Part 1: About solvents

When we think of solvents, we immediately think of water, and indeed water is a very good solvent. However, there are now many excellent solvents besides water, some of which are widely used in electrode reactions.
These solvents can be divided into 1) molecular solvents consisting mainly of molecules and 2) ionic solvents consisting of anions and cations.
Molecular solvents can be divided into two main categories: aqueous and non-aqueous solvents. Non-aqueous solvents can be further divided into organic solvents and other molecular solvents, such as hydrogen fluoride, liquid ammonia, sulfur dioxide, etc. Solvents other than water are collectively referred to as non-aqueous solvents. Most ionic solvents can be divided into high temperature molten salts, which are electrolytes, and ionic liquids, which have recently received much attention as room temperature liquids.

 

Fig. 1-1 Schematic diagram of solvent types

 

Water is widely used as an excellent electrode reaction solvent. On the other hand, when suitable solvents other than water are used for electrode reactions, various effects that differ from those of aqueous solutions can be obtained.
For example:
1) Substances insoluble in water can be dissolved.
2) Substances (electrode materials, electrode reactants, intermediates or products, etc.) that are unstable due to reaction with water in aqueous solution can be stabilized.
3) Electrochemical reactions can be measured over a wider potential range, pH range and temperature range than in aqueous solutions.
4) By changing the dissolution state and reactivity of the solute, the reaction mechanism can be made more compatible with the intended application, etc.

The use of non-aqueous solvents for electrochemical experiments is very effective when it is necessary to increase the solubility of the active substance of the electrode or to limit the participation of hydrogen ions in electrochemical reactions and when measurements at low temperature are required to extend the lifetime of the product.
Moreover, the electrochemical method is also the most basic and effective means to analyze the characteristics of the solvent itself and the behavior of the solute in it.

Before discussing solvents for electrode reactions, it is necessary to review the definitions of two physical quantities, the dielectric constant and the relative dielectric constant.
Dielectric constant ε: the constant determined by the response (dielectric polarization) produced by atoms (or molecules) in a substance when an electric field is applied from outside.
Relative permittivity εr: the ratio between the dielectric constant of a medium and the dielectric constant of the vacuum. It is dimensionless quantity.

The relative permittivity εr of the solvent is the most important property affecting the solvation of ions and the dissociation of electrolytes.

Part 2: Effect of relative permittivity of the solvent (1)

The solvation energy of ions is related to several elements of the ion-solvent interaction, where the electrostatic solvation energy ΔGel can be expressed by the following Born formula[1]。

 

 (2) 

Assuming that the constant of the association reaction between the solvated cation and solvated anion is Kass, logKass can be roughly expressed by the following Fuoss approximation equation (3).

 

 (3) 

where z+e and z-e are the charges of M+ and X- and α is the closest distance between M+ and X- ions .
From equation (3), it can be seen that logKass is almost linearly related to the inverse of αεr, and it can be predicted that if the relative permittivity εr is smaller, or the nearest distance α between ions is smaller, the easier it is to form ion pairs whose solution conductivity is reduced.


The relationship between log Kass and εr inverse for tetrabutylammonium picrate with larger values of α is seen below, and a better linear relationship can be seen between them.

 

 

 

Fig. 2-1 Relationship between the association constants of Bu4NPic (tetrabutylammonium picrate) and the relative permittivity of the solvent εr
solvents: ➀ C6H5NO2, ➁ Ac, ➂ Py, ➃ CH2ClCH2Cl, ➄ CH3CHCl2, ➅ C6H5Cl, ➆ m-C6H4Cl2
(Y. H. Inami et al., J. Phys. Chem. 83, 4745 (1961).
The dashed line is the relationship between the degree of conformance α and log(C Kass ) (molar concentration of C: Bu4NPic mol dm-3).

 

Assuming that the analytical concentrations of the tetrabutylammonium cation and picrate anion in solution are C M (M = mol dm-3), there is a relationship between the degree of association α between M+ and X- and log(C Kass ) as shown by the dashed line in Fig. 2-1. For example, for 0.01 M tetrabutylammonium picrate, it can be seen that more than 80% dissociation occurs when the εr of the solvent used is >30, while more than 90% exists as ion pairs when the εr of the solvent is <10.

Reference
[1] A. J. Bard, ed., Electroanalytical Chemistry, Vol. 3, C. K. Mann, Non-aqueous　solvents for electrochemical use, p. 57 (1969), Marcel Dekker.

Part 3: Efect of relative permittivity of the solvent (2)

The reaction in which a solid electrolyte is dissolved in a solvent and dissociates into free ions can be divided into two steps: the solid is dissolved in a solvent to form a solvated ion pair (enter↓), and the solvated ion pair is further dissociated to form a solvated cation and a solvated anion.

For the above two processes, the larger the relative permittivity of the solvent (or other factors that make the solvation of ions easier to occur), the easier it is to move to the right. The solvent used for the electrode reaction should be able to dissolve the supporting electrolyte, and must be able to dissociate into ions to a considerable extent, so a solvent with a relatively large relative permittivity (εr>20) is often used.

 

Table 1. Physical properties of organic solvent used for electrode reaction.

          

 

Some typical solvents used in electrochemistry and their physical properties are exemplified in Table 1.
It can be seen that the relative permittivity of solvents commonly used in electrochemistry, such as acetonitrile, DMF, PC, DMSO, methanol, etc., is much higher than 20.
The special mention should be made of the fact that the εr of water is very large, so water is a very good solvent for electrochemical measurements.
The solvents used for electrode reactions should be able to dissolve the supporting electrolyte and must be able to dissociate into ions to a considerable extent, so solvents with large relative dielectric constants (εr > 20) are often used.
However, solvents with low relative dielectric constants, such as THF, can also be used for electrode reaction measurements by using a suitable supporting electrolyte.

 

Table 2. Solubility of tetraalkylammonium salts and specific resistance of solutions (25℃).

 

Table 2 shows the solubility and resistivity of various tetraalkylammonium salts in four solvents, acetonitrile, DMF, DME, and THF, at a concentration of 0.6 or 1.0 M.[2][3]
From the solubilities and resistivities in the table, for acetonitrile, DMF, which have relative dielectric constants much greater than 20, the various tetraalkylammonium salts are well dissolved in the solvents, yielding electrolyte solutions with low resistivities.
However, for DME and THF, which are solvents with small relative dielectric constants, if the alkyl group of the ammonium salt is ethyl, the solubility of these electrolyte salts in DME and THF solvents is very small, and it is very difficult to dissolve them, and the resistivity of the solution cannot be measured. However, when the alkyl group of the ammonium salt is butyl, the solubility of the ammonium salt in DME and THF solvents is greatly increased, and the resistivity of the solution can also be measured.


Reference
[2] H. O. House, E. Feng and N. P. Peet, J. Org. Chem. 36, 2371 (1971).
[3] K. Rousseau, G. C. Farrington and D. Dolphin, ibid. 37, 3968 (1972).

Part 4: Solvent donating and accepting properties and solvent classification

The electron (pair) donor and acceptor properties of a solvent, together with the relative permittivity are factors that affect many reactions and equilibrium that occur in solution. In particular, when comparing the solute behavior of various solvents with high relative permittivity used in the electrode reaction, the effects of the differences in the donor and acceptor properties of the solvents are more pronounced than those in the relative permittivity.

As a measure of the strength of solvent donating and accepting, the donor number (Donor number, expressed in DN) and acceptor number (Acceptor number, expressed in AN) advocated by Gutmann are widely used[4][5].

 

 (6)

 

 

On the other hand, the receptor number is a measure of the strength of the receptivity, and the receptor number is measured. If there is such an interaction between triethylphosphine oxide dissolved in the sample solvent (receptor) and the solvent, in which case the NMR low magnetic field shift δ of phosphorus 31 is measured using n-hexane as a reference, the receptor number AN in n-hexane is regarded as 0, and the receptor number AN (Acceptor number) at the time of the interaction between antimony pentachloride and triethylphosphine oxide in ethylene chloride is expressed as 100.

 

 (7)

The acceptor number AN of the solvent can be calculated by Equation (7). A higher AN value indicates a stronger (electron) acceptability of the solvent.

Part 5: Factors involved in solvation of ions (1)

The solvation of ions involves a variety of factors that are interrelated in the ion solvent interaction.
These factors include:
1) Electrostatic interactions expressed by Brown's equation
2) Donor-acceptor interactions
3) Interaction with anion through hydrogen bonding provided by solvent
4) Interactions of hard and soft acid-base
5) Interaction of electrons from d10 cation giving back to solvent molecule
6) Interactions due to structure formation and structure destruction of solvent

The energy from electrostatic interactions accounts for a significant portion of the total solvation energy, but other factors tend to be more influential when comparing the solvation energies of commonly used solvents with high relative dielectric constants.

a) The solvation of cations is generally closely related to the donor DN (alkalinity) of the solvent

 

Fig. 5-1 The free energy of K+ ion transfer from acetonitrile to other solvents (ΔGt0(K+)AN → S) (○), and variation of hydrogen electrode potential (●) as a function of the solvent donor number DN [8][9].

 

Usually the solvation of cations is closely related to the donor (alkalinity) of the solvent, and solvation tends to be stronger in solvents with higher DN. For example, Fig. 2 shows the free energy (ΔGt0(K+)AN → S)(○) of K+ ion transfer from acetonitrile to other solvents as a function of solvent donor number DN, and the hydrogen electrode potentials (which have a linear relationship with the solvation energies of the H+ ions)(●) in various solvents as a function of solvent donor number DN.
It can be seen that there is a nearly linear relationship between the solvation energy of K+ ions and the hydrogen electrode potential (which is linearly related to the solvation energy of H+ ions) (●) and the solvent donor number DN.

b) Ion solvation is closely related to the acceptor property (acidity) of the solvent.

 

Fig. 5-2 The solvation energy of Cl- Cl- ions transferred from acetonitrile solvent to other non-aprotic solvents (ΔGt0(Cl-)→ S) linearly changes with the acceptor number AN[8][9 ]

 

The solvation effect of anions is closely related to the acceptability (i.e. acidity) of the solvent. The greater the acceptor number AN of the solvent, the stronger the solvation effect on the anions. In general, small anions such as fluoride, chloride, and hydroxide ions, as well as anions such as acetate, whose negative charge is concentrated on the smaller oxygen atom, have strong hydrogen bond acceptability, so they form in water or alcohols. It has a strong solvation effect. However, these ions have weak solvation in non-aprotic solvents that cannot provide hydrogen bonds and are in a rather high reactive state.

For some large anions, such as iodide ions and perchlorate ions, on the one hand, their solubility in water and alcohol solvents becomes weak because of their weak ability to accept hydrogen bonds, but on the other hand, due to the The stronger the polarity, the stronger the dispersion force will be with non-aprotic solvents of similar polarity. This is why the solvation energies of perchlorate ions in water and alcohols are not much different from those in non-aprotic solvents.


Reference:
[8] V．Gutmann，“The　Donor－Acceptor　Approach　to Molecular　Interactions”, (1978），Plenum Press．
[9] U．Mayer，Monatsh. Chem．108，1479 （1977）．

Part 6: Factors involved in solvation of ions (2)

(c) The structure of water molecules that can form hydrogen bonds between them, so their entropy value is low.
The structure of water molecules can form hydrogen bonds between them, so its entropy value is low. When hydrophilic ions (many inorganic ions are hydrophilic) enter the water, the strong interaction between the water molecules and the ions causes the overall structure of the water around the ions to be disrupted, increasing their entropy.
However, when hydrophobic ions such as tetraalkylammonium ions (NR4+) and tetraphenylborate ions (Ph4B-) enter water, the water molecules around the ions, which are distant from the ions, further bind and increase their hydrogen-bonded structure (structure formation), which decreases their entropy.
As a result, these hydrophobic macro ions become unstable in water, while they can be more stable in organic solvents without hydrogen bonding structures (see Table 5).

 

Table 5. Standard free energy, enthalpy and entropy of ion transfer from water to organic solvents (25℃).
Based on the exothermic thermodynamic assumptions. The relationship of ΔGt0(Ph4As+) = ΔGt0(Ph4B+), ΔHt0(Ph4As+) = ΔHt0(Ph4B+), ΔSt0(Ph4As+) = ΔSt0(Ph4B+) are established. The unit is kcal mol-1.

 

 

Fig. 6-1 Comparison of half-wave potentials of metal ions in N-methylpyrrolidone (NMP) and N-methylthiopyrrolidone (NMTP) (vs. E1/2of bisphenyl chromium (I))

 

Part 7: Acid-base equilibrium and pH range in organic solvents (1)

The reaction of dissociation of HA-type acid in solvent is shown in equation (8). It can be divided into two stages.

 

(8)

The first step is for HA to enter the solvent and become a solvated ion pair. In the second step, the solvated ion pair further dissociates into solvated H+ and solvated A- ions.
The equilibrium constant of the ionization reaction process in the first step is represented by KI, and the equilibrium constant of the dissociation process in the second step is represented by KD (Equation 9). The ionization equilibrium constant Ka obtained by the potentiometric method or conductivity method can be expressed by Equation 10.

 

(9)

 

(10)

During the ionization process, the solvent presses

 

The sequence acts as a donor and an acceptor, and the H-A bond breaks into an ion pair of solvated H+ , and solvated A- . This reaction process is more likely to occur if that H-A bond itself is more easily broken, or if the solvent is more strongly solvated with the H+ and A- ions.
In addition, from the previously mentioned Fuoss equation (3), it can be seen that the larger the relative permittivity of the solvent and the larger the closest distance between the H+ and A- ions, the easier the dissociation of the solvated ion pairs (H+, A- ) will be.

 

（3）

For acids of type HA, in addition to the dissociation reaction, such homoconjugation reactions can occur, and the values of the homoconjugation reaction constants, KfHA2- are shown in parentheses in Table 6.

 

Table 6 pKa and homogeneous conjugate reaction constants of acids (KfHA2-)

 

Water, with its relatively strong donor and acceptor properties and high relative dielectric constant, is a solvent that easily dissociates acids.
On the other hand, in acetonitrile solvents, where both donor and acceptor properties are weak, solvation of H+ is difficult, and solvation of A- ions is often difficult as well. As a result, the pKa of the acid is very large, and there is almost no acid that can be completely dissociated. However, in DMSO, which is a strong donor, H+ is strongly solvated, so the pKa is smaller than that in acetonitrile, and acids such as picric acid, which solvate anions relatively easily, can be completely dissociated.
Table 6 shows the pKa for the dissociation of BH+ ⇔ B + H+ for acids of the BH+ type, which is affected by the strength of solvation of BH+, B, and H+, with the effect of solvation of H+ being relatively large. Thus, the pKa in acetonitrile (AN) is much larger than in DMSO. pKa in DMSO is usually approximately the same as in aqueous solutions.


Reference:
[10] I. M. Kolthoff and P. J. Elving,Treatise on Analytical Chemistry, 2nd Ed. Part I, Vol. 2 (1979).