Method of optimizing composite preparation for electrical properties: maximum capacitance electrodes

Composites of a matrix of metal fibers and carbon fibers interlocked in and interwoven among a network of fused metal fibers are inherently capable of displaying a broad range of values of a particular physical property. Where the composite is made by sintering a preform of the fiber network dispersed in a matrix of an organic binder, the value of the physical property of the resulting composite is a function of several independent variabiles which can be controlled during composite fabrication. With particular regard to the capacitance of a stainless steel-carbon fiber electrode, there is described a method of optimizing capacitance during electrode fabrication.

BACKGROUND OF THE INVENTION 
The maximum energy and/or power densities obtainable from carbon based 
electrodes in liquid double layer capacitors, batteries, and fuel cells 
often depend on various physiochemical rate phenomena occurring at the 
electrode-electrolyte interface. The energy density in liquid double layer 
capacitors, for example, increases with increased surface area of the 
carbon electrode material presented to the electrolyte [Tiedemann, W., and 
Newman, J., J. Electrochem. Soc., 122, 70, (1975)], while the power 
density is controlled and limited by the diffusion of electrolyte through 
the microporous electrode material [Rose, F., in "Proceedings of the 33rd 
International Power Sources Symposium", Cherry Hill, N.J., June 13-16, 
1988, The Electrochemical Society, Inc., p. 572 (1988)]. As a result, 
electrode capacitance depends on an interplay between increased 
diffusional processes and higher levels of surface area. Since higher 
levels of surface area entail smaller characteristic dimensions and 
smaller diffusional pathways, high energy density and high power density 
are often mutually exclusive. 
For Li/SOCl.sub.2 and other battery systems, reaction products tend to clog 
normal carbon cathodes at higher current densities (&gt;10 mA/cm.sup.2) 
[Mammone, R. J., and Binder, M., J. Electrochem. Soc., 134, 37, (1987)] as 
a result of preferential precipitation at the exterior of the electrode. 
High power density cathode materials are required which are flexible and 
which have varying and adjustable porosities and void volumes so as to 
accommodate reaction products without significant loss in accessibility. 
In H.sub.2 -O.sub.2 fuel cells and other electrocatalytic processes, the 
power level and/or reaction selectivity and activity may be restricted by 
heat and mass transport limitations which occur at the electrode surface 
[Ticianelli, E. A., Derouin, C. R., Redondo, A., and Srinivason, S., J. 
Electrochem. Soc., 135, 2209, (1989)]. Porous and flow-through 
electrocatalysts are desired which incorporate high specific surface areas 
of supported electrocatalysts such as platinum, palladium, nickel, gold, 
carbon, etc., while also being present in an easily accessible 
configuration to facilitate mass transport to active surface regions. 
Previous work in this laboratory [Kohler, D. A., Zabasajja, J. N., A. 
Krishnagopalan, and Tatarchuk, B. J., J. Electrochem. Soc., 137, 136, 
(1990)] has resulted in a procedure for preparing metal-carbon electrodes 
which appear to address many of the above mentioned problems associated 
with double layer capacitors, batteries, and fuel cells. Free standing 
electrodes, with variable porosities and void volumes, can be manufactured 
from a wide variety of metal fiber and carbon fiber sources. We now 
disclose a method of optimizing an electrical property in the preparation 
of composite electrodes made of high surface area carbon fibers and 
conductive stainless steel fibers. Stainless steel fibers were chosen 
because of their commercial availability in small diameters (.ltoreq.4 
.mu.m) and their compatibility with a number of electrolytes. 
SUMMARY OF THE INVENTION 
This invention relates to optimizing some physical property of a composite 
comprising a network of metal fibers and carbon fibers having a plurality 
of bonded junctions at the fiber crossing points where the composite is 
made by sintering a preform of the network of fibers dispersed in a matrix 
of an organic binder. Optimization is performed by determining the rate 
equations, including apparent activation energies, for the domain within 
which the physical property increases and the separate domain where the 
physical property decreases. The optimal sintering time is determined 
within the envelope of independent variables, and the physical property is 
optimized separately with respect to each of the other independent 
variables. In a specific embodiment the composite is a stainless 
steel-carbon fiber article designed as an electrode, and the physical 
property in question is its capacitance. In a more specific embodiment the 
envelope is bounded by a maximum and minimum sintering temperature, and a 
maximum and minimum weight ratio of stainless steel fibers to carbon 
fibers. Other embodiments will be apparent from the description which 
follows.

DESCRIPTION OF THE INVENTION 
The composites which we have chosen as electrode materials result from a 
marriage of carbon and metals in such a way that this combination of 
dissimilar and normally incompatible materials forms a physically stable 
composite structure which exhibits properties that are intermediate to the 
constituent materials. These composites are prepared most effectively by 
making a uniform dispersion of carbon fibers, metal fibers, and solid 
cellulosic binder in a liquid medium, collecting the wetted uniform solid 
dispersion and removing the liquid medium from it to afford a preform, and 
heating the preform in a gaseous atmosphere at conditions sufficient to 
vaporize at least 99% of the binder and to fuse the metal fibers. We have 
now found a method of optimizing a given electrical property of such 
composites during their preparation. Although most of the ensuing 
discussion will focus on the capacitance of the composites, we emphasize 
that the general method described is applicable to other properties as 
well such as void volume, electrochemical power density, surface area per 
unit weight, electrical conductivity, thermal conductivity, EMI/RFI 
damping, mechanical strength and toughness, and so on. 
As stated above, the composite of this invention is a matrix of carbon 
fibers interlocked in and interwoven among a network of fused metal 
fibers. The composite is a network of metal fibers and carbon fibers 
having a plurality of bonded junctions at the fiber crossing points, where 
"bonded junctions" refers to those crossing points in the network where 
the fibers are securely physically connected in some sort of permanent 
union. Although it should be apparent that "carbon" in the phrase "carbon 
fibers" includes and encompasses graphite, we here specifically note that 
in the context of the remainder of this specification and in the claims 
"carbon fibers" includes carbon blacks and graphitic materials. The carbon 
fibers constitute from about 1 to about 98 weight percent of the final 
composite, although the range between about 20 to about 98 weight percent 
is preferred. There is no significant upper or lower limit for the 
diameter of the carbon fibers as regards the composite itself. That is, 
the diameter of the carbon fibers used in the composite influences its 
final properties rather than imposing limitations on the composite itself. 
Carbon fibers have been reported with a surface area from about 1500 
m.sup.2 /g to 1 m.sup.2 /g and less, and with a diameter from 20 nm to 
about 1 mm. As an example, and as will become clearer from the 
descriptions within, for use in liquid double layer capacitors, H.sub.2 
/H.sub.3 PO.sub.4 /O.sub.2 fuel cells, and Li/SOCl.sub.2 batteries, carbon 
fibers having a surface area of from 250 m.sup.2 /g to about 1000 m.sup.2 
/g are most desirable with fibers having a diameter from 1 to about 10 
microns, with a carbon content of the composite ranging from 30 to about 
90 weight percent. 
The carbon fibers generally are present as bundles. Single fibers tend to 
be brittle, whereas bundles or aggregates of fibers afford a composite 
with more desirable mechanical properties. As the diameter of the carbon 
bundles increases, the weight of metal fibers needed to keep the bundles 
interwoven or interlocked is decreased. The physical properties of the 
final composite also depend on the physical properties of the carbon 
fibers used; thermal stability, surface area, mean pore diameter, 
mechanical flexibility, resistance to electrolytes and acids, and 
electrocatalytic properties are examples of composite properties which are 
influenced by the properties of the constituent carbon fibers and any 
electroactive materials impregnated on the fibers. It should be emphasized 
that the surface area of the carbon fibers used largely determines the 
surface area of the final composite. Since different applications require 
different characteristics, the choice of carbon fiber properties often 
will be dictated by composite application. For example, where used in 
double layer capacitors one generally wants a certain minimum pore size, 
which in turn limits the surface area. In batteries mass transfer is more 
important and one wants a higher void volume, preferably with a bimodal 
pore size distribution. A graded porosity also is possible to attain using 
this invention and may be important in particular applications. However, 
what needs to be emphasized is that many of the composite properties are 
not only variable but are under the control of the investigator or 
fabricator within quite broad and flexible limits. 
The carbon fibers are interwoven among, and interlocked in, a network of 
metal fibers. The metal fibers which may be used in the practice of this 
invention must be electrically conducting when used in an electrode, must 
be chemically inert under the conditions of their contemplated use, and 
must provide structural integrity and mechanical stability to the final 
composite under the contemplated conditions of use. So, for example, the 
final composite generally needs to retain its overall shape, and to retain 
the carbon fibers in the network relatively rigid and immobile. Examples 
of metal fibers which may be used in the practice of this invention 
include aluminum, titanium, vanadium, chromium, iron, cobalt, nickel, 
copper, zinc, zirconium, niobium, molybdenum, ruthenium, rhodium, 
palladium, silver, cadmium, indium, tin, hafnium, tantalum, tungsten, 
rhenium, osmium, platinum, gold, antimony, beryllium, iridium, silicon, 
and combinations of the above. Metal alloys also may be used in the 
practice of this invention, as exemplified by constantan, hastelloy, 
nichrome, inconel, monel, carpenter's metal, and various steels, 
especially stainless steels, and other iron alloys. As can be appreciated, 
there is enormous flexibility in the choice of metal fibers. Because of 
their general availability and relatively modest cost, as well as 
favorable physical and chemical properties, various stainless steels are 
the materials of choice, especially in many electrode applications. 
The diameter of the metal fibers used is largely dictated by their 
availability. Although in principle there is no upper or lower limit to 
metal fiber diameter there may be significant operational restrictions. 
For example, if the metal fiber diameter is greater than ten times, or 
less than one-tenth, the carbon fiber diameter, then the fused metal 
network may not hold the carbon fibers together adequately. Stated 
differently, the metal fiber diameter D.sub.m relative to the carbon fiber 
diameter D.sub.c is in the range 0.1 D.sub.m .ltoreq.D.sub.c .ltoreq.10 
D.sub.m. Another operational limitation is related to the number of 
metal-metal contacts, or fusion points, which are largely responsible for 
supporting the carbon fibers in the composite. Calculations show that the 
number of metal-metal contacts varies inversely with the square of the 
metal fiber diameter, hence there is a requirement for small diameter 
metal fibers where it is desirable to increase the overall weight fraction 
of carbon and surface area of the resulting composite. But in the context 
of novel composites per se, the diameter of the metal fiber used is not 
critical. The method of preparation and attainment of composites is not 
limited by metal fiber diameter, at least up to about 50 microns. In the 
context of composite properties, however, the diameter of the metal fiber 
is important and in practice it is desirable to have metal fibers with a 
diameter no more than about 10 microns but at least 0.1 micron. It would 
be most desirable to use metal fibers with a diameter in the range from 
about 0.5 microns to about 4 microns, but it needs to be emphasized again 
that the nature and diameter of the metal fibers used in the practice of 
this invention are limited largely by their availability rather than by 
any theoretical considerations. 
The amount of metal in the final composite depends on how much surface area 
per gram is important, and, perhaps even more importantly, how good a 
contact is desired between the metal and the carbon fibers. It should be 
clear that the better the contact wanted, the higher the necessary 
percentage of metal fiber (at constant fiber diameter) in the final 
composite. Generally the composites of this invention will have a metal 
content ranging from about 2 up to about 99 weight percent, i.e., a metal 
to carbon weight ratio from about 0.02 to about 99, with a weight ratio 
between about 0.02 and 10 being preferable. As metal content increases, 
the composite shows reduced resistance and higher power density per gram 
with a lower surface area and lower energy density per gram. 
One significant and important advantageous feature of our composites is 
that they are readily prepared via a preform, which is a solid containing 
a non-woven dispersion of the carbon and metal fibers in a binder. The 
binder provides a matrix in which the fibers of the carbon and metal are 
dispersed. The purpose of the binder is to permit the fabrication of a 
solid preform containing an otherwise structurally unstable dispersion of 
the elements of the final composite, -i.e., carbon and metal fibers-which 
can be shaped, stored, and otherwise handled prior to creation of an 
interlocked network via fusion of the metal fibers. The binder merely 
provides a stable, although weak, physical structure which maintains the 
spatial relationship of the components of the final composite prior to the 
latter's formation. Although the preform is only a temporary structure, it 
is an important one in the fabrication of the final composite. The binders 
used in preparation of the preform also may contain adjuncts, such as pore 
and void formers. 
One critical property of the binders which may be used in the practice of 
this invention is that they volatilize at least to the extent of 90 weight 
percent, and preferably at least 99 weight percent, under conditions used 
for fusion of the metal fibers. The binder has no function in the 
composite, hence its presence should be minimal. Among binders which may 
be used in the practice of this invention are cellulose, organic resins 
such as polyvinyl alcohols, polyurethanes, and styrene-butadiene latex, 
and thermosets such as epoxies, urea-formaldehyde resin, 
melamine-formaldehyde resin, and polyamide-polyamine epichlorohydrin 
resin. Cellulose appears to be the premier binder because it volatilizes 
completely at relatively low temperatures with little ash formation and is 
unreactive toward the other components of the composite. 
The binder is present in the preform at a range from about 2 up to about 80 
weight percent. The minimum amount of binder is that which is necessary to 
give a stable preform, that is, one which can be handled, shaped, and so 
forth, an amount which depends upon carbon fiber loading, fiber size, and 
so forth. The amount of binder present in the preform will influence the 
void volume of the final composite, with a higher binder content affording 
a higher void volume, hence the binder can be used as one independent 
variable to control this property. Using cellulose with carbon fibers and 
stainless steel fibers as an example, a range from about 10 to about 60 
weight percent of cellulose is a typical one. 
The carbon and metal fibers are mixed with the binder and with a liquid of 
appropriate viscosity. The purpose of the liquid is to provide a medium 
for the facile and effective dispersion of the solids, for one wants as 
uniform a dispersion as is feasible in the final preform. Other than the 
need for the liquid being unreactive with the components, there are no 
other important limitations on the liquid which may be used. In the case 
of cellulose water normally will be the liquid, although water-alcohol 
mixtures, especially water-glycol, may be used. Illustrative examples 
include methanol, ethanol, propanol, ethylene glycol, propylene glycol, 
butylene glycol, poly(ethylene glycol)s, poly(propylene glycol)s, and so 
forth. The liquid medium also may contain salts where desirable. 
After a dispersion is attained, the solids are collected, as on a mat. 
Excess liquid may be removed, such as by pressing, and the resulting solid 
dispersion is then dried. Where a thermosetting binder is used, the 
temperature of drying is important. However, in the more usual case there 
is nothing particularly critical in the drying process, and drying may be 
performed in air, under elevated temperatures, or in a flowing gas. The 
mass also may be compacted to a greater or lesser extent to affect void 
volume; the greater the compaction, the lower will be the void volume. 
Fusion or sintering of the metal fibers in the dried preform, whose 
preparation was described above, is the final stage in the fabrication of 
the composite, and the particular conditions of sintering to optimize a 
given electrical property is the subject of our invention. In general, the 
preform is heated under conditions effecting sintering of the metals to 
provide a network of fused metal fibers. Fusion of the metal fibers at 
their points of contact rigidly locks the carbon fibers in place to afford 
a rigid structure by defining a matrix of carbon fibers interwoven or 
interlocked in a network of metal fibers with the structural rigidity 
arising from a multiplicity of fused points of contact. Sintering 
typically is done in a gas containing hydrogen at a partial pressure which 
is about 5 times the partial pressure of water in the gas stream, the 
water typically arising from the binder and from oxides on the surface of 
the metal. At the temperature of metal fusion, the metal also usually 
promotes gasification of carbon via its reaction with hydrogen to afford 
methane. The combination of sinter-fusing the metal fibers, forming good 
electrical contacts between the metal fibers and carbon fibers 
accompanying sintering, and the decrease in carbon content accompanying 
gasification of the carbon fibers gives rise to composites with varying 
electrical properties. When the composite is intended to be used as a 
capacitor it would be highly desirable to prepare the composite in such a 
way as to optimize its capacitance. The following will disclose just such 
a method of preparation, thereby enhancing even further the usefulness of 
our composites. 
At this point we emphasize again that a stainless steel-carbon fiber 
composite is but representative of the composites which may be used, and 
capacitance is but illustrative of the properties which may be optimized 
according to our invention. For simplicity and clarity of exposition the 
following description is specific to the capacitance of a stainless 
steel-carbon fiber composite, but our invention is not limited thereto and 
is of far broader scope and greater universality. 
The conductivity and capacitance of the sintered-matrix will depend on a 
number of variables including the relative amounts of metal and carbon 
used and on the sintering conditions employed during the preparation 
process. Using a stainless steel fiber-carbon fiber composite as 
exemplary, composite electrodes were characterized by measuring their 
capacitances, a direct measure of the active carbon surface area 
electrically connected to the electrolyte; see Tiedemann and Newman, 
op.cit. The capacitance, measured using AC impedance, potential step, and 
cyclic voltammetry methods, was correlated to kinetic parameters 
describing the sintering of metal fibers to each other and to the 
metal-catalyzed gasification of carbon. The observed kinetics were in turn 
used to predict the maximum attainable capacitance with respect to the 
composition of the electrode preform, sintering temperature, and sintering 
time. Energy densities of completed electrodes were then estimated. 
EXPERIMENTAL 
Materials 
Materials used during electrode fabrication were: carbon fibers (Charcoal 
Cloth, Ltd.), 316L stainless steel fibers (Bekaert Steel Wire Corp.), 
cellulose fibers (a mixture of soft and hard woods) and 316L stainless 
steel foils (Arnold Engineering). Individual carbon fibers (N.sub.2 BET 
surface area of 790 m.sup.2 /gm) were 2-3 .mu.m in diameter and were used 
in the form of 20 .mu.m diameter bundles ca. 5 mm in length. Stainless 
steel fibers were 2 .mu.m in diameter and 2 mm in length. Cellulose fibers 
were 20-30 .mu.m in diameter and 100-1000 .mu.m in length. Stainless steel 
foils were 5 .mu.m in thickness. 
Paper Preforms 
Carbon-stainless steel-cellulose composite papers (i.e., paper preforms) 
were prepared as 16 cm diameter circular sheets as outlined previously 
[Kohler et al., ibid.]. A series of paper preforms with constant amounts 
of carbon and cellulose (1.0 gm/sheet and 0.5 gm/sheet, respectively) and 
different loadings of stainless steel fibers were made to examine the 
effects of stainless steel loading on electrode performance. The amounts 
of stainless steel in the various sheets were 0.1, 0.2, and 0.5 gm of 
fiber per sheet. 
Stainless steel-cellulose composite papers were also made. These preforms, 
containing 0.5 gm cellulose/sheet and 0.5 gm stainless steel/sheet, were 
used as an overlayer covering to enhance electrical contact and protect 
the active carbon-containing layer from abrasion during handling [Kohler 
et. al., ibid.] 
Electrode Fabrication and Sintering 
Paper preforms were cut and assembled, and the layered electrode preform 
heat treated as described in Part I of this investigation [idem, ibid.]. 
Sintering was performed in an atmosphere of pure hydrogen (99.995%, Liquid 
Air) with a linear flow rate of 2.6 cm/min (STP) at a total pressure of 
101 kPA. Heat treatment was performed at 1323K, 1373 K, and 1423 K for the 
paper preform containing 0.5 gm stainless steel/sheet to examine the 
effects of sintering temperature on electrode performance. Additional 
experiments were performed at 1323 K for paper preforms containing 0.1, 
0.2, and 0.5 gm stainless steel/sheet to examine the influence of 
stainless steel loading. 
Weight Loss Measurements 
The amount of carbon retained in the electrode after sintering was 
established from weight change measurements and the earlier observation 
that cellulose was quickly removed during heat treatment [idem, ibid.]. 
These measurements were obtained on a Sartorius Model R 160 D semimicro 
balance with an accuracy and a precision of 0.02 mg. 
Electrochemical Measurements 
Electrodes were spot welded to 0.25 mm diameter nickel wires (99.995%, 
Johnson Matthey Inc.) to allow for electrical contact. The connecting wire 
was mounted inside a 23 cm long flint glass Pasteur pipette (Fisher 
Scientific), and sealed with quick set epoxy (Duro) to separate the 
connecting wire from the test solution. 
The experimental cell (Electrosynthesis, Inc.) was of the H-type design. 
The cell featured a platinum wire mesh counter electrode (99.9%, Johnson 
Matthey Inc.) and a saturated calomel (SCE) reference electrode (Fisher 
Scientific). The working and counter electrode chambers were separated by 
a microporous film (Celgard 3401, Hoechst Celanese Corp.). 
Electrode characterization was conducted in a deoxygenated solution of 1.0M 
Na.sub.2 SO.sub.4 (99.97% pure Na.sub.2 SO.sub.4 crystals, Fisher 
Scientific) at 300 K. Distilled and deionized H.sub.2 O was utilized in 
solution preparation. The selection of this particular electrolyte was 
based on: (i) a slow corrosion rate of stainless steel of less than 50 
.mu.m of penetration/yr [Schweitzer, P. A., "Corrosion Resistance Tables", 
Marcel Dekker, Inc., 1062, 1976], (ii) a solution conductivity of ca. 83 
mmho/cm [Weast, R. C. (ed.), "CRC Handbook of Chemistry and Physics, 64th 
Ed.," The Chemical Rubber Co., D-305, 1983], and (iii) an electrolyte 
dielectric constant of 67.0 [Conway, B. E., "Electrochemical Data", 
Elsevier Publishing Co., 47, 1952]. 
Electrochemical measurements were made using an EG&G Princeton Applied 
Research System. The measurement system included an EG&G C Model 273 
Potentiostat/Galvanostat, Model 5208 Two Phase Lock-in Analyzer, and an 
IBM Model 30 micro-computer. 
Electrode Assessment 
Electrode capacitance was determined by three independent methods: 
admittance plots of AC impedance data, single potential step measurements, 
and cyclic voltammetry. AC impedance measurements were made over the 
frequency range from 0.002 Hz to 100 kHz at the open circuit potential 
(.apprxeq.-550 mV vs SCE). Single potential step measurements (magnitude 
of 5 mV) were also carried out at -550 mV vs SCE. Cyclic voltammetry was 
performed over the potential range from -800 to 800 mV vs SCE. A scan rate 
of 100 mV/sec was applied for five sweeps. 
Electrochemical Model 
The electronic model used to determine electrode performance is a series RC 
circuit. This simple model included terms for the total effective 
resistance of the composite electrode system (R.sub.T) and the electrode's 
double layer or interfacial capacitance (C) [Shih, H., and Pickering, H. 
W., J. Electrochem. Soc., 134, 1943, (1987)]. Capacitance values obtained 
using this model by AC impedance, potential step, and cyclic voltammetry 
were in good agreement and supported the use of this relatively simple 
model (see FIGS. 1-3). The total electrode capacitance obtained included 
the capacitance due to double layer charging and the capacitance due to 
faradaic reactions, which are parallel processes. 
For AC impedance, the capacitance was determined from an admittance plot, 
where the capacitance was found from [Mansfeld, F., Kendig, M. W., and 
Tsai, S., Corrosion, 38, 570, (1982)]: 
##EQU1## 
where Y" is the imaginary admittance and .OMEGA. is the angular frequency. 
Data obtained from an electrode made from a paper precursor containing 0.5 
gm stainless steel/sheet and sintered at 1323 K for 40 minutes are shown 
in FIG. 1. The sintered electrode contained 0.00528 gm carbon. The AC 
impedance data in the admittance plot were fitted to various equivalent 
circuit models which yielded similar values of the total capacitance. 
While a distribution of relaxation times is often observed from 
microporous systems [De Levie R., "Advances in Electrochemistry and 
Electrochemical Engineering", Vol. 6, 329 (1967)], it should be noted that 
the active surface area in the electrodes was contained within the pores 
of contiguous carbon fibers (2 .mu.m diameter, ca. 800 m.sup.2 /gm, 2.0 nm 
diameter internal porosity) [Kohler et. al.,ibid.] Since the vast majority 
of the active surface area was contained in pores of ca. 2.0 nm, while the 
fibers themselves were quite accessible and interspaced with larger 
dimensions (ca. 50 .mu.m), it is likely that the predominance of a single 
time constant reflects a strong overall dependence of capacitance on 
intraparticle/intra-fiber mass transfer. 
For the potential step method, the current varied by the relationship 
[Bard, A. J., and Faulkner, L. R., "Electrochemical Methods, Fundamentals 
and Applications", John Wiley and Sons, 11, (1980)]: 
EQU i=i.sub.o exp(-t/.tau.), [2] 
where i.sub.o is the peak current and: 
EQU .tau.=CR.sub.T. [3] 
The values of .tau. and i.sub.o were determined by least squares analysis 
of ln i versus t data, where .tau. equaled the negative inverse of the 
resulting slope and i.sub.o was the intercept. R.sub.T was calculated 
using: 
EQU R.sub.T =DV/i.sub.o, [4] 
where DV is the potential step perturbation. The capacitance was then found 
from Equation [3]. Potential step data obtained from an electrode made 
from a paper precursor containing 0.5 gm stainless steel/sheet and 
sintered at 1323 K for 40 minutes are shown in FIG. 2. The sintered 
electrode contained 0.00528 gm carbon and is the same electrode shown in 
FIG. 1. 
For cyclic voltammetry, the average capacitance over the scanned potential 
region was calculated from the charge stored (q) in the resulting I-V 
envelope [Yeo, R. S., Orehotsky, J., Visscher, W., and Srinivasan, S., J. 
Electrochem. Soc., 128, 1900, (1981)], using the equation: 
##EQU2## 
where v is the sweep rate, and .DELTA.t is the time it takes to scan in 
one direction. The factor of 2 in the denominator accounts for scanning in 
both the anodic and cathodic directions. Voltammetric data obtained for an 
electrode made from a paper precursor containing 0.5 gm stainless 
steel/sheet and sintered at 1323 K for 40 minutes are shown in FIG. 3. The 
sintered electrode contained 0.00528 gm carbon and is the same electrode 
used in FIGS. 1 and 2. Since faradaic and pure capacitive features are 
noted in FIG. 3, a comparison of the capacitive charging current versus 
sweep rate was made and a linear dependence obtained, indicating that the 
charging process was reversible. 
DISCUSSION OF RESULTS--THE OPTIMIZATION MODEL 
To better understand our results and the subsequent development of a 
working hypothesis leading to optimization of an electrical property--in 
the foregoing examples, capacitance--in the fabrication of the class of 
composites in question, it appears useful to briefly summarize what we 
believe is the phenomenological basis of our invention. What we have found 
is that at a given ratio of stainless steel to carbon fiber and sintering 
temperature, the capacitance of the resulting composite initially 
increases but then decreases, with the capacitance showing a definite 
maximum with sintering time. Although initially puzzling, reflection led 
to the following hypothesis which appeared to at least qualitatively 
account for these observations. 
Two concurrent and independent reactions take place during sintering. One 
is the sinter-fusing of the stainless steel fibers at a multiplicity of 
their crossing points within the network to form a rigid three-dimensional 
matrix. Within this matrix there are multiple fusion points of the 
stainless steel fibers with excellent electrical contact at such nodes. In 
addition, formation of the rigid three-dimensional matrix results in the 
carbon fibers becoming enmeshed in the stainless steel fiber network 
resulting in a multiplicity of contact points between the carbon and 
stainless steel fibers and good electrical as well as physical contact 
between the dissimilar fibers. Consequently, the initial stages of 
sintering manifest the results of increasing the number of electrical 
contact points. 
The other reaction occurring during sintering is the metal-catalyzed 
gasification of carbon, that is, the reaction of carbon with hydrogen to 
form gaseous methane. Metal catalyzed gasification is not uniform along 
the carbon fiber, but rather is localized at the stainless steel-carbon 
fiber junctions. Consequently, following the formation of a junction, 
gasification of the carbon at the junction tends to break the electrical 
contact; the longer the sintering time, the more the gasification, the 
more electrical contacts between carbon and the metal fibers will be 
broken, all of which lead to a decrease in capacitance. 
Although the sinter-fusing of the metal fibers and the gasification of 
carbon are quite independent and concurrent reactions, nonetheless they 
are competing reactions in the context of the capacitance of the resulting 
composite. Using the aforegoing phenomenological description one can then 
construct a basis for optimizing capacitance, or any other electrical 
property, based on the kinetics of two competing reactions. In particular, 
one can determine the kinetic equations describing the increase in 
capacitance and the kinetic equations describing the capacitance decrease. 
Both equations will incorporate the independent variables of time, 
temperature, and stainless steel (or more generally, metal) to carbon 
fiber ratio, and also will implicitly yield the activation energy for the 
processes of capacitance increase and capacitance decrease. From these 
equations one then can calculate the sintering time for maximum 
capacitance at any sintering temperature and metal loading. One then can 
generate data by varying sintering temperature and metal fiber to carbon 
fiber loadings to determine the maximum capacitance on a total weight 
basis. This will then afford a composite whose capacitance has been 
maximized with respect to metal fiber to carbon fiber ratio, sintering 
temperature, and sintering time. The ensuing sections are a more detailed 
exposition of our method. 
RESULTS 
Weight Loss Measurements 
The loss of carbon, due to catalyzed gasification, was monitored by the 
change in electrode weight beyond the removal of cellulose after sintering 
for various lengths of time. These calculations were based on the complete 
removal of cellulose after short sintering times (ca. 5 min at 1323 K), 
and were verified during control studies using stainless steel-cellulose 
preforms which did not contain carbon. The gasification rate was defined 
as: 
EQU r.sub.g =-(1/M.sub.co)(dM.sub.c /dt)=k.sub.go exp(-E.sub.g 
/RT)[SS].sup.ng,[6] 
where r.sub.g is the gasification rate (min).sup.-1, M.sub.co is the 
initial mass of carbon (gm), M.sub.c is the mass of carbon (gm) at any 
time t (min), k.sub.go is the rate constant for gasification (min.sup.-1 
(gm stainless steel).sup.-ng), E.sub.g is the apparent activation energy 
for gasification (kJ/mol), [SS] is the weight of stainless steel fibers 
used in the paper precursor sheet (gm/sheet), and ng is the order of 
reaction in stainless steel. The reaction rate was considered zero order 
in carbon since its level was held constant in the paper preforms and 
since the metal catalyst particles arising from the stainless steel fibers 
were supported by and therefore always in contact with excess carbon 
during sintering. Integrating Equation [6], at constant temperature and 
stainless steel content, with the boundary condition, M.sub.c =M.sub.co at 
t=0 yields: 
EQU M.sub.c =M.sub.co -r.sub.g M.sub.co t=M.sub.co (1-r.sub.g t).[7] 
By defining the fractional conversion of carbon, X.sub.c as: 
EQU X.sub.c =(M.sub.co -M.sub.c)/M.sub.co, [8] 
the equation: 
EQU 1-X.sub.c =1-r.sub.g t, [9] 
can be developed for assigning r.sub.g as the negative slope of a plot of 
1-X.sub.c versus t. Data obtained for a paper precursor containing 0.5 gm 
stainless steel/sheet sintered at 1323 K, 1373 K, and 1423 K are shown in 
FIG. 4, while data for paper precursors containing 0.1, 0.2, and 0.5 gm 
stainless steel/sheet, sintered at 1323 K, are shown in FIG. 5. 
Electrochemical Measurements 
Capacitance versus sintering time profiles for various stainless steel 
loadings and temperatures are shown in FIGS. 6 and 7. Initially, as 
sintering time increased, the measured capacitance, on a per gram of 
carbon basis, rapidly increased. After passing through a maximum, the 
capacitance slowly decreased with sintering time. A series reaction scheme 
was proposed as a simple model relating sintering time to the observed 
capacitance data. The series reaction is shown schematically in FIG. 8, 
where carbon first becomes electrically activated or contacted by the 
formation of sintered metal-metal joints (r.sub.1) and the removal of 
cellulose. This contacted carbon may then be converted to gaseous products 
by the catalytic pathway (r.sub.2). The reaction rates are defined as: 
EQU r.sub.1 =dC/dt=k.sub.1o exp(-E.sub.1 /RT)[SS].sup.n1 for 
0&lt;t.ltoreq.t.sub.1,[10] 
EQU r.sub.2 =-dC/dt=k.sub.2o exp(-E.sub.2 /RT)[SS].sup.n2 for t.sub.1 
.ltoreq.t&lt;t.sub.2, [11] 
where r.sub.1 and r.sub.2 are reaction rates (F (gm carbon).sup.-1 
min.sup.-1), C represents the measured capacitance (F/gm carbon), k.sub.1o 
and k.sub.2o are measured rate constants (F (gm carbon).sup.-1 min.sup.-1 
(gm stainless steel).sup.-ni), E.sub.1 and E.sub.2 are apparent activation 
energies (kJ/mol), [SS] is the weight of stainless steel fibers used in 
the paper precursor sheet (gm/sheet), n.sub.1 and n.sub.2 are orders of 
reaction, t.sub.1 is the time (min) where sintering is complete, and 
t.sub.2 is the time (min) where all carbon has been gasified. Integrating 
Equation [10] at constant temperature and stainless steel content, with 
the boundary condition C=0 at t=0, which was an experimentally verified 
point, gives: 
EQU C=r.sub.1 t. [12] 
Integrating Equation [12] at constant temperature and stainless steel 
content yields: 
EQU C=-r.sub.2 t+b.sub.2, [13] 
where b.sub.2 (F/gm carbon) is a constant. 
Determination of Kinetic Parameters 
In order to determine the roles of sintering temperature and stainless 
steel loading, two sets of experiments were performed. In the first set, 
sintering temperature was varied as the stainless steel loading was held 
constant. In the second set, the amount of stainless steel was varied at 
constant sintering temperature. FIGS. 4 and 6 provide gasification and 
capacitance data versus sintering time as obtained at 1323 K for a 
stainless steel loading of 0.5 gm. These data were linearly regressed 
using Equations [9], [12], and [13]. Parameters describing gasification, 
sintering, and capacitance loss rates for differing stainless steel 
loadings and sintering temperatures were obtained and are shown in Table 
I. 
Effects of Stainless Steel Loading 
Reaction rates (r.sub.g, r.sub.1, r.sub.2) were fit to Equations [6], [10], 
and [11] at constant temperature for determination of the order of each 
reaction in stainless steel. The plot of capacitance loss (r.sub.2) versus 
stainless steel loading ([SS]) is shown in FIG. 9. Orders of reaction for 
gasification (n.sub.g), sintering (n.sub.1), and capacitance loss 
(n.sub.2) are presented in Table II. 
Temperature Effects 
Reaction rates, at constant stainless steel loading, were also fit to 
equations [6], [10], and [11] to determine the individual activation 
energies for the reactions. Arrhenius plots for gasification (r.sub.g) and 
sintering (r.sub.1) are shown in FIGS. 10 and 11, respectively. Apparent 
activation energies for gasification (E.sub.g), sintering (E.sub.1), and 
capacitance loss (E.sub.2) are listed in Table II. 
Rate Constants 
With knowledge of the activation energy and order of reaction, the rate 
constant for each reaction was determined using a least squares analysis. 
Results are again given in Table II. 
DISCUSSION 
Capacitance Versus Sintering Time Profiles 
The general shape of the profile of capacitance versus sintering time 
exhibited two distinct regions. The increasing region is attributed to 
sintering, where the formation of stainless steel-stainless steel contacts 
or joints provides interconnected pathways to electrically contact the 
active capacitive material, carbon. The region of capacitance decrease 
(t.gtoreq.t.sub.1) may be due to the loss of carbon, or more likely the 
loss of stainless steel-carbon contacts. If all carbon in the electrode 
structure contributed equally to the capacitance, as carbon was gasified, 
the capacitance on a per gram of carbon basis, should be constant. This 
would yield a horizontal capacitance versus time profile for the region 
(t.gtoreq.t.sub.1). Deviations from this behavior indicate that all carbon 
does not contribute equally to capacitance. The region where carbon is 
most likely to gasify first is in the neighborhood of stainless 
steel-carbon contacts where the metal catalyst contacts the carbon. 
Therefore, as carbon gasifies, the ability to contact carbon through the 
stainless steel network decreases resulting in an overall drop in 
electrode capacitance even though significant levels of carbon are still 
retained. 
Effects of Stainless Steel Loading 
The orders of reaction in stainless steel for gasification (n.sub.g), 
sintering (n.sub.1), and capacitance loss (n.sub.2) varied from near zero 
to almost 0.5. These non-integer orders suggest a complex series of events 
may be taking place. 
For carbon gasification (r.sub.g), the observed reaction order (n.sub.g), 
as determined from Equation [6] was 0.072.+-.0.030 (95% confidence level). 
Within the limits of the experimental data, a plot of reaction rate versus 
stainless steel loading was linear with a rather shallow slope. 
Extrapolation of these data to zero stainless steel loading predicted a 
gasification rate of 0.0030 min.sup.-1, not zero as assumed by Equation 
[6]. Because of this, the gasification rate of carbon in the absence of 
stainless steel, was experimentally determined at 1323 K and found to be 
ca. 0.0003 min.sup.-1. This non-zero rate may be due to uncatalyzed 
gasification, low levels of impurities in the carbon fibers themselves 
and/or the result of catalytically active impurities in the quartz 
sintering equipment. However, since the measured background gasification 
rate was an order of magnitude less than the catalyzed rate, the 
background rate was considered negligible and the determined rate Equation 
[6] assumed to be valid. 
The near zero order dependence of gasification on stainless steel loading 
is unexpected and unexplained at present. Calculations according to the 
procedure of Bird et al., "Transport Phenomena," J. Wiley and Sons (1960), 
p. 529, did not suggest that the reaction was under diffusion control and 
changing the rate of H.sub.2 flow past the preform from 10 to 50 cc/min 
(STP) during sintering did not alter the gasification rate. 
The rate of sintering (r.sub.1), as related to electrode capacitance, 
increased with stainless steel loading to the power of 0.17.+-.0.01. This 
order of reaction (n.sub.1) suggested a somewhat weak interrelationship 
between the sintering rate and the amount of stainless steel present. 
Since the sintering rate was measured indirectly by relating the 
capacitance to the sintering time, any rigorous evaluation of the reaction 
order is unwarranted. The fact that the rate increased with stainless 
steel content was considered satisfactory since the number of stainless 
steel-stainless steel contacts should increase with increased stainless 
steel content. However, since many fibers form redundant contacts with 
other fibers already contacted at other locations, the order determined by 
capacitance measurements cannot be strictly related to either the order of 
the surface reaction (i.e., sintering by surface diffusion) or the 
absolute number of metal contacts. 
For the rate of capacitance loss (r.sub.2), the measured order of reaction 
(n.sub.2) was determined to be 0.49.+-.0.14. This value differs 
significantly from that obtained for gasification and again indicates that 
all carbon does not impact equally on the capacitance. As additional 
stainless steel was added, the gasification rate changed rather slowly 
while the capacitance decreased much faster. The observed order of 
reaction can be rationalized by considering the electrical contacting of 
carbon to stainless steel. Since stainless steel-carbon contacts are 
broken after prolonged sintering due to the catalytic gasification of 
carbon by the metal, increased numbers of metal contacts can provide 
enhanced contacting at short sintering times but also lead to the loss of 
capacitance, and the scission of contiguous carbon fibers (as can be 
readily seen in a scanning electron micrograph), at longer sintering 
times. The net result of such behavior is a loss in capacitance which is 
much more pronounced on stainless steel loading than overall carbon 
removal, and a maximum in capacitance per gram of electrode at 
intermediate loadings, as discussed subsequently. 
Temperature Effects 
The apparent activation energies for gasification (E.sub.g), sintering 
(E.sub.1), and capacitance loss (E.sub.2) were determined from Arrhenius 
plots of appropriate reaction rates. Values were compared with those 
obtained for iron, the dominant surface species in 316L stainless steel 
(5). 
For gasification, the apparent activation energy (E.sub.g) was found to be 
80.+-.5 kJ/mol. This value compared favorably with the literature value of 
98.6 kJ/mol as reported for the catalyzed gasification of graphite by iron 
in hydrogen in the temperature range from 900 to 1100 K (16). The 
discrepancy between these two values may be the result of temperature 
differnces, measurement errors in the earlier work (16), and/or inherent 
differences between the amorphous carbon used in this study and graphite 
(16). 
The activation energy of sintering (E.sub.1) was determined to be 204.+-.19 
kJ/mol. In the literature, an initial activation energy of 270 kJ/mol for 
gamma-iron powders sintered from 1336 to 1666 K has been reported (17). 
This value appears to be in reasonable agreement, especially considering 
the indirect method used in this study to assess sintering behavior. 
For capacitance loss, the observed activation energy (E.sub.2) was 80.+-.9 
kJ/mol, nearly identical to that determined for carbon gasification. This 
again suggests the correspondence between gasification and capacitance 
loss, when carbon located at or near carbon-stainless steel contacts is 
removed. 
Optimization of Capacitance 
Since one possible use of stainless steel-carbon composite electrodes is in 
liquid double layer capacitors, a procedure was developed to determine the 
sintering time, temperature and stainless steel loading which maximized 
the capacitance on a total weight basis (viz., carbon plus stainless steel 
in the carbon containing layer). 
The maximum capacitance on any particular capacitance versus time curve 
occurred at the intersection of the sintering (r.sub.1) line with the 
capacitance loss (r.sub.2) line. The location of this intersection was 
calculated by combining Equations [12] and [13] and rearranging so that 
##EQU3## 
where t.sub.1 is the optimal sintering time (min). The maximum capacitance 
C.sub.opt (in faradays per gram carbon) was found by substituting Equation 
[14] for t into Equation [12] which gave: 
##EQU4## 
C.sub.opt was then corrected to C.sub.opt,corr, to reflect the added 
weight of stainless steel in the electrode by: 
##EQU5## 
The amount of carbon, M.sub.c, at time t.sub.1 was given by Equation [7]. 
Substituting for M.sub.c in Equation [16] yields: 
##EQU6## 
The rates r.sub.g, r.sub.1, r.sub.2 were each temperature and composition 
dependent as defined by Equations [6], [10], and [11]. A similar 
expression was developed for b.sub.2 such that: 
EQU b.sub.2 =Aexp(B/T)[SS].sup.C, [18] 
where A=1.4 F/gm C gm SS.sup.0.22, B=5400 K, and C=0.22. 
Sintering temperature and stainless steel loadings were then varied to 
determine the maximum capacitance on a total weight basis. The capacitance 
versus stainless steel loading curves for 1323, 1373, and 1423 K are shown 
in FIG. 12. The maximum occurred at 1323 K with a stainless steel loading 
of 0.24 gm stainless steel/gm carbon and the capacitance reaching 45.3 
F/gm (carbon plus stainless steel in the carbon containing layer). 
Of particular interest was the occurrence of the maximum capacitance at the 
lowest experimental temperature. This can be most easily explained by 
considering the experimentally determined reaction rates for sintering and 
capacitance loss at different temperatures. FIG. 13 shows the least 
squares fits of capacitance (F/gm C) versus sintering time obtained at a 
constant stainless steel loading of 0.5 gm/sheet at different 
temperatures. Experimental data points have been omitted from this figure 
since these are the same lines/rates determined from the data shown in 
FIG. 6. As temperature is increased, the rates of sintering and 
capacitance loss each increased, but the value of b.sub.2 (the capacitance 
intercept) decreased. The decrease of the capacitance intercept appears 
most responsible for decreases in capacitance at higher temperatures. 
Efforts to identify the physical significance of b.sub.2 are under way 
(18). Preliminary data suggest that electrodeposition of a metal such as 
nickel onto the electrode structure to reform lost metal-carbon contacts 
(with a corresponding increase in capacitance and upward shifting of 
b.sub.2) may be an avenue for better understanding the physical nature of 
the capacitance intercept. 
At constant temperature, as the amount of stainless steel was increased, 
the capacitance initially grew as the ability to contact carbon improved. 
A level of addition was reached, however, where the increase in 
capacitance was no longer large enough to overcome the additional weight 
of the stainless steel or the increased rate of gasification. Further 
increases in stainless steel loading decreased the capacitance. 
The maximum capacitance of 45.3 F/gm (carbon+stainless steel) was used to 
estimate the expected electrode energy density. The energy density was 
calculated using E=1/2 CV.sup.2 where E is the energy density, C is the 
maximum capacitance and V=2 volts is the estimated potential range for 
1.0M Na.sub.2 SO.sub.4 at pH 7. Resulting energy densities in the range of 
90 kJ/kg of electrode were calculated. 
TABLE 1 
______________________________________ 
Parameters describing gasification, sintering, 
and capacitance loss profiles 
Temp.sup.a 
SS.sup.b r.sub.g.sup.c 
r.sub.1.sup.d 
r.sub.2.sup.e 
b.sub.2.sup.f 
______________________________________ 
1323 0.1 0.00307 2.42 0.127 
50.7 
1323 0.2 0.00315 2.71 0.204 
56.1 
1323 0.5 0.00343 3.20 0.298 
70.9 
1373 0.5 0.00453 6.62 0.378 
61.2 
1423 0.5 0.00571 11.7 0.495 
53.2 
______________________________________ 
.sup.a Temp = Sintering temperature (K) 
.sup.b SS = Stainless steel loading (gm stainless steel/sheet) 
.sup.c r.sub.g = Rate of gasification 
.sup.d r.sub.1 = Rate of sintering (F (gm carbon).sup.-1 min.sup.-1) 
.sup.e r.sub.2 = Rate of capacitance loss (F (gm carbon).sup.-1 
min.sup.-1) 
.sup.f b.sub.2 = Ordinate intercept of capacitance loss data at t = 0 
(F/gm carbon) 
TABLE II 
__________________________________________________________________________ 
Parameters describing reaction rates.sup.1 
Rate Rate Apparent Activation 
Order of Reaction In 
Process Constant.sup.2 
Energy (kJ/mol) 
Stainless Steel 
__________________________________________________________________________ 
Gasification 
k.sub.go = 5.1 .+-. 0.5 
E.sub.g = 80 .+-. 5 
n.sub.g = 0.072 .+-. 0.030 
Sintering 
k.sub.1o = 4.0 .+-. 0.1 .times. 10.sup.8 
E.sub.1 = 204 .+-. 19 
n.sub.1 = 0.17 .+-. 0.01 
Capacitance loss 
k.sub.2o = 580 .+-. 10 
E.sub.2 = 80 .+-. 9 
n.sub.2 = 0.49 .+-. 0.14 
__________________________________________________________________________ 
.sup.1 Associated errors are for a 95% confidence level 
.sup.2 Units of rate contants 
k.sub.go [=] min.sup.-1 (gm stainless 
k.sub.1o [=] F (gm carbon).sup.-1 min.sup.-1 (gm stainless 
k.sub.2o [=] F (gm carbon).sup.-1 min.sup.-1 (gm stainless 
steel).sup.-0.49