Commercial grade ursodeoxycholic acid drug was purchased from Lupin Pharmaceuticals Ltd., India. All other chemicals (AR grade) were purchased from s.d. chemicals Pvt. Ltd., India. Silica gel prepared from sodium metasilicate of specific gravity 1.06 g/cm³ was used as crystal growth medium. Test tubes were used as crystal growth vessels. Crystal growth by single diffusion method was employed for the crystallization. The pH of the gel was set using acetic acid. 5% w/v of UDCA dissolved in methanol was placed over the set gel taken in the test tube. The experiment was carried out at room temperature (≈27˚C).

Enraf-Nonius CAD-4 Diffractometer, with MoKα (λ = 0.71073 Å) radiation was used to obtain the accurate cell parameters of the grown UDCA single crystal at room temperature. Cell parameters were obtained from least-squares refinement of the setting angles of 346 reflections.

Simultaneous thermogravimetric analysis (TGA) and differential thermal analysis (DTA) was carried out for the powdered sample of as grown crystals in the temperature range 40˚C to 350˚C under a constant heating rate of 10˚C/min using Perkin Elmer Diamond thermal analyzer. The crucible used was made of alumina which served as a reference for the sample.

Transparent, rectangular platy crystals of size: 3.5 × 1.5 × 0.5 mm³ were crystallized in a week’s time. The crystals were removed after a growth period of few weeks and photographed (Figure 1(b)).

The unit cell parameters were determined from the collected X-ray data. Lattice parameters of orthorhombic ursodeoxycholic acid form are: a = 26.56(15) Å, b = 13.25(5) Å, c = 12.31(4) Å, and the space group is P2₁2₁2₁. These values agree well with the reported values in the literature [13] .

TGA/DTA plot is presented in Figure 2. TGA/DTA of ursodeoxycholic acid showed no appreciable mass loss before the melting point (200.6˚C) which reasonably agrees with the literature value [14] . Absence of an endothermic peak around the boiling of point of water confirmed the anhydrate nature of the title compound. The DTA exhibits exothermic trend except two endothermic peaks (200.6˚C and 380˚C). The thermal process around 200.6˚C initiated the decomposition of the aliphatic chain into CO₂, C₂H₄ and CH₄ molecules and the mass loss at this stage supported this argument. Further the decomposition of the aromatic moieties happened above 380˚C with the release of methane and water molecules.

The TGA data was analyzed using Origin Lab [15] and was fitted into the Coats

and Redfern relation [16] ―Equation (1) to determine the values of activation energy (E), frequency factor (A) and order of the reaction (n).

log [ 1 − ( 1 − α ) 1 − n T 2 ( 1 − n ) ] = log [ A R β E ( 1 − 2 R T ¯ E ) ] − [ E 2.303 R T ] (1)

where, α is fraction of original substance decomposed at time t and is calculated from TGA data using Equation (2),

α = m o − m t m o − m f (2)

where m_t is the mass at a given time, m_o and m_f are the initial and final masses of the sample respectively. R denotes gas constant.

To determine the activation energy, frequency factor and order of reaction,

the plot of log [ 1 − ( 1 − α ) 1 − n T 2 ( 1 − n ) ] versus 1/T is drawn for different values of n

(Figure 3) and the best linear plot gives the correct value of n. This equation is valid for all values of n except n = 1. The best linear plot is obtained for n = 0.25. The activation energy and frequency factor are determined from the slope and intercept of the plot. The calculated values of activation energy and frequency factor are 172.581 kJ/mol and 3.10 × 10¹⁰ s⁻¹ respectively. Using kinetic parameters, Arrhenius equation can be written ask k = Ae^−E/RT. The Arrhenius equation for is k = 3.10 × 10¹⁰ e^−172581/RT mol⁻¹・s⁻¹.

The Thermodynamic parameters of ursodeoxycholic acid: entropy of activation

(ΔS), enthalpy of activation (ΔH) and Gibbs free energy (ΔG) were calculated using Equations (3)-(5).

A = ( k T / h ) e ( Δ S / R ) (3)

where h and k are Planck’s constant and Boltzmann constant respectively.

Δ H = E – R T (4)

Δ G = Δ H – T Δ S (5)

The values of ∆S, ∆H and ∆G are −50.47 J/Kmol, 167.22 kJ/mol and 199.76 kJ/mol respectively. Positive value of ∆G shows that the decomposition reaction of ursodeoxycholic acid is non-spontaneous.