Ind. Eng. Chem. Res. 2009, 48, 3855–3859
3855
Factors Affecting Bubble Size on Foamed Polymer-Paperboard Composites Sriram K. Annapragada and Sujit Banerjee* Institute of Paper Science and Technology, School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, 500 Tenth Street NW, Atlanta Georgia 30332-0620
Foamed paperboard is a composite material with applications in the consumer products industry. The composite comprises a layer of paperboard sandwiched between two polymer films. One film foams upon heating while the other acts as a barrier. Foaming is caused by the vaporization of the small amount of moisture present in the board. The resulting increase in pressure bubbles the heat-softened polymer. During growth, the vapor driving force, which depends on the rate of vaporization, overcomes the opposing sheet resistance. Upon continued heating, the vapor escapes through the molten polymer film and from the sides of the board. Less than 2% of the total initial moisture accumulates inside the foam. The average bubble size is about five times lower than the maximum possible bubble size because of moisture losses. The final bubble size and foam thickness are dictated by the degree of bubble coalescence. Introduction Foaming on paperboard is a relatively new technique where the paperboard is faced with polymers on both sides and heated. The polymers are of different densities and the lowerdensity side melts and is bubbled by the vapor generated from the board moisture. The vapor bubbles the hot lowdensity polymer film and creates a rough insulated surface.1 The product is used commercially for the manufacture of disposable coffee cups and other containers for hot foods and liquids. The foamed material combines the advantages of traditional polymeric foam2-10 with the environmental benefits of paperboard. In previous work we have shown that initial bubble growth is driven by the vapor pressure of the moisture contained in the paperboard and is principally controlled by the pore size across the paper-polymer interface.11 We have also previously shown that the number of bubbles created in the process is not influenced by the properties of the polymer and the film thickness. In contrast, the properties of the polymer and the level of bonding to the paper surface, which depends on the speed at which it is extruded on to the board, are some of the factors that govern the initial bubble size.12 The final bubble size depends upon the degree of coalescence, which, in turn, is influenced by factors such as the rate of bubble growth and collapse. In this final paper of the series we discuss some of these factors and their contribution to foam quality. Experimental Details Procedures for the preparation of the foamed paperboard have been detailed earlier,11-13 Briefly, paperboard samples were prepared from a 3:1 mixture of Southern hardwood and softwood pulps. Three low density polyethylenes (EC 476, EC 479, EC 482) with melt points between 106 and 110 °C (obtained from Westlake Polymers) were extruded on one side at 61-213 m/min to give a 17-45 µm thick polymer layer as described earlier.11,13 A 17-45 µm thick polymer coating was applied. Successful foaming requires the opposite side of the composite structure to have a higher melting barrier layer. The barrier layer serves to direct the vapor to the lower melt side. In this study, the opposite side of the * To whom correspondence should be addressed. E-mail: sb@ gatech.edu.
board was sealed with packaging tape to form a barrier layer. No significant difference in foaming was found between the use of packaging tape or the extruded higher density polyethylene.11 The composites were foamed in a convective oven at 132 °C11 for various periods so as to allow the foam to expand to various thicknesses. A schematic of the composite structure and the cross section of a foamed board are illustrated in Figure 1 panels a and b, respectively. The void volume, calculated as the fraction of gas volume present in the polymeric phase, was 73-92%. The loss of vapor from different parts of the board was measured by foaming 9 × 7 cm board samples in a convective oven at 132 °C for periods ranging between 0 and 1000 s. The loss of total moisture was determined by taking the difference in the weights of board before and after foaming. The samples were cooled for 3 min before weight measurements were made in order to remove any effects of recondensation. For the determination of moisture loss through the surface the edges of the board were sealed with epoxy. Difference measurements between the sealed and control boards provided the quantity of moisture lost from the edges. The moisture accumulated inside the foam was estimated from the foam volume by assuming that the bubbles only contained water vapor. The bubble size was determined by image analysis as described earlier.11,13 A paper sheet is a complex structure containing several tortuous channels and pores. The pore size distribution in paperboard was determined from SEM images, an example of which is provided in Figure 2. The exact size distribution of pores was difficult to determine for each of the various paper samples used in foaming. Hence, the pore distribution was approximated by manually determining the areas of 500
Figure 1. (a) Schematic of the extruded board composite; (b) cross section of the finished foam structure.
10.1021/ie8015413 CCC: $40.75 2009 American Chemical Society Published on Web 03/10/2009
3856 Ind. Eng. Chem. Res., Vol. 48, No. 8, 2009
Figure 2. SEM image of paperboard used in foaming with the pore areas marked on the right panel.
Figure 3. Typical variation in foam thickness with time.
Figure 5. Rate of moisture loss from paperboard.
Figure 4. Vapor loss during foaming.
Figure 6. Development of foam moisture.
individual pores on the paper surface from eight different regions of the paperboard with Image J software.14 Figure 2 shows an example of the different areas in the SEM image identified as pores.
points during foaming. The results from the vapor loss measurements are shown in Figures 4 and 5. Figure 5 is a subset of Figure 4 and highlights the changes in moistureloss over the first 120 s. All of the polymers used showed similar levels of moisture loss during foaming. The percentage of vapor lost through the molten polymeric film, either through bubbles bursting or through diffusion, is a significant percentage of the total vapor lost. Earlier work11 has shown that the vapor escaping through the surface (Figure 5) originates from the collapse of smaller bubbles. Diffusion across the polymer film is unlikely to occur over such short time scales. Figure 5 also shows that the vapor loss through the edges occurs at roughly the same rate as that through the surface, which is expected because both are governed by the vaporization rate. Moisture is lost earlier from the edges because the melt points of the polymers were 106-110 °C, and no loss through the polymer film would occur until it softened. The accumulation of moisture in the board is about 1% as shown in Figure 6. Pore Size Analysis. The pore size distribution obtained from SEM analysis varied between 2 and 30 µm as shown in Figure 7. This is to be compared with the bubble size range of 20-100 µm, which is also illustrated in Figure 7. If the two spikes in the bubble radius plot are removed and the
Results and Discussion Vapor Loss Measurements. The development of foam thickness upon continuously heating the filmed board is illustrated in Figure 3. The thickness, which is related to the size of the bubbles in the foam, reaches a maximum value after which bubble collapse returns it to its initial prefoamed level. Similar behavior was noted in previous results obtained from videos taken during foaming.11 Clearly, the heating time and temperature must both be optimized for high foam quality. The maximum bubble size depends on the balance between the forces that drive growth and those that oppose it. During growth, the vapor driving force, which depends on the rate of vaporization, overcomes the opposing sheet resistance.11 If heating is continued beyond the optimal range, the vapor escapes through the molten polymer layer and from the sides of the board, and the foam eventually collapses. To obtain a mass balance of the sheet moisture, the moisture distribution in the sheet was measured at various
Ind. Eng. Chem. Res., Vol. 48, No. 8, 2009 3857
Figure 7. Pore size (left) and bubble size (right) distributions on paperboard.
for the pores. If we assume that the pore structure at the board/polymer interface is a frustum (truncated cone), then for a given cone, the diameter of the larger opening “R1” will be linearly related to that of the smaller opening “R2” if the cone is truncated at different planes perpendicular to the axis. Since the vapor driving force controls bubble growth,11 the maximum bubble size can be estimated from the rate of vapor flow into the pore. Vapor transport should create a pressure gradient across the board in the thickness direction and lead to convective bulk flow of the type observed during paper drying.15 The maximum bubble volume can be estimated from Figure 8. Comparison of pore radius and bubble radius frequencies from Figure 7.
Figure 9. Relationship between bubble and pore radius for various pore sizes.
Figure 10. Variation in the number of bubbles with foam thickness.
distributions are lined up, a smooth relationship is found between the distributions of bubbles and pores as shown in Figure 8. The overall similarity of the two profiles in Figure 7 suggests that the bubble distribution is governed by that
d (FV) ) FVr·πr2 dt
(1)
where V is the volume of the bubble (m3), Vr is the flow rate of the vapor into the pore (m/s), F is the density of water vapor (kg/m3), t is the time (sec) and r is the pore radius (m). The transport rate (Vr) into the pore should depend on the rate of vaporization and the resistance offered by the porous structure, that is, the permeability. To account for the different sizes of pores on paper surface, we varied the R1/R2 ratio between 0.1 and 10. The maximum bubble radius calculated from eq 1 for the corresponding pore radii between 0.02 and 400 µm is illustrated in Figure 9. The maximum theoretical bubble size for the pore size range considered is 1200 µm. However, as shown later, the actual bubble size varies between 20 and 260 µm. Thus, on average, the bubbles do not grow to their maximum possible size because most of the vapor is lost through the surface. Effect of Coalescence on Final Bubble Size Distribution. The pores on paperboard can be very closely spaced and the associated bubbles can coalesce, in which case the growth of a given bubble would also depend upon those of its neighbors. It is known that interbubble contact is inevitable if the void volume of the final foam exceeds 75%.16 The void fractions for the various cases studied here are much larger than 75%, which should force a high degree of coalescence. Coalescence (calculated as the percentage decrease in the number of bubbles from the maximum number) increases foam thickness as shown in Figure 10. The plot was obtained by measuring values at various stages of bubble growth. To determine the effect of coalescence on foam thickness, the bubbles were divided into three different size bins: 0-30 µm (bin 1), 31-140 µm (bin 2), and 141-690 µm (bin 3). Their distribution in the final foam is illustrated in Figure 11. The foam thickness is relatively insensitive to the number of bin 1 bubbles once a thickness of about 150 µm is reached.
3858 Ind. Eng. Chem. Res., Vol. 48, No. 8, 2009
Figure 11. Bubble count distribution in the final foam.
Figure 12. Bubble volume distribution in the final foam.
On the other hand, the fraction of bin 2 bubbles decreases with increasing foam thickness and the corresponding percentage of bin 3 bubbles increases. We have shown11 that bin 1 bubbles are mostly formed from the pores present on the paper board, whereas those in bins 2 and 3 are formed by coalescence. Thus the coalescence of bin 2 and bin 3 bubbles controls the final foam thickness. The distribution of bubbles measured by the total bin volume at each time across the three size bins is shown in Figure 12. The volumes of bin 1 and bin 2 decrease with foam thickness because of coalescence, which leads to the formation of the larger bin 3 bubbles. A thicker foam would thus be expected to have a smaller number of large-sized bubbles (bin 3 bubbles) as is evident in Figure 11. Conclusion The bubbles initially formed in the foam are primarily controlled by the pore size distribution, the vapor driving force, and the polymer thickness. The thickness of the polymer film limits the size to which a bubble can grow before bursting. The pore size distribution is governed by the uniformity of the paperboard surface.11 The vapor driving force depends on the bonding ability of the polymer with the paperboard; poorer bonding of polymer with paper leads to a lower driving force and reduces the bubble size.12 Higher polymer extrusion speeds and lower coated weights contribute to poorer bonding of paper with polymer.12 Other factors such as temperature, the polymer melt index, and moisture content are less important. The larger bubbles are principally created by coalescence and depend on the vapor driving force, the distance between bubbles, and the size of the bubbles initially formed. Coalescence leads to thicker foams due to the formation of larger sized bubbles. The insulation properties directly relate
to the amount of gas dispersed in the foam;17 hence a thicker foam provides better insulation. But coalescence also reduces the bubble count. Optimal insulation would be obtained if the degree of coalescence could be reduced and the individual bubbles were allowed to grow larger. Literature Cited (1) Iioka A. Method for producing a heat-insulating paper container from a paper coated or laminated with a thermoplastic synthetic resin film. U.S. Patent 4435344, 1984. (2) Lee S. T.; Ramesh, N. S. Polymeric Foams: Mechanisms and Materials; CRC Press; Boca Raton, 2004. (3) Lee S. T.; Park C. B.; Ramesh, N. S. Polymeric Foams: Science and Technology; CRC Press; Boca Raton, 2007. (4) Venerus, D. C.; Yala, N.; Bernstein, B. Analysis of diffusion-induced bubble growth in viscoelastic liquids. J. Non-Newtonian Fluid Mechanics 1998, 75, 55. (5) Feng, J. J.; Bertelo, C. A. Prediction of bubble growth and size distribution in polymer foaming based on a new heterogeneous nucleation model. J. Rheol. 2004, 48, 439. (6) Ramesh, N. S.; Rasmussen, D. H.; Campbell, G. A. Numerical and experimental studies of bubble growth during the microcellular foaming process. Polym. Eng. Sci. 1991, 31, 1657. (7) Amon, M.; Denson, C. D. A study of the dynamics of foam growth: Analysis of the growth of closely spaced spherical bubbles. Polym. Eng. Sci. 1984, 24, 1026. (8) Joshi, K.; Lee, G. L.; Shafi, M. A.; Flummerfelt, R. W. Prediction of cellular structure in free expansion of viscoelastic media. J. Appl. Polym. Sci. 1998, 67, 1353. (9) Arefmanesh, A.; Advani, S. G.; Michaelides, E. E. A numerical study of bubble growth during a low pressure structural foam molding process. Polym. Eng. Sci. 1990, 30, 1330. (10) Han, J. H.; Han, C. D. Bubble nucleation in polymeric liquids. Part II: Theoretical considerations. J. Polym. Sci., Part B 1990, 28, 743. (11) Annapragada, S. K.; Patterson, T.; Banerjee, S. Mechanism of foaming on polymer-paperboard composites. AIChE J. 2008, 54, 537. (12) Annapragada, S. K.; Patterson, T. F.; Banerjee, S. Effect of polymer properties on bubble growth in polymer-paperboard composites. J. Appl. Polym. Sci. 2008, 109, 3786.
Ind. Eng. Chem. Res., Vol. 48, No. 8, 2009 3859 (13) Annapragada, S. K. Mechanism of foaming on polymer-paperboard composites. Ph.D. Thesis. Georgia Institute of Technology, Atlanta, GA, 2007. (14) Rasband W. S. Image J. National Institutes of Health. Bethesda, Maryland; http://rsb.info.nih.gov/ij/, 1997-2004. (15) Devlin, P. An investigation of mechanism of high intensity drying. Ph.D. Thesis. Georgia Institute of Technology, Atlanta, GA, 1986. (16) Weaire, D.; Hutzler, S. The Physics of Foams. Oxford University Press; New York, 2000.
(17) Priester R. D.; Turner, R. B. In The Morphology of Flexible Polyurethane Matrix Polymers, Low Density Cellular Plastics; Hilyard, N. C., Cunningham, A., Eds.; Chapman & Hall; London, 1994; Chapter 4.
ReceiVed for reView October 13, 2008 ReVised manuscript receiVed February 7, 2009 Accepted February 17, 2009 IE8015413
