Predicting the permeability and tensile properties of multilayer films from the properties of the individual component layers

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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

proper-y

To whom correspondence should be addressed (Tel: +886-7-3814526 ext 5418, Fax: +886-7-3835015, E-mail: chhuang.ac87g@nctu.edu.tw, cchuang@cc.kuas.edu.tw).

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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.

EXPERIMENTAL

Materials

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/

cm3].

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

Permeability

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

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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.

Tensile Behavior

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

Permeability (ml-mm/m

2 -day-atm)

PA-6 LDPE

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

Permeability (ml-mm/m

2-day-atm)

PA-6 LDPE

Figure 2. Nitrogen (N2) permeabilities of three-layer films as a function of volume fraction of PA-6 layer.

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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

calculated by

"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)

2

Figure 5. Engineering stress–strain curves of PA-6 and LDPE films.

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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 Strain

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

True Strain

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)

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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.

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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:

0MexpðM



"TÞ ¼PA-60PA-6expðPA-6



"TÞ

þLDPE0LDPEexpðLDPE



"TÞ

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:

0M¼PA-60PA-6þLDPE0LDPE ð8Þ

and the strain hardening parameter of the three-layer film is defined as:29

Mð"Þ ¼

@ ln M

@"

¼@½PA-60PA-6expðPA-6



"Þ þ LDPE0LDPEexpðLDPE



"Þ @"

ð9Þ

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 Strain

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.

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Table III). A good agreement also exists between these systems with regard to their tensile moduli.

CONCLUSIONS

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.

REFERENCES

1. J. K. Rogers, Mod. Plast., 67, 46 (1990).

2. S. Hosoda, Y. Seki, and H. Kihara, Polymer, 34, 4602 (1993).

3. J. Culter, J. Krohn, and W. Todd, Packag. Tech. Eng., 8, 30 (1999).

4. S. J. Liu and C. H. Yang, Adv. Polym. Technol., 20, 108 (2001).

5. G. L. Wooddell, Tappi Notes, 1986, 21.

6. M. S. Pucci and R. N. Shroff, Polym. Eng. Sci., 26, 569 (1986).

7. J. F. Graham, M. Predrag, and N. B. Sati, Polym. Int., 48, 461 (1999).

8. S. A. Jabarin and W. J. Kollen, Polym. Eng. Sci., 25, 1156 (1988).

9. P. M. Subramanian, Polym. Prepr., 30, 28 (1989). 10. D. C. Climenhage, Packaging, 32, 39 (1987). 0 10 20 30 40 50 95100 0.0 8 9 10 11 12 13 14 15 16 17 LDPE PA-6 additive rule experimental data

Volume fraction of PA-6 (%)

True yield stress (MPa)

(a) 0 10 20 30 40 50 95100 0.0 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 LDPE PA-6 additive rule experimental data

Volume fraction of PA-6 (%)

Strain hardening parameter

(b)

Figure 12. Comparison of mechanical parameter between ad-ditive rule and experimental data as a function of PA-6 content. (a) The true yield stress; (b) the strain hardening parameter.

0 10 20 30 40 50 95100 0.0 100 120 140 160 180 200 220 240 260 280 300 320 LDPE PA-6 additive rula experimental data

Volume fraction of PA-6 (%)

Tensile Modulus (MPa)

Figure 13. Comparison of tensile modulus between additive rule and experimental data as a function of PA-6 content.

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11. S. Eichler and J. Miltz, J. Appl. Polym. Sci., 50, 2095 (1993). 12. Y. P. Khanna, E. D. Day, M. L. Tsai, and G. Vaidyanathan,

J. Plast. Film Sheet., 13, 197 (1997).

13. M. Eldridge, J. Wanger, and R. John, J. Plast. Film Sheet., 17, 221 (2001).

14. H. Tanaka, H. Shigemoto, and H. Kawchi, J. Plast. Film Sheet., 12, 279 (1996).

15. M. G. Botros, J. Plast. Film Sheet., 12, 195 (1996). 16. G. W. Kamykowski, J. Plast. Film Sheet., 16, 237 (2000). 17. S. Bahadur, Polym. Eng. Sci., 13, 266 (1973).

18. Y. Wang, A. J. Easteal, and X. D. Chen, Packag. Tech. Sci., 11, 169 (1998).

19. S. Y. Lee and S. C. Kim, Polym. Eng. Sci., 37, 463 (1997). 20. S. Bianchi, S. Cantagallo, G. Consolati, M. Laporta, M. Pegoraro, G. Tieghi, and L. Zanderighi, J. Appl. Polym. Sci., 86, 559 (2002).

21. G. F. Akbar, J. Plast. Film Sheet., 15, 194 (1999). 22. J. B. Faisant, A. Aı¨t-Kadi, M. Bousmina, and L. Descheˆnes,

Polymer, 39, 533 (1998).

23. W. J. Schrenk and T. Alfrey, Polym. Eng. Sci., 9, 393 (1969).

24. Automatic Manometric Gas Permeability Tester Operator Manual, Model L100-5000, Lyssy AG (2001).

25. Automatic Manometric Water Vapor Permeability Tester Operator Manual, Model L80-5000, Lyssy AG (2001). 26. A. Peterlin, J. Mater. Sci., 6, 490 (1971).

27. M. Al-Hussein and G. Strobl, Macromolecules, 35, 8515 (2002).

28. V. Gaucher-Miri, G. K. Jones, R. Kaas, A. Hiltner, and E. Baer, J. Mater. Sci., 37, 2635 (2002).

數據

Table I. Thickness and volume fraction of PA-6 layer in three-layer films

Table I.

Thickness and volume fraction of PA-6 layer in three-layer films p.2
Figure 1. Oxygen (O2) permeabilities of three-layer films as a function of volume fraction of PA-6 layer.

Figure 1.

Oxygen (O2) permeabilities of three-layer films as a function of volume fraction of PA-6 layer. p.3
Figure 4. Water vapor permeabilities of three-layer films as a function of volume fraction of PA-6 layer.

Figure 4.

Water vapor permeabilities of three-layer films as a function of volume fraction of PA-6 layer. p.3
Figure 3. Carbon dioxide (CO2) permeabilities of three-layer films as a function of volume fraction of PA-6 layer.

Figure 3.

Carbon dioxide (CO2) permeabilities of three-layer films as a function of volume fraction of PA-6 layer. p.3
Figure 5 displays the engineering stress–strain curves for the monolayer films of PA-6 and LDPE

Figure 5

displays the engineering stress–strain curves for the monolayer films of PA-6 and LDPE p.3
Figure 7. Modeling of Ln true stress–strain of PA-6 and LDPE films.01340102030405060PA-6LDPEEngineering Strain

Figure 7.

Modeling of Ln true stress–strain of PA-6 and LDPE films.01340102030405060PA-6LDPEEngineering Strain p.4
Figure 6. True stress–strain curves of PA-6 and LDPE films.

Figure 6.

True stress–strain curves of PA-6 and LDPE films. p.4
Figure 5. Engineering stress–strain curves of PA-6 and LDPE films.

Figure 5.

Engineering stress–strain curves of PA-6 and LDPE films. p.4
Figure 10. Modeling of Ln true stress–strain of three-layer films as a function of volume fraction of PA-6 layer.

Figure 10.

Modeling of Ln true stress–strain of three-layer films as a function of volume fraction of PA-6 layer. p.5
Figure 8. Comparison of true stress–strain curves between modeling curves and experimental data of PA-6 and LDPE films.

Figure 8.

Comparison of true stress–strain curves between modeling curves and experimental data of PA-6 and LDPE films. p.5
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

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 p.5
Table III. Tensile moduli of LDPE, PA-6 and three-layer films

Table III.

Tensile moduli of LDPE, PA-6 and three-layer films p.6
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.

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. p.6
Table III). A good agreement also exists between these systems with regard to their tensile moduli.

Table III).

A good agreement also exists between these systems with regard to their tensile moduli. p.7
Figure 12. Comparison of mechanical parameter between ad- ad-ditive rule and experimental data as a function of PA-6 content

Figure 12.

Comparison of mechanical parameter between ad- ad-ditive rule and experimental data as a function of PA-6 content p.7

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