This section will provide a summary of structural and mechanical properties of plastics, discuss per-meability theory and equations used for calculating permeability and shelf life, and describe common traits and uses of thermoplastics for food packaging.
Figure 5.9. Photo of an injection-molded parison (center) and injection stretch blow molded bottles for hot fill processes (left) and aseptic process (right).
STRUCTURALPROPERTIES
The structural and mechanical properties of plastics discussed in this chapter are among those most com-monly considered for the design of food packages.
The structural properties described are molecular weight, glass transition temperature, and crystalline melting temperature. More detailed information on these topics can be found in basic polymer textbooks such as Billmeyer (1971) and Sperling (1992).
Molecular Weight
Plastic polymers are comprised of repeating units of a variety of monomer structures (ethylene, propy-lene, etc.). The degree of polymerization (DP) is used to describe the average number of each of these monomers in a polymer. For example, the DP for polyvinylidene chloride (PVDC) is 100–10,000 (Andrady 1999). During the formation of polymers, chains with many different lengths and DPs are pro-duced; therefore, polymers have average molecular weights rather than molecular weights (shown in Table 5.1). Depending on how molecular weight is measured, different types of averages are obtained (number average or weight average). Number aver-aged molecular weight (M—
n) is the total weight of molecules divided by the total number of molecules, shown in Equation 5.1.
5.1
—M
nis independent of molecular size and is sensi-tive to small molecules in the mixture (Robertson 1993). Most of the thermodynamic properties of polymers (colligative properties, osmotic pressure, freezing point depression) depend on M—
n(Billmeyer 1971).
Weight averaged molecular weight (M—
w) is more complex and is calculated as shown in Equation 5.2.
5.2
Heavier molecules become more important in the calculation of M—
w, and most of the bulk properties of polymers (viscosity, strength) depend on M—
w.
Above their critical molecular weight, polymers begin to show strength and toughness, which drasti-cally influence processing capability. Critical molec-ular weight depends on polymer chain entanglement.
Increasing entanglement increases a polymer’s lecular weight and brings it closer to the critical mo-lecular weight (Sperling 1992). Tensile strength of polymers first increases with increasing molecular weight but then reaches a maximum at the critical molecular weight. Viscosity increases continuously with increasing molecular weight. This increase in viscosity makes polymers nonprocessible above their critical molecular weight.
Glass Transition and Crystalline Melting Temperatures
The temperature at which a polymer changes from a glassy state to a rubbery state is called the glass tran-sition temperature (Tg). Tg is a characteristic of amorphous polymers, which do not form regular structures due to the interference of chain and pen-dant groups. The crystalline melting temperature (Tm), on the other hand, is the temperature at which a crystalline polymer undergoes a transition from a crystalline solid to a liquid. Above Tm, a polymer is in a liquid (melted) state. Since most plastic poly-mers used in food packaging are semicrystalline (they contain both amorphous and crystalline re-gions), they have both Tgand Tm(as shown in Table 5.1). At temperatures below Tg, amorphous regions of polymers are in the glassy state. In the glassy state, molecules have no segmental motion but vi-brate slightly. Structures in the glassy state do not have the regularity of crystalline structures, but the physical properties of glassy and crystalline struc-tures (such as hardness and brittleness) are similar.
At temperatures above Tg, amorphous structures are in the rubbery state, and the polymer becomes soft and flexible as molecular movement increases. In the section on package filling, the importance of se-lecting plastics with Tgabove temperatures encoun-tered during food processing is described.
Crystalline and glassy regions in a plastic poly-mer provide barriers to permeants, and a plastic is more permeable above its Tgdue to the decrease in glassy regions. Therefore, knowledge of the Tgand Tmof a plastic is essential for designing good food packages with the desired barrier properties. The mobility of the polymer chain is the determining factor for Tg; therefore, factors that restrict the rota-tional motion of the molecules cause an increase in M
5 Food Packaging 113
Tg (e.g., increasing intermolecular forces and in-creasing numbers of bulky pendant groups), and fac-tors that increase molecular movement and flexibil-ity cause a decrease in Tg (e.g., plasticizers and flexible pendant groups) (Sperling 1992). Increasing the number of polar side groups will form stronger intermolecular forces and lead to higher Tg. Bulky pendant groups such as benzene rings can restrict the rotational freedom of neighboring chains and in-crease Tg; however, flexible pendant groups such as aliphatic chains can limit chain packing and de-crease Tg. Increasing the cross-linking of polymers will decrease free volume, restrict molecular rota-tional motion, and raise Tg. Addition of low molec-ular weight plasticizers to a plastic will increase the flexibility of the polymers, weaken the intermolecu-lar forces between the polymer chains, and lower Tg. MECHANICALPROPERTIES
Mechanical properties of polymers describe their behavior (strength, stiffness, brittleness, and hard-ness) under stress. Tensile properties, tear strength, and impact strength are measures used to describe mechanical properties. Understanding these proper-ties is important for designing proper packages to withstand stresses and forces encountered during processing, shipping, distribution, warehousing, and consumer use.
Tensile properties include tensile strength, yield strength, elongation, and Young’s modulus. Tensile properties are determined from stress-strain curves that are constructed by plotting the change in the length (strain) of the polymer with respect to tensile stress applied to the polymer (as shown in Fig.
5.10). Tensile strength is the maximum stress a poly-mer can sustain at its break point. This property is quite important for polymers that need to be stretched and is an indication of the resistance of the polymer to continuous stress (as in a screw cap on a bottle) (Hanlon et al. 1998). Polymers with low ten-sile strength can be used for packaging dry soup, coffee, or confectionery products; however, high tensile strength is needed for packaging bulk prod-ucts (Soroka 1999). The strain at the break point of a polymer is called elongation at break, and it is ex-pressed as the percent change of the original length of the polymer. Elongation is a good measure of toughness and the ability of a plastic material to conform to an irregular surface (Hanlon et al. 1998).
Polymers with low elongation are used for packag-ing heavy products. Yield strength is the stress at the
point of a nonelastic deformation of a polymer. The slope of the stress-strain curve over the range for which this ratio is constant (the initial slope of the stress-strain curve) is called Young’s modulus.
Young’s modulus is a good measure of the intrinsic stiffness of a polymer.
The shape of the stress-strain curve also provides information about other mechanical properties of the polymer. Toughness is measured from the area under the stress-strain curve, and is a measure of the energy a polymer can absorb before it breaks. Over-all toughness is also related to the impact strength of the polymer. Impact strength is the resistance to breakage or rupture as a result of a sudden stress, while tensile strength is a measure of the resistance to breaking as a result of a slowly applied stress.
PERMEABILITY
Since plastic packaging materials, unlike glass and metal, are not absolute barriers, they allow the trans-port of gases and odors to and from the package. This exchange of gases, or permeability, has a drastic im-pact on the shelf life, quality, and safety of food products. Therefore, permeability characteristics are one of the most important properties of plastics for the design of food packages. This section provides a brief theoretical background for permeability and discusses factors affecting the permeability of gases through plastics. The next section provides sample permeability and shelf-life calculations based on the equations presented here.
Figure 5.10. An example of a typical stress-strain curve.
5 Food Packaging 115
The permeability coefficient is described by the following equation (Crank 1975):
5.3
where P is the permeability coefficient that de-scribes the total mass transport at a steady state through a film; D is the diffusion coefficient, which is a measure of how fast the permeant molecules are moving in the plastic polymer; and S is the solubil-ity coefficient that measures how many permeant molecules are moving in the plastic polymer. A polymer with low permeability will have low diffu-sion and solubility coefficients. Permeation of mol-ecules through polymers involves the following stages (Ashley 1985): (1) absorption of the perme-ant onto the surface of the polymer, (2) solubiliza-tion of the permeant in the polymer matrix, (3) dif-fusion of the permeant through the polymer along a concentration gradient, and (4) desorption of the permeant from the other polymer surface as shown in Figure 5.11. These stages, and therefore the per-meability of plastic packaging materials, are influ-enced by the properties of the plastic polymers, the properties of the permeating molecules, the degree of interaction between the polymer and the permeat-ing molecules, and the environmental conditions (temperature and pressure). The properties of poly-mers that affect permeability include crystallinity;
polarity; chain-to-chain packing ability; glass
transi-tion temperature; size, shape, and polarity of the permeant; temperature; and pressure (Pascat 1986, Robertson 1993, Sperling 1992).
Crystallinity. Because diffusion of molecules oc-curs in the amorphous regions of a polymer, the permeability of highly crystalline polymers is sig-nificantly less than the permeability of highly amor-phous polymers, as shown in Figure 5.12. For exam-ple, the oxygen (O2) permeability of high-density polyethylene with 80% crystallinity is about 4.5 times lower than the O2permeability of low-density polyethylene with 50% crystallinity (Pascat 1986).
Polarity. Highly polar polymers are excellent bar-riers to nonpolar permeant molecules (such as oxy-gen) but poor barriers to polar permeant molecules (such as water vapor). An increase in relative humid-ity will cause an increase in the permeabilhumid-ity of polar polymers. The two nonpolar polymers com-monly used in food packaging are polyethylene and polypropylene; most other polymers for food pack-aging are polar.
Chain-to-Chain Packing Ability. Linear polymers with simple molecular structures have higher (more dense) chain packing and lower gas permeability than more complex and branched polymers. Poly-P= ×D S
Figure 5.11. Diagram of how solubility and diffusivity relate to permeability. As described by Ashley (1985), a per-meant molecule must absorb at the surface of the polymer, solubilize in the polymer matrix, diffuse through the poly-mer along a concentration gradient, and desorb at the opposite polypoly-mer surface.
mers with bulky side chains have poor packing abil-ity and higher permeabilabil-ity. HDPE has a more linear structure than LDPE, and the permeability of HDPE is lower than that of LDPE.
Glass Transition Temperature (Tg). The free vol-ume and mobility of polymer molecules below their Tgare reduced. Therefore, at temperatures below the Tg, a polymer has fewer voids, permeating mole-cules have a more tortuous path to travel through the polymer, and permeability is reduced. Polymers with Tgs higher than their end-use temperature for food packaging have improved barrier properties.
Table 5.1 shows Tg, Tm, O2permeability, and H2O permeability values for select polymers.
Size, Shape, and Polarity of the Permeating Species.
Smaller molecules more readily diffuse through polymers than larger molecules. For example, for LDPE the diffusion coefficient of carbon dioxide (CO2), which has a 3.4 angstrom (Å) molecular di-ameter, is 0.37106cm2⋅s1, while the diffusion coefficient for the smaller O2with a 3.1 Å diameter is 0.46106 cm2⋅s1 (Pascat 1986). However, since permeability is affected by both diffusivity and solubility (refer to Eq. 5.3), smaller molecules may not always have higher permeability. Also, the meability of linear molecules is greater than the per-meability of molecules with bulky side chains. If the polarities of both the permeating molecule and the polymer are the same, the permeating molecule may easily diffuse through the polymer. However, when the polarity of the permeating molecule is opposite that of the polymer, interaction will occur between
the permeant and the polymer, and permeability will decrease.
Temperature and Pressure. Permeability (P) is in-dependent of pressure if there is no interaction be-tween the polymer and the permeant. However, P becomes pressure dependent and increases with in-creasing pressure for polymers having an interaction with the permeant. Permeability, diffusion, and sol-ubility coefficients vary exponentially with temper-ature according to the Arrhenius law:
5.4
5.5
5.6
where P0, D0, and S0are pre-exponential constants;
EP, ED, and Es are activation energies for perme-ation, diffusion, and sorption, respectively; R is the universal gas constant; and T is the absolute temper-ature. Since the permeability coefficient is the prod-uct of the diffusion coefficient and the solubility co-efficient (Eq. 5.3), the activation energy for the permeation is equal to
5.7
Calculations for permeability of food packages are based on Fick’s first law. Fick’s first law is used to describe the permeation of a molecule, called the permeant, through a plastic film at a steady state.
Ep=ED+Es S=S0 exp(−Es/RT) P=P0 exp(−Ep/RT) D=D0 exp(−ED/RT)
Figure 5.12. Diagram of the influence of crystalline regions on permeation of a molecule through a package.
For unidirectional diffusion, Fick’s first law is given by
5.8
where J is the flux or the amount of permeant diffus-ing per unit area per unit time, D is the diffusion co-efficient or diffusivity, c is the concentration of the permeant in the film, and x is the distance across which the permeant travels (package thickness). If (1) steady state mass transport, (2) negligible con-vective transport, and (3) a constant diffusion coef-ficient are assumed, Equation 5.8 can be integrated across the total thickness of the package (l) to give Equation 5.9:
5.9
where c1and c2are permeant concentrations at the package surfaces and l is the package thickness. The flux, J, of a permeant in a film can be defined as the amount of permeant (Q) passing through a surface of unit area (A) in one direction of flow during unit time (t). The equation for calculating flux is
5.10
where Q is the total amount of permeant passing through per unit area per unit time.
Equation 5.10 can be substituted into Equation 5.9 to give Equation 5.11. Equation 5.11 enables the calculation of the total amount of permeant passing through a film with an area A in a period of time t:
5.11
When measuring gas permeation, it is more con-venient to measure the partial pressure of the perme-ant rather than its concentration. According to Henry’s law, the concentration of the permeant in the film (c) is expressed as:
5.12
where S is the solubility coefficient and p is the par-tial pressure of the permeant in the gas phase.
By combining Equation 5.11 with Equation 5.12, Equation 5.13 is formed:
5.13
Since the product of D and S is the permeability coefficient, P (as shown in Eq. 5.3), Equation 5.13 can be rewritten as:
5.14
According to the SI system, the units of P are
As a molecule permeates through a package, an unsteady-state diffusion precedes the steady-state diffusion of the permeant through the polymer (Fig.
5.13.). Mass transfer during unsteady-state diffusion can be described by Fick’s second law. The solution of Fick’s second law yields Equation 5.15 for a sys-tem with (1) a concentration-independent diffusion constant, (2) a polymer that is initially free from per-meant, and (3) only one surface of the polymer ex-posed to the permeant gas at pressure p1 (Comyn 1985):
5.15
If the linear portion of steady-state line in Figure 5.13 is extrapolated to Q = 0, then the intercept on the x-axis, which is known as time lag (τ), can be ex-pressed as
5.16
Equation 5.16 provides the basis for calculating diffusivity, D.
Mutilayer or laminate films are composed of sev-eral layers of different types of polymers in order to maximize functional properties while minimizing cost. For calculating the permeability coefficient (P) for a multilayer film that consists of n layers of dif-ferent types of plastics (Fig. 5.14.), the following se-ries of equations can be used. If it is assumed that the flux of the permeant molecules is at a steady state and the areas where permeation takes place are equal, the following equation can be used to express Q of the layered package:
5.17
For multilayer films, Equation 5.14 can be written as:
5 Food Packaging 117
5.18
5.19
And for multilayer films, the permeability coef-ficient PT can be calculated from the following equation:
5.20
In addition to passing through plastics by perme-ation, gases also may pass through plastics via pores, pinholes, cracks, defective seals, or other defects. Packages must be intact for the permeabil-ity equations described above to be valid. If the packages have pores, holes, or defects, the perme-ability calculations will underestimate permeabil-ity, and the shelf-life calculations will overesti-mate shelf life. Package testing procedures (de-scribed in the section Finished Product, below) are designed to detect leaks or defects that could limit package performance beyond the shelf life and per-meability calculated using the equations described above.
P l
l P l P l P
T
n n
=( /1 1) (+ 2/ 2)+……+( / )
Δp p p p p p p
p p
n n
= − = − + −
+ − −
( ) ( ) ( )
(
0 1 2 2 3
+…… 1 nn)
Q P A p p
l
P A p p l P A
T
n
= 1 0− 1 = − =
1
2 1 2
2
( ) ( )
(
……
= pp p
l
n n
n
−1− )
Figure 5.13. An example of a typical permeation curve.
Figure 5.14. A diagram of permeation through a multilayer plastic film. This diagram is used for calculating permeability through multilayer films as described by Equations 5.17–5.20 in the text.
SAMPLEPERMEABILITYCALCULATIONS
Example 1: Calculation of Permeability through a Monolayer Film
How much oxygen would permeate through a 20 cm
20 cm plastic bag made of linear low-density poly-ethylene (PO2 = 4.18108 cm3⋅cm⋅cm2⋅s1⋅ atm1) or PET (P = 1.671010cm3⋅cm⋅cm2⋅s1⋅ atm1) per second? The thickness of the plastic is 0.2 cm, and the partial pressure of oxygen across the film is 0.21 atm.
Using Equation 5.14:
for linear low-density polyethylene (LLDPE)
for PET
Example 2: Calculation of Permeability through a Multilayer Film
How much oxygen would permeate through a 20 cm
20 cm multilayer plastic bag made of polyethyl-ene (PO2 = 4.18108 cm3⋅cm⋅cm2⋅s1⋅atm1) and PET (PO2 = 1.671010 cm3⋅cm⋅cm2⋅s1⋅ atm1) per second? The thickness of each plastic layer (PE and PET) is 0.1 cm, and the partial pres-sure of oxygen across the film is 0.21 atm.
PTcan be calculated from Equation 5.20:
and QTis
Example 3: Calculation of the Shelf Life of a Food Product Packaged in a Monolayer Film A food product becomes rancid when it absorbs 2.1 ml of O2. What is the shelf life of this product if it is packaged with LDPE (PO2 = 4.18108 cm3⋅cm⋅
cm2⋅s1⋅atm1)? What is the shelf life of the prod-uct if it is packaged with a PET film (PO2 = 1.671010cm3⋅cm⋅cm2⋅s1⋅atm1)? The surface area of the package is 400 cm2, and the package thickness is 0.1 cm. The partial pressure of oxygen across the package is 0.21 atm.
This problem can be solved using Equation 5.14:
The t in Equation 5.14 is the shelf life of the prod-uct (ts) for this example. Equation 5.14 can be rewritten as
For LDPE:
Thus, LDPE will not provide the needed O2 bar-rier properties for this product.
For PET:
Thus, PET will provide a much better shelf life for this product than LDPE.
USES OFTHERMOPLASTICS FORFOOD
PACKAGING
Types of thermoplastics used in food packaging in-clude polyolefins (polyethylenes, polypropylene), substituted olefins (polystyrene, polyvinyl alcohol,
t
5 Food Packaging 119
polyvinyl chloride, polyvinylidene chloride, polyte-trafluoroethylene), copolymers of ethylene (ethylene-vinyl acetate, ethylene-(ethylene-vinyl alcohol), polyesters (polyethylene terephthalate), polycarbonates; poly-amides (nylons), and acrylonitriles (styrenes) (Ro-bertson 1993). The chemical composition of each thermoplastic will influence its performance in pro-cessing, forming, and use of packages as well as its performance and interactions with a variety of foods. Therefore, specific food applications gener-ally use select thermoplastics that will function well in the parameters of the application. When an indi-vidual thermoplastic cannot provide all the func-tions necessary or is too expensive for a certain product, a laminate system is often used. A laminate
polyvinyl chloride, polyvinylidene chloride, polyte-trafluoroethylene), copolymers of ethylene (ethylene-vinyl acetate, ethylene-(ethylene-vinyl alcohol), polyesters (polyethylene terephthalate), polycarbonates; poly-amides (nylons), and acrylonitriles (styrenes) (Ro-bertson 1993). The chemical composition of each thermoplastic will influence its performance in pro-cessing, forming, and use of packages as well as its performance and interactions with a variety of foods. Therefore, specific food applications gener-ally use select thermoplastics that will function well in the parameters of the application. When an indi-vidual thermoplastic cannot provide all the func-tions necessary or is too expensive for a certain product, a laminate system is often used. A laminate