Soft Polymer Magnetic Nanocomposites: Microstructure Patterning by Magnetophoretic. Transport and Self-Assembly. Suvojit Ghosh and Ishwar K.

Transcription

1 Electronic Supplementary Material (ESI) for Soft Matter Thi journal i The Royal Society of Chemitry 1 Soft Polymer Magnetic Nanocompoite: Microtructure Patterning by Magnetophoretic Tranport and Self-Aembly Suvojit Ghoh and Ihwar K. Puri Supplementary Material Supplement 1 Determination of Magnetic Field The experimental etup conited of a pair of 1 inch cube N5 grade NdFeB magnet (K & J Magnetic, Inc.), hown in the chematic in Figure 1 (d), that are placed 1.7 mm apart. Magnetic nanoparticle were dipered in diluted prepolymer and cured in platic cuvette at three poition relative to thee magnet, labeled A, B and C. Numerical value for B are obtained from the Finite Element Method Magnetic (FEMM) oftware at the ubtrate poed by the cuvette wall and confirmed by uing a Hall probe magnetometer. Value of db / dx are obtained from thi by a central difference cheme. A map of thee value i hown in Figure S1 pointing out poition ued to determine the magnetic control variable which are eparated from the urface of the magnet by the thickne of cuvette wall. The value are lited in Table 1. Figure S1 (a) Map of magnetic field trength B with value of the x-component of (b) B, and (c) it gradient db / dx determined from FEMM oftware.

2 Thi journal i The Royal Society of Chemitry 1 Supplement Scaling analyi relating magnetophoretic velocity to particle ize Each ole i an MNP cluter of ubmicron length. The particle inertia thu play a negligible role in it dynamic o that the magnetophoretic force i balanced only by the fluid drag. From Stoke formulation, the drag on a pherical particle in a fluid F 6 au, (S.1) where a denote the particle radiu and the dynamic vicoity of the fluid. For nonpherical particle, the drag force F ~ magnetophoretic force, i.e., au where a i an etimate of the particle ize. Thi equal the ( m ) B ~ au. (S.) The magnetic moment ~ am m where M i the aturation magnetization of the contituent material. Thu, it follow from Eq. S. that the magnetophoretic peed of a particle cale a U ~ a. (S.) Supplement Scaling Analyi for Structure Aniotropy The aniotropy metric i a repreentative meaure of the cone angle of the filament. Thu, a lower value of indicate higher hape aniotropy. It lowet value i achieved for a ingle chain of ole that repreent the highet conceivable hape aniotropy. The ource of microtructure aniotropy i the long range orientation of the ole-ole bond in the direction of the field. A larger B induce greater alignment of thee bond and thu lead to maller. However, increae monotonically with the gradient of the ernal magnetic field db, a een in Figure (i), while it variation with B i not monotonic. Thi i

3 Thi journal i The Royal Society of Chemitry 1 eemingly counterintuitive but i clarified by conidering that ole-ole bond are oriented not along B but along the local direction of the magnetic field. Thi above analyi i thu valid only when B ~ B. For a nonhomogeneou field, the magnetophoretic force due to the magnetic field gradient alo influence the aniotropy. In order to analyze the dependence of microtructure aniotropy on the magnetic control variable Figure S A implified two particle ytem demontrate how aniotropy increae with increaing gradient of the magnetic field. B and db, we conider a imple ytem compried of the two ole hown in Figure S. In a homogeneou ernal field, tronger magnetic field induce greater alignment of the ole and thu a higher aniotropy. However, a the field trength increae above a critical value, the degree of alignment aturate. Thi critical value can be etimated by comparing B with the field produced at a point due to neighboring ole, a noted above. For the configuration in Figure S (b), the magnetic field at the center of ole 1 due to the preence of it neighbor i B1 /4 e. Conidering magnetite particle, M x M Am -1 lead to B1 ~.T, which i an order of magnitude maller than the applied value of B in our experiment. A B i directed along ( x), the net magnetic field experienced by ole 1 i alo imilarly directed toward the ernally impoed field. It i reaonable to aume that all ole in the ytem encounter a local magnetic field that i directed along ( x), and the alignment effect of the magnetic field i well pat aturation.

4 Thi journal i The Royal Society of Chemitry 1 Correponding to our experiment, we conider B B( x) e. The total potential energy of the ytem x U 1 ( 1 )( ) o mm mr mr mb ( r ) 5, (S.1) i r r tot i i where r denote the poition vector of one ole relative to the other. Thu, the potential energie for cae (a) and (b) in Figure S are, repectively, m 4a a tot ( ( ) ( )), and (S.) U m B a B a U b tot m 8a mb( a). (S.) Here, a denote the radiu of the olar particle. The difference between thee two value indicate whether aniotropic chain are formed along the magnetic field or if all nanoparticle are pulled to the ubtrate. Thi difference, m 8a Utot m B( a) B( a). (S.4) A two-particle chain tranition to a morphology where both particle lie on the ubtrate when. Approximating B( a) B( a)~ db( a), the criteria for thi tranition i, U tot 16 a db 1. M (S.5) Thu, a larger magnitude of the magnetic field gradient render a maller aniotropy in the reultant tructure. In more complicated ytem that conit of everal ole, implified

5 Thi journal i The Royal Society of Chemitry 1 expreion for uch equation cannot be determined. However, the dimenionle number obtained from Eq. (S.5), a db (S.6) M provide guidance about the aniotropy of the ytem. Smaller value of lead to higher aniotropy in the microtructure, forming long filament with mall wherea a high value of will drag all ole to the ubtrate forming an uniform coating with the highet conceivable value of.