Abstract
Developing process-structure relationships that predict the impact of the filler-matrix interfacial thermodynamics is crucial to nanocomposite design. This work focuses on developing quantitative relationships between the filler-matrix interfacial energy, the processing conditions, and the nanoparticle dispersion in polymer nanocomposites. We use a database of nanocomposites made of polypropylene, polystyrene, and poly(methyl methacrylate) with three different surface-modified silica nanoparticles under controlled processing conditions. The silica surface was modified with three different monofunctional silanes: octyldimethylmethoxysilane, chloropropyldimethylethoxysilane, and aminopropyldimethylethoxysilane. Three descriptors were used to establish the relationship between interfacial energy, processing conditions, and final nanoparticle dispersion. The ratio of the work of adhesion between filler and polymer to the work of adhesion between filler to filler (descriptor: \( W_{\text{PF}} /W_{\text{FF}} \)) and the mixing energy for the production of the nanocomposites (descriptor: E γ ) are used to determine the final dispersion state of the nanoparticles. The dispersion state is described using a descriptor that characterizes the amount of interfacial area from TEM images (descriptor: \( \bar{I}_{\text{filler}} \)). In order to capture the descriptors accurately, the TEM images of the nanocomposites are binarized using a pixel-wise neighbor-dependent Niblack thresholding algorithm. The significance of the microstructural descriptors was ranked using supervised learning and the interfacial area emerged as the most significant descriptor for describing the nanoparticle dispersion. Our results show a stronger dependence of the final dispersion on the interfacial energy than the processing conditions. Nevertheless, for the final dispersion state, both descriptors have to be taken into account. We also introduce a matrix-dependent term to establish a quantitatively non-linear relationship between the processing and microstructure descriptors.
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References
Ramanathan T, Abdala AA, Stankovich S et al (2008) Functionalized graphene sheets for polymer nanocomposites. Nat Nanotechnol 3:327–331
Ramanathan T, Liu H, Brinson LC (2005) Functionalized SWNT/polymer nanocomposites for dramatic property improvement. J Polym Sci, Part B 43:2269–2279
Tyan HL, Liu YC, Wei KH (1999) Thermally and mechanically enhanced clay/polyimide nanocomposite via reactive organoclay. Chem Mater 11:1942–1947
Ash BJ, Siegel RW, Schadler LS (2004) Mechanical behavior of alumina/poly(methyl methacrylate) nanocomposites. Macromolecules 37:1358–1369
Hussain F, Hojjati M, Okamoto M, Gorga RE (2006) Review article: polymer-matrix nanocomposites, processing, manufacturing, and application: an overview. J Compos Mater 40:1511–1575
Jordan J, Jacob KI, Tannenbaum R, Sharaf MA, Jasiuk I (2005) Experimental trends in polymer nanocomposites—a review. Mater Sci Eng, A 393:1–11
Paul DR, Robeson LM (2008) Polymer nanotechnology: nanocomposites. Polymer 49:3187–3204
Yano K, Usuki A, Okada A, Kurauchi T, Kamigaito O (1993) Synthesis and properties of polyimide clay hybrid. J Polym Sci Polym Chem. 31:2493–2498
Zhu A, Cai A, Zhang J, Jia H, Wang J (2008) PMMA-grafted-silica/PVC nanocomposites: mechanical performance and barrier properties. J Appl Polym Sci 108:2189–2196
Ophir A, Dotan A, Belinsky I, Kenig S (2010) Barrier and mechanical properties of nanocomposites based on polymer blends and organoclays. J Appl Polym Sci 116:72–83
Hanemann T, Szabó DV (2010) Polymer-nanoparticle composites: from synthesis to modern applications. Materials. 3:3468–3517
Villmow T, Kretzschmar B, Pötschke P (2010) Influence of screw configuration, residence time, and specific mechanical energy in twin-screw extrusion of polycaprolactone/multi-walled carbon nanotube composites. Compos Sci Technol. 70:2045–2055
Villmow T, Pötschke P, Pegel S, Häussler L, Kretzschmar B (2008) Influence of twin-screw extrusion conditions on the dispersion of multi-walled carbon nanotubes in a poly (lactic acid) matrix. Polymer 49:3500–3509
Kasaliwal G (2011) Analysis of multiwalled carbon nanotube agglomerate dispersion in polymer melts. PhD dissertation, University of Dresden
Natarajan B, Li Y, Deng H, Brinson LC, Schadler LS (2013) Effect of interfacial energetics on dispersion and glass transition temperature in polymer nanocomposites. Macromolecules 46:2833–2841
Rauwendaal C (2014) Polymer extrusion. Hanser, Munich
Gacitua W, Ballerini A, Zhang J (2005) Polymer nanocomposites: synthetic and natural fillers a review. Maderas Ciencia y tecnol 7:159–178
Wang M (2003) Developing bioactive composite materials for tissue replacement. Biomaterials 24:2133–2151
Ahmed M (1979) Coloring of plastics: theory and practice. Van Nostrand Reinhold, New York
Parfitt GD (1969) Fundamental aspects of dispersion, dispersion of solids in liquids: with special reference to pigments, chap 3. Elsevier, Amsterdam, pp 81–121
Hartley PA, Parfitt GD (1985) Dispersion of powders in liquids. 1. The contribution of the van der Waals force to the cohesiveness of carbon black powders. Langmuir 1:651–657
Wang Y, Lee WC (2004) Interfacial interactions in calcium carbonate–polypropylene composites. 2: effect of compounding on the dispersion and the impact properties of surface-modified composites. Polym Compos 25:451–460
Socher R, Krause B, Müller MT, Boldt R, Pötschke P (2012) The influence of matrix viscosity on MWCNT dispersion and electrical properties in different thermoplastic nanocomposites. Polymer 53:495–504
Alig I, Pötschke P, Lellinger D et al (2012) Establishment, morphology and properties of carbon nanotube networks in polymer melts. Polymer 53:4–28
Yamada H, Manas-Zloczower I, Feke DL (1998) Observation and analysis of the infiltration of polymer liquids into carbon black agglomerates. Chem Eng Sci 53:1963–1972
Levresse P, Manas-Zloczower I, Feke DL, Bomal Y, Bortzmeyer D (1999) Observation and analysis of the infiltration of liquid polymers into calcium carbonate agglomerates. Powder Technol 106:62–70
Vaia RA, Jandt KD, Kramer EJ, Giannelis EP (1995) Kinetics of polymer melt intercalation. Macromolecules 28:8080–8085
Washburn EW (1921) The dynamics of capillary flow. Phys Rev Lett 17:273–283
Lozano T, Lafleur PG, Grmela M, Thibodeau C (2004) Effect of filler dispersion on polypropylene morphology. Polym Eng Sci 44:880–890
Atkins P, de Paula J (2010) Physical chemistry. Oxford University Press, New York
Gendron R, Binet D (1998) State of dispersion: polypropylene filled with calcium carbonate. J Vinyl Addit Technol 4:54–59
Khan J, Harton SE, Akcora P, Benicewicz BC, Kumar SK (2009) Polymer crystallization in nanocomposites: spatial reorganization of nanoparticles. Macromolecules 42:5741–5744
Kitazaki Y, Hata T (1972) Extension of Fowkes’ equation and estimation of surface tension of polymer solids. Nippon Setchaku Kyokaishi. 8:131
Wu S (1971) Calculation of interfacial tension in polymer systems. J Polym Sci Polym Symp 34:19–30
Khoshkava V, Kamal MR (2013) Effect of surface energy on dispersion and mechanical properties of polymer/nanocrystalline cellulose nanocomposites. Biomacromolecules 14:3155–3163
Dee GT, Sauer BB (1992) The molecular weight and temperature dependence of polymer surface tension: comparison of experiment with interface gradient theory. J Colloid Interface Sci 152:85–103
Chung CI (2000) Extrusion of polymers. Hanser, Munich
Starr FW, Douglas JF, Glotzer SC (2003) Origin of particle clustering in a simulated polymer nanocomposite and its impact on rheology. J Chem Phys. 119:1777–1788
Stöckelhuber KW, Das A, Jurk R, Heinrich G (2010) Contribution of physico-chemical properties of interfaces on dispersibility, adhesion and flocculation of filler particles in rubber. Polymer 51:1954–1963
Wang M-J (1998) Effect of polymer-filler and filler-filler interactions on dynamic properties of filled vulcanizates. Rubber Chem Technol 71:520–589
Good RJ, Girifalco LA (1960) A theory for estimation of surface and interfacial energies. III. Estimation of surface energies of solids from contact angle data. J Phys Chem 64:561–565
Owens DK, Wendt RC (1969) Estimation of the surface free energy of polymers. J Appl Polym Sci 13:1741–1747
Fowkes FM (1964) Attractive forces at interfaces. Ind Eng Chem 56:40–52
Mezger TG (2006) The rheology handbook: for users of rotational and oscillatory rheometers. Vincentz Network GmbH & Co KG, Hannover
Edmondson IR, Fenner RT (1975) Melting of thermoplastics in single screw extruders. Polymer 16:49–56
Tadmor Z, Duvdevani I, Klein I (1967) Melting in plasticating extuders theory and experiments. Polym Eng Sci 7:198–217
Fukase H, Kunio T, Shinya S, Nomura A (1982) A plasticating model for single-screw extruders. Polym Eng Sci 22:578–586
Donovan RC (1971) A theoretical melting model for plasticating extruders. Polym Eng Sci 11:247–257
Abeykoon C, Kelly AL, Brown EC et al (2014) Investigation of the process energy demand in polymer extrusion: a brief review and an experimental study. Appl Energy 136:726–737
Abeykoon C, Li K, McAfee M, Martin PJ, Deng J, Kelly AL (2010) Modelling the effects of operating conditions on die melt temperature homogeneity in single screw extrusion. In: UKACC International Conference on CONTROL 2010, pp 42–47
Lai E, Yu DW (2000) Modeling of the plasticating process in a single-screw extruder: a fast-track approach. Polym Eng Sci 40:1074–1084
Kapur JN, Sahoo PK, Wong AKC (1985) A new method for gray-level picture thresholding using the entropy of the histogram. Comput Vision Graph 29:273–285
Otsu N (1975) A threshold selection method from gray-level histograms. Automatica. 11:23–27
Kittler J, Illingworth J (1986) Minimum error thresholding. Pattern Recogn 19:41–47
Weszka JS, Nagel RN, Rosenfeld A (1974) A threshold selection technique. IEEE Trans Comput 100:1322–1326
Xu H, Dikin DA, Burkhart C, Chen W (2014) Descriptor-based methodology for statistical characterization and 3D reconstruction of microstructural materials. Comput Mater Sci 85:206–216
Khurshid K, Siddiqi I, Faure C, Vincent N (2009) Comparison of Niblack inspired binarization methods for ancient documents. In: IS&T/SPIE Electronic imaging, vol 7247, pp 72470U–72470U-9
Niblack W (1985) An introduction to digital image processing. Strandberg Publishing Company, Birkeroed
Zhao H, Li X, Huang Y, Schadler L, Chen W, Brinson LC NanoMine—a material data resource for polymer nanocomposites: database, data analytics and predictive tools (manuscript under review)
Borbely A, Csikor FF, Zabler S, Cloetens P, Biermann H (2004) Three-dimensional characterization of the microstructure of a metal–matrix composite by holotomography. Mater Sci Eng, A 367:40–50
Rollett AD, Lee SB, Campman R, Rohrer GS (2007) Three-dimensional characterization of microstructure by electron back-scatter diffraction. Ann Rev Mater Res. 37:627–658
Tewari A, Gokhale AM (2004) Nearest-neighbor distances between particles of finite size in three-dimensional uniform random microstructures, Mater Sci Eng. A. 385:332–341
Pytz R (2004) Microstructure description of composites, statistical methods, mechanics of microstructure materials, CISM courses and lectures. Springer, New York
Scalon JD, Fieller NRJ, Stillman EC, Atkinson HV (2003) Spatial pattern analysis of second-phase particles in composite materials. Mater Sci Eng, A 356:245–257
Xu H, Li Y, Brinson C, Chen W (2014) A Descriptor-Based Design Methodology for Developing Heterogeneous Microstructural Materials System. J Mech Design. 136:051007
Torquato S (2002) Random heterogeneous materials: microstructure and macroscopic properties. Springer, New York
Sundararaghavan V, Zabaras N (2005) Classification and reconstruction of three-dimensional microstructures using support vector machines. Comput Mater Sci 32:223–239
Basanta D, Miodownik MA, Holm EA, Bentley PJ (2005) Using genetic algorithms to evolve three-dimensional microstructures from two-dimensional micrographs. Metall Mater Trans A 36:1643–1652
Quiblier JA (1984) A new three-dimensional modeling technique for studying porous media. J Colloid Interf Sci. 98:84–102
Jiang Z, Chen W, Burkhart C (2012) A Hybrid Optimization Approach to 3D Porous Microstructure Reconstruction via Gaussian Random Field. In: ASME 2012 international design engineering technical conferences & computers and information in engineering conference (Chicago), IDETC2012-71173
Grigoriu M (2003) Random field models for two-phase microstructures. J Appl Phys 94:3762–3770
Ganesh VV, Chawla N (2005) Effect of particle orientation anisotropy on the tensile behavior of metal matrix composites: experiments and microstructure-based simulation. Mater Sci Eng, A 391:342–353
Thomas M, Boyard N, Perez L, Jarny Y, Delaunay D (2008) Representative volume element of anisotropic unidirectional carbon–epoxy composite with high-fibre volume fraction. Compos Sci Technol. 68:3184–3192
Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11:357–372
Xu H, Liu R, Choudhary A, Chen W (2014) A machine learning-based design representation method for designing heterogeneous microstructures. In: ASME 2014 international design engineering technical conferences and computers and information in engineering conference, V02BT03A009-V02BT03A009
Acknowledgements
The support from NSF for this collaborative research: CMMI-1334929 and DMR-1310292 (Northwestern University) and CMMI-1333977 (RPI), is greatly appreciated.
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Hassinger, I., Li, X., Zhao, H. et al. Toward the development of a quantitative tool for predicting dispersion of nanocomposites under non-equilibrium processing conditions. J Mater Sci 51, 4238–4249 (2016). https://doi.org/10.1007/s10853-015-9698-1
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DOI: https://doi.org/10.1007/s10853-015-9698-1