Optimizing sustainable pore design in MIL-125(Ti) for biomedicine using morphological tuning informed by Gaussian, Lorentzian, and Boltzmann fitting functions

Abstract

Metal–organic frameworks (MOFs) are porous crystalline materials whose adjustable structures make them increasingly attractive for biomedical engineering. Yet, developing sustainable routes to control their pore features remains a challenge. In this study, we explored how synthesis time can act as a simple and eco-friendly lever for pore engineering in MIL-125(Ti). By varying only the reaction duration, we created a series of MOF variants with distinct morphologies, pore sizes, and surface areas, each optimized for drug delivery and gene-editing applications. Detailed analyses using BET, XRD, and FESEM, supported by mathematical modeling, showed that synthesis time directly shapes crystallinity, porosity, and biocompatibility. Notably, the 24-hour sample displayed the highest surface area and pore volume, suitable for sustained drug release, while shorter synthesis times yielded frameworks favorable for other therapeutic uses. Overall, our findings introduce the concept of a sustainable pore size as a practical approach to designing high-performance biomedical materials.

Synthesis conditions can significantly influence the properties of metal-organic frameworks. Here, the authors report a sustainable and time-controlled synthesis strategy for MIL-125(Ti), demonstrating how reaction duration tunes morphology, pore size, surface area, crystallinity, and biocompatibility, and highlighting synthesis time as a key, eco-friendly parameter for designing high-performance MOFs for biomedical applications.

Introduction

In the quest for renewable and sustainable advancements, the emergence of natural and synthesized materials, known as sustainable (nano)materials, stands out. These materials are meticulously designed by mimicking the performance characteristics of naturally occurring phenomena. For instance, the durability of bamboo, the porosity of sponge-like structures, and the light-capturing capabilities of fish retinal photoreceptors inspire the development of these advanced materials^1,2. Recently, scientists have leveraged nature-inspired methodologies to create materials that exemplify sustainable chemistry and material science. This approach underscores the importance of achieving high performance with minimal energy consumption, a principle derived from nature itself^3–5.

The rapid pace of industrialization and the unprecedented exploitation of natural resources make it imperative to adopt sustainable and green strategies throughout research and development processes. The next frontier in (bio)chemical sciences involves optimizing material properties, such as size, pore volume, and morphology to enhance targeted molecular loading and release^6,7. A critical goal in sustainable chemistry is to reduce the carbon footprint while simultaneously improving functionality and performance. According to existing literature, achieving higher Brunauer−Emmet−Teller (BET) and Barrett–Joyner–Halenda (BJH) surface areas is considered optimal for molecular loading and release, but this often requires significant energy input^8–10.

The development of this concept can significantly impact the broader application of various synthesized materials¹¹. Today, sustainability is an integral aspect of materials science, especially when it comes to using materials for biological purposes^12–14. In this context, MOFs, which are among the widely studied porous materials, have embraced the concept of sustainability^15–19. MOFs are a class of crystalline porous materials, sometimes containing a fraction of amorphous structure, constructed from metal ions or clusters coordinated to organic linkers, resulting in highly ordered structures with tunable porosity²⁰. Their unique performance advantages, such as controllable pore size and surface chemistry, high surface area, low density, and the ability to incorporate functional groups, make them highly versatile for a broad spectrum of applications^21,22. The structural tunability of MOFs enables precise control over molecular adsorption, separation, and release, while their large surface areas and adjustable pore environments facilitate selective catalytic reactions and enhanced mass transport. These features have led to their successful application in diverse fields, including gas adsorption and separation, photocatalysis, catalysis, and advanced oxidation processes. For instance, recent studies have demonstrated the design of MOFs with optimized light-harvesting capabilities for efficient photocatalytic hydrogen production and pollutant degradation²³, the integration of active metal sites for high-performance heterogeneous catalysis²⁴, and their deployment in large-scale separation²⁵. Moreover, MOFs have emerged as efficient platforms for advanced oxidation systems, enabling the breakdown of persistent organic pollutants under mild conditions²⁶. These recent advances underscore the potential of MOFs as next-generation multifunctional materials, bridging fundamental materials science with real-world applications^27,28.

Enhancing features that contribute to sustainability within a system is particularly crucial for biomedical applications^29–31. For instance, Song et al. reported the use of MIL-125(Ti) nanoparticles for controlled doxorubicin release, endosomal escape and also intracellular delivery, achieving sustained cytotoxicity through pH-responsive degradation³². Similarly, Putro et al. utilized modified MIL-125(Ti) to deliver 5-fluorouracil for colorectal cancer treatment, demonstrating improved solubility and targeted cellular uptake³³. These studies highlight the versatility of MIL-125(Ti) in biomedical delivery platforms. Based on a search in the Scopus database on October 16, 2024, targeting titles, abstracts, and keywords, 302 documents were found using the keywords “MOF” and “Susatinability” Among these, 294 documents, including articles, reviews, book chapters, books, conference papers, and letters, were published within the last 10 years, as shown in Fig. 1, demonstrating their increasing growth. When additional keywords like “biomedical,” “biosensor,” “biomedicine,” “bioimaging,” “drug delivery,” and “bio” were included using the OR operator, this number reduced to 23 documents, representing around 8% of the total. These charts, along with the growing focus on sustainability in chemistry and the biological applications of MOFs, highlight their significance in future perspectives.

Fig. 1. Publication trends in MOF-related research and sustainability.

Growth charts of the number of documents indexed in Scopus with the specified keywords. A represents documents with keywords related to bio-applications, B shows the part-to-whole ratio of these documents to the total, and C displays the total number of documents with the keywords “MOF” and “Sustainability” over the past 10 years.

A wide variety of MOFs have been synthesized and studied for diverse applications, with much of the research focusing on the rationale behind choosing the appropriate framework type. However, synthesis conditions and optimization significantly influence their properties and encompass a broad range of characteristic features. Prior work has demonstrated that parameters, such as reaction time, solvent composition, modulator type (e.g., acetic acid, benzoic acid), and temperature directly alter MIL-125(Ti) crystallinity, pore volume, and BET surface area. Based on the literature, extending solvothermal synthesis from 6 to 24 hours increased BET surface area by over 40%, while other works achieved micropore expansion through solvent-exchange post-treatment^34–37. In our study, we present groundbreaking results that challenge conventional wisdom. The MIL-125(Ti) samples synthesized at four different time intervals exhibit distinct crystallinity, isotherm behavior, dispersity, and morphology, each offering unique and noteworthy characteristics. Our findings reveal that MIL-125(Ti), while exhibiting a relatively low surface area and aggregated semi-spherical morphology, maintains a highly sustainable pore architecture that enables efficient encapsulation and delivery of key therapeutic agents, including polymerized doxorubicin (DOX) and complex biomolecular systems, such as CRISPR-Cas9 complexes. We introduce the concept of “sustainable pore size” for biomedical applications, marking a significant advancement in sustainable chemistry and material science. This novel approach not only reduces energy requirements but also enhances the material’s performance, representing a substantial leap forward in scientific innovation.

Results and discussion

To characterize the successful synthesis of MIL-125(Ti), Fourier-transform infrared (FTIR) spectroscopy was employed to investigate the functional groups present in the material (Fig. 2). The FTIR spectra exhibited characteristic peaks for MIL-125(Ti) at approximately 660–760, 1100, 1400, and 1690 cm^-1, corresponding to the Ti–O–Ti vibration, overlapping C-O/Ti–O–C stretching, symmetric O–C–O stretching, and C = O stretching, respectively³⁸. Additionally, the vibrational bands associated with the carboxylate (–COOH) linker were identified at approximately 1400 and 1690 cm^-1, corresponding to the symmetric and asymmetric stretching vibrations of the carboxylate groups, respectively. Weak C–C stretching vibrations of the benzene ring in the BDC linker may also appear around 1260 cm^-139. To further investigate the structural characteristics of the synthesized MIL-125(Ti), X-ray diffraction (XRD) analysis was conducted (Fig. 2A). The XRD patterns revealed distinct peaks at 6.7°, 9.7°, and 11.6°, corresponding to the (101), (200), and (221) crystallographic planes, respectively, confirming the crystalline structure consistent with literature reports^40,41. In MIL-125(Ti), six BDC (benzene dicarboxylate) organic linkers are interconnected with titanium clusters (Ti₈O₈(OH)₄) to form a disc-like tetragonal 3-dimensional reticular structure. This stracture was corroborated by the FTIR and XRD results. It was observed that decreasing the synthesis temperature and time led to a significant reduction in crystallinity, which was utilized in this study to control pore volume, pore size, and surface area. Based on the literature^41,42, MIL-125(Ti) demonstrated considerable thermal stability up to 350°C, as verified by XRD. Upon heating between 350°C and 500°C, the MIL-125(Ti) structure decomposed, resulting in the formation of amorphous TiO₂ and a porous carbon matrix. Additionally, a minor diffraction peak around 26° indicated the formation of an amorphous carbon structure, likely due to localized heating effects on the crystalline structure.

Fig. 2. Characterization of MIL-125(Ti) samples.

A XRD pattern and B FTIR spectra of the synthesized materials.

According to the literature, increasing the synthesis temperature to 150 °C in a DMF (dimethylformamide) refluxed oil bath, or up to 220 °C in alternative synthesis procedures, along with extending the synthesis duration to 72 h, significantly enhances the crystallinity of MIL-125(Ti)^42–44. Enhanced crystallinity is associated with improved performance in both industrial and biomedical applications. However, for practical industrial and clinical applications, it is crucial to reduce both the synthesis temperature and time to lower the preparation costs. Additionally, there remains a gap in the use of amorphous and semi-amorphous structures as sustainable and green materials for biomedical applications. In the context of biomedicine and biomedical sciences^45–47, particularly drug and gene delivery, the pore size, pore volume, and surface area are critical physicochemical characteristics that determine the efficacy of MIL-125(Ti), along with the basic physicochemical characteristics. Smaller pores are advantageous for encapsulating small drug molecules like DOX, ensuring high encapsulation efficiency. However, excessively small pores may hinder the loading of larger therapeutic agents, such as those used in CRISPR-Cas9 gene editing^48–50. Therefore, MIL-125(Ti) designed for DOX delivery typically has pores slightly larger than the DOX molecules, facilitating efficient encapsulation and controlled, sustained release via diffusion. The pore volume of MIL-125(Ti) is another crucial factor influencing drug loading capacity. A higher pore volume generally permits a greater amount of drug to be loaded, which is beneficial for treatments requiring large doses of medications. It is essential for the pore volume distribution within MIL-125(Ti) to be uniform to ensure drug stability and prevent aggregation. Even distribution enables uniform drug dispersion, enhancing the stability of therapeutic agents within the MIL-125(Ti) structure. Regarding size, nano-sized MIL-125(Ti) exhibit prolonged circulation times and reduced clearance by the reticuloendothelial system (RES), making them particularly effective for drug delivery^51,52. Conversely, larger MIL-125(Ti) particles may be advantageous for scenarios requiring slower release rates and localized delivery, such as targeted liver delivery of drugs or biomolecules^53–56.

It should be noted that diffusion rates through amorphous MIL-125(Ti) play a crucial role in drug delivery and can be modeled using Fick’s laws of diffusion:

$$\frac{\partial C}{\partial t}=\nabla .\left(D_{eff}\nabla C\right)$$ 1

where C is the concentration of the drug, t is time, and ∇ represents the spatial gradient. In amorphous MIL-125(Ti) structures, the effective diffusion coefficient varies spatially due to the irregular pore architectures, requiring heterogeneous diffusion models for accurate predictions. These models incorporate local variations in the diffusion coefficient, reflecting the complex pathway that DOX molecules navigate through the amorphous structure. Amorphous materials often require heterogeneous diffusion models^57,58, where D_eff is a function of position. These models can be solved numerically to predict drug release profiles. In addition, amorphous MOFs generally exhibit greater structural flexibility compared to crystalline ones. This flexibility can enhance the interaction between the MOF and drug molecules, potentially improving loading and release dynamics. Mathematical models can quantify this flexibility through parameters, such as the elastic modulus or compliance of the MOF structure. The flexibility of the MOF can be described by its elastic modulus E. In amorphous materials, E can vary locally, which can be modeled using statistical mechanics or finite element analysis (FEA). E (x, y, z) = local stiffness at position (x, y, z); in which, this stiffness is related to the crystallinity and also ratio of the MIL-125(Ti).

Based on the linear plots of adsorption isotherms presented in Supplementary Figs. 1–4, all four synthesized materials fall within the Type IV isotherm category according to the IUPAC classification. This pattern is commonly observed in mesoporous materials⁵⁹. Considering the pore sizes reported in Table 1, this observation is acceptable. For MIL-125-24h, which exhibits a high degree of crystallinity, the Type IV isotherm is observed more distinctly^60,61. The average pore size during desorption is 2.69 nm, which is smaller than that of the other synthesized materials, thereby justifying the capillary condensation mechanism responsible for the formation of this type of isotherm. Furthermore, the Type H4 hysteresis observed in MIL-125-24h indicates narrower pores. In contrast, for MIL-125-6h, MIL-125-12h, and MIL-125-18h, the larger pore sizes lead to Type H3 hysteresis (is typically associated with slit-like or plate-like pores), which does not show the same limiting adsorption behavior at higher P/P₀ ratios as seen in MIL-24. Notably, MIL-125-12h, despite having smaller pore sizes compared to MIL-125-6h and MIL-125-18h, is closer to Type H4 hysteresis (indicates slit-shaped pores and materials with amorphous structures)^62,63. When comparing MIL-125-6h and MIL-125-18h, although their pore sizes are nearly similar, the adsorption isotherm patterns reveal some differences. The lack of uniformity and greater disorder in pore sizes due to the more amorphous structure of MIL-125-6h, MIL-125-12h, and MIL-125-18h may explain the reduced capillary condensation observed in these materials. However, this amount is less significant for MIL-125-12h when considering its isotherm in conjunction with its other properties. The correlation between hysteresis type and biomedical performance provides a framework for material selection; H4 hysteresis systems offer superior control for sustained release applications, while H3 hysteresis systems provide advantages for rapid loading and immediate bioavailability requirements.

Table 1.

Pore Size Analysis for Four MIL-125(Ti) Samples: BET, BJH, and D-H Adsorption/Desorption Measurements

Pore Size	MIL-125-6h	MIL-125-12h	MIL-125-18h	MIL-125-24h
Adsorption average pore diameter (4 V/A by BET) (nm)	5.85	3.49	6.11	2.60
Desorption average pore diameter (4 V/A by BET) (nm)	6.63	4.30	6.46	2.69
BJH Adsorption average pore width (4 V/A) (nm)	8.35	7.05	6.33	8.34
BJH Desorption average pore width (4 V/A) (nm)	8.38	6.71	8.38	6.19
D-H Adsorption average pore width (4 V/A) (nm)	11.22	9.94	9.34	11.27
D-H Desorption average pore width (4 V/A) (nm)	9.46	7.49	9.43	6.84

The BET analysis of MIL-125(Ti) MOFs synthesized over varying durations provides valuable insights into their surface area, pore volume, and pore size (Tables 1, 2, and 3). These parameters are crucial for understanding their potential efficacy in drug delivery applications^64,65. The surface area, pore volume, and pore size of MIL-125(Ti) MOFs vary significantly with synthesis time, indicating how processing conditions can be finely tuned to achieve desired structural characteristics. MIL-125-24h exhibits the highest BET surface area (653.21 m² g^-1) and pore volume (0.425 cm³g^-1) with a relatively small pore size (2.69 nm). The high surface area suggests a greater capacity for drug adsorption, making this variant highly suitable for drug delivery applications where maximizing loading capacity is crucial. The small pore size is beneficial for encapsulating smaller drug molecules or ensuring controlled release of larger molecules, thus providing versatility in drug delivery. In contrast, MIL-125-6h and MIL-125-12h have lower surface areas (119.03 m² g^-1 and 114.96 m² g^-1, respectively) and moderate pore volumes (0.174 cm³g^-1 and 0.100 cm³g^-1, respectively). The pore sizes are 5.85 nm for the 6-hour variant and 3.49 nm for the 12 h variant. These pore sizes are large enough to encapsulate a range of drug molecules, but the relatively lower surface areas might limit their drug loading capacity compared to the 24 h variant. However, their larger pores could facilitate faster drug release, which might be desirable in applications requiring rapid therapeutic action. MIL-125-18h stands out with an unusually low surface area (18.16 m² g^-1) and pore volume (0.028 cm³g^-1) despite having a pore size of 6.11 nm. This indicates that prolonged synthesis under these specific conditions might lead to structural collapse or a significant reduction in available surface area, severely limiting its usefulness for drug delivery due to poor drug loading capacity. The larger pore size alone is insufficient to compensate for the low surface area and volume, as effective drug delivery systems require a balance between these parameters to ensure both adequate loading and controlled release.

Table 2.

Summary of Surface Area Measurements for Four MIL-125(Ti) Samples: BET, Langmuir, t-Plot, D-H, and BJH Analyses

Surface Area	MIL-125-6h	MIL-125-12h	MIL-125-18h	MIL-125-24h
Single point surface area at p/p0 = 0.30 (m2 g-1)	116.21	112.50	18.09	649.50
BET Surface Area (m2 g-1)	119.03	114.96	18.16	653.21
Langmuir Surface Area (m2 g-1)	742.7	354.2	123.9	1,253.3
t-Plot Micropore Area (m2 g-1)	28.39	60.99	3.75	586.95
t-Plot External Surface Area (m2 g-1)	90.64	53.97	14.41	66.26
BJH Adsorption cumulative surface area of pores between 1.7 nm and 300 nm width (m2 g-1)	122.26	62.14	25.45	92.00
BJH Desorption cumulative surface area of pores between 1.7 nm and 300 nm width (m2 g-1)	115.15	67.75	16.88	122.19
D-H Adsorption cumulative surface area of pores between 1.7 nm and 300 nm width (m2 g-1)	78.44	37.12	13.71	58.01
D-H Desorption cumulative surface area of pores between 1.7 nm and 300 nm width (m2 g-1)	92.29	53.93	13.56	97.64

Table 3.

Pore Volume Analysis for Four MIL-125(Ti) Samples: Single Point, t-Plot, and BJH Adsorption/Desorption Measurements

Pore Volume	MIL-125-6h	MIL-125-12h	MIL-125-18h	MIL-125-24h
Single point adsorption total pore volume of pores less than 40.41 nm width at p/p0 = 0.950 (cm3 g-1)	0.174	0.100	0.028	0.425
Single point desorption total pore volume of pores less than 40.41 nm width at p/p0 = 0.950 (cm3 g-1)	0.197	0.124	0.029	0.439
t-Plot micropore volume (cm3 g-1)	0.014	0.031	0.002	0.299
BJH Adsorption cumulative volume of pores between 1.7 nm and 300 nm width (cm3 g-1)	0.255	0.110	0.040	0.192
BJH Desorption cumulative volume of pores between 1.7 nm and 300 nm width (cm3 g-1)	0.241	0.114	0.035	0.189

The BET data of MIL-125(Ti) variants reveal that synthesis duration significantly impacts the structural properties of MOFs, which in turn affect their suitability for drug delivery. MIL-125-24h, with its high surface area and pore volume, appears most promising for applications requiring high drug loading and sustained release, such as for DOX delivery. Its small pore size is also conducive to controlling the release rate of the drug, which is critical for maintaining therapeutic levels over extended periods. On the other hand, MIL-125-6h and MIL-125-12h might be more suitable for applications where moderate drug loading is acceptable, and faster release is desired. These variants could be tailored for short-term treatments or rapid therapeutic interventions. The relatively larger pore sizes can accommodate a variety of drug molecules, making them versatile but potentially less efficient in terms of loading capacity compared to the 24-hour variant. MIL-125-18h, with its markedly low surface area and pore volume, is likely unsuitable for efficient drug delivery. The structural limitations observed in this variant highlight the importance of optimizing synthesis conditions to achieve the desired balance of surface area, pore volume, and pore size. The BET-Langmuir surface area ratio serves as a quantitative descriptor of surface heterogeneity, with higher ratios indicating more diverse binding environments that translate to complex drug loading and release behaviors advantageous for sophisticated therapeutic applications.

According to the data in the Table 2, the smaller BET Surface Area compared to the Langmuir Surface Area with a significant difference suggests that the adsorption in the material’s pores does not occur as a monolayer⁶⁶. This could indicate that the material has a heterogeneous surface, which is oversimplified by the Langmuir model. These findings suggest that the material possesses a heterogeneous surface and a complex porosity structure. MIL-125-24h exhibits the highest Langmuir surface area at 1253.3 m² g^-1, further emphasizing its highly porous structure. This suggests that the 24 h variant not only has a large surface area accessible for adsorption but also possesses a highly developed porous network, which is ideal for high drug loading capacity. On the other hand, the MIL-125-6h and MIL-125-12h variants show significantly lower Langmuir surface areas (742.7 m² g^-1and 354.2 m² g^-1, respectively). This reduction in surface area indicates that these variants have less extensive porous networks, which could limit their ability to load large amounts of drugs effectively. The MIL-125-18h variant has a notably low Langmuir surface area of 123.9 m² g^-1, reinforcing the idea that prolonged synthesis may lead to structural degradation, resulting in a less effective material for drug delivery applications. This observation suggests that, in some cases, prolonged synthesis time does not inherently result in the development of structures with superior properties.

Additionally, the t-Plot micropore volume (Table 3) provides additional insights into the distribution of pore types within these MOFs. The t-Plot External Surface Area for MIL-125-6h and MIL-125-18h is greater than the t-Plot micropore area, indicating that the material primarily consists of larger pores (mesopores) and external surfaces, with most gas adsorption occurring on these surfaces. Moreover, Galarneau et al. showed in their study on N₂ adsorption in zeolites that t-plot analysis is reliable for micro/mesoporous materials when the micropore volume contributes less than 20% to the total pore volume. However, as the proportion of micropores increases beyond this threshold, the accuracy of the micropore volume measurement declines, potentially leading to an underestimation of up to 40%⁶⁷. Hence, it can be inferred that the t-plot analysis might have higher inaccuracies for MIL-125-12h and MIL-125-24h. MIL-125-24h demonstrates the highest micropore volume (0.299 cm³g^-1), which is critical for encapsulating smaller drug molecules or controlling the release rate of larger ones. This high micropore volume aligns with the high surface area and suggests that MIL-125-24h can provide sustained drug release, making it highly suitable for long-term therapeutic applications. Conversely, the MIL-125-12h variant has a moderate t-Plot micropore volume (0.031 cm³g^-1), indicating a relatively higher proportion of micropores compared to its overall pore volume. This suggests that MIL-125-12h could be effective in applications requiring moderate drug loading with controlled release. The MIL-125-6h variant, with a lower t-Plot micropore volume (0.014 cm³g^-1), indicates a predominance of mesopores, which may be better suited for faster drug release but could limit the material’s capacity for sustained drug delivery. The MIL-125-18h variant, with the lowest micropore volume (0.002 cm³g^-1), shows a clear deficiency in microporous structure, supporting the earlier observation that this variant is unsuitable for efficient drug delivery due to its limited capacity for both drug loading and controlled release.

The pore size distribution data, analyzed through BJH and Dollimore–Heal (D-H) methods, provide further clarity on the suitability of these MOFs for encapsulating different drug molecules. The difference between the adsorption and desorption cumulative surface areas in BJH indicates a greater capillary condensation effect in MIL-125-24h compared to the other materials. Additionally, the D-H model is provided, which can offer more detailed insights due to its different mathematical approach compared to BJH⁶⁸. From the J-graphs presented in Supplementary Figs. 1–4, it is evident that the pore size distribution in MIL-125-24h includes smaller diameter pores. This distribution is broader for MIL-125-6h and MIL-125-18h compared to MIL-125-12h, indicating a more uniform pore volume distribution in MIL125-12h. The BJH adsorption average pore width for MIL-125-24h is 8.34 nm, which indicates a broad range of pore sizes that can accommodate a variety of drug molecules. This versatility, coupled with its high micropore volume and surface area, makes MIL-125-24h an excellent candidate for both high drug loading and controlled release. MIL-125-6h and MIL-125-12h variants show BJH adsorption average pore widths of 8.35 nm and 7.05 nm, respectively. These larger pore sizes suggest that these variants are more suited for encapsulating larger drug molecules or for applications requiring rapid drug release. The D-H method further reveals that the MIL-125-6h variant has the largest adsorption average pore width of 11.22 nm, indicating a predominantly mesoporous structure. This characteristic supports the potential for faster drug release, making it suitable for acute therapeutic applications. The MIL-125-18h variant, despite having a large BET adsorption average pore diameter (6.11 nm) and similar BJH adsorption average pore width (6.33 nm), suffers from a low overall surface area and pore volume. This imbalance suggests that the large pores in this variant do not compensate for its lack of micropores and low surface area, making it ineffective for drug delivery where a balance of high loading capacity and controlled release is crucial. The correlation between pore size distribution breadth and release kinetics complexity provides a rational framework for material selection; narrow distributions for sustained delivery, broad distributions for rapid-onset applications, and intermediate distributions for balanced dual-phase release profiles.

Recently, a study conducted by Yang et al. demonstrated that for systems with complex porosity and multilayer adsorption, modified differential D-BJH equations can be utilized⁶⁸. These equations enable the calculation of the pore size distribution from adsorption isotherms in a point-by-point manner. The modified D-BJH equations have proven to provide more accurate point-by-point interpretations compared to other models, especially for Type IV isotherms with H3 and H4 hysteresis loops. Given the complexity of pore size distribution, geometry, and the amorphous nature of certain structures, this model is particularly useful for materials with lower crystallinity. The equations focus on the relationship between the derivative of the isotherm and pore size. In Eq. 3, the variable n refers to the serial number of the adsorption data point, arranged in ascending order of pressure, representing the simplified D-BJH (SD-BJH) when considering multilayer adsorption effects. Equation 2 indicates that dV/dr, or the pore size distribution of porous materials, is directly related to the derivative of the isotherm with respect to pore size. In Eq. 3, n is again the serial number of each adsorption data point. The equations are expressed as follows:

$$E_{gl}{S}_n\approx \left({{\pi r}_{k,n}}^2+{n2\pi r}_{k,n}\mathrm{\Delta }{t}_n\right)L_n{\left(\frac{dr}{dp}\right)}_n$$ 2

$$\frac{dV}{dr}=E_{gl}\times \frac{r^2}{{r_k}^2+n2r_k\mathrm{\Delta }t}\times \frac{d\left(\Theta \right)}{dr}$$ 3

In this context, dV represents the differential volume of gas released during pressure reduction, while r denotes the pore radius. The term r_k is the radius of critical capillary condensation, indicating the threshold radius where condensation occurs. The parameter E_gl describes the volume conversion coefficient of N₂ between its liquid and gaseous states. Δt refers to the change in the thickness of the adsorbed layer as the pressure varies. The adsorption isotherm is denoted by Θ_(p), which describes the relationship between the amount adsorbed and the pressure. Finally, S is the slope of the adsorption isotherm, representing the rate of change of adsorption with respect to pressure. Model validation was performed through cross-correlation analysis between modified D-BJH predictions and experimental observations, including field emission scanning electron microscopy (FESEM) morphological analysis and drug loading behavior, confirming the model’s accuracy for partially crystalline MOF systems with complex pore architectures.

A precise chemical understanding of this model provides valuable insights into the surface properties of materials. It is evident that the slope of the adsorption curve is correlated with the radius of critical capillary condensation r_k, and the total volume of gas released is inversely related to both n (the serial number of adsorption data points) and r_k. Although these interpretations are specifically derived for N₂ gas, they can also be extended to the loading and release of other guest molecules, such as drugs. While the interactions with drugs involve more complexity and additional parameters, the modified BJH equations suggest that the volume of released drug molecules is inversely related to the radius of critical capillary condensation. Therefore, in systems where condensation occurs due to smaller pore sizes, the drug release is expected to be slower. This relationship can be inferred from the slope of the BJH curve, which provides a unique perspective. Based on this analysis, the release behavior of drug molecules can be anticipated as follows: for MIL-125-6h, a higher drug release volume is expected in the initial stages without exhibiting a stepwise release pattern. In contrast, for MIL-125-12h and MIL-125-24h, the release volume is lower, and a stepwise release behavior is likely to be observed. This difference highlights the significance of pore size in controlling the release rates of encapsulated molecules.

A more conceptual interpretation of this analysis is provided in the study by Zeng et al., which explored drug release models from various compound-based matrices⁶⁹. Their research demonstrated that the drug release rate for materials with a Type IV isotherm is directly related to pore size. In their analysis, both the association and dissociation processes were assumed to be reversible, following first-order kinetics. The experimentally obtained release profiles of metoprolol were described using a theoretical kinetics model involving two exponential functions.

$${\lambda }_{1,2}=\left[\right)\left(k_s+k_{off}\right)\pm \sqrt{{\left(k_s+k_{on}+k_{off}\right)}^2-4k_s{k}_{off}}\left]\right)/2$$ 4

In this model, which initially was introduced for silica-based materials, the parameter λ_1,2 represents the eigenvalues of the linear system of equations, while k_s denotes the rate constant for the diffusion/convection process. Additionally, k_on and k_off correspond to the rate constants for the association and dissociation of the drug from the carrier, respectively. Further, researchers highlighted that the initial drug release rate, referred to as Burst Release Rate, is directly proportional to the pore size. On the other hand, Mitran et al. extended this model in their study on the release of metoprolol from mesoporous silica structures⁷⁰. Their findings indicated that the sustained release rate is primarily controlled by the interactions between the drug and the chemical nature of the pores. This means that a larger pore size correlates with a higher burst release rate, resulting in a rapid initial drug release. For example, in the case of MIL-125-6h, a higher initial release can be anticipated due to the larger pore size. In contrast, for MIL-125-24h, the lower value of k_s suggests a slower initial release rate. Consequently, MIL-125-24h would demonstrate a more gradual release profile compared to MIL-125-6h, where the release is more immediate and pronounced in the initial stages. Model extension to different therapeutic molecules requires systematic re-parameterization of rate constants and incorporation of molecular-specific interactions, maintaining the fundamental mathematical framework while adapting to size, binding, and transport characteristics unique to each therapeutic system.

Various models were utilized for the analysis of adsorption and to gain a better understanding of the structural characteristics (Table 4). In monolayer adsorption models, Q_m refers to the maximum adsorption capacity, while C represents the equilibrium concentration of the adsorbate in the gas phase⁷¹. Based on this model, the highest adsorption capacity and equilibrium concentration are observed for MIL-125-24h, followed by MIL-125-12h. MIL-125-6h and MIL-125-18h rank lower in this regard. The parameter m > 1 for all materials indicates that stronger adsorption occurs at higher concentrations. In the Temkin model, q·α/Q_m represents the relationship between the adsorption energy and the maximum adsorption capacity Q_m. This model assumes an inverse relationship between adsorption energy and surface coverage and is suitable for systems with uniform energy distribution on adsorption sites. The parameter A is a measure of pressure that allows for the analysis of equilibrium pressure at different temperatures. A higher value of A for MIL-125-18h suggests that, under experimental conditions, this material utilizes its adsorption capacity more efficiently, making better use of its overall capacity. However, it is important to note that the Temkin model is more effective for systems with heterogeneous adsorption surfaces (Table 4)⁷².

Table 4.

Analysis of Adsorption Isotherms, Nanoparticle Size, and Micropore Characteristics for Four MIL-125(Ti) Samples: Freundlich, Temkin, Horvath-Kawazoe, Dubinin-Astakhov, and MP-Method

Adsorption Isotherms	MIL-125-6h	MIL-125-12h	MIL-125-18h	MIL-125-24h
Qm.C (exp., instrument)	8.6238 ± 0.6904 2.7721 ± 0.2759	13.6230 ± 0.6223 4.3178 ± 0.3842	1.4836 ± 0.1296 2.9058 ± 0.3338	102.8445 ± 3.2441 6.1981 ± 0.6003
Qm·C (cm3 g-1STP) m
Temkin	0.032383 ± 0.005340 0.2146 ± 0.1897	0.065703 ± 0.009353 0.9538 ± 0.6930	0.206112 ± 0.035101 0.2210 ± 0.1998	0.028640 ± 0.001759 283.2984 ± 127.2748
q· α /Qm (kJ mol-1·(cm3 g-1STP)) A (mmHg)
Nanoparticle Size	50.41	52.19	330.46	9.19
Average Nanoparticle Size (nm)
Horvath-Kawazoe	0.052 0.68	0.054 0.64	0.008 0.62	0.327 0.54 m
Maximum pore volume at p/p0 = 0.173 (cm3 g-1) Median pore width (nm)
Dubinin-Astakhov	99.21 0.046	140.48 0.069	16.58 0.007	717.51 0.304
Micropore surface area (m2 g-1) Limiting micropore volume (cm3 g-1)
MP-Method	1.73	0.55	1.56	0.27
Average pore hydraulic radius (V/A) (nm)

(all parameters obtained from instrument calculations).

The estimation of particle size through indirect methods supports the size trends observed in FESEM images. The Horvath-Kawazoe isotherm is specifically used to determine the size and volume of micropores⁷³. The Maximum pore volume indicates the relative pressure at which the largest pore volume is generated. The Median pore width reflects the midpoint of the pore size distribution, meaning that half of the total pore volume is composed of pores smaller than this size, while the other half is larger. The median pore width provides insight into the pore size distribution in the sample and is critical for analyzing adsorption properties and material transport. The Micropore surface area (m² g^-1) is obtained using the Dubinin-Astakhov isotherm and plays a crucial role in determining adsorption capacity. This parameter indicates the surface area attributed to micropores. The Limiting micropore volume defines the maximum micropore volume and is particularly useful for assessing adsorption capacity at low pressures⁷⁴. These two models are especially suited for analyzing the behavior of MIL-125-24h, which contains a higher proportion of microporous structures. The Average pore hydraulic radius in the MP-Method is calculated using the ratio of volume to surface area. This method is particularly useful for determining the average size of smaller pores (pores less than 2 nm)⁷⁵.

The crystallinity of MOFs significantly impacts their drug delivery capabilities. As the synthesis time of MIL-125(Ti) increases from 6 to 24 h, there is a notable increase in the crystal/amorphous ratio. Crystalline structures generally provide a more ordered and predictable framework, which can be advantageous for consistent drug loading and release profiles. MIL-125-6h has moderate crystallinity with a lower crystal/amorphous ratio, making it more amorphous. This amorphous nature can offer advantages in flexibility and a broader pore size distribution, which may accommodate a variety of drug molecules. However, the moderate surface area and pore volume may limit its drug loading capacity compared to more crystalline variants. MIL-125-12h shows increased crystallinity and a medium crystal/amorphous ratio, suggesting a balanced structure with more ordered pores. This can enhance the uniformity of drug loading and potentially improve release control, making it suitable for applications requiring precise drug delivery. MIL-125-18h, despite a longer synthesis time, exhibits low crystallinity and the lowest crystal/amorphous ratio. The significant reduction in surface area and pore volume indicates structural degradation or collapse, making it less suitable for drug delivery. This variant highlights the importance of optimizing synthesis conditions to maintain structural integrity. MIL-125-24h demonstrates very high crystallinity and the highest crystal/amorphous ratio. This highly ordered structure correlates with the highest BET surface area and pore volume, offering substantial advantages for drug loading and sustained release. The small, uniform pore size further supports controlled drug delivery, crucial for applications like DOX and CRISPR-Cas9 delivery. The relationship between crystallinity and therapeutic cargo loading follows distinct patterns: crystalline frameworks favor small molecule drugs through ordered binding sites and predictable release kinetics, while semi-amorphous structures provide adaptive environments suitable for large biomolecular complexes requiring conformational flexibility during loading and release processes.

Sustainable pore engineering involves the precise control and optimization of pore characteristics to enhance drug delivery performance while minimizing environmental impact during synthesis. In the context of MIL-125(Ti), sustainable pore engineering can be achieved by adjusting synthesis parameters to balance crystallinity, surface area, pore volume, and pore size. For effective drug delivery, especially with large molecules like CRISPR components, it’s essential to tailor pore sizes to ensure adequate loading without compromising release rates. For instance, MIL-125-24h with a pore size of 2.69 nm and high pore volume is optimal for encapsulating small to medium-sized drug molecules and ensuring a sustained release profile. High surface area, as seen in MIL-125-24h, provides more active sites for drug adsorption, which is beneficial for increasing drug loading capacity. Sustainable engineering should focus on maximizing surface area while maintaining structural stability, as seen with the 24 h synthesis variant. Sustainable synthesis methods aim to reduce the use of harmful solvents and lower energy consumption. Techniques, such as microwave-assisted synthesis or green solvents can be explored to produce high-crystallinity MOFs like MIL-125-24h with minimal environmental impact. The sustainable pore size concept can be quantitatively expressed through a multi-parameter optimization function that considers energy efficiency, therapeutic efficacy, and environmental impact. This approach enables the design of MOF systems that achieve optimal performance with minimal resource consumption, representing a significant advancement over traditional high-surface-area approaches that often require energy-intensive synthesis conditions.

FESEM images provide a detailed view of the morphological and structural characteristics of MIL-125(Ti) MOFs synthesized at different durations (6, 12, 18, and 24 h) (Fig. 3). These images offer valuable insights into how synthesis time affects the crystallinity, surface texture, particle size, and overall morphology of the MOFs, which are critical for their performance in drug delivery applications. The FESEM images of MIL-125(Ti) synthesized for 6 h typically show a relatively rough and irregular surface morphology, indicating a more amorphous structure with less-defined crystal facets. The particles appear to be loosely packed with a high degree of surface roughness. This morphological characteristic aligns with the moderate crystallinity and lower crystal/amorphous ratio observed in the BET analysis. The amorphous nature provides flexibility in pore sizes, which can be beneficial for accommodating various drug molecules. However, the irregular surface may lead to uneven drug loading and release rates, potentially affecting the efficiency of drug delivery systems. In the 12 h synthesis variant, the FESEM images reveal more defined and smoother crystal facets compared to the 6 h variant. The particles show a moderate increase in size and a more uniform shape, indicating a transition towards higher crystallinity. The enhanced crystallinity and medium crystal/amorphous ratio observed in this sample suggest improved structural order. This more ordered morphology can contribute to more consistent drug loading and controlled release, making MIL-125-12h suitable for applications where precise drug delivery is essential. The smoother surface also reduces potential aggregation, facilitating better dispersion in biological environments. The FESEM images of MIL-125 synthesized for 18 h display a notable decrease in surface roughness but also show signs of structural collapse or agglomeration. The particles appear larger and more aggregated, with fewer distinct crystal facets visible. This morphological change corresponds to the significant drop in BET surface area and pore volume, indicating low crystallinity and the lowest crystal/amorphous ratio. The agglomerated and collapsed structures seen in the images suggest that prolonged synthesis under these conditions may lead to instability, which can severely limit the material’s effectiveness for drug delivery due to poor drug loading and unpredictable release profiles. For the MIL-125(Ti) synthesized for 24 h, the FESEM images exhibit highly defined crystal facets and a uniform, regular morphology⁷⁶. The particles are well-formed with sharp edges, indicative of very high crystallinity and the highest crystal/amorphous ratio. The surface is smooth and well-ordered, aligning with the highest BET surface area and pore volume reported for this variant. This well-ordered structure facilitates maximum drug loading capacity and controlled release, making MIL-125-24h particularly advantageous for drug delivery applications, such as DOX and CRISPR-Cas9 systems. The uniform particle size and shape enhance dispersibility and reduce the risk of aggregation, further improving biocompatibility and efficacy in biomedical contexts. Additionally, the EDS data and mapping analysis confirm the presence of the main structural elements in the samples, as well as their uniform distribution. Moreover, the range of atomic percentages in each sample is consistent with the reported sources, and the ratios in the synthesized samples are deemed acceptable^77,78.

Fig. 3. Morphological and elemental characterization of MIL-125(Ti) samples.

A,B MIL-125-6h, C,D MIL-125-12h, E,F MIL-125-18h, G,H MIL-125-24h: FESEM images and EDS results of the synthesized materials, respectively. Additionally, mapping analyses are shown in figures I–L for MIL-125-6h, MIL-125-12h, MIL-125-18h, and MIL-125-24h, respectively. Elemental maps labeled “K” correspond to X-ray emission from K-shell electron transitions (primarily the Kα line) detected by EDS. K-series lines provide strong, well-resolved signals for reliable mapping of mid-Z elements.

The progressive morphological transformation of MIL-125(Ti) with synthesis time, as revealed through surface height histograms, is deeply embedded in the mathematical nature of the fitting functions, each encoding distinct physical regimes of growth, surface energy distribution, and crystallinity. The transition from Boltzmann to Gaussian to Lorentzian and back to Gaussian represents not only changes in statistical morphology but also encapsulates a dynamic shift in the dominant physical forces and chemical kinetics during crystal formation. At 6 h, the Boltzmann bent step function^79,80 approximates a sigmoidal curve, where x₀ is surface height, x₀ (previously denoted as h₀) is the inflection point, w (corresponding to Δh) represents the characteristic slope width, and A is the amplitude (Figs. 4 and 5). This model captures the existence of a transitional boundary between low and high height populations, typically indicative of incomplete nucleation and/or aggregation. Physically, this corresponds to a system far from equilibrium, where the free energy landscape is rugged, and heterogeneous nucleation sites dominate⁸¹. The surface is governed by stochastic growth kinetics, with low activation barriers and high configurational entropy. In this regime, coordination between titanium centers and organic ligands is partial, and the rate of monomer addition is highly variable. Such surfaces are dominated by high surface energy zones and lack coherent long-range order, which is reflected in the wide range of curvature radii observed across the height domain.

Fig. 4. 2D and 3D FESEM morphological analysis of MIL-125(Ti) samples.

FESEM images restructured (both 2D and 3D) by using ImageJ software, for MIL-125-6h, MIL-125-12h, MIL-125-18h, and MIL-125-24h. To minimize analysis error, images were taken using a consistent scale. Additionally, both 2D and 3D images were selected from relatively particle-saturated areas, uniformly chosen within a 5 × 5 µ dimension.

Fig. 5. Mathematical fitting of morphological height distributions in MIL-125(Ti) samples.

Mathematical function fitting was performed on 5 × 5 µm² locked FESEM images of the four synthesized samples using Gwyddion software. The height distribution was analyzed using three applied models: the Boltzmann bent step function (f(x) = y₀ + (h/2)tanh(ξ/w) + αξ + βξ², ξ = x − x₀), the Gaussian function (f(x) = y₀ + a·exp [−(x − x₀)²/b²]), and the Lorentzian function (f(x) = y₀ + a/[b² + (x − x₀)²]. The fitted functions for each sample are also illustrated in the corresponding figures. Height histogram analysis was performed using calibrated FESEM images processed through ImageJ software for height extraction and Gwyddion software for statistical fitting. The methodology provides quantitative validation of morphological transitions with precision comparable to traditional profilometry techniques.

At 12 h, the emergence of a Gaussian height distribution^82,83, suggests the minimization of local free energy and the onset of a quasi-equilibrium regime, where particle growth is more uniform and thermodynamically driven. Here, x₀ (corresponding to μ) denotes the mean height, and b (related to σ by b ≈ √2σ) is the width parameter corresponding to the surface roughness root-mean-square (RMS) value^84,85. In physical terms, lower σ implies reduced variance in growth rates across nucleation and/or aggregation sites, indicating improved synchronization in crystal face development. The isotropic nature of this distribution is critical: it reflects a phase space where the chemical potential of the building blocks is spatially homogeneous, leading to symmetric crystal facets and coherent domain alignment. These conditions are known to maximize surface packing density, reduce fractal dimension, and facilitate anisotropic diffusion of small molecules—ideal for achieving controlled diffusion kinetics in drug delivery.

The transition to a Lorentzian profile^86,87 at 18 h is mathematically characterized, where x₀ denotes the peak position, and b (corresponding to γ) represents the half-width at half-maximum (HWHM). Unlike the Gaussian, the Lorentzian has heavier tails, implying a higher probability of extreme height deviations. Physically, this reflects an increase in long-range height correlations and a dominance of specific crystallographic planes or facets that grow faster than others. The power-law behavior in the tails suggests a surface morphology shaped by self-similar growth mechanisms, possibly involving screw dislocation propagation or kinetic roughening phenomena. This behavior is typical of systems near critical points, where fluctuations become scale-invariant. Such surfaces often exhibit enhanced surface fractality and higher Hausdorff dimension^88,89, promoting heterogeneous interactions with biomolecules—an advantage in systems requiring multiplexed cargo loading or hierarchical release patterns. Notably, Lorentzian morphology implies a non-zero kurtosis excess, mathematically quantified, where μ₄ is the fourth central moment of the distribution. High kurtosis reflects heavy-tailed distributions and localized sharp features on the surface, which can serve as energy-focusing points during cell membrane penetration or endosomal escape. Moreover, surface structures described by Lorentzian statistics are associated with non-Markovian surface energy fluctuations, where the temporal correlation in local growth events leads to clustered defect formation—potentially exploitable in stimuli-responsive release applications. By 24 h, the system re-stabilizes into a narrow Gaussian profile with reduced σ, indicating completion of the coordination-driven self-assembly process. This mature phase is characterized by the emergence of a global minimum in the Gibbs free energy surface, where ligand orientation, coordination number, and metal-ligand bond angles reach an optimal configuration. At this stage, surface strain is minimized, and lattice periodicity becomes dominant. The spatial correlation function of height fluctuations, exhibits exponential decay, a hallmark of smooth, well-ordered topographies. In this regime, parameters, such as autocorrelation length and spectral density become relevant for predicting adsorption behavior of therapeutic payloads.

Importantly, this evolution can be viewed through the lens of dynamic scaling theory, where w is the surface width (RMS roughness), L is system size, t is time, α α is the roughness exponent, and z is the dynamic exponent. The transition from Boltzmann to Gaussian to Lorentzian and back reflects a crossover in the governing exponents, signifying changes in the universality class of the underlying growth process—from random deposition (α ≈ 0.5, z ≈ 2.0) to Edwards-Wilkinson-type kinetics and eventually to Kardar-Parisi-Zhang-type behavior in the Lorentzian regime (α ≈ 0.8, z ≈ 1.6)^90–93. These critical exponents provide a deeper theoretical basis for predicting how synthesis conditions influence final surface morphology and, by extension, therapeutic efficacy. Finally, the mathematical nature of the height distributions is directly linked to the surface’s topological entropy and information content. Surfaces with Gaussian height distributions have low entropy and are easily parameterized, while Lorentzian surfaces possess higher entropy, reflecting greater structural diversity and complexity. From a systems design perspective, higher entropy may correlate with more robust performance under varying physiological conditions, making them advantageous for in vivo delivery of sensitive biomolecules, such as CRISPR/Cas complexes or siRNAs. Conversely, the deterministic regularity of Gaussian surfaces is ideal for applications requiring high fidelity, such as single-molecule sensing or targeted release in microfluidic environments. Overall, the synthesis time-dependent evolution of MIL-125(Ti)’s surface morphology can be rigorously described through a fusion of statistical mechanics, surface physics, and reaction kinetics, each embodied in the fitting equations used to model the height distributions. These mathematical models serve not only as descriptors but as predictive tools for tuning MOF surface properties for specialized biomedical functions.

The mathematical foundation for statistical function selection in morphological analysis is based on established principles of statistical mechanics and surface physics. Each function type represents probability distributions that naturally emerge from specific physical regimes during crystal growth and aggregation processes. The Boltzmann function describes transitional systems between discrete energy states, arising from the statistical mechanical principle P(E) ∝ e ^(-E/kBT), where surface regions probabilistically switch between growth and dormant states. Gaussian distributions emerge when multiple independent random processes contribute to surface variations, following the central limit theorem where individual molecular addition events sum to create normal height distributions. Lorentzian profiles characterize critical phenomena with scale-invariant growth, exhibiting heavy tails that follow power-law decay P(h) ∝ h^-2, indicating long-range correlations and fractal-like surface structures. Parameter fitting was performed using least-squares regression with comprehensive statistical evaluation including coefficient of determination (R²), reduced chi-squared (χ²_red), and Akaike Information Criterion (AIC) for objective model comparison. The fitting procedure involved: (1) height histogram extraction from calibrated FESEM images, (2) distribution normalization for statistical comparison, (3) iterative non-linear fitting using Levenberg-Marquardt algorithm, and (4) uncertainty estimation for fitted parameters. Comparative analysis revealed optimal function selection based on synthesis time: Boltzmann functions for 6-hour samples (R² = 0.94 ± 0.02), Gaussian functions for 12 and 24 h samples (R² = 0.97 ± 0.01), and Lorentzian profiles for 18-hour morphology (R² = 0.92 ± 0.03). The parameter evolution provides quantitative metrics for synthesis optimization, with Gaussian standard deviation decreasing from 2.1 nm (12 h) to 1.8 nm (24 h), demonstrating progressive surface smoothing and enabling rational material design through mathematical modeling.

The physical interpretation of fitting parameters provides direct insights into synthesis mechanisms and material properties. The Boltzmann inflection point (x₀) corresponds to the critical height threshold for sustained crystal growth, while the slope width (w) quantifies the sharpness of nucleation and/or aggregation transitions. For Gaussian distributions, the width parameter (b, related to σ by b ≈ √2σ) directly measures surface roughness and growth uniformity, with smaller values indicating more controlled synthesis conditions. Lorentzian half-width at half-maximum (b, corresponding to γ) parameters correlate with surface feature correlation lengths, providing quantitative measures of structural coherence. These mathematical descriptors enable predictive modeling of material properties and rational optimization of synthesis conditions for specific applications.

The dynamic light scattering (DLS) results for the four synthesized materials, analyzed using the Cumulants method, are presented in Table 5. Additionally, the intensity, number, and volume distribution graphs are shown in Supplementary Fig. 5. According to the data, the polydispersity index (PDI) for the MIL-125-12h sample is significantly lower than that of the other samples. This notable difference is evident in Fig. 6. The comparison of the hydrodynamic size obtained from DLS using the cumulant method with FESEM images indicates significant aggregation of the MIL-125-24h sample in the aqueous solvent. The influence of larger particles is more apparent in the intensity-based distribution peaks⁹⁴. Furthermore, the volume-based distribution can provide a more accurate estimation of the particle size distribution function⁹⁵. As seen in Supplementary Fig. 5, a well-defined distribution based on intensity, number, and volume is observed for MIL-125-12h, which is noteworthy. Considering the more complex distributions of the samples, the Laplace and SBL results offer complementary insights into the particle size behavior⁹⁶. These models, similar to the Cumulant analysis, also reveal a larger number-based distribution for MIL-125-18h, which is consistent with the FESEM images. Additionally, similar trends in size distribution based on volume and intensity are observed for MIL-125-6h, MIL-125-12h, and MIL-125-24h. The correlation between particle uniformity (low PDI) and colloidal stability has significant implications for drug delivery consistency, with MIL-125-12h representing an optimal balance of material performance and formulation stability for pharmaceutical applications.

Table 5.

DLS data including Z-average size and PDI of the synthesized MOFs

Parameters	MIL-125-6h	MIL-125-12h	MIL-125-18h	MIL-125-24h
PDI	0.545	0.041	0.264	0.712
Z avarage (nm)	587.02	468.25	743	479.89

Fig. 6. Dispersion behavior of MIL-125(Ti) samples in water.

Images of four MIL-125(Ti) samples dispersed in deionized water, 4 h after sonication in a water bath.

Understanding the interaction between nanomaterials and biological systems is essential for advancing safe and effective biomedical technologies^97–99. Among various nanomaterials, MOFs have attracted increasing interest for their tunable physicochemical properties, large surface area, and potential for drug delivery, imaging, and biosensing applications. Assessing the biocompatibility and cytotoxicity of these materials is a critical step in ensuring their suitability for clinical translation^100,101. In this context, MIL-125(Ti) MOFs, known for their structural versatility, offer a compelling platform for exploring structure–activity relationships in biomedical environments. The MTT assay results provide crucial insights into the cellular toxicity and biocompatibility of MIL-125(Ti) MOFs, particularly when considering their potential applications in drug delivery (Fig. 7). In this study, two different structures of MIL-125(Ti), synthesized over 6 h (amorphous structure) and 24 h (crystalline structure), were evaluated for their impact on cell viability in the MCF-7 breast cancer cell line after 24 h of treatment. The observed differences in cell viability between these two structures highlight important considerations regarding their suitability for biomedical applications. The amorphous structure of MIL-125(Ti) synthesized over 6 h exhibited lower cell viability in the MTT assay compared to its crystalline counterpart. This reduced cell viability can be attributed to several factors inherent to the amorphous nature of the material. Amorphous materials generally possess a higher density of surface defects and active sites due to their lack of long-range order. These sites can interact more readily with cellular components, potentially leading to increased production of reactive oxygen species (ROS) and subsequent oxidative stress within cells. This increased reactivity can compromise cell membrane integrity and overall cell health, resulting in lower cell viability. The FESEM images indicated that the amorphous MIL-125-6h particles have a rough and irregular surface morphology, which can contribute to higher levels of aggregation in biological media. Aggregated particles may induce greater physical disruption to cells and provoke a more pronounced inflammatory response, both of which can contribute to cytotoxic effects and reduced cell viability. The amorphous structure is inherently less stable than its crystalline counterpart, which may lead to faster degradation and release of potentially toxic metal ions from the MOF framework. This degradation can exacerbate cytotoxicity, further compromising cell viability.

Fig. 7. Cytotoxicity of MIL-125(Ti) samples on MCF-7 cells.

MTT assay results for the amorphous structure of MIL-125-6h and the crystalline structure of MIL-125-24h on MCF-7 cells after 24 hours of treatment. Data are presented as Mean ± SD, where SD represents the variation across the three tested concentrations (MIL-125-6h: 54.33 ± 6.46; MIL-125-24h: 84.57 ± 14.27). Analysis was performed using Prism software.

In contrast, the crystalline structure of MIL-125(Ti) synthesized over 24 h demonstrated better cell viability in the MTT assay, suggesting superior biocompatibility. Several factors contribute to the improved performance of the crystalline structure. The highly ordered crystalline structure of MIL-125-24h provides greater stability, reducing the likelihood of rapid degradation and the release of toxic metal ions. This stability helps maintain the integrity of the MOF and minimizes adverse interactions with cellular components. Crystalline structures typically have fewer surface defects and active sites compared to amorphous structures. This reduction in surface reactivity decreases the generation of ROS and minimizes oxidative stress on cells, thereby enhancing cell viability. The FESEM images revealed that MIL-125-24h has well-defined crystal facets and a more uniform particle size. This uniformity reduces the tendency of particles to aggregate, leading to more predictable and less disruptive interactions with cells. The reduced aggregation also lowers the likelihood of provoking inflammatory responses, contributing to higher cell viability. Although not directly measured in this assay, the high crystallinity and controlled pore size distribution of MIL-125-24h can facilitate a more controlled and sustained release of therapeutic agents. This controlled release can enhance therapeutic efficacy while minimizing cytotoxic effects, further supporting better cell viability.

The MTT assay results underscore the importance of optimizing the structural properties of MOFs for biomedical applications. The better cell viability observed with the crystalline structure of MIL-125-24h highlights its potential as a more biocompatible and stable platform for drug delivery. The stability and reduced reactivity of the crystalline MOF make it a safer choice for in vivo applications, where minimizing cytotoxicity is crucial. In drug delivery, particularly for treatments involving sensitive biological systems^102,103, the choice of MOF structure can significantly impact therapeutic outcomes. The crystalline MIL-125-24h provides a promising candidate due to its high surface area, controlled pore size, and excellent biocompatibility. These properties ensure efficient drug loading, sustained release, and minimal adverse effects on healthy cells, making it ideal for applications, such as DOX and CRISPR-Cas9 delivery. Conversely, the amorphous MIL-125-6h structure, while potentially beneficial for certain applications due to its broader pore size distribution, requires careful consideration of its cytotoxic effects. Strategies to mitigate these effects could include surface modifications or the incorporation of stabilizing agents to enhance its biocompatibility. Furthermore, in predicting the development of understanding and correlating structural features with cell viability, the interplay of morphology on the toxicity toward normal or cancerous cells can be more effectively analyzed, enabling a more efficient design of systems.

Conclusion

This study underscores the importance of sustainable material design in the advancement of biomedical applications, particularly in drug and gene delivery. By focusing on MIL-125(Ti), we have expected that a lower surface area and aggregated semi-sphere morphology can achieve highly efficient molecular loading and release, challenging the conventional emphasis on high surface areas. Our concept of “sustainable pore size” offers a novel approach to enhancing material performance while reducing energy consumption, aligning with the principles of sustainable chemistry. MIL-125(Ti) synthesized over 24 h exhibited the highest surface area, pore volume, and crystallinity, making it the most suitable for high drug loading and sustained release, particularly for applications involving small to medium-sized molecules like doxorubicin and CRISPR components. In contrast, shorter synthesis durations produced materials with varying pore sizes and surface areas, offering different release profiles that may be advantageous for specific therapeutic needs. Notably, the 6 h and 12 h variants, with larger pores, may be more appropriate for rapid drug release applications. The evolution of MIL-125(Ti) surface morphology during synthesis can be quantitatively characterized by integrating statistical mechanics, surface physics, and reaction kinetics into height distribution models. These models provide valuable quantitative parameters for system design, though they require a deeper understanding of the underlying physicochemical properties. Additionally, we demonstrated that MIL-125-12h, with its superior crystallinity compared to MIL-125-6h and MIL-125-18h, represents a transition state for MIL in the synthesis pathway, characterized by high dispersibility in water. The study also highlights the potential of semi-amorphous and amorphous MOFs in biomedical applications, emphasizing the need for tailored synthesis conditions to balance crystallinity, pore structure, and surface area. The findings suggest that while crystalline structures provide predictable frameworks for drug delivery, amorphous structures offer flexibility and a broader range of pore sizes, which can be beneficial in certain contexts. This work presents a significant step forward in sustainable material science, offering new perspectives on the design of MOFs for biomedical applications. By optimizing synthesis parameters and embracing the concept of sustainable pore size, we can develop materials that not only meet the functional demands of drug delivery systems but also adhere to the principles of green chemistry. Future research should explore the scalability of these synthesis methods and further refine the balance between material performance and environmental impact. For industrial scale-up and commercial applications, MIL-125-12h represents the optimal balance between performance, sustainability, and economic viability, providing a practical pathway for widespread adoption of sustainable MOF synthesis in biomedical manufacturing.

Materials and methods

Synthesis of MIL-125(Ti)

There are numerous studies in the literature regarding the synthesis of MIL-125(Ti)^104,105. However, we have modified the existing method to focus on performance and sustainability. Briefly, we dissolved the BDC linker (5.3 mmol) in DMF (12.5 mL) and stirred the mixture in a round-bottom flask at a lower temperature (as per literature) for less than 1 h. Next, methanol (3.5 mL) was added to the homogenized solution, which was then stirred for an additional hour under reduced temperature reflux conditions. Subsequently, Ti(BuO)₄ (1.05 mL) was introduced into the solution, and this new phase was allowed to react for 6, 12, 18, and 24 h in a glass autoclave system at approximately 110 °C. After the reaction, the product was cooled to room temperature, washed five times with methanol, and then dried in an oven at 80 °C for 24 h.

Preparation sample for N₂ adsorption & desorption and DLS analyses

A quantity of 100 mg of each synthesized material was placed in a vacuum oven at 80 °C for 24 h. After drying, the samples were transferred to the analyzer, where their N₂ adsorption was measured using an analysis bath at a temperature of approximately -196.9 °C. The resulting isotherm data were then obtained from the measurements. For the DLS test, 2 mg of each material was added to 1 mL of deionized (DI) water and subjected to probe ultrasonication for 15 min at a power of 50 W in a pulsed mode (3 s on, 3 s off). After sonication, the samples were left undisturbed for 3 h, and the supernatant solution was collected for the DLS analysis.

MTT assay

MCF-7 human breast carcinoma cells (obtained from the Pasteur Cell Line Bank, Tehran, Iran) were cultured in Dulbecco’s Modified Eagle Medium (DMEM; Gibco) supplemented with 10% fetal bovine serum (FBS; Gibco) and 100 IU ml^-1 penicillin–streptomycin (Invitrogen) at 37 °C in a humidified 5% CO₂ incubator. The cells were used as supplied, following institutional biosafety and ethical guidelines. Cytotoxicity of the synthesized MIL-125(Ti) samples was evaluated using the MTT assay (3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazolium bromide). MIL-125-6h and MIL-125-24h, representing the amorphous and crystalline structures, respectively, were tested at concentrations of 0.5, 0.75 and 1 μg ml^-1. Cells were seeded in 96-well plates at a density of 1 × 10⁵ cells per well and incubated for 24 h before treatment. After 24 h exposure to the nanomaterials, 100 μl of MTT solution (5 mg ml⁻¹ in PBS) was added to each well and incubated for 3 h. The medium was then replaced with absolute DMSO to dissolve the formazan crystals, and absorbance was measured to quantify cell viability.

Materials characterizations

To evaluate the sustainable performance of the synthesized MIL-125(Ti) variants, the materials were characterized using FTIR, XRD, BET, and FESEM. XRD measurements were employed to investigate the crystalline structures using a Bruker D8 instrument with Cu Kα radiation (1.54 Å at 40 kV, 40 mA). For consistency and comparability, each MOF sample was pressed with uniform pressure onto a glass slide to create a semi-homogeneous surface for XRD measurements. To analyze surface chemical compositions and functional groups, FTIR spectra were recorded using a Bruker Optics Tensor-27 device, after preparing KBr pellets and recording the background. Additionally, a MicroActive for TriStar II Plus 2.03 instrument was used to analyze the BET surface area, along with other data related to pore structure and isotherms. DLS data were recorded using a Cordouan Tech VASCO2 device. The MTT results were obtained by reading the plates at 570 nm using an ELISA reader, ELX808 BioTek. The energy efficiency of our synthesis approach was evaluated by monitoring temperature, time, and solvent consumption compared to conventional methods. Energy calculations were based on heating requirements, reaction duration, and auxiliary equipment operation, demonstrating significant reductions in overall energy demand while maintaining material performance suitable for biomedical applications.

Author contributions

H.D. conceived and designed the study, administered the project, developed the methodology, performed the investigation, curated the data, visualized the results, and wrote the original draft. M.B. supervised the project and contributed to writing – review & editing. S.S. curated data and contributed to writing – original draft and review & editing. N.R. conceived and designed the study, administered the project, developed the methodology, performed the investigation, curated the data, visualized the results, and wrote the original draft.

Peer review

Peer review information

Communications Chemistry thanks Shang-Hsiu Hu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Data availability

All Supplementary Figs. for this study are provided in the accompanying Supplementary Information file. Additional datasets generated and analyzed during this work, including XRD, FTIR, BET, FESEM, and DLS data, can be requested from the corresponding author by emailing [bagherzadeh@sharif.edu].

competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s42004-025-01845-z.