Predictions of Storage Modulus of Glass Bead-Filled Low-Density-Polyethylene Composites

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1 Materials Sciences and Applications, 2010, 1, doi: /sa Published Online Deceber 2010 ( 343 Predictions o Storage Modulus o Glass Bead-Filled Low-Density-Polyethylene Coposites Ji-Zhao Liang College o Industrial Equipent and Control Engineering, South China University o Technology, Guangzhou, P.. China. E-ail: scutjzl@sohu.co eceived April 14 th, 2010; revised June 21 st, 2010; accepted Noveber 17 th, ABSTACT The actors aecting storage odulus (E c ) and quantitative characterization o polyer coposites illed with inorganic particles were discussed in this paper. On the basis o Eshelby s ethod and Mori s work, an equation describing the relationship between the E c and the iller volue raction, particle geoetry as well as interacial orphology was proposed. The E c o the glass bead illed low-density-polyethylene (LDPE/GB) coposites was estiated by eans o this equation under experiental conditions with teperature range o C, requency o 1 Hz and the aplitude o 0.6, and copared with other equations proposed in literature. The results showed that the predictions or this equation were close to the easured data ro the LDPE/GB coposites. Keywords: Polyer, Coposite Materials, Storage Modulus, Prediction 1. Introduction Viscoelasticity is one o iportant paraeters or characterization o processing and use properties o polyeric aterials. For polyer blends or inorganic particle-illed polyer coposites, the relationship between structure and properties tends towards ore coplexity owing to the oration o an interace between coponents, as well as between the illers and atrix. The viscoelastic paraeter o polyer aterials ay be easured using a dynaic echanical analysis instruent, such as storage odulus, loss odulus and echanical daping, etc. In addition, dynaic echanical easureents over a range o teperatures provide valuable insight into the structure, orphology and properties o polyeric blends and coposites. A lot o dynaic echanical analyses on polyeric blends and coposites have been done [1-4]. Zhang et al. [1] easured dynaic echanical properties o coposites illed with SMA particles and short ibers, and ound that the storage odulus reaches the axiu at the SMA phase transoration teperature o approxiate 120 C. Karoui and Duour [2] predicted the rheology paraeters, such as storage odulus, loss odulus, strain, tanδ and coplex viscosity, o ripened sei-hard cheeses using luorescence spectra in the UV and visible ranges recorded at a young stage. Miyagawa and his colleague [3] studied the characterization and therophysical properties o unsaturated polyester-layered silicate nanocoposites. The results showed that a higher storage odulus enhanceent was obtained when the organo-clay nanoplatelets were delainated and ore hoogeneously dispersed. Kolarik [4] researched the Phase structure and theral and echanical properties o heterogeneous polyaide 66/syndiotactic polystyrene blends, and ound that storage odulus (125 C) noticeably declined with weight raction and thus showed that sps did not iprove the diensional stability o the blends at elevated teperatures. Since 1998, Liang et al. [5-9] have investigated the eects o glass bead content and size on the viscoelastic properties o illed polyolein coposites, and get soe useul indings. Storage odulus is an iportant index or easuring the stiness and elasticity o polyeric aterials, and it has been paid extensively attention by researchers. For particulate illed coposites, a nuber o equations or prediction o the odulus have been derived with dierent ethods. Aong these ethods, Eshelby s equivalent inclusion ethod is ore noticeable, which is a ethod to analyze average stress ield distribution in the case o only an inclusion an ininite body [10]. It is necessary to odiy Eshelby s ethod in the case o existence o a lot o inclusions and their interaction. Mori and Tanaka [11] proposed a odiication ethod in order that the ethod was available or the case o con-

2 344 Predictions o Storage Modulus o Glass Bead-Filled Low-Density-Polyethylene Coposites taining a nuber o elliptic sphere inclusions. Taya and Chou [12] urther developed Mori-Tanaka ethod and presented a odel including several types o inclusions. To calculate the elastic odulus Benveniste [13] proposed an equation group based on the odiied Mori- Tanaka ethod. The ocus o this paper is to investigate the actors aecting the storage oduli o polyer coposites illed with inorganic particles, and to propose a quantitative characterization based on the previous work stated above. Moreover, to veriy it soe easured data o the dynaic echanical properties o glass bead-illed low density polyethylene coposites will be used. 2. Theory 2.1. Factors Aecting Storage Modulus E For polyer coposites, relative storage odulus ( ) is usually used to characterize the relationship between storage odulus and other paraeters, which is deined by E = E / E (1) c where E c and E are the storage odulus o coposite and atrix resin, respectively. For a given atrix resin, the ajor actors aecting E are iller content, geoetry, size and its distribution, the distribution and dispersion status o the inclusions in the atrix resin, as well as the interacial orphology between the. That is ( E = φ, d, ξ, ) (2) where φ is the iller volue raction, d is the particle diaeter, ξ is the paraeter related to the dispersion o the particles in atrix and interacial adhesion strength Quantitative Description o Storage Modulus For a rando distribution o spherical particles in atrix, i there is no interacial slide, then E ay be described with the aous Einstein Equation [14]: E = φ (3) Guth generalized the Einstein equation concept by introducing a particle interaction ter and proposed a ollowing equation or spherical particles [15]: E = φ φ 2 (4) Halpin and Tsai derived a siple and generalized equation to approxiate the results o ore exact icroechanics. The Halpin-Tsai equation is as ollows [16] 1+ ζηφ E = (5) 1 ηφ and 1 η = + ζ where ζ is a easure o reinorceent, and it depends on iller geoetry, packing geoetry, and loading conditions. For spherical particles, ζ = 2. = E / E, E is the iller particle storage odulus. On the basis o Eshelby s ethod [10] and Mori s work [11], a sipliied storage odulus equation ay be proposed as ollows: ξφ E = 1+ (7) 1 φ λ and ( ) 7 5ν λ = 15 1 ( ν ) where ξ is the coeicient related to iller shape and packing property. ν is the atrix resin Poisson ratio. 3. Experiental 3.1. aw Materials A atrix resin used in this experiental was a low-density-polyethylene with trade-ark o LDPE G812 (Polyolein, Singapore). The resin elt low index and density were 35 g/10 in (2.16 kg, 190 C) and g/c 3, respectively. The elting teperature was 106 C. A set o solid glass beads (GB) with dierent diaeter, 114 μ (GB2227), 93 μ (GB2429) and 11 μ (GB 5000), was used as iller in this test. The GB trade ark was Spheriglass and was supplied by Potters Industry Inc. in USA. The GB density was 2.5 g/c 3, and the GB surace was pretreated with a silane coupling agent (CP-01) by the supplier Specien Fabrication The LDPE and glass beads were blended in a twin screw extruder (Brabender) ater siply ixing to produce the coposites. The blending ratios o LDPE/GB were 90/10, 80/20, 70/30, and 60/40, respectively. The extrusion teperature varied ro 160 C to 180 C. The speciens or dynaical testing were olded with an injection achine, with width, thickness, and length o 12.9, 3.2, and 55, respectively. The injection teperature was ro 180 C to 200 C Apparatus and Methods The viscoelasticity property easureents o the LDPE/ GB coposites were conducted using a dynaical echanical analyzer (DMA 983, Du Pont Instruents, USA). The test teperatures varied ro 150 C to (6) (8)

3 Predictions o Storage Modulus o Glass Bead-Filled Low-Density-Polyethylene Coposites C, and the teperatures were increased at 2 C per inute. The ixed requency was 1 Hz and the aplitude was esults and Discussion 4.1. Dependence o Storage Modulus on Teperature Figure 1 shows the dependence o the storage odulus ( E c ) o LDPE/GB5000 coposites on teperature. When teperature is lower than 100 C and glass bead content is low (weight raction ( φ ) 20%), E decreases rapidly, and then it decreases gently as teperature lower than 50 C. In a teperature range o 50 C 25 C, E decreases quickly with a rise in teperatures, and then it decrease slightly. In other words, the turning points o storage odulus-teperature curves are at about 100 C, 50 C, and 25 C, respectively. When φ is ore than 20%, the turning points o storage odulus-teperature curves are at about 35 C and 25 C, respectively. It indicates that when teperature is ixed E changes with variation o the glass bead content, especially in a case o higher iller concentration. Figure 2 shows the dependence o the storage odulus ( E c ) o LDPE/GB2429 coposites on teperatures. When teperature is lower than 100 C and within 50 ~ 0 C, E c decreases rapidly, but it decreases gently in other teperature range with a rise in teperatures. In other words, the turning points o storage odulus-teperature curves were around 125 C and 25 C, respectively. It was ound in urther studies that one o peaks o loss odulus-teperature curves o these coposites located around 25 C [6,9]. This indicates that the glass transition teperature or these coposites is about 25 C. Figure 3 shows the dependence o the storage odulus ( E c ) o LDPE/GB2227 coposites on teperatures. When teperature is lower than 50 C and glass bead content is low (weight raction ( φ ) 10%), E decreases roughly linearly. In a teperature range o 50 C 25 C, E decreases quickly with a rise o teperatures, and then it decrease slightly. In other words, the turning points o storage odulus- teperature curves are at about 50 C and 25 C, respectively. When φ is ore than 20%, the turning points o storage odulus- teperature curves are at about 125 C, 50 C and 25 C, respectively? It also indicates that E changes with va- riation o the glass bead content when teperature is ixed, especially in a case o higher iller concentration. It can be seen ro Figure 1 to Figure 3 that when teperature is ixed the E c changes with variation o the glass bead content, and the dierence increases with a reduction o teperatures. In general, the interaction between the glass beads and the LDPE atrix increases and the certain elastic shear deoration is generated under dynaic shear load when teperature is constant, leading to oring the elastic storage energy in the coposite syste. With a rise o teperature, the otion ability o olecular chain in the resin enhances and the relaxation process o the elastic storage energy is quickened, resulting ro the reduction o the storage odulus (see Figures 1-3). Moreover, the interaction between the glass beads and the LDPE atrix increases is enhanced and the dependence o the storage odulus o the illed systes on teperature is increased with an addition o the glass beads, especially in the case o high iller concentration such as φ = 40% (see Figures 1 and 2). Figure 1. Dependence o storage odulus on teperature o LDPE/GB5000 coposite. Figure 2. Dependence o storage odulus on teperature o LDPE/GB2429 coposite.

4 346 Predictions o Storage Modulus o Glass Bead-Filled Low-Density-Polyethylene Coposites E (GPa) LDPE φ = 10 % φ = 20 % φ = 30 % Teperature ( o C) Figure 3. Dependence o storage odulus on teperature o LDPE/GB2227 coposite elationship between elative Storage Modulus and GB Content Figure 4 illustrates the relationship between the relative storage odulus ( E ) o the LDPE/GB coposites and the glass bead volue raction ( φ ) as teperature is 25 C. It ay seen that the E increases nonlinearly with an increase o φ. In addition, the E is estiated by eans o Equation (7) under these test conditions. The results indicate that the calculations and the experiental easured data are roughly close to each other. In this paper, ν = 0.38, ξ = 2.0. For inorganic particles, a relationship between weight raction and volue raction is given by [17]: φ χ φ = 1 φ + φ χ (9) where χ = ρ / ρ, ρ and ρ are the density o the iller and atrix resin, respectively. When teperature is 0 C, the relationship between the relative storage odulus o the LDPE/GB coposites and the glass bead volue raction is showed as in Figure 5. Siilarly, the E increases nonlinearly with an addition o φ. Furtherore, the E is also estiated by eans o Equation (7) under these test conditions. The results show good agreeent between the estiations and the experiental easured data. It can also be observed ro Figures 4 and 5 that the relative storage odulus o LDPE illed with sall diaeter GB is obvious greater than that o LDPE illed with big ones. This because that the saller the size o particles is, the ore speciic surace area o the iller is, leading to increase o the contact area between the inclusions and atrix. Furtherore, the particle nuber increases with an reduction o iller size under the sae volue raction, and the interaction between the inclusions and atrix is enhanced correspondingly, resulting in increase o the storage odulus o polyer coposites, especially in a case o unior dispersion o iller in resin atrix. Figures 6-8 are respectively the racture surace photographs o the scanning electron icroscope (SEM) o the LDPE/GB2227, LDPE/GB2429 and LDPE /GB5000 illed systes when the glass bead weight raction is 20%. It can be observed that the dispersion o the glass beads in LDPE atrix was roughly unior. As stated above, the interaction between the glass beads and the LDPE atrix increases is enhanced and the dependence o the storage odulus o the illed systes on teperature is increased with an addition o the glass beads, especially in the case o high concentration o the ine particles, leading to the dierence between the predictions and the easured storage odulus o the E o C d = 11 μ d = 93 μ d = 114 μ Equation (7) Figure 4. elationship between relative storage odulus and GB volue raction at 25 C φ (%) Figure 5. elationship between relative storage odulus and GB volue raction at 0 C.

5 Predictions o Storage Modulus o Glass Bead-Filled Low-Density-Polyethylene Coposites 347 Figure 6. SEM photograph o racture surace o LDPE/GB2227 coposite. Figure 7. SEM photograph o racture surace o LDPE/GB2429 coposite.

6 348 Predictions o Storage Modulus o Glass Bead-Filled Low-Density-Polyethylene Coposites Figure 8. SEM photograph o racture surace o LDPE/GB5000 coposite. LDPE coposites increases (such as LDPE/GB5000 coposite, see Figures 4 and 5). This indicates that the paraeter ζ would be greater than 2 or the LDPE coposite illed with sall size glass beads. 4.3 Coparison between Predictions o elative Storage Modulus Figure 9 shows the relationship between the relative storage odulus o the LDPE/GB2429 coposites and E T = 25 o C Experiental Equation (4) Equation (5) Equation (7) Equation (3) φ (%) Figure 9. Coparison between predictions o relative storage oduli o LDPE/GB2429 syste at 25 C. the glass bead volue raction as teperature is 25 C. Siilarly, the E increases nonlinearly with an addition o φ. In addition, the values o the E are calculated respectively by using o Einstein equation, Guth equation, Halpin-Tsai equation and Equation (7) under these test conditions, and the results are showed as in Figure 4. It can be seen that the predictions by application o Equation (7) were closer to the easured data ro the experients o the coposites than the other equations. When inorganic particles are blended into atrix resin, they will play a role o raework in polyeric coposite because their stiness is uch greater than that o the atrix. In addition, they will block the oveent o the olecular chains o the atrix resin, leading to increase the stiness o illed polyer coposite aterials. Thereore, i the distribution or dispersion o the inclusions in the atrix is unior, the ore the inorganic particles in the atrix, the higher the stiness o polyeric coposites is. In this case, the storage oduli o polyer coposites will increase with an increase o the iller particles (see Figures 4,5,9). 5. Conclusions The storage odulus o LDPE/GB coposites decreased with rising teperature when the glass bead content was constant, and the turning points o storage odulusteperature curves were around 125 C and 25 C, re-

7 Predictions o Storage Modulus o Glass Bead-Filled Low-Density-Polyethylene Coposites 349 spectively. The storage odulus o LDPE/GB coposites increased nonlinearly with an increase o the volue raction o the glass beads under given experiental conditions. Equation (7) describes a relationship between the storage odulus and volue raction o inorganic particles or illed polyer coposites. The relative storage odulus o LDPE/GB coposites was estiated by using this equation, and these estiations were copared respectively with the calculations by eans o Einstein equation, Guth equation and Halpin-Tsai equation. The results showed that the predictions o the relative storage odulus by eans o Equation (7) were closer to the easured data ro the experients o the coposites than the other equations. EFEENCES [1]. X. Zhang, Q. Q. Ni, T. Natsuki and M. Iwaoto, Mechanical Properties o Coposites Filled with SMA Particles and Short Fibers, Coposite Structures, 2007, Vol. 79, No. 1, pp [2]. Karoui and E. Duour, Prediction o the heology Paraeters o ipened Sei-Hard Cheeses Using Fluorescence Spectra in the UV and Visible anges ecorded at a Young Stage, International Dairy Journal, 2006, Vol. 16, No. 12, pp [3] H. Miyagawa, A. K. Mohanty,. Burgueno, L. T. Drzal and M. Misra, Characterization and Therophysical Properties o Unsaturated Polyester-Layered Silicate Nanocoposites, Journal o Nanoscience and Nanotechnology, 2006, Vol. 6, No. 2, pp [4] J. Kolarik, L. Fabri, M. Slou and D. Konecny, Heterogeneous Polyaide 66/Syndiotactic Polystyrene Blends: Phase Structure and Theral and Mechanical Properties, Journal o Applied Polyer Science, 2005, Vol. 96, No. 3, pp [5] J. Z. Liang, C. Y. Tang,. K. Y. Li, S. C. Tjong and K. C. Yung, A Study o the Elastic Storage Moduli o Glass Bead Filled LDPE Coposites, Key Engineering Materials, 1998, Vol , pp [6]. K. Y. Li, J. Z. Liang and S. C. Tjong, Morphology and Dynaic Mechanical Properties o Glass Beads Filled Low Density Polyethylene Coposites, Journal o Materials Processing Technology, 1998, Vol. 79, No. 1-3, pp [7] J. Z. Liang,. K. Y. Li and S. C. Tjong, Eects o Glass Bead Content and Surace Treatent on Viscoelasticity o Filled Polypropylene/Elastoer Hybrid Coposites, Polyer International, 1999, Vol. 48, No. 11, pp [8] J. Z. Liang,. K. Y. Li and S.C. Tjong, Eects o Glass Bead Size and Content on the Viscoelasticity o Filled Polypropylene Coposites, Polyer Testing, 2000, Vol. 19, No. 2, pp [9] J. Z. Liang,. K. Y. Li and S. C. Tjong, Dynaic Mechanical Analysis o Low-Density Polyethylene with Glass Beads, Journal o Theroplastic Coposite Materials, 2000, Vol. 13, No. 1, pp [10] J. D. Eshelby, Elastic Inclusion and Inhoogeneities. Progress in Solid Mechanics, Asterda, 1961, Vol. 2, pp [11] T. Mori and K. Tanaka, Average Stress in Matrix and Average Elastic Energy o Materials with Misitting Inclusions, Acta Metallurgica, 1973, Vol. 21, No. 5, pp [12] M. Taya and T. W. Chou, On Two Kinds o Ellipsoidal Inhoogeneities in an Ininite Elastic Body: An Application to a Hybrid Coposite, International Journal o Solids and Structures, 1981, Vol. 17, pp [13] Y. Benvensite, A New Approach to the Application o Mori-Tanaka Theory in Coposite-Materials, Mechanics o Materials, 1987, Vol. 6, pp [14] E. Guth, Theory o Filler einorceent, Journal o Applied Physics, 1945, Vol. 16, No. 1, pp [15] L. E. Nielsen, Mechanical Properties o Polyer and Coposites, Marcel Dekker, New York, [16] L. E. Nielsen, Generalized Equation or the Elastic Moduli o Coposite Materials, Journal o Applied Physics, 1970, Vol. 41, No. 11, pp [17] J. Z. Liang and. K. Y. Li, Measureent o Dispersion o Glass Beads in PP Matrix, Journal o einorced Plastics and Coposites, 2001, Vol. 20, No. 8, pp