Polymer crystal basic structure

Among the numerous challenges faced in understanding the formation and evolution of hierarchical structures in polymer crystallization, we restrict ourselves to explain the essential basic features of folded lamellae. Specihcally, we consider (1) molecular origin of enhanced scattered intensity before any crystallographic features are apparent, (2) spontaneous selection of small lamellar thickness, (3) molecular details of growth front, and (4) formation of shish-kebab structures in the presence of a flow. 

In polymer crystallization the challenge is to identify and clarify the transformations by which chain molecules pass from a disordered, molten state to the ordered supra-molecular organization known as the semi-crystalline state. The subject is highly relevant in terms of both basic science and technology it is indeed clear that many modern applications require complete control of the structure and the morphology of polymers from macroscopic dimensions down to below the nanoscale. As a simple example, making the crystallites in a polymer liber equally oriented and reducing the number of chain folds (or hairpins) therein, usually turn out to be very favorable requisites for mechanical performance. 

While in volumes 180 and 181 of this series several basic aspects of morphology, inter-phase structure and disorder were addressed, in the present volume, molecular interactions, modeling, phase transformation and crystallization kinetics are considered (see the subject index including keywords from volumes 180 and 181 at the end of the book). Needless to say, in spite of substantial success over 60 years or more we are still far from having a complete and unambiguous picture of polymer crystallization. We firmly believe that a fruitful approach to such a complex problem requires one to give way to many different and sometimes conflicting viewpoints, as we have attempted to do in these volumes. We do hope that they are not only a time-capsule left for... 

Many polymers have the capability to crystallize. This capability basically depends on the structure and regularity of the chains and on the interactions between them. The term sernicrystalline state should be used rather than crystalline state, because regions in which the chains or part of them have an ordered and regular spatial arrangement coexist with disordered regions typical of the amorphous state. X-ray diffraction studies of samples of polymers crystallized from the melt reveal diffuse zones, char-... 

The basic structure of low molecular mass liquid crystals or monomers of liquid crystalline polymers is schematically shown below... 

In the majority of polymer systems designed for an SiC synthesis, the atom ratio C/Si is significantly >1. Therefore, in the crystallization model described by Monthioux and Delverdier [147] the excess carbon is considered to play a very important role. By means of HRTEM it was observed that more or less in all the systems investigated the formation of the so-called Basic Structure Units (BSU) of the free carbon - i.e. the formation of small stacks of only a few polyaromatic layers - seems to be the first step for the following nucleation mechanism of SiC. Such BSUs (graphenes) have lateral extensions in the order of 1 nm, are laterally saturated by hydrogen atoms and piled up in a... 

Whereas crystallization from dilute solutions may result in the formation of single polymer crystals, this perfection is not achieved when deahng with polymers cooled from the melt. The basic characteristic feature is still the lamellar-hke crystallite with amorphous surfaces or interfaces, but the way these are formed may be different, based on the careful investigation of melt-crystallized polymers using neutronscattering techniques. The two models that have been proposed to deseribe the fine structure of these lamellae and their surface characteristics in semicrystalline polymers differ mainly in the way the chains are thought to enter and leave the ordered lamellae regions. These are ... 

The molecules displaying LC phases are highly anisotropic. They might be seen as rigid rods or ellipsoids of revolution with I d. The basic structure of low molecular mass liquid crystals or monomers of LC polymers is given in Figure 5. 

The phase transition from disordered states of polymer melt or solutions to ordered crystals is called crystallization-, while the opposite process is called melting. Nowadays, more than two thirds of the global product volumes of synthetic polymer materials are crystallizable, mainly constituted by those large species, such as high density polyethylene (HOPE), isotactic polypropylene (iPP), linear low density polyethylene (LLDPE), PET and Nylon. Natural polymers such as cellulose, starch, silks and chitins are also semi-crystalUne materials. The crystalline state of polymers provides the necessary mechanical strength to the materials, and thus in nature it not only props up the towering trees, but also protects fragile lives. Therefore, polymer crystallization is a physical process of phase transition with important practical relevance. It controls the assembly of ordered crystalline structures from polymer chains, which determines the basic physical properties of crystalline polymer materials. 

Basic Structure Crystal orientation Crystallite content Homogeneity Precursor Polymer composition Appropriate fiber tension High density and compactness Prevent filament coalescence... 

An enlargement of the experimental data range is obviously of interest also for a better understanding of basic phenomenon. Indeed, despite the large number of papers concerning polymer crystallization, the role of mesomorphic phase in the formation of the crystalline structures is not completely... 

The outline of the paper is as follows. In Sect. 2 we describe the basic RISM and PRISM formalisms, and the fundamental approximations invoked that render the polymer problem tractable. The predicticms of PRISM theory for the structure of polymer melts are described in Sect. 3 for a variety of single chain models, including a comparison of atomistic calculations for polyethylene melt with diffraction experiments. The general problem of calculating thermodynamic properties, and particularly the equation-of-state, within the PRISM formalism is described in Sect. 4. A detailed application to polyethylene fluids is summarized and compared with experiment. The develojanent of a density functional theory to treat polymer crystallization is briefly discussed in Sect. 5, and numerical predictions for polyethylene and polytetrafluoroethylene are summarized. 

In most cases, structural analysis of polymer crystals is carried out using uniaxially oriented samples (fibers or films). The basic procedures include (1) determination of the fiber period (2) indexing (hkl) diffractions and determining the unit cell parameters (5) determination of the space group symmetry (4) structural analysis and (5) Fourier transforms and syntheses and Patterson functions. The first three aspects of the procedure are discussed here, and the last two aspects are left for further references. 

Polymer crystals are always semicrystalline, and thus, they are far from perfect. Limited crystal sizes and complicated aggregates make the basic understanding of the structure-property relationships very difficult. To simplify, two types of properties in general exist for crystals of small molecules structure-insensitive and structure-sensitive properties. The structure-insensitive properties include... 

A large and perfect crystal scatters electrons into a diffraction pattern of sharp spots. General interpretation of this pattern requires a knowledge of crystallography. There are many texts in this field [18-20], with some specifically aimed at microscopists [21, 22]. Books on crystal optics (Section 2.3) contain basic summaries [23, 24]. There are also many texts on diffraction from materials 125-27], some concentrating on electron diffraction [28, 29]. The most common use of a crystal diffraction pattern is to find the orientation of a crystal of known structure. Wunderhch [30] contains a listing of many polymer crystal structures. 

In Crystallization of Polymers, second edition, Leo Mandelkern provides a self-contained, comprehensive, and up-to-date treatment of polymer crystallization. All classes of macromolecules are included and the approach is through the basic disciplines of chemistry and physics. The book discusses the thermodynamics and physical properties that accompany the morphological and structural changes that occur when a collection of molecules of very high molecular weight are transformed from one state to another. 

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