Oxidative Thermolysis of Sulfobutyl-Ether-Beta-Cyclodextrin Sodium Salt: A Kinetic Study

Featured Application

The results of this paper can be used by both researchers and industry for the development of supramolecular structures containing SBECD, since it presents spectral and diffraction data and the thermal stability range of a highly used cyclodextrin in the pharmaceutical field. SBECD is often used in formulations to enhance the solubility of poorly water-soluble drugs. If its thermal stability is compromised, this could affect its ability to form stable inclusion complexes with the drug, which could lead to inconsistent drug release or reduced bioavailability. Therefore, maintaining thermal stability is essential to ensure the consistent performance of the excipient in solubilizing the drug.

Abstract

Sulfobutyl-ether-beta-cyclodextrin sodium salt (SBECD) is a modified cyclodextrin widely used in the pharmaceutical industry to enhance the solubility and stability of poorly water-soluble drugs. As a derivative of beta-cyclodextrin, it is produced by introducing sulfobutyl ether groups into the beta-cyclodextrin molecule, which significantly increases its water solubility and decreases its toxicity compared to unmodified cyclodextrins. This study investigates the spectral and PXR diffraction characterization of SBECD, its thermal stability profile, and decomposition mechanism using isoconversional methods. Since the simple ASTM E698 method does not provide realistic data, the Flynn–Wall–Ozawa, Friedman, and NPK methods were employed, leading to the kinetic triplet that characterizes the oxidative thermolysis of this compound.

1. Introduction

In the ever-evolving landscape of pharmaceutical formulations, the solubility and bioavailability of active pharmaceutical ingredients (APIs) remain critical challenges. Many promising drug candidates exhibit poor water solubility, which can hinder their therapeutic effectiveness and limit their clinical applications [1]. To address this, novel excipients such as sodium salt of sulfobutyl-ether-beta-cyclodextrin (SBECD) have emerged as powerful tools to improve drug solubility and stability [2,3].

SBECD stands out due to its unique chemical structure, which includes negatively charged sulfobutyl groups attached to the beta-cyclodextrin core [4]. This modification not only improves the water solubility of hydrophobic drugs but also provides a safer and more biocompatible profile compared to traditional solubilizing agents [4,5]. When inclusion complexes are formed with APIs, SBECD can significantly enhance the dissolution rate, protect drugs from degradation, and reduce irritation in sensitive tissues. These attributes make it a versatile excipient in various dosage forms [6], including injectables [7], oral tablets [8,9], and ophthalmic solutions and gels [10].

In the realm of parenteral formulations [11], SBECD plays a critical role in increasing the solubility of intravenous drugs, thereby making it suitable for this pathway of administration. Also, it seems that formulations containing SBECD showed reduced nephrotoxicity, and even if decreased renal function causes reduced SBECD clearance and increased exposure, this compound continues to exhibit a good safety and tolerability profile in intravenous formulations [7,12]. In oral dosage forms, it improves drug absorption by enhancing solubility in the gastrointestinal tract, leading to better therapeutic outcomes. Additionally, its ability to reduce drug toxicity and improve patient tolerance underscores its value in designing safer and more effective pharmaceuticals [12,13]. The structural formula of SBECD is presented in Figure 1, along with the structure of the parent compound, the naturally occurring beta-cyclodextrin.

According to Cyclolab [14], there are currently 13 APIs on the market (voriconazole, carfilzomib, amiodarone, ziprasidone, maropitant, aripiprazole, posaconazole, carbamazepine, melphalan, delafloxacin, brexanolone, remdesivir, fosphenytoin) and at least 150 further in development in formulations containing SBECD.

Some physico-chemical properties of SBECD are reported in the literature, as well as in the certificates of analysis that are emitted by the producers of this modified cyclodextrin. The composition of SBECD can be typically denoted as C₄₂H_70–nO₃₅(C₄H₈SO₃Na)_n, where “n” represents the degree of substitution [15], which can be modified by choosing an adequate synthesis protocol [16]. The molecular mass of SBECD varies depending on the degree of substitution, typically ranging from approximately 2000 to 3000 daltons [15].

The stability of SBECD and its decomposition are reported in several scientific papers, but also on the website of Cyclolab. It seems that in solution, SBECD starts decomposing at pH values of around 4.2–4.4, being more rapid as the pH decreases under 4.0 [14]. Regarding the solid state, it seems that SBECD showed no degradation when stored for 2 weeks in an inert atmosphere at 70 °C [14]. Kinetic studies were carried out in solution for the hydrolytic degradation of cefixime in the presence of Captisol^® (a SBECD produced by Ligand Pharmaceuticals) [17], suggesting the strong stabilizing influence of the cefixime–Captisol complexation against aqueous-mediated degradation [18], and for the aqueous degradation of Salinosporamide A, where Captisol^® had a similar stabilizing effect [19]. Also, the stability of azithromycin in buffered aqueous solution at pH 6.7 was investigated in the presence of different cyclodextrins, and the most effective stabilization of the drug was obtained by using SBECD, which maintained the azithromycin amount in solution at 99% for up to 6 months at room temperature [20].

Isoconversional kinetic studies are essential in the field of pharmaceutical sciences, particularly for understanding the decomposition of drugs, providing valuable insights into the thermal stability and degradation behavior of APIs, which are critical for ensuring the safety, efficacy, and shelf-life of pharmaceutical products [21,22,23]. APIs often undergo complex degradation processes that can involve multiple reaction steps, and isoconversional methods help in understanding these mechanisms by analyzing the reaction kinetics without assuming a specific model. By determining how apparent activation energy (E_a) changes with conversion (α), researchers can identify whether the decomposition follows a single-step or multi-step mechanism [24,25,26,27].

This article explores the thermal stability and evaluation of the decomposition kinetics of pharmaceutical-grade SBECD, since to our knowledge, the thermal degradation of this valuable compound was not investigated up until now. As investigational tools, SBECD was characterized by FTIR spectroscopy and PXRD under ambient conditions, and by thermoanalytical methods (TG/DTG/HF) in an oxidative atmosphere, in non-isothermal heating conditions. Thermoanalytical data were processed by two isoconversional kinetic methods, one integral (Flynn–Wall–Ozawa, FWO) and one differential (Friedman, FR), and later by the employment of the modified NPK method, to separate the contribution of each individual process to the global process of decomposition for this compound.

2. Materials and Methods

2.1. Materials

Sulfobutyl-ether-beta-cyclodextrin sodium salt with a degree of substitution n = 6.5 (SBECD, batch No. CYL-5127, Dexolve^TM, molar mass for anhydrous analyte 2163 g·mol⁻¹, molar mass for decahydrate analyte 2335 g·mol⁻¹) was received as a free sample from Cyclolab R&L Ltd. (Budapest, Hungary), and was used as received, without any a priori preparation.

For Karl Fischer titration, anhydrous methanol (Combimethanol, Water ≤ 0.01%) was purchased from Merck (Darmstadt, Germany). Molecular sieves, 3A were purchased from Sigma Aldrich (Darmstadt, Germany). Titrant 5 apura^®, solvent apura^®, and water standard 1% apura^® were purchased from Merck (Darmstadt, Germany).

2.2. Instrumental Investigations

A Perkin Elmer SPECTRUM 100 device (Perkin-Elmer Applied Biosystems, Foster City, CA, USA) FT-IR spectrometer equipped with an ATR device was used to record FTIR spectra. The spectral data were obtained directly from solid samples in the spectral range of 4000–650 cm⁻¹. The obtained spectrum was built using a spectral resolution of 1 cm⁻¹. The investigation was repeated three times to ensure the accuracy of the results, with the data showing no differences between the performed evaluations. For each analysis, the FT-IR spectrometer performs 32 scans, the resulting spectrum being the mean of these determinations. The spectral range of 2300–1900 cm⁻¹ has no spectroscopic significance, since it represents the noise signal of the ATR crystal.

The PXRD profile was recorded on a Bruker D8 Advance powder X-ray diffractometer at ambient temperature, between 5 and 35° (2θ), using CuKα radiation (40 kV, 40 mA) and an Ni filter.

Thermoanalytical data were simultaneously collected as TG (thermogravimetric/mass curve), DTG (derived thermogravimetric/mass derivative), and HF (heat flow curve) in a dynamic air atmosphere (100 mL·min⁻¹) using open aluminum crucibles on a Perkin-Elmer DIAMOND instrument (Perkin-Elmer Applied Biosystems, Foster City, CA, USA). The samples were heated under a dynamic synthetic air atmosphere (Linde, Timişoara, Romania) at a flow rate of 100 mL·min⁻¹, with heating rates of 2, 4, 6, 8, and 10 °C·min⁻¹, over a temperature range of 40–500 °C.

The determination of the water content for SBECDs was performed using the Karl Fischer titration (KFT) method of two components, comprising Component 1: Titrant 5 apura^® and Component 2: Solvent apura^®. Measurements were carried out with a Karl Fischer 701 Titrando apparatus (Metrohm AG, Herisau, Switzerland), supplemented by a 703 Ti Stand mixing system and a Metrohm 10 dosing system (Metrohm AG, Herisau, Switzerland). Anhydrous methanol (dried on molecular sieves, 3 Å) was used as an additional solvent. Approximately 0.05 g of SBECD was used per determination.

The method parameters were as follows: I(pol) was set to 50 μA, endpoint and dynamics at 250 mV, a maximum rate of 5 mL/min, and drift was used as the stop criterion, with a stop drift of 20 μL/min. The extraction time was 300 s.

All instrumental measurements were performed in triplicate.

2.3. Kinetic Study

To investigate the kinetics of SBECD decomposition under thermal stress under oxidative conditions, the DTG data that were obtained as mentioned in Section 2.2. were processed as follows: the kinetic study (ASTM E698, Friedman and Flynn–Wall–Ozawa methods) was conducted in the first step of decomposition, occurring between 220 and 310 °C, which corresponds to the decomposition of anhydrous SBECD. The analysis was performed using AKTS Thermokinetics Software version 4.46 (AKTS AG TechnoArk, Siders, Switzerland). The mathematical framework and the significance of applying isoconversional kinetic methods have been widely documented in the literature [28,29,30,31]. The decomposition mechanism of SBECD was assessed using the modified NPK method, following a protocol previously established by our research group.

The abbreviations used follow the traditional notation in the field of thermal analysis, as recommended by the International Confederation for Thermal Analysis and Calorimetry (ICTAC) Kinetics Committee, as follows:

α: Conversion degree;

t: Time;

β: Linear heating rate (°C·min⁻¹);

A: Pre-exponential factor according to the Arrhenius kinetic model (min⁻¹);

k(T): Temperature-dependent reaction rate function;

f(α): Differential conversion function;

g(α): Integral conversion function;

E_a: Activation energy (kJ·mol⁻¹);

R: Universal gas constant (J·mol⁻¹·K⁻¹);

r: Reaction rate;

T: Absolute temperature (K);

Δm: Mass loss over a specific temperature interval.

3. Results and Discussion

The UATR-FTIR (Universal Attenuated Total Reflection Fourier Transform Infrared Spectroscopy) instrumental technique is widely used in the field of pharmaceutical research since it is able to provide reliable results in a very short amount of time, allowing the identification and purity evaluation of each compound. In the case of SBECD, the obtained FTIR spectrum was drawn up and is presented in Figure 2. Considering the structure of the compound (Figure 1), the identity of the compound was evaluated by comparing the obtained results with the available literature data [32,33,34,35].

As such, the presence of the main structural characteristics of SBECD were revealed on the FTIR spectrum. The presence of the O–H bonds can be correlated with the broad band seen in the 3700–3050 cm⁻¹ spectral range determined by the stretching vibrations of these bonds. The characteristic stretching vibrations of the methylene groups are revealed at 2932 cm⁻¹ (the asymmetric stretching vibration of the C–H bond) and 2885 cm⁻¹ (the symmetric stretching vibration of the same bond type). A well-defined signal can be seen at 1643 cm⁻¹, its presence being due, according to the literature data, to the bending vibration of the H-O-H bonds belonging to the water molecules intercalated in the structure of SBECD [16,36]. The two low-intensity bands observed at 1411 and 1365 cm⁻¹ may be correlated with the association of the in-plane bending vibration of the O-H bonds with the wagging deformation vibration of the C-H bonds present in the structure of SBECD.

The vibrations of the C–O bonds, that are usually visible in the 1260–1000 cm⁻¹ spectral range [34], cannot be observed since their low intensity is masked by the presence of other bands.

The presence of the sulfonate anion in the structure of SBECD determines the most intense spectral signals, with two wide bands being revealed with peaks at 1149 and 1026 cm⁻¹, representing the asymmetric and symmetric stretching vibrations, respectively, of the S=O bond. The results are in good agreement with reported data [16].

Figure 3 presents the PXRD pattern of SBECD, which reveals only one broad peak centered in the 18.20–19.55° interval (with maximum intensity at 18.20°), indicating the amorphous nature of the sample, even if this cyclodextrin contains in the structure a saline sulfone–sodium ionic moiety.

The thermoanalytical profile of SBECD recorded in dynamic air flow at a heating rate of β = 10 °C·min⁻¹ (Figure 4) reveals a dehydration step between 40 and 137 °C, with a corresponding Δm = 8.16%, leading to a water content of 10.67 mol water per mol anhydrous SBECD. The water content from the SBECD sample was also determined using a two-component Karl Fischer titration based on the methodology published by Hădărugă, Hădărugă, and Isengard [37], revealing a total water content of 8.02 ± 0.27%. The good agreement between the KFT method and thermal analysis suggests that this mass loss process is solely due to the presence of water in the structure of SBECD, and no other volatile compounds. Anhydrous SBECD seems stable for a large temperature range, namely between 137 and 239 °C, when a continuous mass loss process takes place up to 434 °C (Δm = 45.79%). In the 434–500 °C temperature range, the residual mass remains constant at 46.05%.

The DTG curve reveals the dehydration process that took place in the 40–137 °C temperature range, followed by another two consecutive processes associated with the decomposition of anhydrous SBECD, namely in the 239–313 °C range (DTG_peak at 273 °C) and in the 313–379 °C range (DTG_peak at 352 °C), followed by another process in the 379–500 °C range (DTG_peak at 394 °C). The HF curve reveals the endothermic water loss—the first process was between 40 and 48 °C (HF_peak at 44 °C)—probably associated with superficial adsorbed water (or so-called surface water) [37,38], and a second water release process between 48 and 137 °C (HF_peak at 67 °C), probably associated with strong bonded water [37]. Another endothermic process takes place in the 248–291 °C range (HF_peak at 274 °C), associated with the melting of SBECD, in good agreement with the literature data that indicate the 266–274 °C interval for this phase transition [39]. It is worth mentioning that such a large interval for melting is due to the amorphous nature of the SBECD sample, as confirmed by the PXRD study.

In order to get an in-depth look into the thermal stability and decomposition of SBECD, we carried out a kinetic study according to ICTAC recommendations, namely the use of isoconversional methods, both integral and differential [40,41,42,43,44]. Isoconversional methods allow for the determination of reaction rates, activation energies, and other kinetic parameters directly from experimental data, without the need to assume a predefined reaction mechanism or model, since in materials science or chemical processes, the reaction mechanism can be complicated, involving multiple steps or stages. In such cases, using a model-free approach allows the data to be analyzed without trying to fit them into a potentially incorrect or oversimplified model. Using both integral and differential methods is required by the ICTAC committee, since the obtained data allow to cross-check the results: if both methods give a similar variation of E_a values vs. conversion degree, it increases the confidence in the accuracy of the kinetic parameters; if there is a discrepancy between the methods, it may indicate that the reaction has multiple stages with different kinetic behaviors, suggesting the need for more detailed analysis.

Kinetic data play a crucial role in various aspects of the pharmaceutical industry, particularly in understanding and optimizing processes related to drug formulation, stability, manufacturing, and quality control. The data provide insights into the rates of chemical reactions, thermal stability, degradation processes, and other key factors, which are essential for ensuring the efficacy, safety, and quality of pharmaceutical products. Kinetic data, especially related to the degradation rates of drugs (such as hydrolysis, oxidation, or photodegradation), can be used to predict the shelf life and stability of pharmaceutical formulations. By understanding the reaction rates at different temperatures, the pharmaceutical industry can predict how a drug will degrade over time and establish storage conditions and expiration dates. Stability testing under accelerated conditions (e.g., elevated temperature and humidity) allows for predicting the long-term stability of the product and how to best store it to extend its shelf life.

As a preliminary method, we have used the ASTM E698 method, which is a standardized approach used to determine the apparent activation energy (E_a) of chemical reactions [45]. This method is widely used in industries such as pharmaceuticals, polymers, and materials science to study the stability and degradation of substances, but can be used only as a preliminary method before carrying out isoconversional studies, since it is based on the hypothesis that the decomposition process follows a single reaction mechanism throughout the entire reaction, which is a limitation when dealing with complex reactions involving multiple steps or changes in mechanisms over time. As a result, the calculated activation energy (E_a) may not be accurate for reactions that exhibit multi-step or overlapping mechanisms [22,46].

The good correlation of the data sets suggested by the ASTM E698 method (Figure 5) may suggest a single-step degradation of SBECD, but this must be further analyzed by employing multi-point model free methods, like the Friedman and Flynn-Wall-Ozawa methods, since one-point model free methods, like ASTM E698, have clear limitations [21,45].

Isoconversional kinetic analysis is a robust tool used to study the degradation behavior of materials, providing a non-mechanistic method for estimating the kinetic parameters of a reaction [28,29,41]. In contrast to model-fitting methods, which rely on predefined reaction mechanisms, isoconversional models determine kinetic parameters solely from the experimental data obtained across various heating rates [29,47].

The investigated process corresponds to the first degradation step of anhydrous SBECD, occurring within the following temperature ranges: 221–289 °C (at β = 2 °C·min⁻¹), 228–298 °C (at β = 4 °C·min⁻¹), 235–303 °C (at β = 6 °C·min⁻¹), 238–309 °C (at β = 8 °C·min⁻¹), and 239–313 °C (at β = 10 °C·min⁻¹). As expected, the process shifts to higher temperatures, and the reaction rate increases with higher heating rates, as shown in the plots of the reaction progress vs. temperature (Figure 6a) and reaction rate vs. temperature (Figure 6b). This behavior is attributed to the thermal inertia of the samples during heat transfer at elevated heating rates.

The analysis of the reaction rate curves from Figure 6b reveal two separate processes that concur at the decomposition of anhydrous SBECD, when the thermal treatment is carried out at low heating rates (≤4 °C·min⁻¹). At higher heating rates, due to thermal inertia, the processes are no longer separated or a change in the decomposition mechanism takes place. To get a clear view of the influence of the heating rate over the decomposition of SBECD, three well-established isoconversional methods were employed, namely Flynn–Wall–Ozawa (FWO), Friedman (FR), and non-parametric kinetics (NPK).

The linear plottings obtained by using the FWO and FR methods are presented in Figure 7a,b, while the corresponding apparent E_a values vs. α (with a variation step for α of 0.05) are shown in

Table 1. Variation in E_a vs. α for SBECD degradation using the FWO and FR isoconversional methods.

Ea/ kJ·mol−1	Conversion degree α										$\overline{{\mathbf{E}}_{\mathbf{a}}}$ ± error/kJ·mol−1
	0.05	0.1	0.15	0.2	0.25	0.3	0.35
FWO	156.6 ± 0.2	154.6 ± 0.1	152 ± 0.1	149.7 ± 0.1	147.8 ± 0.1	146.3 ± 0.1	145.2 ± 0.1
Friedman	156.7 ± 0.9	130.7 ± 0.1	125.1 ± 0.4	123 ± 1.0	124.1 ± 1.6	127.2 ± 2.0	131.5 ± 2.5
	Conversion degree α
	0.4	0.45	0.5	0.55	0.6	0.65	0.7
FWO	144.5 ± 0.2	144.3 ± 0.2	144.5 ± 0.2	145 ± 0.3	146 ± 0.4	147.4 ± 0.6	149.3 ± 0.8
Friedman	136.7 ± 2.7	143.2 ± 3.0	149.6 ± 3.3	155.5 ± 3.6	161.7 ± 3.8	166.8 ± 4.2	172 ± 4.9
	Conversion degree α
	0.75	0.8	0.85	0.9	0.95
FWO	151.6 ± 1.1	154.6 ± 1.6	158.1 ± 2.3	162.7 ± 3.9	169.7 ± 8.0						151.0 ± 9.5
Friedman	177.4 ± 6.2	181.5 ± 7.9	186.3 ± 10.7	191.2 ± 16.5	207.6 ± 28.7						155.2 ± 37.7

, along with corresponding errors.

By analyzing the data presented in Table 1 and Figure 8, it can be observed that the data processing by the integral and differential protocols reveals a similar trend regarding the variation of E_a with the advance of the reaction, namely at low conversion degrees (α ≤ 0.2 for FR and α ≤ 0.5 for FWO), and the decrease in E_a was observed, followed by an increasing trend as the conversion increases (α > 0.2 for FR and α > 0.5 for FWO).

$\overline{{\mathrm{E}}_{\mathrm{a}}}$ Regarding the uncertainty of each E_a value vs. conversion degree, it can be observed that the integral processing of the data reveals that the modification of the decomposition mechanism takes place only when α is higher than 0.9, and when all the other values are placed in the confidence interval of $\overline{{\mathrm{E}}_{\mathrm{a}}}$± 0.1·$\overline{{\mathrm{E}}_{\mathrm{a}}}$ (or between 0.9$\overline{{\mathrm{E}}_{\mathrm{a}}}$and 1.1$\overline{{\mathrm{E}}_{\mathrm{a}}}$), with namely a 10% accepted variation around the mean value (Figure 8). However, the differential processing of the data reveals a complex pathway of decomposition, since the dependence of activation energy values with the conversion degree falls outside the above-mentioned confidence interval of 10% accepted variation around the mean value at low conversion degrees (α between 0.1 and 0.4, and α > 0.75). The variation of E_a vs. α may be explained by the modification of activation parameters during the decomposition process, by the complexity of the heterogenous process, or by the heat and mass transfer influence over the reaction rate [30,31,48]. Vyazovkin et al. [49,50,51] associated the aspect of the E_a vs. conversion dependencies with the mechanism of the complex processes, suggesting that an increase in E_a with α takes place when the process involves parallel or successive reactions, and a decrease in E_a with α takes place when the process involves a reversible step or the process involves a diffusion transition.

If the variation of E_a is non-monotonous, like in this case, the process is complex and the data cannot be processed solely by classic isoconversional methods, like FWO and FR.

Following this conclusion, that SBECD is thermally degraded by a complex mechanism, we have chosen to thirdly investigate the kinetic method, the modified non-parametric kinetic method (NPK), proposed by J. Sempere, Rosa Nomen, and R. Serra in 1998 [52,53,54,55] and later modified by T. Vlase, Gabriela Vlase, and N. Doca [56,57,58]. In our previous studies, we have presented the theoretical background of this method and its use in obtaining the kinetic triplet (A, E_a, and f(α)), describing the heterogenous decomposition process of drugs and pharmaceutical formulations [21,23,59,60].

The NPK method is conducted without assuming a predefined model for k(T) or f(α), and based solely on the axiom that the reaction rate (r) can be represented as the product of two independent functions: one dependent only on temperature and the other only on conversion.

$$r={\displaystyle \frac{\mathrm{d}\alpha }{\mathrm{d}t}}=\mathrm{k}(T)·\mathrm{f}(\alpha ),$$

(1)

where the parameters of the equations are presented in Section 2.3.

The temperature function k(T) is usually modeled by the Arrhenius equation, even if in the field of solid non-isothermal thermolysis processes are discussions regarding the dependence or independence of the preexponential factor A vs. temperature, respectively, over the significance of the activation energy Ea. The conversion function f(α) can be chosen on formal considerations or assuming a priori a mechanism of degradation; in this case, several approximations must be implemented, which can affect the results of the kinetic analysis. Following these aspects, to avoid approximations or supplementary axioms, the conversion function proposed by Šestak–Berggren can be used, as follows:

$$\mathrm{f}\left(\alpha \right)={\alpha }^m·{(1-\alpha )}^n·{[-\ln \left(1-\alpha \right)]}^p$$

(2)

where the significance of the m, n, and p parameters are specific for the investigated process, associated with physical transformations (m), chemical reactions (n), and homomolecular reactions in the melted state (p).

The Šestak–Berggren equation is a generalization of the conversion functions proposed and validated in the literature, and this generality is important in kinetic analysis, due to the fact that it does not involve the use of approximations. Following this, it is clear that the Šestak–Berggren equation is utilized in the formal description of phenomena where the mass loss is influenced both by the degradation of the molecular architecture of compounds and also of the resulted fragments [5].

The thermoanalytical data obtained by carrying out experiments at five heating rates led to a family of curves (presented in Figure 9 as red dots) that generated an interpolated 3D surface of the reaction rate (green lines), by multivariate regression.

Based on the experimental points and the generated reaction rates’ surface, the corresponding matrix was generated by the partition of the surface and applying the SVD algorithm, which generated the results presented in

Table 2. The results of the NPK method obtained during the thermal degradation of SBECD.

Compound	Process	λ /%	A /s−1	Ea /kJ·mol−1	n	m	Šestak–Bergreen Eq.	R2	$\overline{{\mathbf{E}}_{\mathbf{a}}}$/kJ·mol−1
SBECD	1	73.6	2.58 × 1015	152.6 ± 0.4	2	1/3	(1−α)2 α1/3	0.998	151.2 ± 0.5
	2	25.6	2.45 × 1014	151.9 ± 0.7	1/3	1/3	(1−α)1/3 α1/3	0.997

. It can be seen that the thermolysis of SBECD is due to two distinct processes, both containing physical and chemical contributions (for the main process, n = 2 and m = 1/3, while for secondary process, n = m = 1/3) with similar values for activation energies (152.6 and 151.9 kJ·mol⁻¹). The total explained variances λ (99.2%) can accurately describe the degradation process.

The total explained variances λ (99.2%) can accurately describe the degradation process, since with the results presented in Table 2, the reconstruction of the reaction rates surface led to good results, as seen in Figure 10.

4. Conclusions

In this paper, anionic cyclodextrin sulfobutyl-ether-beta-cyclodextrin sodium salt (SBECD) was investigated by FTIR spectroscopy, PXR diffractometry, KF titration, and thermal analysis in dynamic oxidative conditions. Thermoanalytical curves TG/DTG/HF were recorded at five different heating rates in non-isothermal conditions, revealing a good thermal stability of this analyte in an anhydrous state of up to ~240 °C, after losing the water content (~8%) in the 40–140 °C temperature range. The main decomposition process of the in situ formed anhydrous SBECD was investigated by kinetic analysis, initially by the employment of the ASTM E698 method, followed by two traditional isoconversional methods (FR and FWO), and later the kinetic triplet was determined using the NPK method.

The NPK method suggested that SBECD is degraded by the contribution of two processes, both containing chemical degradations and physical transformations.