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 !