Viscoelastic and Permeation Theory of Carbon Black Particle Mixture

Key words: carbon black dispersion; permeation theory; viscoelasticity; electrical conductivity; agglomerated structure CLC number: O373 Document code: A Abstract: Experimental testing of thick dispersion carbon black particles/ethylene-vinyl acetate mixtures It was found that the viscoelasticity of the molten dispersion was related to the three-dimensional network structure formed by the dispersed particles, but the main influencing factor when the dispersion was in the solid state was not the cohesive structure but the viscoelasticity of the dispersion medium. The density of the three-dimensional network structure can be calculated by image analysis to determine the ratio of its effective connection. Under the condition of less deformation, the elastic modulus can be expressed by introducing the penetration probability parameter and the results can be consistent with the cubic mesh model. When the carbon black particle mass fraction reaches the percolation critical value, the conductivity of the mixture in the solid state increases with the increase of the carbon black particle mass fraction, which indicates that there is a jumping effect in the electron transport process. 0 Introduction Carbon black particles are a dispersion system formed by dispersing carbon black particles with extremely fine particles in a certain medium and are widely used in printing inks, coatings, polymers, cables, automobile tires and Other industrial fields. For example, as a cable coating, the dispersion conditions of the carbon black particles and their cohesive structure have a great influence on the electrical conductivity of the cable processing coating. In general, the rheological properties of the dispersions are tested to evaluate the dispersion conditions of the dispersions and the agglomerated structures formed by the particles. In general, when the concentration of dispersed particles reaches a certain threshold, the particles are connected to each other to form a three-dimensional network structure. The process of testing the rheological properties of dispersions is, in fact, the process of destruction and reformation of such networks. According to rubber elasticity theory, the elastic modulus (also called the elastic modulus) of a dispersion depends on the density of the network structure formed by the dispersed particles. Since the carbon black particles have a certain conductivity, their electrical conductivity will also be affected by the density of the network structure formed by the dispersed particles or the degree of mutual aggregation of the particles. A number of studies have shown that many infiltrating systems have different index values ​​and percolation thresholds, which are mainly caused by differences in the system's cohesive structure and evaluation methods. From the perspective of permeation theory and exponential law, this study focuses on the influence of the agglomerate structure formed by the carbon black particles in the carbon black/ethylene-vinyl acetate copolymer dispersion on the rheological properties and electrical conductivity of the dispersion. 1 Experiments This study used acetylene black as dispersed particles and ethylene-vinyl acetate copolymer as a dispersion medium. The main physical properties of carbon black particles: particle size 42 nm, oil absorption 250 ml 100 g, specific surface area 70 cm2/g. The ethylene-vinyl acetate copolymer has a glass softening temperature of -40°C and exhibits viscoelastic solid properties at room temperature. The dispersion of the carbon black particles was carried out at 150° C. using a heatable barrel grinder. Carbon black particle mass fraction of 9% to 38%, divided into 6 levels. The storage elastic modulus G and the loss elastic modulus G" were measured using an RDS (Rheometrics Dynamic Spectrometer) rheometer. The shear test was carried out in the form of a parallel plate at 130C, and the tensile test was performed at 25C. Investigate the effect of 2-1 temperature and frequency on viscoelasticity For a carbon black particle sample with a mass fraction w(C) = 38%, the test temperature t is stored at a deformation r = 1 % and angular frequency w = 10 rad/s. The effect of the elastic modulus G, the loss elastic modulus G", and the elastic tangent tgσ is shown in FIG. The temperature dependence of the viscoelasticity of the dispersion is similar to that of a polymer dispersion medium, exhibiting the characteristics of a polymer. The glass softening temperature is -20°C and another point of curvature occurs at t=70°C. The dispersion exhibits viscoelastic solid properties at room temperature. When t>130°C, the system becomes fluid dynamic (liquid). Under the flow dynamics, the system exhibits the characteristics of viscoelastic properties that depend on the dense structure of the agglomerated structure formed by the dispersed particles. Fig. 1 The logarithmic relationship between storage elastic modulus G loss elastic modulus G" and elastic tangent tgσ and temperature t for w(C) = 38% dispersions for different mass fractions of carbon black particle samples at t = 130°C, r = Under the condition of 0.2%, the relationship between G, G" and w is tested. The results are shown in Fig. 2 and Fig. 3 respectively (because the numerical span is large, they are represented by logarithmic coordinates.) As can be seen from the two figures, the GG" values ​​are With the increase of the mass fraction of carbon black particles, the GG value increases rapidly with the increase of w in the low mass fraction sample, but the change of the mass fraction w(C) = 29% is very small. This phenomenon shows the characteristics of a typical thick and loose system. The reason is mainly attributed to the condensed structure formed by the carbon black particles in the dispersion. The reason is mainly attributed to the condensed structure formed by the carbon black particles in the dispersion. When the carbon black particle mass fraction is low, the agglomerated structure formed by the dispersed particles cannot exist throughout the entire system but exist as separate aggregates. When w increases, this condensate is easily destroyed, resulting in a change in the value of GG; after the carbon black particle mass fraction reaches a certain threshold, the aggregates formed by the dispersed particles are distributed throughout the system, and the aggregates are interconnected and shaped. Into a three-dimensional network structure, when w increases the desire to destroy such aggregates, the system itself will produce a reaction against it and maintain the existence of the network structure.The relaxation time of the test dispersion also proves that the carbon black particles have a large mass fraction. Dispersion system, its cohesive structure density is also large, long relaxation time.Figure 2 different mass fraction of the dispersion at temperature t = 130 °C storage elastic modulus in the logarithm relationship between G and angular frequency w Figure 3 different mass fraction dispersion system in The logarithmic relationship between the loss elastic modulus G" and the angular frequency w at temperature t=130°C 2-2 The effect of deformation on viscoelasticity The dispersion of different mass fractions is stored at w=10 rad/s, and the elastic modulus of storage G, loss elasticity The relationship between rate G" and deformation r is shown in Fig. 4 and Fig. 5, respectively. In the region of low mass fraction (w(C) < 23% =, the G, G" values ​​are almost constant when the deformation r increases. However, when the particles When the mass fraction w(C)>29%, G, G" shows clearly The deformation dependence, and G is more significant than G. Amari and Watanabe have pointed out: In this angular frequency domain, G, G" shows a strong dependence on the long-relaxation network formed by dispersed particles. The density of this network structure decreases with the increase of deformation, resulting in a decrease in G and G. In the area of ​​low mass fraction, the dispersed particles do not form such a three-dimensional network structure, so G and G cannot be observed. "Deformation dependence. Payne observed the same phenomenon with dispersions of carbon black particles dispersed in vulcanized rubber. He pointed out that for solid materials, the magnitude of elastic modulus and dependence on deformation depend mainly on the carbon black particles. The dispersion (dispersion state) and the viscoelasticity of the polymer itself as the dispersion medium Figure 4 Logarithmic relationship between the storage elastic modulus G and the deformation r for different mass fraction dispersion systems at an angular frequency w = 10 rad/s For the angular frequency w=10rad/s, the logarithmic relationship between the loss elastic modulus G" and the deformation r for different mass fraction dispersion systems 2-3 The influence of the dispersed particle mass fraction on the viscoelasticity of the system The dispersion structure of the dispersion is composed of dispersed particles The density of the agglomerated structure formed by the dispersed particles is related to the mass fraction of the particles, the larger the mass fraction, the tighter the agglomerated structure and the higher the density.When the mass fraction of the dispersed particles exceeds a certain threshold, the agglomerated structure expands to the entire dispersion system. A three-dimensional network structure will be formed.Figures 6 and 7 show the relationship between measured G, G" and dispersed particle mass fraction at an angular frequency w = 10 rad/s and a test temperature t = 130C. In this area, the elastic modulus is mainly determined by the density of the agglomerated structure formed by the dispersed particles.When the mass fraction of the dispersed particles exceeds a certain critical value, G, G" will increase linearly with the increase of the mass fraction of the particles. The critical mass fraction of the dispersion is approximately 3.5. As the deformation increases, the network structure is partially destroyed. Therefore, the dependency of G on the mass fraction becomes small, and the slope of the straight line also becomes smaller. Amari et al. have reported that carbon black particles are dispersed in the dispersion of linseed oil. When the carbon black particle mass fraction w(C)>2%, the dependence of G on the particle mass fraction can be observed. This shows that the carbon black particles are more likely to form an agglomerate structure in the linseed oil than in the ethylene-vinyl acetate copolymer. In other words, in the carbon black particle/ethylene-vinyl acetate copolymer dispersion, the agglomerate structure formed by the particles is more fragile. This property is necessary for the material used as a cable coating process. Fig. 6 The relationship between the storage elastic modulus G′ and the carbon black particle mass fraction w(C)Fig. 7 The relationship between the loss elastic modulus G′′ and the carbon black particle mass fraction w(C)Fig. 8 shows the storage elastic modulus G, conductivity ∑ The relationship with the carbon black particle mass fraction.Storage elastic modulus G" was tested at a temperature t=25°C and an angular frequency w=10 rad/s. The conductivity ∑ test temperature is 25 °C. Compared with the elastic modulus tested under high temperature conditions, the trend of G increases with the mass fraction slightly. This is due to the fact that the system is solid at low temperatures, and the factors affecting the elastic modulus of the dispersion, in addition to the mass fraction of carbon black particles, have a great influence on the viscoelastic properties of the dispersion medium itself. For conductivity enthalpy, when the mass fraction of carbon black particles w (C) <23%, the system is almost non-conductivity; when the mass fraction of carbon black particles w (C)> 23%, the conductivity ∑ with particle mass fraction Increase and increase rapidly. For this phenomenon, it can be considered that the agglomerated structure formed by the small particle mass fraction is not sufficient to constitute a three-dimensional network structure, and the electron transport channel has not yet been formed, so the dispersion system does not have the conductive property. When the mass fraction of particles exceeds the critical value (this system is approximately 25%0), the agglomerated structure formed by the particles constitutes a three-dimensional network structure and communicates the channels for electron transport. The greater the mass fraction of dispersed particles, the greater the density of the three-dimensional network structure and the increase of electron transport channels. As a result, the conductivity ∑ increases sharply with the increase of the particle mass fraction. Fig.8 Relationship between storage elastic modulus G'[○], conductivity ∑[●], and carbon black particle mass fraction w(C) 2-4 Permeation theory of carbon black particle dispersion system Elastic modulus of carbon black particle dispersion system in a molten state The relationship between particle mass fraction and deformation depends on the density of the agglomerated structure formed by the particles under vibration. When the link between the particles reaches a certain threshold of water, the network formed by the particles will expand to the entire system. This phenomenon can be explained by the penetration theory. As mentioned earlier, in a thinly dispersed system, the mass fraction of particles is low and only relatively small aggregates can be formed. As the mass fraction of particles increases, this small aggregate gradually fills the space of the system. When the particle mass fraction reaches a critical value, it eventually forms a three-dimensional network structure throughout the entire system and becomes a permeate system. In the infiltration system, the effective connecting chain Peff between particles and its effect on the elastic properties of the system can be evaluated by statistical methods. For carbon black particle/ethylene-vinyl acetate copolymer dispersions, according to the exponential law, conductivity ∑ and elastic modulus G can be written as follows: ∑ = (P -- Pc)t (1) G' = (P - Pc) f (2) where P is the statistical probability of the link between the dispersed particles, PC is the probability of the critical link (the chain that the particle mass fraction reaches a critical value), and t and f are the conductivity and elasticity, respectively. The rate of evaluation index. For the three-dimensional cubic grid model, the index of the chain penetration model is 1.6±0.1 (1.5±0.1 for the position penetration model). Sieradzki and Li have reported that the fission stress and Yang elastic modulus use an aluminum mesh model with a definite mesh ratio to confirm that the index method can be applied. The index of its fissile stress is 1.7, and the index of Yang's elastic modulus is 3.1. Adams et al. studied the application of chain permeation theory in polymer reaction, and considered that the ratio of chain presence in the polymer reaction system can be determined by the reaction time. The reaction of the polymer can be predicted by the penetration theory and has a higher index. Deptuk et al. studied the relationship between conductivity, Young's elastic modulus and silver powder volume fraction of the submicron silver powder sintering mixture. It is believed that the permeation theory is suitable for this system, and the permeation indexes of conductivity and Yang elasticity are 2.15±0.25, respectively. 8±0.5. Mall and Russel pointed out that when discussing permeation theory, the volume fraction of particles must consider both ratio and position ratio. In fact, due to the cohesive structure formed by the particles and the particle size, the interaction between the particles, and the interaction between the particles and the dispersion medium, it is difficult to establish a simple mathematical relationship between the particle volume fraction and the formation of the particle chain. In this study, the image analysis method was used to evaluate the effective particle-linking chain of the dispersion, and to establish the relationship between the elasticity and conductivity of the dispersion. The specific method is: the dispersion is cut into thin slices under certain conditions, photographed into an image with a microscope, and then processed appropriately by an image analysis system.