introduction to plastic foamsfoams/presentations/friday13/friday13... · introduction to plastic...
TRANSCRIPT
Introduction Introduction to to Plastic FoamsPlastic Foams
AndrAndréé MoreiraMoreiraPolymer Polymer PhysicsPhysics, BASF AG, BASF AG
Ludwigshafen, GermanyLudwigshafen, Germany
Les Les HouchesHouches, Jan. 2006, Jan. 2006
AcknowlegmentsAcknowlegments::
H.H. WeiWeißß V. V. SchSchäädlerdlerP. P. MMüüllerller M. M. RRüüllmannllmannE. E. WaWaßßnerner H. H. SchuchSchuchK. HahnK. Hahn C. C. ExnerExnerM. M. AllmendingerAllmendinger P. LopesP. LopesB. B. SowartSowart A. A. AlteheldAlteheldD. LongoD. Longo K.K.--H. H. WaWaßßmermerT. FrancisT. Francis F. F. HeilmannHeilmannM. M. RRüüllmannllmann M.M. BotheBothe
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Global summaryGlobal summary
Introduction
Plastic foams: Physics and Chemistry
Plastic foams: industrial processes
Mechanical properties
Acoustic properties
Thermal properties
Nanoporous foams: the future?
Part I
Part II
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Summary: Part IISummary: Part II
Mechanical propertiesStress strain behaviorBendingCrash simulation of foams
Acoustic propertiesSound and sound managementAcoustic impedance and sound reflectionSound dissipation in porous media
Thermal propertiesThermal conductivity: definitionConductivity through the matrixRadiative contributionConductivity through the gas
Nanoporous foams: the future?
Mechanical propertiesMechanical properties
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Mechanical mapMechanical map
Source: Gibson & Ashby
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Bending work, bending strength
Compressive strength
Testing materials (some examples)Testing materials (some examples)
Tensile strength
Source: Gibson & Ashby, Cellular solids , 2nd Ed., Cambridge (1997)
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
OpenOpen-- and and closedclosed--cell foamscell foams
Open-cell foams are generally weaker than closed-cell foams
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Model foam: HoneycombsModel foam: Honeycombs
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Example: stressExample: stress--strain curve strain curve of a rigid foam (experimental)of a rigid foam (experimental)
Source: Gibson & Ashby
σpl
( ) ( )termpressuregas+−+
≈
S
F
S
F
S
F
EE
ρρ
φρρ
φ 12
φ: fraction of material in the edges(=1 in open-cell foams)
Open- and Closed-cell foams (G & A)
( ) ( )termpressuregas+−+
≈
S
F
S
F
ys
pl
ρρ
φρρ
φσ
σ1
2/3
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
0 0.2 0.4 0.6 0.8 1rel. density
0
0.2
0.4
0.6
0.8
1
ler.
gnuoYdo
m.
0 0.2 0.4 0.6 0.8 1rel. density
0
0.2
0.4
0.6
0.8
1
ler.
gnuoYdo
m.
Comparison between Gibson & Ashby and simulations (linear regime )
2
≈
S
F
S
F
EE
ρρ
( )S
F
S
F
S
F
EE
ρρ
φρρ
φ −+
≈ 1
2
2
φ: fraction of material in the edges
Cubic closed cells (G & A)
Cubic open cells (G & A)
ES=3.4 GPa
Cubic foamsCubic foams: linear : linear elasticityelasticity
Simulation
G&A
Simulation
G&A
Horst Weiss, Peter Müller, Frank Heilmann, BASF
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
§ Polymer matrix:
§ Molecular weight distribution
§ Linear, branched
§ Additives and fillers
§ Homogeneity of foam structure
§ Cell density
§ EPS: fusion of the beads
Properties that influence the Properties that influence the mechanical behavior of foamsmechanical behavior of foams
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
On On passingpassing: : Why isWhy is an an inhomogeneous inhomogeneous foam weakerfoam weaker??
Initial 10% compression
Extreme bending of struts near irregular cells!
Homogeneous compression In homogeneous Foams!
Density ~ 40 g / l
Horst Weiss, Peter Müller, Frank Heilmann, BASF
Acoustic propertiesAcoustic properties
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
8 Hz – 20 kHz
25 – 80 kHz
40 – 50 kHz
1 – 5 Hz
Fre
quen
cy (
Hz)
1
10
102
103
104
105
343
34.3
3.4
0.34
0.034
0.0034
Wav
elen
gth
(m)
Air: c = 343 m/sρ = 1.3 kg/m³
SoundSound
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Threshold of hearing measured at 1 kHz:
Lowest Intensity: I0 = 10-12 Watt / m²Highest Intensity: 10 Watt / m²
Lowest Pressure: 2 x 10-5 Pa = 2 x 10-10 bar Highest pressure: 60 Pa = 0.6 mbar
Decibel system:
I(db) = 10 Log10(I / I0)
Lowest value: 0 db (I = I0)
Highest value (threshold of pain): 130 db
20 50 100 200 500 1000 2000 5000
20
40
60
80
100
120
Conversation
Music
Threshold of pain
Threshold ofhearing
Frequency (Hz)
Inte
nsity
(dB
)
Source: Veit, Teschnische Akustik
SoundSound
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Absorption:
Isolation:
Insulation:
Absorb and dissipate sound generated in a room. Low sound reflection.
Keep sound out of a room through reflection.
Avoid sound propagation though solids by coupling rigid parts to resilient materials.
Foams OK
Foams OK
Foams KO
Sound Sound management management in in buildingsbuildings
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
cZ ρ=Acoustic impedance: Reflection factor:
12
12)(
)(
ZZZZ
pp
r i
r
+−
=≡1 2
incident
absorbed
reflectedp(r) reflected pressurep(i) incident pressure
The higher is the modulus of r, the better is the reflexion…Bulky materials reflect better (higher contrast with the air)
Absorption factor:21 r−=α
Source: Gibson and Ashby, Cellular Solids
Interfaces and Interfaces and sound absorptionsound absorption
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG Source:K.W. Suh et al., Adv. Mat. 12, 1779 (2000)
Sound Sound absorption absorption ((open cell foamsopen cell foams))
(effect of moisture)
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
tp
pctp
gas ∂∂Ξ
−∇=∂∂
ρ22
2
2
Combining (1) Navier-Stokes with dissipation, (2) mass conservation and (3) the equation-of-state for the medium (gas), one obtains:
Traveling 1d plane wave solution (damped!):
)(0
tzkiz eepp ωξ −−−=
Dispersion relation: 04 22
222242 =
Ξ−−
gasckkc
ρω
ω
c: velocity of soundΞ: dissipative factor
ckc gas
/
2
ω
ρξ
Ξ=
Dispersion relation (c=343 m/s)
0
1000
2000
3000
4000
5000
6000
0 5 10 15 20 25 30
kr
om
ega low diss.
high diss.
air
Penetration length:
Sound Sound dissipationdissipation: : the wave equation the wave equation in in porous porous mediamedia
penetration length (m)
0
0.1
0.2
0.3
0.4
0.5
0 200 400 600 800 1000 1200
frequency (Hz)
len
gth
(m
)
low diss.
high diss.
What do we know about Ξ ?It has a maximum at some porosity
It decreases the amount of “blind ends”(connection to the Rayleigh model)
Ξ = 5 x 103 Ns/m4
Ξ = 100 x 103 Ns/m4
Thermal Thermal propertiesproperties
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
25Air
800 – 1200Concrete
41Glass wool
38Cork (low dens.)
46Balsa
25 – 35PUR
15Aerogel
400 – 800Brick
4VIP
30 – 35Styropor
35 – 40Styrodur
150Polystyrene
700 – 800Glass
TC (mW / K m)TC (mW / K m)MaterialMaterial
Source: Handbook of Chemistry and Physics, 56th Ed.
Thermal Thermal conductivityconductivity
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Transport propertiesTransport properties
φα∇−=Jr
tJ
∂∂
−=⋅∇φr
(1) The flux of φ is against its gradient
Pos
itive
gra
dien
t
(2) Sources of flux responsible for change in time
Combining (1) and (2) leads to: φαφ 2∇=
∂∂
t
ρρ 2∇=
∂∂
Dt
Transport of matter: Transport of heat: Tct
T 2∇=∂∂
ρλ
ρ: Density field
D: Diffusion coefficient
T: Temperature fieldλ: thermal conductivity (W / K m)c: specific (mass) heat capacityρ: (mass) density of the material
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Heat transport across materials:Heat transport across materials:oneone--dimensional casedimensional case
nrr JJJ +=
Two contributions to the heat flux: radiative and non-radiative (convection plays no role for air at length scale below a few mm)
xT
J nr ∂∂
−= λ
( ) xKr eTTJ −−= 4
04
1σβT1 T0
β: constant (below 1 for real surfaces, 1 for black body)
σ: Stefan’s constant
Kp: extinction coefficient of polymer
λ: thermal conductivity (W / K m)
Jr
Jnr
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
NonNon--radiativeradiative heat transport across heat transport across composites: onecomposites: one--dimensional casedimensional case
Two limiting cases:
xT
J nr ∂∂
−= λ
T1 T0
T1 T0
2
1
1
1 11λ
ϕλϕ
λ−
+=
1
1
2
22111 )1( λϕλϕλ −+=
(a) Serial (eg. coextrusion)
(b) Parallel
REMEMBER! conductivity = 1 / Resistivity
ϕ1: vol. frac. of mat. 1
λ1: thermal cond. of mat. 1
Parallel X Serial
01234567
0 0.2 0.4 0.6 0.8 1
Vol. frac. of component 1λ
/ λ2 parallel
21 6 λλ =
serial
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Heat transport across foams:Heat transport across foams:oneone--dimensional casedimensional case
( )LK
pp
Fg
P
F p
Fp
eTTxT
J ρρ
σβλρρ
τλρρ −
−+∂∂
+
−−= 4
04
11
ρF: density of the foam (usually <300 g/l)
ρp: density of the polymer (~1 kg/l)
τ: tortuosity factor (empirically found to be ~ 2/3)
β: constant (below 1 for real surfaces, 1 for black body)
σ: Stefan’s constant
Kp: extinction coefficient of polymer
L: thickness of foam across x-axis
T1 T0
L x
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Heat transport across foams:Heat transport across foams:oneone--dimensional casedimensional case
( )radiationmatrixgaseff LTT
Jλλλλ ++≈
−−≡
10
Effective Thermal Conductivity
0
10
20
30
40
50
60
0 20 40 60 80 100
Foam density (g/l)
TC (
mW
/ K
m)
polymer
gas
radiation
total
T1 T0
L x
( )LK
pp
Fg
P
F p
Fp
eTTxT
J ρρ
σβλρρ
τλρρ −
−+∂∂
+
−−= 4
04
11
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Side note: RSide note: R--values in architecturevalues in architecture
RLTTJ eff 1
10
≡=−
−λ
Inne
r wal
l
Ther
mal
isol
atio
n (fo
am)
Out
er w
all
LTT
Jeff
10 −−≡λ
outerfoaminnertotal RRRR ++=
outer
outer
foam
foam
inner
inner LLLλλλ
++=
JTT
JTT
JTT
JTT
Rofi
total01011111 −
−=−′′
−′′−′
−′−
−=
ofi JJJ ==
Proof:
Conservation of energy:
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Effective Thermal Conductivity
0
10
20
30
40
50
60
0 20 40 60 80 100
Foam density (g/l)
TC
(m
W /
K m
)
polymer
gas
radiation
total
Thermal conductivity of foams:Thermal conductivity of foams:low density systemslow density systems
TC dominated by radiative contribution!
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Styropor®
IR-Absorber:Graphite
l 25% lower thermal conductivity (at density of 10 g/l)l 50% lower amount of Material needed (for thermal conductivity of 33 mW / K m)
NeoporNeopor®®
Increasing the KIncreasing the K--factorfactor
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
NeoporNeopor®® versusversus StyroporStyropor®®
Styropor®Neopor®
IR Camera
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Thermal conductivity of foams:Thermal conductivity of foams:intermediate density systemsintermediate density systems
Effective Thermal Conductivity
0
10
20
30
40
50
60
0 20 40 60 80 100
Foam density (g/l)
TC
(m
W /
K m
)
polymer
gas
radiation
total
TC dominated by gas contribution!
Nanoporous foamsNanoporous foams::The futureThe future??
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
25Air
800 – 1200Concrete
41Glass wool
38Cork (low dens.)
46Balsa
25 – 35PUR
15Aerogel
400 – 800Brick
4VIP
30 – 35Styropor
35 – 40Styrodur
150Polystyrene
700 – 800Glass
TC (mW / K m)TC (mW / K m)MaterialMaterial
Source: Handbook of Chemistry and Physics, 56th Ed.
Thermal Thermal conductivityconductivity
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Knudsen effect in PU-foam (pore diameter ~ 400 µm)
8
13
18
23
28
33
-2 -1 0 1 2 3 4
log(pore diameter/mean free path)
Ther
mal
con
duct
ivit
y (m
W/
K m
)Freon 12
CO2
N2
PUR foam, porosity 0.88, pore size ~400 µm
Experimental data from Harper and Sahrigi, I & EC Fundamentals 3, 318 (1964)
Mean free path of N2 at 10 C ~ 100 nm
Why Why nanoscopicnanoscopic pores are good:pores are good:the Knudsen effectthe Knudsen effect
Mean free path(from kinetic
theory):
22 dPTk
l B
π≈
d: diameter of the molecule
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Gas conductivity in usual foamsGas conductivity in usual foams
Thermal conductivity through diffusion & collision, no conductivity through convection (for air below 1mm typical length scale)
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Gas conductivity in Gas conductivity in nanoporous nanoporous mediamedia
In words: in a gas, heat is transported either by radiation or by diffusion à reducing diffusion length means reducing the heat flux through the gas!
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Knudsen made easy:Knudsen made easy:thermal transport in the ideal gasthermal transport in the ideal gas
vl0=τ Frequency of collision = mean free path / mean molecular velocity
In a bulk system (no walls):
τ1
=p Probability of collision per unit time
Ideal gas confined between 2 walls:
wmmm ppp ,, +=Lll111
0
+=
L
l is the effective mean free path of the system, i.e., the distance that a molecule on average travels before collision (either with another molecule or with a wall)
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Knudsen made easy:Knudsen made easy:thermal transport in the ideal gasthermal transport in the ideal gas
z=0n: number density of molecules
321 n
Molecules move, on average, in the z+ direction…
z
)(61
lnv −…of which cross z=0 per unit time and area without experiencing collision
So the particle flux is:zn
lvlnvlnvJ z ∂∂
−≈+−−=31
)(61
)(61
10
0 131
31 −
+==
Ll
lvlvD
Mass transport:
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Knudsen made easy:Knudsen made easy:thermal transport in the ideal gasthermal transport in the ideal gas
z=0n: number density of molecules (no gradient!)
ε: mean energy per molecule
321 n
Molecules move, on average, in the z+ direction…
z
)(61
lnv −ε… transporting average energy across z=0 per unit time and area without collision
So the energy flux is:zT
TlvJ z ∂
∂∂∂
−≈ε
31
Heat transport (non-radiative):
cT
=∂∂ε Specific heat per
molecule
Dcn=λ
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Knudsen made easy:Knudsen made easy:thermal transport in the ideal gasthermal transport in the ideal gas
Dcn=λ1
00 1
31 −
+=
Ll
lvD 20 2 dPTk
l B
π=
Knudsen effect in PU-foam (pore diameter ~ 400 µm)
8
13
18
23
28
33
-2 -1 0 1 2 3 4
log(pore diameter/mean free path)
Ther
mal
con
duct
ivit
y (m
W/ K
m)
Freon 12
CO2
N2
0
0.2
0.4
0.6
0.8
1
1.2
-4 -3 -2 -1 0 1 2 3 4
Log(L / l0)
D /
D0
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Small Pores: 10 - 100 nmLow density: 1 - 100 g/literTherm. cond.: 15 - 25 mW/K*m
Discovered in the 1931 by Kistler (Nature 127, 741 (1931))
Silica Silica aerogelsaerogels
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Si(OR)4 + H2O g Si(OR)3OH + ROH (Hydrolysis)
2 Si(OR)3OH g (RO)3SiOSi(OR)3 + H2O (Condensation)
R: Hydrogen, alkyl or silicate group
0 200 400 600 800 1000radiusHnmL
2
4
6
8
10
rotcaferpni
ecalpaLHrabL
θγ
cos2R
PP lg =−
liqliq
gas gas
Fw
FlFt
Fw
Fl
Ft
-Ft
-Ft
θ
0
20
40
60
80
100
120
140
160
180
200
220
240
50 100 150 200 250 300 350 400
Temperature (C)
Pre
ssur
e (b
ar)
water
isoprop.
CP
CPSupercriticaldrying path
Silica Silica aerogelsaerogels
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
Duromers (gels)
Use the right components: Avoid supercritical drying
Thermoplastics
Use the right nucleating agents/processing
NanofoamsNanofoams@BASF@BASF
Dr. AndrDr. Andréé MoreiraMoreira, BASF AG, BASF AG
"eierlegende Wollmilchsau“Egg-laying, wool- and milk-producing pig
Plastic foams arePlastic foams are......