Utilizing the allyl-terminated copolymer methoxy(poly(ethylene glycol))-block- poly(jasmine lactone) in the development of amorphous solid dispersions A comparative study of functionalized and non-functionalized polymer

Molecular interactions are crucial to stabilize amorphous drugs in amorphous solid dispersions (ASDs). Most polymers, however, have only a limited ability to form strong molecular interactions with drugs. Polymers tailored to fit the physicochemical properties of the drug molecule to be incorporated, for instance by allowing the incorporation of specific functional groups, would be highly sought-for in this regard. For this purpose, the novel allyl-terminated polymer methoxy(polyethylene glycol)- block-poly(jasmine lactone) (mPEG-b -PJL) has been synthesized and functionalized to potentially enhance specific drug-polymer interactions. This study investigated the use of mPEG-b -PJL in ASDs, using carvedilol (CAR), a weakly basic model drug. The findings revealed that the acidic functionalized form of the polymer (mPEG-b -PJL-COOH) indeed established stronger molecular interactions with CAR compared to its non-functionalized counterpart mPEG-b -PJL. Evaluations on polymer effectiveness in forming ASDs demonstrated that mPEG-b -PJL-COOH outperformed its non-functionalized counterpart in miscibility, drug loading ability, and stability, inferred from reduced molecular mobility. However, dissolution tests indicated that ASDs with mPEG-b -PJL-COOH did not significantly improve the dissolution behaviour compared to amorphous CAR alone, despite potential solubility enhancement through micelle formation. Overall, this study confirms the potential of functionalized polymers in ASD formulations, while the challenge of improving dissolution performance in these ASDs remains an area of further development.


Introduction
Overcoming the low solubility of poorly water-soluble drugs is a key challenge in pharmaceutical development.One of the well-recognized solutions is utilizing the amorphous form of the drug, which possesses higher energy and higher apparent water solubility compared to its crystalline form (Hancock and Zografi, 1997).However, the higher free energy of the amorphous form also increases recrystallization risks during formulation or storage (Laitinen et al., 2013).To overcome this, polymeric materials are used to create amorphous solid dispersions (ASDs) to stabilize an amorphous form of the drug (Chiou and Riegelman, 1971;Iyer et al., 2021;Janssens and Van den Mooter, 2009;Shah et al., 2014;Van den Mooter, 2012).The stabilization mechanism of ASDs largely relies on kinetically reducing the mobility of the amorphous drug, achieved through the anti-plasticizing effect of the polymer, and the formation of drug-polymer molecular interactions (Yu, 2001).Molecular interactions between drug and polymer are crucial for an enhanced stability as they inhibit phase separation and recrystallization in ASDs (Frank and Matzger, 2018;Matsumoto and Zografi, 1999).Enhanced molecular interactions in ASDs may lead to improved miscibility (Chan et al., 2015), higher drug loading ability (Alshahrani et al., 2015), and sustained drug supersaturation during dissolution (Taokaew et al., 2020), thereby potentially enhancing the overall efficacy of ASD formulations.Most existing ASDs focus on systems that form hydrogen bonds (Anderson, 2018;Baghel et al., 2016).Considering that ionic bonds are generally stronger than hydrogen bonds, polymers capable of forming ionic bonds with the drug could offer prolonged stabilization.Functional polymers, which have free functional groups on their backbone or side chains, can potentially form ionic bonds with drugs (Weuts et al., 2005).However, only a few acidic functional polymers are on the market, e.g.poly(glutamic acid) (Huang et al., 2023), poly(acrylic acid) (Gui et al., 2021), hydroxypropyl methylcellulose acetate succinate (Bapat et al., 2024), hydroxypropyl methylcellulose phthalate (Van Duong et al., 2022), and methacrylic copolymers (known by the commercial name Eudragit®L100/S 100/L100-55) (Patra et al., 2017).Applications of these polymers in ASDs are limited due to their insufficient acidic functionality, which might not effectively protonate weakly basic drugs (Song, 2015).
The novel block copolymer methoxy(polyethylene glycol)-block-poly (jasmine lactone) (mPEG-b-PJL) is introduced as a promising polymer in this context.This allyl-terminated functional polymer has the potential to incorporate specific functional groups of interest, via addition to its unsaturated hydrocarbons (allyl groups) (Bansal et al., 2021;Rahman et al., 2022).The polymer was first synthesized by Bansal et al. in 2021 via a facile, highly controllable, and well-established ring-opening polymerization methodology using the renewable food additive jasmine lactone as a starting material (Bansal et al., 2021).The postpolymerization functionalization of this polymer was achieved using simple, solvent-free UV-mediated thiol-ene click chemistry.The introduction of hydroxyl, carboxyl, and amine functionality to mPEG-b-PJL has been successfully established with a highly efficient conversion rate, especially for hydroxyl and carboxyl groups.mPEG-b-PJL is a semicrystalline polymer, possessing both crystalline and amorphous domains.The crystalline domain stems from the mPEG part of the polymer, resulting in a distinct melting behaviour at around 50 • C, which is considerably lower than the glass transition temperature (T g ) of most amorphous polymers (Bertoni et al., 2023;Van Duong and Van den Mooter, 2016).This characteristic makes mPEG-b-PJL a promising candidate for solvent-free manufacturing technologies with low processing temperatures, offering potential economic, energetic, and environmental benefits.Despite the numerous benefits, the use of semicrystalline polymers in ASDs is limited by their physical instability, primarily due to the low T g (− 17 to − 53 • C for PEG with different molecular weights) (Baird and Taylor, 2011).This highlights the importance of semi-crystalline polymers to form strong drug-polymer interactions, to impact the performance of the resulting ASDs (Zhu et al., 2012).Moreover, mPEG-b-PJL is amphiphilic and it has been demonstrated to self-assemble into micelles in solution (Ali et al., 2022;Bansal et al., 2021).Micelles formed with carboxylic acid terminated mPEG-b-PJL (mPEG-b-PJL-COOH) showed a remarkable enhancement in the water solubility of clotrimazole, 334 times higher than that achieved with Soluplus®-based micelles (Bansal et al., 2023a).Moreover, research on the potential commercial use of this polymer is ongoing (Bansal et al., 2023b).However, there remains a gap in understanding the impact of using these polymers in ASDs, particularly in terms of drug-polymer molecular interactions and their ability to form ASDs and with respect to the in vitro performance of the resulting ASDs.
This study explored the application of mPEG-b-PJL in ASD formulations, using carvedilol (CAR) as the model drug.The acidfunctionalized polymer, mPEG-b-PJL-COOH, was synthesized to enhance molecular interactions within the ASDs, according to the basic nature of CAR.Non-functionalized mPEG-b-PJL was used for comparison.The initial step involved assessing whether mPEG-b-PJL-COOH could form stronger molecular interactions with CAR than its nonfunctionalized counterpart, using thermal analysis, solid-state nuclear magnetic resonance (ssNMR), and Fourier transform infrared spectroscopy (FTIR) combined with principal component analysis (PCA).The study also evaluated drug-polymer miscibility and drug loading ability and assessed the stability of the resulting ASDs by examining molecular mobility.Dissolution tests were also carried out on the ASDs formulated with both the mPEG-b-PJL-COOH and the non-functionalized mPEG-b-PJL.

Sample preparation
Physical mixtures (PMs) of CAR -mPEG-b-PJL or CAR -mPEG-b-PJL-COOH with crystalline CAR at different ratios (w/w) were prepared by mixing (total weight of the mixtures: 500 mg) using a mortar and pestle.The respective ASDs were prepared by quench-cooling of the PMs.The samples were placed on an aluminum foil over a preheated hot plate (140 C) until complete melting was visually observed.Subsequently, the molten samples were cooled by placing the foil (with molten samples on top) on a stainless-steel block (stored at around − C).Additionally, pure amorphous CAR was prepared by the same method.

Investigation of molecular interactions -Mid-range Fourier transform infrared spectroscopy (FTIR) and principal component analysis (PCA)
FTIR spectra were collected with a mid-range FTIR Spectrometer MB3000 (ABB, Zürich, Switzerland) coupled with a MIRacle™ single reflection attenuated total reflection (ATR) system (PIKE Technologies, Fitchburg, WI, USA) equipped with a diamond lens.Dry nitrogen gas flow was used to constantly purge the ATR unit to avoid interference from water vapour and carbon dioxide.Data were collected using the Horizon MB™ FTIR software (Version 3.2.5.2,ABB, Zurich, Switzerland).Each spectrum was measured as the mean of 64 scans at a wavenumber range from 4000 to 600 cm − 1 with a resolution of 4 cm − 1 .The spectral ranges of 1000-1800 cm − 1 and 3300--3400 cm − 1 were selected for additional analysis of CAR -mPEG-b-PJL samples to observe the potential formation of hydrogen bonds.For CAR -mPEG-b-PJL-COOH samples, the ranges of 1300-1800 cm − 1 and 3300-3400 cm − were chosen to observe the potential formation of ionic bonds.The selected regions were normalized with standard normal variate transformation and subsequently subjected to PCA using Simca 18 software (Version 18.0.0.372,Sartorius,Göttingen,Germany).
Theoretical spectra for CAR-polymer PMs and ASDs at various mixing ratios, were calculated by combining the FTIR spectra of the individual components.No drug-polymer molecular interactions are reflected in the calculated PMs and ASDs spectra (C-PMs and C-ASDs).Therefore, the molecular interaction between CAR and polymer can be observed by comparing C-PMs and C-ASDs with the measured PMs and ASDs spectra.
-Solid-state nuclear magnetic resonance (ssNMR) Magic angle spinning (MAS) 13 C NMR spectra were obtained with a Bruker AVANCE-III NMR system, operating at 100.6 MHz for 13 C, equipped with a Bruker 4 mm cross-polarization MAS probe in doubleresonance mode tuned to 1 H and 13 C frequencies.All experiments were conducted at 298 K with a MAS frequency of 10 kHz, and samples were packed in 4.0 mm rotors.Data acquisition and processing were performed using Bruker TopSpin software (Version 4.3.0,Billerica, Massachusetts, United States) and MestReNova software (Version 6.0.2,Santiago de Compostela, Spain), respectively.

Thermal analysis − differential scanning calorimetry (DSC)
The thermal behaviour of CAR-polymer PMs with various mixing ratios was investigated by using a Discovery DSC (TA instruments, New Castle, DE, USA) with a constant nitrogen gas flow (50 mL/min).Data acquisition and analysis were performed using Trios software (version 5.1.1,TA Instruments, New Castle, DE, USA).Samples (2-5 mg) were loaded into hermetically sealed aluminum pans.The temperature was increased from − 20 C to 130 C at a rate of 10 C/min to observe the thermal behaviour.The melting behaviour of CAR-polymer PMs with various mixing ratios was used to evaluate drug-polymer miscibility and solubility.After observing the melting behaviour, the samples were equilibrated at − 70 C.Following this, the samples were reheated to 130 C at a rate of 10 C/min, and the T g s were determined from the heat capacity step change in the second heating process.The T g values were used to evaluate the molecular interactions using the Gordon -Taylor (G-T) equation and for the construction of the temperature-composition diagrams.All measurements were performed in independent triplicates.
Enthalpy relaxation, as a function of aging time, was assessed for amorphous CAR, 50 % CAR -mPEG-b-PJL ASD, and 50 % CAR -mPEGb-PJL-COOH ASD.The samples were prepared by quench-cooling in the DSC as follows: samples were heated at a rate of 10 C/min to 130 C, cooled at maximal cooling rate and then equilibrated at − 70 C. Subsequently, the prepared samples underwent annealing at a temperature 10 C below their respective T g for 1, 2, 4, 8, and 16 h.The samples were then reheated to 40 C at a rate of 2 C/min with a sinusoidal modulation (amplitude of 0.212 C and period of 40 s).The relaxation enthalpy was determined from the area under the curve of the endothermic peak in the non-reversing flow at the T g during reheating.The enthalpy relaxation behaviour observed with DSC was used in the molecular mobility investigation, as described in Theoretical methods section 3.2.4.The instrument was calibrated using indium.The obtained enthalpy relaxation behaviour was used for molecular mobility evaluation.

Solid state characterization − x-ray powder diffraction (XRPD)
The solid state of the samples was investigated with an X'Pert PRO diffractometer (PANalytical, Almelo, The Netherlands), equipped with a copper anode (Cu Kα radiation, λ = 1.54187Å).The generator voltage was 45 kV, and the tube current was 40 mA.Samples were scanned from 5 ˚to 35 ˚2θ in reflection mode, at a scan rate of 0.067 ˚2θ/s and a step size of 0.026 ˚2θ.A Bragg-Brentano parafocusing geometry was used.XRPD data was collected and analyzed using X'Pert Data Collector and X'Pert Highscore Plus software (version 2.2.4,PANalytical, Almelo, The Netherlands), respectively.

Physical stability test
The stability test was conducted under dry conditions (0 % relative humidity using phosphorus pentoxide) at room temperature (around C).Samples were regularly measured using XRPD (weekly for the first month, and every two weeks thereafter) until recrystallization was detected.

In vitro drug release -Dissolution test
The dissolution profiles of the samples were measured using a μ-Diss Profiler (Pion Inc., Billerica, MA, USA).Samples containing 1 mg of CAR were added to each vial containing 10 mL of 0.1 M phosphate buffer (pH 7.2, 37 C) and a cross-shaped magnetic stirring bar (at a stirring rate of 100 ± 3 rpm).A pH value of 7.2 was chosen to keep consistency with previous related studies on co-amorphous systems (Liu et al., 2020a).Ultraviolet probes, with a 5 mm path length, were inserted in each vial to detect the in situ absorbance of dissolved CAR for 24 h at the wavelength range of 200 to 700 nm, and each probe was calibrated before the dissolution experiments.Second derivative pre-processing was applied on the whole spectra (200 to 700 nm) to remove the influence of the baseline.Absorbance at the range of 278 to 289 nm was used for concentration determination.In all cases, the dissolution profiles are presented as an average of three independent replicates.All data were  obtained and processed by using Au PRO software (Version 5.5.2.3974, Pion Inc., Billerica, MA, USA).

Evaluation of molecular interactions -Calculation of theoretical T g using Gordon -Taylor (G-T) equation
The theoretical T g s of homogenous binary mixtures without molecular interactions can be estimated by using the G-T equation (Equation (1) (Gordon and Taylor, 1952), coupled with the Simha-Boyer rule (Equation (2) (Simha and Boyer, 1962).Deviations of experimental T g s from the theoretical T g s can suggest phase separation, molecular interactions, or the presence of a plasticizer (Hancock and Zografi, 1994).This approach has been widely utilized in various studies to evaluate molecular interactions within binary systems (Di et al., 2021;Liu et al., 2020b;Xu et al., 2023).
Where ω is the mass fraction and subscripts 1 and 2 represent the amorphous drug and polymer, respectively.K is a constant and can be estimated as follows: Where ρ is the density of the amorphous components.The density of the crystalline CAR and polymer is used in this experiment, as the density of the amorphous polymer cannot be determined due to fast recrystallization.For CAR, as a small molecule material, using the crystalline density as an approximation has been proven to be valid (Hancock et al., 2002).

Evaluation of miscibility -Calculation of Flory-Huggins (F-H) interaction parameter χ
A lattice-based, statistical mechanics prediction model was introduced by Flory and Huggins, where drug-polymer miscibility can be linked to the interaction parameter χ (Flory, 1942;Huggins, 1941).The interaction parameter χ can be calculated using Equation (3) by investigating the drug melting point depression behaviour with DSC (Baird and Taylor, 2012;Marsac et al., 2006).
Where, T Mix m and T drug m are the T m of the drug with and without the carrier, respectively, R is the gas constant (R = 8.314 J K − 1 mol − 1 ), ΔH fus is the heat of fusion of the pure drug, m is the molecular volume fraction of the carrier to the drug, and ϕ drug and ϕ polymer are the molecular volume fractions of the drug and the polymer, respectively, in the binary mixtures.
To obtain the interaction parameter χ, the equation can be rearranged to Equation (4).
By plotting a graph with ϕ polymer as yaxis and ϕ polymer 2 as x-axis, the interaction parameter χ can be determined as the slope value.

Evaluation of drug loading ability
-Construction of temperature-composition diagrams − Temperature-composition diagrams are useful to guide the development of ASD formulations (Qian et al., 2010).They are typically constructed using drug-polymer solubility data and the T g s of the ASDs at different drug-to-polymer ratios.The T g s at various compositions were measured by DSC, while drug-polymer solubility was determined based on drug melting point depression also observed with the DSC.Drug-polymer solubility at temperatures near the T g is extrapolated from solubility data at higher temperatures.A schematic diagram of ASDs with an amorphous polymer is shown in Fig. 2. The diagram can be divided into four regions (I to IV) according to the drug-polymer solubility and the T g s.Region I represents the ideal conditions for ASDs.The intersection of the solubility and the T g lines indicates the maximum drug loading.

Evaluation of molecular mobility -Calculation based on the Kohlrausch-William-Watts (KWW) equation
The molecular mobility of amorphous materials at a temperature below T g can be evaluated investigating the enthalpy relaxation behaviour by using DSC measurements combined with the KWW equation (Equation ( 5)) (Cowie et al., 1997;Hancock et al., 1995;Sertsou et al., 2010;Williams and Watts, 1970;Xu et al., 2023).
Where τ is the average relaxation time constant, β is the stretch parameter, t is the annealing time (which is 1, 2, 4, 8, and 16 h for this study), ΔH t is the relaxation enthalpy for the sample annealed at temperature T for time t, ΔH ∞ is the relaxation enthalpy for the sample annealed at temperature T for infinite time, which can be calculated with Equation (6).ΔC p is the heat capacity change at T g .

Comparison of experimental T g s with theoretical T g s
The initial focus of the study was to compare acidic functionalized polymers with non-functionalized polymers with regard to the molecular interactions between the drug and the polymers in ASDs.This was done by contrasting experimental T g s obtained from DSC measurements, with the theoretical T g s, derived from the G-T equation, as illustrated in Fig. 3. Positive deviations from theoretical T g s are indicative of molecular interactions (Di et al., 2021;Liu et al., 2020b;Xu et al., 2023).All ASDs exhibited a single T g , indicating homogeneous amorphous, singlephase systems.For CAR -mPEG-b-PJL ASDs, the theoretical and experimental T g s aligned closely, indicating the absence of strong drug-polymer molecular interactions.In contrast, for CAR -mPEG-b-PJL-COOH ASDs, notable positive deviations of the experimental form the theoretical T g s were observed, suggesting stronger drug-polymer molecular interactions, particularly at a 50 % mixing ratio (w/w), indicating the strongest molecular interaction at this mixing ratio.

Spectroscopic method -ssNMR
Although the above DSC results indicate relatively strong molecular interactions between CAR and mPEG-b-PJL-COOH, they do not offer structural or molecular insight into the interactions.Therefore, 13 CNMR R. Di et al. spectra were acquired for the polymers, amorphous CAR, 50 % CAR -mPEG-b-PJL both as PM and ASD, and 50 % CAR -mPEG-b-PJL-COOH both as PM and ASD (Fig. 4).The polymer spectra showed distinct sharp resonances, indicating ordered material (crystalline or semi-crystalline), whereas amorphous CAR and the binary samples showed broad resonances, indicating highly disordered materials (amorphous).The carboxylic acid group peak in mPEG-b-PJL-COOH, centered around ppm, shifted to 176 ppm when CAR -mPEG-b-PJL-COOH PM and ASD were measured, indicating the existence of ionized carboxylic acid groups in both PM and ASD and thus the potential salt-formation between the polymer and CAR.However, since the signal-to-noise ratio is relatively low and the resonances are broad, the carbon spectra do not provide definitive conclusions about the drug-polymer interactions.

Spectroscopic method combined with multivariate data analysis -FTIR combined with PCA
FTIR combined with PCA was employed to investigate the molecular interactions formed by CAR with the polymers from a structural perspective.FTIR spectra of the single components and the respective drug-polymer C-PMs, PMs, C-ASDs, and ASDs were used for PCA.The score plot for the CAR -mPEG-b-PJL-COOH systems is shown in Fig. 5a.The first principal component (PC-1) captured 67.5 % of the variation and can be explained by the various mixing ratios, as shown by the corresponding loading plot in Fig. 5b.Positive and negative loadings correspond to the spectra of CAR and mPEG-b-PJL-COOH, respectively in PC-1.In contrast, the score plot (Fig. 5a) showed clear negative deviations between the calculated and the experimental spectra for both PMs and ASDs in the second principal component (PC-2), which captured 23.0 % of the spectral variation.This indicates the existence of molecular interactions between CAR and mPEG-b-PJL-COOH in both PMs and ASDs.The maximum negative deviation was observed at 50 % CAR -mPEG-b-PJL-COOH.In the corresponding loading plot, the most prominent positive peaks corresponded to the stretching vibration of the C = O band of the carboxylic acid group (ν (C=O) : 1708 cm − 1 ), and the stretching and bending vibrations of the secondary amine (ν (N-H) : cm − 1 , δ (N-H)chain : 1501 cm − 1 respectively) (Pearson and Slifkin, 1972;Smith, 1998).The most prominent negative peaks corresponded to the symmetric and antisymmetric stretching of deprotonated carboxylic acid (ν s(COO-) : 1390 cm − 1 , ν as(COO-) : 1565 cm − 1 ) (Oomens and Steill, 2008;Pearson and Slifkin, 1972), and the bending vibration of the protonated secondary amine (δ (NH2+)chain : 1579 cm − 1 ) (Smith, 1998).From the loadings plot, PC-2 can be explained as follows: C-PM and C-ASD samples contain unbound carboxylic acid groups and secondary amine groups, while PMs and ASDs contain deprotonated carboxylic acid groups and protonated secondary amine groups.Therefore, it can be concluded that ionic bonds were formed between the carboxylic acid in mPEG-b-PJL-COOH and the secondary amine of the aliphatic chain in CAR for both PMs and ASDs samples.The results also indicated that the   strong interactions between mPEG-b-PJL-COOH and CAR were already established during the initial mixing process, observed as ionic bonds in the PMs.This might be due to the fact that the mixing process was conducted at room temperature (around 25 C), which is significantly above the T g of the polymer.Therefore, the polymer exhibits high molecular mobility during the mixing, providing the opportunity to form ionic bonds.Another phenomenon to note is that the stretching vibration of the secondary amine (ν (N-H)chain and carbazole : 3340 cm − 1 ) was observed in the C-PM and PM but not in the C-ASD and ASD.That is attributed to the secondary amine in the carbazole participating in forming hydrogen bonds within amorphous CAR.This finding aligns with previous studies that amorphous CAR can form dimers by forming hydrogen bonds through the secondary amine in the carbazole (Yathirajan et al., 2007).
As for CAR -mPEG-b-PJL samples, the PCA score plot (Fig. 6a) again showed that PC-1, which captures 75.4 % of the variation, mostly explains the different mixing ratios, which is supported by the loading plot of PC-1 in Fig. 6b.However, PMs showed a more narrow distribution with regard to the CAR concentrations compared to C-PMs, along PC-1.This might indicate that in the PM samples, the CAR particles were physically covered by the polymer.The preparation of the PMs was conducted under room temperature which is far above the T g of the mPEG-b-PJL (− 55 C) but below its T m (50 C), resulting in the polymer existing in a 'soft' solid state, which could facilitate their coverage of the CAR particles.Considering that mid-IR can only measure the sample surface approximately up to 25 μm deep (Delbeck and Heise, 2021;Maeno et al., 2023), this might lead to seemingly lower CAR concentrations compared to the theoretical values (where homogenous mixing was expected).PC-2 explained the differences between crystalline and amorphous CAR, and concentration variations that were not covered by PC-1.PC-2 also indicated molecular interactions between the drug and the polymer, as deviations were observed between C-ASDs and ASDs in PC-2.From the loading plot of PC-2 (Fig. 6c), peaks corresponding to the vibrations of ester, ether, alcohol, and secondary amine (ν (C-O) : 1000-1300 cm − 1 , δ (N-H) : 1500 cm − 1 and ν (N-H) : 3342 cm − 1 ) are responsible for most of the variations in the PC-2 values.This suggests the potential formation of hydrogen bonds between the ester, ether, alcohol, and amine groups of CAR and mPEG-b-PJL.
Overall, the molecular interaction investigation indicated that mPEG-b-PJL-COOH is effective in forming strong molecular interactions with the weakly basic drug CAR compared to mPEG-b-PJL without functionality, which can only form hydrogen bonds with CAR.

Investigation of miscibility by using melting point depression behaviour combined with Flory-Huggins theory
The FTIR-PCA investigation demonstrated that mPEG-b-PJL-COOH forms stronger molecular interactions with CAR than mPEG-b-PJL.However, forming successful ASDs fundamentally relies on achieving homogeneous molecular-level mixing of drug and polymer, i.e. achieving drug-polymer miscibility (Qian et al., 2010).Thus, subsequently, drug-polymer miscibility was evaluated.Both CAR -mPEG-b-PJL and CAR -mPEG-b-PJL-COOH binary systems exhibited melting point depression behaviour (Fig. 7a and b), which indicated that both

Investigation of drug loading ability
Understanding their drug loading ability is also crucial for ASD formulations, particularly because supersaturated ASDs, being thermodynamically unstable, might undergo phase separation or recrystallization during formulation or storage (Mahieu et al., 2013).Supersaturated ASDs are also more susceptible to the influence of mechanical stress during downstream processing (Yang et al., 2014).Temperaturecomposition phase diagrams (Fig. 8) were plotted to evaluate the drug loading ability of the polymer.
Due to the semi-crystalline nature of the polymers, two melting events were observed for samples with high drug contents.Consequently, this led to the division of the composition-temperature diagrams into five or six distinct regions, rather than the usual four regions, as described in the method section for amorphous polymers.In Region III (shown in Fig. 8), the ASDs are supersaturated, which can lead to phase separation and recrystallization of supersaturated drugs.The stability of the ASD is thus dependent on the stability of the amorphous drug.These ASDs might be kinetically stabilized by storing at low temperatures, but this region is generally not ideal for ASD formulations.In Region IV, there are two sub-regions (IVa and IVb).In both, samples are supersaturated, with a risk of recrystallization for the polymer (IVa) and the drug (IVa and b).Region IV should thus be avoided in any case.In Region I, ASDs are thermodynamically stable but low drug loading and low storage temperatures are required due to the low T g values of the ASDs, which might not be practical for ASD formulation in an applied setting.In Region II b, the samples are in a thermodynamically stable liquid state.However, this region requires high temperatures that are above the T m of the polymer (50 C), which is also impractical.Region II a is considered ideal for ASD formulations because samples are thermodynamically stable.Samples are above the T g , but below the T m of the polymer, in a liquid or semi-liquid state.This indicates that there is a risk of the recrystallization of the mPEG part of the polymer, which could lead to supersaturation of the drug.
To validate the temperature-composition diagrams, stability tests, at 25 • C under dry conditions, were conducted for CAR -mPEG-b-PJL and CAR -mPEG-b-PJL-COOH ASDs with 20 %, 33 %, and 43 % CAR (marked as stars in the diagrams in Fig. 8).Results are shown in Figure S2 (Supplementary material).The amorphous CAR in CAR -mPEG-b-PJL ASDs in region IVa (with 20 %, 33 %, and 43 % CAR) recrystallized within two weeks.In contrast, in CAR -mPEG-b-PJL-COOH ASDs, the amorphous CAR stayed amorphous throughout the testing period (ten months for samples containing 20 % and 33 % CAR,   and seven months for the sample containing 43 % CAR).It is important to note that the stability tests were conducted at a temperature much higher than the T g of the ASDs (− 40 to 5 • C).This further suggests that the enhanced stabilization in CAR -mPEG-b-PJL-COOH ASDs is primarily attributed to the strong drug-polymer interactions.
The temperature-composition diagrams of the CAR -mPEG-b-PJL-COOH and CAR -mPEG-b-PJL systems were compared, and it is obvious that the CAR -mPEG-b-PJL-COOH system has significantly larger areas for regions I, II a, and II b than the CAR -mPEG-b-PJL system.This indicated enhanced drug loading ability of mPEG-b-PJL-COOH.Additionally, it suggests that ASDs formulated with mPEG-b-PJL-COOH are more resilient to temperature fluctuations during storage.

Investigation of molecular mobility by determining enthalpy relaxation
To evaluate the stability of the resulting ASDs, molecular mobility was investigated.Molecular mobility was found to correlate with physical processes such as crystallization (Aso et al., 2004), and it is normally a significant factor in comparing the stability differences between samples.The DSC thermograms and the volume fraction of unrelaxed amorphous material change with aging time, are shown in Fig. 9.The ASD 50 % CAR -mPEG-b-PJL-COOH showed the slowest relaxation behaviour compared to the ASD 50 % CAR -mPEG-b-PJL and pure amorphous CAR.To quantify the relaxation behaviour, the experimental data were fitted to the KWW equation, and the parameters τ and β are summarized in Table 2.In general, increased τ values indicate reduced molecular mobility in single-component amorphous systems.However, for more complex multi-component amorphous systems, like ASDs, knowing the relaxation time constants from the fit of the KWW equation is not sufficient to evaluate the molecular mobility (Graeser et al., 2009;Matsumoto and Zografi, 1999).In this condition, the time required to reach the semi-relaxed state (t ((φ)=0.5) ) can be calculated with Equation (7) for quantitative comparison (Bansal et al., 2010): The t ((φ)=0.5)values are summarized in Table 2, and both 50 % CAR -mPEG-b-PJL ASD and 50 % CAR -mPEG-b-PJL-COOH ASD showed much higher t ((φ)=0.5)values compared to amorphous CAR, which means they both exhibited slower relaxation.Considering reduced enthalpy relaxation normally indicates reduced molecular mobility in the systems (Bhugra et al., 2008;Hancock et al., 1995), this suggests that both polymers, particularly the acidic functionalized polymer, can stabilize amorphous CAR.The significantly reduced molecular mobility in functionalized polymer ASDs, compared to both amorphous CAR and ASDs with non-functional polymer, is likely due to the stronger molecular interactions in the functionalized polymer ASDs (Bansal et al., 2010).

In vitro drug release -Dissolution study
To investigate if there is a correlation between molecular interactions and improved stability with ASD performance, dissolution profiles of crystalline and amorphous CAR and the PMs and ASDs of % CAR-polymer (w/w) were determined and are shown in Fig. 10a.The.
PMs and ASDs existed in a 'soft' solid state, as the sample preparation was conducted under room temperature which is far above the T g of the polymers (− 55 C) and the ASDs (− 25 C to 5 C).The solubility of crystalline CAR was identified as 19.3 ± 0.9 μg/mL after 60 h, aligning with a previously reported saturation solubility of CAR at 19.1 ± 1.5 μg/mL (Hamed et al., 2016).Amorphous CAR exhibited a higher saturation concentration (28.0 ± 7.5 μg/mL) after 24 h, with noticeable variations between different samples possibly due to different recrystallization speeds during the dissolution.The initial drug release rate was significantly enhanced in CAR -mPEG-b-PJL PM and ASD samples (compared to crystalline CAR) within the first hour.However, the final drug concentration of PMs only exhibits slight supersaturation (20.7 ± 0.4 μg/ mL) compared to crystalline CAR.The ASDs showed supersaturation initially, but this was followed by precipitation, leading to a lower final concentration compared to crystalline CAR.This implies that amorphous CAR may recrystallize into less soluble hydrate forms in the presence of mPEG-b-PJL.This finding aligns with results from another study where amorphous CAR, in the presence of the polymer HPMC, recrystallized into CAR hydrates (Liu et al., 2020a).For CAR -mPEG-b-PJL-COOH samples, both PM and ASD samples showed a gradual increase in dissolved drug concentration, with PMs maintaining higher concentrations throughout the dissolution experiments.The areas under the dissolution curves (AUC) were calculated and are shown in Table 3. Surprisingly, neither PMs nor ASDs showed significant improvement in dissolution, with ASDs even exhibiting a worse profile than PMs, likely due to the recrystallization of amorphous CAR into CAR hydrates.Comparable findings were noted in other research utilizing carbamazepine (CBZ), where amorphous CBZ recrystallized into its dihydrate  form, resulting in a reduced final dissolved concentration of CBZ compared to its crystalline form (Jensen et al., 2017;Savolainen et al., 2009).Additionally, research utilizing amorphous riboflavin also reported its recrystallization into a dihydrate form during the dissolution process (Henaff et al., 2023).
To further understand the observed dissolution results, additional experiments were conducted using a medium containing dissolved polymer (with the same quantity as in the PMs and ASDs).The pH of the medium was measured both before and after dissolving the polymer, and no substantial alterations were observed.
The dissolution of both crystalline and amorphous CAR in this medium was examined and the results are shown in Fig. 10b.In the medium with dissolved mPEG-b-PJL-COOH, both crystalline and amorphous CAR showed a significantly higher final dissolved drug concentration than their respective CAR -mPEG-b-PJL-COOH ASDs and PMs (as shown in Fig. 10a).This outcome could be attributed to the ability of mPEG-b-PJL-COOH to form micelles and substantially increase the apparent drug water solubility, as demonstrated by previous studies (Ali et al., 2022;Bansal et al., 2023a).The less enhanced dissolution observed in CAR -mPEG-b-PJL-COOH PMs and ASDs could potentially be attributed to the CAR-polymer salt formation.This is supported by a recent study indicating that ASDs with ionized basic drugs (clotrimazole, loratadine, or cinnarizine) and ionized HPMCAS tend to form insoluble complexes during dissolution due to electrostatic interactions, leading to poorer release performance (Bapat et al., 2024).
Crystalline CAR, in the medium with pre-dissolved mPEG-b-PJL, showed a dissolution profile similar to the CAR -mPEG-b-PJL PMs.For amorphous CAR in pre-dissolved mPEG-b-PJL, two different patterns were observed.In the first case, amorphous CAR rapidly recrystallized and showed similar dissolution behaviour to crystalline CAR.In the second case, amorphous CAR recrystallized more slowly and demonstrated dissolution patterns similar to those of CAR -mPEG-b-PJL ASDs, but with delayed supersaturation and precipitation.In general, CAR in medium with dissolved mPEG-b-PJL did not show significant differences compared to the respective ASD and PM.Overall, the ASD formulations did not demonstrate significantly improved dissolution behaviour.

Conclusion
As expected, the acidic functionalized polymer mPEG-b-PJL-COOH formed stronger molecular interactions (ionic bonds) with CAR compared to the non-functionalized mPEG-b-PJL (hydrogen bonds).Moreover, the strong drug-polymer interactions between CAR and mPEG-b-PJL-COOH were already formed during grinding.Both polymers were miscible with CAR, and mPEG-b-PJL-COOH showed superior drug-polymer miscibility and enhanced drug loading ability.Additionally, mPEG-b-PJL-COOH demonstrated a better potential for stabilizing the amorphous drug by significantly reducing the molecular mobility of resulting ASDs, despite the rather low T g s of the mPEG-b-PJL-COOH.Even stored at a temperature far above its T g , the ASDs formed with mPEG-b-PJL-COOH remain physically stable, mainly due to the strong drug-polymer interactions.Despite these advantages, ASDs with mPEGb-PJL-COOH did not notably improve dissolution, although they exhibited potential in micelle formation for solubility improvement.Improving the dissolution performance of the ASDs created with mPEGb-PJL-COOH remains a challenge to be addressed in future research.

Fig. 3 .
Fig. 3. Comparison of the experimental T g s with the theoretical T g s of CAR -mPEG-b-PJL and CAR -mPEG-b-PJL-COOH ASDs at various mixing ratios (from 30% to 90% CAR, w/w).The bars represent the deviations of the experimental T g s from the theoretical T g s.

Fig. 4 .
Fig. 4. 13 C NMR spectra of mPEG-b-PJL, mPEG-b-PJL-COOH, amorphous CAR, PM, and ASD of 50% CAR -mPEG-b-PJL, and PM and ASD of 50% CAR -mPEGb-PJL-COOH.The Blue, red, and pink lines indicate the resonances of ester, carboxylic acid, and deprotonated carboxylic acid groups, respectively.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 6 .
Fig. 6.(a) Score plot of CAR and mPEG-b-PJL and the respective C-PMs, PMs, C-ASDs, and ASDs with different mixing ratios.(b) Loading plot of PC-1 together with the FTIR spectra of CAR and mPEG-b-PJL.(c) Loading plot of PC-2 together with the FTIR spectra of crystalline CAR, amorphous CAR, 50% CAR -mPEG-b-PJL C-ASDs, and ASDs.

Fig. 8 .
Fig. 8. Temperature-composition diagram of (a) the CAR -mPEG-b-PJL systems; and (b) the CAR -mPEG-b-PJL-COOH systems.The red dashed line represents the T g s of the ASDs.The black dashed line represents the drug-polymer solubility.The stars mark the conditions of the ASDs for the stability test.The green stars () indicate the amorphous drug in the ASDs remained stable throughout the test, whereas the yellow stars () indicate the amorphous drug in the ASDs recrystallized during the testing period (ten months).(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 10 .
Fig. 10.Dissolution profiles of (a) crystalline CAR, amorphous CAR, the PMs and ASDs of CAR-polymers containing 50% CAR; (b) crystalline CAR, amorphous CAR, crystalline CAR in medium with dissolved polymers, and amorphous CAR in medium with dissolved polymers.

Table 3
Areas under the dissolution curves shown in Fig.10(n = 3).