Landscapes and fragilities

M.

Goldstein

, , ().

F. H.

 

Stillinger

and

T. A.

 

Weber

,  , ();

F. H.

Stillinger

and

T. A.

Weber

, , ().

The total number of inherent structure of the PEL is the product of $ΩN$ times the trivial factor $N!$ due to particle permutation.

C. A.

 

Angell

,  , ();

C. A.

 

Angell

,  , ();

R.

Böhmer

,

K.

Ngai

,

C. A.

Angell

, and

D. J.

Plazek

, , ().

C. A.

Angell

, , ().

A. P.

Sokolov

,

E.

Rössler

,

A.

Kisliuk

, and

D.

Quitmann

, , ().

S.

Yannopoulos

and

G.

Papatheodorou

, , ().

R.

Hall

and

P.

Wolynes

, , ().

J. C.

Dyre

,

N. B.

Olsen

, and

T.

Christensen

, , ().

J. C.

Dyre

, , ().

J. C. Dyre and N. B. Olsen, cond-mat/0211042.

K.

Ngai

, , ().

R.

Bohmer

and

C. A.

Angell

, , ().

I. M.

Hodge

, , ().

T.

Scopigno

,

G.

Ruocco

,

F.

Sette

, and

G.

Monaco

, , ().

X.

Xia

and

P. G.

Wolynes

, , ().

U. Buchenau and A. Wischnewski, cond-mat/0401088.

M. L.

Ferrer

,

H.

Sakai

,

D.

Kivelson

, and

C.

Alba-Simionesco

, , ().

C. A.

Angell

,

K.

Ngai

,

G. B.

McKenna

,

P. F.

McMillan

, and

S. W.

Martin

, , ().

P. G.

Debenedetti

and

F. H.

Stillinger

, , ().

F. H.

Stillinger

, , ().

B.

 

Doliwa

and

A.

 

Heuer

,  , ();

B.

Doliwa

and

A.

Heuer

, , ().

C. A.

Angell

, , ().

C. A.

Angell

, , ().

R. J.

Speedy

, , ().

S.

Sastry

, , ().

R.

Richert

and

C. A.

Angell

, , ().

J. L.

Green

,

K.

Ito

,

K.

Xu

, and

C. A.

Angell

, , ().

L.

Wang

,

V.

Velikov

, and

C. A.

Angell

, , ().

J. P.

Garrahan

and

D.

Chandler

, , ().

H.

 

Vogel

,  , ();

G. S.

 

Fulcher

,  , ();

G.

Tamman

and

W.

Hesse

, , ().

L.-M.

Martinez

and

C. A.

Angell

, , ().

A remarkable exception is represented by vitreous silica, which is one of the strongest systems according to the kinetic fragility while it turns out very close to glycerol (an intermediate value of $mA)$ as far as the T dependence of the excess entropy is concerned.

G.

Adam

and

J. H.

Gibbs

, , ().

H.

Tanaka

, , ().

F. H.

 

Stillinger

and

T. A.

 

Weber

,  , ();

C. A.

 

Angell

and

S.

 

Borick

,  , ();

S. Corezzi, L. Comez, and D. Fioretto, cond-mat/0211379;

D.

Prevosto

,

M.

Lucchesi

,

S.

Capaccioli

,

R.

Casalini

, and

P. A.

Rolla

, , ().

R. J.

Speedy

, , ().

R. J.

Speedy

and

P. G.

Debenedetti

, , ().

R. J.

Speedy

, , ().

F. H.

Stillinger

, , ().

S.

 

Büchner

and

A.

 

Heuer

,  , ();

A.

Heuer

and

S.

Büchner

, , ().

S.

 

Mossa

,

E.

 

La Nave

,

H. E.

 

Stanley

,

C.

 

Donati

,

F.

 

Sciortino

, and

P.

 

Tartaglia

,  , ();

S.

 

Mossa

,

E.

 

La Nave

, and

F.

 

Sciortino

,  , ();

S.

 

Mossa

,

E.

 

La Nave

,

P.

 

Tartaglia

, and

F.

 

Sciortino

,  , ();

E.

La Nave

,

S.

Mossa

,

C.

De Michele

,

F.

Sciortino

, and

P.

Tartaglia

, , ().

F. W.

Starr

,

S.

Sastry

,

E.

La Nave

,

A.

Scala

,

H. E.

Stanley

, and

F.

Sciortino

, , ().

Actually, the microcanonical definition of temperature is $T−1=dS/dE,$ where S it the (total) entropy. At low enough temperature, the latter quantity can be separated in a “configurational” entropy Σ term—that counts the (logarithm of the) number of minima of the PEL—and a “vibrational” term $(Sv),$ that measure the entropy associated to the vibrational motion within the basin of attraction of a given minima. In the harmonic approximation, and with the further assumption that the curvature of the PEL at its minima do not depend on the energy elevation of the minimum itself, $Sv=const$ and, therefore, $dS/dE=dΣ/dE.$

F.

 

Sciortino

,

W.

 

Kob

, and

P.

 

Tartaglia

,  , ();

F.

Sciortino

,

W.

Kob

, and

P.

Tartaglia

, , ().

C. A.

Angell

and

W.

Sichina

, , ().

P. G. Debenedetti, F. H. Stillinger, and C. P. Lewis, preprint.

P. G. Debenedetti, Metastable Liquids. Concepts and Principles (Princeton University Press, Princeton, 1996).

P. G.

Debenedetti

,

F. H.

Stillinger

, and

M. Scott

Shell

,  , ().

C. A.

 

Angell

,

B. E.

 

Richards

, and

V.

 

Velikov

,  , ();

C. T.

Moynihan

, and

C. A.

Angell

, , ().

E.

La Nave

,

S.

Mossa

, and

F.

Sciortino

, , ().

F.

Sciortino

,

E.

La Nave

, and

P.

Tartaglia

, , ().

R. J.

Speedy

, , ().

Note that Eq. (8) in Ref. 26 defines a fragility index with the dimension of energy. In the caption of Fig. 1, Sastry clarifies that—in order to have a dimensionless fragility index—a dimensional quantity is needed in going from from $TSc,$ which is a dimensional quantity and fragility that is dimensionless. In the absence of a good way to calculate ℰ, Sastry choose the Lennard-Jones energy scale $εAA,$ finding support for such a choice in the numerical data. This choice leads to the approximation $K=(ε̄α/2εAA)(1+TK/T),$ to be compared with the exact expression $K=(ε̄α/2E)(1+TK/T),$ reported in Eq. (51).

D.

Huang

and

G. B.

McKenna

, , ().

The existing correlation between thermodynamic $(mT)$ and kinetic $(mS)$ fragilities—as experimentally observed in Ref. 32—is NOT in contradiction with the statement that $Σ(T)$ alone is not sufficient to determine fragility. Indeed, the experimentally observed correlation between $mT$ and $mS$ [discussed in Eq. (11) of the manuscript] can be derived—beyond assuming the proportionality between configurational and excess entropy—from (i) the definition of $mT$ [Eq. (7)]; (ii) the definition of $mS$ [Eq. (2)]; and (iii) the AG relation. We stress that Eq. (11) is independent from whether or not the fragility could be derived from $Σ(T)$ only. Note that, as shown in Eq. (7), the evaluation of $mT$ requires the knowledge of two thermodynamic quantities (the excess entropy and the T derivative of it), but also the knowledge of one dynamical quantity $(Tg).$ The presence of $Tg$ in the definition of $mT$ highlights the need for dynamical information in the evaluation of the fragility.

D.

Perera

and

P.

Harrowell

, , ().

J.

Horbach

and

W.

Kob

, , ().

B. W. H.

van Beest

,

G. J.

Kramer

, and

R. A.

van Santen

, , ().

C. A.

 

Angell

,  , ();

K.

Ito

,

C. T.

Moynihan

, and

C. A.

Angell

, , ().

F.

Starr

,

F.

Sciortino

, and

H. E.

Stanley

, , ().

M.

Hemmatti

,

C.

Moynihan

, and

C. A.

Angell

, , ().

I.

Saika-Voivod

,

P. H.

Poole

, and

F.

Sciortino

, , ().

R. J.

Speedy

, , ().

G. Tarjus, D. Kivelson, S. Mossa, and C. Alba-Simionesco cond-mat/0309579, 2003.