Photoactive Hybrid Materials with Fractal Designs Produced via 3D

Research Article Cite This: ACS Appl. Mater. Interfaces 2019, 11, 24771−24781

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Photoactive Hybrid Materials with Fractal Designs Produced via 3D Printing and Plasma Grafting Technologies Yoann de Rancourt de Mimeŕ and,* Kun Li, and Jia Guo Key Laboratory for Green Chemical Process of Ministry of Education, Wuhan Institute of Technology, Wuhan 430205, China

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S Supporting Information *

ABSTRACT: The present paper partly aims at exploring the potential of fractal geometry for concrete applications in the field of materials science. It is more specifically a study about the conception of hybrid polymer-based materials with photocatalytic activity. The concept behind this work is to investigate the use of polymer fractal structures manufactured by 3D-printing technology, as a highly ordered substrate with an important surface area to immobilize catalyst nanoparticles, by means of plasma grafting technology. Two types of fractal units, fractal pyramids (fracmids) and fractal cones (fracones), have been described and the former has been extensively characterized on a geometrical aspect. Various complex superstructures have also been described using fractal units as building blocks. 3D structures based on the aforementioned theoretical models have been designed using computer-aided design (CAD). On the basis of CAD models, several structures have been 3D-printed with PLA using fused deposition modeling. PLA substrates have been successfully coated with nanoparticles of ZnO using a combination of core− shell synthesis and plasma grafting. Finally, the photocatalytic activity of a hybrid material has been assessed with a positive outcome, showing the relevance of the concept developed in this study. KEYWORDS: fractal, FDM, hybrid materials, polymer, interface, CAD, plasma grafting, superstructure, photocatalyst

1. INTRODUCTION The word fractal was coined by mathematician Benoit Mandelbrot, who extensively worked on their discovery and potential applications in science.1 Although fractals had already been known for many years before him,2 they were regarded as a sort of mathematics oddity. Fractals are objects, structures, or functions that are built by a recursive repetition of patterns at many or infinite scales. In other words, a fractal would show the same or very similar pattern independently of the scale of observation. The most famous example of such a phenomenon must be the Mandelbrot set,3 illustrating the notion of selfsimilarity. In the material field, most studies focus on the use of fractal geometry for antennas,4 the fractal mechanical analysis of fatigue and rupture in materials,5 or the fabrication of metal fractal structures using laser beams.6 Huang et al. also reported the use of fractals in metamaterials for absorbing low frequency microwaves.7 So far, there are relatively few articles reporting the use of 3D-printing technology for manufacturing fractal materials. Jun et al. used additive manufacturing (AM) to fabricate three-dimensional metal fractal antennas based on the Sierspinki tetrahedron geometry.8 More specifically, they used a binder jetting metal process to manufacture antennas to be used in wireless communication technologies. Another application of AM and fractals has been described by Warner et al., who used maskless stereolithography to 3D print various fractal patterns in the form of hydrogel structures.9 They hence managed producing biomimetic designs for biological © 2019 American Chemical Society

applications. Davis et al. assessed the wetting properties of three-dimensional nanostructured fractal surfaces created by two-photon photolithography.10 Now, to the best of our knowledge, no one reported the use of fused deposition modeling (FDM) technology to produce fractal structures. The creation of a fractal pyramid pattern presented in this study came from a reflection about the famous Koch snowflake,11 actually a curve, discovered by the Swedish mathematician Helge von Koch. His curve, using simple triangles, allows obtaining a figure of increasing complexity with fractal rank and a perimeter tending toward infinity. A question wondered was, following the same rather simple principle, would it be possible to create a three-dimensional figure that could be as simple to build and practically usable in a structured material. Its fractality would be used to artificially increase the surface area of a polymer substrate. The fracmid (portmanteau for fractal pyramid, for simplicity) has been conceived with such aim and requirements. The geometrical parameters of this fractal unit have been described and analyzed here using simple mathematical tools. In this study, another fractal unit, fractal cone or fracone, has been conceived, based on observation of the Romanesco broccoli inflorescence structure,12 but once again with an approach Received: April 22, 2019 Accepted: June 17, 2019 Published: June 17, 2019 24771

DOI: 10.1021/acsami.9b06982 ACS Appl. Mater. Interfaces 2019, 11, 24771−24781

Research Article

ACS Applied Materials & Interfaces Scheme 1. Illustration Displaying the Different Stages of Manufacturing and Usage of the Photocatalysta

a

Steps (a) and (b) are simultaneous. (a) Nanoparticles of ZnO are functionalized to produce core/shell nanoparticles. The shell is a carboxylic acid-bearing polymer. (b) PLA fractal substrates are printed with FDM, layer by layer. (c) Fractal substrates are activated by plasma (stage 1); then nanoZnO@polymer(CO2H) core/shells are applied to the substrate’s surface and left to graft (stage 2). (d) The hybrid photocatalyst is immersed in wastewater and activated by direct sunlight to produce hydrogen by water splitting. The orange stars symbolize the organic pollutants, used in the process as sacrificial agents.

not only potentially allow producing substrates with important specific surface areas and with a hierarchically arranged configuration but also make it possible, thanks to FDM, to produce such substrates in a single and cost-effective processing step, which is an important aspect for sustainable production of materials. A wide range of techniques already exist to produce polymer materials with high surface area. While some rely on chemical methods, by synthesizing highly porous polymers20 or through the use of wet etching21 for instance, others can be based on physical processing, like laser22 or plasma etching,23 or even mechanical modification.24 Some common limitations to these techniques can be about the necessity to use successive processing steps, chemical additives (porogen, surfactants, solvents, gases, oxidizing chemicals, etc.), and/or costly/energy-intensive equipment. An important point of this study is to immobilize the mineral catalyst on a substrate to fix the secondary removal issue, which is very energy- and time-consuming in heterogeneous catalysis processes. In other words, we propose an innovative process: the use of fractal superstructures to obtain 3D-printed polymer substrates with high interface efficiency, combined with plasma grafting functionalization, for applications in the field of catalysts. More specifically, concerning the plasma treatment used in this study, we propose the term “aqueous phase plasma-aided grafting” (APPAG). Following the same principle as in the aforementioned work,16 it relies on the plasma activation of a polymer substrate, followed by the grafting of mineral or core/shell nanoparticles dispersed in a liquid, here specifically water. In a recent study, Son et al. created ZnO-based hierarchical structures using 3D printing and hydrothermal reactions for photocatalytic applications.25 While their work is of great importance, we used a different approach and propose an alternative, with a process that needs fewer steps, using milder conditions and more complex 3D-printed substrates. Indeed,

guided by simplicity. For complexity reasons, this fractal unit has not been analyzed like the previous unit. Nevertheless, it has been successfully designed by computer-assisted design (CAD) and used for the 3D conception of complex structures as well. The emergence of three-dimensional printing technologies, and their improvement, potentially opens the way for a new industrial revolution. Indeed, 3D printing offers a wide range of applications, from biomaterials13 to the automotive industry,14 for instance. Also, the possibility of manufacturing materials possessing highly complex morphologies allows for the creation of advanced and innovative materials. Plasma grafting technology is a well-known technique in the domain of materials, and its ability to modify or functionalize the surface of polymers has been extensively studied.15 It is a technology of choice for the manufacturing of advanced, high value-added materials. It allows the efficient and convenient grafting of a very wide range of compounds at the surface of polymeric substrates, making it a valuable tool in hi-tech industrial processes. But not only organic molecules can be grafted onto surfaces. Indeed, in a previous work, plasma grafting technology was successfully used for grafting zinc oxide nanoparticles onto the surface of a flat polypropylene substrate.16 The aim was to produce antibacterial surfaces for medical applications. But, in addition to its well-studied antibacterial activity,17 zinc oxide is also known and increasingly utilized for its photocatalytic properties. Indeed, ZnO nanoparticles have the ability, under solar irradiation, to degrade organic molecules18 and also to produce hydrogen gas.19 Hence, in this study, we investigate the feasibility of using CAD-conceived fractal structures for 3D printing polymer substrates onto which ZnO nanoparticles are subsequently plasma-grafted, for photocatalytic applications. One of the aims of using fractal materials is to significantly enhance the interface nanoparticles/fluid. Fractal structures 24772


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ultrasonic treatment. Also, it is necessary to remove oxygen from the dispersion by bubbling N2 gas. This avoids the poisoning of radical reactionswhich makes the grafting possibleduring the plasma grafting treatment. Finally, right after plasma activation, the PLA substrate is immersed in the ZnO dispersion and left to react. This allows ZnO core/shell nanoparticles to graft onto PLA. Subsequently, all nongrafted nanoparticles are removed from the surface by thorough ultrasonic cleansing. The nanocomposite thus formed is then ready for being used as a photocatalyst. This hybrid photocatalyst is expected to be used for the production of H2 gas, using organic pollutants as sacrificial agents, and through direct sunlight activation, hence promoting the revalorization of wastewaters containing organic contamination, e.g., chemical or pharmaceutical byproducts, bacterial or fungal waste, etc. In this study though, the photoactivity of the nanocomposite has been assessed by testing the photocatalytic degradation of Rhodamine B dye.

we found the combination of 3D-printed fractal substrate and plasma grafting to be really suitable for producing hybrid photocatalysts. Although we chose to focus on a very specific application, we believe the principles and the process described in this study can be useful in other domains of materials science, for numerous applications (energy production and storage, optics, electronics, water purification, etc.), and could have significant implications in the field. For instance, the materials produced in this study could also be used for the disinfection of water, thanks to the antimicrobial property of nanoZnO.16,17 It is also possible to imagine the replacement of the grafted ZnO by nano zeolites for their catalytic properties26 or for adsorption of pollutants.27 Photonic crystals or more generally metamaterials might also be produced using our approach, by grafting various mineral nano- or microparticles on the polymer substrates.28 The first three parts of this article will focus on the study and conception of fractal units and superstructures, and the last section will describe the actual fabrication of hybrid photocatalytic material as well as testing its photocatalytic activity. Finally, this study will not specifically focus on the core/shell synthesis, nor on the plasma grafting, which will be the object of another publication.

4. THEORETICAL CALCULATIONS AND RESULTS 4.1. Important Aspects. 4.1.1. Fractal Units. In this article, fractal units will refer to the fractal elements partly composing the structures. For practical applications, not only due to the technical limits of printing processes but also considering the level of complexity of 3D modeling, data processing, time of printing, only a few ranks of fractality might be used. An equilibrium should be found between the size of units (dimensions of rank 0 objects), and the rank of fractals. It is obvious that, limited by the accuracy of 3D printers, there is a minimum size of details that can be given to 3D elements. Either it is decided that the units will be built relatively big but with a high fractal rank or units will be relatively small, but hence the fractal rank achievable would be lower. Such considerations are crucial, because the result in terms of spatial geometry is critically different. In simple words, having a layer of big fractal units with high fractal rank cannot be equivalent to a similar-dimensioned layer of small fractals with lower fractal rate, partly because, in the former case, there would be a lot of useless empty space and also a wasteful amount of material used, considering the fact that only fractal unit surfaces are useful. 4.1.2. General Structure. Once fractal units are conceived, in most cases, they cannot be used on their own but rather need a scaffold to be ordered spatially in an optimal manner. While the fractal units would be responsible for the effective quality of the interface, the scaffold, giving birth to the general structureor superstructurewould provide a real threedimensional aspect to the materials, hence optimizing its spatial efficiency. The scaffold has for a goal not only the optimum arrangement of units together but also, in the case of an interface composite/fluid, factors like flowability or accessibility of the fractal units to the fluid or the content of the fluid, for instance, bacteria or micropollutants. The scaffold has nothing to do with the fractality of the units but rather is a simple mechanical support. That means the overall superstructures are just partially fractal, only at the scale of the fractal units. Different types of scaffolds can be imagined, aiming at different applications (Figure 1). For instance, a panel, or multilayer arrangement, would most likely be adapted to a photocatalytic application. But an infinity of other supports can be foreseen, for instance, rodlike structures, tubes, sponge-like structures, metal scaffold-like structures, and so on.

2. MATERIALS AND METHODS All fractal units and structures have been conceived without the aid of fractal generating software. Later, AutoCAD 2013 has been used for the 3D design of fractal units as well as superstructures. Calculations have been handled with Excel. All models and structures have been 3D-printed with an A85 FDM printer provided by JGAurora. The parameters have been set as follows: printing nozzle diameter, 0.4 mm; nozzle temperature, 210 °C; print bed temperature, 60 °C; layer thickness, 0.1 mm; print speed, 20 mm/s, travel speed, 80 mm/s; fill density, 20%. Translucent PLA filaments of 1.75 mm diameter have been used for printing. Plasma grafting experiments were conducted with an all-integrated 20 MHz SPV-50 plasma reactor from Sindin Co. Ltd., equipped with a quartz plasma chamber, working under a vacuum of 10 Pa, and using a gas flow rate of 30 mL/min. ZnO nanoparticles with an average diameter of 30 nm were purchased from Maikun Chemical. A 30% solution of poly(acrylic acid) in water from Damao was used for the functionalization of ZnO. Plasma grafted samples were analyzed by a Zeiss GeminiSEM 300, equipped with an Oxford X-MaxN EDS detector. A photocatalytic degradation test has been done with one of the hybrid materials, using a 5 mg/L solution of Rhodamine B dye, and light activation by a xenon lamp (300 W, PLS-SXE300C/300CUV, Beijing Trusttech Co., Ltd.)

3. DESCRIPTION OF THE MANUFACTURING PROCESS As mentioned in the Introduction, the project behind this study specifically targets the production of photocatalysts with ZnO nanoparticles, for generating hydrogen gas. The synthesis process is described in Scheme 1. First, PLA fractal substrates need to be printed by FDM. Meanwhile, ZnO nanoparticles are functionalized with polymer bearing carboxylic acid functions. Indeed, even though pure ZnO nanoparticles can be grafted on a polymer by plasma,16 the use of a polymer shell containing carboxylic acids around ZnO nanoparticles promotes higher plasma grafting rates. More specifically, we use poly(acrylic acid) (PAA) as a coupling agent. After these simultaneous steps are completed, N2 or O2 plasma discharge is used to activate the surface of the PLA substrate. In the meantime, ZnO@PAA core/shells are dispersed in water, using 24773


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case, the fractal surface would be globally convex, in the second case, concave. With this definition, a porous sponge-like structure would be a negative morphology, getting its advantageous interface created by its network of connected pores. A natural occurrence would be lung bronchioles. An example of positive morphology would be the intestine, with the surface of intestinal villus creating an important specific surface area. In this paper, only positive morphologies will be considered. In addition to such considerations, it is possible to predict that fractal structures could be used in two different ways, in static or continuous-flow reactors, if they are to be used in chemical processes. 4.1.6. Surface Accessibility. Accessibility is a key notion here. One of the points of using fractal structures is to improve the spatial arrangement of nanoparticles. If the case of a catalyst is taken, it is easy to imagine that a simple powder of nanoparticles might not have an optimal interface, partly because nanoparticles sometimes have a strong tendency to aggregate, resulting in a reduced accessibility of their surface. Also, it can be imagined that, in certain situations, something similar to fouling might happen at the particles interface, because of powder compaction. Now if a thin layer of such nanoparticles can be grafted onto the surface of a fractal structure, the highly ordered arrangement would make these particles much more accessible spatially, with potentially reduced chemical hindrance. In other words, the surface of nanoparticles would be more available for adsorption by a fluid, and at lower scale, by molecules. In the case of a continuous-flow reactor, the use of optimized fractal structures might also make it possible to improve the flowability and interaction with a liquid medium. 4.1.7. 3D-Printed Surfaces. Notions of unit surface efficiency and spatial interface density are important for the conception of structures. Nevertheless, in reality, surfaces produced by 3D-printing techniques, including FDM, are far from smooth. This is inherently due to the technique of layerby-layer deposition, which creates rough topographies. This is something that is referred to as the stair/step (or stair stepping) effect.29 Hence, it is hard to predict accurately the actual spatial interface density of 3D-printed structures. Whereas this stair/step effect can be a significant drawback for materials where aesthetics is relevant, in the present case of substrates produced for immobilization of active nanoparticles, it can be advantageous, since it increases the surface area of structures (compared to theoretical models created by CAD). It is true if deposition layers are reasonably thin. In the case of layers that are too thick, the stair/step effect would become detrimental to the shape of units, especially the smaller constituents of it. In FDM specifically, the stair/step effect is mostly influenced by the slicing thickness and the printing nozzle diameter. 4.1.8. Advantages of the Overall Process and Materials. The most obvious advantage of using fractal substrates is about producing interfaces with high surface area and that would be easily accessible, thanks to a hierarchical spatial configuration. Moreover, the use of fractal geometry, especially for FDM, makes it possible to get substrates with an advantageous interface in a single processing step, using only one substance (the printed polymer) and a relatively low amount of energy in the process, with no postmodification needed. Another important point of the process exposed in this article is about the chemical immobilization of catalyst particles. Indeed, in heterogeneous catalytic processes, the secondary removal of

Figure 1. Three examples of scaffolds to aid for the creation of superstructures. (a) Columnar scaffold; (b) metal scaffold-like structure; (c) multilayer panel scaffold.

4.1.3. Fractal Rank. Increasing the fractal rank of units is a convenient method to raise the interface efficiency. Indeed, when the rank increases, the general structure is not altered and there is only a slight increase of apparent size of units. The most obvious advantage of fractals is that, with the rank increasing, the surface of fractal units grows exponentially, while their volume only changes a little. In other words, an easy way to increase the surface without modifying the superstructure itself is to increment the fractal rank of units. One crucial advantage is that a structure can be designed and then, depending on the efficiency of the material aimed, the fractal units can be interchanged without having to change the overall structure parameters. Of course, the maximal rank attainable, and thus the quality of the material interface, depends on the printing technique used, the accuracy of printers, and the state of the art of 3D-printing technologies. One parameter cannot be ignored. It is easy to realize that the higher the rank, hence the finer the structure, the more time it would take to print a material. A compromise has to be found between complexity of the structure and processing time of materials. 4.1.4. Spatial Efficiency. Spatial efficiency is a complex and relative notion, which would greatly vary with the targeted application. Different subparameters can be associated with it, like the value of specific surface area (SSA), the availability, or accessibility, of such a surface, the density of fractal units per volume, etc. Two important mathematic parameters can be described: • Unit surface ef f iciency, or surface/volume ratio: the amount of available surface per volume of material composing a fractal unit, m2/m3 or m−1. • Spatial interface density: amount of interface (or available surface) per volume occupied by the structured material (fractal units + scaffold), m2/m3 or m−1. The spatial interface density reflects the way fractal units are packed in the general structures. The more compact a structure is, the greater the value of interface density should be. But it is also directly influenced by the unit surface density and thus the fractal rank and unit size. Finally, compared to classic specific surface area, expressed in surface per mass unit, the spatial interface density described here has the advantage of being independent of the material used and only influenced by the geometrical features of structures. 4.1.5. Structure Morphology. Fractals offer a wide range of morphologies. Two main morphologies could be differentiated, positive and negative morphologies. For the former, the interesting interface would be on the outside, whereas, for the latter, the interface would be in the inside. Indeed, fractal structures can be virtually conceived either by addition of matter or by simple removal from a bulk material. In the first 24774


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ACS Applied Materials & Interfaces catalyst from the reaction medium is a serious issue, costing a lot of energy and time in separation processes. Here, the use of plasma grafting allows for a permanent immobilization of zinc oxide nanoparticles on the polymer substrate, suppressing any need for separation steps after reaction. It should also be noted that plasma technology is categorized in clean processes, which is an important point of this project. Another significant advantage of our process is that all the synthesis steps can be carried out in water and at room temperature. All of these aspects contribute to a green chemistry approach of material manufacturing. Finally, about the combination of FDM and plasma technology: FDM can produce interesting and cheap polymer substrates, and we believe plasma is an interesting technique because it allows grafting active nanoparticles on the surface, where it is the most useful, by comparison to cases where mineral nanoparticles are just dispersed in a polymer matrix by mixing. Indeed, in the latter case, nanoparticles situated within the matrix cannot be as active as the ones on the surface, since their activity would greatly depend on diffusion mechanisms and kinetics. There is no specific influence of the FDM process on plasma grafting, meaning that the grafting efficiency mostly depends on plasma parameters. Of course, the grafting rate should partly depend on the surface area of the substrate. Though, theoretically at least, the plasma process could be used to graft ZnO-based (or other mineral nanoparticles) core−shells on any type of organic substrate produced by any printing process. Concerning the fabrication of 3D substrates, we are well aware that laser 3D-printing technologies would be more adapted than FDM so as to obtain structures with better accuracy and higher fractal rank. However, we believe FDM holds some significant advantages, for instance, the accessibility of the technique and the possibility to upscale its use for substrate printing. The use of FDM allows for the low-cost fabrication of substrates made from renewable resources and biodegradable polymer in the case of PLA. Also, a key point is that PLA is a reasonably affordable feedstock, especially compared to expensive photosensitive resins used in laser printing applications. 4.1.9. Potential Enhancement of the Substrate Interface. Owing to the physical limitations of the FDM technology, in practice, reaching higher fractal ranks and thus high definition of the substrate superstructures can be challenging. A potential improvement of the interface of polymer substrates could be achieved using a technology called colloidal lithography (CL), which is a low-pressure reactive ion etching process.23 This treatment allows the formation of a nano- or microarray structure at the surface of polymers treated. This technique could be used on FDM-printed PLA fractal structures in order to increase their specific surface. Later, there would be more surface area available to plasma graft nanoZnO. 4.2. About the Fractal Units. 4.2.1. Building the Fractal Units. 4.2.1.1. Fracmids. A simple analogy can be made between Koch snowflakes and fracmids. Following a similar logic for their construction, fracmids would be a sort of 3D version of the former. The construction of a fracmid is relatively easy compared to many other fractal structures. The first step, which is rank zero (r0), is a square base “perfect” pyramid with top faces being equilateral triangles (Figure 2a and Figure S1a). This can be considered as the unit core. The core could have been a triangle base pyramid (tetrahedron) as well, but the square pyramid has been chosen for practical reasons. Indeed, it is much easier to arrange fracmids in rows

Figure 2. From (a) to (d): fracmid units created by CAD, from r0 (pyramidal core unit) to r3.

when they have a square base. Since the starting unit, or core, is different from the next ranks units, fracmids are not strictly fractal in the traditional definition of the term, albeit it is not a real concern. The next step consists in virtually growing new pyramids, this time tetrahedral pyramids, on the surface of each top face of the starting unit. These new pyramids are also “perfect” pyramids, or regular tetrahedrons, with all faces being equilateral triangles. The way these smaller pyramids are built is the following: the three corners of their base are placed at the exact center of the three edges of each one of the four top faces of the primal square base pyramid. It should be noted that the base of the core unit will not be altered along the process of “fractalization”. So basically, at rank one (r1), there are four new pyramids (or tetrahedrons) appearing. For the next step, or r2, the same operation is repeated, with all new faces, or facets, created at the previous step, receiving a new tetrahedron. The exact same operation is iterated over and over for the following ranks, and can virtually be incremented for an infinite number of ranks. Images of polymer 3D-printed fracmid models (ranks 2 and 3) can be found in the Supporting Information (Figure S2). 4.2.1.2. Fracones. Concerning the conception of fracones, all important parameters, like the solid angle of the core unit, the number of branches along the main cone, as well as around the central axis, their sizes, and spacing, have been set purely empirically. In addition, and although the general structure could be compared to that of Romanesco broccoli, it has been simplified a lot (Figure 3), compared to the natural occurrence.

Figure 3. Fracone units obtained by CAD. (a) The conical core unit, r0; (b) r1 fracone; (c) r2 fracone.

Indeed, for the latter, the arrangement of fractal units follows a complex spiral configuration. It means the spatial architecture of fracone units is far from optimal but also much easier to construct with CAD, and thus used for real applications like 3D printing. Now, compared to fracmids, the construction process is a lot more baffling for fracones (Figure S1e−h). The first step, or r1, consists in adding smaller cones on the surface of the core unit. These smaller cones are reduced versions of the core. Six of these cones are aligned along the axis of the core, getting progressively smaller toward the apex of the main cone. This row of six cones is radially repeated four times around the core. So, the final amount of small cones is 24, all orderly placed on the surface of the core. At this stage, the structure looks like a fir tree, with the core cone being the trunk, and the smaller 24775


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ACS Applied Materials & Interfaces cones being the branches. In order to obtain r2, the structure created in the previous step is virtually copied and reduced, and each branch is to be replaced by a copy of the structure, in a mise en abyme process. The same operation can be incremented for the next ranks. It is to note that the analogy with trees is not irrelevant, since, when increasing the rank, the obtained structure looks more and more vegetal-like, somewhat mimicking vegetal growing processes (Figure S1g,i). 4.2.1.3. Respective Advantages of Fracmid and Fracone Units. Fracmids offer many advantages as a fractal structure. First of all, the concept of their structure is rather simple and virtually easy to build compared to other potential 3D fractal structures. As well, it is easy to predict the evolution of their geometrical parameters, like surface and volume, with increasing fractal rank since mathematical functions allow exact calculations of such parameters. Finally, owing to their morphology, fracmids are very adapted to flat substrates. We also believe they would be well adapted to photocatalytic applications specifically, partly because their pyramidal shape makes them suitable to receive sunlight from different incident angles. The flat facets generated by fractality might also partially deflect light and scatter it deep into the structures. Also, at sufficient fractal ranks, some sort of cavities appears on the surface of fracmids due to their geometry. Such cavities might be interesting to trap light and improve the photocatalytic performance of the hybrid materials. Whereas fracones have similar advantages compared to fracmids concerning their fractality, their parameters are hard to control and they are much more complex. Owing to the higher height/width ratio of their main unit (the cone trunk), fracones would be well adapted to a round-shaped scaffold substrate, like a rod or the inner wall of a tube. This, in addition of their rounded surfaces which would give them a decent flowability, would make it particularly adapted for a use in continuous-flow reactors. Oppositely, fracmids would most likely be more adapted to static reactors. 4.2.2. Calculations and Observations. 4.2.2.1. Determining Surface Area and Volume Formulas. In this section, only fracmids are analyzed, fracones being too complex and changeable for any mathematical deep analysis. Indeed, fracmids only have a strict and single way of construction, while fracones on the other hand can be obtained in an infinity of ways with slight variations in their geometrical parameters. For surface calculations, the base of the pyramidal core will be neglected since fracmid units are supposed to be laying on a substrate, meaning that their base would not be an accessible surface. The surface area of the core pyramid, or S0, for surface area at fractal rank 0, is very easy to obtain: S0 = 4 × a02

Scheme 2. Geometrical Considerations About the Fracmid Unitsa

a

(a) A face of the fracmid at rank 1. A tetrahedral pyramid can be observed in the middle, with its apex in the middle of the figure. The side of new facets is a1 and is equal to a0/2. (b) Illustration of the interfracmid gap, with four r1 fracmid units, top view. (c) Side view of an r1 fracmid. Trigonometry allows calculating x, equivalent to half of the interfracmid gap.

A general formula can be found so as to calculate the surface area of units at any rank, Sn. This area is equal to the number of facets of rank n, multiplied by the surface area of such facets. Since each new pyramid on a face makes six new facets appear, we can guess the number of facets of rank n: n facet(rn) = 4 × 6n

Since each new facet surface area of rank n is equal to 1/4 of that of rank n − 1 i1y i1y 3 Sfacet(rn) = jjj zzz × Sfacet(r0) = jjj zzz × a02 4 k4{ k4{ Combining the two last formulas n

i3y Sn = n facet(rn) × Sfacet(rn) = jjj zzz × a02 3 k2{ n

i3y Sn = jjj zzz × a02 3 k2{ The side of facets can also be calculated at any rank: a an = n0 2 The volume formula is more complex to reach. The number of new pyramids at rank n can be deduced from the fact that each facet of rank n − 1 gives rise to a new pyramid at rank n. n

3 = a02 3 4

As well, the volume of the unit at rank 0 is easily found, with the formula V = 1/3 × a × h: V0 =

n

a a3 1 × a02 × 0 = 0 3 2 3 2

n pyramid(rn) = 4 × 6(n − 1)

Observing one face of the core pyramid at rank 1 (Scheme 2a), with one new tetrahedral pyramid appearing in the middle, it can be observed that a1, the side of the new facets, is equal to half of a0. And the surface area of facets of rank 1, of side a1, is equal to one-fourth of that of rank 0 faces.

Their volume can be obtained from their dimensions, or an: Vpyramid(rn) = 24776

an3 a3 = 3n 0 6 2 2 ×6 2 DOI: 10.1021/acsami.9b06982 ACS Appl. Mater. Interfaces 2019, 11, 24771−24781

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Figure 4. (a) Evolution of the surface area of a fracmid unit with the fractal rank (black curve) and of the unit volume with fractal rank (orange curve), for a0 = 1 mm; (b) unit surface efficiency (surface/volume ratio) as a function of the fractal rank.

since the conception of this unit, due to its rounded surfaces, uses significantly more RAM than fracmids. Of course, it should be mentioned that it would be possible and most likely easier to obtain 3D models of the fractal units using programs resulting in an automated fractal generator. Though the aim of the study was other: First, we intended to prove that such fractal units are geometrically “viable”, i.e., correct and conceivable, second that they can be employed to design more complex structures (superstructures), and finally translated from virtual/digital models into materials, thanks to 3D printing technology. 4.3.2. Complex Structures. 4.3.2.1. Fracmid Simple Lamellar Structure. Figure 5 shows an example of a simple

To conclude, the general formula for the volume calculation of fractal units is a sum of the volume of the core pyramid V0 with the volume of all the new pyramids appearing at each iteration (rank): n

Vn = V0 +

∑ npyramid(r ) × Vpyramid(r ) n

n

k=1

Vn =

a03 + 3 2

n

∑ (4 × 6n− 1) × k=1

a03 23n × 6 2

4.2.2.2. Surface, Volume, and Unit Surface Efficiency Evolution with Fractal Rank. On the basis of previously found formulas, Tables S1 and S2 compile the values of calculated surface, volume, and unit surface efficiency of the fracmid unit, for fractal rank ranging from 0 to 10. Calculations have been carried out with two different core unit dimensions (a0), 1 mm and 0.1 mm, in order to assess how surface efficiency evolves with the size of units. Only for a0 = 1 mm, curves have been traced to show the evolution of the surface, volume, and surface/volume ratio (unit surface efficiency) features, with fractal rank (Figure 4). The results of calculations confirm the fact that, when the fractal rank is incremented, the surface of fractal units rises in an exponential way while their volume only slightly increases to eventually reach a plateau. As a consequence, the unit surface efficiency improves greatly with increasing fractal rate, exponentially as well. Comparing the size of fracmids, it appears that the unit surface efficiency is strictly inversely proportional to the dimensions of the fractal unit. When side dimensions of units are divided by 10, its surface efficiency is increased by 10. As a consequence, the calculations clearly prove that the smaller the fractal units, the higher their surface/ volume ratio. As a conclusion, for fracmids, and most likely for other fractal units like fracones, the rank is not the only parameter of importance; the size of the unit core is also crucial to be able to control the surface area. 4.3. 3D Conception and Design by CAD. 4.3.1. Fractal Units. Fracmids have been conceived by CAD from fractal rank 0 to 3 (Figure 2a−d). Fracone units, only allowed for a CAD conception of rank 2 maximum (Figure 3a−c). Indeed, a more powerful computer would be necessary for higher ranks,

Figure 5. (a) Side view of a single level of simple lamellar structure made with r2 fracmids; (b) 3D view of the same single level, made of fractal units and a thin tray as a support; (c) the full simple lamellar structure is simply obtained by piling up single levels on the top of each other.

lamellar structure with r2 fracmids lying on the top side of substrate thin trays. The full structure is made by assembling levels on the top of each other. Figure 7b also shows crossshaped venting made in the trays, in the space between fracmid units. This could be useful for a better accessibility of fracmid units deep inside the structure, as well as a better penetration of light in the structure. Also, in the specific case of H2 production, it would make it easier for the gas to permeate through the material. Interfracmid distance calculation: Between the fracmids exists a gap (Scheme 2b), because of the tetragonal pyramids appearing at rank 1. Trigonometry calculations enable determining the value of this gap (Scheme 2c). 24777


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ACS Applied Materials & Interfaces a0 ji zy i 1 yz zz b = arccosjjjj 2 zzzz = arccosjjjj jzz 3 z{ k k {

First of all, angles b, c, and d need to be determined:

ij h yz i 2 yz zz c = arcsinjjj 1 zzz = arcsinjjjj z ja z k 3{ k 1{ d = 180° − b − c

Figure 7. (a) Multilevel pellet based on the simple lamellar structure; (b) top view, evidencing cross-shaped venting in the supporting trays, in between the fracmid units.

ij x yz cos(d) = jjj zzz ja z k 1{

From this, x can be deduced:

ij i yy i 1 zy zz − arcsinjjjj 2 zzzzzzzz x = a1 × cosjjj180 − arccosjjjj z j z k 3{ k 3 {{ k Since the gap is actually equal to 2x, for a fracmid of core dimension 1 mm (a0), a gap value of 0.333 mm is found. This gap value has been confirmed during the 3D conception of fracmids. 4.3.2.2. Fracmid Double-Layered Lamellar Structure. This structure (Figure 6) is similar to the previous configuration,

Figure 8. (a) A single column, obtained with fracmids of rank 1; (b) a repetition of the previous column creates a structured material.

4.3.2.5. Comparison of Structures Based on Fracmid Units. The three types of structures, namely, simple lamellar structure, double-layered lamellar structure, and columnar structures, might have different uses, depending on their geometrical features. For instance, lamellar structures seem more adapted to a photocatalytic application. Indeed, this configuration allows for a proper exposure of the fractal units from a light source (possibly sunlight) above, especially for the simple lamellar structure, in which fractal units are all facing upward, thus ideally oriented to capture light efficiently. Of course there must be an optimal number of levels in the structures, which could only be determined by experimental work. Now, comparing the two types of lamellar structures, despite a higher spatial interface density, the double-layered configuration might be a little detrimental to the penetration of light in the structure. On the other hand, the columnar structure would be more adapted in applications where only the interaction between a fluid medium and the substrate matters (catalytic applications, adsorption, decontamination, etc.) and where no light activation is needed. An interesting aspect of this structure is that it offers different packing possibilities, making it possible to modulate its density. It also minimizes the use of supportive material (from the scaffold), compared to the simple lamellar, albeit the double-layered lamellar structure is better for this matter since it does not need any scaffold for its structure, apart from a base support. 4.3.2.6. Fracone Columnar Structure. Fracone columns basically follow the same concept as for fracmid columns, albeit using a cylinder-shaped rod instead of a square section rod. The different horizontal levels of fracone units alternate in an

Figure 6. (a) Side view of a single level of double-layered lamellar structure with r2 fracmids; (b) 3D view of the first level; (c) the full double-layered lamellar structure is made by adding layers of fractal units on the top of the base level.

except that each level contains two layers of fracmids, one facing up and one facing down. Considering there are A and B fracmid layers, B being the “upside down” fracmids, there is a shift of a0/2 on x and y axes for the B layer, relatively to the A layer. Figure 6a displays the way fracmids are packed in a layer. A specificity of this architecture is that, except for the first one, levels do not require the use of trays for mechanical support. For this reason, the structure is naturally aerated and does not need venting. 4.3.2.3. Fracmid Pellets. Pellets have been designed, on the basis of the same model as the simple lamellar structure. Figure 7 displays different views of pellets with r1 fracmids. Even though they would find practical use and allow easy handling, they might be too inconvenient to manufacture using the FDM technique. Though, they might be produced using other AM techniques. 4.3.2.4. Fracmid Columnar Structure. This kind of structure uses square section rods (hollowed out to increase the spatial interface density) as a mechanical support for fracmids (cf. columnar scaffold in Figure 1a), instead of flat horizontal trays. Figure 8a shows a single column bearing r1 fracmids and Figure 8b the resulting structure, when the number of columns increases. Figure S3 also shows different methods for packing columns together, which enables obtaining superstructures with various compacity. 24778


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ACS Applied Materials & Interfaces ABABA sequence along the rod, with B levels being radially tilted, relatively to A, for a tighter packing of the units on the surface of the cylinder. This can be observed on Figure 9a,

Figure 9. (a) Sample of a fracone column composed of r1 units, evidencing the way each level is packed by being radially tilted compared to the one below; (b) the resulting structure; (c) section of a tube with inside wall covered with r2 fracones.

which shows a sample of a column with r1 fracones. As previously seen for fracmid structures, the cylinders can identically be hollowed out. Figure 9b gives an overview of the full structure, with several columns. This columnar configuration of fracones could be advantageously combined with a metal scaffold-like substrate (Figure 1b) to form an interesting fractal network. 4.3.2.7. Fracone Tubular Structure. This structure uses the same kind of configuration as above, except that the fractal units now cover the inner wall of a tube of substrate. Figure 9c only shows a small section of the tube configuration, for clarity purposes. It is easy to imagine that the fracones could be longer, in order to cover more of the inside section area of the tube, and have more interactions with a hypothetical fluid. This configuration could be interesting for the manufacturing of continuous-flow reactors. 4.4. Materials Fabrication and Testing. This section intends at proving that the principles described in this study can be used to produce real functional materials. Although there are many parameters that need to be managed for the creation of the hybrid materials (fracmid dimensions and fractal rank, 3D-printing parameters, core−shell synthesis conditions, plasma grafting settings, etc.), these aspects will not be described here. Indeed, we only want to attest the feasibility of the overall process. 4.4.1. 3D-Printed Structures. Fracone units did not show an acceptable printability, owing to their sharp morphology. We believe other types of 3D-printing technologies than FDM would be more adapted to them. On the other hand, a number of structures based on the fracmid units have been successfully printed by FDM. Three examples of structures, with lamellar and columnar morphologies, are displayed in Figure 10 (scales of the models are shown in Figure S4). Interestingly, these models show an appreciable cohesion and robustness. The visual aspect of the printed fracmids can be observed more clearly in Figure S5. Figure 10d,e gives an overview of the surface of printed fracmids as well as their morphology. The typical stair/step topography can be seen in these images. Even though there are still improvements that can be made, such as reducing the scale of the structures, increasing the fractal rank and printing accuracy, it is already an important step, to show that the structures described here are printable and viable, but also that geometry inspired by fractal principles can be used in concrete 3D-printing applications using FDM technology. It is to note that using a printing nozzle of smaller diameter should make it possible to get smaller units, with

Figure 10. (a) Photograph of a PLA 3D-printed simple lamellar structure bearing r2 fracmids; (b) double-layered lamellar structure with r2 fracmids; (c) columnar structure made with r1 fracmids; (d) SEM image of the side part of an r2 fracmid of 5 mm side (scale: 2 mm); (e) SEM of the top part of the same r2 fracmid (scale: 2 mm).

higher fractal rank and better definition. However, we met difficulties while using a smaller nozzle (0.1 mm diameter), notably adhesion issues between the models and the printer bed. Finally, it should be noted that the quality of the printed substrates significantly depends on the accuracy of the equipment, and not only the printing parameters. 4.4.2. Synthesis of the Hybrid Photocatalyst. As seen in the SEM photograph in Figure 11, nanoZno@PAA core/shells

Figure 11. SEM images of ZnO@PAA agglomerates plasma grafted on PLA surface (the scales represent 4 μm). (a) The darker areas correspond to the PLA substrate left apparent. (b) Here, the amount of poly(acrylic acid) is lower. As a consequence, agglomerates are smaller, and the coating is more uniform.

have successfully been grafted on the surface of PLA. The EDX spectrum in Figure S6 from the Supporting Information corroborates the fact that the agglomerates visible on the top of the PLA surface are mainly made of zinc oxide. The carbon peak is most likely due to the PAA shell, according to our observations. The zinc oxide layer is apparently a few micrometers thick. The agglomerates are composed of core/ shell particles of average diameter around 30 nm, packed together. Tuning the PAA grafting rate partially allows controlling the size of agglomerates, as well as the uniformity 24779


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5. CONCLUSION A number of superstructures have been conceived and later designed by CAD, using two types of fractal units, namely, fracmids and fracones, in addition to a scaffold. Calculations allowed evidencing what influence the fractal rank plays on the fractal unit surface. Concretely, incrementing the fractal rank makes the interface of superstructures rise exponentially. In a predictable way, decreasing the dimensions of fractal units also permits an improvement of the interface of structures. Using the geometrical principles exposed here, different structures have been 3D-printed with PLA using FDM. PLA samples have been successfully functionalized with nanoZnO@PAA by plasma grafting. Finally, the photoactivity of one sample of hybrid material has been positively tested, with a result of 63% degradation of Rhodamine B dye after 5.5 h. Even if the application exposed in this study is specifically about the conception of photocatalysts using ZnO nanoparticles and plasma grafting, the concept developed here actually opens the way for a wide range of applications where architecture and interface of materials play an important role. Finally, the principles described in this study realistically allow for the preparation of fully functional structured hybrid nanomaterials.

of the grafted layer. For instance, Figure 11b displays a much more uniform layer, with smaller agglomerates, thanks to a lower amount of PAA in the shells. We assume these agglomerates are the result of a chain reaction during the plasma grafting, making the PAA chains react not only with the PLA surface but also between one another, promoting the formation of interchain boundaries and thus covalent junctions between neighbor core−shell particles. To conclude, the APPAG (aqueous phase plasma-aided grafting) process revealed to be very efficient and highly reproducible for the functionalization of a PLA substrate by zinc oxide-based nanocore/shells, which makes it a perfectly adapted tool to be combined with FDM 3D printing. We believe these interesting results could be extended for the fabrication of other materials, using different AM processes and other types of polymer substrates and nanoparticles, through the use of various coupling agents (other than PAA). 4.4.3. Photoactivity of the Hybrid Nanocomposite. The photocatalytic activity of a hybrid material has been investigated, to prove that zinc oxide is still photoactive, even after surface functionalization and plasma grafting. The sample (Figure S7) is made of nanoZnO@PAA plasma-grafted (N2 plasma) on a PLA substrate made of a single layer of r2 fracmids. Whereas we faced difficulties finding the precise mass of ZnO grafted onto the surface of the sample, we know with certainty that it is less than 1 mg. Figure 12 actually displays

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.9b06982. One figure showing the different steps of fractal units conception; images of fracmid units 3D-printed by FDM and fractal structures; two tables with geometrical parameters related to fractal units; one figure showing CAD columnar structures; images of 3D-printed structures; an EDX spectrum of PLA surface coated with nanoZnO@PAA; an image of a hybrid photocatalyst (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +86 15071028704. ORCID

Yoann de Rancourt de Mimérand: 0000-0002-3120-7616

Figure 12. Degradation kinetics of Rhodamine B dye by the hybrid photocatalyst (PLA-g-ZnO@PAA). The inset graph displays the visible absorbance curves of Rhodamine B throughout the photodegradation experiment.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding

This research has been funded by the Youth Science Foundation of Wuhan Institute of Technology.

the results for a second cycle of Rhodamine B photodegradation. The test appeared conclusive since 63% of the dye has been degraded after 5.5 h of test, thus showing that the manufactured nanocomposite can effectively be used in photocatalytic applications. This proves that the surface functionalization of nanoparticles of ZnO by PAA did not, or at least not significantly, restrain their photoactivity. Also, the photocatalytic efficiency is relatively important, considering the small amount of nanoZnO engaged in the test. Finally, this experiment also proves that the sample can be recovered, washed in thorough conditions, and reused successfully, confirming the fact that the ZnO coating obtained by plasma grafting is permanent and robust.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The department of Chemical Engineering and Pharmacy of Wuhan Institute of Technology (WIT) is deeply acknowledged for their support (grant number 16QD53).

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REFERENCES

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