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 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

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

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?

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?

Enthalpy

Heat Capacity

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

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!

Thermal Model (Circuit)

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

ThermalQuantityElectric Temperature T Voltage Heat Q Charge PowerPCurrent ResistanceR Heat capacityCpCp Capacitance Thermal / Electric Analog

TYPE II Differential Scanning

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

THE Enthalpy: What DSC sees: DSC POV of Enthalpy

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

TYPE I Modulation (AC)

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 (~ mrad/s) T ac - Amplitude of temperature oscillations (~ 2-15 mK) AC-C: Basic View

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

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

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

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

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

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

Application: Calorimetric Spectroscopy

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.

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

AC-C*: Complex C p ( ) If c << s, then i = ii. The Real and Imaginary parts of C p ( ) are: Complex frequency dependence contained in.

Complex C p : 8CB+Aerosil

Complex C p : Glycerol+Aerosil

Application: RF-Calorimetry

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

Driving Frequency Sweep: 8CB+Aerosil Fitting Results (driven damped oscillator): A 0 = mK Q = 12 0 = Mrad/s ( f 0 = MHz ) * No features seen for empty cell *

RF-C: 8CB+Aerosil I-N: K N-SmA: K

RF-C: 8CB+Aerosil

Application: Isothermal Concentration Scanning Calorimetry

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 C p under many different conditions. ACC done at one T as function of time = ICSC.

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

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

VERY Recent Novel Systems

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 Mg 2+.

Protein+Ligand Unfolding

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