mer e Netzwerke: ktur, Theorie und Anwendung - ipfdd.de · zeigen dyna sehr großen h einen einzig...
Transcript of mer e Netzwerke: ktur, Theorie und Anwendung - ipfdd.de · zeigen dyna sehr großen h einen einzig...
PolyStru
48
Prof. Dr. Jens
Sommer
Tel.: 0351 465
sommer@ipfd
Prof. Dr. Gert
Tel.: 0351 465
gheinrich@ipf
ymeruktur
s-Uwe
58-750
dd.de
Heinrich
58-360
fdd.de
re Ner, The
Durch die VeFlüssigkeitseFestkörpereLösungsmittneue Klasse durch die Veentsteht, ermUntersuchunthermodynaminsbesonderSolche „OlymSimulation ezunehmendeüberraschender nicht-affwelche durchsich räumlic(Phys. Rev. LArbeiten liefeVerständnis chemisch vePolymernetzfunktionalenEigenschafteMagnetfeldeTheoretischeder Verteilundie magnetoKopplungsei(2014)). VerneEigenschafteZeitbereich, universellen können. Durdie Spektraldwelcher versunterschiedlist es gelungdynamischenPolymernetzder Zeit zu b4813 (2014)). Die Arbeiten Bereich des zwei Preise: anlässlich dedem Young Sdas hohe Inteseinen Ergebder dehnungNaturkautscDissertation Elastomer-NRooj den FörKautschuk-G
etzweeorie
ernetzung voneigenschaftenigenschaften telbeständigkevon Netzwerkrhakung von R
möglicht die gng der Rolle dmischen Eigee die Quellun
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Lett. 112, 23800ern auch eineder Rolle der rnetze Gele. S
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e Untersuchunng und der Pr-elastischen genschaften (etze Polymereen über einen die nicht durc Prozess bescch einen Multdichte der Relschiedene dynlichen Zeitbergen das Verhan Moduls für uzwerke über 14eschreiben (M
im anwendunST3 erfuhren Dr. Karsten B
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Brüning wurdexpo 2014 in Körd ausgezeicheifenindustrieufklärung derKristallisationegelt. Für seiniet der funktiote erhielt Dr. SDeutschen Die experimen
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Das Gebiet funNanokompositPublikationen wEvidence for ahase in ionic e4(2014) 3463),hospholipids
n carbon nanoomposites” (PUnmodified Lnd the develolastomer comechnol. 87(20
ung
ung elastomees Work-Shope Charakterisie5 Teilnehmern
die hohe Anweer Arbeiten imktioneller Elae wurde durcweiter ausgeban in situ deveelastomers” (, „The role of in the rubber-
otube filled naPolymer 55(20DH as reinforpment of flam
mposites” (Rub14) 606).
erer Werkstoffps „Nicht-erung von Gun vorwiegend
endungsrelevam ST3 unterstrastomer-h eine Reihe vbaut, z. B. eloped polyme(Macromoleculinked -filler-interac
atural rubber 014) 4738) undrcing filler for me-retardant bber Chem.
fe war
mmi“, aus
anz reicht.
von
er ules
ction
XNBR
PolyStru
The swellin Michael Lanand Jens-Uw Olympic gelpolymers (“topological Fig. 1, with texclusively by the linkin
Fig. 1:
Top left: sketch
desinterspersi
The scaling of t
function of the
polymer volum
line indicates a
unscaled data.
This particupolymer netmaterials athe pristine thermodynaaccessible. reveal the requilibrium which is an physics. Sincoined by dechallenge tobeen maste
ymeruktur
ng of olympic
ng, Jakob Fiscwe Sommer
ls [1, 2] are nerings”) conneinclusion of ptheir elastic pon the entang
ng of the rings
h of an Olympic g
ion of non-concat
the equilibrium d
degree of polym
me fraction at pre
a scaling accordin
ular differencetworks and gen interesting effect of enta
amic propertieIn particular, ole of entangl swelling of poutstanding p
nce the term Oe Gennes [1], ho synthesize s
ered yet, altho
re Ner, The
gels
cher, Marco W
tworks made ected by the molymer strandroperties dep
glements that s.
gel. Top right:
tenated strands.
degree of swellin
erization, N, and
paration conditio
ng to Q ∝ N-0.28φ0-0
e to conventioels makes themodel system
anglements ones of polymersuch gels cou
lements for tholymer netwo
problem in poOlympic gels hhowever, the such materialsugh possible
etzweeorie
Werner,
of cyclic mutual
ds, see pending
are fixed
Bottom:
g as
the
ons, φ0. The 0.72. Inset:
nal ese m, since n the s is uld he orks, lymer
has been
s has not
ppRctstOaosplipwnTboacceppsaopo
wdfp
Tt
wmsmlc
erke:e und
pathways for tproposed [2,3Recently [4], wcomputer simtheir topologicswelling in anthat the equiliOlympic gels ias function of of the rings, sstandard modpredict an inclarger N. We sis a direct conprocess originwhich allows no elastic defoThe key to undbehavior is thoverlapping riapproximatelyconcatenationconcatenated equilibrium swpairs of rings preparation coswelling. Sincand the numbon N and the ppreparation coof an Olympic
Q ∝ N
with the samedifferent scalifor a fully affinpolymer netw
Q ∝ N
The good agrethat fits best t
Q ∝ N
with equation model describswelling of Olymore striking larger equilibcorrelated wit
Anw
their synthesi]. we constructe
mulations in orcal state and t a-thermal soibrium degreeis described bthe degree ofee Figure 1, in
dels of networreasing degreshowed in Ref
nsequence of anally proposedpolymer ringsormation. derstand this e observationings in the swy the same asns per ring. Th
rings remainwelling, whilethat were oveonditions des
ce the degree ber of overlapppolymer volumonditions, φ0, gel could be
N - 0.19 φ0
- 0.75,
e parameters ing as the textne swelling of
work,
N 0.57 φ0
- 0.25.
eement of ourto
N - 0.28 φ0
- 0.72
(1) is a first inbes the main fympic gels. A result is that
rium degree oth a larger no
wendu
s have been
ed Olympic gerder to characto simulate isolvent. We foue of swelling, by a negative pf polymerizatin marked conrk swelling [5]ee of swelling f. [4] that this a desintersped by Bastide [6s to swell in p
unusual swel that the num
wollen state is s the number ohus, only in overlap at non-concate
erlapping at intersperse dof concatenatping rings depme fraction atswelling equiexpressed [4]
(1)
but at a cleart-book estimaf a convention
(2)
r simulation d
(3)
ndication, thatfeatures of thesecond, prob for Olympic gof swelling mun-affine contr
ung
ls by cterize sotropic und Q, of power on, N, trast to that for result rsion 6], art at
lling mber of
of
nated
uring tion pend t librium ] by
rly ate [5] nal
ata,
t our e
bably gels, a ust be ri-
Keywords
olympic gel
desinterspersio
non-affine swel
Monte-Carlo sim
49
on
lling
mulation
PolyStru
50
Keywords
in-situ synthe
polyurethane
nitrile butadie
self-compatib
structural/me
characterizati
ymeruktur
esis
-urea
ene rubber
bilization
echanical
ion
re Ner, The
bution to sweconfirmed byThe results opotential to rthe equilibriuconventionaltime it was pcontribution swelling. Curfocus on the conventionalnon-affine coknown since theoretical d Sponsor: Deutsche FoProjekt LA 27 [1] P. G. De
PolymerIthaca (1
[2] E. RaphaJ.Stat.P
[3] G. T. Pic(2006).
[4] M. LangSomme2380001
[5] M. RubinOxford U
[6] J. BastidJ.Macro
etzweeorie
elling. This tey our simulatiof our study [4revolutionize oum degree of l polymer netw
possible to estto the equilibrrent investigtransfer of th
l networks in ontributions to decades [6],
description.
rschungsgem735/2-1
Gennes, Scalr Physics, Cor1979). ael, C. Gay, P.hys. 89, 111-11
ckett, Europhy
, J. Fischer, Mr, Phys. Rev. L. nstein, R. ColbUniversity Prede, C. Picot, S
omol.Sci.Phys
erke:e und
ndency was aon results.
4] have enormour understanswelling of
works: for thetimate the nonrium degree oations, theref
hese results toorder to quano swelling, whbut still lack a
meinschaft,
ling Concepts rnell Universit
G. de Gennes8 (1997).
ys.Lett. 76, 616
M. Werner, J.-Lett. 112 (2014
by, Polymer Pess, Oxford, UK. Candau, . B19, 13 (1981)
Anw
lso
mous nding of
e first n-affine of ore, o
ntify hich are a
in ty Press,
s,
6-622
-U. )
Physics, K (2003).
).
Npp
MLW
PeptocdmcinlomhuinthuutereInmepthsT(Psyd(NSeateN
Fi
Sc
st
fo
wendu
Nitrile butadieolyurethane-roperties
Muhammad TaLandwehr, KlaWießner, Gert
Polyurethane-ngineering mrofile of supeo the range ofonstituents (diamines) and
morphologies. haracteristicsncorporated inogies to obtain
materials. Howave been reporeas with rub
ntensive solvehe reported rerea blends shrethane-ureaemperatures einforcing to sn the present
method is inveffectively the olyurethane-uhe heat build-oftening of poo follow this mPUU) with higynthesized inuring blendinNBR) in an intubsequently, xtracted fromddition polymerminated pre
NMR spectrosc
ig. 1:
cheme of reactive
tructure of NBR a
or the in situ PUU
ung
ene rubber/in-urea blends w
ahir, Regine Bus Werner StHeinrich
ureas are higaterials that hrior mechanicf available chadiisocynataes,unique heteroThe distingui
s of polyurethan rubbers by bn advanced mwever, only a forted on blendbers by a time
ent-blending mesults of rubbhow that the da phase gets sand its effect softening. work, a simplstigated to incuseful characureas in rubbe-up concerns dolyurethane-umethod, polyuh content of h-situ via a preg with nitrile ernal mixer [1the PUU phas
m blends to chamerization of is
epolymer withcopy.
e blending metho
and the reative pr
.
-situ synthes with improve
Boldt, Maria Auöckelhuber, S
h performanchave distinguical propertiesaracteristic polyols and ophase structshed mechanane-ureas cablending methulticomponen
few investigatding polyurethe and energy method. In addber/ polyureth
ispersed polyoften at high transforms fr
le reactive blecorporate cteristics of ers and to adddue to the rea phase (Fi
urethane-ureahard segmentsepolymer routbutadiene rub1, 2]. se is solvent-aracterize the
socyanate-h diamine by 1H
odology showing
repolymer and di
sized d
uf der Sven
ce shed
s due
tural nical n be hodo-nt ions hane-
dition, ane-
y-
rom
ending
dress
g. 1). a s is e bber
e
H
amine
PolyStru
After structcompoundemixing mill compressiothe stress-swhich reflecreinforcemein-situ synth
0 500
1
2
3
4
5
6
Str
ess
(M
Pa)
Fig. 2:
Stress-Strain c
profile of NBR
The elastic increase anwith the loacharacterizeNBR/PUU bblends, as omechanicaldemonstratheight of losin the storatransition replateau reg180°C. Scanning Elenergy dispEDX) investioxygen-richdispersed in
ymeruktur
ural verificatied with curativ
to get blend von moulding. Fstrain curves cts concentraent of nitrile bhesized PUU.
100 150 200
NBR/P
Str
curves showing im
upon incrementa
modulus and d elongation ading of stiff Pes self-compa
blend system. observed from behavior of be a progressivss factor and ge modulus thegion towardsion at high tem
lectron Microsersive X-ray sigation of blen
h distinguishedn continuous N
re Ner, The
on, blends areves on a two-rvulcanizates bFig. 2 demonsof blend vulcation dependen
butadiene rub
250 300 35
UU 70/30
NBR/PUU 80/20
NBR/PUU 90/
rain (%)
mprovement in th
al loading with PU
tensile strengat break decreUU phase, whatibilization ofThe reinforce
m the dynamic blend vulcanizve drop in thea correspondhrough the NBs a stable rubbmperatures u
scopy coupledspectroscopic nd vulcanizated PUU domainNBR matrix (F
etzweeorie
e roll by trates
anizates, nt ber by
50 400 450
/10 NBR
he tensile
UU.
gth eases
hich f ed ates,
e peak ing rise BR bery pto
d with (SEM-
es shows ns Fig. 3).
Isdcrmpimspaai
CDMH
[
erke:e und
In-situ synthestrong interfadelamination cryogenic fracroughness of mechanical inphases and eximprovement mechanical chsystem. The ppossess new pand are cost-eapplications liimpellers, ind
Co-operation:Dr. Nasir MahMartin-LutherHalle (Saale),
[1] M. Tahir, G. HeinricPatent ApEuropeanEP2014/0
[2] M. Tahir, MahmoodMacromo10.1002/m
Anw
esized PUU docial adhesionfrom continuo
cturing. In adinterfacial bo
nterlocking bexplains the unin the mecha
haracteristicsprepared blenprofile of attraeffective mateike rubber rol
dustrial wheel
hmood, Institur-Universität Germany
N. Mahmoodch, A. Das, R. pplication DE n Patent Appli68245 K. W. Stöckel
d, H. Komber,ol. Mater. Engmame.2014002
PUU
NBR
wendu
mains develo, which preveous NBR phasdition, the undary promo
etween two disnprecedented nical and dyn
s of NBR/PUU d vulcanizatesactive properterials for llers, belting, s etc.
ut für Chemie,Halle Wittenb
, K.W. StöckelJurk, German102013217661.cation
lhuber, N. G. Heinrich: . (2014), DOI:
298.
ung
p nts its se on
otes stinct
amic-blend
s ties
pump
berg,
lhuber, n 9 &
S
w
Fig. 3:
SEM-EDX microg
with elemental o
mapping shows o
rich PUU domain
dispersed in NBR
51
graphs
xygen
oxygen-
s (blue)
R matrix.
PolyStru
52
Keywords
soft magnetic
magneto-indu
deformation
controllable s
modelling
ymeruktur
c elastomers
uced
stiffness
re Ner, The
Mechanical pelastomers:mechanics aapproaches Dmytro IvaneMarina Saph Magneto-sento a class of to change eaapplied magMSEs very pesensors, robother industr MSEs consisparticles diselastomeric magnetic promagnetizatiopreparation. with isotropidistribution owith anisotroexternal magthe melt befoshown experparticle distrthe mechanidescribe thisproposed. Wmacroscopicaddressing tstudies incluapproach whparticle distrthe magnetosamples, it isapproaches. To this aim, wtheoretical fothe mechanidifferent shadistributionsconsidered athe aspect racontains maganisotropic s
etzweeorie
properties of unification of
and microscop
eyko, Vladimirhiannikova, Ge
nsitive elastomsmart materi
asily the shapenetic field. Therspective maotics, actuatorial applicatio
st of micron-spersed withinmatrix. Carbooperties and hon is common
It is possible c and anisotroof the particleopic particle agnetic field shore the curingrimentally tharibution has a cal properties
s effect many While most of tc continuum-mhe shape effe
uding ours utilhich describesribution [4]. Too-mechanical s necessary to
we developedormalism whical behavior o
apes and diffes [5]. The MSEas an ellipsoidatio / (gnetic particlespatial distrib
erke:e und
magneto-senf the continuupic theoretica
r Toshchevikoert Heinrich
mers (MSEs) bals due to thee and stiffnessese features
aterials for deors, dampers aons [1].
ized magneticn a non-magneonyl iron with high saturatioly used for thto produce M
opic spatial es. To producearrangement thould be applig process [1,2]t the microscstrong influe
s of MSEs. To theories havehem are base
mechanics apects [3], a few lize the micros explicitly theo be able to pbehavior of reo combine the
recently a rigich allows to aof the MSEs wrent particle sample is
d of revolutionsee Fig. 1) thaes with isotroution.
Anw
nsitive um-al
ov,
belong eir ability s under make
esign of and for
c etic soft soft n e MSE SEs
e MSEs the ed to ]. It was opic nce on
e been ed on the proach recent scopic
e redict eal MSE ese two
gorous analyze
with
n with at pic or
Fi
M
m
se
m
el
TcwdxfipracdththmbddCothpcaHmcfust
wendu
ig. 1:
Microscopic mode
magnetic field H0,
emi-axes of rotat
microsphere. The
llipsoid.
he spatial disharacterized
which is defineistances betw- and y-directeld in a given oint in Fig. 1), adius r0 arounhosen to be mistance betwehe magnetic fhe particles th
microsphere. Wution dependsistribution, wepends only oonstructing thf elastic and mhe latter depearameter analculate a mand a change o
/2Here is the modulus in theoefficients of unctions of thtructural para
ung
l of an MSE under
applied along the
tional ellipsoid, r0
function rθ defin
tribution of paby the anisotr
ed as the ratioween neighbortions. To calcupoint inside twe introduce
nd this point. Tmuch larger theen neighboriield contains hat are inside We show that s only on the lhile the seconon the shape ohe free energymagnetic freeends now on thnd anisotropygneto-induce
of the elastic m and Δ
permeability oe absence of fproportionalite initial aspecameter as s
r a uniform exter
e x-axis. A and B
0 is the radius of
es the boundary
articles is ropy parameteo of the averagring particles ulate the maghe sample (re
e a microspheThe value of r0
han an averagng particles. Tcontributions and outside othe first contrlocal particle nd contributioof the sample y of MSE as a energies, whhe shape
y parameter ed deformationmodulus Δ :
/2. of vacuum, ield. The ty and act ratio andhown in Fig. 2
rnal
are the
of the
er , ge along netic
ed re of
0 is e Thus, from
of the ri-
n .
sum here
, we n
is the
are the
2.
PolyStru
Fig. 2:
The coefficient
aspect ratio of
( 0.8, 0.9),
structures, mo
lattice. The vol
susceptibility o
In particulainduced defelastic modnegative, deMSE sampledistribution the mechanarrangemenbeen considleads to a pwhereas theleads to themicroscopic Sponsor: The currentfunds of the Co-operatioDr. Dmitry BTechnische
ymeruktur
ts and as f
the sample , c
isotropic ( 1
odeled on the hex
lume fraction
of particles 1
r, we found thormation andulus can be e
epending on the and on the lof particles. B
nical coupling nt and the samdered. The absure macroscoe presence of
e main contribc approach [5]
t work was sue DFG grant G
on: Borin, Dr. MarUniversität D
re Ner, The
functions of the in
calculated for the
1.0) and plane-lik
xagonal close-pac
0.3 and magne
1000.
hat the magne the change oither positive he initial shapocal spatial Besides, the ebetween the
mple deformasence of this copic approachthe strong co
bution of the ].
pported from R 3725/6-1.
rkus Kästner resden
etzweeorie
nitial
e chain-like
ke ( 1.2)
cked
etic
eto-of the
or pe of the
effect of particle
ation has coupling ,
oupling
the
[
[
[
[
[
erke:e und
[1] G. FilipcsM. Zrínyi:206 (2007
[2] C. HintzeV. ToshchG. HeinricKunststof
[3] Y. L. RaikPhysics L
[4] D. IvaneyM. SaphiaMacromo20 (2011),
[5] D. IvaneyM. Saphia10 (2014),
Anw
sei, I. Csetneki: Advances in 7) 137-189 , D. Y. Borin, Dhevikov, M. Sach: Kautschukffe 67/4 (2014)
kher, O. V. StoLetters 26 (200ko, V. Toshchannikova, G. Holecular Theor
411 424 ko, V. Toshchannikova, G. H2213 - 2225
wendu
i, A. Szilágyi, Polymer Scie
D. Ivaneyko, aphiannikova, k Gummi ), 53 - 59 lbov: Technica00), 156-158 evikov,
Heinrich: ry and Simula
evikov, Heinrich: Soft
ung
nce
al
ations
Matter
53
PolyStru
54
Keywords
polymer-matr
composites
fracture tough
particle size d
ymeruktur
rix
hness
distribution
re Ner, The
Effect of plaswith a size dpolymer com Bernd Lauke 1. IntroductioCrack resistapolymers is aparticles. Disdebonding, mvoiding, are rmechanical bcontribution on particle sdissipation eafter debondthis structurgrowth mech[2] and in Rethe particle s 2. Crack resiThe energy npropagation toughness, rthe crack conew fracturethe same timmatrix yieldiwithin a largcalled the yiegiven by the and the relevthe dissipatiointegral over
(1) pc RR
where my isyielding enerfrom the craunder remotcan be appro
tensile stres
where is ais the compowidth of the
cy ERminimum rain the matrix
etzweeorie
stic void growistribution on
mposites
e
on ance of particaffected by thssipation mecmatrix shear bresponsible fobehaviour. Asof particle deize distributio
energy causedding from the ral parameterhanism was mf. [3] and is exsize distributi
stance, fractunecessary to iis called crac
respectively. Dnsumes energ
e surface in thme energy, Rdz
ng around deer zone of widelding zone. Tproduct of mavant volume fon zone energr all local cont
mdzpz RR
s the volume srgy, is the dck tip. The mu
te mode I loadoximated by a
s, 0 : 0 )( a zone shape aosite modulusdissipation zo
2min,0c /E wit
dial stress whx shell around
erke:e und
wth around pan toughness o
le reinforced e size distribu
chanisms, as pbands or plastor the fracture the energy
ebonding may on [1] also the d by matrix voimatrix depen. The plastic v
modelled by Wxtended hereion effect.
ure toughnessnitiate crack
ck resistance, During crack ggy, Rpz, to form
he process zon, is dissipatedbonded particdth, y2 , subseThe zone eneratrix toughnesraction, vm, plgy which is thetributions:
y
0
mymm 2v
specific matrixistance coordultiaxial stresding at the pos
uniform radia
cc /ER and size facto. Consequent
one, y , is give
th min,0 as t
here plastic yid a particle sta
Anw
articles of
ution of particle tic e
depend
iding ds on
void Williams
n for
s
Rc, or growth, m the ne. At d by cles equently gy is ss, Rm, us e
y d)(
x dinate s field
sition al
2/1
or and Ec ly the en by:
he
elding arts. The
incinre
th
E
(2
w
s
3Acis
F
S
ra
Tv~
u
c
dp
(3
waP
wendu
ntegration overack plane cantegration oveeplacement:
he normalizat
Eq. (1) can be r
2) 4dz RR
with as th
mins and maxs
. Single particA spherical paral polymer mas considered.
ig. 1:
ingle particle, ra
adius, r0; ry yield
he local parti 30p rrv~ . Th
nder uniform
oncentrations
erived the debarticle/matrix
3) dmrr
with the specifnd m as the m
Poisson’s ratio
ung
er the distancen be transform
er the stress. W R2d
tion, 0 /s rewritten as:
max
min
2
1s
smy
ccER
he matrix yield
as defined be
cle model rticle embeddatrix under unThe geometry
adius, rp, within
ding radius.
cle volume fra
he representa
stress, 0 , le
s, 0mij /
bonding stresx interface as:
/(EG8 md
ic debonding matrix Young’o, respectively
e, , from themed into With the
30cc d)(E
my , the integ
3)()(my dsss
d strength an
elow.
ded within a spniform radial sy is shown in F
matrix materia
action is defin
ative element
eading to stres
. Williams [2]
ss at the :
))1(d( mp
energy, Gd, an’s modulus any.
e
0 and
gral in
ds
d
pheri-stress Fig. 1.
l of
ned by:
is
ss
]
nd Em nd
Polymere Netzwerke: Struktur, Theorie und Anwendung
55
1.0
1.2
1.4
1.6
1.8
10 20 30 40 50 60 70 80 90
Mean particle diameter, dp [m]
Nor
mal
ized
cra
ck r
esis
tan
ce ,
Rc/
Rm
sN=20m
sN=10m
sN=5m
Gd=10J/m2
4. Particle size distribution It is assumed that the Gaussian normal distribution function provides a mathematical description of the probability density, fn(dp), for the particle size and describes more or less exactly the measured values. With fn and the particle volume density, np, the particle volume fraction, v, is given by:
pppn
d
d
3pp Vn
6ddfdn
6v
max,p
min,p
.
The particle diameters lay between the limits dp,min and dp.max and the number of particles of a special size is given by: pnpj ddfnn .
5. Energy of plastic voiding, crack resistance The yielding energy is derived by the product of applied force, F0, with displacement, u , at the matrix shell of radius, r0:
ur4uFW 02
00my .
This displacement was calculated in [3] to be
mm00 E/),v~,s(C~
ru with the
functionality given therein. With this value the yielding energy of the matrix shell around one debonded particle was calculated as:
m2
my3
0my E/C~
)s(r4W . The volume
density of yielding energy is now given by:
(4) pn
d
)s(d
mypmy ddfWn)s(max,p
p
The value of the lower limit of particle diameter, dp(s), results from Eq. (3) to be:
)s)1/((EG8)s(d 222mymmdp .
Inserting this into Eq. (2) and then into Eq. (1) provides the composite toughness to be: (5)
max
min
max,p
p
s
s
pn
d
)s(d
3p
pm
c
m
m
c
ds]ddfd[)s(C~
s
1
v~v
VE
E121
v
R
R
with 3/)v~1(2smin and 3/v~ln2smax .
6. Results The proposed model is applied for glass-sphere-filled polyethylene with the following material properties for the spheres: Ep= 64 GPa, p= 0.2. The elastic properties of the polyethylene matrix are: Em= 520 MPa, m= 0.35 and the matrix yield stress: MPa27my .
As can be seen in Fig. 2 the composite toughness increases at lower mean particle sizes and remains constant for larger values.
For particle size distributions with larger standard deviations, sN, fracture toughness becomes rather independent of mean particle size. This behaviour is caused by the fact that smaller particles demand higher stresses for debonding and subsequent matrix yielding. The fraction of particles that do not debond do not induce matrix yielding in the neighbourhood. [1] B. Lauke: Computational Mater. Sci.
77(2013), 53-60 [2] J.G. Williams: Comp. Sci. a. Technol.70
(2010), 885-891 [3] B. Lauke: Compos. Sci. and Technol.
86(2013),135-141
Fig. 2:
Fracture toughness (crack
resistance) as a function of
mean particle diameter for
different standard de-
viations, sN, of a Gaussian
normal distribution of
particles of the size
between dp,min=1m and
dp,max=100m, .05.0~ vv
PolyStru
56
Keywords
PVT analysis
epoxy shrinka
crosslinking k
phase transiti
ymeruktur
age
kinetics
ion
re Ner, The
PVT als MethVernetzungsübergängen Jürgen Piont Die Analyse dermöglicht nspezifischen Abhängigkeisondern aucübergängen Abbaureaktiound anderenÄnderung deverbunden ssuchungen ekinetischer PEine SammluDaten von koziellen Polymfindet sich inmit einem GNInc., BoulderGenauigkeit von 0,004 cmspezifischen Temperaturbermöglicht, wVolumen bei Temperatur sind. DerartiKompressibiund die TemAbhängigkeithermischenerhalten. Abcarbonats, gDruckaufbauTemperatur. Der Bereich instabil und (Abb. 1b, die Abhängigkeivom Druck) wwährend desDaten werdeSpritzgusspr
etzweeorie
hode zur Charsreaktionen u von Polymer
teck
der PVT-Datenicht nur die B Volumens vot von Druck uh die Analyse der Polymereonen, Vernetz
n Phänomenenes spezifischeind. Zeitabhän
erlauben die BParameter. ung von im IPommerziellenmeren, Kompon [1]. Die UnterNOMIX-PVT-Dr, CO 80304, Uvon 0,002 cm³
m³/g) bei der B Volumens (Vs
bereich bis 20wobei Änderu konstantem von 0,0002 cmge Daten werilität, die therperatur von Pt vom Druck u
n Vorgeschichtb. 1a zeigt Datemessen als
u von 10 bis 20
zwischen dendie AbweichuGerade kennzt der Glasübewird durch des Druckaufbauen z.B. für die rozesses benö
erke:e und
rakterisierunund Phasen-ren und Mono
n von PolymeBestimmung dn Polymeren nd Temperatuvon Phasen-
en, Polymerisazung, Umestern, die mit einen Volumens ngige Unter-Bestimmung
F gemessene und nichtkomositen und Blersuchungen e
Dilatometer (GUSA), das eine³/g (oberhalb
Bestimmung d
sp) im Druck- u00 MPa bzw. 4ngen im spezDruck und
m³/g nachweisrden benötigt, mische Ausde
Phasenübergäund von der te der Materiaten eines PolyIsotherme un
00 MPa bei jed
n beiden Geradng von den Isozeichnet hier drgangstempe
en Glasübergaus verursachtModellierung
ötigt.
Anw
ng von
meren
eren des in
ur,
ationen, rung er
en PVT-mmer-ends erfolgten GNOMIX 240 °C
des und 00 °C
zifischen
sbar um die
ehnung ngen in
alien zu y-ter
der
den ist obaren die
eratur ang . Solche
g des
A
PV
(a
IndMorucanpthdmCbsdis
wendu
bb. 1:
VT-Daten von Po
a) oder isobare (
n reaktiven Syer Umsetzung
Materials, veruder Vernetzunung eines Epoarboxyltermincrylonitril)-Kaachgewiesen,räparation einhermische Staichte hat. Wer
mit dem EpoxidTBN-Kautschessere Werteamen Mischeer Härtung (M
st bei Methode
ung
olycarbonat, erh
(b) Messungen
ystemen lässt g anhand des ursacht durchng, verfolgen.oxids mit SiC-niertem Poly(bautschuk (CTB, dass die Art nen deutlicheabilität und dirden die SiC-Ndharz gemisc
huk eingemisce erhalten als n aller drei Ko
M1). Auch der Ve 2 um 10 % ve
halten über isoth
sich der VerlSchrumpfes d Polymerisati Bei der ModiNanofasern ubutadien-co-BN) wurde der Proben-n Einfluss aufe VernetzungsNanofasern erht und dann d
cht (M2), werdbeim gemeinomponenten vVolumenschrerringert (Abb
herme
auf des on fizie-
und
f die s-rst der den -vor umpf b. 2).
PolyStru
Abb. 2:
Einfluss von Si
der Verarbeitu
den Volumensc
PVT-Dilatomet
SiC beschleCTBN dieseZähigkeit de Auch in niedbeeinflusst durch AnpaParameter a(z.B. Simhagleichung) dihre PhasenLeitfähigkeiGlasübergaPVT-Analysstimmt für dCarvediloldiEin Vergleicrelaxationendaten und eRückschlüsmechanism KooperationProf. S. ThoKottayam, IProf. M. PalPoland
ymeruktur
iC-Nanofasern un
ungsmethode auf
chrumpf eines Ep
ter (10 MPa, Abbil
unigt die Vern etwas verlan
es Epoxids erh
dermolekulardas freie Volussen der geman Phasenzus-Somczynski-die Beweglichnübergänge soit. Die Druckangstemperatue oder dielektdie protische ihydrogenphoch der beobacn mit druckab
elektrischen Lse auf den Leus von dieser
nen: omas, Mahatmndien; luch, Universi
re Ner, The
nd CTBN-Kautsch
die Vernetzungs
poxids, analysiert
ldung aus [2] ada
netzung, währgsamt, jedochhöht [2].
en Verbindunumen, bestimm
messenen PVTstandsgleichu-Phasenzustahkeit der Moleowie die elektbhängigkeit dur bestimmt ütrische Spektrionische Flüssphat gut übehteten Strukt
bhängigen VisLeitfähigkeiteneitfähigkeits-r ionischen Flü
ma-Ghandi-Un
ty of Silesia, K
etzweeorie
huk sowie
kinetik und
t mittels
aptiert).
rend h die
gen mbar -ngen nds-
eküle und trische der über roskopie sigkeit
erein [3]. ur-kositäts-n erlaubt
üssigkeit.
niversität
Katowice,
[
[
[
erke:e und
[1] J. PiontecPropertiePropertie(Edts): Laand Funcand TechAdvancedVolume 6Polymer Springer,
[2] P. PoorniHuczko, DThomas: nanofiberVolume spropertie46.
[3] Z. WojnarGrzybowsHigh Presthe ConduLiquids, P
Anw
ck, M. Pyda: Tes – pVT-Data es; in K.-F. Arnandolt-Börnstctional Relationology- New S
d Materials an6: Polymers, SSolids and Po, Heidelberg 2ma Vijayan, J
D.. Puglia, J.. Liquid rubber
r modified eposhrinkage, cures; Comp. Sci.
rowska, Y. Waska, A. P. Sokossure as a Keyuctivity MechaPRL 111, 22570
wendu
Thermodynamand Thermal
ndt, M. D. Lecein, Numerica
onships in ScieSeries, Group
nd TechnologieSubvolume A: olymer Melts, 2014 . Pionteck, A..M. Kenny, S.. r and silicon coxy nanocompre kinetics andTech. 102 (20
ang, J. Piontecolov, M. Palucy Factor to Ideanism in Proti03 (2013)
ung
mic
chner al Data ence p VIII: es,
Part 2,
.
carbide posites: d 14) 39-
ck, K. ch: entify ic Ionic
57
PolyStru
58
Keywords
polymer netw
linear dynami
multiscale ap
statistical-phy
theory
ymeruktur
works
ic moduli
proach
ysical
re Ner, The
Multiscale aanalysis of u Marina SaphIgor Gazuz, G The understathe dynamic-polymers anconsiderablymolecular dyacademic intaccurate desrelationshipsthe polymer processing apolymer prodtheir dynamiNowadays, thproperties ofrepresented multiscale arelaxation refrequencies,intermediateat low frequemotivated mused for the applied to th Recently we multiscale alinear dynamcrosslinked frequency dodependent dyapproach arelogarithmic srelaxation timform of a pieFig.1) that costatistical−pdifferent freqrelaxation prfrequencies,polymer chaRouse relaxafrequencies,time relaxati
etzweeorie
pproach to dyunfilled rubbe
hiannikova, VlaGert Heinrich
anding of the -mechanical pd their molec
y improved witynamics theorterest of molescription of ths is of the highand rubber in
as well as finaducts are direc-mechanicahe linear dynaf entangled poreasonably w
pproach whicegimes: glassy followed by R
e frequencies encies [1]. Howultiscale apprpolymer melte crosslinked
elaborated a pproach for d
mic moduli of tpolymer netwomain [2]. Theynamic modue calculated ospectral densmes )(H . Thecewise-poweombines the idhysical theoryquency regimrocesses at ex (2) the bendinin at high freqation processe and finally (4ion processes
erke:e und
ynamic-mechers
adimir Toshch
relationship bproperties of ular structureth the developries. Besides ecular theoriee structure/phest importanndustry, as thel properties o
ectly governedl behaviour. amic-mechanolymer melts
well using a h combines dy regime at ve
Rouse regime and reptation
wever, a physiroach similar ts has not bee networks.
versatile theoescription of tthe randomly
works across ae frequency-li in the multi
on the base of ity function of
his function har-law (see in
deas developey of polymers es: (1) nonpolyxtremely highng modes of tquencies, (3) tes at intermed
4) extremely los at low freque
Anw
anical
hevikov,
between
e has pment of the s, the roperty
nce for e of d by
ical can be
ifferent ery high
at the n regime ically to that
en yet
oretical the
a broad
scale the
f the as the sert of
ed in the for ymeric he he diate ong-encies.
Fi
Fi
fo
ap
sp
se
TreintithsdmecleKthafrm
OreledareG
fuuscstpdhstmo
wendu
ig. 1:
its of the master
or the unfilled S-S
pproach. Insert s
pectral density H
eparated by the c
he structural elaxation regin literature. Cme relaxation
heoretical apppectrum is caynamics of da
multiscale appxperimental dharacteristicsength of the K
Kuhn segmenthe active netwnd in danglingractions of act
material.
Only after takinelaxation procength scales, ynamic moduchieved. Fig. 1elaxation part
eqGG , and tunctions of thnfilled S-SBRulfur. Here G
orresponds totorage modularameters of ensity and theave been obtatrain depende
model of the ruther material
ung
curves for the sto
SBR rubber with
hows schematica
() in which four d
characteristic rela
origin of the lme is still a momparing then spectrum wiproaches, we aused by a slowangling chainsproach allows data based ons of polymer m
Kuhn segmentts in an entangwork strands bg chains as wetive chains an
ng into accouncesses on varan excellent dli of unfilled r1 shows exemt of the storagthe loss modue angular freq
R rubber crosseqG is the plate
o the limiting vlus at low freqS-SBR rubbe
e density of enained from theences using thubber elasticiparameters h
orage and loss m
the multiscale
ally the logarithm
different regimes
axation times.
long-time matter of discu form of the loith different conclude thatw reptation s [3]. The propus to interpre structural
materials as th, the numbersgled fragmentbetween junctell as the volud dangling
nt this richnesious time anddescription of rubbers was
mplarily the ge modulus, ulus, G , as quency forslinked with 1 eau modulus wvalue of the
quencies. Struers - the crossntanglementse fitting of strehe extended tuty [4]. The valhave been
moduli
mic
s are
ussion ong-
t this
posed et
he s of t, in tions ume
ss in
r the phr which
uctural s-link - ess-ube ues of
Polymere Netzwerke: Struktur, Theorie und Anwendung
59
extracted from the fits and are found to correlate well with the actual values for the S-SBR copolymer used in the studied samples. So, we extract the molar mass of the Kuhn segment Ms 300 g/mol, which is in close agreement with the value Ms = 353 g/mol, obtained from the mathematical analysis of the chemical structure of S-SBR [5]. The newly proposed multiscale approach allows to fit and to describe the dynamic moduli of unfilled S-SBR rubbers over 16 frequency decades with a limited set of parameters (relaxation times, scaling exponents). All parameters have a clear physical meaning and obey the relations motivated by the statistical−physical theory of polymer melts and polymer networks. The multiscale approach can be generalized for the case of filled polymer networks, which is of extraordinary importance for the tire applications in automobile industry. Co-operation: Dr. Stephan Westermann and Dr. Frank Petry, Goodyear Innovation Center Luxembourg [1] O. Byutner, G.D. Smith: Macromolecules
34 (2001), 134-139 [2] M. Saphiannikova, V. Toshchevikov,
I. Gazuz, P. Petry, S. Westermann, G. Heinrich: Macromolecules 47 (2014), 4813-4823
[3] J.G. Curro, D.S. Pearson, E. Helfand: Macromolecules 18 (1985), 1157-1162
[4] M. Kaliske, G. Heinrich: Rubber Chem. Technol. 72 (1999), 602-632
[5] B. Huneke, M. Klüppel: Kautsch. Gummi Kunstst. 59 (2006), 242-250