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
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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].
4 Physical behaviour of polymeric foams - an overview
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
6 Physical behaviour of polymeric foams - an overview
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
8 Physical behaviour of polymeric foams - an overview
(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
10 Physical behaviour of polymeric foams - an overview
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
12 Physical behaviour of polymeric foams - an overview
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.
14 Physical behaviour of polymeric foams - an overview
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=
16 Physical behaviour of polymeric foams - an overview
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,
18 Physical behaviour of polymeric foams - an overview
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.
20 Physical behaviour of polymeric foams - an overview
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
Reaction chemistry 25
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
26 Polyurethane flexible foam formation
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
Reaction chemistry 27
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
28 Polyurethane flexible foam formation
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
Reaction chemistry 29
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
30 Polyurethane flexible foam formation
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)
Reaction chemistry 31
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.
32 Polyurethane flexible foam formation
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
34 Polyurethane flexible foam formation
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.
Morphology development 35
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.
36 Polyurethane flexible foam formation
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).
Morphology development 37
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.
38 Polyurethane flexible foam formation
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).
40 Polyurethane flexible foam formation
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.
Morphology development 41
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