Theoretical insights into influence of additives on sulfamethoxazole crystal growth kinetics and mechanisms

doi:10.1007/s11705-022-2294-4

Front. Chem. Sci. Eng.

2023, Vol. 17

Issue (10) : 1503-1515 https://doi.org/10.1007/s11705-022-2294-4

RESEARCH ARTICLE

Theoretical insights into influence of additives on sulfamethoxazole crystal growth kinetics and mechanisms

Qiao Chen, Mingdong Zhang, Yuanhui Ji(

)

Jiangsu Province Hi-Tech Key Laboratory for Biomedical Research, School of Chemistry and Chemical Engineering, Southeast University, Nanjing 211189, China

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Abstract

In this work, the influence of the initial chemical potential gradient, stirring speed, and polymer type on sulfamethoxazole (SMX) crystal growth kinetics was systematically investigated through density functional theory (DFT) calculations, experimental measurements and the two-step chemical potential gradient model. To investigate the influence of different conditions on the thermodynamic driving force of SMX crystal growth, SMX solubilities in different polymer solutions were studied. Four model polymers effectively improved SMX solubility. It was further found that polyvinylpyrrolidone (PVP) and hydroxypropyl methyl cellulose (HPMC) played a crucial role in inhibiting SMX crystal growth. However, polyethylene glycol (PEG) promoted SMX crystal growth. The effect of the polymer on the crystal growth mechanisms of SMX was further analyzed by the two-step chemical potential gradient model. In the system containing PEG 6000, crystal growth is dominated by the surface reaction. However, in the system containing PEG 20000, crystal growth is dominated by both the surface reaction and diffusion. In addition, DFT calculations results showed that HPMC and PVP could form strong and stable binding energies with SMX, indicating that PVP and HPMC had the potential ability to inhibit SMX crystal growth.

Keywords insoluble drugs polymer inhibition crystallization crystal growth kinetics DFT calculations

Corresponding Author(s): Yuanhui Ji

Online First Date: 17 May 2023 Issue Date: 07 October 2023

Cite this article:

Qiao Chen,Mingdong Zhang,Yuanhui Ji. Theoretical insights into influence of additives on sulfamethoxazole crystal growth kinetics and mechanisms[J]. Front. Chem. Sci. Eng., 2023, 17(10): 1503-1515.

URL:

https://academic.hep.com.cn/fcse/EN/10.1007/s11705-022-2294-4
https://academic.hep.com.cn/fcse/EN/Y2023/V17/I10/1503

Fig.1 Chemical structures of (a) SMX, (b) PVP, (c) HPMC, and (d) PEG.

Initial concentration/ (g?L^?1)	$Δ μ$ /(J?mol^?1)	Stirring/(r?min^?1)	Polymer	Polymer concentration/ (g?L^?1)
1.34	2 × 10³	100	–	–
1.32	2 × 10³	200	–	–
1.32	2 × 10³	250	–	–
1.17	1.7 × 10³	200	–	–
1.46	2.2 × 10³	200	–	–
1.83	2 × 10³	200	PEG 6000	20
2.32	2 × 10³	200	PEG 6000	40
1.95	2 × 10³	200	PEG 20000	20
2.58	2 × 10³	200	PEG 20000	40
1.32	2 × 10³	200	PVP	0.5
1.32	2 × 10³	200	HPMC	0.5

Tab.1 Experimental conditions for the measurement of the crystal growth kinetics of SMX

Fig.2 SMX solubilities in polymer/water solutions: (a) PEG 6000/water, (b) PEG 20000/water, (c) PVP/water, and (d) HPMC/water.

Fig.3 Crystal growth kinetics of SMX in solutions at different conditions: (a) the different initial chemical potential gradients, (b) stirring speed, (c) PVP, (d) PEG 6000, (e) PEG 20000 and (f) HPMC. The inset was the crystallization ratio as a function of time according to Eq. (16). In Fig.3(a), the triangles, circles and squares represent the crystal growth kinetics of SMX at the initial chemical potential gradients of 1.7 × 10³, 2 × 10³ and 2.2 × 10³ J?mol^?1, respectively. The dashed, full and dotted lines denote the crystallization ratio with the initial chemical potential gradient of 1.7 × 10³, 2 × 10³ and 2.2 × 10³ J?mol^?1, respectively. In Fig.3(b), the circles and squares denote the crystal growth kinetics of SMX at 200 and 250 r?min^?1. The full and dotted lines denote the crystallization ratio at 200 and 250 r?min^?1. In Fig.3(c), the stars denote the crystal growth kinetics of SMX in the aqueous solutions containing 0.05% PVP content. In Fig.3(d), the circles, triangles and squares represent the crystal growth kinetics of SMX at 0%, 2% and 4% content of PEG 6000, respectively. The full, dashed and dotted lines denote the crystallization ratio at 0%, 2% and 4% content of PEG 6000, respectively. In Fig.3(e), the circles, triangles and squares represent the crystal growth kinetics of SMX at 0%, 2% and 4% content of PEG 20000, respectively. The full, dashed and dotted lines denote the crystallization ratio at 0%, 2% and 4% content of PEG 20000, respectively. In Fig.3(f), the triangles denote the crystal growth kinetics of SMX in the aqueous solutions containing 0.05% HPMC content.

Fig.4 SEM images of SMX: (a) seed crystals; the crystalline products obtained from the initial chemical potential gradient of (b) 1.7 × 10³, (c) 2 × 10³, and (d) 2.2 × 10³ J?mol^?1 at 310.15 K and 200 r?min^?1 in the aqueous solutions; (e) the crystalline products obtained at 250 r?min^?1, 310.15 K in aqueous solutions; and the crystalline products obtained in the aqueous solutions containing (f) 2% PEG 6000, (g) 4% PEG 6000, (h) 2% PEG 20000, and (i) 4% PEG 20000 at 310.15 K and 200 r?min^?1.

Fig.5 PXRD patterns of (a) seed crystals and the crystalline products obtained in solutions without polymer, and (b) the crystalline products obtained in solutions with polymer.

Fig.6 PXRD patterns of the crystalline products dried for 24 h in vacuum at 343.15 K.

$Δ μ$ / (J?mol^?1)	Stirring/ (r?min^?1)	Polymer	k_d	k_s	k_t^a)	ARD%	Average ARD%
$Δ μ$ / (J?mol^?1)	Stirring/ (r?min^?1)	Polymer	k × 10⁴/(mol?m^?2?s^?1)			ARD%	Average ARD%
1.7 × 10³	200	–	18.6	3.99	3.29	2.8	4.6
2 × 10³	200	–	28.2	5.98	4.93	3.5
2.2 × 10³	200	–	42.0	6.45	5.59	7.1
2 × 10³	250	–	34.7	8.21	6.64	4.9
2 × 10³	200	2% PEG 6000	29.6	12.9	8.98	6.2	5.1
2 × 10³	200	4% PEG 6000	79.1	14.9	12.6	5.2
2 × 10³	200	2% PEG 20000	18.0	19.2	9.30	3.7
2 × 10³	200	4% PEG 20000	29.5	24.6	13.4	5.1

Tab.2 Surface-reaction rate constant and diffusion rate constant obtained from the two-step chemical potential gradient model, and the ARDs between the modeled results and experimental dat

Fig.7 Diffusion rate constants and surface-reaction rate constants for SMX crystal growth in (a) the aqueous solutions and (b) the aqueous solutions containing PEG.

Fig.8 The noncovalent interactions between SMX and (a) PEG 6000, (b) PEG 20000, (c) PVP and (d) HPMC. White, red, blue, cyan and yellow balls represent H, O, N, C and S, respectively.

$k d = A × e ? E R T + B × ω (Δ μ × 10 ? 3) 2$			$k s = C × e ? E R T + D × ω (Δ μ × 10 ? 3) 2$		$k d$ /(mol?m^?2?s^?1)	$k s$ /(mol?m^?2?s^?1)
A/(mol?m^?2?s^?1)	B/(J²?m^?2?s^?1?r^?1?min)		C/(mol?m^?2?s^?1)	D/(J²?m^?2?s^?1?r^?1?min)	$k d$ /(mol?m^?2?s^?1)	$k s$ /(mol?m^?2?s^?1)
30.95	3.39 × 10^?5		24.92	?3.37 × 10^?6	1.84 × 10^?3	7.16 × 10^?4

Tab.3 Predicted surface-reaction rate constant and the diffusion rate constant of SMX at 100 r?min^?1 and 310.15 K^a)

Fig.9 The crystal growth kinetics of SMX in aqueous solutions at 310.15 K and 100 r?min^?1. The circles represent the experimental results. The dashed line represents the predicted results using the two-step chemical potential gradient model.

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