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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 Through a conductor passes an electric current I, A Joule heat is created : Production of entropy: ΔQJ = I ⋅ U ⋅ Δτ Δi S 1 ΔQJ I ⋅ U = ⋅ = T Δτ T Δτ 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 !