Notes 3 of fe 501 physical properties of food materials
1. FE-501
PHYSICAL PROPERTIES OF
FOOD MATERIALS
ASSOC PROF. DR. YUS ANIZA YUSOF
DEPARTMENT OF PROCESS & FOOD ENGINEERING
&
FACULTY OF ENGINEERING
UNIVERSITI PUTRA MALAYSIA
4. INTRODUCTION
• There are many methods for measuring water activity
of foods.
• This session provides information about the theory of
water activity, its prediction and measurement
methods, and preparation of sorption isotherms.
• W t
Water activity of f d can b measured using
ti it
f foods
be
d
i
methods based on colligative properties, isopiestic
transfer, and hygroscopicity of salts and using
hygrometers.
h
t
• Moisture sorption isotherm describes the relationship
between water activity and the equilibrium moisture
content of a food product at constant temperature.
5. IMPORTANCE OF WATER ACTIVITY
• Water activity (aw) is one of the most critical
factors in determining quality and safety of foods.
• W t
Water activity affects th shelf lif
ti it
ff t the h lf life, safety,
f t
texture, flavor, and smell of foods.
• While temperature, pH and several other factors
can influence if and how fast organisms will grow
in a product, water activity may be the most
important factor in controlling spoilage
spoilage.
• Most bacteria, for example, do not grow at water
,
activities below 0.91, and most molds cease to
grow at water activities below 0.80.
6. IMPORTANCE OF WATER ACTIVITY
• By measuring water activity, it is possible to
predict which microorganisms will and will not be
potential sources of spoilage.
i l
f
il
• Water activity‐‐not water content‐‐determines
the lower limit of available water for microbial
growth. In addition to influencing microbial
spoilage, water activity can play a significant role
in determining the activity of enzymes and
vitamins in foods and can have a major impact
their color, taste, and aroma.
h
l
d
7. IDEAL SOLUTION‐ RAOULT’S LAW
• A solution can be defined as ideal if the cohesive forces inside
a solution are uniform. This means that in the presence of two
components A and B, the forces between A and B, A and A,
and B and B are all the same
same.
• Gibbs free energy in terms of partial molar quantities and
since the partial molar free energy is the chemical potential,
for compound A in a solution:
(4.1)
• where is the molar volume of component A in solution
which is the volume divided by the number of moles of A.
which is the volume divided by the number of moles of A.
8. IDEAL SOLUTION‐ RAOULT’S LAW
• Using ideal gas law and Eq. (4.1), μA can be related to the
g
g
q ( ),
partial vapor pressure by:
( )
(4.2)
• If μ0A is the value of chemical potential when the pressure is 1
atm, integrating Eq. (4.2):
atm integrating Eq (4 2):
(4.3)
(4.4)
9. IDEAL SOLUTION‐ RAOULT’S LAW
• Partial vapor pressure of a component, which is a measure of
p p
p
,
tendency of the given component to escape from solution
into the vapor phase, is an important property for solutions.
For a solution in equilibrium with its vapor:
(4.5)
• Thus, chemical potential of component A in solution is related
to the partial vapor pressure of A above the solution.
Equation (4 5) i true only when vapor b h
E
i (4.5) is
l
h
behaves as an id l
ideal
gas.
10. IDEAL SOLUTION‐ RAOULT’S LAW
• A solution is ideal if the escaping tendency of each
p g
y
component is proportional to the mole fraction of that
component in the solution. The escaping tendency of
component A from an ideal solution as measured by its
solution,
partial vapor pressure, is proportional to the vapor pressure
of pure liquid A and mole fraction of A molecules in the
solution. This can be expressed by Raoult’s law as:
(4.6)
11. IDEAL SOLUTION‐ RAOULT’S LAW
• where PA is the partial vapor pressure of A, XA is its mole
p
p p
,
fraction, and P0 A is the vapor pressure of pure liquid A at the
same temperature. If component B is added to pure A, vapor
pressure is decreased as:
(4.7)
(4.8)
(4 8)
• Equation (4.7) (relative pressure lowering) is useful for
solutions of a relatively nonvolatile solute in a volatile solvent.
• Inserting Eq. (4.6) into Eq. (4.5), Eq. (4.9) can be obtained:
(4.9)
12. HENRY’S LAW
• Consider a solution containing solute B in solvent A. If the
d
l
l
l
f h
solution is very dilute, a condition is reached in which each
molecule B is completely surrounded by component A. Solute
p
y
y
p
B is then in a uniform environment irrespective of the fact
that A and B may form solutions that are not ideal at higher
concentrations.
concentrations In such a case the escaping tendency of B
case,
from its environment is proportional to its mole fraction,
which can be expressed by Henry’s law as:
(4.10)
• where k is the Henry’s law constant.
• H
Henry’s l
’ law i not restricted t gas–liquid systems. It i valid
is t
t i t d to
li id
t
is lid
for fairly and extremely dilute solutions.
13. COLLIGATIVE PROPERTIES
• Colligative properties d
ll
depend on the number of solute
d
h
b
f
l
molecules or ions added to the solvent. Vapor pressure
lowering, boiling point elevation, freezing point depression,
g
g p
g p
p
and osmotic pressure are the colligative properties. These
properties are used to determine the molecular weights and
to measure water activity
activity.
14. COLLIGATIVE PROPERTIES
BOILING POINT ELEVATION
• If a small amount of nonvolatile solute is d
f
ll
f
l l
l
dissolved in a volatile
l d
l l
solvent and the solution is very dilute to behave ideally, the
lowered vapor pressure can be calculated from Eq. (4.7). As a
p p
q ( )
result of lowered vapor pressure, the boiling point of solution
is higher than that of the pure solvent.
• A di
As discussed b f
d before, chemical potentials of th volatile A f
h i l t ti l f the l til
for
liquid and vapor phases are equal to each other at
equilibrium:
(4.11)
• The chemical potential of A in liquid phase is expressed as in
Eq. (4.9):
E (4 9)
(4.9)
15. COLLIGATIVE PROPERTIES
BOILING POINT ELEVATION
• At constant temperature the f
h first two terms are constants and
d
independent of composition. Therefore, they can be
combined to simplify the equation:
p y
q
(4.12)
• where μ0L’A is the chemical potential of pure liquid A.
• At boiling point at 1 atm, μVA = μ0V’A . Thus, Eq. (4.12)
becomes:
(4.13)
• For a pure component A, the chemical potentials are identical
with molar free energies. Thus:
(4.14)
16. COLLIGATIVE PROPERTIES
BOILING POINT ELEVATION
(4.15)
• This equation involves both the Gibbs free energy and
temperature derivative of Gibbs free energy and it is more
convenient to transform it so that only a temperature
derivative appears. This can be achieved by first
differentiating (G/T ) with respect to temperature at constant
p
pressure:
(4.16)
17. COLLIGATIVE PROPERTIES
BOILING POINT ELEVATION
• Using Eqs. (
(4.15) and (
) d (4.16), the Gibbs‐Helmholtz equation is
) h
bb
l h l
obtained:
(4.17)
(
)
• Substituting Eq. (4.14) into (4.17) and differentiating:
(4.18)
• where
Thus:
is the molar latent heat of vaporization (λv).
(4.19)
(4 19)
18. COLLIGATIVE PROPERTIES
BOILING POINT ELEVATION
• Equation (
(4.19) can b integrated b using the l
)
be
d by
h limits of pure
f
solvent (XA = 1) at temperature T0 to any arbitrary XA and T
values.
(4.20)
(4.21)
• B ili
Boiling point elevation (T – T0)
i
l
i (T
) can be expressed as TB. When
b
d T Wh
boiling point elevation is not too large, the product of T times
T0 can be replaced by T 02 .
19. COLLIGATIVE PROPERTIES
BOILING POINT ELEVATION
• Considering the mole f
d
h
l fraction of solute as XB, the mole
f l
h
l
fraction of solvent is XA = 1 − XB
• ln (1 – XB) can be expanded in a power series as:
(4.22)
• For dilute solutions where XB is a very small fraction, higher
order terms in Eq. (4.22) can be neglected. As a result:
• where
(4.23)
(4.24)
(4 24)
20. COLLIGATIVE PROPERTIES
BOILING POINT ELEVATION
• I which wB and wA are th masses of solute and solvent,
In hi h B d A
the
f l t
d l t
respectively and MB and MA are the molecular weights of the
solute and solvent, respectively. Substituting Eq. (4.23) into
Eq. (4.22):
E (4 22)
(4.25)
• where lv is the latent heat of vaporization per unit mass.
• The term (wB/wAMB) is expressed in terms of molality as
(m/1000). Then:
( /1000) Th
(
(4.26)
)
• where KB is the molal boiling point elevation constant.
23. WATER ACTIVITY
• Consider a f d system enclosed in a container. All the
d
food
l d
ll h
components in the food are in thermodynamic equilibrium
with each other in both the adsorbed and vapor phases at
p p
constant temperature. Considering moisture within the food
system and the vapor in the headspace, their chemical
potentials are equal to each other:
(4.28)
• The activity of water in foods can be expressed as:
y
p
(4.29)
• If the water activity is expressed in terms of pressures, the
following equation is obtained:
(4.30)
24. WATER ACTIVITY
• F
Fugacity coefficients of water vapor i equilibrium with
it
ffi i t
f
t
in
ilib i
ith
saturated liquid are above 0.90 at temperatures between
0.01°C and 210°C and pressure values between 611 Pa and
19.1×10 Pa (Rizvi, 2005).
19 1 105 P (Ri i 2005)
• Therefore, it can be approximated to 1, which means
negligible deviation from ideality. Thus, water activity in foods
can be expressed as:
(4.31)
• Therefore water activity can be defined as the ratio of the
Therefore,
vapor pressure of water in the system to the vapor pressure of
pure water at the same temperature. It can also be expressed
as the equilibrium relative humidity (ERH) of the air
surrounding the food at the same temperature.
25. WATER ACTIVITY
• Water activity is an important property in f d systems. Most
food
chemical reactions and microbiological activity are controlled
directly by the water activity. In food science, it is very useful
y y
y
y
as a measure of the potential reactivity of water molecules
with solutes.
• W t activity d i t f
Water ti it deviates from R
Raoult’s l
lt’ law at hi h solute
t higher l t
concentrations. The variation of solute and solvent molecule
size results in a change of intermolecular forces between the
molecules, leading them to behave as nonideal.
26. WATER ACTIVITY
• The intermolecular f
h
l l forces b
between solvent molecules, solute–
l
l l
l
solute and solute–solvent interactions and solvation effects
cause the solution to behave nonideally. If the solute
y
completely dissociates into ions when dispersed in a solvent it
causes nonideality. The presence of insoluble solids or porous
medium cause a capillary action that decreases vapor
pressure and shows deviation from ideal behavior.
28. WATER ACTIVITY
WATER ACTIVITY
• Definition of relative humidity in a mixture of air and water
y
vapor is the ratio of amount of water vapor in the mixture
divided by the maximum amount of water vapor that could be
held by the air at that condition (saturation) Mathematically
(saturation). Mathematically,
this ratio is the same as the ratio of water vapor partial
pressure divided by saturation pressure, as expressed in
equation (
(4.32):
)
(4.32)
29. WATER ACTIVITY
WATER ACTIVITY
• By substituting this definition in the BET equation,expression
y
g
q
, p
(4.33) is derived, and transformation of variables plotted on
the graph in Figure 4.1, allows for the determination of the
constants,
constants as shown in the previous section Thus we can see
section. Thus,
how water activity (or equilibrium relative humidity) can take
the place of partial pressure as the parameter plotted on the
x‐axis for obtaining water vapor sorption isotherms.
(4.33)
• Another possibility to further simplify the use of water
sorption isotherms, is to use the water content instead of m
(mass of the water absorbed).The water content is what we
know as moisture content of the food.
31. MOISTURE CONTENT
• For general purposes, the moisture content of a food is
g
p p
,
normally expressed simply as the percent moisture in the
food substance. Mathematically, this is the ratio of the mass
of water contained in the food sample (adsorbent) over the
total mass of food sample containing the moisture
(adsorbate), expressed as a percent. However, moisture
content used as the variable plotted on the vertical axis of
vapor sorption isotherms often is expressed as the ratio of
(
)
y
y
mass of water mW (adsorbate) divided by mass of dry matter
mdm, only (absorbent), as expressed in equation (4.34):
(4.34)
(4 34)
32. MOISTURE CONTENT
• These two different methods for expressing moisture content
in a f d sample are k
food
l
known as “
“wet b ”( b) and “d
basis”(wb) d “dry
basis”(db), respectively. The distinction between both
methods of expression, as well as the ability to quickly
calculate one from the other must be well understood
understood.
• The illustration in Figure 4.2, shows a vertical bar representing
a 100 g food sample composed of 20 g water and 80 g dry
matter,
matter and shows how these quantities are used to correctly
express moisture content on either basis.
• For example, in this case the moisture content on a wet basis
is 20/100 = 20% But on a dry basis it is 20/80 = 25%
20%. But,
25%.
• Refer also to Table 4.1 for further elaboration on the
difference between the two expressions and how to convert
the quantities from one to another.
35. HYGROSCOPICITY
• Hygroscopicity is a term used to describe how readily a
yg
p y
y
material will take up moisture when subjected to a given shift
(change) in relative humidity.
• Th t
The term i often used i i d t i l practice t i di t
is ft
d in industrial
ti to indicate
materials that quickly become problematic in the presence of
the least increase in surrounding relative humidity.
• For example, certain powdered ingredients are said to be very
hygroscopic if they become sticky and cause caking problems
that prevent free flowing from the storage hopper in a food
process.
• In this regard the term is used in a relative qualitative sense,
and no quantitative scale has ever been assigned to
hygroscopicity.
36. HYGROSCOPICITY
• There is no means to quantify what is the difference between
q
y
strong and weak hygroscopic behavior.
• It may be possible to consider hygroscopicity as a material
property th t could b quantified if we understand th t thi
t that
ld be
tifi d
d t d that this
type of moisture uptake behavior in response to change in
relative humidity can be observed from the shape of the
sorption isotherm for this material.
• For example, a highly hygroscopic powder will show a much
higher uptake of water when shifted from 45% to 75% relative
humidity than a powder would with lower hygroscopicity.
37. BET EQUATION FOR FOODS
• In the case of water vapor sorption in foods, when the
p
p
,
isotherms are obtained as plots of moisture content (db)
versus water activity, the BET equation gets the form
(4.35)
• where
38. BET EQUATION FOR FOODS
• If the quantity 1/xW ∙ aW/(1−aW) were plotted against water
q
y /
/(
p
g
activity aW, a straight line is obtained (see Figure 4.3).The
monolayer moisture content xW, a as well as the BET constant,
can then be obtained from the slope and intercept of the line
line.
The value of xW, a is usually the moisture content at which the
water is tightly bound with water molecules in a single
monolayer, and it cannot participate as a solvent. Thus, it is
the moisture content that should be reached for maximum
y
y
stability of dehydrated foods
41. BET – ONE POINT METHOD
• For the purpose of rough estimation, the straight line BET plot
p p
g
,
g
p
can be approximated by constructing a straight line from the
origin of the coordinate axes through a single data point. The
single data point should be taken at value of water activity at
which the monolayer is fully developed (saturated) but no
multiple layer formation exists. As a rule of thumb for most
foods, this value is normally chosen in the range of water
activity between 0.3–0.4.
42. BET – ONE POINT METHOD
• The BET parameters for the monolayer moisture content xW, a
p
y
and BET constant C can be estimated from the slope of this
straight line, and will normally serve sufficiently well for most
purposes of approximating the profile of the sorption
isotherm for the given food substance, as shown by equation
(4.37). Because of a = 0 we can say:
(4.37)
• and
d
(4.38)
43. THERMODYNAMICS OF WATER VAPOR
O
CS O
O
SORPTION IN FOODS
• Similar to the d
l
h discussion on thermodynamics of sorption
h
d
f
isotherms presented earlier in this chapter, the temperature
dependency of the BET constant C can be obtained from an
p
y
Arrhenius plot of log C over reciprocal absolute temperature
T. The excess enthalpy of adsorption, or monolayer‐bonding
enthalpy ∆hC, can be obtained from the slope m of the
straight‐line Arrhenius semi‐log plot, as given by equation
(4.39):
(4.39)
45. THERMODYNAMICS OF WATER VAPOR
O
CS O
O
SORPTION IN FOODS
• The specific sorption enthalpy hs,mono will b f
h
f
h l
ll be found at the
d
h
drying condition which leaves only the monolayer, but fully
intact. At this point the monolayer is a complete layer of
p
y
p
y
water molecules tightly bound to the boundary surface of the
food material, and the enthalpy at this point marks the
distinction between “free” and “bound” water in the food
free
bound
food.
• As explained earlier, the BET theory covers a monolayer only
and there is no regard for multilayers (like in the GAB model,
see below). That means water in the second layer is treated
like “free” water. So in the BET theory the “excess” monolayer
bonding enthalpy ∆hC disappears and plays no further role.
46. THERMODYNAMICS OF WATER VAPOR
O
CS O
O
SORPTION IN FOODS
• In this case, water is f l available to b h
h
freely
l bl
behave as normal water
l
(vaporize, condense, freeze, sublime and thaw), and only the
enthalpy of vaporization (in the case of desorption), or
condensation (in the case of adsorption) applies. In the opposite
direction when the “excess” monolayer bonding enthalpy ∆hC
takes on high values, the bonding strength at the monolayer
g
,
g
g
y
surface becomes very strong.
• Further water removal beyond this point through normal drying
processes becomes very costly and time consuming Therefore
consuming. Therefore,
it is of critical importance to identify this point of distinction
with respect to the “excess” monolayer bonding enthalpy ∆hC in
order to design and specify optimum drying, storage and
f
packaging conditions to assure long‐term stability of dehydrated
foods.
47. THERMODYNAMICS OF WATER VAPOR
O
CS O
O
SORPTION IN FOODS
• A f method f quickly estimating this “
fast
h d for
kl
h “excess” monolayer
”
l
bonding enthalpy hC is possible by comparing water activity
of a food at different temperatures, and determining the
p
g
temperature dependency of water activity for the given food.
This can be done with the Clausius–Clapeyronequation:
(4.42)
49. GAB MODEL
• The GAB model is a semi theoretical multi molecular
adsorption model intended for use over a wide range of water
activity, and can be written as a three‐parameter model:
(4.44)
• where
50. GAB MODEL
• The GAB isotherm equation is an extension of the two
two‐
parameter BET model which takes into account the modified
properties of the adsorbate in the multilayer region and bulk
liquid (“free” water) properties through the introduction of a
third parameter k. If k is less than 1, a lower sorption is
p
predicted than that by the BET model, and allows the GAB
y
,
isotherm to be successful up to water activity of 0.9.The GAB
equation reduces to the BET equation when k = 1. The
constants in the GAB equation (k and C) are temperature
dependent, and are the means by which we can extract
information when we construct and refer to sorption
isotherms at different temperatures.
55. SHELF LIFE OF FOOD RELATED TO WATER ACTIVITY
• The normally high moisture content in most fresh foods is
y g
largely the reason they are so perishable.
• If left unprotected without being processed or preserved in
any way, th will d t i t rapidly as a result of various
they ill deteriorate
idl
lt f
i
microbial, chemical and biochemical reactions.
• In order for these reactions to proceed, most of them require
p
,
q
abundant availability of free water to act as a solvent and for
hydraulic transport of molecules across semi‐permeable
membranes,
membranes essential for microbial metabolism within the
metabolism,
food.
56. SHELF LIFE OF FOOD RELATED TO WATER ACTIVITY
• For this reason one of the most effective methods of food
preservation is to reduce the moisture content until the water
activity is low enough that the amount of free water needed
to support any of the degradation reactions that might take
place is not available.
• This is the principle behind the storage stability and long shelf
life of dehydrated foods.
• As the water activity is brought below 1 and lowered further
in a food the rates of these reactions begin to slow down
food,
down.
• They proceed more slowly with further lowering water
activity, which translates into longer and longer shelf life.
57. SHELF LIFE OF FOOD RELATED TO WATER ACTIVITY
• The actual shelf life of any specific food product at a given
y p
p
g
water activity may vary depending on structure and
composition of the food material, and spoilage mechanism of
concern.
concern
• The shelf life of a food will be limited by any one of a series of
spoilage mechanisms that can destroy the food. These include
microbial activity (bacteria, yeasts and moulds), enzyme
activity, browning reactions, and lipid oxidation (rancidity).
• Of all these reactions microbial activity is by far the most
reactions,
sensitive to water activity, having the greatest need for
available free water.
• Table 4.5 lists the minimum values of water activity needed
for the growth of different microorganisms.
60. SHELF LIFE OF FOOD RELATED TO WATER ACTIVITY
• Water activity dictates whether or not a reaction will take
y
place in a food, and if so, at what rate.
• Therefore the objective of most food dehydration processes is
to bring the food
t b i th f d product t a specified water activity.
d t to
ifi d t
ti it
• However, the engineer responsible for the design and
operation of the food dehydration process can only be
p
y
p
y
concerned about moisture content.
• The food drying equipment is designed only to remove
moisture, and only moisture content can b measured and
i
d l
i
be
d d
controlled on the factory floor (not water activity).
• The sorption isotherm becomes the fundamental tool by
which it is possible to specify the moisture content needed
that will assure the required water activity.
61. LABORATORY DETERMINATION OF SORPTION ISOTHERMS
• In order to obtain a sorption isotherm for any material
substance, It is necessary to be able to accurately measure
both the moisture content and the water activity of a sample
after it has come into equilibrium relative humidity at
different known levels of relative humidity. The moisture
content must be on a dry basis (db).
62. LABORATORY DETERMINATION OF SORPTION ISOTHERMS
LABORATORY DETERMINATION OF SORPTION ISOTHERMS
Measurement of Water Activity
• Different procedures are available f
ff
d
l bl for measuring water
activity, but they usually fall into one of three general
methods of approach. Water activity can be measured
pp
y
through:
– Sample being brought into equilibrium with a closed
atmosphere of known constant relative humidity (isopiestic
technique or desiccators method)
– Equilibrium head space atmosphere surrounding sample is
measured f i relative h idi with the sample (
d for its l i
humidity i h h
l (water
activity meter)
– Dynamic method in which samples are exposed to atmospheres
of various relative humidity and weighed simultaneously.
64. LABORATORY DETERMINATION OF SORPTION ISOTHERMS
LABORATORY DETERMINATION OF SORPTION ISOTHERMS
Measurement of Moisture Content
• The standard classic procedure f accurate d
h
d d l
d
for
determination of
f
the moisture content in a sample of food material is the
g
gravimetric oven method.
• In this method, a sample of known initial weight is placed into
a drying oven at 105 °C, and weighed periodically until no
further i ht loss i d t t d
f th weight l
is detected.
65. LABORATORY DETERMINATION OF SORPTION ISOTHERMS
LABORATORY DETERMINATION OF SORPTION ISOTHERMS
Measurement of Moisture Content
• There are various types of l b
h
f laboratory “
“moisture meters”
”
available for more rapid determination of moisture content
(
(within 10–30 minutes). These work on the principles of
)
p
p
either measuring electrical conductivity, which depends on
moisture content, or by driving the moisture out of the
sample more rapidly than a drying oven using infrared
radiation from an infrared lamp. These methods, however,
can often give erroneous results because of various
limitations, and must b used with great caution.
li i i
d
be
d ih
i
