HeatCapacityandStability

Howdoyoudefineandmeasurethestabilityofnanosystems(thatyoucan’tsee)

Thesimula:onshowsthatyoucanfindthemel:ngtemperaturebymeasuringtheheatcapacityasafunc:onofT

h=p://propka.ki.ku.dk/~jhjensen/calorimetry.html

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Thesimula:oncomputesTasafunc:onofUHereweswitchtheaxes

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Thedataisnoisyprimarilybecauseofthefasthea:ngrateWesmoothitbyfiPngittoapolynomial(bluecurve)

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Fromthesmootheddata(bluecurve)wecancomputetheheatcapacity(redcurve,righty‐axis)

CV =∂U∂T

⎛⎝⎜

⎞⎠⎟V

≈U(T2 ) −U(T1)

T2 − T1

Figurefrom:h=p://dx.doi.org/10.1016/S1631‐0705(02)01326‐9Thisar:cleisalsointes:ng:h=p://dx.doi.org/10.1021/ja802389d

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Reallifeapplica:ons

Whyistheheatcapacityhighestataphasetransi:on?

Heatcapacityandenergyfluctua:ons

CV =∂U∂T

⎛⎝⎜

⎞⎠⎟V

=E − E( )2kT 2

(Page230‐231inMolecularDrivingForcesrememberthat)U = E

Thesystemchangesmostataphasetransi:onsotheenergyfluctua:onsarelargesthere

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h=p://propka.ki.ku.dk/~jhjensen/cvandt.html 7

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h=p://propka.ki.ku.dk/~jhjensen/cvandt.html 8

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h=p://propka.ki.ku.dk/~jhjensen/cvandt.html 9

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