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Review of Modern Calorimetry for Complex Fluids and Biology

Review of Modern Calorimetry for Complex Fluids and Biology. Germano Iannacchione Department of Physics Order-Disorder Phenomena Laboratory Worcester Polytechnic Institute Worcester, MA. The Usual Suspects. The Order-Disorder Phenomena Laboratory Aleks Roshi Saimir Barjami

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Review of Modern Calorimetry for Complex Fluids and Biology

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  1. Review of Modern Calorimetryfor Complex Fluids and Biology Germano Iannacchione Department of Physics Order-Disorder Phenomena Laboratory Worcester Polytechnic Institute Worcester, MA

  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

  3. The Order-Disorder Phenomena Lab • (Soft) Condensed Matter: Interdisciplinary. • New Experimental Techniques. • Current Projects: • Novel Phases in Liquid Crystals. • Quenched Random Disorder Effects. • Thermal Properties: CarbonNanotubes. • Protein Unfolding • Frustrated Glasses

  4. Why Calorimetry? Why Not? • DQ and DT are experimental parameters. • No other technique has Direct Access to a material’s: • Enthalpy ( H ) • Entropy ( S ) • Free Energy (really important!)

  5. OK. Why Free Energy? The Free Energy of a material or system is essentially the “solution” for all the thermodynamic parameters at all temperatures. ( That’s a good reason. ) BUT WAIT, there is more than one Free Energy! So, which is it? At constant pressure: Gibbs Free Energy ( G ) Favored by experimentalists At constant volume: Helmholtz Free Energy ( A ) Favored by theorists ( no work )

  6. Enthalpy

  7. Heat Capacity

  8. Two Types of Calorimetry I.FixDQ input and measure resulting DT. Relaxation, Modulation (AC), etc. II.ControlDQ input to maintain a fixedDT. Differential Scanning Calorimetry (DSC)

  9. Temperature The temperature increase due to an applied heating power is : Re - external thermal resistance linking the sample+cell to the bath. P - applied heating power (heat current). What a minute! Looks like “Ohm’s Law”!

  10. Thermal Model (Circuit)

  11. Heat Flow Balance (Continuity) The heat current continuity for each element : A classic set of coupled Differential Equations. * Need Tq (what is actually measured).

  12. Thermal / Electric Analog

  13. TYPE IIDifferential Scanning

  14. Typical DSC Setup Technical Notes 1999: TA Instruments, Inc. Technical Notes 1999: TA Instruments, Inc.

  15. DSC POV of Enthalpy THE Enthalpy: What DSC sees:

  16. New Technique:Modulation DSC • Combination of Type I and II Calorimetry • Differential Heat Flow (Power): • dQ/dt = DT/R = Cpb + f(T, t) • Add a modulation to the heating ramp • “Kinetic” heat flow, f(T, t), contains the induced T-oscillations

  17. TYPE IModulation (AC)

  18. AC-C: Basic View • P. F. Sullivan and G. Seidel, Phys. Rev. 173, 679 (1968). • Applied AC power induces temperature oscillations: Cp - Heat capacity P0 - Amplitude of the applied power (~ 0.1 mW)  - Heating frequency (~ 100-200 mrad/s) Tac- Amplitude of temperature oscillations (~ 2-15 mK)

  19. Heating Power Modulation Applying heating power sinusoidally as: will induce sinusoidal temperature oscillations: Tb - bath temperature. TDC - DC temperature rise ( rms heating ). Tac e j(t+)- temperature oscillations.

  20. Modulation Amplitude From a one-lump thermal model, the temperature oscillation amplitude is : e = Re C - external time constant. ii- internal time constant: tii2 = s2 + c2( root-sum-squared ) Rs- sample thermal resistance. Re- external thermal resistance. C = Cs + Cc-TOTAL heat capacity.

  21. Modulation Phase Shift • In the “plateau”, THE phase shift is F ~ -p/2: • The reduced phase shift f ( w, T ) is : te = ReC -external time constant. i = s + c -internal time constant (sum). • For small w (small angle):

  22. AC-C: Heat Capacity The total heat capacity of the cell+sample is : If : Then : What?!? After all that, we’re back where we started!

  23. Complex Fluid Example • Nano-colloidal dispersion: Liquid Crystal + Aerosil • LC = 8CB (4-cyano-4’-octylbiphenyl) • Aerosil = type 300 ( 7 nm, –OH coated, SiO2 spheres) Mass-fractal, weak H-bonded, gel. • Sample: 8CB+aerosil with rS = 0.10 g cm-3.

  24. AC-C: 8CB+Aerosil ~ 20 mg of Sample Constant Applied Power ( Joule heating ) f = 15 mHz I – N = 312.24 K N – SmA = 305.31 K

  25. Application:Calorimetric Spectroscopy

  26. Cp a Dynamic Response Function? • Of course, any thermodynamic quantity results from an ensemble and time average. • Cp “looks” static because it fluctuates too fast! • The experimental time (frequency w) 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 t. When w ~ t-1, Cp(w) will be complex.

  27. Linear Response Theory Slowly Relaxing Enthalpy Fluctuation: Enthalpy Correlation Function: Complex Heat Capacity: Static Part: Fast Part:

  28. AC-C*: Complex Cp(w) • If tc << ts, then ti = tii. • The Real and Imaginary parts of Cp(w) are: • Complex frequency dependence contained in f.

  29. Complex Cp: 8CB+Aerosil

  30. Complex Cp: Glycerol+Aerosil

  31. Application:RF-Calorimetry

  32. RF (Dielectric) Heating • Electric fields couple directly to electric dipoles. • The Polarization may be permanent or field induced.

  33. Driving Frequency Sweep: 8CB+Aerosil Fitting Results (driven damped oscillator): A0 = 8.4 ´ 10-10 mK Q = 12 0 = 5.0554 Mrad/s ( f0 = 0.805 MHz ) * No features seen for empty cell *

  34. RF-C: 8CB+Aerosil I-N: 312.21 K N-SmA: 305.35 K

  35. RF-C: 8CB+Aerosil

  36. Application:Isothermal Concentration Scanning Calorimetry

  37. Concentration Driven Transitions • Concentration dependent states of matter (phases) are important in many systems. • Phase Diagrams ® Temperature scans at fixed composition. • Temperature FIXED ® Heat WILL flow. • Composition scanned ® System may not be CLOSED. • Volume = Thermodynamic Variable. • ACC can measure Cp under many different conditions. • ACC done at one T as function of time = ICSC.

  38. ICSC: 8CB+Hexane Initial Hexane X = Isotropic phase 301.3 K = SmA of 8CB 1st peak = N phase 2nd feature = SmA phase X8CB at transition = Mean-interaction length.

  39. AC-C: 8CB+Hexane • 8CB+Hexane after ICSC: • Heating-scan • (line) • Multiple Phases! • 1 hr vacuum • Cooling-scan • (line+symbol)

  40. VERY Recent Novel Systems

  41. Biological Example • Stability of ubiquitous membrane proteins (Prof. José M. Argüello, WPI). • Unfolding (denaturing) of the active protein under various conditions. • Aqueous sample with 10 mg/ml protein. Two Samples: • Bare protein (without legand). • Protein with legand containing 5 mM ATP and 5 mM Mg2+.

  42. Protein+Ligand Unfolding

  43. FINE • Calorimetry is an extremely powerful tool in the study of Soft-Condensed Matter. • Interdisciplinary by nature! • Calorimetry to suit any taste: • DSC, MDSC • ACC, ACC*, RFC • ICSC

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