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Oscillatory RheologyMeasuring the Viscoelastic Behaviour of Soft Materials

Masuring this tim dpndnt strss r-

spns at a sing frqunc immdiat rvas

k diffrncs btwn matrias, as shwnschmatica in figur 1(b). If th matria is an

ida astic sid, thn th samp strss is pr-

prtina t th strain dfrmatin, and th pr-

prtinait cnstant is th shar mduus f th

matria. Th strss is awas xact in phas

with th appid sinusida strain dfrmatin.

In cntrast, if th matria is a pur viscus

fuid, th strss in th samp is prprtina t

th rat f strain dfrmatin, whr th pr-

Sft matrias such as cida suspnsins,

musins, fams, r pmr sstms ar ubiq-

uitus in man industris, incuding fds, phar-macuticas, and csmtics. Thir macrscpic

mchanica bhaviur is a k prprt which

ftn dtrmins th usabiit f such matrias

fr a givn industria appicatin. Charactrising

th mchanica bhaviur f sft matrias is

cmpicatd b th fact that man matrias ar

viscastic, s thir mchanica prprtis i

btwn that f a pur astic sid and that f

a viscus iquid. Using sciatr rhg, it is

pssib t quantif bth th viscus-ik and

th astic-ik prprtis f a matria at diffr-

nt tim scas; it is thus a vauab t fr un-

drstanding th structura and dnamic prpr-tis f ths sstms [1, 2].

Oscillatory Rheology

Th basic princip f an sciatr rhmtr is

t induc a sinusida shar dfrmatin in th

samp and masur th rsutant strss r-

spns; th tim sca prbd is dtrmind b

th frqunc f sciatin, , f th shar d-

frmatin. In a tpica xprimnt, th samp is

pacd btwn tw pats, as shwn in figur

1(a). Whi th tp pat rmains statinar, a

mtr rtats th bttm pat, thrb imps-ing a tim dpndnt strain (t)=sin(t) n

th samp. Simutanus, th tim dpndnt

strss(t) is quantifid b masuring th trqu

that th samp impss n th tp pat.

Fig. 1: (a) Schematic representation of a typical rheometry setup, with the sample placed betweentwo plates. (b) Schematic stress response to oscillatory strain deformation for an elastic solid, aviscous fluid and a viscoelastic material.

Prof. David Weitz, Dr. Hans Wyss, Ryan Larsen,Harvard University

Soft materials such as emulsions, foams, or dispersions are ubiquitous in

industrial products and formulations; they exhibit unique mechanical

behaviours that are often key to the way these materials are employed in a

particular application. Studying the mechanical behaviour of these materials

is complicated by the fact that their response is viscoelastic, intermediate

between that of solids and liquids. Oscillatory rheology is a standard

experimental tool for studying such behaviour; it provides new insights

about the physical mechanisms that govern the unique mechanical

properties of soft materials. Pht: 108 (phtcas)

G.I.T. Labratry Jurnal 3-4/2007, 68-70, GIT VERLAG GmbH & C. KG, Darmstadt www.gitverlag.cm www.pRo-4-pRo.cm

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prtinait cnstant is th viscsit f th fuid.

Th appid strain and th masurd strss ar

ut f phas, with a phas ang =/2, as

shwn in th cntr graph in figur 1(b).

Viscastic matrias shw a rspns that

cntains bth in-phas and ut-f-phas cntri-

butins, as shwn in th bttm graph f figur

1(b); ths cntributins rva th xtnts f

sid-ik (rd in) and iquid-ik (bu dttd

in) bhavir. As a cnsqunc, th tta strss

rspns (purp in) shws a phas shift with rspct t th appid strain dfrmatin

that is btwn that f sids and iquids,

0

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sca f this raxatin is xpctd t dpnd n

th strain rat f dfrmatin; th raxatin

spds up if th sstm is subjctd t shar [4,

810]. As th strain ampitud f dfrmatin is

incrasd in a strain-swp masurmnt, th

strain rat incrass and th charactristic fr-

qunc f th sw raxatin prcss mvs t-

wards highr frquncis. As a cnsqunc, a

pak in th ss mduus is bsrvd at th pintwhr this charactristic frqunc bcms

cmparab t th sciatin frqunc f th

strain dfrmatin, . Thus, th bsrvd bhav-

iur at arg strains dirct rfcts th structur-

a raxatin f th matria.

This bhaviur is xpitd in a nw ap-

prach t sciatr rhg, Strain-Rat Fr-

qunc Suprpsitin (SRFS) [5], whr th am-

pitud f strain rat is kpt cnstant as is

varid. examps f such masurmnts ar

shwn in figur 2(d) fr diffrnt strain rat am-

pituds f shar dfrmatin. At a strain rats,

th frqunc dpndnc f th rspns

shws th bhaviur xpctd fr a sw struc-

tura raxatin prcss, with a prnuncd pak

in th ss mduus. Th data shw that with in-

crasing strain rat ampitud th rspns

mvs twards highr frquncis; hwvr, th

gnra shap f th rspns is surprising in-

snsitiv t strain rat, as shwn in figur 2().

B scaing th frqunc and th magnitud f

ach data st, w caps th data rcrdd at

diffrnt strain rats nt a mastr curv with

th crrspnding scaing factrs shwn in th

inst. Whi th magnitud scaing factr, a(),

dpnds n wak n th appid strain rat,

th frqunc scaing factr b() shws a in-ar dpndnc n ; thus, within th rang

studid, th charactristic raxatin frqunc

is prprtina t th appid strain rat. Surpris-

ing, ntab diffrncs in th shap f this

shar-drivn raxatin ar bsrvd btwn

diffrnt samps [5]. Thus, th shap f th r-

axatin is nt gvrnd b th sing tim sca

inducd b th shar but is instad gvrnd b

a samp-dpndnt spctrum f raxatin

tims. In th xamp shwn th unusua

brad shap f th pak indicats that th rax-

atin spctrum f this sstm cntains a rmark-

ab brad rang f tim scas.

Th bhaviur bsrvd suggsts that vauab

infrmatin abut th structura raxatin f

sft matrias can b accssd frm such nnin-

ar viscastic masurmnts, vn if th rax-

atin ccurs at tim scas that ar nt accssi-

b t inar sciatr rhg.

Conclusions

osciatr rhg is a vauab t fr stud-

ing th mchanica bhavir f sft matrias.

Rcnt studis suggst that th nninar visc-

astic bhavir cntains vauab infrmatin

abut th dnamics f ths sstms. Thus ma-

surmnts at arg strain dfrmatins shud

ad t a bttr undrstanding f th phsica

mchanisms that gvrn thir bhaviur.

References

[1] W. Macsk: Rhg: Princips, Masurmnts

and Appicatins, Wi-VCH, Nw yrk, 1994

[2] larsn R.G.: Th structur and rhg f cm-

px fuids, oxfrd Univrsit Prss, Nw yrk,

1999

[3] Hu Z. and Xia X.: Adv. Matrias 16, 305 (2004)

[4] Miazaki H.M. et al.: eurphs. ltt. 75, 915

(2006)

[5] Wss H.M. et al.: cndmat/0608151 (2006)

[6] Sich P. et al.: Phs. Rv. ltt. 78, 2020 (1997)

[7] Cats M.e. and Sich P.: J. Rhg 48, 193

(2004)

[8] Fuchs M. and Cats M.e.: Phs. Rv. ltt. 89

(2002)

[9] Fuchs M. and Cats M.e.: Farada Discuss. 123,

267 (2003)

[10] Miazaki K. et al.: Phs. Rv. e 70, 011501 (2004)

C o n t a c t

Dr. Hans M. Wyss

Ryan J. Larsen

Prof. David A. Weitz

Harvard Univrsit

Phsics & DeAS

Cambridg, USA

T.: +1 617 496 80 49

Fax: +1 617 496 95 64

hwss@das.harvard.du

www.das.harvard.du/prjcts/witzab/