# Bulletin of the American Physical Society

# APS March Meeting 2022

## Volume 67, Number 3

## Monday–Friday, March 14–18, 2022; Chicago

### Session Y16: Molecular Glasses

8:00 AM–11:00 AM,
Friday, March 18, 2022

Room: McCormick Place W-184A

Sponsoring
Units:
DPOLY DSOFT DCP DMP

Chair: Rodney Priestley, Princeton University

### Abstract: Y16.00007 : Rigorous foundation of the Adam-Gibbs relation*

9:36 AM–9:48 AM

#### Presenter:

Takashi Odagaki

(Kyushu University & RISE Inc.)

#### Author:

Takashi Odagaki

(Kyushu University & RISE Inc.)

_{??RR}>=N/L. Denoting the probability of finding the k-th CRR of size ??

_{??}by ??

_{??}, I find that the configurational entropy is given by ??

_{??}= <−??

_{??}lnΠ

_{??=1}

^{??}??

_{??}> =????

_{??}

^{∗}=??

_{??}

^{∗}??∕<??

_{??RR}> with ??

_{??}

^{∗}=??

_{??}ln2. The transition rate within the k-th CRR can be written as ??

_{??}=??

_{0}exp (−Δ?? ??

_{??}/??

_{??}??), where Δ?? is the activation free energy per particle and ??

_{0}is the attempt frequency. Then, the average transition rate is given by

*W*(

*T*)= (Π

_{k=1}

^{??}

*W*

_{??})

^{1/??}=??

_{0}exp (−Δ?? Σ

_{??=1}

^{??}??

_{??}/??k

_{??}??).Therefore, the transition rate is given by

*W*(

*T*)= ??

_{0}exp [−Δ?? ????

_{??}

^{∗}/??

_{??}????

_{??}(??)], which is the Adam-Gibbs relation. With the proper definition of CRR and the configurational entropy, I assess various estimations of the size of CRR reported before.

*This work was supported in part by JSPS KAKENHI (C) (18K03573).

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