Method for selecting adsorptive composite barriers for packaging applications
View Patent ↗A method of selecting an appropriate resin bonded sorbent composition which may be used at least for in part making an enclosure to protect contents from external humidity including the steps of: a) selecting a plurality of resins, a plurality of sorbents and a plurality of ratios therebetween to form a plurality of composites; b) calculating a plurality of failure times for the plurality of composites, wherein each failure time of the plurality of failure times is based on when an internal relative humidity of each composite of the plurality of composites is equal to the maximum internal relative humidity; c) determining which of the plurality of failure times is greater; and, d) selecting one composite of the plurality of composites based on the result of step (c).
1. A method of selecting an appropriate resin bonded sorbent composition which may be used at least for in part making an enclosure to protect contents from external humidity, wherein said enclosure has an internal headspace volume V, a thickness L and a surface area A, said enclosure surrounded by an environment having an external relative humidity h out which is a fraction of a saturated water vapor density ρ sat at a temperature T, said internal volume having a maximum internal relative humidity, said method comprising the steps of:
a) selecting a plurality of resins, a plurality of particulate sorbents and a plurality of ratios therebetween to form a plurality of composites, wherein each resin of said plurality of resins has an effective water vapor diffusivity D m and a water vapor solubility coefficient S m and each composite of said plurality of composites has a volume fraction of said resin φ m and a volume fraction of said sorbent φ d ;
b) calculating a plurality of failure times for said plurality of composites, wherein each failure time of said plurality of failure times is based on when an internal relative humidity h in of each composite of said plurality of composites is equal to said maximum internal relative humidity;
c) determining which of said plurality of failure times is greater; and,
d) selecting one composite of said plurality of composites based on the result of step (c).
2. The method of selecting a resin bonded sorbent composition of claim 1 , wherein each particulate sorbent of said plurality of particulate sorbents is stoichiometric and each composite of said plurality of composites has a stoichiometric coefficient μ, an initial mass concentration R 0 and a concentration C out of water vapor dissolved at an external surface, said internal relative humidity after a lag time t LR is calculated according to the equation:
h
i
n
(
t
)
=
h
out
[
1
-
exp
(
-
ϕ
m
D
m
S
m
A
(
t
-
t
LR
)
L
(
ρ
sat
V
+
1
2
ϕ
m
S
m
AL
)
)
]
,
wherein: t is a time to reach said internal relative humidity h in ; and,
t LR is said lag time of said enclosure having said thickness L.
3. The method of selecting a resin bonded sorbent composition of claim 2 , wherein said lag time is calculated according to the equation:
t
LR
=
L
2
6
D
m
(
1
+
3
Ψ
)
,
wherein
:
Ψ
=
μ
R
0
C
out
.
4. The method of selecting a resin bonded sorbent composition of claim 1 , wherein each particulate sorbent of said plurality of particulate sorbents has a water vapor sorption isotherm, said water vapor isotherm is linear and has a water vapor solubility coefficient S d , and each composite of said plurality of composites has a pseudo stoichiometric coefficient μ, an initial mass concentration R 0 and a concentration C out of water vapor dissolved at an external surface, said internal relative humidity after a lag time t LL is calculated according to the equation:
h
i
n
(
t
)
=
h
out
[
1
-
exp
(
-
ϕ
m
D
m
S
m
A
(
t
-
t
LL
)
L
(
ρ
sat
V
+
1
2
S
eff
AL
)
)
]
,
wherein: t is a time to reach said internal relative humidity h in ;
t LL is said lag time of said enclosure having said thickness L; and,
S eff =φ m S m +φ d S d .
5. The method of selecting a resin bonded sorbent composition of claim 4 , wherein said lag time is calculated according to the equation:
t
LL
=
L
2
6
D
m
(
1
+
Ψ
h
out
)
,
wherein
:
Ψ
=
μ
R
0
C
out
.
6. The method of selecting a resin bonded sorbent composition of claim 1 , each particulate sorbent of said plurality of particulate sorbents has a water vapor sorption isotherm, said water vapor sorption isotherm is dual sorption mode and has a hole saturation constant C max , a Langmuir affinity constant b, and said internal volume has an initial internal relative humidity h in.0 , said internal relative humidity after a lag time t LD is calculated according to the equation:
t
=
t
LD
+
a
1
a
3
a
5
(
1
+
bh
out
)
[
ln
1
+
bh
i
n
1
+
bh
i
n
.0
-
ln
h
out
-
h
i
n
h
out
-
h
i
n
.0
-
ln
(
1
+
bh
out
)
(
1
1
+
bh
i
n
-
1
1
+
bh
i
n
.0
)
]
-
a
2
a
3
+
a
4
a
5
ln
h
out
-
h
i
n
h
out
-
h
i
n
.0
,
wherein: t is a time to reach said internal relative humidity h in ;
t LD is said lag time of said enclosure having said thickness L;
a
1
=
ϕ
d
C
max
b
;
a
2
=
ϕ
m
S
m
;
a
3
=
AL
2
;
a
4
=
ρ
sat
V
;
and
,
a
5
=
ϕ
m
D
m
S
m
A
L
.
7. The method of selecting a resin bonded sorbent composition of claim 6 , wherein said lag time is calculated according to the equation:
t
LD
=
L
2
6
D
m
(
1
+
ϕ
d
ϕ
m
C
max
b
S
m
6
y
3
[
1
2
y
2
+
y
-
(
1
+
y
)
ln
(
1
+
y
)
]
)
,
wherein: y=bh out .
8. The method of selecting a resin bonded sorbent composition of claim 1 wherein said resin bonded sorbent composition is formed with the aid of a coupling agent or a compatibilizing agent, wherein the coupling agent or compatibilizing agent is chemically compatible with each resin of said plurality of resins and improves adhesion or coupling of each particulate sorbent of said plurality of particulate sorbents with each resin of said plurality of resins.
9. The method of selecting a resin bonded sorbent composition of claim 8 wherein said coupling or compatibilizing agent is selected from the group consisting of reactive and non-reactive agents.
10. The method of selecting a resin bonded sorbent composition of claim 9 wherein said compatibilizing agent is selected from the group consisting of a metal, a metal oxide, an acrylate, a stearate, a block copolymer, a maleate, an epoxy, a silane, a titanate, an organo-metal ligand and mixtures thereof.
11. The method of selecting a resin bonded sorbent composition of claim 1 wherein said resin bonded sorbent composition is compounded in a twin screw extruder.