# Electrokinetic Properties of 3D-Printed Conductive Lattice Structures
## 1 Introduction  
Metamaterials are artificial structures or assemblies specially designed to reach specific properties that natural materials do not have [1]. Artificial media can be created by different means, among which additive manufacturing offers several advantages for making objects with a complex shape [2, 3]. Before adopting a new manufacturing process such as 3D printing, the merit of the process must be evaluated with care. Sustainability criteria are becoming more and more stringent in the process assessment. Reduced consumption of both energy and natural resources, a small volume of waste, environmental issues, life cycle of the manufactured products, etc., must be weighted with specific tools against other constraints, such as cost and ease of production, human labor, etc. [4]. Among the advantages of additive manufacturing, one may cite (i) the possibility to produce a large variety of prototypes or functional components with complex geometry, (ii) substantial automation of the technological process, and (iii) a reduction in the number of manufacturing steps [5, 6, 7]. Disadvantages include (i) the limited number of materials that can be involved in the process, (ii) a longer fabrication time, and (iii) a higher energy consumption in comparison with conventional methods. Due to its advantages, additive manufacturing is actively used in diverse such areas as aerospace, automotive, medical, architecture, education, etc. [8]. Different 3D printing technologies include stereolithography [3, 9] and extrusion printing method [10]. The latter approach has been successfully applied to produce conductive cellular structures [10, 11]. For this production, ink made of polymer with embedded conductive inclusions at a concentration above the percolation threshold is used. Despite the low cost and wide prevalence of 3D printing technology based on extrusion of polymer material, this method is limited to the production of overhanging structures. It requires special support media that complicate the manufacturing process [12]. In contrast, the selective laser sinteringfabrication process can deal with a shape sample of any complexity. It can potentially be applied for the fabrication of 3D cellular structures with, however, a larger mass of material used in the fabrication process [13]. Nowadays, sub-mm spatial resolution can easily be reached with commercially-available printers. At this length scale and above, one may think of myriads of mechanical, acoustical, electrical, etc., applications, including the fabrication of molds for the manufacture of special pieces [4]. In particular, 3D printing is providing new opportunities for the fabrication of electromagnetic metamaterials with unusual behavior for electromagnetic radiation in the radio wave and microwave domains [14; 15]. For instance, suitably-structured dielectrics behave like an effective anisotropic media for microwaves [16]; a periodic array of small metallic inclusions in a polymer matrix may be seen as a diamagnetic effective medium [17]. When deposited on a metallic foil, 3D-printed all-dielectric resonators lead to broad-band absorption in the microwave range [18; 19]. Many other applications are under investigation, which range from DC electrical circuits [20] to GHz antennas [21]. The structure of interest in this work is a periodic network of interconnected beams defining a 3D mesh. Figure 1 is an example representing a diamond lattice. Light 3D lattices of that kind can easily be produced by additive manufacturing [22; 23], including the largely-diffused 3D-printing technology based on polymer materials, such as fused deposition modeling (FDM). Recent examples of FDM products are: Kagome mesh structures made of acrylonitrile butadiene styrene (ABS) polymer [24] and simple-cubic lattices made of conducting nanocarbon-doped polylactic acid (PLA) [25]. In that case, the lattice parameter is a few millimeters wide or larger.