2.density and porosity - suranaree university of...

30/07/52 Density and porosity/S.T.Rattanachan

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Density and porosity

Asst. Prof. Dr. Sirirat T. Rattanachan


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Density and porosity

Density: terms• Bulk density• True density• Theoretical density• Apparent density

Porosity: terms• Total porosity• Open porosity• Close porosity


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Bulk density

� Bulk density = อัตราสวนมวลรวมตอปริมาตรทีร่วมรพูรนุดวย หรือ ปริมาตรจําเพาะ

� Bulk density ของชิน้ Ceramic มักเปนปรมิาตรที่มีรูพรนุดวย ซึง่รวมรพูรุนแบบเปด และแบบปด (bulk volume/external volume)

� Bulk density ≠ True density

A

B

CBulk volume = A+B+CA = solid volume or True volume ∼ Theoretical densityB = Open pore volumeC = Closed pore volumeBulk volume �� ก� � ��

C)B(A volumeTotal

Mass density Bulk

++=


4

A

C

C)(A olumeApparent v

Mass density Apparent

+=

Apparent density �� ก!


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Density

volumetrue

mass density True =

C)(A olumeapparent v

mass density Apparent

+=

C)B(A ebulk volum

mass density Bulk

++=

cellunit a of volume

cellunit a of mass density lTheoretica =


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Theoretical density� �� "#! �$ TD� X-ray density �%&�'(��( unit cell )*+��,�-�� unit cell

volume .(&� �/-��'ก*�� 1 unit cell �� 1 unit cell

3

24323

2

85.115.00.85

cmg 5.480

)10()A 131.5(6.03x10

4(1.85O) Ca) 4(0.15 Zr)4(0.85 TD

A 5.131 parameter cellunit , cell)unit /)(4(ZrO sitesanion 8

sites,cation 4 : structure Fluorite is Zr:Example

=

°

++=

°=

−

OCa

100density true

densitybulk density al theoretic% x=


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Liquid pycnometer techniques:true density

� ��ก� �%&�/-�ก)'��'�ก)��

� �-�ก��()�� 0��1��&� )*��

20ก ก&�

��( pycnometer50 ml

%'��/-��'ก��(��)�� W1

�+�@��'�� 1/3 )&�%'��/-��'ก W2

��A��/-�ก)'��)�.��ก$B��A�

.)�C��ก�D ��&��A� %'�� W3

��A��/-�2��A� )&�%'��/-��'ก W4

)()( 2314

12

WWWW

WW

−−−

−=ρ


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Archimedes method

� Bulk volume

� Bulk density

� Apparent volume

� Apparent density


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Apparent solid Volume = �� = the difference between dry weight ( D ) and the immersed weight ( I ) of piece.

� S – I = volume of open pores + sealed pores + solid� S – D = Vol. open pores� D – I = Vol. of sealed pore + solid

Bulk densityWeight = DApp. Vol. S –I

True density = WeightTrue Vol.

Apparent solid density = Weight = DApp. – solid Vol D –I

Where D = wt. Of dry piece ( g )S = wt. Of soaked piece ( g )I = wt. Of soaked immersed piece ( g )

Density Density Density Density ตางๆตางๆตางๆตางๆ


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Porosity

� Open pores

� Close pores

� Techniques:

� Archemedes

� Instrument


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Porosity

�� ก��

Apparent Porosity = Ratio of open pore volume to total volume% App. Porosity = open pore vol. x 100

Total vol.= S – D x 100S – I

Water absorption = Ratio of open pore vol . to weight of the test piece% Water absorption = open pore vol. x 100

wt.= S – D x 100

D


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True porosity

: All the pores ( open and sealed )% True Porosity = Volume of all pores x 100

Total vol. of the test piece= App. Vol – True vol. x 100

App. Vol.

= 1 - True Vol. x 100

App. Vol.

True Vol./App. Vol. = =

where Da = Apparent density = weight App. Vol.

Dt = True density = weight True. Vol.

% True porosity = 1 - Sa x 100� St

� Sa = Apparent specific gravity� St = True specific gravity

t

a

a

t

D

D

D

weightD

weight

= 100)1( xD

D

t

a−


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Pore volume measurement

� Gas absorption ��$� pore � ��( < 800Aº

� Mercury penetration (Porosimeter techniques) ��$��( pore > 800 Aº

John I. D’Souzae

Pore size limits of gas adsorption (BET) and mercury intrusion porosimetry


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Gas adsorption � BET

� 2�ก monolayer adsorption �%& low P/P0 ratio

� 2�ก multilayer adsorption �%& P/P0 0.05-0.3

� ,&� higher pressure gas 2*�ก�(ก� condense ก)��)� P/P0 0.6-0.99


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BET equation

re temperatuadsorption T

kJ/(K.mol) (8.31constant gas R

wallpore and liq.between anglecontract

liquid of memolar volu V

interfacevapor -liq. tension surface

surface planeon liq. of pressure gas saturated P

cos2ln

equationKelvin

(P), scapillariein

pressure and (r) radius with scapillarie cylindicalin condense gasat support th

L

LV

0

0

=

=

=

=

=

=

=

θ

γ

θγ

RTr

V

P

P LLV


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BET equation

m

PPx

PPRT

Vr

molmV

mN

N

LLV

L

µθγ

θ

γ

0

4

0

36-

23-

LV

2

log

1005.4

ln

cos2

0

10 x 34.68

10 x 8.72

K) (77point boilat gas,

−

==

=

=

=

,&��B�� P/P0 +��,�� r .(& �� P/P0 � ��*+��$ 0.6-0.99 2*.(&�� r 2-100 nm


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Mercury porosimeter

� % porosity,

� pore volume distribution,

� pore size distribution,

� surface area distribution,

� particle size distribution,

� bulk and apparent density.


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Phenomenon of capillary rise

θ = contact angleWater wet the well

θ < 90º (wetting liq.)

θ = contact angleHg wet the well

θ > 90º (non-wetting liq.) � depressed


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Mercury porosimeter

� placing a sample into a container,� evacuating the container to remove contaminant gases

and vapors (usually water) and, while still evacuated, allowing mercury to fill the container. (a solid, a non-wetting liquid (mercury), and mercury vapor)

� Next, pressure is increased toward ambient while the volume of mercury entering larger openings in the sample bulk is monitored.

� When pressure has returned to ambient, pores of diameters down to about 12 mm have been filled.

� The sample container is then placed in a pressure vessel for the remainder of the test. A maximum pressure of about 60,000 psia (414 MPa) is typical for commercial instruments and this pressure will force mercury into pores down to about 0.003 mm in diameter.

� The volume of mercury that intrudes into the sample due to an increase in pressure from Pi to Pi+1 is equal to the volume of the pores in the associated size range ri to ri+1, sizes being determined by substituting pressure values into Washburn’s equation.


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Mercury porosimeter

� pore diameter, total pore volume, surface area, and bulkand absolute densities.

� The technique involves the intrusion of a non-wetting liquid(often mercury) at high pressure into a material through theuse of a porosimeter.

� The pore size can be determined based on the externalpressure needed to force the liquid into a pore against theopposing force of the liquid's surface tension.

� A known as (Washburn's equation) for the above material having cylindrical pores is given as:� PL = pressure of liquid � PG = pressure of gas� σ = surface tension of liquid� θ = contact angle of intrusion liquid� DP = pore diameter

PGL D

PPθρ cos4

=−


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Mercury porosimeter

LP P

D213

=

Since the technique is usually done under vacuum, the gaspressure begins at zero. The contact angle of mercurywith most solids is between 135° and 142°, so an averageof 140° can be taken without much error. The surface tension of mercury at 20 °C under vacuum is 480 mN/m. With the various substitutions, the equation becomes:

As pressure increases, so does the cumulative pore volume.From the cumulative pore volume, one can find thepressure and pore diameter where 50% of the totalvolume has been added to give you the median porediameter.


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Nitrogen gas adsorption


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Mercury Porosimeter

2.density and porosity - suranaree university of...

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