Download and macro-world of thermal science

Macro/meso/micro/nano world: temperature and thermal physics
Jaroslav Šesták
New Technology - Research Center in the
Westbohemian Region, West Bohemian
University, Universitni 8, CZ-30114 Plzeň;
Division of Solid-State Physics, Institute of
Physics of the Academy of Sciences ČR,
Cukrovarnická 10, CZ-16200 Praha,
both Czech Republic; E-mail:
[email protected]
optical ~ 600 nm
(set-up of crystals)
Zacharias Janssen (1580-1658);
Galileo Galilei (1564-1742)
size
Max von Laue (1879-1960)
William Lawrence Bragg (1890-1971)
Gustav H.J. Tammann (1861-1938)
Nikolaj S. Kurnakov (1860-1941)
Sigmund Freud (1856-1939)
X-ray ~ 0.5 nm
(ordering of atoms)
Thermodynamics
Thermodynamics
Meaning of the Second Law
Two aspects:
• We cannot use the energy as we desire
• Intriguingly heat becomes the entropy
The Law or rather/mere statistics? At macroscopic scales
The Second Law is perfectly valid. however,
what happens at meso- and micro-scales?
MACRO
‐ΔW
Mechanical work applied to or by the system is conventionally defined within the so called MACRO‐
WORLD in which we use to live
ΔE
Total change of the energie of systemu includes all processes done on the macro‐ and micro‐
scales; E is the state function. MESO
ΔQ
„Heat, describes energy transfer on microscopic level and provides basis for the derived quantity called entropy, which describes the extent of deposition/distribution of energy on the microscopic level
(so called „degradation of energy“)
ΔE = ‐ΔW + ΔQ
MICRO/NANO
Thermal analysis at micro/meso scales?
We should understand thermodynamics at those ranges
?
‐ΔW
MACRO
ΔE
May the work be defined at some meso‐scopic scales? Does there exist a barrier line (horizon) demarcating the upper MICRO‐WORLD?
MESO
MICRO
NANO
ΔQ
What is „work“ in micro scales?
ΔE = ‐ΔW + ΔQ
‐ΔW
MACRO
Mechano-measurements
~ 10 μm (>10-2 mm)
Optical-measurements
~ 600 nm (5.10-4 mm)
MESO
novel
Electron microscopy
~ 10 nm (10-5 mm)
MICRO
NANO
ΔQ
X-ray-measurements
~ 0.5 nm (10-7 mm)
An alternative viewpoint including
the distinction between ORDER and CHAOS macro: dW = pdV
? micro
ΔU/ΔV=p ⇒ ordered process
ΔU/ΔS = T ⇒ chaotic
process
ΔE = ‐ΔW + ΔQ
= PdV + TdS
Biological structures
How we can define
temperature/ heat at
macro/meso/micro
scales of our inquiry?
Material structures
Ordinary horizon (physical sight of scales)
Newton mechanics
E = mv2, F = (m1 m2)/d2
agreed units [sec, m, g, oC]
Euclid's geometry
(flat Earth, right angles)
Thermal state, time flow
⇒ certainty (~laws)
Imaginary macro‐world ⇐ our world of termal analysis
Speed √
( 1‐v 2/ c2
)
Spec. theory of relativity
COSMIC-SCALE MACRO
Space density
Theory of gravitation
g
c
Riemann
(saddle space)
Lobačevsky (globular –”-)
QUANTUM-SCALE MiCRO
Scientific horizon Uncertainty
Quantum mechanics
h
Sharpness
Basic constant of our Universe
c = 2.99 10 8 speed of light
m/s
g = 6.67 10 11 gravitation constant m 3 /(kg s 2 )
h = 6.63 10 -34 Planck constant
Js
k = 1.38 10 -23 (R/NA) Boltzmann const. J/K
e = 1.6 10 -19 charge of electron
C
Structure of the Universe
α= 1/137 Fine structure constant ( μ c e 2 /(2 h )
10 -34
Planck unit length
(g h c 3 ) 1/2
10 -43
Planck unit time
(g h c 5 ) ½
5 10 -18 g unit of mass
(h c/ g) 1/2
2.6 10 -4 Quantum ohm
(h /e 2 )
10 32 K
maximum temperature
(h c/ g) ½(c 2/k)
2.4 10 -12 Compton´s length
⇐ h / mc ⇒
E = mc2 = hc/λ relating energy and mass
h ≤ Δx Δv Heisenberg uncertainty principle
1840
mass ratio of proton versus electron
s
i
The creation of Universe - selfcooling
n
Absolute
g
u symmetry
Gravity l “boring state”
gravitons
a
r
i
Symmetry
Strong force t
gluons
breaking
y
10 32 K
Δt ≅ 10 -25 sec
Weak force
15
ΔT ≅ 10 K
B
e
g
i
n
n
i
n
g
Temperature
TA
Electromagnetic
- ⇔ + photons
Analogy to phase
transformations
time
Asymmetry
continuation
Flowing – intervening
in the complex space - τ
τ = (k T) + (i h/t) ↔ (k T) + (i h ω)
i h ω
Compton´s cut off: (h ω)/(exp (h ω)/(kT)) k T
Historical experience of ever-spread heat
We can postulate warmness multiplicity
non‐relativistic temperature, T (but flowing similarly as time, t) Mach’s „Wärmezustand“ = ‘omnipresent’ thermal state = ever present warmth condition
There exists an ordered continuous set of a
property intrinsic to all bodies called
hotness manifold
Macro-case:
Relativistic transformations of temperature
Thermodynamics gives ambiguous solutions e.g.
T = T0√(1 −v2/c2)
T = T0 /√(1 −v2/c2)
⇒ T = T0
K. v. Mosengeil (1907)
H. Ott (1963)
P. T. Landsberg (1966)
⇒ One century of controversy in solution of a fundamental
problem of relativistic thermal physics
⇒ Our suggestion: relativistic constants, e.g.,
⇒ k = k0√(1 −v2/c2), R = R0√(1 −v2/c2)
J.J. Mareš. P. Hubík, J. Šesták „Relativistic transformation
of temperature “ Physica E 42 ( 2010) 484-487
Micro-case:
Ultra-fast processes: rapid quenching
A laser
beam
A piece of
metal
Propagation
of a thermal
wave
∂T
∂ 2T
+τ
− κ ΔT = 0
2
∂t
∂t
What is a meaning of
thermal field ? Gradient Δ?
The process is so fast that
local thermal equilibrium is
not capable to be set up !
Micro processes and the state of gradients and temperature
Local equilibrium, however, cannot be a generally valid assumption!
The temperature at fast processes
contrivance of thermodynamics
What happens if there
is no time for the system
fast-enough equilibration?
“T“
ΔT
T
T´ (?)
what says thermodynamics ?
Detailed family tree of thermodynamics:
THERMOMETRY
CALORIMETRY
CONDUCTION
OF HEAT
Sadi Carnot
Clapeyron
Fourier
Duhamel
CARNOT LINE
(dissipationless work)
FOURIER LINE
(workless dissipation)
Clausius
(thermodynamics based
on 1st and 2nd laws)
Kelvin
(absolute
temperature)
THERMODYNAMICS
Stokes
Kelvin
DISSIPATION LINE
Kirchhoff
THERMOSTATICS
(Gibbs)
Clausius-Planck inequality
(Planck)
THERMAL ANALYSIS PRACTICE AND THEORY
Clausius-Duhem inequality
(Duhem)
de Donder
Meixner
Prigogine
THERMODYNAMICS OF IRREVERSIBLE PROCESSES
Reveal an evident contradiction:
THERMOMETRY
CALORIMETRY
Sadi Carnot
Clapeyron
CONDUCTION
OF HEAT
NO TIME!
CARNOT LINE
(dissipationless work)
Clausius
(thermodynamics based
on 1st and 2nd laws)
EQUILIBRIUM!
TIME!
FOURIER LINE
(workless dissipation)
Kelvin
(absolute
temperature)
THERMODYNAMICS
THERMOSTATICS
(Gibbs)
Fourier
Duhamel
Clausius-Planck inequality
(Planck)
THERMAL ANALYSIS PRACTICE AND THEORY
FIELD Stokes
Kelvin
DISTRIBUTION OF DISSIPATION LINE
TEMPERATURE IN SPACE!
Kirchhoff
Clausius-Duhem inequality
(Duhem)
de Donder
Meixner
Prigogine
THERMODYNAMICS OF IRREVERSIBLE PROCESSES
WHY ? engines
CONDUCTION
OF HEAT
Sadi Carnot
(1796 – 1832)
Fourier
Duhamel
CARNOT LINE
(dissipationless work)
Clausius
(thermodynamics based
on 1st and 2nd laws)
EQUILIBRIUM!
?
Kelvin
(absolute
temperature)
THERMODYNAMICS
THERMOSTATICS
(Gibbs)
Clausius-Planck inequality
(Planck)
THERMAL ANALYSIS PRACTICE AND THEORY
Mach’s „Wärmezustand“ =
‘omnipresent’ thermal state
called ‘hotness manifold’
FOURIER LINE
(workless dissipation)
FIELD Stokes
Kelvin
DISTRIBUTION OF DISSIPATION LINE
TEMPERATURE IN SPACE!
Kirchhoff
Clausius-Duhem inequality
(Duhem)
de Donder
Meixner
Prigogine
THERMODYNAMICS OF IRREVERSIBLE PROCESSES
Smart and practical solution
CONDUCTION
OF HEAT
Fourier
Duhamel
CARNOT LINE
(dissipationless work)
FOURIER LINE
(workless dissipation)
Clausius
(thermodynamics based
on 1st and 2nd laws)
TEMPERATURE
Stokes
Kelvin
THERMODYNAMICS
LOCAL EQUILIBRIUM
DISSIPATION LINE
EQUILIBRIUM!
Kirchhoff
THERMOSTATICS
(Gibbs)
Clausius-Planck inequality
(Planck)
THERMAL ANALYSIS PRACTICE AND THEORY
Clausius-Duhem inequality
(Duhem)
de Donder
Meixner
Prigogine
THERMODYNAMICS OF IRREVERSIBLE PROCESSES
Equilibrium
at small cells
Thermodynamics beyond local equilibrium
RATIONAL THERMODYNAMICS
EXTENDED THERMODYNAMICS
Truessdell, Noll, Coleman, Silhavy, …
Jou, Casas-Vasquez, Muller, …
PRINCIPALLY GENERAL
AT MINIMAL GENERALIZATION
Temperature as well as heat and
entropy are axiomatic concepts !
Fluxes are new independent
thermodynamics variables , Δq
Perfect mathematical background!
(a generalization of local equilibrium)
“T“
“T“
T
T´ (?)
T, q
THERMAL ANALYSIS PRACTICE AND THEORY ⇒ << ΔT ??
T´ (q) (?)
Local equilibrium
explains the meaning of thermal fields:
T(x,t)
T ≈ const (thermodynamic temperature)
“T“
“T“
If thermometer
is small enough
T
T´ (?)
T
T
⇒Importance of the determinability of flows (gradients Δ)
♣ an innate state in nature ♥
Everyday:
Flux example:
a shining bulb
ƒ Through a conductor passes an electric current I,
ƒ A Joule heat is created :
ƒ Production of entropy:
ΔQJ = I ⋅ U ⋅ Δτ
Δi S 1 ΔQJ I ⋅ U
= ⋅
=
T
Δτ T Δτ
ƒ Thermodynamic flux is proportional to
U
I =k⋅
T
the ratio of voltage over temperature
Local equilibrium ⇒ formulation of Thermodynamics of Irreversible Processes
Production of entropy (internal dissipation):
r
r r
r
Δi S r
μi
ρ
−1
v
1
1
&
= q ⋅ ∇T − T Ρ : ∇v − ∑ J i ⋅ ∇ T + T ∑ Aeξ e + T ε ⋅ i
Δτ
Thermal phenomena
P
Mechanical friction
Diffusion
(Fourier) q = λ∇T
(Fick) J = D ∇c
(Ohm)
etc. (Schrödinger)
Chemical reactions
Electromagnetic processes
DISSIPATIVE STRUCTURES
stable
unstable
macro
Δq
I = r ∇u
micro
Bénard instability
J. Šesták, P. Hubík, J. J. Mareš,
„Thermal analysis scheme aimed at
better understanding of the Earth’s
climate changes due to the alternating
irradiation” J. Thermal Anal. Calor. in
print 2010
Macro-scale (climate, weather):
J.J. Mareš, J. Šesták “An attempt at
quantum thermal physics“ J. Thermal
Anal. Calor. 82 (2005) 681
Organized Bernard cells illustrating ever existing effect of contrary
fluxes (due to opposite outcome of heat and gravitation)
Micro-scale
(casing, self-organization):
Nature tends to simple commandments
Analogies of the Newton Law
F=ma
Diffusion (Fick, Δx)
Heat transfer (Fourier ,ΔT)
Electric conduction (Ohm, ΔU)
Shift of momentum in liquids (Stokes, Newton)
⇒ Quantum mechanics (Schrödinger)
⇓
♥ principles of least ♣
action (optimalization)
smart nature
Fermat principle (1662)
Pierre de Fermat
(1601 – 1665)
The Fermat's principle of least time
“the Nature acts via the easiest and the most accessible way
reached within the shortest time”.
Maupertuis in 1744 envisaged least action that
"when some change takes place in nature, the quantity of action
necessary for the change is the smallest possible. The quantity of
action is the product obtained by multiplying the mass of the bodies
by their velocity and the distance traveled“….. m v λ= ђ
⇓
J.J. Mareš, J. Stávek, and J. Šesták, „Quantum aspects of self-organized
periodic chemical reaction“ J. Chem. Phys. 121 (2004) 1499.
Entering quantum territory
Kinetics of
periodic
reactions
Brownian
motion
Classical
diffusion
Fick law: D ≈ kT/ξ
Mvλ=h
Quantum
criterion D = i DQ
= i h/2M
Hausdorff’s
dimension &
measure (≈ 2)
Thermal noise (< 4 k)
Gravitation effect (< in space)
Doubtful territory of thermodynamics
The Law or mere/rather statistics? At macro-scopic scales
The Second Law is perfectly valid
but
What happens at meso/micro/nano-scales?
size in nm
Decreasing the number
of acting molecules to a
nano-limit to only a few
But what happen if there is a
very small, but intelligent being
controlling the piston/door?
Just only few molecules
Or imagine a sophisticated nano-machine ?
Maxwell demon:
A creature, a nano-device, biological
system, microcomputer or anything
else being able to separate molecules
at molecular scales without an energy
consumption.
NANO-SCALE
All proofs of impossibility have been
defeated but the demon action needs
information ≡ energy
Heat, entropy and information
PROCESS
According to the thermodynamic laws
Or just interpreting information from its environment
Entropy Statistical physics Information
Q/T =S= ? kB ln W (1/ln2) ln C
Q – heat W – complexion/arrangement C – system coding
T – temperature kB – Boltzmann const. (1.38 10 ‐23 )
(energy exchange via energy transducers during any measurement)
J/K = 1023 bit
Localized thermal
investigation
vopt… defined movement (like a piston)
laser
a solvent
x
F
optical trap
x0
630 nm (a latex particle)
F = -k (x – x0 ) ≈ 10-12 N = pN
δ W
t
=
∫
v opt ⋅ F ( s ) ds
0
Negative production of entropy
The work is defined because
vopt is given and F may be
calculated by measuring the
position of the particle.
But how far is thermodynamics valid at these scales ?
Wang. G.M., et al, Phys. Rev. Lett., vol 89, No 5., 2002
Second Law has statistical character and the
situation at small time and length scales may become
problematic (special circumstances at nano-scales)
Experimerntazl resul;ts: Wang. G.M., et al, Phys. Rev. Lett., vol 89, No 5., 2002
t = 0.02s
t = 2s
Negative production of entropy
D. M. Price, M. Reading, A. Hammiche, H. M. Pollock: Micro-thermal
analysis: scanning thermal microscopy and localised thermal analysis. Int. J.
Pharmaceutics 192 , 85-96 (1999) \
Specific territory of thermodynamics
Corrections toward nano‐scale? At macro-scopic scales
The Laws are perfectly valid
but
what happens at nano-scales (interfaces)?
Decreasing number of
bulk molecules to a
nano-limit narrowed by
interface layer energy
ΔT
Interaction between the sample holder (cell)
and the entire sample surface (competition
between the bulk ~ r3 and surface ~ r2 )
going behind
1. At small space scales we must be very careful when applying
the first and second law of thermodynamics.
If we measure heat, for example, we should justify
what we really do (modulated techniques at small samples)
2. The second law has a statistical character at small
scales ! (special applications)
3. At fast processes seems the situation becomes alike
that of quantum mechanics, i.e., the coincident measure
of accurate temperature and/or heat emerge awkward
4. There are other open questions (gradients, interfaces,
crystal size, contacts, fractal behavior, etc.) due to
experimental set ups.
ΔQ ΔT = ?Δ?
Uncertainty principle in quantum mechanics
Δp Δx = h
CURVES
ANALOGY
Crystal order by
X-ray diffraction
crystal
interface
Thermal order by
thermal analysis
base- line
singularity
X-ray
DTA
Identity
“fingerprint“
Identity
“fingerprint“
Position
Symmetry
Quality
Position
Uniformity
Quality
Quantity
Intensity
Area
Quantity
Size
Area
Shape
Broadening
Crystal size
Shape
Structure
Kinetics
Base line - steady
thermal state of
structural makeup
Affected by the
sample set up and
trial/experimental
arrangements
Effect, singularity:
due thermal state
response upon the
structural changes
Theoretical background of thermal analysis
1964
1979
1984
2005
Shorty-range disorder
via X-ray background
imperfections
Crystal interface
surface tension
Thermal vibration
disorder (Cp) via TA
curve background
Modern approach: investigating the baselines
Base line: thermal state
of structural makeup
distorted by defects
and other imperfections
Base line: thermal state
of structural makeup
distorted by interface
tension of the outside
straightening out layer
Temperature modulation
<Δ T <Δt
M. Reading, „Modulated dDSC: a new way forward in materials
characterization“ Trends Polym. Sci. 1, 1993, 248-253
B. Wunderlich, Y. Jin, A. Boller, „Mathematical description of DSC based on
periodic temperature modulation“, Thermochim. Acta 238 (1994) 277-293.
Temperature quenching
Phase change
Freeze-in state
x
x
x
x
x
x
>>Δ T <<Δt
S.A. Adamovsky, A.A. Minakov, C. Schick. Scanning
microcalorimetry at high cooling rate. Thermochimica Acta 403
(2003) 55–63; and: Ultra-fast isothermal calorimetry using thin
film sensors Thermochimica Acta 415 (2004) 1–7
Ultrafast changes in temperature in
nano-scale and its determinability
ΔQ ΔT = ?Δ?
Where is the operate limit of
uncertainty principle
ΔT/Δt = ?Δ?
Where is the operate limit of
recordable temperature changes
ΔT = ?Δ?
Where is the limit of readable and
reproducible temperature gradient
B. Wunderlich “Calorimetry of Nanophases “ Int.J. Thermophysics
28 (2007) 958-96; M. Reading, A. Hammiche, H. M. Pollock. M. Song:
Localized thermal analysis using a miniaturized resistive probe.
Rev. Sci. Instrum. 67, 4268-4275 (1996)
Introduction
of micro-analysis methods using:
* ultra-small samples and
* mili-second time scales .
It involved a further peculiarity of truthful temperature
measurements of nano-scale crystalline samples in the particle
micro range with radius (r) which becomes size affected due to
increasing role of the surface energy usually described by an
universal equation:
Tr/T∞ ≅ (1 – C/r)p
where ∞ portrays a standard state and C and p are empirical
constants ranging ≈ 0.15 < C < 0.45 and p = 1 and/or ½
Guisbier G, Buchaillot L. Universal size/shape-dependent law for
characteristic temperatures. Phys. Lett. A 2009; 374; 305
Any experiment always provides certain data on
temperature and other measured variables!
It seems that thermoanalysts believe that a mere
replacement of thermocouples by thermocouple
batteries or by highly sensitive electronic chips
moreover renaming DTA principle to variously
termed DSC´s is a sufficient solution toward
theoretical rations.
It’s the responsibility of researcher to know to
what extent spans his true conscientiousness!
One never gets to see that his work is so secret
that he does not even know what he is doing !
(~allied to blindness trust to instrumental outputs)
Various scientific views compete each other
It’s not politics; is the best one only
the one which is the loudest one?
I appreciate that you kindly waited until the end of my long lecture, thank you !