Introduction

Chitosan, which is made up of at least 50 % deacetylated chitin, is one of the natural polycationic polymers that can be used for many applications due to its unique character and has been used for defluoridation of drinking water because it is harmless to humans and possesses excellent biological properties [1]. Chitosan also has been used as a polymer host to make biocompatible polymer electrolytes [2, 3]. In the present study, chitosan mixed with oxalic acid has been used to form solid polymer electrolytes. Plasticization has proven to be an effective way to enhance conductivity of solid polymer electrolytes [4]. Plasticization will make the polymer electrolyte more amorphous and will assist in the dissociation of the salt thereby increasing the number of mobile charge carriers [5, 6]. Polyol plasticizers suchlike sorbitol, glycerol and polyethylene glycol (PEG) are small molecules that are able to intersperse and intercalate among and between polymer chains, disrupting hydrogen bonding and spreading the chains apart [7]. Glycerol was selected as the plasticizer in this work as it is expected to improve the conductivity further due to the presence of hydroxyl groups [8]. In this work, we report the maximum conductivity that can be achieved in the chitosan-oxalic acid polymer electrolyte system and investigate the role of glycerol in enhancing this conductivity further.

In the development and characterization of ionic conductors such as polymer electrolytes, the estimation of transport parameters such as ionic mobility (μ) and carrier density (n) is crucial since conductivity is the product of n, μ and electron charge, e [9]. Some of the methods that have been used to determine the transport parameters of ionic conductors are based on electrochemical impedance spectroscopy (EIS), pulsed magnetic field gradient-NMR measurements, potentiometry and amperometry [9, 10]. Among these techniques, EIS is the most favoured one since it is a relatively easier non-destructive method [11]. Bandara et al. [12] have developed a direct method for calculating the number density, mobility and diffusion coefficient of conducting ions using the method of broadband dielectric response (BDR). EIS and Fourier transform infrared (FTIR) methods are used in this study to determine the transport parameters of the chitosan-oxalic acid polymer electrolyte system. While the EIS method utilizes the impedance equations based on the equivalent circuits that will fit the Nyquist plots of the electrolytes, the FTIR method is based on the deconvolution of the peaks obtained. The results obtained for chitosan-oxalic acid system from the EIS and FTIR methods will be compared with the results obtained from BDR method in order to check the suitability of the EIS method in determining the transport parameters. The findings will be verified using the highest conducting chitosan-oxalic acid-glycerol plasticized electrolyte.

Theory

The ionic conductivity, σ of a polymer electrolyte can be expressed as:

$$ \sigma ={n}_{\hbox{--} }e\left|{Z}^{-}\right|{\mu}_{\hbox{--} }+{n}_{+}e\left|{Z}^{+}\right|{\mu}_{+} $$
(1)

where n − and n + are the numbers of negative and positive charge carriers per unit volume, e is the electronic charge, μ − and μ + are the mobilities of the negative and positive charge carriers and Z − and Z + are the valences of the negative and positive charge carriers, respectively [9]. It has been reported by Bandara et al. [12] that the real and imaginary parts of impedance measured by sandwiching an electrolyte between two blocking electrodes can be written as:

$$ {Z}_r=\frac{R}{1+{\left(\omega RC\right)}^2} $$
(2)
$$ {Z}_i=\frac{\omega {R}^2C}{1+{\left(\omega RC\right)}^2}+\frac{2}{\omega {C}_e} $$
(3)

where Z r and Z i are, respectively, the real and imaginary parts of the impedance, Ω is the angular frequency, C e is the electrical double layer (EDL) capacitance at each electrode, C is the bulk geometrical capacitance and R is the bulk resistance of the electrolyte. These equations are valid when the Nyquist plot is a perfect semicircle with a vertical spike at low frequencies. The vertical spike represents a perfect capacitor, and this is represented by the second term of the right-hand side of Eq. (3) with the factor 2 indicating two EDL layers on both sides of the electrolyte, which are in contact with the blocking electrodes. When ions accumulate at the electrode/electrolyte interfaces, EDLs will be formed. The double-layer capacitance is given by:

$$ {C}_{\mathrm{e}}=\frac{\varepsilon_r{\varepsilon}_0A}{\lambda } $$
(4)

And the geometrical capacitance is given by:

$$ C=\frac{\varepsilon_r{\varepsilon}_0A}{2d} $$
(5)

In Eqs. (4)–(6), the thickness of the electrolyte is represented as 2d. The bulk resistance R is given by:

$$ R=\frac{2d}{\sigma A} $$
(6)

Here, ε r is the dielectric constant of the electrolyte, ε 0 is the vacuum permittivity (8.85 × 10−14 F cm−1), λ is the thickness of each electrical double layer and A is the electrode/electrolyte contact area. The dissipative loss parameter, following the BDR or Bandara-Mellander (B-M) approach, is given by [12]:

$$ \tan \left(\varphi \right)=\frac{\omega \tau \sqrt{\delta }}{1+{\left(\omega \tau \right)}^2} $$
(7)

And the peak of the dissipative loss curve is given by:

$$ {\left( \tan \left(\varphi \right)\right)}_{\max }=\frac{\sqrt{\delta }}{2} $$
(8)

Here, Ω is the angular frequency and τ (\( =\frac{1}{\omega } \)) is the characteristic time constant corresponding to the maximum in the dissipative loss curve, and δ \( =\frac{d}{\lambda } \). The B-M approach assumes that the ions have a single relaxation time and defines the diffusion coefficient (D), mobility (μ) and number density (n) of the mobile ion by the following equations [12]:

$$ D=\frac{d^2}{\tau_2{\delta}^2} $$
(9)
$$ \mu =\frac{e{d}^2}{kT{\tau}_2{\delta}^2} $$
(10)
$$ n=\frac{\sigma kT{\tau}_2{\delta}^2}{e^2{d}^2} $$
(11)

As the values of τ 2 and δ can be evaluated from the dielectric measurement, Eqs. (9)–(11) can be used to determine D, μ and n. However, these equations are valid only for an ideal system with Nyquist plot having a perfect semicircular ark and a vertical spike. In contrast, the Nyquist plots obtained by impedance measurements, in general, have the following features: (a) a depressed semicircle, which is best represented with an equivalent circuit comprising a constant phase element (CPE) or leaky capacitor connected in parallel to a resistor; (b) a tilted spike, which is best represented by a resistor in series with a CPE; or (c) a depressed semicircle and a tilted spike, which can be represented by an equivalent circuit comprising a parallel combination of CPE and a resistor that is in series with a second CPE. While the spike represents the electrical double layer, the depressed semicircle represents the bulk material [11].

The real and imaginary parts of the Nyquist plot consisting of a depressed semicircle and tilted spike are given by the equations [11]:

$$ {Z}_{\mathrm{r}}=\frac{R+{R}^2{k_1}^{-1}{\omega}^{p_1} \cos \left(\frac{\pi {p}_1}{2}\right)}{1+2R{k_1}^{-1}{\omega}^{p_1} \cos \left(\frac{\pi {p}_1}{2}\right)+{R}^2{k_1}^{-2}{\omega}^{p_1}}+\frac{ \cos \left(\frac{\pi {p}_2}{2}\right)}{{k_2}^{-1}{\omega}^{p_2}} $$
(12)
$$ {Z}_{\mathrm{i}}=\frac{R^2{k_1}^{-1}{\omega}^{p_1} \sin \left(\frac{\pi {p}_1}{2}\right)}{1+2R{k_1}^{-1}{\omega}^{p_1} \cos \left(\frac{\pi {p}_1}{2}\right)+{R}^2{k_1}^{-2}{\omega}^{p_1}}+\frac{ \sin \left(\frac{\pi {p}_2}{2}\right)}{{k_2}^{-1}{\omega}^{p_2}} $$
(13)

The term k 1 −1 is the geometrical capacitance of the polymer electrolyte, and k 2 −1in Eqs. (12) and (13) is the capacitance due to the EDL formation at the electrode/electrolyte interface during the impedance measurement which is equivalent to the capacitance C e in Eq. (4) of the B-M approach. The parameters R, p 1 and p 2 are defined in the paper by Arof et al. [11]. Equations (12) and (13) are valid for the Nyquist plot with a depressed semicircle and a tilted spike. The values of k 1 −1 and k 2 −1 can be obtained by trial and error to fit the experimental Nyquist plot. The diffusion coefficient (D), mobility (μ) and number density (n) of the mobile ion can be calculated by the following equations:

$$ D=\frac{{\left({k}_2{\varepsilon}_r{\varepsilon}_0A\right)}^2}{\tau_2} $$
(14)
$$ \mu =\frac{e{\left({k}_2{\varepsilon}_r{\varepsilon}_0A\right)}^2}{k_bT{\tau}_2} $$
(15)

where k b is the Boltzmann constant (1.38 × 10−23 J K−1), T is the absolute temperature in Kelvin and e is the electron charge (1.602 × 10−19 C). The number density of charge carriers n can be determined from σ using:

$$ \sigma =n\mu e $$
(16)

Experimental

Sample preparation

Chitosan with more than 75 % degree of deacetylation procured from Aldrich and oxalic acid (C2H2O4.H2O) from R&M Chemicals were used for the preparation of the polymer electrolytes by the solution casting method. The membrane samples have been prepared according to the procedure described by Fadzallah et al. [13]. Five polymer membranes were prepared with 10, 20, 30, 40 and 50 wt% oxalic acid contents and the samples were named as OA10, OA20, OA30, OA40 and OA50, respectively. The highest conducting polymer of chitosan-oxalic acid system was added with glycerol as a plasticizer. Different amounts of glycerol 10, 20, 30, 40, 50 and 60 wt% were added to OA40 membrane, and the samples were designated as OG10, OG20, OG30, OG40, OG50 and OG60, respectively.

Sample characterization

Electrical impedance spectroscopy (EIS)

Impedance measurements on the sample membranes were performed using the HIOKI 3532-50 LCR Hi-Tester impedance analyser as a function of frequency ranging from 50 Hz to 1 MHz at room temperature 300 K. The procedure used and the ionic conductivity calculation have been reported in Fadzallah et al. [14].

Fourier transform infrared spectroscopy

Fourier transform infrared (FTIR) data for the sample membranes were obtained from 4000 to 650 cm−1 using the Thermo Scientific Nicolet iS10 spectrophotometer operating at a resolution of 4 cm−1. The characteristic bands between 1400 and 1800 cm−1 were deconvoluted using the OMNIC software. The absorbance peaks were fitted to a straight baseline using the Gaussian-Lorentzian function, and the area of the deconvoluted bands were calculated. According to Yalcinkaya et al. [15] and Ritthidej et al. [16], the absorption peak of NH2 deformation appears at around ~1559 cm−1 and the presence of NH3 + at ~1600 cm−1. In the deconvolution process, peaks due to the complexation between chitosan and oxalic acid were selected and the sum of the intensity of all the deconvoluted peaks was ensured to fit the original spectrum. The peak at around 1600 cm−1for NH3 + was assigned to free ions. The area under the peak was determined, and the percentage of free ions was calculated using the following equation:

$$ \mathrm{Percentage}\ \mathrm{of}\ \mathrm{free}\ \mathrm{ions}\ \left(\%\right)=\frac{A{}_f}{A_f+{A}_u}\kern0.5em \times 100 $$
(17)

Here, A f is the area under the peak of the protonated amine, NH3 +, and A u represents the area under the peak of the unprotonated amine, NH2.

Results and discussion

Chitosan-oxalic acid electrolyte system

The room temperature ionic conductivity value of chitosan-based sample membranes increased gradually with OA content and reached a maximum at 40 wt% OA with a value of 4.95 × 10−7 S cm−1. The increase in ionic conductivity value can be attributed to the increases of mobility and number density of charge carriers. However, the number density of mobile ions might decrease due to ion reassociation or recombination processes [11]. The Nyquist plots for the samples and their corresponding fitting plots are shown in Fig. 1. From the Nyquist plots, the values of parameters k 1 −1 and k 2 −1 were obtained by trial and error method until the fitted points give a good fit to the experimental points with a regression value R 2 ~ 1. The values of k 2 −1 together with those of n, μ and D obtained using Eqs. (14–16) are listed in Table 1. To calculate these values, the dielectric constant ε r was required.

Fig. 1
figure 1

Nyquist plots (circle) and their corresponding fitted lines (line) for a OA10, b OA20, c OA30, d OA40 and e OA50 samples

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Table 1 The values of k 2, ε r , τ 2, D, μ and n for the chitosan-oxalic acid electrolyte system obtained using the proposed EIS method
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To obtain ε r , log ε r versus log f was plotted for all samples and is shown in Fig. 2 with the enlarged region (inset a) between log f = 5.8 and log f = 6. The value of ε r in this enlarged region was taken as the dielectric constant because log ε r versus log f showed a constant value. In other regions, i.e. at lower f values, ε r increases as the frequency decreases due to the accumulation of charges in the space charge region and the value of ε r cannot be considered as the dielectric constant value. The ε r values at 1 MHz have been taken as dielectric constant values. Hence, ε r  = 0.16, 1.44, 2.30, 8.70 and 6.62 for OA10, OA20, OA30, OA40 and OA50, respectively. The inset (b) in Fig. 2 shows that the values of the ionic conductivity and k 2 −1 increased linearly with oxalic acid content reaching maxima at 40 wt% with the highest k 2 −1 value of 74.07 × 10−7 F. The ionic conductivity is mainly controlled by n and μ as shown by Eq. (16). From Table 1, one can see that OA40 exhibits the highest μ and D values. The values of n, μ and D of the charge carriers were validated using results obtained from FTIR spectroscopy. The FTIR spectra were published in reference [14]. The absorption peaks from 1800 to 1400 cm−1 were deconvoluted. In the deconvolution process, peaks due to the complexation between chitosan and oxalic acid were selected and the sum of the intensity of all the deconvoluted peaks was ensured to fit the original spectrum. The peak at around 1600 cm−1 for NH3 + was assigned to free ions. The three parameters of n, μ and D were calculated using the Eqs. (14), (15) and (16). Table 2 lists the parameter values.

Fig. 2
figure 2

The dielectric constant, ε r for samples with different amounts of OA versus log f at room temperature, 300 K (the inset (a) shows the enlarged plots at high frequencies, and inset (b) shows the variation of conductivity and k 2 −1 with different amounts of oxalic acid)

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Table 2 The values of V total, the free ions (%), n, μ and D for the chitosan-oxalic acid electrolyte system obtained using the FTIR method
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Table 2 shows that n and μ influenced the ionic conductivity. The highest conducting membrane OA40 exhibits the highest μ and D values. For comparison purposes, the impedance data obtained from the experiment can be transformed into loss tangent formalism, tan (φ), as shown in Fig. 3. It can be seen that the fitting is not that good at low and high frequencies. This might be due to the type of Nyquist plot used to develop the B-M method. In this method, no parameter can be adjusted since δ used in this equation is directly from a tan (φ) versus frequency curve based on the experimental impedance data. The parameters τ 2 and δ obtained by curve fitting are used to determine the transport parameters n, μ and D by the broadband dielectric response or the B-M method, and the parameter values obtained are listed in Table 3.

Fig. 3
figure 3

Dielectric loss tangent (tan ϕ), (circle) and their corresponding fitted lines (line) as a function of frequency for sample membranes a OA10, b OA20, c OA30, d OA40 and e OA50

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Table 3 The values of τ 2, δ, n, μ and D for the chitosan-oxalic acid electrolyte system determined using the B-M method
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The highest conducting membrane OA40 shows the lowest τ 2 value, 0.53 × 10−4 s. The ionic conductivity is mainly controlled by n and μ values. Table 3 shows that OA40 exhibits the highest μ and D values. Figures 4, 5 and 6 compare the OA concentration dependence of the charge carrier density, n, charge carrier mobility, μ, and diffusion coefficient, D, values calculated based on FTIR method, EIS method and the B-M method. The results obtained from the EIS method [11] and the FTIR method are in reasonably good agreement compared to the results from the B-M approach.

Fig. 4
figure 4

Plot of log charge carrier density, n, against OA (wt%) content obtained from the proposed method, FTIR and B-M method for the chitosan-OA electrolyte system

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Fig. 5
figure 5

Plot of log charge carrier mobility, μ, against OA (wt%) content obtained from the proposed EIS method, FTIR and B-M method for the chitosan-OA electrolyte system

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Fig. 6
figure 6

Plot of log diffusion coefficient, D, against OA (wt%) content obtained from the proposed EIS method, FTIR and B-M method for the chitosan-OA electrolyte system

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Chitosan-oxalic acid-glycerol electrolyte system

The proposed EIS method was tested on the plasticized chitosan-based electrolytes with different amounts of glycerol as well. The n, μ and D values calculated based on the proposed EIS method were compared with results obtained from FTIR spectroscopy and B-M method.

The Nyquist plots for all the plasticized chitosan electrolytes and their corresponding fitting plots are shown in Fig. 7. Log ε r versus log f curves plotted in order to obtain dielectric constants (ε r ) are shown in Fig. 8 with the enlarged regions between log f = 5.8 and log f = 6 in inset (a). The constant values seen in inset (a) were taken as the dielectric constants. In other regions, i.e. at lower f values, ε r increases as the frequency decreases due to the accumulation of charges in the space charge region and the value of ε r cannot be considered as the dielectric constant value. Hence, dielectric constants of the membranes (values of ε r at f = 1 MHz) are 8.21, 8.86, 8.93, 12.47, 13.40 and 19.82 for OG10, OG20, OG30, OG40, OG50 and OG60, respectively. The values of k 2 −1 together with those of n, μ and D obtained from the proposed EIS method are listed in Table 4. The inset (b) in Fig. 8 shows the values of the ionic conductivity and k 2 −1 increased linearly with glycerol content. The k 2 −1 reaches maximum at 60 wt% with a value of 58.82 × 10−6 F. The ionic conductivity is mainly controlled by n and μ calculated from Eq. (16). From Table 4, one can see that OG60 exhibits the highest μ and D values.

Fig. 7
figure 7

Nyquist plot (circle) and their corresponding fitted points (line) for a OG10, b OG20, c OG30, d OG40, e OA50 and f OG60

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Fig. 8
figure 8

The dielectric constant ε r for samples with different amounts of glycerol versus log f at room temperature 300 K. The inset (a) shows the enlarged plot at high frequencies and inset (b ) shows the variation of conductivity and k 2 −1 with different amounts of glycerol

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Table 4 The values of k 2 −1, ε r , τ 2, D, μ and n for the glycerol-chitosan with 40 wt% oxalic acid electrolyte system obtained using the proposed EIS method
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The values of n, μ and D of the charge carriers obtained from the proposed EIS method are validated using the results obtained from FTIR spectroscopy. The three parameters of n, μ and D were calculated using the FTIR data and listed in Table 5. For comparison purposes, the impedance data obtained from the experiment can be transformed into loss tangent formalism, tan (φ), as shown in Fig. 9. It can be observed that the fitting is not that good at low frequencies. Table 6 lists the values for the transport parameters obtained using BDR method. Figures 10, 11 and 12 compare glycerol concentration dependence of charge carrier density, n, charge carrier mobility, μ, and diffusion coefficient, D, values calculated using FTIR method, EIS method (this work) and the B-M method. The results obtained from the EIS method [6] and the FTIR method are in good agreement compared to the results from the B-M approach.

Table 5 The values of V total, the free ions (%), n, μ and D for the glycerol-chitosan with 40 wt% oxalic acid electrolyte system obtained using the FTIR method
Full size table
Fig. 9
figure 9

Dielectric loss tangent (tan ϕ), (circle) and their corresponding fitted lines (line) as a function of frequency for sample membranes a OG10, b OG20, c OG30, d OG40, e OG50 and f OG60

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Table 6 The values of τ 2, δ, n, μ and D for the glycerol-chitosan with 40 wt% oxalic acid electrolyte system using the B-M method
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Fig. 10
figure 10

Plot of log charge carrier density, n, against glycerol (wt%) content obtained from the proposed EIS method, FTIR and B-M method for the plasticized electrolyte system

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Fig. 11
figure 11

Plot of log ionic mobility, μ, against glycerol (wt%) content obtained from the proposed EIS method, FTIR and B-M method for the plasticized electrolyte system

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Fig. 12
figure 12

Plot of log diffusion coefficient, D, against glycerol (wt%) content obtained from the proposed EIS method, FTIR and B-M method for the plasticized electrolyte system

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Figure 13 shows the comparisons of transport properties and conductivities for electrolytes having 0 and 60 wt% glycerol contents. The 0 wt% of glycerol here stands for the highest conducting membrane of the non-plasticized chitosan-based electrolyte OA40. The addition of 60 wt% glycerol increased the conductivity value from 4.95 × 10−7 to 4.13 × 10−5 S cm−1. All three methods show that the number density of charge carriers increase when glycerol is added to the electrolyte (Fig. 13a) The changes in the values of the number density of charge carriers, n, for FTIR method, proposed EIS method and B-M method against the glycerol contents were observed in Fig. 13a. However, the addition of glycerol did not increase the ionic mobility, μ, and diffusion coefficient, D, as shown in Fig. 13b, c. The number density of charge carriers increase substantially in glycerol-added samples due to the prevention of ion association because of the high dielectric constant of the glycerol. However, the high viscosity of glycerol-added samples reduces the mobility and diffusion rate of the ions slightly. The higher number density of change carriers is responsible for the observed high ionic conductivity of the glycerol-added sample.

Fig. 13
figure 13

Plot of n, μ, D and σ against the glycerol content. Note that the 0 wt% of glycerol here stands for the highest conducting membrane of the non-plasticized chitosan-based electrolyte OA40

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Conclusions

The proposed EIS method shows that the values of number density, mobility and diffusion coefficient of mobile ions can be calculated solely from the impedance data without depending on the EDL layer as in the case of the broadband dielectric response approach. The values obtained from the EIS method are in reasonably good agreement with the values from FTIR spectroscopy compared to the values from the broadband dielectric response approach. The values of k 2 −1 calculated from the impedance data reach maxima at 40 wt% oxalic acid (OA40) and 60 wt% (OG60) glycerol with values of 74.07 × 10−7 and 58.82 × 10−6 F, respectively. The ionic conductivity of oxalic acid and plasticized membranes are mainly influenced by n and μ. The highest conducting membranes OA40 and OG60 exhibit the lowest τ 2 values, 0.53 × 10−4 and 0.38 × 10−5 s, respectively. The addition of glycerol increased the ionic conductivity by increasing the number density of charge carriers but did not increase the ionic mobility, μ, and diffusion coefficient, D. The results obtained from the EIS method and the FTIR method are in good agreement compared to the results from the B-M approach.