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KINETICS OF CRYSTALLIZATION PHENOMENA OF SPHERULITES IN POLY(ETHYLENE TEREPHTHALATE)

A study of the influence of temperature, molecular weight, and additives by light depolarization measurements

S T E L L I N G E N

1

De verklaring van Clough et al. voor het feit dat het mogelijk is met de lichttrans-missietechniek - zoals gebruikt door o.a. Magill - de kristallisatiekinetiek van sferu-lieten te onderzoeken is in vele gevallen onvoldoende.

Clough, S., Rhodes, M. B. en R. S. Stein, J. Pol. Sci. C 18 (1967), 1. Magill, J. H., Polymer 2 (1961), 221.

Dit proefschrift, hoofdstuk 4 (Fig. 4.5).

2

De formule van Mandelkern et al. voor de beschrijving van de groeisnelheid van sferulieten in het gehele temperatuurgebied van kristallisatie is een te grove benadering.

Mandelkern, L., Jain, N. L. and H. Kim, J. Pol. Sci. A-2, 6 (1968), 165. Suzuki, T. and A. J. Kovacs, Pol. J. 1 (1970), 82.

Dit proefschrift, hoofdstuk 4.

3

De verschillende temperaturen van maximale sferulietgroeisnelheid, bij kristallisatie uit de smelt en uit de glastoestand, zoals gevonden door Baranov et al. voor PETP, is waarschijnlijk te verklaren door een onjuiste voorbehandeling van de onderzochte preparaten.

Baranov, V. G., Kenarov, A. V. and T. I. Volkov, J. Pol. Sci. C 30 (1970), 271.

4

De bij een trekproef van vaste polymeren optredende maximale spanning wordt ten onrechte met de term vloeigrens betiteld.

Jackel, K., Kolloid Z. J37 (1954), 130. 5

De wijd verbreide, foutieve idee dat natuurvezels geen of weinig last hebben van electrostatische oplading, dit in tegenstelling tot kunstvezels, wordt grotendeels ver-oorzaakt door het feit dat in de winter de relatieve vochtigheid in de huizen vroeger hoger was dan tegenwoordig.

6

Het publiceren van mechanische eigenschappen van polyamiden zonder dat vermeld wordt of de testvoorwerpen geconditioneerd zijn, is voor andere dan commerciële doeleinden volstrekt zinloos.

7

Op grond van recente metingen van Uiers en Haberkorn blijkt dat bij kristalliniteits-bepalingen van semikristallijn polymeer materiaal niet zonder meer van een constante amorfe dichtheid mag worden uitgegaan.

Uiers, K.-H. en H. Haberkorn, Makromol. Chem. 146 (1971), 267. 8

Het is niet te rechtvaardigen dat het nog altijd mogelijk is in octrooiaanvragen voor-beelden op te nemen die bij nawerken niet realiseerbaar blijken te zijn.

9

Het moet ernstig worden betwijfeld, of plastics die onder invloed van zonlicht verpul-veren een bijdrage tot een verminderde vervuiling van het milieu kunnen vormen.

KINETICS OF

CRYSTALLIZATION PHENOMENA

OF SPHERULITES IN

POLY(ETHYLENE TEREPHTHALATE)

A study of the influence of temperature, molecular weight, and additives

by light depolarization measurements

/ L V - /

/

PROEFSCHRIFT

TER V E R K R I J G I N G VAN DE G R A A D VAN D O C T O R IN DE T E C H N I S C H E W E T E N S C H A P P E N AAN DE T E C H N I S C H E H O G E S C H O O L DELFT OP G E Z A G VAN DE RECTOR M A G N I F I C U S I R . H . R . V A N NAUTA LEMKE,

H O O G L E R A A R IN DE A F D E L I N G DER E L E K T R O T E C H N I E K , VOOR EEN COMMISSIE UIT DE SENAAT TE V E R D E D I G E N

OP W O E N S D A G 1 DECEMBER I 9 7 I TE I4.OO UUR

D O O R

FRANS VAN ANTWERPEN

N A T U U R K U N D I G INGENIEUR GEBOREN TE MONSTER

BI.>LlOTHt^K

DER

TECHNISCHE HOGESCHOOLi

DELFT

r

DIT P R O E F S C H R I F T IS G O E D G E K E U R D DOOR DE P R O M O T O R : P R O F . DR. D. W. VAN KREVELEN

Aan mijn ouders Aan mijn vrouw

D A N K B E T U I G I N G

Aan de Raden van Bestuur van Akzo N.V. en van Akzo Research & Engineering N.V. betuig ik mijn dank voor de toestemming tot publikatie van dit onderzoek.

Voorts dank ik de heren E. H. Boasson, J. Boon en J. J. van Aartsen voor de waardevolle adviezen die zij tijdens het schrijven van dit proefschrift gegeven hebben en de heer M. Vaalburg voor zijn taalkundig advies.

De heer S. Willemsen ben ik erkentelijk voor het uitvoeren van de experimenten en de heer R. F. Veldhuyzen van Zanten voor zijn berekeningen met de computer.

Tenslotte wil ik in mijn dank een ieder betrekken die op enigerlei wijze heeft mee-gewerkt aan het tot stand komen van dit proefschrift.

C O N T E N T S

I N T R O D U C T I O N 11

1 T H E O R Y OF C R Y S T A L L I Z A T I O N IN POLYMERS 15

1.1 Introduction 15 1.2 General theory of phase transitions 15

1.3 Nucleation in polymers 16 1.3.1 Introduction 16 1.3.2 Homogeneous nucleation 16 1.3.3 Heterogeneous nucleation 18 1.3.4 Rate of nucleation 19 1.4 Growth in polymers 20 1.4.1 Introduction 20 1.4.2 Growth by coherent secondary nucleation 21

1.4.3 Growth rate 21 1.5 Overall crystallization 23

1.5.1 Introduction 23 1.5.2 Constant number of nuclei 24

1.5.3 Constant nucleation rate 24 1.5.4 Overall rate of crystallization 25

1.6 Secondary crystallization 25

References 25 2 T H E O R E T I C A L ASPECTS OF THE M E A S U R I N G METHOD . . . . 27

2.1 Introduction 27 2.2 Light scattering by perfect spherulites 27

2.3 Light scattering by imperfect spherulites 30

References 32 3 M E A S U R I N G A P P A R A T U S AND M E A S U R I N G METHOD . . . . 33

3.1 Introduction 33 3.2 Operation of the apparatus 35

3.3 Sample fabrication 36 3.3.1 Polymer 36 3.3.2 Fabrication of the test specimens 36

3.4 Determination of the number-average molecular weight of PETP . . 36

3.5 Description of the apparatus 37

3.5.1 Light source 37 3.5.2 Crystallization oven 37

3.5.3 Analyzer 38 3.5.4 The electronic recording and computing system 38

References 42 4 G R O W T H RATE OF THE S P H E R U L I T E S 43

4.1 Introduction 43 4.2 Preparation of the test specimens 43

4.3 The spherulite radius as a function of the crystallization time . . . 45

4.4 Growth rate of the spherulites in plain PETP 47 4.5 Growth rate of the spherulites in PETP containing liquid additives . . 53

4.6 Growth rate of the spherulites in PETP containing solid additives . . 55

4.7 Discussion 55 4.8 Conclusions 60 References 61 5 M A X I M U M S P H E R U L I T E R A D I U S 62

5.1 Introduction 62 5.2 Maximum spherulite radius of plain PETP 62

5.3 Maximum spherulite radius of PETP containing liquid additives . . . 66 5.4 Maximum spherulite radius of PETP containing solid additives . . . 67

5.5 Discussion 69 5.6 Conclusions 70 References 70 6 O V E R A L L C R Y S T A L L I Z A T I O N 71

6.1 Introduction 71 6.2 Overall crystallization of plain PETP 72

6.3 Overall crystallization of PETP containing liquid additives . . . . 74 6.4 Overall crystallization of PETP containing solid additives . . . . 75

6.5 Discussion 80 6.6 Conclusions 85 References 85

A P P E N D I C E S 1 C O M P A R I S O N O F S P H E R U L I T E R A D I I AS C A L C U L A T E D F R O M H ^ S C A T T E R I N G P A T T E R N S W I T H A N D W I T H O U T T A K I N G I N T O A C -C O U N T THE R E F R A -C T I V E INDEX 86 2 C A L I B R A T I O N OF THE E L E C T R O N I C A P P A R A T U S 88 A2.1 Introduction 88 A2.2 Elimination of the error caused by a delay in the electronic circuit. . 88

A2.3 Elimination of the error caused by the choice of the level of

discrimina-tion of the differentiator signal 89 A2.4 Measurements after calibration 90

3 D E T E R M I N A T I O N OF THE E Q U I L I B R I U M M E L T I N G P O I N T A N D

HEAT O F F U S I O N OF PETP 91

References 92

4 P R I N C I P L E S OF THE USED R E G R E S S I O N ANALYSIS M E T H O D S . . 93

A4.1 Introduction 93 A4.2 Multiple linear regression 93

A4.3 Non-linear regression 94

5 E X P E R I M E N T A L DATA OF THE S P H E R U L I T E G R O W T H RATE

MEASUREMENTS 96

SUMMARY 106

I N T R O D U C T I O N

It is known that already in the second half of the last century macromolecules, among which polyesters and polyamides, were incidentally obtained in the laboratory [1.1]. However, the concept of macromolecules was first introduced in 1920 by Staudinger [1.2]. On the basis of Staudinger's concept Whinfield and Dickson [1.3] prepared poly(ethylene terephthalate) (PETP) in 1941. This polyester with the repeating unit

O _ O —CH^—CH,—O—C^(^ o \ — C — O —

appeared to be extremely suitable for the manufacture of man-made fibres and films. For application as a plastics material PETP was too brittle.

Owing to a modified method of preparation developed by the Akzo (former AKU)-Research Laboratories this polymer can now also be processed into a plastics ma-terial [1.4].

For properties such as tensile strength, hardness and maximum service temperature it is desirable for many applications that the material should be in the crystalline state rather than in the glassy state. Therefore it was necessary that a further study be made of the crystallization behaviour of PETP and an investigation be carried out into the possibilities of influencing this behaviour.

The investigations to this end are described in this thesis.

The properties of a plastics material are determined by the structure of the polymer chain (molecular structure), the ordering of the chain molecules and the mutual ar-rangement of the ordered regions (supramolecular structure). Though it is known that supramolecular structures may form below the glass transition point [1.5-7], atten-tion has mostly been directed to the formaatten-tion of these structures above this transi-tion point.

For the investigation into the formation of supramolecular structures above the glass transition point (crystallization) one may apply different methods. All these methods are based on the measurement of the change of a physical property connected with crystallization. Examples are caloric measurements [1.8], determination of the change in the mass density [1.9] and the light depolarization method [1.10]. Espe-cially suitable for determining the growth rate of supramolecular structures (mostly spherulites) are light microscopy [1.11] and light scattering measurements [1.12].

Whether a particular method can be applied, depends on various factors. Decisive for the choice of a measuring method are generally the rate of crystallization and the maximum spherulite radius.

In this investigation special attention has been paid to the growth rats of spherulites at a constant crystallization temperature. But also the maximum spherulite radius and the overall rate of crystallization have been dealt with.

Up till now the growth rate of spherulites in PETP has only been given for one molecular weight measured at two crystallization temperatures (Keller [1.13]). The lack of further determinations of the spherulite growth rate for this polymer is probably to be attributed to the experimental inaccessibility of this quantity in the case of PETP. This is especially due to the small maximum spherulite radius. How-ever, during the present investigation Baranov et al. [1.14] published spherulite growth rates for PETP with a molecular weight (M„) of 13,000 measured in the whole tem-perature range in which crystallization takes place.

By using the principle of the light scattering method developed by Stein [1. 15], it is possible to determine the growth rate of spherulites in PETP in the entire range of crystallization temperatures. This method is suitable in the case of spherulites with a radius of about 0.5 to a few microns. Following this principle, we have built an apparatus with which it is possible continuously to record the spherulite radius as a function of time during crystallization.

In this investigation the overall rate of crystallization of PETP is measured by making use of the light depolarization method developed by Magill [1.10]. This method can b ; used for PETP in the whole temperature range between the glass transition point and the melting point. However, measuring this quantity for PETP at each crystallization temperature may also be done by other methods [1.16, 17].

The overall rate of crystallization is made up of two components, viz. the number of crystallization nuclei present and their growth rate. Both quantities may be in-fluenced by the addition to the polymer of particular agents. The influence of these additives, both on the number of nuclei and on the growth rate of the spherulites, is described in this thesis for PETP mixed with small quantities ( < 1 % by mass) of a solid or a liquid. Also this part of the investigation is carried out by applying the above-mentioned methods.

By quenching PETP, from temperatures above the melting point to temperatures below the glass transition point, no noticeable crystallization occurs. As a result, it is possible to investigate the isothermal crystallization of this polymer by heating from the glassy state. Many investigations of PETP described in the literature have been carried out in this way [1.13, 16-18]. Besides investigating crystallization from the glassy state, we investigated isothermal crystallization of PETP from the melt. This thesis has been divided into the following chapters:

Chapter 1 gives a description of the crystallization theory as far as necessary for the interpretation of the measuring results.

Chapter 2 describes the theoretical background of the method for measuring the growth rats of spherulites (light scattering method) and of that for measuring the overall rate of crystallization (light depolarization method).

Chapter 3 deals with the fabrication of the specimens and gives a description of the measuring apparatus.

Chapter 4 contains the results of the growth rate measurements on spherulites in PETP. Special attention has been paid to the influence of the molecular weight and the crystallization temperature. These results are compared with theory. Moreover, it is shown that the growth rate of spherulites can be influenced by small quantities of liquid additives.

Chapter 5 deals with the results of the measurements on the maximum spherulite radius. It appears that especially solid additives may highly influence the maximum spherulite radius.

In Chapter 6 the results of the measurements of the overall rate of crystallization are described.

R E F E R E N C E S

1.1 Flory, P. J., Principles of Polymer Chemistry, Cornell University Press, Ithaca, New York (1953), p. 12, 14.

1.2 Staudinger, H., Berichte 53 (1920), 1073.

1.3 Whinfield, J. R. and J. T. Dickson, Brit. Pat. 578.079.

1.4 van Krevelen, D. W., Bussink, J., Huntjens, F. J. and J. L. Voigt, Proc. Int. Plastics Congress Amsterdam (1966), 167.

1.5 Kargin, V. A. and S. J. Berestnewa, Plaste und Kautschuk 14 (1967), 719. 1.6 Yeh, G. S. Y. and P. H. Geil, J. Macromol. Sci. B-1, 2 (1967), 235. 1.7 Frank, W. and H. A. Stuart, Koll. Z. Z. Pol. 225 (1968), 1. 1.8 Inoue, M., J. Pol. Sci. A 1 (1963), 2697.

1.9 Boyer, R. F., Spencer, R. S. and R. M. Wiley, J. Pol. Sci. / (1946), 249. 1.10 Magill, J. H., Polymer 2 (1961), 221.

1.11 Aggerwal, S, L., Marker, L., Kollar, W. L. and R. Geroch, J. Pol. Sci. A-2, 4 (1966), 715. 1.12 Picot, C , Weill, G. and H. Benoit, J. Pol. Sci. C 16 (1968), 3973.

1.13 Keller, A., Lester, G. R. and L. B. Morgan, Phil. Trans. Roy. Soc. (London) A 247 (1954), 1.

1.14 Baranov, V. G., Kenarov, A. V. and T. I. Volkov, J. Pol. Sci. C 30 (1970), 271. L15 Stein, R. S. and M. B. Rhodes, J. Appl. Phys. 31 (I960), 1873.

L16 Cobbs, W. H. and R. L. Burton, J. Pol. Sci. 10 (1953), 275.

1.17 Mayhan, K. G., James, W. J. and W. Bosch, J. Appl. Pol. Sci. 9 (1965), 3605.

C H A P T E R I

T H E O R Y O F C R Y S T A L L I Z A T I O N IN P O L Y M E R S

1.1 I N T R O D U C T I O N

The characteristic morphological structure of bulk crystallized polymers is a spheru-litic one [1. la]. The spherulites can be regarded as a more or less orderly arrangement and orientation of crystallites embedded in an amorphous mass. So a crystallized polymer is semicrystalhne. The maximum crystallinity generally is between 30 and 90%, dependent on the type of polymer and the crystallization conditions.

The crystallites are considered to be highly ordered regions with parallelized molecular chains which are mostly folded back and forth, as can be seen in Fig. 1.1 [1.2].

>

Radial direction

Fig. 1.1 Model of part of a spherulite. A. Amorphous regions. C. Crystalline lamellae made up of crystallites.

For the description of the crystallization in polymers use is made of the classical theory of phase transitions as developed for systems consisting of small molecules. This phase change takes place in two steps: nucleation and growth.

1.2 G E N E R A L THEORY OF PHASE T R A N S I T I O N S

The general theory of phase transitions was developed by Gibbs [1.3]. Later on this theory was extended by, among others, Becker and Döring [1.4] and TurnbuU and

Fisher [1.5]. The derivation is based on the assumption that in supercooled melts and in supersaturated solutions and vapours fluctuations occur which lead to the forma-tion of a new phase.

The phase transformations begin with the appearance of a number of very small particles of the new phase.

The replacement of the old phase by the new phase is accompanied by a decrease of Gibbs free energy, whereas the formation of a surface between the two phases causes the free energy to increase. For small particles the decrease of bulk free energy is exceeded by the increase in the interfacial free energy. So the growth of new particles depends on the ratio of surface area to volume. There is a critical volume V* separa-ting those particles whose free energy of formation increases during growth from those whose energy decreases. So, the small particles will tend to re-dissolve, and the large ones will tend to grow. A particle with a volume smaller than V* is called an embryo, whereas the one with a volume larger than V* is referred to as a nucleus.

1.3 N U C L E A T I O N IN POLYMERS

1.3.1 Introduction

The nucleation for bulk crystallized polymers*), the so-called primary nucleation, will now be described by the theory summarized in the foregoing section.

As a model of nuclei in polymers one often takes a rectangular prism [1.6, 7] which is connected with the long polymer chains. In a crystallized polymer these chains are folded back and forth as was first suggested by Keller [1.8] for a polymer crystallized from a dilute solution. It is now evident that this folding also occurs in crystalHzation of polymers in bulk [1.9, 10].

The three-dimensional nucleus can be formed:

homogeneously, i.e. nucleation is effected only by molecules of the polymer; heterogeneously, i.e. nucleation takes place on foreign bodies.

It must be pointed out that the following treatment of the theory in the literature has been derived for crystallization at moderate supercoolings. However, the equa-tions can also bs used for the whole temperature range between the glass transition point and the melting point [1.11, 12].

1.3.2 Homogeneous nucleation

The model of homogeneous nucleation is shown in Fig. 1.2. The folds of the chains are in the surface ab, and the polymer chains are parallel to the c axis. The symbols for the different interfacial free energies**) are given in the figure.

*) Bulk crystallization as distinct from crystallization during orientation, e.g. during the drawing of fibres and films.

**) Interfacial free energy can be defined as:

Fig. 1.2 Model of homogeneous nucleation.

The change in the Gibbs free energy of formation (AFJ for this model is:

AF^ = - a b c A F , + 2aba, + 2(ac + bc)a (1.1) with AF„ being the change in bulk free energy. The dependence of AF^ on temper-ature is normally given by [1.13]:

AT

AF„ = AH (1.2)

with AHf being the heat of fusion; AT = T„ —T the supercooling; T„ the melting point and T the crystallization temperature.

Strictly speaking, eq. 1.2 only holds for low supercoolings. As in our measurements we have to do with moderate to high supercoolings we prefer, for theoretical reasons, to use a more general equation derived earlier by the same author [1.14]:

AHfTAT AF„ =

T„ (1.3)

For the formation of a nucleus of critical dimensions the change in free energy can be found by the conditions:

aAF, ^AF|; i'AFk

da db The critical dimensions appear to be:

a = b = dc = 0 4cr AR •G' = 4a^ AF„ (1.4) (1.5) (1.6) The free energy of formation of a nucleus of these dimensions can be found by substituting a*, b* and c* in eq. 1.1. This leads to:

* 32a a,

A F K , 3 * = —

1.3.3 Heterogeneous nucleation

For polymers in bulk heterogeneous nucleation is the most common nucleation [1.15-17]. This is mainly to be attributed to the great number of heterogeneities, e.g. catalyst residues which are inevitably present in the polymer. The model for this type of nucleation is given in Fig. 1.3, with the foreign body being a flat substrate.

Fig. 1.3 Model of heterogeneous nucleation on a flat substrate.

The arrangement of the chain molecules is as described for the homogeneous nucleus.

The Tree energy of formation for a nucleus is now given by:

AF|; = — abcAF^-l-2abaj + 2bcCT + aca-l-ac(0' —aj (1.8a)

(1.9)

(1.8b) It is convenient to define a factor

Aa = (a-h a'— as,)/2

With eq. 1.9 the equation for the free energy of formation reads: AF|j = — abcAF,, + 2aba^-i-2bca-l-2acAa

The calculation of the critical dimensions is analogous to that for homogeneous nucleation. This leads to

4a AF; 4Aa AF, 4a, a* = b* = c* = AF„ (1.10) (1.11) (1.12) The critical free energy corresponding to these dimensions is:

AF,,3* = ^ 32(Aa)aae

(AF,)^ (1.13)

From eqs. 1.7 and 1.13 it can be seen that if Aa < a, the substrate promotes the nucleation.

It is obvious that if such a substrate contains steps, cracks, ridges, etc., it will have a more favourable effect on the nucleation than a flat one; the interfacial free energy will then be decreased on more surfaces of one and the same nucleus.

1.3.4 Rate of nucleation

The rate of nucleation can be calculated by using Boltzmann's law and kinetic con-siderations.

According to Boltzmann's law the probability w that an embryo occurs with a (Gibbs) free energy AF^^* at constant pressure and temperature is proportional to exp ( —AFk^*/kT). In this expression k is the Boltzmann constant and T the absolute temperature. It must be pointed out that AF,^* is temperature-dependent. Because embryos with a free energy AF^* can grow into nuclei, the rate of nucleation N, in its turn, is proportional to w. So

N = Z exp ( - AFk*/kT) (1.14) where Z is a proportionality factor which is written as

Z = N o e x p ( - A E / k T ) (1.15) where NQ is a constant, and the term exp( —AE/kT) the probability that a chain

segment is transported from the supercooled to the crystalline phase; AE is the tem-perature-dependent free energy of activation of this process.

The temperature dependence of this activation energy is given by Hoffman [1.13], using the empirical viscosity relation of Williams, Landel and Ferry (WLF) [1.18], which properly speaking may only be applied between Tg and Tg-HlOO. This led to the following expression for the activation energy of one mole:

AE' = CiT/(C2-hT-Tg) (1.16) Tg is the glass transition point of the polymer. C^ and Cj are constants. Further,

AE' = N A A E (1.17) where N^ is the number of Avogadro and kN^ = R (the gas constant), so that the

expression for Z becomes

(1.1 ) From relaxation measurements WLF found that Cj = 17.2kJ/mol*)andC2 =51.6K are universal constants. With crystallization measurements on various polymers, how-ever, others found other values of Ci and/or C2 giving the best fit to the experimental data [1.19-22]. In principle, this means that the expression of the activation energy only has the same mathematical form as the WLF relation.

•) The units used are those of the International System of Units (SI units) given in Recommendation R 1000 of the International Organization of Standardization (ISO).

Z = No exp - C,

The expression for the rate of nucleation for the homogeneous nucleation we now find by substituting eq. 1.7 combined with eq. 1.3 and eq. 1.18 in eq. 1.14. This leads to (1.19) N = = No exp ( Ci \ . „ „ / R(C2 + T - r g ) / " " ' ^ \ 32a^a;r^^ \ k(AHf)^T^(AT)V

For heterogeneous nucleation the expression for the rate of nucleation reads:

(1.20) N = No exp - -—— ——- exp

R ( C 2 + T - T . ) / " \ k(AHf)2T^(AT) 32a(Aa)aeT„'*

In these expressions the temperature dependencies of a and a^ are neglected, a is weakly dependent on temperature due to vibrations of the molecular chains. A decrease of a^ with decreasing temperature is caused by the formation of more irre-gular folds at low crystallization temperatures [1.23, 24]. For this situation, however, the nucleation is mainly governed by the transport term.

1.4 G R O W T H IN POLYMERS

1.4.1 Introduction

In the foregoing sections dealing with nucleation there was only need to describe the nucleation of one crystallite. But in the treatment of the growth it is necessary to con-sider aggregates of crystallites. In bulk crystallization these aggregates are mostly spherulites.

In the case of homogeneous nucleation the spherical shape is gradually approached via the intermediate sheaflike structure [1.25].

With crystallization in bulk in the presence of nucleating agents the spherical growth is thought to occur as a result of nearly simultaneous nucleation of crystallites at numerous points on the surface of the foreign particle followed by dendritic growth [1.26].

From Fig. 1.1 it can be seen that the growth rate of a spherulite is equal to the growth rate of the radial lamellae.

Already the earliest quantitative studies on the growth rate of spherulites for several polymers demonstrated that this growth rate is constant with time and the process nucleation-controlled [1.15, 27]. This latter conclusion is deduced from the large negative temperature coefficient characteristic for the growth rate in the vicinity of the melting point.

The nucleation takes place on an already existing crystal face consisting of crys-tallized polymer. This process is called secondary nucleation.

1.4.2 Growth by coherent secondary nucleation

As a model of the growth of crystallites one normally takes a model of coherent secondary nucleation [1.13]; i.e., crystallographically the new layer is merely an extension of the underlying crystal.

This model is the same as the model of heterogeneous nucleation; but now the sub-strate, which consists of the crystallized polymer, is fully wettable. So Aa (eq. 1.9) is equal to zero. The new layer has the same thickness as that of the polymer chain (bg). So the secondary nucleation is a two-dimensional nucleation.

The free energy of formation is given by

AF|j = — abocAFy + 2aboae-l-2boCo (121) The critical dimensions for the formation of a new layer are found by

3AFk ^AFk da dc 0 (1.22) 2a This leads to a* = (1.23) AF„ 2a^ AF. (1.24) ^ 4boaae A F . , * = — 5 — - (1.25) "•' AF„ ^ 1.4.3 Growth rate

With regard to the growth of spherulites the basic assumption is made that the growth rate is limited by the frequency of formation of successive monolayers. Thus, com-pared with the nucleation of a monolayer, the lateral growth is assumed to be a fast process*).

Analogous to eq. 1.14 combined with eq. 1.15 the equation for the rate of two-dimensional nucleation is given by [1.28]

I = lo exp (-AE/kT) exp (-AFk,2*/kT) (1.26) In this equation I is the rate of nucleation on a surface unity; IQ a frequency factor.

Since the growth rate is determined by the rate of formation of nuclei on the sub-strate surface, eq. 1.26 may be modified to represent the spherulite growth rate G. Then one obtains the expression

G = Go exp (-AE/kT) exp (-AFk,2*/kT) (1.27) with Go = bglo being a constant.

*) In a revision of the classical nucleation theory, however, Binsbergen (Koll. Z. Z. Pol. 2J7(1970), 289) no longer considers the lateral growth to be a much faster process than the formation of the successive monolayers.

By substituting the expressions for AE and AFi^ 2* in eq. 1.27 the growth rate of spherulites is found to be:

n n I ^' \ I 4 b o a a J „ ^ \ R ( C 2 + T - r ^ ) / \ KAHfT^AF/

Properly speaking, the expression for the growth rate G must contain a factor that depends on the size of the substrate surface area; for the formation of more nuclei on the same layer only gives rise to one new monolayer of thickness bo. Hence the growth rate G is proportional to the number of nuclei that gives rise to a new monolayer. This number depends on the sur-face area and can be given by f(A)I(A—A*). A is the substrate area. A* is the sursur-face area with critical dimensions, and I the rate of nucleation per surface unity.

For a very small substrate area the function f (A) approaches unity; for then the rate of nucleation on surface A is so small that the probability of two or more nuclei being formed on a layer at the same time tends to be zero. For a large substrate area f(A)I(A—A*) will be a constant.

The above demands are satisfied by the expression

« A ) = l ~ e x p ( - ^ ^ ^ ) (1.29) with Ao being a parameter.

For the growth rate we can now write

G = b o [ l - e x p ( - ^ ^ - ^ ^ ) J I(A - A*) (1.30) The curve of this expression is shown in Fig. 1.4.

Fig. 1.4 The growth rate as a function of the substrate surface area

So, only a constant growth rate can be found at a particular crystallization temperature if in the course of the crystallization the substrate area remains a constant; or in the case of a fluctuating substrate area this is so large that it varies in that part of the curve in Fig. 1.4 where a constant level has been reached.

1.5 O V E R A L L C R Y S T A L L I Z A T I O N

1.5.1 Introduction

Since we know the expressions for nucleation and growth rate, also expressions for the overall crystallization can be determined.

We make use of the equation derived by Avrami [1.30] and, obtained in a simpler way, by Evans [1.31]. This equation reads:

a = l - e x p ( - K t " ) (1.31) where a is the volume fraction transformed into the spherulitic state; K and n are

parameters, which are called rate constant and constant of Avrami, respectively. These parameters are determined by the types of growth and nucleation.

The volume fraction a can be derived from the mass density of the sample by assuming that the crystallizing polymer consists of a two phase system, i.e. the spherulitic state and the amorphous state outside the spherulites. We can then write

m = m^-Fm^ (1.32) where m is the mass of the polymer sample;

m^ is the mass of the spherulitic state;

m^ is the mass of the amorphous state outside the spherulites. By using the mass densities of the two states eq. 1.32 can be written as

pv = PsVs + P.v, (1.33) where the p and v terms refer to the mass densities and volumes of the respective

regions.

By substituting a, which is defined as vjv, into eq. 1.33 and rearranging the equa-tion, one obtains

a = ( 1 . J 4 )

P s - P a

As remarked already, the parameter n gives information about the various types of nucleation and growth. This is shown in Table 1.1.

T A B L E 1.1

Values of the Avrami exponent n for various types of nucleation and growth [1.1b, 32a]

Growth habit

Three-dimensional Two-dimensional One-dimensional

Linear growth

Instantaneous nucleation Sporadic nucleation 3 3 < n < 4 2 2 < n < 3 1 1 < n < 2

For the case of three-dimensional growth combined with two special cases of primary nucleation the parameters K and n will be derived below.

1.5.2 Constant number of nuclei

For the case of a constant number of nuclei N per unit volume, the spherulitic crystallized volume fraction a' at a time t is given by

a' = f7r(Gt)^N (1.35) where impingement of spherulites is neglected.

If the impingement of the spherulites is to be taken into account the real trans-formed volume fraction of spherulitic material can be found by using

da = ( 1 - a ) da' (1.36) Eq. 1.36 expresses the fact that the effect of impingement is small when the amount

of crystallized material is small, and that da/da' must decrease to zero as the crys-tallization approaches completion.

Taking into account that for a' = 0 also a = 0 integration of this equation leads to

a = l - e x p ( - a ' ) (1.37) The combination of the eqs. 1.35 and 1.37 compared with eq. 1.31 leads to

K3 = y N G ^ (1.38) n = 3 (1.39) 1.5.3 Constant nucleation rate

By a constant nucleation rate N is meant that the nucleation rate per unit volume untransformed material remains a constant.

If at a time x the untransformed volume fraction is equal to 1 — a(x), the number of nuclei forming in a short time interval between x and x + dx is N{1—a(x)} dx. In the case of free growth these nuclei lead to a volume fraction of spherulitic material at a time t of [1. Ic]

An

— G ' ( t - x ) ^ N { l - a ( x ) } d x (1.40) Integration from 0 -» t gives

a' = ^ G ^ N f ( t - x ) ^ { l - a ( x ) } d x (1.41)

3 .' 0

Allowing for the impingement eq. 1.37 is used again. This leads to

For small values of t, when a < 1, 1—a(x) approaches unity. Then integration leads to a = l - e x p | - - G ^ N f * j (1.43) Thus K = - G ^ N (1.44) 3 n = 4 (1.45) For larger values of a, n depends on G and N and can have all values between

four (N large, G small) and three (N small, G large). 1.5.4 Overall rate of crystallization

The half-time of crystallization t^ is normally taken as a measure of the overall rate of crystallization. The time tj. is the time necessary to reach the value a = 0.5. Sub-stitution of t^ and a = 0.5 in eq. 1.31 gives, after rearranging this equation, the following expression

I i l 2 \ ' ' "

1.6 S E C O N D A R Y C R Y S T A L L I Z A T I O N

With many polymers the Avrami or primary crystallization as described in the fore-going sections is followed by a slow secondary crystallization [1.19, 33, 34].

For the phenomenon of secondary crystallization there are two possibilities [1.19]: a. a crystallization of a more difficultly crystallizable component

b. an increase in the perfection of the existing crystallites.

According to Sharpies [1.32b] the second possibility is the more acceptable one. In support of this view it should be mentioned that upon the polymer being annealed the fold period shows an increase [1.35].

R E F E R E N C E S

1.1 a. Mandelkern, L., Crystallization of Polymers, McGraw Hill, New York (1964), p. 326; b. p. 228; c. p. 226.

1.2 Koenig, J. L. and J. Hannon, J. Macromol. Sci. Bl (1967), 119.

1.3 Gibbs, J. W., Collected Works Vol. 1, Longmans, New York (1928), p. 94. 1.4 Becker, R. and W. Döring, Ann. Phys. 24 (1935), 719.

1.5 TurnbuU, D. and J. C. Fisher, J. Chem. Phys. 17 (1949), 71. 1.6 Price, F. P., J. Pol. Sci. 42 (1960), 49.

1.7 Boon, J., Thesis Delft (1966). 1.8 Keller, A., Phil.Mag. 2 (1957), 1171.

1.10 Geil, P. H., Yeh, G. S. Y. et al., J. Macromol. Sci. Bl (1967), 793. 1.11 Boon, J., J. Pol. Sci. C 16 (1967), 1739.

1.12 Magill, J. H., Polymer 6 (1965), 367. 1.13 Hoffman, J. D., SPE Trans. 4 (1964), 315. 1.14 Hoffman, J. D., J. Chem. Phys. 28 (1958), 1192. 1.15 Price, F. P., J. Am. Chem. Soc. 74 (1952), 311.

1.16 von Falkai, B. and H. A. Stuart, Kolloid Z. 162 (1959), 138. 1.17 Sharpies, A., Polymer J (1962), 250.

1.18 Williams, M. L., Landel, R. F. and J. D. Ferry, J. Am. Chem. Soc. 77(1955), 3701. 1.19 Hoffman, J. D. and J. J. Weeks, J. Chem. Phys. 37 (1962), 1723.

I .20 Magill, J. H., J. Appl, Phys. 35 (1964), 3249.

1.21 Boon, J., Challa, G. and D. W. van Krevelen, J. Pol. Sci. A-2, 6 (1968), 1791. 1.22 Suzuki, T. and A. J. Kovacs, Pol. J. / (1970), 82.

1.23 Lauritzen, J. 1. and E. Passaglia, J. Res. NBS 71A (1967), 261. 1 .24 Hoffman, J. D., Lauritzen, J. I. et al., Koll. Z.Z. Pol. 231 (1969), 564. 1 .25 Keller, A. and J. R. S. Waring, J. Pol. Sci. 17 (1955), 447.

I .26 Geil, P. H., Polymer Single Crystals, John Wiley & Sons, New York (1963), p. 223 ff. 1.27 Flory, P. J. and A. D. Mclntyre, J. Pol. Sci. 18 (1955), 592.

1.28 Burnett, B. B. and W. F. McDevit, J. Appl. Phys. 28 (1957), 1101. 1.29 Hoffman, J. D., Ind. Eng. Chem. 58 (1966), 41.

1.30 Avrami, M,, J. Chem. Phys. 7(1939), 1103; 8 (1940), 212; 9 (1941), 177. 1.31 Evans, U. R., Trans. Far. Soc. 41 (1945), 367.

1.32 a. Sharpies, A., Introduction to Polymer Crystallization, Edw. Arnold, London (1966), p. 50; b. p. 64.

1.33 Zachmann, H. G. and H. A. Stuart, Macromol. Chem. 41 (1960), 131. 1.34 Rabesiaka, J. and A. J. Kovacs, J. Appl. Phys. 32 (1961), 2314. 1.35 Hoffman, J. D. and J. J. Weeks, J. Chem. Phys. 42 (1965), 4301.

C H A P T E R 2

THEORETICAL ASPECTS OF THE MEASURING METHOD

2.1 I N T R O D U C T I O N

The crystallization measurements in this investigation are divided into measurements of the growth rats of spherulites, the maximum spherulite radius, and the overall rate of crystallization.

The measurements of the growth rate and the maximum spherulite radius are based on the light scattering theory of perfect spherulites as developed by Stein and Rhodes [2.1].

The overall rate of crystallization is determined by measuring the change in the transmission of depolarized light. This method was first used by Magill [2.2]. The existence of transmitted depolarizsd light may be attributed to the spherulites being imperfectly formed, for instance as a result of the presence in the spherulites of •"random orientation" crystallites. The light scattering theory of "random orienta-tion" crystallites has been discussed by Stein and Wilson [2.3]. Keijzers [2.4a] applied this theory to spherulites containing "random orientation" crystallites.

A review of both theories is given by Stein in a monograph [2.5]. 2.2 L I G H T S C A T T E R I N G BY P E R F E C T S P H E R U L I T E S

The model of a perfect spherulite is a homogeneous anisotropic sphere in an isotropic medium [2.1]. The light scattering pattern of these spherulites is calculated by the amplitude method. This means that first the total amplitude per spherulite is cal-culated, followed by squaring, giving the intensity of the scattered light. This method is the most useful for systems of known geometry.

The amplitude of scattering by the i"" volume element of a system is given by the classical formula [2.6]

Ai = K(Mi . O) cos {k(ri. S)} (2.1) where K is a proportionaUty constant. M; is the dipole induced in the i"' volume

element located at a distance FJ from an origin. O is a unit vector perpendicular to the propagation direction of the scattered beam and lies in a plane through the polarization direction of the analyzer, perpendicular to the analyzer plane, k is the wave number Iti/X, where X is the wave length inside the material. S is equal to

So —S where So is a unit vector in the direction of the incident light beam and S is a unit vector in the direction of the scattered light beam.

The amplitude of the light scattered by a sphere is expressed in terms of the general integral [2.6]

A = K (M . O) COS {k(r . S)}r^ sin a da dQ dr (2.2) J r = o J n = o J a = 0

where r, a and Q are the polar coordinates. Starting from the integral as given in eq. 2.2, Stein and Rhodes [2.1] calculated scattering patterns for spherulitic crystal-lized samples placed between a polarizer and an analyzer. With the polarizer and the analyzer placed as denoted in Fig. 2.1 (H^ position) this calculation gives the so-called H^ scattering pattern. H^ designates vertical orientation of the polarizer and horizontal orientation of the analyzer.

1. Polarizer 2. Sample 3. Analyzer 4. Screen

Fig. 2.1 The coordinate system for H, scattering from anisotropic spheres.

For the light intensity of this scattering pattern the authors [2.1] derived the expression

3 ^ ^ I„^ = A„^^ = K'V^

u-

where K' is a proportionality constant. V is the scattering volume of the spherulites. a, and a^ are the tangential and the radial polarizability of the spherulites, respsctively. 9 is the polar scattering angle and \i the azimuthal scattering angle (Fig. 2.1). SiU designates the integral

SiU r sin X J 0 X dx U is a form factor given by

4JCR 9 U = sin

--K 2

(2.4)

(2.5) where R is the mean spherulite radius.

Attention is drawn to the fact that at zero scattering angle, where U = 0, the light intensity is zero. This can be shown by developing the product

(3/U^) (4 sin U - U cos U - 3 SiU) in a series and taking the limit for U -» 0.

The scattering pattern as given by eq. 2.3 is shown in Fig. 2.2. The lines represent contours of constant light intensity. The numerical values of these contours are the logarithms of the light intensity.

Fig. 2.2 Calculated light intensity contours for H, scattering by an anisotropic sphere 12.5]. The maximum light intensity is found at an azimuthal angle n = 7r/4 rad. The form factor corresponding to this maximum has the value U = 4 . 1 .

Also in the case of a narrow distribution of the spherulite sizes the form factor has the value 4 . 1 . The value of U decreases as the distribution becomes broader. This has been calculated by Keijzers [2.4b] both for various gaussian and block distribu-tions.

Now the mean spherulite radius can be calculated by determining the scattering angle corresponding to the point of maximum light intensity (9„); substituting this angle and U = 4.1 into eq. 2.5 results in the following equation for the mean spheru-lite radius:

It should be pointed out that X and 9„ used in this expression are ths wave Isngth and scattering angle in the polymer sample. Calculations in Appendix 1, however, show that if into eq. 2.6 the wave length and scattering angle in air are substituted, no considerable error is introduced, provided that the spherulites are not unduly small.

A spherulite, of course, is not perfectly formed. This results in the presence of light scattered by heterogeneities (Section 2.3). Yet the spherulite radii calculated from Hy scattering patterns are in very good agreement with those measured by microscope. This is shown in Fig.2.3 for spherulites whose radii can bs determined by the light scattering method as well as by microscope. The polymer used for this comparison. is nylon 6.This polymer has been chosen because it readily allows of realizing spheru-lites of the required order of magnitude.

ÏÏ ((jm)-microscope

Fig. 2.3 A comparison of spherulite radii measured by light scattering and by microscope. For t h e drawn line Rscait is identical with R.nicr.

2.3 L I G H T S C A T T E R I N G BY I M P E R F E C T S P H E R U L I T E S

In the foregoing section it has been shown that in the centre of the H^ scattering pattern of a perfect spherulite no light intensity is present.

However, when a real H^ scattering pattern of spherulites (Fig. 3.1) is considered, light intensity in the centre of the pattern is observed. This may be attributed to one or more of the following factors:

a. Orientation of amorphous regions in or outside the spheruhtes b. "Random orientation" crystallites within the spherulites [2.4a, 7]

c. Impingement of the spherulites which causes the spheres to grow into polyhedrals. The light intensity due to these factors added to the scattered light intensity of the perfect spherulites gives the total scattered light intensity of the sample.

The light scattering pattern of "random orientation" crystallites has been calculated by Stein and Wilson [2.3]. The scattered light intensity is calculated by the correlation function method, and can bs expressed by

I' = X Z AiAj = K^ ƒ ƒ (Mi. O) ( M j . O) cos {k(ri. S)} cos {k(rj. S)} dr^ dr^ (2.7) where the meaning of the symbols is the same as for eq. 2.1.

From this integral Stein and Wilson [2.3] calculated the H^ scattering pattern for "random orientation" crystallites. This led to the expression

, r " sin(hr) ,

I'H. = A K i 6 ' J f(r)Kr) - ^ r^ dr (2.8)

where Kj is a proportionality constant. 5 is the mean anisotropy in polarizability per unit volume (expressed in a formula: 5 = (a||)ay —(aj^)^^). h is equal to 4n sin (9/2)/^. f(r) and n(r) are two spherical symmetric correlation functions for elements sepa-rated by a distance r.

f(r) is the orientation correlation function which can be approximated by [2.8]

f(r) = x e x p f - y + ( l - x ) e x p f - ^ j (2.9) in which b and c are characteristic correlation distances. In applying the theory t»

"random orientation" crystallites which are present within spherulites, as done by Keijzers [2.4a, 7], b may be considered a measure of the irregular centre of the spherulites [2.4c]. c is supposed to originate from the non-spherulitically crystallized part of the material within the whole spherulite [2.4c]. x is a factor lying between zero and unity.

The expression for p(r) reads [2.7]

<il'>

K r ) = l + ^ Y ( r ) (2.10) a

where <T|^> is the mean-square polarizability fluctuation (T), = a , - a ) , a is the mean polarizability of the sample. y(r) is the density correlation function [2.8].

Since <Ti'^>/a'^ <^ 1 and Y(r) < 1, n(r) = 1 is a good approximation for all values. ofr.

Now it is possible to solve the integral in eq. 2.8. This leads to the following expression for I'H^ [2.4d]:

x b ' V ' t / h ' b ' \ ( l - x ) c ' V ' t / h V ^

In the centre of the scattering pattern h = 0 and so the light intensity in the centre satisfies the formula:

I'H.,o = 7;^KiO^[xb^ + ( l - x ) c ' ] (2.12) oU

It is unknown how the parameters in this expression are connected with the spheru-lite radius. So it is impossible to predict the connection between the intensity of the transmitted light and the overall crystallization. This light intensity moreover is influenced by the unknown contribution of the factors mentioned under a. and c. at the beginning of this section.

Besides, there is the practical complication of the photo-cell having a particular aperture angle. Consequently, also scattered light with a scattering angle smaller than the aperture angle contributes to the intensity of the "transmitted" light.

For these small scattering angles the scattered light intensity of a perfect spherulite is proportional to R ' ° . This can be shown by developing the product

(3/U^) (4 sin U - U cos U - 3 SiU)

from eq. 2.3 in a series. For small angles the product is by first approximation propor-tional to U'^ and, hence, with R^. The spherulitic scattering volume is proporpropor-tional to R^. Now it can be seen from eq. 2.3 that for small scattering angles I^^ is propor-tional to R ' ° .

In view of the above it is clear that the connection between the "transmitted" light intensity and the overall crystallization can only be found empirically.

R E F E R E N C E S

2.1 Stein, R. S. and M. B. Rhodes, J. Appl. Phys. 31 (1960), 1873. 2.2 Magill, J. H., Polymer 2 (1961), 221.

2.3 Stein, R. S. and P. R. Wilson, J. Appl. Phys. i i (1962), 1914. 2 . 4 a. Keijzers, A. E. M., Thesis Delft (1967); b. p. 22ff; c. p. 61; d. p. 58.

2.5 Stein, R. S., Proceedings of the Interdisciplinary Conference on Electromagnetic Scattering, ed. by M. Kerker, Pergamon Press, London (1963), p. 439 ff.

2.6 Guinier, A. et al , Small Angle Scattering of X-rays, Wiley, New York (1955), Chapter 2. 2.7 Keijzers, A. E. M., van Aartsen, J. J. and W. Prins, J. Am. Chem. Soc. 90 (1968), 3107. 2 . 8 Keijzers, A. E. M., van Aartsen, J. J. and W. Prins, J. Appl. Phys. 36 (1965), 2874.

CHAPTER 3

M E A S U R I N G A P P A R A T U S A N D M E A S U R I N G M E T H O D

3.1 I N T R O D U C T I O N

As already mentioned, the aim of this investigation is to obtain some insight into the growth rates of spherulites and overall rates of crystallization of poly(ethylene tereph-thalate) (PETP) under various crystallization conditions. So to this end a suitable measuring method had to be found.

A simple method of measuring spherulite growth rates is the one in which use is made of a microscope. However, this procedure is impracticable because the maxi-mum spherulite radius of most PETP samples is too small. Instead, use is made of the light scattering method developed by Stein (Section 2.2). With this method it is possible to measure spherulite radii of half a micron to a few microns.

In order to determine growth rates with this method it is necessary to record the Hy scattering pattern during crystallization. This can be done by photographing this scattering pattern, as is done by Picot [3.1] and Baranov [3.2]. An example of our own results obtained with this technique is given in Fig. 3.1. Here some photos of a series taken with a recording camera (Agfa typs RBC) are shown. From these photo-graphs the spherulite radii can be calculated with the use of eq. 2.6 by determining the point of maximum light intensity in the lobes. Since the corresponding crystalliza-tion times are known, the growth rate can be calculated. However, this method is very time-consuming.

We therefore built an apparatus with which it is possible immediately to record the spherulite radius during crystallization. This is realized by scanning the H^ scat-tering pattern with a photo-cell which moves back and forth along a line through the centre of the scattering pattern and the point of maximum light intensity in a lobe. This line has an azimuthal angle \i of 7r/4 rad (Fig. 2.2). The photo-cell is connected to an electronic device which determines the position of the point of maximum light intensity, from which the spherulite radius is computed.

In Fig. 3.2 an example is given of the light intensity measured by the photo-cell across a clover-leaf. This figure has been obtained by connecting the photo-cell directly to an oscilloscope (Tektronix type 549 storage) and photographing the curve arising on the screen.

Scattering angle (rad): tcr>st(S) '• Fig. 3.1 0 58 0 nl6 0 nl6 16 25

H, scattering patterns of crystallizing PETP (M„ = 35,400). Crystallization temperature: I75°C. The polarization directions are vertical and horizontal.

Also the overall rate of crystallization can be determined in several ways. Which method is the most suitable depends on the rate of crystallization. For PETP this rate can be fast due to factors such as low molecular weight and crystallization temperature.

A convenient method (developed by Magill [3.3]) for measuring high overall rates of crystallization is the measurement of the change in the intensity of transmitted depolarized light.

It should be pointed out that this method only gives a measure of the overall crys-tallization (Section 2.3). An advantage of the method is that it can be combined with

mm

• •

•••!••

• • • • •

•

•

•

1

m

Fig. 3.2 The light intensity of an H» scattering pattern along a line with an azimuthal angle of 7r/4 rad.

the method applied for measuring growth rates. So the spherulite radius and the overall rate of crystallization can be determined simultaneously during crystallization. 3.2 O P E R A T I O N OF THE A P P A R A T U S

The operation of the apparatus will be described with reference to the schematic representation in Fig. 3.3. A description of the different devices used is given in Section 3.5.

> !

-1 2

1. Laser 2. Diaphragm 3. Oven and sample 4. Analyzer 5. Photo-cell

4 5 6 6. Recorder (overall crystallization)

7. Moving photo-cell

8. Electronic recording and computing system

9. Recorder (spherulite radius) Fig. 3.3 Schematic representation of the apparatus.

The parallel, vertically polarized light beam radiated by the laser is scattered by the crystallizing PETP sample placed in the oven. The sample has a thickness of about 100 pm. The analyzer has a horizontal orientation which leads to what is called the Hy scattering pattern. The shape of this pattern is shown in Fig. 3.1.

The Hy scattering pattern is scanned by a photo-cell (7) which moves back and forth along a line having an azimuthal angle of 7r/4 rad and in a plane which is perpendicular to the optical axis of the light scattering system. Consequently, the line passes through the points of maximum light intensity in two lobes. Photo-cell (7) has its neutral position at a fixed distance from the centre of the scattering pattern. The photo-cell (7) is connected to an electronic device (8) with which the position of the photo-cell is determined when it measures the point of maximum light intensity in the first lobe. This position is indicated by a voltage which is the input for a computing device whose output is a voltage representing the spherulite radius. This radius is registered by a recorder (9).

In the centre of the scattering pattern there is also a photo-cell (5). This photo-cell measures the transmitted depolarized light intensity which is a measure of the overall crystallization (Section 2.3). This light intensity is also registered by a recorder (6).

3.3 S A M P L E F A B R I C A T I O N

3.3.1 Polymer

The PETP used in the investigations is from a single commercial autoclave batch. The polymer contains catalyst remnants of 76 ppm Mn, 208 ppm Ge, and 30 ppm P. The diethylene glycol content amounts to 1.58 mass per cent; this percentage is hardly changed by the heat treatments carried out to get the desired samples. When it leaves the autoclave the polymer is chopped into chips. The polymer chips have a number-average molecular weight of 22,100.

Polymer chips with a higher number-average molecular weight are obtained by polycondensation of the chips. In this way polymer chips have been obtained with number-average molecular weights between 22,100 and 45,000, depending on the time of polycondensation.

3.3.2 Fabrication of the test specimens

The test specimens for the crystallization measurements are in the form of tapes. These tapes are produced by melting the polymer chips in an extruder (30 mm Reifen-hauser extruder) and extruding the molten polymer through a narrow slit. Immediately after it has left the slit, the polymer which has now the form of a tape is quenched in a water bath to keep it amorphous. The tape is 15 mm wide and has a thickness of about 100 pm.

For investigations on PETP containing small amounts of additives, tapes are ex-truded of chips dusted with the desired quantities of these additives.

3.4DETERMINATIONOFTHENUMBER-AVERAGE MOLECULAR WEIG HT OF PETP For brevity's sake, we will hereinafter refer to "number-average molecular weight" as "molecular weight".

Molecular weights are determined via measurements of the viscosity ratio, which is defined as the ratio of the viscosity of a polymer solution and the viscosity of the solvent. We apply a 1"{, mass over volume solution of the polymer in metacresol. The respective viscosities are determined at 25 °C, using a standard Ubbelohde viscom-eter [3.4].

At Akzo Research Laboratories an empirical relationship used between viscosity ratio (rir) and molecular weight ( M J determined from end group titrations runs as follows [3.5]:

„ . , ( , , _ „ . . - = | ( . P., ,3.)

provided that the viscosity ratio has a value larger than about 1.40. P„ is the mean number of monomer units in a polymer chain.

3.5 D E S C R I P T I O N OF THE A P P A R A T U S 3.5.1 Light source

The light source is a continuous wave helium-neon gas laser (type G 3) developed by Reyrolle Parsons Automation Ltd., New Castle upon Tyne, England. A laser is used because of its parallel, monochromatic beam of light of high intensity. Moreover, with the laser type used the light is linearly polarized. The parallel bundle obviates the use of lenses. The high light intensity makes it possible to scan the changing scattering pattern. The wave length of the laser is in the red region (0.6328 |xm).

The laser also radiates incoherent light. Therefore it must be positioned in a separate room in order to keep the photo-cells in the dark. Mounted in the wall is a diaphragm by which the coherent laser beam enters the room containing the other part of the apparatus.

3.5.2 Crystallization oven

Isothermal crystallization measurements are carried out starting from the glassy state as well as from the melt. The oven is schematically represented in Fig. 3.4.

MO melting oven A heated air CO crystallization oven L light beam C clamp for slide

In principle the heating in the crystallization oven (CO) is carried out with heated air which is blown past the sample at a constant speed. Heating elements are used to keep the walls of the oven at the same temperature as that of the air passing through it. The outside of the oven is isolated. The crystallization temperature is kept constant within 0.5 °C.

The light beam enters the crystallization oven through a pin hole. The light being scattered by the crystallizing polymer sample leaves the oven by a conical hole.

The crystallization measurements are done on square pieces of material cut from taps, which are placed between glass slides with a thickness of 150 ^im, which are inserted in the clamp (C). The specimens are then melted in the electrically heated melting oven (MO) at 285 °C for 30 seconds (Section 4.2).

With crystallization from the melt the clamp is subsequently pulled out of the melting oven and moved into its correct position in the crystallization oven (CO). This operation is practically instantaneous.

With crystallization measurements from the glassy state the clamp is at first fully pulled out and the specimen is quenched in heptane in order to obtain the PETP sample in the glassy state. After that the clamp (C) is brought into the crystallization oven (CO).

3.5.3 Analyzer

The orientation of the analyzer is perpendicular to the polarization direction of the laser light. So only depolarized light can pass through the analyzer.

3.5.4 The electronic recording and computing system*)

In Fig. 3.5 a block diagram is given of the system for continuously scanning the scattering pattern and computing the spherulite radius from the measured points of maximum light intensity in the lobes.

The operation of the system is as follows:

A photo-cell (I), a solar-cell, moves back and forth once every second, along a line with an azimuthal angle of nj4 rad and in a plane which is perpendicular to the optical axis of the light scattering system. The photo-cell (1) furnishes a voltage which is proportional to the light intensity. The conversion of this signal by various devices is schematically shown in Fig. 3.6, which also represents the integrator signal and some trigger signals. Some calibrating difficulties which have not been dealt with in this schematical treatment are considered in Appendix 2. A further description of the system is given with the Figs. 3.5 and 3.6.

In order to get rid of the noise, the signal of the photo-cell (1) is rectified (3). For checking purposes this signal is made visible on an oscilloscope (22) (Tektronix type 549 storage). A differentiator (4) differentiates the signal, after which it is the input *) The electronic recording and computing system was constructed by mr. Korzilius and mr. Lendering (Akzo Corporate Research).

for the discriminator (5) whose output is a block-voltage. The leading edge of this signal designates the moment at which the maximum light intensity is measured. The leading edge of the block-signal also denotes the moment for the sample and hold amplifier (7) to sample the output signal from the integrator (12).

supply - - - 3 ; - > ^ tight 3 4 5

W 3

0

7. Sample and hold amplifier 8. Resistor 9. Resonator 10. Amplifier 11. Flip-flop 12. Integrator 13. Computing device

(diode function generator and anti-log) 14. Recorder 15. Amplifier 16. Resistor 17. Resonator 18. Amplifier 1 9. Switch 20. Photo-cell 21. Recorder 22. Oscilloscope S, S' Metal strips SM Servomotor SH Shaft P Pulley ST String

Fig. 3.5 Block diagram of the electronic circuit.

After having been reset, the integrator (12) starts to operate as soon as the photo-cell (1) leaves its neutral position, i.e. when the metal strip S leaves the resonator (9). At that very moment the resonator (9) is not deadened any longer and begins to resonate. This means that a minimum current is drawn from the power supply. This gives a sudden voltage drop across the resistor (8). This drop is, via the flip-flop (11), the signal for starting the integrator (12). At the moment the maximum light intensity is measured the signal for stopping the integrator (12) is given by the leading edge of the block-voltage from the discriminator (5). The resulting maximum output voltage

of the integrator (12) designates the position of the point of maximum light intensity in the lobe which is the first to be scanned by the photo-cell (1) after it has left its neutral position. The output voltage remains constant until the integrator (12) is reset to its initial position by the leading edg; of the block voltage across resistor (8).

discriminatcr(5)

integrator (12)

resistor(8)

resistor (16)

Fig. 3.6 Time-relation of the signals appearing in the first half of a scanning cycle.

Via the sample and hold amplifier (7) the sampled output signal of the integrator (12) is supplied to a computing device (13) which computes the spherulite radius which is registered by a recorder (14) (Philips type PM 8100). The computing circuit is an electronic analogon for the expression of the spherulite radius given by eq. 2.6. The photo-cell (1) is mounted on a rail and moved back and forth by a string (ST) which is driven by a servomotor (SM). The direction of rotation of the servomotor (SM) is controlled by the resonating circuits (9) and (17). When one of the metal strips, S or S', enters a resonating circuit, the respective resonator is deadened. Then the voltage across resistor (8) or (16) increases and toggles the switch (19) for the servomotor (SM). The light intensity in the centre of the Hy scattering pattern which is related to the overall crystallinity (Section 2.3) is measured with a photo-cell (20). This photo-cell (20), a solar-cell, furnishes a voltage which is proportional to the measured light intensity. The voltage is recorded by a recorder (21) (Honeywell type 18).

An advantage of this set up is that the spherulite radii and the overall rate of crys-tallization can be determined simultaneously. Photo-cell (20), however, must be so

small that the maxima of light intensity in the lobes are not hidden from the scanning photo-cell (1).

For a photograph of the detecting device, see Fig. 3.7.

PC, Scanning photo-cell (growth rate) S, S' Metal strips PC2 Fixed photo-cell (overall P Pulley

crystallization) SM Servomotor Fig. 3.7 Photograph of the detecting device

R E F E R E N C E S

3.1 Picot, C , Weill, G. and H. Benoit, J. Pol. Sci. C 16 (1968), 3973.

3.2 Baranov, V. G., Kenarov, A. V. and T. 1. Volkov, J. Pol. Sci. C 30 (1970), 271. 3.3 Magill, J. H., Polymer 2 (1961), 221.

3.4 ASTM D 445 - 65.

CHAPTER 4

GROWTH RATE OF THE SPHERULITES

4.1 I N T R O D U C T I O N

With the apparatus described in Chapter 3 crystallization phenomena have been in-vestigated on PETP for isothermal crystallization both from the glassy state and from the melt. These investigations have been carried out on PETP samples with molecular weights (M„) in the range of 19,000 to 39,000, obtained from chips with various molecular weights (Section 3.3.1). In the entire range of molecular weights investi-gated the weight-average molecular weight is about 2.4 times the number-average molecular weight (determined by gel permeation chromatography).

In this chapter the results for the growth rates of spherulites are described. The simultaneously measured overall rate of crystallization is dealt with in Chapter 6.

4.2 P R E P A R A T I O N OF THE TEST SPECIMENS

The test specimens are amorphous tapes with a thickness of 100 pm, the fabrication of which is described in Section 3.3.2. These tapes contain about 0.35% water by mass. This quantity of water causes an inadmissible hydrolytic degradation of the polymer when the samples are melted. It is therefore necessary that the tapes should be dried. For experimental reasons it is preferred that during drying the tapes should keep amorphous. Therefore the tapes are dried for 24 hrs at 50 °C and a pressure of 13.3 N/m^ (0.1 mm Hg). In this way the end value of the moisture will be about 0.01 % m/m. The tapes are kept under vacuo at 50 °C until they are used for the

measurements.

In order to prevent thermal oxidative degradation of the specimens during melting the dried samples are placed between glass slides with a thickness of 150 pm. As a result of the above precautions degradation will be only slight.

In order to remove any differences in thermal and mechanical history of the tapes, they are all melted prior to crystallization regardless as to whether isothermal crys-tallization from the glassy state or from the melt is investigated. The temperature programmes used for the two types of crystallization are schematically shown in Figs. 4.1 and 4.2.

The cooling time from the melting temperature to Tj.rys, or the heating time from Troon, to Tj,rys, must be as short as possible. Fig. 4.3 shows the actual variation of

T (°C). 300 100-— _ Tcryst. 1 I _ 30 -Time (s) T CC). 300 200 100 'room O-l 'cryst.

i_

Fig. 4.1 Temperature programme prior to isothermal crystallization from the melt.

Fig. 4.2 Temperature programme prior to isothermal crystallization from the glassy state.

Time (s)

Fig. 4.3 Temperature versus time for heating a sample from 25 "C to 220 °C.

temperature with time when heating a sample from T^o^jto the adjusted crystalliza-tion temperature of 220 °C. This curve has been obtained with the aid of visual observations of the onset of melting of pure substances having different melting points.

The temperature and duration for melting the PETP samples have been chosen from the measurements shown in Fig. 4.4. The maximum spherulite radius reached after crystallization from the melt at 190 °C is taken as a measure of the number of nuclei in the melt. When an increase in melting temperature and/or melting time does not cause an increase in the maximum spherulite radius measured, there is no need to choose a higher melting temperature and/or a longer melting time.

From Fig. 4.4 it appears that use may be made of any temperature-time combina-tion which gives for this sample a maximum spherulite radius of 2.12 pm upon crys-tallization at 190 °C. We have chosen a melting time of 30 sat a temperature of 285 °C.

e 0-^ me[ting time :30s 0 melting time : 60s meUingtime; 90s 260 270 280 290 300 . ^ - Melting temperature (°C)

Fig. 4 . 4 The maximum spherulite radius of PETP (M„ = 39,100), upon crystallization from the melt at 190 °C, as a function of melting temperature and melting time.

4 . 3 T H E S P H E R U L I T E RADIUS AS A F U N C T I O N OF THE CRYSTALLIZATION TIME

The change in the position of the maximum light intensity in the lobes of an Hy scattering pattern can be seen in Fig. 4.5. This figure shows that during crystallization the point of maximum light intensity in the lobes moves to the centre of the scattering pattern. The light intensity increases with the crystallization time.

The picture was taken from the screen of the oscilloscope and shows the curves of light intensity registered by the scanning photo-cell during the crystallization process. In order also to make visible in Fig. 4.5 the light intensity in the centre of the scatter-ing pattern, the photo-cell for measurscatter-ing this light intensity first had to be removed from its position in front of the scanning photo-cell.

From the position of the maximum light intensity in the lobe of the clover leaf the spherulite radius is determined by the electronic circuit. The spherulite radius as a function of the crystallization time is registered by a recorder (Section 3.5.4). The recorded curve is a step function because the scanning photo-cell scans the maximum light intensity in the lobe only once per second. An example of such a curve is given in Fig. 4.6.