Polymer Processing:
„Engineering activities concerned with operations
carried out on polymeric materials to enhance their utility“
Prof. Dr. Klaus Ruhland
Z. Tadmor, C. G. Gogos, Principles of Polymer Processing, Wiley-Interscience
T. A. Osswald, Polymer Processing Fundamentals, Hanser Verlag
M. D. Lechner, K. Hehrke, E. H. Nordmeier, Makromolekulare Chemie, Birkhäuser Verlag
B. Tieke, Makromolekulare Chemie, VCH Verlag
M. Brahm, Polymerchemie kompakt, Hirzel Verlag
J. Hoinkis, E. Lindner, Chemie für Ingenieure, Wiley-VCH Verlag
Monomer Polymer compound Plastic final productpoly-reaction adding/mixing shaping
Thermal and mechanical impact
compoundingsynthesis
Polymer Recycling
Processing of Polymers
1. Introduction to Polymers
2. Thermal behaviour3. Mechanical behaviour
4. Extrusion5. Mixing
6. Injection molding
7. Secondary Shaping8. Other Important Polymer Processes
(Calendering, Coating, Foaming)
Historical Evolution of Polymer Processing
taken from „principles of polymer processing“
Monomer: Smallest molecule(s), a polymer can be synthesized from
Polyreaction: Chemical transformation in which monomers are transformed into polymers
Repeat unit: Smallest entity, with which the stoichiometry of a polymer can be described,
just by multiplication (sometimes inconsistent: PE).
Oligomer: (oligos – some, meros – part) Molecule consisting of several repeat units. If one
repeat unit is added, the property under focus changes measurably.
Polymer: (polys – much, meros – part) Molecule consisting of manyrepeat units. If one repeat unit is added, the property under focus does not change.
Degree of polymerization: Pn = Mpolymer/Mrepeat unit
Polymer compound: a mixture of polymers composed of the same repeat unit, but with different
degree of polymerization.
Polymer blend: a mixture of polymer compounds, in which the different compounds are
composed of different repeat units.
Co-Polymer: Polymer consisting of more than one type of repeat unit
Additives: External non-polymer materials, added to the polymer compound to improve its
properties
Plastics = Polymer compound or blend + Additive(s)
Polymer processing: engineering activity concerned with operations carried out on
polymeric materials to enhance their utility.
Introduction into Polymer Chemistry: Definition of some terms
Classification of Monomers
Bifunctional acyclic:
Terephthalic acid
Adipinic acid
Phosgene
Glycole
Bisphenol A
Hexamethylene diamine
Hexamethylene diisocyanate
Monofunctional cyclic:
ε-Caprolactame
Laurin lactone
Ethylene oxide
Cyclooctene
Monofunctional acyclic
(multiple bond):
Ethylene
Styrene
Tetrafluor ethylene
Vinyl chloride
Methyl metacrylate
(butadiene)
(isoprene)
COOHHOOC
HOOC
COOH
Cl
O
Cl
HO
OH
HO OH
NH2
H2N
NCO
OCN
O
NH
O
O
O
H
H
H
H
HH
H
F
F
F
F
H
Cl
H
H
CH3
COOCH3
H
H
Classification of Polyreactions
Polyreaction
monofunctional monomerbifunctional monomer
Chain-growth reaction:growing chain reacts only with monomer
step-growth reaction:all components in the system react simultaneously
Poly-condensation
Poly-addition
Poly-recombination
Poly-elimination
Poly-merization
anionic radical cationic insertion group-transfer
Averaged degree of polymerization in dependence of the conversion:
a) step-growth reaction
b) chain-growth reaction without chain termination reaction (living polymerization)
c) chain-growth reation with chain termination raction
Structure of Polymers
repeat unit
polymer (intra-chain)
polymer compound (inter-chain)
Isomerism in Chemistry
Isomerism(same stoichiometry, different structure)
stereo isomers(same type of bonds, different orientation)
constitution isomers(different types of bonds)
configurational isomers(superimposition only with bond cleavage)
conformational isomers(superimposition by rotation about bond)
syn-periplanar
syn-clinal
anti-clinal
anti-periplanar
polymerizationisomers
(CH2)5 (CH2)6
sequenceisomers
chiral isomers
enantiomers(mirror images)
diastereomers
A
B DC
A
BDC
RR
R
RR R
R
R
geometric isomers
Structure of Polymers
repeat unit
polymer (intra-chain)
polymer compound (inter-chain)
Structure of Polymer Compounds (repeat unit)
H H
H H
n
conformationalisomers PE
H
H RR
HHR
H HR
HHH
R
H
R
HHR
H
H
R
HH
H H
H CH3
n
configurationisomers PP
H H
H CH3
n
H H
H3C H
n
n
geometricisomers IR n
(
)n
n
constitutionisomers BR n
n
1,4-BR 1,2-BR
Structure of Polymers
repeat unit
polymer (intra-chain)
polymer compound (inter-chain)
Structure of Polymer Compounds (polymer I)
H H
H H
n
conformationalisomers PE
H
R
H
R
HH
H
R HR
HH
R
H HR
HH
R
H
H
R
HHH
H
R
R
HH H
R
H
R
HH
H
H RR
HH
α
L0
L = n L0 sin(α/2)
<r2>0 = n L0
2 (1-cos(α))
(1+cos(α))
(1+cos(β))
(1-cos(β))
α: bond angleβ: averaged torsional angle
σ: empirical steric factor
<r2>0 = n L0
2 (1-cos(α))
(1+cos(α))σ2
σ(PE) = 1.85
σ(PS)at = 2.2σ(PMMA)at = 1.9σ(PMMA)i = 2.2
σ(PMMA)syn = 1.9σ(PP)a = 1.7σ(PP)i = 1.6σ(PP)syn = 1.8
i: isotacticat: aticticsyn: syndiotactic
coiling takes relaxation timeRandom coil
Structure of Polymer Compounds (polymer II)
H H
H CH3
n
configurationisomers PP
H H
H CH3
n
H H
H3C H
n
isotactic
syndiotactic
atacitc
hem-isotactic
block-isotactic
Tm = 176 °C
Tm = 165 °C
Tm = 120-176 °C
Tm: melting temperature
Structure of Polymer Compounds (polymer III)
n
constitutionisomers PP
n n
CH3CH3
CH3
head to head tail to tail
Structure of Polymer Compounds (polymer IV)
constitutionisomers
n n nPE
HDPE ρ = 0.94-0.96 g/mLTg = 127-135 °C
LLDPE ρ = 0.93-0.94 g/mLTg = 123 °C
LDPE ρ = 0.91-0.93 g/mLTg = 105-115 °C
Tg: Glas temperature
Structure of Polymers
repeat unit
polymer (intra-chain)
polymer compound (inter-chain)
Structure of Polymer Compounds (polymer compound)
Polymerization „isomers“
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 100 200 300 400 500 600 700 800
degree of polymerization
Mo
lecu
lar
Weig
ht
Mn
Mw Mn
Mw= 2 -
1
Pn
Most probable distribution (Schulz/Flory)
Mn = Σ ni Mi / Σ ni
Mw = Σ ni Mi2 / Σ ni Mi
σ2 = Σ ni (Mi-Mn)2 / Σ ni = Mn (Mw - Mn) σ: standard deviation of distribution
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 100 200 300 400 500 600 700 800
degree of polymerization
Mole
cula
r w
eig
ht
Poisson distribution (living polymerization)
Mn
Mw= 1 +
1
Pn
Mn Mw
Thermal behaviour of polymers
Thermal Behaviour of Polymer compounds
Tm Tc
melt
Tg
dQ
dt
Tg
Viscous solid
solid (amorphous or semicristalline)
Tc
Viscous solid
Tm
meltViscous solid/semicrystalline
Viscous solid/semicrystalline
∆Hm
∆Hcrys
amorphous orsemicrystalline
solid
viscoussemicrystalline
solid
melt depolymerizationdecomposition
glass transition partial crystallization melting depolymerization
endo-therm
exo-therm
Tcrys
S R
∆T = 0
Q
QS
dQ
dt= const.
QR
Differential Scanning Calorimetry
Thermal Behaviour of Polymer compounds
Tg: torsional rotation in the amorphous regions becomes excessable• no phase transition• heat capacity Cp increases (entropic effect, rather enthalpic)• density of polymer decreases above Tg (larger free volume)• value is dependent on the heating/cooling rateTg
0: Tg measured with cooling rate of 10-5 °C/s
V0: mass-filled volume in the Polymer
Vf: empty volume in the polymer
V
Thermal Behaviour of Polymer compounds
Tg(P) = Tg0 - K P-1
For linear chains Tg increases with increasing degree of polymerization
Thermal Behaviour of Polymer compounds
Tg decreases with increasing amount of added plasticizer
The plasticizer serves as a poor solvent for the polymer compound
xW: molar fraction of added plasticizer
Thermal Behaviour of Polymer compounds
In statistical co-polymers Tg can be settled between Tg1 and Tg2 of the two
homo-polymers by the molar composition of the co-polymer
TgPAN: 60 °C
TgBR: -60 °C
Tgco-polymer: xAN Tg
PAN + (1-xAN) TgBR
xAN: molar fraction of acrylonitrile in the co-polymer
Thermal Behaviour of Polymer compounds
In homo-polymers there exists a relation between Tg and Tm:
Tg ≈ ⅔ Tm
Thermal Behaviour of Polymer compounds
Increment calculation of Tg0:
Tg0 = Σ Yi/ Σ Mi
184,272000Ph-S-Ph
180,284000Ph-CO-Ph
108,137400O-Ph-O
5920000O-CO-NH
6020000O-CO-O
82,922000CCl2
48,519400CHCl
3212400CHF
90,136100CH(Ph)
96,241300CH(cyclohexyl)
56,119900CH(iPr)
288000CH(CH3)
142700CH2
[g/mol][g K/mol]
Mi
Yi
Structure unit i
• Polar substituents increase Tg
• sterically flexible substituents increase Tg
• cross-linking increases Tg
• large energy barriers for torsional rotation
increase Tg
188cis-1,4-BR
373PS
323Nylon 66
424PEK
250PP
360PVC
Tg
0 [K]Polymer
Crystallinity in Polymer compounds
Molten polymer compound Solid state (semi-crystalline) Solid state (fiber, oriented)
Diffractogram of a
semicrystalline
polymer compound
amorphous semi-crystalline semi-crystalline
oriented
Chain length: 10-5 m
Interactions between polymer molecules:
•Van der Waals
•Dipole/Dipole
•Hydrogen bonds
•No chemical bonds (crosslinking)
Crystallinity depends on prior thermo-mechanical treatment of the polymer compound
Fib
er
direction
Thermal Behaviour of Polymer compounds
Tm is dependent on the heating and cooling rate, because the
reorientation of the polymer chains takes time.
Tm0 is defined as that temperature when Tm = Tcrys and Pn = ∞
It holds: Tcrys ≤ Tm ≤ Tm0
meltViscous solid/semicrystalline
Tm
Thermal Behaviour of Polymer compounds
1/Tm(P) = 1/Tm0 + (2 R/∆Hm) P-1
PE
For linear polymer chains the end groups serve as „impurities“
lowering the melting point.
meltViscous solid/semicrystalline
Tm
Thermal Behaviour of Polymer compounds
Increment calculation of Tm0:
Tm0 = Σ Yi/ Σ Mi
Tm = ∆Hm/∆Sm
• Polarizable substituents increase Tm (∆H)
• Polar substituents increase Tm (∆H)
• Opportunity for hydrogen bonds increases Tm (∆H)
• Uniformity increases Tm (∆H, ∆S)
• Rigidity in the back bone increases Tm (∆S)
1518000NH
1613500O
48,527500CHCl
3217400CHF
90,148000CH(Ph)
56,135300CH(iPr)
2813000CH(CH3)
146000CH2
[g/mol][g K/mol]
Mi
Yi
Structure unit i
450PS
459PP
415PEK
Tm
0 [K]Polymer meltViscous solid/semicrystalline
Tm
Thermal Behaviour of Polymer compounds
Depolymerization:
COOMe COOMe COOMe
Tc = 60°C
COOMe COOMe COOMe
∆Hp, ∆Sp
Tc = ∆Hp/∆Sp
Since ∆Sp is negative, ∆Hp must be exothermic for a polymerization,
to be thermodynamically feasable (∆Gp<0).As a consequence there exists a temperature Tc (ceiling temperature),
starting from which depolymerization is thermodynamically favored for
entropic reasons.
melt
Tc
Cross-linking in Polymer compounds
EPDM
S8 S1.6 H2S + S5.4
hot vulcanisation
Chemical bonding between the polymer molecules
1,4-BR
Thermoplast Elastoplast Elastomer ThermosetFluidoplast
viscous solid
fluid
no glass transitionTgTgTg
fluid
no melt transition
Viscous solid
TmTm
solid (amorphous or semicristalline)
solid(cristalline block domains)
solid solid
no melt transition
meltmelt
elastomer elastomer solid
solidelastomer
TF
TCTCTC
TF: fluid temperature, Tg: glass temperature, Tm: melt temperature, Tc:ceiling temperature, TD: decomposition temperature
TD TD
no melt transition
Chain fixation increases
Tem
peratu
rein
creases
Room
temp.
fluidoplast/thermoplastlow gas permeabilityisobutenepolyisobutylenePIB
fluidoplast/elastomerlow temperature elastomerdimethylchlorosilanepolydimethylsilanePDMS
duroplasturea, formaldehydeUrea/formaldehyde resinUF
duroplastmelamin, formaldeyhdemelamin/formaldehyde resinMF
thermoplast/fiberprecursor to carbon fibersacrylic nitrilePolyacrylnitrilePAN
duroplastmotor housings, telephonesphenol, formaldehydephenol/formaldehyde-resin, BakelitePF
thermoplastClothes1,6-adipodiamine, adipinic acidpolyamide 66PA 66
thermoplastFormaldehydePolyoxomethylenePOM
thermoplasttoys, garden equipmentacrylnitrile, butadiene, styreneacrylnitrile, butadiene, styreneABS
thermoplastCDs, DVDs, unbreakable bottlesbisphenol A, phosgenepolycarbonate, MakrolonPC
thermoplastDiversevinylchloridepolyvinyl chloridePVC
elastomer after vulcanisationtires and tubesisopreneisoprene rubber, natural rubberIR
elastomer after vulcanisationsolvent-resistent rubber, glovesacrylic nitrile, butadienenitrile/butadiene rubberNBR
elastomer after vulcanisationtires and tubesbutadienebutadiene rubberBR
styrene, acrylic nitrilestyrene/acrylnitrile co-polymerSAN
thermoplastbottles, clothesglycole, phthalic acidpolyethyleneterephthalatePET
thermoplastbullet-proved jacketsphthalic acid chloride, phthalic aminepoly(para-phenylene-amide), KevlarPPTA
thermoplast/duroplasthigh-temperature resistencetetrafluoroethenepoly(tretafluoroethene)PTFE
thermoplastLenses, „plexi glass“methyl metacrylatepoly(methylmetacrylate)PMMA
thermoplast/elastoplastheat-resistentpropenepolypropylenePP
thermoplastfoilsethene, 1-octadecenelinear low-density-polyethyleneLLDPE
thermoplasttransport containeretheneHigh-density-polyethyleneHDPE
thermoplastfoilsetheneLow-densitiy-polyethyleneLDPE
elastomeraging-resistentethene, propene, 1,5-hexadieneethylene/propylene/diene-monomersEPDM
elastomer after vulcanisationtires and tubesstyrene, butadienestyrene/butadiene rubberSBR
thermal classificationapplicationmonomer(s)nameabbriv.
Some important polymers
styrene
butadiene ethene propene 1,5-hexadiene
1-octadecene
COOMemethyl-metacrylate
FF
F F
tetrafluoroethene
COClClOC phthalic acid chloride
COOHHOOC phthalic acid
NH2H2N phthalic amine
HOOH
glycole
CNacrylic nitril
isoprene
Cl
vinyl chloride
OHHO
Bisphenol-A
Cl
O
Cl
phosgene
O
HH
formaldehyde
N
N
N
NH2
NH2H2N
melamin
H2N NH2
O
urea
isobutylene
Me Si
Cl
Cl
Me
dimethylsilylchloride
Some important monomers
Some important polymers
PE (polyethylene)
COOMe COOMe COOMe COOMe COOMe COOMe COOMe
PP (polypropylene)
PMMA (polymethylmetacrylate)
PTFE (polytetrafluorethylene)
F F
F F
F F
F F
F F
F F
F F
F F
F F
F F
F F
O
HN
O
NH
HNO
PPTA (poly(para-phenylene-amide)
O
O
O
O
O
O
O
O
PET (polyethyleneterephthalate)
O
O
O OO
O
Makrolon
O O O O O O O O O O
POM (poly-oxymethylene)
OSi
OSi
OSi
OSi
OSi
OSi
OSi
OSi
OSi
PDMS (polydimethylsiloxan)
PIB (polyisobutylene)
Economic importance
90%
Plastics-
production in
dependence of
time
Further Modification of Polymer Compounds
Polymer Compound
chemical modificationphysical modification
-polymer-analogousreactions
-chemical blowing
mixing
Additives:-Plastizers-Flame retardants-Stabilizers-Fillers-Blowing agents
other Polymers:Polymer blends
shaping
post-reactor phase
preperation forprocessing
processing phase
Additives
Plasticizers Stabilizers Fillers Antistaticagents
Blowingagents
thermal light mechanic active inactive
flameretardant
heat
atmosphere
oxygen moisture
FibersUV-absorbers
Anti-oxidants
hydro-phobics
Lead-organyls
extenders:fill volume lower the price
color pigmentsanti-shrinkingself-healing
-act as "poor solvent" forthe polymer-decrease the operatingtemperature for shaping
absorbe heat by de-composing into less-reactive products
internal extinguishers:Al(OH)3 H2OXBrn n BrXPn "PO"coating
Mechanical behaviour of polymers
Mechanical Behaviour of Polymer compounds
(energy-elastic) (visco-elastic) (viscous)
solid liquidthermoplast
Newton-Modell:
σ = ηdεdt
Hook-Modell:
σ = E ε
Voigt-Modell:
ε = ε1 = ε2
σ = σ1 + σ2
Maxwell-Modell:
σ = σ1 = σ2ε = ε1 + ε2
0
0,2
0,4
0,6
0,8
1
1,2
0 50 100 150 200 250 300 350 400 450
time
ten
sio
n σσ σσ solid
thermoplast
liquid
0
0,2
0,4
0,6
0,8
1
1,2
0 50 100 150 200 250 300 350 400 450
time
elo
ng
ati
on
εε εε
solid
thermoplast
liquid
0
0,2
0,4
0,6
0,8
1
1,2
0 50 100 150 200 250 300 350 400 450
time
ten
sio
n σσ σσ solid
thermoplast
liquid
0
0,2
0,4
0,6
0,8
1
1,2
1,4
0 50 100 150 200 250 300 350 400 450
time
elo
ng
ati
on
εε εε
solid
thermoplast
liquid
Elastomere
σ
α
L0
L = n L0 sin(α/2)
Reforming driving force:multiple microstates of random coil
(solely entropic!)
Mechanical Behaviour of Polymer compoundsT
ensi
on σ
Rel. Elongation ε
oriented
(a)
(b)(c)
(d)
(e)
Stabilization of polymer compounds towards tension by orienting streching
Tg Tm
Mechanical Behaviour of Polymer compounds
elastomer
melt
Log(E
/(N
m-2
))
elastomer
HookVoigt-
Maxwell
Newton-
like ?!
elongation in %
Non-Newtonian behaviour in polymeric melts
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
2
0 2 4 6 8 10 12 14 16 18 20
shear rate dεεεε/dt
vis
co
sit
y ηη ηη
Newtonian behaviour
Polymer compound
shear rate ε
relaxation rate 1/λ
Deborah number De =chain relaxation time
processing time=
λtP
= λ ε
De << 1 De = 1 De >> 1
σ = ηdεdt
= η εNewtonian:
σ = ηdεdt
= η ε
Polymer:
σ = η(ε) ε = m(T) ε n, 0 < n < 1
for De << 1
for De ≈ 1 m(T) = m0 e-a (T-T0)
Shear thinning effect!
Non-Newtonian behaviour in polymeric melts
L
R
p1
p2
∆p = p1 - p2
flow Q
Newtonian flow field: Polymer compound flow field:
vz(r) =∆p
4 L η R2 - r
2vz(r) =
∆p
4 L mR
1+1/n - r
1+1/n1
1 + 1/n
1/n
σ = ηdεdt
= η ε σ = η(ε) ε = m ε n, 0 < n < 1
-1774600
-1574600
-1374600
-1174600
-974600
-774600
-574600
-374600
-174600-1333 -833 -333 167 667 1167
radius r
vz(
r)
-738000
-638000
-538000
-438000
-338000
-238000
-138000
-38000-848 -648 -448 -248 -48 152 352 552 752
radius r
vz(
r)
Reduction during extrusion Swell during extrusion
Q =π R4
8 L η∆P Q =
π R3
1/n +3 ∆P
2 m L
1/nR 1/n
vz(r)
Hagen-Poisseuille
Classification of Polymer Processing
Classification of Polymer Processing
1. Die forming (fiber, film, sheet, tube, wire)
2. Calendering and coating (knife, roll)
3. Mold coating (powder, rotation)
4. Molding and casting (injection, transfer, react. inj.)
5. Strech shaping (thermoforming, blowmolding)
continuous
cyclic
The Extruder
The Navier-Stokes equation (incompressible fluids)
dv
dtρ = P + η ∆v + ρ g
acceleration of fluid
externalpressure
internalpressure
gravitationalpressure
The velocity field of an extruder
x
y
zux
y/h
0
uz 0
x/W
= P + η ∆v
externalpressure
internalpressure
0
The Extruder
Brinkmann number:
Br =
=
Viscous dissipation
Heat transport
η V02
k (Ta - Tb)
Solid bed profile
The Extruder
The die design
Rules of thumb:• avoid thick sections
• minimize the number of hollow sections
• generate profiles with constant wall thickniss.
The Extruder
The coat hanger die (films, sheets, foils)
W
xα
R
extrudate extrudate
R(x) =(3 + s)/π * h
2n+1 (W-x)
n
2n (s + 2)
n * sin(α)
1/(3n + 1)
for uniform flow in the land
(s = 1/n)
(shear thinning effect)
diebarrel with screw
Characteristic curve of an extruder
die shape
m.
∆p
open
discharge
closed
discharge
N, H
2 N, H.. N: screw rate
H: channel depth of screw
.N, 2 H.
Non-Newtonian flow
Newtonian flow
m = ∆Pk
m = k' ∆P1/n
∆ps ∆pd
m.
HWDB
Ls LD
RD
Characteristic curve of an extruder
die shape
Mixing of polymers
Mixing of polymers
Compatibility of polymers
16666666666LDPE
1
LDPE
16665666666HDPE
1666666666PP
161563266PVC
15665666POM
1161144PMMA
162256PC
16645PA
1166ABS
166SAN
16HIPS
1PS
HDPEPPPVCPOMPMMAPCPAABSSANHIPSPS
1 = very compatible, 6 = incompatible
Hildebrand-parameters
∆Hmix = Vges x1 x2 (δ1 - δ2)2
Two polymers mix with each other if ∆δ ≤ 0.1(cal cm-3)½
(J cm-3)0.5
Polyethylene 15,8-17,1
Polystyrene 16,8-18,8
Poly(methylmetacrylate) 16,0-16,6
Polypropylene 17,4-19,0
Poly(vinylchloride) 19,2-22,1
Nylon 66 25,8-29,1
Polyacrylonitrile 25,6-31,5
Poly(propylenoxid) 15,4-20,3
δ2 = ρ Σ Fi/Mi
structure unit Fi Mi
-CH3 303 15
-CH2- 269 14
C(quart) 65,5 12
-CH(CH3)- 479 28
-C(CH3)2- 672 42
-CH=CH- 497 26
-OH 462 17
-O- 235 16
-CO- 538 28
-COOH 1000 45
-COO- 668 44
Mixing of polymers
Mixing mechanisms
Distributive mixing Dispersive mixing
Distributive mixing
Dispersive mixing
notmixed
well-mixeddispersively and
distributivelymixing = tension + reorientation
Mixing of polymers
distributive dispersive
Mixing of polymers
Flow number: λ =
Capillary number: Ca = Deviatoric stress
Surface tension=
τ Rσs
γγ + ω
..
Mixing devices
Mixing devices
Injection molding
Injection molding
A
B
C
D
A
B
C‘/C
D
C‘
A
BC‘C
5. S
crew
back
(ch
eck
valv
eopen)
Injection molding
Injection molding
Injection blow molding
Extrusion blow moldingParison programming
by die-temperature as function of t
by die opening as function of t
by screw rate as function of t
Film blowing
Biaxial stretching!
Film blowing
Blow-up ratio:
BR =
draw ration:
DR =
ratio of film thickness:
h0/hf = DR BR
Rf
R0
vf
v0
Rotational molding
Thermoforming
plug-
assisted
vacuum
Calendering
Calendering
Calendering
The velocity field of a calender
R
h0 h1
x
y
h0 h1h-1
h2h2
N
vx(y) = 2 πNR + y2 - h2
h12
1 -h1
h
h1
h
23
2
h = h0 + R - √R2 - x2
dP
dx= η
d2vx
dy2
Calendering
n: viscosity-power-law index
Ribbing in roll coating
Ca = η N
σsN: roll rate
Fiber-spinning
Fiber-spinning
Take-up
Final take-up
Heater:Stretching/molecularorientation
Extruder
Spinneret
Fiber-spinning
Fiber-spinning
DR = vz/v0 De = 3(n-1)/2 (m/G) (v0/L)
viscosity η = m ε(n-1).
Thermosets/Reactive molding
Thermosets/Reactive molding
curing byheatmixinglightmoisture
hv
Welding
thermal friction