Crystalline stem length

Fig. 11 Monomer distributions of 32-mers with Ef/Ec = 0.1 at Ec/k /T =0.174 vs. variable crystalline-stem lengths changing with time during isothermal crystallization at a specific temperature. The evolution time is denoted by the numbers (times 1000 Monte Carlo cycles) near the curves. The curves are shifted vertically with an interval of 300 for clarity. We can see that with time the peak shifts from one third to half of the chain length [56]...

Provided the crystalline stem length t,c is known and a stacked lamellar structure is assumed, the thicknesses of the interphase and amorphous phase can be evaluated from these data by the Eqs. (6) and (7) ... 

Figure 8. Orientation of the lamellae and the molecular chains with respect to the extrusion direction. The angles uand cji represent tilting of the lamellar normal and the chains from the extrusion direction, respectively. L and L show the crystalline stem length and the lamellar long period, respectively.

Crystallisation of synthetic 3 5-l,4-polyisoprene at-20 °C in hexane and amylacetate solutions gave chain-folded a-type crystals with 53% and 57% crystallinity, respectively. Selective ozonolysis degradation of the isoprene units in the surface folds associated with high-resolution GPC measurement was used to determine the crystalline stem length, stem length distribution and fold surface structure of TPI crystals. 

In view of this disagreement, as well as of evidence from polymer mesophases and MD simulations, we also propose an alternative model, based on the concept that the attractive interactions are so short-lived as to be effectively delocalized. As a consequence, bridges separating consecutive bundles are also taken into account in the evaluation of the average stem length of the growing crystal, in addition to the crystalline stems and to the loops... 

Figure 4.7 Stem length distribution in crystalline PE. ( 4) Progressive etching of the lamellar crystals in LLDPE—fuming nitric acid at 60°C (i) 24 h (ii) 144 h (iii) 480 h (iv) 960 h. (B) Comparison of the stem length distribution determined by different techniques (i) analysis of the DSC determined melting curve (ii) SEC of etched stems (iii) Raman spectroscopy (iv) calculated, assuming fractionation by stem length and random branch distribution.

Fig. 2.1. Cylinder model for the single crystal. The cross-section contains /i crystalline stems of length m. The (tight) folds and ends are comprised in an excess free energy Cf. Almost all monomers are considered to be contained in the crystalline fraction...

Fig. 2.2. Two-phase model for a cylindrical polymer crystal, (a) Loops and tails are explicitly considered as an amorphous fraction in thermodynamic equilibrium with the crystalline fraction. The height of the amorphous layers is denotes by h, keeping the notation for m as the length of the crystalline stems. Both length scales are considered in units of statistical segments, (b) Illustration of the thermodynamic equilibrium system. Segments can be exchanged between two phases and the temperature is considered to be lower than equilibrium melting temperature...

The free-energy change for secondary crystal nucleation can be estimated in a way similar to the above primary nucleation. Assuming a rectangular bundle of crystalline stems with the lateral size a and the stem length I,... 

Figure 4 Schematics depicting the basics of the Lauritzen-Hoffman secondary nucleation theory. G indicates the lateral rate of grovrth accessible in the experiments, while stands for the propagation rate of the nucleus in the row direction until it reaches a dislocation defect or impinges on a neighboring nucleus /.stands for the so-called persistence length of the lamellar crystal while /c is the fold length of the lamella a and b are the lateral dimensions of a crystalline stem and a are the surface energies for the fold and lateral surface, respectively.

The crystal structure of NR is orthorhombic (space group Pbca) The (002) diffraction line, that is originated by lattice planes perpendicular to the c chain axis, is particularly informative. The corresponding average crystallite dimension, Z.002, assessed by the Scherrer equation, is often called in the literature the stem length and is used to describe the size of rubber crystallites. The (200) and (120) reflections correspond to lattice planes parallel to the chain direction. A very widespread procedure for measuring the crystallinity or rubber is based on the Mitchell method ... 

The longitudinal acoustic mode (LAM), measured by Raman spectroscopy, continues to be a powerful means of measuring the average stem length in crystalline polymers. Its application has been extended to polyethers, poly-thioether," and also polytetrafluorethylene and its oligomers. ... 

The intended role of the glycylalanine repeats in this design is the formation of p-sheet crystalline stems,7.8 while residues X and Y are chosen to form reverse tums.9,10 In each case, the selection of local sequence elements was based on information about the conformational properties of known polypeptides poly(glycylalanine) has been reported to form p-sheet crystals, , and Sibanda and Thornton have identified five X,Y pairs that appear to favor p-hairpin formation in globular proteins.9,10 As of this writing, we have expressed six different sequence variants of 1, and several chain-length variants as well. Detailed structural analysis by x-ray scattering and spectroscopic methods is underway and will be repotted elsewhere. 

Fig. 2. Sketch of a chain connecting two crosslinks. The end-to-end length is r, the solid line stands for a crystalline stem at an angle 0 with the direction represented by r. Statistical-segment discontinuities are disregarded.

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