PHB/LCAB PHB/HCAB
3.3 Temperature Dependence of the WAXD Profiles of PHB/CAB (50/50) Blend
Figure 4 presents temperature-dependence of WAXD profiles of the blend measured in the heating process from 25 to 180 OC. Peaks at 2e - 8.8 and 11.0O are due to (020) and (110) diffractions from PHB crystals in the blend, while the peaks at 2e - 5.1, 6.5, 8.1, 10.0, 11.5 O are assigned to CAB crystals in the blend. The overall trend in the T-dependence of WAXS profiles is highlighted in the inset (a) and (b) for the particular diffraction profiles at 2e z 5.10
for CAB and at 2e i 10.0 O for PHB. The T-dependence of the WAXD profiles can be
classified into Low-T, Crossover-T, and High-T Regions as in the case of the T-dependence of the SAXS profiles.In Low-T Region, the (110) diflliraction peak intensity from PHB crystals increases and the Bragg angle at the peak shifts toward smaller 2e with T, indicating that the C. C. of PHB proceeds and the PHB crystals become more perfect with T. On the other hand CAB still remains amorphous, as evidenced by the diffraction profiles at 2e cr 5.1 O. in Crossover-T Region, the partial melting ofPHB and recrystallization into more perfect crystals occur with increase T, as evidenced by the decreasing (200) diffraction intensity of PHB and a shift of the diffraction peak toward small 20. 0n the contrary, the CC of CAB starts to proceed, so
-113- ,
that the peak intensity and width of the diffraction at 2e ! 5.1 O increases and narrows,
respectively. In High-T Region, the PHB crystals continue to melt up to -173 OC and
eventually transform to a complete melt, as evidenced by the decrease of the (1 1O) diffractionpeak intensity with almost no peak shift. The CC of CAB continues to progress, as
evidenced by the increasing diffraction peak intensity at 2e i 5.1 O.
It is important to note some differences in the T-dependence of the WAXD and SAXS profiles in this High-T Region: (1) the SAXS peak intensity at q g O.3 nm-i, apparently reflecting the long spacing of the CAB crystals, decreases with T, while the WAXD peak intensity at 2e i 5.10 keeps increasing and hence the CC of CAB continues to progress; (2) the SAXS peak at g i O.9 nm-i, reflecting the long spacing ofPHB lamellar crystals, cannot be obviously observed, though the PHB crystals still remains to exist. These apparent discrepancies will be clarified later in section 4.4.
3.4 Temperature-dependence of the SAXS Intensities at q z O.2 and O.9 nm-i in PHB/CAB (50/50) Blend. Figure 6 displays temperature dependence of typical SAXS
intensities at (a) q = O.9 nm-i relevant to the PHB long period in the blend and (b) g = O.2 nm-i relevant to the CAB long period in the blend taken in the heating process for pure PHB, PHBICAB (20/80, 25175, 30/70, 50/50, and 60/40) blends, and pure CAB. The inflection point shown by the arrow with a specified temperature in I(g = O.9 nm'i) vs T (part a) was assigned to be the onset temperature Tcc,pHB for CC of PHB in the blend. The Tg,h,sAxs for each blend as indicated in part (b) was estimated from the inflection point at the lower temperature (as shown by the arrow with a specified temperature), while the Tcc,cAB was estimated from that inflection point at the higher temperature (shown by the red arrow with a specified temperature). In order to display these inflection points more clearly than part (b), the SAXS intensities at g :O.2 nm-i at from 100 to 120 OC and from 130 to 150 OC are enlarged and shown in part (c) and (d), respectively. Moreover, the Tcc,pHB and Tcc,cAB ofthe blends were confirmed also from T-dependence of the WAXD peak intensities of (110) and (020) lattice plane PHB crystals and at 2e cr 5.10 from the CAB crystals, respectively, as will be shown later in conjunction with Figure 1O(b) in section 4.4.
4. Discussion
4.1. Scaling Analysis of SAXS Profiles in Low-T Region. It is reasonable to assume that the CC ofPHB in Low-T Region, as evidenced in Figures 3(b) and 4(a), involves growth of one-dimensional assemblies of PHB lamellae under the condition where the assemblies
themselves are randomly oriented in three-dimensional space. The scattering from a randomly oriented one-dimensional assembly in which centers-of-mass of particles are
oriented in the paracrystalline lattice, Itheor(g), is given by
Itheor(q)q2 - [<Lf(q)l2>-l<Lf(q)>l2]+(11 ij ) I< f (q)> 12z(q)" ls(q) 12 (3)
where i<Lf(g)>l2 is the form factor of the particle (lamella of thickness D, in our case) in the assembly; Z(g) and IS(g) 12 are the paracrystalline lattice factor and the shape factor of the assembly; the symbol * designates the convolution product, v is the volume per lattice, and
< > designates the average oflf(q)21 or.f(q) with respect to the polydispersity in the particle size and orientation fluctuations ofthe particles within the assembly.
'
For a qualitative analysis oflc(q) with Itheor(q), we can neglect the diffuse scattering term [the first term ofthe right hand side (rhs) ofeq 1] due to the polydispersity ofthe particle size and the orientation fluctuations of the particle. Moreover, IS(q)12 is assumed to be given by delta function or the zeroth-order scattering from the assemblies as a whole is assumed not to give significant effects on Ic(g) over the q-range covered in this work. In this case, eq 3 is simply given by
Itheor(g)q2 N (1/ii) l<f(q)> 12Z(g)
(4)
Noting that u"' oc LpHB (the long spacing ofthe PHB lamellae in our case) and 1/(g)12 is given by
v(q)l2•- Ap2D,,,., Si("iif,ei•,PIH2B)/,2) (5)
where Dc,pHB is the PHB lamellae thickness, eq 4 is given by
Itheorq2 •- Ap2ÅëZ,pHBqiiiiD,,pHB Si("ii{,Åë,k',P.")B,X) Z(q) ' (6)
Here Ajo is the electron density difference between PHB lamellae and their matrix, ÅëL, is the average volume fraction of the PHB lamellae in the assembly given by gZt,pHB = Dc,pHBILpHB,
and
qm ii 2n/LpHB;xE q/gm. - (7)
Then from eqs (6) and (7), one obtains
Ith,., (x)x2 qmN Ap2 qbZ,pHBF(x) (8)
with
sin2 (Tt(PLx)
Z(q) (9)
("eLx)2
Consequently, if ÅëL,pHB and Ap?! is kept constant with T in Low-T Region, the scaled structure factor F(x) becomes universal with T, and hence the scaled scattering function Itheor(x) x2qm also becomes universal with T. F(x) gives the scaling function for the structure factor from the self-similarly grown one--dimensional assembly of the lamellae with T. It should be noted that the above equation is derived for the scattering from a single assembly. If there are many assemblies or grains, the rhs of eq 8 should be multiplied by the number of the assemblies (or grains) GM.
Figure 7 displays the plot of the experimental scaled scattering function Ic(x) x2gm(7) vs x in Low-T Region in the double logaritimic scale. The value qm(7) obtained from Figure 3(b) and used to construct the scaled scattering function in Figure 7 is shown later in Figure
10(d). In part (a), the peak intensity of the scaled scattering function increases with T,
which is due to an increase ofthe prefactor Ap2ÅëL,pHB2GM with T. We think that an increase of GM, hence the increase oftotal number ofPHB lamellae, is more likely than an increase of Ap?shL2. In part (b), the experimental scaled scattering in vertically shifted in the double logaritlmic scale, so that the fUnction at the peak position ofx=(q/qm) =1 becomes identical to that at 140 OC. The vertical shift is mathematically equivalent to multiply the temperature dependent shift factor a(7) to the scaled scattering function I,(x) x2gm(7), where a<7) is defined by
a(7) iii [Ic(x-1) g.] T==i4o Oc1 [Ic(x-1) qm]T (1O)
The vertically shifted scaled scattering ftmctions facilitate to compare the shape of the functions at various Ts.
Figure 7(b) reveals that the shape of the scaled scattering fimction is almost universal with T in the T range satisfying 25STXfTg,hillOOC. Thus, in this temperature range, the one-dimensional assemblies of PHB lamellae grow self-similarly with T as schematically illustrated in Figure 8(a). The deviation seems to be remarkable at RTg,h, though the deviation is seen to be still small at 125 OC but large at 140 OC in the small g-range at q/qm <
1. The smaller the q-value is, the large is the deviation. We found that the deviation is
caused by an evolution of the new scattering ftmction, which tends to increase with
decreasing q in the g-range smaller than gm, with increasing T;EtrTg,h, in excess to the scattering from the one-dimensional assemblies of the PHB lamellae. It is quite important to recall here that, in Low-T Region, CAB remains amorphous and only PHB is crystallized with the crystallinity in the blend smaller tan O.28.30 The evolution of the excess scattering at the small q-range reveals itself evolution of the electron density fluctuations at the length scale r much larger than 2nlqm or 70 nm as a consequence of the evolution of the large length-scale composition fluctuations between PHB and CAB in the interstitial amorphous matrix among the PHB lamellar assemblies as illustrated in Figure 8(b).
Figure 8(a) schematically presents one-dimensional assemblies ofPHB lamellae crystals Gi to GM formed in Low-T Region with the long spacing LpHB, the lamellar thickness Dc,pHB, the interlamellar amorphous layer thickness DapHB, and total number of the assemblies GM.
The unit vector n showing the assembly axis is randomly oriented in 3D space. Figure 8(b) presents a Fourier mode of the composition fluctuations with wave number q in the 1arge length-scale composition fluctuations evolved at RTg,h in Low-T Region in the interstitial