Introduction

Vitamins are organic compounds that are necessary for metabolism, generally in small amounts. Vitamins are usually classified by their biological and chemical activities and not their molecular structure. By now, there are thirteen vitamins universally recognized, namely nine water soluble (B1, B2, B3, B5, B6, B7, B9, B12 and C) and four liposoluble (A, D, E and K).

Vitamins of B-group play important roles in the human organism: vitamin B1 plays a central role in energy production, vitamin B2 is essential in Szent-Györgyi–Krebs cycle and beta-oxidation of fatty acids and vitamin B6 is important for the metabolism of lipids and amino acids [1, 2]. The structural formulas of the analysed vitamins are presented in Scheme 1.

Scheme 1
scheme 1

Structural formulas of the analysed vitamins: a thiamine hydrochloride (vitamin B1), b riboflavin (vitamin B2) and c pyridoxine hydrochloride (vitamin B6)

Full size image

High concentration of vitamin B1 is found in yeast, wheat germ, pork, brown rice, vegetables, potatoes, liver and egg yolk. Generally, manufactured food presents a lower quantity of thiamine [2]. The main sources for vitamin B2 are dairy products (milk and cheese), fruits and vegetables (bananas, green beans and leafs), almonds, etc. and for vitamin B6 (as pyridoxine) are soybeans and beans, bananas, walnuts, brown rice, potatoes, etc. Rucker et al. described extensively the biosynthesis, occurrence in food, absorption and transport, diseases associated with deficiency of these vitamins, and the effect of exposure to high doses [2]. Even if the influence of several factors such as pH, moisture, oxidative atmosphere/oxygen, radiation/light and temperature over the stability of vitamins was described, a study regarding the thermal behaviour and kinetic analysis of the decomposition process was not realised, according to our knowledge. The vitamin degradation can occur during food or pharmaceutical product processing and formulation, but as well during storage under impropriate conditions. According to these premises, we set our goal in the study of thermal behaviour of three vitamins from B-class, namely B1, B2 and B6, and as well for the analysis of their kinetic degradative process.

The study of thermal behaviour of pharmaceutical active substances is essential for the estimation of the possible interactions that can occur in solid dosage forms [3–5]. These estimations can be obtained by various methods, but of great importance and reproducibility are the methods that are based on kinetic data, including the ones obtained under non-isothermal conditions.

In our previous studies [6–13] we realised both kinetic analysis regarding the thermal stability of pharmaceuticals and compatibility studies of active pharmaceutical ingredients (API) with different excipients. The differences obtained for the kinetic parameters were easily correlated with the differences in the molecular architecture of API.

In the present paper, we applied a similar strategy for the kinetic analysis, but on significantly different molecular structures (see Scheme 1), even if the physiological role of these compounds are comparable.

Materials and methods

The vitamins are commercial products and used as received without further purification. The vitamins B1 (purity >99 %) and B6 (purity >99 %) were obtained from Acros Organics, Geel, Belgium and vitamin B2 (purity >98 %) was obtained from Fisher Bioreagents, Geel, Belgium. The samples were kept in a desiccator during the study to avoid moisture absorption.

TG/DTG/HF measurements were performed on a Perkin-Elmer DIAMOND TG/DTA instrument. The experiments were carried out using about 7 mg of sample which was weighted into an open aluminium crucible. The furnace temperature was programmed to rise under non-isothermal conditions from ambient temperature to 550 °C linearly at a heating rate of 10 °C min−1. The experiments were completed in a synthetic air atmosphere at a flow rate of 100 mL min−1. For kinetic analysis, the TG/DTG/HF data obtained at heating rates β = 5, 7, 10, 12 and 15 °C min−1 were used.

Results and discussion

  1. 1)

    Thermoanalytical data

Figure 1a–c present the thermoanalytical curves TG, DTG and HF.

Fig. 1
figure 1

TG/DTG/heat flow obtained in air at 10 °C min−1 for a vitamin B1; b vitamin B2; c vitamin B6

Full size image

Thermal decomposition of the studied vitamins in air atmosphere occurs at temperatures higher than 200 °C with DTGpeak = 246 °C for B1, 296 °C for B2, and 212 °C for B6, respectively. For all the three vitamins, the thermodegradation process is an endothermic one with mass loss of 43.9 % for B1, 42.4 % for B2 and 21.6 % for B6, respectively.

Kinetic analysis of the non-isothermal data

The reaction rate r defined by

$$ r = {\text{ d}}\alpha /{\text{d}}t $$
(1)

becomes

$$ r = \beta \left( {{\text{d}}\alpha /{\text{d}}T} \right) $$
(2)

in non-isothermal conditions, where β is the heating rate and the temperature T depends on time (t) by T = T 0 + βt. In Eq. (2), β(dα/dT) represents the value from the DTG curve at the temperature T.

According to the generally accepted hypothesis, the reaction rate can be expressed as a product of two separable functions, one depending on temperature, k(T), another on conversion, f(α), respectively:

$$ r = k\left( T \right)f\left( \alpha \right). $$
(3)

With Eq. (2), it becomes

$$ \beta \left( {{\text{d}}\alpha /{\text{d}}T} \right) \, = k\left( T \right)f\left( \alpha \right). $$
(4)

Accepting an Arrhenius dependence on temperature, Eq. (4) can be rewritten as

$$ { \ln }\left[ {\beta \left( {{\text{d}}\alpha /{\text{d}}T} \right)} \right]_{\alpha } = { \ln }\left[ {Af\left( \alpha \right)} \right] \, {-}E/RT. $$
(5)

This is the Friedman (FR) method [14] for determining the activation energy by plotting the left member of Eq. (5) versus 1/T, at different values of conversion degree (α). So the Friedman method is a differential isoconversional model-free method (‘model free’ because the conversion function f(α) is not explicit described).

The results are presented in Fig. 2. The standard deviation from the mean value does not exceed 10 %, this being an indication of a single-step process.

Fig. 2
figure 2

Activation energy (E) versus α by Friedman’s method for vitamins: a B1, b B2 and c B6

Full size image

If Eq. (4) is integrated, it becomes

$$ \beta g\left( \alpha \right) \, = \, \int k\left( T \right){\text{d}}T $$
(6)

with

$$ g\left( \alpha \right) \, = \, \int {\text{d}}\alpha /f\left( \alpha \right). $$
(7)

Equation (6) is a starting point for a series of isoconversional integral and model-free methods. The analytical forms depend on the approximation used for solving the temperature integral (∫k(T)dT). We used two well-known methods:

  • The Fynn–Wall [15] and Ozawa [16] method (FWO) based on the equation:

    $$ \left( {{ \ln }\beta } \right)_{\alpha } = { \ln }\left[ {AE/\left( {Rg\left( \alpha \right)} \right)} \right]{-} 5. 3 3 1{-} 1.0 5 2E/\left( {RT} \right). $$
    (8)

  • The Kissinger–Akahira–Sunose [17, 18] method (KAS), with the equation:

$$ \ln (\beta /T^{2} ) = \ln [AE/(Rg(\alpha ))]{-}E/\left( {RT} \right). $$
(9)

Figures 3 and 4 present the results obtained by applying these methods.

Fig. 3
figure 3

Activation energy (E) versus α by FWO method for vitamins: a B1, b B2 and c B6

Full size image
Fig. 4
figure 4

Activation energy (E) versus α by KAS method for vitamins: a B1, b B2 and c B6

Full size image

By both the integral methods, the standard deviation of E versus α does not exceed 10 %, this being an indication of a single-step process in these cases, too.

The non-parametric kinetics (NPK) method [19–23] represents a special approach for processing the kinetic data. The method introduces a new point of view in kinetic analysis which is based on the single-step kinetics approximation. The experimental values of reaction rates are arranged in a matrix which is expressed as a product of two vectors containing information on k(T) and f(α). As a matter of fact, this mathematical model is a consequence of Eq. (3). The most important feature of the method is that it enables to decouple the submatrix related to the temperature (V) and conversion functions (U), without the need of any assumptions about their functionality. The data were obtained by analysing the vector u (the first column of U) in respect to a kinetic model suggested by Šesták and Berggren [24]: f(α) = α m(1 − α)n, respectively, the vector v (the first column of V) for an Arrhenius type T dependence. The value of the explained variance, λ, expresses the contribution of each simultaneous steps to the whole thermodegradation process, so that Σλ i = 100 %. If λ < 10 %, we consider that the discussed step can be neglected.

The results on NPK method are systematized in Table 1. The data indicate that the differences in the thermal behaviours of the three vitamins are due to both the different temperature dependences (A and E values), and the different conversion dependences (m and n parameters). Also, different thermal behaviours were observed: by B1 it is clear that there is only one significant process depending on the reactant (1 − α), in case of B6 there are two parallel processes, with 65 and 33 % contributions to the observed thermal behaviour.

Table 1 Kinetic analysis for the three vitamins, the NPK method
Full size table
Table 2 The main values of the activation energy obtained by the four kinetic methods
Full size table

Whatever used kinetic method would be analysed, the values of the activation energy indicate that vitamin B2 presents the higher thermal stability by the three studied vitamins. The use of certain value determined for activation energy in the estimation of the thermal stability is risky. Even if the standard deviation of E values obtained by certain methods exceed 15 % from the mean value for each compound, it is reasonable to avoid any quantitative comparisons using only the model-free methods. In our case, it is certain that the thermal stability decreases in order:

$$ {\text{B}}_{ 2} > {\text{B}}_{ 1} > {\text{B}}_{ 6}. $$

The NPK method assures the obtaining of realistic kinetic parameters, even if the decomposition process is a complex one, due to the fact that all kinetic parameters (A, E, m and n) were obtained without any approximations regarding the temperature and the conversion integral.

The high thermal stability observed for vitamin B2 was somehow unexpected due to the presence of the carbohydrate moiety in the molecular structure, although the increased stability can be explained by the presence of N-heterocyclic aromatic benzo[g]pteridine moiety, which is known to be a stabilizing structure. Furthermore, the degree of aromaticity of vitamin B2 is considerably higher than that of B1 and B6, respectively. It is known that double bonded nitrogen and/or oxygen can also be part of a conjugated structure, as well as single bonded due to the lone pair orbital which can become part of an extended conjugated aromatic system. It can be noticed that in the case of vitamin B2, a conjugated system containing 16 atoms is formed. As a further simple proof for the extended conjugation and high aromaticity of this vitamin is the fact that it absorbs light complementary to yellow in the visible spectrum.

For the case of vitamin B1, a lower degree of aromaticity is expected. This vitamin is formed by two aromatic moieties, namely 4-amino-2-methyl-pyrimidin-5-yl and methyl-thiazolyl nuclei. The extended conjugation is, however, interrupted by the presence of connecting methylene ‘bridge’, determining a lower stability comparative to the one of vitamin B2. The simplest structure, the one of pyridoxine, consists of a classic Hückel aromatic system. For the formation of hydrochloride, pyridinic nucleus is protonated forming a positively charged aromatic polyatomic ion. By kinetic analysis, it is confirmed that the degree of aromaticity of vitamin B6 is lower than that of vitamin B1 (Scheme 2).

Scheme 2
scheme 2

The aromaticity evaluation of the analysed vitamins: a thiamine hydrochloride (vitamin B1), b riboflavin (vitamin B2) and c pyridoxine hydrochloride (vitamin B6)

Full size image

Conclusions

A study on the thermal behaviour of B1, B2 and B6 vitamins was performed. All the three compounds present a relatively high thermal stability, the most stable being vitamin B2.

A kinetic analysis based on four different methods confirms the higher thermal stability of vitamin B2. The individual values of the activation energy obtained by isoconversional methods differ in range of 15 %, so an estimation using only one method is risky, especially by such cases of compounds with significant different molecular architectures.

A way for avoiding this difficulty is the use of Non-Parametric Kinetic method, which allows a separation between the temperatures and the respective conversion dependence on the reaction rate, without any a priori hypothesis. The data processing strategy offers a complete description of the reaction rate of the thermally induced degradation of the vitamins. In order to realise a correlation between structure and stability of the analysed vitamins, the aromaticities of these compounds were analysed.