Creation of
Moisture Sorption Isotherms
for Hygroscopic materials
Dr. Ted Labuza
Creation of
Moisture Sorption Isotherms
for Hygroscopic materials
Dr. Ted Labuza
Sorption Isotherm Methods
page # 2
A. Creation of constant humidity environments
1. Primary humidity generators
The basic or primary methods of producing a known constant humidity (usually expressed as
relative humidity at a particular temperature) involve devices controlling the variables of the
fundamental gas laws. Relative humidity is the ratio of the partial pressure of water vapor present
to that which could be present at saturation, times 100. The saturation vapor pressure is
determined only by the temperature of the (ideal) gas. Therefore, assuming behavior in
accordance with the gas lows, known humidities can be created by manipulation of the
temperature and pressure of saturated gas or by dilution of the saturated gas with an extremely
dry gas, or by a combination of these techniques.
These basic methods of producing known humidities require expensive equipment and exacting
techniques, and they assume complete saturation of the gas at a particular temperature and
pressure. This last condition is a theoretical assumption and the degree of completeness can vary
with the design of the equipment, external factors, such as temperature and barometric pressure,
and the skill of the operator.
2. Secondary humidity generators
Known constant humidities can also be created by secondary methods, by materials whose
affinity for water regulates the water vapor pressure in the atmosphere surrounding the material.
Among the more readily controllable materials are salt solutions and acid solutions. Numerous
lists of the humidities created by various salts and acid concentrations appear in the literature,
inferring a certain ease of producing the specified humidity conditions. An ease of maintenance of
these humidity conditions with high accuracy is also inferred since the temperature dependency is
very small. The ease of handling and low cost of salts has promoted the widespread use of salt
solutions as humidity generators.
a. Conflicting humidity data for salt solutions from published tables
Saturated salt solutions can provide a stable humidity condition; however, the condition
created is not necessarily the relative humidity cited in the literature. Particularly, since the
various references disagree as to the humidity created. Tests at the U.S. National Bureau of
Standards were compared with the published results of various investigations (1). In general the
scattering of reported values were within a band of ± 1.5% RH. from the NBS results.
Therefore, only a qualified expression of the humidity created should be made, with the particular
salt and reference source cited.
b. Requirements for saturated salt solutions
While interpretation of the humidity values created by the various salt solutions is questionable,
the humidity created can be reproducible and stable. Attainment of stable humidity values is
governed by the purity of the salt, by the purity of the water, by the preparation of the salt
solution, by the water vapor equilibrium rate between the liquid and vapor, by the temperature
equilibrium between the liquid and vapor and by the presence of hygroscopic materials within the
vapor space.
Sorption Isotherm Methods
page # 3
(1). Chemical Purity Essential
Obviously the purity of the salt and the purity of the water will determine the equilibrium
humidity condition. Small amounts of contaminants can, in some cases, seriously affect the end
results. Chemically pure salts and distilled water must be used.
Many air borne contaminants are water soluble and may be of a mineral or hygroscopic nature.
Since these contaminants may cause a shift in the equilibrium humidity condition, reliability
requires that stale solutions be replaced with fresh solution. In addition to this shift, some salts
react chemically with the container or air borne contaminants, altering the composition of the
solution and thus the equilibrium humidity.
(2)."Solution" Not a Solution, But a Slush
The preparation of the salt solution is a very important but frequently overlooked
consideration. The solution should be a slash consisting of a solution with excess undissolved
crystals (2). Too much water, as in a true solution, even with undissolved crystals at the bottom,
can result in a layer of less-than-saturated solution at the surface which will produce a higher
humidity than anticipated. Conversely, solid crystals protruding above the surface of the liquid
can reduce the humidity. A good solution can usually be made by adding distilled water slowly,
with constant stirring, until about half the salt crystals are dissolved.
(3). Large Solution Surface Area and Small Vapor Space Desirable
The diffusion rate of moisture from a saturated salt solution is exponential, with a quick
approach to the near equilibrium value, but a very gradual final approach to the actual end point.
The diffusion rate is governed by the difference in water vapor pressure of the solution and of the
vapor and by the attraction of the salt for the water. With some salts, the attainment of complete
equilibrium requires days. In stagnant air even the approach can take considerable time. For
faster stabilization ( to the near equilibrium condition) it is recommended that the surface area of
the solution be as large as practical, that the vapor space be as small as practical and that the air
be circulated over the solution.
(4). Temperature Importance
A saturated salt solution has a definite water vapor pressure at a given solution temperature.
The relative humidity created in the vapor space is determined by the water vapor pressure and
the saturation water vapor pressure at the temperature of the vapor. For example, a saturated
solution of sodium chloride at 77°F generates a vapor pressure equal to 75.8% RH. if the vapor is
also at 77°F but the relative humidity is now 83.1% RH. at the vapor temperature of 75°F. At
these particular conditions a temperature difference of only 2°F between solvent and vapor causes
a non-apparent error of approximately 5% RH.
(5). Allow Fresh Solution to Cool
The effect of temperature differences between solution and vapor can be compensated for if
reasonably constant. Unfortunately this effect is frequently overlooked upon initial preparation of
Sorption Isotherm Methods
page # 4
solutions when the heat of reaction of the salt and water can raise the temperature of the water
very significantly. Fresh solutions should be made up well in advance of actual use at a
temperature higher than the storage temperature and sufficient time allowed to cool at the storage
temperature before use.
B. The Method of Desiccators
1. Eight to nine desiccators with salts to give a
w
s of 0, 0.11, 0.33, 0.44,
0.54, 0.62, 0.75, 0.85, and 0.92 at different temperatures are
recommended for a complete isotherm.
Note that fish tanks make excellent desiccators if an internal platform is
used to raise the samples off the floor.
2. For dry products, the desired range of 0-82% RH with 6-8 points
is generally enough. For semi-moist products use 50-92%% RH .
3. Salt solutions at high temperatures should be prepared at
those temperatures to ensure saturation. Solutions should
be
slurries with about a 2 mm liquid layer above the crystals.
Plastic vacuum
desiccators or fish tanks are the best to use.
4. A layer of glass wool over the desiccator plate or platform will
prevent solution from contaminating dishes when a vacuum is
pulled or the desiccator is handled.
5. Correct the a
w
value for temperature from equations or tables.
6. Samples stored at 11% (LiCl2), 42% (K1Cr2O3) and 62% (NaNO2)
should "not" be taste tested because of toxicity of the salts.
Sorption Isotherm Methods
page # 5
C. a
w
values for salts
a. -general saturated salt a
w
values from Labuza’s lab
Salt 25°C 30°C
Drierite
< 0.01
< 0.01
LiCl
0.112
0.115
K-acetate
0.227
0.225
MgCl
2
0.328
0.329
KCO
3
0.432
0.447
Mg (NO
3
)
2
0.529
0.520
NaBr
0.576
0.574
CoCl
2
0.649
--
NaNO
2
0.643
0.649
SrCl
2
0.709
--
NaNO
3
0.743
--
NaCl
0.753
0.769
KBr
0.809
--
(NH)
2
SO
4
0.810
--
KCl
0.843
0.850
Sr(NO
3
)
2
0.851
--
BaCl
2
0.902
0.920
KNO
3
0.936
--
K
2
SO
4
0.973
0.977
Sorption Isotherm Methods
page # 6
b. Greenspan values for saturated salts used by FDA
______________________________________________________________________________________
Temp
Cesium
Lithium
Zinc
Potassium
Sodium
°C Fluoride Bromide Bromide Hydroxide Hydroxide
0
7.75 ± 0.83
5
5.52 ± 1.9
7.43 ± 0.76
8.86 ± 0.89
14.34 ± 1.7
10
4.89 ± 1.6
7.14 ± 0.69
8.49 ± 0.74
12.34 ± 1.4
15
4.33 ±1.4
6.86 ± 0.63
8.19 ± 0.61
10.68 ± 1.1
9.57 ± 2.8
20
3.83 ± 1.1
6.61 ± 0.58
7.94 ± 0.49
9.32 ± 0.90
8.91 ± 2.4
25
3.39 ± 0.94
6.37 ± 0.52
7.75 ± 0.39
8.23 ± 0.72
8.24 ± 2.1
30
3.01 ± 0.77
6.16 ± 0.47
7.62 ± 0.56
7.38 ± 0.56
7.58 ± 1.7
35
2.69 ± 0.63
5.97 ± 0.43
7.55 ± 0.25
6.73 ± 0.44
6.92 ± 1.5
40
2.44 ± 0.52
5.80 ± 0.39
7.54 ± 0.20
6.26 ± 0.35
6.26 ± 1.2
45
2.24 ± 0.44
5.65 ± 0.35
7.59 ± 0.17
5.94 ± 0.29
5.60 ± 1.0
50
2.11 ± 0.40
5.53 ± 0.31
7.70 ± 0.16
5.72 ± 0.27
4.94 ± 0.85
55
2.04 ± 0.38
5.42 ± 0.28
7.87 ± 0.17
5.58 ± 0.28
4.27 ± 0.73
60
2.03 ± 0.40
5.33 ± 0.25
8.09 ± 0.19
5.49 ± 0.32
3.61 ± 0.65
65
2.08 ± 0.44
5.27 ± 0.23
8.38 ± 0.24
5.41 ± 0.39
2.95 ± 0.60
70
2.20 ± 0.52
5.23 ± 0.21
8.72 ± 0.30
5.32 ± 0.50
2.29 ± 0.60
75
2.37 ± 0.62
5.20 ± 0.19
1.63 ± 0.64
80
2.61 ± 0.76
5.20 ± 0.18
85
5.22 ± 0.17
90
5.26 ± 0.17
95
5.32 ± 0.16
100
5.41 ± 0.17
______________________________________________________________________________________
Temp
Lithium
Calcium
Lithium
Potassium
Potassium
°C Chloride Bromide Iodide Acetate Fluoride
0
11.23 ± 0.54
5
11.26 ± 0.47
21.68 ± 0.30
10
11.29 ± 0.41
21.62 ± 0.50
20.61 ± 0.25
23.38 ± 0.53
15
11.30 ± 0.35
20.20 ± 0.50
19.57 ± 0.20
23.40 ± 0.32
20
11.31 ± 0.31
18.50 ± 0.50
18.56 ± 0.16
23.11 ± 0.25
25
11.30 ± 0.27
16.50 ± 0.20
17.56 ± 0.13
22.51 ± 0.32
30.85 ± 1.3
30
11.28 ± 0.24
16.57 ± 0.10
21.61 ± 0.53
27.27 ± 1.1
35
11.25 ± 0.22
15.57 ± 0.08
24.59 ± 0.94
40
11.21 ± 0.21
14.55 ± 0.06
22.68 ± 0.81
45
11.16 ± 0.21
13.49 ± 0.05
21.46 ± 0.70
50
11.10 ± 0.22
12.38 ± 0.05
20.80 ± 0.62
55
11.03 ± 0.23
11.22 ± 0.05
20.60 ± 0.56
60
10.95 ± 0.26
9.98 ± 0.06
20.77 ± 0.53
65
10.86 ± 0.29
8.65 ± 0.07
21.18 ± 0.53
70
10.75 ± 0.33
7.23 ± 0.09
21.74 ± 0.56
75
10.64 ± 0.38
22.33 ± 0.61
80
10.51 ± 0.44
22.85 ± 0.69
85
10.38 ± 0.51
23.20 ± 0.80
90
10.23 ± 0.59
23.27 ± 0.93
Sorption Isotherm Methods
page # 7
______________________________________________________________________________________
Temp
Magnesium Sodium Potassium
Magnesium
Sodium
°C Chloride Iodide Carbonate Nitrate Bromide
0
33.66 ± 0.33
43.13 ± 0.66
60.35 ± 0.55
5
33.60 ± 0.28
42.42 ± 0.99
43.13 ± 0.50
58.86 ± 0.43
63.51 ± 0.72
10
33.47 ± 0.24
41.83 ± 0.83
43.14 ± 0.39
57.36 ± 0.33
62.15 ± 0.60
15
33.30 ± 0.21
40.88 ± 0.70
43.15 ± 0.33
55.87 ± 0.27
60.68 ± 0.51
20
33.07 ± 0.18
39.65 ± 0.59
43.16 ± 0.33
54.38 ± 0.23
59.14 ± 0.44
25
32.78 ± 0.16
38.17 ± 0.50
43.16 ± 0.39
52.89 ± 0.22
57.57 ± 0.40
30
32.44 ± 0.14
36.15 ± 0.43
43.17 ± 0.50
51.40 + 0.24
56.03 ± 0.38
35
32.05 ± 0.13
34.73 ± 0.39
49.91 ± 0.29
54.55 ± 0.38
40
31.60 ± 0.13
32.88 ± 0.37
48.42 ± 0.37
53.17 ± 0.41
45
31.10 ± 0.13
31.02 ± 0.37
46.93 ± 0.47
51.95 ± 0.47
50
30.54 ± 0.14
29.21 ± 0.40
45.44 ± 0.60
50.93 ± 0.55
55
29.93 ± 0.16
27.50 ± 0.45
50.15 ± 0.65
60
29.26 ± 0.18
25.95 ± 0.52
49.66 ± 0.78
65
28.54 ± 0.21
24.62 ± 0.62
49.49 ± 0.94
70
27.77 ± 0.25
23.57 ± 0.74
49.70 ± 1.1
75
26.94 ± 0.29
22.85 ± 0.88
50.33 ± 1.3
80
26.05 ± 0.34
22.52 ± 1.0
51.43 ± 1.5
85
25.11 ± 0.39
22.63 ± 1.2
90
24.12 ± 0.46
23.25 ± 1.4
95
23.07 ± 0.52
100
21.07 ± 0.60
______________________________________________________________________________________
Temp
Cobalt
Potassium
Strontium
Sodium
Sodium
°C Chloride Iodide Chloride Nitrate Chloride
0
75.51 ± 0.34
5
73.30 ± 0.34
77.13 ± 0.12
78.57 ± 0.52
75.65 ± 0.27
10
72.11 ± 0.31
75.06 ± 0.31
77.53 ± 0.45
75.67 ± 0.22
15
70.98 ± 0.28
74.13 ± 0.06
76.46 ± 0.39
75.61 ± 0.18
20
69.90 ± 0.26
72.52 ± 0.05
75.36 ± 0.35
75.47 ± 0.14
25
64.92 ± 3.5
68.86 ± 0.24
70.85 ± 0.04
74.25 ± 0.32
75.29 ± 0.12
30
61.83 ± 2.8
67.89 ± 0.23
69.12 ± 0.03
73.14 ± 0.31
75.09 ± 0.11
35
58.63 ± 2.2
66.96 ± 0.23
72.06 ± 0.32
74.87 ± 0.12
40
55.48 ± 1.8
66.09 ± 0.23
71.00 ± 0.34
74.68 ± 0.13
45
52.56 ± 1.5
65.26 ± 0.24
69.99 ± 0.37
74.52 ± 0.16
50
50.01 ± 1.4
64.49 ± 0.26
69.04 ± 0.42
74.43 ± 0.19
55
48.02 ± 1.4
63.78 ± 0.28
68.15 ± 0.49
74.41 ± 0.24
60
46.74 ± 1.5
63.11 ± 0.31
67.35 ± 0.57
74.50 ± 0.30
65
46.33 ± 1.9
62.50 ± 0.34
66.64 ± 0.67
74.71 ± 0.37
70
46.97 ± 2.3
61.93 ± 0.38
66.04 ± 0.78
75.06 ± 0.45
75
48.80 ± 2.9
61.43 ± 0.43
65.56 ± 0.91
75.58 ± 0.55
80
52.01 ± 3.7
60.97 ± 0.48
65.22 ± 1.1
76.29 ± 0.65
85
60.56 ± 0.54
65.03 ± 1.2
90
60.21 ± 0.61
65.00 ± 1.4
Sorption Isotherm Methods
page # 8
______________________________________________________________________________________
Temp
Ammonium Potassium Ammonium
Potassium
Strontium
°C Chloride Bromide Sulfate Chloride Nitrate
0
82.27 ± 0.90
88.61 ± 0.53
5
85.09 ± 0.26
82.42 ± 0.68
87.67 ± 0.45
92.38 ± 0.56
10
80.55 ± 0.96
83.75 ± 0.24
82.06 ± 0.51
86.77 ± 0.39
90.55 ± 0.38
15
79.89 ± 0.59
82.62 ± 0.22
81.70 ± 0.38
85.92 ± 0.33
88.72 ± 0.28
20
79.23 ± 0.44
81.67 ± 0.21
81.34 ± 0.31
85.11 ± 0.29
86.89 ± 0.29
25
78.57 ± 0.40
80.89 ± 0.21
80.99 ± 0.28
84.34 ± 0.26
85.06 ± 0.38
30
77.90 ± 0.57
80.27 ± 0.21
80.63 ± 0.30
83.62 ± 0.25
35
79.78 ± 0.22
80.27 ± 0.37
82.95 ± 0.25
40
79.43 ± 0.24
79.91 ± 0.49
82.32 ± 0.25
45
79.18 ± 0.26
79.56 ± 0.65
81.74 ± 0.28
50
79.02 ± 0.28
79.20 ± 0.87
81.20 ± 0.31
55
78.95 ± 0.32
80.70 ± 0.35
60
78.94 ± 0.35
80.25 ± 0.41
65
78.99 ± 0.40
79.85 ± 0.48
70
79.07 ± 0.45
79.49 ± 0.57
75
79.16 ± 0.50
79.17 ± 0.66
80
79.27 ± 0.57
78.90 ± 0.77
85
78.68 ± 0.89
90
78.50 ± 1.0
95
100
______________________________________________________________________________________
Temp
Potassium
Potassium
°C Nitrate Sulfate
0
96.33 ± 2.9
98.77 ± 1.1
5
96.27 ± 2.1
98.48 ± 0.91
10
95.96 ± 1.4
98.18 ± 0.76
15
95.41 ± 0.96
97.89 ± 0.63
20
94.62 ± 0.66
97.59 ± 0.66
25
93.58 ± 0.55
97.30 ± 0.45
30
92.31 ± 0.60
97.00 ± 0.40
35
90.79 ± 0.83
96.71 ± 0.38
40
89.03 ± 1.2
96.41 ± 0.38
45
87.03 ± 1.8
96.12 ± 0.40
50
84.78 ± 2.5
95.82 ± 0.45
Sorption Isotherm Methods
page # 9
c. Hygrodynamics technical bulletin
Saturated Salt Solution
Formula
Percent Relative Humidity at Stated Temperatures
68°F(20°C) 77°F(25°C) 86°F (30°C)
Lithium Chloride
LiCl
.
H
2
0 12.4
12.0
11.8
Potassium Acetate
KC
2
H
3
O
2
23.3
22.7
22.0
Magnesium Chloride
Mg Cl
2
.
6H
2
O
33.6
33.2
32.8
Potassium Carbonate
K
2
CO
3
2H
2
O 44.0
43.8
43.5
Potassium Nitrite
KNO
2
49.0
48.1
47.2
Magnesium Nitrate
Mg (NO
3
)
2
6H
2
O 54.9
53.4
52.0
Sodium Nitrite
NaNO
2
65.3
64.3
63.3
Sodium Chloride
NaCl
75.5
75.8
75.6
Ammonium Sulfate
(NH
4
)
2
SO
4
80.6
80.3
80.0
Potassium Nitrate
KNO
3
93.2
92.0
90.7
Potassium Sulfate
K
2
SO
4
97.2
96.9
96.6
d. temperature effect equations for salts
principle ln a
w
= [
∆
H/R] [1/T] + c T=°K
salt equation
LiCl
ln a
w
= 500.95 [1/T] -3.85
K
2
C
2
H
3
O
2
ln a
w
= 861.39 [1/T] -4.33
MgCl
2
ln a
w
= 303.35 [1/T] -2.13
K
2
CO
3
ln a
w
= 145.00 [1/T] -1.30
MgNO
3
ln a
w
= 356.60 [1/T] -1.82
NaNO
2
ln a
w
= 435.96 [1/T] -1.88
NaCl
ln a
w
= 228.92 [1/T] -1.04
KCl
ln a
w
= 367.58 [1/T] -1.39
e. references
(1)A. Wexler and S. Hasegawa, "Relative humidity-temperature relationship of some saturated
salt solutions in the temperature range 0° to 50°C". J. Research NBS 53, 19 (1954).
(2) A. Wexler and W.G. Brombacher, "Methods of measuring humidity and testing hygrometers",
NBS Circular 512 (1951).
(3) S. Martin, "The control of conditioning atmospheres in small sealed chambers", J. Sci. Instru.
39, 370 (1962).
(4)
C.P. Hedlin and F.N. Trofimenkoff (Division of Building Research National Research
Council, Saskatoon, Sask., Canada), "Relative humidities over saturated solutions of nine salts in
Sorption Isotherm Methods
page # 10
the temperature range from 0 to 90°F", Paper presented at 1963 International Symposium on
Humidity and Moisture.
(5)
J. Chirifie a
w
of salt J. Food Sci. 49:1486, 1984
(6) Wilmer A. Wink (Institute of Paper Chemistry), "Salt Solution, Equilibrium Relative
Humidity", Industrial and Engineering Chemistry, April 1946, page 251.
(7) F.E.M. O'Brien, "The control of humidity by saturated salt solutions-a compilation of data", J.
Sci. Instr. 25, 73 (1948)
(8) International Critical Tables, 1, 68 (McGraw-Hill Book Co. New York, N.Y.)
(9) Handbook of Chemistry and Physics (Chemical Rubber Publ. Co., Denver CO
Sorption Isotherm Methods
page # 11
D. Temperatures for isotherms
1. The temperatures of choice are 20, 25, 30, 35, 45°C for most dry
foods. At least two temperatures should be used if thermodynamic
parameters are required. This would facilitate many other aspects of
product development research. Someone should have the responsibility
for setting the policy for use of the desiccators.
E. Equilibrium Time
1. A general policy of a maximum of three weeks for any one study
could be set unless there is a problem of recrystallization or
nonequilibrium at high a
w.
Given this, only an initial and final
weighing are necessary.
F. Initial sample preparation step options:
1. Dry all samples down to zero moisture by holding in a
vacuum oven for 48 hours at 30°C with a LN2 or dry
ice/methanol in the trap for the pump. This will give an
adsorption isotherm.
2. Dry all samples over desiccant (Drierite) for three weeks. This
will occur faster if a vacuum is used. This will then give an
adsorption isotherm.
3. Use samples directly as is and correct for initial moisture by
using dry desiccator value from isotherm study or measure
initial moisture by some other method. This will give a combined
adsorption/desorption working isotherm.
Sorption Isotherm Methods
page # 12
G. Sample weighing
1. Weigh duplicate or triplicate samples (1-5 grams) into glass petri
dishes to 0.1 mg or better. Dishes should be stored in a dry
desiccator or fish tank to keep dry.
2. Different kinds of samples can be done at same time but do not
overload the desiccator. Don't combine adsorption/desorption samples
3. Generally, the sample volume should be < 1/20 of volume of air.
4. Weigh samples after 21 days for single reading. If two times are used
(14 and 21 days) and no change of greater than 1 mg/gram dry solids
(0.1% error) occurs, end the experiment. If there is a greater change
than
that, continue to weigh. This may occur at high aw. An alternative is
to assume
three weeks is enough and weigh only once.
5. To facilitate weighing, prevent condensation, and the
problem of cooling of samples from high temperatures,
the samples can be transferred into an "empty" desiccator and
brought down to room temperature to weigh (20 minutes). The
high a
w
samples at high temperatures may cause condensation so the
dry desiccator should
be prewarmed to the higher temperature.
6. Lids are not necessary if the weighings are done rapidly.
The balance should be periodically checked.
7. Pulling a vacuum on the desiccator would reduce the overall time
to 3-7 days, but requires more care and set-up. Also, pulling
the
vacuum could cause bubbling and contamination of the
samples with
salts.
Sorption Isotherm Methods
page # 13
H. Calculation of moisture content.
1. Non-dried samples (sample prep Method F-3) "Working Isotherm"
m
==
[
w
2
−−
w
1
]
++
%
H
2
O
100
w
1
w
1
100
−−
%
H
2
O
100
==
g
water
g
solids
W1 = initial weight
W2 = final weight
% H2O = initial moisture content of sample (wet basis) done by
some other method or from the dry desiccator.
2. For pre-dried samples (sample prep Method F-1 or F-2)
m
==
[
w
2
−−
w
1
]
w
1
==
g
water
g
dry
solids
w
2
- w
1
= moisture gained in grams
w
1
= grams dry solids of sample
3.. To convert from dry basis to wet basis.
%H
2
O
==
m
1
++
m
100
==
g water
100
g total
Sorption Isotherm Methods
page # 14
I. Moisture Isotherm plot.
1. To obtain the moisture sorption isotherm, plot moisture (dry basis)
versus a
w
on linear paper. A smooth curve should be used to
connect the points. Outliers should be discarded and the data
point repeated. Most food isotherms "should" have a general
sigmoidal shaped curve. For best results use an computer solution
2. Some samples high in amorphous state sugar will show an
increase and then decrease in weight with time due to
recrystallization. Thus, a true isotherm cannot be made (see
J. Food Sci. 45:1231) but the data are still useful.
J. BET Isotherm
1. Calculate a/(1-a)m for each isotherm data point and plot versus aw
2. Only use values up to 0.55 a
w
.
3. Use a linear regression program to get the intercept I and slope S.
4. Calculation
m
o
= monolayer value in g/H
2
O solids = 1
I + S
Sorption Isotherm Methods
page # 15
K. GAB isotherm plot
1. The GAB equation is:
m
==
m
0
k
b
ca
1
−−
k
b
a
[[
]]
1
−−
k
b
a
++
ck
b
a
[[
]]
kb ranges from about 0.7 to 1
1 < c< 200
a = water activity at moisture m
2. To solve for each parameter:
a. use a nonlinear regression program
b. use polynomial solution
a
m
==
k
b
m
o
1
c
−−
1
a
2
++
1
m
0
1
−−
2
c
a
++
1
m
0
k
b
c
a
m
==
αα
a
2
++
ββ
a
++
εε
αα
==
k
b
m
0
1
c
−−
1
ββ
==
1
m
0
1
−−
2
c
εε
==
1
m
0
k
b
c
Using the binomial equation, the GAB solution is:
k
b
==
ββ
2
−−
4
ααεε
−−
ββ
2
εε
c
==
ββ
εε
k
b
++
2
m
0
==
1
εε
k
b
c