Predicting the Permeability and Tensile Properties of Multilayer Films
from the Properties of the Individual Component Layers
Chi-Hsien HUANG, Jiann-Shing WU, and Chun-Chin HUANG;y
Department of Applied Chemistry, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan, R.O.C. Department of Mold and Die Engineering, National Kaohsiung University of Applied Science, Kaohsiung 807, Taiwan, R.O.C.
(Received October 10, 2003; Accepted February 7, 2004; Published May 15, 2004)
ABSTRACT: We have fabricated typical three-layer ﬁlms (A/B/C multilayer structures), comprising polyamide-6 (PA-6), low-density polyethylene (LDPE), and adhesive (low-density ethylene grafted with maleic anhydride, LDPE-g-MAH), by a coextrusion blown-ﬁlm process using various compositions of the three layers. With the goal of predicting the permeability and tensile properties of the three-layer ﬁlms, we examined model predictions and the properties of the individual component layers to provide an economical and eﬃcient pathway to designing desired multilayer structures. We used the series model for predicting permeability; a good agreement exists between experimental data and this model for predicting both gas and water vapor permeabilities of three-layer ﬁlms having various contents of PA-6. By using the additive rule model, we can also predict the tensile properties, including the true yield stress, strain hard-ening parameter, and tensile modulus of the three-layer ﬁlm from those of the individual component layers, with par-ticularly high accuracy in the true stress–strain relationship. [DOI 10.1295/polymj.36.386]
KEY WORDS Coextrusion / Multilayer / Permeability / Plastic Deformation / Strain Hardening / Tensile Property /
Coextrusion is a process in which two or more polymers are extruded simultaneously and joined to-gether to form a single structure having diﬀerent prop-erties in each layer. This process is used to achieve a broad range of properties in the ﬁnal material that are not available in any of the individual materials alone. Coextrusion has become an attractive and economical method to fabricate, for example, multilayer sheets, blown ﬁlms, cast ﬁlms, tubing, and containers.1–4
The choice of component materials depends on the quired end-use applications. The most important re-quirements for such ﬁlms are their permeability prop-erties and mechanical strengths.
Low-density polyethylene (LDPE) and polyamide 6 (PA-6) are two important classes of polymers used in coextrusion that are very popular in the packaging in-dustry. LDPE is employed widely because of its low cost, high barrier properties toward moisture, good op-tical properties, and ease of processing,5–7but its poor barrier property toward oxygen and many organic sol-vents limits its applicability.8,9 On the other hand, PA is a good barrier resin toward oxygen, aromas, and or-ganic solvents and it has high tensile strength, but is relatively expensive and a poor barrier for water va-por.10–13It is possible to combine these two resins into
a single structure by using a coextrusion process to form multilayer sheets, ﬁlms, or containers possessing a multitude of properties. Because of the chemical dis-similarities between these two resins, however, an
ex-trudable adhesive is often incorporated into the struc-ture as a tie layer that holds the two resins together. By combining graft and polymer blending, Tanaka et al.14have successfully developed a new generation
of tie layer adhesives that maintain high adhesive strengths after thermoforming and orientation. Bo-tros15 studied three-layer ﬁlms (tie/EVOH/tie) using a coextrusion cast-ﬁlm process and found that the tie layers bind to EVOH through covalent and hydrogen bonding. Kamykowski16 studied the adhesive proper-ties of ﬁve-layer coextruded cast ﬁlms and found that adhesion generally can be improved upon increasing the overall ﬁlm thickness or the relative amount of the adhesive. The molecular weight of the grafted res-in has a small aﬀect on adhesion. Homopolymer di-luents outperform random copolymers with respect to their adhesion properties. Because of the incorpora-tion of the tie layer, the single structure comprises a typical three-layer A/B/C conﬁguration (LDPE/tie/ PA-6) with multiple properties arising from the indi-vidual component layers.
Previous reports have described the properties, such as permeability and tensile strength, of monolayer ma-terials, such as LDPE and PA-6.12,17–21With the goal of designing a method for eﬀectively predicting the speciﬁc properties of a multilayer structure from the properties of its individual component materials, in this paper we examine the permeabilities, including those toward gas and water vapor, and tensile
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ties of three-layer ﬁlms fabricated by a coextruded blown-ﬁlm process using the series model22 and the
additive rule23 as predicting methods, respectively. These models are economical and eﬃcient tools for designing multilayer sheets, ﬁlms, and containers to be prepared by coextrusion processes.
Commercial-grade low-density polyethylene [LDPE; 6030 F; M.I. (g/10 min, 190C, 2.16 kg) = 0.27; density = 0.922 g/cm3] was supplied in pellet form by Formosa Plastic Corp. (Taiwan). The poly-amide-6 (PA-6; Novamid 1030; M.I. (g/10 min, 240C, 2.16 kg) = 5; density = 1.14 g/cm3) was
pro-vided in pellet form by Mitsubishi Engineering-Plas-tics Corp. (Japan). The adhesive, Modic-AP L502, which was obtained in pellet form from Mitsubishi Chemical Corp. (Japan), is a low-density polyethyl-ene-grafted maleic anhydride [LDPE-g-MAH; M.I. (g/10 min, 190C, 2.16 kg) = 1.0; density = 0.93 g/
Preparation of Multilayer Films
Prior to processing, PA-6 was dried in a vacuum oven for a period of 12 h at 90C. PA-6, LDPE, and
LDPE-g-MAH were coextruded through a three-layer coextrusion blown-ﬁlm die (inner diameter = 97.6 mm; gap thickness = 1.2 mm) at 250C. Above the
exit of the die, the three-layer ﬁlm was inﬂated and cooled with air and stretched by a take-up device. Monolayers of PA-6 and LDPE ﬁlms were also fabri-cated using the same blown-ﬁlm apparatus. Before measuring their permeability and tensile behavior, all samples were placed for 14 d in cabinet maintained at 25C with a relative humidity of 50%. The overall
thickness of three-layer multilayered ﬁlms was ca. 200mm. Because the tie layer generally was very thin (ca. 5mm in this study) during the coextrusion proc-ess, and the main molecular structure was LDPE, we consider the tie layer to be part of the LDPE layer and neglect its eﬀect on permeability and tensile be-havior. Table I presents the thicknesses and volume
fractions of the PA-6 layers; we controlled these com-positions using gear pumps.
Measuring Gas Permeability
The gas permeability, including that toward oxygen (O2), nitrogen (N2), and carbon dioxide (CO2), was
measured using a Lyssy L-100-5000 Gas Permeability Tester,24 following the ASTM Standard Method D1434. The gas permeability of the samples was measured at 23C and at a relative humidity of 0%. The temperature was controlled by a water bath. Measurements were taken on 5 replicate samples; average values are reported.
Measuring Water Vapor Permeability
Water vapor permeability was measured using a Lyssy L-80-5000 Water Vapor Permeability Tester,25 following the ASTM Standard Method E96. The per-meability of the samples was measured at 38C and at a relative humidity of 90%. The temperature was con-trolled by a water bath. Measurements were taken us-ing 5 replicate samples; average values are reported.
Measuring Tensile Behavior
We conducted uniaxial tensile measurements using a Hung-Ta Instrument 2102AP with test samples that were 20 mm wide and 20 mm long. Samples were test-ed with a crosshead spetest-ed of 20 mm/min at a temper-ature of 25C and a relative humidity of 50%. Engi-neering stress–strain curves were determined from load-extension data based on the geometry of the ini-tial specimen. Measurements were taken on 5 repli-cate samples; average values are reported.
RESULTS AND DISCUSSION
The gas permeabilities of PA-6 and LDPE ﬁlms, in-cluding those toward O2, N2, and CO2 as shown in
Figures 1–3. We see that the PA-6 ﬁlm has much bet-ter barrier properties than LDPE toward all these gas-es, with permeabilities for both ﬁlms increasing in the order CO2> N2> O2. In these ﬁgures, the gas
perme-abilities of three-layer ﬁlms as a function of the vol-ume fraction of the PA-6 layer. The values of gas per-meabilities all lie between those of the individual component layers for all the gases. As expected, the permeability toward all gases decreased upon increas-ing the volume fraction of the PA-6 layer. Because of the lamellar structure of the three-layer ﬁlms, we ap-plied a series model to predict the gas permeability of a three-layer ﬁlm from that of its individual compo-nent layers:22
Table I. Thickness and volume fraction of PA-6 layer in three-layer ﬁlms
Thickness of PA-6 layer Volume fraction of PA-6 layer
(mm) (%) 20 10 40 20 60 30 80 40 100 50
1 PM ¼ PA-6 PPA-6 þLDPE PLDPE ð1Þ
where PM is the permeability of the three-layer ﬁlm,
PPA-6 and PLDPE are the permeabilities of the
mono-layer ﬁlms of PA-6 and LDPE, respectively, and PA-6 and LDPE are the volume fractions of PA-6
and LDPE (including the tie layer) in the three-layer ﬁlm, respectively. Figures 1–3 also show the gas per-meabilities of three-layer ﬁlms toward O2, N2, and
CO2, respectively, for the series model. We can see
that a good agreement exists between the experimen-tal data and the model’s predictions for all these gases. Figure 4 shows the water vapor permeabilities of PA-6 and LDPE ﬁlms. In contrast to their gas barrier properties, we see that the LDPE ﬁlm has enhanced water vapor barrier properties relative to those of the PA-6 ﬁlm. The ﬁgure also presents the water vapor permeabilities of the three-layer ﬁlms as a function of the volume fraction of the PA-6 layer. Similarly to the gas permeabilities, the values of water vapor permea-bilities all lie between those of the individual compo-nent layers. For the sake of comparison, this ﬁgure al-so presents the predictions made by the model using Eq 1. The water vapor permeabilities increase upon increasing the PA-6 content and agree reasonably well with the series model.
Figure 5 displays the engineering stress–strain curves for the monolayer ﬁlms of PA-6 and LDPE. We see that the PA-6 ﬁlm exhibits a ductile mechan-ical behavior. Upon initial deformation of the ﬁlm sample, the engineering stress increases steadily with the engineering strain. As the engineering strain in-creases, the engineering stress almost remains con-stant and a so-called cold drawing takes place before
0 10 20 30 40 50 95100 2 4 6 8 10 12 14 series model experimental data
Volume fraction of PA-6 (%) O2
Figure 1. Oxygen (O2) permeabilities of three-layer ﬁlms as a function of volume fraction of PA-6 layer.
0 10 20 30 40 50 95100 0 5 10 15 20 25 30 35 40 45 series model experimental data
Volume fraction of PA-6 (%)
CO 2 Permeability (ml-mm/m 2 -day-atm) PA-6 LDPE
Figure 3. Carbon dioxide (CO2) permeabilities of three-layer ﬁlms as a function of volume fraction of PA-6 layer.
0 10 20 30 40 50 95100 0 2 4 6 8 10 12 14 16 18 1000 1200 LDPE PA-6 series model experimental data
Volume fraction of PA-6 (%)
Water vapor permeability x10
2 (g-mm/m 2 -24hr)
Figure 4. Water vapor permeabilities of three-layer ﬁlms as a function of volume fraction of PA-6 layer.
0 10 20 30 40 50 95100 0 1 2 3 4 series model experimental data
Volume fraction of PA-6 (%) N2
Figure 2. Nitrogen (N2) permeabilities of three-layer ﬁlms as a function of volume fraction of PA-6 layer.
the engineering strain becomes 1. After the value of strain, the engineering stress increases with the in-crease of engineering strain due to the molecular alignment;26 this eﬀect is known as strain hardening. On the other hand, the LDPE ﬁlm exhibits a lower level of engineering stress and deforms in a manner that is characteristic of a rubbery material by its con-tinuous increase of engineering stress with increasing strain.
We calculated the engineering stress and strain by considering the original geometry of the sample ﬁlms, but, in fact, the cross-sectional area of a ﬁlm sample changed continuously during deformation. The engi-neering stress and strain cannot represent the actual stress and strain at any one instance. It is necessary and more instructive to plot the true stress–strain curves to describe the tensile behavior. Because the deformation behavior of both the PA-6 and LDPE ﬁlms were homogeneous, as presented in Figure 5, and a constant volume was assumed during deforma-tion, the true strain, "T, and the true stress, T, were
"T¼lnð1 þ "EÞ ð2Þ
T¼Eð1 þ "EÞ ð3Þ
where "Eand Eare the engineering strain and the
en-gineering stress, respectively.17,27 Figure 6 displays the true stress–strain curves of the PA-6 and LDPE ﬁlms as calculated using Eqs 2 and 3.
To model the deformation behavior of ﬁlm, we in-troduced the following empirical constitutive equa-tion:17,28
¼ 0expð"TÞ ð4Þ
where 0and are the true yield stress and the strain
hardening parameter, respectively. The constitutive equation can also be presented in the following form:
ln ¼ ln 0þ"T ð5Þ
The plot of the natural logarithm of true stress (ln ) vs. true strain ("T) should be linear in the region of
plastic deformation. The intercept and slope of the least-squares approximation correspond to the natural logarithm of the true yield stress (ln 0) and the strain
hardening parameter (), respectively. Figure 7 pres-ents the experimental data and ﬁtted curves of the nat-ural logarithm of the true stress versus true strain for the PA-6 and LDPE ﬁlms. A linear relationship ap-pears to exist over the range of true strains from 0.3 to 1.6 where correlation coeﬃcients are all > 0.98 with respect to the approximation. The parameters of the constitutive equation for the PA-6 and LDPE ﬁlms are summarized in Table II. Figure 8 displays a comparison of the experimental true stress–strain data and the modeling curves. A good correlation ex-ists between the experimental data and the modeling curves for the plastic deformation of the PA-6 and
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 50 100 150 200 250 PA-6 LDPE True Strain
True Stress (MPa)
Figure 6. True stress–strain curves of PA-6 and LDPE ﬁlms.
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 1 2 3 4 5 6 7 PA-6 LDPE True Strain Ln True Stress
Figure 7. Modeling of Ln true stress–strain of PA-6 and LDPE ﬁlms. 0 1 3 4 0 10 20 30 40 50 60 PA-6 LDPE Engineering Strain
Engineering Stress (MPa)
Figure 5. Engineering stress–strain curves of PA-6 and LDPE ﬁlms.
LDPE ﬁlms. It is obvious that the model is only ap-propriate within the plastic deformation range.
Figure 9 presents a plot of the engineering and true stress–strain curves of three-layer ﬁlms with respect to various compositions of PA-6. It is clear that these curves lie between those obtained for monolayers of PA-6 and LDPE. The stress level increases upon in-creasing the volume fraction of the PA-6 layer and, in addition, the strain hardening behavior becomes more obvious. In the range of volume fractions of PA-6 that we investigated, all the three-layer ﬁlms de-form homogeneously. As Figure 11 indicates, a linear relationship also appears to exist for the three-layer ﬁlms over the same range of true strains (0.3–1.6) as it did for the PA-6 and LDPE ﬁlms. The correlation coeﬃcients are also all > 0.98 with respect to the ap-proximation. The corresponding parameters of the constitutive equation for the three-layer ﬁlms with various volume fraction of PA-6 are presented in Table II. The values of these parameters, including the true yield stress and strain hardening parameters, also lie between those of the individual component layers. Figure 11 displays a comparison of the exper-imental true stress–strain data and the modeling curves. A good correlation also exists between the ex-Table II. True yield stress (0) and strain hardening parameter
() of LDPE, PA-6 and three-layer ﬁlms Volume fraction of PA-6 layer 0
(%) (MPa) 0 (LDPE) 9.49 1.27 10 10.05 1.31 20 10.66 1.41 30 11.72 1.42 40 12.00 1.48 50 12.61 1.51 100 (PA-6) 16.44 1.60 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 50 100 150 200 250 PA-6 LDPE Line: modeling curves Symbol: experimental data
True Stress (MPa)
Figure 8. Comparison of true stress–strain curves between modeling curves and experimental data of PA-6 and LDPE ﬁlms.
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.0 2 3 4 5 50% 40% 30% 20% 10% Line: modeling curves Symbol: experimental data
Ln True stress
Figure 10. Modeling of Ln true stress–strain of three-layer ﬁlms as a function of volume fraction of PA-6 layer.
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0 5 10 15 20 25 30 35 40 45 50 55 LDPE PA-6 50% 40% 30% 20% 10% Engineering Strain
Engineering Stress (MPa)
(a) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 20 40 60 80 100 120 140 160 180 200 220 240 260 LDPE PA-6 50% 40% 30% 20% 10% True Strain
True Stress (MPa)
Figure 9. Stress–strain curves of three-layer ﬁlms as a func-tion of volume fracfunc-tion of PA-6 layer. Thick solid lines represent the component layer of PA-6 and LDPE, respectively. (a) Engi-neering; (b) True.
perimental data and the modeling curves for the plas-tic deformation of the three-layer ﬁlms having various volume fractions of PA-6.
Similar to what we reported above for predicting permeability, we used a simple theoretical additive rule model23 to predict the tensile behavior of a
three-layer ﬁlm from those of its individual compo-nent layers:
M ¼PA-6PA-6þLDPELDPE ð6Þ
where Mis the true stress of a three-layer ﬁlm, PA-6
and LDPEare the true stresses of the PA-6 and LDPE
layers, respectively, and PA-6 and LDPE are the
vol-ume fractions of PA-6 and LDPE (including the tie layer) layers, respectively.
From Eqs 4 and 6, the relationship between the true stress–strain of the three-layer and individual compo-nent layer ﬁlms is:
ð7Þ where 0M is the true yield stress of the three-layer
ﬁlm, 0PA-6 and 0LDPE are the true yield stresses of
the PA-6 and LDPE layers, respectively, and M,
PA-6, and LDPE are the strain hardening parameters
of the three-layer ﬁlm, PA-6, and LDPE layers, re-spectively. It is reasonable to believe that the true yield stress of the three-layer ﬁlm alone follows the additive rule:
and the strain hardening parameter of the three-layer ﬁlm is deﬁned as:29
@ ln M
¼@½PA-60PA-6expðPA-6"Þ þ LDPE0LDPEexpðLDPE"Þ @"
We calculated the parameters 0M and M for the
ad-ditive rule by using the parameters of the individual component layers in Table II. Figure 12 presents the dependence of these parameters obtained by additive rule and the experimental data (from Table II) with re-spect to the ﬁlms’ compositions. The good agreement existing between the experimental data and the addi-tive-rule model suggests that this rule can be used to accurately predict the plastic deformation of the three-layer ﬁlms.
As we mentioned above, the constitutive equation is only valid in large-strain plastic deformation. In small-strain deformation, modulus is the most impor-tant mechanical property. Thus, we also examined the validity of the additive rule with respect to the modu-lus. Table III lists the tensile modulus of the individ-ual component layers of PA-6 and LDPE. We see that the PA-6 ﬁlm performance is stiﬀer and more rigid than that of LDPE. The tensile moduli of three-layer ﬁlms are also presented in Table III. The tensile mod-ulus increases upon increasing the PA-6 content. The
model of the additive rule can be stated as follows: MM¼PA-6MPA-6þLDPEMLDPE ð10Þ
where MM is the tensile modulus of the three-layer
ﬁlm, and MPA-6 and MLDPE are the tensile moduli of
the PA-6 and LDPE layers, respectively. Figure 13 provides a comparison between the moduli obtained by the additive rule and the experimental data (from
Table III. Tensile moduli of LDPE, PA-6 and three-layer ﬁlms
Volume fraction of PA-6 Tensile modulus
(%) (MPa) 0 (LDPE) 111.52 10 129.04 20 154.08 30 162.03 40 194.57 50 209.56 100 (PA-6) 297.21 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 20 40 60 80 100 120 140 160 180 50% 40% 30% 20% 10% Line: modeling curves Symbol: experimental data
True Stress (MPa)
Figure 11. Comparison of true stress–strain curves between modeling curves and experimental data of three-layer ﬁlms as a function of volume fraction of PA-6 layer.
Table III). A good agreement also exists between these systems with regard to their tensile moduli.
We have successfully fabricated three-layer ﬁlms, which are typical multilayer structure A/B/C ﬁlms, by a coextruded blown-ﬁlm process. We have investi-gated the permeabilities, including those toward three gases and water vapor, and tensile behaviors of mon-olayers of PA-6 and LDPE and their multilayer ﬁlms. We examined the relationships between the properties of the monolayers of the component materials and those of the three-layer ﬁlms by predictions using a series model and an additive rule to obtain the perme-abilities and tensile behaviors, respectively. We found that predicting the gas permeability, with respect to O2, N2, and CO2, of the three-layer ﬁlms based upon
those of the individual component layer ﬁlms occurs
in good agreement with the experimental data when using the series model. This model is also useful for predicting the water vapor permeability with respect to the volume fraction of PA-6. The tensile behavior of the component-layer and multilayer ﬁlms can be expressed by a constitutive equation having two pa-rameters in the true stress–strain relationship, i.e., the true yield stress and the strain hardening parame-ter. We can also predict the tensile properties—in-cluding the true yield stress, strain hardening, and ten-sile modulus—of the three-layer ﬁlm from those of the individual component layers with good agree-ments in the true stress–strain relationship by using the additive rule.
As mentioned above, these model predictions pro-vide an economical and eﬃcient tool for designing multilayer structures, formed by a coextrusion proc-ess, that possess speciﬁc permeability and/or tensile properties.
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