Kinetic Characteristics of Ion Exchange

Nanostructured titanates, produced by the alkaline hydrothermal treatment of TiO2, are characterized by an open, mesoporous morphology, which facilitates the transport of ions from a liquid towards the surface of nanotubes. Figure 4.2 shows the dynamics of pH change in an aqueous suspension of nanostructured titanate and titania after the addition of aqueous LiOH. For a blank solution of pure water, the addition of LiOH results in a very rapid increase in pH up to a value of 11.5, with an almost constant value after 60min. A small decrease of pH is attributable to the reaction with atmospheric CO2, which leads to the formation of lithium carbonate. The addition of an identical amount of LiOH to a suspension of TiO2 nanoparticles (Degussa P-25; characterized by spheroidal particles of ca. 20 nm diameter), results in a rapid increase in pH up to 11, followed by an insignificant drop. In contrast, the addition of an identical amount of LiOH to a suspension of titanate nanotubes and nanofibres, results in an initial, rapid rise in pH to approximately 11, followed by a slow decrease in pH to the values 7.3 and 8.1, respectively. The characteristic time for the pH decrease is in the range of several tens of minutes.

The specific surface area of Degussa P-25 (ca. 50m2g_1) is lower than that of titanate nanotubes7 (ca. 200 m2g-1), but higher than that of titanate nanofibres (ca. 20m2g-1). Thus, such an insignificant drop in pH after the addition of alkali to P-25 cannot simply be explained in terms of a small surface area. Rather, such a high degree of pH variation for nanostructured titanates can be explained by the leaching of protons from the crystal structure of the

Xanax Pharmacokinetics
Figure 4.2 Graph showing pH as a function of time, following the addition of 50 mL of LiOH (1 mol dm-3) to a suspension of 0.1 g of TiO2 nanoparticles (P-25), titanate nanotubes or titanate nanofibres in 10 mL water at 25 °C. The initial pH of water is ca. 4.5. (Data are adapted from ref. 8).

protonated titanates, which arises from the substitution of protons by lithium cations, as shown in reaction (4.13). The dynamics of pH change reflect the kinetic regularities of ion-exchange in nanotubular and nanofibrous titanates.

The pH of a solution is related to the concentration of protons using a logarithm, pH = —log([H+]. The typical kinetic curve of proton concentration growth in a suspension of protonated titanate nanotubes after addition of LiOH, had the "S"-shape shown in Figure 4.3. The curve indicates a short induction period, followed by monotonic growth and saturation. The release of protons from the titanate nanotubes to the bulk solution can be illustrated using the following sequence of processes:

Lisurface ! Liintercalate (4:15)

Liintercalate b H2Tin°2n+1 ! LiHTin02n+1 b ^tercalate (4.16)

Hintercalate ! Hburface (4.17)

Hsurface ^ Hbulk

Chemical Properties, Transformation and Functionalization 91 0.3-n-

Figure 4.3 Graph showing proton concentration growth with time (□) after addition of 40 mL of LiOH (lmoldm-3) to a suspension of 0.1 g of protonated titanate nanotubes in 10 mL water at 25 °C. The line was fitted using Equation (4.20). (Data are adapted from ref. 8).

Time / min

Figure 4.3 Graph showing proton concentration growth with time (□) after addition of 40 mL of LiOH (lmoldm-3) to a suspension of 0.1 g of protonated titanate nanotubes in 10 mL water at 25 °C. The line was fitted using Equation (4.20). (Data are adapted from ref. 8).

The resultant process corresponds to reaction (4.13), with Li1 as the intercalating ion and x = 1. Step (4.14) represents the adsorption of lithium ions from bulk solution onto the surface of the nanotubes, whilst step (4.15) is the transport of lithium ions inside the crystal to the ion-exchange centres. Reaction (4.16) represents the ion-exchange which occurs inside the crystal. Steps (4.17) and (4.18) represent the reverse transport of protons from the crystal to the surface, then into the bulk solution. It has been shown that the length of nanotubes affects the overall rate of ion-exchange.8 This may indicate that the transport of lithium ions and protons between the layers inside the nanotube wall are the rate-limiting steps. The above scheme can therefore be simplified by the exclusion of fast processes in two consecutive stages, namely the diffusion of lithium ions (A to B) and the diffusion of protons (B to C) inside the nanotube walls:

where k1 and k2 are reaction constants. Scheme (4.19) is deliberately oversimplified in order to demonstrate the appearance of an induction time in the kinetic curve of proton concentration growth. More detailed treatments should consider the transformation from A to B, not as a chemical reaction, but rather as a diffusion process inside the nanotube. The analytical solution for the accumulation of C from scheme (4.19), using the law of mass action, has the form:9

C{t) = -—V M1 - e—k1t) - k1 (1 - e-k2t)) (4.20)

k2 — k where A0 is the infinity concentration of protons, and k1 and k2 are parameters characterising the diffusion of lithium ions and protons inside the nanotubes, respectively.

Equation (4.20) is fitted to the experimental kinetic curve of proton concentration growth in Figure 4.3. The proposed scheme (4.19) is in agreement with experimental kinetics and explains the reasons for the induction period in the kinetic curve. The growth in proton concentration in suspension following the addition of strong LiOH, is due to a leaching of protons from the solid nanotubes as a result of ion exchange with the lithium cations diffused inside the nanotubes. At zero time, the concentration of lithium ions inside the nanotubes and the rate of the proton leaching are both equal to zero. As soon as lithium ions diffuse into the nanotubes, the reverse leaching of protons occurs after an induction time.

Although the mechanistic scheme (4.19) does not correspond exactly to the process of ion diffusion in solid materials described, a general solution for diffusion in a cylinder10 can be used to show the relation of the reaction constant k1 to the diffusion coefficient:

tube where DLi is the diffusion coefficient of lithium ions inside the titanate nano-tubes, and Ltube is the nanotube length.

An analysis of k1 reaction constants for samples of nanotubes having differing average lengths, shows that Equation (4.21) is valid.8 The values of k1 were obtained by fitting experimental kinetic curves describing proton concentration growth for nanotubes of differing lengths (see Figure 4.3) to Equation (4.20). Average values for nanotube length were used, with determination using SEM microscopy. The determined values for k1 and Ltube are consistent with Equation (4.21), indicating that the transport of lithium ions in titanate nanotubes probably occurs along the length of the nanotube. The value of the diffusion coefficient was estimated in the order of magnitude of 10—11 cm2s—1, which is much smaller than the diffusion coefficient of caesium ions in zeolite, but of a similar order of magnitude to that of cancrinite.11 Similar diffusion coefficient values were also observed for zirconium thiophophates.12 For a more accurate determination of the diffusion coefficient, an improved model for the forward and reverse diffusion of ions in cylindrical particles is required.

Nanofibrous titanate nanostructures demonstrate similar ion-exchange properties to those of titanate nanotubes. Although the amount of ion-exchangeable centres in nanofibres is less than that in nanotubes, the characteristic time of ion-exchange between protons and lithium ion from aqueous solution is of the same order of magnitude (see Figure 4.2). Studies of the kinetic regularities of alkaline metal ion intercalation into nanofibrous titanates of differing length and width, have shown that changes in the dimensions of nanofibres facilitate ion-exchange without changing the extent of the process, confirming that the ion transport inside nanofibres is a rate-limiting stage.8

In addition, crystallographic studies of intercalated alkaline ions inside titanate nanotubes and nanofibres have clarified the directions of ion flow in nanostructures. Figure 4.4 shows the transformation of titanate nanosheets to nanotubes or nanofibres, with a consistently oriented crystallographic axis. During the growth of nanosheets, under alkaline hydrothermal conditions, the bending of nanosheets around axis b occurs followed by a closing of the loop, and growth along direction b. If the formation of a nanotube does not occur, the nanofibres produced have a length corresponding the direction c, and a thickness corresponding to both directions a and b (see Figure 4.4). As described above, the transport of alkaline metal cations in titanate nanotubes occurs preferentially along the nanotube length, which corresponds to axis b. In

Metal Nanosheets
Figure 4.4 Titanate nanostructures (nanosheets, nanofibres and nanotubes with crystallographic axis) and the directions of cation transport during ionexchange.

the case of nanofibres, the transport of cations occurs preferentially along axes b and c. The length of the nanotubes (in the hundreds of nanometres range) is of the same order of magnitude as the thickness of nanofibres (along direction b). Taking into account that the characteristic time of ion-exchange for both nanotubes and nanofibres is similar, it may be concluded that the transport of ions in nanofibres in direction b is dominant.

The diffusion of alkaline metal ions inside nanotubes occurs between the titanate layers, which are characterized by a zigzag structure and an average spacing of ca. 0.72 nm. The sizes of the alkaline metal ions in aqueous solution are smaller and have the following ionic diameters: Li1 (0.09nm), Na1 (0.116nm), K1 (0.152 nm), Cs1 (0.181 nm) for a coordination number of 6 (ref. 13). Despite the differences in the size of alkali metal cations, the apparent rate of intercalation is very similar for all of the ions studied. This unusual result of the absence of selectivity of titanate nanotubes in terms of alkali metal transport is consistent with the observation of crystal structure alterations following the substitution of protons by alkali metal cations in nanotubular titanates, showing an increase of interplanar distance d2oo from 0.88 nm to 1.18 nm.8 Surprisingly, the interplanar distance d200 = 1.18 nm is almost identical for many of the nanotubular titanates of alkaline metals, including: Li1, Na1, K1 and Cs1.

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