S Wachowiak

F Danede

J F Willart

F Siepmann

J Siepmann

Dr Mounira Hamoudi
email: mounira.hamoudi@univ-lille.fr

PLGA implants for controlled dexamethasone delivery: Impact of the polymer chemistry

Keywords: PLGA, implants, controlled release, dexamethasone, swelling

The aim of this study was to better understand the impact of the chemistry of poly(lactic-coglycolic acid) (PLGA) polymers on the resulting drug release kinetics from implants prepared by melting and molding. Dexamethasone was incorporated as the drug. The polymer molecular weight of the PLGA, lactic acid:glycolic acid ratio and type of end groups (ester versus free acid) were varied. The implants were characterized using optical macroscopy, SEM, X-ray powder diffraction, DSC, gravimetric monitoring of dynamic changes in the systems' dry and wet mass upon exposure to the release medium as well as drug release and pH measurements.

Interestingly, the shape of the drug release profiles was similar in all cases: No noteworthy burst effect was observed. Dexamethasone release set on after a lag time, the length of which strongly depended on the PLGA chemistry: The lag time decreased with decreasing polymer molecular weight, increasing glycolic acid content and was shorter for -COOH end groups compared to ester end groups. In all cases, drug release set on as soon as a critical hydrophilicity and polymer molecular weight were reached and substantial system swelling started: The penetration of large amounts of water into the implants allowed for complete dexamethasone dissolution and relatively rapid diffusion of the dissolved drug molecules through a highly swollen PLGA gel up to 100 % drug release.

Introduction

Implants are often used to provide controlled release of drugs during periods ranging from days to years, in order to reduce the administration frequency, increase patient comfort, minimize undesired side effects, enhance the efficacy of the treatment and limit the overall drug dose [START_REF] Kleiner | Evolution of implantable and insertable drug delivery systems[END_REF][START_REF] Brandão De Paiva | Sirolimus-Loaded Intravitreal Implant for Effective Treatment of Experimental Uveitis[END_REF][START_REF] Costello | Drug release mechanisms of high-drug-load, melt-extruded dexamethasone intravitreal implants[END_REF][START_REF] Li | An in vitro gel-based system for characterizing and predicting the long-term performance of PLGA in situ forming implants[END_REF]. Biodegradable polymers offer the advantage of avoiding the removal of empty remnants upon drug exhaust. Frequently, synthetic aliphatic polyesters, such as poly(glycolic acid) (PGA), poly(lactic acid) (PLA) and poly(lactic-co-glycolic acid) (PLGA) are used for this purpose [START_REF] Hirota | Characterizing release mechanisms of leuprolide acetate-loaded PLGA microspheres for IVIVC development I: in vitro evaluation[END_REF][START_REF] Shah | A biomimetic approach to active self-microencapsulation of proteins in PLGA[END_REF][START_REF] Zhang | Minimizing acylation of peptides in PLGA microspheres[END_REF][START_REF] Costello | Reverse engineering the Ozurdex dexamethasone intravitreal implant[END_REF][START_REF] Carlier | Development of mAb-loaded 3D-printed (FDM) implantable devices based on PLGA[END_REF][START_REF] Utomo | Development of intranasal implantable devices for schizophrenia treatment[END_REF][START_REF] Desai | Effect of formulation parameters on 2methoxyestradiol release from injectable cylindrical poly(DL-lactide-co-glycolide) implants[END_REF].

PLGA offers several key advantages as polymeric matrix former in biodegradable, controlled release implants, including:(i) complete biodegradability into nontoxic degradation products, which can be safely eliminated and do not cause foreign body reactions [START_REF] Vert | The complexity of the biodegradation of poly(2-hydroxy acid)-type aliphatic polyesters[END_REF][START_REF] Shive | Biodegradation and biocompatibility of PLA and PLGA microspheres[END_REF],

(ii) good biocompatibility with tissues and cells [START_REF] Shive | Biodegradation and biocompatibility of PLA and PLGA microspheres[END_REF][START_REF] Fournier | Biocompatibility of implantable synthetic polymeric drug carriers: focus on brain biocompatibility[END_REF] and (iii) the possibility to adjust desired drug release rates during time periods ranging from a few days up to several months [START_REF] Marquette | Stability study of full-length antibody (anti-TNF alpha) loaded PLGA microspheres[END_REF][START_REF] Ahmed | Preparation of preformed porous PLGA microparticles and antisense oligonucleotides loading[END_REF][START_REF] Wischke | Principles of encapsulating hydrophobic drugs in PLA/PLGA microparticles[END_REF][START_REF] Maturavongsadit | Biodegradable polymeric solid implants for ultra-long-acting delivery of single or multiple antiretroviral drugs[END_REF][START_REF] Bach | Implications of changes in physical state of drugs in poly(lactide-co-glycolide) matrices upon exposure to moisture and release medium[END_REF][START_REF] Suh | Effect of implant formation on drug release kinetics of in situ forming implants[END_REF][START_REF] Parent | PLGA in situ implants formed by phase inversion: critical physicochemical parameters to modulate drug release[END_REF][START_REF] Dorta | Potential applications of PLGA filmimplants in modulating in vitro drugs release[END_REF].

Several drug products have been approved by the FDA for parenteral controlled drug delivery [START_REF] Wang | Drug release from in situ forming implants and advances in release testing[END_REF][START_REF] Park | Evolution of drug delivery systems: From 1950 to 2020 and beyond[END_REF][START_REF] Park | Injectable, long-acting PLGA formulations: Analyzing PLGA and understanding microparticle formation[END_REF]. A variety of PLGA grades are used, differing in their polymer molecular weight, lactic acid:glycolic acid ratio, and type of end groups: free acid versus ester groups [START_REF] Santoveña | hGH release from directly compressed hGH-PLGA biodegradable implantable tablets: Influence of physicomechanical factors[END_REF][START_REF] Thalhauser | Silica particles incorporated into PLGA-based in situ-forming implants exploit the dual advantage of sustained release and particulate delivery[END_REF][START_REF] Santoveña | Rheological properties of PLGA film-based implants: correlation with polymer degradation and SPf66 antimalaric synthetic peptide release[END_REF][START_REF] Zlomke | Polymer degradation induced drug precipitation in PLGA implants -Why less is sometimes more[END_REF][START_REF] Kempe | Non-invasive in vivo evaluation of in situ forming PLGA implants by benchtop magnetic resonance imaging (BT-MRI) and EPR spectroscopy[END_REF][START_REF] Ghalanbor | Interdependency of protein-release completeness and polymer degradation in PLGA-based implants[END_REF]. The specific chemistry of each PLGA determines its key characteristics, such as hydrophilicity, degradation rate and permeability for the drug. Consequently, the PLGA chemistry can strongly affect the resulting drug release kinetics [START_REF] Ibrahim | Optimization of injectable PLGA insitu forming implants of anti-psychotic risperidone via Box-Behnken Design[END_REF][START_REF] Li | Effective sustained release of 5-FU-loaded PLGA implant for improving therapeutic index of 5-FU in colon tumor[END_REF][START_REF] Saraf | Influence of PLGA End Groups on the Release Profile of Dexamethasone from Ocular Implants[END_REF]. Differences in PLGA chemistry are also important for other fields of application, e.g. for the stabilization of emulsions [START_REF] Robin | Tuning morphology of Pickering emulsions stabilised by biodegradable PLGA nanoparticles: How PLGA characteristics influence emulsion properties[END_REF].

A variety of manufacturing procedures can be used to prepare PLGA-based controlled release implants, for example: hot melt extrusion [START_REF] Lehner | Intracochlear PLGA based implants for dexamethasone release: challenges and solutions[END_REF][START_REF] Zheng | Hot melt extrusion: An emerging manufacturing method for slow and sustained protein delivery[END_REF][START_REF] Major | Hot Melt Extruded and Injection Moulded Dosage Forms: Recent Research and Patents[END_REF], melting and molding [START_REF] Yamakawa | Release behavior of poly(lactic acid-co-glycolic acid) implants containing phosphorothioate oligodeoxynucleotide[END_REF], compression [START_REF] Hamoudi-Ben Yelles | PLGA implants: How Poloxamer/PEO addition slows down or accelerates polymer degradation and drug release[END_REF][START_REF] Beugeling | The mechanism behind the biphasic pulsatile drug release from physically mixed poly(dl-lactic(-co-glycolic) acid)-based compacts[END_REF], or 3D printing [START_REF] Serris | Development of 3D-printed layered PLGA films for drug delivery and evaluation of drug release behaviors[END_REF]. In addition, liquid formulations can be injected into the patient, which form solid implants in-situ in the patient's body [START_REF] Kempe | Do in situ forming PLG/NMP implants behave similar in vitro and in vivo? A non-invasive and quantitative EPR investigation on the mechanisms of the implant formation process[END_REF].

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d Despite the great practical importance of PLGA-based implants, the underlying mass transport mechanisms are often not fully understood. This can be attributed to their complexity [START_REF] Beugeling | The mechanism behind the biphasic pulsatile drug release from physically mixed poly(dl-lactic(-co-glycolic) acid)-based compacts[END_REF][START_REF] Ford | Mathematical modeling of drug delivery from autocatalytically degradable PLGA microspheres-a review[END_REF][START_REF] Fredenberg | The mechanisms of drug release in poly(lactic-co-glycolic acid)-based drug delivery systems-a review[END_REF][START_REF] Vert | Biodegradation of PLA/GA polymers: increasing complexity[END_REF]. Upon exposure to aqueous media, water penetrates into the system and initiates polymer degradation. The rate of water penetration is much higher than the rate of ester bond cleavage. Thus, the entire device is degrading and undergoing "bulk erosion". If the drug is present in the form of solid particles, it can dissolve upon contact with water and diffuse out of the implant. The diffusion pathways can be either water-filled pores, the polymeric matrix, or a combination of both. Furthermore, autocatalytic effects might play a role: The rate at which acidic degradation products are generated within the implant can be higher than the rate at which they are neutralized or diffuse out of the system [START_REF] Ford | Mathematical modeling of drug delivery from autocatalytically degradable PLGA microspheres-a review[END_REF]. Consequently, the micro pH within the dosage form can locally drop and accelerate PLGA degradation and drug release [START_REF] Siepmann | How autocatalysis accelerates drug release from PLGA-based microparticles: a quantitative treatment[END_REF]. Recently, polymer swelling has been reported to play an "orchestrating" role for drug release from PLGAbased implants prepared by hot melt extrusion [START_REF] Bode | Often neglected: PLGA/PLA swelling orchestrates drug release: HME implants[END_REF]. After a certain lag-time, the polymeric matrix becomes sufficiently hydrophilic, the polymeric network weak enough, and the osmotic pressure within the implant sufficiently high to allow large amounts of water to penetrate into the system (amounts, which are much higher than those initially penetrating into the much more hydrophobic and denser polymeric device upon first contact with aqueous media). These high amounts of water lead to substantially increased drug mobility and accelerated drug release.

However, the relative importance of all these phenomena can very much depend on the polymer chemistry. So far, relatively little is known on how the PLGA chemistry affects the underlying drug release mechanisms in controlled release implants.

The aim of this study was to prepare PLGA implants loaded with dexamethasone by melting and molding and to characterize the systems thoroughly before and after exposure to phosphate buffer pH 7.4 at 37°C. The impact of the chemistry of the PLGA on implants properties was studied, in particular of the: (i) lactic acid:glycolic acid blend ratio, (ii) type of This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d end groups: ester versus acid, and (iii) polymer molecular weight. Dexamethasone was chosen as drug for several reasons: (i) It does not act as a plasticizer for PLGA. (ii) It is neither acidic nor basic (and does, thus, not accelerate polyester hydrolysis). (iii) It has a limited aqueous solubility. Thus, even a saturated drug solution does not exhibit a high osmotic pressure. (iv) It is a widely used glucocorticoid and used for example in the marketed drug product Ozurdex ® : a PLGA implant which is injected into the eye to treat adults with impaired vision caused by macular oedema.

Optical macroscopy, SEM, X-ray powder diffraction, DSC, gravimetric monitoring of dynamic changes in the systems' dry and wet mass upon exposure to the release medium and pH measurements of the bulk fluid were performed to better understand the underlying drug release mechanisms.

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d

b. Implant preparation

Cylindrical, flat-faced implants were prepared by melting and molding drug-polymer powder blends (10:90, w:w, %). The latter were obtained using a cryo-mill (1 g batches; Retsch, Germany), equipped with 50 mL zirconium oxide jars, containing 20 mm diameter zirconium oxide beads (1 bead per jar). The blends were cooled to -196 °C for 20 min, followed by cryomilling for 5 min at 30 Hz. Ten mg cryo-milled drug-polymer powder blend was filled into a cylindrical mold (2 mm diameter) and heated to 95°C for 15 min, followed by cooling to room temperature.

c. Optical macroscopy

Pictures of implants before exposure to the release medium were taken using a Nikon SMZ-U macroscope (Nikon, Tokyo, Japan), equipped with an AxioCam ICc1 camera.

The lengths and diameters of the implants were determined using the ImageJ software (US National Institutes of Health, Bethesda, Maryland, USA).

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d. Practical drug loading

Implants were dissolved in 5 mL acetonitrile followed by filtration (0.45 µm PVDF Syringe Filter, Millex-HV, Merck Millipore, Tullagreen, Ireland) and drug content determination by HPLC-UV analysis using a Thermo Fisher Scientific Ultimate 3000 Series HPLC, equipped with a LPG 3400 SD/RS pump, an auto sampler (WPS-3000 SL) and a UV-Vis detector (VWD-3400RS) (Thermo Fisher Scientific, Waltham, USA). Ten μL samples were injected into an A C18 RP column (Gemini 3 μm C18 110 Å, 100 mm x 4.6 mm; Phenomenex, Le Pecq, France). The mobile phase consisted of a 33:67 (v/v) acetonitrile:water mixture, the flow rate was 1.5 mL/min. The detection wavelength was λ = 254 nm. All experiments were conducted in triplicate. Mean values +/-standard deviations are reported.

e. X-ray powder diffraction

X-ray diffraction patterns of raw materials and drug loaded implants were recorded with a Panalytical X'pert Pro diffractometer (Cu anode tube of wavelength Kα1 = 1.541 Å and Kα2 = 1.544 Å) (Panalytical, Almelo, Netherlands). Rotatory Lyndemann capillaries (diameter: 0.7 mm) were used.

f. Differential scanning calorimetry (DSC)

DSC thermograms of raw materials and drug loaded implants were recorded using a DSC 1 Star (Mettler Toledo, Greifensee, Switzerland). Approximately 3-5 mg samples were accurately weighed in sealed aluminum pans. The pans were heated from 20 to 300°C, cooled to -70°C and reheated to 300°C, at a rate of 10°C/min (in nitrogen atmosphere). Each experiment was conducted in triplicate. Mean values +/-standard deviations are reported.

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P r e p r i n t n o t p e e r r e v i e w e d g. In vitro drug release

Implants were placed in 2 mL Eppendorf tubes (1 implant per tube), filled with 2 mL phosphate buffer pH 7.4 (USP 42), and horizontally shaken (80 rpm, 37°C, GFL 3033; Gesellschaft fuer Labortechnik, Burgwedel, Germany). At pre-determined time points, the entire release medium was completely withdrawn and replaced with 2 mL pre-heated, fresh phosphate buffer pH 7.4. The amount of dexamethasone in the withdrawn, filtered (0.45 µm PVDF Syringe Filter, Millex-HV, Merck Millipore, Tullagreen, Ireland) bulk fluid was determined by HPLC-UV analysis, as described above in section 2.d. In this case, the injected volume was 100 μL. All experiments were conducted in triplicate. Mean values +/standard deviations are reported.

h. Implant swelling

Implants were treated as for the in vitro drug release measurements described in section 2.g. At pre-determined time points:

where mass (t = 0) represents the implant mass before exposure to the release medium.

All experiments were conducted in triplicate. Mean values +/-standard deviations are reported.

i. Implant erosion and PLGA degradation

(a) Implants were treated as for the in vitro drug release measurements described in section 2.g. At pre-determined time points, implant samples were withdrawn, freeze-dried The dry mass (%) (t) was calculated as follows:

(
dry mass (𝑡)% = dry mass (t) mass (t=0) × 100% (3)
where mass (t = 0) is the implant's mass before exposure to the release medium.

All experiments were conducted in triplicate. Mean values +/-standard deviations are reported.

(b) The decrease in polymer molecular weight of different PLGA during drug release was determined by gel permeation chromatography (GPC). Implants were treated as described for the in vitro drug release measurements in section 2.g. At predetermined time points, implants were withdrawn and freeze-dried. Three mg of the obtained lyophilisates were dissolved in 1 mL tetrahydrofuran. One hundred mL samples were injected into an Alliance system

(

j. Scanning electronic microscopy (SEM)

The internal and external microstructures of the implants before and after two weeks exposure to the release medium were studied using a JEOL Field Emission Scanning Electron Microscope (JSM-7800F, Japan), equipped with the Aztec 3.3 software (Oxford Instruments, Oxfordshire, England). Samples were fixed with a ribbon carbon double-sided adhesive and covered with a fine carbon layer. Implants, which had been exposed to the release medium, were treated as described in section 2.g for the in vitro drug release measurements. After two weeks, implant samples were withdrawn, freeze-dried (as described in section 2.i) and cut using a scalpel to observe cross sections.

Results and discussion

The aim of this study was to better understand the impact of the polymer chemistry of PLGA-based implants on the resulting drug release kinetics, in particular of the (i) lactic acid:glycolic acid blend ration, (ii) type of end groups: ester versus acid, and (iii) polymer molecular weight. Dexamethasone loaded implants were prepared by melting and molding. The implants were thoroughly characterized before and after exposure to phosphate buffer pH 7.4:

with respect to the physical states of the drug and PLGA, dynamic changes in dry and wet mass of the systems, inner and outer morphology, polymer swelling and degradation, changes in the pH of the release medium and drug release.

a. Physico-chemical key properties of the implants

The optical microscopy pictures on the left hand side of Figure 1 show implants based on

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d PLGA 50/50 A (38 kDa), PLGA 50/50 A (92 kDa), PLGA 75/25 A (70 kDa) and PLGA 50/50 E (50 kDa). The ratio "50/50" or "75/25" indicates the lactic acid:glycolic acid ratio, "A" and "E" indicate the nature of the end groups (acid or ester), and the polymer molecular weight is indicated in the brackets. The theoretical dexamethasone loading was 10% in all cases, the practical loading 9.1 +/-0.3% (and homogeneous in different parts of the implants). As it can be seen, the obtained implants were white, had a smooth surface and appeared to be homogeneous, irrespective of the PLGA grade. The SEM pictures on the left hand side of Figure 2 show surfaces and cross-sections of dexamethasone loaded implants before exposure to the release medium. In all cases, the systems looked dense (with a certain micro-porosity) and homogeneous.

Figure 3 shows the X-ray diffraction patterns of the raw materials (drug and polymers) as well as of the dexamethasone loaded implants before exposure to the release medium. Clearly, the drug powder as received was crystalline. Its melting point was 264°C, as evidenced by a sharp endothermic peak in its DSC thermogram (Figure S1). In contrast, all PLGA raw materials and dexamethasone loaded implants were X-ray amorphous (Figure 3). DSC thermograms of the PLGA raw materials and of drug loaded implants are illustrated in Figure 4. In the case of the raw materials, 2 nd heating cycles are shown (the thermal history of the samples not being of interest), whereas in the case of the implants 1 st heating cycles are illustrated (the thermal history being of interest). As it can be seen, glass transitions were clearly visible in all cases. Table 1 lists the corresponding temperatures. Interestingly, the Tgs did not substantially differ between the polymer raw materials and the drug loaded implants, indicating that the manufacturing procedure did not seem to significantly degrade the PLGA and that the presence of the drug did not alter the Tg. This might indicate that the dexamethasone is present in the form of amorphous particles distributed throughout the PLGA matrices (and is not dissolved). The limited PLGA degradation during implant manufacturing was also evidenced of drug release (illustrated by the dotted lines in Figure 5).

b. Dexamethasone release kinetics and mass transport mechanisms

It has previously been reported that drug release from PLGA and PLA based implants might be "orchestrated" by substantial polymer swelling (Figure 6) [START_REF] Bode | Often neglected: PLGA/PLA swelling orchestrates drug release: HME implants[END_REF]: Initially, the polymeric matrices are rather hydrophobic and only limited amounts of water rapidly wet the entire implants. Once water gets into contact with the ester bonds, polymer degradation sets on throughout the systems (bulk degradation). Upon each ester bond cleavage, 2 new hydrophilic end groups are created: a -COOH and a -OH end group, rendering the matrices more and more "water loving". In addition, the degree of polymer chain entanglement decreases, leading to a

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d decreasing mechanical resistance against substantial swelling. Furthermore, a steadily increasing osmotic pressure is created within the implants due to the generation of water-soluble degradation products. At a certain time point (at the end of the above discussed lag phase), the matrices are sufficiently hydrophilic, mechanically fragile and osmotically active that they attract considerable amounts of water: The solid implants are transformed into highly swollen PLGA gels. This fundamentally alters the conditions for drug release: The drug particles can dissolve in the high amounts of water and can rather easily diffuse out into the release medium.

Depending on the chemistry of the PLGA, this time point is more or less rapidly reached: For example, comparing the behavior of implants based on PLGA 50/50 A (38 kDa) and PLGA 50/50 A (92 kDa) (blue versus orange curves in Figure 5), it can be seen that the lag time increased when increasing the polymer molecular weight (while keeping the monomer ratio and type of end groups the same). This is consistent with the above described release mechanism:

If the initial polymer molecular weight is higher, it takes more time to reach the "critical" molecular weight to allow for substantial system swelling. Also, when changing the lactic acid:glycolic acid ratio from 50/50 to 75/25, the lag time increased (orange versus red curves in Figure 5, despite a higher initial molecular weight). This can likely be explained by the higher hydrophilicity of PLGA 50/50 compared to PLGA 75/25: It contains less lactic acid, which is more hydrophobic than glycolic acid, due to an additional methyl group. If the system allows more water to come in initially, polymer degradation is faster. Furthermore, comparing the black and orange curves in Figure 5, it becomes obvious that the lag time is higher in the case of PLGA with ester end groups compared to free acid end groups (even if the molecular weight is lower). The PLGA terminal end groups influence the degradation rate. For instance, carboxyl terminal groups can catalyze the hydrolysis of ester bonds, thus producing more acidic groups and potentially leading to autocatalytic effects, accelerating polymer degradation [START_REF] Félix Lanao | In vitro degradation rate of apatitic calcium phosphate cement with incorporated PLGA microspheres[END_REF]. In addition, free acid end groups render the implants less hydrophobic from the beginning,

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d allowing more water to penetrate into the system. Both, this lower initial hydrophobicity as well as the potential acid catalysis lead to faster polymer degradation. Thus, it takes less time to reach the critical molecular weight (as it can be seen in Figure 5C).

Figure 7 shows further experimental evidence for the hypothesized drug release mechanisms and impact of the PLGA chemistry: The dynamic changes in the implants' volume, dry mass and in the pH of the release medium are shown. The dotted lines show the same lag times as in Figure 5. As it can be seen, the implants' volume substantially increased after the lag times, due to the penetration of considerable amounts of water into the systems (Figure 7A).

This coincides with the onset of important dry mass loss (Figure 7B). The latter can in part be explained by drug release but is in major part caused by the leaching of water-soluble degradation products into the release medium: Analogous to dissolved dexamethasone molecules, water-soluble short chain acids are rather mobile in the highly swollen PLGA gels and diffuse out, due to concentration gradients. This leads to significant drops in the pH of the bulk fluid (Figure 7C). The optical microscopy pictures in Figure 1 Furthermore, please also note that at t = 2 weeks, only the implants based on PLGA 50/50 A (38 kDa) were entering the "substantial system swelling phase". Comparing these pictures to those on the left hand side of Figure 2 (taken before exposure to the release medium), signs for polymer degradation throughout the matrices are visible (indicating bulk degradation).

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Conclusion

In this study, the chemistry of PLGA did not fundamentally change the underlying drug release mechanisms from dexamethasone loaded implants, neither the shape of the observed release patterns. But the polymer chemistry determined the length of the lag time, after which drug release set on. This could be explained by the fact that the polymer molecular weight, "lactic acid:glycolic acid ratio" and type of end groups (free acids versus esters) affect the time point, at which a sufficient system hydrophilicity and macromolecular chain length are reached to allow the beginning of substantial implant swelling. The latter fundamentally changes the conditions for drug release. This improved understanding of the importance of the polymer chemistry on the control of drug release can be expected to facilitate the development of innovative biodegradable implants.

Declaration of interests

The Editor-in-Chief of the journal is one of the co-authors of this article. The manuscript has been subject to all of the journal's usual procedures, including peer review, which has been handled independently of the Editor-in-Chief.

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d Fig. 6 Schematic presentation of the mass transport phenomena involved in the control of drug release from the investigated implants. Polymer swelling "orchestrates" drug release:

after a certain lag time, it fundamentally changes the conditions for drug dissolution and diffusion, and drug release sets on. Reprinted from [START_REF] Bode | Often neglected: PLGA/PLA swelling orchestrates drug release: HME implants[END_REF], with permission. This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d

  ,L-lactic-co-glycolic acid) (PLGA) 50/50 A [50:50 lactic acid:glycolic acid, -COOH end groups, Mw = 92 kDa], PLGA 50/50 E [50:50 lactic acid:glycolic acid,ester end groups, Mw = 50 kDa] and PLGA 75/25 A [75:25 lactic acid:glycolic acid, -COOH end groups, Mw = 70 kDa] (Ashland, Dublin, Ireland); PLGA 504H [50:50 lactic acid:glycolic acid, -COOH end groups, Mw = 38 kDa] (Evonik, Darmstadt, Germany); dexamethasone (Discovery Fine Chemicals, Dorset, UK); acetonitrile and tetrahydrofuran (Carlo Erba, Val-de-Reuil, France).

  (a) Pictures of implants were taken with a Nikon SMZ-U macroscope. Dynamic changes in the systems' volume were estimated considering cylindrical geometry using the following equation: change in volume (𝑡)% = volume (t)-volume (t=0) volume (t=0) × 100% (1) (b) Implant samples were withdrawn, excess water was carefully removed and weighed [wet mass (t)]. The wet mass (%) (t) was calculated as follows: wet mass (𝑡)% = wet mass (t) mass (t=0) × 100%

Figure

  Figure5Ashows the experimentally measured dexamethasone release kinetics from the

  further illustrate the fundamental changes in the conditions for drug release: Depending on the PLGA grade, after a certain lag time, the implants substantially swell. SEM pictures of surfaces and cross-sections of the different types of implants are shown in Figure 2: On the right hand side, implants based on PLGA 50/50 A (38 kDa), PLGA 50/50 A (92 kDa), PLGA 75/25 A (70 kDa) and PLGA 50/50 E (50 kDa) are illustrated after 2 weeks exposure to phosphate buffer pH 7.4. Please note that the samples had been dried prior to analysis, thus, artefact creation is highly likely.

Figure captions Fig. 1

 captions1 Figure captions

Fig. 2

 2 Fig. 2 SEM pictures of surfaces and cross-sections of dexamethasone loaded PLGA implants

Fig. 3 X

 3 Fig. 3 X-ray diffraction patterns of the raw materials and dexamethasone loaded PLGA

Fig. 4

 4 Fig. 4 DSC thermograms of the raw materials (second heating cycles) and of the investigated

Fig. 5

 5 Fig. 5 Impact of the PLGA chemistry on: (A) dexamethasone release, (B) dynamic changes in

Fig. 7

 7 Fig. 7 Dynamic changes in the: (A) volume of the implants, (B) dry mass of the implants and

Figure 2

 2 Figure 2

Figure 5

 5 Figure 5

Figure 6

 6 Figure 6

  with molecular weights between 1,480 and 70,950 Da (Polymer Laboratories, Varian, Les Ulis,

	France).
	refractometer detector: 2414 RI, separation module e2695, Empower GPC software; Waters,
	Milford, USA), equipped with a PLgel 5 μm MIXED-D column (kept at 35 •C, 7.8 × 300 mm;

Agilent). Tetrahydrofuran was used as mobile phase at a flowrate of 1 mL/min. Molecular weights were calculated using the Empower GPC software (Waters) and polystyrene standards This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d

Table 1 :

 1 Glass transition temperatures (Tgs, °C) of the raw materials (as received, second heating cycles) and of the investigated dexamethasone loaded PLGA implants (first heating cycles) before exposure to the release medium. The lactic acid/glycolic acid ratio, type of end groups (A: acid,

	E: ester) and initial polymer molecular weight are indicated in the left column. Mean values +/-
	standard deviations are reported.
	PLGA grade	Raw materials	Drug loaded implants
	50/50 A (38kDa)	43.3 ± 0.2	43.6 ± 0.2
	50/50 A (92kDa)	47.0 ± 0.1	46.8 ± 0.2
	75/25 A (70kDa)	46.9 ± 0.2	47.1 ± 0.2
	50/50 E (50kDa)	45.9 ± 0.1	46.0 ± 0.1

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d

Figure 7

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d

Supplementary material

PLGA implants for controlled dexamethasone delivery: Impact of the polymer chemistry This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4427814 P r e p r i n t n o t p e e r r e v i e w e d


de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

-Google reviews (Google Reviews API) for several spatial entities in each city, including urban riverfronts² → Confront the previously identified issues with potential problems that are discussed by social actors.

III. Material & methods

Global scale approach of socio-environmental stakes and conflicts related to floodplain urbanisation This project is part of an interdisciplinary research program GloUrb, which aims to characterize the urbanisation process of floodplains since the 80's. Floodplains, which can be defined as "areas of low-lying land that are subject to inundation by lateral overflow water from rivers or lakes with which they are associated" 1 , are the "attractors" and "fixing" areas of such global urbanisation. Floodplain ecosystems are simultaneously vulnerable to socio-environmental transformations and essential to their inhabitants wellness. However, the impact of floodplain urbanisation on humans has been overlooked and understanding stakes and potential conflicts is needed to promote public debates and discuss potential solutions. -OpenStreetMap (OSM): food production, engineering, amenities, entertainment, nature -Wikidata: "dam", "powerplant", "park", "canal", "bridge", etc. "Ahmedabad AND Sabarmati" Results : water, level, mark, flow, danger, etc. Results : Riverfront, city, India, bank, waterfront, etc. Proper noun FALSE TRUE

II. Study sites

  , L.Vaudor, H. Piégay This work is funded by the French National Research Agency (ANR) (Project GloUrb n° ANR-22-CE03-0005). It is also cofunded by the Labex IMU (ANR-10-LABX-0088) and the EUR H2O'Lyon (ANR-17-EURE-0018) of Université de Lyon, within the programme 'Investissements d'Avenir' operated by ANR. 1. Sofia, G., Roder, G., Dalla Fontana, G., & Tarolli, P. (2017). Flood dynamics in urbanised landscapes : 100 years of climate and humans' interaction. Scientific Reports, 7(1), 40527. https://doi.org/10.1038/srep40527 2. Dempsey, N., Velarde, C. L. M., Samuel, M., Bakshi, Y., & Baradi, M. (2020). From river to Riverfront : How meanings and cultural heritage change. The case of the Sabarmati Riverfront project, Ahmedabad, Gujarat. Town Planning Review, 91(6), 643-666. https://doi.org/10.3828/tpr.2020.89 3. Comby, E., Le Lay, Y.-F., & Piégay, H. (2014). How chemical pollution becomes a social problem. Risk communication and assessment through regional newspapers during the management of PCB pollutions of the Rhône River (France). Science of The Total Environment, 482-483, 100-115. https://doi.

-

  Main methodological challenge = using remotely accessible sources -Progressive selection according to a top-down, multi-scale approach → From global to local scale IV. Outcomes • Explore socio-environmental conflicting situations related to floodplain urbanisation at local to global scales • Understand the diversity of situations and how urbanisation exacerbates socio-environmental stakes • Stimulate public debate on floodplain artificialisation in a context of climate change Collection of geospatial data and attributes on :

  Map of Ahmedabad with OSM basemap and layer regarding natural items → Provide a global scale typology of socio-environmental issues related to floodplains -300 urban agglomerations of over 300K inhabitants that intersect rivers larger than 30-60 m -Selection along a gradient of demographic growth patterns The approx. 300 selected sites and their population growth (%) between 1980 and 2018 → Highlight tensions between the perceived space, the conceived space and the living space Map of Delhi with OSM basemap and layer regarding engineering items (basemap : Stamen Design) The Yamuna Floodplain, in Delhi, a sensitive area in term of conservation Selection of conflicting situations, which induced public debates and discourses 3 to these documents Text mining & content analysis on: -A set of press articles and web pages (n > 15 000):"Delhi AND Yamuna"Frequency of occurrence of lemma when using the Search Engine Page Results (SERP)


Murad Abuaisha
email: murad.abuaisha@minesparis.psl.eu

Ahmed Rouabhi

Faouzi Hadj-Hassen

David W Eaton

Firas Tayeb

Alain Valtz

Thermal effects on the kinetics of gas dissolution in brine: A case study of CO 2 storage in salt caverns (a non-dimensional model)

Understanding the dissolution kinetics of CO 2 in brine is important for efficient management of cycled CO 2 in underground salt caverns.

One promising clean energy resource is methanation, a technique used to convert carbon dioxide to methane using hydrogen. Methanation is supposed to reply to the energy fluctuating demand, which necessitates large storage of its production elements (H 2 and CO 2 ). This study focuses on CO 2 storage and cycling in salt caverns in the context of clean energy transition [1].

Conclusion Abstract

The underground storage system can be divided into three domains: (1) the well which extends from the ground surface to the cavern;

(2) the cavern itself; and (3) the rock mass that surrounds the cavern and the well (Fig. 1).

The cavern brine has initially low concentration of CO 2 . As CO 2 is injected into the cavern, a concentration gradient develops at the brine interface. This concentration gradient forms the driving force for the Fickian diffusion.

Consequently, convection is created in the brine due to changes in the density field. A thermal convection is further developed due to cycling temperature changes at the brine interface, which interacts with the geothermal gradient of the brine. The velocity field that emerges due to both types of convection is expected to enhance the dissolution of CO 2 in the brine. This research introduces a non-dimensional model that couples cavern thermodynamics [2] with the dissolution mechanisms in the brine. Since the model is non-dimensional, once validated by the laboratory measurements, it can be applied to other scales. This model can also be adapted to study the dissolution of other gases. Experimental work is required, some of it considered in this study, in order to establish the key model parameters.

The DECOVALEX 2023 conference, November 14-16 2023 | Troyes, France Before applying the non-dimensional model on the cavern scale, experimental validation is needed. Laboratory experiments are performed based on a pressure decay test using a PVT (Pressure-Volume-Temperature) cell. In this setup, the CO 2 gas is injected from a tank into the cell that is partially filled with saturated brine. The cell temperature is controlled by placing it into a temperature-controlled basin (Fig. 3). Once gas is injected, it starts dissolving in the liquid phase. The kinetics is strongly influenced by natural convection, which is caused by density changes related to the concentration of dissolved gas as well as thermal changes driven by CO 2 cycling and the effects of the geothermal gradient. Based on a novel non-dimensional model that couples cavern thermodynamics with the dissolution mechanisms, this study investigates how the natural convection related to mass and thermal changes impacts dissolution kinetics. The numerical model is validated using laboratory measurements, and thereupon upscaled to typical dimensions of a salt cavern. Although our simulations show that the total dissolved mass is relatively minor compared to the initial stored mass/cycled mass, it is nevertheless important to quantify other loss phenomena, particularly gas permeation into the host rock salt. The developed model can also be adapted easily to study the kinetics of dissolution of other gases, such as hydrogen and methane. The results of the numerical model correlate well to the experimental data. The black curves represent the numerical solutions while considering only the diffusion phenomenon. For these solutions to correlate to the experimental data, the diffusion coefficient needs to be enhanced.

Thermal effects are quantified numerically. Fig. 5 shows the numerical model that is used for this purpose. This model represents a cylinder with a radius that is 3 times the radius of the laboratory cell. Nevertheless, the same height-radius ratio is adopted. In the first scenario, a temperature difference of 3 °C is applied over the model height. In the second scenario, the difference is reduced to 0.1 °C.

Simulations -Cavern Scale I

To consider the full cavern scale, the numerical model represents a cylindrical volume ∼42412 m 3 in an infinite rock salt domain (Fig. 6). The cavern brine occupies almost 11% of the volume over a height of 1.5 m.

The cycling program envisaged for this research: a weekly utilization of the cavern with four cycles spreading over ∼28 days. Cycling leads to reasonable mass variations where the cycled CO 2 stays always in its supercritical state. The novelty of this research stems from the fact that it presents and quantifies the effects of thermal convection on the gas-liquid dissolution process. Simulations demonstrate that the ultimate total dissolved mass is approximately 0.32% of the initial stored mass. Although this loss may seem insignificant, the quantification of this loss, during cycling becomes important when other loss mechanisms are studied, particularly the permeation of gas into the rock domain.

Fig. 1 .

 1 Fig. 1. Schematic representation of CO 2 storage in salt caverns and its transport mechanisms between the cavern phases

Fig. 2 .

 2 Fig. 2. The workflow of this study

Fig. 3 .

 3 Fig. 3. Schematic representation of the pressure decay PVT cell used to study the CO 2 dissolution in the brine and to validate the mathematical model

Fig. 4 .

 4 Fig. 4. A comparison between the numerical and the experimental pressure histories for the two laboratory tests: (a) ! "0 = 12.9 MPa and (b) ! "0 = 16.87 MPa. The black curves represent the numerical solutions while considering only pure diffusion (# app = 8.6 x 10 -8 m2/s)

Fig. 5 .

 5 Fig. 5. Schematic representation of the numerical model. Evolution of the volume averaged CO 2 concentration. The figure shows how the thermal effects due to different temperature gradients accelerate the dissolution process.

Fig. 5

 5 Fig.5shows how even a small temperature difference of 0.1 °C accelerates the dissolution process.

Fig. 6 .

 6 Fig. 6. Schematic diagram of the boundary value problem: it represents a cylindrical cavern created at a depth of 600 m in a surrounding rock salt domain

Fig. 8

 8 Fig.8shows the cavern thermodynamics as well as the brine CO 2 volume averaged concentration as function of cycling. Fig.8(c) shows how the brine CO 2 concentration increases linearly due to cycling.

Fig. 8 .

 8 Fig. 8. Cavern CO 2 pressure (a) and temperature (b) as function of the relative mass variations during 6.5 months

Fig. 9 .

 9 Fig. 9. The evolution of the brine average temperature during the CO 2 cycling. (b) The brine CO 2 concentration averaged over its surface and volume. The surface averaged concentration shows clearly the effects of cycling

Fig. 10 .Fig

 10 Fig. 10. Contours at 10 days of weekly cycling

Schaaf, T., Grunig, J., Schuster, M. R., Rothenfluh, T., Andreas, O., 2014. Methanation of CO 2 -storage of renewable energy in a gas distribution system. Energy, Sustainability, and Society, 4,

2. AbuAisha, M., Rouabhi, A., 2019. On the validity of the uniform thermodynamic state approach for underground caverns during fast and slow cycling. International Journal of Heat and Mass Transfer, 142, 118424.

Acknowledgements

Introduction and Methodology

Methodology and Laboratory Work

Thermal Effects


domain: phys spi

text:
Enrico ; Lia

Indra ; Ghosh

Stephen M ; Hanham

Benjamin ; Walter

Fuanki ; Bavedila

Marc ; Faucher

Andrew P ; Gregory

Leif ; Jensen

Jan ; Buchholz

Horst ; Fischer

Ulrich ; Altmann

Rüdiger Follmann

Rüdiger Follmann

Novel mm-Wave Oscillator Based on an Electromagnetic Bandgap Resonator

Abstract-This paper introduces a novel millimeter-wave oscillator concept based on an electromagnetic bandgap (EBG) resonator (also called a photonic crystal resonator). To realize an ultra-low phase noise MMIC oscillator, an EBG resonator is developed by introducing a periodic structure into an ultra-high resistivity silicon wafer to create an electromagnetic bandgap which confines a localized resonant mode with a reduced mode dielectric filling factor of 47%. The measured results of the resonator demonstrate an unloaded Q-factor of 108,300 can be achieved at 45 GHz. Measured oscillator phase noise levels of -91.5, -121.5 and -133 dBc/Hz are obtained at offset frequencies of 1, 10 and 100 kHz, respectively. Index Terms-dielectric materials, dielectric resonator, microwave oscillators, MMICs, photonic crystals.

I. INTRODUCTION

owadays, reference oscillators based on quartz resonators are limited in frequency of operation to a few hundred megahertz. Deriving gigahertz range signals from such a reference requires frequency multiplication or frequency synthesis. However, the multiplication process increases the phase noise of the output signal according to 20log10 of the multiplication factor, as well as increasing the complexity of the circuit. In this sense, it is advantageous to have a LO signal generated directly at the fundamental frequency in the millimeter (mm-) wave band. This requires, however, a high quality (Q-) factor resonator operating preferably at several gigahertz. Traditional passive resonators employing metal cavities have their Q-factor limited by the resistive losses in the metal. Alternatively, oscillators operating directly at the fundamental frequency based on ceramic resonators offer average phase noise and are normally not available above 25 GHz. Indra Ghosh, Jan Buchholz, Horst Fischer, Ulrich Altmann, and Rüdiger Follmann are with IMST GmbH, Germany (email: indra.ghosh@imst.de; jan.buchholz@imst.de; horst.fischer@imst.de; ulrich.altmann@imst.de; ruediger.follmann@imst.de).

Dielectric resonators made of low dielectric loss and high resistivity materials are an interesting alternative to overcoming the problem of limited resonator Q-factors in the mm-wave band. One approach is to fabricate the dielectric resonator from an ultra-high resistivity silicon wafer [START_REF] Krupka | High Q-Factor Millimeter-Wave Silicon Resonators[END_REF]. An emerging type of mm-wave dielectric resonator that can be implemented using a silicon wafer is an electromagnetic bandgap (EBG) resonator, also known as a photonic crystal resonator [START_REF] Joannopoulos | Photonic Crystals: Molding the Flow of Light[END_REF][START_REF] Otter | 100 GHz Ultra-high Q-factor Photonic Crystal Resonators[END_REF]. Such a resonator is realized by engineering an EBG in the silicon wafer through the introduction of periodic holes in order to confine a localized resonant mode. A resonator designed in this manner may have a Q-factor limited only by material loss. This material loss may be reduced by designing the resonator in such a way as to concentrate most of the energy outside the silicon and in air. This approach allows the realization of extremely high Qfactors which is a key aspect to achieving very low phase noise in oscillator applications.

Research papers and laboratory demonstrations [START_REF] Jensen | High Resistivity (HiRes TM ) Silicon for GHz & THz Technology[END_REF][START_REF] Krupka | Measurements of Permittivity and Dielectric Loss Tangent of High Resistivity Float Zone Silicon at Microwave Frequencies[END_REF] have shown that dielectric resonators made from low-loss materials such as high resistivity silicon may become an interesting alternative to conventional room-temperature passive mmwave resonators used in reference and high frequency oscillators, and important components for future mm-wave applications.

This work aims to demonstrate that low-loss ultra-high resistivity silicon resonators can be utilized for high frequency oscillators with significant advantages in obtaining high Qfactor and therefore low phase noise compared to multiplied quartz crystal and traditional high frequency oscillators. In this paper, the novel experiment of using a silicon EBG resonator exhibiting a reduced dielectric filling factor of its resonant mode in an oscillator operating at 45 GHz is demonstrated successfully, establishing a route towards overcoming the Stephen M. Hanham is with the Dept. of Electrical, Electronic and Systems Engineering, University of Birmingham, U.K. (email: s.hanham@bham.ac.uk).

Benjamin Walter, Fuanki Bavedila, and Marc Faucher are with Vmicro SAS, France (email: benjamin.walter@vmicro.fr; fuanki.bavedila@vmicro.fr; marc.faucher@vmicro.fr). Marc Faucher is also with the University of Lille, CNRS, Centrale Lille, University Polytechnique Hauts-de-France, UMR 8520 -IEMN -Institut d'Electronique de Microélectronique et de Nanotechnologie, F-59000 Lille, France.

Andrew P. Gregory is with the National Physical Laboratory, U.K. (email: andrew.gregory@npl.co.uk).

Leif Jensen is with TopSil GlobalWafers A/S, Denmark (email: lej@gwtopsil.com).

Color versions of one or more figures in this letter are available at XXX. Digital Object Identifier XXX Novel mm-Wave Oscillator Based on an Electromagnetic Bandgap Resonator problem of excessive phase noise affecting high frequency oscillators operating in the mm-wave band.

II. ULTRA-HIGH Q-FACTOR RESONATOR DESIGN

Low-loss and high-performance dielectric materials are crucial for realizing dielectric resonators as part of oscillators in high performance telecommunication systems. The dielectric material chosen for the investigation and characterization of the resonator is the High Resistivity Silicon for GHz and THz Applications supplied by TopSil GlobalWafers A/S [START_REF] Jensen | High Resistivity (HiRes TM ) Silicon for GHz & THz Technology[END_REF].

The design of the silicon EBG resonator relies upon the creation of a surrounding region of the silicon exhibiting an EBG and this is realized using a triangular lattice of air holes perforating the planar silicon wafer. The resulting transverse electric (TE)-like bandgap is defined according to the substrate parameters (e.g., its height as well as the hole diameter and the lattice constant). The neutron-irradiated high-resistivity silicon (HRS) used has a measured permittivity 𝜀 𝑟 equal to 11.68 and loss tangent 𝛿 𝑙𝑜𝑠𝑠 of 1.2 × 10 -5 (294 K), including both dielectric and finite conductivity losses. The substrate has a thickness of 1000 µm, the holes have a radius of 863.5 µm and a lattice constant of 1831 µm. The periodic EBG structure prohibits propagating modes within its bandgap and the energy stored inside a localized mode cannot be transported through this region of the silicon wafer.

The resonator is formed by the concatenation of unit cells with a small increase in horizontal width period from the central unit cell to the outer unit cells, as shown in Fig. 1, to confine the resonant mode. The unit cell analysis is performed assuming infinite periodicity in the x-axis directions. The unit cells are engineered so that the majority of the propagating mode's energy is concentrated in an air gap rather than the silicon. The approach introduced here employs the idea of reducing the dielectric filling factor of the resonator to reduce overall dielectric loss of the resonator. The filling factor  is defined as the ratio of the electromagnetic energy of a resonator stored inside the silicon to the total stored electromagnetic energy. By lowering  the achievable quality factor increases according to 1/( tan 𝛿) with tan 𝛿 being the loss tangent of the silicon substrate material.

The filling factor can be expressed as follows:

 = ∭ 𝜖 𝑠𝑖 |𝐸| 2 𝑑𝑣 𝑉 𝑠𝑖 ∭ 𝜖(𝑣)|𝐸| 2 𝑑𝑣 𝑉 𝑡 , ( 1
)
where 𝑉 𝑠𝑖 is the volume of the silicon forming the EBG resonator and 𝑉 𝑡 is the total volume containing the resonant mode. The denominator represents the total energy of the mode.

To minimize out-of-plane losses, it is necessary to shape the electric and magnetic field in the resonator to reduce wavevector components inside the light cone [START_REF] Tanaka | Design of Photonic Crystal Nanocavity with Q-Factor of ~10 9[END_REF][START_REF] Akahane | High-Q Photonic Nanocavity in a Two-dimensional Photonic Crystal[END_REF]. A common approach is to create a Gaussian envelope of the field by linearly increasing reflection from the center to outer unit cells. This is achieved by varying the horizontal period (width) of the unit cells quadratically with the distance in the ±x-directions, as shown Fig. 1. The EBG resonator design has been simulated using a range of tools implementing different techniques such as Meep with FDTD (time-domain) and rectangular grid meshing, CST Studio with FEM and tetrahedral meshing, and Empire XPU tool. After careful optimization of the parameters and best simulation results obtained, the EBG resonator was manufactured. An NTD float zone silicon wafer with high resistivity (>400,000 Ω.cm), 150 mm diameter and 1000 µm thickness is etched using the deep reactive-ion etching (DRIE) method, which is a highly anisotropic process to achieve deep etch depths with steep-sided holes and trenches in wafer substrates.

The measurement results of the full two-port S-parameters achieved an outstanding loaded Q-factor (𝑄 𝐿 ) of 52,400 with insertion loss peak (𝑆 8,7 ) of -5.75 dB, shown in Fig. 2. The unloaded Q-factor (𝑄 𝑢 ) is calculated to be 108,300 at 45.77 GHz using 𝑄 𝑢 = 𝑄 𝐿 /(1 -|𝑆 8,7 (𝑓 0 )|), where 𝑄 𝐿 is calculated from the forward transmission 𝑆 8,7 using the 3 dB method and 𝑓 0 is the resonant frequency. It is important to highlight the importance of obtaining an insertion loss of approximately -6 dB to achieve the best phase noise results in oscillator applications [START_REF] Everard | Low Noise Oscillators[END_REF][START_REF] Lia | High Q-Factor Silicon Resonator for High Frequency Oscillators[END_REF]. The design approach of the active circuit is based on a monolithic microwave integrated circuit (MMIC) voltagecontrolled oscillator (VCO) using a high-performance 130 nm SiGe BiCMOS semiconductor technology process from IHP Microelectronics with cutoff frequency 𝐹 𝑇 up to 250 GHz and maximum frequency Fmax = 340 GHz. The oscillator has been realized in feedback topology: the MMIC contains a two-stage loop amplifier (black and red regions in Fig. 3) whose 2 nd stage has been designed in a balanced configuration, a 10 dB coupler (yellow) which serves to supply the oscillator signal to the output. This is followed by an electronic phase shifter realized by a 90° hybrid coupler (blue) which is terminated by varactor diodes at two ports. The total gain realized within the oscillator loop is 12.5 dB. To couple to the TE10 mode in the feed waveguides, the input and output of the circuit are connected through bond-wires to waveguide (WR-19) to microstrip transition probes. The waveguides include a waveguide bandpass filter and fine and coarse phase-shifters, and connect to the EBG resonator through triangular tapers created on the edge of the silicon substrate which protrude inside a standard WR-19 waveguide to couple to the 𝑇𝐸 10 mode. The output of the RF signal is obtained after an output amplifier (green region in Fig. 3) with a gain of 7.8 dB connected in the same way to a waveguide to coaxial adapter.

IHP Microelectronics provides an SG13S design kit for the ADS (Advanced Design Systems) simulation tool used in the design of the oscillator.

Figure 4 shows the block diagram for the MMIC oscillator and Fig. 5 shows the assembled oscillator inside its housing. The total power consumption of the oscillator is 215 mW, size is 157 x 88 x 29 mm and the weight is 442 g, including all connectors. The loss tangent of the silicon has a sharp increase for temperatures higher than 290 K [START_REF] Krupka | Electrical properties of as-grown and proton-irradiated high purity silicon[END_REF]. To avoid this region, a nominal operation temperature for the oscillator of 263 K is chosen as a compromise between increased cooling power requirements and higher Q-factor. Figure 6 shows the measured phase noise levels of -94.6, -120.3 and -142.6 dBc/Hz obtained at offset frequencies of 1, 10 and 100 kHz, respectively, with an output power of -1.2 dBm at a nominal impedance of 50 Ω at 263 K with zero tuning voltage. The oscillator also works at room temperature (290 K) with a corresponding degradation of 2 -6 dB in terms of single sideband (SSB) phase noise. Owing to the temperature variation of the silicon permittivity and the reduced dielectric filling factor of the resonator of 47%, the temperature drift of the oscillator frequency is 1 MHz/K. By means of PID temperature-control and thermally isolating the oscillator from the environment it is expected that a temperature stability of < ±0.05 K can be achieved resulting in a remaining frequency variation of ±50 kHz. The electrical tuning range of the oscillator is 239 kHz (0 to 3 Volts), which is limited by the operation of the phase shifters within the narrow passband of the resonator. Further precise frequency adjustment can be carried out by means of the tuning voltage or varying the resonator temperature.

Table 1 compares the overall performance of the oscillator with other microwave and mm-wave oscillators described in the literature. It can be seen that the oscillator compares favourably in terms of phase noise and FOM performance with state-ofthe-art oscillators. The oscillator 𝐹𝑂𝑀 is defined as 𝐹𝑂𝑀 = 𝐿(Δ𝑓) -20log (𝑓 0 /Δ𝑓) + 10log (𝑃 𝐷𝐶 /1mW), where 𝐿(Δ𝑓) is the phase noise in dBc/Hz at the frequency offset Δf from the oscillator frequency 𝑓 0 , and 𝑃 𝐷𝐶 is the total power consumption.

IV. CONCLUSION

This paper demonstrates a novel mm-wave oscillator employing a low-loss high-resistivity silicon resonator with a reduced dielectric filling factor of its resonant mode, leading to an improved Q-factor and thereby addressing the problem of excessive phase noise affecting high frequency oscillators operating in the mm-wave band. The oscillator also benefits from small size and low power consumption. Future work is to increase the Technology Readiness Level (TRL) of the oscillator, improve the frequency stability and tunability, and realize scaled versions operating at higher fundamental mode frequencies.

Fig. 1 .

 1 Fig. 1. (a) The EBG resonator with its dimensions and variable periodicity (𝑎 𝑛 ) along the x-axis. (b) The Gaussian envelope of the resonant mode achieved by linearly increasing the reflection from the center to the outer unit cells.

Fig. 2 .

 2 Fig. 2. (a) The measured results of the two-port S-parameters (amplitude and unwrapped phase of the forward transmission 𝑆 8,7 , and input reflection 𝑆 7,7 and 𝑆 8,8 amplitudes) coefficients and (b) the EBG resonator in its test jig interfaced with the waveguide-to-coaxial adapters.

Fig. 3 .

 3 Fig. 3. Layout of the MMIC VCO circuit.

Fig. 4 .

 4 Fig. 4. The complete block diagram of the MMIC VCO.

Fig. 5 .

 5 Fig. 5. The final MMIC VCO assembly in its housing (top half removed).

Fig. 6 .

 6 Fig. 6. Measured SSB phase noise of the oscillator at 263 K.

Table 1 .

 1 Comparison of state-of-the-art microwave and mm-wave oscillators. All SSB phase noise values were normalised to a 45 GHz carrier frequency and estimated values, shown in grey, were estimated based on the intercept within the slope regions.

	Ref. Description	Pout	SSB PN	FOM
		[dBm]	[dBc/Hz] @ offset	[dBc/Hz]
	[11] Tunable DRO @	+17.0	-33 @ [100 Hz]
	12.8 GHz		-65 @ [1 KHz] -96 @ [10 KHz]
			-122 @ [100 KHz
			-141 @ 1MHz
			-150 @ 10 MHz

This article has been accepted for publication in IEEE Microwave and Wireless Technology Letters. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/LMWT.2023.3268090 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information.