Kinetic, thermodynamic, and Adam-Gibbs Fragilities Srikanth Sastry - PowerPoint PPT Presentation

Kinetic, thermodynamic, and Adam-Gibbs Fragilities Srikanth Sastry TIFR Centre for Interdisciplinary Sciences, Hyderabad, India Jawaharlal Nehru Centre for Advanced Scientific Research Bengaluru, India Symposium on Fragility, JNCASR, Bengaluru, India January 8, 2014

In collaboration with: Anshul Deep Singh Parmer (TCIS) Shiladitya Sengupta (JNCASR/TCIS) Frederic Affouard (Lille) Filipe Vasconcelos (Lille) Sengupta et al , J Chem Phys, 135, 194503 (2011) + ongoing (unpublished) work

Outline  How do we understand the rapid rise of structural relaxation times in glass forming liquids?  How does fragility – the rapidity of rise of relaxation times - depend on the nature of the interparticle interactions ?  Can we understand the fragility in terms of the variation of the configurational entropy?  What role is played by the high temperature activation energy? Approach: Study relaxation times and configurational entropy in model liquids using computer simulations to address these questions.  Tune the “softness” of the interaction potential  Configurational entropy and relaxation times for different softnesses  Tune the barrier heights and study its role in determining fragility.

The glass transition  Viscosities of supercooled liquids rise rapidly at low temperatures, well described (but not uniquely) by Vogel-Fulcher-Tammann relation  The glass transition – When viscosity reaches 10 13 poise, they stop flowing on experimental time scales (relaxation times ~ 100 s)  “Laboratory glass transition” seen for wide range of substances, and is a kinetic effect.  How do we understand the rapid rise of viscosities, relaxation times?

Fragility (kinetic definition)  Data collapse when T scaled with Tg? – No, Instead, a range of behavior.  How rapidly the viscosity changes is called the fragility of the glass former.  Well described by the VFT (Vogel Fulcher Tammann) form.     1 h  h 0 exp     K VFT T T 0  1         K VFT – kinetic fragility index ฀  Fig: C. A. Angell, Jl. of Non-Crystalline Solids , 102 , 205 (1988).

The Adam-Gibbs Relation • Builds on Gibbs-DiMarzio (GD) theory describing the glass transition as an entropy vanishing transition. • Connection to dynamics. • Views a liquid as divided into cooperatively rearranging regions of size z. • Probability of rearrangement: • Entropy of each CRR roughly constant regardless of size. • Total entropy of the system • Results in expression for relaxation times: • Tested and found to be a good description of experimental and simulation data. • Configurational entropy in simulations estimated via the multiplicity of local energy minima, or inherent structures.

Fragility (thermodynamic definition)  Thermodynamic definition of fragility (K T )   A      exp from configuration entropy 0   TS  Kinetic and thermodynamic definitions c   connected if AG relation holds T      TS 1   c T   T  Relation with energy landscape of the liquid: K Broader distribution of potential energy minima  more fragile Potential energy minima = Inherent Structures (IS) Fig.: S. Sastry, Nature , 409 , 164 (2001) Ref.Talk by Shiladitya Sengupta But, can we say something about how fragility depends on the nature of interatomic interactions?

Fragility and the nature of interactions I softness of interactions Computer simulation study using (p,q) potentials [Bordat et al PRL 2004] Fragility from VFT fits to relaxation times Bordat et al found that as the interaction potential became softer, the fragility increased. The slope is proportional to fragility.

Fragility and the nature of interactions Weitz and co-workers studied colloidal fluids of microgel particles, whose softness can be varied. Mattson et a l Nature 2009 They find: Hmm…

Fragility and the nature of interactions: What to expect? Intuitively, a system with softer interactions can have better and more robust packing of particles, a narrower distribution of energies, and therefore should be stronger. Various findings are consistent with this intuitive expectation:  "..more deformable molecules fill space better than hard molecules, leading to stronger fluids that are less sensitive to the structural changes induced by temperature variation.” (Douglas & coworkers JCP 2007).  Fragility decreases with increasing polydispersity (Bagchi & co- workers PRL 2008). So: Are the simulation results incorrect, or they are telling us something new?

Tuning softness to tune fragility  Simulation * of model glass formers with tunable LJ like interactions  kinetic fragility increases with increasing softness  soft is fragile ?    q p     r r         min min V ( r ) p q        p q r r    Experiments ** on deformable Softness is a measure of how colloid particles  kinetic fragility steeply the repulsive interaction rises decreases with increasing softness  soft is strong ?  What about thermodynamic fragility ? Not known. Study the model systems of Bordat et al, and do thermodynamic analysis, by • P. Bordat, F. Affouard and M. Descamps, calculating the configurational entropy. Phys. Rev. Lett., 93 , 105502 (2004). ** J. Mattsson et. al., Nature , 462 , 83 (2009) C. A. Angell and K. Ueno, Nature , 462 , 45 (2009) (News and views)

Simulation Details 80:20 binary mixture, N = 1500. Density = 1.2 Model I: q = 12, p =11 Model II: q = 12, p = 6 Model III: q = 8, p = 5 Temperatures above and below onset temperature. 3 – 5 sample runs for each temperature, each run > 100  a  Diffusion coefficients and relaxation times (from overlap function q(t)) to obtain kinetic fragilities. Configurational entropy to obtain thermodynamic fragility. 

Kinetic Fragility vs. softness Relaxation time Diffusivity Increasing Increasing softness softness Fragility plot Diffusivity Activation energy E(T) scaled by high T value E 0 vs. k B T / E 0 Increasing Increasing softness softness Relaxation time Kinetic fragility increases with increasing softness  supporting Bordat et. al. (2004)

Thermodynamic fragility vs. softness   T      TS 1   c T   T K K T = slope Increasing softness Thermodynamic fragility decreases with increasing softness  How to reconcile the opposite trends?  Possibility 1: Kinetic (K VFT ) and thermodynamic (K T ) fragility are unrelated. Incorrect if Adam Gibbs relation holds for all softness.  Possiblity 2: Coefficient A in AG relation depends on softness/system.

Reconciling the trends : AG fragility Diffusivity Relaxation time Increasing Increasing softness softness    Adam Gibbs relation holds for all softness.     1    exp     0  Estimate kinetic fragility using full AG T      K 1   VFT      T  relation: 0 K     T A K (assuming T T )      exp AG 0 K A 0   TS c  Both K T and „A‟ decreases with softness.   T      TS 1    kinetic fragility increases. c T   T K

Understanding softness dependence of „A‟  Extrapolate AG relation to high T Diffusivity  Estimate „A‟ and AG fragility from high T activation energy Increasing     A E softness          0 ( T ) exp exp     0 0     TS ( T ) k T c B  E S ( )  est 0 c A k B K  T K AG est A I = kinetic fragility from VFT fit. K VFT II = kinetic fragility from VFT fit using T 0 = T K K VFT Diffusivity Relaxation time Diffusivity Relaxation time I II I II K VFT K VFT K AG K VFT K VFT K AG A est A est Model A A 0.34 0.24 0.22 0.20 0.19 0.14 I 2.27 2.52 2.88 3.91 0.38 0.26 0.27 0.21 0.19 0.17 II 1.35 1.20 1.79 1.87 0.40 0.30 0.32 0.26 0.21 0.21 III 0.71 0.65 1.02 1.00 Kinetic fragility estimate using full AG relation (K AG ) and high T behaviour II ). agrees quantitatively with direct values (K VFT Partial success predicting A behavior on density scaling (not shown).

Fragility and the nature of interactions II Dependence on high T activation energy Recap :     A E          0 ( T ) exp exp     Contribution from thermodynamics 0 0     TS ( T ) k T c B  E S ( )  Contribution from high temperature est 0 c A k Activation energy B K  T K AG est A Can we tune the interatomic interaction such that static structure and thermodynamics remains same but the kinetics are different ?  Previous work (Saika-voivod et al ., PRE, 90, 041401, 2004) suggests that this is indeed possible by adding a barrier of finite height h but infinitesimal width to the interparticle potential  Expectation : tunable barrier height “h” changes the bond lifetime (kinetics) without changing the static structure and thermodynamics

Anticipated by Angell..by pure thought..?! Angell, in NATO ASI E 188:133 (1990)