Why Is the Sensory Response of Organic Probes within a Polymer Film Different in Solution and in the Solid-State? Evidence and Application to the Detection of Amino Acids in Human Chronic Wounds

We anchored a colourimetric probe, comprising a complex containing copper (Cu(II)) and a dye, to a polymer matrix obtaining film-shaped chemosensors with induced selectivity toward glycine. This sensory material is exploited in the selectivity detection of glycine in complex mixtures of amino acids mimicking elastin, collagen and epidermis, and also in following the protease activity in a beefsteak and chronic human wounds. We use the term inducing because the probe in solution is not selective toward any amino acid and we get selectivity toward glycine using the solid-state. Overall, we found that the chemical behaviour of a chemical probe can be entirely changed by changing its chemical environment. Regarding its behaviour in solution, this change has been achieved by isolating the probe by anchoring the motifs in a polymer matrix, in an amorphous state, avoiding the interaction of one sensory motif with another. Moreover, this selectivity change can be further tuned because of the effectiveness of the transport of targets both by the physical nature of the interface of the polymer matrix/solution, where the target chemicals are dissolved, for instance, and inside the matrix where the recognition takes place. The interest in chronic human wounds is related to the fact that our methods are rapid and inexpensive, and also considering that the protease activity can correlate with the evolution of chronic wounds.


S3. The behaviour of the sensory film at different pH.
The study of the behaviour of the material at different pH was carried out dipping discs of F(3)-Cu-D in 5 ml of water solutions with pHs between 0 and 14 overnight. These solutions were prepared from HCl and NaOH in water in different concentrations until the pH range was completed (1-14). 1.66·10 -2 0.83 100.00 This procedure runs a principal component analysis. The purpose of the analysis is to obtain a reduced number of linear combinations of the 2 variables that explain the greatest variability in the data. In this case, a component has been extracted, since it is the only component with an eigenvalue greater than or equal to 1, Which explains 99.17% of the variability in the original data.      The  table also shows tabulated p*, a, and b parameters for the Taft-Kamlet solvatochromic model, describing the polarity of the solvent, the acidity or ability to donate a proton to a hydrogen bond (HBD) and the basicity or ability to accept a proton from a hydrogen bond (HBA) respectively.

S6. Diffusion of species in solution into the swelled film.
In this paper, we study the interaction of amino acids with the F(3)-Cu-D sensor. This substrate is a 100-micron thick membrane, with a receiving unit containing copper attached to a dye, Figure S11. The number of receiving units will depend on the weight of the latter used. When the sensor is in contact with a solution of amino acid, adsorption of the latter occurs first. Subsequently, the substitution of the dye by the amino acid takes place, the first one being out of the film and colouring the solution. To clarify the mechanism that takes place during this process, a kinetic study with several amino acids is carried out. Finally, from an amino acid mixture, the adsorption rate constant is determined to construct a calibration curve and to determine their concentration in a sample of collagen, elastin and epidermis.
There are so many examples in the related literature studying different adsorption processes of substances, generally pollutants, in different substrates with variable particle size. In the present work, the objective is to synthesize an amino acid sensor that will act as an adsorbent.
This, instead of being presented in particles of a certain size, is a 100 µm thick membrane.
In the adsorption processes in solution several stages of transport take place in series: 1. External transport of the solute that moves from within the solution to the film surrounding the adsorbent. This is a quick process.
2. Diffusion of the solute through the film towards the surface of the adsorbent or external mass transfer.
4. Adsorption itself on the active centres.
There are two approaches in mathematical modelling for the kinetic study of adsorption: a) Surface reaction model (SRM), where the mass transfer is assumed to be rapid and the adsorption reaction (step 4) is the stage that limits speed.

b)
Model of mass transfer reaction (MTM), mass transfer is the slow stage while the adsorption reaction is rapid. In this model, one can find one (single resistance model) or both (dual resistance model) diffusion processes (steps 2 and 3) that control speed.
The obvious drawback of any of the types of modelling (SRM or MTM) is that the apparent numerical value of a speed parameter, obtained by adjusting the model to the data, may not reflect the actual value of the model, but maybe a grouped parameter that incorporates the effect of other processes that were not included in the model derivation. This problem is especially important if the parameter in question (e.g., the diffusion coefficient) needs to have a general validity so that it can be used in different circumstances.
Before the approach of the two models, it is necessary to consider the mass balance, whose differential expression is given by equation (1).
Where qt is the milligrams of adsorbate per gram of adsorbent at a time t, Co and Ct are the milligrams per litre of initial adsorbate and at time t respectively, V is the volume of the solution in litres and M is the grams of the adsorbent.
To calculate qt, the concentration of adsorbed amino acid must be measured. For this, it is considered that for each mole of adsorbed amino acid one mole of dye is released. The concentration of dye released is determined by measuring the absorbance at each time. Known the molar extinction coefficient at the working wavelength, 431 nm, and the volume of solution, the moles of released dyes that are the same as the adsorbed amino acid are determined. From here, it is possible to calculate qt at each time.

a) Fixed-bed kinetics: SRM
Several empirical equations allow the study of adsorption kinetics. Two of the most used are the Lagergren [1] equation, pseudo-first-order, and Ho's [2], pseudo-second-order. The theoretical approach of these two models is proposed by Azizian [3], concluding that the obtained speed constants depend on the adsorption rate constants, desorption and the initial concentration of the adsorbate. In the approach developed by Azizian, the cases where the initial adsorbate concentration is much higher than the adsorbed concentration, the equation obtained corresponds to the pseudo-first-order model, equation (3). In this work, the concentration of amino acid in solution practically remains constant, the pseudo-first-order model being the one that best fits the experimental data.
Where qe are the milligrams adsorbed when equilibrium is reached, and the speed constant of the process is reached. From a non-linear adjustment by least squares, these parameters are determined. Figure S12 shows the adjustment obtained for one of the amino acids analysed. The results obtained for the different amino acids studied are shown in Table S13. In this mathematical model, there can be up to two stages that control the kinetic process. Therefore, it is necessary to first consider the two types of transfer: diffusion through external film and intraparticle diffusion.
The diffusion through the external film is modelled according to a linear driving force that assumes that the mass transfer rate depends linearly on the difference in concentration between the concentration in solution and the concentration on the external surface of the adsorbent:

b1. Single resistance: intraparticle-diffusion models
In this model, it is assumed that diffusion occurs in a homogeneous solution of limited volume. The membrane is considered to have a thickness 2l, where the space occupied by it is -l ≤ x ≤ l, while the solution is limited to space -l-a ≤ x ≤ -l, l ≤ x ≤ l + a. The concentration of the solute in the solution is always uniform and is initially Co, while in the membrane the initial concentration is zero. Crank provides the analytical solution [4], assuming that intraparticle diffusion is the only stage of speed control.
Where gn is the non-zero positive roots of: The parameter a is the relationship between the volume of the solution and the membrane and can be calculated employing equation (8) Calculated α, the values of gn are determined and by a non-linear adjustment by least-squares Ds is optimized. Figure S14 shows the adjustment obtained for one of the amino acids. This model has been used by other researchers for spherical particles [5]. Following the results obtained, Figure S14, suggests that, although intraparticle diffusion is important, it is the two stages that intervene in the adsorption process, without ruling out that it is intraparticle diffusion that controls speed.

b2. Single resistance: film-diffusion models.
Considering a finite volume, equation (2) and a linear isotherm (qe = KCe) (where Ci is in equilibrium with q as Ce with qe) Ct and Ci can be substituted in equation (4) in terms of Co and qt to obtain equation (9), which can be integrated giving rise to equation (10).
The exponential term in equation (10) is constant for any set of experimental data, and this is equivalent to equation (3). Comparing both equations, it can be argued that the kinetic rate constant k1 is a function of SA, K, M, V and kf. On the other hand, the empirical model of Boyd [6] and Reichenberg [7] used to study intraparticle diffusion also establishes a linear  (3) of pseudo-first-order, intraparticle diffusion equation (11) and diffusion through the external film equation (10).
Although the experimental data conform to equation (10), (the same result is obtained as with equation (3), Figure S12), it is not conclusive given all the above, but the assumption that the diffusion of the film is the stage of speed control.

b3. Dual resistance model (intraparticle and film diffusion)
Crank [4] derived the model analytically with a more realistic solution that includes both broadcasts, equation (12). Where βn are the positive roots of: The Bi parameter depends in turn on kf, DS and l, equation (14), With equations (12) to (14) and using the Origin program, the parameters Ds and kf were optimized by a non-linear adjustment by least squares. Figure S16 shows the results obtained for some of the amino acids. This model, for spherical particles, has been used by other researchers [8,9]. From the results obtained, it is confirmed that the two diffusion processes are involved in the adsorption reaction. Table 2 (manuscript) shows the parameters obtained in the adjustment with equation (12).
Once the external and internal diffusion coefficients for a given adsorption system have been determined, the speed limitation step can be determined in terms of the number of Biot, Bi, which relates the external mass transfer resistance to the resistance of internal mass transfer, equation (14). When the Bi >> 1, the adsorption process is mainly controlled by intraparticle diffusion, and if Bi<< 1, it is the external diffusion that primarily controls the speed [10,11].
Once the values of Bi have been checked, table 2, the stage that mainly controls this adsorption process is the diffusion on the boundary layer or external mass transport.

S7. Complex formation between the polymer, Cu(II) and dye.
The complex that forms within the film is composed of 1 metal centre (Copper) and two different types of ligands: the compound (3) and the dye.
We have tried to see the complex formed between (3) and Cu(II), but we have not been able to absorb it in the same area. However, we assume that the complex within the membrane is 1: 1 since it is prepared by immersing the material in a brutal excess of copper.
In the second step, the film is immersed in a dye solution. In this case, the 1:1 complex is also going to be formed for the same reason as before.

S10. Calculation of initial rates at 1 and 5 min.
As previously seen, the most accurate is to measure the reaction rate constant. However, depending on the concentration this measure could last for hours, so we think about using that same philosophy (measuring the kinetics) but in short times.
To obtain an easy-to-use calibration curve, the value of the initial rate in the first minutes of the reaction is determined and plotted against the glycine concentration. The initial rate was obtained from the origin of the graphical representation of absorbance/time versus time. This linear trend is only maintained during the first minutes of the adsorption process, thus, we have calculated the value of the initial rate with the absorbance data at 1 and 5 minutes by equation (16).
Calculated the initial rate and represented against the concentration of glycine, Figure S25 is obtained. A linear variation is observed, with ordinate (1.2±0.2) 10 -3 min -1 , slope 23.8±0.3 min -1 M -1 and a value of R = 0.9992.
To determine the concentration of an unknown sample, a sensor disc is introduced to a solution of this and measurements are taken at one minute (A1) and five minutes (A5). With the help of equation (7), the initial rate, vo. To determine the concentration, equation (8) Once the concentration of Glycine, CGly, and taking into account the steps taken to prepare these samples, the starting concentration, Cp, is determined as Cp = 21 CGly. To calculate the mass, m, in milligrams of this initially present m = 75.07 Cp V, where V is the ml of starting solution.
This last method depends on the membrane used, so before using it would be necessary to perform a pre-calibration for each of these. Once tested for glycine, we tested it for the epidermis. The results are shown in Table S26 and Figure S27.

S12. Proof of concept 1. Hydrolysis of a sample of food matrix (beef, loin cut).
• Reference method [12]. To prepare the sample, 12.5 g of the food matrix showed in Figure S31 (5% substrate to the total volume) and 62.5 mg of the enzyme "papain" (0.5% to the substrate) were weighed and made up to 250 ml with pH 7 buffer solution. The mixture was incubated at 50 o C, and aliquots of 5 mL were taken at t= 21, 40, 62, 120, 180, 240, 300, 360, 420, 480, 540 and 5772 minutes. These aliquots were boiled at 100 o C for 10 min to stop hydrolysis. Finally, they were hot filtered. Finally, 50 µl of the filtered solutions were mixed at room temperature with 3 ml of OPA solution within the cuvette. The mixture stood for exactly 2 min before being read at 330 nm in the spectrophotometer. Each sample is measured by triplicate.
The degree of hydrolysis (DH%) under the following formula. The samples were simultaneously measured with our proposed material, by UV-Vis technique and RGB method.
•  Different types of samples ( Figure S33) from the same chronic wound were analysed. Each sample was boiled in a pH 7 buffer solution for 10 min (20 ml of pH 7 buffer solution per gram of sample). Finally, the samples were hot filtered.

S14. Reversibility of the material
The reversibility of the material was studied by the RGB method as explained below: • Charge & recharge The charging procedure was performed as depicted in Manuscript (Preparation of the sensory film).