Chain crystals

The effect of different types of comonomers on varies. VDC—MA copolymers mote closely obey Flory s melting-point depression theory than do copolymers with VC or AN. Studies have shown that, for the copolymers of VDC with MA, Flory s theory needs modification to include both lamella thickness and surface free energy (69). The VDC—VC and VDC—AN copolymers typically have severe composition drift, therefore most of the comonomer units do not belong to crystallizing chains. Hence, they neither enter the crystal as defects nor cause lamellar thickness to decrease, so the depression of the melting temperature is less than expected. 

Fig. 31 Trajectories of seven crystallizing chains (thick lines) selected at random from 640 chains during crystallization at 330 K a at 0.128 ns, b at 6.4 ns, c at 12.8 ns, and d at 19.2 ns. Also shown are the growing crystalline domains (thin parallel lines). Pictures are all side view along the x-axis...

The end-to-end vector r of any non-crystallized chain portion comprising n skeletal bonds with a length l will be taken as Gaussian-distributed, i.e.,... 

Figure 2.46 Model of packing of conformationally disordered chains of sPP in disordered modifications of form II presenting kink bands.189,190 Chains drawn with thick and thin fines are at 0 and 0.5 along b. In the ordered portion of crystal chains are in ordered twofold (T2G2)B helical conformation, whereas in the defective portion (delimited by dashed lines) chains are in T2G2T6 conformation.

Many semicrystalline polymers are polymorphic and exist in different crystal forms. When PBT fiber is uniaxially stretched [75], the contracted gauche-trans-gauche a-crystal chain is extended to a fully trans conformation of a y-crystal. Above 20% strain, the crystal form is 100% y-crystal with a longer c-axis triclinic cell dimension. Thus, it is reasonable to ask whether the... 

AMI calculations on dimers of nitroanilines are of interest in investigating the inter-molecular forces which orientate the individual molecules in crystal chains. Dimerization in solid crystal may be considered responsible for the differences in molecular geometry between solid and gas phases97. 

The. folded-chain lamella theory arose in the last 1950s when polymer single crystals in the form of thin platelets termed lamella, measuring about 10,000 A x 100 A, were grown from polymer solutions. Contrary to previous expectations, X-ray diffraction patterns showed the polymer chain axes to be parallel to the smaller dimension of the platelet. Since polymer molecules are much longer than 100 A, the polymer molecules are presumed to fold back and forth on themselves in an accordionlike manner in the process of crystallization. Chain... 

If the growth front is frozen, the crystallization at the growth front depends crucially on the commensurability between the thickness of the growth front and the length of crystallizing chains. For details, see Ref. 49. A collection of polydisperse chains gets effectively fractionated at the growth front. 

Thus, they are in rather close contact with each other. In crystals chains of hydrogen-bonded atoms may be formed. In phosphatidylethanolamine the phosphate and -NH3+ ions may alternate in these chains.132... 

The crystal structure of I strongly resembles the relaxed crystal dimer structure (B). In the case of II, structure IIB would require a bend in the crystal chain that might be very difficult to accommodate. 

AMI calculations on the dimers of nitroanilines and substituted benzoic acids are of considerable value in predicting their crystal structures. In particular, the intermolecular forces that dictate the relative orientations of the individual molecules in the crystal chains can be understood. It is likely that this methodology will be useful for modelling the kinds of interactions that might occur in other crystals. 

Conditions required to generate A- and B-type crystal conformations are reasonably well-understood. Under cool, wet conditions (such as in a potato tuber), B-type starch crystals form, while in warmer, drier conditions (e.g. in a cereal grain), the A allomorph is preferred. Chain length also affects the selection of crystal form, chains of DP <10 do not crystallize, chains with a DP from 10 to 12 tend to form A-type crystals, and chains with a DP >12 tend to yield the B form.37,38 This is likely the result of differences in loss of entropy on crystallization experienced by chains of different lengths.39 An irreversible transition from B-type starch to A-type starch can be accomplished under conditions of low humidity and high temperature. This so-called... 

The answer is very simple. Putting aside crystal chains which terminate at the interface (only significantly available in low molecular weight material) there are two possibilities (fig. 2). 

Philpotts A. R., Shi J., and Brustman C. (1998) Role of plagioclase crystal chains in the differentiation of partly crystallized basaltic magma. Nature 395, 343-346. 

Figure 4.10 shows a plot of He as a function of f for different PE and paraffin samples crystallized from the melt. The calculated continuous curve was derived using b = 20 nm. The deviation of the experimental data from the calculated curve is due to the wide range of b values obtained (b = 6-26 nm), corresponding to the widely different structures examined (CEPE crystals, chain-folded lamellae, low-density (LD) PE and linear paraffins). Comparison of experimental and calculated He data for PE emphasizes the parallel increase in the b parameter derived from mechanical data (14-26 nm) and in determined thermodynamically (79-91 mJ m ) for a series of samples with different molecular weights (56000-307000) (Balta Calleja et al, 1990b) (see also Section 4.3). 

Figure 15. Aggregated nanoparticles of titania forming a single-crystal chain, an example of oriented aggregation. From Penn and Barrfield (1999) with permission from Elsevier, pubhshers of...

Figure 51. A series of fluctuations at the crystal growth face. The squares represent crystallized chain segments, (a) Steps allowed in the Frank-Tosi model,226 (b and c) some other possible steps (after ref 4).

Keywords Block copolymers, Crystallization, Chain folding... 

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