multiple glassy states and anomalous ......we observe diffusion anomaly and reentrance due to...

GAYATRI DAS

Under the supervision of Prof. Francesco Sciortino and Dr. Emanuela Zaccarelli

In collaboration with Nicoletta Gnan and Dr. Matthias Sperl

Dipartimento di FisicaUniversita di Roma La Sapienza

MULTIPLE GLASSY STATES AND ANOMALOUS BEHAVIOR OF COLLOIDAL SYSTEMS:

SIMULATIONS AND THEORY

XXVI Ciclo

OUTLINEOUTLINE

Introduction

Recent studies of multiple glasses in colloids

Attractive colloids Soft colloids

Square shoulder system: theoretical predictions

Square shoulder system: numerical results

Conclusions

1

COLLOIDAL GLASSESCOLLOIDAL GLASSES

At low temperatures and/or high concentrations the system can show a dynamical arrest

Compression Cooling

Glass Crystal

We suppress the crystallization by adding polydispersity to the system

2

Experimental Phase diagram

Pham et al., Science 296, 104 (2002)

Theoretical predictions and numerical/experimental evidences show a reentrant region (creates multiple glass transitions) in the dynamical phase diagram

3

ATTRACTIVE COLLOIDSATTRACTIVE COLLOIDS

MCT Prediction

reentrant fluid region

repulsive glass

attractive glass

Dawson et al., Phys. Rev. E 63, 011401 (2001)

Mode Coupling Theory (MCT)

glass glasstransition

Square Well (SW) potential

Binary mixture of colloidal particles interacting via SW potential

r

V (r)

Δ

4

Theory Experiments

Mayer et al., Nature Materials 7, 780 (2008)

Star polymer

Binary mixture of star polymersfor different density and size ratio

softness

Soft potential

SOFT COLLOIDSSOFT COLLOIDS

r

V (r)

SQUARE SHOULDER SYSTEMSQUARE SHOULDER SYSTEM

Δ=0.13

U /k BT

Δ=0.15

G

L

U /k BT

G

G

G

L

Sperl, Zaccarelli, Sciortino, Kumar, Stanley, Phys. Rev. Lett. 104, 145701 (2010)

control parameters

and

MCT predictions:

● existence of glass-glass line with end point higher order singularities

● presence of diffusion anomalies along the liquid-glass line

5

MODE COUPLING THEORY

ϕ ,T Δ

glass1

2

NUMERICAL INVESTIGATIONNUMERICAL INVESTIGATION

6

SIMULATION TECHNIQUES:

The system can be quenched to lower temperature at higher packing fraction compared to one-component system

σ AA/σBB=1.2We simulated a mixture of particles of size ratio N=200050 :50

Event Driven molecular dynamics simulations

● NVT ensemble

● NVE ensemble

Δ=0.15

● We performed MCT calculations using as input the static structure factors obtained within molecular dynamics simulations

● We estimated the location of two higher order singularities by superimposing the MCT line on the arrest line evaluated from simulations. We then performed the following bilinear transformation

ϕ → 1.1046ϕ+0.0038

T → 0.9052T−0.0111

PHASE DIAGRAM FOR

7

Das et al., J. Chem. Phys. 138, 134501 (2013)

NUMERICAL INVESTIGATIONNUMERICAL INVESTIGATION

DYNAMICS CLOSE TO HIGHER ORDER SINGULARITIESDYNAMICS CLOSE TO HIGHER ORDER SINGULARITIES

MEAN SQUARE DISPLACEMENT (MSD) Δ=0.15PHASE DIAGRAM FORϕ=0.525

A characteristic subdiffusive behavior was observed at intermediate times for

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0.1≤tD0≤10 T<0.4

DENSITY AUTO CORRELATION FUNCTION Δ=0.15PHASE DIAGRAM FORϕ=0.525

The fitting is done with general asymptotic decay law for the correlation function for aset of qvectors close to the higher order singularity A3

Φq(t )∼ f q+hq(1) ln (t /τ )+hq

(2)(ln (t /τ ))2

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DENSITY AUTO CORRELATION FUNCTION Δ=0.15PHASE DIAGRAM FOR

● The transition from concave-to-convex in the shape of density auto-correlation function at the critical value of indicates the presence of higher order singularity

● For this critical value of the density auto-correlation function shows a pure logarithmic behavior in the vicinity of higher order singularity

ΦqAA(t)

q

q

A3

ϕ=0.525


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Since the singularities are buried in the glassy phase, we can observe their presence only indirectlyand their influence on the liquid phase is weak

Δ

Δ=0.15PHASE DIAGRAM FOR

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The only higher order singularity accessible from the liquid phase is the predicted from MCT

can be obtained by finely tuning the value of the control parameter A4

A4

A3


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II. Numerical investigations for Δ=0.17

Mapped the MCT lines onto the arrested glass curve obtained from simulationswith the following bilinear transformation

ϕ → 1.115668ϕ+0.0135

T → 0.741929T+0.0061

NUMERICAL INVESTIGATION


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ϕ=0.50

T

DYNAMICS CLOSE TO A3 HIGHER ORDER SINGULARITY

MEAN SQUARE DISPLACEMENT

● We investigated the presence of higher order singularity moving along the isochore

● The appearance of subdiffusivity in mean square displacement on lowering temperature indicates the presence of higher order singularity

A3

13


A3

The fitting is done with general asymptotic decay law for the correlation function for aset of qvectors close to the higher order singularity


(2)(ln (t /τ ))2

DENSITY AUTO CORRELATION FUNCTION

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ϕ=0.585

● We studied the dynamics in order to locate the presence of higher order singularity.

● A characteristic subdiffusive behavior of mean square displacement observed for ϕ=0.585, T=0.325

A4

MEAN SQUARE DISPLACEMENT

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We did the fitting with general asymptotic decay law for the correlation function for aset of qvectors close to the higher order singularity A4


(2)(ln (t /τ ))2

DENSITY AUTO CORRELATION FUNCTION

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, T=0.325Δ=0.17PHASE DIAGRAM FOR


LOGARITHM APPROACHING A4

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The density auto-correlation function shows logarithmic behavior to three decades in magnitude even at high packing fraction, .ϕ=0.58

We tried to explore the endpoints of glass-glass line by studying the isodiffusivity lines associated to the invariant dynamics

invariant dynamicsThis seems the glass-glass line brings a new dynamics named

The dynamical features are indistinguishableclose to middle points (rather than endpoints) of the putative glass-glass line

PECULIAR DYNAMICS CLOSE TO THE SINGULARITIES

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INVARIANT DYNAMICS ALONG ISODIFFUSIVITY LINE

D /D0=3.6E-4, 5.5E-05, 9.5E-06

● We observed invariant dynamics along isodiffusivity lines

● The dynamics are indistinguishable along the invariant line

We have drawn invariant dynamics along three lowest normalized isodiffusivity lines

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DYNAMICS ALONG ISODIFFUSIVITY LINE

● We investigated, whether the two higher order singularities, not having any distinctive feature with respect to other points along the glass-glass line

● We compare MSD and for invariant state points with respect to other state points along isodiffusivity line D /D0= 5.5E-05

ΦqAA(t )

20

21

DYNAMICS ALONG ISODIFFUSIVITY LINE

Mean square displacement and exactly coincides with each other for the invariant state points along isodiffusivity line D /D0=5.5E-05

ΦqAA(t )

INVARIANCE BREAKS

The invariant dynamics breaks for non-invariant state points along isodiffusivity . The thick line represents the invariant dynamics as a reference.D /D0=5.5E-05

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23


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III. Glassy behavior of the SS system in zero temperature limit

DIFFUSION ALONG ISOCHORES ARRHENIUS BEHAVIOR OF DIFFUSIVITY

DYNAMICAL PROPERTIES

The sharp drop in the diffusion along isochoresindicates that the system is approaching theglassy phase for T →0

The temperature dependance of the diffusivity shows an Arrhenius behavior at low and remains constant with increasing

TT

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LOW DENSITY PHASE DIAGRAM

Δ=0.15

In the low density region the system shows a crossover from fragile to strong behavior at low temperature T

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DO WE HAVE A STRONG GLASS FORMER?

The fitting of density autocorrelation functionsis made with the stretched exponential

Φq(t )=Aq e[−(t / τq)

βq ]

DENSITY AUTOCORRELATION FUNCTIONS ALONG ISOCHORE

BEHAVIOR OF STRETCHING EXPONENT ALONG ISOCHORES

● The value of approaches highest value for most Arrhenius isochores 0.39,0.395

βq

● A highest value of characterizes the strong glass behavior

βq

25

BREAKDOWN OF STOKES-EINSTEIN (SE) RELATION

RELAXATION TIME ALONG ISOCHORE RELAXATION TIME ALONG ISOCHORE

● The behavior of relaxation time with is similar with fitting of stretched exponential and

τ

1 /e● The decay in follows the Arrhenius law

along isochoreτ

● The divergence in the diffusivity at low reflects the violation of SE relation

D τT

● The simple isotropic interaction can enhance the diffusivity and violates the SE relation

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CONCLUSIONS

● We observe diffusion anomaly and reentrance due to cooling for

● A bilinear transformation in and with the scope of mapping the theoretical curve onto the numerical one, allow us to locate numerically two higher order singularities

● Simulations confirm the presence of higher order singularities in terms of subdiffusive behavior in MSD and logarithmic behavior of density autocorrelation functions for some state points in the liquid region

● On increasing , we could see a stronger influence of a higher order singularity due to the presence of a close sign

● Investigating the exact location of higher order singularity in equilibrium phase by exploring different values of (on going work ...)

● The simple competition between two length scales has revealed a new invariant dynamics along the the putative glass-glass line

● We explore the low and region of the phase diagram for and achieve the glass transition in low density region for

● The system retains strong like character in the small region of the phase diagram (i.e. the crossover from fragile to strong behavior)

● A significant violation of SE relation is observed in analogy to other glass-forming systems

ϕ TA3

Δ=0.17A4

A4

Δ=0.15

Δ

T →0ϕ T Δ=0.15

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THANK YOU

multiple glassy states and anomalous ......we observe diffusion anomaly and reentrance due to...

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