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Flexible Food Packaging
for the 21st Century and Beyond
Dr. Kenneth S. Laverdure
Frito-Lay, Inc.
Packaging Research and Development
Sustainability and Advance Materials Group
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A Little Quote
“Knowledge and Timbers
shouldn‟t be much used
‟till they are seasoned.”
Oliver Wendell Holmes, 1858
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Outline
• Review of classical multi-layer film structure
• Understanding the Physics of Mass Transport
• Practical Knowledge of Barrier
• Barrier Technologies
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Typical Opaque Laminated Film
FunctionCross-Section
• Barrier
• Stiffness
• SealingEPB Copolymer
Polypropylene
Metal Layer
inside
• Barrier Film
Film Gauge:
0.0025”• Inter-layer
Adhesion• Lamination Layer LDPE
• Clarity
• GraphicsPrint
Polypropylene
EPB Copolymer
• Print Film
• Sealing
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Typical Packaging Film Structure
Outer Web
Tie Layer
Inner Web
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Typical Layer Materials
Oriented Polypropylene
Polyethylene
Metalized Oriented Polypropylene
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Flex. Pkg.- Materials Key Attributes
Print web: gloss (or matte), stiffness, machine-ability
Tie layer: stiffness, barrier
Barrier web: sealant, stiffness
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Outer Web
OPP Core
Ink Layer
Slip layer
Print layer
The Outer web is typically a three layer structure,
Featuring a core, a slip layer, and a print surface.
Graphics are reverse printed by the converter.
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Tie Layer
Polyethylene
Polyethylene
Polypropylene (Or EVOH)
The tie layer bonds inner/outer webs together,
provides stiffness, package opening for the consumer,
and occasionally O2 barrier
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Inner Web
OPP Core
High energy receptive surface
Sealant Layer
Vacuum deposited Aluminum
The inner web is typically a three to four layer film,
which provides heat seal, stiffness, and barrier against
oxygen, moisture, and light.
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Typical Packaging Film Structure
OPP Core
High energy receptive surface
Sealant Layer
Vacuum deposited Aluminum
Polyethylene
Polyethylene
Polypropylene (Or EVOH)
OPP Core
Ink Layer
Slip or Sealant layer
Print layer
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MASS TRANSPORT:
THE MATHEMATICS
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“Do not worry about your
difficulties in Mathematics.
I can assure you mine are
still greater.”
Albert Einstein
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Continuity Equation and Mass Transport
• General case of
diffusion
• One dimensional case of
diffusion
X
Y
Zc
tjx
xjy
yjz
z 0
c
t
jx
x
C
C
1
2
X C(x,t)
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Fick’s Laws of Diffusion
• Diffusion coefficient, D, relates concentration profiles
to flux within a film (polymer).
• Fick‟s first law:
• Fick‟s second law:
– Case of 1-D unsteady state transport through a
membrane
ja Dabca
x
2
2
x
cD
t
c aab
a
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Different Cases of Mass Transport
Time
M
M t
Fickian Diffusion Fickian Diffusion (time1/2)
Time1/2
M
M t
SuperCase II (Activated) Diffusion
Time
M
M t
Accelerated
Adsorption
Case II, or Solvent Front Transport
Time
M
M tPossible
Dissolving
of Polymer
Adsorption linear
with square root of time.
These behaviors may be observed by measuring the weight of a film over time. A film surrounded by water vapor for example.
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Determining Transport Case
• Mass Uptake versus time:
– Where Mt = mass at time t
M∞ = mass at equilibrium
k = proportionality constant
n = power index
– Power Index (n) determines Transport Case
• May be determined plotting by weight uptake over time
nt ktM
M
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Ad/desorption Comparison
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2 2.5
Time (hrs)
Fra
cti
on
al
Lo
ss
or
Gain
Frac. Gain
Frac. Loss
Time (Hours)
Desorption
Adsorption
Fickian Diffusion -- Curve of CO2 Ad/desorption within Polymer Film
Example of Fickian Diffusion
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Fickian Diffusion – Demonstration of linear behavior
Fickian Diffusion vs. Time1/2
Adsorption in Square Root of Time
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60 80 100 120
Time^(1/2) [s^(1/2)]
Fra
cti
on
al M
as
s U
pta
ke
Frac. Gain
Initial Slope
Fra
ctional M
ass G
ain
ed o
r Lost
Square Root of Time (s1/2)
1 hr = 3600s;
√3600 = 60
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Diffusion Coefficient by ‘Initial Slope’ Method
• „Initial Slope Method‟
• For short times and Fickian diffusion,
0
2/1
2/1
2/1
24
128m
mt
Dt
mLierfc
L
Dt
M
M
2/1
2/18
tD
LM
M t
Crank, “Mathematics of Diffusion”, 1975.
• Fickian diffusion
– Initial slope of mass uptake
is linear with t1/2.
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Other Methods to Extract Deff
• „Half-time Method‟
• „Limiting Slope Method‟
Mt
M
18
2
1
2m 1 2exp
4D 2m 1 2 2t
L2
m0
2
2
2
48ln1ln
L
tD
M
M t
Slope of
D L2
42t1/ 2
Ln16
2D from half time of mass uptake:
Crank, “Mathematics of Diffusion”, 1975.
Berens, A. R., Polymer 1977, 18, 697.
M
M t1ln
versus time
2
24
L
D
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Other Methods to Extract Deff
• „Half-time Method‟
• „Limiting Slope Method‟
Mt
M
18
2
1
2m 1 2exp
4D 2m 1 2 2t
L2
m0
2
2
2
48ln1ln
L
tD
M
M t
Slope of
D L2
42t1/ 2
Ln16
2D from half time of mass uptake:
Crank, “Mathematics of Diffusion”, 1975.
Berens, A. R., Polymer 1977, 18, 697.
M
M t1ln
versus time
2
24
L
D
Plenty of methods to compute Deff,
each has its own built-in
assumptions and accuracies.
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Lag Time Method
Time
Lag Time, tL
Ma
ss T
hro
ug
hp
ut
L
ieff
t
LD
6
2
effPslope
Employed with Permeation Cells
Permeate
Feed
StreamRetentate
Polymer Membrane of
separation unit.
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Solubility
• Solubility coefficient, S
– Partitioning of a component within
two different phases
• Gas solubility in a solid
– Henry‟s Law: ci Sipi
Atmosphere
Polymer
Gas Molecules
Gas at
Atmosphere/
Polymer
interface
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MASS TRANSPORT:
THE APPLICATION
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“Permeation by the Units”
• Permeation, Diffusion, and Solubility
Coefficients:
P = D * S
• D [=] cm2/s ≡ cm * (cm/s)
• S [=] cc (STP) /(cm3 {polymer} * atm)
• P [=] (cc (STP) * cm) / (cm2 * s * atm) ≡
(cc(STP)/cm2 * s) * cm* (1/atm)
Penetration distance
Penetration Velocity
Volume of Adsorb Gas
Volume of Solid
Driving
Force
Flux Gauge
Driving
Force
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Permeation, Permeance, and
Transmission Rate
• Permeation Coefficient
– P [=] mass * film gauge / (area * time * (delta)
pressure)
– Mass Transport normalized to gauge and conditions
• Permeance
– Permeance [=] mass / (area * time * (delta) pressure)
– Mass Transport normalized to conditions for a specific
film gauge
• Transmission Rate
– TR [=] mass / (area * time) ≡ flux
– Mass Transport at specific gauge and conditions.
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Methods of Mass Transport Measurement
• Gravimetric Sorption– Easy to identify types of transport
behavior.
– Samples may exhibit a low
mechanical integrity.
– Fluids must have a high solubility
in the polymer to observe
transport.
• Permeation Cell– Standardized characterization
technique.
– Samples must form mechanically
stable, continuous film.
– Fluids are not required to be highly
soluble in order to observe
transport behavior.
Mocon Permatran
(http://www.mocon.com)
Permeate
Feed
StreamRetentate
Polymer Membrane
inside separation unit.
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Oxygen vs. Water:
Differences in Barrier
Property Oxygen Water Vapor
Composition of Atmosphere 21% 1%
Gas Permanent Condensable
Polarity Non-Polar Polar
Diffusion Fickean Fickean and Type II
Solubiilty
Low for all
polymers
Low for polyolefins (hydrophobic) and
High for cellulose/EVOH (hydrophilic)
Permeation Control Diffusion Diffusion and Solubility
Barrier Effectiveness Pin Hole Defects Surface Area Coverage
Oxygen requires only a diffusion barrier;
Water requires both diffusion and solubility barriers.
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Transmission Rates;
An example from the web.
Source: http://www.matweb.com
Red = PP with functional barrier, PVDC or metallization
Blue = PP with no functional layers
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Transmission Rates: The Literature
R. Tock, Advances in Polymer Technology, Vol. 3, No. 3 (1983), pp. 223-231
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Select Coefficients for Film
P. DeLassus, “Barrier Polymers,” H. Tung, Ed., Kirk-Othmer Encyclopedia
of Chemical Technology – 4th Ed., Vol. 3 (1992), pp. 931-962.
(Multiple References)
Diffusion and Solubility Coefficient Data is difficult to obtain from literature.
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Permeation Coefficients:
A Comparison
Permeation Coefficients
Coefficients from different sources generally agree.
Some error is present in Mass Transport measurements.
P = D * S
P. DeLassus (Dow Chemical Data), “Barrier Polymers,” H. Tung, Ed., Kirk-Othmer Encyclopedia
of Chemical Technology – 4th Ed., Vol. 3 (1992), pp. 931-962.
(Permeation data from Dow Chemical Brochure)
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BARRIER
TECHNOLOGY
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Vacuum Metallization
• Properly prepared roll of
OPP placed inside
vacuum chamber
• Vacuum drawn to <
10-4 mm Hg (10-6 atm)
• Rewound and passed
over molten Al
• Al vapor deposited on
surface of film
Vacuum Chamber
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Nanotechnology Barrier
• Clay Platelet
– Aspect Ratio 100 to 1000
for length to gauge.
– Impenetrable to
permeate gas.
• Barrier formed by
tortuous path of platelet.
– Platelet perpendicular to
direction of permeation
gives maximum barrier.
• Application methods
– Aqueous solutions
– Extrusion
Polymer film with nanoparticle platelets
• Diffusion controlled by
number and orientation of
platelets.
• Solubility controlled by
polymer binder.
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IN
CONCLUSION
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Summary
• Packaging film structures are complex
assemblies with specialized layers for barrier.
• The type of mass transport, Fickian vs. Case II
(solvent front), will determine the type of
measurements and models employed.
• Permeation: P = D * S
• Consider both diffusion and solubility for barrier.
– Oxygen requires only a diffusion barrier;
Water requires both diffusion and solubility barriers.
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A Final Word
“Knowledge is power.”
Sir Francis Bacon (1561 - 1626)
Whatever technology is employed to obtain
barrier in the 21st century, knowledge of mass
transport fundamentals will allow you to leverage
that technology to the fullest.