2007 place conference september 16-20 st louis, mo ... · pdf file• 1855: graham...
TRANSCRIPT
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2007 PLACE Conference
September 16-20
St Louis, MO
Permeation and Measurement Techniques
Presented by:Joel FischerLab Manager and ScientistMOCON, Inc.
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WHY A PACKAGE ???
• CONTAINMENT• PROTECTION• MARKETING
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ALLMATERIALS
PERMEATE!!!
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Permeation basics
• Permeation is simply the flux of molecules through a material normalized to the pressure gradient
• Units of permeation “explain” the mechanism:– SI units
( )Pascm
cmPaKcm××
××2
53 10013.1;15.273volume of gas at STP material thickness
area time pressure drop, driving force
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Isostatic Permeation Methodology(Oxygen transmission rate test)
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Permeation basics
atmdaymmilcc××
×2
daymcc×2
Permeation rate
Transmission rate
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History of Permeation Theory• 1829: Graham observed permeation of CO2 into a wet
pig’s bladder• 1831: Mitchell discovered balloons collapse at different
rates when filled with different gases• 1855: Fick proposed his law of mass diffusion as by
analogy with Fourier’s law for heat conduction and Ohm’s law for electrical conduction
• 1855: Graham postulated “colloidal diffusion”, dissolution of the penetrant followed by transmission of the dissolved species through the membrane
• 1879: Von Wroblewski observed Henry’s Law with gases in rubber and combined this with FICK’S Law to obtain the relationship between permeation and the area and thickness of the membrane.
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Solution-diffusion mechanism(Graham’s colloidal diffusion)
The gas is sorbed at the entering face and dissolved
The dissolved penetrant molecules then diffuse through the membrane and
Desorb at the exit face.
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Permeation
The relationship between the rate of permeation And the concentration gradient is embodied in Fick’s First law:
xCDJ∂∂
−=
Where J is the flux per unit area of permeant through the polymer, D is the diffusion coefficient, and δc/δx is the concentration gradient of the permeant across a thickness δx
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Permeation
Fick’s second law:
2
2
xCD
tC
∂∂
=δδ
Applies under circumstances where diffusion is limited to the x-direction and D is indendent of concentration
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Pasternak’s Solutionof Fick’s Law
Assumptions:The diffusion coefficient D is not a function
of the concentrationThe surface concentration is proportional to
the pressure of the permeantThe swelling of the polymer is negligible.
F(x) = -D(dc/dx)
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Pasternak’s Solutionof Fick’s Law
Boundary conditions:c = 0 x = 0 t = 0c = 0 0 ≤ x ≤ l t = 0c = cf x = 0 t > 0c = 0 x = l t ≥ 0c = cf(l-x)/l 0 ≤ x ≤ l t = ∞
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Pasternak’s Solutionof Fick’s Law
{ }XXJJ
−⎟⎠
⎞⎜⎝
⎛=ΔΔ
∞
exp4π
00.10.20.30.40.50.60.70.80.9
1
0 1 2
1/X = (4D/l2)t
Nor
mal
ized
Flu
x J/
J
Theoretical permeation Theoretical permeation curve for constant diffusion curve for constant diffusion coefficientcoefficient
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• Permeability can be defined as the product of the solubility coefficient and the diffusion coefficient
P = S x D
Permeability
Solubilitycoefficient
Diffusioncoefficient
• Generally, P and S can be directly measured and D can be calculated.
• However, there are indirect methods for measuring D as well.
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DiffusionDiffusion is the process by which matter is
transported from one part of a system to another as a result of random molecular motions.
Diffusion refers to the net transport of material within a single phase in the absence of mixing.
In Fickian systems, D is independent of concentration.
Units of D:sec
2cm
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Diffusion Coefficient vs. TempO2 Diffusion through Rubber
0
10
20
30
40
50
60
-20 0 20 40 60
Temp C
cm2
/ sec
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Solubility
Solubility represents the dissolution of permeant into polymer and relates the concentrations within the film to the partial pressure of the permeant.
Solubility is dependent upon permeant concentration or driving force.
Units of S: mmHgcmSTPcm
−3
3 )(
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Real-life Solubility
• 2-liter bottle material used in a variety of food and beverage applications.
• At 23C with room air (20.9% oxygen) exposure, the bottle walls contained 0.48 cc’s of oxygen
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Solubility vs. TemperatureOxygen Solubility in Water
00.010.020.030.040.050.06
0 20 40 60 80
Degree C
ccO
2 / c
cH2O
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Temperature Impact on Permeation?
• As Temp Increases Diffusion increases• As Temp Increases Solubility decreases
• P = S x D
• D over-rides S in the above equation and….
• Generally: For every 10C increase in Temp, the Permeation Rate Doubles
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Henry’s Law
The concentrations are related to the partial pressures by a solubility coefficient, S (the reciprocal of Henry’s Law coefficient)
CA=PASA
CA
CA1
PA1
PA2
CA2
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Chemical PotentialChemical potential, μ, is the actual driving force
for permeation.Chemical potential is a thermodynamic property
related to pressure.
μL
μV
vapor
liquid
For Vapor Liquid Equilibrium (VLE),
μL = μV
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Permeation
PPwvwv=x=xPPnitrogennitrogen=y=y
water vaporwater vapor nitrogennitrogen
filmfilm
water vaporwater vapor vacuumvacuum
filmfilm
PPwvwv=x=x
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Temperature
Arrhenius equation:
RTE
ePP−
= 0P = Permeation rateP0 = Permeability constantE = Activation energyR = Gas constantT = Temperature
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Polymeric (MATERIAL) properties influencing package performance
• Structure• Moisture and other possible interactants
with the chains.• Polymer surface • Additives• Thickness• Multiple layers
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Effect of the actual chemical substituent on the polymer backbone
• Polymer chains must “move aside” or “open up”to allow permeation.
• The weaker the forces holding the chains together, the more rapidly the permeation will occur.
• The chain-to-chain forces are determined by the chemical nature of the backbone.
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POLYMER STRUCTURE OXYGEN PERMEATION* COMMENTS
Polyethylene 480 Low polarity, very little cohesion between chains
Polypropylene 150 Chains are a little stiffer, but very little cohesion or attraction
Poly(methyl methacrylate) 17
Chains are much stiffer due to steric hindrances; polarity results in chain-to-chain attraction superior to hydrocarbon polymers
Poly(vinyl chloride) 8
Chain-to-chain attraction very high due to chlorine electrons; movement of chains restricted
Effect of the actual chemical substituent on the polymer backbone
H2C CH
C O
OCH3
H2C CH
Cl
H2C CH
CH3
H2C CH2
* cc-mil/100 in2-day-atm
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The degree of packing, crystallinity, and orientation of the molecular chains
• Close packing and/or high crystallinity results in low free volume and better barrier.
• Orientation results in better barrier by creating a more tortuous diffusion path.
POLYMER MORPHOLOGY O2 PERMEATION* COMMENTS
PET (poly(ethylene
terephlate)) 10% crystalline 10.0
PET 50% crystalline 5.0 Higher crystallinity reduces the available sites for permeation
PET 50% crystalline and oriented 3.0
Crystallinity and orientation produces more tortuous path for permeation
* cc-mil/100 in2-day-atm
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The susceptibility to moisture and other possible interactants with the chains
• Some chemical species are adversely affected by moisture absorption and thus barrier is reduced.– Water enters the polymer and interacts with the bonds that
hold the chains together– The polymer swells and the chains become “floppy” thus
allowing permeation to increase.• Water, which is highly polar, will only react this way with
polar polymer groups that depend upon hydrogen bonds.– Hydroxyl – Amide
• Other polar groups, although they might absorb water, are not affected since their barrier properties do not depend upon hydrogen bonds.– Ester– Cyano
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Effect of Relative Humidity on OTR(1011mL*cm/cm2*sec*cmHg @25oC)
28.828.8LDPE6.66.6HDPE
0.060.06ABS9.03.3PVA0.30.06Nylon 6
12.00.0078Uncoated Cellophane
1.50.0006PVOH100%RH0%RHPolymer
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The susceptibility to moisture and other possible interactants with the chains
0.001
0.01
0.1
1
10
0 20 40 60 80 100Rh (%)
O2 P
erm
eatio
n
(cc-
mil/
100
in2 -d
ay-A
TM) NYLON 6 @ 23C
SELAR® PA @ 23C
NYLON MXD6 @ 23C
44% EVOH @ 20C
30% EVOH @ 20C
SELAR® OH PLUS @ 23C
Note: Selar ® PA is commerically available. SELAR® OH PLUS is currently out of commercial production.Data on ‘OH PLUS’ is for reference only. SELAR® is a registered trademark of E.I. du Pont de Nemours & Co.
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The nature of the polymer surface contacting the permeant
• The nature of the surface can determine the permeability as much as the polymer bulk.
• An example is hydrocarbon permeation through polyethylene:– Polyethylene polymer is very nonpolar and thus a
very poor barrier to nonpolar permeants such as hydrocarbon liquids.
– By treating the surface with fluorine gas, the fluorine adds on to the chains at or near the surface and by virtue of its bulk and polarity prevents hydrocarbon liquids from entering the polymer
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Additives used in manufacturing or modifying the polymer
• Depending upon the chemical nature, as well as the manner which the additive is blended, the barrier can be either enhanced or reduced.
PVC Poly (vinyl chloride)
Material state Pure, rigid PVC
Plasticized, soft PVC
O2 Permeation rate (cc-mil/100 in2-day-atm) 8 150
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Presence of Co-permeantExample – ethyl acetate and limonene, used with BOPP
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Thickness
• Typically the transmission rate is inversely proportional to the thickness of the material
thickness permeation rate• This may not apply for very thin materials
where structural changes or surface phenomena may have occurred.
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Multiple layers
• Multi-layer materials obeying Fick’s can be mathematically “added” by means of the Parallel Resistance Equation.
L++=BAtotal TRTRTR
111
A CB
TRtotal
TRA TRB TRC
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Measurement Techniques
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Basic test methods for measuring permeation
• Gravimetric• Isostatic
– Flow-through– Accumulation / Speciation
• Accumulation II
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Gravimetric method (dry cup - weight gain)
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Gravimetric method (wet cup - weight loss)
0.00000
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Gravimetric method Data collection
00.050.1
0.150.2
0.250.3
0.35
0 5 10 15 20
TIME (days)
WE
IGH
T L
OSS
(gra
ms)
Y = 0.03x - 0.15 0.03 g/day lostsample area: 30 cm2
thickness: 1 mil
driving force: 230 mm Hg
P=(0.03 g/day)(1 mil)/(30 cm2)/(230 mm Hg)
P= 0.043 g-mil/m2-day-mm Hg
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Isostatic Permeation MeasurementFlow-through technique
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Isostatic Permeation MeasurementFlow-through technique
permeant
detector
Carrier gas
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Isostatic Permeation MeasurementData collection
0
10000
20000
30000
40000
50000
60000
0 1 2 3 4 5 6
TIME (hours)
PER
ME
AT
ION
RA
TE
(g
-mil/
m2 -d
ay-m
m H
g)
P = 51,232 g-mil/m2-day-mm Hg
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Isostatic Permeation MeasurementAccumulation / separation technique
TRAP column
detectorpermeant
Carrier gas
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Isostatic Permeation Measurement Data collection
050
100150200250300350400
0 50 100 150 200 250
TIME (hours)
PER
ME
AT
ION
RA
TE
(g
-mil/
m2-
day-
mm
Hg)
Minutes34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
Vol
ts
0.02
0.04
0.06
0.08
0.10
0.12
Vol
ts
0.02
0.04
0.06
0.08
0.10
0.12
tcd
card ar unstressedName
0
100
200
300
400
500
600
0 50 100 150 200 250
TIME (hours)
PER
ME
AT
ION
RA
TE
(g
-mil/
m2-
day-
mm
Hg)
0
100
200
300
400
500
600
0 50 100 150 200 250
TIME (hours)
PER
ME
AT
ION
RA
TE
(g
-mil/
m2-
day-
mm
Hg)
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Accumulation IIASTM E398
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QUESTIONS??
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Thank YouPRESENTED BY
Joel FischerLab Manager and ScientistMOCON, [email protected]
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