research internship thesis - final report - ankit kukreja

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University Duisburg-Essen Faculty of Engineering

Mechanical Engineering, IVG Thermodynamics

PROJECT REPORT

Measurement of Vapor Pressures and Gaseous Diffusion Coefficient of Some Selected Organic and Metalorganic

Compounds

Ankit Kukreja

Supervisor: Dr. rer. nat. M. A. Siddiqi


CERTIFICATE

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

Universität 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.


ACKNOWLEDGEMENT

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.


TABLE OF CONTENT

1. Introduction……………………………………………………………………………………………...5

2. Techniques to measure vapour pressure………………………………………………………………6

2.1 Langmuir effusion method…………………………………………………………………………6

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 coefficient……………………………………………………………………………………14

4.1 Quartz crystal microbalance(QCM)……………………………………………………………..17

4.2 Piezoelectric effect………………………………………………………………………………...18

4.3 Measurement technique…………………………………………………………………………..18

5. Experimental materials and procedure………………………………………………………………22

5.1 Knudsen method experimental setup……………………………………………………………22

5.2 Diffusion coefficient measurement………………………………………………………………27

6. Results and discussion…………………………………………………………………………………30

6.1 Vapour pressure…………………………………………………………………………………..30

6.1.1 Anthracene……………………………………………………………………………….30

6.1.2 Aluminium acetylacetonate……………………………………………………………..31

6.1.3 Glycine……………………………………………………………………………………31

6.2 Diffusion coefficient……………………………………………………………………………….32

7. Summary………………………………………………………………………………………………..34

8. Reference……………………………………………………………………………………………….35

APPENDIX A

Table A1 : Experimental values for diffusion coefficient……………………………………………36

Table A2 : Antoine constants and enthalpy of sublimation………………………………………...37


1. INTRODUCTION

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 liquid’s or solid’s 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.


2. TECHNIQUES TO MEASURE VAPOUR PRESSURE

The most widely used methods for the compounds having low vapour pressure [1] 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 [2] shown below:

RT

MP

dt

dm

2 (1)

where, dt

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, α = 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, α

can no longer be assumed to be unity. Therefore, by rearranging Equation (1) gives

kvP (2)

where, Rk 2

which can be evaluated by calibration with substances of known vapour pressure and,

M

T

dt

dmv


Since the Langmuir’s 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 [3].

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 Dalton’s 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 [1]

below

MV

RTmP a

(3)

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 [4]:

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.


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 day’s 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 [1]. 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

m

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:


RT

MPA

t

m

2

, (4)

where, Δm = 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

small thickness.

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 [1] 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 [5] 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:

KRT

MPA

t

m

2 (5)

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.

M

RTP

2

tKA

m

(6)

The Clausing factor, K, of the orifice can be calculated by using the following equation [1]:

Developed by Ankit Kukreja. Copyrights protected. Contact: +1(832)388-9932, [email protected] of

37

2

2.05.01

r

l

r

lK (7)

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 [6]:

VdPSdTdG (8)

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


37

throughout the phase.

The transitions of a pure substance from one phase to another can be represented by the

equation below:

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

dPVdTSdPVdTS 1122

dTSSdPVV )(( 12)12

V

S

VV

SS

dT

dP

)(

)(

12

12 (14)

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

HS

, 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


37

)( sv

sub

VVT

H

VT

H

dT

dP

(15)

where, subHH = the heat of sublimation of solid

T = the temperature

sv VVV

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:

P

RTVv (16)

By substituting the value to Equation (15), the following equation is formed:

2RT

PH

TV

H

dT

dP sub

v

sub

,

2

1

RT

H

dT

dP

P

sub

2

ln

RT

H

dT

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

BT

dT

R

HP sub

2

ln

BTR

HP sub

1ln (18)


37

where, B = the constant of integration

This can be compared with the equation of a straight line, which is commonly shown as

cmxy (19)

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)

from:

R

Hmslope sub

(20)

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

K-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.

)/()/ln(

i

ii

CKT

BAPaP

(22)

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

Antoine equation.


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P

P’

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 [6]. 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 M

AJ is represents a

mole flux in a mixture of A and B, M

AJ is then the net mole flow of A across the boundaries

of a moving plane and can be express as

B

A


37

( )M

A 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

M

AJ and a bulk flow contribution ( )A A Bx N N .

For equimolar counter diffusion,

A BN N (24)

M

A AJ N (25)

Definition of another flux M

BJ which relative to the plane of no net volume flow is:

M M

B AJ J (26)

and if V

AJ and V

BJ represent vectorial molar fluxes of A and B, then , by definition,

V V

B B A AJ V J V (27)

V MBA A

VJ J

V and V MA

B B

VJ J

V (28)

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)

V

AJ = M

AJ (30)

Diffusion coefficients for a binary mixture of A and B are defined by

M AA AB

dxJ cD

dz (31)

M BB BA

dxJ cD

dz (32)

where c is the total molar concentration and diffusion is in the z direction.


37

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 Adxc

dz.

For an isothermal, isobaric binary system,

V AA AB

dcJ D

dz And V B

B AB

dcJ D

dz (34)

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

10-9

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 [7]. 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. [8] 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.


37

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)


37

The equation (35) describes the piezoelectric effect with the caused piezoelectric P

, the

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)

where

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/μg

Thus, Sauerbrey equation depends on a linear sensitivity factor, Cf, which is a fundamental

property of the quartz crystal.

2

02f

q q

nfC

(38)

where

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.


37

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 [8]

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

Fick’s diffusion law is shown below [8]:

,0 ,0 ,0( ) ( ) ( )

f f f

AB

D D D D D D

m X m X m XD

A t t

(39)

Where

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

= 0

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, ρD can be determined from ideal gas law:


37

D

pM

RT (40)

The vapor pressure was calculated by an Antoine type equation (with pressure in kPa and

temperature in K):

ilog i

i

BpA

TkPaC

K

(41)

Where

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

following relationship:

0

0

( )

( )

f

f

f

m f fm

t C t t

(43)

where

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:


37

0

0

( )

( )AB

D f

f f XD

t t C

(44)

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

substances.


37

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)

3. Glycine

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


37

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 70µm. 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

foil (mm)

Surface area of orifice,

A (mm2)

Clausing factor

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


37

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:


37

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.


37

y = 0.967x + 14.869

330

340

350

360

370

380

390

400

410

330 340 350 360 370 380 390 400

Rubotherm Temperature / K

Co

rrec

ted

T e

mp

era

ture

/

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.


37

Specifications

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.

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.


37

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.

COATING METHOD

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 [8].

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

material.

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.


37

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 powder’s 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.


37

6 RESULTS AND DISCUSSION

6.1 VAPOUR PRESSURE

6.1.1 Anthracene

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 [9]. 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)).

0.001

0.01

0.1

1

10

100

0.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.003 0.0031 0.0032 0.0033

1/T 1/K

Vap

ou

r p

ress

ure

/ P

a

Antonie equation-Self

Self- Magnetic Suspension Balance

Self- Conventional Knudsen Method

Ref. 12

Ref. 10

Ref. 11

Figure 6.1: Vapour pressure of anthracene


37

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



0.001

0.01

0.1

1

10

100

0.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.003

1/T / 1/K

Va

po

ur

pre

ssu

re /

Pa

Ref. 13

This work-knudsen cell

Antonies equation

Ref. 14

Ref. 15

Figure 6.2: Vapour pressure of aluminium acetylacetonate

6.1.3 Glycine

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. [16] 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


37

compared with the value measured by DeKruiff et al. [17]. The molar enthalpy of



0

0

0

1

10

100

0.0021 0.00215 0.0022 0.00225 0.0023 0.00235 0.0024 0.00245 0.0025

1/T / 1/K

Vap

ou

r p

ress

ure

/ P

a

Ref. 15

This work-Knudsen cell

Ref. 16.

Antonies Equation

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.

[12]. 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.


37

Table 6.1: Experimental values of diffusion coefficient of copper acetylacetonate in air

Temperature / K df/dt Diffusion coefficient / cm² /s

343.15 0.0016 0.34285003

373.15 0.0992 0.75178611

353.15 0.006 0.39590474

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

340 345 350 355 360 365 370 375

Temperature / K

DA

B /

cm

² s-1

Figure 6.4: Diffusion coefficient of copper acetylacetonate in air.


37

7 SUMMARY

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 ºC to 100 ºC. A quartz crystal microbalance with a high resolution of 10 ng cm-2

is

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.


37

8 REFERENCE

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,

(1993) 175.

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 Leitão, 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:

10.1021/je9001653).

13. M . A. Siddiqi, R. A. Siddiqui, B. Atakan, Surface & Coating Technology, 201,

(2007), 9055.

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

(Engl.Transl.).

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),

651.


37

Appendix A

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


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


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


37

Table A2 : The Antoine constants and the enthalpies of sublimation for the substances

studied in this work.

Substance Ai Bi ΔsubHm(exp)(Temperature) ΔsubHm (lit) (Temperature)

/ kJ ∙ mol-1

/ kJ ∙ mol-1

Anthracene 11.10 5099.99 97.65 (350-399 K) 97.63± 1.27a

(339-399 K)

100 ± 2.8b

(318-363 K)

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

(453-471 K)

136.5h (408-431 K)

a) Ref. [12]; b) Ref. [10]; c) Ref. [11]; d) Ref. [13]; e) Ref. [14]; f) Ref. [15]; g) Ref. [16]; h)

Ref. [17]

research internship thesis - final report - ankit kukreja

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