331

Article

Nihon Reoroji Gakkaishi Vol.41, No.5, 331~336(Journal of the Society of Rheology, Japan)©2013 The Society of Rheology, Japan

1. INTRODUCTION

Cellulose fiber dispersions are used widely in various engineering fields such as paper, fiberboard, fiber-reinforced plastic, and so on. The viscoelastic properties of the cellulose fiber dispersions, especially their relationship with the fiber concentration, are the most important characteristics in practical use. In the papermaking process, for example, pulp fiber suspensions are in the condition of wet networks on the wire prior to drying. The properties of the suspension change drastically during the process: inter-fiber bonding occurs as the concentration rises from about 1 % to 20 %; the suspension becomes a mat-like; and the elastic modulus of the suspension increases rapidly. The relationship between the fiber concentration and the elastic modulus of the suspension is important from both of practical and academic standpoint.

We have investigated the viscoelastic properties of cellulose fiber disperse systems, especially their concentration dependence.1-3) As a result, a power law correlation was found between the storage modulus, G', and the concentrations of the network, c, as follows:

G' = kc α. (1)

Where k is a parameter independent of c and the exponent, α ,

was 9/4 for fiber disperse systems with random networks1,2) and was 3 for fiber disperse systems having laminated network structures.3) This indicates α reflects the properties of the network structure. However, quantitative explanations have not been made in the exponent yet. For a further detailed discussion on the relationship between G' and c, we thus focused on a theoretical analogy between mechanical and electrical models as described below.

A model consisting of springs and dashpots is usually applied to describe the properties of a viscoelastic system.4) This mechanical model has a mathematical analogy with an electrical model5) as shown in Fig. 1A and B. A spring and a dashpot in a mechanical model are numerically equivalent to a capacitor and a resistance in an electrical circuit.6,7) It is thus possible to describe a mechanical model as an electrical one.

To describe fiber networks using an electrical model, electrical conductivity should be given to the fiber networks. Carbonization can give them conductive properties. The electrical properties for carbonized fibrous networks reflect

Relationship between Viscoelasticity and Electrical Conductivity of Carbonized Cellulose Fiber Networks

Liwei Yu*, Daisuke TaTsumi*,**, and Mitsuhiro moriTa*,**

*Graduate School of Bioresource and Bioenvironmental Sciences, Kyushu University**Faculty of Agriculture, Kyushu University, Japan

(Received : December 6, 2012)

Cellulose fibers were carbonized at 900 ºC to make fiber networks having conducting properties. Dynamic viscoelasticity and electrical conductivity of the conductive fiber networks were examined. The storage modulus, G', of the networks increased with the network concentration, c, and a power law was found between G' and c: G' = kc α. The exponent, α , was almost the same as that of the other power law for non-carbonized cellulose fiber networks. The electrical conductivity, σ , of the conductive fiber networks also increased with c, and another power law was found between σ and c: σ = k’c β. The value of exponent, β , was almost the same as α . The coincidence of the exponents for the power law relationships indicates that both of the viscoelastic and electric behaviors of the networks were expressed with the same formula attributed to transfer phenomena, that is momentum and electron transfer, respectively. Key Words: Dynamic viscoelasticity / Electrical conductivity / Fiber network / Power law

** Tel & Fax: +81-92-642-2998, E-mail: tatsumid@agr.kyushu-u.ac.jp 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan Fig. 1. The analogy between mechanical model (A) and electrical model (B).

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the network structure. The changes in AC and DC electrical conductivities of cellulose fibers during its transformation into carbon fibers have been measured.8) The changes in electrical conductivity were correlated with the structural evolution of the fiber networks. Concerning network evolution, electrical conductivity and elastic moduli of carbon materials have been measured as a function of their density.9-12)

In this study, we prepared conductive networks from cellulose fibers. The cellulose fiber networks were carbonized to give them electrical conductivity. Not only the viscoelastic behavior of the cellulose fiber network but also the viscoelastic and the electrical conductive behavior of the conductive networks were discussed to find the relationship of the exponent between viscoelasticity and electrical conductivity of the conductive networks.

2. EXPERIMENTAL

2.1 Sample Preparation

Cellulose fibers used in this study was commercially available softwood dissolving pulp which was supplied by Nippon Paper Chemicals Co., Ltd, Japan. A 33 g of the pulp was dispersed in 2 L of distilled water, and then disintegrated by a standard disintegrator. The pulp suspension was filtered with a glass filter and pressed to remove water to obtain a disk consist of wet fiber network. By changing the direction of water removal, we obtained the laminated and longitudinal directed cellulose fiber networks, and then they were freeze-dried to keep their structures. The random directed fiber networks were prepared without filteration. The orientation directions of cellulose fiber network were observed with a scanning electron microscope (SEM: JSM-5600LV, JEOL, Ltd., Japan).

The fiber networks were carbonized by using an electric oven at 900 ºC for 1 hour, and then let them soak in distilled water for 24 hours to investigate the concentration dependence of the electrical conductivity and the dynamic storage modulus of the carbonized cellulose fiber networks.

2.2 Rheological Measurements

Rheological measurements were carried out using a parallel-plates type rheometer (Rheosol-G2000, UBM Co., Ltd., Japan). The diameters of the plates were 30 mm. The dynamic viscoelastic properties were measured at 35 ºC for various concentrations. The concentration of the carbonized cellulose fiber network was varied by pressing to remove water with changing the gap between the plates of the rheometer, as shown in Fig. 2. The samples kept their original disk-like shape, and moreover, the orientation of fiber was maintained

even after pressing. The detail of this method was shown in our previous paper.3) The concentration of the specimen was calculated using an equation as follows:

C = W0Wi

× 100% (2)

where W0 and Wi are bone-dry weight and the weight after pressing of specimens. Because Wi is in proportion to the thickness of the specimen, it was calculated from initial and final weight of specimens by using a calibration line.

The dynamic strain, γ , was 0.1 % to measure linear viscoelastic properties of the fiber networks. Normal stress measurements were carried out using an ARES rheometer (Rheometric Scientific Inc.) with the plates of 50 mmφ.

2.3 Electrical Conductivity Measurements

The conductive fiber networks used for electrical conductivity measurements were a size of 22 mm in diameter and 5~6 mm in thickness. The specimen was placed between the parallel-plates of the rheometer, and then measured electrical resistance of the conductive fiber network through the direction of thickness with changing the thickness of the fiber networks, as shown in Fig. 2. The electrical conductivity of the specimen was calculated using the following equation:

σ = 1/ρ = H/SR (3)

where σ and ρ are electrical conductivity and resistivity, H and S are the thickness and the contact area between the specimen and plates, and R is resistance measured.

3. RESULTS

3.1 The Orientation Directions of Fibers in Cellulose

Fiber Networks

The SEM images of laminated (a), random (b) and longitudinal directed (c) non-carbonized cellulose fiber

Fig. 2. Rheological measurements and electrical conductivity measurements of carbonized cellulose fiber networks.

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networks are shown in Fig. 3. Arrows in the images signify the orientation directions of fibers in the cellulose fiber networks. Depending on the direction of water removal, the cellulose fiber networks showed the different orientation. The SEM images of laminated (a), random (b) and longitudinal directed (c) carbonized cellulose fiber networks are shown in Fig. 4. Comparing Fig. 3 with Fig. 4, the cellulose fiber networks are found to keep the original structure even after carbonization.

3.2 The Effects of Stress Relaxation on the Rheological

Properties of Cellulose Fiber Disperse Systems with

Laminated and Longitudinal Directed Network Structure

The frequency dependence of G' of the laminated (a) and longitudinal directed (b) cellulose fiber networks with waiting time after pressing to remove water from the fiber networks are shown in Fig. 5. The normal stress relaxation occurred after pressing of the fiber networks. The moduli were almost unchanged with time in the laminated network and the longitudinal directed cellulose fiber networks. These

figures show that there is almost no influence of normal stress relaxation induced by pressing on the rheological properties of cellulose fiber networks.

3.3 Correlation between Dynamic Storage Modulus

and Concentration for Non-Carbonized Cellulose

Fiber Networks

The concentration dependence of G' of the laminated (a), random directed (b) and longitudinal directed (c) non-carbonized cellulose fiber networks are shown in Fig. 6. A linear relationship was obtained between log G' and log c for different orientation direction of the fiber networks. In other words, it shows that a power law was also found between G' and c: G' = kcα. The slope values, α , were 3.7 for the laminated fiber networks and 2.3 for the random networks. These values were consistent with those found in our previous studies.1-3) In contrast, the value of α was 1.4 for longitudinal directed fiber network. This lower value should be due to its fiber network structure as discussed later.

(b)

Fig. 3. SEM images of laminated (a), random (b) and longitudinal directed (c) non-carbonized cellulose fiber networks.

(b)

Fig. 4. SEM images of laminated (a), random (b) and longitudinal directed (b) carbonized cellulose fiber networks.

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3.4 Correlation between Dynamic Storage Modulus and

Concentration for Carbonized Cellulose Fiber Networks

The relationship between G' and c for the wet carbonized cellulose fiber networks with laminated (a), random (b), and longitudinal directed (c) structure are shown in Fig. 7. Regardless of the orientation direction in the fiber, the storage modulus of the networks increased with c, and a power law was found between G' and c: G' = kcα. The values of exponent, α , were ca. 4.3, 2.6 and 1.1 for the carbonized cellulose fiber networks with laminated, random, and longitudinal directed structure, respectively. They are close to those of the other power law for the non-carbonized cellulose fiber networks. The comparison of the concentration dependence for the carbonized and non-carbonized networks was not carried out in the same concentration range, it is because of the water absorption of the cellulose fiber become poor after carbonization.

3.5 Correlation Between Electrical Conductivity and

Concentration for Carbonized Cellulose Fiber Networks

The concentration dependence of the electrical conductivity, σ , of the laminated (a), random (b) and longitudinal directed (c) carbonized fiber networks are shown in Fig. 8. The σ increased with c, as same as c dependence of G'. Linear relationships were obtained between log σ and log c for the carbonized fiber networks, that is, another power law was found between σ and c: σ = kc β. This behavior is very similar to that of G' vs. c as shown in Fig. 7. Furthermore, the value of exponent, β , was almost the same with α for the carbonized and non-carbonized cellulose fiber networks. These results suggest an obvious relationship between the viscoelastic and the electrical properties.

4. DISCUSSION

Comparing the values of exponent, α and β , we can find that these two exponents for the carbonized cellulose fiber

Fig. 6. Logarithmic plots of dynamic moduli, G', versus fiber concentration, c, for laminated (a), random (b) and longitudinal directed (c) non-carbonized cellulose fiber networks.

Fig. 5. Dynamic storage modulus, G', versus angular frequency, ω, for laminated (a) and longitudinal directed (b) cellulose fiber network at various waiting time.

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networks were almost the same. They were moreover almost as same as that the other power law of the concentration dependence of G' for non-carbonized cellulose fiber networks. These results suggest an obvious correlation between the viscoelastic and the electrical properties. This is due to the fact that the stress and the conductivity are both related to the transfer phenomena. In other words, they are described as the transfer of momentum and electron, respectively. The coincidence of the exponents for the power law relationships indicated the viscoelastic and electric behaviors of the networks can be expressed with a similar formula.

The values of exponent for the cellulosed fiber networks with laminated structure were larger than that of a longitudinal directed structure. This is due to a difference in the structure of the laminated and longitudinal directed fiber networks. In our previous study3), the exponents have been discussed with the orientation of fibers. According to the discussion, the reason of the difference of the exponents should be as follows. When the specimens were pressed to increase concentration, the

number of interfiber contact points increased with increasing c. When fibers lie on a plane, they can contact each other easily. However, the increase of the interfiber contact points in longitudinal directed networks should be smaller than that of laminated or random networks because the direction of pressing and the fiber orientation is the same. As the result, the stress or the conductivity of longitudinal directed networks showed smaller dependence on concentration than the other networks.

5. CONCLUSION

Dynamic viscoelastic behavior and electrical conductive behavior of the conductive fiber networks were investigated. The storage modulus of the cellulose fiber networks increased with concentration of fiber, a power law was found between G' and c: G' = kcα. The exponent of carbonized cellulose fiber networks was almost the same as that of the other power law for non-carbonized fiber networks. This is due to the similar

Fig. 7. Logarithmic plots of dynamic moduli, G', versus fiber concentration, c, for laminated (a), random (b) and longitudinal directed (c) carbonized cellulose fiber networks.

Fig. 8. Logarithmic plots of electrical conductivity, σ , versus fiber concentration, c, for laminated (a), random (b) and longitudinal directed (c) carbonized cellulose fiber networks.

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structure between before and after carbonized cellulose fiber networks.

The concentration dependence of electrical conductivity was as same as that of storage modulus in the carbonized cellulose fiber networks. This suggests an obvious correlation between viscoelastic and electrical properties of the carbonized fiber network. The coincidence of the exponents for the power law relationships indicates that the viscoelastic and electric behaviors of the networks were described with similar mechanisms. The results show that it is possible to presume the viscoelastic properties of cellulose fiber network by measuring its conductivity, which is more preferable in the online measurements.

ACKNOWLEDGMENTS

Authors wish to express their gratitude to Professor Songlin Zuo, Nanjing Forestry University, for his kind help on carbonization. Authors also wish to thank Professor Takuya Kitaoka, Kyushu University, for his allowing us to use the standard paper machine.

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