Clarification and Questions on “Growing Length and Time Scales in Glass-forming Liquids”

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Clarification and Questions on “Growing Length and Time Scales in Glass-forming Liquids”

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Clarification and Questions on “Growing Length and Time Scales in Glass-forming Liquids”

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Clarification and Questions on“Growing Length and Time Scales in Glass-forming Liquids”

Ryoichi Yamamoto

Kyoto University

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Introduced a “temporal quantity Q(t0)” which is sensitive to particle motions associated with a microscopic length scale “a” and a lag time ”t”.

Then, set “a=0.3s ” and “t=t4”.

average part (later)

fluctuating part

Examined FSS for χ4 and B.

consistent

OK, FSS seems to work for the “fluctuating” part.

Next, examined FSS for the structural relaxation time.

FSS doesn’t work for the average relaxation time...

Summary so far...

Q1: FSS seems to work well for the “fluctuation part” but fails for the “average part”. Does this statement make sense?

Finaly, try FSS for Configurational Entropy.

Very interesting results, but still confusing...

FSS seems to work for Sc, but the fitted values of x do not mach with those from χ4 or B at all.

The relaxation time fits very well with AG fitting.

Q2: What does this result suggest ? Decoupling of glowing time scale and glowing length scale with decreasing system size??

fluctuations in “order parameter “

time-space correlation (2-point)

Langevin Eq.

need MCT

This is so-called critical slowing-down. Glowing length directly leads to the slowing-down!!

fluctuations in “local dynamics”

time-space correlation (4-point)

RY&Onuki (’97, ‘98), Glotzer (‘99), Berthier (‘04), Weeks (?), IMCT (‘06),...

average relaxation

any physics??

4-point relaxation time

(migration time of DH)

coupling??

2-point relaxation time

(usual relaxation time)

- What is the true identity of the DH and glowing length scale ξ?
- Any correspondence with static properties?
- Mosaic phase? Hidden order parameters? CRR? How can we identify them???

- What is the main role of the glowing length scale ξ?
- We have no proper theory for bridging between glowing length scale (ξ) and glowing time scales (t4,k, tqm).
- GT vs. CP-> more differences than similarities.
- Does ξ contribute to slowdown the system, or accelerate it? (Remember Weeks’ talk.)
- Is ξ nothing more than a by-product of slowing-down?

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