f (1) A Model for Permeability Reduction in Polymer Nanocomposites

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1 A Model for Permeability Reduction in Polymer Nanocomposites Man Chio Tang 1, Sushant Agarwal 1, Fares D. Alsewailem 2, Hyoung J. Choi 3 and Rakesh K. Gupta 1 1 Department of Chemical and Biomedical Engineering, West Virginia University, Morgantown, WV King Abdulaziz City of Science and Technology, Riyadh, Saudi Arabia 3 Department of Polymer Science and Engineering, Inha University, Incheon , Korea Abstract A simple theory that builds on the tortuous path concept is developed to quantitatively predict mass transport through a polymer containing dispersed nanoplatelets, and data are presented on polylactic acid (PLA)-matrix nanocomposites. PLA is a bioderived biodegradable polymer that is being employed in food packaging where the plastic is discarded after a single use. However, the poor water vapor barrier property of PLA limits its use in this regard, and it is of interest to reduce moisture permeability through this polymer. In the present work, Cloisite 30B, an organoclay that is compatible with PLA, was dispersed in the polymer via melt-mixing, and processing conditions were optimized to reduce platelet agglomeration. Nanocomposite morphology was characterized with transmission electron microscopy, and moisture permeability was measured as a function of clay content. There was good agreement with the proposed theory, and it was found that at a 5.3 vol% filler loading the water vapor permeability was reduced by almost 70%. Introduction Polymers are widely used as packaging materials. Most of them are typically derived from crude oil which is not a renewable resource. Also, the polymers are, in general, neither biodegradable nor compostable. Moreover, these non-degradable packaging materials are usually discarded after a single-use, and they end up in landfills as solid waste. As a consequence, concerns over pollution and sustainability have led to enormous scientific investigations on bio-derived and biodegradable polymers such as polylactic acid (PLA). PLA has been considered as a good substitute for conventional synthetic non-biodegradable polymers because it has high strength, excellent transparency, and good processability when compared to conventional polymers. 1-5 However, low gas barrier properties limit the applications of PLA as a packaging material. An efficient way to enhance PLA barrier properties is through the incorporation of nanoplatelets such as nanoclays into the PLA matrix. Here, it is helpful to have a theory that predicts the improvement in diffusivity and permeability as a function of filler content and filler aspect ratio. Proposed Theory One of the earliest theories is due to Nielsen 6 who calculated the increase in path length experienced by a diffusing molecule as it follows a tortuous path around the dispersed barriers. This concept is illustrated in Figure 1. A consequence of the increased path length, in the absence of any change in the imposed concentration difference, is a reduction in both the concentration gradient and the mass flux. In terms of Fick s law of diffusion, then, it appears as if the diffusion coefficient D has decreased if the concentration gradient is assumed to remain at its original value. For gas transport, there is a corresponding proportionate reduction in the permeability. This is a purely geometric effect and its magnitude was calculated by Nielsen for barriers having a volume fraction f, thickness t and width h (see Figure 1). The quantity h/t is generally known as the barrier aspect ratio. The estimated value of D, based on Nielsen s model, is given by 6 :! "! = 1 + & '( f (1) where D 0 is the diffusivity in the absence of any barriers, and a small correction related to the change in polymer volume fraction has been neglected. SPE ANTEC Anaheim 2017 / 704

2 The presence of barriers has one additional major effect besides the increase in path length. This is a reduction in the area for mass transfer. As a practical matter, one is interested in the rate of mass transport through a polymer film rather than just the flux of the diffusing species. Since the rate of mass transport is the product of the flux with the area for mass transfer, it is essential to compute the latter quantity as well. This has been done using a variety of models by Cussler and co-workers Using one of the proposed models, the effective diffusivity is predicted to be given by 7-10 :! " = 1 + (! +, - )/ f / 0(12f) (2) where h is defined in Figure 1, and it exceeds h, in general. However, h approaches h as the filler concentration increases. It is seen that Cussler s theory has the diffusivity depending more strongly on both the aspect ratio and the filler volume fraction. It has been our experience that, while Eq 2 is able to represent experimental data, it does so with a value of the aspect ratio that is different from the one revealed by TEM pictures. In view of this, we propose a new model that is based on Nielsen s ideas 6, and this is illustrated in Figure 2. From an examination of Figure 2, it must be clear that if the path length doubles, the area for mass transfer must be reduced by a factor of 2. It the path length increases by a factor of 3, the area for mass transfer must reduce by a factor of 3. In general, then, if the path length increase by a factor of (1 + (hφ)/2t), the area for mass transfer must reduce by the same factor. As a consequence, it must be true that:! "! = (1 + & '( f)' (3) where D 0 is again the diffusivity through the polymer without nanoplatelets, and D is the diffusivity through the polymer in the presence of nanoplatelets. Eq 3 is the final result of the proposed model, and it is subjected to quantitative testing in the work described in the rest of this manuscript. More details are given in the dissertation 11. Experimental Details Materials Polylactic acid PLA 6752D was provided by NatureWorks LLC (Minnetonka, MN). The nanoclay used in this study was Cloisite 30B from Southern Clay Products (Austin, TX). Cloisite 30B is a natural montmorillonite modified with a quaternary ammonium salt. In this nanoclay, the organic and inorganic fractions were determined to be 20.2% and 79.8%, respectively by TGA measurements. PLA Nanocomposites Preparation All the materials used in this work were dried (90 C in an oven for 4h) before use. The desired concentrations of Cloisite 30B (inorganic content) and PLA were mixed in a Haake Polydrive internal mixer at C and 80 rpm for 5 min. These process conditions were determined after extensive experimentation. Unfilled PLA was also meltprocessed under the same conditions to prepare a reference material. The PLA nanocomposite was then compression molded into 0.5 mm-thick films at C and 10 ton load for 5 min. Measurement of Water Vapor Permeability Before being used, the PLA film was dried in a desiccator for 7 days. The water vapor barrier property of the film was determined using a PERMATRAN W3/33 instrument purchased from MOCON (Minneapolis, MN) which measures the water transmission rate across the film. Prior to sample testing, the test cell was flushed with nitrogen to remove any moisture. Once a low transmission rate was obtained, the film was placed into the test cell of the machine. 100% relative humidity was applied by placing a sponge soaked with HPLC grade water. The temperature was set at 25 o C.When steady state was reached, the permeability was calculated from the steady water vapor transmission rate. Measurement of Water Vapor Solubility Besides directly measuring the permeability, the solubility of moisture in the nanocomposite was determined independently. In a solubility experiment, the initial weight of a dried sample is measured. Then the sample is placed in an environmental chamber at the desired temperature and relative humidity (RH). The weight of the sample is measured on a regular basis until it reaches equilibrium. Since the volume of one mole of any gas is L at STP, the equilibrium moisture concentration in the sample C eq in units of cc of water vapor at STP per cc of sample is calculated by the following equation 12 : C 45 = (626 ")'' " (4) where W is the weight in grams of the polymer containing absorbed water at equilibrium, W 0 is the SPE ANTEC Anaheim 2017 / 705

3 weight in grams of the dried polymer, and ρ is the density of PLA nanocomposite which is about the same as PLA (1.2 g/cm 3 ). The gas solubility can then be obtained from the following equation: S = : ;< =.8=?@ (5) where S is the solubility of water vapor in units of (kg/pa/m 3 ), C eq is the previously determined equilibrium concentration of moisture in the polymer, and p is the saturated water vapor pressure measured in Pa. All the values reported here are the average of measurements on at least 3 samples. The diffusivity can then be obtained by dividing the permeability by the solubility. Transmission Electron Microscopy The dispersion of Cloistie 30B organoclay in the polymer was examined by a Phillips CM200 Transmission Electron Microscope (TEM). A cryoultramicrotome was used to prepare thin samples. Results and Discussion Figure 3 shows the water vapor permeability through PLA and PLA containing Cloisite 30B. As expected, the permeability decreased with the incorporation of Cloisite 30B due to the tortuous effect created by the dispersed Cloisite 30B nanoplatelets. These nanoplatelets acted as impermeable barriers and forced the diffusing water molecule to travel a longer path in the PLA matrix. For PLA and PLA containing 5.3 vol% of Cloisite 30B, the permeabilities were 1.58±0.03 and 0.49± kg/(m Pa s) respectively. Thus, at the highest clay concentration, moisture permeability was reduced by 69% compared to neat PLA. This makes the moisture permeability in the nanocomposite be similar to the value of moisture permeability in PET 13, a polymer used commonly for packaging applications. It is also seen that there is a linear relationship between permeability reduction and clay concentration except at the highest loading level. This is most likely due to agglomeration of Cloisite 30B in the PLA matrix. Transmission electron microscopy was used to investigate the dispersion state of Cloisite 30B in the PLA matrix and also to determine the filler aspect ratio. The TEM images of PLA containing different amounts of Cloisite 30B are presented in Figures 4 (a)- (d). A representative region was chosen for each of the samples. At the same magnification, it is clear that there are more nanoplatelets available as barriers when the loading of Cloisite 30B is increased. These pictures indicate that the clay platelets are reasonably well dispersed and randomly oriented in the PLA matrix. The clay platelets form both intercalated and exfoliated structures in the PLA matrix. However, as the loading of Cloisite 30B is increased, there are more intercalated structures and even some aggregated structures present. The average aspect ratio of the platelets as measured from these pictures is Figure 5 shows the water vapor solubility through PLA and PLA containing Cloisite 30B. The incorporation of Cloisite 30B increased the solubility because the nanoclay was relatively hydrophilic and could attract water molecules when exposed to a humid environment. For PLA and PLA containing 5.3 vol% of Cloisite 30B, the solubilities were 2.70±0.05 and 4.5± kg/(pa m 3 ) respectively. The solubility in PLA containing 5.3 vol% of Cloisite 30B increased by 67% as compared to neat PLA. On the other hand, the solubility and the loading showed a linear relationship for up to 2.6 vol% of Cloisite 30B. This was a direct result of the increase in clay surface area available for moisture absorption and not because of an increase in water concentration in the polymer itself. However, the solubility increased less than linearly when the loading reached 5.3 vol% because of filler agglomeration at the high loading. To quantify and confirm this effect, let us consider unit volume of the nanocomposite. The moisture contained in this unit volume is c N, and this is the sum of the moisture on the clay surface and the moisture dissolved in the polymer. Thus, c BCDE = c F c HIJ (1 φ) (6) where c clay is the moisture on the clay surface, c PLA is the equilibrium water vapor concentration per unit volume of unfilled PLA, and f is the volume fraction of Cloisite 30B. Using Eq. (6), the mass of water absorbed on the clay surface per unit volume of the nanocomposite as a function of clay content is plotted in Figure 6. As the loading of nanoclay increased, the clay surface increased and so did the amount of moisture absorbed on the surface. Indeed, there was a linear relationship between the moisture absorbed by the clay and the amount of clay added except at 5.3 vol% of Cloisite 30B. At this concentration, there was some filler agglomeration and the lowered surface area results in less than expected absorption of moisture. This was confirmed by the TEM images shown earlier in Figure 4. SPE ANTEC Anaheim 2017 / 706

4 Diffusivity is obtained by dividing permeability by solubility. Based on the above discussion, it can be concluded that the percent reduction in diffusivity has to be the same as the percent reduction in permeability since moisture solubility in PLA remains the same for all PLA nanocomposites. Having established this, one can examine theoretical predictions employing the barrier aspect ratio obtained by analyzing TEM images shown in Figure 4 using ImageJ software. Figure 7 shows the comparison of the diffusivity data with the predictions based on Eqs. (1-3). The aspect ratio used is It is evident that the proposed model, as embodied in Eq. 3, does an excellent job of explaining all the experimental results. The Cussler s theory should have a slightly higher aspect ratio, but it did not affect the prediction significantly. Conclusions Nanoclay Cloisite 30B was incorporated in polylactic acid (PLA) via melt blending. The water vapor permeability was reduced to a level similar to that in PET by the addition of 5.3 vol% of nanoclay. A new model was proposed to describe all the experimental data. The predictions of this model appear to be quantitatively correct and provide a better fit to the data than the two currently popular models. 8. Eitzman, D. M., R. R. Melkote, and E. L. Cussler, AIChE Journal, 42: 2-9 (1996). 9. Falla, W. R., M. Mulski, and E. L. Cussler, Journal of Membrane Science, 119: (1996) 10. Moggridge, G. D., N. K. Lape, C. Yang, and E. L. Cussler, Progress of Organic Coatings, 46: (2003). 11. Tang, M. C. Effect of Nanoclay and Polymer Crystallinity on Moisture Diffusion through Polylactic Acid (PLA). Ph.D. dissertation, Department of Chemical and Biomedical Engineering, West Virginia University, Siparsky, G. L., K. J. Voorhees, J. R. Dorgan, and K. Schilling. Journal of Environmental Polymer Degradation 5 (1997): Auras, R. A., S. P. Singh, and J. J. Singh. Package Technology and Science 18 (2005) Acknowledgement This research was made possible by a grant from the King Abdulaziz City of Science and Technology in Riyadh, Saudi Arabia. References 1. Katiyar, V., N. Gerds, C. B. Koch, J. Risbo, H. C. B. Hansen, and D. Plackett, Journal Applied Polymer Science, 122: , (2011). 2. Park, S.H., S. G. Lee, and S. H. Kim, Composites: Part A, 46: 11-18, (2013). 3. Fukushima, K., D. Tabuani, M. Arena, M. Gennari, and G. Camino, Reactive & Functional Polymers, 73: , (2013). 4. Wu, F., X. Lan, D. Ji, Z. Liu, W. Yang, and M. Yang, Journal of Applied Polymer Science, 1-9, (2013). 5. Rhim, J. W., S. I. Hong, and C. S. Ha, LWT Food Science and Technology, 42: , (2009). 6. Nielsen, E. L., Journal of Macromolecular Science (Chemistry), A1: (1967). 7. Cussler, E. L., S. E. Hughes, W. J. Ward, and R. Aris, Journal of Membrane Science, 38: (1988). Figure 1: Tortuosity path concept. Figure 2: Illustration of the new model showing reduction in the area for mass transfer with an increase in path length. SPE ANTEC Anaheim 2017 / 707

5 Permeability ( kg/(m-pa-s)) Solubility ( 10 3 kg/(pa-m 3 )) Figure 3: Water vapor permeability through PLA nanocomposites ( kg/pa/m/s). Figure 5: Water vapor solubility through PLA nanocomposites ( 10 3 kg/pa/m 3 ). Moisture content per unit volume (cm 3 STP) Figure 6: Moisture content on Cloisite 30B as a function of volume % of Cloisite 30B. Figure 4: TEM images of PLA containing Cloisite 30B (a) 0.5 vol%; (b) 1.5 vol%; (c) 2.6 vol%; (d) 5.3 vol%. SPE ANTEC Anaheim 2017 / 708

6 D 0 /D Experimental data Nielsen's model Cussler's model Our model Figure 7: Comparison of the proposed model and two existing models with experimental data of diffusivity through PLA nanocomposites. SPE ANTEC Anaheim 2017 / 709