April 2007 Constant Current EPID of Fiber-Reinforced Ceramic Composites 1067 1.0 0.8 ￥王 u0.4 40 000.51.0152.0253.03.54.04.55.0 x/a Current(mA) Fig 12. Electric field Ex along the center of the two-dimensional slit. 10. Infiltrated alumina volume percentage versus deposition cur H modifies the particle surface charge and that of the fibers rendering the latter and the former to have the same sign surface even though the fiber concentration is 8.5 vol%. In fact, the field charge, i. e, both are positively charged. Thus, electrosteric(or penetration depth is only double the fiber spacing. The EPD driving force is the electric field, i.e., no field electrostatic)repulsion develops between the fibers and the par- iving force. During deposition, the particles initially deposi between the fibers on the surface of the outer conductive fibers. If the deposit re- or an ionically-stabilized susp sistance is the suspension resistance, the particles deposit on between charged surfaces consists of van der Waals attraction the outer fibers and their surface becomes insulating, i.e., they and electrical double-layer repulsion. As the filament diameter exert no"shielding " contribution. Thus, the electric field car (12 um)is far larger than the particle size(0. I um), the fiber fil- now penetrate further and particles deposit on the inside fibers ament is assumed to be an infinitely large, fat surface. Assuming However, if the fiber bundle is large, the outer fiber layer be that the fiber is pure alumina, the van der Waals interaction, VA comes clogged before the inside voids are filled and a central between an alumina filament and cavity is inevitable. This explains why no particles deposit at the fiber bundle center when the conductive-fiber bundle is large Galor et al.2 reported deep electrophoretic infiltration of olloidal silica particles into a porous conductive carbon sul rate(48 vol% porosity with an average pore size of 60 um) here rp is the particle radius(0.05 um), A is the Hamaker con They, however, reported a maximum weight gain of 3%. A tant for alumina across ethanol (3.37 x 10-J), and d is the suming that the theoretical density of the carbon substrate is paration distance between the fiber and particle. The electrical double-layer interaction potential between a pore volume. They argue that full infiltration can be achieved if spherical alumina particle in an ionically stabilized suspension ive full infiltration due to the electric field shielding effect. Prac- tically, it is concluded that conductive- fibers cannot aid the VR=2nErp-psr formation of dense fiber-reinforced ceramics by EPD or EPID (2) Repulsive Interaction Between the Fiber Filaments and the particles Electrophoretic infiltration deposition involves p:(1) electrophoresis of particles in the suspension, (2 ation the particles through the fiber preform, and (3) tion on the electrode behind the fiber preform s) particke. infiltrate, they must pass through the fiber preform to deposit on the back electrode and as the process continues, they build into ess. To maintain this backfilling process, no particle should de- osit in the fiber perform on the way through. The oxide fibers will also adsorb the PEl (or H)when dipped into the alumina uspension; thus, electrosteric (or electrostatic) interaction oc- curs between the fibers and the particles via the co-adsorbed P (or H)and influences the efficiency of the backfilling. PEl or (0.0) Fig. 13. Potential distribution in a conductive fiber array( white circles Fig. 11. Boundary conditions of a two-dimensional slit.even though the fiber concentration is 8.5 vol%. In fact, the field penetration depth is only double the fiber spacing. The EPD driving force is the electric field, i.e., no field, no driving force. During deposition, the particles initially deposit on the surface of the outer conductive fibers. If the deposit re￾sistance is  the suspension resistance, the particles deposit on the outer fibers and their surface becomes insulating, i.e., they exert no ‘‘shielding’’ contribution. Thus, the electric field can now penetrate further and particles deposit on the inside fibers. However, if the fiber bundle is large, the outer fiber layer be￾comes clogged before the inside voids are filled and a central cavity is inevitable. This explains why no particles deposit at the fiber bundle center when the conductive-fiber bundle is large (Fig. 3). Galor et al. 28 reported deep electrophoretic infiltration of colloidal silica particles into a porous conductive carbon sub￾strate (48 vol% porosity with an average pore size of 60 mm). They, however, reported a maximum weight gain of 3%. As￾suming that the theoretical density of the carbon substrate is 2.25 g/cm3 , their deposited SiO2 only occupies 5.5 vol% of the pore volume. They argue that full infiltration can be achieved if surface deposition is avoided. However, it is impossible to ache￾ive full infiltration due to the electric field shielding effect. Prac￾tically, it is concluded that conductive-fibers cannot aid the formation of dense fiber-reinforced ceramics by EPD or EPID. (2) Repulsive Interaction Between the Fiber Filaments and the Particles Electrophoretic infiltration deposition involves three steps: (1) electrophoresis of particles in the suspension, (2) infiltration of the particles through the fiber preform, and (3) particle deposi￾tion on the electrode behind the fiber preform. When particles infiltrate, they must pass through the fiber preform to deposit on the back electrode and as the process continues, they build into the fiber preform from back to front, i.e., a ‘‘backfilling’’ proc￾ess. To maintain this backfilling process, no particle should de￾posit in the fiber perform on the way through. The oxide fibers will also adsorb the PEI (or H1) when dipped into the alumina suspension; thus, electrosteric (or electrostatic) interaction oc￾curs between the fibers and the particles via the co-adsorbed PEI (or H1) and influences the efficiency of the backfilling. PEI or H1 modifies the particle surface charge and that of the fibers, rendering the latter and the former to have the same sign surface charge, i.e., both are positively charged. Thus, electrosteric (or electrostatic) repulsion develops between the fibers and the par￾ticles via their double-layer overlap. The particles thus ‘‘stream’’ between the fibers. For an ionically-stabilized suspension, the interaction energy between charged surfaces consists of van der Waals attraction and electrical double-layer repulsion. As the filament diameter (12 mm) is far larger than the particle size (0.1 mm), the fiber fil￾ament is assumed to be an infinitely large, flat surface. Assuming that the fiber is pure alumina, the van der Waals interaction, VA, between an alumina filament and an alumina particle is29 VA ¼ Arp 6D 1 þ D 2rp þ D þ D rp ln D 2rp þ D 
(6) where rp is the particle radius (0.05 mm), A is the Hamaker con￾stant for alumina across ethanol (3.37
1020 J 30), and D is the separation distance between the fiber and particle. The electrical double-layer interaction potential between a spherical alumina particle in an ionically stabilized suspension and an alumina filament (assumed flat) is31,32 VR ¼ 2perpzpzf
ln 1 þ expðkDÞ 1 expðkDÞ  ðz 2 p þ z 2 fÞ 2zpzf ln 1½  expð2kDÞ ( ) (7) 40 45 50 55 0 0.2 0.4 0.6 0.8 1 Current (mA) Vol% pores Fig. 10. Infiltrated alumina volume percentage versus deposition cur￾rent after complete infiltration. x y φ= φo a φ= 0 (0,0) φ= 0 (0,a) (∞, 0) y=a/2 x=a (∞, a) Fig. 11. Boundary conditions of a two-dimensional slit. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 x/a Ex=4φo/a Fig. 12. Electric field Ex along the center of the two-dimensional slit. Fig. 13. Potential distribution in a conductive fiber array (white circles are fibers). April 2007 Constant Current EPID of Fiber-Reinforced Ceramic Composites 1067