Crystals and Crystallinity in Polymers E-Book

Claudio De Rosa

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 1340

Veröffentlichungsjahr: 2013

Beschreibung

Provides the tools needed to master and apply the fundamentals of polymer crystallography Using core concepts in physics, chemistry, polymer science and engineering, this book sheds new light on the complex field of polymer crystallography, enabling readers to evaluate polymer crystallization data and determine the best methods to use for their investigations. The authors set forth a variety of tested and proven methods for analyzing ordered and disordered structures in polymer crystals, including X-ray diffraction, electron diffraction, and microscopy. In addition to the basics, the book explores several advanced and emerging topics in the field such as symmetry breaking, frustration, and the principle of density-driven phase formation. Crystals and Crystallinity in Polymers introduces two new concepts in crystallinity and crystals in synthetic polymers. First, crystallinity in polymeric materials is compatible with the absence of true three-dimensional long-range order. Second, the disorder may be described as a structural feature, using the methods of X-ray scattering and electron diffraction analysis. The book begins by introducing the basic principles and methods for building structural models for the conformation of polymer crystal chains. Next, it covers: * Packing of macromolecules in polymer crystals * Methods for extracting structural parameters from diffraction data * Defects and disorder in polymer crystals * Analytical methods for diffuse scattering from disordered polymer structures * Crystal habit * Influence of crystal defects and structural disorder on the physical and mechanical properties of polymeric materials Crystals and Crystallinity in Polymers examines all the possible types of structural disorder generally present in polymer crystals and describes the influence of each kind of disorder on X-ray and electron diffraction patterns. Its comprehensive, expert coverage makes it possible for readers to learn and apply the fundamentals of polymer crystallography to solve a broad range of problems.

Leseprobe

Table of Contents

Title page

Copyright page

Preface

1: Configuration and Conformation of Macromolecules in Polymer Crystals

1.1 Crystals of Polymers

1.2 Constitution and Configuration of Crystalline Polymers

1.3 Conformation

1.4 Relationships among Internal Parameters of Macromolecules

1.5 Conformation of Polymer Chains in the Crystalline State

1.6 Helical Conformations in Isotactic and Syndiotactic Polymers

1.7 Conformational Energy Calculations

1.8 Helical Conformation and Optical Activity

1.9 Alternating Copolymers

1.10 Polydienes

1.11 Nonhelical Chain Conformations of Isotactic Polymers

2: Packing of Macromolecules in Polymer Crystals

2.1 General Principles

2.2 The Principle of Density (Entropy)-Driven Phase Formation in Polymers

2.3 Symmetry Breaking

2.4 Impact of Chain Folding on Crystal Structure Symmetry

2.5 Frustrated Polymer Crystal Structures

2.6 Chiral Crystallization of Polymers with Helical Chain Conformations

2.7 Packing Effects on the Conformation of Polymer Chains in Crystals: The Case of Aliphatic Polyamides

3: Methods in Crystal Structure Determination from X-Ray Diffraction

3.1 X-Ray Diffraction of Semicrystalline Polymers

3.2 Fourier Synthesis and the Phase Problem in Crystallography

3.3 X-Ray Fiber Diffraction Analysis

3.4 Determination of Parameters of the Unit Cell and Indexing of the Diffraction Pattern

3.5 Measure of the Integrated Intensities of the Reflections and Corrections for Geometric (Lorentz), Polarization, and Absorption Factors

3.6 Calculation of Structure Factors

3.7 Structural Refinement

3.8 Form of Diffraction Pattern and Broadening due to the Laue Function

4: Defects and Disorder in Polymer Crystals

4.1 Classification of Different Types of Structural Disorder

4.2 Crystals with Partial Three-Dimensional Order (Class A): Disorder with Three-Dimensional Periodicity Maintained for Only Some Characterizing Points of the Structure

4.3 Solid Mesophases

5: Methods of Analysis of Diffuse Scattering from Disordered Structures of Polymers

5.1 Structural Disorder and Diffuse Scattering

5.2 Methods of Diffraction Analysis from Disordered Crystals

5.3 Long-Range Order in Disordered Lattices of Class A

5.4 SRO in Disordered Crystals of Class A

5.5 Short-Range Order in Disordered Crystals with Substitution-Type Disorder

5.6 Short-Range versus Long-Range Order in Disordered Crystals of Classes B and C (Solid Mesophases)

5.7 Disordered Models with Perturbations Occurring over Continuous Ranges

5.8 Basic Formulas for the Calculation of X-Ray Diffraction Intensity from Disordered Model Structures of Polymers

5.9 Examples of Calculation of Average Diffracted Intensity of Structures Disordered in One Dimension

5.10 Line and Surface Integration Method of Diffraction Intensity for Fibers and Powders of Polycrystalline Samples

6: Crystal Habits

6.1 Basic Remarks

6.2 Rounded Lateral Habits

6.3 Chain Folding, Molecular Orientation, and Sectorization

6.4 Twinning and Secondary Nucleation Theory

6.5 Homoepitaxy, Morphology, Stem Orientation, and Polymorphism

7: Influence of Crystal Defects and Structural Disorder on the Physical and Mechanical Properties of Polymeric Materials

7.1 Introduction

7.2 Stress-Induced Phase Transformations during Deformation

7.3 Isotactic Polypropylene (iPP)

7.4 Syndiotactic Polypropylene (sPP)

Index

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Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

De Rosa, Claudio.

Crystals and crystallinity in polymers : diffraction analysis of ordered and disordered crystals / by Claudio De Rosa, Dipartimento di Chimica Paolo Corradini, Universitá di Napoli Federico II, Complesso Monte Sant' Angelo, Napoli, Italy, Finizia Auriemma, Dipartimento di Chimica Paolo Corradini, Universitá di Napoli Federico II, Complesso Monte Sant' Angelo, Napoli, Italy.

pages cm

Includes bibliographical references and index.

ISBN 978-0-470-17576-7 (hardback)

1. Crystalline polymers. 2. Crystallization. I. Auriemma, Finizia. II. Title.

QD382.C78D43 2013

547'.7–dc23

2013011106

Preface

With this book, we are indebted to our late mentor, Paolo Corradini. He introduced us into the fascinating world of the Fourier space and diffraction, and taught us the invaluable importance of crystallography for understanding the macroscopic properties of polymers at the molecular level. Several concepts illustrated in the book are the result of our long, illuminating, and tireless discussions with Paolo Corradini, which were animated in the framework of his own remarkable researches. We absorbed his unique way of looking at macromolecules and crystals due to his never-ending teaching ability.

Polymer crystallography is an essential part of materials science and is of fundamental importance in physics, chemistry, and engineering courses. This book takes an interdisciplinary approach to the subject of polymer crystallography and is, therefore, suitable for undergraduate students in all those courses. The book is also addressed to postgraduates and specialists in the field of polymer science and strikes a balance between the need for resorting to a rigorous crystallographic approach for structural analysis and the large variability of the crystalline state of polymers due to their high tendency of including a large amount of disorder inside the crystals.

The book is divided into seven chapters. Chapter 1 introduces the basic postulates and methods that allow building of structural models for the conformation of the chains in the crystals, whereas Chapter 2 illustrates the methods that allow building of models for the packing mode of the chains inside the crystals. In Chapter 2, several examples of polymer crystals are provided and the useful concepts of limit ordered and limit disordered model structures are introduced. Chapter 3 is devoted to the illustration of the basic methods for the extraction of structural parameters from diffraction data, whereas Chapters 4 and 5 cover the important issue of structural disorder in polymer crystals. In Chapter 4, the different classes of disordered crystal structures of polymers, based on their diffraction patterns, are introduced, providing several examples of these classes, according to a unified view, whereas in Chapter 5, the methods for analysis of disordered structures from diffuse scattering measurements are derived. In Chapter 6, some basic elements of the morphology of single crystals of polymers are remarked upon, with particular emphasis to the cases where morphology could be linked to the arrangement of the chains in the crystals (geometric morphology). Finally, Chapter 7 covers the relationships between the crystal structure and final properties of polymers and illustrates the importance of understanding material properties at the molecular level.

Some sections of the book are concerned with more advanced topics, such as the concepts of symmetry breaking and frustration and the principle of density (entropy)-driven phase formation in polymer crystallography (Chapter 2), the methods that allow finding the helical parameters for noncommensurable helical structures (Chapter 3), the diffraction modeling method, which is illustrated in Chapter 5, and some concepts of geometrical morphology that are reviewed in Chapter 6. These advanced topics make this book suitable also to postgraduate students and experts in polymer science.

The concepts of crystal and crystallinity in polymeric materials are complex and very far from the ideal concept of crystal as a periodic array of identical motifs that implies a complete three-dimensional long-range order of all atoms. Although this ideal concept is valid for the solution of the crystal structure of polymers (see the classic books of polymer crystallography, Structure of Crystalline Polymers by H. Tadokoro and X-Ray Diffraction by Polymers by M. Kakudo, N. Kasai), it is useful only for establishing limit ordered models of the crystal structure to which real macromolecular systems approach when they crystallize in conditions close to the thermodynamic equilibrium.

In polymer crystals, indeed, the true three-dimensional long-range order of all atoms is never present and the structural disorder inside crystals is a rule rather than an exception. One of the main characteristics of polymeric materials is that, at variance with other crystalline materials such as metals, they are never completely crystalline. They are semicrystalline and are generally composed of crystals (lamellae) embedded into an amorphous phase, producing a highly interconnected network. The peculiar semicrystalline character of polymers, associated with the presence of structural disorder in the crystals and polymorphism phenomena, determines their outstanding physical properties.

In this book, a new view of the concepts of crystallinity and crystals in synthetic polymers is presented. The first concept is that crystallinity in polymeric materials is compatible with the absence of true three-dimensional long-range order. Second, the disorder may be described as a structural feature, using the methods of interpretation of the X-ray scattering and electron diffraction. The structures of semicrystalline polymers are discussed in terms of idealized limit models of crystals, where long-range order may be achieved only for some structural features that are not necessarily coincident with single atoms and are not necessarily point centered. Typical examples of non-point-centered structural features are straight lines, corresponding, for instance, to the chain axes of polymer molecules. In this case, the order regards only the positioning of the chain axes and no lateral correlations between atoms of neighboring chains are present.

All the possible types of structural disorder generally present in crystal of polymers are analyzed and the influence of every kind of disorder on the X-ray and electron diffraction patterns is described. Simple rules for the interpretation of the diffuse scattering present in the diffraction patterns of polymers are given. This can be very useful to recognize the disorder present in polymer crystals just from inspection of the diffraction pattern. The methods for the analysis of disordered structures in polymer crystals are illustrated from theoretical and practical perspectives. The important role of X-ray diffraction techniques in the wide angle are outlined, providing numerous examples and practical rules that allow the use of our book also as a “manual” and textbook.

Moreover, the concept that for polymers the methods of crystal structure determination that make use of sole diffraction data cannot be used is described. Due to the presence of disorder, and the fact that the crystalline regions always coexist with the amorphous ones, contain a large number of defects, and are of small average dimensions, the diffraction patterns of semicrystalline polymers are characterized by few and very broad reflections, rapidly vanishing with increasing diffraction angle. However, in general, for the resolution of the crystal structures of polymers, the paucity and overlap of diffraction data, even in the cases where electron diffraction patterns of single crystals are available, are compensated by use of indirect methods. These methods involve the construction of molecular models of the conformation of polymers in the crystals and of the packing mode of the chains within the unit cell using crystallographic information obtained by diffraction experiments and molecular modeling. Methods for building models of macromolecules in the crystals are based on the basic principles of polymer crystallography, that is, the principles of equivalence and ofminimum internal conformational energy. These methods, illustrated in the Chapter 1, allow building of reasonable low-energy models of the chain conformation of polymers in the crystals and, hence, models of packing. Various examples are reported in the Chapter 2 to show how the principle of equivalence is a working postulate that affords finding, generally, the exact symmetry of the chain conformation and the conformation of lowest energy. The structure factors of the trial model structures are thus calculated and compared with the corresponding experimental values derived from the observed diffracted intensities. As illustrated in Chapter 3, the method of resolution of the crystal structure is, therefore, a trial-and-error procedure where the trial models are modified, under the constraints imposed by the equivalence principle, and refined up to reach a satisfactory agreement. The process as a whole is therefore inductive rather than deductive as in traditional crystallography. This point is described in the book starting from a deep analysis of the stereochemistry of polymers and of the methods for the determination of the conformation of chains in the crystalline phase only based on the application of the equivalence principle.

In Chapters 2 and 4, the use of electron diffraction, and electron microscopy in general, to obtain information about the crystal structure and the presence of disorder are presented. In particular, as shown in Chapter 2, recent studies from other laboratories by electron microscopy of polymer single crystals have demonstrated that only by using selected area electron diffraction of single crystals it is possible to find the correct symmetry (the space group) during the solution of the crystal structure. Since a very small area of the crystal is in diffraction, this technique, associated with dark-field imaging of the single crystal, allows finding that the intensities of some symmetric reflections are, very often, different, indicating a packing of the chains with a symmetry lower than the symmetry that can be obtained from X-ray diffraction. Moreover, as shown in Chapter 4, the presence of different microdomains in the single crystals, where the orientation of the chains may be different, and the consequent presence of stacking faults, can be easily visualized using these techniques. Finally, in the electron diffraction patterns of single crystals, the presence of streaks around some reflections can also be visualized. The study of these streaks is a powerful method to describe the type of disorder that is present in the crystal. Sections of Chapter 2 are dedicated to the recent concepts of symmetry breaking and frustration that have been described thanks to the use of electron diffraction and electron microscopy. The differences between the two necessarily complementary techniques of X-ray diffraction and electron diffraction are outlined. The selected area electron diffraction allows finding the true local order and the correct symmetry, whereas with X-ray diffraction only the average structure and the long-range order can be obtained.

Finally, in Chapter 7, it is pointed out that the structural organization of polymers, determined by conditions of crystallization, associated with polymorphism and disorder phenomena, may strongly influence the physical and mechanical properties of a given material. The relationships between the conditions of crystallization, the types of defects present in the crystals, the presence of disorder in the packing, and the mechanical properties of various polymers are described. Defects in the crystals may be due to the presence of microstructural defects in the single macromolecules (defects of stereoregularity, regioregularity, and constitution), which may be included in the crystals. Correlations between physical properties of the materials and inclusion of microstructural defects in the crystals are also discussed. Numerous examples are provided that illustrate the concept that if, on one hand, departures from the ideal long-range order may be considered as a disturbance, in practice, these “deviations” from the ideal may turn out to be useful since they may induce additional and desirable properties in the final products.

Many books on the crystallization of polymers and on the description of the methods of X-ray diffraction for studying the crystal structure of polymers are available. However, the description in a comprehensive manner of the disorder as a structural feature (Chapters 4 and 5), and of the methods for studying the structure of disordered systems by using a combination of all the diffraction techniques (X-ray and electron; Chapters 2 and 4) and microscopy imaging (Chapter 6), and the impact of the presence of defects and disorder on the physical and mechanical properties of polymers (Chapter 7), is missing. Our book is aimed to fill this gap.

CLAUDIO DE ROSA

FINIZIA AURIEMMA

Naples, Italy

1

Configuration and Conformation of Macromolecules in Polymer Crystals

1.1 Crystals of Polymers

A crystal is a portion of solid matter in which some kind of long-range positional order exists on the level of atomic dimensions in three-dimensional space (1,2). This definition corresponds to a reasonable and generally valid working hypothesis, implying a complete long-range positional order of most of atoms (2). The crystalline state should be, therefore, characterized by the presence of three-dimensional order. “Periodicity” is intended as the quality of a motif recurring at equal intervals in the space. In the ideal limit case, the repetition is endless, whereas in real cases, it extends up to the scale considered as appropriate for the description of material properties (1). In the ideal limit case, the corresponding model crystal is designated as ideal crystal.

In the case of polymers, the concepts of crystal and crystallinity are complex and very far from the ideality because in polymer crystals, the three-dimensional long-range order is never present and the structural disorder inside crystals is a rule rather than an exception (3–10). First of all, at variance with other crystalline materials, such as metals, polymeric materials are never completely crystalline. They are semicrystalline and are generally composed of crystals (lamellae) embedded into an amorphous phase, producing a highly interconnected network (11) (Fig. 1.1). The peculiar semicrystalline character of polymers determines their outstanding physical properties.

Figure 1.1. Models of the microstructure of semicrystalline polymers. (A) Each chain may run through several crystalline and amorphous regions. (B) Model of a tightly folded lamella crystal. (C) Fringed micelle model (11). (Reproduced with permission from Reference 7. Copyright 2006 by the American Chemical Society.)

In crystals of polymers, the macromolecules are longer than the unit cell parameters and each chain passes through many unit cells. Accordingly, the concept of an ideal crystal of polymers requires infinite molecular mass, completely regular constitution of the macromolecules, completely regular configuration of the units in the macromolecules, and completely regular conformation of the chains (3).

In a slightly enlarged recent definition, a crystal is any solid having an essentially discrete diffraction diagram (12). This definition implies the presence of some kind of long-range three-dimensional periodicity but not necessarily a complete three-dimensional order of atoms. This concept well corresponds to the partial order present in polymer crystals. The requirement of three-dimensional long-range order appears to be violated in polymer crystals, unless it is considered as a limit, mainly for the following reasons: (a) The macromolecules of a polymer are not uniform; that is, they have different molecular masses, a distribution of molecular masses being always present (13); (b) constitutional, configurational, and conformational disorders along the polymer chains are always present (4); and (c) the dimensions of the crystals are very small, mostly in the nanometer range (they are often indicated as crystallites) (11).

Moreover, even in the case of regular constitution, configuration, and conformation, disorder may be present in the crystals due to the presence of defects in the mode of packing. Disorder in the packing may occur while some structural feature, for instance, some atoms or the axes of helical macromolecules, maintain periodic positions (4). The degree of disorder in the packing or in the single macromolecules is sometimes so high that it is difficult to define this state as crystalline, even though we can still observe crystalline entities with a regular shape by microscopy (optical or electronic). This state can be more properly indicated as intermediate between amorphous phase and ordered crystals (4–7). These crystalline forms that present large amounts of disorder with lack of periodicities in one or two dimensions (e.g., along or normal to the chain axes) are very common in solid semicrystalline polymers and are generally indicated solid mesophases (4–10). In solid mesophases, the presence of a high amount of disorder frequently prevents the definition of a unit cell and only average periodicities along some lattice directions may be defined (4,6).

The issue of long-range versus short-range order in polymer crystals has been extensively treated in the scientific literature (4–10). A modern view of crystallinity and crystalline order in polymers implies that the crystallinity and the capability of polymers to crystallize (crystallizability) are compatible with the presence of a high degree of disorder and the absence, in many cases, of long-range three-dimensional order. This view implies the need to describe the disorder in polymer crystals as a structural feature (4–7) and has required many efforts for the development of experimental techniques and theoretical methods for the study of different types of disorder and the evaluation of the degree of disorder present in the crystals (6,7) (Chapter 5). These methods are part of modern polymer crystallography.

The complex nature of macromolecules in polymeric materials, which always include constitutional and configurational defects along the chain, the polydispersity of the molecular masses, the easy inclusion of defects inside the crystallites, generally prevents obtainment of single crystals of a suitable size for the collection of X-ray diffraction data with the techniques normally used for single crystals of low-molecular-weight compounds (14). The dimensions of polymeric single crystals are instead suitable for electron diffraction. The structural analysis is further complicated by the fact that crystalline polymers are always characterized by a complex morphology, consisting of amorphous, crystalline, and intermediate regions, and the transition from noncrystalline to crystalline regions is considered to be a continuum (11) (). In polymeric materials of high crystallinity, the major part of the material is made up of small crystals, called crystallites, forming platelets in which the chains run perpendicular to the most highly developed surfaces. The thickness of the platelets is a few hundred angstroms long. The usual length of the molecular chain is, in general, far greater than the size of crystallites. Hence, each macromolecular chain is considered to pass through several crystalline and noncrystalline regions successively (11) (A).