Both (120) and (200) peaks become narrower as the
reeling speed increases (Figure 6.8). These data imply that the orientation function
undergoes a tremendous increase with the reeling speed, from 0.68 for 1 mm s −1
to 0.97 for 100 mm s −1 .

6.3.2.3 Intercrystallite Distance
Assuming that the scatter are the crystallites embedded in the amorphous silk
region, and that they have cylindrical symmetry along the fiber axis, the Small
Angle X-ray Scattering (SAXS) intensity in the equatorial direction can be given
as [89]

Kl c

I = (6.6)

l c q 2 ) 3 / 2 (1 +

where q is

the wavelength of the X-ray, K is a constant, and l c is the correlation length, which
can be determined from the intercept and slope of a plot of I −2 / 3 versus q 2 .For
the scattering along the meridional direction, Equation 6.6 takes a slightly different
form:

= 4 π sin θ/λ is the scattering wave vector, θ is the scattering angle, λ

Kl c

I = (6.7)

1 + l c q 2

The correlation length l c along the meridian is determined from the intercept
and slope of the plot of I −1 versus q 2 . The correlation lengths can be related
to intercrystallite distance. A similar analysis was used in the SAXS study of
the semicrystalline fibers [90] and the small-angle neutron scattering study of
poly(vinyl alcohol) gels in which the cross-linking points are crystallites [91].
However, unlike the gels, silk has a fiber axis with different material properties