1 Introduction

The liquid-phase micro extraction (LPME) is a green sample preparation method for a kind of substances from complex sample matrices (Liu and Dasgupta, 1996; Jeannot and Cantwell, 1996) and offers analytical chemists a good chance to combine it with GC and LPLC (Xu et al., 2007; Porto et al., 2012; Lee et al., 2006; Potter et al., 1991; Xue et al., 2013) and other analytical methods (Green and Abraham, 2000; Sparrenberger et al., 2004). Electrochemical methods are based on carbon paste electrode (CPE) (Lawrence et al., 2002) with some unique adhesion properties (Khoo and Ye, 2000; Salinas et al., 1990) in organic phase and in aqueous phase(Strong and Dasgupta, 1989; Krishnan et al., 1993). The combination of LPME with electrochemistry at CPE had been used in amperometric electrochemical detection of electrochemical active substances such as bromide (Hao et al., 2009) and iodide (zhu et al., 2010) by cyclic voltammetry or differential pulse voltammetry. The voltammetric methods cannot directly be used for electrochemical detection of an inactive species after the extraction. In this case, potentiometric methods such as open circuit potential method, or other potential measurement methods are favorable. Open circuit potential method not only serves in the detection of substance with or without electrochemical activity (Wilburn et al., 2004; Slowinska et al., 2003) with higher sensitivity and applicability, but also gives out the dynamic information about chemical process occurred at the electrode surface (Brotons et al., 1995).

Alkyl phenols are toxic compounds in the environment (Ghambarian et al., 2012), and widely used in dye-chemical, medicine and petrochemical, cosmetic, and food industries. In the environment, dye-chemical productions and petrochemical industries as regards detections, we not only pay more attention to single compound, but also want to know how much amount of alkyl phenols in the samples. In this case, the extraction, detections and removals of all phenols are really important, and attract many people’s attention. Some analytical methods have been developed such as liquid chromatography (Faraji et al., 2010) with liquid–liquid micro extraction and fluorescent detection (Neto, 2012) and high performance liquid chromatography with Carrier-mediated liquid phase extraction (Zhang et al., 2008).

Among the alkyl phenols, 4-tert-butylphenol (TBP) is a typical one, with a larger alkyl group, tert-butyl, which makes the molecule weakly acidic and strongly hydrophobic, and a phenol group which makes it have moderate oxidation. The electrochemical behavior of TBP is not obviously defined due to the strong hydrophobicity and weaker solubility in water, so that amperometry in the detection of TBP has to be done with a modified electrode by means of electrochemical catalysis and phase-transition catalysts. If the potentiometry was combined with micro extraction, the detection may be done without the need of electrochemical catalysts, and the detection is not only on a single molecule, but also on whole kind of molecules with similar properties.

The extracted molecules in aqueous solution are surrounded by a large amount of water molecules, and are called hydrated molecules. In the liquid–liquid extraction process, the hydrated molecules must loss the surrounded water molecules and extracted into organic phase. There are very complex molecular interactions of extracted molecules with water molecules and organic extractant molecules, and the interactions take place only in few molecular layers. The common experimental methods are not totally reliable to get some information from the interactions. Electrochemical method is an interface monitoring method. Quantum chemical methods can give some information about molecular structure, molecular interactions as well as the thermodynamic properties. Among the several quantum chemical calculation methods, PM6 in MOPAC2009 (Stewart, web: http://OpenMOPAC.net; Stewart, 2007) is a semi-empirical quantum chemistry method, which can hold larger molecular systems, has increased calculation speed, is easy to use without special requirement for computers, usually personal computers, and attracts more and more people’s attention to be applied in their research works. In the present paper, the potentiometry was combined with liquid–liquid micro extraction for the detection of 4-tert-butylphenol, the molecular mechanism of the micro extraction was suggested according to the quantum chemical calculation, and the quantum chemical results accord well with the experimental data. Some interested results are described here.

2 Theoretical descriptions

According to the thermodynamic principles (Callen, 1985), the tendency of a chemical process can be estimated with the change of Gibbs free energy at given temperature: ΔG_r < 0 for spontaneous forward reaction; ΔG_r = 0 for equilibrium and ΔG_r > 0 for the spontaneous backward reaction. For a given reaction system including m components of reactants and n components of products, the changes of Gibbs free energy of the reaction (ΔG_r) can be calculated as,

The models of individual molecules such as 4-tert-butylphenol, trioctyl phosphate and water are directly drawn out in ACDLABS 12 software (http://www.acdlabs.com). The model of hydrated 4-tert-butylphenol was built with a model of salvation in a box (Zhang et al., 2006; Fennell et al., 2011) just surrounding the whole molecule with 18 water molecules. In organic binder liquid, the model of clusters of trioctyl phosphates in its liquid phase and trioctyl phosphate interacting with 4-tert-butylphenol was built according to the interaction model of length chain molecules self assembling in liquid interface (Abdel-Mottale et al., 2005; Page and Warr, 2004). In this model, the two trioctyl phosphate molecules crossover together into a cluster as a dimer, in which each side of the molecular cluster has three length chains with a larger contact area. A molecular cluster model composited of one 4-tert-butylphenol and one dimer with the tert-butyl group lain on the two carbon chain plane, and the hydroxyl group of phenol forming a hydrogen bonding with the one oxygen of one phosphate. All of the three molecular clusters are shown in Fig. 1.

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Figure 1

Molecular clusters composited of 4-tert-butylphenol, water and trioctyl phosphate. TBP-18w: 4-tert-butylphenol with 18 water molecules; ToP₂: a dimer of trioctyl phosphate; ToP₂–TBP: one dimer interacts with one 4-tert-butylphenol.

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All the models were constructed with ACDLABS 12 (http://www.acdlabs.com), and further optimized with EF in MOPAC2009. The quantum chemical calculation was performed with MOPAC2009 software (Stewart, web: http://OpenMOPAC.net; Stewart, 2007) with parameters of PM6, EF, GNORM = 0.01, THERMO, LET, at 25 °C under vacuum conditions.

3 Experimental

4 Results and discussion

4.1

4.1 Potentiometric studies of the micro extraction

4.1.1

4.1.1 Potentiometric curves of 4-tert-butylphenol

Open circuit potential experiments were performed in 0.25 M KCl electrolyte solution (pH 3.0) without (1) and with 1.0 × 10⁻⁶ M TBP (2) on the CPE, the obtained potential–time curves are shown in Fig. 1. The CPE in 0.25 M KCl electrolyte solution without TBP gives out a decline curve with regression equation as Harris model,

(4)

$$E=1/(0.2333t^{0.4136}-12.65)\text{;}{R}^2=0.9367\text{;}\mathit{SD}=0.0015$$ The CPE in 0.25 M KCl including 1.0 × 10⁻⁶ M TBP gives out a exponential association curve with the regression equation of,

(5)

$$E=0.116-0.03352e^{-0.00676t}\text{;}{R}^2=0.9262\text{;}\mathit{SD}=0.0024$$ Removing the influence of the electrolyte solution and subtracting curve 2 from curve 1, a new curve was obtained as curve 3 in Fig. 2.This is a typical exponential association curve with the regression equation of,

(6)

$$E=0.2194-13.78e^{-0.01685t}\text{;}{R}^2=0.9999\text{;}\mathit{SD}=2.93x{10}^{-6}$$ This curve also serves as the liquid–liquid micro extraction dynamic responding curve of the CPE to TBP, from which the apparent first extraction kinetic rate constant of 0.01685 s⁻¹ was obtained.

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Figure 2

The potentiometric curves of trioctyl phosphate carbon paste electrode without (1), with 4-tert-butylphenol (2) and background solution (3) in 0.25 M KCl electrolyte solution (pH 3.0). Concentration of 4-tert-butylphenol is 1.0 × 10⁻⁶ mol/L.

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4.1.2

4.1.2 The effects of solution pH

The solution pH is an important factor, which influences not only the existing forms of TBP but also the adsorption ability of trioctyl phosphate. The solution pH was controlled by disodium hydrogen phosphate-citric acid buffer system in the range of 2.2–8.0, and the OCP experiments were performed in 0.3 M KCl electrolyte solution including 1.0 × 10⁻⁴ M TBP. The open circuit potential differences at 500 s were plotted against solution pH, a complex curve was obtained as shown in Fig. 3.

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Figure 3

The relationship between differences of open circuit potential and solution pH.

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In the pH region from 2.2 to 6.0, the open circuit potential differences have a similar value around 26 mV with the maximum point located at pH = 3.0. In the range of pH >6, the potential difference goes down to the negative range, due to the acid–base reaction of 4-tert-butylphenol with hydroxyl in solution, which is not favorable for the extraction. So pH = 3.0 was chosen as the optimal pH condition in the following experiments.

4.1.3

4.1.3 The concentration influence of 4-tert-butylphenol

Under the optimal experimental conditions, the open circuit potential experiments were performed in 0.5 M KCl electrolyte solution including different concentrations of TBP in the range of 1.0 × 10⁻⁴–5.0 × 10⁻⁷ mol/L. The obtained open circuit potential differences at 500 s were plotted against concentration of TBP as an exponential association function shown in Fig. 4A with the regression equation of,

(7)

$$\mathrm{\Delta }E=0.0459-0.0302e^{-38372c}\text{,}{R}^2=0.9976\text{,}\mathit{SD}=0.0011$$ The exponential function curve can be easily transferred into a logarithm as shown in Fig. 4B. The regression equation for the plot of open circuit potential difference against logarithm of TBP concentration is as follows,

(8)

$$\mathrm{\Delta }E=0.0998+0.01382\times \text{log}(c\text{,}M)\text{;}{R}^2=0.992\text{,}\mathit{SD}=0.0013$$ The linear slope of 0.0138 in the equation indicates that each cluster of trioctyl phosphate can extract up to 3–4 of 4-tert-butylphenol molecules, that is n = 3–4. This liquid–liquid micro extraction potentiometry can be used in the determination of 4-tert-butylphenol with the detection limit of 5.0 × 10⁻⁷ mol/L. The experiments were performed for 5 times at 5.0 × 10⁻⁷ mol/L in composed water sample (drinking water addition of 5.0 × 10⁻⁷ mol/L 4-tert-butylphenol), so we obtain the detection limit of 5.0 × 10⁻⁷ mol/L (n = 5, ratio of signal/noise = 3).

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Figure 4

The plot of open circuit potential difference against TBP concentration (A), and logarithm of TBP concentration (B). The other experimental conditions were as same as in Fig. 1.

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4.2

4.2 The molecular mechanism of the micro extraction by quantum chemistry

The 4-tert-butylphenol (TBP) molecule was built, optimized and calculated with MOPAC2009. The entropy and heat of formation of TBP were obtained as 0.431885 kJ·K⁻¹·mol⁻¹ and −187.531 kJ·mol⁻¹ (listed in Table 1).

Table 1 The summary of thermodynamic calculation results.

Item/298 K	Entropy, S (kJ·K−1·mol−1)	Heat of formation, Hf (kJ·mol−1)	Free energy change ΔGr (kJ·mol−1)
TBP	0.431885	−187.531
TBP–W18	1.80522	−3067.679	200.633
W18	1.57092	−3473.234
ToP	1.01617	−1359.005
ToP2	1.1523125	−1221.707	879.613
ToP–TBP	1.02785	−406.622	1256.135
ToP2–TB	1.846969	−1773.711	−542.750
ToP2–TB2	2.021217	−1687.173	−1149.502
ToP2–TB3	2.17344	−1572.971	−1662.553
ToP2–TB4	1.895057	−1592.322	3112.553

The TBP molecule was hydrated with 18 water molecules (W₁₈) in a water box, and forms a molecular cluster including 18 water molecules and one TBP molecule,

(9)

$$\text{TBP}+18\text{W}\to {\text{TBP-W}}_{18}$$ The reaction entropy of 1.80522 kJ·K⁻¹·mol⁻¹ and heat of formation of −3067.679 kJ·mol⁻¹ were calculated. The free energy change of the reaction at 298 K was calculated as 200.633 kJ·mol⁻¹ (listed in Table 1) according to Eq. (1). This value of free energy change indicates that the TBP molecule in aqueous solution is not favorable in thermodynamic terms, and it is not easy to dissolve TBT in water with small solubility.Trioctyl phosphate (ToP) in liquid phase may form some kinds of clusters in order to obtain the stability. The semi-empirical quantum chemical calculation indicates that two trioctyl phosphate molecules form a dimer structure with two phosphates in the middle and three carbon chains crossover together as shown in Fig. 1.

(10)

$$\text{ToP}+\text{Top}\to {(\text{ToP})}_2$$ The entropy and heat of formation of the dimer cluster were calculated as 1.15 kJ·K⁻¹·mol⁻¹, and −1221.707 kJ·mol⁻¹ (listed in Table 1).The free energy change for the reaction (Eq. (10)) was calculated as 879.6132 kJ·mol⁻¹ (listed in Table 1). The value indicates that the model for the dimer structure is not a stable one. In the real liquid trioctyl phosphates, the molecules are not the stiff ones but each molecule may be surrounded by several other molecules and forms trimer, tetramer and so on. The dimer may be the simplest one, but it indicates that several trioctyl phosphate molecules are combined together for the extraction of one extractant molecule, so it still manful calculation for the implication case.

During the micro extraction process, the hydrated tert-butyl phenol was extracted into trioctyl phosphate phase, and remove out all water molecules and interaction with trioctyl phosphate dimmer in the polar region and forms a molecular cluster as describes in the following reaction,

(11)

$${(\text{ToP})}_2+\text{nTBP}-{\text{W}}_{18}\to {(\text{ToP})}_2-{\text{TBP}}_{\text{n}}+{\text{nW}}_{18}(n=1\text{,}2\text{,}3\text{,}4)$$ The free energy changes according to Eq. (11) for different numbers of TBP molecules (n = 1, 2, 3, 4) were obtained as −542.750 kJ mol⁻¹, −1149.502 kJ mol⁻¹, −1662.788 kJ mol⁻¹ and 3112.553 kJ mol⁻¹ (listed in Table 1). At this stage we can seen that the extraction is a favorable process (called as spontaneous process) with very larger negative free energy changes. The enthalpy change, entropy and free energy change for the reaction were plotted against number of TBP as shown in Fig. 5.

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Figure 5

The plot of reaction free energy against number of TBP molecules.

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The change of fee energy for the reaction keeps a linear decrease with number of TBP with the regression equation of,

(12)

$$\mathrm{\Delta }{G}_{\text{r}}=-826.636-278.461\times n\text{,}{R}^2=0.9995\text{,}\mathit{SD}=13.55$$ The change of enthalpy in the reaction decreases with an increase in the number of TBP up to 3, and then goes down further, while the entropy change decreases with the number of TBP, and becomes the negative value after 4. This result means that one dimer is most likely to extract three TBP molecules and then the further extraction is favorable for enthalpy but unfavorable for entropy. So the fourth TBP molecule was extracted only in the higher concentration of TBP in aqueous solution. This result also accords well with the open circuit potential measurement result in the plot of open circuit potential difference against logarithm of TBP concentration with the slope = 0.01382 (Eq. (8)).

5 Conclusions

In summary, the liquid–liquid micro extraction of 4-tert-butylphenol from aqueous solution on to the trioctyl phosphate organic phase can be monitored by potentiometry with carbon paste electrode, and theoretically studied by semi-empirical quantum chemistry methods with MOPAC2009, and applied in the determination of 4-tert-butylphenol. Some important results are obtained as follows.

• The liquid–liquid micro extraction dynamic curve of 4-tert-butylphenol from aqueous solution to trioctyl phosphate organic phase can be monitored by potentiometry, and follows a typical exponential association function with the apparent first extraction kinetic rate constant of 0.01685 s⁻¹.

• The open circuit potential changes with concentration of 4-tert-butylphenol and follows an exponential association function, linearized as a working curve for the detection of 4-tert-butylphenol in aqueous solution in the concentration range of 1.0 × 10⁻⁴–5.0 × 10⁻⁷ mol/L with the detection limit of 5.0 × 10⁻⁷ mol/L.

• The quantum chemical studies with MOPAC2009 indicate that the interactions of hydrated 4-tert-butylphenol with trioctyl phosphate dimer are thermodynamically favorable for the micro extraction of 4-tert-butylphenol from aqueous solution into the organic phase. Each trioctyl phosphate dimer can interact with up to four 4-tert-butylphenol molecules, which accords well with the slope of potential–logarithm of concentration curve. The quantum chemical calculation gives out the molecular mechanism of the micro extraction process.