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Viscoelastic properties of a pitch and coke-pitch disperse system
VISCOELASTIC PROPERTIES OF A PITCH AND COKE-PITCH DISPERSE SYSTEM ~OTOTSUGU SAKAI? Omachi Plant, Showa-Denko Co., Ltd., Omachi, Nagano, 398, Japan
Abstract-V~sc~~astic properties of a pitch and a coke-pitch disperse system were studied by using a Weissenberg rheogoniometer and a simple compressive creep apparatus. Dynamic modulus and steady shear viscosity of the pitch, and creep compliance of the disperse system were determined. The pitch examined was found to be a Ne~onian non-elastic fluid over a wide range of experimental conditions. whereas the coke-pitch disperse system showed a transition from non-elastic to viscoelastic fluid at about 50 wt% of coke content. It has also been shown that the time-temperature superposition principle is applicable to the disperse system. the temperature dependence of the shift factor being independent of coke content.
Various types of disperse systems are found in natural and artificial products. Many of them exhibit so unique and useful ch~acterist~cs as to open new fields in science and technology. Variation in the mixing ratio of filler and medium brings about a variety of characteristics extending over an almost infinite range of values. However, their practical appIication as industri~ materials have been limited to a rather narrow range, mainly because of the lack of understanding of their characteristics as well as of the underlying mechanisms. A systematic study by rheological methods is expected to be a most appropriate approach for getting useful information as to the preparation of such disperse systems, and also as to the filler-medium and filler-filler interactions resulting from the nature of constituent molecular species. In the case of carbon paste used as raw material for various artificial carbon products, the rheological characteristics provide important clues for understanding mixing and shaping processes, being governed mainly by the viscosity of pitch and the elasticity of coke grains. The rheology of such disperse systems depends on the shape and size of coke grains as well as on the mixing ratio of coke to pitch. Some studies of the viscosity of various coke-pitch disperse systems with rather low contents of coke were made[l,2f, in which an extensive study of steady state viscosity was made by using capillary- and coaxial cyIinder-viscometer. The systems with high content of coke show remarkabfe non-lined response and/or occurrence of cracking of the molded pieces in the ordinary strain or stress region; this was preventing the clari~cation of its rheological properties for many years. On the other hand, the systems with very low content of coke show liquid-like properties, in contrast to the solidlike behavior of the former. The industrial carbon pastes span the wide intermediate range of coke content, and SPresent address: School of Materials Science, Toyohashi University of Technology, Tempaku-cho Toyohashi, Aichi 440, Japan.
behave as viscoelastic materiaIs between the two extremes. In other words, past studies putting stress just on the viscosity measurements seem to be insufficient for cla~fication of the matter. Hereupon, we have attempted to make a systematic study of the viscoelastic properties of pitch and coke-pitch disperse system, changing the com~sition stepwise over a wide range of coke contents. 2.EXPERIMENTAL
2.1 Samples A coal tar pitch prepared by Kawatetsu Chemical Industry Co., Ltd was examined in the present work, with softening point as determined by the ring-ball method of 84S”C. As-received pitch was dried at 15O”C, and then pulverized at room temperature to less than 250&m size. The pitch powder was kept in a brown colored desiccator with silica gel. The coke used was a product of Petro Coke Co., Ltd., having a needle-like texture and grain size of 53 to 44pn-r. The coke was dried in wxo at 15O”C,and kept also in a desiccator. In preparation of the disperse system, coke and pitch powder were mixed at room temperature with various weight ratios as shown in the first column of Table 1. The powder mixtures were then molded into cylinders of about 26 mm in diameter and 80 mm in height, under a pressure of 181kg/cm’ at temperatures shown in Table 1. The pitch itself (without coke) was formed by pouring it into a mold at 1SO“C. To remove residual strains produced by molding, samples were annealed at temperatures given in Table 1. For the creep measurements, cylindrical test pieces of 25.0 mm in diameter and 30.0 mm in height were machined carefully from molded samples. The bulk density of each machined sample was determined from its weight and volume (Table 1). 2.2 Apparatus The ~iessenberg rheogoniometer Model R-18 manufactured by Sangamo Controls, Ltd. was used to measure steady-state viscosity and complex modulus of molten pitch; this is a cone-and-plate viscometer with 139
140
M.
SAKAI
Table 1. Shaping conditions, annealing conditions and bulk densities of creep samples
content of coke WC
(%I
molding erature
temp-
( “C)
annealing
temp-
erature
bulk dens'
(OC) ty
(g/cmt
0.0
150
30.0
75
55
1.37
40.0
80
35
1.46
50.0
90
45
1.52
55.0
95
60
1.57
60.0
100
80
1.58
70.0
125
90
1.49
facilities for normal force measurements. Details of the
instrument are given in the literature[3,4]. In order to decide whether the pitch is Newtonian or not, the shear rate dependence of steady shear viscosity n was examined in the range of shear rate from 1.13 to 113set-‘. Also, the distinction between elastic and nonelastic fluids was made on the basis of measurements of dynamic shear viscosity n’ and stored shear modulus G’ under oscillations from 3.14 to 314 set-‘. The creep compliance of pitch itself and coke-pitch disperse systems was measured on a simple compressive creep apparatus, shown schematically in Fig. 1. A test piece placed in the middle of a cylindrical electric furnace (of inside dimensions dia. 30 and length 300 mm) was kept at various temperatures between 20 and 150°C for an hour, and then subjected to a compressive stress, the deformation being detected by a transducer and recorded as a function of time. The temperature fluctuations during the creep measurements were less than + O.z”C. The creep compliance J(t) was calculated from IS]
where L and D are height and diameter of the sample, respectively, F compressive force and AL(r) the
,... ri=o
Dial gauge
naoter Alumina md Furnace
ij Fig. 1. Creep apparatus.
1.30
compressive deformation recorded as a function of time. E,,(= AZ&)/L) and P, ,(= 4F/77DZ) represent compressive strain and stress, respectively. When the coke-pitch disperse system had a yield stress the creep compliance was calculated using the following equation;
(2) where P?, is the yield stress. 3. RESULTS AND DISCUSSION
3. I Viscoelastic properties of the pitch Table 2 gives the steady shear viscosity (9) of molten pitch as a function of shear rate (i), and the dynamic shear viscosity (v’) and stored shear modulus (G’) as functions of frequency (w). 17 and q’ are almost in. dependent of + and w, respectively, and G’ is zero at least in the ranges of w and temperature examined; which leads to an important conclusion that the molten pitch is a Newtonian and non-elastic fluid. It will be shown later through the creep ex~riment that the pitch is still non-elastic even at such low temperatures as 4O-WC far below the softening point. Such a non-elastic behaviour of pitch comes presumably from the rigid structure of constituent molecules. Since the pitch is found to be a simple non-elastic fluid, one can make a quantitative analysis of the elastic properties of these disperse systems on the basis of the elasticity of filler (coke grain), ignoring the contribution of medium. 3.2 Viscoelastic properties of the coke-pitch disperse sassed In Fig. 2 are shown the representative changes of compressive strain (E,,) with time for various compressive stress (P,,) at constant coke content (WC) and temperature. The same data are reproduced in the form of E,, vs PI, plot in Fig. 3. Although beautiful linear relations are commonly observed between l1, and PII, an essential difference does take place in the following two groups; all the plots in Fig. 3(a) for which WC= 40.0 wt% go through the origin of diagram, while those in Fig. 3(b) for which W, = 55.0 ~4% converge to a finite value of PI1 at et1 = 0.0, viz. the latter exhibits a yield stress (Pt,) of 3.92x 104dynelcmz at 53.9”C. The samples with the coke content (WC) higher than 50 wt% were found to show well-defined yield stresses, whose magnitude increases with W,.
Viscoelastic properties of a pitch and a coke-pitch disperse system
141
Table 2. Steady shear viscosity n as a function of shear rate r, and dynamic shear viscosity n’ and stored shear modulus G’ as a function of frequency o for the pitch melted
at
7
I
116.Z°C
7
(poise)
fand
G' at 112.OOC
I (poise) ‘7
(see-l)
~ UJ
G'
(dyne/cm21
0.00
1.13
69.7
3.14
149
2.26
76.6
6.28
147
0.00
3.57
70.6
9.92
149
0.00
7.16
74.9
144
0.00
146
0.00
11.3
75.3
22.6
76.6
35.7
70.6
71.6
73.0
113
19.8 31.4
75.3
q, x 10-3,dyne/cm’ (a)
'r t, min 2
(a)
“0 ;
w=
0
Fig. 3. The relation between compressive strain (e,,) and compressive stress (PI,) for different values of time. The changes of the creep compliance J(t) with time f are shown in Fig. 4. In accordance with the time50 t.
loo
min
(W
Fig. 2. The change of compressive strain (c, ,) with time (t) under different compressive stresses (PI,).
temperature superposition principle[5], all of the curves at different temperatures can be shifted so as to form a master curve at a reference temperature by using appropriate values of shift factor aT. The reference temperature was selected at about the middle of temperatures actually used; i.e. 376.9”K for highest coke content (WC = 70.0 wt%) and 303.7”K for pitch. In Fig. 5
M.
‘/
SAKAI
I
(a)
B-
I -4
I -2 [i/T-I/T,]
I 0
x104,
I
2
I 4
K
Fig. 6. The temperature dependence of shift factor aT for different coke contents.
c
7 log t.
3
1
41
5ec
Fig. 4. The creep compliance function (J(t)) at different temperatures.
where T and To are the temperature of measurement and the reference temperature in absolute unit, respectively. One can readily see that the temperature dependence of aT is expressed by Arrhenius-type equation independently of the coke content; (3)
Fig. 5. The master curves of J(t) for different coke contents,
reference temperaturebeing 7O.O”C. the master curves for various samples are shown by normalizing the as-obtained curves to a constant temperature of reference 7O.O”C.For the samples with the coke content lower than 40.0 wt%, including the pitch itself (WC= 0.0 wt%), the master curves do not have any plateau and show straight part with the slope of 1.0 in the long time region; which means that these samples are non-elastic fluids. For the specimens with coke content higher than 5Owt%, each master curve indicates a definite plateau which extends over a wide time region and becomes more flat with the increase in the coke content. This means that the higher the coke content the more elastic this disperse system is. In Fig. 6, the shift factors al- for different samples at different temperatures are plotted against l/T - l/To,
The value of AHJR has been evaluated from the slope to be 1.35~ lO*K. It is worthwhile to notice that the temperature dependence of uT for all samples, not only the coke-pitch disperse systems but the pitch itself, can be expressed by using the same value of AHJR. In other words, the temperature dependence of viscoelastic properties of the disperse systems is entirely controlled by the pitch used as medium. In fact, this is very important technical information for manufacturing artificial carbon products, and agrees well with our experience that a change in pitch produces remarkable changes in processing conditions of the carbon paste. 3.3 Analysis of creep compliance function J(t) For amorphous materials in the range of stress-strain linearity, the creep compliance function J(t) is usually described in terms of three responses as follows; J(t)=&+
- L(T)( 1 - e-I”) d(ln 7) + t/q. I -_
(4)
The glassy compliance J, represents a time-independent deformation which is attributed to the stretching and bending of intra- and inter-molecular bonds. The retardation term, the second term in eqn (4), is a monotonically increasing function of time and has a finite value at infinite time, indicating a form of the time-dependent
Viscoelastic properties of a pitch and a coke-pitch disperse system
recoverable deformation. The third term representing permanent deformation is linear with respect to time and inversety propo~ion~ to viscosity. For sufficiently long times, J(t) is approximated by the third term of eqn (4) only. Then, one can calculate the steady-state viscosity +j from the straight portion of each master curve for J(t) having the slope 1.0. In Fig. 7, +j at 7O.o”C for the disperse systems with coke contents of 0.0, 30.0 and 40.0 wt% are shown as a function of the volume fraction of coke (I&). The volume fraction is given by
where d is the bulk density of sample and d, is the density of pitch itself (see Table 1). The experimental points fall on Mooney’s curve[4,7]; In ($*0) = 2.5&/U - k4~),
(6)
with a crowding factor k of the tiller of 1.6. They do not fit the Einstein’s equation ($jO = 1+ 2.5&}[8] as shown in Fig. 7. The steep increase of rif+, with (bc is probably due to the strong interaction between coke grains. Elastic property of the disperse systems with coke content higher than 5Owt% may appropriately be analysed in terms of the elastic energy stored in the material. From the dimensional analysis, the elastic stored energy o, is given by[9] o. = A . J,
. P :,,
where A is a proportionality constant and J, the steadystate compliance. In general, 5, is given by the plateau level of the master curve of J(t). Since the master curves in Fig. 5 exhibit slight slopes even in the plateau range, we have defined the value of 3, as the compliance at the
Fig. 7. The relation between relative viscosity (~/~*) and volume fraction of coke (&) at 70.0%, where Mooney’s equation is represented by solid line and Einstein’s equation by broken line.
Fig. 8. The dependence of steady-state compliance J, on coke content W,..
inflection point, and its change with coke content W, is shown in Fig. 8. The rapid decrease of .I, with increasing W, seems to be due to the increasing interaction between coke grains. In the range of W, above ~.O~%, the matter may appropriately be looked at as a threedimensional network or structure of coke-bridges.
4. CONCLUDING REMARKS By means of static and dynamic measurements of viscoelastic properties, a coal tar pitch was found to be a Ne~onian and non-elastic fluid at tem~ratures between 40 and 150°C. Such a non-elastic behaviour under stress is possibly attributed to the high rigidity of constituent molecules. Since some pitches, such as petroleum pitches, are supposed to contain flexible high polymers as constituents, further extensive studies on viscoelastic properties of various pitches are necessary and desirable to be made in future. By using the same pitch as medium, disperse systems of petroleum coke were prepared, and their viscoelastic properties examined in simple compressive creep experiments. Aiplying the time-temperature superposition curves of creep smooth master principle, compliance J(t) were obtained by using appropriate shift factors independent of the coke content. This implies that the temperature dependence of viscoeiastic properties of the given coke-pitch disperse systems is governed just by the pitch used as medium. The master curves indicate that with increasing coke content a t~nsition from non-elastic to viscoelastic fluid takes place at about 5Owt%. For the disperse systems with coke content lower than 4Owt%, relative viscosity is explained by using Mooney’s equation. On the other hand, for the systems with viscoelastic behavior, the rapid decrease in the steady-state compliance 1, is observed with the increase in coke content, which can be qu~i~tively ascribed to the increasing interaction between coke grains.
144
M.
Acknow~edgeme~s-I am very gratefui to Showa-Denko Co., Ltd. for emission to publish this article. I also express my thanks to Mr. I’. Komatsu and Mr. J. Ken of Showa-~nko Co., Ltd. for their encouragement in this work, and Prof. M. Inagaki of Toyohashi University of Technology for many helpful discussions. RgIXlZENCEs 1. G. Bhatia, Carbon 11(5),437 (1973);M(6), 315,319 (1976). 2. G. Bhatia, R. K. Aggarwal, S. S. Chari and G. C. Jam, Carbon 15(4),219 (1977). 3. K. Weissenbe~, Tesfing of materials by Means of the Rheo-
SAKAl
gon~ometer. San8amo Controls Ltd., Bogner Repis, Er@and. 4. A. Jobhng and J. E. Roberts, Weisse~e~ Rheogo~~o~eter ~nst~~ion ~aa~a~. San8amo Controls Ltd., Bogner Regis, England. 5. J. D. Ferry, Viscoelastic Properties of Polymers. Wiley, New York (l%l). 6. M. Mooney, J. Colloid Sci. 6, 162(1951). 7. D. C. Bogue and J. L. White, Engineering Analysis of NonNewtonian Fluids. The Agardograph Series of the North Atlantic Treatv Organization (1970). 8. A. Einstein, Am. ?hys. 19,289 (1906);34, 591 (1911). 9. B. D. Coleman and H. Markovitz, f. Appl. Phys. 35, 1 (1964).
Abstract-V~sc~~astic properties of a pitch and a coke-pitch disperse system were studied by using a Weissenberg rheogoniometer and a simple compressive creep apparatus. Dynamic modulus and steady shear viscosity of the pitch, and creep compliance of the disperse system were determined. The pitch examined was found to be a Ne~onian non-elastic fluid over a wide range of experimental conditions. whereas the coke-pitch disperse system showed a transition from non-elastic to viscoelastic fluid at about 50 wt% of coke content. It has also been shown that the time-temperature superposition principle is applicable to the disperse system. the temperature dependence of the shift factor being independent of coke content.
Various types of disperse systems are found in natural and artificial products. Many of them exhibit so unique and useful ch~acterist~cs as to open new fields in science and technology. Variation in the mixing ratio of filler and medium brings about a variety of characteristics extending over an almost infinite range of values. However, their practical appIication as industri~ materials have been limited to a rather narrow range, mainly because of the lack of understanding of their characteristics as well as of the underlying mechanisms. A systematic study by rheological methods is expected to be a most appropriate approach for getting useful information as to the preparation of such disperse systems, and also as to the filler-medium and filler-filler interactions resulting from the nature of constituent molecular species. In the case of carbon paste used as raw material for various artificial carbon products, the rheological characteristics provide important clues for understanding mixing and shaping processes, being governed mainly by the viscosity of pitch and the elasticity of coke grains. The rheology of such disperse systems depends on the shape and size of coke grains as well as on the mixing ratio of coke to pitch. Some studies of the viscosity of various coke-pitch disperse systems with rather low contents of coke were made[l,2f, in which an extensive study of steady state viscosity was made by using capillary- and coaxial cyIinder-viscometer. The systems with high content of coke show remarkabfe non-lined response and/or occurrence of cracking of the molded pieces in the ordinary strain or stress region; this was preventing the clari~cation of its rheological properties for many years. On the other hand, the systems with very low content of coke show liquid-like properties, in contrast to the solidlike behavior of the former. The industrial carbon pastes span the wide intermediate range of coke content, and SPresent address: School of Materials Science, Toyohashi University of Technology, Tempaku-cho Toyohashi, Aichi 440, Japan.
behave as viscoelastic materiaIs between the two extremes. In other words, past studies putting stress just on the viscosity measurements seem to be insufficient for cla~fication of the matter. Hereupon, we have attempted to make a systematic study of the viscoelastic properties of pitch and coke-pitch disperse system, changing the com~sition stepwise over a wide range of coke contents. 2.EXPERIMENTAL
2.1 Samples A coal tar pitch prepared by Kawatetsu Chemical Industry Co., Ltd was examined in the present work, with softening point as determined by the ring-ball method of 84S”C. As-received pitch was dried at 15O”C, and then pulverized at room temperature to less than 250&m size. The pitch powder was kept in a brown colored desiccator with silica gel. The coke used was a product of Petro Coke Co., Ltd., having a needle-like texture and grain size of 53 to 44pn-r. The coke was dried in wxo at 15O”C,and kept also in a desiccator. In preparation of the disperse system, coke and pitch powder were mixed at room temperature with various weight ratios as shown in the first column of Table 1. The powder mixtures were then molded into cylinders of about 26 mm in diameter and 80 mm in height, under a pressure of 181kg/cm’ at temperatures shown in Table 1. The pitch itself (without coke) was formed by pouring it into a mold at 1SO“C. To remove residual strains produced by molding, samples were annealed at temperatures given in Table 1. For the creep measurements, cylindrical test pieces of 25.0 mm in diameter and 30.0 mm in height were machined carefully from molded samples. The bulk density of each machined sample was determined from its weight and volume (Table 1). 2.2 Apparatus The ~iessenberg rheogoniometer Model R-18 manufactured by Sangamo Controls, Ltd. was used to measure steady-state viscosity and complex modulus of molten pitch; this is a cone-and-plate viscometer with 139
140
M.
SAKAI
Table 1. Shaping conditions, annealing conditions and bulk densities of creep samples
content of coke WC
(%I
molding erature
temp-
( “C)
annealing
temp-
erature
bulk dens'
(OC) ty
(g/cmt
0.0
150
30.0
75
55
1.37
40.0
80
35
1.46
50.0
90
45
1.52
55.0
95
60
1.57
60.0
100
80
1.58
70.0
125
90
1.49
facilities for normal force measurements. Details of the
instrument are given in the literature[3,4]. In order to decide whether the pitch is Newtonian or not, the shear rate dependence of steady shear viscosity n was examined in the range of shear rate from 1.13 to 113set-‘. Also, the distinction between elastic and nonelastic fluids was made on the basis of measurements of dynamic shear viscosity n’ and stored shear modulus G’ under oscillations from 3.14 to 314 set-‘. The creep compliance of pitch itself and coke-pitch disperse systems was measured on a simple compressive creep apparatus, shown schematically in Fig. 1. A test piece placed in the middle of a cylindrical electric furnace (of inside dimensions dia. 30 and length 300 mm) was kept at various temperatures between 20 and 150°C for an hour, and then subjected to a compressive stress, the deformation being detected by a transducer and recorded as a function of time. The temperature fluctuations during the creep measurements were less than + O.z”C. The creep compliance J(t) was calculated from IS]
where L and D are height and diameter of the sample, respectively, F compressive force and AL(r) the
,... ri=o
Dial gauge
naoter Alumina md Furnace
ij Fig. 1. Creep apparatus.
1.30
compressive deformation recorded as a function of time. E,,(= AZ&)/L) and P, ,(= 4F/77DZ) represent compressive strain and stress, respectively. When the coke-pitch disperse system had a yield stress the creep compliance was calculated using the following equation;
(2) where P?, is the yield stress. 3. RESULTS AND DISCUSSION
3. I Viscoelastic properties of the pitch Table 2 gives the steady shear viscosity (9) of molten pitch as a function of shear rate (i), and the dynamic shear viscosity (v’) and stored shear modulus (G’) as functions of frequency (w). 17 and q’ are almost in. dependent of + and w, respectively, and G’ is zero at least in the ranges of w and temperature examined; which leads to an important conclusion that the molten pitch is a Newtonian and non-elastic fluid. It will be shown later through the creep ex~riment that the pitch is still non-elastic even at such low temperatures as 4O-WC far below the softening point. Such a non-elastic behaviour of pitch comes presumably from the rigid structure of constituent molecules. Since the pitch is found to be a simple non-elastic fluid, one can make a quantitative analysis of the elastic properties of these disperse systems on the basis of the elasticity of filler (coke grain), ignoring the contribution of medium. 3.2 Viscoelastic properties of the coke-pitch disperse sassed In Fig. 2 are shown the representative changes of compressive strain (E,,) with time for various compressive stress (P,,) at constant coke content (WC) and temperature. The same data are reproduced in the form of E,, vs PI, plot in Fig. 3. Although beautiful linear relations are commonly observed between l1, and PII, an essential difference does take place in the following two groups; all the plots in Fig. 3(a) for which WC= 40.0 wt% go through the origin of diagram, while those in Fig. 3(b) for which W, = 55.0 ~4% converge to a finite value of PI1 at et1 = 0.0, viz. the latter exhibits a yield stress (Pt,) of 3.92x 104dynelcmz at 53.9”C. The samples with the coke content (WC) higher than 50 wt% were found to show well-defined yield stresses, whose magnitude increases with W,.
Viscoelastic properties of a pitch and a coke-pitch disperse system
141
Table 2. Steady shear viscosity n as a function of shear rate r, and dynamic shear viscosity n’ and stored shear modulus G’ as a function of frequency o for the pitch melted
at
7
I
116.Z°C
7
(poise)
fand
G' at 112.OOC
I (poise) ‘7
(see-l)
~ UJ
G'
(dyne/cm21
0.00
1.13
69.7
3.14
149
2.26
76.6
6.28
147
0.00
3.57
70.6
9.92
149
0.00
7.16
74.9
144
0.00
146
0.00
11.3
75.3
22.6
76.6
35.7
70.6
71.6
73.0
113
19.8 31.4
75.3
q, x 10-3,dyne/cm’ (a)
'r t, min 2
(a)
“0 ;
w=
0
Fig. 3. The relation between compressive strain (e,,) and compressive stress (PI,) for different values of time. The changes of the creep compliance J(t) with time f are shown in Fig. 4. In accordance with the time50 t.
loo
min
(W
Fig. 2. The change of compressive strain (c, ,) with time (t) under different compressive stresses (PI,).
temperature superposition principle[5], all of the curves at different temperatures can be shifted so as to form a master curve at a reference temperature by using appropriate values of shift factor aT. The reference temperature was selected at about the middle of temperatures actually used; i.e. 376.9”K for highest coke content (WC = 70.0 wt%) and 303.7”K for pitch. In Fig. 5
M.
‘/
SAKAI
I
(a)
B-
I -4
I -2 [i/T-I/T,]
I 0
x104,
I
2
I 4
K
Fig. 6. The temperature dependence of shift factor aT for different coke contents.
c
7 log t.
3
1
41
5ec
Fig. 4. The creep compliance function (J(t)) at different temperatures.
where T and To are the temperature of measurement and the reference temperature in absolute unit, respectively. One can readily see that the temperature dependence of aT is expressed by Arrhenius-type equation independently of the coke content; (3)
Fig. 5. The master curves of J(t) for different coke contents,
reference temperaturebeing 7O.O”C. the master curves for various samples are shown by normalizing the as-obtained curves to a constant temperature of reference 7O.O”C.For the samples with the coke content lower than 40.0 wt%, including the pitch itself (WC= 0.0 wt%), the master curves do not have any plateau and show straight part with the slope of 1.0 in the long time region; which means that these samples are non-elastic fluids. For the specimens with coke content higher than 5Owt%, each master curve indicates a definite plateau which extends over a wide time region and becomes more flat with the increase in the coke content. This means that the higher the coke content the more elastic this disperse system is. In Fig. 6, the shift factors al- for different samples at different temperatures are plotted against l/T - l/To,
The value of AHJR has been evaluated from the slope to be 1.35~ lO*K. It is worthwhile to notice that the temperature dependence of uT for all samples, not only the coke-pitch disperse systems but the pitch itself, can be expressed by using the same value of AHJR. In other words, the temperature dependence of viscoelastic properties of the disperse systems is entirely controlled by the pitch used as medium. In fact, this is very important technical information for manufacturing artificial carbon products, and agrees well with our experience that a change in pitch produces remarkable changes in processing conditions of the carbon paste. 3.3 Analysis of creep compliance function J(t) For amorphous materials in the range of stress-strain linearity, the creep compliance function J(t) is usually described in terms of three responses as follows; J(t)=&+
- L(T)( 1 - e-I”) d(ln 7) + t/q. I -_
(4)
The glassy compliance J, represents a time-independent deformation which is attributed to the stretching and bending of intra- and inter-molecular bonds. The retardation term, the second term in eqn (4), is a monotonically increasing function of time and has a finite value at infinite time, indicating a form of the time-dependent
Viscoelastic properties of a pitch and a coke-pitch disperse system
recoverable deformation. The third term representing permanent deformation is linear with respect to time and inversety propo~ion~ to viscosity. For sufficiently long times, J(t) is approximated by the third term of eqn (4) only. Then, one can calculate the steady-state viscosity +j from the straight portion of each master curve for J(t) having the slope 1.0. In Fig. 7, +j at 7O.o”C for the disperse systems with coke contents of 0.0, 30.0 and 40.0 wt% are shown as a function of the volume fraction of coke (I&). The volume fraction is given by
where d is the bulk density of sample and d, is the density of pitch itself (see Table 1). The experimental points fall on Mooney’s curve[4,7]; In ($*0) = 2.5&/U - k4~),
(6)
with a crowding factor k of the tiller of 1.6. They do not fit the Einstein’s equation ($jO = 1+ 2.5&}[8] as shown in Fig. 7. The steep increase of rif+, with (bc is probably due to the strong interaction between coke grains. Elastic property of the disperse systems with coke content higher than 5Owt% may appropriately be analysed in terms of the elastic energy stored in the material. From the dimensional analysis, the elastic stored energy o, is given by[9] o. = A . J,
. P :,,
where A is a proportionality constant and J, the steadystate compliance. In general, 5, is given by the plateau level of the master curve of J(t). Since the master curves in Fig. 5 exhibit slight slopes even in the plateau range, we have defined the value of 3, as the compliance at the
Fig. 7. The relation between relative viscosity (~/~*) and volume fraction of coke (&) at 70.0%, where Mooney’s equation is represented by solid line and Einstein’s equation by broken line.
Fig. 8. The dependence of steady-state compliance J, on coke content W,..
inflection point, and its change with coke content W, is shown in Fig. 8. The rapid decrease of .I, with increasing W, seems to be due to the increasing interaction between coke grains. In the range of W, above ~.O~%, the matter may appropriately be looked at as a threedimensional network or structure of coke-bridges.
4. CONCLUDING REMARKS By means of static and dynamic measurements of viscoelastic properties, a coal tar pitch was found to be a Ne~onian and non-elastic fluid at tem~ratures between 40 and 150°C. Such a non-elastic behaviour under stress is possibly attributed to the high rigidity of constituent molecules. Since some pitches, such as petroleum pitches, are supposed to contain flexible high polymers as constituents, further extensive studies on viscoelastic properties of various pitches are necessary and desirable to be made in future. By using the same pitch as medium, disperse systems of petroleum coke were prepared, and their viscoelastic properties examined in simple compressive creep experiments. Aiplying the time-temperature superposition curves of creep smooth master principle, compliance J(t) were obtained by using appropriate shift factors independent of the coke content. This implies that the temperature dependence of viscoeiastic properties of the given coke-pitch disperse systems is governed just by the pitch used as medium. The master curves indicate that with increasing coke content a t~nsition from non-elastic to viscoelastic fluid takes place at about 5Owt%. For the disperse systems with coke content lower than 4Owt%, relative viscosity is explained by using Mooney’s equation. On the other hand, for the systems with viscoelastic behavior, the rapid decrease in the steady-state compliance 1, is observed with the increase in coke content, which can be qu~i~tively ascribed to the increasing interaction between coke grains.
144
M.
Acknow~edgeme~s-I am very gratefui to Showa-Denko Co., Ltd. for emission to publish this article. I also express my thanks to Mr. I’. Komatsu and Mr. J. Ken of Showa-~nko Co., Ltd. for their encouragement in this work, and Prof. M. Inagaki of Toyohashi University of Technology for many helpful discussions. RgIXlZENCEs 1. G. Bhatia, Carbon 11(5),437 (1973);M(6), 315,319 (1976). 2. G. Bhatia, R. K. Aggarwal, S. S. Chari and G. C. Jam, Carbon 15(4),219 (1977). 3. K. Weissenbe~, Tesfing of materials by Means of the Rheo-
SAKAl
gon~ometer. San8amo Controls Ltd., Bogner Repis, Er@and. 4. A. Jobhng and J. E. Roberts, Weisse~e~ Rheogo~~o~eter ~nst~~ion ~aa~a~. San8amo Controls Ltd., Bogner Regis, England. 5. J. D. Ferry, Viscoelastic Properties of Polymers. Wiley, New York (l%l). 6. M. Mooney, J. Colloid Sci. 6, 162(1951). 7. D. C. Bogue and J. L. White, Engineering Analysis of NonNewtonian Fluids. The Agardograph Series of the North Atlantic Treatv Organization (1970). 8. A. Einstein, Am. ?hys. 19,289 (1906);34, 591 (1911). 9. B. D. Coleman and H. Markovitz, f. Appl. Phys. 35, 1 (1964).