low density cellular plastics: physical basis of behaviour

Edited by
N. C. Hilyard Honorary Research Fellow, Materials Research Institute, Division of Applied Physics, Sheffield Hallam University, UK
and
A. Cunningham Company Science and Technology Associate, International R&T Centre, ICI Polyurethanes, Everberg, Belgium
ID n I SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
First edition 1994
© 1994 Springer Science+Business Media Dordrecht Originally published by Chapman & Hali in 1994 Softcover reprint ofthe hardcover Ist edition 1994
ISBN 978-94-010-4547-6 ISBN 978-94-011-1256-7 (eBook) DOI 10.1007/978-94-011-1256-7 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the UK Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored, or transmitted, in any form or by any means, without the prior permission in writing of the publishers, or in the case of reprographic reproduction only in accordance with the terms of the licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms oflicences issued by the appropriate Reproduction Rights Organization outside the UK. Enquiries concerning reproduction outside the terms stated here should be sent to the publishers at the London address printed on this page.
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Contents
Preface xiii
1 Physical behaviour of polymeric foams - an overview 1 A. Cunningham and N.C. Hilyard
1.1 General 1 1.2 Foam formation 3 1.3 Cell structure 4 1.4 Matrix polymer morphology 7 1.5 Thermal behaviour 9 1.6 Stress-strain behaviour 11 1.7 Energy management 14 1.8 Final comments 19 References 20
2 Polyurethane flexible foam formation 22 Luis D. Artavia and Christopher W Macosko 2.1 Introduction 22 2.2 Reaction chemistry 23 2.3 Morphology development 33 2.4 The cell opening mechanism 47 2.5 Conclusions 51 Acknowledgements 51 References 52
3 Characterizations of polymeric cellular structures 56 M. B. Rhodes 3.1 Introduction 56 3.2 Background 57 3.3 Quantitative characterization 60 3.4 Stereology 64
vi Contents
3.5 Difficulties associated with measurement 67 3.6 Optical microscopy 70 3.7 Final comments 75 Acknowledgements 76 References 76
4 The morphology of flexible polyurethane matrix polymers 78 R. D. Priester, Jr and R. B. Turner 4.1 Introduction 78 4.2 The dynamics of phase separation 78 4.3 The morphological characterization of foams 84 4.4 Summary 101 Acknowledgements 101 References 102
5 Heat transfer in foams 104 Leon R. Glicksman 5.1 Introduction 104 5.2 Conduction heat transfer 106 5.3 Radiative heat transfer 121 5.4 Gas conduction 135 5.5 Overall conductivity 139 Acknowledgements 143 Appendix A: Lower limit analysis 144 Appendix B: List of symbols 148 References 150
6 Thermal ageing 153 C. J. Hoogendoorn 6.1 Introduction 153 6.2 Theory and modelling 155 6.3 Experimental methods 169 6.4 Different testing methods 181 Appendix: List of symbols 184 References 185
7 The elastic behavior of low-density cellular plastics 187 Andrew M. Kraynik and William E. Warren 7.1 Introduction 187 7.2 Elastic behavior of perfectly ordered two-dimensional foams 190 7.3 Elastic behavior of three-dimensional foams 210 7.4 Future directions 220 Acknowledgements 223 References 223
Contents Vll
8 Hysteresis and energy loss in flexible polyurethane foams 226 N. C. Hilyard 8.1 Introduction 226 8.2 Mechanical response 227 8.3 Definitions and relationships 230 8.4 Mechanisms 238 8.5 Static hysteresis 251 8.6 Dynamics hysteresis 257 8.7 Ball rebound resilience 261 8.8 Conclusions 264 Appendix: List of symbols 267 References 268
9 Impact response 270 N. J. Mills 9.1 Introduction 270 9.2 Macroscopic deformation geometry 272 9.3 Cell geometry and deformation mechanisms 276 9.4 Impact properties 283 9.5 Relation of impact properties to microstructure 291 9.6 Packaging design 300 9.7 Complex impacts 307 9.8 Discussion 316 References 317
10 Acoustic characteristics of low density foams 319 Walter Lauriks 10.1 Introduction 319 10.2 Single-wave approximation for foams with a low flow
resistivity 321 10.3 Acoustic properties of foams of medium and high flow
resistivity 331 10.4 Matrix representation of layered porous materials 339 10.5 Conclusion 353
Appendix A: Matrix elements 354 References 359
Index 362
Contributors
Luis D. Artavia Escuela de Ingenieria Quimica Universidad de Costa Rica Ciudad Universtaria Rodrigo Facio San Jose Costa Rica
A. Cunningham ICI Polyurethanes Everslaan 45 B-3078 Everberg Belgium
Leon R. Glicksman Massachusetts Institute of Technology Cambridge Massachusetts MA 082139 USA
N.C. Hilyard Materials Research Institute Division of Applied Physics Sheffield Hallam University Sheffield SI 1WB UK
C. 1. Hoogendoorn Heat Transfer Group Applied Physics Department Delft University of Technology Delft The Netherlands
x
Andrew M. Kraynik Sandia National Laboratories Albuquerque New Mexico 87185-0834 USA
Contributors
Christopher W. Macosko Department of Chemical Engineering and Materials Science University of Minnesota Minneapolis MN 55455-0132 USA
N. J. Mills School of Metallurgy and Materials University of Birmingham Birmingham B15 2TT UK
R. D. Priester PUjTPU Product Research, B1470D Dow Chemical USA Freeport Texas 77541 USA
M. B. Rhodes Chemistry Department University of Massachusetts Amhurst Massachusetts MA 01003-0035 USA
R. B. Turner PUjTPU Product Research, B1470D Dow Chemical USA Freeport Texas 77541 USA
Contributors
William E. Warren Department of Civil Engineering Texas A&M University College Station Texas 77843-3136 USA
Xl
Preface
Foams are gas filled integral structures in which the gas is finely dispersed throughout a continuously connected solid phase. The bulk density is usually substantially lower than that of the solid component, and for the foams which form the focus for this book the volume fraction of the gas phase is considerably greater than 0.5 and in most instances in excess of 0.9. Many of the materials encountered in every day experience, such as bread,
plants and trees, structural materials for buildings, comfort materials for domestic and automotive seating, shock absorbers or car bumpers and materials for noise control, have one thing in common - the cellular nature of their physical structure. Why are these structures so important in the natural and man-made world?
The reasons are both technical and commercial. From a technical viewpoint cellular materials offer:
1. high specific stiffness and strength - making them suitable for structural applications;
2. close to ideal energy management - hence their use in thermal and acoustic insulation, vibration damping, acoustic absorption and shock mitigation; and
3. comfort - hence their use for domestic and automotive seating.
The commercial driving force is cost reduction and legislation, such as weight saving and noise reduction in the automotive and industrial sectors. Density reduction can be converted directly to cost savings and it is this reason which ensures that commercially produced foams are inexorably being driven towards their lowest possible density for a given application. As densities become ever lower the control and optimisation of the cellular structure and physical properties becomes more complex. To facilitate progress in this respect there is a need for a better understanding of the fundamental relation ships between composition, cellular structure, matrix morphology and the physical properties. This will facilitate the identification of key factors that control behaviour and performance in use and thereby enable the selection of appropriate chemical and processing variables.
XIV Preface
This book brings together a worldwide group of authors from industry and academia who are at the forefront of research into the physics of low-density solid polymer foams. They report, explain and quantify, using empirical data, phenomenological modelling and mathematical analysis the current understanding of fundamental issues concerning foam formation and physical behaviour, and in so doing bring to the readers' attention the many new and exciting possibilities in foam development which have potential for commercial exploitation. Unlike other books on polymeric foams, which concentrate on the chemistry and process technology of foams, it focuses on the essential material science issues of the quantification and mathematical modelling of physical behaviour whether it be mechanical, pneumatic, thermal or acoustic. The book addresses fundamental issues concerning the physics of low density cellular plastics and is intended for any researcher, whether they be chemist, physicist, material scientist or advanced postgraduate student majoring in cellular materials, who may be involved in the development or application of new low-density cellular polymer products. It deals for the most part, but not exclusively, with polyurethane foams and includes chapters by Cunningham (ICI Polyurethanes, Belgium, the Overview), Artavia and Macosko (University of Minnesota, USA, although Artavia is now based at Cindad Universtaria Rodrigo Facio, Costa Rica), foam formation; Rhodes (University of Massachusetts, USA), cell structure characterization; Priester and Turner (Dow Chemical USA), morphology of flexible polyurethane matrix polymers; Glicksman (Massachussets Institute of Technology, USA), heat transfer; Hoogendoorn (Delft University, the Netherlands), thermal ageing; Kraynik and Warren (Sandia National Laboratories, USA, although Warren is now based at Texas A&M), elastic behaviour; Hilyard (Sheffield Hallam University, UK), hysteresis and energy loss; Mills (University of Birmingham, UK) impact response; Lauriks (University of Leuven, Belgium) acoustic absorption and insulation. Editorial change has been kept to the minimum required and the editors would wish to thank contributors for their forebearance over the prolonged time the book has been in preparation.
N.C. Hilyard A. Cunningham
A. Cunningham and N. C. Hilyard
1.1 GENERAL
Over the last decade, the markets for low-density cellular plastics increased considerably, the major product sectors being domestic, automotive, aero space and industrial. Applications include comfort cushioning, thermal insulation and energy management systems. The reasons for this growth are:
1. cost reduction; 2. improved functional performance; 3. potential for integrated design; and 4. legislation concerning, for example, automobile weight reduction, drive past noise reduction, flammability and smoke reduction and building insulation standards.
Improvements to performance have come about through the development of a better understanding of the relationships between chemical, processing and physical variables. The purpose of this book is to provide the reader with a state of the art review and discussion of these issues from a pre dominately physics perspective. As new and improved materials are introduced classification becomes more
complex. Differentiation between low-density foams is based mainly on:
1. base polymer; 2. cell structure; 3. physical properties; and 4. application.
Thus:
1. Base polymers include thermosets (e.g. polyurethane, phenolics, polyphos phazene, malamine formaldehyde, polymethacrylamide) and thermoplastics (e.g. polystyrene, polypropylene, polyvinyl chloride and polyethersulphone).
2 Physical behaviour of polymeric foams - an overview
2. Cellular structures may be reticulated or closed cell, or somewhere between depending on formulation, processing and post-processing operations.
3. Physically the foam may be, for example, rigid or flexible, combustion modi fied or non-flammable. Even these categories have developed sub-divisions; flexible foam, for instance, can be high hysteresis (HHF), viscoelastic (VEF) or high resilience (HRF).
4. Applications include the thermal insulation of appliances and the walls and roofs of domestic and industrial buildings, comfort cushioning for both domestic and contract furniture (including aircraft and public transport) and energy management systems. This last category is broad and includes, for example, automotive seating, shock mitigation (e.g. vehicle front and side impact protection) and noise control.
The physical properties offoams depend in a complex way on many factors, some ofwhich cannot be varied independently. They fall into two categories:
1. material related; and 2. the test regime.
Material factors include: the composition of the base polymer and formula tion; the morphology of the solid polymer comprising the cell elements of the foam; cell structure; foam density; post-processing operations and environ mental conditions during and after processing; and the nature of the fluid enclosed by the matrix. Since the cell structure geometry of most manufactured foams is anistotropic (cells being elongated in the direction of foam expansion), property values (such as thermal, mechanical and flow) are expected and found to be dependent on the direction of measurement. The test regime, i.e. the conditioning environment (temperature and relative humidity) and test specification (strain rate, frequency of deformation, mech anical conditioning, etc.) also influence measured parameters. Furthermore, the response of a foam subject to large physical inputs is non-linear so property values depend on the intensity of the input whether it be thermal, mechanical, pneumatic or acoustic. To compare physical data given by different researchers, the test regimes must be specified in detail. Other factors remaining the same, such as the test environment and the
conditioning of the foam test piece, a physical property value X r can be represented by the functional relationship
X f = ff(composition, structure, morphology), (1.1)
where composition refers to the starting formulation, structure to the geometry and connectivity of the cellular matrix and morphology to the molecular and super-molecular structure of the matrix polymer. This book develops the theme given in (1.1). It first considers the dynamics of the foam formation process, methods of characterizing the cellular struc ture within a foam and the morphology of the polymer comprising the cell
Foam formation 3
structure elements in foams. It continues by considering relationships be tween physical behaviour and structural and compositional factors. The behaviours addressed include heat transfer and thermal ageing, the relation ship between stress and strain, static and dynamic hysteresis, impact behaviour and acoustic absorption.
1.2 FOAM FORMATION
The majority of cellular polymers result from the nucleation, growth and expansion of gas bubbles in a melt or reacting liquid system. Representations of idealized structures at different stages of the expansion process are given in Fig. 1.1. In the first instance the bubbles are dispersed throughout the liquid and if stabilized at this stage the foam would have high density, Fig. 1.1(a). For spherical bubbles of uniform size the lowest value of density is when the bubbles are close packed, Fig. 1.1(b). If the expansion process is allowed to continue the bubbles touch and distort to fill the interstrices, forming, in the three-dimensional case, polyhedral structures which are often represented in the literature by the idealized form of a pentagonal
•••••••••• • • • (al
(bl
(dl
(e)
Fig. 1.1 Idealized two-dimensional cellular structures at different stages of foam expansion [1].
dodecahedron (Fig. 1.1(c». Such a representation is used in several chapters of this book. Depending on the physical states of the liquid system, such as viscosity and surface energy, gravitational and other forces may cause the liquid material to concentrate at the intersection of the elements of the repeating cells to form Plateau borders which are usually tricuspid in cross sectional shape, Fig. l.l(d). At this stage the foam is oflow density and is closed cell. However, the membranes between the cell struts which result from the intersection of the spherical bubbles (the 'windows') may be ruptured. In the case of polyurethane foams this can be achieved by means of a chemically based cell-opening mechanism or by post-processing treatment (reticulation). These procedures give open cell foams with varying degrees of connectivity (Fig. 1.1(e». Even with the same generic type of polymer this can depend on the starting formulation and process conditions. As Artavia and Macosko describe in Chapter 2, the formation of polyurethane foam is a complex physico-chemical process in which many variables combine to control the final poduct.
1.3 CELL STRUCTURE
Figure 1.2(a) schematically illustrates the idealized cell structure for an open cell foam. The pentagonal dodecahedron provides tetrahedral junc tion elements which closely approximate the ideal angles essential in the maintenance of stable foam structures and comes close to forming a space filling geometry. However, it does not, in either case, exactly meet these requirements. For foams that have had time to reach thermodynamic equilib-
(8)
I I I I I I I I )~deff~1
(bl
I
I
:+--deff~1
Fig. 1.2 Schematic representation of cell structures in polyurethane open cell flexible foams: (a) low density (Pr < 30 kgjm3), the classic pentagonal dodecahedron; and (b) high density (Pr> 50kgjm3), a shell with windows.
Cell structure 5
rium (e.g. aqueous and naturally occurring foams) three rules have been identified (see, for example, [2-5]):
1. The average number of faces per cell is 14. 2. The average number of sides per face is 5.143. 3. The tetrahedral junction angles are 1090 28' 16".
The only space-filling structure so far identified that statisfies all of these conditions is the p-tetrakaidecahedron proposed in [5]. It should be noted that to meet these rules the edges are curved, which is a commonly observed feature of low-density foams (both aqueous and synthetic). The curvature of the edges/struts which form the load-bearing matrix of the foam reinforces the dominance of strut bending as the primary deformation mode. This is mathematically derived and analysed in great detail in Chapter 7. For rapidly formed synthetic foams in which non-equilibrium structures can be frozen-in deviations from the ideal can take place. Suprisingly, these deviations are not great. Table 1.1 compares the percentage of four-, five- and six-sided windows in a rapidly formed polyurethane to those in a pentagonal dode cahedron and a- and p-tetrakaidecahedrons.
It is most important to relate any discussion on the description of cell structure to the density (or volume fraction of polymer) under considera tion. For foams below a solid volume fraction of about 0.05 a polyhedral description holds. However, increasing the solid volume fraction above this level can alter the cellular structure rapidly. Figure 1.3 shows micrographs of low-density and high-density high-resilience polyurethane cushion foams. It is seen in Fig. 1.3(a) that with the low-density foam the dimensions of the cell strut elements, strut length 10 and thickness t, can be evaluated with reasonable certainty. However, the geometry of the higher density foam (Fig. 1.3(b» does not conform to the classic model and is better described by an ellipsoidal shell with windows, as illustrated schematically in Fig. 1.2(b).
Table 1.1 Percentage of four-, five- and six-sided faces measured in four large cell and two small cell polyurethane rigid foam systems compared with ideal structural models
Large cell foam Small cell foam 4 5 6 4 5 6
16 65 18 15 53 27 18 61 21 16 58 23 18 59 22 20 56 21
Pentagonal dodecahedron 0 100 0 fJ-tetrakaidecahedron 14 57 29 a-tetrakaidecahedron 43 0 57
Fig. 1.3 Electron micrographs of HR polyurethane cushion foams illustrating the effect of volume fraction of polymer on cell structure: (a) Pr = 26 kg/m3 and (b) Pr = 60 kg/m3.
In the latter case it is difficult to define the cell structure in terms of par ameters 10 and t. Consequently, the characterization of cell structures is not straightforward and has become a study in its own right. Basically, there are two types of approach:
1. quantification of the dimensions of the cell elements (structs and windows) and their geometrical arrangement, as used by Glicksman in his analysis
Matrix polymer morphology 7
given in Chapter 5 for heat transfer through closed-cell rigid foams and Kraynik and Warren in their micro-mechanical analysis of unit cell deformation for the relationship between stress and strain (Chapter 7);
2. the statistical evaluation of average cell size, such as the effective cell diameter deff of closed or open cells.
The latter is used in the development of theoretical models and interpreta tion of data for heat transfer behaviour (Chapter 5), gas diffusion behaviour (Chapter 7), fluid flow behaviour (Chapter 8) and acoustic absorption behaviour (Chapter 10). As argued by Rhodes in Chapter 3 the structural characterization undertaken depends on the use to which the information is to be put and she describes and critically compares currently available methods. The most important statistical structural parameters which affect physical behaviour are:
I. cell size; 2. cell size distribution; 3. anisotropyjcell orientation; 4. proportion of cell struts and windows; and 5. porosity.
The statistical characterization of cell structure is complicated further by the fact that in some material systems there may be bimodal cell size distributions. Figure 1.4 shows a typical distribution of polyurethane foam cells as a function of the number of faces per cell where f is the fraction of cells containing nF faces. From Fig. 1.4(b) it is seen that the number of faces per cell nF increases in proportion to the average cell diameter diso. Consequently, the data in Fig. 1.4(a) indicates that with this material there was both a bimodal and a very broad distribution in cell diameter. Broad cell size distributions will influence elastic collapse, heat transfer
and gas transfer, all of which are cooperative processes.
1.4 MATRIX POLYMER MORPHOLOGY
The common theme throughout this book is the attempt to express (1.1) in mathematical terms. The study of polymer morphology and its represen tation in terms of functional relationships has proved particularly difficult because of the modifying effect of the superimposed cellular structure. One of the most complex of polymer morphologies occurs in flexible polyure thane foam and two chapters of the book are devoted to this understanding. Chapter 2 looks at the complexities of molecular network formation and phase separation, which is the precursor to the development of the final solid polymer morphology. Chapter 4 extends the analysis to the fundamental characterization of this final state. A major restriction on the determination of morphological and, ultimately, intrinsic matrix polymer properties has been the practical difficulty of making direct measurements on individual
(a)
I I I I
23456
10 t-
Fig. 1.4 Quantification of the cell structure in rigid polyurethane foams: (a) the distribution of cells with respect to the number of faces per cell, illustrating both a broad and bimodal distribution; and (b) the number of faces per cell as a function of cell diameter for large-celled foams [6].
Thermal behaviour 9
foam struts. All attempts to remove the cellular superposition by application of pressure and temperature tend to modify the matrix polymer morphology. With thermoplastic foams modification can occur through the relaxation of internal stresses induced during processing, and for semi-crystalline polymers there is the added complication of modification via post annealing. For thermoset polymers the existence of a cross-linked network, often in
combination with a phase-separated morphology, make the fusing of a foam into a measurable plaque impossible without severe disruption of the initial molecular state. In recent years, therefore, a range of techniques have arisen specifically tailored to extracting information on the matrix molecular state in the presence of the cellular macro-structure. Most prominant of these has been the increasingly successful use of SAXS as a probe of the micro morphology of flexible polyurethane foam (see, for example, Chapter 4). Recent extension of this technique to real-time measurements by Najima et al. [7] demonstrates that the full benefits of this approach have yet to be exploited. The physical models developed for foams subjected to small deformations all lead to equations in the form of separated variables where the intrinsic matrix property is independent of the foam strain. Although the practical applications of rigid cellular materials are usually confined to such low strains (pre-buckling), flexible foams invariably have to perform their design function under large deformations. Research by Hilyard and Cunningham [8] has shown that for polyurethane flexible foams the intrinsic polymer loss mechanism under dynamic conditions is strongly dependent on the level of absolute strain. Future mathematical representations of large strain behaviour, therefore, will have to incorporate such a matrix dependence, which is central to the true description of the non-linear viscoelastic response of these foams.
1.5 THERMAL BEHAVIOUR
It is well known that the three modes of heat transfer in cellular materials are convection, conduction and radiation. Although air possesses a much lower thermal conductivity than any solid substance the full benefit of this could not be harnessed because of the large convective heat losses gen erated in air gap structures. Early experimental studies demonstrated that convective losses could be eliminated if air was entrapped in a porous medium with pore dimensions less than a few millimetres. This led to the development of the open fibre and inorganic powder insulations which even today form the vast majority of airgap insulation. The low densities of these products meant that the elimination of convection far outweighed the heat transfer increase due to solid conduction. As new applications were developed that demanded high insulation efficiency coupled to load bearing capability (e.g. appliances and cold stores) the need for new forms of insulating structure increased. Attention was, therefore, focused on the second of the heat transfer
mechanisms - conduction. Replacing air with a substitute gas of much lower thermal conductivity could provide the required improvements. To do this, however, closed cell foams were needed to encapsulate the gas in cells sufficiently small to prevent convection. The development in the early 1960s of a range of CFC blowing agents (in particular CFC-11) provided the low conductivity gases needed for this approach. Benefits were immediate, with insulation efficiencies increasing by over 40%. Over the last 25 years the thermal ageing performance of insulation foams
has been studied extensively, with results in line with the pioneering work of Norton [19] and Cuddihy and Moacanin [10]. In 1987, however, the Montreal Protocol eliminated CFCs as an ongoing gas option for plastic foams. This protocol, coupled to increasing energy conservation trends (particularly in the USA) provided a unique double stimulus to the further improvement of cellular insulating materials. The result has been an explosion of research and development within both industry and academia in an attempt not only to characterize and predict the long-term ageing performance of foam based on CFC-ll gas substitutes, but also to improve still further the insulating efficiency of the foam. To do this attention was focused on to the last remaining heat transfer mechanism - radiation. In the 1980s extensive work by Glicksman and Cunningham (see, for example, [11-13]) established the level of radiative heat transfer in low-density rigid polyurethane foam to be approximately 30% of the overall foam thermal conductivity (Table 1.2). This was far higher than previously assumed and provided a new research focus for insulation improvement.
Table 1.2 Estimated radiative heat transfer contribution in a polyurethane rigid foam
Mechanism Free-rise Free-rise Contribution laminate laminate in the rise
All (WjmK) ,1..1 (WjmK) direction
(%)
Gas 0.008 0.008 45 conductivity
Plastic 0.004 0.002 20 conductivity
Estimated radiative 0.006 0.004 35 conductivity
Stress-strain behaviour 11
Today, therefore, the two most critical issues in the research and develop ment of improved cellular foam insulation are:
1. the elimination of internal radiative heat transfer through the redesign of cellular structure; and
2. the long-term thermal ageing performance of possible CFC-ll alternatives.
Both of these areas are thoroughly reviewed and developed in Chapters 5 and 6.
1.6 STRESS-STRAIN BEHAVIOUR
The relationship between stress and strain is central to most applications of low-density polymeric foams, whether they be structural, comfort-related or for energy management. Consequently, it is worthwhile to review the current understanding of this relationship for both small and large strains.
1.6.1 Stiffness and strength
For a given chemical system and test regime the most important variable is foam density Pc, or, more importantly, the density of the foam relative to that of the solid polymer which comprises the cellular matrix. This is usually expressed as the volume fraction of polymer ¢ = PelPs' Low-density foams may be considered as those in which ¢ < 0.1. All foam manufacturers and researchers have at one time or another examined the correlation between physical parameters and density (e.g. modulus, hardness, strength, air flow and resistivity). For mechanical properties Xc a power law relationship has been found to apply in most cases;
(1.2)
where X s refers to property of the solid matrix parameter and the exponent ndepends on the property in question. It usually lies in the range 1.0 < n < 2.0 (Table 1.3).
Table 1.3 Examples of theoretical values of the exponent n for the mechanical properties of low-density foams (the subscripts C and T refer to compressive and tensile deformation, respectively)
Source Foam structure Property n
Gibson and Ashby [15] Open cell Ecc 2
O"Cel 2 Menges and Knipschild [16] Closed cell O"CB 2
1B 2 Ecc 2
Both Gibson and Ashby [14] and Menges and Knipschild [15], found good agreement between empirical values of n and those predicted from their respective theoretical models based on the micromechanics of cell element deformation. Rusch [16] proposed a purely empirical relationship for the modulus of flexible open cell foams in compression, namely
ECf = Es(4)l12)(2 + 7¢ + 3¢2).
Analysis ofthe experimental data ofGent and Thomas [17] and Lederman [18] by Hilyard [19] for rubber latex foams showed, for a range of ¢ values that the behaviour could be represented quite well by (1.2) with the value of the exponent in the range 1.4 < n < 1.7. For other physical behaviours, such as heat transfer, air flow and acoustic absorption the simple power law expressed in (1.2) does not apply. An insight to the origin of the difference in the value of n for mechanical behaviour, both theoretical and empirical, is obtained from the work of Kraynik and Warren presented in Chapter 7. They show, using a formalized micromechanical approach, that the value of the exponent n for the elastic modulus Ef depends critically on foam microstructure and whether the predominant deformation mode is cell element bending or cell element stretching/compression. For most practical situations tetrahedral strut junctions predominate. However, the degree of cell regularity varies from foam to foam, depending on the type of foam and process conditions. Consequently, it is not unexpected that the exponent n lies in the range 1.0 < n < 2.0. Above, and in the historical investigations cited, it has been assumed for the most part that the mechanical properties of the solid matrix polymer are constant and the same as those of the bulk polymer. This is not the case in general. It is now quite clear, as explained in Chapter 8, that with some foams the chemical/processing methods used for controlling foam density influence the physical properties of the solid matrix polymer so that the density Ps, modulus Es and loss tangent tan Os are not always independent variables.
1.6.2 Stress-strain relationship
Ignoring the influence of the enclosed fluid, deformation rate and frequency, the mechanical response of a low-density foam is controlled by the way in which the cell elements behave cooperatively under localized strain whether it be small or large. Relatively recent theoretical studies have shown that deformation under small forces (i.e. pre-buckling) is associated with cell element bending [14, 20] rather than normal deformation ofthe struts parallel to the force vector, as assumed in earlier work by, for example, Gent and Thomas [17]. The majority of theoretical investigations have been aimed at predicting single point property values such as elastic moduli, Poisson's ratio
Stress-strain behaviour 13
and strength, and, as explained above, in this respect these models have met with some success. More recently, Kraynik and Warren, after intensive work over many years, have developed a micromechanical modelling approach (described in Chapter 7) which allows the prediction of the non-linear stress-strain response of an elastomeric cellular plastic up to the point of elastic collapse. This is a major step forward. From a practical viewpoint, however, and a focus for future work is the modelling of the compressive stress-strain response at large strains (10% < e < 80%) in terms of compositional, structural and morphological variables. An early example of such work is that of Dement'ev and Tarakonov [21-23], which, like Gibson and Ashby in their later pub lications, divides the static mechanical response into three regions: Hookean, plateau and densification. They relate the stress-strain behaviour of flexible foams to the cell structure variable b = t/lo, where t is the strut width, and 10 is the undeformed strut length. The basis of their theoretical argument is that in bulk compression cell struts bend and that tranverse changes in the test specimen are small. The boundaries to the three strain regions are defined in terms of critical com pressive strains e < eel> eel < e < ee and e> ee, where eel is the elastic collapse strain and ee the strain at the onset of strut interaction, i.e. densification. In the post-collapse and densification regions the stress is related to strain by elliptic integrals of the first and second kind. The predictions of their model for a flexible foam is compared schematically with a practical mechanical response in Fig. 1.5 and it is seen that it is similar to that of the model representation of Gibson and Ashby.
I/) I/) 11.1 a: l I/)
•• C7el - ••••
STRAIN
Fig. 1.5 Schematic illustration of the CFD stress-strain relationship for a flexible foam given by the model of Dement'ev and Tarakonov. The line is the predicted behaviour and the data points national experimental values.
Mathematical development yields the following values for the critical strains
and ec = 1- f3/(1 + f3/4)cos n/4,
with the density ratio being given by
prlPs = 3 j2.p2/(2 + {3)2.
(1.3)
(1.4)
(1.5)
Equations (1.3) and (1.5) predict that for low-density flexible foams having volume fraction of polymer </J in the range 2%-10%, the value of the buckling strain eel is in the range 1.5%-7%. The mean value is about the same as that found in practice for cushion foams (Chapter 8) but the lower limit is too small. The corresponding strains for the onset of densification ec is in the range 76%-90% which is too large. As explained above, a major difficulty associated with the application of this type of micromechanical model representation is that with higher density flexible foams, such as polyurethane cushion foams with Pr > 50 kg/m3, it is difficult to estimate the characteristic dimensions, 10 and t, of the cell strut elements. Furthermore, models of this type indicate that the stress post-elastic collapse is parallel to the strain axis up to the point of densification. This is the case with rigid (friable) foams but not with flexible (elastomeric) foams.
1.7 ENERGY MANAGEMENT
The management of energy in its various physical forms is one of the major applications of rigid and flexible low-density polymer foams. This importance is reflected by the fact that three chapters of the book are devoted to this subject, excluding thermal energy management which is treated separately. The forms of energy addressed include static mechanical, dynamic mech anical, impact and acoustic. Applications in which these physical behaviours are significant include comfort cushioning, automotive seating, shock miti gration and noise and vibration control.
1.7.1 Hysteresis
Hystresis plays an important role in mechanical energy management and the cellular plastic materials available for this purpose range from high resiliency cushion foams, with room temperature small-strain loss tangent (tan (5) about 0.1, through noise insulating viscoelastic foams, with tan £5 in the range about 0.2-0.5 to high hysteresis vibration control foams which typically have tan £5 in the range 0.5-1.0. Here we must differentiate between loss tangent, tan £5, and hysteresis.
Conventionally, hysteresis is measured under constant strain rate static
Energy management 15
conditions at large strains, whereas tan {) is a measure of the ratio of energy loss to energy stored under small strain harmonic deformation. As explained by Hilyard (Chapter 8) the micromechanics of the deformation of the cell elements is different in each case. The application of foams in automotive seating presents an interesting illustration of the importance of both static and dynamic performance. A major function of seat foam is the provision of comfort. This can be differentiated into two forms: static (or show-room) comfort and dynamic (in-ride) comfort. Static comfort is governed for the most part by firmness (hardness index), support (SAG or SAC factor) and recovery (resiliency); high resilience, i.e. low hysteresis, foams are preferred. However, dynamic comfort is governed to a large extent by the transmission of vibration through the cushion. Like other mass-spring arrangements the person-seat system exhibits resonance, and the criteria for the engineering design of the foam are to ensure that the resonance frequency is about 3Hz to 4Hz and the transmissibility at resonance is small, typically 2.8 to 3.0. This raises two issues.
1. Low transmissibility at resonance requires a large loss factor, which implies a resiliency lower than that needed for superior static comfort.
2. In order to design the foam so that it satisfies the criteria, quantitative knowledge of the effective dynamic stiffness and loss factor under large static compressions (40-60%) is required.
Hilyard addresses this issue in Chapter 8, but this work is only the first step in the development of our understanding. Much more investigation is needed of the morphological and structural factors which govern dynamic mechanical behaviour under large quiescent strain conditions.
1.7.2 Impact
Impact is a process involving a high rate of deformation, in which, for flexible foams under flat platten compression, the relationship between displace ment and time is approximately a half sinusoid. When modelling the impact response it is usual to make simplifying assumptions. One of these is that the idealized shock motion can be represented by a velocity step y= 0 at t < 0 and y= Vi at t = 0 where Vi is the speed of the body of mass M at the instant of impact. The subsequent displacement y of the foam can be analysed using the equation of motion
My + F(y,y) = 0
f Y=
where Wi is the impact energy and Ym is the maximum deflection of the mitigator. The modelling of the force of reaction F(y,y), which is both deformation and rate dependent, is central to the analysis, and if the function is known for the unloading part of the mechanical response the rebound energy Wr can be evaluated, as well as Ym' However, at present this is not possible because unlike the loading part of the cycle which can be modelled using, for example, the Rusch equation or the Gibson-Ashby equation there is no equivalent model for the unloading part of the cycle. The difficulty arises from the fact that:
1. the maximum deflection varies with M and Vi so Ym is not known until the numerical integration is complete (i.e. when v=0); and
2. the mechanical response, hence F(y,y), in the unloading part of the deflection cycle depends on Ym'
What is required is an analytic expression that will represent both the loading and unloading phases for any maximum deflection. This is not yet available. Unlike the comfort cushioning market, which is dominated by flexible polyurethane foams, shock mitigating materials include thermoplastic foams such as polyethylene and polystyrene as well as semirigid and rigid polyurethanes. As a consequence, when considering mechanisms governing the relationship F(y, y) between the reactive force, F, deformation, Y, and defomation rate, y, account must taken of the molecular/morphological origin of the yield processes involved in crystalline slip in semi-crystalline matrix polymers and in crazing in amorphous rigid matrix polymers, as well as domain disruption in block copolymer and segmented molecular structures. The mechanics of large-strain deformation in thermoplastic foams is considered by Mills in Chapter 9.
1.7.3 Acoustic
All foams absorb noise to varying degrees, and a range of generic types and grades are available commercially for noise insulation and absorption. They include open and closed cell low-density foams such as cellullar polyurethane and expanded polyimide, polyethylene and chlorosulphanated polyethylene. By appropriate formulation and post processing they can be engineered to give optimum acoustic performance. Although polymer foams have been used for this purpose for many years there is no unified theory which relates performance to independently measured variables. A formalized theoretical approach to absorption and insulation behaviour is given in Chapter 10. An introduction to the more practical aspects is given below. The energy in a sound wave is directly proportional to the square of the pressure amplitude P, and when a sound wave with acoustic pressure Pi is incident on a foam, part of the energy is absorbed and part Pr is reflected. This is illustrated for normal incidence in Fig. 1.6(a). The absorption coefficient
Energy management
n=3
n=5
Fig. 1.6 (a) The incident and reflected acoustic energy on a foam absorbing layer with rigid backing having infinite acoustic impedance Z. (b) The pressure profiles in the foam layer illustrating odd order resonances [25].
is the ratio of the energy Er in the reflected wave to that in the incident wave, Ej ,
The reflectivity r = Pr/Pi of an acoustic surface is governed by its acoustic impedance Z, which is defined as the ratio of the instantaneous acoustic pressure to the particle velocity p/v of the sound wave in the material. The acoustic impedance Wo of free air is Poco, where Po is the density of air and Co the speed of propagation in air. Within a porous material the air is not free and the system is reactive, so the impedance is a mathematically complex quantity Z = R +jx. The values of the real and imaginary parts, R and X,
are governed by many parameters including the frequency of the sound wave and the flow resistivity, tortuosity, density, stiffness and damping of the foam. For sound waves incident normally on a foam layer of thickness I bonded to a rigid backing (having infinite acoustic impedance) the acoustic absorption coefficient is, from [24]
an = 1 -I(Z - Wo)/(Z + WoW·
In acoustic absorption applications the function of the cellular material is to allow the acoustic pressure field to penetrate the surface with the smallest possible reflection so that the energy of the incident field is dissipated within the material. Energy dissipation takes place in two ways:
1. the viscous interaction of the air wave within the open pores of the cellular matrix, which is the predominant mechanism; and
2. the damping of the frame wave propagating through the cellular matrix.
Unlike the high modulus fibrous absorbers which were the subject of early theoretical studies (e.g. [25]), the stiffness of the 'frame' in cellular plastics approaches that of the enclosed air, so coupling between the air and frame waves is likely. Coupling between the two wave systems and its effect on the acoustic absorption behaviour of elastic porous materials have been the subject of intense theoretical study (see, for example, [26,27]) and is discussed in some detail in Chapter 10. When a layer of cellular plastic acoustic material of thickness I is bonded to a 'rigid' surface 1/4-wave resonances occur through interference between the incoming and reflected waves, as illustrated in Fig. 1.6(b). Resonance and anti-resonance conditions create maxima and minima in the acoustic absorption response. According to Zwikker and Kosten resonances, and consequently absorption maxima, occur at
COr = n(nv/2/),
where n = 1,3,5, etc. The speed of propagation v = (E/p)1/2, where E are p are the effective bulk modulus and density of the system. Anti-resonances, and hence absorption minima, occur when n is even. These maxima and minima are illustrated in Fig. 1.7 which shows the influence of air flow resistance on the acoustic absorption response of a polyurethane acoustic foam. Reticulation was achieved by controlled mechanical crushing between nip rollers. The highest flow resistivity corresponds to no crushing operation and the lowest to five operations. It is seen that not only does the flow resistivity affect the value of the absorption coefficient, it also influences the resonance frequency, intially shifting it to lower frequencies with decreasing resistivity but then to higher frequencies. The crushing operations had no effect on the foam density and only a very small effect on the dynamic modulus and loss tangent of the bulk foam. The strong influence of air flow resistivity on acoustic absorption behaviour is clearly seen and as a rough
Final comments 19
0<
0.2
FREQUENCY 1Hz
~ 0 ~ -A- 2 -- 3 --e- 4 -- 5 Fig. 1.7 Normal incidence acoustic absorption (SWT) response for a low-density closed cell polyurethane acoustic foam with different levels ofmechanical reticulation, 0-5 [28].
guide optimum absorption response is obtained when the flow resistance of the absorbing layer R = 3poco '" 1200 Rayl. However, as Rogers [28] argues, to achieve the best results the absorber should be tailored to the noise spectrum.
1.8 FINAL COMMENTS
Although our understanding of the relationship between compOSItion, morphology and structure for the thermal insulation behaviour and the single point mechanical properties of low-density solid foams is now well advanced this is not case for other physical behaviours, such as the relationship between stress and strain at large strains, how compositional factors affect static and dynamic hysteresis, and the influence of cell structure and matrix polymer damping on acoustic absorption behaviour. As explained above, there are many gaps in our appreciation, and understanding of the origin ofthe physical behaviour. This understanding is central to the engineering design of low density foams for future applications. The editors hope that the ideas and concepts presented in the following chapters will provide the background for future research into the physical basis of their behavior.
REFERENCES
1. Hilyard, N. c., and Young, J. (1982) Introduction, in Mechanics of Cellular Plastics, (Ed. N. C. Hilyard), Applied Science Publishers, London, Ch. 1.
2. Matze, E. B. (1946) The three-dimensional shape of bubbles in foam - analysis of the role of surface forces in three dimensional cell shape determination. J. Botany, 33, 58-80.
3. Marvin, 1. W. (1939a) The shape of compressed lead shot and its relation to cell shape. Am. J. Botany, 26, 280-8.
4. Marvin, J. W. (1939b) Cell shape studies in the pith of Euratorium Purpureum. Am. J. Botany, 26, 487-504.
5. Williams, R. E. (1964) Space filling polyhedron: Its relation to aggregates of bubbles, plant cells and metal crystallites. Science, 161, 276-7.
6. Cunningham, A. (1987) A structural model of heat transfer through rigid polyurethane foam, in Heat and Mass Transfer (eds 1. Bougard and N. H. Argan), Hemisphere Publishing Corporation, pp. 32-43.
7. Najima, S., Kato, K., Ono, M. and Askida, T. (1992) Time resolved SAXS study ofmorphological change in a binary blend of poly e-kaprolactone and polystyrene oligomer. Macromolecules, 25, 1922-8.
8. Hilyard, N. c., Lee, W. L. and Cunningham, A. (1991) Energy dissipation in polyurethane cushion foams and its role in dynamic ride comfort. Proc. Cellular Polymers-Forum Hotel. London. UK, 20-22 March 1991. RAPRA Technology Ltd, 187-91.
9. Norton, F. 1. (1967) Thermal conductivity and life of polymeric foams. J. Cellular Plast., 3, 23-36.
10. Cuddihy, E. F. and Moacanin, 1. (1967) Diffusion of gases in polymeric foams. J. Cellular Plast., 3, 73-80.
11. Shuetz, M.A. and Glicksman, L. R. (1984) A basic study of heat transfer through foam insulation. J. Cellular Plast., 20(2), 114-21.
12. Valenzuela, J. A. and Glicksman, L. R. (1981) Thermal resistance and aging of rigid urethane foam insulation. Proc. DO£-0N RL Workshop on Mathematical Modeling of Roofs, Con! 811. Nov. 79-261.
13. Cunningham, A. and Sparrow, D. J. (1986) Rigid polyurethane foam: What makes it the most effective insulant? Cellular Polymers, 5, 327-42.
14. Gibson, L. J. and Ashby, M. F. (1988) Cellular Solids-Structure and Properties, Pergamon Press, Ch. 5.
15. Menges, G. and Knipschild, F. (1982) Stiffness and strength-rigid plastic foams in Mechanics ofCellular Plastics (ed. N. C. Hilyard), Applied Science Publishers, London, Ch. 2A.
16. Rusch, K. C. (1969) Load-compression behaviour of flexible foams. J. Appl. Polym. Sci., 13, 2297-311.
17. Gent, A. N. and Thomas, A. G. (1963) Mechanics of foamed elastic materials. Rubber Chem. Tech., 36, 597-602.
18. Lederman, J. M. (1971) Prediction of the tensile properties of flexible foams. J. Appl. Polym. Sci., 15, 693-703.
19. Hilyard, N. C. (1982) Mechanics of cellular Plastics (ed. N. C. Hilyard), Applied Science Publishers, London, 80-81.
20. Warren, W. E. and Kraynik, A. M. (1988) The linear elastic properties of open-cell foams. J. Appl. Mech., 55, 341-6.
21. Dement'ev, A. G. and Tarakanov, O. G. (1970a) Effect of cellular structure on the mechanical properties of plastic foams. Polymer Mech. USA, 6(4), 594-602.
22. Dement'ev, A. G. and Tarakanov, O. G. (1970b) Model analysis of the cellular
References 21
structure of plastic foams of the polyurethane type. Polymer Mech. USA, 6(5), 744-9.
23. Dement'ev, A. G. and Tarakonov, O. G. (1973) Deformative properties of flexible foams in compression. Polymer Mech. USA, 9(3),395-400.
24. Zwikker, C. and Kosten, C. C. (1949) Sound Absorbing Materials, Elsevier, Amsterdam, pp. 15 et seq.
25. Beranek, L. L. (1960) Noise Reduction. McGraw-Hill, New York, pp. 257-9. 26. Lambert, R. F. (1982) The acoustical structure of highly porous open-cell foams.
J. Acoust. Soc. Am., 72(3), 879-87. 27. Allard, J.-F., Aknine, A. and DepolJier, C. (1986) Acoustical properties of partially reticulated foams with high and medium flow resistance. J. Acoust. Soc. Am., 79(9), 1734-40.
28. Rogers, C. G. (199Ia, b) A Technical and Commercial Analysis ofthe Manufacture, Supply and Properties of Noise Control Foams, MPhil Thesis, Sheffield City Polytechnic, Sheffield, UK, Ch. 5, Ch. 6.
2
2.1 INTRODUCTION
Plastic and elastomer foams may be considered as filled plastic composites, where particles, or cells of gas, are the filler. Produced by injection molding and extrusion, or by pouring in place, these materials are either open or closed cell, or somewhere between the two. In open cell foams the gas cells are interconnected, while in a closed cell foam each cell is totally enclosed by thin plastic walls [1-4]. The cellular structure could be the result of:
1. whipping air into a solution or suspension of the plastic, which is then hardened by heat and/or catalytic action (i.e. silicone-based foam);
2. reducing the pressure imposed on the system such that a gas dissolved in the resin suddenly expands (i.e. foamed vinyls);
3. a liquid component of the mix such as hexane or CFC-ll is volatilized by heat (i.e. polystyrene foam);
4. carbon dioxide gas is produced within the mass by chemical reaction (i.e. flexible urethane foams);
5. nitrogen is released within the mass by thermal decomposition of a chemical blowing agent such as azobisformamide or azobisisobutyronitrile (i.e. ex truded low-density polyethylene); or
6. tiny beads of resin or glass (e.g. hollow microballoons) are incorporated in a plastic mix such as "syntactic foam' [2,3].
The scope of applications of cellular materials includes insulating foam, cushioning foam and structural foam. Insulating foam is a low-density material used for heat insulation of buildings and cold storage areas. Cushioning foam is soft and resilient and finds uses in carpet underlay, weatherstripping, seat cushions, upholstery and packaging. Structural foams are stronger and stiffer
Reaction chemistry 23
than the other types and are therefore capable of supporting stress. This type has a dense, hard skin encasing a lighter foamed core. Either type of foam may be possible in some plastics, for example polyurethane [2-4]. The family of urethane foams is one of the most versatile members of the cellular plastics group. One reason for this continued growth is the versatility of the polyurethane chemistry. Depending on the starting ingredients, it is possible to produce a range of products from extremely soft flexible foams through tough rigid foams and integral-skinned foams to molded articles, films or fibres [1,3,5-7]. This chapter focuses on the formation of flexible urethane foams. There are three important processes which determine the final properties of these cellular polymers:
1. Bubble nucleation and growth, which determines the number and size of the foam cells;
2. microphase separation of hard and soft segments, as discussed in Chapter 4, which leads to open cell structure and the control of mechanical and thermal properties; and
3. polymerization of liquid monomers to produce a covalently bonded polymer network.
A delicate balance must develop among these three processes in order to produce a quality foam. Future development of flexible polyurethane foams will depend on expanding our understanding of the chemistry and physics of the foam processing. However, relatively fast rates of reaction, large exotherms, high rates ofchange ofvolume and viscosity and the heterogeneity of the reacting foam complicate the study of the foam formation process. In this chapter, we consider the formation of flexible urethane foams, as the foaming process is presented in terms of the competition between micro phase separation and covalent network formation.
2.2 REACTION CHEMISTRY
The foaming process is an example of the chemistry of the isocyanate group. In the first reaction, water and a diisocyanate compound interact to release carbon dioxide gas (as the 'blowing agent') and form isocyanate-terminated ureas:
20CN-R-NCO + H 20 ---+OCN-R-NH-CO-NH-R-NCO + CO2 j. (2.1)
While (2.1) indicates the principal products of the isocyanate-water reaction, the actual mechanism may be more complicated (Fig. 2.1). Sequence I is considered the most likely reaction path during foaming [1,8-11]. In the second reaction, a hydroxyl-terminated polyether and the same diisocyanate react to produce a crosslinked polyurethane network ('gelling
24 Polyurethane flexible foam formation
~ p P"7 [R.N-e-O<:.N.R~
\I Q -~ R-N~ I;IQ~ R·NCO +1Ip- R·N-e-oH I' :r..:...:: j:N:.R
[R-Nd-OJ [R-
reaction'):
(2.4)
(2.5)
Formation of allophanates (2.3) or biurets (2.4), although possible, is not significant under typical foaming conditions [6,9,12].
R /
R /
CO-NH-R'
Isocyanurate formation is another important reaction of isocyanates used in the production of rigid foams (2.5). The addition process is catalysed by strong bases such as alkali acetates or formates [5,13].
R I
.( \ / ""RC /I o
2.2.1 Chemical system
The basic ingredients of a flexible foam formulation are polyol, diisocyanate, water, catalysts and surfactant. The structure, molecular weight, composition and functionality of the isocyanate or polyol play significant roles in determin ing the final properties of the polymer. In general, aromatic diisocyanates are used to produce urethane foams. Polyols with low equivalent weights (70-800) and high functionality (3-8) are used in rigid foams, and polyols with equivalent weights in the range of 500 to 3000 and low functionality (2.5-3.0) are used in flexible foams. Other ingredients such as flame retardant additives, pigments, fillers and mold release agents are added for specific applications [1,5,14-16]. The main ingredients of a typical flexible foam formulation (Table 2.1), and their roles in the process of foam formation are discussed in the following sections. All components are commercial products used in conventional
Table 2.1 Chemical system
Description
A 3100MW polyether polyol (nominal functionality in = 3; 87% propylene oxide, 13% ethylene oxide
A 3000MW polyether polyol (nominal functionality in = 3; 100% propylene oxide, all secondary hydroxyls)
Deionized water (Corning ACS Mega-Pure system)
An 80:20 mixture of the 2,4- and 2,6-isomers oftoluene diisocyanate (TDI)
Silicone surfactant
Amine catalyst, 70% bis (2-dimethylaminoethyl) ether solution in dipropylene glycol
Producer
Union Carbide Corporation
Table 2.2 Foaming systems l
Formulation V3I37 H2O TD! T-9 D33LV A-I Batch V (g) (g) (g) (g) (g) (kg) (l/kg)
STD2.0902 100.0 2.0 25.0 0.2 0.3 1.54 19.7 STD2.11O 100.0 2.0 30.6 0.2 0.3 1.61 20.3 STD2.130 100.0 2.0 36.2 0.2 0.3 1.67 22.4 STD3.11O 100.0 3.0 41.2 0.2 0.3 1.31 27.0 STD4.090 100.0 4.2 44.2 0.2 0.3 0.90 30.5 STD4.110 100.0 4.2 54.0 0.2 0.3 0.96 33.0 STD4.130 100.0 4.2 63.8 0.2 0.3 1.02 36.7 STD4a.ll0 100.0 4.0 51.8 0.2 0.3 STD5.110 100.0 5.0 62.5 0.2 0.3 1.00 39.5 STD6.090 100.0 6.0 59.8 0.2 0.3 1.00 40.3 STD6.11O 100.0 6.0 73.1 0.2 0.3 1.08 41.6 STD6.130 100.0 6.0 86.4 0.2 0.3 1.16 MOD2.01 3 100.0 2.0 30.6 0.2 0.28 1.16 20.3 MOD2.02 100.0 2.0 30.6 0.1 0.1 1.16 15.5 MOD4.01 100.0 4.2 54.0 0.2 0.2g 0.96 31.9 MOD4.02 100.0 4.2 54.0 0.4 0.96 38.1 MOD4.03 100.0 4.2 54.0 0.1 0.1 0.96 28.0 MOD4.04 4.2 54.0 0.2 0.3 0.96 33.0 MOD6.01 100.0 6.0 73.1 0.2 0.2 0.96 40.3 MOD6.02 100.0 6.0 73.1 0.4 0.96 49.6
11.0pphp of surfactant (L6202) was added to all formulations. 2 Last three digits indicate isocyanate index for the standard polyol-water package. 3Modifications to the polyol or catalyst package at a constant 110 TDI index are indicated.
slabstock foaming. Table 2.2 summarizes the foaming systems discussed in this chapter.
(a) Polyols
Flexible foams are made primarily from hydroxy-terminated triols with molecular weights ranging from 3000 to 4000. Polyethers are prepared by addition of alkylene oxides, usually propylene oxide, onto trifunctional initiators such as glycerine or trimethylolpropane. Polyether diols, made using glycol initiators, are also combined with triols in making high-elonga tion foams and elastomers.
(b) Isocyanates
Polyurethane foams are prepared mainly with toluene diisocyanate (TOI), diphenylmethane diisocyanate (MOl) and their derivatives. An 80:20 mixture of 2,4-TOI and 2,6-TOI is the most important commercial product, although
a 65:35 mixture is also used in large-scale production of flexible foams. The 65:35 blend yields a foam which can bear higher loads and is sometimes used as an admixture to the 80:20 isomer mix. The functionality of TDI can be increased by allophanate branching (2.3) or by the addition of trimer (2.5) for subsequent use in the production of both slabstock and molded high resilience foams. Special MDI prepolymers and mixtures of TDI and MDI are also be coming competitive in some areas such as self-skinning foams, high-quality cushioning foams, and high resilience foams [17]. MDI is the preferred isocyanate for use in rigid and semi-rigid foams, in addition to microcellular elastomers produced by reaction injection molding [5-7]. The isocyanate index or amount of NCO groups required in a formulation
is given by:
NCO = fNCO*(fwatmwat/Mwat + fpmp/Mp)*r/MNCO, (2.6)
where: fp and fwat are the functionalities of water and polyol; mp and mwat are the masses of water and polyol used in the formulation; MNCO' M p and Mwat are the molecular weights of the isocyanate containing compound (174.2 g/mole for TDI), polyol (3100 g/mole) and water (18 g/mole); and r is the stoichiometric imbalance. Thus, for a 2pphp water foam at 110 TDI index (STD2.110), the amount of TDI needed is as indicated in Table 2.2:
( c) Blowing agents
Blowing of flexible urethane foams is carried out primarily by the isocyanate water reaction (2.1), even though chlorofluorocarbons may be used. Increasing the water content while keeping constant the isocyanate index (2.6) increases the amount of carbon dioxide given off and the ratio of urea to urethane in the finished foam. In the range of commercial applications (2 to 6 parts of water per hundred parts of polyol, pphp), the lowered density and increased urea hard segment content compensate for each other [18, 19]. Above 6pphp of water, foam properties decline due to the high exotherm generated and extremely low density [6]. Growing concerns about the impact of chloro fluorocarbons on the environment are leading to their elimination from reactive urethane foaming [20-22].
(d) Catalysts
A foam system usually contains a tertiary amine and an organometallic tin compound to adjust the foaming chemistry to desirable processing conditions. Tertiary amines accelerate both the isocyanate-water and isocyanate-hydroxyl reactions. Meanwhile, organometallic tin compounds such as dibutyltin
dioctoate, dibutyltin dilaurate, stannous oleate and stannous octoate are powerful catalysts for the isocyanate-hydroxyl reaction. The synergistic character of tin and tertiary amine catalysis was particularly helpful in the development of the one-shot process [1,5,23].
(e) Surfactant
During foaming, surfactants help to mix incompatible components of the reaction mixture and to stabilize bubble expansion according to the Plateau Gibbs-Marangoni effect [24-29]. Polydimethylsiloxane (PDMS) polyether graft copolymer surfactants are the most widely used in industry. Surfactants are designed for specific applications by changing the length of the PDMS backbone, the number and length of the pendent polyether chains and the ratio of ethylene oxide (EO) to propylene oxide (PO) within these pendent chains. In general, the ratio of siloxane to ether controls the activity of the surfactant, and the ratio of EO to PO controls the solubility of the surfactant in the foam mix [30-31].
2.2.2 The foaming process
The formation of flexible polyurethane foam is relatively fast (2-4 min), highly exothermic (75-160 °C total temperature rise) and involves a large increase in volume (20-50 x). Consequently, the foaming mixture undergoes changes in macroscopic morphology including bubble nucleation and growth, bubble packing, cell opening and curing. These changes are illustrated in Fig. 2.2. However, the reaction chemistry has important implications for the develop ment of macroscopic morphology. If the foam has not gelled by the time of cell rupture, it will collapse. If the foam is tightly crosslinked (i.e. it has gelled too much), it will shrink. Thus, information on reaction speed is essential for evaluating different polymerizations and comparing catalysts, improving blowing efficiencies, and especially for relating the buildup of structure during processing. Therefore, reaction kinetic data combined with an understanding of the structural changes due to crosslinking and phase separation are necessary to optimize the formation of flexible urethane foams.
( a) Foam exotherm
Figure 2.3 presents a comparison between predicted and measured total temperature rise (.1Trxn ) values as the water and/or TDI content is increased in the formulation. Calculation of the .1 Trxn is based on complete conversion of the limiting reagent and heats of reaction obtained from fitting adiabatic temperature rise data (125.5 kJ/mole of urea formed for the isocyanate-water reaction and 93.9 kJ/mole of urethane formed for the alcohol-isocyanate reaction). For the 90 TDI index systems it is further assumed that residual
Time - 60s Bubble packing during foaming Onset of phase segregation G' - 100 Pa (bubble network)
-'::.'.
:"-'.:.-.'"
Time=O To,Vo G' - O.(lO] Pa Mi;ting
./; :,. / ...:~ . .~. r ":.:.': . '::'/. :.:
Fig. 2.2 Macroscopic view of morphology development during processing of flexible polyurethane foam.
water evaporates, consuming 560 caljg at an average temperature of 70°C [32]. Typical values of LiHrxn for (2.1) and (2.2) are presented in Table 2.3. Differences are the result of multiple experimental conditions (i.e. bulk v. solution polymerization), chemical systems and assumptions (i.e. heat capacity values) made during data analysis [7]. Perfect agreement between model and experimental data is indicated by
a line drawn at 45°. Calculated Li Trxn values are within ± 6°C of the experi mental LiTrxn • The predicted LiTrxn for formulation STD6.110 was 10°C lower than the value obtained experimentally. This is probably due to the forma tion of secondary products. Formulation STD6.110 reached a maximum temperature of 181.4°C, where formation of secondary products and/or opening of the urethane bond may be thermally induced [1,37]. Whereas trimer formation is unlikely in the absence of a suitable catalyst [13], biuret
170
160
" 150
e 110 <> '1: G)
100Po. ~ A STD.130~ 90
• STD.ll0 80 o STD.090
80 90 100 110 120 130 140 150 160 170
Calculated ~T rxu
Fig. 2.3 Comparison of calculated v. observed ATrxn v. water level (2-6pphp) and isocyanate content (<) - 90 index, • - 110 index and /::, - 130 index) in the formulation (Table 2.2). Formation of 0.0763 mole of biuret (41.4 kJ/mole [35]) improves the prediction of A7;xn for formulation STD6.110 (.). Agreement between calculated and experimental values is illustrated by a line drawn at 45°. Predictions are within ±6°C of the experimental data.
Table 2.3 Heats of reaction [6,7,13,32-35]
Reaction Heat of reaction (kllmo/e)
Source
A. Urethane formation -NCO +HO-----+-O-CO-NH
83.6, 103, 105 100.5 94.5 82.4-92.5 (range) 88.9 83.7 92.7 94.6 93.9
B. Urea formation -NCO +H2N-----+-NH-CO-NH
91.3-112
C. B/owing reaction 2-NCO +H20 ----+C02 + -NHCONH
188.4 104.7-146.6 (range) 146.6 133.3 (amorphous) 125.5
Macosko [7] Woods [6] Vespoli and Alberino [13] Steinle et al. [33] Aleksandrova et al. [34] Hager [35] Literature average value Standard heat of reaction Artavia [32]
Pannone and Macosko [36]
Woods [6] Hager [35] Literature average value Average standard heat of reaction Artavia [32]
(2.8)
and allophanate formation are possible if more than 20% excess of TOI is used in the formulation [38-42]. Even though the experimental L1Trxn for formulation ST06.130 is in good agreement with model predictions, the foam was found collapsed at the end of the experiment. Monomer conversion can be related to the temperature rise profile through
adiabatic reactor analysis [7,36,43]. Once heat loss has been compensated for, fractional conversion is estimated by comparing the temperature rise at time t and the total temperature rise for the reaction:
rL1T r(T - To) (1(=--= ,
L1Trxn Tad - To
where (I( indicates conversion, r~ 1 is the ratio of functional group concen tration and Tad is the maximum temperature attained in the adiabatic experiment. Conversion profiles determined for formulations differing only in the amount of water are presented in Fig. 2.4. Modifications to the water and/or isocyanate level of the formulation do not change significantly the shape of the foam exotherm (Fig. 2.5). Thus, two regions could be identified in Fig. 2.4: (i) 0 < t. < 60s and (ii) 60 ~ til < 150s. In region I, the rate of reaction consistently increases as the amount of water or TOI is increased in the formulation, suggesting that urea and urethane formation predominate in this region. Meanwhile, region II is highlighted by a sudden acceleration in the rate of reaction as reported in the literature [9,44-47]. An apparent correlation exists between the magnitude of the rise in dT/dt and the amount of water or TOI in the formulation. It is tempting to explain the rise in the
1.0
0.9
a 0.8 ~
Eo-< 0.7 <I f:; 0.6 <I II 0.5 = .~ 0.4 -0- STD2.110 > 0.3 -0- STD3.110 =0 --0-- STD4.110
U 0.2 ~STD5.110
0.1 --a-- STD6.110
0.0 0 30 60 90 120 150 180 210 240
Time (s)
Fig. 2.4 Conversion is calculated using (2.8). A sudden acceleration in the rate of reaction (dlX/dt) is observed as the water level is increased in the formulation. Profiles correspond to formulations listed in Table 2.2.
1.0
0.9
0.1 -¢-- CODv6.090
0.0 0 20 40 60 80 100 120 140 160 180 200
Time (s)
.~ 0.4 (B) STD4.NCO ~
~ 0.3 ---tl-- CODv42.130
8 0.2 ........ CoDv42.110
0.1 -¢-- CODv42.090
0.0 0 30 60 90 120 150 180 210 240 270 300
Time (s)
.~ 0.5
0 0.2 ........ CoDv2.1I0U 0.1 -¢-- CODv2.090
0.0 0 40 80 120 160 200 240 280 320 360 400
Time (8)
Fig. 2.5 Unbalanced stoichiometry. Data correspond to formulations (a) STD6.11O, (b) STD4.11O, (c) STD2.110 (Table 2.2). As the level of water and/or isocyanate is increased in the formulation a sudden rise in dlX/dt is more easily appreciated (at about 60% conversion).
Morphology development 33
rate of reaction as due to the decomposition of a carbamic acid anhydride as shown in Fig. 2.1 [1,8,10,48,49]. However, significant levels of carbamic acid or its anhydride have not been identified during foaming, even though those intermediates would be expected to show a characteristic infrared absorption at about 1760-1800cm- 1 [50]. A more suitable explanation for the sudden rise in the rate of reaction is offered here. The proposed mechanism postulates the segregation of regions with a high concentration of urea and unreacted species (water and TOI), therefore increasing the rate of the isocyanate-water reaction and the overall rate of reaction during foaming.
2.3 MORPHOLOGY DEVELOPMENT
The mechanical properties of a cured foam depend both on the macroscopic cell structure of the foam and the morphology of the material within the cell struts [51]. Furthermore, hydrogen bonding interactions playa critical role in the final properties ofthe polymer. Ureas produced during the isocyanate water reaction (2.1) begin to segregate out of the soft segment phase, changing the morphology of the polymer so that it resembles that found in segmented urethane block copolymers.
2.3.1 Dynamics of phase separation
Phase separation in foams is partially restricted when triols or higher functional polyols or isocyanates are used or when biurets or allophanates are formed. In these cases, hard segment packing is disrupted, and the ratio of urea to urethane functional groups and the thermal history of the foaming reaction are changed. The use of a mixture of TDI isomers is also believed to eliminate hard segment crystallization, as this can occur in many segmented elastomers that may utilize symmetric diisocyanate moieties. Phase separation is further complicated by the fact that hard block chain extension and urethane polymerization occur simultaneously [24,51,52]. Infrared spectroscopy has been used to identify the sequence of chemical reactions involved during the manufacture of conventional slabstock foam. These studies bring out the possibility of microphase separation (hydrogen bonded urea) well before (urethane) polymerization is complete and is there fore important for an understanding of the morphology of these systems. Previous investigations found a growing urea carbonyl absorption at 1715 cm - 1
early in the reaction. At about half of the volume rise profile, this peak shifted to 1640cm -1 and continued to grow [24,53,54]. Model studies using diphenyl urea indicated that the carbonyl absorption was noted at 1715 cm -1 in solution, and at 1640 cm - 1 when segregated in a separate phase (Table 2.4). This suggests that during foaming a condition is reached at which the synthesized urea is no longer soluble in the foam mix and it precipitates out. If most of the hydrogen bonding occurs within the hard segment domains
Table 2.4 Band assignments for infrared studies of polyurethane foams
Frequency Assignment Reference (cm- 1)
1730 Free urethane [37,55,56]
1715-1710 Soluble urea [52,54-59]
1700-1650 Loosely associated urea [59]
1661 Intermediate urea [9,57]
1640 Urea hard segments [23,58,61] Bidentate H-bonded urea [59] '3D H-bonded urea' [62,63]
1631 (D)-urea hard segments [58]
Hp H H--__-+. - N-C-~ ----+
ocAJ CH3
(2270 em-I)
o II
o II
-r-e-()MM. H
Fig. 2.6 Band assignments for infrared studies of flexible polyurethane foams. The development of hydrogen bonding interactions is used to monitor the dynamics of urea phase separation during the processing of foam. Bonart et al. [62] and Sung et al. [63] suggested the development of three-dimensional hydrogen bonding as a result of urea microphase separation. This is illustrated by the bidentate hydrogen bonded urea structure at 1640cm -I.
and both the urea NH and C=O groups are almost completely hydrogen bonded, each urea C=O has to bond with two urea NH groups (Fig. 2.6). Thus the development of a three-dimensional hydrogen-bonded structure is supported [62,63]. This type of structure would explain the fact that systems with urea hard segments tend to have much better mechanical properties than conventional urethane systems [51,64-66].
1.8
Q) 1.4g '" 1.2-e 0
'" 0 0 13 163Ocm- 1 0 0 ~ 0.4 (.
0 0 0
Time (min) (a)
1.8 Adiabatic foaming
1.6 Q) Hard segmentD-urea • to) 1.4 163Ocm· 1c: 13 •.... 1.2 ~0
'" •.rJ
':J 1697 em ~ 0 0 0
~ 0
Time (min) (b)
Fig. 2.7 Water was replaced with 4.6 pphp D20 (Aldrich Chemical Co.) in formulation STD4.110 (Table 2.2). (a) Isothermal foaming: soluble D-urea increases steadily, asso ciation of D-ureas is not significant within 3min of reaction. (b) Adiabatic foaming: onset of associated 'hard' D-ureas is noted at about 90 s into the reaction.
It becomes clear that during foam formation, urea precipitation leads to the development of a phase-separated morphology. The importance of reproducing the thermal history during characterization is illustrated in Fig. 2.7, where infrared data were collected under isothermal and adiabatic foaming conditions [52]. Figure 2.7(a) describes the evolution of deuterated (0-) ureas at 25°C. Figure 2.7(b) shows the corresponding traces for the adiabatic experiments, where the concentration of soluble O-urea (1697 cm- 1
in Table 2.4) increases steadily until a plateau is reached at 90 ± 15 s after addition of TOI. The concentration of soluble urea remains constant, but the concentration of O-urea hard segments (1630cm- 1) rises sharply. This is taken as the onset of hard segment formation [57,58]. Figure 2.8 illustrates the evolution of the urea and urethane carbonyl absorptions during foaming. The onset of urea hard segment formation for the ST02.11O system occurs at 150± 15 s, once the concentration of soluble urea had reached a steady value [52,59]. As it was shown in Fig. 2.7, temperature plays a critical role during hard segment formation. Since changes in the catalyst package will significantly alter the rate of temperature rise, the dynamics of urea microphase separation must also be related to such modifications. Figure 2.9 illustrates the evolution
Spectral data for STD2.l10
WAVENUMBER (cm-')
Fig. 2.8 Typical spectral data during foaming at 2.0 pphp water (STD2.110, Table 2.2).
2 3 Time (s)
~.c 0.8
& 0.2
Fig. 2.9 Evolution ofurea microphase separation in formulation STD4.1lO (Table 2.2) as a function of catalyst level in the system: (a) 0.1 g T-9 and 0.1 g Dabco 33LV (Table 2.1); (b) 0.1 g T-9 and 0.3 g Dabco 33LV; and (c) 0.2 g T-9 and 0.3 g Dabco 33LV.
of hydrogen-bonded urea for the STD4.110 system at three catalyst levels. As the catalyst concentrations increase in the formulation from Fig. 2.9(a) (lowest level) to Fig. 2.9(c) (highest level), the critical time to reach an 'optimized foam morphology' decreased from 150 ±15 s to 90 ±15 s [52,59]. Further more, the data shows that the onset of urea hard segment formation occurs early in the process (at about 50-60% conversion of isocyanate groups), well before a crosslinked polymer network develops in the foaming mixture. For the 2.0 pphp water-based foam, urea formation (2.1) occurs at a slightly faster rate than the urethane formation reaction (2.2). As the amount of water is increased in the formulation, the rate of the isocyanate-water reaction becomes significantly faster, thus generating a microphase-separated morphology at a lower isocyanate conversion [52,53,59,66].
2.3.2 Modulus buildup
The evolution of rheological properties during foaming is divided into four independent regions, as shown in Fig. 2.10 [66].
tt1 g. ~ <: o C ~
0 10
10
0
Fig. 2.10 Four regions of rheological development during reactive urethane foaming. Bubbles nucleate and grow into a space filling network which acts like a low-modulus solid (1). Continued bubble growth is just balanced by the density decrease (2.10) to give a plateau (2). Finally, enough urea is formed to phase separate, leading to a rapid rise in polymer modulus (3) and cell opening. After about 6 minutes the reaction is complete and the final modulus is reached (4). Measurements were made for STD2.110 (Table 2.2) at 5% strain and 6.28radjs. G" value at t=Omin, is that for the unreacted polyol. Independent volume measurements on the same formulation [32,53] indicate that the foaming mixture reaches rf>b;3 0.85 within 50 s of reaction (- - - -).
39Morphology development
(a) Region 1: bubble nucleation
Since self-nucleation does not occur during urethane foaming [1,16,26,28], bubble nucleation results from dissolved gases in the monomers and dispersion of air or other gases into the system by mechanical mixers or frothing devices. During this stage, dissolved air nucleates bubbles and subsequent generation of carbon dioxide by the isocyanate-water reaction (2.1) causes the bubbles to grow into a space-filling network (as observed by Kanner and Decker [26]). This region is estimated to be no more than 30 s long for the STD2.110 foam. The modulus of the reactive foam changes dramatically during this first stage (the loss modulus rises over two decades). At the end of this zone, the storage modulus has a higher value than the loss modulus, indicating 'solid-like' behaviour. The apparent gel time (i.e. G' '" G") is estimated at about 20 s for the STD2.11O foam [66,68].
(b) Region 2: liquid foam
Towards the end of region 1, the reacting mixture shows solid-like behavior (G' > G") characteristic of liquid foams [69-71]. It is still a relatively low modulus gel that keeps expanding as a result of continued CO2 generation. The gel is formed by the interaction of the closely packed bubbles. The material in the cell walls is still of relatively low molecular weight and low viscosity. Conversion of isocyanate is about 60% at the end of this region [52,53]. The weight average molecular weight of formulation STD2.11O is not expected to become infinite due to network formation until at least 84% conversion of the available isocyanate (Table 2.5). The model developed by Princen and Kiss [72] for highly concentrated
emulsions may explain the fact that the foam modulus remained fairly constant during this period:
(2.9)
Table 2.5 Gel conversions during foaming at 110 TDI Index
Formulation ex 1 (Xexp 12time(s) Ctexp2 3time(s) rw iii•.HSI N•.HS2c
STD2.110 0.84 0.70 ± 0.05 121 0.82 ± 0.10178 0.63 2.7 1.5 STD3.11O 0.86 0.58 ± 0.0587 0.66 ± 0.10100 0.70 1.9 1.4 STD4.11O 0.88 0.53 ± 0.0570 0.57 ± 0.1076 0.75 1.6 1.3 STD5.11O 0.89 0.46 ± 0.0569 0.54 ± 0.1077 0.77 1.4 1.2 STD6.11O 0.90 0.41 ± 0.0564 0.50 ± 0.1073 0.79 1.3 1.2
1Calculated with (2.11) assuming a homogeneous well-mixed system, and no secondary reactions. Formulations are listed in Table 2.2. 2From Fig. 2.12 using a two tangents technique described by Yang and Macosko [37]. 3Determined from Fig. 2.12 after bubble bursting (BB).
where G is the elastic shear modulus of the foam or emulsion, r is the inter facial tension, R 32 is a surface-volume mean drop radius and <Pb is the volume fraction of the dispersed phase (<Pb > 0.75). Since r is not significantly affected by moderate increases in temperature or molecular weight of the resin [73], and R 32 ::::::: <Pb1/3 for the volume changes observed during foaming (2.9) reduces to:
(2.10)
Equation (2.10) indicates that the foam modulus becomes relatively insensitive to any further increments in the gas content of the foam for <Pb ~ 0.85. Independent volume measurements (Fig. 2.10) indicate that the foaming mixture reaches <Pb ~ 0.85 within 50 s of reaction.
( c) Region 3: phase separation
At about 60% conversion of isocyanate (150 s under adiabatic conditions), infrared measurements on fonnulation STD2.110 indicate significant hydrogen bonding interactions between urea groups [52,59]. This signals phase separa tion of hard segment domains, which strongly increases polymer modulus [37,51,74]. Phase separation is also observed in the rheological data. At
lif STD2.110
Ai I:.
.~ I~ ~~¢<i' • ¢
.... b 10°
10" 0 1.6 3.2 4.8 6.4 8 9.6 11.2 12.8 14.4 16
Time [min.]
Fig.2.11 Modulus buildup as a function of water level: STD2.110 (open symbols) and STD4.110 (closed symbols) as described in Table 2.2. As the amount of water is increased, the foaming process is accelerated (section 2.2). Thus, the time for the onset of phase separation (region 3, Fig. 2.10) decreases.
2.5 min, G' rises 2.5 decades and G" rises 1.5 decades. Whereas the rapid modulus rise in region 1 is due to formation of a bubble network, here it is due to stiffening of the polymer. During the phase separation (polymer stiffening) process, the chemical
reactions (2.1) and (2.2) continue and carbon dioxide pressure builds up locally. At about 40-70% conversion of NCO groups, the combination of urea microphase separation and pressure buildup bursts the cell walls and volume change stops.
(d) Region 4: foamed elastomer
After cell opening, the foaming reaction continues but becomes diffusion controlled [1,75]. The foam reaches its maximum temperature and modulus. The modulus ofthe foam is now dominated by the polymer modulus [76,77]. In some cases, G" appears to decrease slightly (Fig. 2.11). This may be due to incorporation of dangling chains into the covalent network, and/or optimiza tion of the hard segment morphology [37].
2.3.3 Phase separation 1'. chemical gelation
Artavia et al. [53] showed that foaming stopped at about 40 to 70% NCO conversion (Table 2.5) as the water level decreases from 6 to 2 pphp (Fig. 2.12). Since the cellular material is not able to flow any longer, this condition is considered the gel point in foams [78]. A simple argument can be used to demonstrate that covalent bonding (i.e. chemical gelation) is not the domi nant factor triggering cell opening. Consider a formulation containing poly ether polyol with a 3000 molecular mass (nominal functionality of 3), water (difunctional) and toluene diisocyanate (TOI) (difunctional). Let us further assume that:
1. equal reactivity of end-functional groups holds; 2. water and polyol react at the same rate with TOI; 3. phase separation does not occur; and 4. there is no allophanate, biuret or trimer formation during the polymeriza tion [13,39,42].
Thus, the minimum conversion of isocyanate groups required to form a network of covalent bonds is given by
(2.11)
where:
fe is the average functionality of water and polyether polyol [79]; ge = 2, the functionality of toluene diisocyanate (TOI); r ~ 1, molar ratio of active hydrogens to isocyanate groups (r = 0.91, unless stated otherwise);
--71L.---=......-- 2 pphp
-,I-:.,....---a-~-~--- 3 pphp
7f:,,-r-------.... 4.2 pphp
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Conversion = !:J.T/!:J.T"a
$
10
Fig. 2.12 Specific volume profiles plotted v. extent of reaction for formulations STD2.11O-STD6.110 (Table 2.2). As the amount of water is increased in the formula tion, foams reach their final volume at lower conversions (Table 2.5).
occ(NCO) is the minimum conversion of TDI required for chemical gelling.
For system STD2.110, (2.11) predicts occ(NCO) = 0.8

low density cellular plastics: physical basis of behaviour

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