Christopher Y Leon-Valdivieso

Alejandro Garcia-Garcia

Cécile Legallais

Fahmi Bedoui

Alejandro Garcia

Electrospinning of biomedically relevant gradient scaffolds: From honeycomb to randomly-oriented microstructure

come

INTRODUCTION

Electrospun mats are promising materials for tissue regeneration since their structural and mechanical properties are able to mimic the physical environment of the extracellular matrix (ECM) of those tissues to be engineered [START_REF] Bölgen | Electrospun materials for bone and tendon/ligament tissue engineering[END_REF][START_REF] Yao | Self-assembly of electrospun nanofibers into gradient honeycomb structures[END_REF]. These non-woven fibrous structures exhibit large surface-to-volume ratio and tunable porosity and pore size [START_REF] Yao | Self-assembly of electrospun nanofibers into gradient honeycomb structures[END_REF][START_REF] Nedjari | Electrospun Honeycomb as Nests for Controlled Osteoblast Spatial Organization[END_REF], parameters that play an important role in cellular adhesion, infiltration and ingrowth [START_REF] Rnjak-Kovacina | Increasing the Pore Size of Electrospun Scaffolds[END_REF]. Moreover, the simplicity of the electrospinning process makes them attractive scaffold candidates for large scale production [START_REF] Persano | Industrial Upscaling of Electrospinning and Applications of Polymer Nanofibers: A Review[END_REF]. They have been widely studied for the engineering of musculoskeletal tissues including bone [START_REF] Bölgen | Electrospun materials for bone and tendon/ligament tissue engineering[END_REF][START_REF] Cirillo | Design of Bioactive Electrospun Scaffolds for Bone Tissue Engineering[END_REF][START_REF] Khajavi | Electrospun biodegradable nanofibers scaffolds for bone tissue engineering[END_REF], tendon [START_REF] Rothrauff | Braided and Stacked Electrospun Nanofibrous Scaffolds for Tendon and Ligament Tissue Engineering[END_REF][START_REF] Orr | Aligned multilayered electrospun scaffolds for rotator cuff tendon tissue engineering[END_REF] and ligament [START_REF] Pauly | Mechanical properties and cellular response of novel electrospun nanofibers for ligament tissue engineering: Effects of orientation and geometry[END_REF][START_REF] Petrigliano | In Vivo Evaluation of Electrospun Polycaprolactone Graft for Anterior Cruciate Ligament Engineering[END_REF]; however, complex structures such as the musculoskeletal interfaces remain a challenge [START_REF] Cross | Nanoengineered biomaterials for repair and regeneration of orthopedic tissue interfaces[END_REF][START_REF] Bayrak | Engineering Musculoskeletal Tissue Interfaces[END_REF][START_REF] Ladd | Co-electrospun dual scaffolding system with potential for muscleâ€"tendon junction tissue engineering[END_REF]. These interfaces connect dissimilar tissues (e.g. bone-tendon or bone-ligament) and play a critical role in the efficient distribution of loads between the tissues, allowing for optimal range of motion and stability [START_REF] Sahoo | Interface Tissue Engineering: Next Phase in Musculoskeletal Tissue Repair[END_REF]. They can be seen mainly as a transition from hard-to-soft tissue where gradients in structure and mechanics are present [START_REF] Bayrak | Engineering Musculoskeletal Tissue Interfaces[END_REF] which is indeed one of the main characteristics to consider to develop scaffolds for interface tissue engineering.

Typically, three different engineering approaches have been studied to mimic the architecture of native tissue interfaces: monolithic, graded and layered scaffolds [START_REF] Cross | Nanoengineered biomaterials for repair and regeneration of orthopedic tissue interfaces[END_REF]. Monolithic scaffolds (comprising only one type of cell-loaded material) are commonly used to model one tissue type, nevertheless they usually fail to mimic the anatomical structure or properties of a multitissue system; the gradient and layered scaffolds represent a better alternative to recapitulate the smooth tissue-to-tissue transition [START_REF] Cross | Nanoengineered biomaterials for repair and regeneration of orthopedic tissue interfaces[END_REF][START_REF] Chainani | Multilayered electrospun scaffolds for tendon tissue engineering[END_REF]. Particularly, the osteotendinous junction has been engineered by several groups by fabricating graded scaffolds; however, much of the research focuses on the preparation of nanofiber composites with a continuous chemicalcomposition gradient [START_REF] Bayrak | Processing of polycaprolactone and hydroxyapatite to fabricate graded electrospun composites for tendon-bone interface regeneration[END_REF][START_REF] Lipner | The mechanics of PLGA nanofiber scaffolds with biomimetic gradients in mineral for tendon-to-bone repair[END_REF][START_REF] Zou | Electrospun fibrous scaffolds with continuous gradations in mineral contents and biological cues for manipulating cellular behaviors[END_REF] while less examples of continuous structure gradient are reported [START_REF] He | Electrospinning of nanofibrous scaffolds with continuous structure and material gradients[END_REF][START_REF] Khandalavala | Electrospun Nanofiber Scaffolds with Gradations in Fiber Organization[END_REF]. One of the latter is the generation of PCL scaffolds with gradation in fiber organization by using a 2-step electrospinning process, which rendered materials with a discreet transition from uniaxially-aligned to random fiber orientation. This method, nonetheless, comprises a non-traditional set-up that yields different thicknesses across the scaffold, which could potentially compromise its mechanical properties and further applications [START_REF] Khandalavala | Electrospun Nanofiber Scaffolds with Gradations in Fiber Organization[END_REF]. Similarly, the development of electrospun layered (or multi-region) scaffolds for interface tissue engineering is limited to "aligned-to-random" fiber orientation.

Xie et al [START_REF] Xie | Aligned-to-random" nanofiber scaffolds for mimicking the structure of the tendon-to-bone insertion site[END_REF] fabricated electrospun multi-region collagen scaffolds to mimic the morphology of the osteotendinous junction; while their approach indeed produced aligned and random fiber organizations, the mechanical properties of the construct varied significantly by region, making the transition other than smooth between the layers.

The microfibrillar scaffold architecture is well-known to influence in a significant manner stem cells fate [START_REF] Kumar | determination of stem cell fate by 3D scaffold structures through the control of cell shape[END_REF], since it provides with appropriate physical cues for nutritional conditions (porosity, pore size) and spatial organization (scaffold's geometry) for cell growth [START_REF] Yang | The Design of Scaffolds for Use in Tissue Engineering. Part I. Traditional Factors[END_REF]. Among all the fibrillar architectures reported, honeycomb-patterned structures have recently attracted the attention of biomaterials research groups because they present high structural stability and good permeability [START_REF] Yao | Self-assembly of electrospun nanofibers into gradient honeycomb structures[END_REF]. These bioinspired scaffolds have been used in cardiac and cartilage engineering [START_REF] Engelmayr | Accordion-like honeycombs for tissue engineering of cardiac anisotropy[END_REF][START_REF] Masuoka | Tissue engineering of articular cartilage with autologous cultured adipose tissue-derived stromal cells using atelocollagen honeycomb-shaped scaffold with a membrane sealing in rabbits[END_REF] but they are also known to promote the proliferation and differentiation of osteoblasts for bone regeneration [START_REF] Yao | Self-assembly of electrospun nanofibers into gradient honeycomb structures[END_REF][START_REF] Nedjari | Electrospun Honeycomb as Nests for Controlled Osteoblast Spatial Organization[END_REF][START_REF] Garcia | 3D Honeycomb Scaffolds for a Cellular Microenvironment Adapted to Maxillofacial Bone Reconstruction[END_REF].

Here, we report the fabrication of an electrospun multi-region material in a single-step process that combines two main fibrillar organizations: honeycomb-like (HC) and randomly oriented (RO). These structures are joined together by an interface that, we hypothesize, could act as a smooth transition between the two moieties due to the presence of smaller macropores (compared to the HC region) which in turn could induce gradual variations in the mechanical properties of the construct by region. Our aim is to propose a strategy to generate multi-region materials with a transitional zone that can potentially be used to engineer the osteotendinous junction. To achieve this goal, we set up an electrospinning collector by using HC-patterned masks which were employed as guides for the HC and interface region, while an adjacent flat aluminum area was used for the RO area. In this work, two polymers were chosen to fabricate the multi-region scaffolds: 1) polycaprolactone (PCL) due to its biocompatibility (FDAapproved) and widely reported uses in electrospinning and tissue engineering [START_REF] Woodruff | The return of a forgotten polymerâ€"Polycaprolactone in the 21st century[END_REF] and 2) polyvinylidine fluoride (PVDF) whose piezoelectric properties generate electrically charged surfaces that induce and favor cellular responses [START_REF] Szewczyk | Surface-Potential-Controlled Cell Proliferation and Collagen Mineralization on Electrospun Polyvinylidene Fluoride (PVDF) Fiber Scaffolds for Bone Regeneration[END_REF][START_REF] Guo | Piezoelectric PU/PVDF electrospun scaffolds for wound healing applications[END_REF][START_REF] Rodrigues | -PVDF Membranes Induce Cellular Proliferation and Differentiation in Static and Dynamic Conditions[END_REF], thus potentially able to ensure promising materials for the design and manufacture of cellular scaffolds for interface tissue regeneration.

MATERIALS AND METHODS

Preparation of electrospinning collector

The collector was set up by taping two HC-patterned metallic templates onto a conductive foil (aluminum) and spaced 1 cm apart from each other. Each template contains also a second macroporous pattern which was used to fabricate the interface region. The final configuration can be seen in Figure 1.

2.2.

Fabrication of multi-region materials via electrospinning

Scanning Electron Microscopy (SEM)

Dried samples (typically 5x5 mm) were mounted in carbon discs, sputter-coated with gold/palladium in a Quorum SC7620 Sputter Coater (Quorum Technologies) and analyzed with a FEI Quanta 250 FEG SEM. Fiber and macropore diameters as well as fibers orientation

were measured with ImageJ (v1.49p, http://rsb.info.nih.gov/ij) on acquired images as follows:

Macropore diameter measurement. The area of both HC and interface macropores was approximated to a circumference and the diameter calculated from it. Images were filtered and tresholded (same value was used for all images) to mark a macropore's contour and quantify it. In each case, at least 70 macropores were measured (n=3 per type of scaffold).

Fiber diameter measurement. Perpendicular transversal lines were drawn between the edges of individual fibers, quantifying the length as their diameter. 175 fibers were counted for each fiber diameter distribution (n=3 per type of scaffold).

Orientation of fibers: Representative images were used to quantify the orientation distribution of fibers in the HC and RO regions of PVDF-20, which was evaluated with OrientationJ (plugin for ImageJ) by setting the number of pixels=2 and the minimum energy and coherency to 10%.

Tensile testing (Elastic modulus)

Uniaxial tensile testing (at room temperature) was used to determine the Elastic modulus (E) of the PCL-20 and PVDF-20 scaffolds; this measurement was performed on the different regions of the scaffolds (HC, interface, RO) as well as in the joined scaffold (HC, interface and RO together). Samples were cut up into stripes (1 cm x 3 cm for HC, RO and joined sccafold; 2 mm x 3 cm for the interface) with an average thickness = 51±15 m which was measured using a precision dial thickness gauge (Mitutoyo Corporation, Japan). All the measurements were made with (at least) n=4 per region. Samples were secured with the metallic grips of the tensile tester (Bose electroforce 3200, TA, USA) and stretched at 0.1 mm s -1 using a 22N load cell. In the case of the joined scaffolds, part of the HC and RO regions were gripped, exposing the rest of them and the interface in the middle of the testing length.

The retrieved force and displacement values were used to derive E: force data was divided by the material's surface area to yield the tensile stress values, which was then plotted against the strain data and fitted to a linear model within the linear range (5-15% strain), obtaining E as result of the fitting to the linear-region slope. The void area of HC and interface regions was estimated from the previously acquired SEM images and taken into account for the calculation of E.

X-Ray diffraction

X-Ray diffraction (XRD) spectra of PVDF-20 samples (HC and RO regions) were obtained using a Bruker D8 Advance Diffractometer system. XRD scans were performed on the top surface of the corresponding films, with 2angles ranging from 5 to 70° and a step interval of 0.02°. Retrieved data was analyzed with Diffrac Plus V4 software (Figure S1, Tables S1, S2

and S3). n = 3.

RESULTS AND DISCUSSION

The ultimate goal of this study is to fabricate multi-region scaffolds that can resemble the complex fibrillar architecture(s) found in native tissue-to-tissue systems. Particularly, we are interested in producing materials that can be potentially used to direct stem cells to differentiate down different lineages: bone and tendon. In addition, the presence of a middle transitional layer was considered; this type of structural functionality is perhaps the main target in interface tissue engineering [START_REF] Cross | Nanoengineered biomaterials for repair and regeneration of orthopedic tissue interfaces[END_REF][START_REF] Bayrak | Engineering Musculoskeletal Tissue Interfaces[END_REF]. Honeycomb-like (HC) and randomly-oriented (RO) microstructures were chosen because they have been studied for bone [START_REF] Garcia | 3D Honeycomb Scaffolds for a Cellular Microenvironment Adapted to Maxillofacial Bone Reconstruction[END_REF][START_REF] Nedjari | Three Dimensional Honeycomb Patterned Fibrinogen Based Nanofibers Induce Substantial Osteogenic Response of Mesenchymal Stem Cells[END_REF] and tendon [START_REF] Chainani | Multilayered electrospun scaffolds for tendon tissue engineering[END_REF][START_REF] Lee | Polymer fiber-based models of connective tissue repair and healing[END_REF] regeneration, respectively. Such morphologies, along with a macroporous interface, were integrated into an electrospinning collector designed in our group (Figure 1).

Further, the collector's configuration rendered symmetrically-structured scaffolds (i.e. HCinterface -RO -interface -HC; Figure 2A) which can be also used to engineer other multitissue platforms, such as the bone-ligament-bone system [START_REF] Font Tellado | Strategies to engineer interface: Biomaterials, cells and growth factors[END_REF].

We explored the versatility of multi-region fabrication by using two different polymers: 1) PCL, because of its FDA approval for clinical use and 2) PVDF, due to its piezo-electrical properties which enhance cellular attachment and bioactivity [START_REF] Guo | Piezoelectric PU/PVDF electrospun scaffolds for wound healing applications[END_REF][START_REF] Rodrigues | -PVDF Membranes Induce Cellular Proliferation and Differentiation in Static and Dynamic Conditions[END_REF], thus both being promising materials for the production of cellular scaffolds.

Multi-region PCL scaffolds

First, we investigated the effect of the volume of electrospun polymer on the final scaffold's structure, while keeping the rest of the parameters constant. To do this, a range of PCL volumes from 0.1 to 0.6 mL was used (corresponding to electrospinning times of 5, 10, 20 and 30 min, respectively; table 1). Among all the fabricated scaffolds, only PCL-5 did not form a film that can be manipulated after the process had ended. The rest of the tested volumes generated stable scaffolds with a thickness that varied from 20 to 70 m. As depicted in Figure 2B, the macrostructural characteristics of the resulting scaffolds changed according to the volume of polymer used. For instance, PCL-10 and PCL-20 presented a dense surface in the RO region and well-defined and open macropores in the HC area, the latter being a favorable characteristic in 3D scaffolds for nutrients exchange, proliferation and migration of cells as well as vascularization [START_REF] Loh | Three-dimensional scaffolds for tissue engineering applications: role of porosity and pore size[END_REF]; nevertheless, PCL-10 was very fragile (scaffold too thin compared to the others) and therefore it presented poor handleability. In contrast, PCL-30 was found to be a more structurally-stable scaffold (thus easy to handle) with relatively smaller yet denser HC pores compared to PCL-10 and PCL-20. Further structural characterization showed that the PCL volume played an important role in the fibrillar density and macropore size of the different regions. First, there is an apparent decrease in the HC macropore diameter with increasing volumes of electrospun polymer (Figures 4A and5A), which is caused by the gradual deposition of fibers from the outside to the inside of the macropore with longer electrospinning times; the latter can be corroborated by comparing the HC macropore diameter of the template with those of PCL-10 and PCL-20

(557±46µm vs 867±74µm and 506±51µm, respectively). PCL-30 showed HC macropores which are fully covered by fibers, however, the shape (thus the size) of the macropores could be still marked. Secondly, the interface macropores were affected in the same PCL-volumerelated fashion; for instance, PCL-10 showed significantly bigger interfacial macropore diameters than the ones in PCL-20 (101±10 and 80±10 nm, respectively; Figures 4B and5B)

while they appeared to be non-existent (i.e. covered with fibers) in PCL-30 as stated before (Figure 3, PCL-30 panel). Third, there was not any apparent structural change in the RO region (Figure 4C) at different volumes of PCL.

Finally, the fiber diameter remained unchanged regardless the volume of polymer used (Figure 5C), the region and/or the fiber spatial location in the scaffold (including the interior or exterior of the HC macropore; Figure 3A panel PCL-30). Interestingly, fibers located only near the HC macropore edges followed the directionality of the contour (PCL-10 and PCL-20), a behavior that has been demonstrated in other electrospun HC systems [START_REF] Yan | Self-Assembly of Electrospun Polymer Nanofibers: A General Phenomenon Generating Honeycomb-Patterned Nanofibrous Structures[END_REF]; other than that they remained randomly aligned as proved elsewhere for motionless electrospinning [START_REF] Khandalavala | Electrospun Nanofiber Scaffolds with Gradations in Fiber Organization[END_REF].

Further characterization was focused only on PCL-20 since we consider it the most relevant for tissue engineering; it represents a good compromise between 1) well-defined and open HC macropores, a type of substrate that is proven to provide stem cells with structural cues to stimulate their proliferation and differentiation into osteoblasts [START_REF] Nedjari | Electrospun Honeycomb as Nests for Controlled Osteoblast Spatial Organization[END_REF][START_REF] Garcia | 3D Honeycomb Scaffolds for a Cellular Microenvironment Adapted to Maxillofacial Bone Reconstruction[END_REF], 2) the presence of a porous interface that could allow for a gradual transition between the HC and RO structures, and 3) the ease to handle the material without causing any damage to the different substructures. where fiber diameter,  = HC macropore diameter and  = interface macropore diameter. Fiber diameter distribution is an average of the three zones since they did not exhibit any significant difference between them (not shown). (*p = .05).

Uniaxial-tensile testing was used to gain more insight about the local and global mechanical properties of the multi-region scaffolds. It is indeed desirable that each region exhibits different and optimal mechanical environment that will drive accurate cellular differentiation;

for instance, differentiation of mesenchymal stem cells into osteoblasts has been demonstrated to be promoted in stiffer substrates compared to softer ones [START_REF] Sun | Extracellular matrix stiffness controls osteogenic differentiation of mesenchymal stem cells mediated by integrin α5[END_REF].

Figure 6A shows that all of the regions presented a linear elastic behavior and are subject to plastic deformation at around 30 % strain. Interestingly, the strain-hardening response of the regions was gradually increased across the scaffold (i.e. RO < interface < HC) which could be an effect of the transverse fiber alignment introduced (to different extents) by the interface and HC macropores. None of the regionss showed failure to tensile stretch within the applied strain. Conversely, variations of the elastic modulus (E) were more discreet (Figure 6B). The interface and RO regions exhibited similar E values (3.6±0.6 and 3.7±0.6 MPa) in spite of the structural differences between them; in comparison, the HC zone displayed a higher E

(5.4±0.7 MPa) which we ascribed to be the result of the directional organization (i.e.

increased anisotropy) of the fibers in the HC macropores, even though it presented a decrease of 43% of the fiber density compared to RO. Moreover, the calculated values of E for all the regions where in agreement with the range of values obtained for similar HC-shaped scaffolds by Wittmer et al [START_REF] Wittmer | Well-organized 3D nanofibrous composite constructs using cooperative effects between electrospinning and electrospraying[END_REF], however, our trend seems to be opposed to the one obtained by them:

while our HC samples exhibit significantly higher E than RO, they found that 3D-HC scaffolds led to a substantial decrease of E by a factor 8.5 compared to their "random" version (HC macropores fully covered with fibers). Factors such as the type of electrospun polymer (polylactic acid) and also the electro-spraying of poly(-ethylene oxide) (PEO) to create the 3D internal microstructure might explain these contrasting results. Finally, it is important to note that the average E of the joined scaffold can be considered as the synergistic effect of the HC and RO zones, and that the presence of an interface does not affect it; as a matter of fact, this connecting layer did not contribute to a gradual variation of E (at macroscale) across the construct. However, it combines features from both neighboring moieties: a porous morphology like HC and similar mechanical properties to the RO side, which in turn could be beneficial for smoothing the hard-to-soft transition between the two types of structure of the multi-region scaffold.

Multi-region PVDF scaffolds

To take a step further on this study, we assessed the reproducibility of our electrospinning process with a semi-crystalline polymer, PVDF, whose β-phase (one of its 5 crystalline polymorphs) is well-known for having piezoelectric characteristics that are relevant in tissue engineering [START_REF] Guo | Piezoelectric PU/PVDF electrospun scaffolds for wound healing applications[END_REF][START_REF] Rodrigues | -PVDF Membranes Induce Cellular Proliferation and Differentiation in Static and Dynamic Conditions[END_REF]. PVDF was electrospun onto the multi-region collector by keeping the same parameters as with PCL-20. SEM characterization showed that the 3 microstructures of the PVDF-based scaffold (PVDF-20) were well-preserved (Figure 7A-C); there are, however, important differences to note when compared to PCL-20 (Figure 7D): first, there was a slight reduction in the macropore size in both HC (506 ±51µm vs. 409±34µm) and interface (80±11µm vs. 60±6µm) regions; secondly, the averaged fiber size (considering all the regions) was substantially decreased (614±125nm for PCL-20 vs. 339±58nm for PVDF-20), which we believe to be the result of the polymer's nature: PVDF possess a permanent electrical polarization which enhances the electrostatic attraction between the charged polymer and the collector, causing the jet (thus the fibers) to be stretched to a higher extent compared to PCL; third, fibers located in the contour of the HC macropores were highly oriented in comparison to the interface and RO zones (insets in Figures 7A-C), and even to HC in PCL-20 (Figure S2). Interestingly, the mechanical properties of PVDF-20 showed a similar trend to PCL-20, although in this case the E values were significantly increased (at least two-fold) for all the regions and the joined scaffold (Figure 7E). XRD analysis suggested that, as proved by Guo et al. [START_REF] Guo | Piezoelectric PU/PVDF electrospun scaffolds for wound healing applications[END_REF], the electrospinning favored the appearance of the crystalline and electroactive β-phase (diffraction angle = 20.7), showing a tenfold increase compared to our control, the injection molding process (32±1.5% vs.

3.4±0.5%; Figure 8A and Table 2). Moreover, a slight but significant increase in the β-phase was found in the HC region in comparison to RO (32±1.5% vs. 29±1.1%, Table 2), which can be correlated with the reduction in fiber's size (251±37nm for HC vs. 353±53 nm for RO, Figure 8B). This is supported by the fact that extensional deformation introduced by electrospinning improves the molecular orientation (β-phase crystal array in this case) in smaller fiber diameters [START_REF] Pai | Mechanical properties of individual electrospun PA 6(3)T fibers and their variation with fiber diameter[END_REF]. Interestingly, we also found a variation in the fiber orientation degree (Figure 8C) between the regions, suggesting that the geometry of the HC substrate provokes an "extra stretching effect" (thus an increase in β-fraction) by dictating the collection of fibers in a highly aligned fashion. β-phase crystal transition is accomplished in electrospinning mainly by two mechanisms: electrical poling and mechanical stretching, both forcing the PVDF chains into a molecular conformation with all the dipole moments aligned in the same direction [START_REF] Lim | of β-phase in PVDF by electrospinning[END_REF]. In addition to this, our results indicate that the degree of polarization was enhanced in the HC region by the highly-aligned deposition of fibers on the macropore's contour, resulting in smaller fiber diameters compared to RO and a higher transition from nonpiezoelectric α-phase to the piezoelectric β-phase PVDF (Figure 9). Whether this variability in β-phase between the RO and HC zones is also related to the different substrates used for the preparation of the electrospinning template (steel for HC and aluminum for RO) is yet to be explored. ). An extra "stretching effect" is given by the substrate used to fabricate the HC region by dictating the fiber alignment on the contour of the macropores, leading to a smaller fiber diameter and higher β-phase content compared to RO. For easy visualization, α-phase regions in the individual fibers are shaded in gray circles.

CONCLUSIONS

In this study, we showed the feasibility of fabrication of PCL or PVDF multi-region materials by exploiting the versatility of electrospinning. The method used here rendered scaffolds with HC and RO fiber arrays, which are joined together by an interface. The structural analysis demonstrated that the macropore size in the HC and interface regions could be tailored by changing the electrospun polymer volume, while the fiber size distribution was regiondependent only in the PVDF-based scaffolds, which is closely related to the polymer's nature, fiber orientation and appearance of piezoelectric β-phase PVDF. Moreover, the mechanical behavior of either PCL-or PVDF-based scaffolds was reproducible, showing a discreet increase in the elastic modulus from the RO to the HC region. Our results demonstrate that we have engineered an interface with shared features with their adjacent regions: macroporous like HC and mechanically similar to RO; this could offer the possibility to smooth the bonetendon transition and thus improve cellular responses toward the regeneration of the multitissue system. Further in vitro studies might reveal the biological performance and applicability of this model in the reconstruction of interface tissues.

  PCL scaffolds: A 10% (w/w) polycaprolactone (PCL, MW= 80 kg/mol -1 , Sigma Aldrich, USA) solution was prepared by dissolving PCL pellets in a dicloromethane (DCM, Sigma Aldrich)/N,N-dimethylformamide (DMF, Reagent Plus ≥ 99%, Sigma Aldrich) mixture (80/20 v/v) and stirring overnight before electrospinning. The PCL solution was then transferred into a 5 mL glass syringe (Fortuna Optima) attached to an 18G blunt-tip needle.The syringe was loaded onto an automatic KDS-100 pump (Kd Scientific) and a flow rate of 0.025 mL/min was set. The distance between the tip of the of the needle and the collector was kept at 17 cm, while a constant potential difference of 15 kV was applied throughout the whole process with a custom-built electrical generator. Four different polymer volumes were used: 0.125, 0.25, 0.5 and 0.75 mL and the resulting scaffolds were named PCL-5, PCL-10, PCL-20 and PCL-30, where the number refers to the corresponding electrospinning time (i.e.5, 10, 20 and 30 min).PVDF scaffolds: 1.876g of Polyvinylidene fluoride (PVDF, FV306300, Goodfellow, Ltd, Cambridge, UK) were dissolved in 10mL of an acetone-DMF mix (60/40 v/v) and stirred (400 rpm) at 70°C during 1h. The PVDF solution (18% w/w) was then left to cool down for another 15 minutes before loading it into the syringe. The electrospinning parameters remained the same as for PCL scaffolds (distance syringe to collector = 17cm; applied voltage = 15 kV). A single polymer volume = 0.5 mL was used (PVDF-20; 20 min electrospinning time).

Figure 1 .

 1 Figure 1. Polymer solution (PCL or PVDF) was electrospun onto a flat collector (A) which was set up by using two metallic templates, each of them displaying 2 different macroporus patterns: 1) macropores witha size = 557±46 µm that form a region made of honeycomb-like (HC) structures, and 2) circular macropores with a size = 14±3 µm that generate the interface zone. These two templates were spaced 1 cm apart, leaving only a flat aluminum foil area in between them to allow the formation of a third region with the deposition of randomly-oriented (RO) fibers; HC and interface (Int) pores are magnified in black boxes, while the RO region is highlighted in the dotted box. After electrospinning (B), multi-region scaffolds showed the expected micro-structural organization of each region (RO, interface and HC; from top to bottom on the SEM images) made of nanofibers within the same diameter distribution.

Figure 2 .

 2 Figure 2. A) Template used for the fabrication of multi-region materials; this configuration allowed the electrospun mats to integrate the following structural array: HC, interface and RO (depicted in the figure as 1, 2 and 3, correspondingly). B) Electrospun mats (scaffolds PCL-10, PCL-20 and PCL-30); the structural rigidity of the constructs as well as the HC macropores can be observed.

Figure 3 .

 3 Figure 3. SEM images of the HC-interface transition for the multi-region template before (No fibers) and after (PCL-10, PCL-20, PCL-30) electrospinning.

Figure 4 .

 4 Figure 4. SEM images of HC (A), interface (B) and RO (C) regions. The HC macropore structure could be observed in PCL-10, PCL-20 and PCL-30, while the interface only was visible on PCL-10 and PCL-20. C focuses on the RO region of PCL-20 which was similar to the other two scaffolds. Fibers deposited either in the inner or the outer side of the HC macropore can be seen in A (PCL-30 panel).

Figure 5 .

 5 Figure 5. HC (A) and interface (B) macropore diameter and fiber diameter (C) distributions for PCL-10, PCL-20 and PCL-30 (white, light gray and gray bars, respectively). A-C results are summarized in (D)

Figure 6 .

 6 Figure 6. Typical Stress vs. Strain (A) curves obtained in the mechanical tensile tests for the different regions of PCL-20; (B) the corresponding Elastic modulus (E) calculated in the strain region 5-15%. (*p = .07)

Figure 7 .

 7 Figure 7. SEM images of PVDF-20 in the HC (A), interface (B) and RO (C) regions; zoom in A (thresholded image) showed alignment of the fibers on the edges of the macropores. (D) Comparison between the macropore size (HC and interface) and average fiber size of PVDF-20 (orange bars) and PCL-20 (light gray bars). (E) Elastic Modulus (E) of PVDF-20 by region. Scale bar in A, B and C insets = 5 µm. Interface macropores in (B) are pointed with black arrows. (*p = .05)

Figure 8 .

 8 Figure 8. (A) X-ray diffraction (XRD) of injection-moulded PVDF (top) and PVDF-20 by region: RO (middle) and HC (bottom); peaks at diffraction angles (2θ) 17.7, 18.3 and 19.9 correspond to the crystalline α-phase while the characteristic β-phase diffraction pattern can be observed at 20.7. (B) Fiber diameter of

Figure 9 .

 9 Figure 9. During electrospinning, the formation of β-phase (all-trans conformation) PVDF is promoted due to electrical poling and mechanical stretching effects, both of them causing the re-arrangement of the polymeric chains from their α-phase (trans-gauche-trans-gauche conformation) into their dipole form (all dipoles aligned in the same chain direction). An extra "stretching effect" is given by the

Table 1 .

 1 Volume of electrospun PCL, the corresponding electrospinning time and thickness of the multi-region samples prepared on this study.

	Sample	Volume (mL) Time (min)	Thickness (m)
	PCL-5	0.1	5	-
	PCL-10	0.2	10	21±10
	PCL-20	0.4	20	51±15
	PCL-30	0.6	30	71±26

Table 2 .

 2 Comparison of the β-phase (%) present on PVDF scaffolds

	obtained by electrospinning (PVDF-20: HC and RO) and simple injection
	molding, according to the XRD results.


I B Denysenko
email: idenysenko@yahoo.com

E Von Wahl

M Mikikian

J Berndt

S Ivko

H Kersten

E Kovacevic

N A Azarenkov

Plasma properties as function of time in Ar/C 2 H 2 dust-forming plasma

Keywords: argon/acetylene plasma, nanoparticles, time-dependence, volume-averaged model

The time-dependent properties of an Ar/C2H2 dusty plasma (neutral, ion and electron densities, effective electron temperature and dust charge) are studied using a volume-averaged model for conditions corresponding to experiments on nanoparticle growth. The calculated density evolution for C2H2, H2 and C4H2 molecules are compared with time-resolved measurement of the mass peaks of the neutral species and the effects of the dust density on the plasma properties are analyzed. Time evolutions of the main positive and negative ions are also obtained thanks to the calculations. As a consistency check the time-dependence of the dust radius is also obtained numerically, assuming that an increase of the dust radius is due to deposition of hydrocarbon ions and C2H radicals on the surface of dust particles. It is shown that for conditions corresponding to the experiment, the ions are the main contributor to the particle growth. The calculated dust growth rate is compared to the time-dependence of the dust particle size obtained in the experimental measurements. The results of the numerical calculations are found to be in a good qualitative agreement with the experimental data.

Introduction

Reactive plasmas containing growing nano-and micrometersized particles (dust particles) are of a great fundamental interest due to various useful technological applications [START_REF]Dusty Plasmas: Physics, Chemistry, and Technological Impacts in Plasma Processing[END_REF][START_REF] Vladimirov | [END_REF][3][4]. For the growth of carbonaceous dust particles, gas discharges from methane, acetylene or ethylene are usually used [5][6][7]. To control the dust particle growth, these discharges have been intensively investigated by many authors [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].

Experiments in Ar/C2H2 plasmas revealed that formation of dust particles is accompanied by a decrease of electron and acetylene densities and by an increase of electron temperature and density of metastable argon atoms [10][11][12][13]. In [13,23], it was also shown that the degree of dissociation of acetylene can be as high as 99%. In [24], nanoparticles from a dusty Ar/C2H2 plasma were extracted and the average dust particle diameter as a function of time was determined. Numerous experiments also revealed that the formation of nanoparticles in Ar/C2H2 plasmas exhibits a periodical behavior [11,15,25]. It is widely accepted that the formation is characterized by a few stages [START_REF]Dusty Plasmas: Physics, Chemistry, and Technological Impacts in Plasma Processing[END_REF]25]. In a first stage which is mainly driven by plasma chemical reactions, stable, nanometer sized protoparticles or clusters are produced [25]. After this nucleation stage, the coagulation stage takes place when the protoparticles frequently collide with each other resulting in the formation of dust particles with sizes up to several tens of nanometers. The third and slowest growth stage is the accretion stage where radicals and ions from plasma stick to the dust particles. However, it is unclear at present which species (ions or radicals) affect more essentially the nanoparticle growth in the accretion stage. In [26], it was found experimentally that the diameter of dust particles increases during the accretion stage nearly linearly in time. It was also concluded that the particles grow nearly monodisperse, i.e., their size distribution is very narrow [24,26]. At the end of the accretion stage the dust particles reach a maximum size (a few hundred nanometers) and leave the discharge because of the interplay of different forces on the dust particles, and then a new growth cycle starts.

C2H2 and Ar/C2H2 RF plasmas have already been studied by computer simulations [16][17][18][19][20][21]27]. The studies allowed to explain the nucleation of nanoparticles in these chemistries. It was shown that both positive and negative ions may participate as precursors in the initial stage of particle formation [17,19]. Meantime, most of these numerical studies considered only the nucleation stage of particle formation and, therefore, they did not account for effects of dust particles on plasma properties, which are usually important as seen in experiments. Effects of dust particles on Ar/C2H2 plasmas in glow and afterglow regimes were studied in [15,28], using a volume averaged model, and the results for the glow plasma were compared with mass spectrometry measurements. It was found that due to collection of electrons and ions by dust particles, the effective electron temperature, the densities of argon ions and metastable argon atoms are larger in the dusty glow plasma comparing with the dust-free case, while the densities of most hydrocarbon ions and acetylene molecules are smaller [15]. Note that most of numerical studies on Ar/C2H2 and C2H2 plasmas were carried out using steady-state models that do not fully consider the dusty plasma dynamics with periodical growth of nanoparticles and variation of dust radius with time.

In this paper, we present the time-dependencies of plasma properties (ion, electron and neutral particle densities, effective electron temperature and dust charge) in an Ar/C2H2 dusty plasma obtained using a global (volume-averaged) model. Effects of growing dust particles in the plasma volume on the plasma properties are investigated. The calculated evolution of the densities of C2H2, H2 and C4H2 molecules are compared to the measured time-dependencies for the mass peaks of the neutral species. We also obtain the dust radius as a function of time for the accretion stage. The calculations are carried out assuming that the growth is due to deposition of hydrocarbon ions and C2H radicals on the dust particles. The calculation results for the dust growth rate are compared to those obtained from experimental measurements.

Theoretical model

Main assumptions and equations

In the model, it is assumed that the Ar/C2H2 gas-discharge plasma has R = 22 cm radius and L = 32.4 cm height and is sustained in a cylindrical stainless-steel chamber. The input fluxes of acetylene and argon are QC2H2 (=1.5 sccm) and argon QAr (=11.0 sccm), respectively. The plasma is driven at a RF power of 9 W by a RF generator. The external parameters are taken to be nearly the same as in the experiment [15,24]. The plasma consists of electrons with density ne, seven positive ions with densities + α n (where the index α = C2H2, Ar, ArH, C4H3, C4H2, C6H4 and C2H3 corresponds to the C2H2 + , Ar + , ArH + , C4H3 + , C4H2 + , C6H4 + and C2H3 + ions, respectively), six neutrals (four nonradical and two radical) with densities α n (where the index α = Ar, C2H2, H2, C4H2 corresponds to the nonradical neutrals Ar, C2H2, H2, C4H2, respectively, and α = C2H, H is for the radicals C2H and H, correspondingly), negatively charged dust particles with density nd, radius ad and charge Zd (in units of electron charge), metastable argon atoms (Arm) with density nm, argon atoms in the resonance 4s states ( 3 P1 and 1 P1) (Arr) with density nr as well as argon atoms in 4p states (Ar(4p)) with density n4p. In our model, the metastable and resonance atom densities nm, nr and n4p represent the density of a composite ( 3 P0 and 3 P2) metastable level, the density of a composite ( 3 P1 and 1 P1) resonance level and the density of a composite 4p state, respectively. The model accounts for main positive ions and neutral species identified in our experimental measurements on mass spectra of positive ions and neutral species [15,28]. We do not account for H + and H2 + ions here because our previous experimental and numerical studies [15,28] showed that the densities of these ions in the Ar/C2H2 gas-discharge are small while the collision rates of H + and H2 + with other plasma species are in the same order of magnitude as the corresponding rates for collisions of other positive ions.

We also assume that the plasma contains negative ions C2H -, C4H -and C6H -with densities nC2H-, nC4H-and nC6H-, respectively. At large ratio nAr/nC2H2, the anions C2H -are the dominant negative ions [20,21]. On the contrary, in pure C2H2 plasmas, larger anions, like C12H -and C6H -are dominant [6,17,18]. The dominant neutral species are argon atoms with density ) /(

g B Ar T k P n ≈
, where P = 4.2 Pa is the pressure of argon gas and B k is the Boltzmann constant. We assume that the energy distribution for ions is Maxwellian, and that the ions and dust particles are at gas temperature Tg (300 K).

It is assumed that the electron energy distribution function (EEDF) F has a Druyvesteyn shape [29]:

1/2 2 1 2 ( ) exp( ), F A A ε ε ε = - ( 1
)
where ɛ is the electron energy and A1 and A2 are functions of the average electron energy [29] eff 0

3 ( ) 2 F d eT ε ε ε ε ∞ = = ∫ and eff
T is the effective electron temperature. The EEDF has the

following normalization 0 ( ) 1. F d ε ε ∞ = ∫
The Druyvesteyn distribution is typical for RF plasmas under conditions considered here [30].

The plasma is assumed to be quasineutral, or

2 4 6 C H H C e C d H d n n Z n n n n α α - - - + = + + + + ∑ . ( 2
)
The density of a species X (ions or neutrals) is obtained from the balance equation

( ) ( ) ( ) , , X X X G i L i i i dn R R dt = - ∑ ∑ , (3) where ) (
,

X i G R and ) ( , X i L
R are, respectively, the rates for reactions describing various generation and loss processes of the species X and t is the time. Here, we consider various processes for the loss and generation of the discharge species, including the processes on plasma walls and dust particles, the collisional processes in the bulk plasma, as well as the pumping of gas in and out of the chamber. The processes are detailed in the next subsection.

The effective electron temperature is found from the power balance equation

P P dt V   = -     (4)
where Pabs = 9 W is the absorbed power, V is the volume of the discharge chamber, the power loss Ploss = Pcoll + Pw + Pd, where Pcoll is the power loss due to elastic and inelastic electron-neutral collisions, Pw and Pd are the power losses due to charged particle fluxes to the walls and to the dust particles, respectively. Here

( )

w j Bj effj i e j P en u A π ε ε + = + ∑ , 2 1 2 3 [ ( )] ( ) ( ) i s V ξ ε ε ξ ξ Γ = + Γ Γ
is the mean kinetic energy lost per ion [31] and , and λs is the screening length, which is of the same order as the Debye length [START_REF]Dusty Plasmas: Physics, Chemistry, and Technological Impacts in Plasma Processing[END_REF].

The balance equations for neutrals and ions, the power balance equation and the equation for dust charge are solved by using the DVODE package [START_REF] Byrne | VODE_F90 Support Page[END_REF]. Solving these equations, we assume that the dust density and dust radius are known at each instant. First, the system of first order differential equations is allowed to reach a steady state, i.e. d/dt = 0, for the case when the dust particles are absent from the plasma. After reaching the steady state, it is assumed that the dust radius increases linearly from 10 nm up to 70 nm at a fixed dust density (~ 10 7 cm -3 ) during 88 s. This is supported by our experimental measurements that show this size evolution with a quite narrow size distribution throughout the entire accretion phase with 10 nm sized particles being the smallest ones having been collected. At the end of the phase (when ad = 70 nm), we suppose that the dust particles leave the plasma (because of effect of different forces on the dust grains). After the particle leaving, it is assumed that the dust particles do not affect much the plasma (nd = 0) during next 20 s. After that, a new growth cycle starts.

Making use of the calculated densities of plasma species, effective electron temperature and dust charge (equations ( 1)-( 5)) at the assumption that dust radius grows linearly with time in the accretion stage, one can find the approximate time-dependence for the dust radius approx d a from the following expression:

2 2 2 2 4 ( ) C H approx d d C H C H d approx d d K m n K m n da dt a α α α α πρ + + + = ∑ , (6)
where

2 C H m
is the mass of C2H molecule, ( )

0.5 2 2 2 π ( ) 8 C H d st d B g C H K a t k T m γ π =
, st γ = 0.9 is the sticking coefficient for collisions of C2H radicals with dust particles, which is taken to be the same as that for collisions of the radicals with the walls [17,[START_REF] Von Keudell | [END_REF]. d ρ is the dust material density and the index α is related to hydrocarbon positive ions. The calculations are carried out for d ρ = 1.0, 1.5 and 2.0 g/cm 3 (typical values for the wide variety of carbon based materials [37,38] ).

Note that equation ( 6) is not used to calculate the timedependence for dust radius self-consistently with other plasma parameters. It is used to estimate impacts of ions and radicals on the growth of nanoparticles.

The rates for various generation and loss processes

The rate due to the flow of acetylene into a chamber of volume V is given by V 39], where [31,40]. γr is the sticking coefficient for the neutral particle on the wall surface,

Q J R H C H C / 10 48 . 4 2 2 17 2 2 × = = [31,
[ ] 1 2 ) /( ) 2 ( 2 / - - + Λ = r thr surf r n n r wall S V D K γ υ γ
r g B thr m T k π υ / 8 =
is the mean velocity of species r, r m is the mass of species r, Ssurf is the wall surface area of the reactor chamber,

n D is the neutral diffusion coefficient, [ ] 2 / 1 2 2 ) / 405 . 2 ( ) / ( - + = Λ R L n π
is the effective diffusion length. The neutral diffusion coefficients were calculated in the same manner as in [17,20]. The binary collision diameters, potential energies and polarizabilities of the background gases, which are necessary for the calculation of the diffusion coefficients of neutrals and ions, were taken from [17,19,41]. The sticking coefficient is a function of the radical species, the surface material, the surface condition (for example, substrate temperature and roughness) and even the plasma parameters (for example, ion flux) [42,43]. Formation of thin films on the chamber walls during the growth of nanoparticles in the plasma volume can also affect the sticking coefficients [44]. The sticking coefficients for C2H and H radical neutrals are assumed to be 0.9 and 0.1, respectively [17,42,45].

For the radical neutrals and metastable argon atoms, it is accounted for their deposition on dust particles, and the rate describing the loss process in equation ( 3) is taken to be , respectively. We do not account for negative ion deposition on dust particles because their energy is essentially smaller than the dust surface potential. To determine the rates describing the ion losses on the plasma walls, we obtained the ion mobility j µ and the ion diffusion coefficient j D for a j-th ion. The mobility of the j- th ions in the mixture of gases can be calculated in the same way as the diffusion coefficient of a neutral particle, by Blanc's law,

∑ = i ij i j tot P P ) / ( / µ µ
, where Ptot is the total gas pressure in pascals and Pi is the partial gas pressure. The ion mobility of the ionic species j in the background gas i (in m 2 V - 1 s -1 ) can be calculated from the following expression [START_REF] Mcdaniel | The mobility and diffusion of ions in gases[END_REF]: , and the ion mean-free path [31], /

tot g i ij ij P T m / ) ( 514 . 0 5 . 0 - = α µ , where i α (in
j j j j B ion D m k T λ υ =
, where j m is the mass of j-th ion, and 8 /

j B ion j k T m υ π =
is its average velocity. Using the expressions, the rate in equation ( 3) describing the loss of the j-th positive ion on the plasma walls is given by

+ = j wj n K R [31], where 2 2 effj wj Bj A K u R L = , Rj Lj effj RLh h R A + = 2 , 2 2
aLj j L h α λ -   ≈ +   +     , 1/2 0 0.8 4.0 1 aRj j R h α λ -   ≈ +   +     , 0 e 3 2 n n α - = , 2 4 6 C H C H C H n n n n - - - - + = + , 1 0 eff 0 1 1 2 2 bLj B ion j eT L h k T α α π λ -       ≈ +     +       , 1 0 eff 0 1 1 2 bRj B ion j eT R h k T α α π λ -       ≈ +     +       , 1 1/2 * eff 3/2 1 ( ) j j cj B ion n n eT h k T n - + -     ≈ +             , * 8 15 1 56 B ion j j recj j k T n m K π λ = [47 -49
] and recj K is the rate for collisions of negative ions with j-th positive ions. recj K = 1.01×10 -7 cm 3 /s, 5.0×10 -8 cm 3 /s, 3.0×10 -8 cm 3 /s, 3.0×10 -8 cm 3 /s and 1.7×10 C2lH -+ C2H2 → C2l+2H -+ H2 1.0×10 -12 [18] C2lH -+ CmHn + → C2lH + CmHn 5.0×10 -8

[18]

C2lH -+ Ar + → C2lH + Ar 1.01×10 -7 [20] C2lH -+ H → C2lH2 + e - 1.6×10 -9 [50]
The main reactions of our model for collisions of C2H2, C4H2 and H2 molecules with plasma species are shown in tables 2, 3 and 4.

( ) ( ) K F d σ ε ε ε ∞ = ∫ .
The collision reactions for electrons with argon atoms, ions with C2H and H radicals are also taken into account in the model (they are described in detail in Supporting Information to [28]). For the reactions of electrons with C4H2, the cross sections of ionization, dissociation and electron attachment are taken to be the same as the corresponding cross sections for the reactions of electrons with C2H2, since no data concerning the cross sections are available in the literature. The cross sections describing the loss of C2H in collisions with electrons are taken from [51]. Considering the collisions of argon atoms in excited states Ar* (Arm, Arr or Ar(4p)) with C2H2 and C4H2 molecules (table 4), we assume that there are a few pathways of the reactions: Ar* + C2H2 (C4H2) → C2H2 + (C4H2 + ) + Ar + e -with the rate 0.9×10 -10 cm 3 /s, Ar* + C2H2(C4H2) → C2H(C4H) + Ar + H with the rate 1.75×10 -10 cm 3 /s, Ar* + C2H2 (C4H2) → C2H2* (C4H2*) + Ar (or C2H2(C4H2) + Ar + ω  ) with the rate 2.65×10 -10 cm 3 /s. Note that at present the rates for these reactions are not known. Meantime, the total rate describing the loss of argon metastable atoms in collisions with C2H2 (kq = 5.6×10 -10 cm 3 /s [61]) was measured. Thus, in this model the total rate for loss of Arm in collisions with C2H2 is nearly the same as the rate in [61]. More information on the different reactions and rates for various generation and loss processes, as well as elastic and inelastic collisions taken in to account in the power balance (equation ( 4)), can be found in [15,28] and in Supporting Information to [28].

Results

Time-dependencies for plasma parameters and their comparison with experimental data

Using the theoretical model presented in section 2, we have analyzed how main plasma parameters (neutral, ion and electron densities, effective electron temperature and dust charge) evolve as dust radius increases with time. These simulations have been performed for conditions similar to our experiments on nanoparticle growth.

Based on our experimental observations, we have made the following assumptions concerning the time-variation of ad: The duration of a nanoparticle-growth cycle is 108 s. Here we shall separate one growth cycle into two phases: During the first 20 s (phase I), the nanoparticle size is small and the nanoparticles do not modify any plasma properties. In the model, it has been assumed that the dust density equals zero for phase I. For the next 88 s (phase II), the dust radius increases linearly from 10 nm up to 70 nm at a fixed dust density (~ 10 7 cm -3 ). At the end of a growth cycle, dust particles leave the plasma (because of effect of different forces) and a new growth cycle starts. Note that in our previous works [15,24] one growth cycle was separated into three phases. The measurable diameter of dust particles was in the range 20-40 nm, 40-50 nm and 50-140 nm for the growth phases I, II and III, respectively. Here, to simplify the 0D model, we divide one growth cycle only in two phases, phase I without particles, phase II with constantly growing particles. Arm + Arm → 2Ar 2.0×10 -7

[49] Arm + Arr → Ar + Ar + + e -2.1×10 -9

[49] Ar(4p) + Ar(4p) → Ar + + Ar + e -

5.0×10 -10

[49]

Arm + Ar → 2Ar 2.1×10 -15 [49] Arr → Ar + ω

 10 5 s -1 [49] Ar(4p) → Ar + ω  3.2×10 7 s -1 [49] Ar(4p) → Arm + ω  3.0×10 7 s -1 [49] Ar(4p) → Arr + ω  3.0×10 7 s -1 [49]
Using the model, we have also calculated the dust radius as a function of time, assuming that the growth of nanoparticles with ad > 10 nm is due to deposition of C2H radicals and different hydrocarbon ions and compared this evolution with the experiment [24].

In figure 1(a), the calculated densities of C2H2, C4H2, H2, C2H and H as a function of time are shown. The timedependencies are obtained assuming that the dust density in the phase II is 1.5×10 7 cm -3 and the phases I and II start at t = 8 s and t = 28 s, respectively. Note that figure 1 shows cycles taken in a middle of a long sequence, so before 8 s it is the end of phase II from another cycle. In figures 1(b), 1(c) and 1(d), the normalized calculated densities of C2H2, C4H2, H2 are compared with the intensities of the mass peaks (in a.u.) measured in our experiments [15]. The calculated densities of C2H2 and C4H2 are normalized on 9.56×10 12 cm -3 to have the calculated maximums of these densities nearly the same as the maximums for the mass peaks in the experiment, while the density of H2 is normalized on 3.346×10 13 cm -3 (this normalization makes the calculated time-averaged density of H2 approximately the same as the averaged measured intensity of H2).

The calculated densities of C2H2, C4H2 and H2 are increasing during phase I. For phase II, C2H2 and C4H2 densities first decrease, reach a minimum and then increase.

The time dependency for C2H2, H2 and C4H2 is caused, in our opinion, mainly by the time variation for argon atoms in excited states, for electrons, C2H radicals and for positive ions since the nonradical species are mainly lost in collisions with these species (tables 2-4). The decrease of C2H2 and C4H2 densities in phase II is due to an enhancement of the losses of these nonradical species in collisions with excited argon atoms, positive ions and radicals. The densities of C2H2 and C4H2 increase at large times in phase II due to a reduction in ne, nm and nC2H (figures 1(a) and 2) with growing dust radius.

Since the loss of C2H2 molecules is essentially affected by their collisions with excited argon atoms and C2H radicals [28], their time-dependency is nearly the inverse to those for Arm and C2H (figures 1(a), 1(b) and 2(a)). Therefore, the minimum in nC2H2 is nearly at the same time as the maximums for Arm and C2H. During phase I (when the effect of dust particles on plasma parameters is small) which follows after phase II, the density of acetylene is growing because of little losses in different collisions. The C4H2 and H2 production is related to the C2H2 density [11], and, as a result, the timedependencies for the C4H2 and H2 densities (for H2, excepting the end of phase II) are similar to that for nC2H2.

Note that due to the loss of acetylene molecules in different collisions, the maximum magnitude of C2H2 density in the non-stationary plasma with growing dust particles (1.08×10 13 cm -3 ) is much smaller than the acetylene density in the chamber in the power-off case (1.38×10 14 cm -3 ).

Results of calculations for C2H2 and C4H2 are similar to the experimental time-dependencies for the mass peaks of C2H2 and C4H2 (figures 1(b) and 1(c)), while for H2 they are partly different (figure 1(d)). In particular, in the experiment the intensity of H2 mass peak in the beginning of phase I is decreasing, while the calculated density increases. Moreover, the difference between maximum and minimum magnitudes of mass peaks is nearly 30%, while the calculated maximum of H2 density is nearly 3 times larger than the minimum (figure 1(a) and figure 1(d)). Meantime, the time-dependence for the calculated nH2 and the measured mass peak intensity of H2 behave nearly the same way during most of phase II.

The density of C2H decreases during phase I, increases in the beginning of phase II, reaches a maximum and then decreases during most of phase II (figure 1(a)). The density of atomic hydrogen increases during phase I and the beginning of phase II and then decreases. The densities of neutral species vary mainly due to the collection of electrons, ions and radicals by the dust particles [15,28]. The reduction of free electrons increases the effective electron temperature during phase II (figure 2(a)) when ad becomes larger.

During phase II, ne slowly drops down by a factor of 10 because of an enhancement of the electron collection by the dust particles. When the dust particles leave the discharge at the end of a growth cycle, the electron density increases rapidly because of vanishing the electron loss and the energy loss of electrons on dust particles. Due to a growing temperature Teff, the density of metastable argon atoms becomes larger in the time interval 28 s < t< 65 s (figure 2(a)). For 65 s < t< 116 s, nm drops because of the reduction in ne. In phase I, the density of metastable argon atoms is dropping because of a lower nm production as compared with the phase II (Teff is smaller in phase I) as well as due to the enhancement of the nm loss in collisions with nonradical neutrals (their densities are growing with time). Furthermore, the increase of Teff in phase II also enhances the production of Ar + in electronatom collisions (figure 3). For the same reason the densities of C2H2 + , C4H2 + , C4H3 + , C6H4 + and ArH + are also increasing at the beginning of phase II. Afterwards, their densities are decreasing because of a reduction of their production at lower electron density and due to the enhancement of their losses in collisions with larger dust particles. The density of C2H3 + is found to be smaller (not shown in figure 3) than that of other ions, which agrees well with results of our previous studies [15]. The C2H -anions are produced in collisions of electrons with acetylene molecules, while they are mainly lost in collisions with positive ions and hydrogen atoms [28]. As a result, the rapid increase of ne in the beginning of phase I (as nd is set to 0) is also accompanied by the rapid increase in C2H - density (figure 2(b)). The density of C2H -anions decreases as ne during phase II and also because of the growing Ar + density, which enhances the C2H -losses. The time-dependencies for C4H -and C6H -are similar to the one of C2H -because their loss mechanisms are the same, and because the production of C4H - and C6H -is, respectively, in collisions of C2H -and C4H -with C2H2 (table 1). During phase II, the dust charge increases in time because of the growing surface of the electron collecting dust particles (figure 4(a)). The dust charge saturates at the end of phase II because of the extreme electron rarefaction and the high current of positive ions Ar + onto the dust.

Using equation ( 6), we have also calculated the dust radius as a function of time (figure 4(b)). The calculations have been carried out for different densities of dust material ρd= 1 g/cm 3 , 1.5 g/cm 3 and 2 g/cm 3 , assuming that the dust radius is 10 nm at the beginning of phase II. The calculated radii are in a good qualitative agreement with the experimental measurements presented in [24]. Naturally, by lowering the dust material density, the calculated dust radius increases (figure 4(b)).

We have also obtained the time-dependences for the dust radius assuming that only C2H radicals take part in the growth of dust particles (in equation ( 6

Effects of dust density variation

The dust density during phase II nd is unknown from our experiments. Therefore, let us analyze how the results of our calculations depend on nd.

In figure 5, densities of nonradical neutrals and nH as a function of time are shown for different dust densities: nd = 5×10 6 , 10 7 , 1.5×10 7 and 1.8×10 7 cm -3 . At small dust density (~ 5×10 6 cm -3 ) densities of nonradical species are monotonically decreasing with time. For larger nd (≥10 7 cm -3 ), densities of C2H2 and C4H2 decrease at the beginning of phase II, reach a minimum and then increase. The minimums are observed at smaller times when nd becomes larger (figures 5(a) and 5(c)). Moreover, densities of C2H2, H2 and C4H2 molecules decrease faster with growing nd at the beginning of phase II (figures 5(a), 5(b) and 5(c)). The nd dependency for C2H2, H2 and C4H2 is caused mainly by the density variation for argon atoms in excited states, for electrons, C2H radicals and for positive ions. The density of atomic hydrogen increases at the beginning of phase II but then decreases during the rest of the phase (figure 5(d)). This increase is mainly due to enhancement of the H production in collisions of excited argon atoms, Ar + ions and C2H radicals (their densities increase at the beginning of phase II (figures 3, 6(a) and 6(b))) with nonradical neutrals, while the decrease is also caused by production changes through the lowering of the nonradical densities at the first half of phase II and through the lowering of Arm and C2H densities at the second half of phase II. The H density becomes larger during phase I mainly because of rising densities of nonradical species, from which H mainly originates. Its decrease with increasing nd during phase II is mainly due to the decrease of the densities of electrons (figure 6(c)) and H2 molecules (figure 5(b)) and due to the decrease of nm and nC2H in the second part of phase II (figures 6(a) and 6(b)). Note that the production of atomic hydrogen in Ar/C2H2 plasmas is mainly due to collisions of Ar* with C2H2, C4H2 and H2, of Ar + with H2 and of C2H with C2H2 and C4H2 , as well as due to electronimpact dissociation and ionization of H2 molecules (Supporting information to [28]).

With higher nd, the density of Arm increases faster in the beginning of phase II (figure 6(a)) due to the likewise accelerated increase of Teff (figure 6(d)). The metastable density then goes to a maximum, which is reached the earlier the higher is the dust density because of the enhancement of their losses in collisions with nonradical neutrals. The densities of C2H2 and C4H2 increase at large times in phase II (figures 5(a) and 5(c)) due to a reduction in ne, nm and nC2H (figure 6) with growing dust density. As it was already noted in previous subsection, the time-dependency for C2H2 is nearly the inverse to those for Arm and C2H (figures 5(a), 6(a) and 6(b)). The faster increase of densities of the latter species in the beginning of phase II is due to, at least in part, an increase of Teff that enhances their production in collisions of electrons with neutrals. The density of negative ions in phase II decreases when nd increases (figure 7(c)), mainly due to the enhancement of the anion losses in collisions with Ar + and C2H2 + ions, whose densities grow with nd (figures 7(a) and 7(b)).

Note that the calculated dust radius approx d a decreases when nd increases (figure 7(d)). This can be explained by a smaller amount of available hydrocarbon positive ions and C2H radicals per dust particle for the same input of acetylene.

Discussion and summary

In this paper, we investigated through 0D simulations the physics and chemistry of an Ar/C2H2 plasma containing growing dust particles. One of the main goals of this work was to obtain the time-dependencies of different plasma parameters (ion, electron and neutral particle densities, effective electron temperature and dust charge) for the conditions of our experiments [24]. Especially, comparisons between the calculated time-dependencies of C2H2, H2 and C4H2 with the time-dependencies of corresponding masspeaks measured experimentally. We also studied how our calculations depend on the density of dust particles, which is unknown from our experiments. The evolution of the dust radius is also calculated during dust particle growth as a function of calculated reactant flux towards their surface. The calculated time-dependencies of C2H2 and C4H2 are in a good agreement with the experimental data. During phase I (when the effect of dust particles on plasma parameters is small), the density of acetylene is growing because of little losses in different collisions. On the contrary, in the beginning of the accretion phase, the acetylene density drops rapidly because of a strong enhancement of the losses with excited argon atoms, positive ions and radicals. These latter species are highly produced due to a Teff increase related to an enhanced collection of electrons and ions by dust particles. Surprisingly, at larger times in the accretion stage, the acetylene density increases again mainly because of smaller losses. While Teff increases, its effect is dominated by the strong decrease of ne (and thus species produced by electron collision) due to electron collection by dust particles.

The minimum in the densities of C2H2 and C4H2 during phase II is non-intuitive. Additionally, we show that it appears earlier when increasing the dust density. This is mainly due to the impact of the dust density on Arm, positive ions and C2H radicals. With the increase of the dust density, the effective electron temperature becomes larger and grows faster, while the electron density in the accretion stage becomes smaller. As a result, the densities of non-radical neutrals drop faster in the beginning of the accretion stage. At the end of phase II, the densities of C2H2 and C4H2 increase with increasing the dust density because of smaller losses of these molecules in collisions with electrons, excited argon atoms and C2H radicals (their densities drop with increasing nd). Note that the non-linear behavior of most densities during the linear growth of particles can be explained in our calculations without variation in the dust density.

The growth of the dust radius during the accretion stage is calculated for different dust material densities and number densities assuming that only C2H radicals and positive hydrocarbon ions take part in the growth. The calculated timedependency appears to be in reasonable agreement with experimental data throughout the dust number density and mass density range used in our calculations (see figures 4 and 7d). This suggests that the positive ion deposition on dust particles is effectively the dominant growth mechanism.

Meantime, there is a discrepancy between our calculations and the experimental data for hydrogen molecules, especially in phase I when dust particles do not affect much the plasma properties. In our opinion, the discrepancy is mainly caused by some simplifications used in the 0D model. In particular, the model here assumes that phase I is immediately followed by the accretion phase without considering any intermediate coagulation stage.

In [62], it was shown that plasma parameters in the coagulation phase may change strongly in argon/silane plasma if the dust density at the end of the coagulation phase is large (>10 8 cm -3 ). Meantime, here we consider much smaller dust densities in the accretion stage (~10 7 cm -3 ), and, therefore, we expect that the effect of the coagulation of nanoparticles in our Ar/C2H2 plasma is not as strong as in [62].

The model does not account for plasma inhomogeneity effects neither, which may be very important, in particular, at the end of the accretion stage when the formation of a void may take place [START_REF] Vladimirov | [END_REF]63]. Moreover, the model does not account for effects of dust particles on the shape of electron energy distribution function. Meantime, it was shown that for sufficiently high dust density and/or size, in a low-pressure argon glow discharge, the Druyvesteyn-like electron distribution in dust-free plasmas can become nearly Maxwellian [64,65]. Hence, the shape of the electron energy distribution function in the dust-free phase may be different from the one in the accretion phase when the plasma contains dust particles with large sizes and densities.

Note that here the approximate time-dependency for the dust radius approx Getting this time-dependency, the densities of plasma species, effective electron temperature and dust charge as a function of time have been obtained from equations ( 1)-( 5), assuming that the dust radius grows linearly with time in the accretion stage. Moreover, equation (6) does not account for any loss of the dust material, in particular due to sputtering from ion bombardment [66]. Here we assume that the loss of dust material due to sputtering is not important because ions bombarding dust particles have rather small energies (a few eV). For example, the energy threshold for argon ions sputtering hydrocarbons is in the order of a few tens of eV.

Regarding the growth of dust particles, we also do not account for chemical etching. Therefore, the model here is applicable only for a qualitative analysis of argon/acetylene plasmas containing growing dust particles and it should be improved by inclusion of effects related to spatial plasma inhomogeneity, changes of the EEDF shape, inclusion of the processes describing the loss of dust material, as well as by inclusion of the coagulation stage.

Meantime, our model has some advantages compared to previous models of argon/acetylene dust-forming plasmas currently available in the literature. Besides accounting for the effect of dust particles on the plasma properties, it allows to obtain the plasma parameters as a function of time. Moreover, the model is rather simple, accounts for main species measured in our experiments and gives a good agreement with experimental data. The obtained results are relevant for many applications involving reactive plasmas [67], especially gas discharges used for the synthesis of various nanomaterials.

  ff

  5 sccm) and the scalar converts sccm to cm -3 s -1 . The rate at which particles X leave the discharge due to pumping is V cm 3 /s. Taking into account that the flow rate of argon is approximately equal to the argon pumping rate (since the plasma is low-ionized), one can estimate the pumping rate

  describing the positive ion and electron losses on dust particles are e

 3 A

 3 ) is the polarizability of the background gas і[17,19,41] and ij m is the reduced ion mass in amu. Then the diffusion coefficient for the j-th ion can be derived from the Einstein relation, temperature. Using the expression for j D , one can get the ambipolar diffusion coefficient for the j-th ion,

Figure 1 .

 1 Figure 1. The calculated densities of neutral species (a). The mass peaks (experiment) and the normalized calculated densities of neutral species (theory) for C2H2 (b), C4H2 (c) and H2 (d).

Figure 2 .

 2 Figure 2. The density of metastable argon atoms and the effective electron temperature (a), and the densities of electrons and negative ions (b) as function of time.

Figure 3 .

 3 Figure 3. The densities of positive ions as function of time.

  The radius evolution for both cases is shown in figure4(c)showing that the growth of dust particles during phase II is mainly related to the deposition of hydrocarbon ions on the surface of dust particles, the C2H radicals do not affecting much the dust particle growth.

Figure 4 .

 4 Figure 4. The dust charge as a function of time (a). The dust radius obtained from equation (6) for different densities of dust material: d ρ = 1.0 (curve 1), 1.5 (curve 2) and 2.0 (curve 3) g/cm 3 and the measured dust radius (circles) from [24] (b).

  both C2H radicals and hydrocarbon ions (curve 1), only hydrocarbon ions (curve 2) and only C2H radicals participate to the growth of dust particles for d ρ = 1.0 g/cm 3 (c). The normalized time 0 and 1.0 in figures 4(b) and 4(c) corresponds to, respectively, t = 8 s and 116 s in figure1.

Figure 5 .

 5 Figure 5. The densities of C2H2 (a), H2 (b), C4H2 (c) and H (d)for different dust densities in the dust-growth phase: nd = 5×10 6 (dash-dotted curves), 10 7 (dotted curves) 1.5×10 7 (dashed curves) and 1.8×10 7 (solid curves) cm -3 .

Figure 6 .

 6 Figure 6. The density of metastable argon atoms (a), C2H density (b), electron density (c) and effective electron temperature (d), for different dust densities in the dust-growth phase: nd = 5×106 (dash-dotted curves), 10 7 (dotted curves) 1.5×10 7 (dashed curves) and 1.8×10 7 (solid curves) cm -3 .

Figure 7 .

 7 Figure 7. Densities of C2H2 + (a), Ar + (b) and C2H -ions (c) and the calculated dust radius (d) for different dust densities in the dust-growth phase: nd = 5×10 6 (dash-dotted curves), 10 7 (dotted curves), 1.5×10 7 (dashed curves) and 1.8×10 7 (solid curves) cm -3 . The other conditions are the same as in figure 6. In figure 7 (d), d ρ = 1.0 g/cm 3 and the normalization of time is the same as for figure 4(b).

  b) and 4 (c)) has not been obtained self-consistently with other plasma parameters.

Table 1 .

 1 -7 cm 3 /s for the reactions C2nH -+ Ar + → C2nH + Ar, C2nH -+ CmHn + → C2nH + CmHn, C2nH -+ ArH + → C2nH + H + Ar, C2nH -+ H + → C2nH + H and C2nH -+ H2 + → C2nH + 2H, respectively.Here n =1,2,3.Considering various collisional processes in the plasma volume, we accounted only for binary collisions. A reaction rate for such reactions is calculated as the product of the reactant densities and the rate coefficient K of the reaction, Reactions for collisions of negative ions with positive ions and neutrals (here l=1,2,3).

	R	=	K	×	α n n	β	, where α n and β
			Reaction		Rate constant	Reference
								(cm 3 /s)
	C2lH -+ ArH + → C2lH + H + Ar	3.0×10 -8	[15]

n are the densities of the reactants. The reactions for collisions of negative ions with positive ions and neutrals, taken into account in our study, are presented in table 1.

Table 2 .

 2 Main reactions for collisions of electrons with C2H2 and H2 molecules.

	Reactions between electrons and hydrocarbons [51, 52]
	e -+ C2H2 → C2H2 + + 2e -	e -+ C2H2 → C2 + 2H + e -
	e -+ C2H2 → H + +C2H + e -	e -+C2H2 →C2H + + H + 2e -
	e -+ C2H2 → C2H -+ H	e -+ C2H2 → C2 + H2 + e -
	e -+ C2H2 → C2H + H + e -	e -+ C2H2 → C2 + + H2 + 2e -
	Reactions between electrons and H2 [53]
	e -+ H2 → 2H + e -	e -+ H2 → H + + H + 2e -
	e -+ H2 → H2 + + 2e -

Table 3 .

 3 Ion-molecular reactions with participation of positive ions accompanied by production and loss of C2H2, C4H2 and H2 molecules.

	Reaction	Rate constant	Reference
		(cm 3 /s)
	Reactions between Ar + /ArH + and neutrals
	Ar + + C2H2 → C2H2 + + Ar	4.2×10 -10	[20, 54]
	Ar + + C4H2 → C4H2 + + Ar	4.2×10 -10
	Ar + + H2 → ArH + + H	8.7×10 -10	[43]
	Ar + + H2 → H2 + + Ar	1.8×10 -11	[43]
	ArH + + C2H2 → C2H2 + + H + Ar 4.2×10 -10
	ArH + + H2 → H3 + + Ar	6.3×10 -10	[43]
	Reactions between hydrocarbon ions and molecules
	C2H2 + + C2H2 → C4H2 + + H2	0.43×1.2×10 -9	[55]
	→ C4H3 + + H	0.49×1.2×10 -9
	→ C4H4 +	0.08×1.2×10 -9
	C2H2 + + C4H2 → C4H2 + + C2H2	0.9×1.4×10 -9	[56]
	→ C6H3 + + H	0.1×1.4×10 -9
	C2H2 + + H2 → C2H3 + + H	1.0×10 -11	[18, 56]
	C2H3 + + C2H2 → C4H3 + + H2	2.4× 10 -10	[18]
	C2H3 + + H → C2H2 + + H2	6.8×10 -11	[56]
	C2H3 + + C4H2 → C4H3 + + C2H2	3.0×10 -10	[57]
	C2H3 + + C2H → C2H2 + + C2H2	3.3×10 -10	[58]
	C2H3 + + C2H → C4H2 + + H2	3.3×10 -10	[58]
	C4H2 + + C2H2 → C6H4 +	2.0×10 -10	[55, 59]
	C4H2 + + C4H2 → C6H2 + + C2H2	0.83×1.4× 10 -9	[56]
	→ C8H2 + + H2 → C8H3 + + H	0.17×1.4× 10 -9 0.01×1.4× 10 -9
	C4H3 + + C4H2 → C6H3 + + C2H2	7.4×10 -10	[56]
	C4H3 + + C2H2 → C6H5 +	2.2×10 -10	[56]
	C6H4 + + C2H2 → C8H6 +	7.0×10 -11	[55]

Table 4 .

 4 Molecule/atom -molecule/atom reactions accounted for in the model. Here

						gK T is the gas
	temperature in K, Ar* denotes argon atoms in
	various excited states including the metastable and
	4s and 4p resonance states.
	Reaction	Rate constant	Reference
		(cm 3 /s)
	Reactions between hydrocarbons
	C2H + C2H2 → C4H2 + H	1.3×10 -10			[18]
	C2H + C4H2 → C6H2 + H	6.5×10 -11			[18]
	C2H + C4H2 → C6H2 * + H 6.5×10 -11			[18]
	Reactions between H/H2 and hydrocarbons
	H + C2H → C2H2	1.66×10 -7 /TgK	[17]
	H + C2H2 → C2H3	7.25 10 ×	12 -	gK T	11.67 -	× [18]
		gK exp (-1212.7/ ) T
	H + C4H2 → C4H3	2.82 10 ×	25	gK T	11.67 -	× [18]
		gK exp (-6441.0/ ) T
	H2 + C2H → C2H2 + H	1.82 10 ×	11 -	×	[18]
		gK exp (-1443.0/ ) T
	Reactions with participation of argon atoms in excited
	states
	Ar* + C2H2 (C4H2) →	0.9×10 -10
	C2H2 + (C4H2 + ) + Ar + e -
	Ar* + C2H2 (C4H2) →	1.75×10 -10
	C2H (C4H) + Ar + H
	Ar* + C2H2 (C4H2) →	2.65×10 -10
	C2H2 (C4H2) + Ar + ω 
	Ar* + H2 → ArH* + H	1.1×10 -10			[54]
	Arm + Arm →	6.2×10 -10			[60]
	Ar + Ar + + e -

ξ ξ ε ε ξ ξ Γ Γ = Γ Γ

Acknowledgements

The authors acknowledge the financial support of the Deutsche Forschungsgemeinschaft in the frame of the project B13 of the SFB/Transregio 24. J B and E K would like to acknowledge the support from French Research Agency via ANR project PLASMABOND.