Post on 30-May-2018
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THE REACTION KINETICS STUDY
Chemical reactions take place at a certain rate and it is defined
as the rate of change of the amount of the reactant(s)/product(s)material(s) per unit time
Parameter(s): pressure; concentration; reaction fraction,
dn/dt = kf(n)
k : rate constant
f(n) : amount function, n
e.g.: Polymer decay
d /dt = k (1 - )
Arrhenius: rate of reaction is
influenced by temperaturek = A exp (-E/RT)
E : activation energy
A : pre-exponential factor, depends on
the orientation and the structure of the
reactants
The rate of reaction is influenced by:
(a) The amount of reactants, and
(b) The temperature
k = A-E/RT
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Three types of chemical reaction
studies by TG, DTA/DSC:(i) The extent of reaction,
intermediates, and products
(i) Energy or heat involved in the
various levels of reaction
(i) Mechanism and kinetics of
reaction
For reactions in solution :
- concentration, cB For solid state reactions:
- reaction fraction,
Solid state endothermic reaction
A (solid) = B (solid) + C (gas)
- heat is absorbed as the gas and mass
lost
The extent of reaction, is a
quantity which has the dimension of
the amount of material
nB = nB,0 + B
nB : the amount of material B
nB,0 : the selected amount of B,
at t= 0
B : the stoichiometric number for B(+ve if B is the reaction product and
ve if B is the reactant)
The Reaction Kinetics
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Despite being measured at a fixed
temperature, rate of reaction changes
with time and the value of
Rate = d /dt = kT f( )
kT : rate constant at temperature T
: mathematical expression for
For a reaction in solution or
radiochemical reaction, f( ) is thesame throughout the sample, but it
may change when the reaction
becomes f( ) due to the chemicalchange, geometrical change, or a
change in reaction mechanism.
(a) Diffusion controlled reaction
d /dt = kT /2 ( )
(b) Two dimensional nucleus growth
(Avrami equation)
d /dt = kT (1 - ) (-ln(1 - ))1/2
(c) First order reaction: random decay of
an active species
d /dt = kT
(1 - )
Examples of relationship betweensolid state reaction and :
Interpretation of reaction kinetics
equation takes into account the
following:- the way reaction begins by
nucleation process- the nucleus growth
- the interaction or interfacial
geometry involved in the reaction
- the reactant decay
The Rate of Reaction
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The Rate Constant, k, is strongly influenced
by temperature and sometimes written as
kT.
Arrhenius equation:
kT = A exp(-E/RT)
A = pre-exponential factor
E = activation energy (J/mole)
R = molar gas constant (8.314 J/(K mole)
The reaction mechanism may change
during the reaction which can influencethe value ofE.
Temperature Control
In a non-isothermal experiment,
temperature is controlled according
to a linear temperature rise, K/min, and at the time t:
Tt = T0 + t
However, in the real situation an
endothermic or exothermic process
will change the actual temperature
and the equation is modified as
follows
Tt = T0 + t + s(t)
wheres(t) is the difference between
the sample temperature and the
programmed temperature.
The Reaction Rate Constant
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Heat capacity change
- estimated by the change in the
baseline of the DSC curve
- independent of the rate of reaction
but dependent on the materials
present in the sample Control of temperature gradient in
the sample- use as small sample size as possible
- instrumental control system.
The rate of a chemical reaction and a
physical change can be influenced bytemperature and H.
Hence, a relationship exists between
- the H and the DSC peak area
- the rate of reaction and the rate of
heat flow, P
DTA/DSC Peak Thermograms
The peaks are divided into several
fractions, each of which represents the
reaction fraction that has takenplace, respectively.
Kinetics study of a single step
reaction, example:
a) Decomposition of free radical initiator
of azobisisobutyronitrile (AIBN) by
DSC method:
4 32 K/min will produce data that is
suitable for first order kinetics and the
activation energy of 125 kJ/mol.
Reaction Kinetics and DSC Curves
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The DSC curve for an exothermic reaction
showing the measurement of partial peak area
b) Measurement of the rate of
polymer crystallization by
using the partial area to
determine the percantage ofthe polymer crystallized.
The results are normally
compatible with the Avrami
equation
[-ln(1 - ]1/ n
= kt
where
: the final crystallinity at thetime t
n : depends on the crystal growth
mechanism, e.g. n = 3 forspherical growth
The Relationship of DSC
Curve and
Figure 8.1
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Evaluation of thermal
hazards by the kinetics data
is a standard method ASTM
E698-79.
The sample is repeatedly heated for several times at various heating rates, , andthe peak temperature of the thermogram is recorded, Tmax . The plot of ln( )
versus 1/ Tmax produces a straight line with the slope ofE/R.
An isothermal DSC curve for polymer
crystallization
ASTM E698-79 Standard Method for
The Evaluation of Thermal Hazards
Figure 8.2
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The DTA curve for calcium
oxalate monohydrate:
(a) in nitrogen,
(b) in the air.
Sample: 10 mg, 10 K/min
Hydration waterOxalatedecomposition
Decomposition
of calcium
carbonate
Calcium oxalate monohydrate (CaC2O4 H2O)
(a)
(b)
CO + O2 CO2
The Application of DSC/DTA On The
Organic and Complex Compounds
Figure 8.3
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(a)
(b)
The DTA curve for copper sulphate
pentahydrate:
(a) unsealed plate
(b) sealed plate and pin-holed
Sample: 6 mg of powdered crystal,10 K/min, air-flow.
I CuSO4 5H2O = CuSO4 3H2O + 2H2O H (373 K) = 100 kJ/mole
II CuSO4 3H2O = CuSO4 H2O + 2H2O H (400 K) = 104 kJ/mole
III CuSO4 H2O = CuSO4 + 2H2O H (510 K) = 72 kJ/mole
Sample decomposition:
CuSO4 = CuO + SO2 + O2
I IIIII
Copper Sulphate Pentahydrate (CuSO4 5H2O)
Figure 8.4
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OPC = Ordinary Portland Cement contains largely calcium sylicates
because it is made by heating clay (alumino-sylicate) and calciumcarbonate
When used, cement is mixed with water that will hydrate the sylicates,
and it is gradually transformed into a good cement material that produces
the final strength in several months.
Figure 8.5: DTA curve for a sample of Portland Cement concrete (50 mg, 20K/min, nitrogen) (Source: H_F 3.38)
Quartz transition: 573o
C
dehydration
Ordinary Portland Cement (OPC)
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The high alumina cement (HAC) is made from bauxite and limestone to produce a calcium aluminate mixture.
When mixed with water, HAC produces cement at a faster rate
than the OPC, hence speeds up the construction process, but
under certain circumstances the HAC concrete beams tend to
break and result in accidents.
During the hardening process CaO Al2O3 10H2O is formed, but this is not the
most stable hydrate and will slowly be converted to a more stable compounds
such as hexahydrate, hydrated alumina or gibbsite.
3CaO Al2O3 10H2O (or C3AH6) and Al2O3 3H2O (or AH3)
3(CaO Al2O3 10H2O) = 3CaO Al2O3 6H2O + Al2O3 3H2O + 18H2O
High Alumina Cement HAC
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Conversion reaction weakens the
concrete because the reactionproduct is denser than the original
concrete and the reacting structure
becomes porous, especially if the
conversion process takes place
rapidly.
Decahydrate, hexahydrate andgibbsite lost their water molecules
when heated as shown in Figure
8.6.
Sampling by drilling of the
concrete should be carried out
carefully
Figure 8.6: DTA curves for standard HAC that has
conversion of 50 % (a) and 70 % (b) (source: H_F 3.39)
Avoid gypsum and plaster, remove the drilling metal pieces 10 100 mg of sample is analysed at 10 30 K/min, nitrogen atmosphere The degree of conversion is determined from the height of the peak
The Degree of
conversion (Dc)(a)
(b)
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100Amount of AH3
Dc =(Amount of AH3 + Amount of CAH10 )
or
100a(Peak height AH3)
Dc =
(aPeak height AH3 + b Peak height CAH10 )
or
100(Peak Height AH3)
Dc =
(Peak height AH3 + Peak height CAH10 )
Where a and b are calibration constants andK= b/a Figure 8.6: DTA curves for standard HAC that has
conversion of 50 % (a) and 70 % (b) (source: H_F 3.39)
Avoid gypsum and plaster, remove the drilling metal pieces 10 100 mg of sample is analysed at 10 30 K/min, nitrogen atmosphere The degree of conversion is determined from the height of the peak
The Determination of Dc
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The calibration constantKis determined by analysing a standard material
that has 50 % dan 70 % conversion. For the 50 % conversion, the peak
height AH3 is 3.5 cm, while the peak height for CAH10 is 3.7 cm.
Hence, 50 % = 100 x 3.5/(3.5 + Kx 3.7)
and K = 0.95
For the unknown sample HAC, the peak height HAC3 is 4.4 cm and for
the peak CAH10 is 2.6 cm
Therefore Dc = 100 x 4.4/(4.4 + 0.95 x 2.6)
= 64 5 % conversion
Calculation for the Determination of Dc
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Figure 8.7: DTA curve for
several types of minerals
(source: H_F 3.40)
Peaks- Single mineral components
e.g. quartz, undergoes phase
transition- Hydrated minerals- Dehydration peaks indicate
hydroxyl
- Carbonate minerals lost CO2
The Application of
DSC/DTA to the Clays
and Minerals
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Figure 8.8: DTA curve for kaolinite
(Source: H_F 3.41)
Hydration water
Dehydroxylation
Formation of mullite crystal
3Al2O32SiO2
Kaolinite
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A complex mineral
Some contains anion that is bound to chained
bondong and not easily dissociated except athigher tempertatures (source: H_F 3.42(b))
M2B6O11 xH2O
Some contains discrete ions that losses water molecules at atemperature below 250 oC (Source: H_F 3.42(a))
Borate Figure 8.9
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a) BaCO3
b) Iron oxide: Fe2O3
c) BaCO3 : 6Fe2O3 mixture
Two levels of crystal transition
Barium hexaferite: BaFe12 O19
- Useful as a solid magnet in
the induction component
High temperature inorganic reactions
produce many new compounds useful for
the electronics industry
Example: heating of a
BaCO3 and Fe2O3 mixture
Synthesis of compounds at
higher temperature
Figure 8.10
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Polymer/oil decays when heated in an
oxidizing atmosphere
The sample is heated in N2 until 200oC
The atmosphere is changed to oxygen and
the temperature maintained at 200 oC
The time required for the sample to achieve
the oxidation process is recorded, or
The polymer is heated in O2 and the
temperature where the oxidation occurs is
recorded.
Figure 8.11: DSC curve for the oxidation ofpolyethylene (PE). The dotted line indicates thechange of atmosphere N2O2.
(a) DSC scan for the PE layer, 10 K/min, oxidation
onset temperature = 220 oC
(b) DSC isotherm for the PE layer at 200 oC; onset
time = 35 min. H_F 3.46
Oxidation Decay of Polymers
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Polymerization: reaction
between small molecules to
produce bigger molecules with
different properties
For unsaturated molecules, such
as styrene and vinyl chloride,
H = -100 kJ/mole (exothermic)
R-NH2 + CH2----CH-R R-NH-CH2-CH-R
R-N(CH2-CHOH-R)2
O OH
a) Reaction takes place at low temperaturebut becomes faster when heated above
100 oC. The initial reaction ofTg is
followed by an exothermic curing
reaction.
b) Re-heating of the cured sample may
produce higher temperature of Tg .
1st heating
2nd heating
Polymer Curing
Figure 8.12
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Proteins (e.g. colagen) can exist as longmolecules such as fibre, or round or
compact molecules such as insulin.
Protein structure:- folded- scrolled- sheet- helix and super-helix
(helix in helix)
The structures are destroyed
when heated or denaturized
under an extreme pH.These changes are endothermic.Complex samples
of animal muscle
protein
Colagen (single material)
800 mg, colagen solution 0.3
%, sealed container, 0.5 K/min
850 mg, sealed container, 0.2 K/min
Protein Denaturation
Figure 8.13
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Figure 8.14 shows DTA curves for the
decomposition of poly(vinyl chloride), PVCand polypropylene (PP) (Source: H_F 3.49 & 3. 50)
PVC
PP
PVC: PVC powder shows a small glasstransition at 80 oC, followed by a small
endothermic process at 300 oC, and
immediately followed by a large exothermicat 550 oC:
- decay process with a loss of HCl
- volatile material
- oxidation of the released carbon
PP: decomposed in a single step processand the product is easily oxidised. Hence, the
endothermic process of melting at 80 oC is
followed by a large exothermic oxidation
peak.
Polymer Decay