–1–
1. Introduction
1.1. Basic concepts
The origins of electrochemistry can be traced back 200 years ago (1791) and is due to Luigi Galvani who first performed an "electrochemical" experiment while dissecting a frog. Nine years later, Volta discovered the first electrochemical cell, having salt water between two plates, made of silver and zinc. In the following years, pioneering work of Nicholson (1800), Davy (1807 – 1808), Faraday (1833), Kohlrausch, Hittorf, Arrhenius, Nernst and Leblanc in the XIXth century lead to the development of electrochemistry as an important branch of science.
We can say that now electrochemistry deals with two major issues: the physical chemistry of ionically conducting solutions or pure substances (such as molten salts) –the ionics – and the physical chemistry of electrically charged interfaces – the electrodics. The ionics describes mainly ions and solvents, as well as the interaction between them. The electrodics is concerned with the interface between an electrode (metal or semiconductor) and an electrolyte and all the phenomena that happen when such interfaces are brought together. In the following we need to define some basic concepts, which will be encountered throughout the course.
An electrolyte is a substance, either dissolved in a solution or in a molten salt, that forms charged species (ions). An electrode consists of a second phase (usually solid, e.g. a metal) which is immersed in an electrolyte. The electrode charged positively, i.e. having a deficit of electrons, is called the anode, while the electrode charged negatively, i.e. having an excess of electrons, is called the cathode. The charged species in solution move towards the electrode having opposite charges and are called cations (positively charged – they move towards the cathode) and anions (negatively charged – they move towards the anode). The terms ion, anion and cation were introduced by Michael Faraday in 1834.
The process of adding electrons to either an ion or a neutral species is called reduction, while the reverse process (i.e., removal of electrons) is called oxidation.
1.2. Solvents and ion solvation
For many years, electrochemistry dealt mostly with aqueous solutions, but in time, with the development of electrochemistry, non-aqueous solvents became important as well. The aluminum industry for example is entirely based on electrolysis in a molten salt system (fused cryolite). There are three types of solvents used in electrochemistry, outlined below.
1. Molecular solvents – which consist of molecules. The forces between solvent molecules range from hydrogen-bond type (water) and other type of "bridges" (oxygen, halogen) – these are highly polar solvents – to dipole-dipole interactions (moderately polar liquids, e.g. acetone) and van der Waals interactions (non-polar liquids, such as hydrocarbons). The latter solvents are dielectrics and do not conduct appreciably; in some of them the autoionization phenomenon occurs, conducting electricity to some extent (very little however):
2H2O H3O+ + OH; 2HgBr2 HgBr+ + HgBr3; 2NO2 NO+ + NO3;
2. Ionic solvents – which consist of ions, and are mostly molten salts. Not all salts yield ions when fused, some form instead molecular liquids (like HgBr2). Usually, molten salts exist at high temperatures (at standard pressure, NaCl is liquid between 800 and ca. 1450 oC), but in the past years "room-temperature" molten salts were discovered, which have low melting points (ethylpiridinium bromide, -114 oC, tetramethylammonium thiocianate, -50.5 oC). In some cases, mixtures of salts (called eutectics) have also low melting points, such as the AlCl3 + KCl + NaCl in the ratio 60:14:26 (mol %) which melts at 94 oC. The ions in these melts can be monoatomic (like Na+ and Cl) or polyatomic (molten cryolite, Na3AlF6, contains Na+, AlF63, AlF4 and F ions).
3. Polymer solvents – which contain polymeric chains capable of dissolving salts. These are (almost) solid electrolytes and they are very important in the manufacturing of solid-state batteries and any other practical device that needs a solid electrolyte. The most important solvents of this type are polyethylene oxide (PEO) and polypropylene oxide (PPO). Ions are dissolved by coordination of the cation by electronegative heteroatoms (such as oxygen), the anions surrounding the polymer chain which adopts a helical structure (Figure 1).
PEOPPO
Figure 1. Schematic structure of a PEO – LiClO4 "complex".
In a fluid medium, most commonly used in electrochemistry, the dissolved ions interact strongly with the solvent molecules: the higher the dielectric constant of the solvent, the stronger the interaction. The solvent-solute interaction is called solvation (or hydration, if the solvent is water). The energy changes accompanying this interaction are very large for ions (~ 400 kJ/mol for single charged ions), and much smaller for non-polar species (~10 – 15 kJ/mol). Transport parameters, such as ionic mobilities and diffusion coefficients, are influenced by the solvation: the ion does not move alone, as a single entity, but carries some solvent molecules (in some cases quite many of them) with it.
Figure 2. Schematic of a hydrated cation, showing the different water layers surrounding the cation.
1.3. Electrolysis, Faraday's law and electrode types.
The electrolysis is an (electro)chemical process which occurs due to the passage of electric current through an electrolyte by applying a large enough voltage between two electrodes.
According to Faraday's law, the amount of substance transformed during the passage of current is related to the charge:
m = KQ = = KIt (at constant current)
where Q is the charge passed, I is the current, t is the electrolysis time and K is the equivalent of the substance:
or
where M is the molar mass of the substance (atomic mass, A, if we deal with an element), F is the Faraday constant (96487 C/mole) and n is the number of transferred electrons.
(A)(B)
(C)(D)
Figure 3. Common electrode processes. (A) – simple electron transfer; (B) – metal deposition; (C) – gas evolution; (D) – surface film transformation.
Some examples of common electrode processes are shown in Figure 3.
(E)
(E)
Figure 3. Common electrode processes. (E) – anodic dissolution.
2. Ionics
2.1. Ion migration and transference numbers
Although positive and negative ions are discharged in equivalent amounts at the electrodes, the anions and cations do not necessarily move with the same velocity in an electric field. The total amount of ions, and hence the corresponding quantity of electricity, carried through the solution is proportional to the sum of the anion and cation velocities.
If u+ is the absolute migration velocity (or mobility) of the cation and u- for the anions (in the same solution), the total amount of electricity passed will be proportional to the sum u+ + u-. The amount of electricity carried by each ionic species, Qi, is proportional to its own mobility. The fraction of current carried by each ionic species is called transference (or transport) number, and for a 1:1 electrolyte it is given by the simple equation:
and ; t+ + t- = 1(1)
In general, for a z+:z- electrolyte, one can write:
and (2)
If z+ = z- = 1 (1:1 electrolyte), then c+ = c- as well, and we recover eq. (1).
Obviously, the faster the ion, the greater its contribution to the total current. If, and only if, the mobilities of anions and cations are exactly the same, the current will be transported in the same proportion (50%) by each species. To calculate the transference number one does not need the absolute mobility of an ion, but only the ratio between the two mobilities. The transference number is not constant with concentration, because the mobilities change with changing the concentration (due to ionic interactions – see ). As a rule, if the transference number is close to 0.5, it changes only slightly with concentration. Also, if the transference number for the cation is less than 0.5, then it decreases with increasing concentration , while if t- > 0.5, it increases with increasing concentration.
The mobilities u represent the migration rate of an univalent ion under a potential gradient of 1 V/m and can be calculated through a force balance: the electric force must balance the frictional force of movement in the fluid medium. The electrical force can be written as:
Fe = zeE(3)
where E is the electric field (dV/dx)
The frictional force is assumed to be given by Stokes law for spherical particles:
Ff = 6rv(4)
where is the solution viscosity (for dilute solutions it can be taken equal to the solvent's viscosity), r is the radius of the ion and v is its speed (in m/s). From the balance of the two forces (i.e., equality of eqs. (3) and (4)) one obtains:
zeE = 6rv, or (5)
Eq. (5) holds well for large ions, but large deviations are seen for small ions, as Stokes' law is not appropriate to describe the movement of very small particles. One can define also an effective hydrodynamic radius if the mobility is known:
(6)
As with eq. 5, the hydrodynamic radius is close to the real radius (including the solvent molecules in the solvation shell!) for large ions, but it is usually larger for small ions.
2.2. Measurement of transference numbers
In metallic conductors the current is carried by electrons only, and for such conductors one can write t- = 1 and t+ = 0. For electrolyte solutions it is often difficult to guess a priori what fraction of the current is carried by positive and negative ions. The simplest method for measuring transference numbers is due to Hittorf, and it is called actually the "Hittorf's method". In general, the number of equivalents removed from any compartment during the passage of current (or electrolysis) is proportional to the speed of the ion moving away from it:
(7)
The total number of equivalents lost from both compartments, which is proportional to u+ + u-, is seen to be equal to the number of equivalents deposited on each electrode; hence:
(8)
and
(9)
Figure 4. Hittorf's apparatus for determining transference numbers.
The two expressions provide a basis for experimental determination of transference number by the Hittorf method (1853). A schematic diagram of a Hittorf cell is shown in Figure 4. Stirring is performed only near the anode and cathode, in order to enhance the mass transfer, while the central part is not stirred. Consider such a cell which is filled with a e.g. HCl solution and let as assume that we pass 1 Faraday charge. The current is carried across the cell by the flow ions, and in view of the definition of the two transference numbers, the passage of 1 Faraday of charge means that t+ equivalents of H+ move towards the cathode and t- equivalents of Cl move towards the anode. The net flow across the cell's section is t+ + t- = 1 equivalents of ions, which corresponds to 1 Faraday of charge. Obviously, the number of equivalents in the middle of the cell is not changed by the passage of current. Let us consider now the changes that occur in the cathode region. The change in equivalent of H+ and Cl due to ion migration is given by the transfer across the cross section line. In addition to migration, there is a removal of 1 equivalent of H+ through the electrode reaction (H+ + e½H2). The net change in the cathode compartment is:
change in equivalents of H+ = electrode reaction + migration = –1 + t+ = t+ – 1 = –t-(10)
change in equivalents of Cl = electrode reaction + migration = 0 – t- = –t- (11)
The passage of 1 Faraday results thus in the removal of t- equivalents of HCl from the cathode compartment. In a similar manner, the change in the anode compartment is:
change in equivalents of H+ = electrode reaction + migration = 0 – t+ = = –t+(12)
change in equivalents of Cl = electrode reaction + migration = –1 + t- = t- – 1 = -t+(13)
Figure 5. Schematic of the Hittorf's cell showing the changes that occur in each compartment.
The net effect at the anode is the loss of t+ equivalents of HCl; the faradaic loss of material can be easily measured using a coulometer. Thus, the experimental procedure for measuring the transference numbers consists in filling the Hittorf cell with the desired solution (e.g., HCl) previously measuring accurately its concentration. Then electrolysis is performed and the charge passed is accurately measured. The anode and cathode compartments are drained and analyzed to give the concentration after passing the current. The concentration change is related to the number of equivalents lost during electrolysis. If the charge passed is not too large and if no mixing occurs in the central compartment, then it is found that the concentration in the central compartment is unchanged. The changes in concentration in the anodic and cathodic compartments will give the transference numbers for the anions and cations; Table 1 shows some measured values for various electrolytes at different concentrations.
Table 1. Transference numbers of cations at various concentrations in water solution.
c (mol/L)Electrolyte / 0 / 0.01 / 0.02 / 0.05 / 0.1 / 0.2
HCl / 0.8209 / 0.8251 / 0.8266 / 0.8292 / 0.8314 / 0.8337
CH3COONa / 0.5507 / 0.5537 / 0.5550 / 0.5573 / 0.5594 / 0.5610
CH3COOK / 0.6427 / 0.6498 / 0.6523 / 0.6569 / 0.6609 / --
KNO3 / 0.5072 / 0.5084 / 0.5087 / 0.5093 / 0.5103 / 0.5120
NH4Cl / 0.4909 / 0.4907 / 0.4906 / 0.4905 / 0.4907 / 0.4911
KCl / 0.4906 / 0.4902 / 0.4901 / 0.4899 / 0.4898 / 0.4894
KI / 0.4892 / 0.4884 / 0.4883 / 0.4882 / 0.4883 / 0.4887
KBr / 0.4849 / 0.4833 / 0.4832 / 0.4831 / 0.4833 / 0.4841
AgNO3 / 0.4643 / 0.4648 / 0.4652 / 0.4664 / 0.4682 / --
NaCl / 0.3963 / 0.3918 / 0.3902 / 0.3876 / 0.3854 / 0.3821
LiCl / 0.3364 / 0.3289 / 0.3261 / 0.3211 / 0.3168 / 0.3112
CaCl2 / 0.4380 / 0.4264 / 0.4220 / 0.4140 / 0.4060 / 0.3953
1/2Na2SO4 / 0.3860 / 0.3848 / 0.3836 / 0.3829 / 0.3828 / 0.3828
1/2K2SO4 / 0.4790 / 0.4829 / 0.4848 / 0.4870 / 0.4890 / 0.4910
1/3LaCl3 / 0.4770 / 0.4625 / 0.4576 / 0.4482 / 0.4375 / 0.4233
1/4K4Fe(CN)6 / -- / 0.515 / 0.555 / 0.604 / 0.647 / --
1/3K3Fe(CN)6 / -- / -- / -- / 0.475 / 0.491 / --
2.3. Electrical conductivity of ionic solutions
Ionic solutions, just like metallic conductors, obey the Ohm's law (provided that the applied voltage is not too large and no electrode reaction takes place), which relates the applied voltage to the current flowing through the electrolyte solution:
(14)
where V is the applied voltage. The resistance of any uniform conductor is proportional to its length, l, and inversely proportional to its cross section area, A, so that:
(15)
The proportionality factor, , is called the specific resistance (or resistivity); in electrochemistry the inverse of the specific resistance, = 1/, is more often used, and it is called specific conductance, its units being -1cm-1, or Scm-1. In the same way, one can define the conductance of the electrolyte solution, as the inverse of the resistance:
(16)
which is measured in -1 (also called Siemens, S, or mho, as the word "mho" is just the reverse of "ohm").
Practical measurement of conductance require a cell with known values of interelectrode distance (l) and electrode area (A), and therefore, since these values are constant for the same cell, their ratio is a constant called cell's constant. Thus, when measuring the conductance of a solution, we can write that:
= (cell constant)(17)
The cell constant is either known from the manufacturer, or it can be determined (as a calibration procedure) by measuring the conductance of a standard solution for which the conductance is known very accurately (e.g. a solution of KCl 0.02 M at 25 oC, having = 2.76810-3-1cm-1).
As the conductance of an electrolytic solution depends on the concentration (because the number of charged species carrying the current usually increases as the concentration increases), it is convenient to define a conductivity, called equivalent conductivity, which measures the conductivity relative to the same equivalent concentration, thus allowing to compare different salts:
(18)
where c is the molar concentration and z is the total (absolute) charge of positive and negative ions. The factor 1000 is the transformation factor for the concentration (which in chemistry is usually measured in mole per liter, while the equivalent conductivity is measured in Scm2mol-1). The molar conductivity has been more often used in the past years (in an effort to stop using the normal, or equivalent, concentration, which is often a source of confusion), defined as:
or (19)
(in the last relationship, one should remember that the concentration must be given in molecm-3 !).
We should also mention that all the quantities defined above for solutions can be used for molten salts too, which are also ionic conductors. Selected values for are shown in Table 2.
The large differences in conductivity between electronic and ionic conductors should be noted and is due to the different conduction mechanism: in electronic conductors charge is carried by electrons, which are small and consequently very fast charge carriers, while in ionic conductors, charge is carried by mobile ions, which are massive and have therefore much smaller mobilities.
The conductivity depends on the concentration of ions and their mobility: more ions means more charge, i.e., larger conductivity, while faster ones means more charge can move in a given time; we can relate to the ion mobility by the following relationship:
(20)
Table 2. Electric conductivities for various conductors and electrolyte solutions.
Electronic conductors / , -1cm-1Cu / 5.6105
Al / 3.5105
Pt / 1.0105
Pb / 4.5104
Ti / 1.8104
Hg / 1.0104
Graphite / 2.5102
Aqueous solutions / , -1cm-1
0.1 mole/L / 1 mole/L / 10 mole/L
NaCl / 0.011 / 0.086 / 0.247
KOH / 0.025 / 0.223 / 0.447
H2SO4 / 0.048 / 0.246 / 0.604
CH3COOH / 0.0004 / 0.0013 / 0.0005
LiClO4 solutions / , -1cm-1
Water / 0.073 (1 M)
Propylene carbonate / 0.005 (0.66 M)
Dimethylformamide / 0.022 (1.16 M)
As the conductivity is expected to depend linearly with concentration, it would appear that the molar conductivity does not depend on concentration. This is not true however; for weak electrolytes, which are not totally dissociated when dissolved, this is obvious, as the concentration of free ions depends on the total concentration in a non-linear manner. For strong electrolytes, like NaCl, it is less obvious, but similar effects occur due to interaction between ions at relatively large concentrations. Only for totally non-interacting ions would the molar conductivity be constant with concentration, but this is only an ideal situation; real electrolyte solutions approach this behavior only in the limit of extremely dilute solutions.
For weak electrolytes it is easy to obtain a dependence of the molar conductivity on the concentration. Let us consider for example a weak acid, HA, dissolved in water and write down the equilibrium:
HA + H2O H3O++ A
initial:c 0 0
equilibrium:(1 – )ccc
where is the dissociation degree (0 < 1). The equilibrium constant (assuming that the water concentration is very large and almost constant) is:
(20)
Figure 6. Dependence of the molar conductivity on the square root of concentration for a strong (HCl) and a weak (CH3COOH) electrolyte.
Figure 7. Plot showing the validity of Ostwald's law for CH3COOH.
Thus, for weak electrolytes the conductivity depends on the concentration because the ion concentration is only c, with depending on concentration according to eq. (20). At the limit of very low concentrations (c 0) the dissociation degree is one ( 1); we can define a limiting molar conductivity, 0, corresponding to c 0, and we can write:
c = 0 or (21)
(note that from eq. 21, the molar conductivity for weak electrolytes decreases as the concentration increases, but the total conductivity, , usually increases. In many cases has a maximum at some concentration, after which it starts to decrease, as an increase in the total concentration, c, will actually lead to a much larger decrease in c – see Figure 6)