Abstract
The mechanical properties of aggregated colloids depend on the mutual interplay of inter-particle potentials, contact forces, aggregate structure and material properties of the bare particles. Owing to this variety of influences, experimental results from macroscopic mechanical testings were mostly compared to time-consuming, microscopic simulations rather than to analytical theories. The aim of the present paper was to relate both macroscopic and microscopic mechanical data with each other and simple analytical models. We investigated dense amorphous aggregates made from monodisperse poly-methyl methacrylate (PMMA) particles (diameter: 1.6 \(\mu\) m via nanoindentation in combination with confocal microscopy. The resulting macroscopic information was complemented by the three-dimensional aggregate structure as well as the microscopic strain field and strain tensor. The measured strain field and tensor were in reasonable agreement with the predictions from analytical continuum theories. Consequently, the measured force-depth curves could be analyzed within a theoretical framework that had been frequently used for nanoindentation of atomic matter such as metals, ceramics and polymers. The extracted values for hardness and effective Young’s modulus represented average values characteristic of the aggregate. On the basis of of these parameters we discuss the influence of the strength of particle bonds by introducing polystyrene (PS) between the particles.
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Alfons van Blaaderen, Science 301, 470 (2003)
Daan Frenkel, Science 296, 65 (2002)
P. Schall, I. Cohen, D.A. Weitz, F. Spaepen, Nature 440, 319 (2006)
Dirk G.A.L. Aarts, Matthias Schmidt, Henk N.W. Lekkerkerker, Science 304, 847 (2004)
R. Besseling, Eric R. Weeks, A.B. Schofield, W.C.K. Poon, Phys. Rev. Lett. 99, 028301 (2007)
Eric R. Weeks, J.C. Crocker, Andrew C. Levitt, Andrew Schofield, D.A. Weitz, Science 287, 627 (2000)
K.A. Dawson, G. Foffi, F. Sciortino, P. Tartaglia, E. Zaccarelli, J. Phys.: Condens. Matter 13, 9113 (2001)
M. Siebenbrger, M. Ballauff, J. Rheol. 53, 707 (2009)
Alessio Zaccone, Miroslav Soos, Marco Lattuada, Hua Wu, Matthäus U. Bäbler, Massimo Morbidelli, Phys. Rev. E 79, 061401 (2009)
C. Schilde, S. Breitung-Faes, A. Kwade, Ceramic Forum Internat. 84, 12 (2007)
C. Schilde, I. Kampen, A. Kwade, Chem. Eng. Sci. 65, 3518 (2010)
C. Schilde, T. Gothsch, K. Quarch, M. Kind, A. Kwade, Chem. Eng. Tech. 32, 1078 (2009)
C. Schilde, A. Kwade, Chem. Ing. Tech. 81, 1155 (2009)
S. Zumer, M. Ravnik, T. Porenta, G.P. Alexander, J.M. Yeomans, Proc. SPIE 7775, 77750H (2010) DOI:10.1117/2.1201009.003168
Y.A. Vlasov, X.-Z. Bo, J.C. Sturm, D.J. Norris, Nature 414, 289 (2001)
M. D’Acunzi, M. Mammen, L. Singh, X. Deng, M. Roth, G.K. Auernhammer, H.-J. Butt, D. Vollmer, Faraday Discuss. 146, 35 (2010)
J. Boussinesq, Applications des Potentiels a l’étude de équilibre et du mouvement des solides élastiques (Gauthier-Villars, Paris, 1885)
H. Hertz, J. Reine Angew. Math. 1882, 156 (1882)
J. Hay, Exp. Tech. 33, 66 (2009)
M.F. Doernera, W.D. Nixa, J. Mater. Res. 1, 601 (1986)
Krystyn J. Van Vliet, Catherine A. Tweedie, J. Mater. Res. 21, 3029 (2006)
A. Gouldstone, K.J. Van Vliet, S. Suresh, Nature 411, 656 (2001)
D. Filip, V.I. Uricanu, M.H.G. Duits, D. van den Ende, J. Mellema, W.G.M. Agterof, F. Mugele, Langmuir 22, 560 (2006)
X. Ling, H.-J. Butt, M. Kappl, Langmuir 23, 8392 (2007)
Lars-Oliver Heim, Jürgen Blum, Markus Preuss, Hans-Jürgen Butt, Phys. Rev. Lett. 83, 3328 (1999)
S. Ecke, R. Raiteri, E. Bonaccurso, C. Reiner, H.-J. Deiseroth, H.J. Butt, Rev. Sci. Instrum. 72, 4164 (2001)
R.R. Agayan, R.G. Smith, R. Kopelman, J. Appl. Phys. 104, 1 (2008)
John C. Crocker, David G. Grier, J. Colloid Interface Sci. 179, 298 (1996)
E. Weeks, Particle tracking using idl, http://www.physics.emory.edu/~weeks/idl, September 2008
Peter Schall, David A. Weitz, Frans Spaepen, Science 318, 1895 (2007)
D. Chen, D. Semwogerere, J. Sato, V. Breedveld, Eric R. Weeks, Phys. Rev. E 81, 011403 (2010)
Subra Suresh, Nat. Mater. 5, 253 (2006)
R.L. Smith, G.E. Sandland, Proc. Inst. Mech. Eng. 102, 623 (1922)
J.A. Brinell, Congr. Int. Meth. Essai Matér. Construct. 2, 83 (1901)
S.I. Bulychev, V.P. Alekhin, M.Kh. Shorshorov, A.P. Ternovskii, G.D. Shnyrev, Zavod. Lab. 41, 1137 (1975)
S.I. Bulychev, V.P. Alekhin, Zavod. Lab. 53, 76 (1987)
M.F. Doerner, W.D. Nix, J. Mater. Res. 1, 601 (1986)
N.H. Oliver, G.M. Pharr, J. Mater. Res. 7, 1564 (1992)
R. Bartali, V. Michelia, G. Gottardia, A. Vaccaria, N. Laidania, Surf. Coat. Tech. 204, 2073 (2010)
J. Malzbender, G. de With, J. Mater. Res. 17, 502 (2002)
W.C. Oliver, G.M. Pharr, J. Mater. Res. 19, 3 (2004)
C. Pathmamanoharan, K. Groot, J.K.G. Dhont, Colloids Polym. Sci. 275, 897 (1997)
L. Antl, J.W. Goodwin, R.D. Hill, R.H. Ottewill, S.M. Owens, S. Papworth, J.A. Waters, Coll. Surf. 17, 67 (1986)
Remco Tuinier, Gerrit A. Vliegenthart, Henk N.W. Lekkerkerker, J. Chem. Phys. 113, 10768 (2000)
P.J. Lu, J.C. Conrad, H.M. Wyss, A.B. Schofield, D.A. Weitz, Phys. Rev. Lett. 96, 028306 (2006)
C.P. Ohtsuka, T. Royall, H. Tanaka, EPL 84, 46002 (2008)
Rei Kurita, Eric R. Weeks, Phys. Rev. E 82, 011403 (2010)
M. Roth, M. Franzmann, M. d’Acunzi, M. Kreiter, G.K. Auernhammer, Arxiv. cond-mat. soft. 1106, 3623v1 (2011)
James B. Pawley, Handbook of biological confocal microscopy (Springer Science + Buisness Media, LLC, 2006)
Marvin Minski, Scanning 10, 128 (1988)
A.D. Dinsmore, Eric R. Weeks, Vikram Prasad, Andrew C. Levitt, D.A. Weitz, Appl. Opt. 40, 4152 (2001)
T. Kawasaki, A. Onuki, cond-mat.soft 1103, 1051 (2011)
K.L. Johnson, Contact mechanics, chapter 4, Normal contact of elastic solids: Hertz theory (Cambridge University Press, 2004) pp. 84--106
M.T. Huber, Ann. Phys. (Leipzig) 316, 153 (2006)
R.M. Davies, Proc. R. Soc. London, Ser. A 197, 416 (1949)
K.L. Johnson, Contact mechanics, chapter 6, Normal contact of inelastic solids (Cambridge University Press, 2004) pp. 153--201
I.S. Choi, M. Dao, S. Suresh, J. Mech. Phys. Solids 56, 157 (2008)
K.-P. Lu, S. Lee, C.P. Cheng, J. Appl. Phys. 90, 1745 (2001)
Y.-T. Cheng, C.-M. Cheng, Appl. Phys. Lett. 73, 614 (1998)
J. Malzbender, G. de With, Surf. Coat. Tech. 135, 60 (2000)
Marcel Roth, Carsten Schilde, Philipp Lellig, Arno Kwade, Günter K. Auernhammer, Chem. Lett. 41, 1110 (2012)
L. Zhang, M. D’Acunzi, M. Kappl, G.K. Auernhammer, D. Vollmer, Langmuir 25, 2711 (2009)
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Roth, M., Schilde, C., Lellig, P. et al. Colloidal aggregates tested via nanoindentation and quasi-simultaneous 3D imaging. Eur. Phys. J. E 35, 124 (2012). https://doi.org/10.1140/epje/i2012-12124-8
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DOI: https://doi.org/10.1140/epje/i2012-12124-8