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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 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

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    University Duisburg-Essen Faculty of Engineering

    Mechanical Engineering, IVG Thermodynamics


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


    Ankit Kukreja

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

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    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.

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    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.

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    1. Introduction...5

    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

    6.1.1 Anthracene.30

    6.1.2 Aluminium acetylacetonate..31

    6.1.3 Glycine31

    6.2 Diffusion coefficient.32

    7. Summary..34

    8. Reference.35


    Table A1 : Experimental values for diffusion coefficient36

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

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    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.

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    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


    Langmuir considered the evaporation from an isolated solid surface into vacuum and

    presented the Langmuir equation [2] shown below:





    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, = 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

    kvP (2)

    where, Rk 2

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





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    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 [3].


    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 [1]



    RTmP a


    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.

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    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.


    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


    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:

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    , (4)

    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

    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:





    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.







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

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    lK (7)

    where l is the thickness of the foil (sheet) and r is the radius of the orifice.


    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.


    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

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    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










    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


    , 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

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    )( sv









    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:


    RTVv (16)

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






    dP sub

















    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




    HP sub



    HP sub

    1ln (18)

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    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)



    Hmslope sub


    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



    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

    Antoine equation.

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    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 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



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    ( )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:

    M M

    B AJ J (26)

    and if VAJ 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 MAB 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)


    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.

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    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

    dcJ D

    dz And V BB 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


    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.

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    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.


    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)

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    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.


    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.



    q q




    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.

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    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

    Ficks diffusion law is shown below [8]:

    ,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

    = 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, D can be determined from ideal gas law:

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    RT (40)

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

    temperature in K):

    ilog i







    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:



    ( )

    ( )




    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:

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    ( )

    ( )AB

    D f

    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


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    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 .


    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

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    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

    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

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    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:

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    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.

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    y = 0.967x + 14.869










    330 340 350 360 370 380 390 400

    Rubotherm Temperature / K




    T e






    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.

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    Load range: 10 g / 100 g

    Resolution: 0.001 mg / 0.01 mg

    Balances: Micro or analytical balances

    Pressure range: Vacuum bis 100 MPa


    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.

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    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 [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


    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.

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    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.

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    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)).







    0.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.003 0.0031 0.0032 0.0033

    1/T 1/K



    r p



    / P


    Antonie equation-Self

    Self- Magnetic Suspension Balance

    Self- Conventional Knudsen Method

    Ref. 12

    Ref. 10

    Ref. 11

    Figure 6.1: Vapour pressure of anthracene

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    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






    re /


    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

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    compared with the value measured by DeKruiff et al. [17]. 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



    r p



    / P


    Ref. 15

    This work-Knudsen cell

    Ref. 16.

    Antonies Equation

    Figure 6.3: Vapour pressure of aluminium acetylacetonate


    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.

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    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


    B /




    Figure 6.4: Diffusion coefficient of copper acetylacetonate in air.

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    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.

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    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 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,

    (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


    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),


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    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 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

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    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

    (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]