1 Introduction

A number of different commercial photocatalytic products have been developed over the years, such as self-cleaning concrete [1], plastic tent/awning/curtain materials [2, 3], tiles [4] and paint [5], the most popular and successful of which is self-cleaning glass [6,7,8,9,10]. All self-cleaning glass comprises a thin, typically ca. 15 nm thick, compact, i.e. non-porous, film of anatase TiO2, usually deposited by Chemical Vapour Deposition, CVD [11]. The major self-cleaning glass companies and others have worked together to develop an internationally recognised standard method, BS EN 1096–5: 2016, for classifying glass samples as self-cleaning, or not, based on the measurement of the haze of purposely soiled glass, before and after irradiation [12]. A key component of the coating solution used to produce the initial haze is stearic acid, SA, possibly because it appears an appropriate test pollutant for self-cleaning glass, given it is one of the most common saturated fatty acids found in nature and is in all fingerprints [13]. Not surprisingly, therefore, in research, the photocatalytic mineralisation of SA, is one of the most commonly employed reactions used to demonstrate the self-cleaning action of new photocatalytic films [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]; the reaction associated with this process can be summarised as follows,

$$ CH_{3} \left( {CH_{2} } \right)_{16} CO_{2} H \, + \, 26O_{2} \underset{{h\nu \rangle E_{bg} }}{\overset{photocatalyst}{\longleftrightarrow}}18CO_{2} + \, 18H_{2} O $$
(1)

where Ebg is the bandgap energy of the photocatalyst, which is ca. 3.2 eV for anatase TiO2, for example. Interestingly, the number of studies of the kinetics of Reaction (1) appear limited, with most focussed on a system in which the SA film is on top of the photocatalytic film [14,15,16,17,18,19,20,21,22,23,24,25,26].

2 SA layer on top of the photocatalytic film

A schematic illustration of the simple SA layer on top of the photocatalytic film system is given in Fig. 1 and applies to all commercial examples of self-cleaning, photocatalytic glass tested for activity via reaction (1), since they invariably utilise a compact, i.e. non-porous, or micro-porous, TiO2 film. Even mesoporous, sol–gel films appear to fit the ‘SA film on top’ architecture illustrated in Fig. 1, provided the SA is dissolved in a hydrophobic solvent, such as chloroform or dichloromethane, DCM, and the solvent is rapidly evaporated, as occurs when the SA solution is deposited by spin-coating.

Fig. 1
figure 1

Schematic illustration of the conventional SA (light blue, solid film)/photocatalytic film (or particles) system in which the SA lies on top of the photocatalytic film

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In the reported kinetic studies of this system, the rate of removal of SA is found to be zero-order with respect to the concentration of SA, [SA], [11, 17], i.e. d[SA]/dt = rSA = −ko, so that the integrated rate equation is as follows,

$$ \left[ {SA} \right]_{t} = \, \left[ {SA} \right]_{o} - k_{o} t $$
(2)

where [SA]t and [SA]o are the concentrations of SA at irradiation times 0 and t, respectively, ko is the zero-order rate constant, and the reaction is complete when t = [SA]o/ko. The generally accepted rationale for such kinetics is that in such a system all the surface reaction sites on the photocatalytic film have the same reactivity, and the SA, which forms a layer on the photocatalyst film, occupies all the reaction sites throughout the photocatalytic process, so that the rate of SA removal, rSA, is independent of [SA]t.

This simple model is nicely illustrated by the results of a study carried out by this group on reaction (1) using thick, i.e. ca. 2.7 μm, anatase, sol–gel TiO2 films [29]. In this work the concentration of SA was monitored as a function of irradiation time for a series of different values of [SA]o, resulting in a series of approximately parallel straight-line decays, as illustrated in Fig. 2, which underline the zero-order nature of the decay kinetics for reaction (1) and show that ko is independent of [SA]o, as predicted by Eq. (2).

Fig. 2
figure 2

Plot of [SA]t vs irradiation time, t, for thick anatase TiO2 photocatalytic film, covered with SA films of different thickness [29]

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It is worth commenting at this point on the units that are often reported for [SA] and ko. In many studies of reaction (1), and in particular studies of the kinetics, the removal of SA is monitored by FT-IR absorbance spectroscopy, through the disappearance of peaks at, (i) 2957.5 cm−1, due to the asymmetric in-plane C–H stretching mode of the CH3 group, and (ii) 2922.8 cm−1 and 2853.4 cm−1, due to the asymmetric and symmetric C–H stretching modes of the -CH2 group, respectively [18]. Although, some have focussed on monitoring the absorbance due to just one of these peaks [18, 30], more usually the integrated area under all these peaks, from 2700 to 3000 cm−1, is used to provide a measure of [SA]t [17, 31,32,33]. In the latter case, an example of which is illustrated by the [SA] vs t decay profiles in Fig. 2, the units of [SA]t are cm−1, where 1 cm−1 is equivalent to ca. 9.7 × 1015 molecules of SA cm−2 [33], and it follows that those for ko are cm−1 min−1. Given the bulk density of SA is 0.9408 g cm−3, it can be shown that an integrated area of 1 cm−1 is associated with a SA film which is ca. 48.7 nm thick; details of this calculation are given in section S1 in the electronic supplementary information (ESI) file.

An interesting, though rarely noted, feature of this system is that the rate of SA removal is proportional to the fraction of UV irradiation absorbed [34], which can be varied, for example, by simply using photocatalytic films of different thickness. A good illustration of this is provided by the results of a study of the kinetics of reaction (1) as a function of CVD TiO2 photocatalyst film thickness illustrated in Fig. 3 [34]. In this work the irradiation source was a germicidal lamp, so that the UV irradiation was predominantly 254 nm, and the fraction of light absorbed, f254, was calculated using the following expression,

$$ f_{254} = 1 - 10^{Abs(254)} $$
(3)
Fig. 3
figure 3

Plot of the measure rate of removal of SA, rSA, as a function of CVD TiO2 film (on quartz) thickness; irradiance = 3 mW cm−2 254 nm radiation. The insert diagram is a plot of the rate data in the main diagram versus the fraction of UVC radiation absorbed, f254 [34]

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where Abs(254) is the measured absorbance of the TiO2 photocatalytic film at 254 nm, i.e. the measured absorbance of the TiO2 film on quartz glass substrate minus that of the quartz glass substrate.

A similar study, but this time using the same sol–gel films used to generate the data in Fig. 2, also showed that rate of removal of SA was directly proportional to the fractions of UVC and UVA absorbed by the sol–gel film of different thicknesses [29]. These results suggest that in this system, regardless of where in the photocatalytic film they are generated, all photogenerated electrons and holes that have avoided geminate pair electron–hole recombination are able to move efficiently and rapidly to the surface where they are able to react with O2 and the stearic acid, respectively. In all this work it is assumed the rate of diffusion of oxygen through the organic layer is rapid compared to the stoichiometric demand [35], and the rate-determining step is the oxidation of the SA. The rapid transport of photogenerated electrons through titania films is well-know in dye-sensitised solar cells, where the electron diffusion length in 2–4 microns-thick TiO2 sol − gel films is ca. 10 μm [36]. Other works shows that the diffusion length of photogenerated holes, or hydroxyl radicals, is ca. 20 μm in such films [37]. The apparent rapid and efficient transport of both the photogenerated electrons and holes from the bulk of a TiO2 photocatalytic film to the surface is most likely through appropriate trap states in the TiO2 particles/microcrystalline domains. Clearly, in order for this process to be efficient, the transfer of photogenerated electrons and/or holes from one TiO2 particle/microcrystalline domain to another must be facile and that this is only possible if all the particles/microdomains are interconnected/networked, i.e. not isolated, from each other.

3 SA layer inside a photocatalytic film of isolated photocatalytic particles

Although, as noted earlier, most of the studies of reaction (1) have reported zero-order kinetics, there are some notable exceptions. For example, Allain and his co-workers observed first order kinetics for reaction (1) when using porous silica films with embedded TiO2 photocatalytic particles [30]. However, in this work, the SA was found to lie inside, as illustrated in Fig. 4, not on top of, the film, AND that the TiO2 particles were isolated from one another by the silica particles that formed the encapsulation medium, i.e. they were not networked.

Fig. 4
figure 4

Schematic illustration of a photocatalytic films in which the SA (light blue) lies inside a photocatalytic film of particles (white) isolated from one another by silica particles (grey)

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The isolation of the TiO2 particles in this system is an important feature, since it means that each particle can only photocatalytically oxidise the SA that surrounds it, via reaction (1), and once that is complete, its only function is as an absorber, i.e. a filter, of the incident UV radiation. In particular, in the photocatalytic system illustrated in Fig. 4, at no time can any of the photogenerated electrons or holes generated on one photocatalytic particle move to another, due to the isolated nature of the photocatalytic particles. The latter feature is in stark contrast to an ‘all-TiO2 film’, as illustrated in Fig. 1, such as found in commercial self-cleaning glass, in which the photocatalytic particles/crystallite domains are extensively networked, thereby allowing the rapid movement of photogenerated electrons and holes throughout the film.

The first order decay kinetics for reaction (1), reported by Allain et al. [30] using the TiO2/SiO2 films illustrated in Fig. 4 were readily explained by David Ollis [35], using a simple model in which the photocatalytic/SA film architecture illustrated in Fig. 4, was broken up into a stack of 5 identical layers of SA and TiO2 particles, with each layer reducing the incident UV irradiance by a factor of 2, so that by the 5th layer the transmitted UV (365 nm) irradiance is 1/16 that of the original (incident) irradiance; note, that this situation translates to the film having an overall absorbance at 365 nm of 1.204. Using this model, and assuming the zero-order rate constant for each layer is proportional to UV irradiance associated with that layer, Ollis showed that although the kinetics of the disappearance of SA in each layer would still be zero-order, UV filtering by the other TiO2 layers would produce a ‘kinetic disguise’ in the form of a first order decay curve for total amount of SA as a function of irradiation time, as observed by Allain et al. [30] for their TiO2/SiO2 films [35].

Although not subsequently developed by Ollis, a closer inspection of this model reveals that the decay kinetics are very sensitive to the overall absorbance of the photocatalytic film, AT, at the wavelength of the incident UV radiation, so that a range of reaction orders are possible depending upon the value of AT. For example, if the overall absorbance of the film at 365 nm is small, say < 0.1, the kinetics will appear approximately zero order, and if the absorbance of the film is >  > 1.204, the kinetics will exhibit an order >  > 1. Indeed, as we shall see, this model, based on a porous film of non-networked photocatalytic particles with the SA inside the film, predicts the observed apparent reaction order for reaction (1) is approximately proportional to AT!

A general, more developed form of the Ollis model, which to date has only been described by the simple 5 layer, single film absorbance (1.204), system outlined above, can be readily created based on the porous, non-networked photocatalytic film, in which the SA is in the film, as illustrated in Fig. 4. In this model it is assumed that the photocatalytic film, (i) comprises NT identical layers (where, NT is 200 in this work), (ii) has an overall (total) absorbance at the wavelength of the ultra-bandgap irradiation, AT, so that the absorbance of each layer is Abs(L) = AT/NT, (iii) has a total SA per cm2 at irradiation time t = 0 equal to [SA]T,o, so that the initial concentration of SA in each layer is [SA]L,o, where [SA]L,o = [SA]T,o/NT, (iv) the kinetics of destruction of the SA in each layer is zero order, with a rate constant, ko, and (v) the rate of destruction of the SA in each layer depends directly upon the UV irradiance received by the layer, which for layer i will be equal to Iox10−i.Abs(L), where Io is the incident irradiance falling on layer 0, i.e. i = 0.

It follows from the above assumptions that for layer 0 (i.e. the first, and therefore topmost, layer of photocatalyst particles plus SA), the variation of the [SA] with irradiation time, t, will be given by the expression,

$$ \left[ {SA} \right]_{0,t} = \, \left[ {SA} \right]_{L,o} - k_{o} \times \left( {1 - 10^{ - Abs\left( L \right)} } \right) \times I_{o} \times t $$
(4)

where, Io is the incident light intensity falling on layer 0. Similarly, for layer 1,

$$ \left[ {SA} \right]_{1,t} = \, \left[ {SA} \right]_{L,o} - k_{o} \times \left( {1 - 10^{ - Abs\left( L \right)} } \right) \times I_{o} \times 10^{ - Abs\left( L \right)} \times t $$
(5)

and for layer 2,

$$ \left[ {SA} \right]_{2,t} = \, \left[ {SA} \right]_{L,o} - k_{o} \times \left( {1 - 10^{ - Abs\left( L \right)} } \right) \times I_{o} \times 10^{ - 2.Abs\left( L \right)} \times t $$
(6)

So that

$$ \left[ {SA} \right]_{T,\tau } /\left[ {SA} \right]_{T,0} = \sum\limits_{n = 0}^{{n = N_{T} }} {\left( {1 - \tau \times 10^{ - n.Abs\left( l \right)} } \right)/N_{T} } $$
(7)

where τ is a unitless time parameter, which is directly proportional to t, and equal to ko × (1–10− Abs(L)) × Io × t/[SA]L,o, which for very large values of NT, simplifies to,

$$ \tau = k_{o} \times A_{T} \times I_{o} \times t/\left[ {SA} \right]_{T,o} $$
(8)

Note that in the summation in Eq. (7), for each value of n, if/when a value of τ is reached where (1 − τ × 10− n.Abs(L)) < 0, then the reaction is complete (all the SA is removed) in that layer and for that, and all subsequent values of τ, the subsequently calculated negative values of (1-τx10− n.Abs(L))) must be returned as zero for that layer n.

Equation (7) was used to generate a series of normalised decay curves for reaction (1) in the form of [SA]T,τ/[SA]T,o vs τ, as a function of photocatalyst film absorbance, AT, and the results are illustrated in Fig. 5.

Fig. 5
figure 5

Plot of [SA]T,τ/[SA]T,o vs τ profiles, calculated using Eq. (7), assuming the following values for AT (from left to right): 0.01, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 2, 2.5 and 3.0 respectively

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Each of the above decay curves can be fitted to the integrated form of the following general rate equation,

$$ d\left[ {SA} \right]/dt = r_{SA} = - k_{o} \left[ {SA} \right]^{m} $$
(9)

where m is the apparent order of reaction. Thus, if AT is < 0.1 then the decay curve fits zero-order decay kinetics, i.e. m = 0, but with increasing value of AT, the value of m increases, as suggested by the shapes of the decay curves illustrated in Fig. 5 and, indeed, a plot of m vs AT, yields a good straight line with a gradient = 1.107, as illustrated in Figure S1 in the ESI file, i.e.

$$ m = \, 1.107 \times A_{T} $$
(10)

Thus, based in this model, a 1st order decay profile would be expected for a photocatalytic film that had an absorbance of 0.903, rather than the value of 1.204 used by Ollis [35]. Interestingly, a UV lamp with a peak at 365 nm was used by Allain et al., and the thickness of the TiO2/SiO2 film, b, was ca. 400 nm, which suggests the absorbance of the film, AT, was 0.87, assuming a value for the reported absorption coefficient at 365 nm for TiO2, i.e. α(365), of 5 × 104 cm−1 [34], since α(λ) = 2.303.AT/b. This estimated value for AT (= 0.87) is close to the model predicted value of 0.903 [30].

Using the profiles illustrated in Fig. 5 it is possible to determine values for the reaction half-life, τ1/2, as a function m, a plot of which is illustrated in Figure S2 in the ESI and which fits the following expression,

$$ \tau_{1/2} = \, 0.5.\exp \, (0.927 \times m) $$
(11)

The above information allows a [SA]T,τ/[SA]T,o vs. τ decay curve, such as illustrated in Fig. 5, which exhibits a specific reaction order, m, to be fitted to any measured [SA]T,t/[SA]T,o vs irradiation time, t, plot which also shows the same order of reaction.

For example, consider the first-order, i.e. m = 1, [SA]T,t/[SA]T,o vs t decay data reported by Allain et al., which is illustrated in Fig. 6 and which has a half-life of 8.01 min [30]. As noted previously, the model also generates a first-order, [SA]T,τ/[SA]T,o vs τ decay profile for a film with AT = 0.903, calculated using Eq. (10), and, from Eq. (11), τ1/2 for this decay will be equal to 1.26. Thus, the model-generated [SA]T,τ/[SA]T,o vs τ plot for a film with AT = 0.903 can be converted to a [SA]T,t/[SA]T,o vs t plot, and compared to the actual decay data reported by Allain et al. [30], by multiplying each of the τ values in the plot by the of ratio of half-lives, i.e. t1/2/τ1/2, here equal to (8.01/1.26) min. The model generated decay profile processed in this manner is illustrated by the solid line in Fig. 6 and provides an excellent fit to the [SA]T,t/[SA]T,o decay data reported by Allain et al. [30], which is also illustrated in Fig. 6.

Fig. 6
figure 6

Solid line plot of the [SA]T,t/[SA]T,o vs irradiation time, t, decay curve calculated using Eq. (7), assuming a value of AT = 0.903, with each value of τ, in the model generated [SA]T,τ/[SA]T,o vs. τ plot for AT = 0.903, multiplied by the value of ratio of half-lives, t1/2/τ1/2, i.e. (8.01/1.26) min. The data points are the actual [SA]T,t/[SA]T,o values vs. t reported for reaction (1) using the TiO2/SiO2 mesoporous film [30]. The insert plot is that of the measured value of k1 vs. [SA]T,o with a line of best fit based on k1 = K/[SA]T,o, where K is a proportionality constant [30]

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Further support for the above model is gained from the measured variation of the first order rate constant, k1, as a function of the initial amount of SA present in the film, i.e. [SA]T,o, reported by Allain et al. [30], the results of which are illustrated in the insert plot in Fig. 6 [30]. These results showed that in this system k1 depends directly upon the reciprocal of [SA]T,o, which Allain et al. rather vaguely credit to the ‘diffusion of radicals within the porous network’ [30]. However, this same (reciprocal) relationship is predicted by the model, since k1 = ln2/t1/2, which, when combined with Eq. (8), reveals,

$$ k_{1} = \, \ln 2.k_{o} \times Abs_{T} \times I_{o} /(t_{1/2} .\left[ {SA} \right]_{T,o} ) $$
(12)

where τ1/2 = 1.26, calculated using Eq. (11), given m = 1. The inverse relationship between k1 and [SA]T,o, is as a direct consequence of the under lying zero-order nature of the kinetics, for which t1/2 = [SA]o/2ko, despite the fact that the overall decay kinetics appear first order.

As is clear from the [SA]T,τ/[SA]T,o vs. τ decay curves illustrated in Fig. 5, and the straight line relationship between apparent reaction order, m, and the absorbance of the film, AT, see Eq. (10), in the case of a porous photocatalytic film with SA inside the film, as illustrated in Fig. 4, the kinetic model predicts that the variation of the apparent order of reaction, m, can be simply changed by altering the value of AT. Obviously, this change can be effected by varying the thickness of the photocatalytic film, b, and fixing the wavelength of the ultra-bandgap irradiation, λex, which is usually 365 nm in the case of TiO2. However, it is also possible to vary AT, and so the model-predicted value of m, by fixing the thickness of the photocatalytic film and varying λex, since this will also vary the value of AT, given the absorption coefficient of TiO2, α(λ) varies markedly with λex; e.g. α(λ) is ca. 5 × 104 cm−1 at 365 nm and ca. 5.1 × 105 cm−1 at 254 nm [34]. A table summarising the various definitions and parameters used in creating the non-networked photocatalytic particles model is given in section S2 in the ESI.

4 SA layer inside a photocatalytic film of networked photocatalytic particles

As we have seen, the developed Ollis model, based on attenuation of the incident UV radiation by the layers of TiO2 particles, provides an excellent fit to the kinetics of reaction (1), when the SA is inside a mesoporous photocatalytic film in which the photocatalytic particles are isolated. But, what if the photocatalytic particles are not isolated, but rather significantly networked, as illustrated in Fig. 7? Such a setup might be expected to be found when using mesoporous powder or sol–gel photocatalytic films.

Fig. 7
figure 7

Schematic illustration of SA layer (light blue) inside a photocatalytic film of networked/connected photocatalytic particles (white)

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Based on what has been found for compact and microporous TiO2 films, see Sect. 2, it might well be expected that in such a film, any photogenerated electrons and holes would be able to move rapidly and efficiently throughout the film and so NOT exhibit the UV filtering effect that underpins the Ollis model described in Sect. 3. In several publications, Ollis, most likely unaware of the significance of photocatalyst particle networking, mistakenly suggests [35, 38] that the isolated particle model of the kinetics of SA removal described in Sect. 3 also applies to networked systems, such as illustrated in Fig. 7. As evidence, Ollis usually cites a reported example of a 90 nm thick film of P25 powder coated with SA, which exhibits approximate 1st order decay kinetics when irradiated with UVA radiation [11, 35, 38], the results of which are illustrated in Fig. 8.

Fig. 8
figure 8

Normalised plot of the measured decrease in [SA] as a function of irradiation time, t, using UVA (black dots) or UVC (open circles) radiation, for a 90 nm film of P25 TiO2 powder film on glass, dip-coated with SA, with [SA]o = ca 11 cm−1 [11]. The irradiances of the UVA (365 nm) and UVC (254 nm) radiation, were 6.9 and 6.0 mW cm−2, respectively. The insert diagram is the reported UV/Vis absorption spectrum of the P25 film, with an absorbance of 0.55 [11]

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As we have seen, the fully developed form of the Ollis model predicts that the order of reaction (1), m, is directly related to the absorbance of the photocatalytic film, see Eq. (10), and that 1st order decay kinetics are only expected if the film absorbance, AT, is ca. 0.904. However, a brief inspection of the reported absorbance spectrum of the 90 nm P25 film, illustrated in the insert plot in Fig. 8, reveals AT to be only ca. 0.55 at 365 nm, and most of this is most likely due to specular reflection and scattering, so that the actual absorbance of the P25 TiO2 film is likely to be much less than 0.55, and so, for this system, the isolated photocatalytic particle model predicted value of m should be nearer to 0 than 1.

The likely low absorbance of the photocatalytic film at 365 nm (after the contributions due to scattering and specular reflection are removed) and yet high value for the apparent order of the decay of [SA] with UVA irradiation time (m = 1; k1(UVA) = 0.003 min−1), strongly suggests that the Ollis model is not appropriate for this and other networked photocatalytic films. However, the most compelling piece of evidence of the inappropriateness of the isolated photocatalytic particle model is the reported decay of [SA] as a function of irradiation time for the same film, when irradiated with UVC radiation, the results for which are also illustrated in Fig. 8 [14]. As we have seen, the Ollis model (for non-networked/isolated photocatalytic particle films) predicts that the greater the value for AT the greater the order of the reaction, see Eq. (10), and we know that the absorption coefficient for TiO2 at 254 nm is ca. 10 times that at 365 nm [34], thus, if m = 1 under 365 nm irradiation, then the Ollis model predicted value for m for the same 90 nm P25 film when exposed to 254 nm radiation should be >  > 1, and yet it is found to be also approximately first order, although much faster with k1(UVC) = 0.057 min−1. This feature of the same value of m, for two very different values of AT, is completely opposite to the behaviour predicted by the Ollis isolated particle model, as is the observation that k1(UVC) >  > k1(UVA). This, and other reported examples, show clearly that networked photocatalytic particle systems, such as illustrated in Fig. 1 and 7, behave very differently to isolated particle systems, such as illustrated in Fig. 4. In addition, reports on the kinetics exhibited by networked photocatalytic films are much more common than those on isolated photocatalytic films, and so it is worth exploring in more depth why such systems might exhibit kinetics for reaction (1), in which m is > 0, when zero-order kinetics are expected. The likely underlying cause is a distribution of activities, i.e. different values of ko, throughout the film; a feature that has reported before for photocatalytic colloids and films, but not so far recognised in photocatalytic films and reaction (1) [39].

5 Conclusions

The kinetics of a photocatalytic removal of SA via reaction (1) are expected, and often found, to be zero-order, i.e. m = 0, when the SA film lies on top of the photocatalytic film, based on a simple model of the system in which the SA occupies all reactive sites for most the observed photocatalytic decay process. However, if the SA lies within the photocatalytic film, and the photocatalytic particles are isolated from one another, then a more fully developed version of the kinetic model first proposed by Ollis [35, 38] shows that the observed reaction order, m, will depend directly upon the overall absorbance of the photocatalytic film, AT. However, such a system is not common and so this isolated photocatalytic particle model will find only limited application. The isolated particle model cannot be used to explain the kinetics for reaction (1), where m > 0, observed for photocatalytic films in which the SA is still inside the film, but where the photocatalytic particles are networked. An example of the latter system is a 90 nm, mesoporous powder film of P25 impregnated with SA, which when irradiated with either UVA or UVC irradiation, yielded 1st order kinetics, with k1(UVC) >  > k1(UVA). A networked film of photocatalytic particles, unlike one comprising only isolated particles, allows the rapid and efficient movement of photogenerated electrons and holes throughout the film. However, such a system, with the SA inside and/or on top of the photocatalytic film, might be expected to exhibit zero-order kinetics, and not, say, the 1st order kinetics exhibited by a 90 nm, mesoporous powder film of P25 TiO2 dip-coated in SA. It appears likely that a distribution of reaction activities, i.e. values of ko, throughout the film are responsible for networked photocatalytic films, such as the P25 film described above, exhibiting decay kinetics for reaction (1), where m > 0. A paper that describes and tests an appropriate kinetic model of such a system is under preparation.