Our experimental system includes two complementary DNA octahedral origami frames with about 30 nm edge length that can self-assemble into crystalline organization with a cubic lattice through vertex-driven sixfold hybridization8. The nucleation and growth of these lattices is closely dependent on the thermal annealing procedure, which starts at 50 °C to obtain a monomeric DNA-frame solution, followed by a slow ramp down of temperature to allow crystallization8,15. The acoustic setup consists of interdigital transducers (IDTs) and wave generator. IDT, fabricated by photolithography, convert electrical signals into acoustic waves through the piezoelectric effect.Acoustic organization of pre-formed crystalsWe first explored the use of acoustic waves for a macroscale organization using preassembled micron-sized DNA crystallites. A sealed glass capillary with the sample solution is placed in between the two IDTs, where the SSAW with a half wavelength of ~100 µm are generated (Fig. 1b, c). This results in the formation of a pattern of linear nodes with a width of several microns, separated by ~50 µm microns39, the length of nodes (~3 mm) is determined by the size of IDT (3.5 mm). While applying the SSAW, the acoustic forces push the DNA crystallites to the node positions within the capillary, creating a linear pattern (Fig. 1d). The entire setup is held in a temperature-controlled chamber which permits controlling DNA hybridization and pathway for crystal assembly and disassembly, while visualizing the process in real time through optical microscopy.The standing acoustic waves are generated in pulses to stimulate crystallites in a specific spatiotemporal way. This leads to local heating at the active region between the IDTs, where the magnitude of the effect is determined by the temporal acoustic field profile (Supplementary Fig. 1). The profile consists of a wave pulse with a duration of 50 ms active SSAW and different time periods between the initiation of each pulse, ranging from 500 to 5000 ms in our experiments. This design allows us to independently control several key parameters of the system: thermal protocol (using the thermal chamber), pulse and period durations. Initially, the crystals are dispersed randomly within the capillary (Fig. 1c), yet when the acoustic field is applied, the crystals move to the nodes, forming a linear arrangement of individual crystals in the nodes (Fig. 1d and Supplementary Movies 1 and 2).Following the successful organization of DNA crystals into linear patterns, we investigated merging the crystals into a single macroscale morphology through thermally controlled fusion. Our thermal protocol (Fig. 2a) includes the reannealing of crystals without their full melting into a single extended unit under the acoustic field. First, preassembled crystals (Fig. 2b) were aligned into the nodes (Fig. 2c). Next, the temperature was elevated to completely dissolve smaller crystals and nuclei, leaving only crystals that were initially larger, which narrowed the size distribution of crystallites (Fig. 2d). Then, the temperature was ramped down slowly to allow the remaining crystals regrowth while the acoustic field kept the growing crystals within the nodes (Fig. 2e). Due to the closely packed linear alignment and confinement to the nodes by the acoustic force, crystals have the propensity to grow one into the other. Scanning electron microscopy (SEM) images show that crystals are fused together during regrowth, creating a single continuous elongated entity formed from organized crystals. The fused crystals are coherently coordinated and form a solitary lattice that spans over several crystallites (Fig. 2f, g). We observed that the cubic crystallites within the nodes exhibit a certain degree of alignment with a preference for facets to be orientated parallel to the transducer surface (Supplementary Fig. 2), likely since such arrangement minimizes their cross-section to the SSAW. However, this orientation effect is suppressed by inter-crystallite attachments due to the hybridization between DNAs on the surfaces of different crystallites (Fig. 2b–h and Supplementary Fig. 3). Our approach for forming DNA-based morphologies by acoustic field is also suitable for lattices with nano-cargo. Such a cargo (gold nanoparticles (AuNPs), proteins, or quantum dots) allows adding a desired functionality to DNA lattices. As an example of this possibility, Fig. 2h shows the linear arrangement of lattices filled with 10 nm AuNP cargo formed under acoustic stimulation.Fig. 2: Fusing crystallites into macroscale materials.a Thermal profile for reannealing preformed crystals. Active acoustic waves pulsing is represented by a dashed blue line; inactive acoustic field (no pulsing waves) is represented by a solid red line. b–e Brightfield microscopy images of crystals subjected to the thermal reanneal protocol and acoustic waves at the different stages of the protocol, corresponding to the numerical notation in (a). f, g SEM images showing that the crystal reanneal protocol induces fusing of the crystals to form elongated macroscale morphology of crystals. h Crystals filled with AuNP aligned using acoustic waves. The red hue is the result of AuNP loaded into the lattice.Crystallization under acoustic stimulationConsidering the ability of SSAW to push preassembled lattices, we were interested in exploring whether lattice formation is affected by the acoustic field. We applied SSAW pulses during the initial crystal nucleation and growth and combined this with a thermal anneal process. While the wave pulse length is set to 50 ms (approximately 1 M wave cycles), the period, i.e., the time between the initiation of each pulse, is altered for different experiments; the period divided by the pulse length is denoted as τ (Fig. 3). Following this procedure, we observed a formation at the nodes of elongated morphologies of tightly packed crystals, whose appearance is similar to the morphologies formed by preformed crystals under SSAW-driven assembly. However, crystallites assembled under acoustic field pulses exhibited a noticeable increase in crystal size, particularly for certain pulse regimes, as we elaborate below (Figs. 3 and 4a).Fig. 3: Crystal size formed with acoustic waves.Crystal size formed with varied τ. The colors of the plotted sample correspond to the frame of the brightfield microscopy image frame. All samples (other than No Wave) were subjected to 50 ms wave pulses with varied periods (τ = period/pulse, as shown in the inset). Box-plot overlayed shows the median, Q1, Q3 and 1.5 Interquartile range whiskers. n is the number of crystals measured for each sample.Fig. 4: Acoustic waves affect nucleation and growth.a Histogram of crystal size distribution with no acoustic waves (blue) and with τ = 20 (red) for a fast temperature decrease rate of 0.03 °C/min (some of the data is shown in Fig. 3 with different representation). The nucleation and growth theory fit (blue line), and the infusion model (red line) account for the effect of the acoustic waves. b Crystal size distribution vs. τ, showing both discrete experimental data points (as shown in Fig. 3) and continuous model-calculated behavior. c, d Slow thermal anneal (temperature decrease rate of 0.01 °C/min) of crystals with no waves applied (c) and with τ = 20. e Fast thermal anneal (0.03 °C/min) with τ = 20, followed by a thermal reanneal to fuse crystals together, results in elongated macroscale structures at the millimetric scale. The width of the capillary (left wall to right wall) is 1 mm. f Measured SAXS structure factor (S(q)) of the crystals assembled under acoustic field and untreated crystals corresponds to modeled S(q) of simple cubic crystal structure.To obtain a quantitative understanding of this phenomenon, we systematically studied the effect of the ratio between period and pulse, τ, on the size of formed crystals. Pulse in a narrow range of τ values yields an increase of the crystal size at a fast thermal anneal of 0.03 °C/min (Fig. 3 and Supplementary Fig. 6). Compared with thermal annealing without acoustic waves (τ → ∞), SSAW treatment also broadens crystal size distribution, which is more prominent in the narrow τ range (Figs. 3 and 4a). Specifically, at τ = 20 (1000:50 ms period to pulse ratio), crystal sizes are significantly larger (nearly doubling in edge length), even compared to the other samples formed under acoustic waves at different τ values (Fig. 3 and Supplementary Fig. 5). We also observed this effect for all explored thermal anneal rates and found that the largest crystals were formed at the same τ = 20 with a slow thermal anneal of 0.01 °C/min (Supplementary Figs. 7 and 8, for more microscopy images, see Supplementary Figs. 9–18).We first analyzed the size distribution in the absence of acoustic waves to gain mechanistic insights into the observed phenomena of larger crystals formed under the acoustic field (Fig. 4a). This distribution arises from the interplay between nucleation dynamics and diffusion-limited crystal growth. We first ruled out the possibility that the acoustic field has an effect on the individual frames since our estimation indicates that the thermal energy exceeds an acoustic energy for ~30 nm objects (see Acoustic field considerations in Supplementary Information). Both nucleation and growth processes depend on the difference in chemical potential between the solution of free monomers frame, \({kT}{{\mathrm{ln}}}{{{\rm{c}}}}\), and the crystal phase, denoted as:$${\mu }_{{cr}}\left(t\right)={kT}\, {{{\mathrm{ln}}}}\, {c}_{0}-\Delta {Srt}$$
(1)
Here, \(r\) represents the cooling rate, and time is measured from \(t=0\), the point at which the crystal would be in coexistence with the solution at the original concentration \({c}_{0}\). \(\Delta S\) denotes the entropy associated with the unbinding of a single frame from the crystal, which corresponds to melting of 12 DNA duplexes. We introduce the quantity \(\Delta \left(t\right)\), that represents the thermodynamic driving force to crystallization, defined as:$$\Delta \left(t\right)\equiv \frac{{kT}\,{{{\mathrm{ln}}}}\,{c}-{\mu }_{{cr}}\left(t\right)}{{kT}}={{{\mathrm{ln}}}}\frac{c}{{c}_{0}}+\frac{\Delta {Srt}}{{kT}}$$
(2)
Let \(a\) be the lattice constant of the cubic crystal, with \(\frac{\Gamma {kT}}{{a}^{2}}\) representing its surface energy, and \(D\) denoting the diffusion coefficient of a free building block. The classical homogeneous nucleation rate for a cubic-shaped crystal can be expressed as follows40:$$\nu \left(t\right)=\frac{{Dc}\Delta }{{a}^{2}\sqrt{\Gamma }}\exp \left(-\frac{32{\Gamma }^{3}}{{\Delta }^{2}}\right)$$
(3)
Once nucleated, each crystal grows at a diffusion-limited rate given by:$$\dot{L}=\frac{4\pi \varsigma }{3}\frac{D{{ca}}^{3}}{L}\left(1-{e}^{\frac{4\Gamma a}{L}-\Delta }\right)$$
(4)
Here, \(L\) represents the edge size of the cube, and \(\varsigma \approx 0.66\) is a numerical constant specific to the cubic geometry. As the number density of crystals \(n\) and their average volume \(\left\langle {L}^{3}\right\rangle\) increase, the solution of the building blocks gets depleted:$$c={c}_{0}\left(1-\frac{n\left\langle {L}^{3}\right\rangle }{{a}^{3}}\right)$$
(5)
By constructing the Fokker–Planck equation and solving it numerically, we obtained the final size distributions, which are in excellent agreement with the experiments conducted without acoustic waves for both fast and slow thermal anneal protocols (Fig. 4a, b). When fitting the data, we used \(\Gamma\) as a single adjustable parameter (the same for all annealing rates), while the rest of the parameters have been determined based on the known geometry of the building blocks, their concentration, and the thermodynamics of DNA hybridization.Once the system is subjected to acoustic stimulation, two new effects must be considered. Firstly, SSAW are expected to suppress the nucleation of crystallites due to local heating in the active region of the acoustic field due to their dissipation (Supplementary Fig. 1). Secondly, the forces associated with the acoustic field result in an influx of small clusters of frames into the active region from adjacent areas in the capillary (Fig. 1b), which act as nuclei for crystal growth. Thus, the number of growing crystals is dictated by both an interplay of acoustically suppressed homogeneous nucleation and the influx of nuclei from the adjacent region. As the time interval between pulses, i.e., τ decreases, both effects become more pronounced, explaining the observed non-monotonic behavior of the τ vs. crystal size relationship (Fig. 3). Namely, as τ decreases, the suppression of homogeneous nucleation is initially offset by a moderate influx of crystals from the surrounding regions. This leads to a reduction in the overall number of crystalline particles and an increase in their average size (since the total amount of material is determined by the initial concentration). Once the homogeneous nucleation is sufficiently suppressed, the further increase in influx reverses the effect, resulting in a greater number of crystalline particles and, consequently, smaller crystal sizes.To describe this effect, we propose a simple model in which nucleation in the active region is suppressed by a factor of \({e}^{-\frac{\epsilon }{\tau }}\), while remaining unaffected in the adjacent region. The infusion process is represented by a single rate proportional to pulse frequency, \(\frac{\kappa }{\tau }\). The size distribution \(f\left(L\right)\) in the region exposed to SSAW evolves according to the Fokker–Planck equation:$$\dot{f}\left(L,t\right)=\nu \left(t\right){e}^{-\frac{\epsilon }{\tau }}{{{\rm{\delta }}}}\left(L-{L}^{*}\right)-{\partial }_{L}\left(f\left(L,t\right)\dot{L}\right)+\frac{\kappa }{\tau }{f}_{0}\left(L,t\right)$$
(6)
Here, the first two terms represent the nucleation and growth processes discussed above, and the last term is due to the infusion of material from the adjacent region unaffected by the acoustic waves. Thus, \({f}_{0}\left(L,t\right)\) is the size distribution without the SSAW effect that obeys the same equation with parameters \(\kappa\) and \(\epsilon\) set to 0.Although oversimplified, this model provides a surprisingly good description of the observed phenomenon. Specifically, it captures the non-monotonic behavior and the observed broadening of the size distribution due to the acoustic field. Furthermore, this simple model gives an impressive quantitative agreement with the observed size distribution in the vicinity of the optimal conditions for larger crystal sizes (Fig. 4a, b and Supplementary Figs. 6–8). Note that the same values of adjustable parameters \(\kappa\) and \(\epsilon\), have been used for different cooling rates and inter-pulse periods. As the τ increases, homogeneous nucleation in the active region returns to its unsuppressed rate. Conversely, more frequent acoustic driving leads to an increased infusion rate κ. Both these effects cause the size distribution to revert to the no-wave case, which is described by the unmodified nucleation and growth theory.In certain cases, the SSAW effect could produce exceedingly large crystallites compared to those assembled without a field, specifically, with a slow thermal anneal (0.01 °C/min) and an acoustic pulse of 50 ms and τ of 20 (Fig. 4c, d). Interestingly, in contrast to the formation of larger single crystals with a slow anneal, pulsing SSAW during a fast annealing (0.03 °C/min) results in assembly of long crystalline morphologies, reaching length of 2 mm (Fig. 4e). Combined with the reannealing and fusing process discussed above (Fig. 2), each of these morphologies is merged into a single unit, as indicated by the fact that such linear structures (highlighted in blue) can hop from one node to another (marked in red) without breaking. We further explored that nanoscale structure of the lattice morphologies assembled under both acoustic driving and annealing using small angle x-ray scattering (SAXS). SAXS measurements reveal that the formed crystals exhibit a simple cubic lattice, similar to crystals without acoustic stimulation (Fig. 4f). This implies that the acoustic-driven assembly does not alter the nano-scale arrangement of the DNA frames in a lattice but only affects the lattice growth at the level of crystallites and a final morphology at the scale of a hundred micrometers up to millimeters.In conclusion, we have demonstrated that acoustic fields with specific spatiotemporal characteristics provide an effective means to drive the formation of DNA-assembled materials at the macroscale. While DNA nanotechnology enables precise spatial control at the nanoscale, achieving controlled organization at larger scales has remained challenging. By combining DNA-guided assembly with acoustically driven processes, we successfully directed the assembly and dictated the morphology of DNA-origami-based crystal lattices at scales ranging from tens of microns to millimeters, while maintaining DNA-defined nanoscale organization. This study shows that the acoustic field can drive the assembly of macroscale morphologies from preformed crystals and monomers under annealing conditions. The macroscale morphology of crystals can be potentially expanded to other geometries, beyond linear structures shown in our work. This can be achieved by changing the boundary conditions of the sample, or by changing the arrangement and geometry of the transducers. For example, complex two-dimensional patterns can be produced, much like Chladni plates41. More broadly, acoustic holography can be potentially employed to form complexly designed patterns of self-assembled materials42,43. Moreover, the acoustic field might enhance the formation of crystals within a certain pulse regime due to the combination of the two new effects caused by the acoustic waves (local heating and influx of nuclei). Our experimental observations are supported by a computational model that incorporated nucleation dynamics, diffusion-limited growth, and the effects of acoustic driving. Given the flexibility in engineering acoustic fields and a broad range of functions of DNA-based materials, our combined DNA and acoustically driven assembly approach potentially allows for the controlling structure formation over 6 orders of magnitude in scale from sub-nm to mm. Combined with an inorganic templating strategy6,15, this approach provides device-scale nanomaterials fabrication for potential applications in photonics, mechanics, electronic devices, and biomaterials.
Acoustically shaped DNA-programmable materials | Nature Communications
