Linear visoelasti behavior

The previoussetionhas learly revealed thatthe thermosensitive suspensions rystallize

if theeetive volume fration

φ ef f

^{isabove 0.49. Moreover, the evolutionof the samples}

as funtion of the time suggests that the indution time until rystallization ours

depends on

φ ef f

^{as expeted for hard spheres system.} Crystallization strongly aets the mehanialpropertiesof the solution. Forthis reason rheologialmeasurements were

arried on onentrated suspensions to explore the rystallization kinetis in further

details.

The linear visoelasti behavior is studied rst for dierent KS2 solutions. For this

purpose the storage modulus

G ^′

^{and the lossmodulus}

G ^′′

^{is measured froma suspension}

with 9.48

wt.%

^{at dierent} temperatures, orresponding to dierent volume frations

200µm

Figure2.32: Comparison between the linear visoelastiity measurement and the polarized

mi-rosopy during the rystallization proess of a 13.01

wt. %

^{KS3 solution at 20}

^o C

(

φ _{ef f} = 0.54

^{). The storage modulus}

G ^′

^{(lled symbols) and the loss modulus}

G ^′′

(opensymbols) are measured asfuntion of time in the linear visoelasti regime at

1

Hz

^{and 1}

%

^{after 5 min of shearing at 100}

s ⁻¹

^{. The results are ompared to the}

polarized mirosopy observationsat20

o C

^{for dierent timesafter afast quenhing}

from 30

o C

^to20

^o C

^.

φ _{ef f}

^{. A} deformation of 1

%

^{and a frequeny of 1}

Hz

^{has been hosen. Additional}

measurements have shown that the linear visoelasti regime is attained for these

parameters. To remove the samples history, all suspensions were sheared for 5 minutes

with a shear rate of 100

s ⁻¹

^{prior analysis. In all ases reported here the time of}

observation was more than one hour.

The solution was measured at 22

o C

^{whih orresponds to an eetive volume fration}

φ ef f

^{= 0.49.}

G ^′

^{is higher than}

G ^′′

^{for the entire time of} observation indiating a stable uid phase. Lowering the temperature to 19

o C

^{leads to a regime where}

G ^′ ≪ G ^′′

where norystallization is expeted. However after anindution time of 700

s

^{a marked}

inrease in

G ^′

^{is observed as shown in g. 2.31.}

G ^′′

^{goes through a slight maximum and}

nally dereases markedly so that

G ^′ ≫ G ^′′

^{in the nal stage attained after a. 1 hour.}

The highest eetive volume fration 0.65 was reahed by lowering the temperature to

8

o C

^{. Note that this very high volume fration an easily be reahed by adjusting the}

temperature. In this ase g. 2.31 demonstrates that

G ^′ >> G ^′′

^{as expeted for the}

glassy state. At this high volume fration loalrearrangements are slowing down whih

is marked by a slow inrease of

G ^′

^{with the time.}

The same experiment has been performedfor the KS3. Fig. 2.32 presents the timesweep

obtained for a 13.01

wt.%

^{solution at 20}

^o C

⁽

φ ef f

^{= 0.54) and is ompared to the}

ob-servation by polarizingmirosopy. The inrease of

G ^′

^{follows the apparition of the rst}

rystallitesafter420

s

^{. After720}

s

orrespondingtotherossoverof

G ^′

^and

G ^′′

^nofurther

hange an be observed from the polarized mirosopy even if the

G ^′

^{is still inreasing.}

The same observation was done on the others solutions investigated in the oexistene

domain. This underlines the goodagreement and the omplementarity of this two

teh-nis. We determined the indution time of the rystallization. This time was estimated

from timesweep experiments as the time where rystallization indues a 10

%

^{inrease of}

2x10 ⁵ 4x10 ⁵ 6x10 ⁵ 8x10 ⁵

0.50 0.52 0.54 0.56 0.58 0.60

f _eff

t i

Figure2.33: Beginning of the rystallization desribed by the dependene of the harateristi

time

τ i

^{onthe eetivevolumefration}

φ _{ef f}

^fordierentonentrations(12.1

wt.%

^:

irles,13.01

wt.%

^{: downtriangles,13.58}

wt.%

^{: squares)atdierent} temperatures.

The dashed lineis here toguide the eyes.

the omplex modulus

G ^∗

^{. This time was then normalized by the diusion time dened}

as

R ² _H /D 0

^{, where}

R H

^{is the} hydrodynami radius and

D 0

^the free-partile diusion on-stant. This gives the harateristi time

τ i

^{. Fig. 2.33 presents the dependene of}

τ i

^on

φ ef f

^{obtained for dierent} onentrations atdierenttemperatures.

τ i

^{rst dereases with inreasing volume frations and reahes a minimum around}

φ _{ef f} = 0.55

^{. An inrease is observed again for higher eetive volume frations. The}

minimum is in good agreement with the literature [123℄. This orroborates the

frame-work of rystallization and growth. Close to

φ ef f,f

^{the growth proess} predominates as the nuleation is slow. This results in a slow rystallization and in the formation of

large rystals. The growth proess dereases with inreasing volume fration inthe

ben-et of a faster nuleation. The rystallization kinetis reahes then a maximum around

φ ef f = 0.55

^{, whih orresponds to the maximum of the nuleation rate for hard spheres}

olloidalsuspensionasfoundexperimentallyinref. [123℄andtheoretially[119℄. Tohigher

φ ef f

^the rystallization is slowed down as the self diusion of the partiles isdereasing.

Moreover the proximity of the nulei hinders the growth of the rystals. For

φ ef f > φ g

the suspensions stillrystallize, at least partially, by the slow growth of large and

irreg-ularly shaped rystals on seondary nulei, suh as the ontainer walls and regions of

shear-alignedstrutures remainingfrom the tumbling ation[121℄.

Hene, we onlude that the rheologial experiments shown in g. 2.31 and g. 2.32

orroboratesallndingsoftheprevioussetion: Crystallizationtakesplaeatsuiently

high volumefrations. However, the kinetis of rystallizationdepends markedlyon

φ ef f

asexpetedfrompreviousinvestigations[122,123,155,156℄. Thestudyofthevisoelasti

behaviorthereforegivesdiretinformationonthe timesaleinwhihthesystemsremains

in the nonergodistate.

This indiates that the thermosensitive ore-shell partilesbehave as hard spheres when

onsidering their rystallization. Moreover, the fat that these systems rystallize again

points tothe narrowsize distribution.

10 ^-3 10 ^-2 10 ^-1 10 ⁰ 10 ¹ 10

10 ^-2 10 ^-1 10 ⁰ 10 ¹ 10 ² 10 ³

dg/dt [s ^-1 ]

s [P a ]

Figure2.34: Shear melting of rystallized suspensions. Shear stress as funtion of shear rate

for a thermosensitive suspension ontaining 9.48

wt.%

^{of the partiles. The open}

symbolsmarkthemeasurementswithinreasingshearratewhereasthe lled symbols

show the results with dereasing shear rate. Parameter of the dierent urves is

the temperature adjusting the eetive volume fration

φ _{ef f}

^{. The eetive volume}

frations

φ _{ef f}

^{are: triangles up: 0.49; irles: 0.52; triangles down: 0.57; squares:}

0.64.

Im Dokument Structure, Dynamics and Association of Thermosensitive Core-Shell Particles (Seite 54-57)