research internship thesis - final report - ankit kukreja
Post on 25-Jan-2017
Embed Size (px)
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 1 of 37
University Duisburg-Essen Faculty of Engineering
Mechanical Engineering, IVG Thermodynamics
Measurement of Vapor Pressures and Gaseous Diffusion Coefficient of Some Selected Organic and Metalorganic
Supervisor: Dr. rer. nat. M. A. Siddiqi
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 2 of 37
This is to certify that ANKIT KUKREJA, student of 4th Year, Mechanical Engineering
Department, Delhi College of Engineering, Delhi has successfully completed his summer internship at
Universitt Duisburg-Essen, Duisburg, Germany for two months from 1st June, 2009 to 31st July, 2009.
He has completed the whole internship as per the project report submitted by him.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 3 of 37
With profound respect and gratitude, I take the opportunity to convey my thanks to complete the
internship here. I do extend my heartfelt thanks to Dr. M. A. Siddiqi for providing me this opportunity to
be a part of this esteemed organization. I am extremely grateful to Prof. B. Atakan and the staff of the
University for their co-operation and guidance that helped me a lot during the course of internship. I have
learnt a lot working under them and I will always be indebted of them for this value addition in me. I
would also like to thank the training in charge of Delhi College of Engineering and all the faculty member
of Mechanical department for their effort of constant co-operation which have been significant factor in
the accomplishment of my internship.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 4 of 37
TABLE OF CONTENT
2. Techniques to measure vapour pressure6
2.1 Langmuir effusion method6
2.2 Transpiration method...7
2.3 Knudsen effusion method.8
3. Temperature dependence of vapour pressure..10
3.1 Heat of sublimation and Clausius Capeyron equation..10
3.2 Antoine equation..13
4. Diffusion coefficient14
4.1 Quartz crystal microbalance(QCM)..17
4.2 Piezoelectric effect...18
4.3 Measurement technique..18
5. Experimental materials and procedure22
5.1 Knudsen method experimental setup22
5.2 Diffusion coefficient measurement27
6. Results and discussion30
6.1 Vapour pressure..30
6.1.2 Aluminium acetylacetonate..31
6.2 Diffusion coefficient.32
Table A1 : Experimental values for diffusion coefficient36
Table A2 : Antoine constants and enthalpy of sublimation...37
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 5 of 37
Sublimation / Vapour pressure
The vapour pressure of a liquid or the sublimation pressure of a solid is the pressure of a
vapour in equilibrium with its condensed phases. All liquids and solids have a tendency to
evaporate to a gaseous form, and all gases have a tendency to condense back into their
original form (either liquid or solid). For a substance at any given temperature, there is a
partial pressure at which the vapour of the substance is in dynamic equilibrium with its
condensed form. This is the vapour pressure of that substance at that temperature.
Equilibrium vapour pressure can be defined as the pressure reached when a condensed phase
is in equilibrium with its own vapour. In the case of an equilibrium solid, such as a crystal,
this can be defined as the pressure when the rate of sublimation of a solid matches the rate of
deposition of its vapour phase. This is often termed as sublimation pressure. Vapour pressure
is an indication of a liquids or solids evaporation rate. It relates to the tendency of molecules
and atoms to escape from a liquid or a solid. A substance with a high vapour pressure at
normal temperatures is often referred to as volatile.
Vapour pressures for the precursor compounds are needed in chemical vapour deposition
(CVD) process to get information about the volatility of the precursor compound. For a
typical CVD process, the precursor molecules are evaporated and mixed with carrier gas then
flown over to a heated substrate, where they react and decompose on the substrate surface to
produce the desired deposition. Thus the knowledge of vapour pressure helps us to determine
the maximum theoretical growth rate and composition.
The precursor compounds used in CVD are generally organometallic compound. Due to
extremely low vapour pressure of these substances and sensitivity to atmospheric air and
moisture, often either no information about their vapour pressures is available or if available,
the data are contradictory.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 6 of 37
2. TECHNIQUES TO MEASURE VAPOUR PRESSURE
The most widely used methods for the compounds having low vapour pressure  are the
1) Langmuir effusion method,
2) Transpiration method
3) Knudsen effusion method
2. 1 LANGMUIR EFFUSION METHOD
Langmuir considered the evaporation from an isolated solid surface into vacuum and
presented the Langmuir equation  shown below:
dm = the rate of mass loss per unit area,
P = the vapour pressure,
M = the molar mass of the effusing vapour,
R = the gas constant,
T = the absolute temperature
and, = the vaporization constant (usually assumed to be 1)
This equation is applicable in molecular flow regime (under high vacuum). In case of a
substance volatilizing into a flowing gas stream at one atmosphere rather than a vacuum,
can no longer be assumed to be unity. Therefore, by rearranging Equation (1) gives
where, Rk 2
which can be evaluated by calibration with substances of known vapour pressure and,
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 7 of 37
Since the Langmuirs equation is valid under molecular flow regime, which means under high
vacuum and it was adopted for ambient pressures, the applied theory is not correct. However,
through careful calibration with substances of comparable diffusion coefficient as the
experimental substance, some good results are reported in literature .
2. 2 TRANSPIRATION METHOD
In this technique the mass loss of the sample maintained at a constant temperature is measured
in the presence of an inert carrier gas flowing over it at a constant rate. The main idea of this
method is that the flowing inert gas is totally saturated by the evaporating substance. By
applying the Daltons law of partial pressure to the carrier gas and knowing the flow rate of
the inert gas, the vapour pressure of the substance can be calculated with the formula 
where, m = the mass flow rate of the transported compound,
M = the molar mass of the compound,
Ta = the temperature at which the mass flow rate is measured,
V = the volumetric flow rate of the inert gas
R = the universal gas constant.
The flow rate of the carrier gas is chosen so that the thermodynamic equilibrium between the
vapour and the vaporizing substance is virtually undisturbed. This can be established
experimentally. The vapour pressure P of the substance under investigation is then calculated
from Equation 3.
Equation 3 is based on the following assumption :
a) The vapour behaves ideally
b) The thermodynamic equilibrium between the vapour and the vaporizing substance is
undisturbed by the flow of the carrier gas.
c) All the vapour is transported by the carrier gas.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 8 of 37
Transpiration experiments are generally performed at a total pressure of one atmosphere, for
which the ideal gas equation can be assumed to be valid. Experiments are also designed to
meet closely the criteria in assumptions (b) and (c) by choosing the appropriate flow rates of
the carrier gas swept over the sample. The range of flow rates is such that the relative
contribution to the mass loss of the sample due to other processes such as diffusion is
insignificant compared to the mass loss caused by the vapour transported by the carrier gas.
Furthermore, it is ensured that the flow rates chosen are not too fast to disturb the
thermodynamic equilibrium between the sample and the vapour.
However, it is difficult to find a flow range at which the 100% saturation of the sample
vapour in the carrier gas is reached. At most of the time, the carrier gas is either under
saturated due to the fast flow rate or is oversaturated due to the slow flow rate of the carrier
gas. The determination of the mass loss from the vapour deposited in the condenser by
weighing it before and after the experiment also gives results of poor accuracy because of the
relatively small increase in the weight of the collector compared to its total weight. Further,
there can also be considerable weighing error caused by the characteristic of the sample (for
example, the sample may be hygroscopic) if adequate care is not exercised during cooling of
the sample. Now days thermogravimetric apparatus are being extensively for the
transpiration method to overcome the above mentioned problems but finding a flow rate range
still remains a difficult task.
2.3 KNUDSEN EFFUSION METHOD
The most common Knudsen effusion method uses conventional mass loss technique, i. e.
weighing the Knudsen cell before and after effusion. The Knudsen effusion method allows the
determination of vapour pressure of a substance at a constant temperature by measuring the
weight loss of the substance for the slow isothermal flow through a small orifice into the
vacuum. The Knudsen effusion method is based on the classical gas kinetic theory . As
soon as the mean free path length is larger than the typical dimension of an orifice with the
area of A, which separates the sublimating substance from its surrounding, the mass loss rate
of the cell, t
is determined solely by the area of the orifice and the vapour pressure. The
mass loss rate here is the rate of the effusion from the Knudsen cell. The formula of the mass
loss rate at steady state effusion is shown as below:
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 9 of 37
where, m = the mass loss of a sample during time t
M = the molar mass of the substance
A = the area of the orifice
R = the universal gas constant
T = the temperature in Kelvin
Equation (4) is strictly valid for an ideal hole, which means a hole in the sheet of infinitely
For the finite sheet thickness, where the height of the orifice is not negligible, an additional
correction factor which is known as the Clausing factor  K, is taken into account. If the
thickness of the sheet is not infinitely small, some molecules which strike the orifice wall will
suffer non-specular reflection and return to the effusion cell  Clausing calculated a factor K
giving the probability that a molecule impinging on an orifice of finite thickness will pass
through it. Thus, Equation (4) is written after applying the correction derived as below:
The main presuppositions for the application of this formula are the very low pressure regime
and the evaporation of non-associated molecules.
Since most of the parameters of the equation are constants, the vapour pressure of a substance
in the cell can be calculated by knowing the value of the mass loss over time, the Clausing
factor and the area of the orifice.
The Clausing factor, K, of the orifice can be calculated by using the following equation :
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 10 of
where l is the thickness of the foil (sheet) and r is the radius of the orifice.
3 TEMPERATURE DEPENDENCE OF VAPOUR PRESSURE
The vapour (or sublimation) pressure of a solid, constant at a given temperature increases
continuously with increase in temperature up to the critical point of the solid. The solid no
longer exists above the critical temperature and consequently the concept of a saturated
vapour pressure is no longer valid. In terms of kinetic theory the increase in vapour pressure
with temperature is easily understandable. As the temperature increases, a larger proportion of
the molecules acquire sufficient energy to escape from the solid and consequently a higher
pressure is necessary to establish equilibrium between vapour and solid.
3.1 HEAT OF SUBLIMATION AND CLAUSIUS - CLAPEYRON EQUATION
Sublimation of a substance means the transition of the substance from solid to gas phase
without the intermediate liquid phase. The enthalpy of sublimation is the energy required to
overcome the intermolecular interactions in the solid material. The enthalpy of sublimation
(or heat of sublimation) is defined as the enthalpy of evaporation from solid phase to the gas
phase at a fixed temperature. The molar enthalpy of vaporization (or sublimation) is the
energy required to convert one mole of the substance (liquid or solid) from liquid (or solid)
state to gaseous state at a constant temperature and pressure. It is related to the temperature
dependence of the vapour pressure as shown below.
For any pure substance in a single phase, any variation in free energy is given by the
following equation :
To have equilibrium in the phase, dG has to be zero at constants T and P. Since dG =0 in the
above equation when
dT = dP = 0, (9)
the phase is in equilibrium when the pressure and the temperature are constant and uniform
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 11 of
throughout the phase.
The transitions of a pure substance from one phase to another can be represented by the
21 GG (10)
for which G is given by
12 GGG (11)
where, 2G = the molar free energy of a substance in the final state
and, G1 = the molar free energy of a substance in the initial state
When G = 0 at constant temperature and pressure, all such transformations will attain
equilibrium. Imposing this condition on Equation (11), we see that 12 GG because all such
transformation will be in equilibrium at constant temperature and pressure when the molar
free energies of the substance are identical in both phases. Suppose that we have two phases
in equilibrium and that the pressure of the system is changed by dP. The temperature of the
system will then have to change by dT in order to preserve the equilibrium. In such a situation
dP and dT can be related as follows: Since 12 GG , then we have also 12 dGdG .
However, dPVdTSdG 222 (12)
and dPVdTSdG 111 (13)
By equating these expressions, we get
dTSSdPVV )(( 12)12
where, 12 SSS is the change in entropy and 12 VVV is the change in volume for
the process. Further with the equation of Gibbs free energy at constant
temperature STHG , with 0G yieldsT
, where H is the change in
enthalpy for the reversible transformation occurring at temperature T. Substituting this value
of S into Equation (14), we obtain
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 12 of
where, subHH = the heat of sublimation of solid
T = the temperature
vV = the volume of the vapour
sV = the volume of solid
Equation 15 is known as the Clapeyron equation and it relates the change in temperature
which must accompany a change in pressure occurring in a system containing two phases of a
pure substance in equilibrium. sV is quite small if compared with vV and it may be neglected.
Further, if we assume that the vapour behaves as an ideal gas, then vV per mole is given by:
By substituting the value to Equation (15), the following equation is formed:
Pd sub (17)
This equation is known as Clausius-Clapeyron equation and the variation of vapour pressure
with temperature can be expressed mathematically by this equation.
Integrating Equation (17) yields
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 13 of
where, B = the constant of integration
This can be compared with the equation of a straight line, which is commonly shown as
So if a graph of ln P ( y) [P should be in Pa] for any substance is plotted against T/1 ( x) [T
should be in K], then the plot should be a straight line with slopeR
H sub ( m)
and the intercept of y with x , B ( c).
Hence, we can calculate the enthalpy of sublimation (vaporization) of the solids (liquids)
or RmH sub (21)
where, subH = the molar enthalpy of sublimation
m = the slope of graph ln P versus T/1
and R = universal gas constant = 8.3145 Jmol-1
3.2 ANTOINE EQUATION
Antoine proposed a simple modification of Equation 18 which is widely used and gives a
better representation of the temperature dependence of vapour pressure.
where Ai, Bi and Ci are the substance specific constants and T is the temperature in Kelvin.
The empirical Antoine constants for each compound can be effectively determined by the
least square curve fit method where the vapour pressure plot for each compound is fitted to
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 14 of
4. DIFFUSION COEFFICIENT
Diffusion describes the movement of molecules in gases, liquids and solids. Diffusion can
result from pressure gradients (pressure diffusion), temperature gradients (temperature
diffusion), external forced fields (forced diffusion), and concentration gradients . In this
work the diffusion due to concentration gradients will be considered. Diffusion is the process
by which molecules, ions, or other small particles spontaneously mix, moving from regions of
relatively high concentration into regions of lower concentration. Diffusion coefficient is a
factor of proportionality representing the amount of substance diffusing across a unit area
through a unit concentration in unit time. The process of diffusion depends upon the nature
(solid, liquid or gas) of the medium in which it is taking place.
In order to discuss the diffusion coefficient in more detail, the diffusion fluxes and diffusion
potentials should be defined clearly. The constant of proportionality between flux and
potential is the diffusion coefficient.
Figure 4.1: Diffusion across plane PP
Figure 4.1 shows the reference plane in which the diffusion is occurring. This plane is
designated by PP and performed by a binary mixture of A and B, that A is diffusing to the
left and B to the right. The diffusion rates of these species should be identical.
Net movement of A is then results from both diffusion and bulk flow. To define a diffusion
coefficient in a binary mixture, a plane of no net mole flow is used. If MAJ is represents a
mole flux in a mixture of A and B, MAJ is then the net mole flow of A across the boundaries
of a moving plane and can be express as
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 15 of
( )MA A A A BJ N x N N (23)
Where AN , BN = fluxes of A and B across PP
Ax = mol fraction of A at PP
Equation (23) shows that the net flow of A across PP is due to a diffusion contribution
AJ and a bulk flow contribution ( )A A Bx N N .
For equimolar counter diffusion,
A BN N (24)
A AJ N (25)
Definition of another flux MBJ which relative to the plane of no net volume flow is:
B AJ J (26)
and if VAJ and V
BJ represent vectorial molar fluxes of A and B, then , by definition,
B B A AJ V J V (27)
V MBA A
V and V MAB B
where AV , BV = partial molar volumes of A and B in the mixture
V = volume per mole of mixture
If it is an ideal mixture,
AV = BV =V (29)
Diffusion coefficients for a binary mixture of A and B are defined by
M AA AB
M BB BA
where c is the total molar concentration and diffusion is in the z direction.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 16 of
With equation (32) follows:
AB BAD D and 0A Bdx dx
dz dz (33)
The diffusion coefficient then represents the proportionality between the flux of A relative to
a plane of no net molar flow and the gradient Adx
For an isothermal, isobaric binary system,
V AA AB
dz And V BB AB
When fluxes are described in relation to a plane of no net volume flow, the potential is
then the concentration gradient.
The knowledge of binary diffusion coefficient of organometallic compounds are needed for
CVD (Chemical Vapor Deposition) application, since it is used for the determination of the
Sherwood and Lewis numbers which used to describe mass transfer processes.
There are various experimental techniques which can be used to determine diffusion
coefficient in a binary gaseous system. Although these methods provide quite satisfactory
results, but the duration of the measurements usually took many hours to several days,
depending on the temperature and examined substances.
By using a piezoelectric quartz crystal microbalance (QCM) which has a high resolution of
g/cm2, the duration for the measurement is dramatically reduced. The possibility of using
piezoelectric quartz resonators as mass sensing device was first explored by Sauerbrey . It
was found that for a mass uniformly deposited over a crystal surface, the shift resonant
frequency is linearly proportional to the mass loss.
Chen et al.  have described a technique that uses a QCM for determining the diffusion
coefficient of naphthalene in air. The measurement uncertainty of the diffusion coefficient of
naphthalene into air was reported to be less than 3%. In the present study, the method of
Chen, et al. is used to determine the diffusion coefficient.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 17 of
4.1 QUARTZ CRYSTAL MICROBALANCE (QCM)
Figure 4.2: QCM Crystals.
QCM is a thickness- shear- mode acoustic wave mass-sensitive detector based on the effect of
an attached foreign mass on the resonant frequency of an oscillating quartz crystal. QCM has
been used as a mass sensor in the vacuum and gas-phase experiments. Figure 4.2 shows a
QCM crystal used in the present study. The crystal on the left shows the active surface, while
the one on the right shows the contact surface.
4.2 PIEZO ELECTRIC EFFECT
Piezoelectricity is a property of certain classes of material including natural crystal of quartz.
In piezoelectric materials, mechanical strain is generated by application of an electric field or,
an electrical polarization is generated by application of mechanical stress conversely.
The piezoelectric effect was discovered in 1880 by Curie brothers and describes how crystals
generate electrical loads by pressure, tension or torsion at the surfaces.
By applying a tension on a crystal, reciprocal piezoelectric effect can be observed, whereby
by the tension deformation is caused.
The piezoelectric effect can be formulated mathematically as follows:
P ex (35)
x d E (36)
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 18 of
The equation (35) describes the piezoelectric effect with the caused piezoelectric P
piezoelectric polarization module e and deformation x
. The equation (36) shows the
connection for the reciprocal piezoelectric effect. Here x
is the resulting deformation, d das
piezoelectric modulus of elasticity and E
is the electrical field. The piezoelectric effect take
placed only in non conductive materials.
4.3 MEASUREMENT TECHNIQUE
From the Sauerbrey equation which relates the mass change per unit area at the QCM surface
to the observed change in oscillation frequency of the crystal can be expressed as:
f ff C m (37)
f = the observed frequency change in Hz,
fm = the change in mass per unit area in g/cm2,
fC = the sensitivity factor for the crystal, Hz cm2/g
Thus, Sauerbrey equation depends on a linear sensitivity factor, Cf, which is a fundamental
property of the quartz crystal.
n = number of the harmonic at which the crystal is driven
0f = the resonant frequency of the fundamental mode of the crystal in Hz
q = density of quartz
q = shear modulus of quartz
The determination of the diffusion coefficient using QCM is based on the method which uses
a closed Stefan tube. The conventional digital balance is replaced by the QCM which having
more highly resolution.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 19 of
A thin layer of solid examined substance is uniformly coated over the active surface of the
QCM. Then the QCM is place onto the upper open surface of the diffusion tube in the closed
Stefan tube. The mass concentration gradient in the diffusion tube is established when the
substance evaporates on the QCM and moves to the activated charcoal (with a high adsorptive
capacity) on the other end of the diffusion tube. The distance between the QCM and adsorbent
is the diffusion length, X.
The diffusion coefficient was determined under the following assumptions 
i. Both the examined substance and air behave as ideal gases.
ii. The diffusion process in the diffusion tube is one dimensional and steady.
iii. The air is not adsorbed by the activated charcoal, only the substance is adsorbed
iv. The gas mixture within the diffusion tube consists only of the air and examined
substance vapor without the presence of temperature and pressure gradients, external
forces, and chemical reactions.
v. The mass concentration of examined substance vapor at the surface of QCM and air
is constant value and is zero on the surface of the activated charcoal.
With the aforementioned assumptions, the equation of the diffusion coefficient, DAB based on
Ficks diffusion law is shown below :
,0 ,0 ,0( ) ( ) ( )
f f f
D D D D D D
m X m X m XD
A t t
A = cross section area for diffusion
fm = mass flux of the examined substance in the diffusion tube
X = diffusion length
D = mass concentration of the examined substance on the QCM surface
,0D = mass concentration of the examined substance on the activated charcoal surface
fm = mass loss on the surface of QCM during time interval t
t = interval time during mass loss
ABD = binary diffusion coefficient
The mass concentration, D can be determined from ideal gas law:
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 20 of
The vapor pressure was calculated by an Antoine type equation (with pressure in kPa and
temperature in K):
iA , iB and iC are the Antoine coefficients and vary from substance to substance.
If the active crystal surface of QCM is coated with a thin and homogeneous layer of examined
substance, its frequency will decrease from qf (without the coating) to the frequency cf (with
the coating) due to an increase in the thickness of the QCM. The frequency of the QCM will
increase when the coating on the surface QCM evaporates in the diffusion tube. Hence, the
frequency shift f is expressed as:
q cf f f (42)
Over a measuring period from 0t to t , the mass flux, fm can be determined from the
m f fm
t C t t
fC denotes the mass sensitivity of the QCM and 0f denotes the frequency shift of the
QCM at time constant 0t .
The f value is smaller than the 0f value if 0t t . After substituting equation (43) into
equation (39), the equation for the diffusion coefficient is derived:
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 21 of
f f XD
t t C
The change in the frequency of the oscillating QCM was plotted with the time. A linear
variation of the frequency change with the time increment was observed for all the substances
studied as shown in the figure.
The value of the slope ( ) increases with the temperature. Substituting the value of the
slope in the equation (44) would yield the gaseous diffusion coefficient in air for the studied
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 22 of
5 EXPERIMENTAL MATERIALS AND PROCEDURE
The substances used for the vapour pressure and diffusion coefficient measurement were :
1. Aluminium acetylacetonate [Al(acac)3] (purity >99.9%, ABCR GmbH & Co. KG),
2. Anthracene (Purity>99.9%, Alfa Aesar)
4. Copper acetylacetonate
All of these substances are commercially available and were used without any further
purification. The molar enthalpy of sublimation was calculated by plotting ln P (P in Pa)
against 1/T (T in K) and determining the best fit slope R
H sub .
5.1 KNUDSEN METHOD EXPERIMENTAL SETUP
The schematic diagram of the experimental setup is shown in the Figure 5.1:
Figure 5.1: Schematic diagram of the experimental setup
The schematic diagram of a Knudsen cell is shown in Figure 5.2
Figure 5.2: Schematic diagram of a Knudsen cell
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 23 of
The setup includes a Knudsen cell (shown in Figure 2), two Pt100 thermometers, a heating
cell, a cooling trap, a diffusion pump, a pre-vacuum pump, a pressure sensor and the display
and operating unit.
The Knudsen cell is home built from stainless steel material with the diameter 12mm and
height 28mm. The upper lid of the Knudsen cell has a central hole with diameter 9mm. The
upper lid is covered with a thin aluminium foil and a small circular effusion hole is drilled on
the foil. The diameter of the orifice is measured with a microscope. Four aluminium foils
were used throughout the experiment. The diameters of the orifice in aluminium foils were
0.8512mm, 1.0359mm, 0.8717mm, and 0.5616mm. The reason of using the foils with
different orifice diameter for the experiment is to control the mass loss of the substance
through the orifice. Smaller orifice limits the mass loss of the substance. This is useful when
there is substance with high vapour pressure especially at high temperature. Larger orifice
allows more mass loss through the orifice and would be useful in the condition where the
substance has low vapour pressure or when measuring at low temperature. The thickness of
the foil was 70m. The upper lid and the aluminium foil are tightened together with screws.
From the ratio of the diameter of the orifice to the thickness of the aluminium foil, the
Clausing factor for the four aluminium foils was calculated. Table 1 show the Clausing factor
corresponded to the orifice diameter respectively.
Table 5.1: The Clausing factor of 70mm thick aluminium foils
Diameter of the Aluminium
Surface area of orifice,
0.8512 2.275 0.923178
1.0359 3.369 0.936079
0.8717 2.385 0.9248
0.5616 0.9903 0.8877
The Knudsen cell is situated in a stainless vessel, also known as a heating chamber, with good
thermal contact around the cell. The heating wires are wrapped around the outer part of the
heating chamber which acts as a thermal reservoir. The heating chamber was well insulated
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 24 of
by using the glass wool and insulating bands. The temperature was measured using two pre-
calibrated Pt100 thermometer inside the heating chamber around the area where Knudsen cell
was placed. The temperature difference between the two thermometers was found to be
0.02K. This value is acceptable within the experimental error limits. Temperature calibration
was carried out before the experiment by getting the temperature just inside the Knudsen cell
in order to determine the temperature at which the vapour effuses out from the orifice.
Temperature calibration was necessary as there was always a difference between the
temperature inside Knudsen cell and heating cell.
A provision for circulating the nitrogen gas was made into the experimental set in order to
prevent the degradation of substances by atmospheric air and moisture. This was done by
making an inlet at the top of heating cell for introducing the nitrogen into experimental setup
and outlet through a valve in the diffusion pump (Figure 5.2). Thus circulation of nitrogen
was ensured during the heating period.
The Knudsen cell was then evacuated with the help of the vacuum system which consists of a
diffusion pump (Pfeifer TMH 071P) and a pre-vacuum pump (Pfeifer MVP 055-3). There is
also a pressure gauge (Pfeifer TPG 261) for monitoring the pressure of the system. The
pressure in the system is always ensured to be below 10-5
mbar during every experimental run.
A cooling trap was introduced between the heating chamber and the vacuum system to ensure
that whatever substance evaporates during the experiment condenses inside the cooling trap
that help in maintaining high level of vacuum during the experiment and preventing
degradation of vacuum pump.
In another modification of the experiment the vacuum microbalance was used to determine
the mass loss data for the calculation of the vapour pressure.
The schematic diagram of the experimental setup is shown in the Figure 4:
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 25 of
Figure 5.3: Schematic diagram of the experimental setup
The technique of weighing using magnetic suspension balance is one of the most accurate
measuring methods. For numerous applications, however, it is not possible or useful to locate
a balance or a weighing instrument in the measuring chamber itself (e.g. at high temperatures,
high pressures, aggressive atmospheres). In many of these cases magnetic suspension
balances could be a suitable solution.
By means of magnetic suspension balances it is possible to accurately measure the weight
changes of a sample located in a closed measuring cell. The balance (a commercial analytical
or micro balance) is located outside the measuring cell at ambient atmosphere and the sample
is continuously weighed throughout the experiment. The temperature of the heating chamber
is taken into calculation with the assumption that the temperature of the Knudsen cell and
heating chamber is same. As vapour pressure is a strong function temperature, and any error
in its measurement would not give the correct vapour pressure values. In order to avoid this
error the temperature calibration of the system was done using some well studied reference
substance whose vapour pressure is well known.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 26 of
y = 0.967x + 14.869
330 340 350 360 370 380 390 400
Rubotherm Temperature / K
Figure 5.4: Temperature Calibration
The key component of the magnetic suspension balance is the magnetic suspension coupling
which consists of an electromagnet (with a soft iron core), a suspension magnet (a permanent
magnet), a position sensor, and a control system. The electromagnet is attached to the
weighing hook of the balance and maintains a freely suspended state of the suspension
magnet. To achieve the freely suspended state of this permanent magnet, its position is
detected by a position sensor and controlled via a direct analog control circuit. The sample is
linked to the permanent magnet via a load coupling and decoupling device (this "measuring
position" is shown in the figure). By means of the magnetic suspension coupling, weight
changes of the sample are transmitted to the balance. To avoid any influence of a zero-point
drift of the balance the sample can be decoupled from the suspension magnet by lowering it to
a zero-point position (tare position) about 5 mm below the measuring position shown in the
figure. All movements of the suspension magnet and the sample vessel are electronically
controlled so that any vibration is avoided. The measuring accuracy at the balance is not
adversely affected by the magnetic suspension coupling.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 27 of
Load range: 10 g / 100 g
Resolution: 0.001 mg / 0.01 mg
Balances: Micro or analytical balances
Pressure range: Vacuum bis 100 MPa
5.2 DIFFUSION COEFFICIENT MEASUREMENT
A schematic of the experimental apparatus for measuring the diffusion coefficient is given in
Figure 5.5: Schematic view of the experimental apparatus
Figure 5.6: Diffusion Cell
The diffusion cell consist of a aluminum diffusion tube with internal diameter of 13 mm and
with diffusion length of 15 mm having a QCM holder at the top. The other end of the tube
ends toward the container having charcoal powder used as adsorbent for vaporizing material.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 28 of
The temperature of the cell was measured using two Pt-100 thermometers at the two different
position thermometers around the vicinity of the diffusion tube. The cover of the diffusion
cell consists of the crystal BNC connector connected with the POGO pins. The QCM
controller connector is a RJ-45 connector used to electrically connect the QCM25 Crystal
Oscillator to the QCM100 Analog Controller.
The whole of the aluminum diffusion cell was wrapped with heating wire and was well
insulated using glass wool and insulation bands. The temperature is controlled by using PID
temperature controller. The temperature recorded by the two thermometers was always the
same during the experiment.
One of the essential requirements of this method is depositing a thin and uniform layer on the
active surface of the QCM. The change in the frequency after deposition should be
maintained at a value of less than 2% of the original resonant frequency of the QCM .
Therefore, the amount of the deposited material should be very small when compared with
original mass of the substance. This means that really thin films are needed for correct
measurements. This was checked by weighing the QCM before and after the deposition of the
The coating was done using a evaporator made up of aluminum. The figure shows the
construction of the evaporator used for deposition
Figure 5.7: Coating Apparatus.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 29 of
The substance is filled in the evaporator and is heated isothermally. The active crystal surface
of the QCM is placed upon the QCM holder in the cover of the evaporator while the active
other side of the QCM was cooled with liquid nitrogen. The substance is evaporated at a
constant temperature. As substance evaporates, the vapor rises upward up to the active crystal
surface of the QCM, where it is allowed to condense due to the cooling provided by liquid
nitrogen. This leads to the formation of thin and uniform layer because the vapors of the
substance condense as soon as it reaches the surface due to the rapid cooling.
After the coating the active surface of the QCM, it was placed on top end of the diffusion tube
at a constant temperature. The vapor of the substance on the QCM surface continually
diffuses into the air and finally reaches the charcoal powders surface after traveling the
diffusion length in the tube. It is adsorbed by the charcoal. As the vaporization proceeds the
mass of the QCM changes and is reflected by the change in the frequency. The acquired
signal is represented on the screen monitor and the data are collected with a personal
computer using a program interface. To display the data, the program Data logger was used.
The program reads the change in the frequency values of the QCM with the time. The data
was recorded every 60 seconds. The experiments were done at a constant temperature which
continued till all the deposited substance got evaporated from the QCM surface and no further
change in the frequency of the QCM was observed.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 30 of
6 RESULTS AND DISCUSSION
6.1 VAPOUR PRESSURE
The system was first checked by measuring the vapour pressure of the reference substance,
Anthracene. For Anthracene, the measurements were performed in the temperature range
353K-403K. The details of the measurement are given in Appendix A (Table A1) and the
results are compared with some of the available literature values . It is found that the
measured values for anthracene as a reference substance agree very well with the available
literature [10-12] values throughout the temperature range studied. This means that the setup
provides reliable vapour pressure values and is therefore used for measuring the vapour
pressure of other substances. The values measured using magnetic suspension balance along
with the conventional weight balance method are shown in the figure. The molar enthalpy of
sublimation was calculated by plotting ln P (P in Pa) against 1/T (T in K) and determining the
best fit slope (Appendix A (Table A2)).
0.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.003 0.0031 0.0032 0.0033
Self- Magnetic Suspension Balance
Self- Conventional Knudsen Method
Figure 6.1: Vapour pressure of anthracene
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 31 of
6.1.2 Aluminum acetylacetonate
The vapour pressures of aluminum acetylacetonate were calculated from the measured mass
loss and the time using Equation (6). This was done between the temperature range 353K-
396K. The details of the experiments are given in Appendix A (Table A1). Figure 10 shows
the plot of the measured values along with the available literature value. Our measured value
of vapour pressure agrees quite well with available literature values. The molar enthalpy of
sublimation was calculated by plotting ln P (P in Pa) against 1/T (T in K) and determining the
best fit slope (Appendix A (Table A2)).
0.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.003
1/T / 1/K
This work-knudsen cell
Figure 6.2: Vapour pressure of aluminium acetylacetonate
The vapour pressures of Glycine were calculated from the measured mass loss and the time
using Equation 6. This was done between the temperature range 379K-427K. The details of
the experiments are given in Appendix B (Table A1). The values for vapour pressure at
different temperature along with the available literature values [16,17] are shown in figure.
Svec et al.  measured the vapour pressure at higher temperatures where as our
measurements were done at lower temperatures. Our measured value at 417 K is lower when
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 32 of
compared with the value measured by DeKruiff et al. . The molar enthalpy of
sublimation was calculated by plotting ln P (P in Pa) against 1/T (T in K) and determining the
best fit slope (Appendix A (Table A2)).
0.0021 0.00215 0.0022 0.00225 0.0023 0.00235 0.0024 0.00245 0.0025
1/T / 1/K
This work-Knudsen cell
Figure 6.3: Vapour pressure of aluminium acetylacetonate
6.2 DIFFUSION COEFFICIENT
The diffusion coefficient of copper acetylacetonate was measured using the QCM method.
The vapour pressure value at different temperature was taken from the work of Siddiqi et al.
. Only the measured values of the diffusion coefficient are shown in figure 12, as no other
literature values are available. The measured values are listed are given below in the table 2.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 33 of
Table 6.1: Experimental values of diffusion coefficient of copper acetylacetonate in air
Temperature / K df/dt Diffusion coefficient / cm /s
343.15 0.0016 0.34285003
373.15 0.0992 0.75178611
353.15 0.006 0.39590474
340 345 350 355 360 365 370 375
Temperature / K
Figure 6.4: Diffusion coefficient of copper acetylacetonate in air.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 34 of
In this study, the vapour pressure of anthracene, a was measured using Knudsen effusion
method using conventional weighing method and vacuum microbalance. The results were
compared with the available literature value which is in good agreement with our measured
values. This means the setup provides reliable vapour pressure value. Therefore, it was used
to measure the vapour pressure of aluminum acetylacetonate and glycine. The molar enthalpy
of sublimation was calculated from the slope of ln P vs 1/T graph. The diffusion coefficient
copper (II) acetylacetonate have been measured using the QCM method in the temperature
range 70 C to 100 C. A quartz crystal microbalance with a high resolution of 10 ng cm-2
used for reducing measuring time over the conventional digital electronic balance. Since no
empirical correlations for organometallic compounds for the measurement of diffusion
coefficient is available so our measured values could not be compared.
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 35 of
1. D. Ambrose, in: B. Le Neindre, B. Vodar (Eds.), Experimental Thermodynamics,
II, Butterworths, London. (1975), 642.
2. Duncan M Price, Michael Hawkins, Thermochimica Acta, 315, (1998) 19.
3. M. Aslam Siddiqi, Burak Atakan, Thermochimica Acta, 452, (2007) 128.
4. S. R. Dharwadkar, A. S. Kerkar and M. S. Samant, Thermochimica Acta, 217,
5. T. A. O Donnell, Australian Journal of Chemistry, 8, (1955) 485.
6. M. J. Moran, H. N. Shahiro, Fundamentals of Engineering Thermodynamics,
Chapter 11, 3rd
. ed. John Wiley & Sons (1998)
7. G. Sauerbrey, Z. Phys. 155, (1959) 206.
8. Ping-Hei Chen, Jr-Ming.Miao, and Ching-Sung.Jiang; Novel technique for
measuring diffusion coefficient of naphthalene into air; Review of Scientific
Instruments 67 (1996), 2831.
9. R. Sabbah, An Xu-wu, J.S. Chickos, M. L. Planas Leito, M. V. Roux, L. A.
Torres, Thermochimica Acta, 331, (1999) 93.
10. Vahur Oja and Eric M. Suuberg, J. Chem. Eng. Data, 43, (1998) 486.
11. X. Chen, V. Oja, W. G. Chan, M. R. Hajaligol, J. Chem. Eng. Data 51, (2006) 386.
12. M . A. Siddiqi, R. A. Siddiqui, B. Atakan, J. Chem. Eng. Data 2009, ASAP (DOI:
13. M . A. Siddiqi, R. A. Siddiqui, B. Atakan, Surface & Coating Technology, 201,
14. J. Sachindis, J. O. Hill, Thermochimica Acta, 35, (1980) 59.
15. I. P. Malkerova, A. S. Alikhanyan, V. B Lazarev, V. A. Bogdanov, V. I.
Gorgoraki, Ya. Kh. Grinberg, Russ. J. Phys. Chem., 292, (1987) 376
16. H.J. Svec, D. D. Clyde, J. Chem. Engg. Data, 10, (1965)151.
17. C. G. DeKruiff, J. Voogd, J. C. A. Offeringa, J. Chem. Thermody., 11, (1979),
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 36 of
Table A1: Experimental values for diffusion coefficient
Temperature/ K 1/T 1/K Vapour pressure (Pa) ln P
Glycine Conventional Knudsen method
427.05 0.002341646 0.423 -0.86135932
422.29 0.002368041 0.322 -1.13456858
431.81 0.002315833 0.736 -0.30680313
412.78 0.002422598 0.113 -2.18031244
417.53 0.002395037 0.200 -1.60905223
422.29 0.002368041 0.277 -1.283907
Anthracene Conventional Knudsen method
388.98 0.002570826 9.940 2.29658958
388.98 0.002570826 9.962 2.2987338
398.5 0.00250941 18.546 2.92024635
393.74 0.002539747 14.710 2.68855083
384.23 0.002602608 7.297 1.9874785
350.92 0.002849652 0.312 -1.16378326
360.44 0.002774387 1.113 0.10712802
369.85 0.002703799 1.816 0.59665589
379.55 0.002634699 4.164 1.42652657
360.45 0.00277431 0.978 -0.022149
Magnetic suspension balance
359.16 0.002784277 0.774 -0.25618341
360.24 0.002775906 0.925 -0.07796154
341.15 0.002931226 0.128 -2.05572502
370.14 0.002701716 2.056 0.72076235
369.80 0.002704189 2.017 0.70141292
378.69 0.002640661 4.440 1.49065438
350.56 0.002852554 0.326 -1.1208579
398.18 0.002511439 17.830 2.88088243
Aluminium acetylacetonate Conventional Knudsen method
395.75 0.002526848 10.598 2.36064211
379.03 0.002638314 2.599 0.95526301
370.66 0.00269789 1.171 0.15770276
362.3 0.002760144 0.479 -0.73531797
353.94 0.002825338 0.160 -1.82963525
Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] Page 37 of
Table A2 : The Antoine constants and the enthalpies of sublimation for the substances
studied in this work.
Substance Ai Bi subHm(exp)(Temperature) subHm (lit) (Temperature)
/ kJ mol-1
/ kJ mol-1
Anthracene 11.10 5099.99 97.65 (350-399 K) 97.63 1.27a
95.56c (320-354 K)
Al(acac)3 13.30 6031.48 115.49 (353-399K) 117.31 1.6d(345-410 K )
111 4e (345-410 K)
126.73f (388-413 K)
Glycine 13.78 7310.25 139.97 (412-432 K) 136.39g
136.5h (408-431 K)
a) Ref. ; b) Ref. ; c) Ref. ; d) Ref. ; e) Ref. ; f) Ref. ; g) Ref. ; h)