Ideal crystals are regularly repeating three-dimensional arrays of atoms. It follows that, if a polymer is to be able to crystallise, even if only to a limited extent, the minimum requirement is that its chains must themselves have regularly repeating units along their lengths and must be able to take up a straight conformation. This chapter is concerned with the types of regularity and irregularity that polymer chains can have, with how regular chains pack together and with the experimental study of the crystal structure at the level of the unit cell, the smallest unit from which the crystal may be imagined to be built by regular repetition of its structure in space, as described in section 2.5.1.

Regular and irregular chains

Introduction

It is a geometrical requirement that if a polymer is to be potentially capable of crystallising, its chains must be able, by undergoing suitable rotations around single bonds, to take up an arrangement with translational symmetry. If a polymer is actually to crystallise there is also a physical requirement: the crystal structure must usually have a lower Gibbs free energy than that of the non-crystalline structure at the same temperature. Consideration of this physical requirement is deferred to later sections; the present section deals only with the geometrical requirement.

Introduction

This chapter is concerned primarily, in section 3.3, with factors that determine the shapes that individual polymer molecules can take up, both on the local scale of a few repeat units and on the scale of the complete molecule. It is shown that, if a polymer molecule is in a particular kind of solution or in a melt of like molecules, its most likely state is a so-called random coil with a statistically well-defined size. This coil has an open structure that can be penetrated by chain segments belonging to other coils, so that the chains in a molten polymer are likely to be highly overlapping, or entangled, if the molar mass is high. In addition, as discussed in the following section, the molecules do not all have the same length. At first sight these two factors appear to make it unlikely that a polymer could crystallise on cooling, so that it might be expected that polymer solids would be rather structureless. However, in section 3.4 experimental evidence showing that this is not necessarily so is presented and the various ordered structures are discussed further in subsequent chapters.

Distributions of molar mass and their determination

In section 1.3.1 it is pointed out that polymers, unlike other chemical compounds, do not have fixed molar masses. The molar masses are very high and there is a distribution of molar masses, or chain lengths, that depends on the polymerisation conditions.

Introduction – the meaning and importance of orientation

Consider a volume within a sample of polymer that is large compared with the size of individual chain segments, crystallites or spherulites, but small compared with the sample as a whole. If equal numbers of the axes of the chain segments or of the crystallites within this region point in every direction in space, the region is isotropic on a macroscopic scale. If all such regions within the sample are isotropic, the sample itself is said to be isotropic, randomly oriented or unoriented. If any region of the sample is not isotropic it is said to be oriented or partially oriented. The sample as a whole may be homogeneously oriented if all regions of it are oriented in the same way, or it may be inhomogeneously oriented. The various types and degrees of orientation that are possible are considered in detail in subsequent sections.

It is important to realise that, even in a sample that is randomly oriented on a macroscopic scale, there may be regions, such as crystallites, in which the molecular chains are oriented on a microscopic scale.

Polymers are not the only materials that can exhibit orientation. Any polycrystalline material, such as a metal, can exhibit orientation and this can confer desirable or undesirable properties on the material. The effects are, however, often much greater for polymers than they are for other materials.

Polymers and the scope of the book

Although many people probably do not realise it, everyone is familiar with polymers. They are all around us in everyday use, in rubber, in plastics, in resins and in adhesives and adhesive tapes, and their common structural feature is the presence of long covalently bonded chains of atoms. They are an extraordinarily versatile class of materials, with properties of a given type often having enormously different values for different polymers and even sometimes for the same polymer in different physical states, as later chapters will show. For example, the value of Young's modulus for a typical rubber when it is extended by only a few per cent may be as low as 10 MPa, whereas that for a fibre of a liquid-crystal polymer may be as high as 350 GPa, or 35 000 times higher. An even greater range of values is available for the electrical conductivity of polymers: the best insulating polymer may have a conductivity as low as 10−18 Ω−1 m−1, whereas a sample of polyacetylene doped with a few per cent of a suitable donor may have a conductivity of 104 Ω−1 m−1, a factor of 1022 higher! It is the purpose of this book to describe and, when possible, to explain this wide diversity of properties.

The book is concerned primarily with synthetic polymers, i.e. materials produced by the chemical industry, rather than with biopolymers, which are polymers produced by living systems and are often used with little or no modification.

Introduction

As indicated in chapter 1, the first electrical property of polymers to be valued was their high electrical resistance, which made them useful as insulators for electrical cables and as the dielectric media for capacitors. They are, of course, still used extensively for these purposes. It was realised later, however, that, if electrical conduction could be added to the other useful properties of polymers, such as their low densities, flexibility and often high resistance to chemical attack, very useful materials would be produced. Nevertheless, with few exceptions, conducting polymers have not in fact displaced conventional conducting materials, but novel applications have been found for them, including plastic batteries, electroluminescent devices and various kinds of sensors. There is now much emphasis on semiconducting polymers. Figure 9.1 shows the range of conductivities that can be achieved with polymers and compares them with other materials.

Conduction and dielectric properties are not the only electrical properties that polymers can exhibit. Some polymers, in common with certain other types of materials, can exhibit ferroelectric properties, i.e. they can acquire a permanent electric dipole, or photoconductive properties, i.e. exposure to light can cause them to become conductors. Ferroelectric materials also have piezoelectric properties, i.e. there is an interaction between their states of stress or strain and the electric field across them. All of these properties have potential applications but they are not considered further in this book.

Introduction

When polymers are applied for any practical purpose it is necessary to know, among other things, what maximum loads they can sustain without failing. Failure under load is the subject of the present chapter.

In chapter 7 the phenomenon of creep in a viscoelastic solid is considered. For an ideal linear viscoelastic medium the deformation under a constant stress eventually becomes constant provided that e3(t) in equation (7.4) is zero. If the load is removed at any time, the ideal material recovers fully. For many polymers these conditions are approximately satisfied for low stresses, but the curves (b) and (c) in fig. 6.2 indicate a very different type of behaviour that may be observed for some polymers under suitable conditions. For stresses above a certain level, the polymer yields. After yielding the polymer either fractures or retains a permanent deformation on removal of the stress.

Just as linear viscoelastic behaviour with full recovery of strain is an idealisation of the behaviour of some real polymers under suitable conditions, so ideal yield behaviour may be imagined to conform to the following: for stresses and strains below the yield point the material has time-independent linear elastic behaviour with a very low compliance and with full recovery of strain on removal of stress; at a certain stress level, called the yield stress, the strain increases without further increase in the stress; if the material has been strained beyond the yield stress there is no recovery of strain.

Introduction and definitions

Introduction

In section 6.1 it is pointed out that, at low temperatures or high frequencies, a polymer may be glass-like, whereas at high temperatures or low frequencies it may be rubber-like. In an intermediate range of temperature or frequency it will usually have viscoelastic properties, so that it undergoes creep under constant load and stress-relaxation at constant strain. The fundamental mechanisms underlying the viscoelastic properties are various relaxation processes, examples of which are described in section 5.7. The present chapter begins with a macroscopic and phenomenological discussion of linear viscoelasticity before returning to further consideration of the fundamental mechanisms.

Consider first the deformation of a perfect elastic solid. The work done on it is stored as energy of deformation and the energy is released completely when the stresses are removed and the original shape is restored. A metal spring approximates to this ideal. In contrast, when a viscous liquid flows, the work done on it by shearing stresses is dissipated as heat. When the stresses causing the flow are removed, the flow ceases and there is no tendency for the liquid to return to its original state. Viscoelastic properties lie somewhere between these two extremes.

There are already a fairly large number of textbooks on various aspects of polymers and, more specifically, on polymer physics, so why another? While presenting a short series of undergraduate lectures on polymer physics at the University of Leeds over a number of years I found it difficult to recommend a suitable textbook. There were books that had chapters appropriate to some of the topics being covered, but it was difficult to find suitable material at the right level for others. In fact most of the textbooks available both then and now seem to me more suitable for postgraduate students than for undergraduates. This book is definitely for undergraduates, though some students will still find parts of it quite demanding.

In writing any book it is, of course, necessary to be selective. The criteria for inclusion of material in an undergraduate text are, I believe, its importance within the overall field covered, its generally non-controversial nature and, as already indicated, its difficulty. All of these are somewhat subjective, because assessing the importance of material tends to be tainted by the author's own interests and opinions. I have simply tried to cover the field of solid polymers widely in a book of reasonable length, but some topics that others would have included are inevitably omitted. As for material being non-controversial, I have given only rather brief mentions of ideas and theoretical models that have not gained general acceptance or regarding which there is still much debate.

Introduction

Many physical techniques are used in the study of solid polymers and some, such as NMR spectroscopy, can give information about a wide variety of features of the structure or properties. On the other hand, some of these features, for instance the degree of crystallinity, can be studied by a wide variety of techniques that give either similar or complementary information. The techniques described in this chapter are those that have a wide applicability within polymer physics or where the description of the technique is most easily introduced by reference to non-polymeric materials. The reader who is already familiar with a particular technique, e.g. X-ray diffraction, may wish to omit the corresponding section of this chapter. It is suggested that other readers should read through the chapter fairly quickly to gain an overall view of the techniques and then look back when applications are referred to in later chapters if they wish to gain a deeper understanding. Techniques that are more specific to polymers are described in the appropriate chapters and only a few, which are generally available only in specialised laboratories, are mentioned without further discussion.

Introduction

Although the properties of the polymers in the three groups considered in this chapter are in some ways very different, they share the possibility, under suitable circumstances, of self-organisation into supermolecular structures that are of different kinds from the crystallites and spherulites typical of the semicrystalline polymers discussed in the earlier chapters. These kinds of organisation give rise to properties that are of great interest both scientifically and commercially and it is the aim of this chapter to indicate some of the factors that control the various kinds of organisation and to give some indication of the wide variety of structures and properties that can be obtained.

Two or more existing polymers may be blended for various reasons. One reason is to achieve a material that has a combination of the properties of the constituents, e.g. a blend of two polymers, one of which is chemically resistant and the other tough. Another reason is to save costs by blending a high-performance polymer with a cheaper material. A very important use of blending is the combination of an elastomer with a rigid polymer in order to reduce the brittleness of the rigid polymer. It is in the latter use that the self-organising feature of some blends is seen to play a part. This feature arises when the components of the blend are incompatible, i.e. they do not mix, and they segregate into different regions within the material.

Introduction to the mechanical properties of polymers

It must be recognised from the beginning that the mechanical properties of polymers are highly dependent on temperature and on the time-scale of any deformation; polymers are viscoelastic and exhibit some of the properties of both viscous liquids and elastic solids. This is a result of various relaxation processes, as described in sections 5.7.2 and 5.7.3, and examples of these processes are given in sections 5.7.4 and 5.7.5.

At low temperatures or high frequencies a polymer may be glass-like, with a value of Young's modulus in the region 109–1010 Pa, and it will break or yield at strains greater than a few per cent. At high temperatures or low frequencies it may be rubber-like, with a modulus in the region 105–106 Pa, and it may withstand large extensions of order 100% or more with no permanent deformation. Figure 6.1 shows schematically how Young's modulus of a polymer varies with temperature in the simplest case. At still higher temperatures the polymer may undergo permanent deformation under load and behave like a highly viscous liquid.

In an intermediate temperature range, called the glass-transition range, the polymer is neither glassy nor rubber-like; it has an intermediate modulus and has viscoelastic properties. This means that, under constant load, it undergoes creep, i.e. the shape gradually changes with time, whereas at constant strain it undergoes stress-relaxation, i.e. the stress required to maintain the strain at a constant value gradually falls.

Introduction

Chapter 4 is principally concerned with the crystal structure of polymers, that is to say the shape and size of the smallest unit of a crystal-the unit cell-and the arrangement of the atoms within it. The present chapter considers the structure of polymers on a scale much larger than the unit cell. Not all polymers crystallise and, even in those that do, there is always some remaining non-crystalline material, as shown for instance by the presence of broad halos in WAXS patterns from unoriented polymers in addition to any sharp rings due to crystalline material. The widths of the rings due to the crystallites indicate that, in some polymers, the crystallite dimensions are only of the order of tens of nanometres, which is very small compared with the lengths of polymer chains, which may be of order 3000nm measured along the chain, i.e. about 100 times the dimensions of crystallites. The following questions therefore arise.

1. (i) How can long molecules give rise to small crystallites?

2. (ii) What are the sizes and shapes of polymer crystallites?

3. (iii) How are the crystallites disposed with respect to each other and to the non-crystalline material?

4. (iv) What is the nature of the non-crystalline material?

These questions are the basis of polymer morphology, which may be defined as the study of the structure and relationships of polymer chains on a scale large compared with that of the individual repeat unit or the unit cell, i.e. on the scale at which the polymer chains are often represented simply by lines to indicate the path of the backbone through various structures.

Introduction

In this chapter an attempt to answer the following questions is made.

1. (i) What kind of theoretical models, or deformation schemes can be envisaged for predicting the distribution of molecular orientations in a drawn polymer?

2. (ii) How do the predictions of these models agree with experimental results for the orientation averages such as 〈P2(cos θ)〉?

3. (iii) How can experimental or theoretical values of the orientation averages be used to predict the properties of the drawn polymer and with how much success?

These questions form the topics of discussion for sections 11.2, 11.3 and 11.4, respectively. In extremely highly drawn material, a great deal of modification of the original structure of the polymer must have taken place and most of the chains are essentially parallel to the draw direction, so that 〈cos2 θ〉 and 〈P2(cos θ)〉 are both close to 1. It is difficult to describe theoretically and in detail how molecular orientation takes place under these circumstances and thus to predict the small departures from unity for such materials. Discussion of the prediction and use of orientation averages is therefore limited to materials of moderate draw ratios. Models used for interpreting the properties of highly oriented polymers are discussed in sections 11.5 and 11.6.