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where p is the volume fraction of the conducting phase above the percolation threshold, pc is the percolation threshold, σ is conductivity of sample at given volume fraction of p, and σc is the conductivity of the sample at the percolation threshold. The conductivity exponent t generally reflects the dimensionality of the system with values typically around 1.3 and 2.0 for two and three-dimensions, respectively(Clerc, Giraud, Laugier, & Luck, 1990). Gubbels et al. found that in a polystyrene (PS)/ polyethylene (PE)/ carbon black (CB) system, t is 2.0 when CB is dispersed within the amorphous phase of pure PE. Its value becomes 1.3 when CB is at the interface of a PE/PS blend with dual-phase continuity(Gubbels, Blacher, et al., 2002; Gubbels, Jerome, et al., 2002). Al-Saleh et al.(Al-Saleh & Sundararaj, 2008) showed that selective localization of CB at the interface of PS/PP blend is possible by introducing SBS copolymer that can selectively localize at the interface and for which CB has the highest affinity. Addition of 5% SBS resulted in reduction of percolation threshold to less than 1%. The classical percolation theory (Equation 2-44) applied to conductive polymer composite systems must meet some definite conditions. First, the system should be randomly distributed, and secondly, particles must be spherical, monodisperse and have an isotropic conductivity. If one or all of these conditions are not fulfilled, the theoretical value will deviate far from the realistic one. For example, Carmona et al. (Carmona, Prudhon, & Barreau, 1984) reported that in short fiber-epoxy resin composites, the exponent t = 3.0 ± 0.6 when the length of fibers ranges between 1.15 mm and 2.85 mm. A simplified view of percolation transition is depicted in Figure 2-19. At low filler loadings the conductive particles act like conductive islands in a sea of electrically insulating resin. Since electrons moving through the composite still encounter the insulating polymer, little or no change in conductivity is observed. Addition of further conductive material leads to the conductive particles being more crowded and more likely to come into contact with each other. Finally, at the percolation threshold, the first complete cluster from the bottom to the top of the sample is generated. 48
Figure 2-19. Approaching the percolation threshold in a binary blend Thereby, continuous chains or networks of conductive material through sample are formed. An electrical charge can now pass through the conductive composite or blend via this network without encountering the low conductivity of the polymer resin. Introducing further conductive material loading beyond the percolation threshold does not greatly increase the conductivity of this material(Bhattacharya, 1986). 2.3.1.1.1 Parameters Influencing the Percolation Threshold of Conductive Fillers There are several ways to decrease the percolation threshold of conductive filler concentration in polymeric matrices, which are mainly based on the use of additives, the polymer properties, the optimization of processing conditions, and the size, distribution and porosity of the filler(Smuckler & Finnerty, 1974; Verhelst, Wolthuis, Voet, Ehrburger, & Donnet, 1977). Therefore, varying these factors can cause strong deviations from the percolation theory. Several important factors influencing the percolation threshold in conductive polymer composites are as follows: • Type and Shape of Conductive fillers The shape of the particle plays a critical role in where (at what filler volume) percolation occurs. The more structured or elaborately shaped the particle, the more likely it is to contact a nearest neighbor and form a continuous network. Perfectly spherical fillers, which arguably have the least elaborate and least structured shape, can require as much as 40% loading in order to reach 49
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© Sepehr Ravati, 2010. UNIVERSITÉ
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DEDICATED To my parents iii
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RÉSUMÉ Cette thèse présente, po
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devenir une structure hiérarchique
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ABSTRACT This thesis presents, for
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system can be increased from 10 -15
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CONDENSÉ EN FRANÇAIS Dans ce trav
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deuxième coquille de PS. Les phase
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structures à percolation multiple
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autre sous-type de morphologie dans
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TABLE OF CONTENTS DEDICATION.......
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xxiii 2.4.1.1.1 Charged Polymer Ads
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5.3.4 Annealing Test ..............
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xxvii REFERENCES ..................
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LIST OF FIGURES xxix Figure 1-1. a)
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Figure 2-12. SEM photomicrograph of
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Figure 2-34. Schematic view of diff
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Figure 4-8. SEM micrographs of vari
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Figure 5-6. a),b) Scanning electron
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and c) triangular concentration dia
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n number of moles p concentration o
Page 43 and 44: AFM atomic force microscopy LIST OF
Page 45 and 46: PS-co-PMMA copolymer of PS and PMMA
Page 47 and 48: 1.1 Introduction CHAPTER 1 - INTROD
Page 49 and 50: Figure 1-2. Human heart, longitudin
Page 51 and 52: One of the applications for porous
Page 53 and 54: On the other hand, a novel tri-cont
Page 55 and 56: 2.1 Polymer Blends CHAPTER 2 - LITE
Page 57 and 58: Based on Sterling’s approximation
Page 59 and 60: Antonoff’s rule (Equation 2-13) i
Page 61 and 62: 2.1.2.1 Binary Polymer Blends 2.1.2
Page 63 and 64: Some other studies(Everaert, Aerts,
Page 65 and 66: where the parameter z is dependent
Page 67 and 68: “compatibilization” was suggest
Page 69 and 70: a) λ BC A and B are matrices, b) C
Page 71 and 72: Reignier & Favis, 2000, 2003a; Reig
Page 73 and 74: measure the interfacial tension of
Page 75 and 76: a) b) Figure 2-6. Dependence of the
Page 77 and 78: Omonov et al. found double percolat
Page 79 and 80: 2.1.2.2.3 Effect of Composition on
Page 81 and 82: a) b) C B A c) Figure 2-12. SEM pho
Page 83 and 84: In the case where PS is the matrix,
Page 85 and 86: Posthuma de Boer, 1999) (Kumin & Ch
Page 87 and 88: lattice, such as square lattice, wi
Page 89 and 90: magnetization, which is a function
Page 91 and 92: Polymers have long been thought of
Page 93: epoxy as a function of nanotube wei
Page 97 and 98: Figure 2-21. Transmission electron
Page 99 and 100: Figure 2-22: Dependence of PE conti
Page 101 and 102: Figure 2-24. Plot of the total numb
Page 103 and 104: chain provides the conductive path
Page 105 and 106: 2.3.1.2.1 Polyaniline One of the mo
Page 107 and 108: CoPA/LLDPE/PANI blend and a poor-qu
Page 109 and 110: Narkis and co-workers extended and
Page 111 and 112: Figure 2-31: Conductivity of PVDF/P
Page 113 and 114: organic thin films, a novel and str
Page 115 and 116: on the topic have been reported in
Page 117 and 118: succeeded in creating thin films wi
Page 119 and 120: Addition of salt to the solution of
Page 121 and 122: different from that of linear homop
Page 123 and 124: Figure 2-39. Macromolecule with a)
Page 125 and 126: polyanion such as hyaluronan (HA)(P
Page 127 and 128: 2.4.1.1.7 Effect of Salt on Multila
Page 129 and 130: 2.4.1.1.8 Overcompensation of the M
Page 131 and 132: important factors determining the g
Page 133 and 134: As shown in Figure 2-44, swelling a
Page 135 and 136: increasing the pH value due to a de
Page 137 and 138: CHAPTER 3 - ORGANIZATION OF THE ART
Page 139 and 140: discussed above, HDPE, PS, PMMA, an
Page 141 and 142: CHAPTER 4 - LOW PERCOLATION THRESHO
Page 143 and 144: or model which predicts where the p
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concentration threshold for the ons
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chemical and weathering resistance,
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Table 4-1. Material Characteristics
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filled with blend pellets. To facil
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4.3.6 Conductivity Measurements DC
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experimentally in this research gro
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a) b) c) d) Figure 4-4. Schematic i
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microstructure of the quaternary bl
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a) b) c) d) Figure 4-6. SEM microgr
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a) b) PVDF PS PMMA c) d) e) HDPE PS
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Uniform layers of PS and PMMA situa
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the concentration of HDPE is increa
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a) b) c) e) Figure 4-11. SEM microg
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melt-processable and contains 25 wt
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One question that should be address
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Conductivity(S/cm) Ternary Blend 1,
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phase(PMMA), the concentration of P
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(6) Virgilio, N.; Desjardins, P.; L
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ONION MORPHOLOGY HDPE PVDF PS Contr
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work described above has focused on
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thermodynamic explanation to predic
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four-point probe increases continuo
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in the rheology tests were compress
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5.3.6 Layer-by-Layer Deposition The
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prepare a polymer blend structure w
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a) b) c) Figure 5-3. Scanning elect
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spontaneously self-assembled. After
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a) b) c) d) e) f) g) h) Figure 5-5.
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Since the ultra-low surface area va
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c) a) b) Figure 5-6. a),b) Scanning
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salt to a PSS polyelectrolyte solut
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A relationship between macropore si
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close together. It is interesting t
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Figure 5-9. Mass increase (%) indic
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In this work the conductance of the
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deposited PANI layers increases unt
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(52) Guo, H. F.; Packirisamy, S.; G
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6.2 Introduction It is well-known t
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modified version of Harkins theory(
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6.3 Experimental 6.3.1 Materials Co
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Complex voscosity (Pa.s) 1,0E+04 1,
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6.3.5.2 Focused Ion Beam (FIB) and
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a) c) b) d) e) f) PMMA PMMA HDPE HD
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y Harkins theory, PS will always si
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a) b) c) d) e) f) PS Figure 6-6. a)
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a) b) HDPE : black PS : grey PMMA :
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6.4.6 Continuity, Co-continuity, an
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c) V III II I VII I IV VI Figure 6-
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Continuity Scheme (a) Figure 6-10.
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Addition of a low concentration of
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Addition of small amounts of HDPE t
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icontinuous network with the HDPE.
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Three examples are shown in Figure
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(9) Mekhilef, N.; Verhoogt, H. Poly
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structures are formed due to the co
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CONCLUSION AND RECOMMENDATIONS In t
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REFERENCES A. K. Gupta, K. R. S. (1
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Caruso, F. (2003). Hollow Inorganic
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Domenech, S. C., Bortoluzzi, J. H.,
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Geuskens, G., Gielens, J. L., Geshe
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Hou, S., Harrell, C. C., Trofin, L.
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Krass, H., Papastavrou, G., & Kurth
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Macdiarmid, A. G., Jin-Chih, C., Ha
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Niziol, J., & Laska, J. (1999). Con
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Reghu, M., Yoon, C. O., Yang, C. Y.
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Shirakawa, H., Louis, E. L., MacDia
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Utracki, L. A. (1991). On the visco
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Yasuda, K., Armstrong, R., & Cohen,
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literature has examined factors inf
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(Reignier & Favis, 2000, 2003a; Rei
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Table A-1.2. Interfacial tensions a
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acquisition of images with a very h
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Table A-1.3. Continuity of the PMMA
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(17) Reignier, J.; Favis, B. D., Ma
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PANI. Theoretically, the extent of
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Equation A-2.7 0( ) 0 1. 5 σ = σ
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Cumulative Mass × 10 5 (g) dipping
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of PANI, and an increase in the con
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Resistance(ohm) 1.0E+12 1.0E+11 1.0
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esistance value. Samples containing
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The results of resistance for PS/PE
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Caruso, F., & Schuler, C. (2000). E
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