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Review of Modern Calorimetry for Complex Fluids and Biology Germano Iannacchione Department of Physics Order-Disorder Phenomena Laboratory Worcester Polytechnic Institute Worcester, MA Slide 2 The Usual Suspects The Order-Disorder Phenomena Laboratory Aleks Roshi Saimir Barjami Floren Cruceanu Dr. Dipti Sharma Klaida Kashuri 12 MQPs, 12 Papers, 27 Presentations Recent Outside Collaborations (Short List) C. W. Garland (MIT) R. Birgeneau (UC-Berkley) N. Clark (U. Colorado, Boulder) R. Leheny (Johns Hopkins) T. Bellini (U. Milano) P. Clegg (U. Edinburgh) Support: NSF, RC, AC-PRF Slide 3 The Order-Disorder Phenomena Lab (Soft) Condensed Matter: Interdisciplinary. (Soft) Condensed Matter: Interdisciplinary. New Experimental Techniques. New Experimental Techniques. Current Projects: Current Projects: Novel Phases in Liquid Crystals. Novel Phases in Liquid Crystals. Quenched Random Disorder Effects. Quenched Random Disorder Effects. Thermal Properties: CarbonNanotubes. Thermal Properties: CarbonNanotubes. Protein Unfolding Protein Unfolding Frustrated Glasses Frustrated Glasses Slide 4 Q and T are experimental parameters. No other technique has Direct Access to a materials: Enthalpy ( H ) Entropy ( S ) Free Energy (really important!) Why Calorimetry? Why Not? Slide 5 The Free Energy of a material or system is essentially the solution for all the thermodynamic parameters at all temperatures. BUT WAIT, there is more than one Free Energy! So, which is it? ( Thats a good reason. ) At constant pressure: Gibbs Free Energy ( G ) Favored by experimentalists At constant volume: Helmholtz Free Energy ( A ) Favored by theorists ( no work ) OK. Why Free Energy? Slide 6 Enthalpy Slide 7 Heat Capacity Slide 8 I. Fix Q input and measure resulting T. Relaxation, Modulation (AC), etc. II. Control Q input to maintain a fixed T. Differential Scanning Calorimetry (DSC) Two Types of Calorimetry Slide 9 The temperature increase due to an applied heating power is : R e - external thermal resistance linking the sample+cell to the bath. P - applied heating power (heat current). Temperature What a minute! Looks like Ohms Law! Slide 10 Thermal Model (Circuit) Slide 11 A classic set of coupled Differential Equations. The heat current continuity for each element : Heat Flow Balance (Continuity) * Need T (what is actually measured). Slide 12 ThermalQuantityElectric Temperature T Voltage Heat Q Charge PowerPCurrent ResistanceR Heat capacityCpCp Capacitance Thermal / Electric Analog Slide 13 TYPE II Differential Scanning Slide 14 Technical Notes 1999: TA Instruments, Inc. Typical DSC Setup Slide 15 THE Enthalpy: What DSC sees: DSC POV of Enthalpy Slide 16 Combination of Type I and II Calorimetry Differential Heat Flow (Power): dQ/dt = T/R = C p + f(T, t) Add a modulation to the heating ramp Kinetic heat flow, f(T, t), contains the induced T-oscillations New Technique: Modulation DSC Slide 17 TYPE I Modulation (AC) Slide 18 P. F. Sullivan and G. Seidel, Phys. Rev. 173, 679 (1968). Applied AC power induces temperature oscillations: C p - Heat capacity P 0 - Amplitude of the applied power (~ 0.1 mW) - Heating frequency (~ 100-200 mrad/s) T ac - Amplitude of temperature oscillations (~ 2-15 mK) AC-C: Basic View Slide 19 Applying heating power sinusoidally as: will induce sinusoidal temperature oscillations: T b - bath temperature. T DC - DC temperature rise ( rms heating ). T ac e j( t+ ) - temperature oscillations. Heating Power Modulation Slide 20 From a one-lump thermal model, the temperature oscillation amplitude is : e = R e C- external time constant. ii - internal time constant: ii 2 = s 2 + c 2 ( root-sum-squared ) R s - sample thermal resistance. R e - external thermal resistance. C = C s + C c - TOTAL heat capacity. Modulation Amplitude Slide 21 In the plateau, THE phase shift is : The reduced phase shift (, T ) is : e = R e C- external time constant. i = s + c - internal time constant (sum). For small (small angle): Modulation Phase Shift Slide 22 The total heat capacity of the cell+sample is : If : Then : AC-C: Heat Capacity What?!? After all that, were back where we started! Slide 23 Nano-colloidal dispersion: Liquid Crystal + Aerosil LC = 8CB(4-cyano-4-octylbiphenyl) Aerosil = type 300 ( 7 nm, OH coated, SiO 2 spheres) Mass-fractal, weak H-bonded, gel. Sample: 8CB+aerosil with S = 0.10 g cm Complex Fluid Example Slide 24 ~ 20 mg of Sample Constant Applied Power ( Joule heating ) f = 15 mHz I N = 312.24 K N SmA = 305.31 K AC-C: 8CB+Aerosil Slide 25 Application: Calorimetric Spectroscopy Slide 26 C p a Dynamic Response Function? Of course, any thermodynamic quantity results from an ensemble and time average. C p looks static because it fluctuates too fast! The experimental time (frequency ) window sets a partition between static and fast relaxations. Static = slow modes/evolution of enthalpy Fast = phonons (rapid thermal transport) Relaxation process has a characteristic time When, C p ( ) will be complex. Slide 27 Linear Response Theory Enthalpy Correlation Function: Complex Heat Capacity: Static Part: Fast Part: Slowly Relaxing Enthalpy Fluctuation: Slide 28 AC-C*: Complex C p ( ) If c