Local configuration types of Cl− ions around a centered Na+ ion.
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Barely three months into the new year and we are happy to announce a monumental milestone reached - 150 million downloads.
\n\nThis achievement solidifies IntechOpen’s place as a pioneer in Open Access publishing and the home to some of the most relevant scientific research available through Open Access.
\n\nWe are so proud to have worked with so many bright minds throughout the years who have helped us spread knowledge through the power of Open Access and we look forward to continuing to support some of the greatest thinkers of our day.
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The phenomena of transport properties in ionic liquids are of great important in the industrial science and technology, as well as in physics and chemistry. In connection with these, a number of experimental and theoretical studies have been published until the present time [1, 2, 3]. Ionic liquids are mainly classified into two categories; one is a group of molten salts and the other is a large number of electrolytic solutions, in particular, aqueous solutions of electrolytes.
In the case of molten salts, Sundheim discovered that the ratio of the partial conductivities of cation and anion were always equal to their inverse mass ratio, namely, σ+(DC)/σ−(DC) = m−/m+ [4].
Later on, this golden rule or a unified rule was theoretically explained by our group [5, 6, 7, 8, 9]. Detailed procedure will be shown in what follows.
Paralleling to above discovery, a number of scientific studies in molten salts have been developed from 1960s by several researchers [10, 11].
In order to study the structural and transport properties in molten salts, experimental investigations and molecular dynamics simulations have also been carried out from mid-70s of the last century [12, 13, 14, 15, 16].
Following to these, we have been engaged in the study of transport properties in molten salts [6, 7, 8, 9, 17]. We have carried out a theoretical study on the electrical conductivity of molten salts, starting from the Langevin equation and the velocity correlation functions for the constituent ions. Subsequently this treatment was successful to obtain the golden rule σ+/σ− = m−/m+ in a microscopic view point.
It remains, however, unclear how the adopted Langevin equation can be effectively solved within a short time region, under an appropriate memory function, because our former theory was only successful to get the partial conductivities.
We like to discuss more generally the correlation between the velocity correlation functions incorporated with the partial DC conductivities and some of useful memory functions which are closely related to the friction constants acting on cations and anions in molten salts.
Preceding the investigation for molten salts, on the other hand, there have been a number of studies for ionic solutions since the discovery of Faraday, in which a typical example is electrolytic solution. During such long-termed history of electrochemistry, it was well established by Kohlrausch that the experimental results on the ionic conductivities in dilute electrolytic solutions indicated the law of independent migration of ions,
The beginning of the modern aspect, in particular, on the thermodynamic and transport properties in electrolytic solutions might be originated from Debye-Hückel theory [18].
In order to explain the ionic conductivity in electrolytic solution, successful works following to Debye-Hückel theory have been reported by Onsager [19], Prigogine [20], and Fuoss and his co-worker [21]. In these theories, Λ0 is treated by the Stokes law and the concentration dependence is mainly explained by the electrophoretic effect and relaxation one. Therefore, these treatments are based on a kind of mixing of the microscopic and partially macroscopic view point.
Starting from the Liouville equation, statistical mechanics of irreversible process for the ionic conductivity in electrolytic solution have been developed by Davis and Résibois [22] and Friedman [23], although they did not derive any explicit expressions for the friction constant in terms of inter-particle interactions.
It has been required to investigate the static and dynamic properties of dissolved ions in aqueous solutions from the microscopic view point. Along this requirement, the technique of molecular dynamic simulation has been applied, using some qualified inter-particle potentials. Various theoretical attempts have been recently tried to establish the dynamical behaviors of dissolved ions in these solutions, which is able to discuss parallel with results obtained by MD simulation [24, 25, 26].
Chandra and Bagchi [27] have developed a new theoretical approach to study the ionic conduction in electrolytic solutions, based on the combination of the mode coupling theory and the generalized Langevin equation, and they were successful to obtain the Onsager equation. However, there still remains the task to obtain how to derive the theoretical formula for Λ0 in terms of inter-particle potentials and corresponding pair distribution functions.
We will apply the linear response theory for the electrolytic solution and to obtain Λ0 and the concentration dependence of the conductivity in terms of pair-wise potentials and pair distribution functions among ions and water molecules, which can compare parallel with dynamical properties of MD simulation [28].
In addition, we will also clarify how the electrophoretic and relaxation effects treated by many researchers are explained in a microscopic view point.
From these, we will see what is similar and what is different for the case of molten salts and that of electrolytic solutions.
Let us consider a molten salt composed of the density n+ = n− = n0 (= N/V0), of the constituent ion’s masses m+ and m−, and of the charge z+ = − z− = z = 1, where N being the total number of cation and/or anion in the volume V0.
A golden rule, σ+(DC)/σ−(DC) = m−/m+, can be obtainable from a generalized Drude theory, as a law of motion under an electric field [5].
As an extension, the generalized Langevin equation for an arbitrary cation or anion in the system under an external field
where ξ±(
After taking the ensemble average, equations of time evolution based on Eq. (1) in respect to the partial ionic conductivities are then written as follows:
and
And the equation of time evolution in relation to the diffusion constants of constituent ions is written as follows:
As was previously illustrated [9], the retarded friction function ξ±(
and
While, in the case of diffusion constants of constituent ions, that is,
It is emphasized that the memory functions γσ±(
Assuming that the ensemble average for the fluctuating force is zero and if we apply the following electric field,
where Re means the real part and ω is the angular frequency, then the averaged ion’s velocity induced by this external filed is equal to
where μ±(ω) is the mobility of cation or anion.
Putting (9) into the equation of motion (1) after taking the ensemble average, we have
where
Therefore, the current density is written as follows:
The partial conductivity is, then, equal to
and in the limit of ω = 0,
Therefore,
According to our previous studies [7, 8, 9], the following relation was recognized:
where
and
ϕ+−(
Therefore, we have a golden rule for the partial conductivities in a microscopic scale as follows:
In the following sections, as a numerical example, the MD simulation on molten NaCl at 1100 K is often utilized, for which the interionic potential functions suggested by Tosi and Fumi [30] for a study of solid alkali halides are applied. In order to make sure that the Tosi-Fumi potential for NaCl can be valid in the liquid state, we have estimated the partial pair distribution functions of molten NaCl liquid, ɡij(r) (i,j = Na+, Cl−) as shown in Figure 1, which agree with those of experimental results obtained by Edwards et al. [31].
Pair distribution functions,
Using these ɡij(r), we have also estimated the total neighboring numbers around arbitrary ions located at the distance r, which describe as nij = 4πʃ0rr2dr, as shown in Figure 2a–c.
(a)
The nearest neighbor number is defined as nij(r1), where r1 is the position of the first minimum of ɡij(r).
Then, the nearest neighbors around a Na+ are nearly equal to 5.0, since the distance r1 is taken at the minimum position of ɡNa-Cl(r) as shown in Figure 2a.
The application of Tosi-Fumi potentials in the MD simulations for viscosity and electrical conductivity is also valid to reproduce their experimental results [5].
Therefore, the following MD simulations for molten NaCl must be reliable to see their microscopic view.
On the other hand, according to our previous investigations [6, 7, 8, 9, 17, 29], the partial DC conductivities σ+(DC) and σ+(DC) are expressed as follows,
where
and
where
Considering the ensemble averages of (19) and (20), it is convenient to define the velocity correlation functions Zσ+(
and
where < > means the ensemble average.
Using (25) and (26), the partial DC conductivities (19) and (20) are written, respectively, as follows:
On the other hand, combining Eqs. (25) or (26) and (1), we have
and/or
Taking the Laplace transformation of ∂{Zσ+(
Here, we have used an evident condition Zσ+(
On the other hand, the right hand side of (29) is given by the following expressions:
Therefore we have,
In a similar way, we have,
If an appropriate memory function γ(
We have already shown the microscopic expressions for Zσ+(
The short-time expansion forms of Zσ+(t) and Zσ−(t) are actually shown in the following forms:
and
Thus, the partial conductivities for cation and anion in a molten salt are written as in the following Kubo-formulae:
and
Using (14), (16), (40) and (41), we have a very interesting relation written in the following form:
However, it is generally difficult to obtain Zσ±(t) from appropriate memory functions, by using the well-known method in statistical mechanics [33].
Under these circumstances, we explore a new method to solve Langevin Eqs. (29) and (30), in order to clarify a detailed correlation between γ(
Many years ago, Mori [34, 35] had generalized the Langevin equation starting from the Hamilton’s canonical equation of motion in a system of a monatomic liquid with the component’s mass as
where γn(
where the Mori coefficient δn is equal to γn(0).
The method of Copley and Lovesey [36] was able to express the short time expansion for the velocity correlation function Z(
Thus, they provided the following relations if several δn’s are known:
Therefore, the problem is ascribed to the derivation of δn’s. Because of a hard task in such repeating calculations, it is difficult to obtain a number of δn’s. However, several applications along these procedures have been carried out [37, 38].
Instead of the method of continued-fraction described in the above, we will provide a simple but new method to obtain the mutual relation between the combined velocity correlation function Zσ±(
Here, we provide a new and useful method to solve the Langevin equation based on recursion process [29]. Its detail is shown below.
Let us consider a Langevin equation for an evolution function being equivalent to (29) and (30), as follows:
The power expansion for q(
and the corresponding expansion formula for y(
Putting (48) and (49) into the right hand side of Eq. (47), we have
where B(n + 1, m + 1) and Γ(n + 1) mean the beta-function and the gamma-function, respectively, and
On the other hand, the left hand side of Eq. (47) is equal to the following formulae:
Compare both expressions (50) and (52), we can get the recursion formulae as follows,
Therefore, Eq. (49) is practically expressed in the following series:
and so on.
And vice versa, qn’s are expressed as follows:
and so on.
This method can be immediately applicable in the following way, comparing with Eqs. (38) and (39).
where
Considering Eqs. (56) and (57), the memory function γ(
where f(0) = 1.
The Laplace transformation of (59) in the long wavelength limit is then written as follows:
Therefore, we have immediately,
On the other hand, the memory function and its Laplace transformation are described as in the following forms, by using the fluctuation dissipation theorem [6, 7, 8, 9],
and
The most simplest expression for <
where <
Putting (64) into (62) and using (59), we have
This equation gives h(
Putting this relation into (62), we obtain again the relation (59), which indicates that the assumption, h(
Therefore, the general form for the memory function γ(
Various analytic forms for memory functions were proposed [7, 8, 12, 39, 40, 41, 42, 43] and all these functions are qualitatively useful to obtain the combined velocity correlation functions, although some of these theories cannot predict the result obtained by MD simulation.
For example, if we use an approximate form for the memory function as
As shown in our previous results [29], the calculated Zσ+(
However, the time expansion forms of Zσ±(
So far, we are successful to obtain the mutual relation between γ(
There are several works to obtain the auto-velocity correlation functions in monatomic liquids from appropriate memory functions γ(t) [39, 41, 42].
However, it is not known what sorts of model functions are suitable for the combined velocity correlation function Zσ±(
Previously we have already carried out the MD simulation for the combined velocity correlation functions Zσ±(
We try two types of power expansion forms in order to fit the combined correlation functions Zσ±(
In the case of the utilization of only even powers, it was quite difficult to get to the simulated Zσ±(
On the other hand, we can get an agreement if we use even and odd serial powers over
Therefore, the method utilizing the odd and even power series has a more rapid convergence for obtaining Zσ±(
The fitting parameters, which are equal to ym’s, are obtained by the non-linear least mean square method as so-called Levenberg-Marquart method [44].
The primary value in this non-linear least mean square method is inferred by utilization of simplex method.
It is inevitable that the coefficients of ym’s (m = 3, 4, …) are slightly variable because of the termination effect in the expansion form. But we have no difficulty to elucidate γ(
By using these obtained ym’s, it is immediately possible to obtain qn’s. And thereafter we can get a fitted curve indicating the curve of γ(
It is therefore emphasized that the utilization of odd terms within the short time region is necessary for the derivation of qn’s from the ym’s obtained by MD simulation.
For references, several analytic functional forms describing γ(
The γ(
However, an inevitable fact is that the theoretical memory function must be an expansion form of only even powers of the time, even though it is numerically close to the exponentially decaying function which includes the odd powers.
Is it possible to get a model function to fit the obtained curve of γ(
where
Using (70) and (71), we could reproduce the obtained curve of γ(
According to Figure 2a, the averaged nearest neighbor’s number around the Na+ ion is equal to 5.0. Any local coordination numbers around a Na+ are possible to be 4, 5, and 6 under the condition of density fluctuation in the liquid state.
It is possible to consider that stable short range configurations seem to be two types. One is the case of cubic structure-type configuration having with the coordination of 6 chlorine ions around the centered sodium ion as shown in Figure 3a, which is similar to the solid type configuration with a sort of lengthen fluctuation of the interionic distance.
(a) A stable short range configuration of 6 Cl− ions around a Na+ ion. (b) Another stable short range configuration of 4 Cl− ions around a Na+ ion.
The other is close to a tetrahedral coordination of chlorine ions around the centered sodium ion as shown in Figure 3b.
For simplicity, here we assume that the decaying or releasing of these two types of rather stable short range configurations is nearly the same, then the combined configurational decaying is given by i = 3 and b3.
On the other hand, there exist two types of rather unstable short range configurations as shown in Figure 4a and b, respectively, in which the surrounded Cl− ions around a Na+ ion are spatially asymmetric.
(a) A rather unstable short range configuration of 5 Cl− ions around a Na+ ion. (b) Another unstable short range configuration of 4 Cl− ions around a Na+ ion.
Totally, the local configuration types of Cl− ions around a centered Na+ ion are listed in Table 1.
Degree of stability | Configuration type | |||
---|---|---|---|---|
Coordination of 4 Cl− ions | Coordination of 5 Cl− ions | Coordination of 6 Cl− ions | Existing probability, ai | |
i = 1 | 0.2 | 0.2 | ||
i = 2 | 0.3 | 0.3 | ||
i = 3 | 0.15 | 0.35 | 0.5 |
Local configuration types of Cl− ions around a centered Na+ ion.
As shown in the previous section, the combined velocity correlation functions Zσ±(
In addition, it is emphasized that the γ(
In conclusion, we have newly obtained the mutual relation between the memory function γ(
Hereafter, we will consider the strong electrolytic solution composed of N+ cations, N− anions and X water molecules in a volume VM. For simplicity, we take that N+ = N− = N and ions charges are equal to z+ = − z− = z. Then the number densities of ions and water molecules are equal to n+ = n− = n = N/VM and
In the present system, a generalized Langevin equation for the cation (or anion) i under an external field
where γ±(
According to Berne and Rice [16], the internal field
where ɡ+−(
If we take
Inserting (74) into (72) and taking ensemble average under the assumption of <
Therefore,
where
The dc current density
On the other hand,
The Laplace transformation of the memory function in the long wavelength limit
In the next section, we will discuss velocity correlation functions.
Eq. (79) is also obtainable from the following simplified Langevin equation:
Its derivation can be easily seen in a standard book of statistical physics.
Starting from Eq. (80) with an infinitesimal external field
and
where the current densities
In order to obtain the partial conductivities based on Eqs. (81) and (82), it is necessary to study the velocity correlation functions, <
In the next section, we will discuss velocity correlation functions described in terms of inter-molecular (or ionic) potentials and pair distribution functions in order to obtain the
The short time expansion of velocity correlation function, <
In the present aqueous solution of electrolyte, the total Hamiltonian of the system is written as follows:
where
Since the water molecule is not spherical in its molecular configuration, it is difficult to define the position of
From the Poisson’s equation of motion,
and
Since the second derivative of the potential term V is independent for the product of momenta, all other terms other than i = j in (87) must vanish on averaging. And in a similar way, the meaningful terms of (88) for averaging must be also equal to the case i ≠ i’ = j. Therefore, taking the ensemble averages for (87) and (88), we have
where
and
In this equation, ɡ+w(
It is emphasized that there is no contribution from ϕ++(
Insertion of (89) into (84) gives us the following form:
In a similar way, the term <
Using this relation, the distinct velocity correlation function is written as follows:
Using (92) and (94), the combined velocity correlation function Zσ+(
where μ is equal to the reduced mass of m+ and m−. In deriving (95), we have assumed the initial conditions as follows:
These initial conditions are confirmed by our own molecular dynamic simulation, which will be shown in the later section. In a similar way, we have
where
ɡ−w(
It is impossible to obtain the partial conductivities by the insertion of (95) and (97) into (81) and (82), because we knew only the terms up to t2 in their explicit forms. However, these equations can be utilized for the derivation of
According to the fluctuation dissipation theorem applied for the present system with the condition of no external field or of infinitesimal external field, the Laplace transformation of the memory function γ±(
The fluctuation dissipation theorem tells us the following relation:
In the long wavelength limit, this relation is expressed by
Let us go back to the memory function γ±(t) and assume a combined exponential decay functions for it as follows, although this assumption is not exactly consistent with Eq. (84), but technically acceptable one as discussed in the case of molten salt [29],
In this equation, the pre-exponential factor γ00± is subject to the interactions between the central ion and surrounding water molecules. The decaying constants are related to the time dependence of its configuration change. The pre-exponential factor, γ01±, is equal to the magnitude of memory function at t = 0 in respect to the friction force acting on the central cation or anion caused by interactions between its central ion and neighboring ions. In other words, the first term on the right hand side of this equation means the case of dilute limit of electrolytic solution and the second one is equal to the effective friction caused by the addition of a moderate amount of electrolyte. Therefore, the first term is related to either <ϕ+w > or < ϕ−w >, while the second one is related to the term <ϕ+− > .
Using (94) and (96), γ00± and γ01± are expressed as follows:
In the dilute limit of n ≪ x, we have
And then we have
At the dilution limit of electrolyte where the contribution of γ1±(
where the auto-correlation function of random fluctuating force <
As seen in Eq. (79), the Laplace transformation of memory function in the long wavelength limit,
<
Insertion of (107) into (106) gives us
Therefore, we obtain
Compare (106) and (109) we have
By the analogy with this relation, we can infer the following relation:
Therefore, Eq. (102) is explicitly written as follows:
And the Laplace transformation of this equation in the long wavelength limit is equal to
Putting Eq. (113) into (79), we obtain the formulae of the partial conductivities, σ+ and σ−, which are expressed in terms of the pair distribution functions and pair potentials as follows [28],
and
If the concentration c is defined as the number of moles of electrolyte in the unit volume (actually taken as 1 cc), then the number density n is equal to cNA, where NA being the Avogadro’s number. Then, the partial conductivities, σ+ and σ−, are written as follows:
and
In these equations, μ+ and μ− are called as the mobility of cation and anion.
The partial molar conductance Λ+ and Λ− are defined as Λ± = σ±/c. Then the total conductance Λc is written as follows:
Under the condition of n(=cNA) ≪ x, they are approximated to as follows:
and
From Eqs. (119) and (120), we have a form of Λc = (Λ+ + Λ−) ≃ Λ0 + Λ1– kc1/2. Λ0 and k are written as follows:
and
As seen in these expressions, Λ0 means the conductance in the dilution limit of electrolyte and Λ1 is the correction term appeared by the so-called relaxation effect. The last term kc1/2 is composed of the so-called electrophoretic effect and the combined term of both effects.
In the case of a moderate concentration of electrolyte, in particular, of relatively weak electrolyte, we have to take account of the degree of association between the opposite ions into the expression for the partial conductivities.
A number of research works to obtain the model potentials in electrolytic solutions have been presented since the Debye-Hückel theory [18]. In particular, various qualified model potentials, which satisfy the experimental data such as the hydration free energy and the enthalpies in condensed and gas phases, have recently been proposed in order to carry out the molecular dynamic simulation. It is not our intension to compare or evaluate these potentials and therefore we like to refer only some of these for our interests [24, 25, 26, 27, 45]. It may be possible to estimate these potentials by using wave mechanical approach. In fact the ion-water molecule interactions were obtained by such an elaborating method [46, 47, 48].
The essential point for these model potentials in electrolytic solutions is that the dielectric character should be concerned. According to Sack [49], the water-molecules around the constituent ion are strongly oriented and the ion’s orientating ability to neighboring water-molecules decreases with increasing of the distance between the ion and those water-molecules. Oka [50] also estimated the change of effective dielectric constant as a function of distance between the ion and water-molecule.
We propose the following model function to satisfy these results as follows:
where ε0 (=78.35) is the dielectric constant of water. Other parameters are numerically equal to r0 = 5 A and κ = 3.44 A−1, respectively.
The insertion of this dielectric function ε(
On the analogy of the inter-ionic potentials in molten salts, ϕ+−(
where A+− is a constant in relation to the magnitude of repulsive force between cation i and anion j. B+− the softness parameter and (di+ + dj−) is the hard core contact between cation i and anion j. A+− and B+− are also given in the literature [27]. The difference between this expression and that of ionic crystal or of molten salt is only ascribed to whether the introduction of the dielectric function ε(
For simplicity, the pair potentials ϕ+ w(
where ϕrep+w(
It is well-known that the above expression is converted to the following form according to Boltzmann law,
On the other hand, a modified Lennard-Jones potential for water molecule, ϕww(
In this equation, the term 4C(dw/
The repulsive part of inter-ionic potential for ϕ++(
Now let us assume that the repulsive potential ϕrep+w(
Insertion of (129) into Eq. (127) gives us the following expression,
In a similar way, the inter-particle potential between anion and water molecule is expressed as follows:
The dipole moment of water molecule is known to be μ = 0.38 (in the unit of e times 1 Å = 1.6 × 10−29 C·m) and l ≒0.5 Å. Therefore, all parameters in (130) and (131) are known. According to Bopp et al. [51], the repulsive parts in (130) and (131) are converted to the exponential decaying functions similar to the repulsive part in (125) [46, 47].
Under these circumstances, it is possible to use either our empirical expressions (130) and (131), or to apply the inter-particle potentials derived by Bopp et al. [51]. It is also possible to estimate the repulsion terms in (130) and (131) by using wave mechanical approach. In fact, the ion-water molecule interactions were obtained by such an elaborating method [33, 52]. However, we will use the above empirical potentials for numerical application, for simplicity.
We will investigate the tag of water molecules by ion’s moving in the electrolytic solutions from the view point of equation of motion under an applied field
Under this situation, the second law of motion for the cation i can be written as follows:
At the time of steady state, τ, after applying the external field
In a similar way, we have
and
In a unit volume, the total summation of the ensemble averages of these momenta is written as follows:
where nw is the number density of water molecules.
The summation of last three terms on the right hand side of this equation is equal to zero, because there is no external force at
Therefore, we have
This equation indicates that the partial conductivity ratio <
Some of water molecules may be simultaneously pulled by the dissolved ions under an external field
Here, xr is equal to the number density of un-pulled water molecules.
Since, the movements of remainder water molecules under the external field must be isotropic, we have xr < mw
Insertion of this equation into (66) gives us the following relation:
Hereafter, we omit the suffix of ion i or k.
Therefore, we have
We cannot apply the above treatment for H+ and OH− ions, because their conduction mechanisms differ from that of all other dissolved ions. Their mechanisms are known as the Grotthus-type conduction which is a kind of hopping conduction of electrons or holes [3].
It is, however, straightforward to obtain the following relation for all dissolved ions in their dilute limits except for H+ and OH− ones,
This relation seems to be valid for all aqueous solutions of equivalent electrolytes in the dilution limit.
Using Eqs. (114) and (115), Eq. (142) for the dilution limit of electrolytic solution is expressed as follows:
This equation may correspond to the inverse mass ratio for the partial conductivities of molten salt [6].
According to the theoretical results we have discussed so far, the pair distribution functions appear in the essential equations [28]. Therefore, how to obtain the pair distribution functions is one of the matters of vital importance.
There are several standard theoretical methods to obtain the pair distribution functions in molecular liquids from the knowledge of inter-particle potentials [33]. In the calculation of site-site distribution function for such a molecular liquid, the reference interaction-site model (RISM) approximation proposed by Chandler and Anderson [52] seems to be useful. Until the present time, the extension of RISM approximation, in order to obtain the potentials of mean force and also the site-site pair distribution functions ɡμν(r)‘s in electrolytic solutions, has been carried out by several authors [53, 54, 55]. These attempts cover the insufficient experimental knowledge for pair distribution functions ɡ+−(
However, we will use the ɡμν(
The interactions between alkali metal cation and halide anion, TIP4P- alkali metal anion, and TIP4P – halide anion are expressed as [58]:
In (144) and (145), i and j stand for the constituent atoms;
Solute | Water (TIP4P) | Cation | Anion |
---|---|---|---|
Li+ Cl− | 10,000 | 112 | 112 |
Na+ Cl− | 10,000 | 112 | 112 |
K+ Cl− | 10,000 | 112 | 112 |
The numbers of ions in MD cell.
The main part of MD is performed using SIGRESS ME package (Fujitsu) at the supercomputing facilities in Kyushu University.
The obtained figures of ɡij(
Pair distribution function of water molecules around a Li + ion,
Pair distribution function of water molecules around a Na + ion,
Pair distribution function of water molecules around a K+ ion,
Pair distribution function of water molecules around a Cl− ion,
Using Eq. (143), that is, σ+/σ− = (m− + x−mw)/(m+ + x+mw), and taking an assumption that the pulling water molecules for Na+ ion is equal to 6.0 although its plausible justification seems to be difficult, then we obtain the pulling water molecules for other ions as shown in Table 3, in which the hydration numbers seen in a text book [62] and our results obtained by MD simulation, for reference.
Ions | Pulling water molecules, x+ or x− | Hydration numbers in the text book [36] | Hydration numbers obtained from MD simulations |
---|---|---|---|
Li+ | 7.6 | 4.3 ± 0.6 | 4.1 |
Na+ | 6.0* | 5.6 ± 1.7 | 5.7 |
K+ | 2.8 | 5.5 ± 1.3 | 6.4 |
Cl− | 2.8 | 6.0 ± 0.7 | 6.5 |
Numbers of pulling water molecules, x+ or x− and hydration numbers.
Assumption that the pulling number x+ of Na+ ion is equal to be 6.0 and also that the pulling numbers of water molecules for Cl− are not changed even for that the pairing positive ions are different.
Using these pulling numbers for the constituent ions, we can estimate the term, (m− + x−mw)/(m+ + x+mw) as shown in Table 4. As seen in this table, agreements for both terms are satisfactory, which is a kind of proof for the assumption x+ is equal to 6.0.
Electrolyte | σ+/σ− | (m− + x−mw)/(m++ x+mw) |
---|---|---|
Li+ Cl− | 0.595 | 0.598 |
Na+ Cl− | 0.659 | 0.655 |
K+ Cl− | 0.963 | 0.960 |
The ratio of ionic conductivity and the calculation results by using Table 3.
It is emphasized that the pulling number of water molecules by moving ion has no relation to the hydration number of water molecules as seen in Table 3. The hydration of water molecules around electrolytic ions is originated essentially by the thermodynamic stability which is related not only to the interaction energies among ions and water molecules but also to the configuration entropy terms. This is because that the pulling number is not always related to the hydration one.
The present theory seems essentially comparable to the treatments developed by Onsager [19], Fuoss et al. [21], Prigogine [20], Friedman [23], Chandra and Bagchi [27], and Matsunaga and Tamaki [28].
Friedman [23] used a technique of diagram expansion starting from Kubo-Green formula for the conductivity of electrolytic solution and the obtained expression was also written in the form of Λc = (Λ+ + Λ−) = Λ0 + Λ1 – kc1/2. However, his theory is very much sophisticated and too mathematical to understand with a physical insight.
Recent theoretical work carried out by Chandra and Bagchi [27] is basically started from a Kubo-Green type theory, that is, the partial conductivities are derived from velocity correlation functions. Their treatment seems to be a modernized and beautiful and therefore it is very much appreciable. However, the friction force of their theory involves various terms which make it difficult to calculate practically the partial conductivities. In fact, there still remains the task to represent a microscopic formula for Λ0.
The present treatment is easily to understand in view of physical insight and is successful for deriving the formula of Λ0.
The short-time expansion forms for <
The rapid growth of global population as well as industrialization has led to a concomitant increase in environmental pollution. This has very negative effects on natural elements that are vital for life on earth such as air and water. It becomes very crucial therefore to find sustainable ways to mitigate pollution in order to provide a clean and safe environment for humans. Photocatalysis has attracted worldwide interest due to its potential to use solar energy not only to solve environmental problems but also provide a renewable and sustainable energy source. An efficient photocatalyst converts solar energy into chemical energy which can be used for environmental and energy applications such as water treatment, air purification, self-cleaning surfaces, hydrogen production by water cleavage and CO2 conversion to hydrocarbon fuels.
\nResearch in the development of efficient photocatalytic materials has seen significant progress in the last 2 decades with a large number of research papers published every year. Improvements in the performance of photocatalytic materials have been largely correlated with advances in nanotechnology. Of many materials that have been studied for photocatalysis, titanium dioxide (TiO2; titania) has been extensively researched because it possesses may merits such as high photocatalytic activity, excellent physical and chemical stability, low cost, non-corrosive, nontoxicity and high availability [1, 2, 3, 4]. The photocatalytic activity of titania depends on its phase. It exists in three crystalline phases; the anatase, rutile and brookite. The anatase phase is metastable and has a higher photocatalytic activity, while the rutile phase is more chemically stable but less active. Some titania with a mixture of both anatase and rutile phases exhibit higher activities compared to pure anatase and rutile phases [5, 6, 7]. When titania is irradiated with light of sufficient energy, electrons from the valence band are promoted to the conduction band, leaving an electron deficiency or hole, h+, in the valence band and an excess of negative charge in the conduction band. The free electrons in the conduction band are good reducing agents while the resultant holes in the valence band are strong oxidizing agents and can both participate in redox reactions.
\nTitania however suffers from a number of drawbacks that limit its practical applications in photocatalysis. Firstly, the photogenerated electrons and holes coexist in the titania particle and the probability of their recombination is high. This leads to low rates of the desired chemical transformations with respect to the absorbed light energy [8, 9]. The relatively large band gap energy (~ 3.2 eV) requires ultraviolet light for photoactivation, resulting in a very low efficiency in utilizing solar light. UV light accounts for only about 5% of the solar spectrum compared to visible light (45%) [1, 10]. In addition to these, because titania is non-porous and has a polar surface, it exhibits low absorption ability for non-polar organic pollutants [10, 11, 12, 13]. There is also the challenge to recover nano-sized titania particles from treated water in regards to both economic and safety concern [14]. The TiO2 nanoparticles also suffer from aggregation and agglomeration which affect the photoactivity as well as light absorption [15, 16, 17, 18]. Several strategies have been employed in the open literature to overcome these drawbacks. These strategies aim at extending the wavelength of photoactivation of TiO2 into the visible region of the spectrum thereby increasing the utilization of solar energy; preventing the electron/hole pair recombination and thus allowing more charge carriers to successfully diffuse to the surface; increasing the absorption affinity of TiO2 towards organic pollutants as well as preventing the aggregation and agglomeration of the nano-titania particles while easing their recovery from treated water. Several reviews have been published in recent years on the development of strategies to eliminate the limitations of titania photocatalysis [1, 19, 20, 21, 22, 23, 24, 25]. Most of these however focus on pollutant removal from wastewater, water splitting for hydrogen production, CO2 conversion and reaction mechanisms [1, 21, 25, 26, 27, 28, 29, 30, 31]. In this chapter, we review some of the latest publications mainly covering the last 5 years, on strategies that have been researched to overcome the limitations of TiO2 for general photocatalytic applications and the level of success that these strategies have been able to achieve. Based on the current level of research in this field, we also present some perspectives on the future of modified TiO2 photocatalysis.
\nA large number of research works have been published on TiO2 modification to enhance its photocatalytic properties. These modifications have been done in many different ways which include metal and non-metal doping, dye sensitization, surface modification, fabrication of composites with other materials and immobilization and stabilization on support structures. The properties of modified TiO2 are always intrinsically different from the pure TiO2 with regards to light absorption, charge separation, adsorption of organic pollutants, stabilization of the TiO2 particles and ease of separation of TiO2 particles.
\nMetal doping has been extensively used to advance efforts at developing modified TiO2 photocatalysts to operate efficiently under visible light. The photoactivity of metal-doped TiO2 photocatalysts depends to a large extent on the nature of the dopant ion and its nature, its level, the method used in the doping, the type of TiO2 used as well as the reaction for which the catalyst is used and the reaction conditions [32]. The mechanism of the lowering of the band gap energy of TiO2 with metal doping is shown in Figure 1. It is believed that doping TiO2 with metals results in an overlap of the Ti 3d orbitals with the d levels of the metals causing a shift in the absorption spectrum to longer wavelengths which in turn favours the use of visible light to photoactivate the TiO2.
\nBand-gap lowering mechanism of metal-doped TiO2.
Doping of TiO2 nanoparticles with Li, Na, Mg, Fe and Co by high energy ball milling with the metal nitrates was found to widen the TiO2 visible light response range. In the Na-doped sample, Ti existed as both Ti4+ and Ti3+ and the conversion between Ti4+ and Ti3+ was found to prevent the recombination of electrons and (e−) and holes (h+). The metal ion doping promoted crystal phase transformations that generated electrons (e−) and holes (h+) [33]. Mesoporous TiO2 prepared by sol gel technique and doped with different levels of Pt (1–5 wt% nominal loading) resulted in a high surface area TiO2 with an enhanced catalytic performance in photocatalytic water splitting for the Pt-doped samples. The 2.5 wt%Pt-TiO2 had showed the optimum catalytic performance and a reduction in the TiO2 band gap energy from 3.00 to 2.34 eV with an enhanced electron storage capacity, leading to a minimization of the electron-hole recombination rate [34]. Noble metal nanoparticles such as Ag [35], Pt [34], Pd [36], Rh [37] and Au [38] have also been used to modify TiO2 for photocatalysis and have been reported to efficiently hinder electron-hole recombination due to the resulting Schottky barrier at the metal-TiO2 interface. The noble metal nanoparticles act as a mediator in storing and transporting photogenerated electrons from the surface of TiO2 to an acceptor. The photocatalytic activity increases as the charge carriers recombination rate is decreased.
\nIn a recent review by Low et al. [21] the deposition of Au onto TiO2 surface is reported to result in electron transfer from photo-excited Au particles (> 420 nm) to the conduction band of TiO2, which showed a decrease in their absorption band (∼550 nm) and the band was recovered by the addition of electron donors such as Fe2+ and alcohols. Zhang et al. [39] reported that the visible light activity of coupled Au/TiO2 can be ascribed to the electric field enhancement near the metal nanoparticles. Moreover, numerous researchers coupled Au and Ag nanoparticles onto TiO2 surface to use their properties of localized surface plasmonic resonance (LSPR) in photocatalysis [40]. Wang et al. [41] and Hu et al. [42] reported an improved photocatalytic performance due to the Pt nanoparticle which increased the electron transfer rate to the oxidant. It was observed that photocatalytic sacrificial hydrogen generation was influenced by several parameters such as platinum loading (wt%) on TiO2, solution pH, and light (UV, visible and solar) intensities [43]. Moreover, complete discoloration and dye mineralization were achieved using Pt/TiO2 as catalyst; the results were attributed to the higher Pt content of the photocatalyst prepared with the highest deposition time. For Pt-TiO2 catalysts the best discoloration and dye mineralization were obtained over the catalyst prepared by photochemical deposition method and using 120 min of deposition time in the synthesis. These results may be due to the higher Pt content of the photocatalyst prepared with the highest deposition time.
\nHaung et al. [44] prepared Pt/TiO2 nanoparticles from TiO2 prepared at various hydrolysis pH values and found that the phase of TiO2 obtained depended largely on the hydrolysis pH. The anatase/rutile intersection of a Pt/TiO2 sample had a lower recombination rate compared to the anatase phase of Pt/TiO2 due to the longer recombination pathway. Though, the Pt/TiO2 anatase phase showed better degradation efficiency than the Pt/TiO2 anatase/rutile intersection. The decrease in the anatase composition of TiO2, and the decrease in the composition of TiO2 resulted in the degradation rate decrease, suggesting that anatase composition in the Pt/TiO2 system played a crucial role of increasing the photocatalytic degradation of Acid Red 1 dye.
\nLiu et al. [45] prepared the palladium doped TiO2 (Pd-TiO2) photocatalyst using chemical reduction method and tested it the photocatalytic degradation of organic pollutant. It was found that the TiO2 grain size was reduced while the specific surface area increased and the absorption of ultraviolet light also enhanced after using chemical reduction method, however, all these changes had no effect on degradation of organic pollutant. But the degradation was significantly improved due to the deposition of Pd nanoparticles; the Pd/TiO2 organic pollutant degradation was 7.3 times higher compared to TiO2 (P25).
\nRepouse et al. [46] prepared a series of noble metal promoted TiO2 (P25) by wet impregnation and found that the dispersion of the small metal crystallites on TiO2 did not affect the optical band gap of TiO2. The Pt-promoted catalyst exhibited the highest photocatalytic efficiency in the degradation of bisphenol A under solar irradiation. They also found the presence of humic acid to considerably improve the reaction rate of Rh/TiO2 but had a clearly adverse effect with P25 TiO2 photocatalyst. Fluorescence data revealed that humic acid is capable of photosensitizing the Rh/TiO2 catalyst.
\nIndium-doped TiO2 have recently been used for photocatalytic reduction of CO2 [47]. Indium doping resulted in an increase in surface area because of suppression of TiO2 particle growth during the TiO2 synthesis. The light absorption ability of the In-TiO2 was enhanced due to the introduction of the impurity level below the conduction band level of the TiO2. The photocatalytic CO2 reduction activity of the In-TiO2 was about 8 time that of pure TiO2 as a consequence of the high surface area and extended light absorption range.
\nThe doping of TiO2 with transition metals such as Cr [48], Co [48], Fe [48, 49, 50], Ni [48, 51], Mn [48, 52], V [53], Cu [54], Ni [51] and Zn [55], has been studied by different research groups. Numerous studies reported that doping of TiO2 with transition metals improve the photocatalytic activity, attributable to a change in the electronic structure resulting in the absorption region being shifted from UV to visible light. The shift results from charge-transfer transition between the d electrons of the transition metals and the conduct or valence band of TiO2 nanoparticles. Inturi et al. [48] compared the doping of TiO2 nanoparticles with Cr, Fe, V, Mn, Mo, Ce, Co, Cu, Ni, Y and Zr and it was found that Cr, Fe and V showed improved conversions in the visible region while, the incorporation of the other transition metals (Mn, Mo, Ce, Co, Cu, Ni, Y and Zr) exhibited an inhibition effect on the photocatalytic activity. The Cr-doped TiO2 demonstrated a superior catalytic performance and the rate constant was found to be approximately 8–19 times higher than the rest of the metal doped catalysts. It was reported that the reduction peaks in Cr-doped TiO2 shifted to much lower temperatures, due to the increase in the reduction potential of titania and chromium. Therefore, the higher photocatalytic efficiency of Cr/TiO2 in the visible light can be attributed to strong interaction (formation of Cr-O-Ti bonds). Fe-doped TiO2 nanoparticles were used in the visible light degradation of para-nitrophenol and it was found that the Fe-dopant concentration was crucially important in determining the activity of the catalyst. The maximum degradation rate of para-nitrophenol observed was 92% in 5 h when the Fe(3+) molar concentration was 0.05 mol%, without addition of any oxidizing reagents. The excellent photocatalytic activity was as a result of an increase in the threshold wavelength response as well as maximum separation of photogenerated charge carriers [49]. On the other hand, Fe-doped TiO2 evaluated for solar photocatalytic activity for the degradation of humic acid showed a retardation effect for the doped catalysts compared to the bare TiO2 specimens, which could be attributed to surface complexation reactions rather than the reactions taking place in aqueous medium. The faster removal rates attained by using bare TiO2 could be regarded as substrate specific rather than being related to the inefficient visible light activated catalytic performance [50]. Ola et al. [56] reported that the properties of V doped TiO2 were tuned towards visible light because of the substitution of the Ti4+ by V4+ or V5+ ions since the V4+ is centred at 770 nm while the absorption band of V5+ is lower than 570 nm. Moradi et al. [57] obtained high photocatalytic activity of Fe doped TiO2 and studied the effects of Fe3+ doping content on the band gap and size of the nanoparticles. It was found that the increase in the doping content decreased the band gap energy and particle size from 3.3 eV and 13 nm for bare TiO2 to 2.9 eV and 5 nm for Fe10-TiO2, respectively.
\nThe rare earth metals doped TiO2 catalyst also have good electron trapping properties which can result in a stronger absorption edge shift towards longer wavelength, obtaining narrow band gap. Bethanabotla et al. [58] carried out a comprehensive study on the rare earth doping into a TiO2 and found that the rare earth dopants improved the aqueous-phase photodegradation of phenol at low loadings under simulated solar irradiation, with improvements varying by catalyst composition. Differences in defect chemistry on key kinetic steps were given as the explanation for the enhanced performance of the rare earth doped samples compared to pure titania. Reszczyńska et al. [59] prepared a series of Y3+, Pr3+, Er3+ and Eu3+ modified TiO2 nanoparticles photocatalysts and results demonstrate that the incorporation of RE3+ ions into TiO2 nanoparticles resulted in blue shift of absorption edges of TiO2 nanoparticles and could be ascribed to movement of conduction band edge above the first excited state of RE3+. Moreover, incorporated RE3+ ions at the first excited state interact with the electrons of the conduction band of TiO2, resulting in a higher energy transfer from the TiO2 to RE3+ ions. But observed blue shift could be also attributed to decrease in crystallite size of RE3+–TiO2 in comparison to TiO2. The Y3+, Pr3+, Er3+ and Eu3+ modified TiO2 nanoparticles exhibited higher activity under visible light irradiation compared to pure P25 TiO2 and can be excited under visible light in the range from 420 to 450 nm. In a similar work on rare earths (Er, Yb, Ho, Tb, Gd and Pr) titania nanotubes (RE-NTs), [60] the RE3+ species were found to be located at the crystal boundaries rather than inside the TiO2 unit cell and an observed excitation into the TiO2 absorption band with resulting RE3+ emission confirmed energy migration between the TiO2 matrix and RE3+. The presence of the rare earth component was found to reduce recombination of the electrons and holes successfully by catching them and also by promoting their rapid development along the surface of TiO2 nanoparticles. Lanthanide ions doping did not impact the energy gap of TiO2 nanoparticles, however this enhanced the light absorption of catalyst. The surface range of TiO2 nanoparticles generally increases by La3+ particle doping by diminishing the crystallite size and accordingly, the doped TiO2 nanoparticle displayed higher adsorption capacity. Based on theoretical calculations, it was proposed that during the electrochemical process, new Ho-f states and surface vacancies were formed and may reduce the photon excitation energy from the valence to the conduction band under visible light irradiation. The photocatalytic activity under visible light irradiation was attributed not to ·OH but to other forms of reactive oxygen species (O2·−, HO2, H2O2).
\nTiO2 nanoparticles have been comprehensively doped at the O sites with non-metals such as C [61], B [62], I [63], F [64], S [65], and N [66]. Non-metal dopants are reported to be more appropriate for the extension of the photocatalytic activity of TiO2 into visible region compared to metal dopant [67, 68]. This can be ascribed to the impurity states which are near the valence band edge, however, they do not act as charge carriers, and their role as recombination centres might be minimized [53]. As shown in Figure 2, the mixing of the p states of the doped non-metal with the O2p states shifts the valence band edge upward and narrows the band-gap energy of the doped TiO2 photocatalyst. The nitrogen and carbon doped TiO2 nanoparticles has been reported to exhibit greater photocatalytic activity under visible light irradiation compared to other non-metal dopants.
\nBand-gap energy narrowing mechanism for non-metal-doped TiO2.
N-doped TiO2 (N-TiO2) appears to be the most efficient and extensively investigated photocatalyst for non-metal doping. Zeng et al. [69] reported the preparation of a highly active modified N-TiO2 nanoparticle via a novel modular calcination method. The excellent photocatalytic performance of the photocatalyst was ascribed to excellent crystallinity, strong light harvesting and fast separation of photogenerated carriers. Moreover, the enhancement of charge separation was attributed to the formation of paramagnetic [O-Ti4+-N2−-Ti4+-VO] cluster. The surface oxygen vacancy induced by vacuum treatment trapped electron and promoted to generate super oxygen anion radical which was a necessary active species in photocatalytic process. Phongamwong et al. [70] investigated the photocatalytic activity of CO2 reduction under visible light over modified N-TiO2 photocatalyst and they have found that the band gap of N-TiO2 photocatalyst slightly decreases with increasing N content. In addition, the sub-band energies related to the impurity energy level were observed in the N-TiO2 photocatalyst because of the interstitial N species and the sub-band gap energies were found to have decreased from 2.18 eV with 10 wt% N-TiO2 photocatalyst. In contrast, the replacement of O by N is difficult because of the radius of N (17.1 nm) being higher compared to O (14 nm) and the electroneutrality can be maintained by oxygen vacancies, that are provided by replacement of three oxygen vacancies by two nitrogen atom [71]. N-TiO2 photocatalyst reduces the oxygen energy vacancies from 4.2 to 0.6 eV, suggesting that N favors the formation of oxygen vacancies [72].
\nIn contrast, O atoms (14 nm) could be substituted easily by F atoms (13.3 nm) because of their similar ionic radius [73]. Yu et al. [64] reported that the F-doped TiO2 (F-TiO2) is able to absorb visible light due to the high-density states that were evaluated to be below the maxima valence band, although there was no shift in the band edge of TiO2. Samsudin et al. found a synergistic effect between fluorine and hydrogen in hydrogenated F-doped TiO2 which enabled light absorption in UV, visible and infrared light illumination with enhanced electrons and holes separation. Surface vacancies and Ti3+ centres of the hydrogenated F-doped catalyst coupled with enhanced surface hydrophilicity facilitated the production of surface-bound and free hydroxyl radicals. Species present on the surface of the catalyst triggered the formation of new Ti3+ occupied states under the conduction band of the hydrogenated F-doped TiO2, thus narrowing the band gap energy [73]. Enhanced photocatalytic performance of N-doped TiO2 over pure TiO2 has also been ascribed to efficient separation of electron-hole pairs as well as an increased creation of surface radicals such as hydroxyl The band gap can also be narrowed by doping TiO2 with S, since replacement of S into TiO2 can be performed easily due to larger radius of S atoms (18 nm) compared to O atoms (14 nm). S incorporation in TiO2 has been reported to change the lattice spacing of the TiO2 with a reduction in the band gap width from 3.2 to 1.7 eV allowing for higher photocatalytic activity [74]. N, S and C co-doped TiO2 samples photocatalytic reduction of Cr(IV) showed that the co-doping and calcination played an important role in the microstructure and photocatalytic activity of the catalysts. The co-doped samples calcined at 500°C showed the highest activities ascribed to the synergistic effect in enhancing crystallization of anatase and (N, S and C) co-doping. The carbon doped TiO2 (C-TiO2) is reported to be more active than N-TiO2, therefore, C-TiO2 has received special attention [75]. Noorimotlagh et al. [76] investigated the photocatalytic removal of nonylphenol (NP) compound using visible light active C-TiO2 with anatase/rutile. It was found that the doping of C into TiO2 lattice may enhance the visible light utilization and affect the structural properties of the as-synthesized photocatalysts. Moreover, it was reported that after C doping and changing the calcination temperature, the band gap was narrowed from 3.17 to 2.72 eV and from 2.72 to 2.66 eV, respectively. Ji et al. [61] reported the preparation of C-TiO2 with a diameter of around 200 nm and the tube wall was composed of anatase TiO2, amorphous carbon, crystalline carbon and carbon element doping into the lattice of TiO2. The C-TiO2 nanotubes exhibited much better performance in photocatalytic activity than bare TiO2 under UV and visible light. The obtained results were ascribed to the C doping, which narrowed the band gap energy of TiO2, extended the visible light adsorption toward longer wavelength and hindered charge recombination.
\nAlthough single metal doped and non-metal doped TiO2 have exhibited excellent performance in decreasing the electrons and holes recombination, but they suffer from thermal stability and losing a number of dopants during catalyst preparation process [77]. Therefore, co-doping of two kinds of atoms into TiO2 has recently attracted much interest [78]. The electronic structure of TiO2 can be altered by co-doping on TiO2 by formation of new doping levels inside its band gap. Abdullah et al. [77] reported that the doping levels situated within the band gap of TiO2 can either accept photogenerated electrons from TiO2 valence band or absorb photons with longer wavelengths. Therefore, suggesting that the TiO2 absorption range can be expanded.
\nZang et al. [79] evaluated the photocatalytic degradation of atrazine under UV and visible light irradiation by N,F-codoped TiO2 nanowires and nanoparticles in aqueous phase. It was found that photocatalytic degradation of atrazine was higher in the presence of N,F-codoped TiO2 nanowires than that of N,F-codoped TiO2 nanoparticles. The higher photocatalytic performance in the presence of N,F-codoped TiO2 nanowires was attributed to the higher charge carrier mobility and lower carrier recombination rate. Moreover, the speed of electron diffusion across nanoparticle intersections is several orders of magnitude smaller compared to that of nanowire because of frequent electron trapping at the intersections of nanoparticles and increasing the recombination of separated charges before they reach the TiO2 nanoparticles surface. Park et al. [80] showed the best performance for novel Cu/N-doped TiO2 photoelectrodes for dye-sensitized solar cells. It was found that the Cu/N-doped TiO2 nanoparticles provided higher surface area, active charge transfer and decreased charge recombination. Moreover, the addition of suitable content of Cu- to N-doped TiO2 electrode effectively inhibited the growth of TiO2 nanoparticles and improved the optical response of the photoelectrode under visible light irradiation. Chatzitakis et al. [81] studied the photoelectrochemical properties of C, N, F codoped TiO2 nanotubes. It was found that increasing surface area is not followed by increase in the photoconversion efficiency, but rather that an optimal balance between electroactive surface area and charge carrier concentration occurs.
\nZhao et al. [82] investigated the photocatalytic H2 evolution performance of Ir-C-N tridoped TiO2 under UV-visible light irradiation. The photocatalytic activity of TiO2 nanoparticles was reported to be improved by Ir-C-N tridoped TiO2 under UV-visible light, due the synergistic effect between Ir, C and N on the electron structure of TiO2. It was found that Ir existed as Ir4+ by substituting Ti in the lattice of TiO2 nanoparticles, whereas the C and N were also incorporated into the surface of TiO2 nanoparticles in interstitial mode. The absorption of TiO2 nanoparticles was expanded into the visible light region and the band gap was narrowed to ~3.0 eV, resulting in improved photocatalytic H2 evolution under UV-visible light irradiation. Tan et al. [83] investigated the photocatalytic degradation of methylene blue by W–Bi–S-tridoped TiO2 nanoparticles. It was found that the absorption edge of TiO2 was expanded into visible-light region after doping with W, Bi and S and the catalytst showed the best photocatalytic activity, than that of TiO2, S-TiO2, W–S–TiO2 and Bi–S–TiO2. This might be attributed to the synergistic effect of W, Bi and S.
\nAmongst the various strategies that have been used to enhance TiO2 photocatalytic activity, improvement of morphology, crystal structure and surface area have also been considered important and widely investigated approach to achieve better photocatalytic performance. The nanotitania crystallinity can simply be enhanced by optimizing the annealing temperature. However, the stability of the structure and geometries have to be considered when annealing [84]. For the nanotitania morphology and surface area, various ordered structures have been studied. TiO2 nanotubes [85, 86], nanowires [79], nanospheres [87], etc. Tang et al. fabricated monodisperse mesoporous anatase TiO2 nanospheres using a template material and found the resulting catalysts to show high photocatalytic degradation efficiency and selectivity towards different target dye molecules and could be readily separated from a slurry system after photocatalytic reaction [87]. Anodic TiO2 nanotubes have been reported to allow a high control over the separation of photogenerated charge carriers in photocatalytic reactions. The nanotube array has as key advantage the fact that nanotube modifications can be embedded site specifically into the tube wall or at defined locations along the tube wall. This allows for engineering of reaction sites giving rise to enhanced photocatalytic efficiencies and selectivities [88].
\nThe design and preparation of graphene-based composites containing metal oxides and metal nanoparticles have attracted attention for photocatalytic performances. For example, Tan et al. [89] prepared a novel graphene oxide-doped-oxygen-rich TiO2 (GO–OTiO2) hybrid heterostructure and evaluated its activity for photoreduction of CO2 under the irradiation of low-power energy-saving daylight bulbs. It was found that the photostability of O2–TiO2 was significantly improved by the addition of GO, at which the resulting hybrid composite retained a high reactivity. The photoactivity attained was about 1.6 and 14.0 folds higher than that of bare O2–TiO2 and the commercial Degussa P25, respectively. This high photocatalytic performance of GO–OTiO2 was attributed to the synergistic effect of the visible-light-responsiveness of O2–TiO2 and an enhanced separation and transfer of photogenerated charge carriers at the intimate interface of GO–OTiO2 heterojunctions. This study is reported to have opened up new possibilities in the development of novel, next generation heterojunction photocatalysts for energy and environmental related applications. Lin et al. [90] also investigated photoreduction of CO2 with H2O vapor in the gas-phase under the irradiation of a Xe lamp using TiO2/nitrogen (N) doped reduced graphene oxide (TiO2/NrGO) nanocomposites. They found that the quantity and configuration of N dopant in the TiO2/NrGO nanocomposites strongly influenced the photocatalytic efficiency, and the highest catalytic activity was observed for TiO2/NrGO nanocomposites with the highest N doping content. Moreover, modified TiO2/rGO demonstrated a synergistic effect, enhancing CO2 adsorption on the catalyst surface and promoting photogenerated electron transfer that resulted in a higher CO2 photoreduction rate of TiO2/NrGO. Qu et al. [91] prepared the graphene quantum dots (GQDs) with high quantum yield (about 23.6% at an excitation wavelength of 320 nm) and GQDs/TiO2 nanotubes (GQDs/TiO2 nanoparticles) nanocomposites and the photocatalytic activity was tested towards the degradation of methyl orange. It was found that the GQDs deposited on TiO2 nanoparticles can expand the visible light absorption of TiO2 nanoparticles and enhance the activity on photocatalytic degradation of methyl orange under UV-vis light irradiation (ʎ = 380–780 nm). Furthermore, the photocatalytic activity of GQDs/TiO2 nanoparticles was approximately 2.7 times as higher than that of bare TiO2 nanoparticles. Tian et al. [92] reported the preparation of N, S co-doped graphene quantum dots (N, S-GQDs)-reduced graphene oxide- (rGO)-TiO2 nanotubes (TiO2NT) nanocomposites for photodegradation of methyl orange under visible light irradiation. It was found that the S-GQDs+rGO + TiO2 nanocomposites simultaneously showed an extended photoresponse range, improved charge separation and transportation properties. Moreover, the apparent rate constant of N, S-GQDs+rGO + TiO2NT is 1.8 and 16.3 times higher compared to rGO + TiO2NT and pure TiO2NT, respectively. Suggesting that GQDs can improve the utilization of solar light for energy conversion and environmental therapy.
\nAnother drawback of TiO2 nanoparticles mentioned above is the formation of uniform suspension in water which makes its recovery difficult, therefore hindering the application of photocatalytic in an industrial scale. As a result, many studies have attempted the modification of TiO2 nanoparticles on support materials such as clays [93, 94] quartz [95], stainless steel [96], etc. Clays have been reported to be a significant support material for TiO2 nanoparticles because of their layered morphology, chemical as well as mechanical stability, cation exchange capacity, non-toxic nature, low cost and availability. Therefore, TiO2/clay nanocomposites have attracted much attention for application in both water and air purification and have been prepared by numerous researchers. Belver et al. [97] investigated the removal of atrazine under solar light using a novel W-TiO2/clay photocatalysts. It was found that the photocatalytic activity of W-TiO2/clay catalyst exhibited higher photocatalytic performance than that of an un-doped TiO2/clay, which was explained by the presence of W ions in the TiO2 nanostructure. The substitution of Ti ions with W resulted in the increase of its crystal size and the distortion of its lattice and moderately narrower band gap of photocatalysts. Mishra et al. [98] reported the preparation of TiO2/clay nanocomposites for photocatalytic degradation of VOC and dye. They found that the photocatalytic performance of TiO2/clay nanocomposites is highly dependent on the clay texture (as 2:1 clays show highest activity than 1:1) apart from their surface area and porosity. Moreover, the reactions involving TiO2/Clay photocatalyst were fast with rate constant of 0.02886 and 0.04600 min−1 for dye and VOC respectively than the other nanocomposites.
\nIn this chapter, we have given an overview of the development of modified TiO2 catalysts and its future prospects from a scientific point of view. We note that the field has experienced major advances in the last 5 years especially in the area of modifying TiO2 with carbon nanomaterials. Based on the literature we have covered here, we believe that there is still quite a lot that can be achieved in improving the performance of TiO2 catalysts for photocatalytic applications.
\nThere are no conflicts of interest to declare.
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I am also a member of the team in charge for the supervision of Ph.D. students in the fields of development of silicon based planar waveguide sensor devices, study of inelastic electron tunnelling in planar tunnelling nanostructures for sensing applications and development of organotellurium(IV) compounds for semiconductor applications. I am a specialist in data analysis techniques and nanosurface structure. I have served as the editor for many books, been a member of the editorial board in science journals, have published many papers and hold many patents.",institutionString:null,institution:{name:"Sheffield Hallam University",country:{name:"United Kingdom"}}},{id:"54525",title:"Prof.",name:"Abdul Latif",middleName:null,surname:"Ahmad",slug:"abdul-latif-ahmad",fullName:"Abdul Latif Ahmad",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"20567",title:"Prof.",name:"Ado",middleName:null,surname:"Jorio",slug:"ado-jorio",fullName:"Ado Jorio",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Universidade Federal de Minas Gerais",country:{name:"Brazil"}}},{id:"47940",title:"Dr.",name:"Alberto",middleName:null,surname:"Mantovani",slug:"alberto-mantovani",fullName:"Alberto Mantovani",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"12392",title:"Mr.",name:"Alex",middleName:null,surname:"Lazinica",slug:"alex-lazinica",fullName:"Alex Lazinica",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/12392/images/7282_n.png",biography:"Alex Lazinica is the founder and CEO of IntechOpen. After obtaining a Master's degree in Mechanical Engineering, he continued his PhD studies in Robotics at the Vienna University of Technology. Here he worked as a robotic researcher with the university's Intelligent Manufacturing Systems Group as well as a guest researcher at various European universities, including the Swiss Federal Institute of Technology Lausanne (EPFL). During this time he published more than 20 scientific papers, gave presentations, served as a reviewer for major robotic journals and conferences and most importantly he co-founded and built the International Journal of Advanced Robotic Systems- world's first Open Access journal in the field of robotics. Starting this journal was a pivotal point in his career, since it was a pathway to founding IntechOpen - Open Access publisher focused on addressing academic researchers needs. Alex is a personification of IntechOpen key values being trusted, open and entrepreneurial. Today his focus is on defining the growth and development strategy for the company.",institutionString:null,institution:{name:"TU Wien",country:{name:"Austria"}}},{id:"19816",title:"Prof.",name:"Alexander",middleName:null,surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/19816/images/1607_n.jpg",biography:"Alexander I. Kokorin: born: 1947, Moscow; DSc., PhD; Principal Research Fellow (Research Professor) of Department of Kinetics and Catalysis, N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow.\r\nArea of research interests: physical chemistry of complex-organized molecular and nanosized systems, including polymer-metal complexes; the surface of doped oxide semiconductors. He is an expert in structural, absorptive, catalytic and photocatalytic properties, in structural organization and dynamic features of ionic liquids, in magnetic interactions between paramagnetic centers. The author or co-author of 3 books, over 200 articles and reviews in scientific journals and books. He is an actual member of the International EPR/ESR Society, European Society on Quantum Solar Energy Conversion, Moscow House of Scientists, of the Board of Moscow Physical Society.",institutionString:null,institution:{name:"Semenov Institute of Chemical Physics",country:{name:"Russia"}}},{id:"62389",title:"PhD.",name:"Ali Demir",middleName:null,surname:"Sezer",slug:"ali-demir-sezer",fullName:"Ali Demir Sezer",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/62389/images/3413_n.jpg",biography:"Dr. Ali Demir Sezer has a Ph.D. from Pharmaceutical Biotechnology at the Faculty of Pharmacy, University of Marmara (Turkey). He is the member of many Pharmaceutical Associations and acts as a reviewer of scientific journals and European projects under different research areas such as: drug delivery systems, nanotechnology and pharmaceutical biotechnology. Dr. Sezer is the author of many scientific publications in peer-reviewed journals and poster communications. Focus of his research activity is drug delivery, physico-chemical characterization and biological evaluation of biopolymers micro and nanoparticles as modified drug delivery system, and colloidal drug carriers (liposomes, nanoparticles etc.).",institutionString:null,institution:{name:"Marmara University",country:{name:"Turkey"}}},{id:"61051",title:"Prof.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"100762",title:"Prof.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"St David's Medical Center",country:{name:"United States of America"}}},{id:"107416",title:"Dr.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Texas Cardiac Arrhythmia",country:{name:"United States of America"}}},{id:"64434",title:"Dr.",name:"Angkoon",middleName:null,surname:"Phinyomark",slug:"angkoon-phinyomark",fullName:"Angkoon Phinyomark",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/64434/images/2619_n.jpg",biography:"My name is Angkoon Phinyomark. I received a B.Eng. degree in Computer Engineering with First Class Honors in 2008 from Prince of Songkla University, Songkhla, Thailand, where I received a Ph.D. degree in Electrical Engineering. My research interests are primarily in the area of biomedical signal processing and classification notably EMG (electromyography signal), EOG (electrooculography signal), and EEG (electroencephalography signal), image analysis notably breast cancer analysis and optical coherence tomography, and rehabilitation engineering. I became a student member of IEEE in 2008. During October 2011-March 2012, I had worked at School of Computer Science and Electronic Engineering, University of Essex, Colchester, Essex, United Kingdom. In addition, during a B.Eng. I had been a visiting research student at Faculty of Computer Science, University of Murcia, Murcia, Spain for three months.\n\nI have published over 40 papers during 5 years in refereed journals, books, and conference proceedings in the areas of electro-physiological signals processing and classification, notably EMG and EOG signals, fractal analysis, wavelet analysis, texture analysis, feature extraction and machine learning algorithms, and assistive and rehabilitative devices. I have several computer programming language certificates, i.e. Sun Certified Programmer for the Java 2 Platform 1.4 (SCJP), Microsoft Certified Professional Developer, Web Developer (MCPD), Microsoft Certified Technology Specialist, .NET Framework 2.0 Web (MCTS). 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