Crystalline dimensions

The cellulose crystallite size is highest in ulvophycean and certain chlorophycean algae (114-169A), lowest in vascular plants (49-62A) and intermediate in Aceiobacter (70-84A) (1). It appears that cellulose crystalline dimensions are independent of the type of terminal cellulose synthesizing complex. The idea that cellulose biosynthesis is not exclusively responsible for determining its crystalline dimensions has been proposed previously by Marx-Figini (52). 

Very little work has appeared in the literature which deals with blends in which the component materials can cocrystallize. It is generally believed (16.17) that a requirement for cocrystallization is that there must be a close matching of the polymer chain conformations and of crystalline dimensions. Also, some level of miscibility should exist between the two polymers and the crstallization kinetics cannot be very different. Certainly, in the case of liquid crystalline polymers, in general, these requirements would be expected to be met. Some of our recent work (8) has suggested, however, that not all liquid crystal polymers do cocrystallize. The present work suggests that in certain cases it may be possible to achieve this effect. 

Figure 6.17 shows that crystalline dimensions affect interlaminar shear strength. Crystalline dimensions on the surface of carbon fibers can be measured by Raman spectroscopy. The ratio of intensity of two bands (1355 and 1575 cm ) is proportional to the crystalline dimensions on the surface. The crystalline width increases considerably from 3 to over 12.5 nm when the temperature of manufacture of carbon fibers is increased from 1000 to 3000°C. The increase in band ratio correlates with an increase in interlaminar shear strength. 

Brockmeier has studied this temperature eflFect at 22-313 K for PE and copolymers of ethylene with propylene (48). The results obtained by monitoring the frequencies of the three doublets could not be attributed to a simple contraction of the unit cell. London dispersion forces and changes in the helix of the molecule were possible complicating factors. Shen et al. have observed the shifting of the rocking doublet, ca. 725 cmfrom 10 K to room temperature for solution-crystallized PE (49). The 731 and 720 cm components are polarized along the a and b axes of the unit cell, respectively. Shen found no preferential correlation of either frequency s shift with x-ray measurements of expansion of a crystalline dimension. However, a linear relation was found for the frequency of the 731 cm" band with the specific volume of the unit cell. In both IR studies, frequency shifts were minimal below approximately 50 K which Brockmeier suggested arose from the lower limit of molecular motion in the crystal (48). 

Recent research efforts have been focused on the synthesis of doped, stabilized zirconia powders, especially with nanometer-sized particles. Nanocrystalline stabilized powders are vital for the preparation of nanocrystalline materials, as their properties are fundamentally different from those of conventional powders, due to the extremely small crystalline dimension, superior phase homogeneity and low-temperature sinterabUity that significantly determines the later-stage processing and sintering properties of ceramics. 

The classical approach to the optical spectra of small partides is presented by Mie scattering theory, which postulates that a nanocrystallite is characterized by the same complex e(A) as the bulk material In the relevant theoretical equation (derived on the assumption that the crystalline dimensions are much less than the optical wavelength A), only the electric dipole term needs to be retained and the extinction cross section a reduces to ... 

For tire purjDoses of tliis review, a nanocrystal is defined as a crystalline solid, witli feature sizes less tlian 50 nm, recovered as a purified powder from a chemical syntliesis and subsequently dissolved as isolated particles in an appropriate solvent. In many ways, tliis definition shares many features witli tliat of colloids , defined broadly as a particle tliat has some linear dimension between 1 and 1000 nm [1] tire study of nanocrystals may be drought of as a new kind of colloid science [2]. Much of die early work on colloidal metal and semiconductor particles stemmed from die photophysics and applications to electrochemistry. (See, for example, die excellent review by Henglein [3].) However, the definition of a colloid does not include any specification of die internal stmcture of die particle. Therein lies die cmcial distinction in nanocrystals, die interior crystalline stmcture is of overwhelming importance. Nanocrystals must tmly be little solids (figure C2.17.1), widi internal stmctures equivalent (or nearly equivalent) to drat of bulk materials. This is a necessary condition if size-dependent studies of nanometre-sized objects are to offer any insight into die behaviour of bulk solids. 

To improve homogeneity, the preformed article is heated to 370—390°C. The time required for heating and sintering depends on the mold dimensions cooling, which affects the crystallinity and product properties, should be slow. 

Poly(vinyl fluoride) [24981-14-4] (PVF) is a semicrystaltiae polymer with a planar, zig-zag configuration (50). The degree of crystallinity can vary significantly from 20—60% (51) and is thought to be primarily a function of defect stmctures. Wide-line nmr and x-ray diffraction studies show the unit cell to contain two monomer units and have the dimensions of a = 0.857 nm, b = 0.495 nm, and c = 0.252 nm (52). Similarity to the phase I crystal form of poly (vinytidene fluoride) suggests an orthorhombic crystal (53). 

In 1921, a discontinuous index of refraction of vitreous Si02 near the a—P transition of quart2 (crystalline Si02) was noted (17). These data and subsequent x-ray investigations of vitreous siHca led to the suggestion (18) that crystaUites on the order of 1.5 nm were present. It was demonstrated, however, that the crystal size would be less than 0.8 nm, and it was suggested that the term crystal loses meaning for these dimensions (19,20). 

These tetrahedra are arranged in a number of ways to give the different zeohtes. The stmctures are unique in that they incorporate pores as part of the regular crystalline stmctures. The pores have dimensions of the order of molecular dimensions so that some molecules fit into the pores and some do not. Hence the zeohtes are molecular sieves (qv), and they are apphed in industrial separations processes to take advantage of this property. Some zeohtes and their pore dimensions are hsted in Table 2. 

Polypropylene. There is an added dimension to the catalytic polymerization of propylene, since in addition to the requirement that the catalyst be sufficiently active to allow minute amounts of catalyst to yield large quantities of polymer, it must also give predominantly polypropylene with high tacticity that is, a highly ordered molecular stmcture with high crystallinity. The three stmctures for polypropylene are the isotactic, syndiotactic, and atactic forms (90) (see Olefin polya rs, polypropylene). 

The complete characterization of a particulate material requires development of a functional relationship between crystal size and population or mass. The functional relationship may assume an analytical form (7), but more frequentiy it is necessary to work with data that do not fit such expressions. As such detail may be cumbersome or unavailable for a crystalline product, the material may be more simply (and less completely) described in terms of a single crystal size and a spread of the distribution about that specified dimension. 

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