Origin 2021b software

Origin 2021b software (OriginLab Co., Northampton, MA, USA) was used for drawing processing. The significance of the data was determined using one-way analysis of variance (ANOVA), followed by Duncan’s multiple range test, via SPSS 26.0 (SPSS Inc., Chicago, IL, USA), with a 95% confidence level, meaning that differences were considered to be statistically significant when p < 0.05.

The FT-IR-ATR spectra were collected on an IRTracer-100 spectrophotometer. All spectra were measured in the mid-infrared area, over the range of 4000–400 cm⁻¹ (400 scans at a resolution of 4 cm⁻¹). Spectra were acquired and analyzed using the LabSolution IR software (version 1.86 SP2, Shimadzu, Kyoto, Japan). The results were interpreted by comparing the FT-IR peaks of pure substances with those of prepared systems.
The molecular geometries of SA and amino acids were optimized using the Density Functional Theory (DFT) method with Becke’s three-parameter hybrid functional (B3LYP), implemented with the standard 6-311G(d,p) as a basis set. Calculations of the normal mode frequencies and intensities were also performed. The PL-Grid platform (website: www.plgrid.pl, accessed on 11 March 2021) equipped with the Gaussian 09 package (Wallingford, CT USA) for DFT calculation was applicated. The GaussView (Wallingford, CT USA, Version E01) program was used to propose an initial geometry of investigated molecules and for visual inspection of the normal modes. The obtained data were analyzed using the Origin 2021b software (OriginLab Corporation, Northampton, MA, USA).

The characterization of the ASD of Hes was carried out by the XRPD method. Diffraction patterns were recorded on a Bruker D2 Phaser diffractometer (Bruker, Germany) with CuKα radiation (1.54060 Å) at a tube voltage of 30 kV and a tube current of 10 mA. The angular range was 5° to 45° with a step size of 0.02° and a counting rate of 2 s $·$ step⁻¹. The acquired data were analyzed using Origin 2021b software (OriginLab Corporation, Northampton, MA, USA).

The FTIR-ATR spectra were collected on an IRTracer-100 spectrophotometer. All spectra were measured between 400 and 4000 cm⁻¹ in the absorbance mode. The following spectrometer parameters were used: resolution 4 cm⁻¹, number of scans 400, apodization Happ–Genzel. The sample was placed directly on the ATR crystal. Solid samples were pressed against the ATR crystal, and the ATR-FTIR spectrum was scanned. All infrared spectra were acquired and further processed (baseline correction, normalize) with LabSolution IR software (version 1.86 SP2, Shimadzu, Kyoto, Japan). The results were interpreted by comparing the FTIR peaks of pure samples with those of prepared systems.
The molecular geometries of Hes were optimized using the Density Functional Theory (DFT) method with Becke’s three-parameter hybrid functional (B3LYP) implemented with the standard 6–311G(d,p) as a basis set. The calculations of normal mode frequencies and intensities were also performed. Applicated to PL-Grid platform (website: www.plgrid.pl, accessed on 11 March 2021) equipped with Gaussian 09 package (Wallingford, CT USA) for DFT calculation. The GaussView (Wallingford, CT USA, Version E01) program was used to propose an initial geometry of investigated molecules and to visually inspect the normal modes. The obtained data were analyzed using the Origin 2021b software (OriginLab Corporation, Northampton, MA, USA).

The XRPD patterns of pure Hed and Het and their binary systems with HP-β-CD were recorded at ambient temperature using a Bruker AXS D2 Phaser diffractometer (Bruker, Germany) with CuKα radiation (1.54060 Å). The tube voltage and current were 30 kV and 10 mA, respectively. The samples were scanned from 5° to 40° with a step size of 0.02° and a counting rate of 2 s·step⁻¹. The analysis of the acquired data was performed using Origin 2021b software (OriginLab Corporation, Northampton, MA, USA).

Thermal analysis was performed using DSC 214 Polyma differential scanning calorimeter (Netzsch, Selb, Germany). DSC was used to study all samples’ glass transition temperature (T_g). A blank aluminum DSC pan was used as the reference sample, powdered samples of 9–10 mg were placed in sealed pans with a hole in the lid, and different sample heating modes were used to observe the T_g (see Tables S5–S8, Supplementary Materials). A nitrogen atmosphere was used with a flow rate of 250 mL $·$ min⁻¹. The obtained DSC data were analyzed using the Proteus 8.0 software (Netzsch, Selb, Germany). The results were visualized using the Origin 2021b software (OriginLab Corporation, Northampton, MA, USA). The theoretical glass transition temperatures were calculated using the Gordon–Taylor equation: $$T_g=\frac{w_1{T}_{g1}+K_{GT}{w}_2{T}_{g2}}{w_1+K_{GT}{w}_2}$$
$w_1, w_2$ —weight fraction of hesperidin and carrier, respectively. $T_g, T_{g1}, T_{g2}$ —predicted glass transition temperature of a binary system; glass transition temperature of hesperidin, and glass transition temperature of the carrier, respectively. $K_{GT}$ —constant indicates a measure of interaction between two components. $K_{GT}$ expressed mathematically: $$K_{GT}=\frac{{\rho }_1{T}_{g1}}{{\rho }_2{T}_{g2}}$$
where ${\rho }_1, {\rho }_2$ —the densities of two components (Hes: 1.7 g $·$ cm⁻³, Sol: 1.082 g $·$ cm⁻³, HPMC: 1.39 g $·$ cm⁻³), $T_{g1}, T_{g2}$ —glass transition temperature of hesperidin and carrier, respectively.

All experiments were carried out in triplicate, and the data were presented as means ± standard deviation. IBM SPSS Statistics 20 software (IBM, New York, USA) was used to analyze the data on fruit quality, nutritional composition, HPLC results, and antioxidant capacities. A one-way analysis of variance (ANOVA) plus post hoc Duncan’s test was performed to analyze the differences among different citrus samples for quality, composition, and antioxidant capacity. Moreover, origin 2021b software (OriginLab Inc., Northampton, MA, USA) was employed to conduct principal component analysis (PCA), hierarchical cluster heatmap analysis, correlation analysis, discrimination analysis and their plots.