Self assembling cluster crystals from DNA based dendritic nanostructures

Cluster crystals are periodic structures with lattice sites occupied by several, overlapping building blocks, featuring fluctuating site occupancy, whose expectation value depends on thermodynamic conditions. Their assembly from atomic or mesoscopic units is long-sought-after, but its experimental realization still remains elusive. Here, we show the existence of well-controlled soft matter cluster crystals. We fabricate dendritic-linear-dendritic triblock composed of a thermosensitive water-soluble polymer and nanometer-scale all-DNA dendrons of the first and second generation. Conclusive small-angle X-ray scattering (SAXS) evidence reveals that solutions of these triblock at sufficiently high concentrations undergo a reversible phase transition from a cluster fluid to a body-centered cubic (BCC) cluster crystal with density-independent lattice spacing, through alteration of temperature. Moreover, a rich concentration-temperature phase diagram demonstrates the emergence of various ordered nanostructures, including BCC cluster crystals, birefringent cluster crystals, as well as hexagonal phases and cluster glass-like kinetically arrested states at high densities.


Fitting parameters
Parameters resulting from SAXS data fit for the G1-P-G1 and G2-P-G2 presented in Supplementary Fig. 2a and Supplementary Fig. 2b, respectively.

SAXS modeling
The SAXS scattering patterns of DNA clusters at high concentrations show a prominent peak structure that corresponds to a BCC lattice with a pronounced unstructured and broad peak at higher scattering vectors q. The overall pattern is described by the scattering of a crystal domain

Ic(q) with a nonconstant background Ib(q) as I(q)=Ic(q)+Ib(q).
The scattering intensity of a crystal domain in powder average is f ( ) = ( ) ( ) with particle density n.
The structure factor S(q) is expresses as [1]: with Miller indices hkl numbering the Bragg peaks, nu being the number of particles in the unit cell, f 2 hkl as unit cell structure factor considering extinction rules, vd as volume of the unit cell, Porod constant c ≈ 1 and peak multiplicity mhkl.
The Debye-Waller factor ( ) = 4Z [ 〈w [ 〉 depends on thermal dislocations with mean square fluctuations 〈 N 〉 = Δ and reduces peak intensities for increasing q.

G1-P-G1
G2 The form factor of DNA clusters is modeled as core-shell particle with polymer linkers in the core and a shell filled by DNA fragments, a schematic of which is shown in the right cartoon of Fig. 3f. The core-shell form factor is ( ) = ‚∑ ",… ‚ , †,… , ‡,….ˆN with the sum running over n = core, shell, and the scattering amplitude fa,n of shell, respectively core (with Ri=0) as [3] : Here Ri, Ro are the inner and outer radius and ∆ … is the scattering contrast to the solvent of shell, respectively core.
The low intensity at low q suggests that the scattering contrast ∆ between core and shell has opposite sign to result in a condition close to matching of the core against the shell at low q with -s-uu ∆ -s-uu ≈ − f ‡w-∆ f ‡w-.
The broad peak around 2 nm -1 is attributed to correlations between DNA fragments that are not covered in the BCC core-shell model. This background is described by the Teubner-Strey model [4]:

A note on modeled G1-P-G1 and G2-P-G2 cluster form-factors
We would like to attract the attention to a particularly interesting observation concerning the shape of the form-factors in the q-region at which the higher-order reflections are observed. For the G1-P-G1, the first minimum of the cluster form-factor is located exactly at the q-position of the fourth-order Bragg peak (blue curve in Supplementary Fig. 2a) and, therefore explains the absence of this reflection in our 1D-SAXS profiles (second panel and third panel from the bottom of Fig. 4a and Fig. 4b, respectively). It is also worth mentioning that the lack of the above-mentioned reflection allowed us to carefully adjust our fitting parameters. In addition, and contrary to the G1-P-G1 system, the second maximum of the G2-P-G2 cluster form-factor (blue curve in Supplementary Fig. 2b) is not superimposed onto the higher order Bragg peaks arising from the BCC lattice, and, hence, its presence and location can clearly be discerned in the experimental data. Interestingly, the position of the G2-P-G2 cluster form-factor peak is not markedly affected by the DNA concentration or temperature, indicating that the cluster size remains invariant under such changes.

Temperature-induced cluster Fluid-to-BCC transition in G1-P-G1.
In Fig. 4b, a cluster fluid-to-crystal transition is presented for the G1-P-G1 at DNA concentration = 255.7 mg/ml, through alteration of temperature. Up to 20 + C, a temperature well below the LCST of the Poxa chain, the G1-P-G1 solution exhibits a cluster fluid structure which progressively becomes more ordered by increasing the temperature. A slight further temperature increase induces a markedly different phase, as can be seen from the SAXS profile acquired at 23 + C. Comparison of the observed Bragg peaks with the first seven allowed reflections for a BCC lattice with _yy = 28.2 nm (red vertical lines) offers a compelling evidence regarding the morphology of this cluster crystal structure. This fluid-to-crystal transition is in accordance with the self-assembly of our dendritic based triblocks into clusters with a temperature-dependent aggregation number. Since the segregation strength between the Poxa and the DNA in our dendritic-based triblocks becomes stronger with increasing temperature, the observations are compatible with an overall cluster size growth through a simultaneous swelling of its core (Poxa chains stretching) and an increase of the aggregation number. This explains why no significant change is seen in neither the SJT -peak position nor in its width over the temperature range between 4 + C and 23 + C.

On the origin of liquid crystalline BCC-like (BCCLC) in G1-P-G1 system.
The two bottom panels of Fig. 7a and the depolarized images of the samples presented in the top panel of Fig. 7b indicate that a transition from BCC-to-BCCLC occurs over a DNA concentration range from 287.7 mg/ml to 300.8 mg/ml, without, however, a change in the BCC lattice constant. Further augmentation of G1-P-G1 concentration leads to a gradual increase in lattice constant by approximately 8% going from 300.8 mg/ml to 337.7 mg/ml (top panel of Fig. 7b). The sample exhibits a strong and colourful birefringence under crossedpolarizers (rightmost image in the top panel of Fig. 7b). In addition, the SAXS profiles of the most concentrated birefringent BCC-like samples show the so-far missing fourth Bragg reflection (marked by the grey circles in the middle panel of Fig. 7a), suggesting that the BCCto-BCCLC transition is followed by a change in shape or size of the clusters. On the basis of the above results, and in conjunction with the requirement of releasing the packing frustration as the almost close packed BCC crystal is further compressed, we surmise that the optical anisotropy of the BCCLC phase can be ascribed to orientationally ordered ellipsoidal-like clusters occupying the sites of the BCC lattice (Fig. 7c). Such a molecular packing scenario is plausible since a nematic-like "cubic" phase may exhibit optical birefringence without a departure from cubic symmetry. Furthermore, we expect that for a small energy cost, a cluster deformation can be allowed, stemming from its moderate occupancy character. In the BCCLC cluster crystal regime (blue region in the phase diagram of Fig. 6a), an increase of +¥¥ from 38 to 53 is found by increasing the G1-P-G1 concentration (bottom panel of Fig. 7b). It is imperative to note that efforts to refine the unit-cell parameters have shown that the changes were too small to decisively demonstrate a non-cubic symmetry, such as in a tetragonal lattice.
However, the G1-P-G1 packing scenario remains a matter of speculation and further work is required for elaborating this conjecture. The theoretical molecular mass (Mw theor ) of each individual DNA strand and the corresponding experimental value (Mw exper ) as determined by Maldi-TOF mass spectroscopy are listed below. These values were provided by the supplier (Biomers).
The cloud point and the corresponding uncertainty ΔT were observed by fitting the data using nonlinear curve Boltzmann fit and determining the temperature at the inflection point of the heating curve.