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⎛ π ⎞ Equation 2-39. Pc = 1− 2Sin⎜ ⎟ ⎝18⎠ Calculation of Pc for a square lattice was an open question for more than 20 years and was finally resolved by Harry Kesten. For three-dimensional systems, Pc’s are unknown and cannot be calculated for now, although the most interesting thing to do is not calculating the Pc. The percolation threshold has a significant application in universality systems. For example, Utracki et al.(Utracki, 1991) used the percolation threshold to predict the phase inversion point based on emulsion theory as follows: Equation 2-40. η ⎛φm φ ⎞ 1 − 2 = η ⎜ φm φ ⎟ 2 ⎝ − 1 ⎠ In this model, m and η refer to the volume fraction of the component at percolation threshold and intrinsic viscosity, respectively. The universality principle describes that the value of Pc is connected to the local structure of the graph, while the behavior of clusters below, at and above Pc are invariants of the local structure, and therefore, in some sense are more natural quantities to consider. 2.2.1 Universality Systems Systems which tend to be chaotic often have a large number of interacting parts. They are called universality systems. Systems display universality in a scaling limit, when a large number of interacting parts come together. As a matter of fact, universality originated in the study of phase transitions in a statistical science, especially in statistical mechanics. The transformation of a thermodynamic system from one phase to another is a phase transition. When the properties of a material change in a dramatic way, a phase transition happens. For example, when a magnet is heated, its magnetism is lost. In this case, the phase transition is characterized by the [ η ] φm 42
magnetization, which is a function of a parameter of the system, such as the temperature. A system’s critical point is the value of the parameter at which the system has a phase transition. For a given parameter, such as (φ ), with a critical value of ( φ ), the order parameter (a) is c approximated by the following equation: Equation 2-41. ( ) t a a φ −φ = 0 The exponent t is a critical exponent of the system and its value is dependent on the dimensions of the lattice(Grimmett, 1999). For a monodispersed distribution of spheres, a value of 0.156 is predicted for onset of the percolation threshold by percolation theory, which has been verified by several works. For example, in the case of an electrically conductive polymer with filler, the effect of filler loading on the composite resistivity follows a nearly universal pattern regardless of which fillers are chosen. 2.3 Conductive Materials In modern society, a life without electronics cannot be imagined. All materials under normal conditions have some resistance to flowing charges. The electrical resistance of a material is defined by Ohm’s law as the ratio of the voltage (V) applied to the electric current (I) which flows through it. A resistance formula is: There are three main groups of materials from an electrical point of view: conductors, semiconductors, and insulators. Materials containing movable charges of electricity are called conductors. These mobile charges are forced to move when an electric potential difference is applied across separate points on a conductor. The measure of the ability of a conductor to carry electric current is conductivity, which is defined as the ratio of the amount of charges passing through a unit area of the conductor per second, divided by the electric field intensity. c 43
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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
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 and 86: Posthuma de Boer, 1999) (Kumin & Ch
Page 87: lattice, such as square lattice, wi
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
Page 137 and 138: 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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