Critical Point Drying Biological specimens MEMS Aerogels Spices

Single film annealed: 16 stages Fig. 1 prl

Single film annealed: 16 stages Fig. 1 prl

Scaling collapse for indicated values of R0 (metallic side, recall Rc=22.67 k)

Measurement of Irreversible magnetization Before go in to the details lets talk about what do we mean by irreversible magnetization. We define it as the difference between field cooled and zero field cooled magnetizations. As shown in the picture the red curve is the zero field cooled magnetization and black one is the field cooled magnetization. Irreversible magnetization deltaM is shown by the vertical dotted arrow. Field cooled (MFC) and Zero field cooled (MZFC) magnetization. ∆M(H,T) = MFC(H,T) – MZFC(H,T) , is the irreversible magnetization

Field dependence of ∆M(H,T) isotherms Ni/AlOx multilayers (Hm(T), ∆Mmax (T)) Increasing T This what the deltaM isotherms looks as a function of magnetic field. Different colour indicates different temperatures. Temperature increases in this direction. Isotherms show a peak. This is expected, as at very low field regime field cooled and zero field cooled is basically same and deltaM must go to zero. At high magnetic field regime in both case magnetization will be saturated and deltaM will be zero. We define the magnetic field corresponds to the peak to be Hm and the value of deltaM at the peak as deltaM max. Both of them decreases with temperature. Now what we did next is scaled the irreversible magnetization my dividing with deltaMmax and observe its behavior as a function of the scaled magnetic field H/Hm. Hm(T) → Magnetic field where maxima of ∆M occures ∆Mmax(T) → Maximum value of ∆M

Scaling collapse of ∆M Ni/AlOx multilayers T ∆M (H,T) = ∆Mmax(T)F(H/Hm) Interestingly all the isotherms fall on each other and a beautiful scaling collapse is observed. This means that the scaled irreprehensible magnetization is independent of temperature when plotted as a function of scaled magnetic field. Now to be honest we do not understand the origin of the scaling collapse. But it can lead to some conclusions. Add arrow to show T decreasing (OK) (T) 8

Scaling collapse in other materials Until now I was talking only about the single domain Ni nanoparticles. We have found that the scaling collapse is equally true for these other materials too. Though the origin of this extraordinary behavior is unknown, can be useful to extract some valuable information about the magnetization reversal processes. This behavior suggest the probable functional form of the deltaM as a function of magnetic field and temperature. The sticking similarity between wide variety of samples also indicates that this behavior must be something in general and may be something to do with the process of ferromagnetization. LPCMO, identify SD & MD Zotev , Orbach et. all, PRB, 2002

Hydrogen Molecules (Quadrapolar Glass)

The combined 1st and 2nd Laws The 2nd law need not be restricted to reversible processes: đQ is identifiable with TdS, as is đW with PdV, but only for reversible processes. However, the last equation is valid quite generally, even for irreversible processes, albeit that the correspondence between đQ & TdS, and đW & PdV, is lost in this case.

Conversion of Heat to Work (a heat engine) Heat reservoir at temperature T2 > T1 Q  heat W  work both in Joules Efficiency (h*): Q2 Heat Engine Q1 Heat reservoir at temperature T1 < T2 *Don’t confuse with Joule-Thomson coefficient

The combined 1st and 2nd Laws If more than one type of particle (constituent) is added, then

Work and Internal Energy Differential work đW is inexact (work not a state variable) Configuration work is the work done in a reversible process given by the product of some intensive variable (y) and the change in some extensive variable (X). đW is the work done on ‘the system’, e.g. đW is positive when a gas contracts. Dissipative work is done in an irreversible process and is always done ‘on the system’, i.e. đWirr > 0 always. Total work (configuration and dissipative) done in adiabatic process between two states is independent of path. This leads to the definition of internal energy (state variable).

Equation of State of an Ideal Gas In chapter 1, we used the zeroth law to show that a relationship always exists between P, V and T. General form: f (P,V,T) = 0 Example: PV = nRT (ideal gas law) n quantifies the amount of the substance. The units of R and n are linked such that their product nR has the dimensions of joules/kelvin. If n measured in kilomoles, then R = 8.314  103 J/kilomoleK If n measured in moles, then R = 8.314 J/moleK Ideal gas law may also be written in intensive form Pv = RT v is the specific volume in either m3/mole or m3/kilomole

Equation of State of a Real Gas Van der Walls’ equation in intensive form: CP

London – van der Waals’ interaction Etotal = K + V = constant So, the addition of particles to a system results in the addition of kinetic energy to the system which almost immediately dissipates to the entire system. Therefore, the addition of particles changes the internal energy of the system. The change in the internal energy dU is proportional to the number of particles dn that are added. The proportionality constant m is called the ‘chemical potential’. dU = TdS – PdV + mdn Thus, we need to modify the combined 1st and 2nd laws: Thermal (kinetic) Mechanical, chemical (potential)

Properties of Heat It is the temperature of a body alone that determines whether heat will flow to or from a body, “Heat energy is transferred across the boundary of a system as a result of a temperature difference only.” However, this does not necessarily imply that the transfer of heat to a body will increase its temperature. It may also undergo a change of state (phase) from e.g. a liquid to a gas, without a change in temperature. Also, if the temperature of a system increases, it does not necessarily imply that heat was supplied. Work may have been done on the system. Therefore, “Heat is the change in internal energy of a system when no work is done on or by the system.”

Heat Capacity and specific heat The heat capacity C of a system is defined as: Heat capacity is an extensive quantity. The specific heat capacity c of a system is: Specific heat is obviously an intensive quantity. SI units are J.kilomole-1.K-1.

Heat Capacity and specific heat Because the differential đq is inexact, we have to specify under what conditions heat is added. the specific heat cv; heat supplied at constant volume the specific heat cP; heat supplied at constant pressure Using the first law, it is easily shown that: For an idea gas, the internal energy depends only on the temperature of the gas T. Therefore,

The Gay-Lussac-Joule Experiment Suggests an experiment: measure temperature change of a gas as a function of volume whilst keeping u fixed; this will enable us to determine how u depends on v. The Joule coefficient For an ideal gas:

Expansivity and Compressibility Two important measurable quantities: Expansivity: Compressibility:

The Second Law of Thermodynamics Clausius’ statement: It is impossible to construct a device that operates in a cycle and whose sole effect is to transfer heat from a cooler body to a hotter body. Kelvin-Planck statement: It is impossible to construct a device that operates in a cycle and produces no other effect than the performance of work and the exchange of heat from a single reservoir. Carnot’s theorem: No engine operating between two reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs.

The Clausius Inequality and the 2nd Law Consider the following cyclic process: P 2 Irreversible Reversible 1 V

The Clausius Inequality and the 2nd Law The Clausius inequality leads to the following relation between entropy and heat: This mathematical statement holds true for any process. The equality applies only to reversible processes. For an isolated system, đQ = 0, therefore The entropy of an isolated system increases in any irreversible process and is unaltered in any reversible process. This is the principle of increasing entropy. This leads to the following statement:

The Carnot Cycle ab isothermal expansion bc adiabatic expansion cd isothermal compression da adiabatic compression W2 > 0, Q2 > 0 (in) W' > 0, Q = 0 W1 < 0, Q1 < 0 (out) W'' < 0, Q = 0 Stirling’s engine is a good approximation to Carnot’s cycle.

Cooling via Work (a Refrigerator) Environment at temperature T2 > T1 Coefficient of Performance (c): Q2 Refrig- erator Q1 Refrigerator Inside, temperature T1 < T2

T2 > T1 đQ đW (1 – T1/T2)đQ T1đQ/T2 T1 < T2 Available energy M Available energy in a reversible cycle: M đW (1 – T1/T2)đQ Unavailable energy: T1đQ/T2 T1 < T2 There exists no process that can increase the available energy in the universe. Efficiency = h

Entropy changes in reversible processes Various cases: For an ideal gas quite generally:

Entropy changes in reversible processes Various cases: Adiabatic process: đqr = 0, ds = 0, s = constant. A reversible adiabatic process is isentropic. THIS IS NOT TRUE FOR AN IRREVERSIBLE PROCESS! Isothermal process:

Entropy changes in reversible processes Various cases: Isochoric process: We assume u = u(v,T) in general, so that u = u(T) in an isochoric process. Therefore, as in the case for an ideal gas, du = cvdT. Thus, provided cv is independent of T over the integration.

Entropy changes in reversible processes Various cases: Isothermal (and isobaric) change of phase: where l is the latent heat of transformation.

Entropy changes in reversible processes Various cases: Isothermal (and isobaric) change of phase: where l is the latent heat of transformation.

Entropy changes in reversible processes Various cases: Isobaric process: More convenient to deal with enthalpy h = h(P,T) in general, so that h = h(T) in isobaric process. provided cP is independent of T over the integration.

The Tds equations

The Joule-Thomson Experiment Thus, a throttling process occurs at constant enthalpy. The experiment then involves throttling the gas for different values of P2. If h depends on P, then T will change during a constant h throttling process (next slide). This contrasts the previous experiment where the search was for a change in T during a constant u expansion.

Enthalpy When considering phase transitions, it is useful to define a quantity h called ‘enthalpy’ Because h depends only on state variables, it too must be a state variable – hence its usefulness. When a material changes phase (e.g. from a solid to a liquid) at constant temperature and pressure, latent heat l must be added. This heat of transformation is related simply to the enthalpy difference between the liquid and solid

Enthalpy and specific heat The specific heat is not defined at any phase transition which is accompanied by a latent heat, because heat is transferred with no change in the temperature of the system, i.e. c = ∞. However, enthalpy turns out to be a useful quantity for calculating the specific heat at constant pressure For an ideal gas, the enthalpy depends only on the temperature of the gas T. Therefore,

The Gibbs function And Chemical Potential Using Euler’s theorem, one can now define an absolute value for the internal energy of a system Thermal (kinetic) Chemical (potential) Mechanical (potential) From this definition, one can easily show that From the above, one readily sees that m = G/n for a system with only one constituent, i.e. m = g. This is not true for mixtures or multi-constituent systems.

Enthalpy When considering phase transitions, it is useful to define a quantity h called ‘enthalpy’ Because h depends only on state variables, it too must be a state variable – hence its usefulness. When a material changes phase (e.g. from a solid to a liquid) at constant temperature and pressure, latent heat l must be added. This heat of transformation is related simply to the enthalpy difference between the liquid and solid

Enthalpy and Pressure Thus, we see the connection between the physics. The main difference is that enthalpy is relevant during constant pressure processes, whereas internal energy is relevant during constant volume processes. The Joule-Thomson coefficient: For an ideal gas:

The Tds equations These equations give: heat transferred (đq = TdS) in a reversible process; the entropy by dividing by T and integrating; heat flow in terms of measurable quantities; difference in specific heat capacities, cP, b, k, T, etc..; relationships between coordinates for isentropic processes. These equations give: