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.
 New Experimental Techniques.
 Current Projects:
 Novel Phases in Liquid Crystals.
 Quenched Random Disorder Effects.
 Thermal Properties: CarbonNanotubes.
 Protein Unfolding
 Frustrated Glasses

Why Calorimetry?
Why Not?
CP ,V
Q
 H 
 S 


  T 
T P ,V  T  P ,V
 T  P ,V
 Q and T are experimental parameters.
 No other technique has Direct Access to a
material’s:
• Enthalpy ( H )
• Entropy ( S )
• Free Energy (really important!)
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 )
Enthalpy
Heat Capacity
Two Types of Calorimetry
CP ,V
Q

T P ,V
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)
Temperature
The temperature increase due to an applied
heating power is :
T  Re P
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”!
Thermal Model (Circuit)
Cell
htr
Rhtr
Sample
Rs , Cs
Re
Temperature Bath

R
Heat Flow Balance (Continuity)
The heat current continuity for each element :
Ch
T  T 
Th
 P (t )  h s
t
Rh
Ts Th  Ts  Ts  Tb  Ts  T 
Cs



t
Rh
Re
R
T Ts  T 
C

t
R
A classic set of coupled Differential Equations.
* Need T (what is actually measured).
Thermal / Electric Analog
Thermal
Quantity
Electric
Temperature
T
Voltage
Heat
Q
Charge
Power
P
Current
Resistance
R
Resistance
Heat capacity
Cp
Capacitance
TYPE II
Differential Scanning
Typical DSC Setup
Technical
Notes
1999:
TA Instruments,
Inc.
Technical
Notes 1999:
TA Instruments,
Inc.
DSC POV of Enthalpy
Sample
H
H
THE Enthalpy:
H
Reference
dH/dt
(Power)
What DSC sees:
TC TM
T(t)
New Technique:
Modulation DSC
 Combination of Type I and II Calorimetry


Differential Heat Flow (Power):
 dQ/dt = T/R = Cpb + f(T, t)
Add a modulation to the heating ramp
 “Kinetic” heat flow, f(T, t), contains the
induced T-oscillations
TYPE I
Modulation (AC)
AC-C: Basic View


P. F. Sullivan and G. Seidel, Phys. Rev. 173, 679 (1968).
Applied AC power induces temperature oscillations:
dQ
Q
Po
dt
Cp 


T p dT Tac
dt
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)
Heating Power Modulation
Applying heating power sinusoidally as:
P(t )  Po 1  cos(t )
will induce sinusoidal temperature oscillations:
T (t )  Tb  TDC  Tac e j (t  )
Tb
TDC
Tac e j(t+)
- bath temperature.
- DC temperature rise
( rms heating ).
- temperature oscillations.
Modulation Amplitude
From a one-lump thermal model, the temperature
oscillation amplitude is :
Po 
1
2 Rs 
2 2
Tac 
1  2 2    ii 

C    e
3 Re 
e = Re C
ii
1
2
- external time constant.
- internal time constant:
ii2 = s2 + c2 ( root-sum-squared )
Rs
- sample thermal resistance.
Re
- external thermal resistance.
C = Cs + Cc - TOTAL heat capacity.
Modulation Phase Shift


In the “plateau”, THE phase shift is  ~ p/2:
The reduced phase shift f ( , T ) is :
 1

f ( , T )     tan 
  i 
2
 e

p
e = ReC
i = s + c

1
- external time constant.
- internal time constant (sum).
For small  (small angle):
f ( )  1R C
e
AC-C: Heat Capacity
The total heat capacity of the cell+sample is :
Po 
1
2 Rs 
2 2
C
1  2 2    ii 

Tac    e
3 Re 
If :
1

1

  e       i 
e

i

Then :
Po
C
C*
Tac
1
2
What?!?
After all that, we’re
back where we started!
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.
AC-C: 8CB+Aerosil
.2
SmA
N
I
~ 20 mg of Sample

C* ( J K )
.3
.2
Constant Applied Power
( Joule heating )
.
.
f = 15 mHz
.
.
I–N
= 312.24 K
N – SmA = 305.31 K
f ( rad )
.
.
.
.
.
.2
3
3
3
32
T(K)
3
32
Application:
Calorimetric Spectroscopy
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 ) 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  ~ , Cp() will be complex.
Linear Response Theory
Slowly Relaxing Enthalpy Fluctuation: H R
Enthalpy Correlation Function:
H R (0)H R (t )
Complex Heat Capacity:
 H R (0)H R (t )
C p ()  C  j 
dt
2
0
k BT
0
p

Static Part: C p0  C p 
Fast Part: C p
H R2
k BT 2
AC-C*: Complex Cp()
 If c << s, then i = ii.
 The Real and Imaginary parts of Cp() are:
C '  C * cos( f)
1
C"  C * sin( f) 
0
Re
 Complex frequency dependence contained in f.
Complex Cp: 8CB+Aerosil
.3

C' ( J K )
.2
SmA
N
I
.2
.
.
C" + 1/Re
.
.
.
.2
32
3
3
3
3
T(K)
32
3
3
Complex Cp: Glycerol+Aerosil
10
C
8
T (K)
 300
 320
 340
 360
 380
0
2.05
6
 (sec)

C', C" ( J K )
2.00
4
1.95
1.90
1.85
C
1.80

2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4
2

1000 / T ( K )
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0

 ( rad s )
3.5
4.0
4.5
5.0
Application:
RF-Calorimetry
RF (Dielectric) Heating


Electric fields couple directly to electric dipoles.
The Polarization may be permanent or field induced.
Driving Frequency Sweep: 8CB+Aerosil
T ( K )





2
Fitting Results
(driven damped
oscillator):
A0 = 8.4  10-10 mK
Q = 12
0 = 5.0554 Mrad/s
( f0 = 0.805 MHz )




d ( rad s



)
* No features seen for empty cell *
RF-C: 8CB+Aerosil

C*/PO ( s K

)

SmA
N
I-N:
312.21 K
I

N-SmA:
305.35 K




3
3
3
32
T(K)
3
32
RF-C: 8CB+Aerosil
2.3
f ( rad )
2.2
2.2
SmA
N
I
2.
3
3
3
32
T(K)
3
32
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 Cp under many different
conditions.
ACC done at one T as function of time = ICSC.
ICSC: 8CB+Hexane
T = 301.324 K
Initial Hexane X =
Isotropic phase
C* ( J K
-1
)
0.124
0.122
301.3 K = SmA of 8CB
0.120
1st peak = N phase
2nd feature = SmA phase
-1.240
X8CB at transition =
Mean-interaction length.
f ( rad )
-1.245
-1.250
-1.255
0
500
1000
1500
2000
Point Number (  Time  X8CB )
2500
AC-C: 8CB+Hexane
0.17
8CB+Hexane after ICSC:
• Heating-scan
(line)
C*cos(f) ( J K
-1
)
0.16
0.15
0.14
0.13
Multiple Phases!
0.12
0.11
1 hr vacuum
• Cooling-scan
(line+symbol)
C*sin(f) ( J K
-1
)
0.07
0.06
0.05
0.04
300
302
304 306
308
310
T(K)
312 314
316
318
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 Mg2+.

Protein+Ligand Unfolding
0.13
0.12
C* ( J K

)
0.11
0.10
0.09
0.08
~ 336.6 K
~ 377.8 K
0.07
300 310 320 330 340 350 360 370 380 390 400 410 420
TPRT ( K )
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
