## 3 Results  
### Sequence Design of Crosslinker and Spacer Strands for DNA Gel Formations  
We constructed DNA hydrogels by mixing crosslinker and spacer modules that associate based on DNA-DNA hybridization, as shown in Figure 1. Four types of crosslinkers (Y-shaped DNA tiles, X-shaped DNA tiles, DNA-CNT conjugates, and DNA-AuNP conjugates) and three different lengths of spacers (Ss, Sm, and Sl; short (33 nt), medium (44 nt), and long (55 nt), respectively) were tested. With these building blocks, we produced two major types of hydrogels: pure DNA hydrogels and DNA/nanomaterial hydrogel composites. For DNA crosslinkers, we used two types of branching crosslinkers called Y-shaped and X-shaped DNA tiles that were assembled from three and four ssDNA strands, respectively. Each arm in the DNA tile carried a sticky end complementary to sticky ends on the spacers. We adopted sequences of strands D\({}_{1}\), D\({}_{2}\), and D\({}_{3}\) from [PERSON] et al. to construct Y-shaped DNA tiles [40]. Similarly, we modified the sequences of strands X\({}_{01}\), X\({}_{02}\), X\({}_{03}\), and X\({}_{04}\) reported by [PERSON] et al. [41] by swapping in our sticky end to construct X-shaped DNA tiles. To construct DNA-CNT conjugates, we applied a DNA sequence containing multiple repeated GT units that wrap around CNTs. Specifically, we adopted Sequence C as reported by [PERSON] et al. [38] and modified their Sequence D with our sticky end to make it compatible with our spacers. The repeated GT units have been proven to efficiently wrap around CNTs well due to strong \(\uppi\)-\(\uppi\) interactions between the CNT sidewall and the nucleobase aromatic rings [38,42]. [PERSON] et al. also demonstrated a systematic study showing that among all DNA sequences that wrap around CNTs, (GT)\({}_{\text{n}}\) gives the highest dispersion efficiency and only requires 30 min sonication to obtain well-dispersed DNA-wrapped individual nanotubes [26]. A longer sonication treatment breaks CNTs and decreases their high aspect ratio [43], which is a property essential to our objective of building percolating networks. Therefore, we chose to make DNA-CNT conjugates with (GT)\({}_{20}\) repeat units to allow a shorter sonication time. Strands of this length tightly wrap around nanotubes, while a longer DNA strand wraps around nanotubes more loosely and may also entangle multiple nanotubes [44]. We examined both single-walled CNTs (SWNTs) and multi-walled CNTs (MWNTs) in this study. According to the vendor's specifications, the SWNTs have an average diameter of 0.78 nm with a median length of 1 \(\upmu\)m. We chose these dimensions because previously reported atomic force microscopy (AFM) studies observed that (GT)\({}_{20}\) can form multiple wraps around SWNTs with an average diameter around 1 nm [44]. We purchased MWNTs of a much larger size with an average outer diameter of 8.7-10 nm and an average length of 10 \(\upmu\)m. The same study showed that DNA wrapping loosens as the nanotubes become larger and mostly only wrap with one turn around MWNTs of greater diameters. Lastly, we utilized DNA-AuNP conjugates as the fourth type of crosslinker. We synthesized AuNPs with an average diameter of 13 nm using a method adapted from the standard citrate reduction procedure [36]. As-synthesized AuNPs were characterized by TEM, as shown in Figure 2a. DNA-AuNP conjugates were created by attaching ssDNA to the surfaces of AuNPs using the method reported by [PERSON] et al. [39]. Briefly, 13-nmAuNPs at neutral pH adsorb DNA strands with polyadenine (A\({}_{\text{n}}\)) as the anchoring block due to the strong interaction between adenine and gold. We designed a DNA sequence to contain 13-mer of polyadenine (A\({}_{13}\)) that is connected with a 12-nt sticky end. The polyadenine sequence strongly adsorbed onto AuNPs with high loading capacity. This method produced DNA-AuNP conjugates with much higher concentrations of DNA and AuNPs compared to another method prepared by polymerase chain reaction (PCR) elongation [45].