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droplets. The results indicate that due to forces and coalescence, each phase joins with same phase, and thus phase sizes become larger. In other words, a complete transition from multiple subinclusion particles within a given shell to a core-shell structure is observed. It can be said that this process is performed similarly to the case of binary blends, as thin parts of each component are being pushed to thick parts of the same component due to capillary forces, which results in an increase in average pore size. Figure 2-15. Experimental pore size growth (points) with the theoretical model (solid lines) for different blends annealed at 200°C. (Yuan, 2005) 2.2 Percolation Theory The behavior of the connected clusters in a random graph in mathematics is described by the percolation theory. The main concept of the percolation theory is the existence of a percolation threshold. Percolation threshold is a mathematical term defined as the formation of long-range connectivity in random systems. Percolation threshold in engineering and material science deals with fluid flow and similar processes which concern the movement and filtering of fluids through porous media. One question that arises is whether a liquid poured on top of a porous material is able to make its way from the top to the bottom. From a mathematical point of view, a regular 40
lattice, such as square lattice, with a random network by randomly occupying sites (vertices) or bonds (edges) with a statistically independent probability is imagined (Figure 2-16). If it is examined as an infinite network corresponding to Kolmogorov`s zero-one law, for a given P, the probability that an infinite cluster exists is either zero or one. There is a critical P (since this probability is increasing) below which the probability is always 0 and above which the probability is always 1. This critical amount Pc is called the percolation threshold, which if we start out at P = 0 and randomly create connections, Pc is defined as a point at which a spanning cluster first appears. It means that for P greater than Pc, a spanning cluster always exists, although some isolated, non-spanning clusters can be present, and for P less than Pc, there are only isolated clusters(Stauffer & Aharony, 1994a). Figure 2-16. Detail of a bond percolation on the square lattice in two dimensions with percolation probability p=51(Stauffer & Aharony, 1994b) Pc may be calculated theoretically in some cases such as for a square lattice in two-dimensions where the percolation threshold has a value of 0.5. For triangular and honeycomb bonds, (Pc) will be respectively as follows: ⎛ π ⎞ Equation 2-38. Pc = 2Sin⎜ ⎟ ⎝18⎠ 41
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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
Page 35 and 36: Figure 4-8. SEM micrographs of vari
Page 37 and 38: Figure 5-6. a),b) Scanning electron
Page 39 and 40: and c) triangular concentration dia
Page 41 and 42: 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: Posthuma de Boer, 1999) (Kumin & Ch
Page 89 and 90: magnetization, which is a function
Page 91 and 92: Polymers have long been thought of
Page 93 and 94: epoxy as a function of nanotube wei
Page 95 and 96: Figure 2-19. Approaching the percol
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
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CHAPTER 3 - ORGANIZATION OF THE ART
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discussed above, HDPE, PS, PMMA, an
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CHAPTER 4 - LOW PERCOLATION THRESHO
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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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