Cellular solids
`
`Structure and properties
`
`Second edition
`
`Lorna J. fiibson
`Department of Materials Science and Engineering,
`Massachusetts Institute of Technology,
`Cambridge, MA 02139, USA
`
`Michael F. Ashby
`Cambridge University Engineering Department,
`Cambridge, UK
`
`
`
`.
`-‘
`
`AMBRID GE
`UNIVERSITY PRESS
`
`PAGE 1 OF 7
`
`BOREALIS EXHIBIT 1012
`
`

`
`Cambridge Solid State Science Series
`
`EDITORS
`
`Professor D. R. Clarke
`
`Department of Materials.
`University of California, Santa Barbara
`
`Professor S. Suresh
`
`Department of Materials Science and Engineering.
`Massachusetts Institute of Technology
`
`Professor 1. M. Ward FRS
`
`IRC in Polymer Science and Technology,
`University of Leeds
`
`PAGE 2 OF 7
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`

`
`PUBLISHED av ‘rue PRBSSSYNDICATBOPTHIZ unlvaltsrrv or cutartlooa
`The Pitt Building. Trumpington Street. Cambridge, Ca: in United Kingdom
`
`camatuoa: UNIVIIRSITY mass
`The Edinburgh Building, Cambridge caz zrtu. United Kingdom
`4o Welt aoth Street. New York. NY root [-421 t, USA
`IO Stamford Road. Oalrleigh. Melbourne 3166, Australia
`
`First edition 0; Lorna J. Gibson and Michael F. Ashby, 1988
`Second edition «,3 Lorna J. Gibson and Michael F. Ashby, 1997
`
`This book is in copyright. Subject to statutory exception
`nnd lo the provisions or relevant collective licensing agreements.
`no reproduction ofany part may take place without
`the written permission ofCambridge liniversily Press
`
`Pint published by Pergamon Press Ltd.. I988
`Second edition published by Cambridge University Press. 1997
`
`Printed in the United Kingdom at the University Press. Cambridge
`
`Typoet in [0 '/./l3 Vzpt Times
`
`A catalogue recordfor this book is availablefrom the British Library
`
`Library ofCongress Cataloguing in Publication data
`Gibson, Lorna J.
`Cellular aolids : structure & properties I Lorna J. Gibson.
`Michael F. Ashby. — and ed.
`p.
`cm. — (Cambridge solid state science series)
`includes bibliographical references and index.
`rsaN O-52!-49560-I (he)
`I. Foarned materials.
`ll. Title.
`III. Series.
`‘M41 8.9.F6o53
`1997
`620.1’ 1-dczo
`
`2. Porous materials.
`
`l.Asl1by. M. F.
`
`96-3157:
`CIP
`
`mm 0521 49560 I hardback
`
`PAGE 3 OF 7
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`

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` 4
`
`Introduction
`
`,
`»
`
`'
`
`(1) Honeycombs
`
`Structures like the honeycomb shown in Fig. l.l(a) can be made in at least four
`ways. The most obvious is to press sheet material into a half-hexagonal profile
`and glue the corrugated sheets together. More commonly. glue is laid in parallel
`strips on fiat sheets, and the sheets are stacked so that the glue bonds them
`together along the strips. The stack of sheets is pulled apart (‘expanded’) to give
`a honeycomb. Paper resin honeycombs are made like this; the paper is glued
`and expanded, and then dipped into the resin to protect and stiffen it. Honey-
`combs can also be cast into a mould; the silicone rubber honeycomb shown in
`the figure was made by casting. And, increasingly, honeycombs are made by
`extrusion; the ceramic honeycombs used to support exhaust catalysts in automo-
`biles are made in this way.
`
`(b) Foams
`
`Difierent techniques are used for foaming dilTerent types of solids. Polymers are
`foamed by introducing gas bubbles into the liquid monomer or hot polymer,
`allowing the bubbles to grow and stabilize, and then solidifying the whole thing
`by cross-linking or cooling (Suh and Skoehdopole, I980). The gas is introduced
`either by mechanical stirring or by mixing a blowing agent into the polymer. Phy-
`sical blowing agents are inert gases such as carbon dioxide or nitrogen; they are
`forced into solution in the hot polymer at high pressure and expanded into bub-
`
`Figure L2 Comparison
`between a cellular solid and
`a solid with isolated pores.
`
`
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`PAGE 4 OF 7
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`
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`Making cellular solids
`
`bles by reducing the pressure. Alternatively. low melting point liquids such as
`chlorofluoro—carbons or methylene chloride are mixed into the polymer and
`volatilize on heating to form vapour bubbles. Microcellular foams, with cell
`sires on the order of 10/1. can be made by saturating, under pressure and at
`room temperature, a polymer with an inert gas and then relieving the pressure
`and heating the supersaturated polymer to the glass transition temperature,
`causing cell nucleation and growth to occur. Chemical blowing agents are addi-
`tives which either decompose on heating, or which combine together when
`mixed to release gas; sodicarbonamide is an example. Each process can produce
`open- or closed-cell foams; the final structure depends on the rheology and sur-
`face tension of the fluids in the melt. Closed-cell foams then sometimes undergo
`a further process called reticulation, in which the faces of the cells are ruptured
`to give an open-cell foam. Finally, low-density microcellular polymer foams
`and aerogels with relative densities as low as 0.002 and cell sizes as small as 0. In
`can be made by a variety of phase separation methods: one is to precipitate the
`polymer as a low-density gel in a fluid and then remove the fluid by evaporation
`(1eMay ezaI., 1990).
`Metallic foams can be made using either liquid or solid state processing (Sha-
`povalov, 1994 and Davies and Zhen, 1983). Powdered metal and powdered tita-
`nium hydride or zirconium hydride can be mixed, compacted and then heated to
`the melting point of the metal to evolve hydrogen as a gas and form the foam.
`Mechanical agitation of a mixture of liquid aluminium and silicon carbide parti-
`cles fonns a froth which can be cooled to give aluminium foam. Liquid metals
`can also be infiltrated around granules which are then removed: for instance, car-
`bon beads can be burned oil‘ or salt granules can be leached out. Metals can be
`coated onto an open-cell polymer foam substrate using electroless deposition,
`electrochemical deposition or chemical vapor deposition. Metal foams can also
`be made by a eutectic transformation: the metal is melted in an atmosphere of
`hydrogen and then cooled through the eutectic point, yielding the gas as a sepa-
`rate phase within the metal. Solid state processes usually use powder metallurgy.
`In the powder sintering method, the powdered metal is mixed with a spacing
`agent which decomposes or evaporates during sintering. Alternatively, a slurry
`of metal powder mixed with a foaming agent in an organic vehicle can be
`mechanically agitated to form a foam which is then heated to give the porous
`metal. Metal foams can also be formed by coating an organic sponge with a
`slurry of powdered metal, drying the slurry and firing to remove the organic
`sponge. In one of the most remarkable processes, single crystal silicon can be
`made porous by anodization: a silicon wafer is immersed in a solution of hydro-
`fluoric acid. ethanol and water and subjected to a current for a brief time (Bellct
`and Dolino, 1994). The anodizing process tunnels, giving an interconnected net-
`work of pores with at cell size of IO nm and a relative density as low as 0.1; yet
`the material remains a single crystal.
`
`PAGE 5 OF 7
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`

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`'f'l:,t|il;’i
`
`Thermal, electrical and acoustic properties
`of foams
`
`7.:
`Introduction and synopsis
`Foams have unique thermal, electrical and acoustic properties. Among these are:
`exceptionally low thermal conductivity. making them a primechoice for thermal
`insulation; very low dielectric loss, allowing transmission ofmicrowaves without
`attenuation orscattering; and the ability to absorb sound. suiting them as materi-
`als for noise abatement.
`in this chapter we survey the thermal. electrical and acoustic properties of
`foams. Where possible, the underlying physical understanding of the behaviour
`is emphasized. since it is this which allows a degree of predictive modelling of
`foam properties. Case studies are used to illustrate some ofthe results.
`
`Thermal properties
`7.2
`More foam is used for thermal insulation than for any other purpose. Closed-cell
`foams have the lowest thermal conductivity of any conventional non—vaeuum
`insulation. Several factors combine to limit heat flow in foams: the low volume
`fraction of the solid phase: the small cell size which virtually suppresses convec-
`tion and reduces radiation through repeated absorption anti rcfleetion at the cell
`walls; and the poor conductivity ofthe enclosed gas. This low thermal conductiv-
`ity is exploited. at one extreme ol‘sophistication. in the insulation for liquid oxy-
`gen rocket tanks and. at the other, in disposable cups for hot drinks. The frozen-
`
`283
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`PAGE 6 OF 7
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`

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`284
`
`Thermal, electrical and acoustic properties of foams
`
`food industry relies on it: the double skins ofrefrigcratcd truck and railway cars
`are filled with foam. And vast quantities of liquefied natural gas are transported
`around the world in tankers lined with foam.
`The specific heat per unit volume, too, is low for foams, making them espe-
`cially attractive for structures with a low thermal mass; this is important, for
`instance, in ultra-low-temperature research to minimize the consumption of
`refrigerant.
`The coeflicicnt of thermal expansion ofmost foams is roughly the same as that
`of the solid from which they are made. But their moduli are much smaller, and
`because of this, the thermal stresses generated by a temperature gradient are
`much smaller, too, giving them good thermal-shock resistance. This is exploited
`in ceramic foams used as heat shields and ablative coatings: a ceramic foam is
`much less likely to stiffer thermal spalling than the solid from which it is made.
`Firebrick. which typically has a relative density of 0.3. is a good example of a
`ceramic foam which exploits all of these properties. The melting point is high;
`the low thermal conductivity reduces heat loss by conduction; the low heat capa-
`city minimizes the energy required to get it up to temperature; and the thermal-
`shoek resistance prevents spalling if there are sudden changes in temperature.
`But this is just one example. Whenever good thermal insulation is required, it is
`worth considering the use of foams. We now examine their thermal properties
`in more detail, relating them to relative density and to structure.
`
`(a) Melting or softening point
`The melting or softening point of a foam is the same as that of the solid from
`which it is made; data are given in Chapter 3 ('l‘ables 3.1, 3.4 and 3. 5). Pure metals
`and ceramics have sharp melting points, Tm. Alloys and two-phase mixtures
`melt over a range of temperatures but the onset of melting (the solidus tempera-
`ture) still corresponds to a sharp discontinuity in mechanical properties. Glasses
`and polymers are different: well below the glass temperature, Tg. they progres-
`sively soften and become viscoelastic.
`The way in which mechanical properties vary with temperature is summarized
`in the deformation maps shown in Chapter 3. The reader should refer to these
`for a broad description of the influence of temperature on modulus and strength.
`
`(b) Thermal conductivity
`Foattns tire remnrluihle for their good thermal insulation. There is considerable
`literature on the subject. from which it fairly complete picture emerges ( Dohcrly
`or «L,
`iotiz; (iriflin and Slmclulopolc.
`io(i4; (iorring and Cliurcliill.
`t<)6I:
`(iuentlicr. I962; Patten and Skoclulopole.
`iqbz; Skochtlopolc. mm: T00“)!-
`io6t;Selutct7.nml (iilicksinan. tut-l_t: Rcitvvm/.. 1983; and (ilicksman. I904)-
`
`
`
`PAGE 7 OF 7