© Copyright by International OCSCO World Press. All rights reserved. 2011 Point of view 585

VOLUME 49

ISSUE 2

December

2011of Achievements in Materialsand Manufacturing Engineeringof Achievements in Materialsand Manufacturing Engineering

Workings of auxetic nano-materialsY.T. Yao a, M. Uzun a,b,*, I. Patel a,c

a Institute for Material Research and Innovation, The University of Bolton, BL3 5AB, Bolton, UK b Department of Textile Educations, Marmara University, 34722, Goztepe, Istanbul, Turkec British University of Egypt, Cairo, Suez Desert Road, El Sherouk City, 11837, Egypt* Corresponding author: E-mail address: m.uzun@marmara.edu.tr

Received 19.10.2011; published in revised form 01.12.2011

Materials

AbstrAct

Purpose: The human mind is consistently interested in new materials having unique properties. Recently, a relatively new field is being investigated which exhibits a negative Poisson’s ratio (NPR), and consequently are termed auxetic materials. Design/methodology/approach: One of the main reason for interest in auxetic materials is due to the possibility of enhanced mechanical properties such as shear modulus, plane strain fracture toughness and indentation resistance compared to non auxetic material. Findings: Auxetic materials were described concerning their classification, characteristic, properties and potential applications.Research limitations/implications: The paper is an overview the modelling structure and deformation mechanisms of auxetic nano-materials.Originality/value: The paper shows the possibilities of auxetic materials application resulting from their mechanical properties.Keywords: Auxetic; Nano-materials; Negative Poisson’a ratio

Reference to this paper should be given in the following way: Y.T. Yao, M. Uzun, I. Patel, Workings of auxetic nano-materials, Journal of Achievements in Materials and Manufacturing Engineering 49/2 (2011) 585-593.

1. Introduction

Auxetic materials are typically divided into two classes in terms of their scale, which are the common auxetic materials (macro-scale) and nano-scale auxetic materials. This paper, mainly concentrates on study of materials having auxetic behaviour at the molecular level and investigating their deformation mechanisms.

When a material is stretched in one direction, it tends to contract (or, rarely, expand) in the other two directions. Conversely, when a sample of material is compressed in one direction, it tends to expand (or rarely, contract) in the other two

directions. A measure of this dimensional change can be defined by Poisson’s ratio ( ),

y

xyx directionloadingtheinstrain

directionlateraltheinstrain

(1) where x and y are the strains in the x and y directions, respectively.

In fact, for most materials this value is positive (Poisson’s ratios ranging between 0 and 0.5) and reflects a need to conserve

1. Introduction

Point of view586

Journal of Achievements in Materials and Manufacturing Engineering

Y.T. Yao, M. Uzun, I. Patel

Volume 49 Issue 2 December 2011

volume. Negative Poisson’s ratio (NPR) material expands (or contracts) laterally when stretched (or compressed), in contrast to ordinary materials. These new types of materials were named “auxetic” by Evans [1]. “Auxetic” comes from the Greek word auxetos, meaning “that which may be increased”. Consider, as an example, auxetic ultra high molecular weight polyethylene (UHMWPE) proposed and fabricated by Alderson & Evans, 1992 to give a general idea as to what is the difference between auxetic and conventional material and to visualize the deformation mechanism (See Fig. 1) [2].

Fig. 1. Schematic diagram of structural changes observed in microporous UHMWPE undergoing tensile loading in the longitudinal direction: Non-auxetic (A) and auxetic (B) deformation due to fibril hinging in a nodule-fibril microstructure [2]

Fig. 1(a) on the top shows schematically the geometry and deformation of a common material undergoing lateral contraction for loading with a tensile longitudinal stress. Fig. 1(b) on the bottom shows auxetic behaviour in which the undeformed material (left) responds to the tensile longitudinal stress with lateral expansion (right).

2. Auxetic materials properties

Recently, the investigation of auxetic materials has attracted significant attention. One of the reasons for interest in auxetic materials comes from the fact that negative Poisson’s ratio can lead to enhancement in other mechanical properties, including: Shear modulus [3,4], Indentation resistance [5,6], Dynamic properties [7,8], Fracture toughness [9].

Shear modulus

Auxetic materials have higher resistance to shear strain, which can be qualitatively explained by the relationships between shear (or rigidity) modulus G, Young’s modulus E, bulk modulus K (the inverse of the compressibility) and Poisson’s ratio . For isotropic materials the relationships between these constants are:

)3

23(21

GKGK

(2)

)1(2EG

(3)

)21(3EK

(4)

GKKGE

39

(5)

The Poisson's ratio of a stable isotropic material cannot be less than -1.0 or greater than 0.5 due to the requirement that the Young’s modulus, shear modulus and bulk modulus have positive values [10]. However, the Poisson’s ratio can exceed that limits in certain direction for anisotropic materials [11].

For isotropic materials, when Young’s modulus (E) remains unchanged, the values of the shear modulus (G) and the bulk modulus (K) can be altered through the changes in Poisson’s ratio ( ) (Eqs. 3 and 4). E is at least twice the value of G for positive Poisson’s ratio materials. Conversely, E reduces to below 2G when is negative. For example, E=G when =-0.5 and E 0 when -1. In other words, when decreasing to -1, the shear modulus tends to very high values and the Young’s modulus decreases to low values, which makes a solid difficult to shear but easy to deform. K also decreases as -1, which means the material becomes hard to shear but highly compressible. When approaches +0.5, the shear modulus (G) is greatly exceeded by the bulk modulus (K), which makes the material incompressible but easy to shear. Indentation response

For isotropic materials, the indentation resistance (or hardness) (H) is inversely proportional to (1- 2) for a given pressure, defined as:

)1( 2

EH (6)

where the value of relates to the theoretical analysis used. 1stands for uniform pressure distribution [12] and 3/2

is for Hertzian indentation [13].

Eq. 6 shows the indentation resistance tends to infinity with increase in the magnitude of Poisson’s ratio ( ) for a given value of Young’s modulus (E). As already noted, the range of Poisson’s ratios for isotropic materials is -1< <0.5, and so auxetic isotropic material show enhancements in indentation resistance when -1< < -0.5. As approaches -1, the indentation resistance towards infinity. Enhanced indentation resistance of auxetic materials has been demonstrated through investigation of synthetic auxetic materials (i.e. polymeric and metallic foams [5,6]; and microporous polymers [14]). A schematic of indentation response is illustrated in Fig. 2 for both non-auxetic and auxetic materials subjected to compressive impact loading [15].

>0

<0

>0

<0

>0

<0

A

B

Oin thperpedefinthe omatethe iminden

Fig. (b) mlatera

3. app 3.1

Wstrucsynthlevelclasswith mateor Yo

Asynthmicroultra polyp[21,2naturand z Appl

AdemoThercan b

Fthrou

On the non-auxethe direction of imendicular to and ne the lateral ‘floother hand, the rial also contractmpact, leading tntation resistance

2. An object material in the al ‘flow’ of mate

Auxetiplications

Classificati

Within the last thtures have bee

hesised, rangingl. Fig. 3 shows tses of materials

auxetic properterials are known oung’s modulus Auxetic materiahesized, such as oporous polytet

high moleculpropylene (PP), 22], several typrally occurring mzeolites [27].

lications

As stated in thonstrated enhaefore, a range obe envisaged. For example, auugh thermomech

tic material, the mpact and the maway from the d

ow’ of material)vertical impact ts laterally-mateto increased dene [15].

hitting a non-vertical directio

erials in each cas

ic mate

ions and typ

hirty years, a vaen discovered, from the molecthat there are ex(polymers, comties, and that naover several ord[16].

als have been polyurethane an

tra-fluoroethylenlar weight polhighly anisotrop

pes of rocks wimolecular auxeti

he above sectiancements in of potential app

uxetic foam withanical processin

force compressematerial spreadsdirection of the i). For the auxeti

compression merial ‘flows’ into sification, theref

-auxetic (a) anon. The arrowsse

erials p

pes

ariety of auxetic designed, man

cular level up toxamples of each

mposites, metals atural and man-ders of magnitud

discovered, fand polyethylene ne (PTFE) [19]lyethylene (UHpic composites [ith microcracksics, e.g. –cristo

ion, auxetic mother physica

plications of aux

th a re-entrant mng was establish

es the material s in directions mpact (arrows ic material, on

means that the the vicinity of

fore, enhanced

nd an auxetic s indicate the

potential

materials and nufactured or o macroscopic h of the major and ceramics) -made auxetic de of stiffness,

abricated and foams [17,18],

] microporous HMWPE) and

20], laminates [23,24], and obalite [25,26],

materials have al properties. xetic materials

microstructure hed to provide

dispersion ohave potent

Fig. 3. Strumaterials fr

Auxetic

fasteners anof the auxethe auxeticfastener is more tightlyprocessing cushions asfoams. Wanbeneficial iand in redu[32]. AuxetUS6412593features in air leaks) an

Aldersoapplication structures wnano-scale particulate variation pdeformation

Huang resistance could be ecase, they hfor the erelatively lmakes themAvellanadsthe design piezocompopassive poland hydroporder of mamatrix assu

1.E-10

Moau- - c

of acoustic wavetial applications

uctured feature rom the macrosc

c cellular solidsnd rivets due toetic fastener is fc material unde

resisted since y in the hole unof auxetic foams another impong and Lakes 20in the preventionuction of pressurtic foam could a3 2002) for ea

forming syncland sound absorpon et al. 2000 re

in filters from with re-entrant (e.g. zeolites), wsize selectivity

properties of n [16].

& Blackburn of ceramics wnhanced by havhave applicationmissions from low bulk modum more sensit, 1998 pointed o

of hydrophonosites consistinglymer matrix anphone receivers agnitude enhanc

umed auxetic pro

1.E-09 1.E-08 1.E-07 1.E-06

s

Sintered c- bismuth-cuprate superc

Molecular uxetics: -cristobalite

cubic metals

es and cut-off frein the absorptio

size and Youngcopic down to th

(i.e. auxetic fothe negative Po

facilitated by thr compression, the fastener ex

nder tension [30]m [31] opens up t

rtant potential a002 reported auxn of pressure sorre-induced discoalso be used in earphone shells astic doubly curption property [3eported auxetic m

the macro-scalhoneycomb and

which could impy capabilities du

auxetic materi

2001 proposeith cellular or ving negative Pns as substrates

internal combulus associated ive to hydrostaout auxetic compnes and other sg of piezoelectricnd used in medof naval sonar

cement in sensitioperties [35,36,3

1.E-05 1.E-04 1.E-03 1.E-02

structural sub-unit size (m)

ceramics:conductors

Composites:- fibre-reinforced

composites- sandwich panel

composites

Honeycombs- polymer/metal

Foams:- polymer/metal

Natural biomaterials:- skin/bone

Microporous polymers:- PTFE

-UHMWPE-PP

equencies, whichn of sound [18,2

g’s modulus of Ae molecular leve

oams) could be oisson’s ratio. Ine lateral contracwhile removal

xpands and lock]. The scaling upthe developmentapplication for xetic cushions cres or ulcers in tomfort in seatedear cushions (USdue to their ex

rved surfaces (re3,34].

materials have ple (e.g. auxetic d auxetic foam)prove filter cleanue to the uniquials wide mec

ed the thermal honeycomb str

Poisson’s ratios.in catalytic con

bustion enginewith auxetic matic pressure, aposites could be sensors. For exc ceramic rods w

dical ultrasonic iwere shown to ivity when the p7].

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+032 1.E-01 1.E+00 1.E+01

Youn

g's

mod

ulus

(GPa

)

Keyed-brick structures:- nuclear

reactor cores

h might 29].

Auxetic el [28]

used as nsertion ction of

of the ks itself p of the t of seat auxetic ould be the sick

d people S Patent xcellent educing

potential cellular

) to the ning and ue pore chanical

shock ructures

In this nverters es. The materials and so, used in

xample, within a imagers lead to

polymer

Youn

gs

mod

ulus

(GPa

)

2. Auxetic materials properties

587

Materials

Workings of auxetic nano-materials

volume. Negative Poisson’s ratio (NPR) material expands (or contracts) laterally when stretched (or compressed), in contrast to ordinary materials. These new types of materials were named “auxetic” by Evans [1]. “Auxetic” comes from the Greek word auxetos, meaning “that which may be increased”. Consider, as an example, auxetic ultra high molecular weight polyethylene (UHMWPE) proposed and fabricated by Alderson & Evans, 1992 to give a general idea as to what is the difference between auxetic and conventional material and to visualize the deformation mechanism (See Fig. 1) [2].

Fig. 1. Schematic diagram of structural changes observed in microporous UHMWPE undergoing tensile loading in the longitudinal direction: Non-auxetic (A) and auxetic (B) deformation due to fibril hinging in a nodule-fibril microstructure [2]

Fig. 1(a) on the top shows schematically the geometry and deformation of a common material undergoing lateral contraction for loading with a tensile longitudinal stress. Fig. 1(b) on the bottom shows auxetic behaviour in which the undeformed material (left) responds to the tensile longitudinal stress with lateral expansion (right).

2. Auxetic materials properties

Recently, the investigation of auxetic materials has attracted significant attention. One of the reasons for interest in auxetic materials comes from the fact that negative Poisson’s ratio can lead to enhancement in other mechanical properties, including: Shear modulus [3,4], Indentation resistance [5,6], Dynamic properties [7,8], Fracture toughness [9].

Shear modulus

Auxetic materials have higher resistance to shear strain, which can be qualitatively explained by the relationships between shear (or rigidity) modulus G, Young’s modulus E, bulk modulus K (the inverse of the compressibility) and Poisson’s ratio . For isotropic materials the relationships between these constants are:

)3

23(21

GKGK

(2)

)1(2EG

(3)

)21(3EK

(4)

GKKGE

39

(5)

The Poisson's ratio of a stable isotropic material cannot be less than -1.0 or greater than 0.5 due to the requirement that the Young’s modulus, shear modulus and bulk modulus have positive values [10]. However, the Poisson’s ratio can exceed that limits in certain direction for anisotropic materials [11].

For isotropic materials, when Young’s modulus (E) remains unchanged, the values of the shear modulus (G) and the bulk modulus (K) can be altered through the changes in Poisson’s ratio ( ) (Eqs. 3 and 4). E is at least twice the value of G for positive Poisson’s ratio materials. Conversely, E reduces to below 2G when is negative. For example, E=G when =-0.5 and E 0 when -1. In other words, when decreasing to -1, the shear modulus tends to very high values and the Young’s modulus decreases to low values, which makes a solid difficult to shear but easy to deform. K also decreases as -1, which means the material becomes hard to shear but highly compressible. When approaches +0.5, the shear modulus (G) is greatly exceeded by the bulk modulus (K), which makes the material incompressible but easy to shear. Indentation response

For isotropic materials, the indentation resistance (or hardness) (H) is inversely proportional to (1- 2) for a given pressure, defined as:

)1( 2

EH (6)

where the value of relates to the theoretical analysis used. 1stands for uniform pressure distribution [12] and 3/2

is for Hertzian indentation [13].

Eq. 6 shows the indentation resistance tends to infinity with increase in the magnitude of Poisson’s ratio ( ) for a given value of Young’s modulus (E). As already noted, the range of Poisson’s ratios for isotropic materials is -1< <0.5, and so auxetic isotropic material show enhancements in indentation resistance when -1< < -0.5. As approaches -1, the indentation resistance towards infinity. Enhanced indentation resistance of auxetic materials has been demonstrated through investigation of synthetic auxetic materials (i.e. polymeric and metallic foams [5,6]; and microporous polymers [14]). A schematic of indentation response is illustrated in Fig. 2 for both non-auxetic and auxetic materials subjected to compressive impact loading [15].

>0

<0

>0

<0

>0

<0

A

B

Oin thperpedefinthe omatethe iminden

Fig. (b) mlatera

3. app 3.1

Wstrucsynthlevelclasswith mateor Yo

Asynthmicroultra polyp[21,2naturand z Appl

AdemoThercan b

Fthrou

On the non-auxethe direction of imendicular to and ne the lateral ‘floother hand, the rial also contractmpact, leading tntation resistance

2. An object material in the al ‘flow’ of mate

Auxetiplications

Classificati

Within the last thtures have bee

hesised, rangingl. Fig. 3 shows tses of materials

auxetic properterials are known oung’s modulus Auxetic materiahesized, such as oporous polytet

high moleculpropylene (PP), 22], several typrally occurring mzeolites [27].

lications

As stated in thonstrated enhaefore, a range obe envisaged. For example, auugh thermomech

tic material, the mpact and the maway from the d

ow’ of material)vertical impact ts laterally-mateto increased dene [15].

hitting a non-vertical directio

erials in each cas

ic mate

ions and typ

hirty years, a vaen discovered, from the molecthat there are ex(polymers, comties, and that naover several ord[16].

als have been polyurethane an

tra-fluoroethylenlar weight polhighly anisotrop

pes of rocks wimolecular auxeti

he above sectiancements in of potential app

uxetic foam withanical processin

force compressematerial spreadsdirection of the i). For the auxeti

compression merial ‘flows’ into sification, theref

-auxetic (a) anon. The arrowsse

erials p

pes

ariety of auxetic designed, man

cular level up toxamples of each

mposites, metals atural and man-ders of magnitud

discovered, fand polyethylene ne (PTFE) [19]lyethylene (UHpic composites [ith microcracksics, e.g. –cristo

ion, auxetic mother physica

plications of aux

th a re-entrant mng was establish

es the material s in directions mpact (arrows ic material, on

means that the the vicinity of

fore, enhanced

nd an auxetic s indicate the

potential

materials and nufactured or o macroscopic h of the major and ceramics) -made auxetic de of stiffness,

abricated and foams [17,18],

] microporous HMWPE) and

20], laminates [23,24], and obalite [25,26],

materials have al properties. xetic materials

microstructure hed to provide

dispersion ohave potent

Fig. 3. Strumaterials fr

Auxetic

fasteners anof the auxethe auxeticfastener is more tightlyprocessing cushions asfoams. Wanbeneficial iand in redu[32]. AuxetUS6412593features in air leaks) an

Aldersoapplication structures wnano-scale particulate variation pdeformation

Huang resistance could be ecase, they hfor the erelatively lmakes themAvellanadsthe design piezocompopassive poland hydroporder of mamatrix assu

1.E-10

Moau- - c

of acoustic wavetial applications

uctured feature rom the macrosc

c cellular solidsnd rivets due toetic fastener is fc material unde

resisted since y in the hole unof auxetic foams another impong and Lakes 20in the preventionuction of pressurtic foam could a3 2002) for ea

forming syncland sound absorpon et al. 2000 re

in filters from with re-entrant (e.g. zeolites), wsize selectivity

properties of n [16].

& Blackburn of ceramics wnhanced by havhave applicationmissions from low bulk modum more sensit, 1998 pointed o

of hydrophonosites consistinglymer matrix anphone receivers agnitude enhanc

umed auxetic pro

1.E-09 1.E-08 1.E-07 1.E-06

s

Sintered c- bismuth-cuprate superc

Molecular uxetics: -cristobalite

cubic metals

es and cut-off frein the absorptio

size and Youngcopic down to th

(i.e. auxetic fothe negative Po

facilitated by thr compression, the fastener ex

nder tension [30]m [31] opens up t

rtant potential a002 reported auxn of pressure sorre-induced discoalso be used in earphone shells astic doubly curption property [3eported auxetic m

the macro-scalhoneycomb and

which could impy capabilities du

auxetic materi

2001 proposeith cellular or ving negative Pns as substrates

internal combulus associated ive to hydrostaout auxetic compnes and other sg of piezoelectricnd used in medof naval sonar

cement in sensitioperties [35,36,3

1.E-05 1.E-04 1.E-03 1.E-02

structural sub-unit size (m)

ceramics:conductors

Composites:- fibre-reinforced

composites- sandwich panel

composites

Honeycombs- polymer/metal

Foams:- polymer/metal

Natural biomaterials:- skin/bone

Microporous polymers:- PTFE

-UHMWPE-PP

equencies, whichn of sound [18,2

g’s modulus of Ae molecular leve

oams) could be oisson’s ratio. Ine lateral contracwhile removal

xpands and lock]. The scaling upthe developmentapplication for xetic cushions cres or ulcers in tomfort in seatedear cushions (USdue to their ex

rved surfaces (re3,34].

materials have ple (e.g. auxetic d auxetic foam)prove filter cleanue to the uniquials wide mec

ed the thermal honeycomb str

Poisson’s ratios.in catalytic con

bustion enginewith auxetic matic pressure, aposites could be sensors. For exc ceramic rods w

dical ultrasonic iwere shown to ivity when the p7].

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+032 1.E-01 1.E+00 1.E+01

Youn

g's

mod

ulus

(GPa

)

Keyed-brick structures:- nuclear

reactor cores

h might 29].

Auxetic el [28]

used as nsertion ction of

of the ks itself p of the t of seat auxetic ould be the sick

d people S Patent xcellent educing

potential cellular

) to the ning and ue pore chanical

shock ructures

In this nverters es. The materials and so, used in

xample, within a imagers lead to

polymer

Youn

gs

mod

ulus

(GPa

)

3. Auxetic materials potential applications

3.1. classifications and types

Point of view588

Journal of Achievements in Materials and Manufacturing Engineering

Y.T. Yao, M. Uzun, I. Patel

Volume 49 Issue 2 December 2011

Ffailurthe fareporprodupostureducthrouPoiss[30,3were polyp3 indemo

Tcompcombor eqproofpostubiomgaske 3.2

Awideuniquderivso arauxetnegat“hingmanyappli

Amechfor thestabcomp 3.3

Atwo cbroad Mole

A

iron pregulSincesinglsuggthat c

BPoiss

For fibre reinfore mechanism. Aailure resistance rted the successfuce the first auxulated that comced fibre pull-ouugh maintainingson’s ratios of th38,39]. Subsequ performed uspropylene fibre ancrease) and eonstrate for the aThere are manyposite materials,bination with othquipment, e.g. inf vest, shin paulated for aux

material, a bandaet.

Limitations

As mentioned ae range of applicue behaviour. Hve their behavioure less stiff thantic materials hative Poisson’s rages” to flex, or “y auxetic materications. A further reasohanisms responshe developmentblished benefits posites containin

Auxetic ma

Auxetic materialcategories: naturdly discussed in

ecular level aux

A negative Poisspyrites [41] as alar geometric arre then negative le crystal phaseested to have a carbon nitride wBaughman & Gson’s ratio is ve

orced compositeAuxetic materials

properties of coful development xetic polymeric

mposites with aut, potentially hg the interface he matrix and fi

uently, comparatsing positive anand enhancemenenergy adsorptiauxetic fibre systy potential appli, such as vehicleher materials fon a crash helmetad, knee pad oxetic fibres inage or wound p

s

above, auxetic cations and are aHowever, most ur from structuren the solids fromave intrinsic poratio (i.e. auxetic “nodules” to sprerials have limit

on for developiible for auxetic

t of auxetic nanofor auxetic mac

ng auxetic nano-

aterials

ls at the molecural and syntheticthe following.

xetics I: Natural

son’s ratio was fa result of crystalrangement and aPoisson’s ratios

es. For examplnegative Poisso

would be harder tGalvao 1993 havery common in

es, fibre pull-ous are also predictmposites. Aldersof a melt-extrus(polypropylene)

auxetic fibres helping to resist

by careful maibre expansion dtive single-fibrend negative Pont in maximum lion (factor of tems [40]. ications for auxe body or car bu

or personal protet, projectile-resior glove. Othernclude fishnet, ressure pad, and

materials potenattracting intere

manmade auxe at micro or mam which they arrosity in order tmaterials need

ead out and so oted potential in

ng an understabehaviour at theo-fibres to realiro-fibres in high

-fibre.

ular level can bec nanoauxetics.

l nanoauxetics

first reported in ls having a tighta twinned crystals have been reple, carbon nitron’s ratios [42]. than diamond. ve also found thcubic crystals w

ut is a major ted to enhance son et al. 2002 sion process to ) fibre. It was could display crack growth, tching of the during loading e pull-out test oisson’s ratio load (factor of

f 3 increase)

xetic fibres in umper; and in ective clothing stant or bullet r applications

replacement d as a seal or

ntially have a st due to their etic materials

acro levels and re made. Most to achieve the space to allow

on). Therefore, n load-bearing

anding of the e nano-scale is se the already h performance

e divided into These will be

single crystal tly constrained l arrangement.

ported in other ide has been It is believed

hat a negative when they are

stretched almechanismstretched alcauses atomto move clatom 1 and along the [However, t

axis cases ato the ribsdirection. Hthe structurleading to a

For tmonocrystain its basabehaviour ialso pointeauxetic beh

Fig. 4. The ratios. (001[43]. [110] principal ax

The maYeganeh-Hsingle cryst

–cristobalframework

The sinanisotropic it has beenwould alsobeen observframework and Cheliko

Auxeticconcurrent axes in the edges) of framework been also d

long the [110] am is illustrated in

long the [110] dms 2 and 4 to seoser together al

d 3). This then co110] and [001] the moving toge

atoms 5 and 6 toconnecting the

Hence, there is anre, accompanyina negative value transversely ialline structure),al plane [44]. is predicted by ed out that 25haviour based on

nanostructure o1) refers to the

and [1 1 0] are xis

ain breakthroughHaeri et al 1992

tal Poisson’s ratite. Fig. 5 shoof corner-sheari

ngle-crystal –cand by employ

n calculated that be auxetic. Neved in -quartz, of SiO4 tetrahe

owsky 1992 [47c behaviour in

dilation and cx-y plane, passthe SiO4 mo

structure. Baseddeveloped for –

and [1 1 0] direFigure 4. Cubic

direction (axis beparate along [1long the [001] dorresponds to exaxes and so Poi

ether of atoms 1

o move apart alse atoms aligninn expansion of t

ng the expansionfor Poisson’s raisotropic zinc the auxetic behAn orthorhombRovati 2003. M% of monoclin

n theoretical anal

of cubic metals wdirection along directions at a

h in inorganic a2, measured abntios (up to -0.5 ows that –crising SiO4 tetrahedristobalite elastiing suitable avean isotropic po

egative Poisson’which also possdral (See Fig. 6)]. –cristobalite is tooperative rotating through the

olecular tetrahed on this ideal, acristobalite and

ction. The deforc elemental metabetween atom 2 10], and atoms direction (axis b

xtension and conisson’s ratio is p and 3 along th

ong the [110] ang towards the

the [1 1 0] dimenn in the [110] diatio [43]. c (with hexhaviour has beenbic alloy with

Meanwhile, Rovanic crystals dislysis [45,46].

with negative Poa cubic princip

90° angle from

auxetics occurrenormally high nfor some directi

stobalite consistdron. ic constants are

eraging techniquolycrystalline ags ratios also ha

sesses a corner-s) as reported by

thought to be dution (about tetrmidpoints of op

edral making an analytical moextended to –q

rmation als were and 4), 1 and 3 between ntraction positive. he [001]

axis due [1 1 0]

nsion of irection,

xagonal n found auxetic

ati 2004 splaying

oisson’s pal axis a cubic

d when negative ions) in ts of a

e highly ues [41], ggregate ave also shearing

Keskar

ue to the rahedral pposing up the

odel has quartz.

Fig.

Fig

Zeonanobeen GrimsimusubseSanc

Atherethat hFor ePeuraplanecharareporfor adirec Mole

Thas deforanaly

5. Illustration of

g. 6. Illustration

olites are anothstructures and ssuggested to po

ma et al. 200ulations. Experimequently been hez-Valle et al.

Apart from thoe are also organihave been very example, crystala et al. in 2006 e for loading aloacterized by x-rarted that cellulosa uniaxial tensiction) [49].

ecular level aux

The re-entrant hbeen identifiedrming through ytically by Abde

f 2x2 -cristobal

of 2x2 -quartz

her important clseveral idealizedossess negative

00 using forcemental confirmat

reported for Z2005 [48].

ose naturally ocic materials withrecently foundline cellulose I as having negatong the z-axis (ay diffraction. Nse II has auxeticile load in the

xetics II: Synthe

honeycomb strucd as having a

flexure. This sel-Sayed et al. an

lite structure in p

z structure in pro

ass of polyhedrd zeolitic cage stPoisson’s ratios

e-field molecultion of auxetic Zeolite NAT

ccurring inorganh monoclinic cryto display auxehas recently beeive Poisson’s ra(cellulose chain

Nakamura and coc behavior in the

z direction (ce

esis of nanoauxe

cture is the first negative Poisso

structure has bnd Gibson et al.

projection x-y

ojection x-y.

ral framework tructures have

s, predicted by ar modelling behaviour has (natrolite) by

nic materials, ystal structure

etic properties. en reported by atios in the x-z

direction), as oworkers 2004 e (1 1 0) plane ellulose chain

etics

structure that on’s ratio by een modelled [50].

Fig. 7(ahoneycombunder stretcand open uratio.

Recent synthesis ofof organic a

Generalapproacheddownscalin1991 succepropose andsingle crysstructure hasuch a strucas -0.94) balso proposthe mechflexyne/reflentrant hexconcurrent molecular nn acetylene a)

b)

Fig. 7. (a) honeycomby-direction.reflexyne [1

While

provide a would lead a result of these particprocessed [in one plancrystallites

a) shows the debs. For a re-entch in the y direcup in the x dire

attention has ff auxetic structuauxetics have belly, the design

d by first designng these to the messfully employd demonstrate t

stalline networksaving auxetic prcture was showny force-field typ

sed a simple 2 dhanical properlexyne (n, m is n

xagons) networkstretching, hing

network. The velinks, respective

Two-dimensionb structure, wh. (b) Auxetic m1]

the re-entrant hpolymer with t

d to a high meltintheir highly cro

cular materials a[55]. Additionalne, and a bulk m

may be not auxe

y

x

y

x

y

x

CCC

C

C

C

C

C

C

C CC

formation mechtrant hexagonal ction the cells election, leading t

focused on the ures on a molecueen proposed. n of molecula

ning auxetic macmolecular or nanyed such a dowhrough modellins based on the roperties (See Fn to be auxetic (pe calculations dimensional analrties of thenumber of triple s. Deformation ging and flexingrtical and diagonely.

nal deformation hich are subjectmolecular honey

honeycomb struthe desired auxng temperature ss-linked structure not likely to bly, the auxetic b

material consistinetic.

C CC

C CC

C

C

C

C

hanism of the regeometry (Fig

ongate along theto a negative Po

theoretical desiular level, and a

ar auxetics is cro structures, anno level [51,52]wnscaling technng polyphenylac

re-entrant honeig. 7(b)). For ex(Poisson’s ratios[53]. Evans et alytical model to ir so-called bond) (conventiwas assumed tog of the ‘arms’nal arms contain

mechanisms in ted to loading

ycomb network:

ucture can in pxetic properties, and poor tractabure [54]. Conseqbe easily synthebehaviour only

ng of randomly o

C

C

C

C

C

C

C

C

-entrant g. 7(a)), e y-axis oisson’s

ign and number

being nd then . Evans

nique to cetylene eycomb xample, s as low al. have predict (n,m)-

onal/re-o be the of the

n m and

auxetic in the

(n,m)-

rinciple it also

bility as quently, sised or appears oriented

3.2. Limitations

3.3. Auxetic materials

589

Materials

Workings of auxetic nano-materials

Ffailurthe fareporprodupostureducthrouPoiss[30,3were polyp3 indemo

Tcompcombor eqproofpostubiomgaske 3.2

Awideuniquderivso arauxetnegat“hingmanyappli

Amechfor thestabcomp 3.3

Atwo cbroad Mole

A

iron pregulSincesinglsuggthat c

BPoiss

For fibre reinfore mechanism. Aailure resistance rted the successfuce the first auxulated that comced fibre pull-ouugh maintainingson’s ratios of th38,39]. Subsequ performed uspropylene fibre ancrease) and eonstrate for the aThere are manyposite materials,bination with othquipment, e.g. inf vest, shin paulated for aux

material, a bandaet.

Limitations

As mentioned ae range of applicue behaviour. Hve their behavioure less stiff thantic materials hative Poisson’s rages” to flex, or “y auxetic materications. A further reasohanisms responshe developmentblished benefits posites containin

Auxetic ma

Auxetic materialcategories: naturdly discussed in

ecular level aux

A negative Poisspyrites [41] as alar geometric arre then negative le crystal phaseested to have a carbon nitride wBaughman & Gson’s ratio is ve

orced compositeAuxetic materials

properties of coful development xetic polymeric

mposites with aut, potentially hg the interface he matrix and fi

uently, comparatsing positive anand enhancemenenergy adsorptiauxetic fibre systy potential appli, such as vehicleher materials fon a crash helmetad, knee pad oxetic fibres inage or wound p

s

above, auxetic cations and are aHowever, most ur from structuren the solids fromave intrinsic poratio (i.e. auxetic “nodules” to sprerials have limit

on for developiible for auxetic

t of auxetic nanofor auxetic mac

ng auxetic nano-

aterials

ls at the molecural and syntheticthe following.

xetics I: Natural

son’s ratio was fa result of crystalrangement and aPoisson’s ratios

es. For examplnegative Poisso

would be harder tGalvao 1993 havery common in

es, fibre pull-ous are also predictmposites. Aldersof a melt-extrus(polypropylene)

auxetic fibres helping to resist

by careful maibre expansion dtive single-fibrend negative Pont in maximum lion (factor of tems [40]. ications for auxe body or car bu

or personal protet, projectile-resior glove. Othernclude fishnet, ressure pad, and

materials potenattracting intere

manmade auxe at micro or mam which they arrosity in order tmaterials need

ead out and so oted potential in

ng an understabehaviour at theo-fibres to realiro-fibres in high

-fibre.

ular level can bec nanoauxetics.

l nanoauxetics

first reported in ls having a tighta twinned crystals have been reple, carbon nitron’s ratios [42]. than diamond. ve also found thcubic crystals w

ut is a major ted to enhance son et al. 2002 sion process to ) fibre. It was could display crack growth, tching of the during loading e pull-out test oisson’s ratio load (factor of

f 3 increase)

xetic fibres in umper; and in ective clothing stant or bullet r applications

replacement d as a seal or

ntially have a st due to their etic materials

acro levels and re made. Most to achieve the space to allow

on). Therefore, n load-bearing

anding of the e nano-scale is se the already h performance

e divided into These will be

single crystal tly constrained l arrangement.

ported in other ide has been It is believed

hat a negative when they are

stretched almechanismstretched alcauses atomto move clatom 1 and along the [However, t

axis cases ato the ribsdirection. Hthe structurleading to a

For tmonocrystain its basabehaviour ialso pointeauxetic beh

Fig. 4. The ratios. (001[43]. [110] principal ax

The maYeganeh-Hsingle cryst

–cristobalframework

The sinanisotropic it has beenwould alsobeen observframework and Cheliko

Auxeticconcurrent axes in the edges) of framework been also d

long the [110] am is illustrated in

long the [110] dms 2 and 4 to seoser together al

d 3). This then co110] and [001] the moving toge

atoms 5 and 6 toconnecting the

Hence, there is anre, accompanyina negative value transversely ialline structure),al plane [44]. is predicted by ed out that 25haviour based on

nanostructure o1) refers to the

and [1 1 0] are xis

ain breakthroughHaeri et al 1992

tal Poisson’s ratite. Fig. 5 shoof corner-sheari

ngle-crystal –cand by employ

n calculated that be auxetic. Neved in -quartz, of SiO4 tetrahe

owsky 1992 [47c behaviour in

dilation and cx-y plane, passthe SiO4 mo

structure. Baseddeveloped for –

and [1 1 0] direFigure 4. Cubic

direction (axis beparate along [1long the [001] dorresponds to exaxes and so Poi

ether of atoms 1

o move apart alse atoms aligninn expansion of t

ng the expansionfor Poisson’s raisotropic zinc the auxetic behAn orthorhombRovati 2003. M% of monoclin

n theoretical anal

of cubic metals wdirection along directions at a

h in inorganic a2, measured abntios (up to -0.5 ows that –crising SiO4 tetrahedristobalite elastiing suitable avean isotropic po

egative Poisson’which also possdral (See Fig. 6)]. –cristobalite is tooperative rotating through the

olecular tetrahed on this ideal, acristobalite and

ction. The deforc elemental metabetween atom 2 10], and atoms direction (axis b

xtension and conisson’s ratio is p and 3 along th

ong the [110] ang towards the

the [1 1 0] dimenn in the [110] diatio [43]. c (with hexhaviour has beenbic alloy with

Meanwhile, Rovanic crystals dislysis [45,46].

with negative Poa cubic princip

90° angle from

auxetics occurrenormally high nfor some directi

stobalite consistdron. ic constants are

eraging techniquolycrystalline ags ratios also ha

sesses a corner-s) as reported by

thought to be dution (about tetrmidpoints of op

edral making an analytical moextended to –q

rmation als were and 4), 1 and 3 between ntraction positive. he [001]

axis due [1 1 0]

nsion of irection,

xagonal n found auxetic

ati 2004 splaying

oisson’s pal axis a cubic

d when negative ions) in ts of a

e highly ues [41], ggregate ave also shearing

Keskar

ue to the rahedral pposing up the

odel has quartz.

Fig.

Fig

Zeonanobeen GrimsimusubseSanc

Atherethat hFor ePeuraplanecharareporfor adirec Mole

Thas deforanaly

5. Illustration of

g. 6. Illustration

olites are anothstructures and ssuggested to po

ma et al. 200ulations. Experimequently been hez-Valle et al.

Apart from thoe are also organihave been very example, crystala et al. in 2006 e for loading aloacterized by x-rarted that cellulosa uniaxial tensiction) [49].

ecular level aux

The re-entrant hbeen identifiedrming through ytically by Abde

f 2x2 -cristobal

of 2x2 -quartz

her important clseveral idealizedossess negative

00 using forcemental confirmat

reported for Z2005 [48].

ose naturally ocic materials withrecently foundline cellulose I as having negatong the z-axis (ay diffraction. Nse II has auxeticile load in the

xetics II: Synthe

honeycomb strucd as having a

flexure. This sel-Sayed et al. an

lite structure in p

z structure in pro

ass of polyhedrd zeolitic cage stPoisson’s ratios

e-field molecultion of auxetic Zeolite NAT

ccurring inorganh monoclinic cryto display auxehas recently beeive Poisson’s ra(cellulose chain

Nakamura and coc behavior in the

z direction (ce

esis of nanoauxe

cture is the first negative Poisso

structure has bnd Gibson et al.

projection x-y

ojection x-y.

ral framework tructures have

s, predicted by ar modelling behaviour has (natrolite) by

nic materials, ystal structure

etic properties. en reported by atios in the x-z

direction), as oworkers 2004 e (1 1 0) plane ellulose chain

etics

structure that on’s ratio by een modelled [50].

Fig. 7(ahoneycombunder stretcand open uratio.

Recent synthesis ofof organic a

Generalapproacheddownscalin1991 succepropose andsingle crysstructure hasuch a strucas -0.94) balso proposthe mechflexyne/reflentrant hexconcurrent molecular nn acetylene a)

b)

Fig. 7. (a) honeycomby-direction.reflexyne [1

While

provide a would lead a result of these particprocessed [in one plancrystallites

a) shows the debs. For a re-entch in the y direcup in the x dire

attention has ff auxetic structuauxetics have belly, the design

d by first designng these to the messfully employd demonstrate t

stalline networksaving auxetic prcture was showny force-field typ

sed a simple 2 dhanical properlexyne (n, m is n

xagons) networkstretching, hing

network. The velinks, respective

Two-dimensionb structure, wh. (b) Auxetic m1]

the re-entrant hpolymer with t

d to a high meltintheir highly cro

cular materials a[55]. Additionalne, and a bulk m

may be not auxe

y

x

y

x

y

x

CCC

C

C

C

C

C

C

C CC

formation mechtrant hexagonal ction the cells election, leading t

focused on the ures on a molecueen proposed. n of molecula

ning auxetic macmolecular or nanyed such a dowhrough modellins based on the roperties (See Fn to be auxetic (pe calculations dimensional analrties of thenumber of triple s. Deformation ging and flexingrtical and diagonely.

nal deformation hich are subjectmolecular honey

honeycomb struthe desired auxng temperature ss-linked structure not likely to bly, the auxetic b

material consistinetic.

C CC

C CC

C

C

C

C

hanism of the regeometry (Fig

ongate along theto a negative Po

theoretical desiular level, and a

ar auxetics is cro structures, anno level [51,52]wnscaling technng polyphenylac

re-entrant honeig. 7(b)). For ex(Poisson’s ratios[53]. Evans et alytical model to ir so-called bond) (conventiwas assumed tog of the ‘arms’nal arms contain

mechanisms in ted to loading

ycomb network:

ucture can in pxetic properties, and poor tractabure [54]. Conseqbe easily synthebehaviour only

ng of randomly o

C

C

C

C

C

C

C

C

-entrant g. 7(a)), e y-axis oisson’s

ign and number

being nd then . Evans

nique to cetylene eycomb xample, s as low al. have predict (n,m)-

onal/re-o be the of the

n m and

auxetic in the

(n,m)-

rinciple it also

bility as quently, sised or appears oriented

Point of view590

Journal of Achievements in Materials and Manufacturing Engineering

Y.T. Yao, M. Uzun, I. Patel

Volume 49 Issue 2 December 2011

Wand pbondcoposprindesigdime

TproceEvanMole a)

b)

Fig. amonbackbanglethe sp

Gmolearrowconta(tessetriang

Wei 2005 develproposed self-a

ded polymer nlymers having

ng-like “soft” (gned which caensional supramoThis hypotheticaessible than thns et al, and thecular Mechanic

8. (a) repeating ng the variable bbone in the doue between the arpring; (b) an exa

Grima and Evanecular networks ws. They are deaining a planellation of a regles at 60° to ea

O

OH

O

OH

O

OH

O

OH

loped the flexynssembled copol

network, showna double-arrow

(-O-CH2-CH2-Oan in principlolecular networkal polymer has e auxetic molehe auxetic prop

cs simulations, in

unit of the self-b, a, and a’, w

uble-arrow and brm and the backbample of double

ns 2000 propose(Fig. 9) also b

escribed as paralnar polyphenylepeat unit havinch other).

bb

a’

Y

bb

a’

Y

N H

N H

[ ]n

N H

N H

[ ]n

ne/reflexyne netymers based on

n in Figure 8w-like “hard”

O- unit) segmenle self-assemblks [56]. the advantage oecular network perty has beenn the plane of the

assembly and thwhere a the halfb the length of tbone, and a’ the -arrow-like mole

ed a series of sbased on polyphllel ‘graphite-liklacetylene infinng two equilate

b

a

bb

a

b

tworks further n a hydrogen-8. Alternating

block and a nt have been le into two-

of being more proposed by

n predicted in e structure.

he relationship f-length of the the arm, the half-length of

ecules [56]

self expanding henylacetylene ke’ layers each nite network eral molecular

XX

O

O H

O

O H

O

O H

O

O H

a)

b)

Fig. 9. (a) energy conf

Negativusing Mechplane y-z (rotation ofnegative Pointeractionsdeformationresponse ofto achieve rigid ‘squar

Grimanetworked blocks. Thmacrostructauxetic behthe molecusynthesised

So far,towards a sis the liqdemonstrate

the structure of figurations of po

ve Poisson’s rathanics simulation

yz=-0.97 and zthe corner-shari

oisson’s ratios as between the dn mechasnism wf auxetic zeoliteauxetic respon

re’ molecular unet al, 2005 hapolymers based

hese were proture shown in haviour. As wiular network s

d. one of the mo

syntheticaly accequid crystallineed by Griffin e

f polytriangles-2olytriangles-7-yn

ios have been ons and maximum

zy=-0.96), and exing triangles. Inare due to a variifferent layers. Twas also used tes [57,58]. Othense through rotanits [48]. ave also proposd on calix[4] areoduced by dowFig. 10, whichith the polypheshown in Fig.

ost simple and essible moleculae polymer coet al 1995; Gri

-yne; (b) the mine at z=0.0 GPa

obtained in 3 dirm auxeticity is fxplained by coopn the plane x-y aiation in the amThe ‘rotating trito interpret the r zeolites are pr

ation of corner-

ed a range of ene molecular bwnscaling the h is known to nylacetylene ne

10(b) is not

promising appar-level auxetic poncept, proposeiffin & Liu 19

inimum a [57]

rections found in perative and x-z,

mount of iangles’ auxetic

redicted -sharing

auxetic building

folded display

etworks, easily

roaches polymer ed and 998 and

showbasedchain‘rigidSomemoletensithe latensichain

Tprincalignforcemate a)

b)

Fig. theormanumole

wn in Fig. 11. Td on site-connecn to achieve auxd’ rod molecule e rigid rods are

ecular, while othle stress, full exaterally attachedle axis to a posns further apart (The main advaciple, as it is liqn the chains, leade transfer [59].erials have as yet

10. (a) The auxretical moleculaufactured in steecular ‘double ca

The liquid crystctivity driven roxetic behaviourinterconnected b attached at the

her rigid rods havxtension of the pd rods from a poition normal to (See Fig. 11). antage of this pquid crystalline,ding to more cov Unfortunately,t failed to measu

xetic macrostrucar system is baeel and marketealix[4]’ network

talline polymersod reorientation . The main chaby ‘flexible’ spa

eir ends to the fve lateral attachmpolymer main chosition roughly it and push the

polymer netwo, it should be mvalent than non-, mechanical te

ure a negative Po

cture (30×30 cmased. The macred as an ‘egg ranalogues [59]

s are designed in their main

ain consists of acer molecule. flexible spacer ment. Under a hain will force parallel to the neighbouring

rk is that in much easier to covalent bond ests on these oisson’s ratio.

m) on which a rostsructure is rack’; (b) the

Fig. 11. (Asynthesisedbased terphpossible spsiloxane (Xproposed malign with sa concomita

Referen [1] K.E.

Molec[2] K.L. A

polyet33/20

[3] J.B. CcellulaMater

[4] J.B. CcellulaMater

[5] R.S. LnegatiMater

[6] N. Chand au231-2

[7] C.P. CmaterPoissoScienc

[8] C.P. Cdynamratio Techn

[9] J.B. Cfoam and a73-83

[10] H. GeJourna1-13.

A

B1

B2

) An example od by Griffin anhenyl transversepacers: methylenX=Si(CH3)2O). mechanism resusurrounding liquant lateral expan

nces

Evans, M.A. Ncular network deAlderson, K.E. Ethylene having (1993) 4435-44

Choi, R.S. Lakar materials withrials Science 27 Choi, R.S. Lakar materials withrials Science 27/Lakes, K.J. Elmive Poisson’s rials 27/12 (1993han, K.E. Evans,uxetic foams, Jo

260. Chen, R.S. Lakeials with convon-ratio foam ce 28/16 (1993) Chen, and R.S.

mic behaviour ofoams, Journ

nolology 118 (19Choi, R.S. Lakmaterials with

analysis, Internat. ercek, Poisson'sal of Rock Mech

O OO

R

---- ( )n

1

2

f one of the liqund co-workers e rods (R=H, n-ne (X=CH2), eth

(B1 and B2) ulting in auxeticuid crystal field; nsion upon stretc

Nkansah, I.J. Huesign, Nature 35Evans, The fabra negative Po

438. kes, Nonlinear h a negative Poi(1992) 5373-538

kes, Nonlinear h a negative Poi/17 (1992) 4678-ms, Indentabilityratio foams, J

3) 1193-1202. , Indentation resournal of Cellul

es, Viscoelatic bventional-Poissoas one-phase, 4288-4298.

. Lakes, Micromof conventional nal of Engine996) 285-288. kes, Fracture toa negative Poistional Journal o

s ratio values fhanics and Minin

OO O

O

uid crystalline po2005 [58]: resoPr, CN, CF3, P

hylene oxide (Xan illustration

c behaviour: (Band (B2) re-orie

ching

utchinson, S.C. 3 (1991) 124. rication of microisson’s ratio, P

properties of misson’s ratio, Jou81. properties of pisson’s ratio, Jou-4684. y of conventionJournal of Com

silience of convelar Plastics 34/3

ehaviour of comon-ration or ne

Journal of M

mechanical analand negative Po

eering Material

ughness of Reson’s ratio, exp

of Fracture 80/1

for rocks, Internng Sciences 44/1

O XO CO

----( ) m

olymers orcinol-

Ph) with =O), or of the

B1) pre-ent with

Rogers,

oporous Polymer

metallic urnal of

polymer urnal of

nal and mposite

entional (1998)

mposite-egative-

Materials

lysis of oisson’s ls and

-entrant eriment (1996)

national 1 (2007)

591

Materials

Workings of auxetic nano-materials

Wand pbondcoposprindesigdime

TproceEvanMole a)

b)

Fig. amonbackbanglethe sp

Gmolearrowconta(tessetriang

Wei 2005 develproposed self-a

ded polymer nlymers having

ng-like “soft” (gned which caensional supramoThis hypotheticaessible than thns et al, and thecular Mechanic

8. (a) repeating ng the variable bbone in the doue between the arpring; (b) an exa

Grima and Evanecular networks ws. They are deaining a planellation of a regles at 60° to ea

O

OH

O

OH

O

OH

O

OH

loped the flexynssembled copol

network, showna double-arrow

(-O-CH2-CH2-Oan in principlolecular networkal polymer has e auxetic molehe auxetic prop

cs simulations, in

unit of the self-b, a, and a’, w

uble-arrow and brm and the backbample of double

ns 2000 propose(Fig. 9) also b

escribed as paralnar polyphenylepeat unit havinch other).

bb

a’

Y

bb

a’

Y

N H

N H

[ ]n

N H

N H

[ ]n

ne/reflexyne netymers based on

n in Figure 8w-like “hard”

O- unit) segmenle self-assemblks [56]. the advantage oecular network perty has beenn the plane of the

assembly and thwhere a the halfb the length of tbone, and a’ the -arrow-like mole

ed a series of sbased on polyphllel ‘graphite-liklacetylene infinng two equilate

b

a

bb

a

b

tworks further n a hydrogen-8. Alternating

block and a nt have been le into two-

of being more proposed by

n predicted in e structure.

he relationship f-length of the the arm, the half-length of

ecules [56]

self expanding henylacetylene ke’ layers each nite network eral molecular

XX

O

O H

O

O H

O

O H

O

O H

a)

b)

Fig. 9. (a) energy conf

Negativusing Mechplane y-z (rotation ofnegative Pointeractionsdeformationresponse ofto achieve rigid ‘squar

Grimanetworked blocks. Thmacrostructauxetic behthe molecusynthesised

So far,towards a sis the liqdemonstrate

the structure of figurations of po

ve Poisson’s rathanics simulation

yz=-0.97 and zthe corner-shari

oisson’s ratios as between the dn mechasnism wf auxetic zeoliteauxetic respon

re’ molecular unet al, 2005 hapolymers based

hese were proture shown in haviour. As wiular network s

d. one of the mo

syntheticaly accequid crystallineed by Griffin e

f polytriangles-2olytriangles-7-yn

ios have been ons and maximum

zy=-0.96), and exing triangles. Inare due to a variifferent layers. Twas also used tes [57,58]. Othense through rotanits [48]. ave also proposd on calix[4] areoduced by dowFig. 10, whichith the polypheshown in Fig.

ost simple and essible moleculae polymer coet al 1995; Gri

-yne; (b) the mine at z=0.0 GPa

obtained in 3 dirm auxeticity is fxplained by coopn the plane x-y aiation in the amThe ‘rotating trito interpret the r zeolites are pr

ation of corner-

ed a range of ene molecular bwnscaling the h is known to nylacetylene ne

10(b) is not

promising appar-level auxetic poncept, proposeiffin & Liu 19

inimum a [57]

rections found in perative and x-z,

mount of iangles’ auxetic

redicted -sharing

auxetic building

folded display

etworks, easily

roaches polymer ed and 998 and

showbasedchain‘rigidSomemoletensithe latensichain

Tprincalignforcemate a)

b)

Fig. theormanumole

wn in Fig. 11. Td on site-connecn to achieve auxd’ rod molecule e rigid rods are

ecular, while othle stress, full exaterally attachedle axis to a posns further apart (The main advaciple, as it is liqn the chains, leade transfer [59].erials have as yet

10. (a) The auxretical moleculaufactured in steecular ‘double ca

The liquid crystctivity driven roxetic behaviourinterconnected b attached at the

her rigid rods havxtension of the pd rods from a poition normal to (See Fig. 11). antage of this pquid crystalline,ding to more cov Unfortunately,t failed to measu

xetic macrostrucar system is baeel and marketealix[4]’ network

talline polymersod reorientation . The main chaby ‘flexible’ spa

eir ends to the fve lateral attachmpolymer main chosition roughly it and push the

polymer netwo, it should be mvalent than non-, mechanical te

ure a negative Po

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438. kes, Nonlinear h a negative Poi(1992) 5373-538

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references

Point of view592

Journal of Achievements in Materials and Manufacturing Engineering

Y.T. Yao, M. Uzun, I. Patel

Volume 49 Issue 2 December 2011

[11] R.S. Lakes, Design considerations for negative Poisson's ratio Materials Journal of Mechanical Design 115 (1993) 696-700.

[12] H. Hertz, Über die Berührung fester elastischer Körper, Journal of Maths (Crelle J) 92 (1881) 156.

[13] S.P. Timoshenko, Theory of elasticity, McGraw-Hill, New York, 1970.

[14] K.L. Alderson, A.F. Fitzgerald, K.E. Evans, The strain dependent indentation resilience of auxetic microporous polyethylene, Journal of Materials Science 35 (2000) 4039-4047.

[15] A. Alderson, A triumph of lateral thought, Chemistry and Industry 10 (1999) 384-391.

[16] K.E. Evans, A. Alderson, Auxetic materials: Functional materials and structures from lateral thinking, Advanced Materials 12/9 (2000) 617-628.

[17] R.S. Lakes, Foam structures with a negative Poisson’s ratio, Science 235/4792 (1987) 1038-1040.

[18] B. Brandel, R.S. Lakes, Negative Poisson’s ratio polyethylene foams, Journal of Materials Science 36 (2001) 5885-5893.

[19] B.D. Caddock, K.E. Evans, Microporous materials with negative Poisson's ratios. II, Mechanisms and interpretation, Journal of Physics D: Applied Physics 22 (1989) 1883-1887.

[20] A.N. Sherbourne, M.D. Pandey, Proceedings of the “Engineering Mechanics Specialty Conference” ASCE’1991, Columbus, 1991, 841.

[21] R.G. Zhang, H.L. Yeh, H.Y. Yeh, A preliminary study of negative Poisson's ratio of laminated fiber reinforced composites, Journal of Reinforced Plastics and Composites 17/18 (1998) 1651-1664.

[22] R.G. Zhang, H.L. Yeh, H.Y. Yeh, A discussion of negative Poisson's ratio design for composites, Journal of Reinforced Plastics and Composites 18/17 (1999) 15461556.

[23] F. Homand-Etienne, R. Houpert, Thermally induced microcracking in granites: characterization and analysis, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 26/2 (1989) 125-134.

[24] A. Nur, G. Simmons, The effect of saturation on velocity in low-porosity rocks, Earth and Planetary Science Letters 7/2 (1969) 183-193.

[25] A. Yeganeh-Haeri, D.J. Weidner, J.B. Parise, Elasticity of -cristobalite: A silicon dioxide with a negative Poisson's ratio, Science 2575070 (1992) 650-652.

[26] A. Alderson, K.E. Evans, Rotation and dilation deformation mechanisms for auxetic behaviour in the -cristobalite tetrahedral framework structure, Physics and Chemistry of Minerals 28/10 (2001) 711-718.

[27] J.N. Grima, R. Jackson, A. Alderson, K.E. Evans, Do zeolites have negative Poisson's ratios, Advanced Materials 12/24 (2000) 1912-1918.

[28] P.J. Stott, R. Mitchell, K.L. Alderson, A. Alderson, A growing industry, Materials World 8 (2000) 12-14.

[29] A. Alderson, J.A. Rasburn, K.E. Evans, An auxetic filter, A tuneable filter displaying enhanced sizes electivity or defueling properties, Industrial and Engineering Chemistry Research 39 (2000) 654.

[30] J.B. Choi, R.S. Lakes, Design of a fastener based on negative Poisson's ratio foam, Cellular Polymers 10 (1991) 205-212.

[31] M.A. Loureiro, R.S. Lakes, Scale-up of transformation of negative Poisson's ratio foam: Slabs, Cellular Polymers 16 (1997) 349-363.

[32] Y.C. Wang, R. Lakes, Analytical parametric analysis of the contact problem of human buttocks and negative Poisson's ratio foam cushions, International Journal of Solids and Structures 39 (2002) 4825-4838.

[33] M. Burke, A stretch of the imagination, New Scientist 154 (1997) 36-39.

[34] P.J. McMullan, Textile fibres engineered from molecular auxetic polymers, http://www.ptfe.gatech.edu/faculty/ mcmullan/paper.php.

[35] X. Huang, S. Blackburn, Developing a new processing route to manufacture honeycomb ceramics with negative Poisson’s ratio, Key Engineering Materials 206-213 (2001) 201-204.

[36] M. Avellanads, P.J. Swart, Calculating the performance of 1-3 piezo composites for hydrophone applications: An effective medium approach, Journal of the Acoustical Society of America 103/3 (1998)1449-1467.

[37] W.A. Smith, US Patent No. 5334903, 1994. [38] K.L Alderson, A. Alderson, G. Smart, V.R. Simkins,

P.J. Davies, Auxetic polypropylene fibres, Part 1, Manufacture and characterisation, Plastics, Rubber and Composites 31/8 (2002) 344-349.

[39] K.E. Evans, Tailoring the negative Poisson’s ratio, Chemistry and Industry 20 (1990) 654-657.

[40] V.R. Simkins, N. Ravirala, P.J. Davies, A. Alderson, K.L. Alderson, An experimental study of thermal post-production processing of auxetic polypropylene fibres, Physica Status Solidi 245 (2008) 598-605.

[41] A.E.H. Love, A Treatise on the mathematical theory of elasticity, Dover, New York, 1944.

[42] Y. Guo, I.W. Goddard, Is carbon nitride harder than diamond? No, but its grith increases when stretched (Negative Poisson’s ratio), Chemical Physics Letters 237 (1995) 72-76.

[43] R.H. Baughman, D.S. Galvao, Crystalline network with unusual predicted mechanical and thermal properties, Nature 365 (1993) 735-737.

[44] V.A. Lubarda, M.A. Meyers, On the negative Poisson ratio in monocrystalline zinc, Scripta Materialia 40/8 (1999) 975-977.

[45] M. Rovati, On the negative Poisson's ratio of an orthorhombic alloy, Scripta Materialia 48 (2003) 235-240.

[46] M. Rovati, Directions of auxeticity for monoclinic crystals, Scripta Materialia 51 (2004) 1087-1091.

[47] N.R. Keskar, J.R. Chelikowsky, Negative Poisson ratios in crystalline SiO2 from first-principles calculations, Nature 358 (1992) 222-224.

[48] C. Sanchez-Valle, S.V. Sinogeikin, Z.A. Lethbridge, R.I. Walton, C.W. Smith, K.E. Evans, J.D. Bass, Ab initio structural, elastic, and vibrational properties of carbon nanotubes Physical Review B 59 (1999) 12678-12688.

[49] K. Nakamura, M. Wada,S. Kuga, T. Okano, Poisson's ratio of cellulose I and cellulose II, Journal of Polymer Science Part B: Polymer Physics 42/7 (2004) 1206-1211.

[50] F.K. Abdel-Sayed, R. Jones, I.W. Burgens, Theoretical approach to the deformation of honeycomb based composite-materials, Composites 10/4 (1979) 209-214.

[51] K.E. Evans, A. Alderson, F.R. Attenborough, Auxetic two-dimensional polymer networks: An example of tailoring

geometry for specific mechanical properties, Journal of the Chemical Society, Faraday Transactions 91 (1995) 2671-2680.

[52] F.R. Attenborough, Ph.D. Thesis, University of Liverpool, UK, 1997.

[53] M.A. Nkansah, K.E. Evans, I.J. Hutchinson, Modelling the mechanical properties of an auxetic molecular network, Modelling and Simulation in Materials Science and Engineering 2 (1994) 337-352.

[54] A.C. Griffin, S. Kumar, P.J. McMullan, NTC Project, M04-GT21, http://www.ptfe.gatech.edu/faculty/mcmullan/paper.php.

[55] P. Aldred, S.C. Moratti, Dynamic simulations of potentially auxetic liquid-crystalline polymers incorporating swivelling mesogens, Molecular Simulation 31/13 (2005) 883-887.

[56] G.Y. Wei, Design of auxetic polymer self-assemblies Physica Status Solidi 242/3 (2005) 742-748.

[57] J.N. Grima, K.E. Evans, Auxetic behaviour from rotating squares, Journal Of Materials Science Letters 19 (2000) 1563-1565.

[58] U.H.F. Bunz, Y. Rubin, Y. Tobe, Polyethynylated cyclic pi-systems: scaffoldings for novel two and three-dimensional carbon networks, Chemical Society Reviews 28/2 (1999) 107-119.

[59] J.N. Grima, R. Gatt, A. Alderson, K.E. Evans, On the auxetic properties of ‘rotating rectangles’ with different connectivity, Journal of the Physical Society of Japan 7/104 (2005) 2866-2867.

593READING DIRECT: www.journalamme.org

Materials

[11] R.S. Lakes, Design considerations for negative Poisson's ratio Materials Journal of Mechanical Design 115 (1993) 696-700.

[12] H. Hertz, Über die Berührung fester elastischer Körper, Journal of Maths (Crelle J) 92 (1881) 156.

[13] S.P. Timoshenko, Theory of elasticity, McGraw-Hill, New York, 1970.

[14] K.L. Alderson, A.F. Fitzgerald, K.E. Evans, The strain dependent indentation resilience of auxetic microporous polyethylene, Journal of Materials Science 35 (2000) 4039-4047.

[15] A. Alderson, A triumph of lateral thought, Chemistry and Industry 10 (1999) 384-391.

[16] K.E. Evans, A. Alderson, Auxetic materials: Functional materials and structures from lateral thinking, Advanced Materials 12/9 (2000) 617-628.

[17] R.S. Lakes, Foam structures with a negative Poisson’s ratio, Science 235/4792 (1987) 1038-1040.

[18] B. Brandel, R.S. Lakes, Negative Poisson’s ratio polyethylene foams, Journal of Materials Science 36 (2001) 5885-5893.

[19] B.D. Caddock, K.E. Evans, Microporous materials with negative Poisson's ratios. II, Mechanisms and interpretation, Journal of Physics D: Applied Physics 22 (1989) 1883-1887.

[20] A.N. Sherbourne, M.D. Pandey, Proceedings of the “Engineering Mechanics Specialty Conference” ASCE’1991, Columbus, 1991, 841.

[21] R.G. Zhang, H.L. Yeh, H.Y. Yeh, A preliminary study of negative Poisson's ratio of laminated fiber reinforced composites, Journal of Reinforced Plastics and Composites 17/18 (1998) 1651-1664.

[22] R.G. Zhang, H.L. Yeh, H.Y. Yeh, A discussion of negative Poisson's ratio design for composites, Journal of Reinforced Plastics and Composites 18/17 (1999) 15461556.

[23] F. Homand-Etienne, R. Houpert, Thermally induced microcracking in granites: characterization and analysis, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 26/2 (1989) 125-134.

[24] A. Nur, G. Simmons, The effect of saturation on velocity in low-porosity rocks, Earth and Planetary Science Letters 7/2 (1969) 183-193.

[25] A. Yeganeh-Haeri, D.J. Weidner, J.B. Parise, Elasticity of -cristobalite: A silicon dioxide with a negative Poisson's ratio, Science 2575070 (1992) 650-652.

[26] A. Alderson, K.E. Evans, Rotation and dilation deformation mechanisms for auxetic behaviour in the -cristobalite tetrahedral framework structure, Physics and Chemistry of Minerals 28/10 (2001) 711-718.

[27] J.N. Grima, R. Jackson, A. Alderson, K.E. Evans, Do zeolites have negative Poisson's ratios, Advanced Materials 12/24 (2000) 1912-1918.

[28] P.J. Stott, R. Mitchell, K.L. Alderson, A. Alderson, A growing industry, Materials World 8 (2000) 12-14.

[29] A. Alderson, J.A. Rasburn, K.E. Evans, An auxetic filter, A tuneable filter displaying enhanced sizes electivity or defueling properties, Industrial and Engineering Chemistry Research 39 (2000) 654.

[30] J.B. Choi, R.S. Lakes, Design of a fastener based on negative Poisson's ratio foam, Cellular Polymers 10 (1991) 205-212.

[31] M.A. Loureiro, R.S. Lakes, Scale-up of transformation of negative Poisson's ratio foam: Slabs, Cellular Polymers 16 (1997) 349-363.

[32] Y.C. Wang, R. Lakes, Analytical parametric analysis of the contact problem of human buttocks and negative Poisson's ratio foam cushions, International Journal of Solids and Structures 39 (2002) 4825-4838.

[33] M. Burke, A stretch of the imagination, New Scientist 154 (1997) 36-39.

[34] P.J. McMullan, Textile fibres engineered from molecular auxetic polymers, http://www.ptfe.gatech.edu/faculty/ mcmullan/paper.php.

[35] X. Huang, S. Blackburn, Developing a new processing route to manufacture honeycomb ceramics with negative Poisson’s ratio, Key Engineering Materials 206-213 (2001) 201-204.

[36] M. Avellanads, P.J. Swart, Calculating the performance of 1-3 piezo composites for hydrophone applications: An effective medium approach, Journal of the Acoustical Society of America 103/3 (1998)1449-1467.

[37] W.A. Smith, US Patent No. 5334903, 1994. [38] K.L Alderson, A. Alderson, G. Smart, V.R. Simkins,

P.J. Davies, Auxetic polypropylene fibres, Part 1, Manufacture and characterisation, Plastics, Rubber and Composites 31/8 (2002) 344-349.

[39] K.E. Evans, Tailoring the negative Poisson’s ratio, Chemistry and Industry 20 (1990) 654-657.

[40] V.R. Simkins, N. Ravirala, P.J. Davies, A. Alderson, K.L. Alderson, An experimental study of thermal post-production processing of auxetic polypropylene fibres, Physica Status Solidi 245 (2008) 598-605.

[41] A.E.H. Love, A Treatise on the mathematical theory of elasticity, Dover, New York, 1944.

[42] Y. Guo, I.W. Goddard, Is carbon nitride harder than diamond? No, but its grith increases when stretched (Negative Poisson’s ratio), Chemical Physics Letters 237 (1995) 72-76.

[43] R.H. Baughman, D.S. Galvao, Crystalline network with unusual predicted mechanical and thermal properties, Nature 365 (1993) 735-737.

[44] V.A. Lubarda, M.A. Meyers, On the negative Poisson ratio in monocrystalline zinc, Scripta Materialia 40/8 (1999) 975-977.

[45] M. Rovati, On the negative Poisson's ratio of an orthorhombic alloy, Scripta Materialia 48 (2003) 235-240.

[46] M. Rovati, Directions of auxeticity for monoclinic crystals, Scripta Materialia 51 (2004) 1087-1091.

[47] N.R. Keskar, J.R. Chelikowsky, Negative Poisson ratios in crystalline SiO2 from first-principles calculations, Nature 358 (1992) 222-224.

[48] C. Sanchez-Valle, S.V. Sinogeikin, Z.A. Lethbridge, R.I. Walton, C.W. Smith, K.E. Evans, J.D. Bass, Ab initio structural, elastic, and vibrational properties of carbon nanotubes Physical Review B 59 (1999) 12678-12688.

[49] K. Nakamura, M. Wada,S. Kuga, T. Okano, Poisson's ratio of cellulose I and cellulose II, Journal of Polymer Science Part B: Polymer Physics 42/7 (2004) 1206-1211.

[50] F.K. Abdel-Sayed, R. Jones, I.W. Burgens, Theoretical approach to the deformation of honeycomb based composite-materials, Composites 10/4 (1979) 209-214.

[51] K.E. Evans, A. Alderson, F.R. Attenborough, Auxetic two-dimensional polymer networks: An example of tailoring

geometry for specific mechanical properties, Journal of the Chemical Society, Faraday Transactions 91 (1995) 2671-2680.

[52] F.R. Attenborough, Ph.D. Thesis, University of Liverpool, UK, 1997.

[53] M.A. Nkansah, K.E. Evans, I.J. Hutchinson, Modelling the mechanical properties of an auxetic molecular network, Modelling and Simulation in Materials Science and Engineering 2 (1994) 337-352.

[54] A.C. Griffin, S. Kumar, P.J. McMullan, NTC Project, M04-GT21, http://www.ptfe.gatech.edu/faculty/mcmullan/paper.php.

[55] P. Aldred, S.C. Moratti, Dynamic simulations of potentially auxetic liquid-crystalline polymers incorporating swivelling mesogens, Molecular Simulation 31/13 (2005) 883-887.

[56] G.Y. Wei, Design of auxetic polymer self-assemblies Physica Status Solidi 242/3 (2005) 742-748.

[57] J.N. Grima, K.E. Evans, Auxetic behaviour from rotating squares, Journal Of Materials Science Letters 19 (2000) 1563-1565.

[58] U.H.F. Bunz, Y. Rubin, Y. Tobe, Polyethynylated cyclic pi-systems: scaffoldings for novel two and three-dimensional carbon networks, Chemical Society Reviews 28/2 (1999) 107-119.

[59] J.N. Grima, R. Gatt, A. Alderson, K.E. Evans, On the auxetic properties of ‘rotating rectangles’ with different connectivity, Journal of the Physical Society of Japan 7/104 (2005) 2866-2867.