Density and porosity
Asst. Prof. Dr. Sirirat T. Rattanachan
30/07/52
Density and
porosity/S.T.Rattanachan
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Density and porosity
Density: terms
• Bulk density
• True density
• Theoretical density
• Apparent density
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Porosity: terms
• Total porosity
• Open porosity
• Close porosity
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porosity/S.T.Rattanachan
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Bulk density
Bulk density = อัตราสวนมวลรวมตอปริมาตรทีร่ วมรูพรุนดวย หรือ ปริมาตร
จําเพาะ
Bulk density ของชิน
้ Ceramic มักเปนปริมาตรที่มรี ูพรุนดวย ซึง่ รวมรูพรุนแบบ
เปด และแบบปด (bulk volume/external volume)
Bulk density ≠ True density
B
A
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Bulk density =
C
Mass
Total volume (A + B + C)
Bulk volume = A+B+C
A = solid volume or True volume ∼ Theoretical density
B = Open pore volume
C = Closed pore volume
Bulk volume ก
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porosity/S.T.Rattanachan
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Apparent density ก!
A
C
Mass
Apparent density =
Apparent v olume (A + C)
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porosity/S.T.Rattanachan
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Density
True density =
Apparent density =
Bulk density =
mass
true volume
mass
apparent v olume (A + C)
mass
bulk volum e (A + B + C)
mass of a unit cell
Theoretical density =
volume of a unit cell
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porosity/S.T.Rattanachan
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Theoretical density
"#! $ TD
X-ray density %&'(( unit cell )*+
,- unit cell
volume .(&
/-'ก* 1 unit cell 1 unit cell
Example : Zr0.85 Ca 0.15 O1.85 is Fluorite structure : 4 cation sites,
8 anion sites (4(ZrO 2 ) / unit cell) , unit cell parameter = 5.131 A °
4(0.85 Zr) + 4(0.15 Ca) + 4(1.85O)
6.03x10 23 (5.131 A °) 3 (10 − 24 )
= 5.480 g 3
cm
TD =
% theoretic al density =
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bulk density
x100
true density
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porosity/S.T.Rattanachan
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Liquid pycnometer techniques:
true density
ก
%&/-ก)''ก)
-ก
()01& )*
W2 − W1
ρ=
(W4 − W1 ) − (W3 − W2 )
20ก ก&
( pycnometer
50 ml
+@' 1/3
)&%'/-'ก W2
.)CกD
&A %' W3
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Density and
porosity/S.T.Rattanachan
%'/-'ก
() W1
A/-ก)')
.ก$BA
A/-2A
)&%'/-'ก
W4
7
Archimedes method
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Bulk volume
Bulk density
Apparent volume
Apparent density
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porosity/S.T.Rattanachan
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Density ตางๆ
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 density
Weight =
App. Vol.
D
S –I
True density = Weight
True Vol.
Weight
=
App. – solid Vol
D = wt. Of dry piece ( g )
S = wt. Of soaked piece ( g )
I = wt. Of soaked immersed piece ( g )
Apparent solid density =
Where
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Density and
porosity/S.T.Rattanachan
D
D –I
9
Porosity
Open pores
Close pores
Techniques:
Archemedes
Instrument
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porosity/S.T.Rattanachan
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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 100
S–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.
=
True Vol./App. Vol. =
1 - True Vol. x 100
App. Vol.
weight
Dt
D
= a
weight Dt
Da
=
(1−
Da
)x100
Dt
where
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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
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porosity/S.T.Rattanachan
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Pore volume measurement
Gas absorption $ pore ( < 800Aº
Mercury penetration (Porosimeter techniques) $
( pore > 800 Aº
Pore size limits of gas adsorption (BET) and mercury intrusion porosimetry
John I. D’Souzae
30/07/52
Density and
porosity/S.T.Rattanachan
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Gas adsorption BET
2ก monolayer adsorption %& low P/P0 ratio
2ก 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
support that gas condense in cylindical capillaries with radius (r) and pressure
in capillaries (P),
Kelvin equation
P 2γ V cos θ
ln = LV L
P0
RTr
P0 = saturated gas pressure of liq. on plane surface
γ LV = surface tension liq. - vapor interface
VL = molar volume of liquid
θ = contract angle between liq. and pore wall
R = gas constant (8.31 kJ/(K.mol)
T = adsorption temperature
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BET equation
N 2 gas, at boil point (77 K)
γ LV = 8.72 x 10-3 N
m2
3
m
VL = 34.68 x 10
-6
mol
θ =0
2γ LV VL cos θ 4.05 x10 − 4
r=
=
µm
RT ln P
log P
P0
P0
,&
B P/P0 +
, r .(& P/P0 *+$ 0.6-0.99 2*.(& r 2-100 nm
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porosity/S.T.Rattanachan
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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 angle
Water wet the well
θ < 90º (wetting liq.)
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θ = contact angle
Hg wet the well
θ > 90º (non-wetting liq.) depressed
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porosity/S.T.Rattanachan
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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 nonwetting 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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porosity/S.T.Rattanachan
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Mercury porosimeter
pore diameter, total pore volume, surface area, and bulk
and absolute densities.
The technique involves the intrusion of a non-wetting liquid
(often mercury) at high pressure into a material through the
use of a porosimeter.
The pore size can be determined based on the external
pressure needed to force the liquid into a pore against the
opposing force of the liquid's surface tension.
A known as (Washburn's equation) for the above material
having cylindrical pores is given as:
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PL = pressure of liquid
PG = pressure of gas
σ = surface tension of liquid
θ = contact angle of intrusion liquid
DP = pore diameter
4 ρ cos θ
PL − PG =
DP
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porosity/S.T.Rattanachan
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Mercury porosimeter
Since the technique is usually done under vacuum, the gas
pressure begins at zero. The contact angle of mercury
with most solids is between 135° and 142°, so an average
of 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:
213
DP =
PL
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As pressure increases, so does the cumulative pore volume.
From the cumulative pore volume, one can find the
pressure and pore diameter where 50% of the total
volume has been added to give you the median pore
diameter.
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porosity/S.T.Rattanachan
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Nitrogen gas adsorption
30/07/52
Density and
porosity/S.T.Rattanachan
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Mercury Porosimeter
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porosity/S.T.Rattanachan
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