Introduction

Despite widespread spectrum of antibiotic applications in various fields like human and veterinary medicine for prevention and treatment of infectious diseases, livestock production for growth promotion, agriculture, and aquaculture [1,2,3,4], these drugs are one of the main environmental pollutants which entered into aqueous environments by excreting urine and feces through human and animal [5], discharge of hospital wastes, and pharmaceutical company garbage [6]. The emergence of antibiotic-resistant bacterial strains [7], disturbance of normal ecological equilibrium, increase in allergic reaction [8], and entering antibiotics in the human food chain by means of daily food production [8] are problems that their high use rates have serious hazards for the human health and aquatic and soil organisms. Considering all the above-mentioned, the sensing and analysis of antibiotics are a very vital issue in water sources. Chromatographic methods are the most conventional analytical techniques for antibiotic detection with accuracy, but often have some shortages such as real-time detection, equipment of experienced staff, and expensive apparatuses [9, 10]. Commercial test kits are available for the rapid detection of antibiotics; however, these kits have low sensitivity [11]. The optical, colorimetric, electrochemical, and other methods have been commonly employed in the antibiotic detection; however, these techniques possess advantages and disadvantages, and need to study for development of sensitive and portable sensors [12]. Hence, the carbon nanomaterials such as carbon nanotubes (CNTs) have been attracted much attention in fabrication of sensors and biosensors [13] due to high surface area, fast electron transfer rate, thermal and chemical stability, conducting or semiconducting behavior, etc. [14, 15]. In fact, the CNTs play a significant role in the development of ultrasensitive sensors because of hollow tubular geometry that allows binding high rate of target molecules on the CNT surface [16]. Also, a field effect transistor (FET) configuration can make portable sensors. In this configuration, the CNT is used as the conducting channel in the distance between the source and drain electrodes. Gate voltage is applied into buffer solution by using Ag/AgCl reference electrode for setting electrostatic potential of solution. Ions are accumulated near the CNT surface and induce opposite charges on the CNT surface; therefore, the CNT channel conductance changes [17]. The conducting channel can be as a CNT or a network of CNTs [18]. This paper focused on the analytical investigation of the antibiotics sensing based on carbon nanoparticle using the I-V characteristics. Also, this simplified sensor is composed of classical amperometric and potentiometric sensors. Various analytical methods have been reported for the separation and determination of antibiotics [19,20,21,22,23]. Electrochemical determination of antibiotic sensitivity using carbon ionic liquid electrode by analysis of cyclic voltammetric response has been reported in the literature [19]. Novel electrochemical sensor for the direct determination of pyrazinamide (PZA) using a poly(glycine)-modified glassy carbon electrode (poly(Gly)/GCE) by cyclic and square-wave voltammetry was applied in the reference [20]. The electrochemical determination and oxidation of ceftriaxone were investigated on a GCE-decorated platinum nanoparticle (PtNPs) and carbon nanotube (CNT) [21, 22], in a phosphate buffer solution, and kinetic parameters using cyclic voltammetric studies were extracted [22]. Other analytical applied methods reported for the electrochemical determination of antibiotics in pharmaceutical formulations include capillary electrophoresis, spectroscopic methods, and chemiluminescence [19, 23].

In the presented paper, a carbon strand (bulk) based sensor is fabricated for electrical sensing of three types of beta-lactam antibiotics (amoxicillin, penicillin, and ampicillin). The carbon strand is synthesized by pulsed arc discharge method in the distance between the source and drain electrodes and high-density polyethylene (HDPE) is used as the carbon source. Adsorption of antibiotic molecules on the carbon strand can change its electrical conductance. For rationalizing of antibiotic adsorption mechanism on the carbon strand containing NSCMs, we assume a MWCNT instead of a carbon strand to facilitate achievable modeling. The current-voltage (I-V) characteristics of synthesized samples as proposed sensor are investigated before and after sensing process in the different concentrations and temperature values of antibiotic solution. At last, the sensor response is analytically modeled for a sensor based on a MWCNT which shows an acceptable agreement with experimental data. Also, the presented sensor can sense β-lactam antibiotic concentration as low as ppm.

Theory and method

Sensor fabrication and experiment

A sensor is a device that converts physicochemical interaction between target and sensing element to a measurable external signal. The target can change the capacitance, conductance, mass, or other properties of the sensing element [24]. In the work presented, a metallic MWCNT-based chemiresistive sensor is proposed for sensing of three types of beta-lactam antibiotics. Arc discharge technique is one of the nanostructured carbon material (NSCM) producing methods that has been developed [25,26,27,28] for using in polyethylene glycol solution as a liquid medium with hollow metallic electrodes. In this work, a high-voltage generator is connected to hollow electrodes mounted in molten HDPE, and this setup is placed on a glassy substrate sheet where the HDPE is heated by a heating system. By this configuration, the NSCM strand grew in the distance between two narrow hollow rods as the conducting channel, as shown in Fig. 1.

Fig. 1
figure 1

A schematic diagram of NSCMs grown into the environment of HDPE between two hollow electrodes

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Carbon nanostructure strand fabrication is entirely explained as sensor at recent researches [25,26,27,28]. Fortunately, in this method, the carbon strand is stably established after cooling of melted HDPE and is connected to electrodes as head-to-head form. Main products of nanomaterial strand are MWCNTs that are randomly localized close to each other and the existence of MWCNTs has been confirmed by analytical techniques in the reference [25]. Using MWCNTs at sensors enhances sensor sensitivity due to their high surface area [29], sensitivity to very small environmental changes [30], and faster electron transfer rate.

In the proposed sensor, hollow rods as metallic electrodes [26] are connected to the drain and source terminals [31] of Autolab probes for measuring of I-V curves of carbon strand as shown in Fig. 2. Hence, I-V curves of the several synthesized samples are measured as bare sensor before entrance of analyte material.

Fig. 2
figure 2

A schematic diagram of solution injection, penicillin-G adsorption on MWCNT, and measuring of I-V characteristics

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Combination of pure antibiotic and distilled water as antibiotic solution is injected by hollow rods to carbon strand with different solution concentrations and temperatures, respectively for approaching to modeling steps. The experiment is done on more than 18 samples for any antibiotic and range of overlap on the same quantities indicates device repeatability/reproducibility. The adsorption of antibiotic molecules (target) onto the surfaces of NSCMs strand can change the I-V characteristics via electrostatic interactions (charge transfer between the NSCMs and target). Capture content of the target molecules between porous surfaces changes of Schottky barrier height at electrode-MWCNT junctions [32]. Also, length and temperature of carbon strand can be other effective factors on the displacement of I-V characteristics. In the next section, the presented model is defined on a MWCNT conductance and contact resistance between the carbon strand and hollow rods is assumed to be small compared to the intrinsic resistance of strand [31].

Proposed model

The aim of this section is to investigate the antibiotic sensing mechanism on a metallic conductor. In the simplified model, electrons can be exited and transported without scattering under non-ballistic conditions [33] in the conductive MWCNT by applying an external potential between two ends of metallic electrodes. In order to elucidate our insight, we will start using MWCNT quantum conductance formula and derive the electrical properties of nanotubes and then employ the bipartite probability of electrons propagating after and before antibiotic injection. MWCNTs are formed of multiple concentric shells dshell of single-walled carbon nanotubes (SWCNTs) with different outer and inner diameters [33]. MWCNTs consisting of more than three shells display metallic characteristics, and even semiconducting shells at room temperature can be quasi-metallic [33]. An ideal state of electron transport in multi-walled nanotube (MWNT) is justified at a one-dimensional (1D) ballistic condition that the strand or nanomaterial dimensions L are much less than mean free path lmfp of electron transport [34, 35]. In addition, nanotubes are connected to reservoirs of electrons; however, reservoir contacts cause identical transparent connections to all shells and electrons can move through the conductor without scattering [33]. Electrical conductance of the MWCNT is a linear sum of the conductance per shell [36]. MWCNTs quantum conductance Gq, mw can be written as a derivative of the ballistic current and applied drain to source voltage V [33]:

$$ {G}_{\mathrm{q},\mathrm{mw}}=\sum \limits_{d_{\mathrm{s}}}\frac{\partial I}{\partial V}={N}_{\mathrm{ch}}{G}_0 $$
(1)

After the expansion of above relation and solution of integrals that are related to hole and electron terms, it leads to a general formula Gq, mw = NchG0 for the MWNTs quantum conductance with shells of arbitrary chirality, where Nch is called total number of propagating channels or modes and \( {G}_0=\frac{2{e}^2}{h} \) is a basic constant unit of quantum conductance [37]. Standard average value of the number of MWNT conducting channels is approximately calculated as a function of the nanotube temperature TMWNT and shell diameter dshell with constants a1 and a2, under low-bias condition [38]:

$$ {N}_{\mathrm{ch},\mathrm{avg}}\left({d}_{\mathrm{shell}},{T}_{\mathrm{MWNT}}\right)\approx {a}_1{d}_{\mathrm{shell}}{T}_{\mathrm{MWNT}}+{a}_2 $$
(2)

Increasing the diameter or temperature linearly increases the number of conduction channels in large shells and also counteracts increasing electron–phonon scattering rate [36, 39]. That is while in small-diameter nanotubes, increasing the temperature or diameter does not change the number of conduction channels [38]. The total number of MWNT channels is a linear sum of the average channels of each shell [33]:

$$ {N}_{\mathrm{ch},\mathrm{avg}}=\sum \limits_{d_{\mathrm{s}}}{N}_{\mathrm{ch},\mathrm{avg}}\left({d}_{\mathrm{s}\mathrm{hell}},{T}_{\mathrm{MWNT}}\right) $$
(3)

Total number of channels in the general form can be achieved by a solution of finite series for a MWNT that depends on the total number of shells, inner-outer diameters, and temperature.

$$ {N}_{\mathrm{ch},\mathrm{avg}}={N}_{\mathrm{shells}}\left({a}_1{T}_{\mathrm{MWNT}}\frac{d_{\mathrm{out}}+{d}_{\mathrm{in}}}{2}+{a}_2\right) $$
(4)

Standard statistical random distribution of nanotube chiralities expresses on average 1/3 (metallic shell) + 2/3 (semiconducting shell) for all of the nanotube shells [33]. Generally, transmission of electron on the conductive nanotube is classified into two theories. One is the ballistic theory that electrons can be able to transport in a conductor without any scattering. Another is diffusive theory that experience periodic scattering during transmission through a lattice [33]. A special state nearby ballistic theory, where the device or nanomaterial dimensions and mean free path lmfp establish scattering condition(L ≫ lmfp), general quantum conductance is improved as Landaur’s formula [33]:

$$ {G}_{\mathrm{q},\mathrm{mw}}={G}_0{N}_{\mathrm{ch},\mathrm{avg}}P $$
(5)

where P is considered as a transmission coefficient or probability of electrons propagating without scattering through the strand channels [33]. Also, elastic scattering can be considered for this quantum conductance that affects the transmission coefficients directly and thereby reduces the conductance [40]. Range of propagating probability is elucidated to 0 < P < 1 and P = 1 satisfies ballistic theory [33]. A MWCNT strand is considered as a conductor consisting of two contactive sections in series at the classical transport theory. An electron can transmit directly into both sections and eventually can transmit after the number of reflections [41]. Therefore, general internal transmission probability is represented by deducing of transmission of classical particles as a function of the conductor length L [36]:

$$ {P}_{\mathrm{int}}=\gamma \frac{l_{\mathrm{mfp}}}{L+{l}_{\mathrm{mfp}}} $$
(6)

where γ as a fitting parameter is derived from overlapping of experimental and theoretical I-V curves and it has a constant number defined in a certain range that is obtained experimentally from several samples with different lengths, mentioned in Table 1.

Table 1 Different values and ranges of sample length (L) and fitting parameters (α, β, and γ) respectively corresponding to various conditions for all three types of antibiotics; their average values of modeling are obtained at investigation of several samples
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The existence of γ coefficient can be caused to the imperfection of MWCNTs replacement, presence of other conductive carbon materials, impurities, and defects in the synthesized carbon strand. The adsorption of antibiotic molecules on the surfaces of carbon strand and their interaction with structural components of strand lead to conversion of its conductance that shown in the form of I-V plots. So it can be derived that antibiotic injection to the MWCNT strand affects directly on transmission probability. Therefore, Pext coefficient as an external factor of probability is been entering to general transmission probability as follows (derived from reference [41]):

$$ {P}_{\mathrm{total}}={P}_{\mathrm{int}}.{P}_{\mathrm{ext}} $$
(7)

It should be mentioned that Pext is entered into the Landaur’s formula in the presence of external factor (antibiotic molecules). In this modeling, we apply the long lengths of MWCNTs equal distance of two electrodes in limits of a few hundred micrometers because long lengths participate at sensible decreasing of conductance in synthesized samples [25, 31]. Checking of two parameters (antibiotic solution concentration and temperature) at experimental linear I-V curves after injection of solution is deduced that sensing rate of antibiotic depends on its solution concentration C and temperatureT. The quantum conductance of MWCNT can be decreased due to exposure and adsorption of ionized molecules by several orders of magnitude [42]. Increasing solution temperature and its equilibrium interaction with carbon strand cause to decreasing of conductance [43] due to shorter lengths of mean free paths [38]. That is while the conductance of short nanotubes increases as temperature rises [38]. These two parameters of antibiotic solution separately affect inversely on the conduction of MWCNT strand \( \left({G}_{\mathrm{q},\mathrm{mw}}\propto \frac{1}{C}\&\frac{1}{T}\right) \). Experimental fitting of two external parameters on the transmission probability assumptively leads to the following formula:

$$ {P}_{\mathrm{ext}}=\frac{\alpha }{C}+\frac{\beta }{T} $$
(8)

where α and β are constant coefficients, arise from antibiotic solution concentration (ppm) and temperature (K), respectively. Also, they are defined in certain ranges that are obtained experimentally for each type of antibiotic from several samples of solutions. The purpose of obtaining the transmission probability is to achieve a real fraction number by existing parameters. More effective adsorption parameters were separately considered in the Hamiltonian, overlap, and coupling matrices based on a tight-binding model [44]. Component effects are compared and the effective adsorption parameters are selected in the matrices. Random-matrix approach [45] is separately used for obtaining of composed transmission probability. Approximation effects on applied parameters are investigated and the proposed method presents antibiotic sensing response which helps to detect certain components in the solution. Consequently, matrix effects are taken an amount into account of solved antibiotic sensing by MWCNTs considering of the different experimental aqueous samples. C and T are macroscopic quantities of solution but they are entered into the quantum formula. It can be said that we assume fractions of macroscopic quantities without any unit, in other words, consider existence of effects of antibiotic solution concentration and temperature on quantum conductance. Generally, quantum coherence of synthesized carbon strand as antibiotic sensor and macroscopic solution parameters is interpreted by mesoscopic regime [41, 46] in our proposed method. According to the presented documents and substituting for Nshells  (Nshells = 1 + (dout − din)/2δ) [47], central result of this section is exposed as a closed-form formula:

$$ {G}_{\mathrm{q},\mathrm{mw}}=\sum \limits_{d_{\mathrm{s}}}\frac{\partial I}{\partial V}={G}_0\left[\left(1+\frac{d_{\mathrm{out}}-{d}_{\mathrm{in}}}{2\delta}\right)\left({a}_1{T}_{\mathrm{MWNT}}\frac{d_{\mathrm{out}}+{d}_{\mathrm{in}}}{2}+{a}_2\right)\left(\gamma \frac{l_{\mathrm{mfp}}}{L+{l}_{\mathrm{mfp}}}\right)\left(\frac{\alpha }{C}+\frac{\beta }{T}\right)\right] $$
(9)

It should be mentioned that Eq. (9) is justified for sensing of antibiotic via linear I-V curves with solution parameters because of entering of external probability Eq. (8) into the Eq. (9). Also, justification of I-V curve in the absence of antibiotic molecules corresponding to a sample fabricated as a bare sensor is yielded without writing of Eq. (8).

Results and discussion

Adsorption and reaction of antibiotic molecules as an external agent with carbon strand affect the slope of the I-V characteristics. So, in this regard, Eq. (8) is used which indicates that the transmission probability is composed of two parts (external and internal probability parts). The internal part is related to fundamental and structural properties of strand, so its term (Pint) is written in the Eq. (9). But, the second part of probability is considered as the reaction coefficient between antibiotic and carbon molecules. This part can be removed or quantified to a value of 1 (one) in the absence of antibiotic as a bare sensor.

The scrutiny of I-V curves demonstrates that the electrical properties of the conductor strand can be justified by quantum conductance of MWCNTs which depends on the number of propagating channels and the conductor length with the fitting parameter γ considering Eqs. 5 and 6. The slope of I-V curve is considered as an equation which has been solved in two steps (antibiotic injection and without injection) for obtaining the fitting parameters. Hence, contents of γ are extracted for each similar sample only without antibiotic injection. Penicillin-G solution is injected to several conductive samples at two steps. One of them is done at constant concentration (C = 0.05 ppm) of penicillin-G solution and tripartite temperature (T = 274, 300, and 315 K), another step at different solution concentrations (C = 0.05, 0.1, and 1 ppm) and room temperature of penicillin-G solution. At every step, at first, antibiotic solution is injected to several samples with nearly equal lengths. Ranges of fitting parameters α and β as shown in Table 1 are extracted by resolution of two equations with two unknowns as for slopes of experimental linear I-V curves. Injection effectiveness of penicillin-G solution at two practical steps is shown in plots of Fig. 3.

Fig. 3
figure 3

Comparison of experimental and modeling I-V characteristics of penicillin-G sensing by conductive carbon strand at different conditions, aC = 0.05 ppm, T = 274, 300, and 315 K and bC = 0.05, 0.1, and 1 ppm, T = 300 K

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Subsequently, these processes are repeated at various samples with different lengths. Ranges of α and β parameters are individually obtained for each sample. To arrive a comprehensive modeling, checking and comparing of applied lengths of samples and particular ranges of fitting parameters with contents of initial selective sample, all samples can be defined at average ranges of initial sample that are presented in Table 1. It is important that all ranges of obtained contents for sensing of a type of antibiotic are placing in ranges of each other in the employed samples, respectively. The investigation of obtained sample ranges found that every three types of antibiotics materials have a defined proprietary range at each parameter.

The linear I-V curves are plotted with details from experimental and modeling data and scrutiny of curves is done. So in this regard, we can justify increasing of conductance with decreasing of penicillin-G solution concentration and temperature. In other words, increasing the solution temperature and its thermodynamic equilibrium with conductor strand causes to increasing of its resistance. Also, existence of penicillin-G molecules and capture of them between porous surfaces and their interaction with context molecules (as bioreceptor) cause to decreasing of electron transmission rate. In I-V plots of several samples, overlapping of theoretical modeling on obtained experimental data and identification of a relation between them are associated with a generalized regulation of penicillin-G sensing that is also confirmed for another antibiotics sensing. In this experience, three types of antibiotics (Penicillin-G, Amoxicillin, and Ampicillin) are sensed by carbon conductor strand that is approximately simulated to a MWCNT. Not only is sense modeling obtained for three particular types of antibiotics but also it can be righted for another material. Chemical and physical antibiotic adsorption and also capture of them between porous surfaces (BET surfaces) on carbon strand cause the disturbance of electron transmission. Therefore, I-V curves conversion after and before injection is originated from this phenomenon. To get data from Table 1 for the MWCNT conductance modeling, we entered numerical contents of G0  (1/G0 ≈ 12.9 kΩ), for dshell > 6 nm, a1 ≈ 3.87 × 10−4 nm−1 K−1, and a2 ≈ 0.2 [33, 37]. The mean free path lmfp at low energies in high-quality CNTs is approximately equal to 1 μm at room temperature [31] and the shell-to-shell spacing δ is about the interlayer spacing in graphite (δ ∼ 0.34 nm) [33]. It should be noted that the range of dout and din is in the references [47,48,49,50]; the total number of shells Nshells is approximately extracted to number 120 [47], and standard average contribution of metallic shells [33] is Nshells = 40 [47]. The total average number of channels mentioned in Eq. (4) for the MWCNT considered at three different equilibrium temperatures is obtained as Nch, avg = 282. Considering of these macroscopic solution parameters (C, T) and their experimental effects on quantum conductance leads us to write an equivalent relation as external probability of antibiotic sensing that is matched with constant fitting parameters expressed in relation (8). It is clear that modeling is originated from electrical conductive properties of carbon strand and every one of antibiotics are sensed with contribution of fitting parameters (α, β, and γ) defined in the certain ranges for any sample. Apart from the three types of antibiotics, we can use other materials with specific fitting parameters obtained experimentally in order to recognize the material type. Adsorption of any antibiotics in the certain temperature and concentration has unique characteristic in the proposed sample. The different samples with different growing conditions have been made and applied for model rationalizing. It is clear that the existence of antibiotic molecules affects electrical conductance of strand. This conversion is observed in other procedures for electrical determination of antibiotic characteristic. It is true that the overlapping of experimental and theoretical I-V curves is not entirely done, but the presented model exactly justifies the behavior of their displacing arrangement. Also, investigation and comparison of them with each other are expressed at all three types of antibiotics that I-V characteristics are followed from quasi-spectrum logic for the sense conditions as shown in Figs. 3, 4, and 5. These investigations are measured on the approximately equivalent samples that have different structural properties such as distance of two electrodes (strand length), strand growing time, defects, impurities, etc., so according to these reasons, before discriminating and interference studies between the three tested antibiotics must be firstly done in the completely identical grown samples from every aspects.

Fig. 4
figure 4

Comparison of experimental and modeling I-V characteristics of amoxicillin sensing by conductive carbon strand at different conditions, aC = 0.05 ppm, T = 274, 300, and 315 K and bC = 0.05, 0.11, and 1 ppm, T = 300 K

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Fig. 5
figure 5

Comparison of experimental and modeling I-V characteristics of ampicillin sensing by conductive carbon strand at different conditions, aC = 0.05 ppm, T = 274, 300, and 315 K and bC = 0.05, 0.1, and 1 ppm, T = 300 K

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Conclusion

Carbon strand (bulk) containing MWCNTs plays an important role in the performance of electrochemical sensors due to their remarkable features. In this study, a metallic carbon strand-based chemiresistive sensor is fabricated for electrochemical sensing of three β-lactam antibiotics (Penicillin-G, Amoxicillin, and Ampicillin) successfully. Also, the effect of important parameters such as antibiotic concentration, solution temperature, total number of channels, inner-outer diameter of the MWCNTs, and conductor length are investigated. The quantum conductance as a sensing platform is considered and effective parameters by three constant coefficients (α, β, and γ) are simulated. Finally, comparison study based on I-V characteristics is carried out and tolerable agreement between the proposed model and experimental results is reported.