Basics of thermodynamics & kinetics презентация

Содержание

1. Basics of thermodynamics & kinetics
2. THERMODYNAMISC & STATISTICAL PHYSICS
3. WHAT IS “TEMPERATURE”? EXPERIMENTAL DEFINITION : = t,oC + 273.15o EXPERIMENTAL DEFINITION
4. Benoît Paul Émile Clapeyron (1799 – 1864)
5. THEORY Closed system: energy
6. COMPARE: Probability1(ε1) = Mt(E-ε1) / M(E) =
7. Josiah Willard Gibbs (1839 –1903)
8. (dSth/dE) = 1/ T P1(ε1) ~ exp(-ε1/kBT)
9. Unstable (explodes, v → inf.)
10. Separation of potential and kinetic energies in
11. IN THERMAL EQUILIBRIUM: TCOORD = TKIN
12. TRANSITIONS: THERMODYNAMICS
13. gradual transition “all-or-none” (or 1st order) phase
14. Second order phase transition change Recently observed in proteins; rare case
15. LANDAU: Helix-coil transition:
16. Лев Давидович Ландау (1908 - 1968) Нобелевская Премия 1962
17. TRANSITIONS: KINETICS
18. n# = n × exp(-ΔF#/kBT) n#
20. phase separation Coil - Coil - ≈Native ≈
21. TRANSITION RATE = SUM OF RATES
22. t0→… →finish ≈ t0→#1→ finish + t0→#2→
23. _ _ TRANSITION TIME IS ESSENTIALLY
24. DIFFUSION: KINETICS
25. Mean kinetic energy of a particle:
26. Friction stops a molecule within picoseconds:
27. Friction stops a molecule within picoseconds:
28. The End
29. For “small part”: Pj(εj) = exp(-εj/kBT)/Z(T);
30. Thermostat: Tth = dEth/dSth
31. Along tangent: S-S(E1) =
32. Separation of potential energy in classic (non-quantum)
33. P(εKIN+εCOORD) ~ exp(-εCOORD/kBT)•exp(-εKIN/kBT) P(εCOORD) = exp(-εCOORD/kBT)
34. “all-or-none” (or first order) phase transition F(T1) ________________

THERMODYNAMISC & STATISTICAL PHYSICS

Слайд 1PROTEIN PHYSICS

LECTURES 7-8

Basics of thermodynamics & kinetics

Слайд 2THERMODYNAMISC
&
STATISTICAL PHYSICS

Слайд 3WHAT IS “TEMPERATURE”?

EXPERIMENTAL DEFINITION :
= t,oC + 273.15o
EXPERIMENTAL DEFINITION

Слайд 4Benoît Paul Émile Clapeyron (1799 – 1864)
William Thomson, 1st Baron Kelvin

(1824 -1907)

Ludwig Eduard Boltzmann (1844 – 1906)

Слайд 5THEORY

Closed
system:
energy
E = const
CONSIDER: 1 state of “small part” with

ε & all
states of thermostat with E-ε. Mall(E-ε) = 1 • Mt(E-ε)

k • ln[Mt(E-ε)] ≡ St(E-ε) ≅ St(E) - ε•(dSt/dE)|E

Mt(E-ε) ≅ exp[St(E)/k] • exp[-ε•(dSt/dE)|E/k] conclusions

WHAT IS “TEMPERATURE”?

S ~ ln[M]

Слайд 6COMPARE:
Probability1(ε1) = Mt(E-ε1) / M(E) =

exp[- ε1• (dSt/dE)|E/k] (GIBBS)
and
Probability1(ε1) = exp(-ε1/kBT) (BOLTZMANN)

One has: (dSt/dE)|E = 1/ T

k = kB
______________________________________________________________
ε ⇒ ε-kBT, M ⇒ M × exp(1) ≡ M × 2.72

Слайд 7Josiah Willard Gibbs
(1839 –1903)
Яков Григорьевич Синай,

1935
Abel Prize 2014
“…связь между порядком и хаосом…” 1/r3

Joseph Liouville
(1809 - 1882)

Слайд 8(dSth/dE) = 1/ T
P1(ε1) ~ exp(-ε1/kBT)
Pj(εj) = exp(-εj/kBT)/Z(T); Σj

Pj(εj) ≡ 1
Z(T) = Σi exp(-εi/kBT) partition function
СТАТИСТИЧЕСКАЯ СУММА

Слайд 9Unstable (explodes, v → inf.)

Unstable (falls)

stable

↑
unstable
↙

Along tangent: S-S(E1) = (E-E1)/ T1
i.e., F = E - T1S = const (= F1 = E1 - T1S1)

Слайд 10Separation of potential and kinetic energies
in classic (non-quantum) mechanics:

P(ε) ~ exp(-ε/kBT)

// Classic: ε = εCOORD + εKIN
εKIN = mv2/2 : does not depend on coordinates
Potential energy εCOORD: depends only on coordinates

P(ε) ~ exp(-εCOORD/kBT) • exp(-εKIN/kBT)

Z(T) = ZCOORD(T)•ZKIN(T) ⇒ F(T) = FCOORD(T)+FKIN(T)

========================================================================================================================

Elementary volume: Δ(mv)Δx ≅ ħ ⇒ (Δx)3 ≅(ħ/|mv|)3
= (ħ2/[mkBT])3/2

Δ(mv) ≅ m|v|, and |mv| ≅ (mkBT)1/2

Слайд 11IN THERMAL EQUILIBRIUM:

TCOORD = TKIN = Touter

We may consider further
only potential

energy:

E ⇒ ECOORD
M ⇒ MCOORD
S(E) ⇒ SCOORD(ECOORD )
F(E) ⇒ FCOORD , etc.

Слайд 12TRANSITIONS:
THERMODYNAMICS

Слайд 13gradual transition
“all-or-none” (or 1st order) phase transition
coexistence
& jump-like
transition
coexistence
(ΔE/kT)(ΔT/T) ~ 1
Transition:

|ΔF1|= |-ΔS×ΔT| ~ kT*

ΔE-T*ΔS=0

Слайд 14Second order phase transition
change
Recently observed in proteins;
rare case

Слайд 15LANDAU: Helix-coil transition:

Melting:
NOT 1-s order phase transition 1-s order phase transition

Helix & coil: 1D objects Ice & water: 3D objects

ΔFhelix_n = Const + n×f ΔFICE_n = C×n2/3 + n×f
1D interface 3D interface
Mid-transition: f = 0
ΔShelix_n ~ ln(N) positions ΔSICE_n ~ ln(N)
N : very large; n ~ αN, α<<1 (e.g., α~0.001)
Const << ln(N) α2/3⋅N2/3 >> ln(N)
phases mix phases do not mix

Слайд 16Лев Давидович Ландау
(1908 - 1968)
Нобелевская Премия 1962

Слайд 17TRANSITIONS:
KINETICS

Слайд 18n# = n × exp(-ΔF#/kBT)
n#
n
→
TRANSITION TIME:
t0→1 = t0→#1→ ≈

≈ τ#→ (n/n#) = τ#→ × exp(+ΔF#/kBT)

Not
“slowly goes”,
but
climbs, falls
and climbs again…

falls

τ#→

Слайд 19

Слайд 20
phase separation

Coil
- Coil

- ≈Native
≈

Слайд 21TRANSITION RATE = SUM OF RATES

(or: ≈the highest rate)

1/TIME = (1/τ#→) × exp(-ΔF1#/kBT) + (1/τ#→) × exp(-ΔF2#/kBT)

PARALLEL REACTIONS:

RATE = 1/ TIME

Слайд 22t0→… →finish ≈ t0→#1→ finish + t0→#2→ finish + …
#
#
start
_
CONSECUTIVE REACTIONS:
TRANSITION

TIME ≅ SUM OF TIMES
(or: ≈ the highest time)

TIME ≈ τ#→ × exp(+ΔF1#/kBT) + τ#→ × exp(+ΔF2#/kBT) + …

steady-state approximation

t0→… → ≈ t0→#1→1 + t1→#2→ 2 + …

start

“long barrier”

“downhill”

“long barrier”:

finish

Слайд 23_
_
TRANSITION TIME IS ESSENTIALLY
EQUAL FOR “TRAPS” AT AND OUT OF

PATHWAYS OF CONSECUTIVE REACTIONS:

TRANSITION TIME ≅ SUM OF TIMES
(or: ≈the longest time)

# main

finish

start

“trap”: on

“trap”: out

main #

Слайд 24DIFFUSION:
KINETICS

Слайд 25Mean kinetic energy of a particle: •mv2/2• ~ kBT

= Σj Pj(εj) ∙ εj v2 = (vX2)+(vY2)+(vZ2) Maxwell :

in 3D

James Clerk

(1831 –1879)

Слайд 26Friction stops a molecule within picoseconds:

m(dv/dt) = -(3πDη)v [Stokes

law], or m(dv/dt) = -(kBT/Ddiff)v
[Einstein-Stokes]
D – diameter;
m ~ D3 ⋅ 1g/cm3 – mass;
η – viscosity

tkinet ≈ 10-13 sec × (D/nm)2
in water

Sir George Gabriel Stokes Albert Einstein
DIFFUSION: (1819-1903) (1879-1995)

During tkinet the molecule moves by Lkinet ~ v•tkinet

Then it restores its kinetic energy mv2/2 ~ kBT from thermal kicks of other molecules, and moves in another random side

CHARACTERISTIC DIFFUSION TIME: nanoseconds

Слайд 27Friction stops a molecule within picoseconds:

tkinet ≈ 10-13 sec × (D/nm)2 in water

DIFFUSION:
During tkinet the molecule moves by Lkinet ~ v•tkinet

Then it restores its kinetic energy mv2/2 ≈ kBT from thermal kicks
of other molecules, and moves in another
random side

CHARACTERISTIC DIFFUSION
TIME: nanoseconds

The random walk allows the molecule
to diffuse at distance D (~ its diameter)
within ~(D/L kinet)2 steps, i.e., within

tdifft ≈ tkinet•(D/Lkinet)2 = D2/Ddiff

≈ 4•10-10 sec × (D/nm)3 in water

→

Слайд 28The End

Слайд 29For “small part”: Pj(εj) = exp(-εj/kBT)/Z(T);

Z(T) = Σj exp(-εj/kBT)
Σj Pj(εj) = 1
E(T) = <ε> = Σj εj∙ Pj(εj)
if all εj = ε : #STATES = 1/P, i.e.: S(T) = kB∙ln(1/P)
S(T) = kB = kB∙Σj ln[1/Pj(εj)]∙Pj(εj)
F(T) = E(T) - TS(T) = -kBT ∙ ln[ Z(T)]
STATISTICAL MECHANICS

Слайд 30Thermostat: Tth = dEth/dSth

“Small part”: Pj(εj,Tth) ~ exp(-εj/kBTth);

E(Tth) = Σj εj Pj(εj,Tth)
S(Tth) = kBΣj ln[1/Pj(εj,Tth)]Pj(εj,Tth)
Tsmall_part = dE(Tth)/dS(Tth) = Tth

STATISTICAL
MECHANICS

Слайд 31Along tangent: S-S(E1) = (E-E1)/ T1

i.e.,
F = E - T1S = const (= F1 = E1 - T1S1)

Слайд 32Separation of potential energy
in classic (non-quantum) mechanics:

P(ε) ~ exp(-ε/kBT)

Classic: ε = εCOORD + εKIN
εKIN = mv2/2 : does not depend on coordinates
Potential energy εCOORD: depends only on coordinates

P(ε) ~ exp(-εCOORD/kBT) • exp(-εKIN/kBT)

ZKIN(T) = ΣK exp(-εK/kBT): don’t depend on coord.
ZCOORD(T) = ΣCexp(-εC/kBT): depends on coord.

Z(T) = ZCOORD(T)•ZKIN(T) ⇒ F(T) = FCOORD(T)+FKIN(T)

========================================================================================================================

Elementary volume: Δ(mv)Δx = ħ ⇒ (Δx)3 =(ħ/|mv|)3

Слайд 33P(εKIN+εCOORD) ~ exp(-εCOORD/kBT)•exp(-εKIN/kBT)

P(εCOORD) = exp(-εCOORD/kBT) / ZCOORD(T)

ZCOORD(T) = ΣCexp(-εC/kBT): depends

ONLY
on coordinates

P(εKIN) = exp(-εKIN/kBT) / ZKIN(T)

ZKIN(T) = ΣK exp(-εK/kBT): don’t depend on coord.

T<0: unstable (explodes)
<εKIN> ⇒ ∞ at T<0
due to
P(εKIN) ~ exp(-εKIN/kBT)

Слайд 34“all-or-none” (or first order) phase transition
F(T1)
________________

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Basics of thermodynamics & kinetics презентация

Содержание

Слайд 1PROTEIN PHYSICS

LECTURES 7-8

Basics of thermodynamics & kinetics

Слайд 2THERMODYNAMISC
&
STATISTICAL PHYSICS

Слайд 3WHAT IS “TEMPERATURE”?

EXPERIMENTAL DEFINITION :
= t,oC + 273.15o
EXPERIMENTAL DEFINITION

Слайд 4Benoît Paul Émile Clapeyron (1799 – 1864)
William Thomson, 1st Baron Kelvin

Слайд 5THEORY

Closed
system:
energy
E = const
CONSIDER: 1 state of “small part” with

Слайд 6COMPARE:
Probability1(ε1) = Mt(E-ε1) / M(E) =

Слайд 7Josiah Willard Gibbs
(1839 –1903)
Яков Григорьевич Синай,

Слайд 8(dSth/dE) = 1/ T
P1(ε1) ~ exp(-ε1/kBT)
Pj(εj) = exp(-εj/kBT)/Z(T); Σj

Слайд 9Unstable (explodes, v → inf.)

Слайд 10Separation of potential and kinetic energies
in classic (non-quantum) mechanics:

P(ε) ~ exp(-ε/kBT)

Слайд 11IN THERMAL EQUILIBRIUM:

TCOORD = TKIN = Touter

We may consider further
only potential

Слайд 12TRANSITIONS:
THERMODYNAMICS

Слайд 13gradual transition
“all-or-none” (or 1st order) phase transition
coexistence
& jump-like
transition
coexistence
(ΔE/kT)(ΔT/T) ~ 1
Transition:

Слайд 14Second order phase transition
change
Recently observed in proteins;
rare case

Слайд 15LANDAU: Helix-coil transition:

Слайд 16Лев Давидович Ландау
(1908 - 1968)
Нобелевская Премия 1962

Слайд 17TRANSITIONS:
KINETICS

Слайд 18n# = n × exp(-ΔF#/kBT)
n#
n
→
TRANSITION TIME:
t0→1 = t0→#1→ ≈

Слайд 19

Слайд 20
phase separation

Coil
- Coil

- ≈Native
≈

Слайд 21TRANSITION RATE = SUM OF RATES

Слайд 22t0→… →finish ≈ t0→#1→ finish + t0→#2→ finish + …
#
#
start
_
CONSECUTIVE REACTIONS:
TRANSITION

Слайд 23_
_
TRANSITION TIME IS ESSENTIALLY
EQUAL FOR “TRAPS” AT AND OUT OF

Слайд 24DIFFUSION:
KINETICS

Слайд 25Mean kinetic energy of a particle: •mv2/2• ~ kBT

Слайд 26Friction stops a molecule within picoseconds:

m(dv/dt) = -(3πDη)v [Stokes

Слайд 27Friction stops a molecule within picoseconds:

Слайд 28The End

Слайд 29For “small part”: Pj(εj) = exp(-εj/kBT)/Z(T);

Слайд 30Thermostat: Tth = dEth/dSth

“Small part”: Pj(εj,Tth) ~ exp(-εj/kBTth);

Слайд 31Along tangent: S-S(E1) = (E-E1)/ T1

Слайд 32Separation of potential energy
in classic (non-quantum) mechanics:

P(ε) ~ exp(-ε/kBT)

Слайд 33P(εKIN+εCOORD) ~ exp(-εCOORD/kBT)•exp(-εKIN/kBT)

P(εCOORD) = exp(-εCOORD/kBT) / ZCOORD(T)

ZCOORD(T) = ΣCexp(-εC/kBT): depends

Слайд 34“all-or-none” (or first order) phase transition
F(T1)
________________

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Basics of thermodynamics & kinetics презентация

Содержание

Слайд 1PROTEIN PHYSICSLECTURES 7-8Basics of thermodynamics & kinetics

Слайд 2THERMODYNAMISC&STATISTICAL PHYSICS

Слайд 3WHAT IS “TEMPERATURE”?EXPERIMENTAL DEFINITION := t,oC + 273.15oEXPERIMENTAL DEFINITION

Слайд 4Benoît Paul Émile Clapeyron (1799 – 1864)William Thomson, 1st Baron Kelvin

Слайд 5THEORYClosedsystem:energy E = constCONSIDER: 1 state of “small part” with

Слайд 6COMPARE:Probability1(ε1) = Mt(E-ε1) / M(E) =

Слайд 7Josiah Willard Gibbs (1839 –1903) Яков Григорьевич Синай,

Слайд 8(dSth/dE) = 1/ TP1(ε1) ~ exp(-ε1/kBT)Pj(εj) = exp(-εj/kBT)/Z(T); Σj

Слайд 9Unstable (explodes, v → inf.)

Слайд 10Separation of potential and kinetic energiesin classic (non-quantum) mechanics:P(ε) ~ exp(-ε/kBT)

Слайд 11IN THERMAL EQUILIBRIUM:TCOORD = TKIN = TouterWe may consider furtheronly potential

Слайд 12TRANSITIONS:THERMODYNAMICS

Слайд 13gradual transition“all-or-none” (or 1st order) phase transitioncoexistence& jump-liketransitioncoexistence(ΔE/kT*)(ΔT/T*) ~ 1Transition:

Слайд 14Second order phase transitionchangeRecently observed in proteins;rare case

Слайд 15LANDAU: Helix-coil transition:

Слайд 16Лев Давидович Ландау (1908 - 1968)Нобелевская Премия 1962

Слайд 17TRANSITIONS:KINETICS

Слайд 18n# = n × exp(-ΔF#/kBT)n# n→TRANSITION TIME:t0→1 = t0→#1→ ≈

Слайд 19

Слайд 20phase separationCoil- Coil- ≈Native≈

Слайд 21TRANSITION RATE = SUM OF RATES

Слайд 22t0→… →finish ≈ t0→#1→ finish + t0→#2→ finish + …##start_CONSECUTIVE REACTIONS:TRANSITION

Слайд 23__TRANSITION TIME IS ESSENTIALLY EQUAL FOR “TRAPS” AT AND OUT OF

Слайд 24DIFFUSION:KINETICS

Слайд 25Mean kinetic energy of a particle: •mv2/2• ~ kBT

Слайд 26Friction stops a molecule within picoseconds: m(dv/dt) = -(3πDη)v [Stokes

Слайд 27Friction stops a molecule within picoseconds:

Слайд 28The End

Слайд 29For “small part”: Pj(εj) = exp(-εj/kBT)/Z(T);

Слайд 30Thermostat: Tth = dEth/dSth“Small part”: Pj(εj,Tth) ~ exp(-εj/kBTth);

Слайд 31Along tangent: S-S(E1) = (E-E1)/ T1

Слайд 32Separation of potential energyin classic (non-quantum) mechanics:P(ε) ~ exp(-ε/kBT)

Слайд 33P(εKIN+εCOORD) ~ exp(-εCOORD/kBT)•exp(-εKIN/kBT)P(εCOORD) = exp(-εCOORD/kBT) / ZCOORD(T)ZCOORD(T) = ΣCexp(-εC/kBT): depends

Слайд 34“all-or-none” (or first order) phase transitionF(T1)________________

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Обратная связь

Что такое ThePresentation.ru?

Слайд 1PROTEIN PHYSICS

LECTURES 7-8

Basics of thermodynamics & kinetics

Слайд 2THERMODYNAMISC
&
STATISTICAL PHYSICS

Слайд 3WHAT IS “TEMPERATURE”?

EXPERIMENTAL DEFINITION :
= t,oC + 273.15o
EXPERIMENTAL DEFINITION

Слайд 4Benoît Paul Émile Clapeyron (1799 – 1864)
William Thomson, 1st Baron Kelvin

Слайд 5THEORY

Closed
system:
energy
E = const
CONSIDER: 1 state of “small part” with

Слайд 6COMPARE:
Probability1(ε1) = Mt(E-ε1) / M(E) =

Слайд 7Josiah Willard Gibbs
(1839 –1903)
Яков Григорьевич Синай,

Слайд 8(dSth/dE) = 1/ T
P1(ε1) ~ exp(-ε1/kBT)
Pj(εj) = exp(-εj/kBT)/Z(T); Σj

Слайд 10Separation of potential and kinetic energies
in classic (non-quantum) mechanics:

P(ε) ~ exp(-ε/kBT)

Слайд 11IN THERMAL EQUILIBRIUM:

TCOORD = TKIN = Touter

We may consider further
only potential

Слайд 12TRANSITIONS:
THERMODYNAMICS

Слайд 13gradual transition
“all-or-none” (or 1st order) phase transition
coexistence
& jump-like
transition
coexistence
(ΔE/kT)(ΔT/T) ~ 1
Transition:

Слайд 14Second order phase transition
change
Recently observed in proteins;
rare case

Слайд 16Лев Давидович Ландау
(1908 - 1968)
Нобелевская Премия 1962

Слайд 17TRANSITIONS:
KINETICS

Слайд 18n# = n × exp(-ΔF#/kBT)
n#
n
→
TRANSITION TIME:
t0→1 = t0→#1→ ≈

Слайд 20
phase separation

Coil
- Coil

- ≈Native
≈

Слайд 22t0→… →finish ≈ t0→#1→ finish + t0→#2→ finish + …
#
#
start
_
CONSECUTIVE REACTIONS:
TRANSITION

Слайд 23_
_
TRANSITION TIME IS ESSENTIALLY
EQUAL FOR “TRAPS” AT AND OUT OF

Слайд 24DIFFUSION:
KINETICS

Слайд 26Friction stops a molecule within picoseconds:

m(dv/dt) = -(3πDη)v [Stokes

Слайд 30Thermostat: Tth = dEth/dSth

“Small part”: Pj(εj,Tth) ~ exp(-εj/kBTth);

Слайд 32Separation of potential energy
in classic (non-quantum) mechanics:

P(ε) ~ exp(-ε/kBT)

Слайд 33P(εKIN+εCOORD) ~ exp(-εCOORD/kBT)•exp(-εKIN/kBT)

P(εCOORD) = exp(-εCOORD/kBT) / ZCOORD(T)

ZCOORD(T) = ΣCexp(-εC/kBT): depends

Слайд 34“all-or-none” (or first order) phase transition
F(T1)
________________