Glass

Selected Properties and Crystallization

Jürn W. P. Schmelzer

• Publisher: De Gruyter
• Year: 2014
• eBook ISBN: 9783110368109
• Edition: 1
• Topic: Technik & Maschinenbau
• Subtopic: Kondensierte Materie

"This book contains overviews on technologically important classes of glasses, their treatment to achieve desired properties, theoretical approaches for the description of structure-property relationships, and new concepts in the theoretical treatment of crystallization in glass-forming systems. It contains overviews about the state of the art and about specific features for the analysis and application of important classes of glass-forming systems, and describes new developments in theoretical interpretation by well-known glass scientists. Thus, the book offers comprehensive and abundant information that is difficult to come by or has not yet been made public." Edgar Dutra Zanotto (Center for Research, Technology and Education in Vitreous Materials, Brazil)

Glass, written by a team of renowned researchers and experienced book authors in the field, presents general features of glasses and glass transitions. Different classes of glassforming systems, such as silicate glasses, metallic glasses, and polymers, are exemplified. In addition, the wide field of phase formation processes and their effect on glasses and their properties is studied both from a theoretical and experimental point of view.

Christoph Schick, Evgeny Zhuravlev, René Androsch, Andreas Wurm, and Jürn W.P. Schmelzer

1 Influence of Thermal Prehistory on Crystal Nucleation and Growth in Polymers

Observations regarding the effect of thermal history of crystallizing polymer melts onto the outcome of crystal nucleation and growth processes are investigated experimentally. Some results can be at least on a qualitative basis explained by classical nucleation theory (CNT) while others are not easy to understand in the framework of CNT. The origin of the respective problems and possible extensions of CNT to overcome them are briefly discussed. We chose polymers as model systems because they allow one a separate investigation of nucleation and growth processes in a wide temperature and time range. Furthermore they are well suited to be analyzed experimentally by the recently developed fast scanning calorimetry. In particular, by applying fast scanning calorimetry we are able to investigate processes in bulk samples and do not need to use droplets to study homogeneous nucleation kinetics. Fast scanning calorimetry enables us to observe homogeneous nucleation in materials crystallizing relatively fast like most of the industrial relevant semicrystalline polymers. Quantitative analysis allowed us to judge the nucleation efficiency of additives in the whole range of temperatures, where polymers crystallize. Besides the observed nucleation and growth below the glass transition information about the nucleation activity of small crystals grown at different temperatures relative to the cold-crystallization temperature range were obtained. Finally we show how relaxation of the under-cooled melt (glass) influences homogeneous nucleation. These data may serve as input for a more general description of the interplay of nucleation-growth and relaxation processes within the framework of a structural order-parameter model.

1.1 Introduction

The basic theoretical concepts underlying the description of crystal nucleation and growth processes were developed 80-90 years ago. In a variety of cases, the classical methods of describing nucleation that result from these ideas, namely classical nucleation theory (CNT) and the classical theory of crystal growth, supply us with a satisfactory description of the respective processes. However, in a not much less, or possibly even larger number of cases severe deviations between the theoretical predictions and experiment are observed.

In this contribution we focus on some observations regarding the effect of thermal history of crystallizing polymer melts onto the outcome of crystal nucleation and growth processes. Some of them can be at least on a qualitative basis explained by CNT while others are not easy to understand in the framework of CNT. We chose polymers as model systems because they allow one a separate investigation of nucleation and growth processes in a wide temperature and time range. Furthermore they are well suited to be studied experimentally by the recently developed fast scanning calorimetry. In particular, by applying fast scanning calorimetry we are able to investigate processes in bulk samples and do not need to use droplets to study homogeneous nucleation kinetics.

The chapter is structured as follows: First we briefly discuss the state of art regarding theory in the framework of structural order-parameter descriptions. It is followed by the description of an experimental technique, differential fast scanning calorimetry, both providing a deeper insight into nucleation of crystals in dependence on melt history. In the main part of the contribution we then focus on experimental aspects applying the differential fast scanning calorimeter. We describe a way to generate samples with essentially no homogeneously formed nuclei at temperatures above and below the glass transition temperature. Since heterogeneities are never completely absent a strategy to minimize their impact on the observed crystallization is discussed. Making use of differential fast scanning calorimeters and combining both approaches finally allows us studying homogeneous nucleation kinetics under isothermal conditions. For experiments below the glass transition we show that nucleation starts only after significant volume and enthalpy relaxation towards the super-cooled liquid state. Here the influence of the state of the quenched melt regarding sub-T_g relaxation is important for nucleation even if the relaxation is not considered to generate order in the sample. Finally, we discuss the question how structures formed at annealing influence crystallization on heating. We show that crystals formed at temperatures above the cold-crystallization range do not act as nuclei there. But nuclei or crystals formed at so low temperatures that they melt on heating before the cold-crystallization range is reached are able to accelerate crystal growth.

1.2 State of the Art

1.2.1 Dependence of the Properties of Glass-forming Melts on Melt History

The proper account of the circle of problems sketched out above is a hard task. Fig. 1.1 shows the typical relationship between the glass transition temperature T_g (for conventional cooling rates) and the temperature T_max where the maximum of the steady-state nucleation rate is reached. It is evident that the maximum of the steady-state nucleation rate is found near to T_g. For this reason, one has to look carefully at the properties of the ambient glass-forming melt in order to determine correctly the thermodynamic driving force of the process of crystallization and the surface energy term.

The typical behavior of the density of glass-forming systems during vitrification is shown in Fig. 1.2. The density increases with decreasing temperature but its values depend not only on the thermodynamic state parameters but also on cooling rate or, more generally on the melt history, i.e. the way how the glass-forming melt was brought into its current state. In order to describe the behavior in thermodynamic terms, one has to introduce, at least one additional structural order-parameter denoted here as ξ which we may associate, for example, with the free volume of the melt under consideration. The rate of change with time of this additional order-parameter can be described for isothermal and isobaric conditions by

(1.1)

Fig. 1.1: (a) Dependence of the steady-state nucleation rates for α-Li₂O₂SiO₂ on temperature as obtained by different authors [1]. T_g is the glass transition temperature and T_m the melting temperature. (b) Relation between the temperature of the maximum nucleation rate and the glass transition temperature for a large class of glass-forming melts. Different systems are specified by the different numbers (for the details see [2]).

Fig. 1.2: (a) Typical dependence of the density of glass-forming melts on temperature during cooling (shown here for a borosilicate glass) for different cooling rates. With an increase of the cooling rate (from 1 → 2 → 3), the glass-transition temperature is shifted to higher values. (b) Qualitative interpretation of this behavior employing one structural order-parameter connected with the free volume of the system under consideration. Curve 3 refers to the equilibrium state of the melt, curve 2 describes cooling at some given rate and curve 3 describes the method of determination of the glass-transition temperature as employed in Fig. 1.2a [1, 3, 4, 5].

Here τ (p, T, ξ) is the characteristic relaxation time which depends on pressure, temperature and the structural order-parameter. It can be shown [5, 6] that such a relaxation equation can easily reproduce the often observed relaxation behavior of the form ξ ~ t^1/2 and can give a key to the theoretical understanding of the stretched exponential relaxation kinetics. In Eq. (1.1), ξ_e is the equilibrium value of the structural order-parameter. For given cooling and heating rates, q = (dT/dt), Eq. (1.1) can be transformed into a relation describing the change of the structural order-parameter with temperature. The solution of this equation for constant cooling and heating rates results in the dependencies shown in Figs. 1.2 and 1.3.

Fig. 1.3: (a) Dependence of the structural order-parameter on temperature for cooling and heating processes performed with the same absolute value of the rates of change of temperature. (b) Dependence of the characteristic relaxation time, τ(T, ξ), on temperature for cooling and heating processes [1, 5]. By a dashed curve (1), the equilibrium value of the relaxation time is shown. The values of the relaxation time in cooling (2) and heating (3) differ due to differences in the respective values of the structural order parameter as shown in Fig. 1.3a.

Since the structural order-parameter is a function of pressure and temperature and of the melt history (cooling and heating rates), the thermodynamic properties of the melt also depend on the same set of parameters. It follows as a consequence that the thermodynamic state parameters of the crystal cluster in the ambient phase are, as a rule, dependent on the melt history as well. Once the bulk properties depend on melt history, the surface properties also have to depend on it. Consequently, the kinetics of crystal nucleation and growth is affected, in general, by melt history and may proceed, in particular, in a different manner for cooling and heating processes. The degree to which such effects are of importance is determined by the ratio of the characteristic time scales for relaxation and criti...

Table of contents

• Also of Interest
• Title Page
• Copyright Page
• Foreword
• Table of Contents
• Preface
• List of contributing authors
• 1 Influence of Thermal Prehistory on Crystal Nucleation and Growth in Polymers
• 2 Early Stages of Crystal Formation in Glass-forming Metallic Alloys
• 3 Crystalline and Amorphous Modifications of Silica: Structure, Thermodynamic Properties, Solubility, and Synthesis
• 4 The Main Silica Phases and Some of Their Properties
• 5 Chemical Structure of Oxide Glasses: A Concept for Establishing Structure–Property Relationships
• 6 Bubbles in Silica Melts: Formation, Evolution, and Methods of Removal
• 7 Regularities and Peculiarities in the Crystallization Kinetics of Silica Glass
• 8 Stress-induced Pore Formation and Phase Selection in a Crystallizing Stretched Glass
• 9 Crystallization of Undercooled Liquids: Results of Molecular Dynamics Simulations
• 10 Crystal Nucleation and Growth in Glass-forming Systems: Some New Results and Open Problems
• Index