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

mpischen Geleeine Abnahmeer Kettenlängende Ergebnis kfinen Deformah die unvollsth durchdringe

Lett. 112, 23800ern auch eineder Rolle der rnetze Gele. S

zwerke stellen Materialien d

en durch Lichtr kontrolliert

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

er TireTechExScientist Awareresse der Rebnissen zur Agsinduzierten huk widerspieauf dem Gebi

Nanokompositrderpreis der Gesellschaft. D

erke:e und

Polymeren wn (Viskosität) m(Formbeständeit) kombinierken, welche nRingpolymereenauere er Topologie anschaften, g von Netzwee“ zeigen in de des Quellgrae. Dieses kann durch diation erklärt wändige Vehakende Ringe en01 (2014)). Die

en neuen ZugaTopologie für

Stimuli-respon eine Klasse dar, deren elat oder äußerewerden könn

ngen zeigen dobengeometr

(Soft Matter 10e zeigen dynasehr großen

ch einen einzigchrieben werdtiskalen-Ansalaxationszeite

namische Prozreichen kombilten des ungefüllte 4 Größenordn

Macromolecul

ngsorientierteein Würdigun

Brüning wurdexpo 2014 in Körd ausgezeicheifenindustrieufklärung derKristallisationegelt. Für seiniet der funktiote erhielt Dr. SDeutschen Die experimen

Anw

werden mit digkeit, rt. Eine ur

en

auf die

rken. er des mit

e Rolle werden, ung der

ntsteht se

ang zum r nsive von

astische en.

die Rolle rie auf

0, 2213 mische

gen den tz für

en, zesse in iniert,

nungen les 47,

en ng durch e ln mit net, der an

r Kinetik n von ne onalen Sandip

ntelle

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wendu

harakterisierGegenstand de

onventionelleer mit über 75er Industrie diesbezügliche

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