Bundle model

Application of the Bundle Model to Selected Experimental Data. 95... 

The bundle model of polymer crystallization will be discussed first. This mean-field approach describes the metastable configurational equilibrium of the undercooled polymer chain in solution or in the melt, and we will summarize and update previous work of ours [7-9]. The concept of the bundle, i.e. an aggregate of a few parallel polymer segments or stems connected by folds (see Fig. 1 see also [10]) and stabilized by attractive crystal-like interac-... 

We will then examine other flexible polymer crystallization instances which may be interpreted, at least qualitatively, in terms of the bundle model. We will concentrate on crystallization occurring through metastable mesophases which develop by quenching polymers like isotactic polypropylene, syndiotactic polypropylene etc. In principle also hexagonal crystallization of highly defective polymers, and order developing in some microphase-separated copolymer systems could be discussed in a similar perspective but these two areas will be treated in future work. A comparison between the bundle approach and pertinent results of selected molecular simulation approaches follows. 

In any state preceding the onset of crystallization at T < To we assume that bundle stability is favored by localized attractive interactions between contacting (short) stems, some enthalpy advantage being balanced by a corresponding entropy loss (see Fig. 3). Depending upon the core structure of the crystalline stems, various bundle models were examined [8,9]. In the present... 

Fig. 3 a Scheme of a bundle (Model A [8,9]). Chain repeating units are evidenced as black dots, crystalline packed stems are shown as thickened straight portions of the chain, dashed lines stand for crystal-like attractions, b A bundle comprising 4 stems, 3 loops (see Appendix). Dashed lines stand for energy attraction between crystal-like stems with a chain atoms n, 7 2, 3 are numbers of chain atoms in the loops... 

Pre-crystalline order in PET has been investigated by a number of different groups and in the present volume the issue is reviewed under different perspectives in two other contributions [25,26]. Nodular structures measuring ca. 7.5 nm and ca 15 nm apart in PET quenched from the melt close to Tg were first described by Geil [27,28]. Such structures are essentially amorphous, albeit characterized by some degree of orientational order and by a significantly higher density as compared to the fully isotropic polymer. They are indeed qualitatively compatible with the bundle model we propose [29]. Apparently... 

Both our bundle model and MMP s may also be useful approaches to represent the first stage of a polymer mesophase formation from an amorphous system, a process which can be considered a specific mode of polymer crys-... 

We note here that all the information presently available on high molecular weight polymer crystal structures is compatible with the bundle model. While very nearly all crystalline polymer polymorphs involve all-parallel chain arrangements, even the only known exception, namely y-iPP [104,105], where chains oriented at 80° to each other coexist, is characterized by bilayers of parallel chains with opposite orientation. This structure is thus easily compatible with crystallization mechanisms involving deposition of bundles of 5-10 antiparallel stems on the growing crystal surface. Also the preferred growth... 

Kohn, W. D., and Hodges, R. S. (1998). De novo design of alpha-helical coiled coils and bundles Models for the development of protein-design principles. Trends Biotech-nol. 16, 379-389. 

A CEC column can be considered as a collection of capillary tubes with the average channel size between the particles corresponds to the diameter of each tube. Using such a capillary bundle model, the following relationship between the mean channel diameter and the particle size was derived [37] ... 

Figure 3 Parallel-bundle model for a supported zeolite FCC catalyst. (From Ref. 12.)...

---