A kinetic analysis methodology to elucidate the roles of metal, support and solvent for the hydrogenation of 4-phenyl-2-butanone over Pt/TiO2

The rate and, more importantly, selectivity (ketone vs aromatic ring) of the hydrogenation of 4-phenyl-2-butanone over a Pt/TiO 2 catalyst have been shown to vary with solvent. In this study, a fundamental kinetic model for this multi-phase reaction has been developed incorporating statistical analysis methods to strengthen the foundations of mechanistically sound kinetic models. A 2-site model was determined to be most appropriate, describing aromatic hydrogenation (postulated to be over a platinum site) and ketone hydrogenation (postulated to be at the platinum–titania interface). Solvent choice has little impact on the ketone hydrogenation rate constant but strongly impacts aromatic hydrogenation due to solvent-catalyst interaction. Reaction selectivity is also correlated to a ﬁtted product adsorption constant parameter. The kinetic analysis method shown has demonstrated the role of solvents in inﬂuencing reactant adsorption and reaction selectivity.


Introduction
Solvents are an indispensable presence in many catalytic liquid-phase reactions. The choice of solvent should not be arbitrary and is one which can be highly beneficial or detrimental to both activity and selectivity of catalytic reactions. Such a fact is well known, with observations of solvent effects originating in works such as those by Menshutkin, who in 1890 stated: 'By means of a proper choice of solvent, decisive acceleration or deceleration of a chemical reaction can be achieved' [1].
Consequently, solvent effects have become very well documented in organic synthesis [2] and, over the past 50 years, have been reported in heterogeneous catalysis [3]. Properties of the solvent such as dielectric constant and polarity play a role in determining the solubilities of gases (such as hydrogen), solvation of reactants and products as well as other mass transfer effects [4]. As well as influencing reactant and product behaviour, the solvent may also interact with the metal and/or support of the catalyst. A classic example of this is shown in the work by Boudart and co-workers [5][6][7] which explored the liquid phase hydrogenation of cyclohexene using a variety of silica supported catalysts with a range of solvents. Therein, the turn-over frequency (TOF) for Pd/SiO 2 was found to be solvent insensitive whilst in contrast, when using a Ni/SiO 2 catalyst, the use of polar or oxygenated solvents resulted in a marked decrease in TOF and a strong adsorption of the solvent itself on the nickel metal.
Ultimately, numerous effects can arise between solvent, catalyst and substrate which result in catalytic reaction systems whose behaviour can be very difficult to predict. This presents a particular challenge to industry where the following problems can be manifested as a result of these difficulties: High E-factors (kg by-products/kg products), in particular for the pharmaceutical industry [8,9]. 'Scale-up confidence' -prediction of plant scale reactor performance. Catalyst, feedstock and solvent choice constraints due to economic feasibility and environmental restrictions.
To understand and predict solvent effects, methodologies are needed that probe reaction behaviour from a fundamental physical http://dx.doi.org/10.1016/j.jcat.2015.06.007 0021-9517/Ó 2015 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). and chemical standpoint but are also pragmatic in nature so that a broad spectrum of application is possible.

Kinetic modelling of solvent effects in the literature
When modelling kinetics to describe solvent effects in catalytic liquid multi-phase reactions it is essential that proposed models have a fundamental mechanistic basis, together with estimated parameters that are physically meaningful in value and are statistically significant to justify their presence. Table 1 provides a summary of rate models that have previously been used for this area of study. Bertero et al. [10] considered a wide range of Langmuir-Hinshelwood (LH) expressions to describe the hydrogenation of acetophenone. Quality of fit (R 2 ) for all models used in this work was very high (0.999) possibly because at least some were parametrically over-determined. Optimal model choice was, therefore, based on the physical meaning of measured parameters (such as discounting models with negative adsorption constants) and using model selection criteria based upon comparison of residuals and degrees of freedom in each final model. Mathew et al. [11] utilised a similar approach and also checked adsorption parameters for thermodynamic consistency.
Mounzer et al. [12] modelled the kinetics of 2-octanol oxidation performed using a variety of n-heptane/dioxane mixtures as solvents. A LH approach including a product ketone desorption parameter, which was experimentally measured, provided the best description. This model was found to be statistically significant via both the F-and T-tests and showed an excellent correlation between solvent compositions, oxidation rate and the ketone desorption parameter.
Other approaches include the use of Michaelis-Menten-type expressions [13]. This method was shown to be pragmatic in describing solvent effects in ethyl pyruvate hydrogenation by discriminating a lumped reaction term from one relating to adsorption. The limited number of parameters in this model compromises quality of fit and, therefore, may be difficult to implement in multi-response systems.
A number of studies have attempted to include a competitive solvent adsorption term, K S , in their models. Kishida and Teranishi [14] developed a model for the hydrogenation of acetone using n-hexane as the solvent and, subsequently, fixed the rate constants in order to measure K S for other solvents. The assumption that the solvent does not influence rate constants was not justified in the work and the study also did not consider the effect of hydrogen solubility as a function of solvent. In contrast, Lemcoff [15] developed models with thermodynamically sound adsorption parameters for a mixture of polar and apolar solvents, again for acetone hydrogenation and found the K s term was only significant in the kinetic expressions for polar solvents such as water and 2-propanol. Recently, Mukherjee and Vannice [16] demonstrated a similar approach for citral hydrogenation. Their model was developed around citral conversion and validated against prediction of product formation. In this work, the assumption that the solvent competes for an active site is based around the fact that Nomenclature Symbol Description A pre-exponential factor (min À1 (for 1st order)) B(t) sensitivity function (-) inhibiting organic species (mol dm À3 ) k rate constant (min À1 (for 1st order)) k H Henry's constant (-) K equilibrium adsorption constant (dm 3 mol À1 (for 1st order)) L length (m) n reaction order (-) N stirred speed (min À1 ) P product organic species (mol dm À3 ) Par number of parameters (-) R rate of reaction (mol dm À3 min À1 (for intrinsic rates unless noted)) r p particle size radius (cm) R reactant organic species (mol dm À3 ) Greek letters A key element which is missing from the aforementioned studies is a detailed statistical analysis which can ascertain the significance of each of the parameters in the models developed. Such an approach could take model critique beyond R 2 and the removal of parameters due to lower or upper bound constraints. A possible approach is afforded by Quiney and Schuurman [17] who described the modelling of the water gas shift reaction kinetics under continuous flow and used a methodology which examined parameter sensitivities, parameter cross correlation and influence of parameter removal on R 2 values via use of the F-test.

Study of 4-phenyl-2-butanone hydrogenation over a Pt/TiO 2 catalyst
In this paper a detailed study of the hydrogenation of 4-phenyl-2-butanone (PBN) has been undertaken. This reaction has two distinctive routes to produce the fully hydrogenated product, 4-cyclohexyl-2-butanol (CBL). Intermediate compounds are 4-phenyl-2-butanol (PBL), produced by hydrogenation of the carbonyl group and 4-cyclohexyl-2-butanone (CBN), by hydrogenation of the aromatic ring. The reaction scheme is shown in Fig. 1 and features two reaction types, namely ketone (dashed arrows) or aromatic ring (solid arrows) hydrogenation.
The reaction system was chosen as the selectivity of the two pathways from the original 4-phenyl-2-butanone reactant can be influenced by the choice of solvent as shown by McManus et al. [18]. Therein, a variety of solvents were tested which were found to impact on the reaction pathway selectivity and rate of reaction. In general, protic, polar solvents (primary and secondary alcohols) favoured selectivity towards ketone hydrogenation whilst apolar, aprotic solvents (alkanes) favoured the aromatic ring hydrogenation route. In terms of the rates, those observed for alkanes and secondary alcohols were much greater than those for aromatic or primary alcohol solvents. A two-site active site model was postulated, whereby the aromatic ring hydrogenation was proposed to be occurring over the Pt, with ketone hydrogenation occurring at the interface between the Pt and the TiO 2 support with activation of the C@O group through adsorption in the titania oxygen vacancies.
In this paper, a kinetic model is presented utilising these data. In this work, an aim is to stress the importance of using established statistical analysis methods in the development of mechanistically based kinetic models, with application in this case to liquid phase hydrogenations and solvent effects. The approach, inspired by the work of Quiney and Schuurman [17], is used to strengthen the foundations of these kinetic models. A fundamental kinetic model for ketone and aromatic hydrogenation catalysis in this system is determined using an expansive dataset which employs n-hexane as the solvent. From this model, the effects of a wide range of solvents have been determined. This information provides a clear demonstration of not only the role of solvents in influencing reaction selectivity and reactant adsorption but also their interaction with the metal and support of the catalyst during reaction.

Experimental reaction studies
The experimental materials and methods are described in detail in the study by McManus et al. [18]; therefore, only a brief recapitulation is given, herein.
The 4% Pt/TiO 2 catalyst was supplied by Johnson Matthey and was prepared by incipient wetness from Pt(NO 3 ) 4 (Johnson Matthey) as the precursor with titania as the support (P25, Degussa). The catalyst was dried for 12 h at 120°C and then calcined at 500°C for 6 h. The catalyst was ground using a mortar and pestle and sieved to 645 lm for all reactions. The BET surface area of the catalyst Pt/TiO 2 (P25) was 56 m 2 g À1 with a pore size of 2.2 nm. The titania had an anatase to rutile ratio of 3:1 as determined by XRD and TEM analysis showed a metal particle size of 2.2 nm with a dispersion of 33%.
Reaction studies were carried out using a 100 ml Hazard Evaluation Laboratory (HEL) autoclave pressure reactor. In all cases, 0.1 g catalyst and 30 ml solvent were added to the autoclave and pre-reduced in situ under 1 bar H 2 pressure, 60°C, stirrer speed Symbols denote the following: r: rate of reaction (mol dm À3 min À1 ), k: rate constant (min À1 (for 1st order)), K: equilibrium constant (L mol À1 (for 1st order)).
[ ]: concentration (mol dm À3 ), R, P, I and S: reactant, product, inhibiting species and solvent respectively. Subscripts a, b, c, d and s: reactant adsorption, surface reaction, product desorption, inhibition and solvent adsorption steps respectively. 800 rpm for 1 h. Following reduction, a solution of 4-phenyl-2-butanone in a further 20 ml solvent was added to the reactor; reactions were carried out at 70°C, 5 bar H 2 and 1400 rpm stirrer speed. The reaction kinetics are intrinsic and not from transport limitations [18]. Table 2 summarises the three strategies of the experimental programme which have been taken in this work to build a mechanistically sound kinetic model that will link selectivity and adsorption constants to the choice of solvent. Series A utilises isothermal data with different starting concentrations of 4-phenyl-2-butanone. This dataset will allow the impact of concentration driving force on the kinetics to be explored. A number of Langmuir-Hinshelwood type models (varying in rate determining step and types of site) will be discriminated on the basis of parameter estimate quality and model response residuals.
The best candidate models will be taken forward to Series B, which incorporates multi-temperature data. Here, the activation energies will be estimated and the models further refined. Model fitting parameters will be strongly criticised from a statistical and physico-chemical perspective. This will further discriminate remaining models and potentially lead to additional fundamental understanding of the prevailing reaction mechanism. The most suitable model will finally be tested against experiments using a range of solvents (Series C) with the purpose of demonstrating the link between solvent, selectivity and the dominant adsorption constant.

Kinetic modelling procedure
Parameter estimation within the kinetic models was carried out using Athena Visual Studio v14.2Ó software [19]. The kinetic models tested within this work contain non-linear parameters (e.g. activation energies in the Arrhenius equation) and also include multiple concentration responses. To handle these challenges, two estimation methods were used in succession, namely, non-linear least squares and Bayesian estimation.
In general, the non-linear least squares method was used for initial discrimination of each of the kinetic models. The objective function of this method is the total residual sum of squares for the entire model. Subsequently the Bayesian estimation method was used to fine tune the parameter estimation outputs. This method considers the error covariance matrix between responses and aligns the objective function accordingly. By this method, any prejudice towards the smaller magnitude responses in the dataset is largely eliminated enabling a sounder basis for multi-response estimation and a stronger critique of model performance [20,21].
All response variables in the 4-phenyl-2-butanone hydrogenation reaction network are dependent upon the multiple reactions shown in Fig. 1, so the models must be solved implicitly using a set of differential equations: In Eq. (1), y denotes model responses, t denotes time and b denotes the model parameters. A direct decoupled method is used to estimate parametric sensitivities [21,25]: In Eq. (2a), B(t) defines the sensitivity function for each model response with respect to the model parameters. In Eq. (2b) it can be seen that defining sensitivities as a function of time allows them to be solved alongside the main system differential equations, improving solver efficiency and performance.
To minimise cross-correlation between the energy (activation energy, E a or equilibrium adsorption energy, DH ads ) and pre-exponential factor (A i ) parameters, a re-parameterised Arrhenius or van't Hoff equation was used: where the base temperature, T base = 343 K and A i,343 is the value of the rate constant k i or K i at 343 K. 343 K is chosen as this temperature was used for the isothermal stage (Series A) of the parameter estimation process. Hence, this provides an accurate initial prediction for the A i parameters during the multi-temperature data fitting stage, thus facilitating a more accurate estimation of E a or DH ads parameters.
The fitting process can be further improved by solving A i,343 as an exponential term and lumping fitted value, E a or DH ads with constants T base and ideal gas constant, R (J K À1 mol À1 ) to give fitting parameter E a,lump or DH ads,lump . This typically brings the values of A i,343 and E a,lump or DH ads,lump into the same order of magnitude (typically ± 1-10) further reducing cross-correlation in this expression: 3. Results and discussion

Kinetic modelling of the effect of initial 4-phenyl-2-butanone concentration in a n-hexane solvent
In the study by McManus et al. the reaction profiles as a function of time were shown to be very similar up to 60 min for all starting concentrations [18]. Initial rates which are independent of initial organic reactant concentrations have also been previously seen for acetophenone hydrogenation [22]. This has been described as an apparent zero order observation as it is relevant to the initial stage of the reaction. Mechanistically, this observation suggests that adsorption of 4-phenyl-2-butanone is strong on the catalyst surface and may dominate in terms of surface coverage. Therefore, it is important to incorporate 4-phenyl-2-butanone Table 2 Experimental data modelled in this study. adsorption within mechanistic descriptions of the kinetics. In all individual experiments however, 4-phenyl-2-butanone shows an apparent order dependence of greater than one with reaction time, irrespective of starting 4-phenyl-2-butanone concentration. These observations are, therefore, consistent with a reaction mechanism that may feature the following:

Series Variables Constants
An adsorption term for the reactant 4-phenyl-2-butanone, as apparent zero order observations in the work of McManus et al. suggest a strong interaction of this species on the catalyst surface. An influence of product adsorption effects, slowing the overall progress of 4-phenyl-2-butanone conversion over time.
In order to explore these effects the following generalised sequence of elementary steps was used as a basis for the kinetic models in this study to describe the dataset in Series A: where * i denotes a particular active site on the catalyst surface (where i = 1, 2, . . ., n). In conjunction with this the following are noted: The rate of hydrogenation of 4-phenyl-2-butanone was found to be apparent first order in H 2 in the study of McManus et al. In the proposed models (Table 3), the hydrogen driving force is always taken as first order. The H 2 pressure varied data in McManus et al. were explored at one starting 4-phenyl-2-butanone concentration (0.26 mol dm À3 ). The need for an additional H 2 adsorption (and/or dissociation) equilibrium constant term was found to be negligible across these data. This suggests either H 2 does not adsorb onto the surface (i.e. plays an Eley-Rideal type role) or its adsorption is significantly weaker than the organics in competing for the same site. In order to explore the above possibilities, an 'apparent' site competition effect will be explored by placing a square term on the denominator of the kinetic expressions, and for the Eley-Rideal-type mechanism the denominator will remain first-order. The first order in H 2 behaviour in the paper of McManus et al. would suggest that H 2 behaves in an associative rather than dissociative manner in the reaction mechanisms. In the latter, an apparent order closer to 0.5 would be expected. H 2 solubility into the liquid phase does change with either solvent choice or temperature. This was incorporated into the kinetic expressions [23].
Based on the elementary steps described in Eqs. (5a-5d), eight candidate models were derived which may be suitable for the 4-phenyl-2-butanone hydrogenation system (see Table 3). These models will systematically explore three key features of the reaction mechanism: Rate determining step of mechanism: organic adsorption (Eq. (5a)) or surface reaction/hydrogen adsorption (Eq. (5b)); the latter two steps cannot be decoupled in the dataset utilised. Apparent competition between organics and hydrogen for a specific active site, or an Eley-Rideal type mechanism with H 2 playing a gas-phase role only. The presence of different active sites for the ketone and aromatic ring hydrogenation reaction routes.
The Series A dataset was fitted to all eight of the models described in Table 3. The dataset comprised 25 independent experimental observations (5 start concentrations Â 5 batch-time sampling points), each containing concentration responses for 4-phenyl-2butanone, 4-phenyl-2-butanol, 4-cyclohexyl-2-butanone and 4-cyclohexyl-2-butanol. Fig. 2 shows the residuals for all concentration responses in the eight models when a first estimation pass was carried out using non-linear least squares.
Inspection of Fig. 2 affords some initial discrimination; models 6b, 6d and 6f systematically contain the lowest residuals for all responses, models 6a and 6e exhibit poorer residuals for the 4-phenyl-2-butanone and 4-cyclohexyl-2-butanone responses and models 6c, 6g and 6h are, in general, poorer in the prediction for all responses. Further inspection of the batch-time predictions of the latter three models showed the experimental results were poorly captured. This was further confirmed by running the parameter estimation routine using the Bayesian approach.
Before selecting a smaller group of strong candidate models, the quality of the parameter estimates was also investigated for the eight candidate models. As models 6a and 6e show a clear compromise in residuals for 4-phenyl-2-butanone and 4-cyclohexyl-2-butanone concentration responses, a further  Fig. 3.
Critically, Fig. 3 shows that the confidence intervals for this reaction are much larger for 6a and 6e than for the 6b, 6d and 6f models. Similar trends were seen for the parameters describing adsorption of 4-phenyl-2-butanone onto the surface. In line with this, models 6b, 6d and 6f were taken forward for further analysis as they provide the best fitted description of the data matched by the best parameter confidence intervals. All three models have apparent site competition between organics and hydrogen in common, which is in line with observations discussed at the start of this section.
Models 6b, 6d and 6f were subsequently tested using the Bayesian estimation method for additional model refinement and to identify parameters of importance in each model. The results are presented in Table 4.
Each model is similar in overall performance, irrespective of the objective function approach (e.g. Bayesian objective function and residual sum of squares). For the rate constant (ln(k)) parameters, a key difference is seen with model 6d which suggests that the onward 4-cyclohexyl-2-butanone to 4-cylohexyl-2-butanol (CBN ? CBL) reaction does not occur. For the adsorption (ln(K)) parameters there is a clear difference in the dominant product inhibition, in both magnitude and confidence interval. The introduction of temperature varied data is a necessary next step to understand the difference between these models and discriminate further.

3.2.
Kinetic modelling of the effect of temperature in a n-hexane solvent  Table 3.   considerably lower and decreases with temperature. These temperature dependent observations suggest that the activation energy for aromatic ring hydrogenation is higher than that for ketone group hydrogenation, which agrees with the literature [22]. Selectivity to the fully hydrogenated product 4-cyclohexyl-2-butanol, increases with both time and temperature. In Fig. 4, after 120 min, the selectivity to 4-cyclohexyl-2-butanol appears to increase with temperature at the expense of 4-phenyl-2-butanol selectivity. 4-Phenyl-2-butanol to 4-cyclohexyl-2-butanol (PBL ? CBL) is an aromatic ring hydrogenation route, again demonstrating the prevalence of this reaction in n-hexane.
The Series B dataset was fitted to the three models taken forward from Section 3.1. The dataset comprised 30 independent experimental observations (6 reaction temperatures Â 5 batch-time sampling points), each containing concentration responses for 4-phenyl-2-butanone, 4-phenyl-2-butanol, 4-cyclohexyl-2-butanone and 4-cyclohexyl-2-butanol. Here the rate and equilibrium constants fitted in Section 3.1 were expanded into full Arrhenius and van't Hoff equation form, as described in Section 2.2.
Models 6b, 6d and 6f comprised 12, 14 and 14 fitting parameters respectively. The parameter values for the three isothermal models displayed in Table 4 were used as the initial predictions for the pre-exponential factors in the fitting in this section.
The first parameter estimation pass using Bayesian estimation revealed similar residuals for all three models and a number of parameters with large 95% HPD intervals. This suggested that all three models were over-parameterised to describe the multi-temperature dataset. Statistical analysis was carried out on each model using a methodology based on Quiney and Schuurman, [17] in order to remove non-influential parameters from the fitting procedure. An example of this process, for a model based on Eq. (6d) is shown in the Supplementary Information.
Each time a parameter is removed from an overall set of rate expressions, an F-test is then invoked which addresses whether the change in residuals of model responses in the 'n À 1' parameter model in comparison with the 'n' parameter one is statistically significant. This is often defined as a 'nested model' problem and the F-statistic can be calculated as follows: where F is the F-statistic, RSS 1 and RSS 2 are the residual sum of squares in the nested and original model respectively, par 1 and par 2 are number of parameters and obs is the total number of observations. The F statistic generated is compared with F crit (p = 0.05) under these constraints. If the F statistic is smaller than F crit , the removal, equating or fixing of a parameter is deemed acceptable as a statistically significant increase in residuals has not been induced. Fig. 5 shows the successive F-statistic values obtained when parameters are removed from each of the model descriptions. Model 6b showed statistically significant changes to the residuals when more than 2 parameters are removed. Up to that point, the model also contained indeterminate parameters when solved. A similar outcome was seen for model 6f, albeit after the removal of a large number of parameters. These models were discarded due to both of these issues. Model 6d was the most successful and did not exceed F crit during the removal of 6 parameters. At this point, the model contained no indeterminate parameters or estimates with 95% HPD intervals greater than 100% of the estimated value.
A finding for all three candidate models was that the parameter reduction procedure contained steps where two activation energies were equated with one another. In each case, this involved 'pairing' of reaction pathways which have the same mechanism: ketone hydrogenation and aromatic ring hydrogenation.
For the most successful model, 6d, the adsorption parameter K ket,PBL , featuring in the ketone hydrogenation routes, was found to be insignificant. Meanwhile K arom,CBN was found to be a highly significant parameter for the aromatic ring hydrogenation route. The removal of the K arom,CBN parameter was found to have a significant effect on the residuals.
The final parameter estimates for model 6d, the most appropriate model to describe the reaction kinetics of the system, are detailed in Table 5. Full details of the final statistical plots (parity, residual) for this model can be found in Supplementary Information. The final rate equations for the model are as follows: Examining the results summarised in Table 5, the E a for the aromatic ring hydrogenation steps is higher than that for ketone hydrogenation, which was discussed following experimental observation in Section 3.2. The E a values estimated are in line with a surface reaction limited mechanism rather than an organic adsorption limited step. Previous work on a similar system, p-isobutyl acetophenone hydrogenation [11] estimated E a,ket and E a,arom to be 42 and 47 kJ mol À1 , respectively, whilst the heat of adsorption of the reactant was À5 kJ mol À1 .
Similarly, in a kinetic study of ketone  hydrogenation [23], heat of adsorption parameters was found to be in the range À5 to À15 kJ mol À1 . In the current study, the fitted heats of adsorption parameters were found to be indiscriminate from zero, which is feasible in line with the low value estimates from previous studies. The removal of these heats of adsorption parameters for model 6d is demonstrated in Table S3 of Supplementary Information. The presence of the parameter K arom,CBN in the final model has significant similarities with the study by Mounzer et al. [12]. This suggests that desorption of this intermediate, the selective product using n-hexane as the solvent, is a critical component of reaction progress and selectivity. In parallel to this, the final model found the subsequent ketone hydrogenation of 4-cyclohexyl-2-butanone to be a negligible parameter, owing to the fact that 4-cyclohexyl-2-butanone shows a preference to adsorb on the aromatic hydrogenation site rather than the ketone hydrogenation site.
The final model confirms that the organic reactants, for both reactions, compete with adsorbed hydrogen. In the study by McManus et al. it was postulated that two active sites were present, namely a Pt site which is largely selective to aromatic hydrogenation and a site at the interface between the platinum and titania support for ketone hydrogenation; C@O adsorption in an oxygen vacancy weakening the C@O bond for hydrogenation. In this study it was discussed that the former site could be suppressed by the use of certain solvents such as aromatics, which could strongly adsorb on the Pt. The success of the two site model gives credence to this postulation and will be further tested for a range of solvents in Section 3.3.
Qualitative discussion may be afforded around partition coefficients of the different reactants and products in this system (based on their relative distribution in octanol vs. water at equilibrium) which could explain the importance of K arom,CBN but not K ket,PBL . An examination of log P values reveals only a small transition when 4-phenyl-2-butanone is converted to 4-phenyl-2-butanol (2.46 ? 2.47) but it is significant when 4-phenyl-2-butanone is converted to 4-cyclohexyl-2-butanone (2.46 ? 2.77). The strength of 4-cyclohexyl-2-butanone adsorption appears to be a critical solvent parameter in this case and more hydrophobic solvents, such as the n-hexane examined, herein, may be critical to assisting this final stage of the aromatic hydrogenation reaction mechanism. This suggests that in developing kinetics of solvent effects through Langmuir-Hinshelwood descriptions, solvation and adsorption of reactants and products may be coupled in many systems and care must be taken in the interpretation.

Kinetic modelling of 4-phenyl-2-butanone hydrogenation in a range of solvents
The kinetic model elucidated in Sections 3.1 and 3.2 can now be applied to a range of solvent types (Series C in Section 2.1). In all cases, individual solvent reaction data were fitted to a two site model with competition between hydrogen and the organics. The parameter reduction method of Quiney and Schuurman [17] used above was again applied to reduce the expression if necessary.
As Fig. 6 shows, the generalised model for 4-phenyl-2-butanone hydrogenation shows a good correlation when applied to a range of different solvents and gives good predictions. The next step is to assess the key parameters (k arom , k ket and K arom,CBN ) across the entire range of solvents. Fig. 7 shows a log-linear plot of fitted adsorption constant, K arom,CBN against 4-cyclohexyl-2-butanone selectivity after 120 min. A good correlation is seen for the majority of the solvents, with acceptable 95% HPD intervals for the individual solvents in most cases. This correlation was also observed at all reaction times (see Supplementary Information, Fig. S4 for an example after 10 min). This relationship suggests that desorption of the 4-cyclohexyl-2-butanone product is a key factor in determining the reaction selectivity in each of the solvents studied. For the alkanes examined, the adsorption constant is low and the 4-cyclohexyl-2-butanone product is easily desorbed into the liquid phase, giving rise to a high 4-cyclohexyl-2-butanone selectivity. In primary and secondary alcohol solvents, the adsorption constant is much higher and desorption of the 4-cyclohexyl-2-butanone product back into the solvent is much more difficult. This may be understood by the weaker solvation of the 4-cyclohexyl-2-butanone in the hydrophilic alcohol solvents due to its greater hydrophobicity. The result, when using these solvents, is a less favourable desorption process for the 4-cyclohexyl-2-butanone product. A weaker trend is found for the aromatic solvents with toluene and p-xylene showing low 4-cyclohexyl-2-butanone selectivity and high K arom,CBN in contrast to tert-butyl-toluene which features an alkyl group in its structure so may display aromatic-alkane hybrid behaviour. Fig. 8 shows the ratio of the rate constants for the two pathways (k arom /k ket ) with solvent. There is a clear connection between the ratios of the rate constants (reflecting selectivity to 4-cyclohexyl-2-butanone) with solvent type: with high values found for solvents with little interaction with the catalyst and low values (61) for solvents which strongly interact with the catalyst. In Fig. 9, the rate constants for ketone and aromatic hydrogenation for the solvents are examined. Whilst the rate of phenyl group hydrogenation (k arom ) is strongly dependent on choice of solvent, the ketone group hydrogenation rate (k ket ) is found to largely independent of the solvent used. The exception to this is the secondary alcohol solvents and these will be discussed later. The change in selectivity as a function of solvent is thus largely driven by its effect on the rate of phenyl group hydrogenation. This is consistent with the proposed dual site nature of the catalyst [18]. Again, the correlations shown in Fig. 9 were observed at all different reaction times (see Supplementary Information, Fig. S5 for an example after 10 min).
An important note is that the normalised cross correlation values between estimates of k arom and K arom,CBN never reached significant values (>0.95) [24]. This statistical observation further shows that the key kinetic parameters used in fitting solvent data describe different effects, in this case availability of sites and/or rate (k ket and k arom-) as well as the ease of desorption of CBN over Pt (K arom,CBN ). Full details of condition numbers for all solvents are given in Supplementary Information.
The aromatic hydrogenation route has been discussed to occur on the Pt sites of the catalyst surface [18]. Based upon this, k arom could be described as k Pt (1 À h solv ) which relates the number of vacant sites available as a function of solvent adsorption strength. The flatness of the k 1,ket parameter across most solvents suggests that solvent inhibition is not a factor over this site. This site is postulated to be the interfacial site which hydrogenates the C@O bond, a functional group not present in any of the solvents used. Product inhibition over the ketone hydrogenation site was ultimately found to be a low sensitivity parameter in Section 3.2.
The clear exception in Fig. 9 is the secondary alcohols which show k arom sites in comparable levels to an alkane solvent and a higher level of k ket sites. In Fig. 6B, the selectivity to 4-cyclohexyl-2-butanone is found to be low in secondary alcohols, which would suggest that these solvents do not strongly adsorb on the Pt sites, but still inhibit reactant adsorption mode via a different mechanism. An examination of dipolarity (p x 1 ) in [26] shows that 1-propanol and 2-propanol have values of 0.52 and 0.48 respectively, whilst n-hexane has a value of À0.08. Hence, the large difference in k arom observed between primary and secondary alcohols suggests that electronic effects are an unlikely cause of this disparity. This indicates that the effect observed is likely to be steric in nature, owing to the difference in adsorption conformation of primary and secondary alcohols.
4-Cyclohexyl-2-butanone selectivity is also low in secondary alcohols as this product does not desorb easily into the liquid phase due to hydrophobicity factors discussed earlier. The higher k ket parameter for secondary alcohols may suggest this parameter may be coupled in this instance, i.e. ketone hydrogenation is  Table 6 depicts the separate parameters which impact selectivity and active site availability. k ket is again largely unchanged across the results, whilst k arom drops by $60% when a small amount of toluene is added to the n-hexane and by $85% when the solvent is completely switched to toluene. Overall, 4-phenyl-2-butanone conversion over 120 min follows a similar trend. Selectivity is tuned much more aggressively by the addition of toluene with a small amount influencing the K arom,CBN parameter.
In Table 6, a comparison is made with parameter estimation results estimated using the competitive solvent adsorption approach described in Table 1, with the aim of comparing the current method with a previous literature approach using concentration varied data. In this model, 5 adsorption parameters are fitted, namely, K arom,CBN , K arom,hexane , K arom,toluene , K ket,hexane, and K ket,toluene . The hexane solvent adsorption terms were found to be insignificant on both sites, as was the adsorption of toluene on the ketone hydrogenation site. A strong adsorption of toluene was estimated, as postulated, and smaller but still significant adsorption strength of 4-cyclohexyl-2-butanone was seen. The K arom,CBN parameter returned a large 95% HPD interval but the removal of this parameter showed a significant drop in model quality as ascertained by the F-test. To further examine this result this parameter was reinstated and the predictions using this model were examined (Fig. 10).
The solvent adsorption parameter model provides a reasonable prediction of 4-phenyl-2-butanone consumption across the three datasets but there are discrepancies in the selectivity prediction of PBL and CBN, chiefly at high toluene concentrations. This is matched by the high uncertainty but remaining importance of the K arom,CBN parameter which suggests that this is changing as a function of solvent concentration. This suggests the observations cannot be related to adsorption strength of the catalyst surface alone and factors such as solubility of the reactants and products in the solvent, as discussed, must play a role in the overall observed kinetics in this system.

Findings in context to previous solvent effects work
In Section 1.1, it was stressed that the pursuit of elucidating solvent effects in liquid-phase reactions via kinetic modelling should incorporate a strong statistical and mechanistic basis. The approach demonstrated in this work is discussed in reference to these critical requirements. The critical pre-determining step in any kinetic study is the number of proposed models to which data are subsequently fitted. Use of a range of models that include different rate determining steps in their mechanism [10,12,24], assumptions of non-competitive and competitive reactant adsorption [16,22], dissociative or associative molecular adsorption [11,22] and inhibition effects [12,16] all defines this scope. At a maximum of these possibilities, model comparison without a systematic statistical analysis is likely to provide limited conclusions which have a physical meaning. In the current work, such a range of steps were condensed down into eight, 'over-parameterised', starting models with different rate determining steps and active site basis. From there, parameter reduction via sensitivity, condition number and F-test analysis takes each model to a defined stop point. In this case, the bi-directional problem of over-simplifica tion/complication of kinetic models can be avoided.
In the work of Bergault et al. [22], the batch-time acetophenone hydrogenation behaviour draws comparison with the current study, particularly with initial rate behaviour at different acetophenone start concentrations. All possible adsorption effects (including inhibition) were considered and led to indeterminacy in their estimation when the data were fitted, as is seen in the current study. This was circumvented by normalising the adsorption constant values; however, therein the statistical significance of the newly estimated parameters is not discussed. Similarly, their proposed model does not link parameters in identical reaction pathways, of which the estimated parameters in the work would suggest to be a viable move. A similar process is found in the study by Mathew et al. [11]. In this work, two E a values for aromatic ring hydrogenation are estimated at 47 and 44 kJ mol À1 but are left unpaired. A parameter pairing approach in the current work was found to have little impact on residuals and freed up extra degrees of freedom to aid in the parameter estimation process, building on these studies.
A parallel can be drawn between the current study and the mixed ketone hydrogenation study of Chang et al. [24]. The latter eliminated parameters based on insignificant t-values and wide 95% confidence intervals. A product desorption term was found to be a significant parameter for the dominant ketone hydrogenation pathway but not the other reaction pathways. Instead, this desorption term appears as an inhibition factor for the other pathways, again as reported in this study. The study also demonstrated that all ketone hydrogenation routes could be adequately lumped together into one expression, which is similar to the linking of the reaction pathways demonstrated in this work.
The importance of a product desorption term is also in line with the work of Mounzer et al. [12], whereby desorption of product P from active sites was driven by solvent composition. In the current work, the ring hydrogenated product, 4-cyclohexyl-2-butanone, Table 6 Parameter estimates and 95% HPD intervals for fits of experimental data using mixtures of n-hexane and toluene as solvent. Comparison with results when fitting all experiments at once using solvent adsorption approach. exhibits greater hydrophobicity than that of the ketone hydrogenated product 4-phenyl-2-butanol. The former has a greater likelihood of removal from the catalyst surface by apolar aprotic solvents such as n-hexane compared with the alcohols. The correlation between solvent selectivity towards 4-cyclohexyl-2-butanone and K arom,CBN may be a reflection of this. It is suggested that for future study, this selective adsorption effect could be explored computationally via the use of density functional theory (DFT), such as the approach used in the work explored in [4].
A further comparison can be made with previous works which have used K S to describe the inhibition role of the solvent [14,15,27]. In the current work, the essence of this parameter is seen in the analysis of the full solvent range; values of k arom are significantly reduced in primary alcohols and aromatic solvents hence providing a measure of inhibition to catalytically active sites compared to solvents which adsorb weakly (e.g. alkanes). As described earlier, solvent to substrate ratios are often high in batch-time kinetic studies and so the magnitude of the [S] variable can induce a bias towards K S in the fitting procedure, swamping the importance of other variables in the regression.
In the current work, the use of the K s fitting approach was explored over three datasets where hexane and toluene solvent concentrations were varied. Whilst this approach clearly highlighted the strong adsorption of toluene over the sites for aromatic ring hydrogenation, it was unable to achieve an encompassing description across the dataset. This was attributed to the changing K arom,CBN -parameter as a function of solvent choice which the authors believe to be linked to ease of product desorption back into the solvent. It is therefore recommended that care is taken when considering the K s parameter in the analysis and a prudent first step is to analyse individual experimental runs without it.

Conclusions
The role of the solvent can be critical in many catalytic liquid phase reactions, in particular influencing adsorption/desorption of reactants and products as well as influencing overall catalytic turnover rates and gas phase solubility. Development of a physically sound model of this role, as well as catalyst metal/support and reactants/products is very complex due to the influence and interdependencies between each of the model parameters. Data from an experimental study of 4-phenyl-2-butanone hydrogenation over a 4% Pt/TiO 2 catalyst have been used to develop a kinetic analysis methodology to elucidate solvent effects and unify solvation, dominant adsorption constant and product selectivity.
The methodology has successfully drawn upon previous mechanistic descriptions proposed in the literature [11,12,22]. The fitting of data to these models has been combined with a rigorous statistical analysis procedure to eliminate non-influential parameters in their descriptions [17]. During this procedure, the physical and chemical meaning of estimated parameters was considered and this led to pairing of similar reaction pathways (e.g. initial reactant and intermediate ketone hydrogenation). The final model assumed the surface reaction of the organic species with hydrogen to be the rate determining step and included a selective product, 4-cyclohexyl-2-butanone, desorption term. Desorption of this product was found to vary with solvent and was directly linked to the observed product selectivity.
The kinetic analysis methodology proposed can quickly elucidate a fundamentally and statistically sound kinetic model for a chosen system even with limited experimental data. This can subsequently be used to understand the link between solvent, dominant mode of adsorption and selectivity as well as predict catalytic turnover rates based on availabilities of different catalytically active sites in the presence of a range of solvents. In terms of 4-phenyl-2-butanone hydrogenation over 4% Pt/TiO 2 , kinetic modelling has confirmed the presence of two active sites, the impact of solvent on availability of Pt active sites and the role of the solvent in assisting desorption of intermediate 4-cyclohexyl-2-butanone [18].

Acknowledgments
We acknowledge EPSRC for funding as part of the CASTech grant (EP/G011397/1) and the Department of Employment and Learning for a studentship (IM). NSB was funded by a PhD scholarship from the University of Birmingham. SKW was supported by an Engineering Doctorate Studentship in Formulation Engineering at the University of Birmingham sponsored by the EPSRC (EP/G036713/1) and Johnson Matthey. The authors would also like to acknowledge Dr Mike J. Watson (of Johnson Matthey) for valuable discussions on this topic.