# Influence of Irradiance, Flow Rate, Reactor Geometry, and Photopromoter Concentration in Mineralization Kinetics of Methane in Air and in Aqueous Solutions by Photocatalytic Membranes Immobilizing Titanium Dioxide

Authors: Ignazio Renato Bellobono; Mauro Rossi; Andrea Testino; Franca Morazzoni; Riccardo Bianchi; Giulia de Martini; Paola Maria Tozzi; Rodica Stanescu; Cristina Costache; Liliana Bobirica; Mauro Luigi Bonardi; Flavia Groppi
Journal: International Journal of Photoenergy
 (2008-02-05)

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## Abstract

Photomineralization of methane in air (10.0–1000 ppm (mass/volume) of C) at100% relative humidity (dioxygen as oxygen donor) was systematically studied at 318±3 K in an annular laboratory-scale reactor by photocatalytic membranes immobilizing titanium dioxide as a function of substrate concentration, absorbed power per unit length of membrane, reactor geometry, and concentration of a proprietary vanadium alkoxide as photopromoter. Kinetics of both substrate disappearance, to yield intermediates, and total organic carbon (TOC) disappearance, to yield carbon dioxide, were followed. At a fixed value of irradiance (0.30 W⋅cm-1), the mineralization experiments in gaseous phase were repeated as a function of flow rate (4–400 m3⋅h−1). Moreover, at a standard flow rate of 300 m3⋅h−1, the ratio between the overall reaction volume and the length of the membrane was varied, substantially by varying the volume of reservoir, from and to which circulation of gaseous stream took place.
Photomineralization of methane in aqueous solutions was also studied, in the same annular reactor and in the same conditions, but in a concentration range of 0.8–2.0 ppm of C, and by using stoichiometric hydrogen peroxide as an oxygen donor. A kinetic model was employed, from which, by a set of differential equations, four final optimised parameters, k1 and K1, k2 and K2, were calculated, which is able to fit the whole kinetic profile adequately. The influence of irradiance on k1 and k2, as well as of flow rate on K1 and K2, is rationalized. The influence of reactor geometry on k values is discussed in view of standardization procedures of photocatalytic experiments. Modeling of quantum yields, as a function of substrate concentration and irradiance, as well as of concentration of photopromoter, was carried out very satisfactorily. Kinetics of hydroxyl radicals reacting between themselves, leading to hydrogen peroxide, other than with substrate or intermediates leading to mineralization, were considered, and it is paralleled by a second competition kinetics involving superoxide radical anion.


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## Body

## 1. Introduction

Air and water pollution is
notoriously a serious problem facing all anthropic activities throughout the
world. To reduce this problem, many physical, chemical, and biological
technologies are available [1]. Conventional methods based on stripping, such
as adsorption by activated carbon, result only in transfer of pollutants from
one phase to another, and not to integral destruction. On another side, thermal
oxidation techniques may be valuable but surely not cost effective, particularly
at low contamination values, due to the added fuel consumption; furthermore these methods contribute
to massive carbon dioxide production. Photocatalytic processes on
semiconductors, on the contrary, are one of the newer advanced oxidation
processes (AOP) techniques. They were developed during the last twenty five
years [1–9], in the presence of catalysts, such as titanium dioxide, with UV
radiation. If the UV radiation is from the sun, the treatment costs are reduced
drastically by transforming photocatalysis in one of the most appealing and
environmentally friendly processes for complete mineralization of organic
pollutants. Furthermore, photocatalytic processes may be used as a pretreatment
of toxic chemicals, in order to convert them into fully biodegradable compounds
to be finally processed by the most economical technology presently available,
that of active sludge [10]. Combination of photocatalysis with active sludge
techniques is undoubtedly one of the most promising technologies to degrade and
mineralize, efficiently and inexpensively, wastes containing toxic compounds.The major problem in
photocatalysis, from the point of view of industrial applicability, is given by
the necessity of immobilizing the semiconductor photocatalyst, by firmly anchoring
it to a suitably reacting structure, and of reaching the highest performance as
possible in photocatalytic reactors, in continuous mode [11]. These two aspects
(kind of immobilization, as linked to kinetic modeling of the whole course of
the photomineralization process, and quantum yields) need therefore to be
considered as priority options for engineering applications. In all preceding
papers of this series (see, e.g., among the most recent ones [12–14]), the main
concern has been devoted to these topics, and immobilization of semiconductor
photocatalyst and its photopromoting agents in a membrane structure has been
the choice, in order to manufacture modular membrane reactors, the performance
of which has been effectively estimated as one of the highest for energy
efficiency [11].From the point of view
of mechanisms of surface photochemical reactions that take place in
heterogeneous systems, a recent article [15] has criticized the a priori assumed validity of the Langmuir-Hinshelwood
kinetic model to interpret the experimental observations, as well as the
assertion that the kinetics of a heterogeneous photoreaction are either
first-order or half-order dependent on photon flow. Such a criticism has
already been emphasized in the literature also from the point of view of
engineering applications, and dates back to earlier pilot plant studies [16],
which have shown, for example, the influence of flow rate on apparent
thermodynamic constant of adsorption/desorption, relative to the
Langmuir-Hinshelwood model, as well as the inadequacy of this model to fit
kinetics of mineralization, other than in the segment of the initial rate
[12–14], particularly when using immobilized photocatalysts, so that this
pseudothermodynamic parameter of the Langmuir-Hinshelwood model should have a,
partly at least, kinetic character.It is well known that,
in carefully deaerated water, and in the absence of any kind of oxygen donors,
following radiation absorption by the semiconductor, photogenerated holes react
with hydroxyl groups of water to give hydroxyl radicals•OH, while
photogenerated electrons reduce hydroxonium ions and cause hydrogen evolution.
On the contrary, in aerated water, the photogenerated conduction-band electrons
reduce dissolved oxygen or other oxygen donors added to this purpose to yield O2•− in acid-base equilibrium with HO2•.  The possibility of the latter reaction to
take place quantitatively is of uttermost importance in environmental
applications of photocatalyis, because, in the last case, oxidation of organic
compounds may be carried out by HO2• together with •OH
radicals. This allows to obtain a fourfold maximum quantum yield with respect
to that permissible if each absorbed photon would be able to produce a single
hydroxyl radical only. This occurrence has been shown as effective [12, 16, 17]
when using, for example, ozone as oxygen donor and when promoting the activity
of the immobilized semiconductor by suitable doping agents, such as Co(III) or
V(V), coimmobilized with the semiconductor itself in a membrane structure and acting as
scavengers of generated photoelectrons.Comparison of efficiency
of different kinds of supported or immobilized photocalysts, and objective,
quantitative characterization of their photocatalytic power are thus the major
problems to define kinetic reactivity. In most of literature works, this kind
of assessment is often made simply by matching qualitatively concentration
profiles of degraded species. In addition, in many cases described in the
literature, no regard is made to total organic carbon (TOC) mineralization, but
merely to the transformation of substrate into some intermediate compound, as
the first step of the complicated reaction mechanism leading finally to carbon
dioxide. Moreover, it is a common practice, even when quantitative evaluations
are made, to consider the photocatalytic process as a first-order reaction,
while it has been definitely ascertained that apparent reaction order varies
with the concentration of substrate [13, 16]. With an evident transition from a
limiting zero-order, at high concentrations, to a limiting first-order at low
concentrations. Modeling of photocatalytic reactions, on the contrary, in a
wide range of concentrations, and over all the kinetic concentration profile of
TOC, leading to full mineralization, has been approached systematically in
previous papers of this series [12–14, 18], mostly for processes carried out in
aqueous solutions. This has been done also from the standpoint of quantum
yields and energy efficiencies, a very important aspect, which is often neglected
in the literature pertinent to photocatalysis.In the present paper,
modeling will be extended to photocatalytic kinetic runs in gaseous phase, by
using methane in air as a model molecule, both to apply the four-parameter
kinetic model used successfully in preceding studies [12–14, 18] for
fitting the whole kinetic profile, and to broaden the application of this
model, as a function of all variables which show an influence on the
photocatalytic kinetics, and consequently play a primary role in all trustworthy
characterization procedures of immobilized materials. The dependence of the
four parameters of the kinetic model cited above [12–14, 18] on flow
rate, on reactor geometry, on radiation flow, and on the concentration of a
proprietary photopromoter coimmobilized with the semiconductor in the
photocatalytic membranes will be first examined. By this way, information,
preliminarly investigated in a previous work [19] on methane in air, will be
implemented and get deeper. Secondly, the influence of these variables on the
same parameters above [12–14], relatively to experiments carried out
in aqueous solutions, will be checked in order to systematically compare
reactivity in liquid and gaseous phases. Finally, the dependence of quantum
yields on the concentration of substrate and on photon flow will be considered
and analyzed, with the goal of attaining, by all these variables expressed in
the most convenient ways, a complete rationalization of the photocatalytic
process, both in liquid and gaseous phases, from the engineering point of view,
as well from the perspective of establishing a reliable standardization method
of the photocatalytic performance of materials.


## 2. Experimental

### 2.1. Materials

Methane was obtained
from Fluka (GC purity greater than 99.8%). It was used as received with no
further purification. Ultra pure water, to be used for preparation of methane
solutions, or to be aerosolized in the reactor, when performing kinetic runs of
methane in air, to maintain a 100% relative humidity at the operating
temperature of the photoreactor (maximum contents of Na+and heavy
metal ions 0.02 and 0.004 mg Kg−1, resp.), was obtained by
cross-flow ultrafiltration on composite membranes immobilizing active carbon
and nuclear grade ion exchange resins, as described [20]. Concentration of
substrate in the gas phase was 10.0–1000 ppm (mass
expressed as carbon/volume), while in aqueous solution it could be varied, for
solubility reasons, only between 0.80 and 2.00 ppm.


### 2.2. Photocatalytic Membranes

The photocatalytic membranes (PHOTOPERM BIT/313), kindly supplied by
B.I.T. srl, Milan, I, were standard photocatalytic membranes, immobilizing 30 ± 3 wt.% of titanium dioxide (P25 by Degussa, Germany) in the absence and in the
presence of a photocatalytic promoter, as cocatalyst. In the latter case, a
proprietary synergic mixture of tri-(t-butyl)-
and tri-(i-propyl)vanadate(V) [10]
was used, by varying the vanadium concentration in the range 0.1–10 mol/mol % with
respect to that of titanium. Photocatalytic membranes [16, 21], and more
generally membranes, prepared by photografting, to immobilize reagents,
catalysts, and sorbents [22–24], were described and characterized in previous
studies. These membranes were prepared (patents pending) by grafting and
graft-polymerizing, onto a nonwoven microporous polypropylene tissue, 250 ± 9 g⋅m−2 of a prepolymeric blend containing 30 ± 3 wt.% of titanium dioxide (P25 by
Degussa, Germany), under rheological control, in the presence of proprietary
photoinitiating and photosensitising systems.


### 2.3. Apparatus and Procedures

The
laboratory-scale photoreactor was substantially the same as that already
described [25], with some differences in the materials and operating
procedures, as it will be specified later on, and the change is that it was
made gas tight to avoid any leakage of substrate and/or intermediates through
the vapour phase, both when operating with gaseous methane in air or with its
aqueous solutions. Contrarily to procedure of previous work [19], in which,
when operating in the gaseous phase, an aqueous solution of hydrogen peroxide
was aerosolized continuously into the reactor, in order to supply the
stoichiometric amount of this oxygen donor, in the present work, only ultra
pure water was aerosolized in the photoreactor, just to maintain a 100%
relative humidity at 318 ± 3 K, which was the operating temperature of the
reactor. This was made, to check the influence on the rate of the oxygen
content of air, instead of using hydrogen peroxide. Stoichiometric hydrogen
peroxide, on the contrary, was always used when operating with aqueous
solutions of methane. Overall volume of gaseous or liquid phase being treated
was 4.000±0.005 L, in standard experiments; the ratio between the overall
reacting volume and the length of the lamp, corresponding to the length of the
irradiated side of the membrane, was 160 ± 6 cm3/cm. A high-pressure
mercury arc lamp with a nominal power of 1.00 KW was employed, kindly supplied
by Chimia Prodotti e Processi (Muggiò, Milan,
Italy): it was
further provided with a step-by-step power regulation device, so that power
absorbed by the membrane, as determined actinometrically, could be varied
between 0.10 and 4.0 W⋅cm−1.
The membrane being
concentric to the lamp in the photoreactor used, absorbed power per unit length
of lamp was also the same, if referred to unit length of membrane. At 0.30 W⋅cm−1,
the overall power absorbed by the membrane, within the absorption range of
immobilized semiconductor, in the experimental conditions of the present work,
was 30 W, corresponding to 4.45 × 10−5 Einstein s−1. In
this paper, as well as in all preceding papers of this series, when concerning
laboratory-scale experiments carried out in the presence of hydrogen peroxide
as an oxygen donor, the radiating flow, unless otherwise stated, being filtered
by a suitable borosilicate glass, corresponded to a radiation wavelength range
from the band gap of TiO2 downwards to 315 nm, so that direct
photolysis of hydrogen peroxide to give hydroxyl radicals was inhibited. Owing
to the refrigeration system of the lamp, by means of water circulating in the
lamp sheath, made of quartz, mean temperature, during the runs, was 318 ± 3 K.In the present, as well
as in previous papers of this series, membranes were placed and fixed coaxially
with the lamp, in such a way that the flow was perpendicular to the membrane.
Owing to the microporous structure of the membrane, the pressure drop was very
modest: it corresponded to 0.9–1.6 mm Hg, when
the flow rate of the liquid system was 4 m3/h in the laboratory-scale
photoreactor.During some of the gaseous
phase experiments, the flow rate was varied between 4 and 400 m3/h.
In these experiments, in order to examine the influence of flow rate on
parameters of kinetic model used, irradiance was fixed at a value corresponding
to 0.30 W⋅cm−1.The standard flow rate
in gaseous phase kinetic runs, to study the influence of irradiance on
parameters above, was 300 m3/h. In this latter experimental
condition of flow rate, the ratio between the overall reaction volume and the
length of the membrane was varied substantially by varying the volume of
reservoir, from and to which circulation of gaseous stream took place. This was
carried out to study the influence of reactor geometry on kinetic parameters
above, and by operating at a constant irradiance, corresponding to 0.30 W⋅cm−1The
disappearance of methane, as such, was followed by GC-MS
quantitative analysis into the injection port of a GC-MS system. A Varian 3400
with a septum-equipped programmable injector was used. In the GC oven, a30⁢m×0.53⁢nm DB5MS megabore column was installed with the following temperature
programme: 20°C for 1 minute followed by a temperature raise of 5°C/min to
240°C, which was held for 4 minutes.As a carrier gas, He was used at a flow
rate of 25 mL/min. The GC was interfaced via jet separator (0.3 mm Hg in the
separator and 0.03 mm Hg in the analyser) and a transfer line (270°C) to an
ITS40 ion trap mass-spectrometer (ITMS). The ion trap was operated at 300°C in
the electron impact mode, scanning from 35 M/Z to 550 M/Z in 1.5 second. The
GC-ITMS data were acquired on a 386/387 Compaq personal computer with Saturn I
software (Varian). Methane was identified by its mass spectrum and standard
samples. Quantification was based on seven-point calibration curves using, as
internal standard, a standard sample containing perdeuterated methane.In
order to study the relationship between the rate of methane disappearance, as
such, and the overall rate of organic carbon disappearance, this latter was
also followed by total organic carbon (TOC) analysis. To this purpose, a Shimadzu TOC-V
instrument was used, by which the contribution of inorganic carbon present was
always evaluated, in order to obtain TOC by difference from total carbon and
inorganic carbon determinations. Determinations were accurate within 20 ppb C.During all the duration of the runs,
no sensible decrease of activity of the immobilized photocatalyst was observed,
as checked both by random repetition of experiments at various initial
concentrations of the hydrocarbons, both in the liquid and in the gaseous
phase, and by reiteration of whole series of tests at the beginning and at the
end of the prolonged period, throughout which experimentation has been carried
out.


### 2.4. Kinetic Modeling

Kinetic modeling was carried
out by generalizing procedures followed in preceding papers [12, 13, 26]. These
procedures have not the goal of proposing and checking photochemical
mechanisms, but simply its
goal is to reproduce closely experimental data, for engineering purposes,
without any strict implication on the true mechanisms.If
mineralization of substrateS to CO2
is supposed to occur through one single
intermediate I, following scheme (1)
(1)S⟶I⟶CO2,
and if both S and I show a
competitive apparent adsorption onto the immobilized semiconductor surface, as
expressed by apparent adsorption constants K1 and K2, respectively, models for experimental
data, used in nonlinear regression analysis, are not expressed in a closed-form  equation
(2)y(calc)=f(x),
but as
the following system of first-order ordinary differential equations in the
dependent variables CS,CI and CCO2:
(3)(dCSdt)=−k1⋅K1⋅CS1+K1⋅CS+K2⋅CI,(4)(dCIdt)=k1⋅K1⋅CS⋅k2⋅K2⋅CI1+K1⋅CS+K2⋅CI,(5)(dCCO2dt)=k1⋅K1⋅CI1+K1⋅CS+K2⋅CI,
where C denotes concentrations of species to which the pertinent suffix
refer, t time; k1 and k2 the kinetic constants relative to
degradation of S and I, respectively. Intermediate I is supposed to simulate the behavior
of all the often uncountable, numerous intermediates, which are on the route
from the substrate S to CO2.
Experimentally speaking, only kinetic profiles of S and CO2 may be easily followed. Even if, for the
molecule chosen in the present investigation, a limited number of intermediates
may be reasonably envisaged from the substrate to CO2, the same is
not true [12, 13, 26] for aromatic and/or heterocyclic compounds, or still for
long-chain aliphatics, which have been the object of previous investigations.Random
errors int can be neglected, and only the random errors in the dependent variables
are considered.The error sum,G(k1,k2,K1,K2)=∑i=1nwi[CS(exp)i−CS(calc)i]2,  is minimized to obtain the best values of the   k1,k2,K1,K2 parameters; CS(exp)i and CS(calc)i represent
the n measured and calculated
substrate concentration values,
respectively, and wi=1/σ2(CS(exp)i)
is the weighting factor.Furthermore the
conservative balance of carbon has to be accounted for and verified
experimentally, all concentrations of substrate and intermediate being
expressed in terms of carbon content, as obtained from TOC analysis(6)Cc⁢(at⁢time⁢t)=CTOC⁢(at⁢time⁢0)=CS⁢(at⁢timee⁢t)+CI⁢(at⁢time⁢t)+CCO2⁢(at⁢time⁢t),
where Cc represents the total carbon, both organic and inorganic, carbon dioxide
representing the final product of the mineralization process
(6a)CTOC⁢(at⁢time⁢0)be⁢ing⁢equal⁢to⁢CS⁢(at⁢time⁢0),(6b)CTOC⁢(at⁢time⁢t)be⁢ing⁢equal⁢to⁢CS⁢(at⁢time⁢t)+CI⁢(at⁢time⁢t).The
major limitation of (6) is to regard only intermediates containing carbon,
which is,  anyway, the most common condition in degradation of organics. If this
should not be the case, (6) should be substituted by
(7)Cc⁢(at⁢time⁢t)=CTOC⁢(at⁢time⁢t)=CS⁢(at⁢time⁢t)=CCO2⁢(at⁢time⁢t)
and substitute (5) by
(8)(dCCO2dt)=−(dCSdt).Equations
(3)–(6) constitute a
suitable model for temporal disappearance of TOC, which is a relevant
analytical parameter to follow environmental pollution problems.Whent=0 (beginning of photodegradation), CI is completely negligible with respect to CS.
Furthermore, the hypotheses that k1⁢~k2 and symmetrically that K1⁢~K2, even if this
is not always true, may be used, in some cases, simply as a starting
approximation. With this approximation, (3) can be simplified  to
(9)r0=k1⋅K1⋅C01+K1⋅C0,
where r0 is the initial rate,
and C0 represents the initial concentration of
substrate S. The reciprocal of (9)
has exactly the same form of the Langmuir-Hinshelwood model (13). Moreover,
being initially CI=0, from (5) and (6) one obtains, at t=0,
(10)(dCCO2dt)=(dCTOCdt)=0.
In other words, the formation of
carbon-containing intermediates, if the latter are not photodegraded yielding
CO2 at a
higher rate than that of the substrate, gives rise to a characteristic plateau
in the curve of TOC content versus
time. This trend is only approximated experimentally, both because there is
often a preferential, even if not prevailing, route to rapid CO2 formation
from S, and because intermediates
are often more reactive than the substrate itself towards photodegradation, so
that TOC disappearance is initially low, particularly in aromatic compounds,
usually around one order of magnitude lower than that of the substrates, but is still measurable.Now,
let us suppose that a timet* exists,
such as that for t>t*,CS≪CI. At time t*, (4) becomes
(11)dCIdt⁢~−k2⋅K2⋅CI1+K2⋅CI,
and as for (6) in these conditions CTOC~CI, (11) becomes
(12)dCTOCdt⁢~−k2⋅K2⋅CTOC1+K2⋅CTOC.
An important experimental result is
thus substantiated and rationalized in these cases, where the rate of
mineralization of intermediates is much lower than that of transformation of
substrate into an intermediate (the cases of aromatic compounds
particularly):  the curve CTOCversus time explicitly follows a Langmuirian-type rate law (13), by which k and K parameters acquire the physical significance of k2 and K2,
as stated above.That
timet* effectively exists, as a time
at which the substrate is completely converted into intermediates, even with a
modest decrease of TOC content and nearly complete mineralization of eventual
heteroatoms present in the substrate, is experimentally recognized by both
literature data [27] and by results of our preceding work [26].In
most cases, bothk and K couples are accessible experimentally,
as starting values from initial-rate data, relative to substrate, and TOC as
well, using the Langmuirian equation (13)
(13)1r0=1k+1k⁢KC0,
where r0 is the initial rate of substrate
disappearance, whether measured by direct analysis of substrate itself (to
obtain the k1 and K1 couple) or by the rate of
decrease of total organic carbon (TOC) as a function of time (to obtain the k2 and K2
couple). The
values drawn from (13) may be used as starting values to find the absolute
minimum in the error sum, G, with respect to k1,K1,k2 and K2 kinetic parameters. In particular cases, as
stated before, when only k2 and K2 values are available experimentally by TOC
measurements, the approximation k1⁢~k2 and K1⁢~K2 can  be
used as a starting point in the minimization algorithm as has been suggested on
a theoretical basis [28]. Variation of kinetic parameters, in order to optimize
the fitting, may additionally be restricted within the expected range of
experimental uncertainty, but also chemical considerations may be of great
help, as well as simultaneous consideration of k and K parameters for
other chemically related substrates and/or intermediates, which may be studied
by the same methodology.


### 2.5. Modeling of Quantum Yields as a Function of Irradiance and of Substrate Concentration

By using the optimized parameters
of the section above, the rates of photomineralization were evaluated as a
function of initial concentration,C0, and consequently, by operating at a certain value of the
photon flow, the corresponding
quantum yields Φ0 were obtained.Quantum yieldsΦ0, calculated from rates, followed an apparently
Langmuirian function of initial concentration of substrate C0, by which Φ∞ values at infinite concentration could be obtained as(14)1Φ0=1Φ∞+1Φ∞C0K,
where the K value substantially coincided with the lowest between the two K1 and K2 constants
above, for many molecules being K1⁢~K2.Finally,
by repeating all sets of experiments, at different values of the absorbed
radiant power per unit length of photocatalytic membrane, which was varied in
the range 0.10–4.0 W⋅cm−1,
and by applying (14) to each set of these experiments, the Φ∞ values, as a function of the absorbed radiant
power, per unit length of photocatalytic membrane, were obtained.


### 2.6. Modeling of Quantum Yields as a Function of Photopromoter Concentration

For experiments in which the
photopromoter was added, the same procedure described in the preceding
paragraph was adopted, and theΦ∞ values obtained at a high value of absorbed irradiance, typically Φ∞ values at 4 W⋅cm−1, much smaller
than the maximum allowable Φ∞ values corresponding to irradiances tending to zero, were plotted as a function
of concentration of photopromoter in the photocatalytic membrane.


## 2.1. Materials

Methane was obtained
from Fluka (GC purity greater than 99.8%). It was used as received with no
further purification. Ultra pure water, to be used for preparation of methane
solutions, or to be aerosolized in the reactor, when performing kinetic runs of
methane in air, to maintain a 100% relative humidity at the operating
temperature of the photoreactor (maximum contents of Na+and heavy
metal ions 0.02 and 0.004 mg Kg−1, resp.), was obtained by
cross-flow ultrafiltration on composite membranes immobilizing active carbon
and nuclear grade ion exchange resins, as described [20]. Concentration of
substrate in the gas phase was 10.0–1000 ppm (mass
expressed as carbon/volume), while in aqueous solution it could be varied, for
solubility reasons, only between 0.80 and 2.00 ppm.


## 2.2. Photocatalytic Membranes

The photocatalytic membranes (PHOTOPERM BIT/313), kindly supplied by
B.I.T. srl, Milan, I, were standard photocatalytic membranes, immobilizing 30 ± 3 wt.% of titanium dioxide (P25 by Degussa, Germany) in the absence and in the
presence of a photocatalytic promoter, as cocatalyst. In the latter case, a
proprietary synergic mixture of tri-(t-butyl)-
and tri-(i-propyl)vanadate(V) [10]
was used, by varying the vanadium concentration in the range 0.1–10 mol/mol % with
respect to that of titanium. Photocatalytic membranes [16, 21], and more
generally membranes, prepared by photografting, to immobilize reagents,
catalysts, and sorbents [22–24], were described and characterized in previous
studies. These membranes were prepared (patents pending) by grafting and
graft-polymerizing, onto a nonwoven microporous polypropylene tissue, 250 ± 9 g⋅m−2 of a prepolymeric blend containing 30 ± 3 wt.% of titanium dioxide (P25 by
Degussa, Germany), under rheological control, in the presence of proprietary
photoinitiating and photosensitising systems.


## 2.3. Apparatus and Procedures

The
laboratory-scale photoreactor was substantially the same as that already
described [25], with some differences in the materials and operating
procedures, as it will be specified later on, and the change is that it was
made gas tight to avoid any leakage of substrate and/or intermediates through
the vapour phase, both when operating with gaseous methane in air or with its
aqueous solutions. Contrarily to procedure of previous work [19], in which,
when operating in the gaseous phase, an aqueous solution of hydrogen peroxide
was aerosolized continuously into the reactor, in order to supply the
stoichiometric amount of this oxygen donor, in the present work, only ultra
pure water was aerosolized in the photoreactor, just to maintain a 100%
relative humidity at 318 ± 3 K, which was the operating temperature of the
reactor. This was made, to check the influence on the rate of the oxygen
content of air, instead of using hydrogen peroxide. Stoichiometric hydrogen
peroxide, on the contrary, was always used when operating with aqueous
solutions of methane. Overall volume of gaseous or liquid phase being treated
was 4.000±0.005 L, in standard experiments; the ratio between the overall
reacting volume and the length of the lamp, corresponding to the length of the
irradiated side of the membrane, was 160 ± 6 cm3/cm. A high-pressure
mercury arc lamp with a nominal power of 1.00 KW was employed, kindly supplied
by Chimia Prodotti e Processi (Muggiò, Milan,
Italy): it was
further provided with a step-by-step power regulation device, so that power
absorbed by the membrane, as determined actinometrically, could be varied
between 0.10 and 4.0 W⋅cm−1.
The membrane being
concentric to the lamp in the photoreactor used, absorbed power per unit length
of lamp was also the same, if referred to unit length of membrane. At 0.30 W⋅cm−1,
the overall power absorbed by the membrane, within the absorption range of
immobilized semiconductor, in the experimental conditions of the present work,
was 30 W, corresponding to 4.45 × 10−5 Einstein s−1. In
this paper, as well as in all preceding papers of this series, when concerning
laboratory-scale experiments carried out in the presence of hydrogen peroxide
as an oxygen donor, the radiating flow, unless otherwise stated, being filtered
by a suitable borosilicate glass, corresponded to a radiation wavelength range
from the band gap of TiO2 downwards to 315 nm, so that direct
photolysis of hydrogen peroxide to give hydroxyl radicals was inhibited. Owing
to the refrigeration system of the lamp, by means of water circulating in the
lamp sheath, made of quartz, mean temperature, during the runs, was 318 ± 3 K.In the present, as well
as in previous papers of this series, membranes were placed and fixed coaxially
with the lamp, in such a way that the flow was perpendicular to the membrane.
Owing to the microporous structure of the membrane, the pressure drop was very
modest: it corresponded to 0.9–1.6 mm Hg, when
the flow rate of the liquid system was 4 m3/h in the laboratory-scale
photoreactor.During some of the gaseous
phase experiments, the flow rate was varied between 4 and 400 m3/h.
In these experiments, in order to examine the influence of flow rate on
parameters of kinetic model used, irradiance was fixed at a value corresponding
to 0.30 W⋅cm−1.The standard flow rate
in gaseous phase kinetic runs, to study the influence of irradiance on
parameters above, was 300 m3/h. In this latter experimental
condition of flow rate, the ratio between the overall reaction volume and the
length of the membrane was varied substantially by varying the volume of
reservoir, from and to which circulation of gaseous stream took place. This was
carried out to study the influence of reactor geometry on kinetic parameters
above, and by operating at a constant irradiance, corresponding to 0.30 W⋅cm−1The
disappearance of methane, as such, was followed by GC-MS
quantitative analysis into the injection port of a GC-MS system. A Varian 3400
with a septum-equipped programmable injector was used. In the GC oven, a30⁢m×0.53⁢nm DB5MS megabore column was installed with the following temperature
programme: 20°C for 1 minute followed by a temperature raise of 5°C/min to
240°C, which was held for 4 minutes.As a carrier gas, He was used at a flow
rate of 25 mL/min. The GC was interfaced via jet separator (0.3 mm Hg in the
separator and 0.03 mm Hg in the analyser) and a transfer line (270°C) to an
ITS40 ion trap mass-spectrometer (ITMS). The ion trap was operated at 300°C in
the electron impact mode, scanning from 35 M/Z to 550 M/Z in 1.5 second. The
GC-ITMS data were acquired on a 386/387 Compaq personal computer with Saturn I
software (Varian). Methane was identified by its mass spectrum and standard
samples. Quantification was based on seven-point calibration curves using, as
internal standard, a standard sample containing perdeuterated methane.In
order to study the relationship between the rate of methane disappearance, as
such, and the overall rate of organic carbon disappearance, this latter was
also followed by total organic carbon (TOC) analysis. To this purpose, a Shimadzu TOC-V
instrument was used, by which the contribution of inorganic carbon present was
always evaluated, in order to obtain TOC by difference from total carbon and
inorganic carbon determinations. Determinations were accurate within 20 ppb C.During all the duration of the runs,
no sensible decrease of activity of the immobilized photocatalyst was observed,
as checked both by random repetition of experiments at various initial
concentrations of the hydrocarbons, both in the liquid and in the gaseous
phase, and by reiteration of whole series of tests at the beginning and at the
end of the prolonged period, throughout which experimentation has been carried
out.


## 2.4. Kinetic Modeling

Kinetic modeling was carried
out by generalizing procedures followed in preceding papers [12, 13, 26]. These
procedures have not the goal of proposing and checking photochemical
mechanisms, but simply its
goal is to reproduce closely experimental data, for engineering purposes,
without any strict implication on the true mechanisms.If
mineralization of substrateS to CO2
is supposed to occur through one single
intermediate I, following scheme (1)
(1)S⟶I⟶CO2,
and if both S and I show a
competitive apparent adsorption onto the immobilized semiconductor surface, as
expressed by apparent adsorption constants K1 and K2, respectively, models for experimental
data, used in nonlinear regression analysis, are not expressed in a closed-form  equation
(2)y(calc)=f(x),
but as
the following system of first-order ordinary differential equations in the
dependent variables CS,CI and CCO2:
(3)(dCSdt)=−k1⋅K1⋅CS1+K1⋅CS+K2⋅CI,(4)(dCIdt)=k1⋅K1⋅CS⋅k2⋅K2⋅CI1+K1⋅CS+K2⋅CI,(5)(dCCO2dt)=k1⋅K1⋅CI1+K1⋅CS+K2⋅CI,
where C denotes concentrations of species to which the pertinent suffix
refer, t time; k1 and k2 the kinetic constants relative to
degradation of S and I, respectively. Intermediate I is supposed to simulate the behavior
of all the often uncountable, numerous intermediates, which are on the route
from the substrate S to CO2.
Experimentally speaking, only kinetic profiles of S and CO2 may be easily followed. Even if, for the
molecule chosen in the present investigation, a limited number of intermediates
may be reasonably envisaged from the substrate to CO2, the same is
not true [12, 13, 26] for aromatic and/or heterocyclic compounds, or still for
long-chain aliphatics, which have been the object of previous investigations.Random
errors int can be neglected, and only the random errors in the dependent variables
are considered.The error sum,G(k1,k2,K1,K2)=∑i=1nwi[CS(exp)i−CS(calc)i]2,  is minimized to obtain the best values of the   k1,k2,K1,K2 parameters; CS(exp)i and CS(calc)i represent
the n measured and calculated
substrate concentration values,
respectively, and wi=1/σ2(CS(exp)i)
is the weighting factor.Furthermore the
conservative balance of carbon has to be accounted for and verified
experimentally, all concentrations of substrate and intermediate being
expressed in terms of carbon content, as obtained from TOC analysis(6)Cc⁢(at⁢time⁢t)=CTOC⁢(at⁢time⁢0)=CS⁢(at⁢timee⁢t)+CI⁢(at⁢time⁢t)+CCO2⁢(at⁢time⁢t),
where Cc represents the total carbon, both organic and inorganic, carbon dioxide
representing the final product of the mineralization process
(6a)CTOC⁢(at⁢time⁢0)be⁢ing⁢equal⁢to⁢CS⁢(at⁢time⁢0),(6b)CTOC⁢(at⁢time⁢t)be⁢ing⁢equal⁢to⁢CS⁢(at⁢time⁢t)+CI⁢(at⁢time⁢t).The
major limitation of (6) is to regard only intermediates containing carbon,
which is,  anyway, the most common condition in degradation of organics. If this
should not be the case, (6) should be substituted by
(7)Cc⁢(at⁢time⁢t)=CTOC⁢(at⁢time⁢t)=CS⁢(at⁢time⁢t)=CCO2⁢(at⁢time⁢t)
and substitute (5) by
(8)(dCCO2dt)=−(dCSdt).Equations
(3)–(6) constitute a
suitable model for temporal disappearance of TOC, which is a relevant
analytical parameter to follow environmental pollution problems.Whent=0 (beginning of photodegradation), CI is completely negligible with respect to CS.
Furthermore, the hypotheses that k1⁢~k2 and symmetrically that K1⁢~K2, even if this
is not always true, may be used, in some cases, simply as a starting
approximation. With this approximation, (3) can be simplified  to
(9)r0=k1⋅K1⋅C01+K1⋅C0,
where r0 is the initial rate,
and C0 represents the initial concentration of
substrate S. The reciprocal of (9)
has exactly the same form of the Langmuir-Hinshelwood model (13). Moreover,
being initially CI=0, from (5) and (6) one obtains, at t=0,
(10)(dCCO2dt)=(dCTOCdt)=0.
In other words, the formation of
carbon-containing intermediates, if the latter are not photodegraded yielding
CO2 at a
higher rate than that of the substrate, gives rise to a characteristic plateau
in the curve of TOC content versus
time. This trend is only approximated experimentally, both because there is
often a preferential, even if not prevailing, route to rapid CO2 formation
from S, and because intermediates
are often more reactive than the substrate itself towards photodegradation, so
that TOC disappearance is initially low, particularly in aromatic compounds,
usually around one order of magnitude lower than that of the substrates, but is still measurable.Now,
let us suppose that a timet* exists,
such as that for t>t*,CS≪CI. At time t*, (4) becomes
(11)dCIdt⁢~−k2⋅K2⋅CI1+K2⋅CI,
and as for (6) in these conditions CTOC~CI, (11) becomes
(12)dCTOCdt⁢~−k2⋅K2⋅CTOC1+K2⋅CTOC.
An important experimental result is
thus substantiated and rationalized in these cases, where the rate of
mineralization of intermediates is much lower than that of transformation of
substrate into an intermediate (the cases of aromatic compounds
particularly):  the curve CTOCversus time explicitly follows a Langmuirian-type rate law (13), by which k and K parameters acquire the physical significance of k2 and K2,
as stated above.That
timet* effectively exists, as a time
at which the substrate is completely converted into intermediates, even with a
modest decrease of TOC content and nearly complete mineralization of eventual
heteroatoms present in the substrate, is experimentally recognized by both
literature data [27] and by results of our preceding work [26].In
most cases, bothk and K couples are accessible experimentally,
as starting values from initial-rate data, relative to substrate, and TOC as
well, using the Langmuirian equation (13)
(13)1r0=1k+1k⁢KC0,
where r0 is the initial rate of substrate
disappearance, whether measured by direct analysis of substrate itself (to
obtain the k1 and K1 couple) or by the rate of
decrease of total organic carbon (TOC) as a function of time (to obtain the k2 and K2
couple). The
values drawn from (13) may be used as starting values to find the absolute
minimum in the error sum, G, with respect to k1,K1,k2 and K2 kinetic parameters. In particular cases, as
stated before, when only k2 and K2 values are available experimentally by TOC
measurements, the approximation k1⁢~k2 and K1⁢~K2 can  be
used as a starting point in the minimization algorithm as has been suggested on
a theoretical basis [28]. Variation of kinetic parameters, in order to optimize
the fitting, may additionally be restricted within the expected range of
experimental uncertainty, but also chemical considerations may be of great
help, as well as simultaneous consideration of k and K parameters for
other chemically related substrates and/or intermediates, which may be studied
by the same methodology.


## 2.5. Modeling of Quantum Yields as a Function of Irradiance and of Substrate Concentration

By using the optimized parameters
of the section above, the rates of photomineralization were evaluated as a
function of initial concentration,C0, and consequently, by operating at a certain value of the
photon flow, the corresponding
quantum yields Φ0 were obtained.Quantum yieldsΦ0, calculated from rates, followed an apparently
Langmuirian function of initial concentration of substrate C0, by which Φ∞ values at infinite concentration could be obtained as(14)1Φ0=1Φ∞+1Φ∞C0K,
where the K value substantially coincided with the lowest between the two K1 and K2 constants
above, for many molecules being K1⁢~K2.Finally,
by repeating all sets of experiments, at different values of the absorbed
radiant power per unit length of photocatalytic membrane, which was varied in
the range 0.10–4.0 W⋅cm−1,
and by applying (14) to each set of these experiments, the Φ∞ values, as a function of the absorbed radiant
power, per unit length of photocatalytic membrane, were obtained.


## 2.6. Modeling of Quantum Yields as a Function of Photopromoter Concentration

For experiments in which the
photopromoter was added, the same procedure described in the preceding
paragraph was adopted, and theΦ∞ values obtained at a high value of absorbed irradiance, typically Φ∞ values at 4 W⋅cm−1, much smaller
than the maximum allowable Φ∞ values corresponding to irradiances tending to zero, were plotted as a function
of concentration of photopromoter in the photocatalytic membrane.


## 3. Results and Discussion

Photomineralization of
methane in air at 100% relative humidity, and in a concentration range
corresponding to 10.0–1000 ppm (mass/volume)
of carbon, was studied at 318 ± 3 K, in a laboratory-scale reactor, by using
dioxygen of air as an oxygen donor, and by photocatalytic membranes immobilizing
30 ± 3% of titanium dioxide, as a function of absorbed power per unit length of
membrane, expressed in W⋅cm−1. The latter was varied in the range
0.15–4.0 W⋅cm−1.
This is a convenient measure of power absorbed per unit apparent geometrical
membrane surface, since, owing to the annular geometry of photoreactor,
absorbed power per unit length, divided by membrane circumference, yields
exactly that value. Kinetics of both substrate disappearance, to yield
intermediates, and total organic carbon (TOC) disappearance, to yield carbon
dioxide, were followed.At a fixed value of
irradiance, corresponding to 0.30 W⋅cm−1, the mineralization
experiments in gaseous phase were repeated as a function of flow rate, which
was varied between 4 and 400 m3⋅h−1. Moreover, at a
standard flow rate of 300 m3⋅h−1, the ratio between the
overall reaction volume and the length of the membrane was varied,
substantially by varying the volume of reservoir, from and to which circulation
of gaseous stream took place.Photomineralization
of methane in aqueous solutions was also studied, in the same reactor and in
the same conditions, but in a concentration range of 0.8–2.0 ppm of
carbon, and by using stoichiometric hydrogen peroxide as an oxygen donor.


### 3.1. Parameters of Kinetic Model as a Function of Absorbed Power per Unit Length of Membrane

Treating of experimental
data by the kinetic model above (see Experimental) allowed to obtain, for all
sets of kinetic runs, performed as a function of concentration, two couples
of  parameters,k1 and K1,k2, and K2, which fitted the whole
photomineralization curve, and not only its initial segment, as the Langmuirian
parameters generally do. These parameters, as a function of absorbed power per
unit membrane length, are reported in Table 1, both for experiments carried out
on methane in aqueous solutions, with hydrogen peroxide as an oxygen donor, as
well as in the gaseous phase, with dioxygen of air as oxygen donor. In this
same Table, the values measured in aqueous solutions, at 0.30 W⋅cm−1,
in a preceding work [14], are also reported. The very satisfactory fitting of
experimental kinetic data by this model, notwithstanding its extreme
simplicity, is shown, as an example, in Figures 1 and 2 for the kinetic curves
of disappearance of methane in air as such, and of its TOC disappearance,
respectively, at the various initial concentrations specified for this
substrate, and at 0.30 W⋅cm−1 of absorbed power per unit length of
membrane.Table 1
Parameters*, k1 and K1, k2 and K2, able
to fit the whole photomineralization curve, following Scheme (2), at various
values of absorbed power per unit length of membrane expressed in W⋅cm−1.
They were obtained by the optimization of kinetic curves, by using the set of
differential equations corresponding to kinetic model of Scheme (2). All the
parameters are expressed in ppm of carbon (mass of C/volume, mg/L) and refer to
the photodegradation of methane in gaseous phase, and in aqueous solutions, in
the presence of stoichiometric hydrogen peroxide (for the aqueous solutions) or
of dioxygen of air (for the gas-phase experiments), as oxygen donors (treated
volume of the gas phase or of the aqueous solutions 4.00 L; membrane length
100.0±0.5 cm; ratio between overall reaction volume and membrane length 160 ± 6 cm3/cm2; PHOTOPERM®BIT/313 membranes immobilizing 30 ± 3 wt.% TiO2, in the absence of
any photopromoter).
Aqueous solutionsAbsorbed power per unit length of membrane (W⋅cm−1)k1
(ppm
C/min)k2
(ppm
C/min)K1
(ppm
C)−1K2
(ppm
C)−10.150.111(3)0.293(3)0.0124(3)0.0086(3)0.30**0.224(1)0.584(2)0.0126(3)0.0089(3)0.700.494(2)1,23(4)0.0130(3)0.0091(3)0.900.589(3)1.45(4)0.0131(4)0.0090(3)1.500.802(4)1.95(4)0.0125(3)0.0086(4)2.000.890(3)2.24(3)0.0133(6)0.0090(2)3.000.896(4)2.39(6)0.0128(3)0.0088(2)4.000.894(5)2.28(7)0.0127(2)0.0086(3)Gas phaseAbsorbed power per unit membrane length
(W⋅cm−1)k1
(ppm
C/min)k2
(ppm
C/min)K1
(ppm
C)−1K2
(ppm
C)−10.150.115(6)0.288(7)0.0127(7)0.0085(7)0.300.223(5)0.581(5)0.0131(9)0.0082(6)0.900.586(3)1.57(4)0.0131(4)0.0091(3)1.500.805(4)1.92(4)0.0125(3)0.0087(2)2.000.891(3)2.33(3)0.0130(3)0.0090(2)3.000.892(4)2.37(5)0.0127(3)0.0088(2)4.000.889(5)2.32(6)0.0129(4)0.0091(2)*Uncertainties are indicated between parentheses and expressed, relatively to the last digits, as probable errors of the means of optimized values from 9 sets of runs in the range of concentrations tested.
**Data relative to these experiments were taken from
[14].Figure 1
Kinetics of disappearance
of methane, as substrate, from the gas phase, with 0.30 W⋅cm−1 of
absorbed radiation power per unit membrane length. Concentrations, CS in mg/L, for methane, are expressed as carbon, which was not transformed into
intermediates, as a function of time, expressed in minutes, as time necessary
to treat 1 L of gas phase. Photocatalytic membranes used in these experiments
did not contain any photopromoting agent.Figure 2
Kinetics of disappearance
of total organic carbon (TOC) from gaseous methane in the laboratory-scale
photoreactor (see Experimental), expressed as concentrations,CTOC in mg/L of carbon,  which was not mineralized, as a function of
time, expressed in minutes, as time necessary to treat 1 L of gas phase.
Absorbed radiation power per unit membrane length was 0.30 W⋅cm−1 during these runs. Photocatalytic membranes used in these experiments did not
contain any photopromoting agent.From the observation of the values
of kinetic parameters reported in Table1, some interesting considerations may
be immediately drawn.(i) First of all, the four parameters above,
obtained from data of the present paper, relatively to photodegradation and
photomineralization of methane in the gas phase, substantially coincide, within
the limits of experimental uncertainty, with those measured during experiments
carried out in aqueous solution, both kind of experiments being performed in
conditions of turbulent flow, at every value of absorbed radiation power per
unit length of membrane. Furthermore, the kinetic parameters obtained in
previous work [14], at a fixed value of irradiance, are in a perfect agreement
with the present ones. At least, this behavior is surely shown by TiO2 immobilized in photocatalytic membranes tested.(ii) Given the coincidence of kinetic parameters of
Table1, remarked in point (i) above,
between experiments carried out in liquid and gaseous phase, Table 1 points out
that, while k1 and k2 appear to be a clear
function of irradiance, showing a saturation behavior at absorbed powers per
unit membrane length greater than about 2 W⋅cm−1, K1 and K2 parameters show an evident independency on
irradiance.(iii) By operating in a gaseous phase saturated by
water vapour, as has been done in the present paper, mineralization proceeds
smoothly and completely, as it occurs in the liquid phase, and as may be
observed in Figures1 and 2. On the contrary, if relative humidity is much less
than 100%, and particularly when using chlorinated hydrocarbons as substrates
[29], the formation of some amounts of relatively photostable intermediates,
such as carbon monoxide and phosgene, has been detected. Complete
mineralization was thus sensibly retarded. This inconvenience, however, may be
completely obviated, other than maintaining a high humidity in the reaction
medium, also by adding suitable photopromoting agents to the membrane [29]. For
methane, evidently, only the first of these two experimental conditions is
already able to assure complete mineralization.(iv) Another aspect stems out from data of Table1.
In experiments of preceding work [19], carried out on gaseous methane at a
fixed irradiance corresponding to 0.30 W⋅cm−1, hydrogen peroxide was
aerosolized in the reactor in order to be able to compare results with those of
methane solutions [14], in which hydrogen peroxide was the oxygen donor.
Anyway, the two kinds of experiments gave substantially equal results. In
experiments of this paper, on the contrary, the addition of hydrogen peroxide
was omitted during gas-phase experiments, thus giving to dioxygen of air the
role of oxygen donor in these experiments. In fact k and K parameters, as
may be checked from results at 0.30 W⋅cm−1, are the same, in gaseous
phase experiments, independently on whether hydrogen peroxide is present or
not, and furthermore coincide with those of liquid phase runs. This should mean
that the scavenging ability of hydrogen peroxide in aqueous solutions is
comparable, or at least undistinguishable from that of dioxygen in air, with
the photocatalytic membranes yielding substantially equal rates, in the two
series of kinetic runs. On the contrary, dissolved dioxygen in water gives
photomineralization rates about ten times lower than those measurable in the
presence of hydrogen peroxide [16, 21]. This marked that the difference of behavior may be
reasonably attributed to the great difference between chemical potential of
dioxygen in air and that of aqueous solutions, even if saturated with air, also
on the light of considerations expounded in the following point (v).(v) By employing the same line of thoughts, as that
deriving from (i) above, we may guess
that, onto photocatalytic membranes, reactions at the interface control the
process. In transport phenomena through the gaseous phase onto polymers, the sorption
and permeation of gases and vapours in polymers have been shown to be well
described over widely varying conditions by the dualmode sorption theory
[30–33], in which sorption by dissolution (Henry’s law) and sorption in
microvoids (Langmuir isotherm) play a significant role. Factors which relate to
the molecular structure of the polymer, such as polarity, hydrogen bonding, cohesive
energy density, chain flexibility, steric hindrance, and cristallinity, will,
among others, all have an influence on transport properties. When dealing with sorbents
or reagents or catalysts immobilized onto a membrane structure, such as in the
photocatalytic membranes of the present work, thermodynamics of sorption and
reaction control appear to be among the most important factors in determining
transport processes [34]. These reactions are ruled kinetically, and also thermodynamically,
by concentration gradients, independently on diffusion and other phenomena in
the bulk, either if the latter is constituted by a liquid or by a gas phase.
The presence of a sorbent in a membrane structure, such as the structure which
has been obtained by the photografting method used to manufacture the
photocatalytic membranes employed in the present work, affords an alternative
concept in membrane science and technology [22], since the endothermic step of
creating a molecular-size cavity in the polymer for the reacting species,
either if arriving from the gas or from the liquid phase, is virtually
eliminated. At the same time, the thinnest of all conceivable membranes may be
realized, consisting in a monolayer where the adsorbed molecules may interact
with its surroundings. Consequently, as it has been shown [22], surface
diffusion and surface reactivity must be the prevailing mechanism for transport
and reaction in these membranes, since a mobile adsorption layer results, which is able to contribute
efficiently to both diffusion and reactivity [22]. This surface diffusion has
been inferred by the activation energy for solubility of species, either from
the gas or from the liquid phase, which nearly equals the desorption enthalpy
[22]. Mass transfer, in the presence of irradiation, is accompanied by the
photocatalytic reactions across these photocatalytic membranes, manufactured by
the photografting nanotechnology, or by similar nanotechnologies, as those used
for the preparation
of photocatalytic membrane structures. As a consequence, this may occur either
by an activated process, most seemingly involving migration of an adsorbed
unimolecular layer across the surface, or by Knudsen diffusion. The first kind
of mechanism should prevail, as has been found [23, 24], when relatively strong
adsorption interactions with active sites arise. This is in fact the case for
photocatalytic membranes.(vi) The similarity of behavior, and the coincidence
of thek and K parameters (see Table 1), between experiments in the gas and in
the liquid phase, is thus fully compatible with, and clearly interpreted by,
the general mechanisms outlined in (v) above, as deduced and commented in previous studies concerning reactive
membranes.(vii) It should be also underlined that consideration
on rates, based exclusively onk values, following a Langmuir-Hinshelwood model, should not be regarded as fully
and absolutely reliable. In fact, it has been shown, since long time and
unequivocally [16, 21], that also K parameters have a kinetic significance, so that these latter are integral part
of a convenient and fitting model, rather than attributing to them a truly and
purely physical meaning in the sense of adsorption. This notwithstanding, a
rough indication based on k values
can be considered, at high concentrations of substrate, as complementary to the
use of the rate equation, the latter being anyway the most reliable method to
treat experimental data, as has been done, for example in kinetic modeling of
data reported in Table 1, in which the kK factor may play the most relevant role. This behavior may be tentatively
attributed to the fact that k parameters
rule the photochemical reactivity properly, while K parameters reflect, partly at least, kinetic aspects tied to flow
rates, and possibly other engineering features of the photoreactors, as it will
be discussed later.


### 3.2. Parameters of Kinetic Model as a Function of Flow Rate in the Photoreactor and of Reactor Geometry

Maximum photomineralization rates,
as shown by the variation ofK values
with flow rates [16], could be attained, when operating in aqueous solutions,
only if the flow rate exceeded about 3 m3/h, corresponding to a
Reynolds regime, in the operating conditions of the plant.Consequently,
it has been deemed useful, in the present work, to perform a similar
investigation in the gas phase, by operating at a fixed value of irradiance
(corresponding to 0.30 W⋅cm−1) and by varying the flow rate in the
range 4–400 m3⋅h−1.
Results are shown graphically in Figure 3. It readily emerges that, while no
influence on k1 and k2 values could be detected,
outside the limits of experimental uncertainty, a variation of both K1 and K2 values with flow rate was operative, similar to that
evidenced in liquid phase [16], so that all experimental runs for
mineralization of methane in air were standardized at a flow rate of 300 m3⋅h−1,
in order to explore the influence of other variables, such as that of
irradiance itself. This again is a clear indication of the fact that the K parameters contain a kinetic
contribution due to diffusion of species towards the interface of the
photocatalytic membrane.Figure 3
Variation ofK1 and K2 parameters, expressed in (ppm C)−1 (see kinetic modeling in
Experimental), as a function of flow rate (m3⋅h−1), for
photomineralization of methane in air, and experiments carried out at a fixed
irradiance corresponding to 0.30 W⋅cm−1. The mean values of k1 and k2 parameters, resulting from modeling of these same
experiments, were sensibly constant (k1=0.225±0.005 ppm C⋅min−1; k2=0.578±0.007 ppm C⋅min−1), independently on values of flow rates.
Photocatalytic membranes used in the relative experiments did not contain any
photopromoting agent.To
examine further the possible influence of reactor geometry, and given that in
the laboratory-scale apparatus, as well as in all the pilot plant-scale
modules, the optical path was already optimized [12, 16], the ratio α between
the overall reaction volume and the length of the membrane was varied, at the
standard flow rate of 300 m3⋅h−1, and at a fixed value of
irradiance corresponding to 0.30 W⋅cm−1. In an annular laboratory-scale
apparatus, suitable to carry out characterization or standardization
procedures, such as that employed in present as well as in preceding studies,
and in which batch operation is the rule, the best way to vary reactor geometry
consists in varying the volume of reservoir, from and to which circulation of
the reacting stream takes place. Consequently, ratio α
above is
the most suitable parameter to define reactor geometry, when reactor diameter,
and optical path maximizing photochemical yields have been chosen and fixed at
the most convenient values. By varying this α
ratio from 80 to 450 cm3⋅cm−1, it was confirmed that k values varied accordingly, with
respect to those relating to the standard value of α=160 cm3⋅cm−1 used, while
the K values remained substantially
unaffected. Consequently, k values,
reflecting the influence of concentrations, and expressed, for example, in
(mg/L)⋅min−1, were transformed into mass reacted per unit time and
per unit apparent surface of membrane (e.g.,
by expressing them in mg⋅min−1⋅m−2), by taking into
account the variable α  above, following the relation κ=k⋅10α/β,
where β  is the circumference of the membrane,
expressed in cm. Then all these k parameters gave a common κ  value, independent on reactor geometry, if
expressed in the mg⋅min−1⋅m−2 units above, or in any
other related unit, which may be preferred. As a result, by this way, data may
be standardized and compared quite easily, even in different experimental
conditions.


### 3.3. Modeling of Qquantum Yields as a Function of Absorbed Power per Unit
Length of Membrane and of Substrate Concentration

By (14), in which the K values substantially coincided with K2 of Table 1, and by
applying the procedure described above (see Experimental), the Φ∞ values as a function of the absorbed radiant
power per unit length of photocatalytic membrane, expressed in W⋅cm−1,
were obtained and reported in Figure 4, both for experiments carried out in the
gas phase (red symbols) and for experiments performed in aqueous solutions
(blue symbols). The practical coincidence between these two sets of values, as
discussed above, readily appears. The mean values of Φ∞ between these two sets of experiments are
reported in Figure 5.Figure 4
Quantum efficienciesΦ∞ (mol/Einstein),
extrapolated by (14) (see Experimental), at infinite concentration of
substrate, for methane in air (red dots) and in aqueous solution (blue dots),
as a function of absorbed power per unit length of irradiated photocatalytic
membrane, expressed as W⋅cm−1. Photocatalytic membranes used in the
relative experiments did not contain any photopromoting agent.Figure 5
Quantum efficienciesΦ∞ (mol/Einstein)
of methane, extrapolated by (17), at infinite concentration of substrate,
evaluated as mean values (black dots) relative to measurements in aqueous
solution and in the gaseous phase, reported in Figure 4, as a function of
absorbed power per unit length of irradiated photocatalytic membrane, expressed
as W⋅cm−1. The blue curve represents the calculated contribution of
reaction (b), as modeled in the
present work, decreasing with increasing power. The red curve represents the
calculated contribution of reaction (b′),
as modeled in the present work, increasing with increasing power. The mauve
curve represents equation modeled in the present work, as a sum of both these
contributions. Photocatalytic membranes used in the relative experiments did
not contain any photopromoting agent.To explain the behavior
of sigmoid curves, such as that of Figures4 or 5, a competition kinetics of the
reaction of hydroxyl radicals with themselves to give hydrogen peroxide,
accompanied by the reaction of these radicals, as well as of superoxide anion
radical and/or its conjugate acid, with the substrate and intermediates,
leading to mineralization, may be envisaged, such as given by reaction
(a)
on one side and reactions (b) and (b′) on the other.Reaction (a) corresponds to the formation of
hydrogen peroxide by recombination of hydroxyl radicals,dCH2O2/dt,
where t is time,
(a)•OH+•OH⟶H2O2
and its rate ra may be written as
(15)ra=ka⋅C•OH2,
where ka is the rate constant of reaction (a), and C•OH is the concentration of hydroxyl radicals.Reaction
(b) is given by(b)•OH+substrate⁢(or⁢intermediates)⟶mineralization,
and its rate rb may be written
as
(16)rb=kb⋅CS⋅C•OH,
where kb is the rate constant of reaction (b), and CS is the concentration of substrate or
intermediates, on the surface of the photocatalytic membrane on to which
mineralization takes place.Reaction(b′) by the O2•−/HO2• superoxide radical couple is given by(b′)O2•−HO2•+substrate⁢(or⁢intermediates)⟶mineralization, and its rate rb′ may be
written as
(17)rb′=kb′⋅CS⋅CO2•−/HO2•,
where kb′ is the rate constant of reaction (b′).At very low photon flows, corresponding to the
upper plateau of curve of Figure4, at which the concentration of hydroxyl
radicals formed by irradiation onto the semiconductor surface is relatively
low, reaction (a) is certainly
negligible, with respect to reaction (b).
Furthermore, in these circumstances, and particularly when operating in the
presence of hydrogen peroxide as an oxygen donor, scavenging of photogenerated
electrons of the conduction band eCb− should be
quantitative and compatible with reactions (c)
and (d) occurring at comparable
rates, and followed by reaction (e)
as
(c)eCb−+H2O2⟶•OH+OH−,(d)eCb−+O2⟶O2•−HO2•.(e)HO2•+•OH⟶O2+H2O If these conditions are working, a
quantum efficiency equal or very near to the maximum one allowable may be
attained. This hypothesis obviously corresponds to stating that each absorbed
photon, in the optimal conditions of a membrane photoreactor, should give rise
to a hydroxyl radical, at every C0 value of (14) C0 values
being the corresponding CS values of (16) and (17),
for each initial concentration of substrate. Following this same hypothesis,
reactivity of conduction-band electrons, in the presence of hydrogen peroxide
as an oxygen donor, should give rise, almost quantitatively, to molecular
oxygen, or, alternatively to reactions (c)–(e), to reduced species, in the
semiconductor lattice or at the interface, by reaction with donors (water
itself included). If these reactions take place quantitatively, also the
contribution of rb′ to the
overall rate r given by
(18)r=ra+rb+rb′
will be negligible. Radical
reactivity leading to integral mineralization of substrate should be controlled
by (18), with both ra and rb′ much lower than rb and consequently  the rb/r factor should reach the
maximum value permissible (approaching the unity). This situation is surely
achieved at very low values of the photon flow, since effectively, in these
conditions, in Figure 4 the maximum allowable quantum yields for methane
mineralization are operative, corresponding to reactivity of hydroxyl radicals
alone, as shown by the apparent upper plateau of this curve. These values are
very near to 0.125 mol/Einstein, which corresponds to the mineralization of
methane by 8 hydroxyl radicals, as required by stoichiometry. Typically, as
stated above (see Experimental), at 0.30 W/cm (a representative value in the
range of 0–0.5 W/cm, where
maximum quantum yields of Figure 4 are operative, and consequently the rb/r ratio is unitary) this photon flow amounted to 4.45×10−5 Einstein s−1. This means that, for each cm of membrane length, and
consequently for each cm of length of the photoreactor, photogeneration of
4.45×10−5 moles (of hydroxyl radicals) s−1cm−1 took place. To transform this value in amount of hydroxyl radicals generated
per unit time and per unit reactor volume, one should consider that in the
laboratory scale module, given its overall volume in standard conditions, and
owing to engineering design, the volume corresponding to each cm of membrane
length was 160 ± 6 cm3/cm (see Experimental). As a consequence, the
production rate of •OH radicals, always at the given absorbed power
per unit length of 0.30 W/cm, was calculated as 1.11 × 10−3 mol s−1 L−1.  This linear relationship
allows to evaluate the production rate of hydroxyl radicals in the upper apparent
plateau of curves such as that of Figure 4, at each value of W/cm.This
mechanism, however could not rule also at high photon flows, when the quantum
yields of Figure5 from the upper apparent plateau begin to decrease with
increasing photon flow, and finally reach an apparent lower second
plateau.  This may be due, on one side,
the fact that the production rate of hydroxyl radicals, at W/cm values higher
than about 0.5, should vary with photon flow by a nonlinear relationship, and
their evaluation is possible, by supposing that C•OH decreases exponentially with increasing W/cm values
(19)C•OH=f⋅e−g(W/cm),
with f and g positive
constants.On the other side, with increasing
photon flow, and with decreasing rate of hydroxyl radicals production, the rate
of the generation of superoxide radical couples,O2•−/HO2•,  increases.  The CO2•−/HO2•, as a function of absorbed power per unit length of membrane, may be
assumed to vary according an equation of the same kind as (19), but with a
negative g constant, as the production of these radicals should increase with
increasing irradiance, in a complementary way by which hydroxyl radicals
decrease.Reaction(b′) thus yields a supplementary
contribution to mineralization, besides that due to the photocatalytic
reactivity of holes onto the semiconductor surface. In other words, to the rb contribution to
mineralization, a further contribution rb′ should be added, deriving from the concentration of superoxide radical
anion and/or its conjugate acid generated by reaction (d). The overall contribution to mineralization, (rb+rb′)/r, can be approximated by a weighted sum of the
two contributions (b) and (b′) as
(20)rb+rb′r≅y(calc)=f1[1+e−g1(W−W1)/cm]+f2[1+e−g2(W−W2)/cm].The error sum,G(f1,g1,W1,f2,g2,W2)=∑i=1nwi[y(exp)i−y(calc)i]2,
is minimized with respect to f1,g1,W1,f2,g2, and W2 parameters, to find the best model (20) that
fits the data. As shown in Figure 5 for methane, the calculated curve
(red curve) perfectly fits experimental data, and gives rise to a sigmoid
curve, with two apparent plateaux values, as found experimentally.In Figure5, the contributions to quantum yields given
by these two processes have been plotted as a function of W/cm. It clearly
appears that the contribution (blue curve) of hydroxyl radicals to mineralization
decreases with irradiance, while the contribution (mauve curve) of superoxide
anion radical and its conjugate acid increases.Finally, if the best
curve(21)y(calc)=0.15088[1+e1.5246(w−1.4629)/cm]+0.020853[1+e−1.7655(w−2.1448)/cm],
calculated for methane, is coupled
with (14), a three-dimensional graph results (see Figure 6), in which quantum
yields Φ0 may be
plotted and rationalized as a function of initial concentration, C0,
and of irradiance, in the form of the absorbed power per unit length of
photocatalytic membrane, W/cm, which has been defined and used in the present
paper.Figure 6
Quantum yieldsΦ0 (mol of methane/Einstein) for
photomineralization of methane, as a function of initial concentration C0, expressed as mg/L of
carbon, and of absorbed power per unit length of lamp (and membrane), expressed
as W⋅cm−1. Quantum yields are expressed as means of values, from
experiments in gaseous phase and in aqueous solutions. Photocatalytic membranes
used in these experiments did not contain any photopromoting agent.To sum up, only the model given by
both reactions (b) and(b′), in competition with (a), is completely compatible with
experimental data, and able to represent, fully satisfactorily, the dependence
of quantum yields on irradiance values.


### 3.4. Modeling of Quantum Yields, at High Irradiance Values, as a Function of
Photopromoter Concentration

For the experiments carried out by
photocatalytic membranes coimmobilizing the photopromoter together with
titanium dioxide, the sigmoid shape of curves such as that of Figure5 changed
with increasing concentration of photopromoter, and the curves were flattened,
as reported in the example of Figure 7, at a concentration of photopromoter
corresponding to 3.0 mol/mol % of photopromoter vanadium with respect to
titanium. This effect may be correlated to the kinetic influence of the
photopromoter, reflected in the relationship between quantum yields and kinetic
parameters. When the Φ∞ values corresponding to the highest irradiances, typically at 4 W⋅cm−1,
were plotted as a function of % molar concentration of photopromoter, Figure 8 was obtained. This
behavior shows that at low values of the % mol/mol concentration of photopromoter vanadium, up to about 0.5, the same Φ∞ values measured in the absence of any
photopromoting agent (see Figure 5) were obtained. When increasing
photopromoter concentration, on the contrary, above this threshold value, Φ∞ values increase considerably and approach the
maximum allowable for methane (0.125 mol/Einstein), starting from about 5% on
of photopromoter vanadium. This should mean that the decrease of quantum yield
brought about by the increase of irradiance, and interpreted (see preceding
paragraph) by a recombination mechanism of hydroxyl radicals may be fully
compensated by the addition of appropriate photopromoters at suitable
concentration. By this way, operation at high irradiance values is possible,
without loosing any efficiency for the mineralization process.Figure 7
Quantum efficienciesΦ∞ (mol/Einstein)
of methane, extrapolated by (17), at infinite concentration of
substrate, relative to measurements carried out in the gaseous phase, as a
function of absorbed power per unit length of irradiated photocatalytic
membrane, expressed as W⋅cm−1. Photocatalytic membranes used in the
relative experiments contained the photopromoter (see Experimental) at a
concentration corresponding to 3.0 mol/mol % of vanadium with respect to
titanium present as main photocatalyst.Figure 8
Quantum efficienciesΦ∞ (mol/Einstein)
of methane, extrapolated by (17), at infinite concentration of
substrate, relative to measurements carried out in the gaseous phase, and
corresponding to an absorbed power per unit length of irradiated photocatalytic
membrane, expressed of 4.0 W⋅cm−1, as a function of mol/mol % of
vanadium, used as photopromoter in the photocatalytic membranes, with respect
to titanium present as main photocatalyst.


## 3.1. Parameters of Kinetic Model as a Function of Absorbed Power per Unit Length of Membrane

Treating of experimental
data by the kinetic model above (see Experimental) allowed to obtain, for all
sets of kinetic runs, performed as a function of concentration, two couples
of  parameters,k1 and K1,k2, and K2, which fitted the whole
photomineralization curve, and not only its initial segment, as the Langmuirian
parameters generally do. These parameters, as a function of absorbed power per
unit membrane length, are reported in Table 1, both for experiments carried out
on methane in aqueous solutions, with hydrogen peroxide as an oxygen donor, as
well as in the gaseous phase, with dioxygen of air as oxygen donor. In this
same Table, the values measured in aqueous solutions, at 0.30 W⋅cm−1,
in a preceding work [14], are also reported. The very satisfactory fitting of
experimental kinetic data by this model, notwithstanding its extreme
simplicity, is shown, as an example, in Figures 1 and 2 for the kinetic curves
of disappearance of methane in air as such, and of its TOC disappearance,
respectively, at the various initial concentrations specified for this
substrate, and at 0.30 W⋅cm−1 of absorbed power per unit length of
membrane.Table 1
Parameters*, k1 and K1, k2 and K2, able
to fit the whole photomineralization curve, following Scheme (2), at various
values of absorbed power per unit length of membrane expressed in W⋅cm−1.
They were obtained by the optimization of kinetic curves, by using the set of
differential equations corresponding to kinetic model of Scheme (2). All the
parameters are expressed in ppm of carbon (mass of C/volume, mg/L) and refer to
the photodegradation of methane in gaseous phase, and in aqueous solutions, in
the presence of stoichiometric hydrogen peroxide (for the aqueous solutions) or
of dioxygen of air (for the gas-phase experiments), as oxygen donors (treated
volume of the gas phase or of the aqueous solutions 4.00 L; membrane length
100.0±0.5 cm; ratio between overall reaction volume and membrane length 160 ± 6 cm3/cm2; PHOTOPERM®BIT/313 membranes immobilizing 30 ± 3 wt.% TiO2, in the absence of
any photopromoter).
Aqueous solutionsAbsorbed power per unit length of membrane (W⋅cm−1)k1
(ppm
C/min)k2
(ppm
C/min)K1
(ppm
C)−1K2
(ppm
C)−10.150.111(3)0.293(3)0.0124(3)0.0086(3)0.30**0.224(1)0.584(2)0.0126(3)0.0089(3)0.700.494(2)1,23(4)0.0130(3)0.0091(3)0.900.589(3)1.45(4)0.0131(4)0.0090(3)1.500.802(4)1.95(4)0.0125(3)0.0086(4)2.000.890(3)2.24(3)0.0133(6)0.0090(2)3.000.896(4)2.39(6)0.0128(3)0.0088(2)4.000.894(5)2.28(7)0.0127(2)0.0086(3)Gas phaseAbsorbed power per unit membrane length
(W⋅cm−1)k1
(ppm
C/min)k2
(ppm
C/min)K1
(ppm
C)−1K2
(ppm
C)−10.150.115(6)0.288(7)0.0127(7)0.0085(7)0.300.223(5)0.581(5)0.0131(9)0.0082(6)0.900.586(3)1.57(4)0.0131(4)0.0091(3)1.500.805(4)1.92(4)0.0125(3)0.0087(2)2.000.891(3)2.33(3)0.0130(3)0.0090(2)3.000.892(4)2.37(5)0.0127(3)0.0088(2)4.000.889(5)2.32(6)0.0129(4)0.0091(2)*Uncertainties are indicated between parentheses and expressed, relatively to the last digits, as probable errors of the means of optimized values from 9 sets of runs in the range of concentrations tested.
**Data relative to these experiments were taken from
[14].Figure 1
Kinetics of disappearance
of methane, as substrate, from the gas phase, with 0.30 W⋅cm−1 of
absorbed radiation power per unit membrane length. Concentrations, CS in mg/L, for methane, are expressed as carbon, which was not transformed into
intermediates, as a function of time, expressed in minutes, as time necessary
to treat 1 L of gas phase. Photocatalytic membranes used in these experiments
did not contain any photopromoting agent.Figure 2
Kinetics of disappearance
of total organic carbon (TOC) from gaseous methane in the laboratory-scale
photoreactor (see Experimental), expressed as concentrations,CTOC in mg/L of carbon,  which was not mineralized, as a function of
time, expressed in minutes, as time necessary to treat 1 L of gas phase.
Absorbed radiation power per unit membrane length was 0.30 W⋅cm−1 during these runs. Photocatalytic membranes used in these experiments did not
contain any photopromoting agent.From the observation of the values
of kinetic parameters reported in Table1, some interesting considerations may
be immediately drawn.(i) First of all, the four parameters above,
obtained from data of the present paper, relatively to photodegradation and
photomineralization of methane in the gas phase, substantially coincide, within
the limits of experimental uncertainty, with those measured during experiments
carried out in aqueous solution, both kind of experiments being performed in
conditions of turbulent flow, at every value of absorbed radiation power per
unit length of membrane. Furthermore, the kinetic parameters obtained in
previous work [14], at a fixed value of irradiance, are in a perfect agreement
with the present ones. At least, this behavior is surely shown by TiO2 immobilized in photocatalytic membranes tested.(ii) Given the coincidence of kinetic parameters of
Table1, remarked in point (i) above,
between experiments carried out in liquid and gaseous phase, Table 1 points out
that, while k1 and k2 appear to be a clear
function of irradiance, showing a saturation behavior at absorbed powers per
unit membrane length greater than about 2 W⋅cm−1, K1 and K2 parameters show an evident independency on
irradiance.(iii) By operating in a gaseous phase saturated by
water vapour, as has been done in the present paper, mineralization proceeds
smoothly and completely, as it occurs in the liquid phase, and as may be
observed in Figures1 and 2. On the contrary, if relative humidity is much less
than 100%, and particularly when using chlorinated hydrocarbons as substrates
[29], the formation of some amounts of relatively photostable intermediates,
such as carbon monoxide and phosgene, has been detected. Complete
mineralization was thus sensibly retarded. This inconvenience, however, may be
completely obviated, other than maintaining a high humidity in the reaction
medium, also by adding suitable photopromoting agents to the membrane [29]. For
methane, evidently, only the first of these two experimental conditions is
already able to assure complete mineralization.(iv) Another aspect stems out from data of Table1.
In experiments of preceding work [19], carried out on gaseous methane at a
fixed irradiance corresponding to 0.30 W⋅cm−1, hydrogen peroxide was
aerosolized in the reactor in order to be able to compare results with those of
methane solutions [14], in which hydrogen peroxide was the oxygen donor.
Anyway, the two kinds of experiments gave substantially equal results. In
experiments of this paper, on the contrary, the addition of hydrogen peroxide
was omitted during gas-phase experiments, thus giving to dioxygen of air the
role of oxygen donor in these experiments. In fact k and K parameters, as
may be checked from results at 0.30 W⋅cm−1, are the same, in gaseous
phase experiments, independently on whether hydrogen peroxide is present or
not, and furthermore coincide with those of liquid phase runs. This should mean
that the scavenging ability of hydrogen peroxide in aqueous solutions is
comparable, or at least undistinguishable from that of dioxygen in air, with
the photocatalytic membranes yielding substantially equal rates, in the two
series of kinetic runs. On the contrary, dissolved dioxygen in water gives
photomineralization rates about ten times lower than those measurable in the
presence of hydrogen peroxide [16, 21]. This marked that the difference of behavior may be
reasonably attributed to the great difference between chemical potential of
dioxygen in air and that of aqueous solutions, even if saturated with air, also
on the light of considerations expounded in the following point (v).(v) By employing the same line of thoughts, as that
deriving from (i) above, we may guess
that, onto photocatalytic membranes, reactions at the interface control the
process. In transport phenomena through the gaseous phase onto polymers, the sorption
and permeation of gases and vapours in polymers have been shown to be well
described over widely varying conditions by the dualmode sorption theory
[30–33], in which sorption by dissolution (Henry’s law) and sorption in
microvoids (Langmuir isotherm) play a significant role. Factors which relate to
the molecular structure of the polymer, such as polarity, hydrogen bonding, cohesive
energy density, chain flexibility, steric hindrance, and cristallinity, will,
among others, all have an influence on transport properties. When dealing with sorbents
or reagents or catalysts immobilized onto a membrane structure, such as in the
photocatalytic membranes of the present work, thermodynamics of sorption and
reaction control appear to be among the most important factors in determining
transport processes [34]. These reactions are ruled kinetically, and also thermodynamically,
by concentration gradients, independently on diffusion and other phenomena in
the bulk, either if the latter is constituted by a liquid or by a gas phase.
The presence of a sorbent in a membrane structure, such as the structure which
has been obtained by the photografting method used to manufacture the
photocatalytic membranes employed in the present work, affords an alternative
concept in membrane science and technology [22], since the endothermic step of
creating a molecular-size cavity in the polymer for the reacting species,
either if arriving from the gas or from the liquid phase, is virtually
eliminated. At the same time, the thinnest of all conceivable membranes may be
realized, consisting in a monolayer where the adsorbed molecules may interact
with its surroundings. Consequently, as it has been shown [22], surface
diffusion and surface reactivity must be the prevailing mechanism for transport
and reaction in these membranes, since a mobile adsorption layer results, which is able to contribute
efficiently to both diffusion and reactivity [22]. This surface diffusion has
been inferred by the activation energy for solubility of species, either from
the gas or from the liquid phase, which nearly equals the desorption enthalpy
[22]. Mass transfer, in the presence of irradiation, is accompanied by the
photocatalytic reactions across these photocatalytic membranes, manufactured by
the photografting nanotechnology, or by similar nanotechnologies, as those used
for the preparation
of photocatalytic membrane structures. As a consequence, this may occur either
by an activated process, most seemingly involving migration of an adsorbed
unimolecular layer across the surface, or by Knudsen diffusion. The first kind
of mechanism should prevail, as has been found [23, 24], when relatively strong
adsorption interactions with active sites arise. This is in fact the case for
photocatalytic membranes.(vi) The similarity of behavior, and the coincidence
of thek and K parameters (see Table 1), between experiments in the gas and in
the liquid phase, is thus fully compatible with, and clearly interpreted by,
the general mechanisms outlined in (v) above, as deduced and commented in previous studies concerning reactive
membranes.(vii) It should be also underlined that consideration
on rates, based exclusively onk values, following a Langmuir-Hinshelwood model, should not be regarded as fully
and absolutely reliable. In fact, it has been shown, since long time and
unequivocally [16, 21], that also K parameters have a kinetic significance, so that these latter are integral part
of a convenient and fitting model, rather than attributing to them a truly and
purely physical meaning in the sense of adsorption. This notwithstanding, a
rough indication based on k values
can be considered, at high concentrations of substrate, as complementary to the
use of the rate equation, the latter being anyway the most reliable method to
treat experimental data, as has been done, for example in kinetic modeling of
data reported in Table 1, in which the kK factor may play the most relevant role. This behavior may be tentatively
attributed to the fact that k parameters
rule the photochemical reactivity properly, while K parameters reflect, partly at least, kinetic aspects tied to flow
rates, and possibly other engineering features of the photoreactors, as it will
be discussed later.


## 3.2. Parameters of Kinetic Model as a Function of Flow Rate in the Photoreactor and of Reactor Geometry

Maximum photomineralization rates,
as shown by the variation ofK values
with flow rates [16], could be attained, when operating in aqueous solutions,
only if the flow rate exceeded about 3 m3/h, corresponding to a
Reynolds regime, in the operating conditions of the plant.Consequently,
it has been deemed useful, in the present work, to perform a similar
investigation in the gas phase, by operating at a fixed value of irradiance
(corresponding to 0.30 W⋅cm−1) and by varying the flow rate in the
range 4–400 m3⋅h−1.
Results are shown graphically in Figure 3. It readily emerges that, while no
influence on k1 and k2 values could be detected,
outside the limits of experimental uncertainty, a variation of both K1 and K2 values with flow rate was operative, similar to that
evidenced in liquid phase [16], so that all experimental runs for
mineralization of methane in air were standardized at a flow rate of 300 m3⋅h−1,
in order to explore the influence of other variables, such as that of
irradiance itself. This again is a clear indication of the fact that the K parameters contain a kinetic
contribution due to diffusion of species towards the interface of the
photocatalytic membrane.Figure 3
Variation ofK1 and K2 parameters, expressed in (ppm C)−1 (see kinetic modeling in
Experimental), as a function of flow rate (m3⋅h−1), for
photomineralization of methane in air, and experiments carried out at a fixed
irradiance corresponding to 0.30 W⋅cm−1. The mean values of k1 and k2 parameters, resulting from modeling of these same
experiments, were sensibly constant (k1=0.225±0.005 ppm C⋅min−1; k2=0.578±0.007 ppm C⋅min−1), independently on values of flow rates.
Photocatalytic membranes used in the relative experiments did not contain any
photopromoting agent.To
examine further the possible influence of reactor geometry, and given that in
the laboratory-scale apparatus, as well as in all the pilot plant-scale
modules, the optical path was already optimized [12, 16], the ratio α between
the overall reaction volume and the length of the membrane was varied, at the
standard flow rate of 300 m3⋅h−1, and at a fixed value of
irradiance corresponding to 0.30 W⋅cm−1. In an annular laboratory-scale
apparatus, suitable to carry out characterization or standardization
procedures, such as that employed in present as well as in preceding studies,
and in which batch operation is the rule, the best way to vary reactor geometry
consists in varying the volume of reservoir, from and to which circulation of
the reacting stream takes place. Consequently, ratio α
above is
the most suitable parameter to define reactor geometry, when reactor diameter,
and optical path maximizing photochemical yields have been chosen and fixed at
the most convenient values. By varying this α
ratio from 80 to 450 cm3⋅cm−1, it was confirmed that k values varied accordingly, with
respect to those relating to the standard value of α=160 cm3⋅cm−1 used, while
the K values remained substantially
unaffected. Consequently, k values,
reflecting the influence of concentrations, and expressed, for example, in
(mg/L)⋅min−1, were transformed into mass reacted per unit time and
per unit apparent surface of membrane (e.g.,
by expressing them in mg⋅min−1⋅m−2), by taking into
account the variable α  above, following the relation κ=k⋅10α/β,
where β  is the circumference of the membrane,
expressed in cm. Then all these k parameters gave a common κ  value, independent on reactor geometry, if
expressed in the mg⋅min−1⋅m−2 units above, or in any
other related unit, which may be preferred. As a result, by this way, data may
be standardized and compared quite easily, even in different experimental
conditions.


## 3.3. Modeling of Qquantum Yields as a Function of Absorbed Power per Unit
Length of Membrane and of Substrate Concentration

By (14), in which the K values substantially coincided with K2 of Table 1, and by
applying the procedure described above (see Experimental), the Φ∞ values as a function of the absorbed radiant
power per unit length of photocatalytic membrane, expressed in W⋅cm−1,
were obtained and reported in Figure 4, both for experiments carried out in the
gas phase (red symbols) and for experiments performed in aqueous solutions
(blue symbols). The practical coincidence between these two sets of values, as
discussed above, readily appears. The mean values of Φ∞ between these two sets of experiments are
reported in Figure 5.Figure 4
Quantum efficienciesΦ∞ (mol/Einstein),
extrapolated by (14) (see Experimental), at infinite concentration of
substrate, for methane in air (red dots) and in aqueous solution (blue dots),
as a function of absorbed power per unit length of irradiated photocatalytic
membrane, expressed as W⋅cm−1. Photocatalytic membranes used in the
relative experiments did not contain any photopromoting agent.Figure 5
Quantum efficienciesΦ∞ (mol/Einstein)
of methane, extrapolated by (17), at infinite concentration of substrate,
evaluated as mean values (black dots) relative to measurements in aqueous
solution and in the gaseous phase, reported in Figure 4, as a function of
absorbed power per unit length of irradiated photocatalytic membrane, expressed
as W⋅cm−1. The blue curve represents the calculated contribution of
reaction (b), as modeled in the
present work, decreasing with increasing power. The red curve represents the
calculated contribution of reaction (b′),
as modeled in the present work, increasing with increasing power. The mauve
curve represents equation modeled in the present work, as a sum of both these
contributions. Photocatalytic membranes used in the relative experiments did
not contain any photopromoting agent.To explain the behavior
of sigmoid curves, such as that of Figures4 or 5, a competition kinetics of the
reaction of hydroxyl radicals with themselves to give hydrogen peroxide,
accompanied by the reaction of these radicals, as well as of superoxide anion
radical and/or its conjugate acid, with the substrate and intermediates,
leading to mineralization, may be envisaged, such as given by reaction
(a)
on one side and reactions (b) and (b′) on the other.Reaction (a) corresponds to the formation of
hydrogen peroxide by recombination of hydroxyl radicals,dCH2O2/dt,
where t is time,
(a)•OH+•OH⟶H2O2
and its rate ra may be written as
(15)ra=ka⋅C•OH2,
where ka is the rate constant of reaction (a), and C•OH is the concentration of hydroxyl radicals.Reaction
(b) is given by(b)•OH+substrate⁢(or⁢intermediates)⟶mineralization,
and its rate rb may be written
as
(16)rb=kb⋅CS⋅C•OH,
where kb is the rate constant of reaction (b), and CS is the concentration of substrate or
intermediates, on the surface of the photocatalytic membrane on to which
mineralization takes place.Reaction(b′) by the O2•−/HO2• superoxide radical couple is given by(b′)O2•−HO2•+substrate⁢(or⁢intermediates)⟶mineralization, and its rate rb′ may be
written as
(17)rb′=kb′⋅CS⋅CO2•−/HO2•,
where kb′ is the rate constant of reaction (b′).At very low photon flows, corresponding to the
upper plateau of curve of Figure4, at which the concentration of hydroxyl
radicals formed by irradiation onto the semiconductor surface is relatively
low, reaction (a) is certainly
negligible, with respect to reaction (b).
Furthermore, in these circumstances, and particularly when operating in the
presence of hydrogen peroxide as an oxygen donor, scavenging of photogenerated
electrons of the conduction band eCb− should be
quantitative and compatible with reactions (c)
and (d) occurring at comparable
rates, and followed by reaction (e)
as
(c)eCb−+H2O2⟶•OH+OH−,(d)eCb−+O2⟶O2•−HO2•.(e)HO2•+•OH⟶O2+H2O If these conditions are working, a
quantum efficiency equal or very near to the maximum one allowable may be
attained. This hypothesis obviously corresponds to stating that each absorbed
photon, in the optimal conditions of a membrane photoreactor, should give rise
to a hydroxyl radical, at every C0 value of (14) C0 values
being the corresponding CS values of (16) and (17),
for each initial concentration of substrate. Following this same hypothesis,
reactivity of conduction-band electrons, in the presence of hydrogen peroxide
as an oxygen donor, should give rise, almost quantitatively, to molecular
oxygen, or, alternatively to reactions (c)–(e), to reduced species, in the
semiconductor lattice or at the interface, by reaction with donors (water
itself included). If these reactions take place quantitatively, also the
contribution of rb′ to the
overall rate r given by
(18)r=ra+rb+rb′
will be negligible. Radical
reactivity leading to integral mineralization of substrate should be controlled
by (18), with both ra and rb′ much lower than rb and consequently  the rb/r factor should reach the
maximum value permissible (approaching the unity). This situation is surely
achieved at very low values of the photon flow, since effectively, in these
conditions, in Figure 4 the maximum allowable quantum yields for methane
mineralization are operative, corresponding to reactivity of hydroxyl radicals
alone, as shown by the apparent upper plateau of this curve. These values are
very near to 0.125 mol/Einstein, which corresponds to the mineralization of
methane by 8 hydroxyl radicals, as required by stoichiometry. Typically, as
stated above (see Experimental), at 0.30 W/cm (a representative value in the
range of 0–0.5 W/cm, where
maximum quantum yields of Figure 4 are operative, and consequently the rb/r ratio is unitary) this photon flow amounted to 4.45×10−5 Einstein s−1. This means that, for each cm of membrane length, and
consequently for each cm of length of the photoreactor, photogeneration of
4.45×10−5 moles (of hydroxyl radicals) s−1cm−1 took place. To transform this value in amount of hydroxyl radicals generated
per unit time and per unit reactor volume, one should consider that in the
laboratory scale module, given its overall volume in standard conditions, and
owing to engineering design, the volume corresponding to each cm of membrane
length was 160 ± 6 cm3/cm (see Experimental). As a consequence, the
production rate of •OH radicals, always at the given absorbed power
per unit length of 0.30 W/cm, was calculated as 1.11 × 10−3 mol s−1 L−1.  This linear relationship
allows to evaluate the production rate of hydroxyl radicals in the upper apparent
plateau of curves such as that of Figure 4, at each value of W/cm.This
mechanism, however could not rule also at high photon flows, when the quantum
yields of Figure5 from the upper apparent plateau begin to decrease with
increasing photon flow, and finally reach an apparent lower second
plateau.  This may be due, on one side,
the fact that the production rate of hydroxyl radicals, at W/cm values higher
than about 0.5, should vary with photon flow by a nonlinear relationship, and
their evaluation is possible, by supposing that C•OH decreases exponentially with increasing W/cm values
(19)C•OH=f⋅e−g(W/cm),
with f and g positive
constants.On the other side, with increasing
photon flow, and with decreasing rate of hydroxyl radicals production, the rate
of the generation of superoxide radical couples,O2•−/HO2•,  increases.  The CO2•−/HO2•, as a function of absorbed power per unit length of membrane, may be
assumed to vary according an equation of the same kind as (19), but with a
negative g constant, as the production of these radicals should increase with
increasing irradiance, in a complementary way by which hydroxyl radicals
decrease.Reaction(b′) thus yields a supplementary
contribution to mineralization, besides that due to the photocatalytic
reactivity of holes onto the semiconductor surface. In other words, to the rb contribution to
mineralization, a further contribution rb′ should be added, deriving from the concentration of superoxide radical
anion and/or its conjugate acid generated by reaction (d). The overall contribution to mineralization, (rb+rb′)/r, can be approximated by a weighted sum of the
two contributions (b) and (b′) as
(20)rb+rb′r≅y(calc)=f1[1+e−g1(W−W1)/cm]+f2[1+e−g2(W−W2)/cm].The error sum,G(f1,g1,W1,f2,g2,W2)=∑i=1nwi[y(exp)i−y(calc)i]2,
is minimized with respect to f1,g1,W1,f2,g2, and W2 parameters, to find the best model (20) that
fits the data. As shown in Figure 5 for methane, the calculated curve
(red curve) perfectly fits experimental data, and gives rise to a sigmoid
curve, with two apparent plateaux values, as found experimentally.In Figure5, the contributions to quantum yields given
by these two processes have been plotted as a function of W/cm. It clearly
appears that the contribution (blue curve) of hydroxyl radicals to mineralization
decreases with irradiance, while the contribution (mauve curve) of superoxide
anion radical and its conjugate acid increases.Finally, if the best
curve(21)y(calc)=0.15088[1+e1.5246(w−1.4629)/cm]+0.020853[1+e−1.7655(w−2.1448)/cm],
calculated for methane, is coupled
with (14), a three-dimensional graph results (see Figure 6), in which quantum
yields Φ0 may be
plotted and rationalized as a function of initial concentration, C0,
and of irradiance, in the form of the absorbed power per unit length of
photocatalytic membrane, W/cm, which has been defined and used in the present
paper.Figure 6
Quantum yieldsΦ0 (mol of methane/Einstein) for
photomineralization of methane, as a function of initial concentration C0, expressed as mg/L of
carbon, and of absorbed power per unit length of lamp (and membrane), expressed
as W⋅cm−1. Quantum yields are expressed as means of values, from
experiments in gaseous phase and in aqueous solutions. Photocatalytic membranes
used in these experiments did not contain any photopromoting agent.To sum up, only the model given by
both reactions (b) and(b′), in competition with (a), is completely compatible with
experimental data, and able to represent, fully satisfactorily, the dependence
of quantum yields on irradiance values.


## 3.4. Modeling of Quantum Yields, at High Irradiance Values, as a Function of
Photopromoter Concentration

For the experiments carried out by
photocatalytic membranes coimmobilizing the photopromoter together with
titanium dioxide, the sigmoid shape of curves such as that of Figure5 changed
with increasing concentration of photopromoter, and the curves were flattened,
as reported in the example of Figure 7, at a concentration of photopromoter
corresponding to 3.0 mol/mol % of photopromoter vanadium with respect to
titanium. This effect may be correlated to the kinetic influence of the
photopromoter, reflected in the relationship between quantum yields and kinetic
parameters. When the Φ∞ values corresponding to the highest irradiances, typically at 4 W⋅cm−1,
were plotted as a function of % molar concentration of photopromoter, Figure 8 was obtained. This
behavior shows that at low values of the % mol/mol concentration of photopromoter vanadium, up to about 0.5, the same Φ∞ values measured in the absence of any
photopromoting agent (see Figure 5) were obtained. When increasing
photopromoter concentration, on the contrary, above this threshold value, Φ∞ values increase considerably and approach the
maximum allowable for methane (0.125 mol/Einstein), starting from about 5% on
of photopromoter vanadium. This should mean that the decrease of quantum yield
brought about by the increase of irradiance, and interpreted (see preceding
paragraph) by a recombination mechanism of hydroxyl radicals may be fully
compensated by the addition of appropriate photopromoters at suitable
concentration. By this way, operation at high irradiance values is possible,
without loosing any efficiency for the mineralization process.Figure 7
Quantum efficienciesΦ∞ (mol/Einstein)
of methane, extrapolated by (17), at infinite concentration of
substrate, relative to measurements carried out in the gaseous phase, as a
function of absorbed power per unit length of irradiated photocatalytic
membrane, expressed as W⋅cm−1. Photocatalytic membranes used in the
relative experiments contained the photopromoter (see Experimental) at a
concentration corresponding to 3.0 mol/mol % of vanadium with respect to
titanium present as main photocatalyst.Figure 8
Quantum efficienciesΦ∞ (mol/Einstein)
of methane, extrapolated by (17), at infinite concentration of
substrate, relative to measurements carried out in the gaseous phase, and
corresponding to an absorbed power per unit length of irradiated photocatalytic
membrane, expressed of 4.0 W⋅cm−1, as a function of mol/mol % of
vanadium, used as photopromoter in the photocatalytic membranes, with respect
to titanium present as main photocatalyst.


## 4. Standardization of Immobilized Photocatalytic Materials

As recalled in Introduction,
comparison of photocatalytic properties of immobilized materials, between
different laboratories, is very difficult, if not impossible, owing to the
variety of procedures employed in the literature. By examining kinetic curves,
such as those of Figures1 and 2, it becomes readily apparent that if criteria
based on rates, either maximum or medium, are adopted, these will depend on
concentration, besides the influence of reactor geometry, such as overall
volume, or ratio between volume and geometrical surface of immobilized
material. The same applies also to criteria based on isotransformation times,
owing to the influence of concentration on reaction order, and obviously also
on criteria based on first-order kinetic constants. Their possible meaning as
internal matching tools apart, these criteria, consequently, should be judged
as inadequate to compare results obtained in different conditions and/or by
different experimental devices, as has been thoroughly discussed in this work.
In the present paper too, the influence of photochemical parameters, such as
irradiance, and of engineering parameters, such as flow rate, has been clearly
evidenced.In
order to reach order and rationalization, first of all a reliable kinetic model
should be employed to modeling of data, such as that based on four-kinetic
parameters, which has been used in the present as well as in previous work,
able to fit the whole mineralization kinetic profile. This model, together with
the knowledge of the influence of all variables outlined, allows to operate in
quite reproducible conditions, both from the point of view of photochemistry (irradiance,
possibility of isolating truly photocatalytic effects from photolysis of
substrate or from photolysis of oxygen donors, influence of substrate
concentration on quantum yields) and from the point of view of more strictly
geometrical or engineering factors (possibility of transformingk into κ
values,
these latter taking into account geometrical aspects of the photoreactor used
for standardization or characterization procedures, as well of the immobilized
material, such as its geometrical surface). Secondly, rationalization of
quantum yields, as a function of substrate concentration and irradiance allows
not only to shed light onto the general photocatalytic mechanisms, at least
from the perspective of modeling, but also to achieve a fully consistent and
trustworthy design of industrial photoreactors.


## 5. Conclusions

A kinetic model was employed to
study photocatalytic mineralization of methane, both in air and in aqueous
solutions, by an annular laboratory-scale membrane reactor, fitted with
photocatalytic membranes immobilizing titanium dioxide. By a set of
differential equations, four final optimized parameters,k1 and K1, k2 and K2, were calculated, able to
fit the whole kinetic profile satisfactorily. The influence of irradiance on k1 and k2, as well as of flow rate on K1 and K2,
could be rationalized by this model. The influence of reactor geometry on k values could also considered, in view
of standardization procedures of photocatalytic experiments, or of
characterization of immobilized photocatalytic materials.The similarity of
behavior, and the coincidence of thek and K parameters, between experiments
in the gas and in the liquid phase, is fully compatible with, and clearly
interpreted by, reactions control at the interface. These reactions are ruled
kinetically, and also thermodynamically, by concentration gradients,
independently on diffusion and other phenomena in the bulk, either if the
latter is constituted by a liquid or by a gas phase, provided conditions of
turbulent flow are assured. The presence of a sorbent in a membrane structure,
such as the structure which has been obtained by the photografting method used
to manufacture the photocatalytic membranes employed in the present work,
affords an alternative concept in membrane science and technology, since the
endothermic step of creating a molecular-size cavity in the polymer for the
reacting species, either if arriving from the gas or from the liquid phase, is
virtually eliminated. At the same time, the thinnest of all conceivable
membranes may be realized, consisting in a monolayer where the adsorbed
molecules may interact with its surroundings.Quantum yields of
mineralization of substrates in annular photoreactors immobilizing the
photocatalyst in a membrane structure show a Langmuirian-type dependency on
initial concentration of substrates themselves, by which limiting quantum
yields, corresponding toinfinite concentration may be calculated,
together with an apparent thermodynamic constant, coinciding with the lowest
between K1 and K2 values, very often being K1⁢~K2.These
limiting quantum yields depend on radiant power absorbed per unit membrane
length, in the cylindrical geometry of photoreactors. In the low radiant power
range, they take the shape of a plateau corresponding to the maximum allowable
quantum yields, evaluated on the basis of a single hydroxyl radical produced
per each absorbed photon, thus showing the excellent performance of the
photocatalytic membrane reactors. On the contrary, at high radiant power
values, another apparent plateau is evident, at a value of about 1/5 (for the
experimental case of methane) with respect to the maximum value. This was
interpreted on the basis of the competition kinetics of hydroxyl radicals with
themselves, leading to hydrogen peroxide formation, other than with substrate
or intermediates molecules leading to mineralization. In this model, the
contribution of hydroxyl radicals to mineralization decreases with irradiance,
while the contribution of superoxide anion radical and its conjugate acid
increases. Two radical reactions thus appear to be responsible for
mineralization, that of•OH radicals, and that of the O2•−/H2O2• radical couple, the last of which acquiring
importance only in the experimental conditions of high radiating power. If
these contributions are considered together, in a weighted form, the calculated
equation perfectly fits experimental data, and gives rise to a sigmoid curve,
with two apparent plateaux values, as found experimentally.Finally,
the action of a photopromoting agent may be easily quantified and rationalized
by measuring quantum yields at infinite concentration, at high irradiance
values, as a function of concentration of photopromoting agent coimmobilized in
the photocatalytic membrane. When increasing photopromoter concentration above
an apparent threshold value, for which no effect could be observed,Φ∞ values increase considerably and approach the
maximum allowable for the investigated molecule. This should mean that the
decrease of quantum yield brought about by the increase of irradiance, and
interpreted by a recombination mechanism of hydroxyl radicals, may be fully
compensated by the addition of appropriate photopromoters at suitable
concentration. By this way, operation at high irradiance values is possible,
without losing any efficiency for the mineralization process.



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*Source: 283741-2008-03-13.xml*