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Macro/meso/micro/nano world: temperature and thermal physics
Jaroslav ŠestákNew 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:
sestak@fzu.cz
X-ray ~ 0.5 nm(ordering of atoms)
optical ~ 600 nm (set-up of crystals)
Thermodynamics
size
Gustav H.J. Tammann (1861-1938)Nikolaj S. Kurnakov (1860-1941)
Max von Laue (1879-1960)William Lawrence Bragg (1890-1971)
Sigmund Freud (1856-1939)
Zacharias Janssen (1580-1658);Galileo Galilei (1564-1742)
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?
Thermodynamics
‐ΔW
ΔE
ΔQ
Mechanical work applied to or by the system is conventionally defined within the so called MACRO‐WORLD in which we use to live
Total change of the energie of systemu includes all processes done on the macro‐ and micro‐scales;
E is the state function.
„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“)
MACRO
ΔE = ‐ΔW + ΔQMICRO/NANO
MESO
?
Thermal analysis at micro/meso scales?We should understand thermodynamics at those ranges
‐ΔW
ΔE
ΔQ
MACRO
ΔE = ‐ΔW + ΔQNANO
MESO
May the work be defined at some meso‐scopic scales? Does there exist a barrier line (horizon) demarcating the upper MICRO‐WORLD?
What is „work“ in micro scales?MICRO
‐ΔW
ΔQ
MACRO
NANO
MESO
MICRO
Mechano-measurements ~ 10 μm (>10-2 mm)
Optical-measurements~ 600 nm (5.10-4 mm)
Electron microscopy~ 10 nm (10-5 mm)
X-ray-measurements~ 0.5 nm (10-7 mm)
novel
An alternative viewpoint including the distinction between ORDER and CHAOS
macro: dW = pdV
? microΔU/ΔS = T ⇒ chaotic
process
ΔU/ΔV=p ⇒ ordered process
ΔE = ‐ΔW + ΔQ= PdV + TdS
How we can define temperature/ heat at macro/meso/micro scales of our inquiry?
Biological structuresMaterial structures
Newton mechanicsE = mv2, F = (m1 m2)/d2
agreed units [sec, m, g, oC]Euclid's geometry (flat Earth, right angles)Thermal state, time flow⇒ certainty (~laws)
Ordinary horizon (physical sight of scales)
Imaginary macro‐world⇐ our world of termal analysis
Spec. theory of relativity
Theory of gravitation
Quantum mechanics
Scientific horizon Uncertainty
c g
h
Riemann (saddle space) Lobačevsky (globular –”-)
Space densitySpeed √ ( 1‐v 2/ c2 )
Sharpness
COSMIC-SCALE MACRO
QUANTUM-SCALE MiCRO
Basic constant of our Universec = 2.99 10 8 speed of light m/sg = 6.67 10 11 gravitation constant m 3 /(kg s 2 ) h = 6.63 10 -34 Planck constant J sk = 1.38 10 -23 (R/NA) Boltzmann const. J/Ke = 1.6 10 -19 charge of electron C
Structure of the Universeα= 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 massh ≤ Δx Δv Heisenberg uncertainty principle1840 mass ratio of proton versus electron
Absolute symmetry “boring state”
Symmetry breaking
Strong force -gluons
Gravity -gravitons
Electromagnetic- ⇔ + photons
Weak force
time
Temperature
Analogy to phase transformations
Asymmetry continuation
Δt ≅ 10 -25 secΔT ≅ 10 15 K
Beginning
singularity
The creation of Universe - selfcooling TA
10 32 K
Flowing – intervening in the complex space - τ
τ = (k T) + (i h/t) ↔ (k T) + (i h ω)
i h ω
k T
Compton´s cut off: (hω)/(exp (hω)/(kT))
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
Historical experience of ever-spread heat
Macro-case:Relativistic transformations of temperature
Thermodynamics gives ambiguous solutions e.g.
T = T0√(1 −v2/c2) K. v. Mosengeil (1907)T = T0 /√(1 −v2/c2) H. Ott (1963)⇒ T = T0 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
The process is so fast that local thermal equilibrium is not capable to be set up !
A laser beam Propagation
of a thermal wave A piece of
metal
Micro processes and the state of gradients and temperature
Local equilibrium, however, cannot be a generally valid assumption!
What is a meaning of thermal field ? Gradient Δ?
02
2
=Δ−∂∂
+∂∂ T
tT
tT κτ
Micro-case:Ultra-fast processes: rapid quenching
The temperature at fast processescontrivance of thermodynamics
T
“T“
T´ (?)
What happens if there is no time for the systemfast-enough equilibration?
what says thermodynamics ?
ΔT
THERMOMETRYCALORIMETRY
CONDUCTIONOF HEAT
Sadi CarnotClapeyron
FourierDuhamel
CARNOT LINE(dissipationless work)
FOURIER LINE(workless dissipation)
Clausius(thermodynamics based
on 1st and 2nd laws)
Kelvin(absolute
temperature)
StokesKelvin
THERMODYNAMICS DISSIPATION LINE
Kirchhoff
THERMOSTATICS(Gibbs)
Clausius-Planck inequality(Planck)
Clausius-Duhem inequality(Duhem)
de DonderMeixner
Prigogine
THERMODYNAMICS OF IRREVERSIBLE PROCESSES
Detailed family tree of thermodynamics:
THERMAL ANALYSIS PRACTICE AND THEORY
THERMOMETRYCALORIMETRY
CONDUCTIONOF HEAT
Sadi CarnotClapeyron
FourierDuhamel
CARNOT LINE(dissipationless work)
FOURIER LINE(workless dissipation)
Clausius(thermodynamics based
on 1st and 2nd laws)
Kelvin(absolute
temperature)
StokesKelvin
THERMODYNAMICS DISSIPATION LINE
Kirchhoff
THERMOSTATICS(Gibbs)
Clausius-Planck inequality(Planck)
Clausius-Duhem inequality(Duhem)
de DonderMeixner
Prigogine
THERMODYNAMICS OF IRREVERSIBLE PROCESSES
Reveal an evident contradiction:
EQUILIBRIUM!FIELD
DISTRIBUTION OF TEMPERATURE IN
SPACE!
NO TIME! TIME!
THERMAL ANALYSIS PRACTICE AND THEORY
CONDUCTIONOF HEAT
FourierDuhamel
CARNOT LINE(dissipationless work)
FOURIER LINE(workless dissipation)
Clausius(thermodynamics based
on 1st and 2nd laws)
Kelvin(absolute
temperature)
StokesKelvin
THERMODYNAMICS DISSIPATION LINE
Kirchhoff
THERMOSTATICS(Gibbs)
Clausius-Planck inequality(Planck)
Clausius-Duhem inequality(Duhem)
de DonderMeixner
Prigogine
THERMODYNAMICS OF IRREVERSIBLE PROCESSES
WHY ? engines
EQUILIBRIUM!
Sadi Carnot(1796 – 1832)
FIELD DISTRIBUTION OF TEMPERATURE IN
SPACE!
?
Mach’s „Wärmezustand“ = ‘omnipresent’ thermal statecalled ‘hotness manifold’
THERMAL ANALYSIS PRACTICE AND THEORY
CONDUCTIONOF HEAT
FourierDuhamel
CARNOT LINE(dissipationless work)
FOURIER LINE(workless dissipation)
Clausius(thermodynamics based
on 1st and 2nd laws)
StokesKelvin
THERMODYNAMICS DISSIPATION LINE
Kirchhoff
THERMOSTATICS(Gibbs)
Clausius-Planck inequality(Planck)
Clausius-Duhem inequality(Duhem)
de DonderMeixner
Prigogine
THERMODYNAMICS OF IRREVERSIBLE PROCESSES
Smart and practical solution
EQUILIBRIUM! TEMPERATURE
LOCAL EQUILIBRIUM
Equilibriumat small cells
THERMAL ANALYSIS PRACTICE AND THEORY
RATIONAL THERMODYNAMICSTruessdell, Noll, Coleman, Silhavy, …
Thermodynamics beyond local equilibrium
EXTENDED THERMODYNAMICSJou, Casas-Vasquez, Muller, …
PRINCIPALLY GENERAL
Temperature as well as heat and entropy are axiomatic concepts !
Perfect mathematical background!
AT MINIMAL GENERALIZATION
Fluxes are new independent thermodynamics variables , Δq
(a generalization of local equilibrium)
T
“T“
T´ (?) T, q
“T“
T´ (q) (?)
THERMAL ANALYSIS PRACTICE AND THEORY ⇒ << ΔT ??
T(x,t)
Local equilibrium explains the meaning of thermal fields:
T ≈ const (thermodynamic temperature)
T
“T“
T´ (?) T
“T“
T
If thermometer is small enough
⇒Importance of the determinability of flows (gradients Δ)♣ an innate state in nature ♥
Flux example: a shining bulb
Through a conductor passes an electric current I,A Joule heat is created :
Production of entropy:
Thermodynamic flux is proportional tothe ratio of voltage over temperature
Δ = ⋅ ⋅ΔJQ I U τ
i 1 ΔΔ ⋅= ⋅ =
Δ ΔJQS I U
T Tτ τ
= ⋅UI kT
Everyday:
Local equilibrium ⇒ formulation of Thermodynamics of Irreversible Processes
∑ ∑ ⋅++∇⋅−∇−∇⋅=ΔΔ − iAJvTqS
TeeTTiv
Ti i
rr&rrr εξ
τρμ 111 :Ρ
Thermal phenomena
Diffusion Chemical reactionsElectromagnetic processes
Mechanical friction
P
stable
unstable
DISSIPATIVE STRUCTURES
Δq
macro micro
Bénard instability
(Fourier) q = λ∇T
(Fick) J = D ∇c
(Ohm) I = r∇u
etc. (Schrödinger)
Production of entropy (internal dissipation):
Macro-scale (climate, weather):Organized Bernard cells illustrating ever existing effect of contrary fluxes (due to opposite outcome of heat and gravitation)
Micro-scale (casing, self-organization):
J. Šesták, P. Hubík, J. J. Mareš, „Thermal analysis scheme aimed at better understanding of the Earth’s climate changes due to the alternatingirradiation” J. Thermal Anal. Calor. in print 2010
J.J. Mareš, J. Šesták “An attempt at quantum thermal physics“ J. Thermal Anal. Calor. 82 (2005) 681
Nature tends to simple commandmentsAnalogies of the Newton Law
F = m a
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
⇓
Pierre de Fermat(1601 – 1665)
Fermat principle (1662)
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.
Kinetics ofperiodicreactions
M v λ = h
Classicaldiffusion
Fick law: D ≈ kT/ξ
Brownian motion
Hausdorff’sdimension &measure (≈ 2)
Quantumcriterion D = i DQ
= i h/2M Thermal noise (< 4 k)
Gravitation effect (< in space)
Entering quantum territory
The Law or mere/rather statistics?
At macro-scopic scales
The Second Law is perfectly valid butWhat happens at meso/micro/nano-scales?
Doubtful territory of thermodynamics
Decreasing the number of acting molecules to a nano-limit to only a few
size in nm
But what happen if there is a very small, but intelligent being controlling the piston/door?
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.
All proofs of impossibility have been defeated but the demon action needs information ≡ energy
NANO-SCALE
Just only few molecules
Heat, entropy and informationPROCESS
According to the thermodynamic laws
Or just interpreting information from its environment
Entropy Statistical physics InformationQ/T =S= ? kB lnW (1/ln2) ln C
Q – heat W – complexion/arrangement C – system codingT – temperature kB– Boltzmann const. (1.38 10 ‐23 )
(energy exchange via energy transducers during any measurement)
J/K = 1023 bit
630 nm (a latex particle)
laser
optical trapF
F = -k (x – x0 ) ≈ 10-12 N = pN
xx0
vopt… defined movement (like a piston)
∫ ⋅=t
opt dssFvW0
)(δThe work is defined because vopt is given and F may be calculated by measuring the position of the particle.
Wang. G.M., et al, Phys. Rev. Lett., vol 89, No 5., 2002
a solvent
But how far is thermodynamics valid at these scales ?
Localized thermal investigation
Negative production of entropy
Experimerntazl resul;ts: Wang. G.M., et al, Phys. Rev. Lett., vol 89, No 5., 2002
t = 0.02s
t = 2s
Second Law has statistical character and the situation at small time and length scales may become problematic (special circumstances at nano-scales)
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) \
Negative production of entropy
Corrections toward nano‐scale? At macro-scopic scales
The Laws are perfectly valid butwhat happens at nano-scales (interfaces)?
Specific territory of thermodynamics
Decreasing number of bulk molecules to a nano-limit narrowed by interface layer energy
Interaction between the sample holder (cell) and the entire sample surface (competition between the bulk ~ r3 and surface ~ r2 )
ΔT
going behind1. 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 toexperimental set ups.
ΔQ ΔT = ?Δ?Uncertainty principle in quantum mechanics
Δp Δx = h
Crystal order by X-ray diffraction
Thermal order by thermal analysis
crystal
interface
ANALOGYCURVES
X-rayIdentity“fingerprint“
PositionSymmetryQuality
QuantityIntensityArea
ShapeBroadeningCrystal size
DTAIdentity“fingerprint“
PositionUniformityQuality
QuantitySizeArea
ShapeStructureKinetics
base- line singularity
Base line - steady thermal state of structural makeup Effect, singularity:
due thermal state response upon the structural changesAffected by the
sample set up and trial/experimental arrangements
Theoretical background of thermal analysis
1979
1984
2005
1964
Shorty-range disorder via X-ray background
Thermal vibration disorder (Cp) via TA curve background
Crystal interface
surface tension
imperfections
Base line: thermal state of structural makeup distorted by interface tension of the outside straightening out layer
Base line: thermal state of structural makeup distorted by defects and other imperfections
Modern approach: investigating the baselines
<Δ T <Δt
Temperature modulation
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 changeFreeze-in state
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
>>Δ T <<Δt
x
xx
xx
x
ΔQ ΔT = ?Δ?Where is the operate limit of
uncertainty principle
Ultrafast changes in temperature in nano-scale and its determinability
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 !
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