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http://molecularmodelingbasics.blogspot.com
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HeatCapacityandStability
Howdoyoudefineandmeasurethestabilityofnanosystems(thatyoucan’tsee)
Thesimula:onshowsthatyoucanfindthemel:ngtemperaturebymeasuringtheheatcapacityasafunc:onofT
h=p://propka.ki.ku.dk/~jhjensen/calorimetry.html
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U(e
V)
T(K)
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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
0
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0.0014
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