Design and applications of a neural networks assisted portable liquid surface tensiometer

Chemicals

Acetone (99.9%) and methanol (99.9%) were from Macron (Poland). Malt extract and sodium dodecyl sulfate (SDS) (>99.0%) were purchased from Roth (Germany). Pleurotus ostreatus (P. ostreatus) and Irpex lacteus (I. lacteus) were isolated and confirmed in the previous studies [14]. Bidistilled water was produced in the laboratory using a Fistreem Cyclon bidistillator (UK).

Sample preparation

For measurement standards, stock solutions were prepared: the required amount of chemical substance was dissolved in 15 ml of bidistilled water and kept in a freezer at –20°C. Before further use, the stock solutions were defrosted and used for preparing the required levels of concentrations. At least ten different levels of concentrations were used for each compound.

The fungi were grown in a miniaturized format according to the previously optimized procedure [13]. In a 10 ml gas chromatography vial, 2.5 ml of the growth medium (0.6% malt extract) was added. Instead of septa in the vial seal, a cotton disc was used to ensure the gas exchange. 0.03 g of fungi was added to the growth medium in the vial and incubated at room temperature c.a. 22°C. After 17 days of growing when the fungi reached the plateau region, measurement of the medium was performed. The growth medium was diluted two times so that 4 ml of measurement solution would be obtained.

For the modelling and determination of residual detergents on the surfaces the following procedure was used: (i) 2 ml of 10 mM concentration SDS in methanol was added onto the (a) stainless steel and (b) glass, (ii) after the evaporation of methanol, (iii) 4 ml of bidistilled water was added onto the application site of the surfactant, (iv) left for 15 min for extraction and (v) 4 ml of water with the dissolved surfactant from the surface was added to the measurement vial and measured.

In situ determination of river water

The selected sites of the rivers Neris (coordinates: 54°53'57.2"N 23°52'34.4"E) and Nemunas (coordinates: 54°53'50.5"N 23°52'34.7"E) were sampled taking 4 ml of river water and directly used for the measurement. Each measurement was repeated five times, and the mean was used as the determining retraction force value, which later was recalculated to the equivalent SDS concentration.

Portable liquid surface tensiometer and measurement procedures

The instrument for measuring the surface tension was developed according to the previously published paper, where similar mechanics and electronics were used for the measurement of the hardness of Actinidia fruit peel [15]. A schematic diagram of portable measurements is represented in Fig. 1.

The sketches of measurement probes were designed using Inkscape – the open-source vector graphics editor software (https://inkscape.org/). The sketches were processed using Ki-Cad – the open-source electronics design software

T. Drevinskas, J. Balevičiūtė, K. Bimbiraitė-Survilienė, G. Dūda, M. Stankevičius, N. Tiso, R. Mickienė ir kt. (http://kicad-pcb.org/). The processed sketches of the probes were manufactured by the printed circuit board production company SEEED (PRC). The copper of measurement probes was tin-plated.

The measurement principle is the following: (a) the vial with the sample (4 ml) is placed on the lifting platform in the instrument, (b) the sample is lifted up, (c) upon the lift up, the force sensor is auto-zeroed, (d) the platform with the sample is lifted down at the selected speed, (e) during the lifting down, the force is measured, (f) the maximum value of the force reading is considered as the value of the surface tension and is sent wirelessly to the control interface (smartphone, laptop, table pc, etc.). For more sensitive readings of the surface tension, the previously developed migration velocity-adaptive moving average method was modified to suit the surface tension measurements [16].

Between the measurements of different samples, the probes were washed, immersing them into bi-distilled water five times.

Data analysis

Means of the measured force, standard deviation and relative standard deviation were calculated, and polynomial and logarithmic curves of the measured force were fit against the equivalent concentration of SDS using the Microsoft Excel software. For the neural network (NN) models, the data was normalized using the mathematical Rstudio software [17]. The NN models were calculated, and predictions were performed using the R-package neuralnet [18]. The NN models were generated using two procedures.

The first NN procedure. All measured force values representing surface tension for the calibration of SDS were treated as separate data points. Totally 140 data points (14 different levels of concentrations in a range of 0.005 and 21.672 µM, 10 repetitions for each level) were used for the generation of the NN model.

The second NN procedure. Similar to polynomial and logarithmic curve fitting, means of the measured force were used. Neural networks are a type of machine learning method that only works effectively with large data sets, and 14 data points (means) were not enough for the satisfactory model. Knowing the relative standard deviation (<2.5%) for the mean of the measured force of a concentration level, additional data points were generated, injecting the errors to the means and concentration levels similarly like it was described in previously published results [19, 20]. Totally 2,000 data points were generated and used for the calculation of the NN model.

Before calculating the NN model, the data were scaled so that the largest number was equated to 1 and the smallest number was equated to 0 following Eq. (1),

$$m_i=\frac{{\chi }_i-{\chi }_{\min }}{{\chi }_{\max }-{\chi }_{\min }},i=\text{1, 2}\mathrm{...}I\text{,}\text{(1)}$$

where m_i is the normalized value, i (i = 1, 2…I) is the record number in the data set (data table), x_i is the original value in the data set, x_min is the minimum value of the data set, and x_max is the maximum value of the data set. The data sets were separated into 2 equally sized segments – one for training the NN model and another for testing the generated NN model. For the characterization of NN models, the mean squared error (MSE) was calculated following Eq. (2),

$$MSE=\frac{1}{I}{\displaystyle \sum _{i-1}^I{(p_i-x_i)}^2},i=\text{1, 2}\mathrm{...}I\text{,}\text{(2)}$$

where MSE is the mean squared error, i (I = 1, 2…I) is the record number in the data set, representing the data set size, p_i is the predicted value, and x_i is the original value.

The coefficients of determination (R²) were calculated for each calibration model: (i) fit polynomial, (ii) logarithmic curves, and actual and predicted values using the NN model generated with (iii) the first NN procedure and (iv) the second NN procedure.

Characterization of measurement procedures

Different circle-shaped probes were used for the characterization and measurement. Dimensions of the probes are represented in Table 1. Five different probes were used that differed in (i) diameter and (ii) thickness of the ring and formed different contact areas. It is mentionable that the measurement had both sides (top and bottom) covered with tin-plated copper. During the measurement, the bottom part of the probe contacts the liquid, but it also must be taken into account that interaction due to surface tension between the top layer and the liquid exists.

Table 1. Dimensions of the probes used for measurements

Two reference solutions were measured using different diameter (d) and thickness (t) probes: (i) bidistilled water and (ii) acetone (Fig. 2). It was observed that in order to retract bigger diameter probes from the surface of the liquid, a higher force (retraction force) was needed (Fig. 2a). In all cases, a lower retraction force was observed for the acetone solvent than for bidistilled water. Moreover, the measurements showed that the same diameter probes having a bigger area needed a higher retraction force (probes 2 vs 3 and 4 vs 5). For analytical instrumentation, the measurement range is important. Therefore it was decided to express it as a retraction range (mN), subtracting the retraction force value of acetone from the retraction force of water (Fig. 2b). Usually, the load cells that measure the force or other instruments with conventional sensors provide similar noise values at different levels of readings. For example, the instrument sensitivity can be increased if a higher perimeter and area probe was used for the measurement, as it was demonstrated for the designed instrument. On the other hand, cases, where minute volumes of samples are investigated, can only be solved using miniature probes (in this case, probe 1 or probe 2). This allowed reducing the sample volume down to 1 ml.

In Fig. 2c, d, the dependency between the probe areas, probe perimeters, retraction force and retraction range is represented. As demonstrated in the Figure, the dependency is complex showing high correlations: (i) the coefficient of determination (R²) for the probe area vs retraction force was 0.78, (ii) R² for the probe perimeter vs retraction force was 0.83, (iii) R² for the probe area vs retraction range was 0.74, and (iv) R² for the probe area vs retraction force was 0.86.

Later calibration, modelling and in situ experiments with real samples were performed using probe 2 (d 15, t 1).

Calibration and measurement of modelled solutions

Attempt to calibrate the designed instrument for the determination of detergents was performed. Fourteen different levels of SDS concentrations were measured. The range (0.005–21 672 mM) was selected so that the critical micellar concentration (8.2 mM) would be covered (Fig. 3).

It was observed that the dependency between the retraction force and the SDS concentration was too complex to generate single linear, polynomial or logarithmic fitting. It was decided to use a conditional calibration procedure. The conditional calibration covers the cases where a full range of data has to be segmented. In classical methods, the conditional calibration is usually avoided because such calculations require more computational intensity, but this is not a problem using modern-day computers. The segmented smoothing approach was demonstrated with the migration velocity-adaptive moving average method, where it was programmed into a 16 MHz 8-bit low-performance microcontroller. The conditional calibration here represents the following statements: (i) if retraction force (F) ≥ 8.5 (mN), then the calculation of concentrations should be done following the polynomial equation, and (ii) if F < 8.5 (mN), the calculation of concentrations should be done following he logarithmic equation. Here 8.5 (mN) is the cross-point of the logarithmic and polynomial curves. The polynomial equation (y = 65187.198 × x² – 895.881 × x + 9.222, where y is the retraction force F and x is the concentration C) represented in Fig. 3 must be transformed so that instead of y value, x should be calculated: x = 0.00021832 × y² – 0.005022 × y + 0.02775609. This procedure is easily calculated in the MS excel, inverting the y-and x-axis. Similarly, the logarithmic equation (y = –1.208 × ln(x) – 0.065, where y is F and x is C) must be transformed into the exponential equation: x = 0.899737 × e^–0.819808 × y.

Neural networks should be considered as conditional dependency between input and output values. The developed NN model is subdivided into multiple segments representing certain ranges, where each range has its own linear equation composed of weights, inputs and outputs [21]. A mathematical model coupled to the neural networks was recently applied to solve another chemical problem – the prediction of the extraction recovery of polycyclic aromatic hydrocarbons [8].

Using two different procedures, (i) the first NN procedure and (ii) the second NN procedure, the neural network model was trained (Fig. 4). In the first NN procedure, 140 data points, with each repetition (10) at different concentration levels (14), were used. The data set was split in two similar size parts: (i) training and (ii) testing. Different combinations of hidden layers and neurons in the hidden layers were used for training. MSE corresponding to the mM concentrations of SDS was calculated for a combination of the trained neural networks. It was determined that two hidden layers, where the first and the second contained 4 neurons, showed the lowest scaled error (0.047) and absolute MSE (4.4 × 10^–7) (Fig. 4b). The training of the network took 254 steps. The coefficient of determination was calculated for the predicted and actual data of the first NN procedure trained network. R² was 0.986. Comparing it to the polynomial (0.992) and logarithmic (0.991) fitting coefficients, the R² for the first NN procedure trained network was lower. On the other hand, the NN training procedure covers all the range of concentrations and equations generated for polynomial and logarithmic fitting are segmented into 2 ranges: (1) from 0.005 to 0.843 mM (polynomial) and (2) from 0.843 to 21.673 mM (logarithmic).

For the second NN procedure, the same combinations of hidden layers and neurons were used as in the first NN procedure training. The data set is composed of 2,000 data points and half of them was used for training, where another half was used for testing. Differently from the first NN procedure, the lowest MSE was observed for a combination of 2 hidden layers, where the first one contained 3 neurons and the second one contained 2 neurons (Fig. 4d). It took 601 steps to train the NN using the second NN procedure. For the second NN procedure trained NN, a scaled error was lower (0.0086) than for the first NN procedure trained network (0.0468). Additionally, the absolute MSE was almost two decades lower for the second NN procedure trained network (7.7 × 10^–9) than for the first NN procedure trained network (4.4 × 10^–7). The R² of the second NN procedure of the predicted and actual data points was 0.999 that can be considered superior to the first NN procedure trained network (R² of actual and predicted data points was 0.986) and superior to the model developed using a polynomial (R² 0.992) and logarithmic (R² 0.991) fitting.

Neural networks are a less intuitive method than linear, polynomial or logarithmic fitting methods typically used by analytical chemists. Using NN, it is difficult to draw a representative plot, similar to Fig. 3 – polynomial and logarithmic fitting of the retraction force and concentrations. On the other hand, NN models are used for numerous different fields, including life sciences, medicine, and analytical chemistry [22–24].

Neural networks is a machine learning method that is efficient with large-sized data sets [25]. In chemical analytical sciences, obtaining large-sized data sets can be problematic and expensive. As it was demonstrated, it is possible to train a neural network model using a moderate-sized data set (in this case 140 data points), where each repetition is treated as the data point. On the other hand, analysts are used to repeating a single data point from 3 to 5 times and calculating a mean, which is later used as the determined data point. The drawback of this procedure is that the size of the data set is reduced significantly and can be solved (as demonstrated in a previous study) by generating additional data points with the injected error. Such procedure requires known statistical evaluations (standard deviation, distributions, confidence intervals, etc.) of the measurements and the instrument.

Often analytical methods and instruments are calibrated using linear equations, and a drawback of such calibration is a reduced dynamic range. In electrochemical impedance spectroscopy, pseudo-linear ranges are used for the determination of chemicals [26]. In certain cases separating multivalent analytes, the calibration curve deviates from predicted concentrations at trace levels as it is known for phosphate ion applying capillary electrophoresis – contactless conductivity detection [27, 28]. In the mentioned cases, where calibration is dynamic, the range can only be increased if the proposed method of conditional calibration was used or neural network models for the prediction of concentrations were used. The proposed techniques are expected to benefit from analytical methods used in electrochemistry, photometry, spectrometry and separation science [5, 29–31].

Real sample analysis in situ

Real samples were analyzed: (i) modelled leftover of surfactants on the surfaces – (a) SDS on stainless steel and (b) SDS on the glass, (ii) river water – (a) Nemunas and (b) Neris, and (iii) fungal growth medium in the plateau region with (a) I. lacteus and (b) P. ostreatus. Further results are described presenting values obtained using the second NN procedure trained neural network. It was observed that more SDS was recovered from the glass (4.1 mM) than from the stainless steel surface (3.0 mM). In the Nemunas River, 2.3 mM of SDS equivalent concentration was determined, and in the Neris River 1.0 mM of SDS equivalent concentration. In the determination of the growth medium of fungi, previous results were confirmed. I. lacteus produced more surface tension modifying compounds than P. ostreatus [13]. The equivalent concentration of SDS for the I. lacteus growth medium was 3.6 mM, and for P. ostreatus it was 0.4 mM.

In Fig. 5 represented concentrations do not perfectly match. It is visible that at higher (>3.0 mM) concentrations, the conditional calibration using polynomial and logarithmic equations show slightly higher concentrations than both of the NN models predict. At lower concentrations (<3.0 mM), the results differ for different NN models. The NN model trained using the first NN procedure shows smaller values of the equivalent SDS concentration except for the last sample, which is 17th-day P. ostreatus growth medium. At lower concentrations (<3.0 mM), the NN model trained using the second NN procedure showed slightly higher values of the equivalent SDS concentrations.

In the future, it is planned to use the developed instruments and procedures for generating reference data and using them with the chromatographic data segmentation method for mining out exactly what substances are responsible for liquid surface tension modifying properties in biological systems and environment samples [7].