Competing interactions in arrested states of colloidal clays

0.6 MB·English

by  B. Ruzicka

Competing interactions in arrested states of colloidal clays
B. Ruzicka1, L. Zulian2, E. Zaccarelli1, R. Angelini1, M. Sztucki3, A. Moussa¨ıd3, and G. Ruocco1
1 SOFT INFM-CNR and Dipartimento di Fisica, Sapienza Universita` di Roma, I-00185, Italy.
2 ISMAC-CNR via Bassini 15, 20133 Milan, Italy.
3 European Synchrotron Radiation Facility. B.P. 220 F-38043 Grenoble, Cedex France.
(Dated: January 22, 2010)
Usingexperiments,theoryandsimulations,weshowthatthearrestedstateobservedinacolloidal
clayatintermediateconcentrationsisstabilized bythescreenedCoulomb repulsion(Wignerglass).
Dilutionexperimentsallowustodistinguishthishigh-concentrationdisconnectedstate,whichmelts
upon addition of water, from a low-concentration gel state, which does not melt. Theoretical
0
modelling and simulations reproduce the measured Small Angle X-Ray Scattering static structure
1
factorsandconfirmthelong-rangeelectrostaticnatureofthearrested structure. Thesefindingsare
0
attributedtothedifferenttimescalescontrollingthecompetingattractiveandrepulsiveinteractions.
2

n PACSnumbers: 82.70.Dd,64.70.P-,64.70.kj,64.70.pv
a
J

2 Dynamicalarrestinsoftcolloidalsystemshasrecently More recently, the static properties of these two states
2 become the subject of an intense research activity. The have been investigated in detail [18], showing that they

fine tuning of control parameters opens the possibility are also characterized by both the very different aging
]
t to tailorthe macroscopicpropertiesofthe resultingnon- behaviors and the shape of the static structure factor
f
o ergodic states. Several mechanisms of dynamical arrest S(Q). While the low Cw state shows typical inhomo-
s have been identified. Building on the knowledge on the geneities, the high C state is homogenous, allowing for
. w
t hard spheres glass [1], it has become recently clear that theidentificationofthesetwoarrestedstatesrespectively
a
m when both attractive and repulsive terms are present in as gel and glass.
the interaction potential, a re-entrant liquid-glass line,
- In this Letter, through the combination of experi-
d surrounded by two distinct glasses, has been predicted
ments,numericalandtheoreticalapproaches,we demon-
n and experimentally observed in short-ranged attractive
strate that the non-ergodic state observed in Laponite
o
colloids at high concentrations [2]. A rich phenomenol-
c samples in salt free water at sufficiently large concentra-
ogy also takes place at low concentrations: here gelation
[ tions (C ≥ 2.0%) is a Wigner glass. By performing
occurs, which may result from different routes [3]. Inter- w
a simple but impressive dilution experiment, we are able
1
estingscenariosarisewhen,inadditiontoashort-ranged
v todistinguishwhetherattractiveorrepulsiveinteractions
attraction, particles have a residual electrostatic charge
7 are dominant in the formation (and stability) of the ar-
4 whichbuildsupalong-rangerepulsionintheeffectivepo- rested structure for both low and high concentration ar-
9 tential. In this case, particles can form equilibrium clus-
rested samples. Moreover, we compare the S(Q) deter-
3 ters [4], which provide the building blocks of arrest [5].
mined by Small Angle X-rays Scattering (SAXS) with
.
1 Recent works have shown that both Wigner glasses [6],
theoreticaland numericalones in the high concentration
0 intended as arrested states formed by disconnected par-
window, providing an estimate for the effective interac-
0 ticlesorclustersandstabilizedbytheelectrostaticrepul-
1 tions between Laponite platelets. These results provide
sion, andequilibrium gels, whichoccur at largerpacking
: clearcut evidence that the resulting large concentration
v fractionswhentheclustersbranchintoapercolatingnet-
arrested state (which is still found at very low packing
Xi work, can form under these conditions [7, 8]. fraction) can be attributed to the residual electrostatic
r repulsion(Wignerglass)[6]. TherebyLaponiteoffersthe
a To investigate the formation of multiple arrested
unique exampleofasystemwhich,notonlydisplaystwo
states, colloidal clays [9, 10] have emerged as suitable
distinctnon-ergodicstatesdifferingonlyincolloidalcon-
candidates. The anisotropy of the particles, combined
centration, but also shows a counter-intuitive scenario
with the presence of attractive and repulsive terms in
whichinvolvesgel-likestructuresatlowerconcentrations
the interactions, makes the phase diagram of such col-
and a (truly) disconnected glass at larger ones. Hence,
loidal systems very complex. Among these, Laponite
the increase of concentration, which normally favours
suspensions have been widely studied not only for their
percolation and branching, here has the opposite effect.
appealingindustrialapplications[11]butalsofortheirin-
We attribute this novel behavior to the interplay of dif-
teresting experimental/theoreticalproperties [12–20]. In
ferenttime-scalesintheinvolvedattractiveandrepulsive
particular, Laponite displays a non-trivial aging dynam-
interactions, a feature that may be found in other com-
ics [15]and(atleast)two finalarrestedstates,whichare
plex colloidal systems.
obtained by a simple increase of Laponite volume frac-
tion from low (C < 2.0%) to moderate (C ≥ 2.0%) To investigate the glassy state formed by Laponite at
w w
values, at fixed salt concentration C = 10−4M [15, 17]. high clay concentration (C ≥ 2.0%) [15, 17, 18], we
s w
2
FIG. 1: Evolution of ahigh concentration sample at Cw =3.0% with time. Theinitially liquid (L) sample (A)ages with time
reaching,after50h,afinalarrestedglassy state(G2)(B).Atthistimeacoloredsolution(inaliquid(L)state)isaddedtothe
arrested sample (C) that starts to fluidize at the interface (D)- 70 h. Finally thewhole sample is liquid again (E) - 120 h.
use a combination of different approaches. Firstly, we We now turnto elucidate the effective interactionsbe-
perform a dilution experiment (adding water to the ar- tween Laponite platelets, by comparing the evolution of
rested state) that provides a direct criterion to establish theexperimentalstaticstructurefactorSM(Q),obtained
the dominant interactions controlling the formation and from SAXS measurements performed at the High Bril-
stability of the arrested state [3]. If this were due to liancebeamline (ID2)[22]atthe EuropeanSynchrotron
attractive interactions, the presence of additional water Radiation Facility (ESRF) in Grenoble, France, as de-
shouldnotaffect the finalstate,because Laponite bonds scribed in [18], with that predicted theoretically Sth(Q),
(of strong electrostaticnature) cannot be brokenby the assuming several effective interaction potentials [23].
mediationofwater. Ontheotherhand,ifrepulsiveinter- In Fig. 2 the comparison between SM(Q) (symbols)
actionsaredeterminingthe formationofthe non-ergodic and optimal Sth(Q) (lines), for fixed t ≃ 50 h in the
w
state,the increaseoffreevolumeallowsarearrangement concentration window 2.0%≤ C ≤ 3.0%, is shown. As
w
of the Laponite platelets onaverageto a largerdistance. it is evident from Fig. 2, as concentration is decreased
Ifsuchdistanceislargerthanthecharacteristicrepulsive fromC =3.0%toC =2.0%thelowQsignalisslightly
w w
length (namely the electrostatic Debye length) the glass increased and the main peak is slightly shifted towards
will be destabilized up to melting to a liquid state. lowerQ values. The position ofthe main peak is around
To obtain reliable and reproducible results [21] Q ∼ 0.17 nm−1, corresponding to a length ≈ 37 nm, a
Laponite RD dispersions are prepared using the same valueclearlylargerthantheplateletdiameterd=25nm,
protocol described in [18]. The starting waiting time pointingtoanon-connectedfinalstructure. Moreover,no
(t = 0) is the time at which the suspension is filtered. evidence of a peak at contact distance is found.
w
Forthedilutionexperimentasampleathighclayconcen- ThetheoreticalSth(Q)iscalculatedbysolvingnumer-
tration, C = 3.0%, is filtered and sealed in small glass ically the Ornstein-Zernike equation with an appropri-
w
bottles. The photographic sequence of this experiment ate closure relation [24] or by direct simulation of the
is shown in Fig.1. The initially liquid (L)((A) panel) effective potential, without a significant change in the
sample ages with time ≈ 50 h [15] until reaching a final description of the experimental data. For simplicity, we
arrested state, as it can be seen in panel (B) where the reportPercus-Yevickresultsinthefollowing. Inthissim-
sample shows its solid like nature (G2). At this point plifiedtreatment,weconsideronlythe centersofmassof
a solution of colored water (of the same volume as that the scattering objects, supposedly single platelets, and
of the Laponite solution) is added to the arrested (col- treatthem as(spherical)points, followingprevious work
orless) sample. The colorant used, Rhodamine B at a on different systems [7]. The main fit parameters in-
−3
concentration10 M, does not play any role in the pro- volved in the description of the experimental data are
cess,asshownbelow,andisusedtobetterdistinguish(C the number density ρ of the scattering objects and the
panel)the arrestedsample (G2) fromthe liquid solution number of counter-ions Nci that dissociate (on average)
(L). After the addition of water, the arrested sample from each platelet when dissolved in water. Our study
starts to fluidize at the interface with the liquid solution indicates that ρ cannot be the same as the number den-
(D panel - t = 70 h). This process evolves with time sity of Laponite discs obtained from the nominal weight
w
until, after 120 h, the whole sample is back into a liq- concentration ρ = 2.4·1022/m3. Indeed, no simple in-
L
uid state (E panel). This result strongly speaks in favor teraction potential is able to reproduce the position of
of the repulsive nature of the C =3.0% arrested state. the main peak using ρ . Hence ρ must be smaller, due
w L
TheexperimentisrepeatedinabsenceofRhodamineand tothefactthatplateletsmaybefoundwithinadistribu-
showsthatthe additionofthedyedoesnotaffectthe re- tion of clusters [25]. We find that the data can be fully
sults. We have monitored that the pH of the solution described, in terms of peak position, peak height and
remains constant throughout the dilution experiment. compressibility, by a Yukawa potential, which accounts
3

Cw=2.4 % SIMU
C =2.0 % Cw=2.4 % THEO
2.5 w 1.0 Cw=3.0 % SIMU
C =2.2 % Cw= 3.0 % THEO
w
C =2.4 % 1.0
2.0 w
0.8
Cw=2.6 % Q)
1.5 C =2.8 % S( 0.8
Q) w 0.6
S( 1.0 Cw=3.0 % Cw=2.4 % 0.6
1.2 0.4 STHIMEUO
1.0 MEAS
0.5 0.8 0.4
C=3.0 % 0.0 0.2 0.4
0.6 MEAwS - Sample1 0.20.0 0.2 0.4
0.4 TMHEEAOS -- SSaammppllee12 Q (nm-1)
0.0 THEO - Sample2
0.2
0.0 0.1 0.2 0.3 0.4
0.00 0.08 0.16 0.24 0.32 0.40 FIG. 3: Comparison between simulated (symbols) and theo-
Q (nm-1) retical (lines) S(Q) for Cw = 2.4% and 3.0% Laponite sam-
ples. Inset: Simulated (cross symbols), theoretical (line) and
FIG. 2: Comparison between measured SM(Q) (symbols) measured (open circles) S(Q) for Cw =2.4%.
and theoretical Sth(Q) (lines) for several high concentration
Laponite samples at tw ≃50 h. For clarity, curveshavebeen
shifted along the vertical axis progressively by 0.3. Inset: fore,we conclude thatno relevantattractivefeaturesare
ComparisonbetweenSM(Q)(symbols)andSth(Q)(lines)for presentinS(Q)inthisconcentrationwindow. Hence,the
two different samples with Cw =3.0%. combinationofthe dilutionexperimentwiththetheoret-
icalanalysisallowstoidentifytheobservedarrestedstate
as a Wigner glass stabilized by the residual electrostatic
inanaverageway[7]forthescreenedelectrostaticrepul- repulsions.
sionbetweenLaponiteplateletsorclusters,inagreement One further comment concerns the robustness and re-
with more sophisticated theoretical approaches [19]. We producibility of our findings for different samples. Al-
use a potential ofthe formVeff =Aξe−r/ξ/r, where ξ is though different measurements can bring small changes
the Debye screening length and A provides a measure of in SM(Q) due to differences in Laponite batches, to the
thestrengthoftherepulsion. Thenumberdensityisfixed filtrationprocedureortorealclayconcentrations,wecan
toρ≃0.38ρL,arelationshipwhichisfoundtoholdinthe fit equally well different samples with the same effective
whole investigated concentration window. This suggests Yukawa potential upon variation of the fit parameters.
that Laponite may be dispersed in a distribution of very This is shown in the inset of Fig. 2 where SM(Q) is re-
small aggregates, possibly due to particles that are not ported for two different samples with C = 3.0%, from
w
completelydelaminated,compatiblywithanAFMstudy differentbatches,measuredintwodifferentruns,incom-
performed under very dilute conditions [25]. The num- parison with Sth(Q). For the second batch, which has a
ber of counterions in solution is optimized to Nci = 60, higher polydispersity, we find Nci =90 and ρ=0.26ρL.
a value well below the bare charge of a single platelet Thetheoreticalapproachwehaveadoptedsofartreats
(700 e), in good agreement both with previous sim- only the correlations between the centers-of-mass of the
ulations [19] and with conductivity measurements [17]. scattering objects. Although such an approach was
With this choice of parameters, the change in nominal proven to be a good (although crude) approximation to
concentrationanditsassociatedscreeninglengthξ,vary- describethestaticcorrelationsbetweenequilibriumclus-
ing between 8 and 10 nm, are able to reproduce SM(Q) ters of non-spherical shape [7], it is crucial to show that
in the full investigated window, as seen in Fig. 2. The this treatment is valid also when we take into account
repulsion strength Aξ/kBT is found to increase in the explicitly the actual disc shape of clay particles. To this
studied range of concentration by a factor of ≈ 2, com- aim, we have performed MonteCarlo simulations of 200
patibly with the behavior of other charged systems [26]. discsatthesameρasthatextractedfromthefits. Weuse
While the Yukawa potential correctly reproduces the the interaction model introduced in [27] where the total
experimentaldata,otherpossiblecandidatesdonot. The negative charge is uniformly distributed over the surface
simple hard sphere model does not capture at all the area, while rim charges are neglected. Each Laponite
softness of the interactions,failing to reproduce the low- platelet is schematized as a rigid disk, composed by 19
Q regime also after one adjusts ρ. On the other hand, sites disposed on a regular mesh. We simulate several
the addition of a short-range attraction to the electro- repulsion parameters and find that the numerical Sn(Q)
static repulsion is (i) not sufficient to explain the low is in goodagreementwith the experimentaland theoret-
Q-position of the main peak; (ii) tends to induce an en- ical ones when the total charge is fixed to 70 e and the
hanced structuring at nearest-neighbour length. There- screening length is 5 nm. Results are shown in Figure
4
Pagina 1 di 1
liquify and does not show any macroscopic changes of
its solid like state, even after waiting additional weeks,
i.e. the same timescale of the arrest process. In this
case the presence of available free volume does not de-
termine any change in the gel-arrested state ((B) and
(C)panels),duetothefactthatwatercannotbreakclay
bonds. The different behavior between the high and low
concentration samples ((C) and (F) panels) observed in
the dilution experiment confirms the different nature of
the corresponding arrested states: a Wigner glass (G2)
and a gel (G1), dominated respectively by repulsive and
attractive interactions at high and low concentrations.

The striking result of a low-concentration gel network
FIG.4: Starting(A),intermediate(B)andfinal(C)statesof
andofahigh-concentrationdisconnectedWignerglassis
alowconcentrationsampleatCw =1.5%: theinitialgelstate
G1 is not macroscopically affected by the addition of water atoddswithpreviousstudiesofsimplersystems[7,8,28].
(C). Starting (D), intermediate (E) and final (F) states of a We attribute this unexpected scenario to the separate
high concentration sample at Cw = 3.0%: after the addition timescalescontrollingtheinteractionsandthe twoarrest
of water (L) the original glassy state G2 fluidizes (F). processes [15]. While repulsion is felt almost immedi-
ately after samples are prepared, attraction, due to its
anisotropic nature and to the presence of an effective
3 for two samples with Cw = 2.4% and Cw = 3.0%, in repulsive barrier, develops on a much longer timescale
comparison with Sth(Q). In the inset, simulated, the- as in reaction-limited aggregation. Long-time attraction
oretical and measured S(Q) for sample Cw = 2.4% are may also affect the repulsive Wigner glass, through the
compared. Hence,the favorablecomparisonofsimplified formation of subsequent additional bonds. Indeed, rhe-
theoryandsimulationswith experimentalmeasurements ological measurements for rejuvenated samples show a
providesevidence thatour effectiveapproachis useful to dependence on the idle time waited after the glass is
describe disc-shaped objects in this regime. formed [29]. To elucidate this point we have performed
file://C:\Roberta\Roma\articoli\aarticoli MIEI\Laponite\LapoWigner\Sottomesso\Accettato_20_01_10\Fig4... 1/22/2010
So far we have reported evidence of the existence of a anadditionaldilutionexperimentonthe highconcentra-
WignerglassstateinLaponitebythecombinationofex- tionsamplewaitingoneweekafterdynamicalarresttakes
periments,theoryandsimulationfor2.0%≤Cw ≤3.0%. place. In this case the system does not melt, probably
At lower concentrations structural measurements have due to intervening long-time attraction which strength-
shown a marked growth of S(Q) at low Q with waiting ens the glass. However the unmelted final state is dif-
time, which was attributed to the presence of attractive ferent from that observed at low concentration, while
interactions determining an arrested state of attractive the latter remains unchanged and water does not pen-
(orgel)nature[18]. Alreadyforthelowestconcentration etrateintoit, theformerseemstoslowlyabsorbwaterin
shownhere(Cw =2.0%),theagreementbetweenSM(Q) the bulk. SAXS measurements show that S(Q) does not
and Sth(Q) is less good in the low Q range, as visible change significantly in this time window demonstrating
in Fig. 2. This might be an indication of the increasing that the disconnected structure of the repulsive glass is
role of attractive interactions upon lowering concentra- preserved despite the intervening attraction, and hence
tion. Hence, we performthe dilutionexperiment alsofor the resulting state cannot be considered an attractive
a low concentration sample expecting a different result glass in the most common sense.
with respect to the high concentration one.
In conclusion, throughthe combinationof dilution ex-
In Fig. 4 the dilution experiment is shown for a low
periments, SAXS experiments, theory and simulations,
(C = 1.5%) and a high (C = 3.0%) concentration
w w
we have shown the presence of a disconnected Wigner
sample. The samples are left to age up to the final cor-
responding arrested states, respectively of gel (G1) and glass state in a screened charged colloidal system. This
glass (G2) nature for low and high concentrations [18]. arises at a larger (but still very low) concentration with
respecttotheonewhereagelnetworkisfound,thanksto
While the sample at C = 3.0% arrests within 50 h,
w
the different timescales controlling the repulsive (short-
the one for C = 1.5% takes several weeks [15, 17]. Af-
w
ter arrest takes place deionized water (L) is added and time) andattractive(long-time)interactions. We expect
thesefindingstoberelevanttoothercomplexliquidswith
panels (A) and (D) show the identical situation for the
competinginteractionsasanisotropicpatchycolloids[30]
two cases. However the evolution of the two samples
and globular proteins [31].
soon becomes dramatically different. The arrested state
of the high concentration sample (G2) starts to fluidify We thank F. Sciortino for fruitful discussions and
((E) panel) up to reach a final liquid state ((F) panel). ESRFforprovisionofbeamtime. EZacknowledgesERC-
On the contrary, the low concentration sample does not 226207-PATCHYCOLLOIDSfor support.
5
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