PHYSICAL REVIEW RESEARCH 4, 033046 (2022)
Smectic-B phase and temperature-driven smectic-B to -A transition in concentrated solutions
of “gapped” DNA
Prabesh Gyawali ,1 Rony Saha,1 Sineth G. Kodikara,1 Ruipeng Li,2 Masafumi Fukuto,2 James T. Gleeson,1
Gregory P. Smith,3 Noel A. Clark,3 Antal Jakli ,1,* Hamza Balci,1 and Samuel Sprunt1,†
1
2
Department of Physics, Kent State University, Kent, Ohio 44242, USA
National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
3
Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
(Received 22 February 2022; accepted 16 May 2022; published 18 July 2022)
The occurrence of a smectic-B (Sm-B) phase is demonstrated in concentrated aqueous solutions of “gapped”
DNA constructs consisting of fully paired duplexes bridged by a flexible, unpaired strand of nucleotides.
The Sm-B phase, identified by small and wide angle x-ray scattering measurements and optical microscopy,
develops from a smectic-A (Sm-A) phase with increasing DNA concentration at room temperature. It transitions
(reversibly) to the Sm-A when the temperature is raised above ∼50 ◦ C.
DOI: 10.1103/PhysRevResearch.4.033046
I. INTRODUCTION
In recent years, studies on mesophasic self-assembly
in aqueous solutions of ultrashort DNA duplexes or their
oligomeric precursors [1–4], together with investigations
of elementary lamellar (smectic-A [Sm-A]) ordering of
“gapped” DNA (GDNA; duplexes bridged by a single strand
[ss] of unpaired nucleotides) [5,6] and of fully paired duplexes
capped at one end by a short hairpin [7], have reinvigorated
research into the liquid crystalline (LC) properties of the
molecule of life. Building on classic work on cholesteric and
columnar LC phases in solutions of duplex DNA [8–12], the
new developments point to richer mesomorphic behavior that
is achievable by simple manipulations of the morphology of
individual DNA constructs.
The Sm-A phase of aqueously dispersed GDNA occurs in
the concentration range cDNA ∼ 230−260 mg/ml, largely at
the expense of the cholesteric state. It exhibits a significant
sensitivity to temperature and, depending on the length of the
gap, features either a mono- or bilayer structure (∼1 or 2 duplex layer spacing, respectively) [6]. The smectic ordering and
its temperature dependence were attributed to a combination
of enthalpic interactions and entropic effects: Hydrophobic
attraction between blunt duplex ends favors end-to-end stacking of the duplex segments between GDNA constructs, while
segregation of the flexible ss “gaps” into layers becomes entropically favorable when the constructs are densely packed.
*
Advanced Materials and Liquid Crystals Institute, Kent State University, Kent, OH 44242.
†
ssprunt@kent.edu; Advanced Materials and Liquid Crystals Institute, Kent State University, Kent, OH 44242.
Published by the American Physical Society under the terms of the
Creative Commons Attribution 4.0 International license. Further
distribution of this work must maintain attribution to the author(s)
and the published article’s title, journal citation, and DOI.
2643-1564/2022/4(3)/033046(7)
033046-1
The present work addresses the questions: What happens
to the Sm-A phase in GDNA, and what role does temperature play at higher DNA density? When concentrated above
the cholesteric state, fully paired duplexes transition to a 2D
hexagonal columnar phase at cDNA ∼ 400 mg/ml and then, at
∼500−700 mg/ml, they form 3D hexagonal and orthorhombic crystals [11,12]. Here we demonstrate that LC solutions of
GDNA constructs transform to a higher-order smectic phase,
which we identify as a lyotropic smectic-B (Sm-B) phase,
at substantially lower concentrations (260−290 mg/ml) and
undergo a thermotropic transition to the Sm-A phase in the
∼55−60 ◦ C temperature range. Our results further expose the
distinct and remarkably rich LC properties of DNA constructs
that incorporate rigid and flexible elements. They are also
compelling since Sm-B phases appear to be relatively rare in
lyotropic systems; to our knowledge, prior reports are limited
to colloidal suspensions of charged, inorganic platelet- [13] or
rod- [14] shaped particles and dense solutions of semiflexible
rodlike viruses [15–17].
II. EXPERIMENTAL DETAILS
The investigated GDNA construct, denoted 48-10T-48,
consists of two, symmetric 48 bp duplexes connected by a ss
“gap” of 10 unpaired thymine bases (Fig. 1). The construct
was synthesized from PAGE-purified oligomers purchased
from ExonanoRNA (Columbus, OH). Details of the synthesis
and the specific nucleotide sequences are described elsewhere [6].
For small/wide angle x-ray scattering (SAXS/WAXS)
studies, we prepared dense aqueous solutions of 48-10T-48
constructs in standard borosilicate capillaries with a 1.25-mm
inner diameter as follows: We first slowly and evenly loaded
a ∼40 μl volume of isotropic solution (cDNA ∼ 80−100
mg/ml) into an open capillary and then very gradually allowed the water component of the buffer to evaporate until
a target volume was reached. The components of the initial
Published by the American Physical Society
PRABESH GYAWALI et al.
PHYSICAL REVIEW RESEARCH 4, 033046 (2022)
FIG. 1. Top: Schematic structure of the 48-10T-48 GDNA construct studied. Middle: Optical texture of smectic FC “fan” domains
in a thin film of 48-10T-48 GDNA solution sandwiched between
glass slides at 25 ◦ C. The dashed yellow line separates distinct
“smooth” and “striated” FC textures (to the left and right of the line,
respectively) that are observed in the presence of a positive DNA
concentration gradient running from left to right. Scale bar = 50 μm.
Bottom: The black/white images on the left and right detail smooth
and striated FC “fan backs” in two samples sealed at lower/higher
GDNA concentration (cDNA ). The accompanying images in color
were taken with a quartz compensator inserted in the optical path.
Relative color shifts observed in radial directions from the “tip” of an
isolated FC that are along and normal to the compensator’s optical
axis (labeled e) confirm radial orientation of the GDNA duplexes.
The textures are consistent with smectic layers that bend along the
azimuthal direction in the FCs and with the formation of a higherorder smectic phase (striated texture) at higher cDNA .
buffer solution were adjusted so that after the water evaporation, the buffer composition was approximately 150 mM
NaCl/10 mM Tris/0.1 mM thylenediaminetetraacetic acid
(EDTA) in deionized water at pH 7.5. From the known cDNA
of the initial solution and the known sample volume after
evaporation, the final cDNA could be estimated to an accuracy
of ±5%. The capillaries were sealed when the DNA concentration was in the range cDNA = 260−290 mg/ml, ∼10
mg/ml above the range of the Sm-A phase previously investigated [6]. They were then stored at 4 ◦ C for several weeks
and monitored optically in order to ensure uniformity prior to
measurements.
Polarizing optical microscopy was performed on samples
of ∼5−10 μm thickness sandwiched between microscope
slides. The samples were sealed by a thin ring of mineral oil
after water had evaporated from the edges of the film to the
point where focal conic (FC) textures appeared, signaling the
development of a smectic phase. To confirm that the orientation of the GDNA duplex segments in the FCs is consistent
with a smectic layer structure, we utilized a wedge-shaped
quartz compensator plate that could be inserted into the optical
path between crossed polarizer and analyzer at a 45◦ angle
to the polarizer axis. By sliding the plate a variable distance
into the optical path, the phase shift between light polarized parallel and perpendicular to the optic axis of the plate
could be varied. The variable retardation, combined with the
birefringence and dispersion of the GDNA sample, enables
one to determine the orientation of the optic axis in the FC
domains by referencing the color of light transmitted through
the sample to a Michel-Levy interference color chart [18].
SAXS/WAXS measurements were carried out on beamline 11-BM at the National Synchrotron Light Source II. The
incident x-ray energy was 17 keV, the incident beam size at
the sample was 0.2 × 0.2 mm, and the SAXS/WAXS area
detectors were positioned 3.0 and 0.26 m from the sample,
respectively. Samples were mounted in a modified commercial hot/cold stage (Instec HCS60) with kapton film windows.
The temperature of the sample was regulated between 5 and
65 ◦ C (safely below the 77 ◦ C denaturation temperature of the
48 bp GDNA duplexes). No evidence of x-ray damage to
samples was observed during stepwise temperature scans with
10−30 s exposures at each step.
III. RESULTS
A. Optical microscopy
Smectic layering in GDNA samples is revealed in the
polarizing microscope by a FC “fan” texture in which the
duplexes orient radially away from the core of individual
FCs. As described in Experimental Details, the orientation
may be deduced using an optical compensation plate. In
order to minimize the cost in elastic energy (i.e., preserve
approximately uniform layer spacing), the smectic layers of
GDNA bend azimuthally around the FC core, and there is a
corresponding splay in the duplex orientation. (By contrast,
fully paired duplexes in the columnar phase orient azimuthally
within similarly appearing FC domains [3] and thus undergo
an orientational bend in these domains).
Figure 1 shows two variants of the fan texture coexisting at
25 ◦ C in a thin film of 48-10T-48 sandwiched between glass
slides and sealed as described above. The DNA concentration
increases from left to right. The dashed yellow line tracks a
boundary between smooth (lower cDNA ) and striated (higher
cDNA ) fan textures to the left and right of the line, respectively.
The images at the bottom of Fig. 1 show details of smooth
and striated FCs with different “fan” orientations, before and
after the compensator plate was inserted. (Its optical axis is
labeled e in the figure.) After the compensator is inserted, the
color shifts (relative to background color) observed between
“fans” oriented along and perpendicular to e, together with
the negative optical anisotropy of DNA duplexes [19–21],
confirm a radial duplex orientation within the FCs.
We previously used the same technique to associate the
smooth fan texture with the Sm-A phase in GDNA [6]. As
water evaporates from the sample edge, the smooth texture
appears first and then evolves after further evaporation to the
033046-2
SMECTIC-B PHASE AND TEMPERATURE-DRIVEN …
PHYSICAL REVIEW RESEARCH 4, 033046 (2022)
FIG. 2. Top left and right: 2D SAXS patterns recorded on oriented domains of a 265 mg/ml 48-10T-48 sample in the Sm-B phase at 15.3 ◦ C
(left) and in the Sm-A phase at 52.8 ◦ C (right). The central image in each case shows the small angle diffraction arising from layering of the
duplex segments (00l peaks, with the l = 1, 2, 4 orders indicated with dashed blue circles for reference). The left and right side images are
blow-ups of the wider angle scattering due to the lateral packing of the duplexes within the layers. In the Sm-B phase, this scattering consists of
narrowly spaced, sharp arcs indicated by the blue dashed lines, whose index is 10l (l = 0 dominating, with much weaker features for l = 2, 3, 4
being just visible). In the Sm-A phase, the arcs are replaced by diffuse scattering. Bottom left and right: 2D WAXS patterns recorded in the
Sm-B and Sm-A phases simultaneously with the SAXS patterns. In the Sm-B phase (bottom left), the dashed blue arcs indicate 100 and (much
weaker) 110 peaks indexed for a 2D hexagonal lattice. Bottom middle: Log of azimuthally averaged x-ray intensity vs q obtained from the
SAXS pattern at top left (Sm-B phase), with six 00l and three resolvable 10l reflections labeled. The SAXS and WAXS patterns are rendered
after the log of the pixel values was taken (with a small offset). The diffuse ring in the WAXS images just beyond the 100 peak is scattering
from kapton windows.
striated texture, which migrates inward from the edge. It is,
therefore, reasonable to attribute the striated texture, developing at higher DNA concentration than the Sm-A, to a distinct,
higher-order smectic phase. In small molecule thermotropic
LCs, a similar textural change occurs at a temperature-driven
Sm-A to a Sm-B phase transition [22], although in that case
the stripes decorating the FC fans fade away as the Sm-B order
equilibrates thermally.
To confirm the nature of the higher-order phase in GDNA
and to explore its temperature dependence, we turn to the
results of SAXS/WAXS measurements.
B. SAXS and WAXS scattering
Figure 2 shows representative 2D SAXS/WAXS patterns
from fairly well-oriented smectic domains (with layer normal
nearly parallel to the detector plane) in a 265 mg/ml 48-10T48 sample at temperatures T = 15.3 and 52.8 ◦ C. At the lower
temperature, six orders of diffraction are recorded at small
angles (Fig. 2, top left). The lowest order (at scattering wave-
number q = 0.187 nm−1 ) corresponds to a spatial periodicity
of dB = 33.6 nm, slightly greater than two duplex lengths. We
index the peaks as 00l with corresponding scattering vector
q00l along the layer normal. Their number and full width at
half maximum (FWHM) indicate domains with a well-defined
layer structure of average length of at least 30 duplexes along
the layer normal. The alternating heights of the odd and even
order peaks (Fig. 2, bottom middle) suggest a combination of
mono- and bilayer components, with layer spacing dB /2 and
dB , respectively, contributing to the overall smectic density
wave.
At wider angles on the SAXS detector, intense scattering,
centered azimuthally about the direction orthogonal to the
smectic layer normal, is recorded at q = 2.19 nm−1 for the
lower temperature (top left in Fig. 2). The sharpness of the
peak and its orientation indicate significant positional correlations of the duplexes within the smectic layers. Weaker
reflections, at 2.22, 2.26, and 2.31 nm−1 (narrowly spaced
from the main peak and indicated by blue dashes in Fig. 2),
are also visible. Additionally, as shown in Fig. 2 (bottom
033046-3
PRABESH GYAWALI et al.
PHYSICAL REVIEW RESEARCH 4, 033046 (2022)
FIG. 3. Temperature dependence of the log of the azimuthally averaged SAXS intensity from a 285 mg/ml 48-10T-48 GDNA sample. The
left panel shows the diffraction from the smectic layer structure with peaks indexed as 00l in the Sm-B phase and 00l in the Sm-A phase, and
the right panel shows a detail of 100 peak diminishing with increasing temperature. Traces in red correspond to heating from the Sm-B to -A
phase, and the traces in blue are obtained after subsequent cooling back to the Sm-B.
left), a very weak peak, also centered on the axis perpendicular to the layering direction, is recorded on the WAXS
detector at q = 3.79 nm−1 . The ratio of wave numbers for the
intense and weak WAXS peaks, 3.79/2.19 = 1.73, matches
the expected relation between the 110 and the 100 reflec√
tions from a hexagonal crystal structure, q110 /q100 = 3.
Based on these assignments, we may index the weaker satellite reflections at 2.22, 2.26, and 2.31 nm−1 √as 10l for l =
2
2
2, 3, 4, since they satisfy the relation q10l = q100
+ q00l
=
√
2
2
2.19 + (l × 0.187) . As indicated by nearly overlapping
blue dashed lines in Fig. 2 (top left), the peak “expected”
at q101 = 2.20 nm−1 is too close to the intense scattering at
q100 = 2.19 nm−1 to be resolved.
Based on the analysis and assignments above, we identify the lower temperature smectic phase as a Sm-B phase,
with layers of hexagonally packed 48 bp duplex segments
of the GDNA constructs stacked so that their blunt ends
are paired, producing a ∼2 duplex periodicity along the
stacking
√ direction. The lateral duplex-duplex spacing is a =
4π /( 3q100 ) = 3.31 nm (center to center), and the typical
lateral size of a monodomain (estimated from the FWHM of
the 100 peak) is 25a.
The Sm-B state of GDNA is strongly sensitive to temperature as well as concentration. At elevated temperatures,
it melts reversibly into a Sm-A phase. In particular, during
heating from room temperature, the intense 100 scattering diminishes continuously and, together with the weak 110 peak,
disappears completely between 50 and 60 ◦ C, leaving only
diffuse scattering from the lateral packing of the duplexes
consistent with fluid smectic layers (Fig. 2, top right). At the
same temperature, the 00l peaks for odd l (associated with
∼two duplex periodicity) also vanish, resulting in a Sm-A
phase with ∼single duplex layer spacing.
Detailed SAXS data vs temperature reveal a temperature range over which the Sm-B phase coexists with the
Sm-A phase. Figure 3 (left panel) shows azimuthally averaged profiles of x-ray diffraction at small angles and various
T from the smectic layer structure of a 48-10T-48 sample
with cDNA = 285 mg/ml. At T ≈ 43 ◦ C, a secondary peak
emerges at a q value just above the 002 peak associated with
the low-temperature (Sm-B) layer structure. This new peak
(designated 002 ) and its weaker harmonic (004 ) grow in
amplitude as the scattering from Sm-B domains diminishes
and eventually (at T ≈ 59 ◦ C) account for all the observed
small-angle scattering. Figure 3 (right panel) shows the simultaneous diminution of the wider angle 100 peak on heating
through the same temperature steps and its replacement with
a broad, diffuse peak. Thus after heating to 59 ◦ C, the Sm-B
phase in the 285 mg/ml sample has completely transformed
to a Sm-A state, with layer spacing dA = 2π /q002 = 16.6 nm
comparable to a single duplex length. When the sample is subsequently cooled back to 22 ◦ C, the Sm-B phase reforms with
the 00l (l = 1−6) and 100 peaks reappearing at their original
positions (Fig. 3, blue traces), although the amplitudes do not
fully recover over a 1-h period after cooling.
The Sm-B to -A transition occurs at a ∼7 ◦ C higher temperature in the 285 mg/ml sample than in the more dilute
(265 mg/ml) sample studied in Fig. 2. The dependence of the
transition temperature on cDNA appears to be significant, but
so far we have not explored it in detail.
IV. DISCUSSION
In addition to hexagonal lateral packing of the duplexes,
a model of the Sm-B phase in GDNA must account for both
mono- and bilayer correlations, as evidenced by the presence
033046-4
SMECTIC-B PHASE AND TEMPERATURE-DRIVEN …
PHYSICAL REVIEW RESEARCH 4, 033046 (2022)
FIG. 4. Proposed schemes for GDNA packing in the smectic-A (left) and -B (middle and right) phases of 48-10T-48 GDNA solutions.
On the left, right, and back sides of the domains shown, the duplexes are depicted as long, light-blue cylinders, the regions occupied by the
ss “gap” segments are shown as short cylinders in a bolder blue, and the blunt duplex ends are highlighted in dark blue. Inside the domains,
the constructs are rendered with transparency to reveal the interior arrangement. Partial layers of duplexes are shown at the top and bottom
of the domain. Left: In the Sm-A phase, the blunt duplex ends are separated, allowing the ss segments to explore space and the duplexes to
disorder within the layer planes. Interdigitation of duplexes from neighboring constructs results in a smectic density wave with ∼single duplex
periodicity. Middle: Sm-B phase with hexagonally packed duplexes in the layers. Paired blunt ends and ss segments microphase separate within
the planes between the layers, leading to a superposition of density variations along the layer normal with ∼one and ∼two duplex periodicity
and a small-angle diffraction profile consistent with the alternating peak intensities in Fig. 3 at low temperature. Right: 3D ordered Sm-B
phase with full segregation of paired blunt ends and ss segments into alternating planes, producing pure bilayer stacking. The harmonics in the
corresponding diffraction profile should then decrease monotonically with q (which differs from the data in Fig. 3).
of odd and even 00l orders of diffraction that alternate systematically in intensity and by the disappearance of the odd
orders at the Sm-B to -A transition (Figs. 2 and 3).
Figure 4 presents schemes for the GDNA packing in the
two phases that satisfy these requirements. The main idea is
that the Sm-B phase forms from a lower concentration (or
higher temperature) Sm-A phase in which the duplex segments from different GDNA constructs interdigitate within
the smectic layers, and their blunt ends are generally separated. As suggested in Fig. 4, this arrangement allows the
flexible ss “gap” segments to explore additional space laterally
while maintaining a relatively dense packing of duplexes in
fluid monolayers (layer spacing comparable to a single duplex
length). In this scenario, entropy prevails over enthalpic endend interactions in minimizing the free energy.
At higher cDNA (or lower temperature), the Sm-B phase
forms as the blunt ends of the duplex segments pair, and the
duplexes pack side by side in a 2D hexagonal lattice. The
attractive interaction between blunt ends—stronger at lower
temperature and higher cDNA —reduces the free energy against
a trade-off in entropy. The blunt end pairing eliminates lateral
space available for the flexible ss segments to explore, and
consequently these extend along the layer normal, expanding
the layer spacing. This accounts for the shift (Fig. 3) of the
002 and 004 peaks in the Sm-A phase to their positions at
slightly lower q in the -B phase.
The development from purely monolayer to substantially
bilayer correlations across the SmA to -B transition can be
viewed in terms of phase separation of a mixture of blunt
duplex ends (shown in dark blue in Fig. 4) and “dressed”
ends (i.e., ends connected to a flexible ss, rendered in lighter
blue) that occupy planes parallel to the layers. From left to
right, Fig. 4 displays a sequence from a disordered, homogeneous mixture within each plane to complete segregation
of blunt and “dressed” duplex ends into alternating planes
with a hexagonal lateral placement. The middle scheme depicts an intermediate state where blunt and “dressed” end-rich
domains coexist in each plane (analogous to two phase coexistence in a binary mixture). The smectic density wave
in this case combines bilayer (spacing dB ) and monolayer
(spacing dB /2) components, described by Fourier series with
harmonics at 2π l/dB for any integer l in the first case and
for even l only in the second. This could produce the pattern of 00l diffraction peaks with alternating heights seen in
Fig. 3.
In the Sm-B phase, pairing of the blunt ends and confinement of the ss connecting the opposing (internal) ends imply
a degree of interlayer coupling of the 2D hexagonal ordering,
which in turn could explain the weak 10l satellites to the
100 peak (Fig. 2, top left). On the other hand, the weak 110
scattering implies that the 2D hexagonal order within Sm-B
layers of GDNA is not as well developed as in the hexagonal
033046-5
PRABESH GYAWALI et al.
PHYSICAL REVIEW RESEARCH 4, 033046 (2022)
crystalline phase of fully paired duplexes (which occurs at
significantly higher cDNA ) [11].
Lastly, we consider the mechanism for the striated optical
texture observed on FCs in smectic GDNA samples (Fig. 1).
Below the Sm-A to -B transition the lateral spacing (a) between duplexes shrinks (compare centers of the diffuse Sm-A
and sharp Sm-B peaks in Fig. 3, right), while the smectic
layer spacing increases at the same time. Assuming this also
happens when the transition occurs due to increasing cDNA (at
constant T ), the lateral strain imposed by reduction in a could
be relieved by a bend modulation in the duplex orientation
along the layer normal, which is not inhibited by a fixed layer
spacing because it is simultaneously changing. The accompanying modulation of the optical birefringence would then
produce a stripe pattern, with the stripes parallel to the layers
(i.e., running azimuthally across the “fan backs” in the optical
texture). If the Sm-B phase equilibrates slowly (due to slow
water evaporation and relaxation of concentration gradients),
the stripe pattern may persist for long times.
the smectic-A phase previously discovered in this system,
and a temperature-driven Sm-B to Sm-A transition occurs at
fixed concentration when the sample is heated a few tens of
degrees above room temperature. These results further support the conclusion that the phase diagram of DNA duplexes
in the concentration range ∼200−300 mg/ml, where LC
phases occur, shifts from exclusively cholesteric/columnar to
predominantly layered (smectic) phases when a sufficiently
long segment of unpaired bases is introduced in the middle
of an otherwise fully paired construct. The flexible internal
linkage and the blunt end-end attractive interaction both play
key roles in stabilizing the smectic phases and determining
their remarkable combination of thermotropic and lyotropic
behavior.
ACKNOWLEDGMENTS
We have described a lyotropic Sm-B phase formed in
solutions of GDNA duplexes with strong temperature dependence. Hexagonal in-layer order develops at room temperature
when the DNA concentration increases above the range of
The Kent State authors gratefully acknowledge support
from the National Science Foundation (NSF) under Grant
No. DMR-1904167. G.P.S. and N.A.C. were supported by
the NSF under Grant No. DMR-2005212. SAXS/WAXS
measurements were conducted at the 11-BM CMS beamline
of the National Synchrotron Light Source II, a U.S. Department of Energy (DOE) Office of Science User Facility
operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DE-SC0012704.
[1] M. Nakata, G. Zanchetta, B. D. Chapman, C. D. Jones, J. O.
Cross, R. Pindak, T. Bellini, and N. A. Clark, End-to-end stacking and liquid crystal condensation of 6 to 20 base pair DNA
duplexes, Science 318, 1276 (2007).
[2] T. Bellini, G. Zanchetta, T. P. Fraccia, R. Cerbino, E. Tsai, G. P.
Smith, M. J. Moran, D. M. Walba, and N. A. Clark, Liquid crystal self-assembly of random-sequence DNA oligomers, Proc.
Natl. Acad. Sci. USA 109, 1110 (2012).
[3] T. P. Fraccia, G. P. Smith, L. Bethge, G. Zanchetta, G. Nava,
M. J. Moran, S. Klussmann, N. A. Clark, and T. Bellini, Liquid
crystal ordering and isotropic gelation in solutions of four-baselong DNA oligomers, ACS Nano 10, 8508 (2016).
[4] G. P. Smith, T. P. Fraccia, M. Todisco, G. Zanchetta, C.
Zhu, E. Hayden, T. Bellini, and N. A. Clark, Backbone-free
duplex-stacked monomer nucleic acids exhibiting Watson Crick
selectivity, Proc. Natl. Acad. Sci. USA 115, E7658 (2018).
[5] M. Salamonczyk, J. Zhang, G. Portale, C. Zhu, E. Kentzinger,
J. T. Gleeson, A. Jakli, C. D. Michele, J. K. G. Dhont, S. Sprunt,
and E. Stiakakis, Smectic phase in suspensions of gapped DNA
duplexes, Nat. Commun. 7, 13358 (2016).
[6] P. Gyawali, R. Saha, G. P. Smith, M. Salamonczyk, P. Kharel, S.
Basu, R. Li, M. Fukuto, J. T. Gleeson, N. A. Clark, A. Jakli, H.
Balci, and S. Sprunt, Mono- and bilayer smectic liquid crystal
ordering in dense solutions of gapped DNA duplexes, Proc.
Natl. Acad. Sci. USA 118, e2019996118 (2021).
[7] K. Gvozden, S. N. Ratajczak, A. G. Orellana, E. Kentzinger,
U. Rcker, J. K. G. Dhont, C. D. Michele, and E. Stiakakis, Selfassembly of all-DNA rods with controlled patchiness, Small 18,
2104510 (2021).
[8] T. E. Strzelecka, M. W. Davidson, and R. L. Rill, Multiple liquid
crystal phases of DNA at high concentrations, Nature (London)
331, 457 (1988).
[9] F. Livolant, A. M. Levelut, J. Doucet, and J. P. Benoit,
The highly concentrated liquid-crystalline phase of
DNA is columnar hexagonal, Nature (London) 339, 724
(1989).
[10] F. Livolant, Ordered phases of DNA in vivo and in vitro,
Physica A 176, 117 (1991).
[11] D. Durand, J. Doucet, and F. Livolant, A study of the structure
of highly concentrated phases of DNA by x-ray diffraction,
J. Phys. II 2, 1769 (1992).
[12] F. Livolant and A. Leforestier, Condensed phases of DNA:
Structures and phase transitions, Prog. Polym. Sci. 21, 1115
(1996).
[13] D. Kleshchanok, P. Holmqvist, J.-M. Meijer, and H. N. W.
Lekkerkerker, Lyotropic smectic B phase formed in suspensions
of charged colloidal platelets, J. Am. Chem. Soc. 134, 5985
(2012).
[14] A. Kuijk, D. V. Byelov, A. V. Petukhov, A. van Blaaderena,
and A. Imhofa, Phase behavior of colloidal silica rods, Faraday
Discuss. 159, 181 (2012).
[15] E. Grelet, Hexagonal Order in Crystalline and Columnar Phases
of Hard Rods, Phys. Rev. Lett. 100, 168301 (2008).
[16] E. Grelet, Hard-Rod Behavior in Dense Mesophases of Semiflexible and Rigid Charged Viruses, Phys. Rev. X 4, 021053
(2014).
[17] A. Repula, M. O. Menegon, C. Wu, P. van der Schoot, and
E. Grelet, Directing Liquid Crystalline Self-Organization of
Rodlike Particles through Tunable Attractive Single Tips, Phys.
Rev. Lett. 122, 128008 (2019).
[18] W. Nesse, Introduction to Optical Mineralogy, 3rd ed. (Oxford
University Press, New York, 2003).
[19] N. C. Stellwagen, Electric birefringence of restriction enzyme fragments of DNA: Optical factor and electric
V. CONCLUSION
033046-6
SMECTIC-B PHASE AND TEMPERATURE-DRIVEN …
PHYSICAL REVIEW RESEARCH 4, 033046 (2022)
polarizability as a function of molecular weight, Biopolymers
20, 399 (1981).
[20] G. Maret and G. Weill, Magnetic birefringence study of
the electrostatic and intrinsic persistence length of DNA,
Biopolymers 22, 2727 (1983).
[21] R. Oldenbourg and T. Ruiz, Magnetic birefringence study of the
electrostatic and intrinsic persistence length of DNA, Biophys.
J. 56, 195 (1989).
[22] G. W. Gray and J. W. Goodby, Smectic Liquid Crystals: Textures
and Structures (Leonard Hill, London, 1984).
033046-7