the purpose of this paper is to deal with the solution of the inverse kinematics problem in robotic...

8/14/2019 The Purpose of This Paper is to Deal With the Solution of the Inverse Kinematics Problem in Robotic Arms

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The purpose of this paper is to deal with the solution of the inverse kinematics problem inRobotic arms. A two links, two degree of freedom (dof) planar robot arm (manipulator) is

simulated using a Multilayer Static Neural Network (MSNN) and animated. For the neurallearning scheme is used an iterative technique (Levenberg-Marquardt algorithm) that can bethought of as a combination of steepest descent and the Gauss-Newton method. When wechanged the error goal, we observed an oscillation on the end-effector of the manipulator dueto increase of the error. Simulation and animation results for a two dof manipulator provideevidence that this approach is indeed successful with respect to an ANFIS structure, in whichthe main characteristic are the qualitative values versus the quantitative values of the staticstructures.

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Electrochemistry Encyclopedia(http://electrochem.cwru.edu/encycl/)

ELECTROCHEMICAL MACHINING (ECM)Joseph McGeoughInstitute for Integrated Micro and Nano SystemsUniversity of EdinburghEdinburgh, EH9 3JL, United Kingdom

(July, 2005)

Michael Faradays early metallurgic researches, from 1818 to 1824, anticipated thedevelopments which have led to widespread use today of alloy steels. Much effort has beenexpended to improve their performance for their service as cutting tools in machining. The aimhas always been to yield higher rates of machining and to tackle recently developed hardermaterials on the principle that the tool material must be harder than the workpiece which is to bemachined. Much progress has been made; however, in recent years some alloys, which areexceedingly difficult to machine by the conventional methods, have been produced to meet ademand for very high-strength, heat resistant materials. Moreover, these new materials oftenhave to take a complex shape. A search has had to be made for alternative methods of machiningsince the evolution of suitable tooling has not kept pace with these advances.

Electrochemical machining (ECM) has been developed initially to machine these hard tomachine alloys, although any metal can so be machined. ECM is an electrolytic process and itsbasis is the phenomenon ofelectrolysis, whose laws were established by Faradayin 1833. Thefirst significant developments occurred in the 1950s, when ECM was investigated as a methodfor shaping high strength alloys. As of the 1990s, ECM is employed in many ways, for example,by automotive, offshore petroleum, and medical engineering industries, as well as by aerospacefirms, which are its principal user.
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Metal removal is achieved by electrochemical dissolution of an anodicallypolarized workpiecewhich is one part of an electrolytic cell in ECM. Hard metals can be shaped electrolytically byusing ECM and the rate of machining does not depend on their hardness. The tool electrode usedin the process does not wear, and therefore soft metals can be used as tools to form shapes onharder workpieces, unlike conventional machining methods. The process is used to smoothsurfaces, drill holes, form complex shapes, and remove fatigue cracks in steel structures. Itscombination with other techniques yields fresh applications in diverse industries. Recentadvances lie in computer-aided tool design, and the use of pulsed power, which has led to greateraccuracy for ECM-produced components.

Theoretical background

Since electrolysis is the basis of ECM, it must be understood before going further through thecharacteristics and other details of the process.

Electrolysis

Electrolysis is

the namegiven to thechemicalprocess whichoccurs, forexample,when anelectriccurrent ispassedbetween twoconductors

dipped into aliquidsolution. Atypicalexample isthat of twocopper wiresconnected to a source ofdirect current and immersed in a solution of copper sulphate in water, asshown in Figure 1. An ammeter, placed in the circuit, will register a flow of current; from thisindication, the electric circuit can be deduced to be complete. A significant conclusion that canbe made from an experiment of this sort is that the copper sulphate solution obviously has the

property that it could conduct electricity. Such solution is termed an electrolyte. The wires arecalled electrodes, the one with positivepolarity being the anode, and the one with negativepolarity the cathode. The system of electrodes and electrolyte is referred to as the electrolyticcell, whilst the chemical reactions which occur at the electrodes are called the anodic or cathodicreactions or processes.

Fig. 1. Electrolysis of copper sulphate solution.
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Electrolytesare differentfrom metallicconductors ofelectricity inthat thecurrent iscarried not byelectronsbutby atoms, orgroup ofatoms, whichhave eitherlost or gainedelectrons, thusacquiringeither positive

or negativecharges. Suchatoms arecalled ions. Ions which carry positive charges move through the electrolyte in the direction of thepositive current, that is, toward the cathode, and are called cations. Similarly, the negativelycharged ions travel toward the anode and are calledanions. The movement of the ions isaccompanied by the flow of electrons, in the opposite sense to the positive current in theelectrolyte, outside the cell, as shown also in Figure 2 and both reactions are a consequence ofthe appliedpotential difference, that is, voltage, from the electric source.

A cation reaching the cathode is neutralized, ordischarged, by the negative electrons on thecathode. Since the cation is usually the positively charged atom of a metal, the result of this

reaction is the deposition of metal atoms.To maintain the cathodic reaction, electrons are required to pass around the external circuit.These are obtained from the atoms of the metal anode, and these atoms thus become thepositively charged cations which pass into solution. In this case, the reaction is the reverse of thecathodic reaction.

The electrolyte in its bulk must be electrically neutral; that is, there must be equal numbers ofopposite charges within it, and thus there must be equal amounts of reaction at both electrodes.Therefore, in the electrolysis of copper sulphate solution with copper electrodes, the overall cellreaction is simply the transfer of copper metal from the anode to the cathode. When the wires areweighted at the end of the experiment, the anodic wire will be found to have lost weight, whilstthe cathodic wire will have increased in weight by an amount equal to that lost by the other wire.

Some examples of the reactions occurring in these processes are shown in theAppendix.

These results are embodied in Faradays two laws of electrolysis:

1. The amount of any substance dissolved or deposited is directly proportional to theamount of electricity which has flowed.

2. The amounts of different substances deposited or dissolved by the same quantity ofelectricity are proportional to theirchemical equivalent weights.

Fig. 2. Electrolytic dissolution of iron.


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A popular application of electrolysis is the electroplatingprocess in which metal coatings aredeposited upon the surface of a cathodically polarized metal. An example of an anodicdissolution operation is electropolishing. Here, the item which is to be polished is made theanode in an electrolytic cell. Irregularities on its surface are dissolved preferentially so that, ontheir removal, the surface becomes flat and polished.

ECM is similar to electropolishing in that it also is an anodic dissolution process. But the rates ofmetal removal offered by the polishing process are considerably less than those needed in metalmachining practice.

Some observations relevant to ECM can be made:

Since the anode metal dissolves electrochemically, its rate of dissolution depends onlyupon the atomic weight and the ionic charge, the current which is passed, and the time forwhich the current passes. The dissolution rate is not influenced by the hardness or othercharacteristics of the metal.

Since only hydrogen gas is evolvedat the cathode, the shape that electrode remainsunaltered during the electrolysis. This feature is perhaps the most relevant in the use ofECM as a metal shaping process.

Characteristics of ECM

In ECM, electrolytesserve asconductors of electricityandOhms law also applies to this type ofconductor. The resistance of electrolytes may amount to hundreds ofohms.

Accumulation within the small machining gap of the metallic and gaseous products of theelectrolysis is undesirable. If growth were left uncontrolled, eventually a short circuit wouldoccur between the two electrodes. To avoid this crisis, the electrolyte is pumped through theinterelectrode gap so that the products of the electrolysis are carried away. The forced movementof the electrolyte is also essential in diminishing the effects both of electrical heating of theelectrolyte, resulting from the passage of current and hydrogen gas, which respectively increaseand decrease the effective conductivity.

Working principles
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Electrochemical machining is founded on the principles outlined. As shown in Figure 3, the

workpiece and tool are the anode and cathode, respectively, of an electrolytic cell, and a constantpotential difference, usually at about 10V, is applied across them. A suitable electrolyte, forexample, aqueous sodium chloride (table salt) solution, is chosen so that the cathode shaperemains unchanged during electrolysis. The electrolyte is also pumped at a rate 3 to 30meter/second, through the gap between the electrodes to remove the products of machining andto diminish unwanted effects, such as those that arise with cathodic gas generation and electricalheating. The rate at which metal is then removed from the anode is approximately in inverseproportion to the distance between the electrodes. As machining proceeds, and with thesimultaneous movement of the cathode at a typical rate, for example, 0.02 millimeter/secondtoward the anode, the gap width along the electrode length will gradually tend to a steady-statevalue. Under these conditions, a shape, roughly complementary to that of the cathode, will bereproduced on the anode. A typical gap width then should be about 0.4 millimeter. Being

understood the characteristics and working principles of ECM, its advantages should be stated inshort before going further through machining processes:

the rate of metal machining does not depend on the hardness of the material, complicated shapes can be machined on hard metals, there is no tool wear.

The schematic of an industrial electrochemical machine is shown in Figure 4, and an actualexample of a cathode tool and anode workpiece are shown in Figure 5.

Fig. 3. Working principles of ECM.


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Fig. 4. Industrial electrochemical machine.


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machining to be so readily flushed from the machining gap. When complex shapes have to beproduced the design of tooling incorporating the right kind of flow ports becomes a considerableproblem.

Surface finish

Type ofelectrolytes used in the process affects the quality of surface finish obtained in ECM.Depending on the material, some electrolytes leave an etched finish. This finish results from thenonspecular reflection of light from crystal faces electrochemically dissolved at different rates.Sodium chloride electrolyte tends to produce an etched, matte finish with steels and nickelalloys.

The production of an electrochemically-polished surface is usually associated with the randomremoval of atoms from the anode workpiece, whose surface has become covered with an oxidefilm. This is governed by the metal-electrolyte combination used. Nonetheless, the mechanismscontrolling high-current density electropolishing in ECM are still not completely understood. Forexample, with nickel-based alloys, the formation of a nickel oxide film seems to be a prerequisitefor obtaining a polished surface; a finish of this quality, of 0.2m, has been claimed for Nimonic(a nickel alloy) machined insaturated sodium chloride solution. Surface finishes as fine as 0.1

m have been reported when nickel-chromium steels are machined in sodium chlorate solution.The formation of an oxide film on the metal surface is considered the key to these conditions ofpolishing.

Sometimes the formation of oxide film on the metal surface hinders efficient ECM and leads topoor surface finish. For example, the ECM of titanium is rendered difficult in chloride andnitrate electrolytes because the oxide film formed is sopassive. Even when highervoltagesabout50 V are applied to break the oxide film, its disruption is so non-uniform that deep grainboundary attack of the metal surface can occur.

Occasionally, metals that have undergone ECM have a pitted surface while the remaining area ispolished or matte. Pitting normally stems from gas evolution at the anode; the gas bubblesrupture the oxide film.

Process variables also affect surface finish. For example, as the current density is raised thefinish generally becomes smoother on the workpiece surface. A similar effect is achieved whenthe electrolyte velocity is increased. In tests with nickel machined in hydrochloricacid solutionthe surface finish has been noted to improve from an etched to a polished appearance when thecurrent density is increased from about 8 to 19 A/squarecentimeterwith constant flow velocity.

Accuracy and dimensional control

Electrolyte selection plays an important role in ECM. Sodium chloride, for example, yields muchless accurate components than sodium nitrate. The latter electrolyte has far better dimensionalcontrol owing to its current efficiency - current density characteristics. Using sodium nitrateelectrolyte, the current efficiency is greatest at the highest current densities. In hole drilling these

high current densities occur between the leading edge of the drilling tool and the workpiece. Inthe side gap there is no direct movement between the tool and workpiece surface, so the gapwidens and the current densities are lower. The current efficiencies are consequently lower in theside gap and much less metal than predicted from Faradays law is removed. Thus the overcut inthe side gap is reduced with this type of electrolyte. If another electrolyte such as sodiumchloride solution was used instead, then the overcut could be much greater. Using sodiumchloride solutions, its current efficiency remains steady at almost 100% for a wide range of


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current densities. Thus, even in the side gap, metal removal proceeds at a rate which is mainlydetermined by current density, in accordance with Faradays law. A wider overcut then ensues.

Shaping

Most metal-shaping operations in ECM utilize the same inherent feature of the process wherebyoneelectrode, generally thecathode tool, is driven toward the other at a constant rate when afixed voltage is applied between them. Under these conditions, the gap width between the tooland the workpiece becomes constant. The rate of forward movement between the tool and theworkpiece becomes constant. The rate of forward movement of the tool is matched by the rate ofrecession of the workpiece surface resulting from electrochemical dissolution.

Three practical cases are of interest in considering some equations derived for the variation ofthe interelectrode gap width:

1. When there is no tool movement, the gap width increases indefinitely with the squareroot of machining time. This condition is often used in deburring by ECM when surfaceirregularities are removed from components in a few seconds, without the need formechanical movement of the electrode.

2. When the tool is moved mechanically at a fixed rate toward the workpiece, the gap widthtends to a steady value. This inherent feature of ECM, whereby an equilibrium gap widthis obtained, is used widely in ECM for reproducing the shape of the cathode tool on theworkpiece.

3. Under short-circuit conditions the gap width goes to zero. If some process conditions,such as too small equilibrium gap width caused by a too high movement of the tooltoward the workpiece, occur, contact between the two electrodes ensues. This causes ashort circuit between the electrodes and hence premature termination of machining.

The equilibrium gap is applied widely in the shaping process. Studies of ECM shaping areusually concerned with three distinct problems:

1.The design of the cathode tool shape needed to produce a required profile geometry ofthe anodeworkpiece.

2. For a given cathode tool shape, prediction of the resultant anode workpiece geometry, forexample, hole drilling by ECM.

3. Specification of the shape of the anode workpiece, as machining proceeds. This is mostreadily predicted for the smoothing of surfaces, although for actual shaping ofcomponents by ECM, estimates of the machining times as the shape develops provideuseful information about the process.

Applications

Smoothing of rough surfaces


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Deburring, orsmoothing, ofsurfaces(Figure 6), isthe simplestand acommon useof ECM. Aplane-facedcathode tool isplacedopposite aworkpiecethat has anirregularsurface. Thecurrent

densities atthe peaks ofthe surfaceirregularitiesare higherthan those inthe valleys.The formerare, therefore,removedpreferentially and the workpiece becomes smooth, admittedly at the expense of stock metal(which is still machined from the valleys of the irregularities, even though at a lower rate).Electrochemical smoothing is the only type of ECM in which the final anode shape may matchprecisely that of the cathode tool.

Electrochemical deburring is a fast process; typical times for smoothing the surfaces ofmanufactured components are 5 to 30 seconds. Owing to its speed and simplicity of operation,electrochemical deburring can be performed with a fixed, stationary cathode tool. The process isused in many industries.

Hole drilling

Fig. 6. Smoothing of rough surfaces.


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Hole drillingis anotherprincipal wayof using ECM(Figure 7).The cathode-tool is usuallymade in theform of atubularelectrode.Electrolyte ispumped downthe centralbore of thetool, acrossthe main

machininggap, and outbetween thesidegap thatformsbetween thewall of thetool and thehole. Reversalof the electrolyte flow can often produce considerable improvement in machining accuracy.

The main machining action is carried out in the gap formed between the leading edge of the drill

tool and the base of the hole in the workpiece. ECM also proceeds laterally between the sidewalls of the tool and component, where the current density is lower than at the leading edge ofthe advancing tool. Since the lateral gap width becomes progressively larger than that at theleading edge, the side-ECM rate is lower. The overall effect of the side-ECM is to increase thediameter of the hole produced. The distance between the side wall of the workpiece and thecentral axis of the cathode tool is larger than the external radius of the cathode. This difference isknown as the "overcut". The amount of overcut can be reduced by several methods. A commonprocedure involves the insulation of the external walls of the tool (Figure 7), which inhibits side-current flow. Another practice lies in the choice of an electrolyte such as sodium nitrate, whichhas the greatest current efficiency at the highest current densities. In hole drilling these highcurrent densities occur between the leading edge of the drill and the base of the workpiece. Ifanother electrolyte such as sodium chloride were used the overcut could be much greater. Thecurrent efficiency for sodium chloride remains steady at almost 100% for a wide range of currentdensities. Thus, even in the side gap, metal removal proceeds at a rate that is mainly determinedby the current density, in accordance with Faraday's law.

Holes with diameters of 0.05 to 75 millimeterhave been achieved with ECM. For holes of 0.5 to1.0 millimeter diameter, depths of up to 110 millimeter have been produced. Drilling by ECM isnot restricted to round holes; the shape of the workpiece is determined by that of the toolelectrode.

Fig. 7. Electrochemical hole drilling.


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Full-form shaping

Full-form shaping utilizes a constant gap across the entire workpiece and the tool is movedmechanically at a fixed rate toward the workpiece in order to produce the type of shape used forthe production of compressor and turbine blades. In this procedure, current densitiesas high as100 A/square centimeterare used, and across the entire face of the workpiece, the current density

remains high.Electrolyte flow plays an even more influential role in full-form shaping than in drilling andsmoothing of surfaces. The entire large cross-sectional area of the workpiece has to be suppliedby the electrolyte as it flows between electrodes. The larger areas of electrodes involved meanthat comparatively higher pumping pressures and volumetric flow rates are needed.

Electrochemical grinding

The main feature of electrochemical grinding (ECG) is the use of a grinding wheel in which aninsulating abrasive, such as diamond particles, is set in a conductingmaterial. This wheelbecomes the cathode tool. The nonconducting particles act as a spacer between the wheel andworkpiece, providing a constant interelectrode gap, through which electrolyte is flushed.

Accuracies achieved by ECG are usually about 0.125 millimeter. A drawback of ECG is the lossof accuracy when inside corners are ground. Because of the electric fieldeffects, radii better than0.25 0.375 millimeter can seldom be achieved.

A wide application of electrochemical grinding is the production of tungsten carbide cuttingtools. ECG is also useful in the grinding of fragile parts such as hypodermic needles.

Electrochemical arc machining

A process that relies on electrical discharges in electrolytes, thereby permitting metal erosion aswell as ECM in that medium, has been developed. Because this process relies on the onset ofarcs rather than sparks, it has been named electrochemical arc machining (ECAM). A spark hasbeen defined as a sudden transient and noisy discharge between two electrodes; an arc is a stable

thermionic phenomenon. Duration discharges of approximately 1 second to 1 millisecond aredescribed as sparks, whereas for durations of about 0.1 second said discharges can be consideredarcs. Because in the ECAM process duration, energy, and time of ignition of sparks are undercontrol, it is valid to regard them as arcs.

An attraction of the ECAM technique is the very fast rates of metal removal attainable by thecombined effects of sparking and ECM. The ECAM technique can be applied in all the waysdiscussed for ECM, thus surfaces can be smoothed and drilled. Turning is also possible, as iswire machining.

One form of this process relies on a pulsed direct current, that is, full-waverectifiedacpowersupply that is locked in phase with a vibrating tool head. The oscillation of the tool gives rise to aset of conditions whereby ECM occurs over each wave cycle. The interelectrode gap narrows as

the tool vibrates over one cycle. During the same period the current rises until sparking takesplace by breakdown of the electrolyte and/or generation of electrolytic gas or steam bubbles inthe gap, the production of which aids the discharge process.

For drilling, the discharge action occurs at the leading edge of the tool, whereas ECM takes placeon the side walls between the tool and the workpiece. The combined spark erosion and ECMaction yields fast rates of metal removal. Because ECM is still possible, any metallurgicaldamage to the components caused by the sparking action can be removed by a short period ofECM after the main ECAM action. Currents of 250 A at 30 V are typically used in the process.


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Economic aspects

The industrial sectors utilizing ECM technology fall into five main categories: tool and die,automotive, aerospace, power generation, and oil and gas industries. Leading the worldsprinciple machine tool manufacturing nations in production and export of tools in the 1980s wereJapan followed by the former West Germany. The United States led in imports and consumption;

consumption was high for both Japan and W. Germany as well. Unconventional machine toolsincluding ECM are generally considered to account for only 1% of total production.Electrodischarge machining (EDM) holds the largest share, possibly as much as 50% and ECMabout 15% lagging behind laser processes which are 20%.

Manufacturing engineers wishing to use ECM processes in industry need to address thechallenge of proper tool design. The cost of design can be as much as 20% of the cost of anelectrochemical machine for complex components. Predictability of overcuts obtained forspecific applications and the particular electrolytes to be used for the alloy metals that have to bemachined must also be considered along with specific controls and limits on the ECM equipmentneeded.

Computer-controlled equipment and sensors are available for electrochemical machining

systems. However in the 1990s practical ECM systems are often favored because the amount ofcontrol and/or monitoring of the process is far less than that which was required in the 1970s.Thus machines are used successfully in which electrical spark detection is eliminated andmachining products control, for example,pHmonitoring, is nonexistent.

The present and future status of ECM

High-rate anodic electrochemical dissolution is a practical method of smoothing and shapinghard metals by employment of simple aqueous electrolyte solutions without wear of thecathodictool. ECM can offer substantial advantages in a wide range of cavity-sinking and shaped-holeproduction operations.

Control of the ECM process is improving all the time, with more sophisticated servo-systems,

and better insulating coatings. However there is still a need for basic information on electrodephenomena at both high current densities and electrolyte flow-rates.

Tool design continues to be of paramount importance in any ECM operation. The use ofcomputer-aided design to predict cathode tool profiles will continue to advance.

Recently developments in ECM practice have dwelt on the replacement of constant dc by pulsedcurrents (PECM). Significant improvements in surface quality have been claimed. Much smallerelectrode gaps may be obtained, for example, below 0.1 millimeterleading to improved controlof accuracy, for example to 0.02 to 0.10 millimeter, with dies, turbine blades, and precisionelectronic components. The key to further advancement in PECM lies in development of a lowcost power supply. Successful development of technique will enable on-line monitoring of thegap size, enabling closer process control.

Despite these attractions, PECM should be regarded as complementary to, and not a substitutefor, established ECM technology; the former is expensive and metal removal rates can be lowerthan these of the latter.

The advent of new technology for controlling the ECM process and the development of new andimproved metal alloys, which are difficult to machine by conventional means, will assure thefuture of electrochemical machining.

Appendix


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Electrolysis

Reactions that occur during the electrolysis of copper sulphate (Figure 1) are as follows. Theanodic reaction is ionizing of copper:

Cu ==> Cu2+(aq) + 2e-

While at the cathode the copper ions are discharged to form copper metal:Cu2+(aq) + 2e- ==> Cu

Reactions that occur during the electrolysis of iron (Figure 2) are as follows. The anodic reactionis ionizing of iron:

Fe ==> Fe2+(aq) + 2e-

At the cathode, the reaction is likely to be the generation of hydrogen gas and the production ofhydroxyl ions:

H2O + 2e- ==> H2 + 2OH-

The net reaction is thus:

Fe + 2H2O ==> Fe(OH)2(s) + H2The ferrous hydroxide may react to form ferric hydroxide:

4Fe(OH)2 + 2H2O + O2 ==> 4Fe(OH)3

Characteristics of ECM

By use ofFaradays laws, if md (kg) is the mass of metal dissolved, and because md = vdwhere v (m3) is the corresponding volume and d (kg/m3) the density of the anode metal, thevolumetric removal rate of anode metal (m3/second) is given by:

Where a (kg/mol) is the atomic weight of the anode metal, I (ampere) is thecurrent flowing,z is the ionic charge of the anode metal, and theFaraday constantF equals 96,487coulombs/mol. If a machining operation has to be carried out on an iron workpiece at a typicalrate of 2.6 10-8 kg/C, for this removal rate to be achieved by ECM, the current in the cell mustbe about 700 A, because a/zF = 29 10-8 and d= 7,860 kg/m3 for iron.

Rates of machining

By use of Faradays laws the rates at which metals can be electrochemically machined can becalculated.

Where md (kg) is the mass of metal electrochemically machined by current I (ampere)passed for a time t (second). The quantity a/zF is called theelectrochemical equivalent of theanode metal as mentioned before.

Table I shows the metal machining rates that can be obtained when a current of 1000A is used inECM. Metal removal rates in terms of volumetric machining are often more useful than mass


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removal rates, and both quantities are included. (It is assumed that the anodiccurrent efficiencyis 100%, that is all the current is used to remove metal, which is not always the case.)


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Bibliography

Table I. Metal machining rates

Metal Atomic Ionic Density Removal rate

weight charge 103 kg/m3 10-3 kg/s 10-6 m3/s

Aluminum 26.97 3 2.67 0.093 0.035

Beryllium 9.0 2 1.85 0.047 0.025

Chromium 51.99 2 7.19 0.269 0.038

3 0.180 0.025

6 0.090 0.013

Cobalt 58.93 2 8.85 0.306 0.035

3 0.204 0.023

Niobium 92.91 3 9.57 0.321 0.034

(Columbium) 4 0.241 0.025

5 0.193 0.020Copper 63.57 1 8.96 0.660 0.074

2 0.329 0.037

Iron 55.85 2 7.86 0.289 0.037

3 0.193 0.025

Magnesium 24.31 2 1.74 0.126 0.072

Manganese 54.94 2 7.43 0.285 0.038

4 0.142 0.019

6 0.095 0.013

7 0.081 0.011

Molybdenum 95.94 3 10.22 0.331 0.0324 0.248 0.024

6 0.166 0.016

Nickel 58.71 2 8.90 0.304 0.034

3 0.203 0.023

Silicon 28.09 4 2.33 0.073 0.031

Tin 118.69 2 7.30 0.615 0.084

4 0.307 0.042

Titanium 47.9 3 4.51 0.165 0.037

4 0.124 0.028

Tungsten 183.85 6 19.3 0.317 0.0168 0.238 0.012

Uranium 238.03 4 19.1 0.618 0.032

6 0.412 0.022

Zinc 65.37 2 7.13 0.339 0.048


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Surface Effects on Alloys Drilled by Electrochemical Arc Machining, A. DeSilva and J.A. McGeough, Proceedings of the Institution of Mechanical Engineers, Part B, Journalof Engineering Manufacture Vol. 200, pp 237-246, 1986.

Analysis of Taper Produced on Side Zone During ECD, V. K. Jain and V. N. Nanda,Precision Engineering, Journal of the American Society for Precision Engineering Vol.8, No. 1, pp 27-33, 1986.

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International Machine Tool Design and Research Conference pp 323-328, B. J. Davies(editor), Macmillan, Manchester, UK 1984.

Drilling Without Drills, G. Bellows and J. D. Kohls, American Machinist pp 178-183,1982.

Deburring-2: Electrochemical Machining, D. Graham, The Production EngineeringVol. 61, No. 6, pp 27-30, 1982.

Comparative Studies of ECM, EDM and ECAM, I. M. Crichton, J. A. McGeough, W.Munro, and C. White, Precision Engineering Vol. 3, pp 155-160, 1981.

Aspects of Drilling by Electrochemical Arc Machining, T. Drake and J. A. McGeough, inProceedings of the 21th Machine and Tool Design and Research Conference pp 362-369, J. M. Alexander (editor), Macmillan, New York, 1981.

Basic Study of ECDM-II, M. Kubota, Y. Tamura, H. Takahahi, and T. Sugaya, JournalAssociation Electro-Machining Vol. 13, No. 26, pp 42-57, 1980.


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Basic Study of ECDM-I, M. Kubota, Y. Tamura, J. Omori, and Y. Hirano, JournalAssociation Electro-Machining Vol. 12, No. 23, pp 24-33, 1978.

Newcomers for Production, G. Bellows, in Non-Traditional Machining Guide 26 pp28-29, Metcut Research Associates Inc., Cincinnati, Ohio, 1976.

Electrochemical machining, J. Kaczmarek, in Principles of Machining by Cutting,

Abrasion and Erosion pp 487-513, Peregrinus, Stevenage UK, 1976.

Principles of Electrochemical Machining, J. A. McGeough, Chapman and Hall, London,1974.

Listings of electrochemistrybooks,review chapters, andproceedings volumes are also availablein the Electrochemistry Science and Technology Information Resource (ESTIR).(http://electrochem.cwru.edu/estir/)

The Encyclopedia is hosted by theErnest B. Yeager Center for Electrochemical Sciences (YCES) and theChemical Engineering Department , Case Western Reserve University , Cleveland, Ohio.Copyright Notice.Edited by Zoltan Nagy ( [email protected] ), Department of Chemistry ,The University of NorthCarolina at Chapel Hill .

Return to: TopEncyclopedia Home Page Table of Contents Author Index Subject IndexSearch Dictionary ESTIR Home Page YCES Home Page

As illustrated in Figure 1, the hydrogen and the oxygen gases are n

Fig. 1. Operating principle of a fuel cell. (Copied from an article onsolid oxide fuel cells.)
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Ot

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CORROSION INHIBITIONCorrosion reactions involve a metal or metal alloy and its fluid surroundings. All metals andalloys are susceptible to corrosion by one or more naturally available or man-made fluids.

These reactions may cause a uniform loss of metal with consequent loss of cohesive strength orsimply an unacceptable change in appearance, for example tarnishing of gold or silver. There canbe local losses involving much less metal but leading to diminished whole piece strength.

Localized corrosion is exemplified bypitting or stress corrosion cracking.Control of the corrosion rate can be affected by reducing the tendency of the metal to oxidize, byreducing the aggressiveness of the medium, or by isolating the metal from the fluid. The lattercan be done by coating the metal with amillimeterthick impervious non-corroding coating.These have wide spread use, but their effect may not be permanent because of breaks in thecoating over time. Also in some systems coating might interfere with the process for which theequipment is used because they might change the heat transfer properties for example.
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In cases where a fairly thick coating is not acceptable, the use of corrosion inhibitors comes intoplay. These chemicals are continually fed into the fluid with the objective of having them moveto the metal-fluid interface. There the intact inhibitormolecule attaches to the metal, or it reactswith the surface to form a thin adherent compound. In the first case they act byadsorption(Toth,2002). In either case, the films are only one to a few molecules thick, that is nanometerthickness.

Some inorganic (non-carbon) chemicals like the chromates function in both ways and do so verywell. However they are hazardous to human and animal health and are not normally used now.Other inorganics like phosphates, borates, nitrites, and silicates function by reaction to formmicrometerthick films. They are used for some metals in near neutral (pH ~ 7)aqueoussolutions, for instance, in water treatment plants.

For many aqueous systems, for elevated temperature equipment, for crude oil production, etc.organic (carbon based) chemicals find more use. These materials are likely to function byadsorption. Here the organic molecule, which orients itself suitably, becomes attached to thesolid surface often via a less than total reaction between the inhibitor molecule and the solidsurface. The attachment does not require a total electron transferin either direction. A coulumbic

force, for example ion-dipole attraction, suffices to attach the inhibitor molecule to the solidsurface. This in turn interferes with access of the corrosive entity to the surface.

The adsorbed layer can be formed all over the surface either in a single layer or as a multilayer ora mixture of both. The more complete the coverage the better. This process has the advantage ofbeing molecularly thin and thus not too intrusive in heat conduction for example.

But there are problems. The amount of a given material adsorbed from a mixture depends on itsconcentration, temperature, fluid flow rate, as well as on the nature of the adsorbent that is, thesolid surface. The film has to be kept intact by continually adding inhibitor to the medium tomaintain a predetermined concentration of inhibitor. The continuing concentration is generallylower than that used initially, but both are at the milli-molarlevel.

That is not all. If temperature or flow rate of the system changes, the amount adsorbed is apt tochange. For temperature, the change is energetic, a basic change in the amount adsorbed. Forfluid flow, the change is dynamic, that is a change of fluid movement at the interface. This mayaffect the amount left at the interface. Faster flow generally causes removal of some of thephysically adsorbed material from the solid surface.

To this point the object was to get you to visualize the system. The point now is to get someinsight into how the efficiency of inhibition is determined. Corrosion rates can be measured in avariety of ways. In fact, corrosion rates can be determined from any measurable changeavailable. Examples are metal weight loss, rate of gaseous production, and changes in solutioncomposition. The basic approach is to expose small pieces of the metal in question to the fluidenvironment, preferably under flow conditions. Measurement of the corrosion rate can be carriedout electrochemically or chemically. It is best to acquire not only the initial rate but also the

steady rate. The latter is more useful for practical purposes.
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For weightloss, plot thechange inweight of eachcleanedcoupon (metalsample) bothbefore andafter exposureusing multiplesamples. Eachone of thesecan beremoved atpredeterminedtimes, see therepresentative

curve Figure 1.The slope ofthe curve at any point is the corrosion rate at that time. Note that the rate past point A is not quiteflat. The bottom curve shows the corrosion rate for the inhibited system. The weight loss of theinhibited coupon divided by the loss of the uninhibited coupon provides a measure of inhibitionefficiency.

To repeat, the rates can be determined from any quantity which changes regularly as a functionof time. Thus, change in solution concentration of iron (for steels),pHof the solution, or weightof metal coupon can be used.

There are some caveats. Laboratory experiments are useful in screening candidate inhibitors.Following that, they should be subjected to a lab system that emulates conditions in the field,

composition of the fluid, temperature and its changes, flow rates and their changes, time, and soon. Then there should be tests in the real system itself, at least long enough to cover anycondition cycles the system may have. However, continuous exposure with ongoing data outputis best.

To repeat, inhibitors are useless if they do not reach the metal surface intact. They can be lost byreaction with chemicals in the stream or to thieves in the system, that is any other solid surfaceexposed to the fluid stream like sand. Also, the inhibitor should not be detrimental to eitherprocess or product. Further, since the system may change with time, so must the corrosioncontrol. Thus the control system must be monitored consistently.

The question may be asked, why go to all of the trouble that is entailed in using corrosioninhibitors? There are two important reasons to do so.

First, there is the matter of safety. Industrial corrosion can lead to process breakdowns thatculminate in explosions or the venting of chemicals dangerous to health. In either case the ounceof prevention looms large over the pound of cure.

Second, there is the matter of cost. An article in 1995 (Battelle) estimated the cost of corrosion inthe United States per year was $300 billion, an appreciable portion of the Gross DomesticProduct. It also estimated that 30% of that amount could be saved by corrosion control, which ofcourse includes corrosion inhibition.

Fig. 1. Weight loss of coupons.


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Related articles

AnodizingElectrochemistry of corrosion

Bibliography

Fundamental Behavior of Model Corrosion Inhibitors, M. Knag, "Journal of DispersionScience and Technology" Vol. 27, pp 587-597, 2005.

Adsorption: Theory, Modeling, and Analysis, J. Toth (editor), Marcel Dekker, New York,2002.

Corrosion Inhibitors: Principles and Applications, V. Sastri, Wiley New York, 1998.

Economic Effects of Metallic Corrosion in the United States, Battelle ColumbusLaboratories, Columbus OH, 1995.

Corrosion Inhibitors: an Industrial Guide (2nd edition), E. Flick, Noyes, Park Ridge NJ,1993.

Chemical Inhibitors for Corrosion Control, B. G. Clubley (editor), Royal Society of

Chemistry, Cambridge, UK 1990.

Organic-Compounds as Corrosion-Inhibitors in Different Environments - a Review, B.Sanyal, "Progress in Organic Coatings" Vol. 9, pp 165-236, 1981.




DIELECTRICS
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William D. Brown,1 Dennis Hess,2 Vimal Desai,3 and M. Jamal Deen41Department of Electrical Engineering, University of Arkansas3217 Bell Engineering Center, Fayetteville, AR 72701, USA2School of Chemical and Biomolecular Engineering, Georgia Institute of Technology311 Ferst Drive, Atlanta, GA 30332, USA3Mechanical, Materials and Aerospace Engineering, University of Central Florida4000 Central Florida Blvd., Orlando, FL 32816, USA4Electrical and Computer Engineering, McMaster University1280 Main Street West, Hamilton, ON L8S 4K1, Canada(May, 2006)

What is a dielectric? An historical perspective

The science ofdielectrics, which hasbeen pursued for wellover one hundred

years, is one of theoldest branches ofphysics and has closelinks to chemistry,materials, andelectrical engineering.The term dielectricwas first coined byFaraday to suggestthat there issomething analogousto current flow

through a capacitorstructure during thecharging processwhen currentintroduced at oneplate (usually a metal)flows through theinsulatorto chargeanother plate (usuallya metal). Theimportant

consequence ofimposing a staticexternal field acrossthe capacitor is thatthe positively andnegatively chargedspecies in thedielectric become

Fig. 1. Schematic representation of differentmechanisms of polarization.
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polarized. Charging occurs only as the field within the insulator is changing. Maxwellformulated equations for electromagnetic fields as they are generated from displacement ofelectric charges and introduced dielectric and magnetic constants to characterize different media.It is generally accepted that a dielectric reacts to an electric field differently, compared to freespace, because it contains charges that can he displaced. Figure 1 illustrates some of the chargeconfigurations and their response (polarization) under the influence of an external field. Becausealmost all material systems are made up of charges (an exception being neutron stars!), it isuseful to characterize materials by theirdielectric constant.

A schematicrepresentation of thereal part of thedielectric constant isshown in Figure 2. Athigh frequencies(>1014Hz), thecontribution comes

solely from electronicpolarization, implyingthat only freeelectrons, as inmetals, can respond tothe electric field. Thatis why metals aresuch good opticalreflectors! Even thevarious thermal andmechanical

properties, such asthermal expansion,bulk modulus,thermal conductivity, specific heat, and refractive index, are related to the complex dielectricconstant, because they depend on the arrangement and mutual interaction of charges in thematerial. Thus, the study of dielectrics is fundamental in nature and offers a unifiedunderstanding of many other disciplines in materials science.

The scope of dielectric science and technology

Fig. 2. Contributions to the frequency-

dependent dielectric constant from the differentcharge configurations.
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In time, the focus ondielectric science andtechnology has broadenedfrom the materials of thetraditional dielectric filmsused insemiconductordevices and capacitors,particularly oxides andnitrides. More recently,materials of uniquedielectric responses havebeen studied and utilized innovel ways. Table I listsmany of the coretechnology areas of interestto those involved indielectric science and

technology.For instance, in the not toodistant past, polymerscientists and technologistsexpanded their horizonsfrom consumer products tothe high technology arena.Particularly notable areinventions intelecommunications, whereplastic fibers are used for

short optical data links, andpolymeric films are usedfor nonlinear opticsapplications. In the field ofmicroelectronics, radiationsensitive polymers(photoresists) have beenformulated for use with awide variety of exposuresystems, from the earlyones using visible light tothose using near ultraviolet,laser, e-beam, and x-raysources, for the fabricationof the sub-micrometerstructures of high speed,high density integratedcircuits. Steady progresshas also been made in thefield ofpassivation, where

Table I. Core Areas of DielectricScience and Technology

Physics/Chemistry/Materials

Science

Polarizability, Relaxation,Ions, Breakdown Phenomena

Elementary Excitations:Polaritons, Excitons, Polarons,Phonons

Phase Transitions, CriticalPhenomena

Bonding, Ionicity,

Crystal/Ligand Fields,Electronic Correlation

Bonding, Reaction, Kinetics,Transport, Energetics,Thermodynamics

Interfaces, Interphases

Properties of Dielectrics

Structural/Mechanical

Thermal

Electrical

Optical

Magnetic

Chemical

Synthesis/Processing

Deposition: Chemical VaporDeposition CVD, Plasma-CVD, Room Temperature(RT)CVD, Physical VaporDeposition (PVD), Sputtering.Evaporation, Dip/Spin/SprayCoating

Growth: Thermal, Anodic,Epitaxial
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various polymeric films are applied to microscopic objects such as integrated circuits and thepackages that house them.

Ceramists have also extended the range of applications; ceramic materials are used in packagesfor semiconductor integrated circuits, as well as in automobile engines, in composites foraerospace vehicles, and in high efficiency power generation stations. A notable advance was the

discovery of high-temperature superconductivity, for which Bednorz and Muller were awardedthe Nobel Prize in Physics in 1987.

Electronic and optical engineers are pushing the limits of the material properties and applicationsof organic and inorganic conductors,semiconductors, and insulators. One example is the revivedinterest in diamond and diamond-like films. These recent efforts resulted in higher speed, higherdensity devices and interconnection schemes, both electrical and optical, for computers andtelecommunication systems. Another example, the low-dimensional (d = 1, 2) nanostructures,which could only be speculated about in the past, are now a reality. This allows researchers totest some fundamental concepts in quantum mechanics. It is probable that more innovativedevices will follow.

Since the mid-1990s, the microelectronics industry has invested heavily, with some success, in

the development of high- and low-k dielectrics (k is the dielectric constant of a material).These materials are required because of the continuing reduction of both horizontal and verticaldimensions of integrated circuits (ICs), which results in an increase of the gate leakagecurrent,and consequently, an increase in heat dissipation. Therefore, high-k materials are needed for thegate dielectric in complementary metal-oxide-semiconductor (CMOS) ICs, storage capacitors,and nonvolatile static memory devices. Similarly, the reduction in spacing of metal interconnectsin both the vertical and horizontal dimensions has created the need for low-k materials that serveas interlevel dielectrics to offset the increase in signal propagation time between transistors,known as RC delay (R is metal wire resistance and C is interlevel dielectriccapacitance). Asa result of these requirements for present and future sub-100nm IC technologies, many newdielectric materials and material combinations have been and must continue to be created and

characterized if the device density of ICs is to continue to increase as anticipated by MooresLaw.

The previous discussion is not intended to suggest that dielectric science and technology is onlyimportant for electronic components. Far from it; dielectrics play important roles in applicationsranging from sensors, isolation forconductorsin the power utility industry, to ceramic cookware.Further, in the rapidly emerging field of biological systems, the dielectric constant is importantbecause electrostatic effects are used to link the structure and function of biological molecules. Ithas been proposed that electrostatic effects play a major role in important biological activitiessuch as enzyme catalysis,electron transfer,protontransport, ionchannels, and signaltransduction. The role of the science and technology of dielectrics is also important in existingfields of sensors, nanotechnology, electronics, photonics, chemical and mechanical systems, andin emerging fields of biology and biochemistry. Thus, it appears inevitable that the dielectricproperties ofnanoscale materials and structures will be critical to developing novel devices forcurrent and future commercial applications. For example, large amounts ofenergy can be storedin nanocomposites that show largepolarizabilities. In addition, dielectric materials such asferroelectric andpiezoelectricnanomaterials offer significant advantages for communicationdevices and data storage systems. Recently, there have been investigations of nanoporouscomposites formed by the incorporation of nanosize air bubbles, leading to a significant decreasein the dielectric constant and the ability to vary the dielectric constant by controlling theconcentration of air bubbles. Furthermore, the continuing trend in miniaturization requires


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increasingly thinner dielectric materials without nanoscale defects. An understanding of materialand interfacial properties at the nanoscale is often facilitated by materials modeling as well as thedevelopment of innovative characterization tools. One such tool is the development of thescanning nonlinear dielectric microscope (SNDM) that can be used to measure the microscopicpoint-to-point variation of the linear and nonlinear dielectric properties of insulators.

Future requirements and achievements in the area of dielectrics can be realized only by thefurther development and fundamental understanding of reliable material synthesis, processing,and characterization technologies, making it possible to tailor dielectric materials, their thin filmstructures, and their interfaces to specific applications. In the past, these technologies have beensuccessfully applied in the microelectronics and other industries that depend on the uniquemechanical, optical, chemical, and electrical properties of high performance dielectric materials.The advent of nanoscale devices in recent years demands that scientists and engineers continueto focus attention on dielectric material design, synthesis, and characterization for enhancedperformance, reliability, and manufacturability.

Figure 3 is an

attempt todepict themultitude ofinteractionsamong themany anddiverse coreareas ofdielectricscience andtechnologythat present

challengingpossibilitiesfor thecommunity ofscientists, engineers, and technologists in research, development, and manufacturing.

Acknowledgement

This article was reproduced from The Electrochemical Society Interface (Vol. 15, No. 1, Spring2006) with permission ofThe Electrochemical Society, Inc. and the authors.

Bibliography

Material Science and Engineering for the 1990s, National Academy of Science Press,Washington, 1989.

Introduction to Ceramics (2nd edition), W. D. Kingery, H. K. Bowen, and D. R. Uhlmann,pp 918 et seq., Wiley, New York, 1976.

Introduction to Solid State Physics (4th edition), C. Kittel, Wiley, New York, 1971.

Solid State Physics, Advances in Research and Applications, F. Seitz, D. Turnbull, andH. Ehrenreich, Academic Press, New York, 1969.

Fig. 3. Interactions among the core areas of dielectric scienceand technology.
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Theory of Quantum Liquids, D. Pines and P. Nozieres, p. 280, Benjamin, New York,1966.






DIELECTRICSWilliam D. Brown,1 Dennis Hess,2 Vimal Desai,3 and M. Jamal Deen41Department of Electrical Engineering, University of Arkansas3217 Bell Engineering Center, Fayetteville, AR 72701, USA2School of Chemical and Biomolecular Engineering, Georgia Institute of Technology311 Ferst Drive, Atlanta, GA 30332, USA3Mechanical, Materials and Aerospace Engineering, University of Central Florida4000 Central Florida Blvd., Orlando, FL 32816, USA4Electrical and Computer Engineering, McMaster University1280 Main Street West, Hamilton, ON L8S 4K1, Canada(May, 2006)

What is a dielectric? An historical perspective
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The science ofdielectrics, which hasbeen pursued for wellover one hundredyears, is one of theoldest branches ofphysics and has closelinks to chemistry,materials, andelectrical engineering.The term dielectricwas first coined byFaraday to suggestthat there issomething analogousto current flowthrough a capacitor

structure during thecharging processwhen currentintroduced at oneplate (usually a metal)flows through theinsulatorto chargeanother plate (usuallya metal). Theimportantconsequence ofimposing a staticexternal field acrossthe capacitor is thatthe positively andnegatively chargedspecies in thedielectric becomepolarized. Chargingoccurs only as thefield within the insulator is changing. Maxwell formulated equations for electromagnetic fieldsas they are generated from displacement of electric charges and introduced dielectric andmagnetic constants to characterize different media. It is generally accepted that a dielectric reacts

to an electric field differently, compared to free space, because it contains charges that can hedisplaced. Figure 1 illustrates some of the charge configurations and their response (polarization)under the influence of an external field. Because almost all material systems are made up ofcharges (an exception being neutron stars!), it is useful to characterize materials by theirdielectric constant.

Fig. 1. Schematic representation of differentmechanisms of polarization.
http://electrochem.cwru.edu/encycl/art-c04-electr-cap.htmhttp://electrochem.cwru.edu/encycl/fig/d01/d01-f01b.jpghttp://electrochem.cwru.edu/encycl/art-c04-electr-cap.htm


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A schematicrepresentation of thereal part of thedielectric constant isshown in Figure 2. Athigh frequencies(>1014Hz), thecontribution comessolely from electronicpolarization, implyingthat only freeelectrons, as inmetals, can respond tothe electric field. Thatis why metals aresuch good opticalreflectors! Even the

various thermal andmechanicalproperties, such asthermal expansion,bulk modulus,thermal conductivity,specific heat, and refractive index, are related to the complex dielectric constant, because theydepend on the arrangement and mutual interaction of charges in the material. Thus, the study ofdielectrics is fundamental in nature and offers a unified understanding of many other disciplinesin materials science.

The scope of dielectric science and technology

Fig. 2. Contributions to the frequency-dependent dielectric constant from the differentcharge configurations.
http://electrochem.cwru.edu/encycl/fig/d01/d01-f02b.jpg


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In time, the focus ondielectric science andtechnology has broadenedfrom the materials of thetraditional dielectric filmsused insemiconductordevices and capacitors,particularly oxides andnitrides. More recently,materials of uniquedielectric responses havebeen studied and utilized innovel ways. Table I listsmany of the coretechnology areas of interestto those involved indielectric science and

technology.For instance, in the not toodistant past, polymerscientists and technologistsexpanded their horizonsfrom consumer products tothe high technology arena.Particularly notable areinventions intelecommunications, whereplastic fibers are used for

short optical data links, andpolymeric films are usedfor nonlinear opticsapplications. In the field ofmicroelectronics, radiationsensitive polymers(photoresists) have beenformulated for use with awide variety of exposuresystems, from the earlyones using visible light tothose using near ultraviolet,laser, e-beam, and x-raysources, for the fabricationof the sub-micrometerstructures of high speed,high density integratedcircuits. Steady progresshas also been made in thefield ofpassivation, where

Table I. Core Areas of DielectricScience and Technology

Physics/Chemistry/Materials

Science

Polarizability, Relaxation,Ions, Breakdown Phenomena

Elementary Excitations:Polaritons, Excitons, Polarons,Phonons

Phase Transitions, CriticalPhenomena

Bonding, Ionicity,

Crystal/Ligand Fields,Electronic Correlation

Bonding, Reaction, Kinetics,Transport, Energetics,Thermodynamics

Interfaces, Interphases

Properties of Dielectrics

Structural/Mechanical

Thermal

Electrical

Optical

Magnetic

Chemical

Synthesis/Processing

Deposition: Chemical VaporDeposition CVD, Plasma-CVD, Room Temperature(RT)CVD, Physical VaporDeposition (PVD), Sputtering.Evaporation, Dip/Spin/SprayCoating

Growth: Thermal, Anodic,Epitaxial
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Theory of Quantum Liquids, D. Pines and P. Nozieres, p. 280, Benjamin, New York,1966.






ELECTROCHEMICAL CAPACITORSTheir Nature, Function, and ApplicationsBrian E. ConwayChemistry Department, University of Ottawa10 Marie Curie StreetOttawa, Ontario K1N 6N5, Canada(March, 2003)

Historical introduction

Electrochemical capacitors provide a mode of electrical charge-andenergy-storage and delivery,complementary to that bybatteries. The first electrochemical capacitor device was disclosed in aGeneral Electric Co. patent in 1957 to Becker but was of a crude nature, employing porouscarbon. Later work by Sohio (1969) described a so-called "electrokinetic capacitor" utilizing

porous carbon in a non-aqueouselectrolyte which enabled it to be charged up to about 3 V,though the operation of the device was not "electrokinetic" in nature, a misnomer. In 1971,Trasatti and Buzzanca recognized that the electrochemical charging behavior of rutheniumdioxide films was like that ofcapacitors. Between 1975 and 1980, the present author and his co-workers, under contract with the then Continental Group Inc., carried out extensive fundamentaland development work on the ruthenium oxide type of electrochemical capacitor (Conway,1997) which behaves as a surface- redoxpseudocapacitance(seebelow). The whole field hasburgeoned since about 1990 and is very active in fundamental, and R&D directions.
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A great deal of scientific and technological research has been reported in the scientific literaturesince about 1990. An extensive and detailed account of this has been given in the author'smonograph on "Electrochemical Supercapacitors: Scientific Fundamentals and TechnologicalApplications" (1999).

Scientific introduction

In order to describe "electrochemical capacitors" and to explain their function and applications, itis necessary first to consider the nature of an ordinary electrostatic capacitor or a "condenser" asit used to be called, and thence the meaning of the term electrical capacitance.

The nature of electricity took a long time to be understood, from the early experiments onelectrostatic electricity in the mid-18th century, for example by Galvani, through the time of theinvention of the first electric battery byAlessandro Volta (Volta's "Pile") in 1800, on toFaradays's and Davy's monumental discoveries on the chemical origin of electricity generated byVolta's pile. At first, two "kinds" of electricity were postulated: "animal electricity", as in theworks of Galvani on stimulation of the frog's leg nerve by contact between two dissimilar metalsand later, "Voltaic electricity" generated chemically from a Volta pile of zinc and silver orcopper plates separated by paper wetted with an acidor salt solution (Conway, 2000).

In parallel with these discoveries were extensive works on electrostatic electricity generated forexample by the rubbing of naturally occurring amber or by the so-called Wimshurst machine (arotating circular plate, containing insets of amber-like material, rubbing against charge-collectorplates connected overall to a Leyden Jar or a spark-gap). It was from this direction of research onelectricity that the invention of the electric condenser arose, referred to as the "Leyden Jar", andcapable of storing electric chargegenerated by a Wimshurst machine. Such a jar had the"capacity", depending on its dimensions and materials of construction, of storing electric chargeby bringing it together in a condensed way (hence the term "condenser") on the surfaces of aLeyden Jar at a certain two-dimensional charge density.

The principle of design and operation of the Leyden Jar and all subsequent regular condensers orcapacitordevices, is as follows. Two metal surfaces that constitute electrodes are separated atsome small distance either in air (or vacuum) or on each side of a liquid or solid film, referred toas the "dielectric", a term first used by Michael Faraday . For a given separation of the electrodeplates, the capacitance developed per unit area of the two plates depends on the properties of thedielectric between the plates characterized by its so-called dielectric constant.
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In the case of the Leyden Jar (Figure1), the material (glass) of the jar itselfserves a the dielectric medium andthe contact plates were metal foilswrapped, inside and out, around thecylindrical surfaces of the jar. Theelectrical contact to the inner surfacefoil was by means of a conductingelectrolyte solution(or originally byordinary water itself) in which wasimmersed a conducting metalelectrode for electrical contact. Thedevice was charged by joining twowires from the inside electrode andthe outside foil to an electrostaticmachine of the Wimshurst type. Inlater experimentation, the Leyden Jar

capacitor was connected to theelectrodes of a Volta's pileorbatteryforcharging. This was the first-generation capacitor forstorageofelectric charge.

The nature of electric charge remained elusive until much later (1897) when J.J. Thomsonidentified and characterized the fundamental entity of electric charge as the "electron", presentubiquitously in all atoms of the Universe and identified, in his experiments, by means ofexperiments on gases at low pressures in gas-discharge tubes (Crookes tubes or neon lights). Theelectron charge was determined independently by Townsend and by Millikan (Glasstone, 1940),and was shown to be equivalent to Faraday's constant for the relation between extent of passageof charge and extent of chemical change (as related byFaraday's Laws) caused by electrolysisof

conducting solutions, when calculated on a "pergram-atom" or "gram-equivalent" basis.Relation of capacitance to geometry and dielectric constant of a capacitor

The capacitance of a capacitor is proportional to the area of the contact plates and the dielectricconstant of the medium between the plates, and it is inversely proportional to the separationbetween the plates (see theAppendix). In relation to electrochemical capacitors, to be discussedbelow, the capacitance of small dielectriccapacitors is very small being on the order ofmicrofarads or nanofarads (millionth or billionth of a farad, respectively) for small devices onthe order ofmm orcmin dimensions. By having very thin insulatingfilms, on the order of 10 to100 nanometers, formed anodically on the plate of a two-electrode capacitor, substantially largerspecific capacitances (that is per cm2) can be attained. Such devices are called "electrolyticcapacitors" because the thin dielectric oxide films are formed on the plates by an anodic

electrolysis procedure applied at metals such as aluminum, tantalum, titanium, niobium, etc.Such capacitors are still of the dielectric type (the dielectric medium being here the thin,insulating oxide film, usually having a relatively high dielectric constant) and should not beconfused with the "electrochemical" capacitor type of device which is the topic of this article.

Electrochemical capacitors are a special kind of capacitor based oncharging and discharging theinterfaces of high specific-area materials such as porous carbon materials or porous oxides ofsome metals. They can store electric charge and correspondingenergy at high densitiesin anhighly reversible way, as does a regularcapacitor, and hence can be operated at specificpower

Fig. 1. LeydenJar, the first

capacitor or"condenser".
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densities (in watts/kg) substantially higher than can mostbatteries. Their capacitance for a givensize of the device is thus much higher, by a factor of 10,000 or so, than those achievable withregular capacitors. For this reason proprietary names such as "Supercapacitors" or"Ultracapacitors" have been coined to describe their performance.

While they function formally like rechargeable batteries instoring or deliveringelectric charge,

their mechanisms of charge storage are quite different, in most cases, from those operating inbatteries. Thus, electrochemical capacitors are not substitutes for batteries but rather are to beregarded as complementary to them for charge storage or delivery. They can offeradvantageously fast charging or discharging rates over most batteries of comparable volume buttheir energy density is usually less, by a factor of 3 to 4, than that of batteries. Their high poweror power densities, however, enables them to be employed in interesting complementary ways inhybrid systems with batteries.

An important difference between charging a capacitor and charging a battery is that there isalways an intrinsic increase of voltage on charge (or decrease on discharge) of a capacitor as thecharge percm2 is increased or decreased. In contrast, an ideal battery has a constant voltageduring discharge or recharge except as thestate of charge approaches 0 or 100%. Although

practical batteries exhibitsome dependence of cell voltage on state of charge, especially lithium-intercalation batteries, the latter for fundamental reasons arising from intercalation. (See theAppendix for further details.)

The double-layer capacitance at electrode interfaces

Nature of electrical double layers


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An importantclass of
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electrochemical capacitors utilizes the co-called double-layercapacitance that arises at allelectrode interfaces with electrolyte solutions orionic melts. The concept and model of thedouble layer arose in the work of von Helmholtz (1853) on the interfaces ofcolloidalsuspensions and was subsequently extended to surfaces of metal electrodes by Gouy, Chapman,and Stern, and later in the notable work of Grahame around 1947. Models of the double layer areshown in Figure 2, with their capacitor-like structures.

Helmholtz envisaged a capacitor-like separation ofanionic and cationiccharges across theinterface of colloidal particles with an electrolyte. For electrode interfaces with an electrolytesolution, this concept was extended to model the separation of "electronic" charges residing atthe metal electrodesurfaces (manifested as an excess of negativecharge densities under negativepolarizationwith respect to theelectrolyte solution or as a deficiency of electron charge densityunder positive polarization), depending in each case, on the correspondingpotential differencebetween the electrode and the solution boundary at the electrode. For zero net charge, thecorresponding potential is referred to as the "potential of zero charge".

In response to positive or negative electric polarization of the electrode relative accumulations ofcations or anions develop, respectively, at the solution side of the charged electrode. If, for

energetic reasons, the ions of the electrolyte are not faradaicallydischargeable (that is noelectron transfercan occur across the interface ("ideally polarizable electrode", for example amercury electrode, Grahame 1947 and Parsons 1954), then an electrostatic electrical equilibriumis established at the

the purpose of this paper is to deal with the solution of the inverse kinematics problem in robotic...

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