Crystallites thickness

Primary crystallization occurs when chain segments from a molten polymer that is below its equilibrium melting temperature deposit themselves on the growing face of a crystallite or a nucleus. Primary crystal growth takes place in the "a and b directions, relative to the unit cell, as shown schematically in Fig. 7.8. Inevitably, either the a or b direction of growth is thermodynamically favored and lamellae tend to grow faster in one direction than the other. The crystallite thickness, i.e., the c dimension of the crystallite, remains constant for a given crystallization temperature. Crystallite thickness is proportional to the crystallization temperature. 

The low-frequency LAM in Raman spectroscopy is a vibrational mode pertaining to ordered sequences in the chain direction. The mode frequency (An) is inversely proportional to the ordered chain sequence length or to the crystallite thickness. This relation was given by Shimanouchi and co-workers [92,93] as ... 

Raman LAM, SAXS and TEM have been used to obtain the dependence of crystallite thickness with molecular weight under rapid crystallization as well as... 

Figure 20 Normalized frequency distributions of crystallite thickness for linear polyethylene fraction, Mn = 76,700, Mw = 80,800 crystallized at 118 °C ( ), electron micrograph histogram ...

Figure 21 Plot of thickness values as a function of molecular weight for linear polyethylene fractions quenched to —78°C. (A), crystallite thickness, Lc (O), interlamellar thickness, La ( ), interfacial thickness, Lb. Reprinted with permission from Ref. [277]. Copyright 1990 American Chemical Society.

Figure 8.40. Computer-simulated IDFs gi (u) of ID two-phase structure formed by the iterated stochastic structure formation process. tt is the thickness of the transition layer at the phase boundary. o> is the standard deviation of a Gaussian crystallite thickness distribution... 

Several computed IDFs of iterated stochastic structures are presented in Fig. 8.40. As long as the crystallite thickness is uniform, the truncated exponentials of the amorphous thickness distributions are clearly identified in the IDF. 

Figure 8.46. Construction of observable distances (dal, Lf) in a paracrystal from its fundamental distances, L (not observable pseudo long-periods), and dcl (observable crystallite thicknesses). Advancing to the bottom the relations to the observable thicknesses of amorphous layers, dm, and the long periods, L , are sketched...

Illite contents of the run products were measured by the techniques of Srodon (43, 44) using crystallite thickness determined from XRD characteristics of the starting smectites. Most illite contents were measured using the 003 and 005 XRD peaks (smectite reflections), but the 003 and 006 peaks (47) were used in the runs that contained muscovite. 

Figure 2. Plot of XRD peak positions (CuK radiation ethylene glycol-solvated samples) for Kinney smectite treated with 0.05 N Na + K exchange solutions. Experimental points are labeled with percentages of K in solution. The graph, used to determine percentage illite layers and glycol-spacing for illite/smectites having crystallite thickness of 1-14 layers, is from (42).

Sample Specific surface area, m2 /g Crystallite Thickness, L, nm Diameter, L, 9 t a nm d Spacing, nm... 

FIGURE 12.3 Charge capacities (Crev at the second cycle) from diverse carbon materials as a function of crystallite thickness. (Reprinted from Endo, M., et al., J. Phys. Chem. Solids, 57, 725, 1996. With permission.)... 

Most of the pressure crystallisation research has been done on polyethylene. Pressures of 3 kbar or higher are required to obtain crystallite thicknesses of 10-7 m. Some other polymers have a much stronger tendency towards extended chain formation. Poly(chloro trifluoro) ethylene shows this effect at about 1 kbar poly(tetrafluoro)ethene already at about 0.3 kbar. 

Crystallite parameters La, crystallite diameter in the plane of the a axis Lc, crystallite thickness in the C axis a, graphite unit cell dimension in the plane of the layers C, twice the interlayer spacing in the graphite matrix. 

Furthermore, intralamellar contrast increases. Finally, at very high molecular weights (M. , = 1.6 X 10 ) only very short crystallite segments are observed. The histograms presented in Fig. 2 show that the crystallite thickness distribution is fairly narrow and that the measured values appear to be unaffected by molecular weight. This is clearly indicated in Fig. 3, where the maximum, average, and minimum crystal... 

Where t is the crystallite thickness (A), B and B are the width in radians of the diffraction peaks (at half maximum height) of the test sample and a highly crystalline standard sample, respectively, and X (A) is the wavelength of the X-ray beam. 

Figure 8.41. Liquid scattering projected on the meridian, / j ( 3), originating from random placement of lamellae along a shish. The form factor of the dilute system is displayed for reference. Structure parameters as in Fig. 8.40. Uniform crystallite thickness leads to characteristic minima in the scattering curves. Note the varying strength of the oscillations...

Drits VA, Srodon J, Eberl DD (1997) XRD measurements of mean crystallite thickness of illite and illite/smectite Reappraisal of the Ktbler index and the Scherrer equation. Clays Clay Minerals 45 461-475... 

Warr LN, Nieto F (1998) Crystallite thickness and defect density of phyllosihcates in low-temperature metamorphic pelites A TEM and XRD study of clay mineral ciystalhnity-index standards. Can Mineral 36 1453-1474... 

It appears that the crystalline lamellar thickness in the block copolymers does not change as much with PS content. This agrees with the observation of the low melting point depression of block copolymers compared with that of the homo-PTHF since the melting point is determined not only by the end interfacial free energy of crystallite but also by the crystallite thickness. 

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