specific heat capacity of a material - ikiu · specific heat capacity of a material ... often use...

Specific Heat Capacity of a

Material

Thermal Analysis : Dr. A. Sedghi

Dr. Arman Sedghi

(IKIU)

Calorimetry

Two types of calorimetry are commonly used:

◦ Constant-pressure Calorimetry

Specific heat

DHrxn or DHsoln

◦ Bomb Calorimetry (Constant Volume Calorimetry)

DHcombustion


Calorimetry

In constant-pressure calorimetry,

◦ Measurements are made in an “open” container.

Reactions occur at constant pressure

◦ Calorimeter is insulated

Assume that the amount of heat gained from or lost to

the surroundings is negligible

any heat gained or lost during a chemical reaction or process

comes from or goes into the solution being studied.


Calorimetry

In constant-pressure calorimetry, the heat

gained or lost by the solution (the liquid

present) is measured.

◦ If heat is lost by the chemicals (or object) during a

reaction or process, then it must be gained by the

solution and vice versa.

The heat lost or gained by the reaction (or object) and

the solution are equal in magnitude but opposite in sign.

qobj = - qsoln or qrxn = - qsoln


Calorimetry

Calorimetry Simulation:

◦ Measuring the specific heat of a metal

How is the experiment performed?

What kind of data is collected?

How are the data used to determine specific heat?


Calorimetry

Determining specific heat or molar heat capacity experimentally:

◦ Heat an object with a known mass to 95-100oC.

◦ Measure initial temperature of object.

◦ Place known mass of water into calorimeter and measure its temperature.

◦ Add hot object to the water

◦ Measure the equilibrium temperature (i.e. final temperature) of the water and object.


Calorimetry

Types of data obtained from or used in a calorimetry experiment often include: ◦ Sample Data Mass of sample (object or compound)

Tinitial (sample)

Tfinal (sample)

◦ Solution Data Mass of solution

Tinitial (solution)

Tfinal (solution)

Csoln Often use specific heat of water if water is the solvent


Calorimetry

Using the data to find specific heat:

◦ Calculate the amount of heat gained by the water:

qwater = Cwater x mwater x DTwater

◦ Calculate the amount of heat lost by the object qobj = - qwater

◦ Calculate specific heat of object

Cobj = qobj

mobj x DTobj


Calorimetry

Example: A 55.0 g piece of aluminum metal at 100.0oC was added to 51.3 g of water at 20.0oC. The equilibrium temperature of the system was 35.0oC. If the specific heat of water is 4.18 J/g.K, what is the specific heat of aluminum?


Given: Cwater = 4.18 J/g.K

mwater = 51.3 g

DTwater = 35.0oC - 20.0oC = 15.0oC = 15.0 K

mAl = 55.0 g

DTAl = 35.0oC - 100.0oC = -65.0oC = -65.0K

Find: CAl

Calorimetry

qwater = Cwater x mwater x DTwater

qwater = 4.18 J x 51.3 g x 15.0 K = 3216.5 J

g.K

q Al = -qwater = -3216.5 J (Note: Keep some extra sig figs at this stage)

CAl = qAl = -3216.5 J

mAl x DTAl 55.0 g x -65.0 K

CAl = 0.900 J/g.K


Calorimetry

For an exothermic process, the heat produced causes the temperature of the solution to increase. (DTsoln >0)


Chemical

particle

Heat released by chemical

particle

q

q

q q

q

q q

Calorimetry

For an endothermic process, the heat gained comes from the reaction mixture and causes the temperature of the solution to decrease (DTsoln < 0)


Chemical

particle

Heat gained by chemical particle

from the rxn mixture

q

q

q

q

q

q

Calorimetry

Bomb Calorimetry

◦ Constant Volume

Calorimetry

◦ Used to study combustion

reactions

◦ Measure DHcombustion


Calorimetry

As combustion occurs,

◦ Heat is released

◦ Heat is absorbed by the calorimeter and its

contents

◦ Temperature of calorimeter & contents increases.

The change in temperature of the calorimeter

and its contents can be used to determine the

heat of combustion.


Calorimetry

Calculate the heat absorbed by the calorimeter and its contents:

qcal = heat capacity (calorimeter) x DT

(Notice that you do not need a mass term because heat capacity has units of J/K)

Calculate the heat lost by the reactants:

qrxn = -qcal


Calorimetry

Calculate molar heat of combustion

(DHcomb per mole reactant)

◦ DHcomb = qrxn

mole reactant


Calorimetry

Example: When 2.00 g of methylhydrazine (CH6N2) is burned in a bomb calorimeter, the temperature of the calorimeter increases from 25.00oC to 32.25oC. If the heat capacity of the calorimeter is 7.794 kJ/oC, what is the molar heat of combustion for CH6N2?


2CH6N2 (l) + 5 O2(g) 2 N2 (g) + 2 CO2(g) + 6 H2O (g)

Calorimetry

Given: Tfinal = 32.25oC

Tinitial = 25.00oC

Ccal = 7.794 kJ/oC

Find: molar heat of combustion


DT = 32.25 - 25.00

= 7.25oC

DHcomb = qcomb

mol CH6N2

Calorimetry

qcal = Ccal x DT

qcal = 7.794 kJ x 7.25 K = 56.51 kJ

K

qrxn = -qcal = -56.51 kJ

DH = - 56.51 kJ x 46.1 g = -1.30 x 103 kJ

2.00 g mole mole


DHcomb = qrxn

mole CH6N2

Hess’s Law

The heats of reaction (DHrxn) have been measured and tabulated for many chemical reactions.

There are two approaches to determining the heat of reaction for a particular chemical reaction:

◦ Calorimetry

◦ Use tabulated DHrxn to calculate the heat of reaction for another reaction of interest


Hess’s Law

The enthalpy change for a reaction or

process is a state function:

◦ Depends only on the amount of reactants and

products used/formed and on their physical

state

◦ Does not depend on how the reaction was

done.

one step vs. multiple steps


Hess’s Law

Hess’s Law:

◦ If a reaction is carried

out in a series of steps,

DH for the overall

(one-step) reaction is

equal to the sum of

the DH for the

individual steps.


Experimental Procedure

There are four main procedures to this experiment

1. Set-up the calorimeter

2. Boil the water containing metal

3. Set-up the GLX computer.

4. Collect the calorimetric data.


Background - Calorimeter


Thermometer

probe insert

Calorimeter

cover or lid

Two styrofoam cups

nested together

containing water and

metal

GLX

Xplorer

Analog

Adapter

GLX

Adapter

USB

Plug

Figure A- GLX Components


Colorimeter

Voltage

Sensor Syringe

Pressure

Sensor

Temperature

Sensor

pH Sensor

Figure B- Sensor Probes


Calorimetric Set-Up


Differential Scanning Calorimetry (DSC)


Analogous to DTA, but the heat input to sample and reference is varied in

order to maintain both at a constant temperature.

Key distinction:

– In DSC, differences in energy are measured

– In DTA, differences in temperature are measured

DSC is far easier to use routinely on a quantitative basis, and has become the

most widely used method for thermal analysis

Differential Scanning Calorimetry (DSC)

Polymer and reference samples are heated in such a way that they are kept

at the same (increasing) temperature.

When a thermal transition occurs thermal energy is supplied to the

polymer or reference.

The energy transferred is equivalent to the energy absorbed or evolved in

the transition.


DSC Instrumentation


There are two common DSC methods

– Power compensated DSC: temperature of sample and reference are kept

equal while both temperatures are increased linearly

– Heat flux DSC: the difference in heat flow into the sample/reference is

measured while the sample temperature is changed at a constant rate

• DSC differs fundamentally from DTA in that the sample and reference are both maintained at the temperature predetermined by the program.

• during a thermal event in the sample, the system will transfer heat to or from the sample pan to maintain the same temperature in reference and sample pans

• two basic types of DSC instruments: power compensation and heat-flux

Differential Scanning Calorimetry

power compensation DSC heat flux DSC


Power Compensation DSC

sample holder • Al or Pt pans

sensors • Pt resistance thermocouples • separate sensors and heaters for the sample and reference furnace

• separate blocks for sample and reference cells

temperature controller

• differential thermal power is supplied to the heaters to maintain the temperature

of the sample and reference at the program value

sample pan

DT = 0

inert gas vacuum

inert gas vacuum

individual heaters

controller DP

reference pan

thermocouple


DSC


sample holder • sample and reference are connected by a low-resistance heat flow path • Al or Pt pans placed on constantan disc

sensors • chromel®-constantan area thermocouples (differential heat flow) • chromel®-alumel thermocouples (sample temperature) furnace

• one block for both sample and reference cells

temperature controller

• the temperature difference between the sample and reference is converted to

differential thermal power, dDq/dt, which is supplied to the heaters to maintain the temperature of the sample and reference at the program value

Heat Flux DSC

sample pan

inert gas vacuum

heating coil

reference pan

thermocouples

chromel wafer

constantan

chromel/alumel wires


Analysis of Heat-Flow in Heat Flux DSC

• temperature difference may be deduced by considering the heat flow paths in the DSC system

• thermal resistances of a heat-flux system change with temperature

• the measured temperature difference is not equal to the difference in temperature between the sample and the reference

DTexp ≠ TS – TR

tem

pera

ture

Tfurnace

TRP

TR

TS

TSP

heating block

DTR DTS

reference

sample

DTL

thermocouple is not in physical contact with sample


Derives H Uses thermocouples

Power Compensation DSC Quantitative DTA “Heat Flux” DSC

Measures H directly Uses platinum resistance

thermometers

Diamond DSC

Pyris 6 DSC

Sapphire DSC

Competitive DSC’s

DSC Technology …


Heat Flux DSC furnace


furnace

The different DSC technologies …

High resolution / high sensitivity research studies

Absolute specific heat measurement

Fast Scan DSC applications (HyperDSCTM)

High throughput laboratories

Thermal Analysis : Dr. A. Sedghi …. are tailored for specific applications

Routine applications

Near / at line testing in harsh environments

Education

Automated operation

Cost-sensitive laboratories


Heat Flux DSC

DSC

Constant Heating Rate

◦ Initial Temp

◦ Final Temp

◦ Heating Rate (°C/min)

Data

◦ Heat flow to sample minus

Heat flow to reference vs Time

(Temp.)

Measures heat of

crystallization


Polymer without weight change in this temperature range

Typical Features of a DSC Trace for a Polymorphic System

sulphapyridine

endothermic events

melting sublimation

solid-solid transitions desolvation

chemical reactions

exothermic events

crystallization solid-solid transitions

decomposition chemical reactions

baseline shifts

glass transition Thermal Analysis : Dr. A. Sedghi

Sample Preparation

• accurately-weigh samples (~3-20 mg)

• small sample pans (0.1 mL) of inert or treated metals (Al, Pt, Ni, etc.)

• several pan configurations, e.g., open , pinhole, or hermetically-sealed pans

• the same material and configuration should be used for the sample and the reference

• material should completely cover the bottom of the pan to ensure good thermal contact

• avoid overfilling the pan to minimize thermal lag from the bulk of the material to the sensor

* small sample masses and low heating rates increase resolution, but at the expense of sensitivity

Al Pt alumina

Ni Cu quartz Thermal Analysis : Dr. A. Sedghi

DSC Calibration

baseline • evaluation of the thermal resistance of the

sample and reference sensors

• measurements over the temperature range of interest

2-step process

• the temperature difference of two empty crucibles is measured

• the thermal response is then acquired

for a standard material, usually sapphire, on both the sample and reference platforms

• amplified DSC signal is automatically varied with temperature to maintain a constant calorimetric sensitivity with temperature


DSC Calibration temperature • goal is to match the melting onset temperatures indicated by the furnace

thermocouple readouts to the known melting points of standards analyzed by DSC

• should be calibrated as close to the desired temperature range as possible Hea

use of calibration standards of known heat capacity, such as sapphire, slow accurate heating rates (0.5–2.0 °C/min), and similar sample and reference pan weights

t flow calibrants • high purity • accurately known enthalpies • thermally stable • light stable (hn) • nonhygroscopic • unreactive (pan, atmosphere)

metals • In 156.6 °C; 28.45 J/g • Sn 231.9 °C • Al 660.4 °C inorganics • KNO3 128.7 °C • KClO4 299.4 °C organics • polystyrene 105 °C • benzoic acid 122.3 °C; 147.3 J/g • anthracene 216 °C; 161.9 J/g


Heat Flow in DSC


DSC Step by Step


Melting Glass transition Recrystallization

Applications of DSC


DSC is usually carried out in

linear increasing-temperature

scan mode (but can do

isothermal experiments)

– In linear scan mode, DSC

provides melting point data

for crystalline organic

compounds and Tg for

polymers

Easily used for detection of bound crystalline water molecules or solvents,

and measures the enthalpy of phase changes and decomposition

DSC trace of polyethyleneterphthalate (PET)

Applications of DSC


DSC is useful in studies o

polymorphism in organic

molecular crystalline

compounds (e.g.

pharmaceuticals, explosives,

food products)

Example data from two

“enantiotropic” polymorphs

DSC of a Pharmaceutical Hydrate


Loss of water

Melt Decomposition

A Differential Scanning Calorimeter (DSC) measures the amount of energy (heat)

absorbed or released by a sample as it is heated, cooled or held at a constant

(isothermal) temperature. The precise measure of sample temperature is also

made with a DSC.


Differential Scanning Calorimetry (DSC) …

High Sensitivity Thermal Analysis DSC family ...


Researc

h

Diamond DSC • Unique Power Compensation

• HyperDSCTM for unmatched

sensitivity

• Highest signal resolution

• StepScan SW for MTDSC

Sapphire DSC • Heat Flux DSC • Oval sensor for high sensitivity • Fully automated • Multiple cooling options and

pan types for broad operation range

Pyris 6 DSC • Heat Flux DSC • Low cost • Rugged and reliable • Fully automated • Built-in mass flow control

Routine

DSC Plot

The resulting plot of differential rate of heating Vs

temperature can be studied to measure Heat capacity, melt

enthalpy and transition temperature.


Completely amorphous polymers won't show any crystallization, or any

melting either. But polymers with both crystalline and amorphous domains,

will show all the features you see above.

Characteristics of a DSC curve

Each substance has a characteristic DSC curve that can

be used for qualitative identification.

Endotherms generally represent physical changes while

exotherms indicate crystallization, polymerization,

curing, decomposition etc.

The area under the peak (trough) is proportional to the

heat evolved or absorbed during the reaction.


Applications of the DSC curve

% Crystallinity

% Crystallinity = D Hf,x/D Hf

= Heat of fusion of sample/heat of fusion of 100% crystal

Rate of reaction

◦ Height of peak is proportional to rate of reaction

Heat of reaction = Heat absorbed or emitted/No of moles

Change in heat capacity

◦ Manifests as a change in baseline.

◦ A sharp increase is typical of Tg. Thermal Analysis : Dr. A. Sedghi

Melting point from DSC curve

Melting point - Can determine the exact melting

point as the temperature at which melting is

complete. The actual melting of the polymer takes

place at a range of temperature.


Definition of Transition Temperature

157.81°C

156.50°C28.87J/g

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

He

at

Flo

w (

W/g

)

140 145 150 155 160 165 170 175

Temperature (°C)

Sample: INDIUM CRIMPED PAN CHECKSize: 7.6300 mgMethod: indiumComment: P/N 56S-107

DSCFile: C:...\10C per min crimped\DSC010920A.3Operator: Ron VansickleRun Date: 20-Sep-01 09:13Instrument: 2920 MDSC V2.6A

Exo Up Universal V3.3B TA Instruments

extrapolated onset temperature

peak melting temperature


Melting Processes by DSC

pure substances • linear melting curve

• melting point

defined by onset temperature

impure substances • concave melting

curve

• melting characterized at peak maxima

• eutectic impurities may produce a second peak

melting with decomposition

• exothermic

• endothermic

eutectic melt


Glass Transitions

• second-order transition characterized by change in heat capacity (no heat absorbed or evolved)

• transition from a disordered solid to a liquid

• appears as a step (endothermic direction) in the DSC curve

• a gradual volume or enthalpy change may occur, producing an endothermic peak superimposed on the glass transition


Enthalpy of Fusion

157.81°C

156.50°C28.87J/g

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

He

at

Flo

w (

W/g

)

140 145 150 155 160 165 170 175

Temperature (°C)

Sample: INDIUM CRIMPED PAN CHECKSize: 7.6300 mgMethod: indiumComment: P/N 56S-107

DSCFile: C:...\10C per min crimped\DSC010920A.3Operator: Ron VansickleRun Date: 20-Sep-01 09:13Instrument: 2920 MDSC V2.6A



Burger’s Rules for Polymorphic Transitions Enantiotropy: transition is irreversible

end

otherm

ic

Heat of Transition Rule • endo-/exothermic solid-solid transition

Heat of Fusion Rule • higher melting form; lower DHf

• exothermic solid-solid transition

• higher melting form; higher DHf

Monotropy:v

end

otherm

ic


Enthalpy of Fusion by DSC

single (well-defined) melting endotherm • area under peak • minimal decomposition/sublimation • readily measured for high melting polymorph • can be measured for low melting polymorph

multiple thermal events leading to stable melt • solid-solid transitions (A to B) from which the transition enthalpy (DHTR)

can be measured*

crystallization of stable form (B) from melt of (A)

DHfA = DHf

B - DHTR

* assumes negligible heat capacity difference between polymorphs over temperatures of interest

DHfA = area under all peaks from B to the stable melt


Purity by DSC

• eutectic impurities lower the melting point of a eutectic system

• purity determination by DSC based on Van’t Hoff equation

• applies to dilute solutions, i.e., nearly pure substances (purity ≥98%)

• 1-3 mg samples in hermetically-sealed pans are recommended

• polymorphism interferes with purity determination, especially when a transition occurs in the middle of the melting peak

Tm = To - .

DHo

RTo2 c 1

f

melting endotherms as a function of purity.

benzoic acid

97%

99%

99.9%


Effect of Heating Rate

• many transitions (evaporation, crystallization, decomposition, etc.) are kinetic events

… they will shift to higher temperature when heated at a higher rate

• the total heat flow increases linearly with heating rate due to the heat capacity of the sample

… increasing the scanning rate increases sensitivity, while decreasing the scanning rate increases resolution

• to obtain thermal event temperatures close to the true thermodynamic value, slow scanning rates (e.g., 1–5 K/min) should be used

DSC traces of a low melting polymorph collected at four different heating rates. (Burger, 1975)


Effect of Phase Impurities

• Lot A: pure low melting polymorph – melting observed

• Lot B: seeds of high melting polymorph induce solid-state transition below the melting temperature of the low melting polymorph

2046742FILE# 022511DSC.1

2046742FILE# 022458 DSC.1 Form II ?

-5

-4

-3

-2

-1

0

He

at

Flo

w (

W/g

)

80 130 180 230 280

Temperature (°C)Exo Up Universal V3.3B TA Instruments

Lot A - pure

Lot B - seeds

• lots A and B of lower melting polymorph (identical by XRD) are different by DSC


Polymorph Characterization: Variable Melting Point

• lots A and B of lower melting polymorph (identical by XRD) appear to have a “variable” melting point

-1.1

-0.9

-0.7

-0.5

-0.3

-0.1

0.1

He

at

Flo

w (

W/g

)

110 120 130 140 150 160 170 180

Temperature (°C)

DSC010622b.1 483518 HCL (POLYMORPH 1)DSC010622d.1 483518 HCL


Lot A

Lot B

• although melting usually happens at a fixed temperature, solid-solid transition temperatures can vary greatly owing to the sluggishness of solid-state processes Thermal Analysis : Dr. A. Sedghi

• the low temperature endotherm was predominantly non-reversing, suggestive of a solid-solid transition

• small reversing component discernable on close inspection of endothermic conversions occurring at the higher temperatures, i.e., near the melting point

Polymorph Characterization: Variable Melting Point

Reversing (heat flow component)

-0.50

-0.45

-0.40

-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

Re

v H

eat

Flo

w (

W/g

)

110 120 130 140 150 160 170 180

Temperature (°C)



Non-reversing (heat flow component)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

Nonre

v H

eat F

low

(W

/g)

110 120 130 140 150 160 170 180

Temperature (°C)



Lot A

Lot B

Lot A

Lot B

reversing heat flow non-reversing heat flow

• the “variable” melting point was related to the large stability difference between the two polymorphs; the system was driven to undergo both melting and solid-state conversion to the higher melting form


• development of “hyphenated” techniques for simultaneous analysis TG-DTA TG-DSC TG-FTIR TG-MS

15.55%(0.9513mg)

24.80°C100.0%

179.95°C84.45%

-1.8

-0.8

0.2

1.2

2.2

3.2

4.2

Te

mp

era

ture

Diffe

ren

ce

(µ

V/m

g)

-40

0

40

80

120

We

igh

t (%

)

20 70 120 170 220 270

Temperature (°C)

Sample: SODIUM TARTRATE (ALDRICH)Size: 6.1176 mgMethod: 25C TO 300Comment: LOT# 22411A0

TGA-DTAFile: C:\TA\Data\Sdtcal\2004\TGA040105A.5Operator: Ron VansickleRun Date: 6-Jan-04 12:09Instrument: 2960 SDT V3.0F


“Hyphenated” Techniques

• thermal techniques alone are insufficient to prove the existence of polymorphs and solvates

• other techniques should be used, e.g., microscopy, diffraction, and

spectroscopy

evolved gas analysis (EGA)

TG-DTA trace of sodium tartrate


Thermal Expansion in one Dimension

(Length Change)

TLL o DD

change in length change in temperature

initial length

coefficient of thermal expansion (depends on the material)

Mechanical Analysis

(TMA / DMA)

A Dynamic Mechanical Analyzer (DMA) measures rheological

behavior of a sample under dynamic conditions (such as

modulus, compliance and damping) as a function of

temperature, time, frequency, stress, atmosphere or a

combination of these parameters.

A Thermomechanical Analyzer (TMA) measures dimension

changes of a sample (such as expansion or contraction) as

a function of temperature, time and force applied to the

sample.


z

Y

X

E” ~ energy loss in

internal motion

E’ ~ elastic

response

TMA

Constant Heating Rate ◦ Initial Temp

◦ Final Temp


Data ◦ Size of Sample vs Time (or Temp.)

Measures ◦ Thermal Expansion Coefficient

◦ Volume change on crystalization or crystal transformations

◦ Sintering

◦ Glass Transitions in Polymers


TMA


Polymer with glass transition

DMA

Constant Heating Rate ◦ Initial Temp

◦ Final Temp


Data ◦ Force vs Time (or Temp.)

◦ Force delay vs Time (or Temp.)

◦ Viscoelastic Properties Storage and Loss Modulus

Measures ◦ Glass Transition

◦ Viscoelastic Properties


Polymer with Glass Transition

PerkinElmer High Sensitivity Mechanical Analysis family ...


Researc

h

Diamond TMA & DMA • Broad force range

• Multiple deformation modes

• Many measuring systems

• Dynamic & static operation

• Advanced cooling system

Thermal conductivity measurement


فاکتور مقاومت به شوک حرارتی

:استاندارد هاي صنعتي براي مواد ديرگداز


1.BS standard

2.ASTM standard

specific heat capacity of a material - ikiu · specific heat capacity of a material ... often use...

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