# Study on the cell structure and compressive behavior of biodegradable poly([epsilon]-caprolactone) foam.

INTRODUCTION

Foam materials have the advantage of low density, high specific strength, low heat conductivity, and good isolation to sound, making them find wide applications in market sectors such as construction, packaging, buoyancy, automotive, medical, etc. Traditional foams such as polyurethane (PU) foam, polyolefin (PO) foam, etc. have been widely used. However, all these traditional polymer foams possess serious environmental problems for their nonbio-degradability. A way to solve this problem is to develop biodegradable polymer foams. There are many studies in foaming degradable polymer foams (1-4); however, much less work has been performed on structure-property relationships of these biodegradable foams.

It is widely accepted that the physical properties of given foam depend on several factors, it can be described in the following equation (5),

X = X([rho], CP, CS, PM, GE, etc) (1)

where X is a physical property, [rho] is the foam density, CP is the chemical composition, CS is the cellular structure, PM is the polymer morphology, and GE is the nature of gas enclosed. There are a number of studies on developing suitable models to reveal the structure-property relationships in polymer foams (6-9), in which Gibson and Ash- by's approach (6) are widely accepted. They have described the mechanics of closed cell foam under compression by using a simple model made of cubic cells. Based on this model, they gave following equation (6),

[E.sub.f]/[E.sub.m] = [[phi].sup.2] [([[rho].sub.f]/[[rho].sub.m]).sup.2] + 1 - [empty set]) ([[rho].sub.f]/[[rho].sub.m]) (2)

where (E.sub.f), (E.sub.m), [[rho].sub.f], [[rho].sub.m] are the Young's modulus and the density of the foam and the polymer matrix, respectively. [phi] is the volume fraction of the solid contained in the cell edges. The model was applied in different foams, and the similar results were achieved (5), (10-13). Most of those studies emphasized the relationship between foam's density and mechanical properties, a few of them considered the possible effect of microstructural parameters such as cell size, cell wall thickness, and cell density on the mechanical properties. Doroudiani and Kortschot prepared polystyrene foam using physical foaming method (14). By controlling the foaming conditions, including saturation pressure, foaming temperature, and foaming time, a wide range of foam densities and cell sizes can be produced. Effect of the microstructure of Polystyrene foams on impact properties was discussed (15). Statistical analysis of the data showed that foam density plays the most important role in controlling the impact strength. Plastic and viscoelastic de-formation in the cell walls is the major source of energy dissipation in these materials. But, cell size in the range of the study does not affect the impact strength significantly. Effect of structure on tensile properties of polystyrene foams was also studied (16). The tensile modulus and strength increased with an increasing foam density, and they decreased slightly when the cell size increased.

In this work, poly ([epsilon]-caprolactone) (PCL) was chosen as the foaming material. PCL is a linear aliphatic polyester with the unique biocompatibility, degradability, and flexibility (17-21). However, its low melting point has been a disadvantage in many applications (22). To improve its melt strength, PCL was crosslinked by using benzoyl peroxide (BPO) (23). The PCL foam can be produced by either physical or chemical method (24). In this work, the chemical foaming method was used. PCL foams with different densities were prepared. The foam structure was investigated by SEM, and the compressive behavior was achieved by uniaxial compression test. The obtained result were compared with those of traditional polymer foams to analyze the contribution factors. Structural parameters such as cell size, cell wall thickness, and cell density were related to compressive modulus, and the effect of these parameters on compressive behavior was evaluated.

EXPERIMENTAL

Materials

A commercial PCL with (M.sub.w) of 8 X [10.sup.5] was purchased from Solvay, United Kingdom. BPO, an initiator for PCL crosslinking, was purchased from Shanghai Chemical Re-agent, China. Azodiformamide (AC), a chemical foaming agent was obtained from shanghai Guanya Chemical, China. Zinc oxide (ZnO) used to lower the decomposition temperature (25) was bought from Beijing Chemical, China. These chemicals were used as received, except for BPO that was recrystallized prior to use.

Preparation of PCL Foam

The foaming experiments were performed in a three-stage batch process as shown in Fig. 1. In the first stage, PCL pellets were mixed with BPO, AC, and ZnO in a laboratory internal mixer at 90[degrees] C and 40 rpm for 5 min. Then, the mixture was hot-compression molded into a sheet with dimension of 20 mm X 20 mm X 2 mm at the pressure of 5 MPa. The temperature of the hot press was 140 [degrees] C, and the press mold time was set 10 min to make sure BPO fully decomposed and PCL crosslinked with about 40% gel fraction obtained (23). The PCL foam was foamed by heating the sheet in an oil bath at 200 [degrees] C for 3 min. Then, the PCL foams were left in air at room temperature foe 48 h before any structural characterization and mechanical testing.

[FIGURE 1 OMITTED]

Characterization of the PCL Foams

Density. According to ASTM D1622-98, the apparent density of the foam was obtained by the ratio of the weight over the volume of each sample. The dimensions were measured with vernier caliper, and the weight was measured with analytical balance. The foam density was calculated according to Eq. 3,

[rho] = m/a x b x d (3)

where [rho] is the density in g/[cm.sub.3], m is the specimen mass in g, a, b, and c are the length, width, and thickness of specimen in cm, respectively. More than five specimens were measured to minimize the errors.

Cell Parameters. The fractured surfaces of the PCL foams were coated with gold and then observed with a scanning electron microscope (SEM). The typical foam structures were shown in Fig. 2, and the PCL foam micrographs were analyzed by Scion Image[R] Software to obtain cell parameters. In general view of cellular structure, the cell size was calculated as average diameter of more than 200 cells. The actual cell diameter is always larger than its measured counterpart because most cells will not be truncated through their maximal cross-section, therefore underestimating the value. According to ASTM D3576, the actual average diameter of a perfectly spherical cell can be calculated by Eq. 4,

[FIGURE 2 OMITTED]

D = 4/[pi] [delta] (4)

where d is the actual average diameter and [delta] is the calculated average diameter. Because of uneven thickness of the cell walls, the middle part was measured as cell wall thickness. Mean, the middle part was measured as well wall thickness. Mean cell size was calculated as average value of more than 100 cell walls. Cell density was calculated by Eq. 5 suggested by Nam et al. (26),

[N.sub.C] [congruent to] [10.sup.4] [1 - ([[rho].sub.f]/[[rho.sub.m])]/[d.sup.3] (5)

where [N.sub.C] is the cell density in cells/[cm.sup.3], [[rho].sub.f] and [[rho].sub.m] are the densities of the foam and the polymer matrix, respectively, and d is the average cell diameter in mm.

Compressive Behavior. The mechanical test in uniaxial compression was carried out at room temperature using an Instron 1221 Testing machine with a 10 kN load cell. A constant crosshead speed of 1.0 mm/min was used and stress-strain curve was obtained. Because the thickness of the foam samples is thin, it is difficult to perform the compression test according to ASTM standards. Therefore the foam specimens were cut into square pieces with dimension of 15 mm X 15 mm, then two or three pieces were piled up to achieve a total thickness of 5-7 mm. At least five specimens with the same density were tested, and uniaxial compressive modulus was calculated as the slope of the initial linear part of stress-strain curve.

RESULTS AND DISCUSSION

The PCL foams were prepared with relative density between 0.03 and 0.25 by changing the AC blowing agent concentration. The effect of AC concentration on the foam relative density is shown in Fig. 3. The relative density of the PCL foams decreases repidly in the initial stage, then decreases slowly when AC content was relatively high. This phenomenon may result from the fact that there is less gas generated for bubble nucleation and cell growth in low AC concentration. As AC content increases, much more bubbles are nucleated and cells are getting much more bigger, which leads to rapid decease in density. In high AC content, the diffusion loss of the blowing gas became considerable, and more AC existed in the PCL melt would lower the melt strength of PCL matrix. Therefore, the relative density of the PCL foams cannot decrease further.

[FIGURE 3 OMITTED]

Typical SEM micrographs of the foams are shown in Fig. 4. It can It be seen that the PCL foams have a closed cell structure. For the PCL foam expands freely with high density in low foaming grade, its cell has elliptic shape and no sign of cell anisotropy is observed (as seen in the Fig. 4a). The cellular structure is regular, the cell size is in the range from 14 to 130 [micro]m, and the distribution is almost uniform. In high foaming grade, the cell shape changes to polyhedron with pentagon faces (as seen in the Fig. 4b, c, d). In this case, the cell faces were stretched and tensed to form pentagonal cell shape. The cell parameters were calculated from these microphotos and shown in the Table 1. It can be seen that decreasing relative density gives larger cell sizes and thinner cell walls, which could related to low cell density.

[FIGURE 4 OMITTED]

Foams with different densities were tested in compression mode at crosshead speed of 1.0 mm/min. Figure 5 were shown the typical stress-strain curves of PCL foams. The compressive stress-strain curve shows three different regions, which are associated with different deformation mechanisms. At lower strain region, the stress-strain relationship is almost linear. Linear elasticity is controlled by cell wall bending and cell face stretching. The plateau region in the curve is associated with the collapse of the cells by elastic bucking or plastic yielding. When the cells are almost completely collapsed, the opposing cell walls are crushed, giving the final region of rapidly increasing stress. When the relative density of PCL foam is high, the stress increases slightly as the strain changes in the plateau region (as seen in Fig. 5, curve 1). In this case, the plateau is formed by elastic buckling according to Gibson and Ashby (6). When the relative density of PCL foam is lower, the stress remains the same as strain increases in the plateau region, which is due to the plastic yielding of cell walls (as seen in Fig. 5, 5 curves 2 and 3). As relative densities decreases, foam's compressive behavior changes from elastic to elastic-plastic.

[FIGURE 5 OMITTED]

According to Gibson and Ashby (6), postcollapse curve can be described by Eq. 6,

[[sigma].sub.f]/[E.sub.m] = 0.05 ([[rho].sub.f]/[[rho].sub.m]) + [P.sub.0][epsilon]/[E.sub.s] (1 - [epsilon] - [[rho].sub.f]/[[rho].sub.m]) (6)

where [sigma]f the postcollapse stress, [P.sub.0] is the initial fluid pressure at the initiation of collapse in a fluid-filled foam. In man-made foams, [P.sub.0] is usually equal to atmospheric pressure. And [gamma] is strain. [P.sub.0][epsilon]/(1 - [epsilon] - [rho]f/[rho]m) is the contribution of the gas when compressing. The postcollapse stress [[sigma].sub.f] was plotted against [epsilon]/(1 - [epsilon] - [rho]f/[rho]m) in Fig. 6 to evaluated the contribution of air enclosed in the foams during the uniaxile compression test. If Eq. 6 was the whole story, plots of [[sigma].sub.f] against [epsilon]/(1 - [epsilon] - [[rho].sub.f]/[[rho].sub.m]) should give straight lines with a slope P0. However, actually, as relative density increased, the slope of the curve increase. The foams with lower density are close to the expect value. It can be concluded that compression of the enclosed in the foam has great contribution to the slope to the postcollapse stress-strain curve. It is the dominant contribution in low density foams (6).

[FIGURE 6 OMITTED]

The relative compressive modulus was calculated from the stress-strain curve and was plotted against relative density in Fig. 7. It can be seen that relative compressive modulus has a power law relation with relative density. The relationship was described in Eq. 7,

[FIGURE 7 OMITTED]

[E.sub.f]/[E.sub.m] = [10.sup. - 0.37] x [([[rho].sub.f]/[[rho].sub.m]).sup.1.57] (7)

This result is in good agreement with Gibson and Ashby's work (6). By comparing traditional polymer foams, such as polyethylene foam (27), polypropylene foam (11), polystyrene foam (11), and polyvinyl chloride foam (28), as shown in Fig. 8, it can be said that the power law indexes and preexponential factors of the equation of these foams are nearly the same. This character can be attributed to that all these foams have similar closed cell structure, so the properties of a certain foam can be predicted if its relative density and [E.sub.m] are known.

[FIGURE 8 OMITTED]

The effect of density on relative compressive stress was also studied. The relative compressive stress taken at the strain of 20% was plotted against relative density in Fig. 9. It can be seen that the relative compressive stress has a power law relation with relative density, which was described in Eq. 8,

[FIGURE 9 OMITTED]

[[sigma].sub.f]/[[sigma].sub.m] = [10.sup. - 0.18] x [([[rho].sub.f]/[[rho].sub.m].sup.1.48] (8)

where [[sigma].sub.f]/[[sigma].sub.m] is relative compressive stress. The Eq. 8 is similar to Eq. 7 except for the different preexponential factors. It means that the relative density has same effect on the relative compressive modulus and relative compressive stress.

In previous works, most of them mainly considered the relationship between relative density and foam properties. The possible effects of microstructural parameters, such as mean cell size, cell wall thickness, and cell density were seldom considered. To understand the relationship between them, the relative compressive modulus and the microstructural parameters were analyzed in this work.

As shown in Fig. 10, the relative compressive modulus of the PCL foam was plotted as function of the mean cell size. It is clearly seen that when the mean cell size increased from 60 to 160 [micro]m, the compressive modulus decreased a little from 0.008 to 0.006. Therefore, it can be said that the mean cell size has no distinct influence on the relative compressive modulus in the range from 60 to 160 [micro]m. It should be pointed out that there is a special point in Fig. 10, that is, the sample with the mean cell size about 40 [micro]m has a high compressive modulus of 0.165, which is much higher than others. The reason should be that the cells were isolated from each other in the PCL matrix, as shown in Fig. 4a.

[FIGURE 10 OMITTED]

For further understanding the effect of the mean cell size on the relative compressive modulus, the samples with similar densities but different mean cell size were selected. The points of relative compressive modulus versus mean cell size were shown in Fig. 11. The data indicated that mean cell size concerned in the range of this study does not affect the compressive modulus. It is similar to Doroudiani's and Kortschot's result (15), (16). It seems that cell size in the range of 50-200 [micro]m has no significant effect on mechanical properties of polymeric closed cell foams.

[FIGURE 11 OMITTED]

The relative compressive modulus as the function of cell wall thickness was shown in Fig. 12. The result showed that there is a linear relationship between compressive modulus and cell wall thickness. The reasonable explanation is that the compressive modulus is calculated as slope of initial stress-strain curve. In this region, the linear elasticity is controlled by cell wall bending and cell face stretching. As cell wall thickness increases, the cell wall bending and cell face stretching become difficult and result in high compressive modulus.

[FIGURE 12 OMITTED]

The relative compressive modulus was plotted as a function of the cell density as shown in Fig. 13. It can be seen that when the cell density is relatively low, the relative modulus is corresponding low. And as the cell density increases, the relative modulus increases evidently. When the cell density is 3.68 x [10.sup.7] cells/[cm.sup.3], the relative modulus is 0.020, increases nearly seven times. This result is consistent with the data from the Refs. (29), (30). Therefore, the high quality polymer foam can be achieved if its cell density is high enough.

[FIGURE 13 OMITTED]

CONCLUSIONS

Biodegradable PCL foam has been prepared by using chemical foaming method. The densities can be controlled in the range from 0.04 to 0.30 g/[cm.sup.3]. The foam microstructure was characterized by SEM and the structural parameters, such as cell size, cell wall thickness, and cell density, were obtained. Uniaxial compression test was used to characterize the mechanical properties of PCL foam.

The PCL foams have closed cell structure. The cell shape changed from elliptic to pentagon as the density decreased, and both the cell wall thickness and the cell density decreased. But the cell size increased. The power law relationship between relative density and relative compressive modulus was obtained, which is in good agreement with Gibson and Ashby's model. The cell wall thickness and the cell density influence the foam mechanical properties evidently. But the cell size, at least in the range of this study, has no distinct effect on the compressive behavior.

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Correspondence to: Lisong Dong: e-mail: dongls@ciac.jl.cn

Contract grant sponsor: National Science Foundation of China; contract grant number: 50473028.

DOI 10.1002/pen.21199

Published online in wiley InterScience (www.interscience.wiley.com).

Hao Liu, Changyu Han, Lisong Dong

State key Laboratory of Polymer physics and Chemistry, Changchun Institute of Applied Chemistry, Changchun 130022, China and Graduate School of Chinese Academy of Science, Beijing 100080, China

Foam materials have the advantage of low density, high specific strength, low heat conductivity, and good isolation to sound, making them find wide applications in market sectors such as construction, packaging, buoyancy, automotive, medical, etc. Traditional foams such as polyurethane (PU) foam, polyolefin (PO) foam, etc. have been widely used. However, all these traditional polymer foams possess serious environmental problems for their nonbio-degradability. A way to solve this problem is to develop biodegradable polymer foams. There are many studies in foaming degradable polymer foams (1-4); however, much less work has been performed on structure-property relationships of these biodegradable foams.

It is widely accepted that the physical properties of given foam depend on several factors, it can be described in the following equation (5),

X = X([rho], CP, CS, PM, GE, etc) (1)

where X is a physical property, [rho] is the foam density, CP is the chemical composition, CS is the cellular structure, PM is the polymer morphology, and GE is the nature of gas enclosed. There are a number of studies on developing suitable models to reveal the structure-property relationships in polymer foams (6-9), in which Gibson and Ash- by's approach (6) are widely accepted. They have described the mechanics of closed cell foam under compression by using a simple model made of cubic cells. Based on this model, they gave following equation (6),

[E.sub.f]/[E.sub.m] = [[phi].sup.2] [([[rho].sub.f]/[[rho].sub.m]).sup.2] + 1 - [empty set]) ([[rho].sub.f]/[[rho].sub.m]) (2)

where (E.sub.f), (E.sub.m), [[rho].sub.f], [[rho].sub.m] are the Young's modulus and the density of the foam and the polymer matrix, respectively. [phi] is the volume fraction of the solid contained in the cell edges. The model was applied in different foams, and the similar results were achieved (5), (10-13). Most of those studies emphasized the relationship between foam's density and mechanical properties, a few of them considered the possible effect of microstructural parameters such as cell size, cell wall thickness, and cell density on the mechanical properties. Doroudiani and Kortschot prepared polystyrene foam using physical foaming method (14). By controlling the foaming conditions, including saturation pressure, foaming temperature, and foaming time, a wide range of foam densities and cell sizes can be produced. Effect of the microstructure of Polystyrene foams on impact properties was discussed (15). Statistical analysis of the data showed that foam density plays the most important role in controlling the impact strength. Plastic and viscoelastic de-formation in the cell walls is the major source of energy dissipation in these materials. But, cell size in the range of the study does not affect the impact strength significantly. Effect of structure on tensile properties of polystyrene foams was also studied (16). The tensile modulus and strength increased with an increasing foam density, and they decreased slightly when the cell size increased.

In this work, poly ([epsilon]-caprolactone) (PCL) was chosen as the foaming material. PCL is a linear aliphatic polyester with the unique biocompatibility, degradability, and flexibility (17-21). However, its low melting point has been a disadvantage in many applications (22). To improve its melt strength, PCL was crosslinked by using benzoyl peroxide (BPO) (23). The PCL foam can be produced by either physical or chemical method (24). In this work, the chemical foaming method was used. PCL foams with different densities were prepared. The foam structure was investigated by SEM, and the compressive behavior was achieved by uniaxial compression test. The obtained result were compared with those of traditional polymer foams to analyze the contribution factors. Structural parameters such as cell size, cell wall thickness, and cell density were related to compressive modulus, and the effect of these parameters on compressive behavior was evaluated.

EXPERIMENTAL

Materials

A commercial PCL with (M.sub.w) of 8 X [10.sup.5] was purchased from Solvay, United Kingdom. BPO, an initiator for PCL crosslinking, was purchased from Shanghai Chemical Re-agent, China. Azodiformamide (AC), a chemical foaming agent was obtained from shanghai Guanya Chemical, China. Zinc oxide (ZnO) used to lower the decomposition temperature (25) was bought from Beijing Chemical, China. These chemicals were used as received, except for BPO that was recrystallized prior to use.

Preparation of PCL Foam

The foaming experiments were performed in a three-stage batch process as shown in Fig. 1. In the first stage, PCL pellets were mixed with BPO, AC, and ZnO in a laboratory internal mixer at 90[degrees] C and 40 rpm for 5 min. Then, the mixture was hot-compression molded into a sheet with dimension of 20 mm X 20 mm X 2 mm at the pressure of 5 MPa. The temperature of the hot press was 140 [degrees] C, and the press mold time was set 10 min to make sure BPO fully decomposed and PCL crosslinked with about 40% gel fraction obtained (23). The PCL foam was foamed by heating the sheet in an oil bath at 200 [degrees] C for 3 min. Then, the PCL foams were left in air at room temperature foe 48 h before any structural characterization and mechanical testing.

[FIGURE 1 OMITTED]

Characterization of the PCL Foams

Density. According to ASTM D1622-98, the apparent density of the foam was obtained by the ratio of the weight over the volume of each sample. The dimensions were measured with vernier caliper, and the weight was measured with analytical balance. The foam density was calculated according to Eq. 3,

[rho] = m/a x b x d (3)

where [rho] is the density in g/[cm.sub.3], m is the specimen mass in g, a, b, and c are the length, width, and thickness of specimen in cm, respectively. More than five specimens were measured to minimize the errors.

Cell Parameters. The fractured surfaces of the PCL foams were coated with gold and then observed with a scanning electron microscope (SEM). The typical foam structures were shown in Fig. 2, and the PCL foam micrographs were analyzed by Scion Image[R] Software to obtain cell parameters. In general view of cellular structure, the cell size was calculated as average diameter of more than 200 cells. The actual cell diameter is always larger than its measured counterpart because most cells will not be truncated through their maximal cross-section, therefore underestimating the value. According to ASTM D3576, the actual average diameter of a perfectly spherical cell can be calculated by Eq. 4,

[FIGURE 2 OMITTED]

D = 4/[pi] [delta] (4)

where d is the actual average diameter and [delta] is the calculated average diameter. Because of uneven thickness of the cell walls, the middle part was measured as cell wall thickness. Mean, the middle part was measured as well wall thickness. Mean cell size was calculated as average value of more than 100 cell walls. Cell density was calculated by Eq. 5 suggested by Nam et al. (26),

[N.sub.C] [congruent to] [10.sup.4] [1 - ([[rho].sub.f]/[[rho.sub.m])]/[d.sup.3] (5)

where [N.sub.C] is the cell density in cells/[cm.sup.3], [[rho].sub.f] and [[rho].sub.m] are the densities of the foam and the polymer matrix, respectively, and d is the average cell diameter in mm.

Compressive Behavior. The mechanical test in uniaxial compression was carried out at room temperature using an Instron 1221 Testing machine with a 10 kN load cell. A constant crosshead speed of 1.0 mm/min was used and stress-strain curve was obtained. Because the thickness of the foam samples is thin, it is difficult to perform the compression test according to ASTM standards. Therefore the foam specimens were cut into square pieces with dimension of 15 mm X 15 mm, then two or three pieces were piled up to achieve a total thickness of 5-7 mm. At least five specimens with the same density were tested, and uniaxial compressive modulus was calculated as the slope of the initial linear part of stress-strain curve.

RESULTS AND DISCUSSION

The PCL foams were prepared with relative density between 0.03 and 0.25 by changing the AC blowing agent concentration. The effect of AC concentration on the foam relative density is shown in Fig. 3. The relative density of the PCL foams decreases repidly in the initial stage, then decreases slowly when AC content was relatively high. This phenomenon may result from the fact that there is less gas generated for bubble nucleation and cell growth in low AC concentration. As AC content increases, much more bubbles are nucleated and cells are getting much more bigger, which leads to rapid decease in density. In high AC content, the diffusion loss of the blowing gas became considerable, and more AC existed in the PCL melt would lower the melt strength of PCL matrix. Therefore, the relative density of the PCL foams cannot decrease further.

[FIGURE 3 OMITTED]

Typical SEM micrographs of the foams are shown in Fig. 4. It can It be seen that the PCL foams have a closed cell structure. For the PCL foam expands freely with high density in low foaming grade, its cell has elliptic shape and no sign of cell anisotropy is observed (as seen in the Fig. 4a). The cellular structure is regular, the cell size is in the range from 14 to 130 [micro]m, and the distribution is almost uniform. In high foaming grade, the cell shape changes to polyhedron with pentagon faces (as seen in the Fig. 4b, c, d). In this case, the cell faces were stretched and tensed to form pentagonal cell shape. The cell parameters were calculated from these microphotos and shown in the Table 1. It can be seen that decreasing relative density gives larger cell sizes and thinner cell walls, which could related to low cell density.

[FIGURE 4 OMITTED]

TABLE 1. Parameters of PCL foams Density Relative Cell size Cell wall thickness (g/[cm.sup.3]) density ([mu]m) ([mu]m) 0.66 0.58 82 a 0.16 0.14 120 3.73 0.073 0.064 151 1.88 0.044 0.039 153 1.48 Density (g/[cm.sup.3]) Cell density (cells/ Relative modulus [cm.sup.3]) 0.66 7.45 X [10.sup.6] 18 X [10.sup.-2] 0.16 4.98 X [10.sup.6] 2.0 X [10.sup.-2] 0.073 2.73 X [10.sup.6] 6.0 X [10.sup.-2] 0.044 2.68 X [10.sup.6] 2.5 X [10.sup.-3]

Foams with different densities were tested in compression mode at crosshead speed of 1.0 mm/min. Figure 5 were shown the typical stress-strain curves of PCL foams. The compressive stress-strain curve shows three different regions, which are associated with different deformation mechanisms. At lower strain region, the stress-strain relationship is almost linear. Linear elasticity is controlled by cell wall bending and cell face stretching. The plateau region in the curve is associated with the collapse of the cells by elastic bucking or plastic yielding. When the cells are almost completely collapsed, the opposing cell walls are crushed, giving the final region of rapidly increasing stress. When the relative density of PCL foam is high, the stress increases slightly as the strain changes in the plateau region (as seen in Fig. 5, curve 1). In this case, the plateau is formed by elastic buckling according to Gibson and Ashby (6). When the relative density of PCL foam is lower, the stress remains the same as strain increases in the plateau region, which is due to the plastic yielding of cell walls (as seen in Fig. 5, 5 curves 2 and 3). As relative densities decreases, foam's compressive behavior changes from elastic to elastic-plastic.

[FIGURE 5 OMITTED]

According to Gibson and Ashby (6), postcollapse curve can be described by Eq. 6,

[[sigma].sub.f]/[E.sub.m] = 0.05 ([[rho].sub.f]/[[rho].sub.m]) + [P.sub.0][epsilon]/[E.sub.s] (1 - [epsilon] - [[rho].sub.f]/[[rho].sub.m]) (6)

where [sigma]f the postcollapse stress, [P.sub.0] is the initial fluid pressure at the initiation of collapse in a fluid-filled foam. In man-made foams, [P.sub.0] is usually equal to atmospheric pressure. And [gamma] is strain. [P.sub.0][epsilon]/(1 - [epsilon] - [rho]f/[rho]m) is the contribution of the gas when compressing. The postcollapse stress [[sigma].sub.f] was plotted against [epsilon]/(1 - [epsilon] - [rho]f/[rho]m) in Fig. 6 to evaluated the contribution of air enclosed in the foams during the uniaxile compression test. If Eq. 6 was the whole story, plots of [[sigma].sub.f] against [epsilon]/(1 - [epsilon] - [[rho].sub.f]/[[rho].sub.m]) should give straight lines with a slope P0. However, actually, as relative density increased, the slope of the curve increase. The foams with lower density are close to the expect value. It can be concluded that compression of the enclosed in the foam has great contribution to the slope to the postcollapse stress-strain curve. It is the dominant contribution in low density foams (6).

[FIGURE 6 OMITTED]

The relative compressive modulus was calculated from the stress-strain curve and was plotted against relative density in Fig. 7. It can be seen that relative compressive modulus has a power law relation with relative density. The relationship was described in Eq. 7,

[FIGURE 7 OMITTED]

[E.sub.f]/[E.sub.m] = [10.sup. - 0.37] x [([[rho].sub.f]/[[rho].sub.m]).sup.1.57] (7)

This result is in good agreement with Gibson and Ashby's work (6). By comparing traditional polymer foams, such as polyethylene foam (27), polypropylene foam (11), polystyrene foam (11), and polyvinyl chloride foam (28), as shown in Fig. 8, it can be said that the power law indexes and preexponential factors of the equation of these foams are nearly the same. This character can be attributed to that all these foams have similar closed cell structure, so the properties of a certain foam can be predicted if its relative density and [E.sub.m] are known.

[FIGURE 8 OMITTED]

The effect of density on relative compressive stress was also studied. The relative compressive stress taken at the strain of 20% was plotted against relative density in Fig. 9. It can be seen that the relative compressive stress has a power law relation with relative density, which was described in Eq. 8,

[FIGURE 9 OMITTED]

[[sigma].sub.f]/[[sigma].sub.m] = [10.sup. - 0.18] x [([[rho].sub.f]/[[rho].sub.m].sup.1.48] (8)

where [[sigma].sub.f]/[[sigma].sub.m] is relative compressive stress. The Eq. 8 is similar to Eq. 7 except for the different preexponential factors. It means that the relative density has same effect on the relative compressive modulus and relative compressive stress.

In previous works, most of them mainly considered the relationship between relative density and foam properties. The possible effects of microstructural parameters, such as mean cell size, cell wall thickness, and cell density were seldom considered. To understand the relationship between them, the relative compressive modulus and the microstructural parameters were analyzed in this work.

As shown in Fig. 10, the relative compressive modulus of the PCL foam was plotted as function of the mean cell size. It is clearly seen that when the mean cell size increased from 60 to 160 [micro]m, the compressive modulus decreased a little from 0.008 to 0.006. Therefore, it can be said that the mean cell size has no distinct influence on the relative compressive modulus in the range from 60 to 160 [micro]m. It should be pointed out that there is a special point in Fig. 10, that is, the sample with the mean cell size about 40 [micro]m has a high compressive modulus of 0.165, which is much higher than others. The reason should be that the cells were isolated from each other in the PCL matrix, as shown in Fig. 4a.

[FIGURE 10 OMITTED]

For further understanding the effect of the mean cell size on the relative compressive modulus, the samples with similar densities but different mean cell size were selected. The points of relative compressive modulus versus mean cell size were shown in Fig. 11. The data indicated that mean cell size concerned in the range of this study does not affect the compressive modulus. It is similar to Doroudiani's and Kortschot's result (15), (16). It seems that cell size in the range of 50-200 [micro]m has no significant effect on mechanical properties of polymeric closed cell foams.

[FIGURE 11 OMITTED]

The relative compressive modulus as the function of cell wall thickness was shown in Fig. 12. The result showed that there is a linear relationship between compressive modulus and cell wall thickness. The reasonable explanation is that the compressive modulus is calculated as slope of initial stress-strain curve. In this region, the linear elasticity is controlled by cell wall bending and cell face stretching. As cell wall thickness increases, the cell wall bending and cell face stretching become difficult and result in high compressive modulus.

[FIGURE 12 OMITTED]

The relative compressive modulus was plotted as a function of the cell density as shown in Fig. 13. It can be seen that when the cell density is relatively low, the relative modulus is corresponding low. And as the cell density increases, the relative modulus increases evidently. When the cell density is 3.68 x [10.sup.7] cells/[cm.sup.3], the relative modulus is 0.020, increases nearly seven times. This result is consistent with the data from the Refs. (29), (30). Therefore, the high quality polymer foam can be achieved if its cell density is high enough.

[FIGURE 13 OMITTED]

CONCLUSIONS

Biodegradable PCL foam has been prepared by using chemical foaming method. The densities can be controlled in the range from 0.04 to 0.30 g/[cm.sup.3]. The foam microstructure was characterized by SEM and the structural parameters, such as cell size, cell wall thickness, and cell density, were obtained. Uniaxial compression test was used to characterize the mechanical properties of PCL foam.

The PCL foams have closed cell structure. The cell shape changed from elliptic to pentagon as the density decreased, and both the cell wall thickness and the cell density decreased. But the cell size increased. The power law relationship between relative density and relative compressive modulus was obtained, which is in good agreement with Gibson and Ashby's model. The cell wall thickness and the cell density influence the foam mechanical properties evidently. But the cell size, at least in the range of this study, has no distinct effect on the compressive behavior.

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Correspondence to: Lisong Dong: e-mail: dongls@ciac.jl.cn

Contract grant sponsor: National Science Foundation of China; contract grant number: 50473028.

DOI 10.1002/pen.21199

Published online in wiley InterScience (www.interscience.wiley.com).

Hao Liu, Changyu Han, Lisong Dong

State key Laboratory of Polymer physics and Chemistry, Changchun Institute of Applied Chemistry, Changchun 130022, China and Graduate School of Chinese Academy of Science, Beijing 100080, China

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Author: | Liu, Hao; Han, Changyu; Dong, Lisong |
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Publication: | Polymer Engineering and Science |

Article Type: | Technical report |

Geographic Code: | 9CHIN |

Date: | Dec 1, 2008 |

Words: | 3655 |

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