New insights on microscopic properties of metal-porphyrin complexes attached to quartz crystal sensor

A quartz crystal adsorbent coated with 5,10,15,20-tetrakis(4-methylphenyl) porphyrin was used to examine the complexation phenomenon of three metallic ions [aluminum(III), iron(III) and indium(III)]. The aim is to select the appropriate adsorbate for metalloporphyrin fabrication. The equilibrium adsorption isotherms of tetrakis(4-methylphenyl) porphyrin were performed at four temperatures (from 300 to 330 K) through the quartz crystal microbalance (QCM) method. Subsequently, the experimental data were analyzed in order to develop a thorough explanation of the complexation mechanisms. The experimental results indicated that the aluminum(III) chloride is the adequate material for metalloporphyrin application. Theoretical investigation was established through physics adsorption models in order to analyze the experimental isotherms. The AlCl3 isotherms were modeled via a single-layer adsorption model which is developed using the ideal gas law. Whereas, the FeCl3 isotherms were interpreted via a single-layer adsorption which includes the lateral interactions parameters (real gas law), indicating the lowest stability of the formed iron-porphyrin complex. The participation of the chloride ions in the double-layers adsorption of InCl3 was interpreted via layer by layer formulation. Interestingly, the physicochemical investigation of the three adopted models indicated that the tetrakis(4-methylphenyl) porphyrin adsorption was an endothermic process and that the aluminum(III) chloride can be recommended for an industrial application because it presents the highest adsorption energy (chemical bonds with porphyrins).

www.nature.com/scientificreports/ The quartz crystal, which is covered with a layer of gold on both sides, is brought into resonance by means of an alternating electric current. For the adsorption measurement, the adsorbent was doped onto the clean crystal surface by spin coating technique. In the bain-marie (reactor with 100 mL of pure water), the adsorption cell was placed in a Teflon probe and it was covered by a ring in order to protect the electrode from the penetration of liquid. The connection of the probe with the frequency-counter monitor was assured by means of a coaxial cable. Then, 15 injections of adsorbate (AlCl 3 /FeCl 3 /InCl 3 ) were added in the reactor in order to increase the concentration of the metallic ions. The frequency-counter monitor indicated the frequency variation corresponding to the final concentration after each adsorbate addition.
A slight frequency variation was observed after each adsorbate solution addition (slight mass variation of one of the crystal electrodes). This effect was modeled by Sauerbrey in 1959 26 (Fig. 3).
According to Fig. 3, oscillating quartz with a thickness h and without deposited mass m gives the following resonance frequency (f 0 ): where, λ (λ = υ * f 0 ) is the propagation of acoustic wavelength which is twice the thickness of the quartz (The resonance condition verifying that a half wavelength is confined in the thickness of the resonator) and υ is the propagation speed of the acoustic wave (3336 × 10 5 cm/s).
Then, the addition of mass to the quartz surface creates an increase in the thickness (∆h) which causes a resonant frequency change (∆f). Therefore, the rise of the thickness (mass) induces a decrease in the frequency in accordance with the following equations: where, the mass variation (∆m) can be written as a function of the crystal density ρ (g/cm 3 ) and the sensitive surface of quartz A (cm 2 ).
By combining these equations, we obtain the following expression 27 : This equation is called the Sauerbrey's equation which can be otherwise written 26,28 :  Experimental data discussion. Firstly, the adsorbed amounts depicted with the adsorption isotherms ( Fig. 4) confirm that the complexation of the tetrakis(4-methylphenyl) porphyrin by the three metallic ions In 3+ , Al 3+ and Fe 3+ was carried out at all the temperatures. It is confirmed that the tetrakis(4-methylphenyl) porphyrin should be a chemical sensor of the three metals.
Secondly, by comparing the performance of the three adsorption systems in terms of quantity, we can note the following order of the adsorption performance: A Q (AlCl 3 ) > A Q (FeCl 3 ) > A Q (InCl 3 ). The adsorbed quantities  www.nature.com/scientificreports/ are the highest for AlCl 3 . Then, the aluminum chloride is the best adsorbate compound for the tetrakis(4methylphenyl) porphyrin complexation. Lastly, it is clear from the experimental data of the three adsorption systems that the AlCl 3 isotherms show a unique stable saturation level for all the temperatures, the adsorbed quantities of FeCl 3 decrease after the saturation level and the InCl 3 isotherms present two stability states. It should be suggested that the tested porphyrin adsorb only one layer of cationic metal for AlCl 3 and FeCl 3 while, many adsorbed layers are formed in the case of InCl 3 . The multi-layers ionic adsorption of the indium chloride takes place via the layer by layer (LBL) process which is based on charge neutralization between particles having opposite charge signs (anions and cations) 20,29 .
In the following section, the microscopic investigation of these experimental observations is carried out through the physical modeling of the experimental data.

Theoretical modeling of adsorption isotherms by statistical physics treatment
Adsorption models development. According to the adsorption isotherms of tetrakis(4-methylphenyl) porphyrin (Fig. 4), we can notice two phenomena: single-layer adsorption of AlCl 3 and FeCl 3 , and LBL multilayers adsorption of InCl 3 . The experimental isotherms can be analyzed via an analytical physical modeling in the light of the statistical physics treatment.
The first progress of this advanced treatment is seen against the oldest empirical equation elaborated by Langmuir et al. 19 . The Langmuir model expects that an adsorbent site can utmost integrate one particle however our statistical physics models guess that one receptor site can suit n particles where n is a variable number. In addition, our statistical physics models assume the presence of various adsorption energies for various receptor sites, while the empirical models just accept the presence of one adsorption energy level for all the adsorbent sites. Furthermore, the statistical physics models give information about the number of adsorbed layers during the adsorption mechanism whereas, the Langmuir model assumes that one adsorbed layer is formed during the adsorption process. It should be also mentioned that in the case of the multi-layers ionic adsorption, we have fundamentally to use a model that reflects a layer by layer adsorption 20 . The empirical models do not assess this supposition.
In reality, the analytical development of the statistical physics models requires to take account of some assumptions: First of all, it is assumed that the adsorption system can be studied through the grand-canonical ensemble of Gibbs demonstrated in previous works 30,31 . Thus, the complexation reaction involving the free phase (AlCl 3 / FeCl 3 /InCl 3 ) and the tested adsorbent (tetrakis(4-methylphenyl) porphyrin) is summarized in Eq. (7 30,32 : where, I is the adsorbate ion in liquid phase, P is the 5,10,15,20-tetrakis(4-methylphenyl) porphyrin molecules in solid state, (I) n -P is the Ion(III)-Porphyrin complex and n is the stoichiometric coefficient of the adsorption reaction. It represents the number of bonded ions per adsorbent site. In general, this parameter can identify the nature of the adsorption process (n ≤ 0.5: multi-interaction process, n ≥ 1 multi-ionic process).
The studied system, which is supposed in the grand-canonical situation, is characterized by the chemical potential (μ) and the temperature (T) imposing from the outside towards the considered system. These variables are included in the general expression of the partition-function of the grand-canonical ensemble (z gc ) which is the starting point for each model development [30][31][32] .
Concerning the adsorption via a formation of one adsorbed layer, we take account of one energy level (− E). For the double-layers and the multi-layers adsorption processes (LBL adsorptions), two energies (− E 1 ) and (− E 2 ) can be responsible for this process. Note that the first energy (− E 1 ) characterizes the adsorption of the first layer; and the second energy (− E 2 ) is in relationship with the formation of the additional formed layers 29,32 .
The next stage of this physical modeling consists of calculating the average number (N 0 ) of identical occupied porphyrins sites (P m ) which has the following expression 30 : Here, we apply the chemical potential coupled to the ideal gas approach (μ p ). In the presence of this mean potential, we can consider that one individual particle has no interaction with the rest of the system like an ideal fermions gas of electrons. It can be written as a function of the partition-function of translation (z Tr ) and the number of adsorbates (N) 29-31 : The same modeling work is also performed using the chemical potential of a real gas (µ r ). In this case, the lateral interactions between the adsorbates at free state are taken into account and the cohesion pressure a and the covolume b are included in the expression of µ r 20,33 : Finally, the adsorbed amount expression (A Q ) of each physical model is determined by the next equation 30,31,33 : Single-layer model Where c1/2 is: Where w1/2 is:

Double-layers model
Where c1 and c2 are: Where w1 and w2 are:

Multi-layers model
Where c1 and c2 are:  Where c1 and c2 are functions of w1 and w2: All models expressions are developed through the statistical physics formalism and constitute advanced forms of the empirical expression of the Langmuir model. The difference between the classical models (ideal gas approach) and the advanced forms(real gas approach) is essentially seen in the number of parameters in the analytical expressions of the models but they contain in their expressions parameters that are important from a physical point of view, unlike empirical forms, whose parameters generally have no physical meaning.
Fitting of adsorption isotherms with the analytical models. The six adsorption models (Table 1) were applied on all experimental isotherms by the intermediate of a numerical fitting program 29 . The criterions to select the best model are the RMSE coefficient (Residual-root-mean-square-error), the AIC coefficient (Akaike-information-criterion) and the determination coefficient R 2 . Table 2 shows the values of the three adjustment coefficients. According to Table 2, the experimental data of AlCl 3 can be interpreted by the single-layer model (ideal gas approach) whereas; the adsorption isotherms of FeCl 3 show the best coefficients of adjustment with the singlelayer model of real gas. This explains that the decline of the FeCl 3 isotherms at high equilibrium concentration is fundamentally due to the lateral interaction impacts and confirms that the aluminum ions are the best compounds for porphyrin complexation in terms of stability. On the other hand, the LBL double-layers model (ideal gas approach) is selected for the theoretical description of the InCl 3 adsorption. In this case, two adsorbed layers are formed based on charge neutralization between cations (In 3+ ) and anions (Cl − ). Table 2. Values of the correlation coefficient R 2 , the residual root mean square coefficient RMSE and the Akaike information criterion AIC deduced from the numerical adjustment of experimental isotherms with the three statistical physics models. The italic values are the values of adjustement coefficients (R 2 /RMSE/AIC) of the best model devoted for the microscopic description of each experimental adsorption system (AlCl 3porphyrin/FeCl3-porphyrin/InCl3-porphyrin)  Table 3. Fitting values of the steric parameters (n and P m ), the Van der Waals parameters (a and b) and the energetic parameters (c 1/2 , w 1/2 , c 1 and c 2 ) affecting the adsorption of AlCl 3 , FeCl 3 and InCl 3 on 5,10,15,20-tetrakis(4-methylphenyl) porphyrin at four temperatures. www.nature.com/scientificreports/ Overall, the numerical fitting results shows that AlCl 3 is the appropriate adsorbate for the tetrakis(4-methylphenyl) porphyrin complexation considering that the complexation process is carried out without lateral interactions influences compared to the FeCl 3 adsorption and considering that the chloride particles (Cl − ) are remained in solution and do not have an effect on the complexation process compared to the InCl 3 adsorption.
It should be noted that the adsorption models (Table 1) presents some physicochemical parameters which should be used for the microscopic interpretation of the three complexation mechanisms: for AlCl 3 , the singlelayer model (ideal gas) includes three parameters (the number of aluminum per porphyrin site n, the density of porphyrin sites P m and an energetic parameter c 1/2 ). For FeCl 3 , the single-layer model (real gas) presents the parameter a (cohesion pressure) and the parameter b (covolume) in addition to the steric parameters n and P m and the energetic parameter w 1/2 . The LBL adsorption of InCl 3 can be interpreted via four physicochemical variables [n and P M (steric variables), and c 1 and c 2 (energetic variables)].
In the next section, the fitting values of these variables are analyzed and discussed versus the temperature in order to investigate the three complexation processes at the ionic level.

Physicochemical interpretation of the three complexation processes
We give in Table 3 all the fitting values of the steric and the energetic variables affecting the reaction of AlCl 3 , FeCl 3 and InCl 3 with the tetrakis(4-methylphenyl) porphyrin at the four temperatures.
Steric study and lateral interactions influence. The parameters n and P M are typified by a steric aspect.
The product of these parameters is the result of the maximum adsorption capacity 34 .
The fitted values of n give information about the number of metallic ions that can be interact with one adsorbent site. Based on Table 3, all n values of the tetrakis(4-methylphenyl) porphyrin adsorption are found inferior to 1 for the three complexation systems. Therefore, it can be concluded that the AlCl 3 , the FeCl 3 and the InCl 3 adsorptions were only governed by a multi-interaction mechanism at all the temperatures 35 .
The fitted values of P m describe the number of porphyrins sites accessible to ions at each temperature. Table 3 demonstrates that the adsorptions of AlCl 3 and FeCl 3 present the highest values of P m at all the temperatures: P m (AlCl 3 ) > P m (FeCl 3 ) > P m (InCl 3 ). In fact, the anions are not involved in the complexation processes of AlCl 3 and FeCl 3 so there is a fast insertion of the metallic ions in the porphyrin cavities. However, the contribution of the anionic particles in the InCl 3 adsorption prevents the complexation of porphyrin by the indium ions because of the interaction between the two adsorbed layers.
Furthermore, despite the AlCl 3 and the FeCl 3 adsorptions are both single-layer adsorption processes, where there is no contribution of the chloride ions at the layer formation, the fitted values of P m are the lowest for FeCl 3 . Thus, the physical model that describes the FeCl 3 adsorption includes the lateral interactions effect by the intermediate of the parameter a (cohesion pressure) and the parameter b (covolume) 20 . It can be concluded that the decrease of FeCl 3 isotherms (Fig. 4b) can be the result of the high adsorbate-adsorbate interaction which reflects a weak binding Fe 3+ -Porphyrin comparing to the Al 3+ -Porphyrin binding.
Overall, it can be concluded that the use of the aluminum chloride guarantees more stability during the metalloporphyrin formation.
Energetic study. The molar adsorption energies should be calculated by means of the energetic coefficients which are deduced from fitting the experimental isotherms with the three physical models 36 .
The single-layer model (ideal gas) includes one energetic variable c 1/2 . The adsorption energy of AlCl 3 can be determined via the following expression: where, S(AlCl 3 ) is the solubility of the aluminum(III) chloride in aqueous solution.
The single-layer model (real gas) gives rise to the parameter w 1/2 . The adsorption energy of FeCl 3 is determined by the intermediate of the adjusted value of w 1/2 through the following formula: where, S(FeCl 3 ) is the water solubility of iron(III) chloride.
For InCl 3 , the double-layers model introduces the variables c 1 and c 2 with energetic aspect:  Table 4, for the indium(III) chloride adsorption, it is obviously remarked that the calculated values of |− E 1 | which characterizes the indium-porphyrin interaction are greater than those of |− E 2 | (interaction between the adsorbed layers 37 ). Therefore, we can conclude that the interaction |− E 1 | should be compared to the others adsorption systems energies (|− ΔE 1/2 |) to evaluate the stability of the formed metalloporphyrin complexes. The adsorption energies |− E 1 | of InCl 3 and |− E 1/2 | of AlCl 3 and FeCl 3 are the determining factors of the choice of the finest adsorbate because they characterizes the direct interaction between the three metallic ions and the tetrakis(4-methylphenyl) porphyrin.
As a conclusion, the steric study and the energetic interpretation confirm the suggestion of the aluminum(III) for the metal-porphyrin complex facrication. www.nature.com/scientificreports/ Temperature influence on the complexation processes. It is noted from Fig. 4 that the temperature exerts exactly the same influence on the three complexation systems: once the temperature increases, the adsorption capacities increase. This can be explained from Fig. 5 which shows that the values of the coefficients n (Fig. 5a) and P m (Fig. 5b) rise with the temperature from 300 to 330 K. It can be concluded that the thermal agitation effect favors the adsorption dynamics which was an endothermic process 38 : the rise of the temperature active other receptor sites to contribute in the complexation process. From Fig. 5c, it is noted that the parameter a decreases with the expansion of the temperature for the FeCl 3 adsorption while the covolume b increases. The decrease of the cohesion pressure indicates that the lateral interactions effect is low at high temperature. The increase of the parameter b reflects a strong distance between the adsorbates 20 . The behaviors of these two parameters explain the highest reproducibility of iron adsorption at 330 K and demonstrate the endothermic criterion of the studied process.
A last remark from Fig. 5d: it can be seen that all the adsorption energies rise with the expansion of the temperature from 300 to 330 K. This can be interpreted by the endothermic character of the three adsorption mechanisms of the metals 38 .

Conclusion
The target of this article is to investigate the metal-porphyrin complexes through the QCM measurements of the experimental adsorption isotherms of AlCl 3 , FeCl 3 and InCl 3 on porphyrins. Based on the adsorption capacities of the three systems, it was discovered that the AlCl 3 was the best adsorbate that can be used for the metalloporphyrin application since the chloride ions do not have any influence on the porphyrin complexation comparing to the InCl 3 adsorption. It was also verified that a single-layer model (ideal gas) can be used for the theoretical characterization of the AlCl 3 adsorption indicating that there is no lateral interactions effect comparing to the FeCl 3 system. Thus, the participation of chloride ions in the double-layers adsorption of InCl 3 and the lateral interactions influencing the FeCl 3 adsorption disfavors the complexation of the tested porphyrin by the two metallic ions iron(III) and indium(III).
Theoretically speaking, the steric study showed that the three complexation mechanisms took place with a multi-interaction mechanism since the number of bonded ions per site n did not exceed 1 for all the temperatures. The density of receptor sites was the highest for AlCl 3 because the anions did not contribute at the adsorption process and the complexation mechanism of aluminum(III) took place without lateral interactions effect. The energetic analysis indicated that the interaction aluminum(III)-porphyrin can be a covalent or ionic bonds whereas the adsorption of iron and indium took place via physisorption process.