Fabricated device and solar cell geometry is shown in Fig. ", Albert Einstein's original PhD dissertation in German. Rheology of the sol-gel transition. [36]. Mode I (GIC) and II (GIIC) Fracture Toughness of the Composite Samples Studied. Also, the procedures involved in the latex technique can be used to promote effective interaction of the CNM in the polymer matrix, as has been demonstrated for a PP–rGO composite [96,97]. Similarly. The authors have also mentioned that the differences in the dispersion indices may be of higher importance for mechanical testing since the agglomerates are expected to act as imperfections in the compounds and impair the mechanical performance. The storage moduli at low frequencies were also higher for the nanocomposites containing functionalized CNTs, indicating better load transfer between the CNT network and the polymer. we found some interesting scaling behaviors that indicated the electrical conductivity of some nanoparticle-doped polymer films scaled in conformance with an theoretical expectatiion. Macromolecules 20:2957, Allain C, Salomé L (1990) Gelation of semidilute polymer solutions by ion complexation: critical behavior of the rheological properties versus cross-link concentration. Irradiation dose, network forming, and soluble fractions influenced by PTC and NTC effects. At low concentrations, the noninteracting nanotubes homogeneously dispersed in the polymer matrix take a very long time to reaggregate provided the matrix viscosity is high enough to suppress fast Brownian motion (or crosslinked into elastomer after dispersion). This is termed as pseudo plastic nature, or shear thinning behavior. Although this approach avoids the challenge of selecting an adequate solvent as is the case in solution mixing, it generally possesses a comparatively lower dispersion of the CNM in the polymer matrix and the materials are usually subjected to high stress; furthermore, the viscosity of the polymers could aggravate the issue of agglomeration/stacking of the CNMs. J Phys A 22:291, Winter HH, Mours M (1997) Rheology of polymers near liquid-solid transitions. Macromolecules 22:2871, Leibler L, Schosseler F (1985) Gelation of polymer solutions: an experimental verification of the scaling behavior of the size distribution function. Dai et al. Cellulose, one of the world’s most abundant renewable biopolymer [27] resources has unique applications in PV [28–30]. Inset: Enlarged images at two different regions of (b). Currently, some of the main methods used in the preparation of composites of polymers and CNMs are solution mixing, melt processing, in situ polymerization, latex technology, chemical grafting, and layer-by-layer assembly (LBLA). [103] prepared graphene nanoplatelets (GnPs) filled SBR based nanocomposites by the solution mixing method. Ma et al. The AgNWs used had a diameter of 70 nm and a high aspect ratio ranging from 300 to 1000. Not affiliated Clarendom Press, Oxford, Bouchaud E, Delsanti M, Adam M, Daoud M, Durand D (1986) Gelation and percolation: swelling effect. The PTC effect was increased while NTC value was decreased to 400 kGy. Table 7–2. The possible reason for this impairment of impact strength after three times extrusion may be the degradation of polymer induced by too much thermal and mechanical loading during extrusion. Optical transmittance of GNPs–CNC film is very high as represented in Fig. All rights reserved. Mitchell et al. The increase in electrical conductivity of polymer nanocomposite after achieving the electrical percolation threshold as a function of filler content could be modeled by a simple power-law equation [213]. This phenomenon is referred as PTC effect. On the other hand, carbon-based nanostructure graphene has raised significant interest due to its extremely high relative specific surface area, and exceptional mechanical, thermal, and electrical properties. De nition 5 The percolation threshold pcis the concentration (occupation probability) pat which an in nite cluster appears for the rst time in an in nite lattice. J Phys Fr 49:333, Durand D, Delsanti M, Adam M, Luck JM (1987) Frequency dependence of viscoelastic properties of branched polymers near gelation threshold. They can be related to fractal dimensions and to geometrical dimensions. The key to process selection would be to achieve effective dispersal of the CNMs in the polymer matrix coupled with good adhesion and/or interaction between the components of the composites. These thresholds depend on the filler content and follow the order: PC elecsoft < PC elec < PC rheorigid. Each polymer needs a different amount of filler concentration to form the percolation threshold. allocation of $\R^d$ to $\Xi$ which is stable in the sense of Gale-Shapley [118] formed three-dimensional (3D) interconnected graphene structures in NR matrix using self-assembly integrating latex compounding technology by exploiting electrostatic adsorption between poly(diallyldimethylammonium chloride) modified graphene (positively charged) (PDDA-graphene) and NR latex particles (negatively charged) as the driving force (Fig. Percolation scaling theory of intramolecular bond cycles. Consequently, it is necessary to include at least one interphase region6 where the structure, chemistry and properties are typical of neither of the bulk phases that were combined to generate the composite. Some polymers that can be used to prepare composites through the solution-mixing method include PMMA [85], poly(vinyl alcohol) (PVA) [86], and PS [87] etc. Interphase volume fraction as a function of nanoparticle volume fraction for different diameter spherical nanoparticles. Phys Rev Lett 80:4907, Plischke M, Vernon DC, Joós B, Zhou Z (1999) Entropic rigidity of randomly diluted two- and three-dimensional networks. Compared with the control sample, it increases from 718 to 1344 J/m2 (an improvement of 87%) for the interleaved one and up to 1578 J/m2 (an improvement of 120%) for those loaded with the AgNWs. By continuing you agree to the use of cookies. Extrudate swell, B, for polystyrene filled with carbon black at 170°C. The carbon plies exhibit an average thickness of about 120–130 μm, whereas the interleaf layer thickness is estimated to be in the range of 10–40 μm. This is because surface groups in general influence the wettability of the CNMs, which in turn affects their dispersion in different solvents. Close contacts between fillers giving rise to a conductive path corresponds to an electrical threshold (PC elec). Nanocellulose (NC) possesses excellent mechanical properties with abundant functional groups, thus it can be modified with different chemical groups [31]. It is commonly accepted that the dispersion state of the nanoparticles within the polymer matrix can result in different properties of nanocomposites. Estimation of Excipient (Polymer) Percolation Thresholds. By the measurement of dielectric properties as a function of frequency, and by an interpretation of results based on the percolation theory, further insights into the qualitative properties of conduction mechanism in CNT/polymer composites are given. al. Solid conductive inorganic materials normally lead to an increase in melt viscosity of the matrix polymer melt.1–7 The melt flow index (volume flow index) is typically reduced. J Chem Soc Faraday Trans II 72:1354, Stockmayer WH (1943) Theory of molecular size distribution and gel formation in branched-chain polymers. Fig. Subsequently, freeze-drying or melt-processing could be utilized to obtain the final composites; since water is usually the solvent used in this case, the process is relatively safe and environmentally friendly. The formation of the polymeric materials that we consider in this chapter is characterized by the existence of a percolation-type transition point; see below. It was explained that GnPs at low volume fractions cannot connect with each other to form a percolated network which is required for electron mobility. J Phys Fr 49:289, Xing X, Muthupadhyay S, Goldbart PM (2004) Scaling of entropic shear rigidity. In general, the shear viscosity is enhanced, especially at low shear rates. The effect strongly depends on the concentration of the filler, especially whether the amount added is below or above the electrical percolation threshold. I do not know the Ni particle size, nor how the composite was prepared. My polymer is regioregular P3HT (regioregularity ~ 90%), From DSC curve, it lost the glass transition peak to totally flat after and its melting point decreases by 7. 8.1, which shows plots of interphase volume fraction as a function of particle volume fraction for a random array of different sized particles from 2.5 to 16 nm diameter. Phys Rev B 30:6217, Parisi G, Sourlas N (1981) Critical behavior of branched polymers in the Lee-Yang edge singularity. A distance close to polymer gyration radius corresponds to a “soft” rheological threshold … INTRODUCTION: The percolation theory studies the critical points or percolation thresholds of the system, where one component of the system undergoes a geometrical phase transition, starting to connect the whole system.The application of this theory to study the release rate of hydrophilic matrices allows to explain the changes in release kinetics of swellable matrix type system and results in a clear …