Giorgio Cinacchi

Self-assembly of hard helices: a rich and unconventional polymorphism

Hard helices can be regarded as a paradigmatic elementary model for a number of natural and synthetic soft matter systems, all featuring the helix as their basic structural unit, from natural polynucleotides and polypeptides to synthetic helical polymers, and from bacterial flagella to colloidal helices. Here we present an extensive investigation of the phase diagram of hard helices using a variety of methods. Isobaric Monte Carlo numerical simulations are used to trace the phase diagram; on going from the low-density isotropic to the high-density compact phases a rich polymorphism is observed, exhibiting a special chiral screw-like nematic phase and a number of chiral and/or polar smectic phases. We present full characterization of the latter, showing that they have unconventional features, ascribable to the helical shape of the constituent particles. Equal area construction is used to locate the isotropic-to-nematic phase transition, and the results are compared with those stemming from an Onsager-like theory. Density functional theory is also used to study the nematic-to-screw-nematic phase transition; within the simplifying assumption of perfectly parallel helices, we compare different levels of approximation, that is second- and third-virial expansions and a Parsons-Lee correction.

Left or right cholesterics? A matter of helix handedness and curliness

Using an Onsager-like theory, we have investigated the relationship between the morphology of hard helical particles and the features (pitch and handedness) of the cholesteric phase that they form. We show that right-handed helices can assemble into right- (R) and left-handed (L) cholesterics, depending on their curliness, and that the cholesteric pitch is a non-monotonic function of the intrinsic pitch of particles. The theory leads to the definition of a hierarchy of pseudoscalars, which quantify the difference in the average excluded volume between pair configurations of helices having (R) and (L)-skewed axes. The predictions of the Onsager-like theory are supported by Monte Carlo simulations of the isotropic phase of hard helices, showing how the cholesteric organization, which develops on scales longer than hundreds of molecular sizes, is encoded in the short-range chiral correlations between the helical axes.

Modeling benzene with single-site potentials from ab initio calculations: A step toward hybrid models of complex molecules

Extensive ab initio calculations at the MP2/6-31G* level have been carried out to sample the energy surface for the interactions of the benzene dimers. This database has been used to parameterize two anisotropic single-site models, meant to be used as building blocks in hybrid models of complex, liquid crystal forming molecules. A quadrupolar Gay-Berne (GBQIII) and an S-function (SF) Corner potentials have been obtained in this way. Their ability to reproduce, qualitatively at least, the phase diagram as well as energetic and structural properties of benzene has been tested with Monte Carlo simulations and compared with previous literature potentials, GBQI [S. Gupta et al., Mol. Phys. 65, 961 (1988)] and GBQII [T. R. Walsh, Mol. Phys. 100, 2867 (2002)]. It turned out that GBQI showed no melting transition in the temperature range explored (100-400 K), while GBQII underwent a phase transition from solid to gas, with no liquid phase. Conversely, both models parameterized on our database of ab initio interaction energies (GBQIII and SF) gave rise to a stable liquid phase. Melting has been observed between 100 and 150 K (GBQIII) and in the range 300-350 K (SF), i.e., substantially below and slightly above the experimental value at ambient pressure, 278 K. The description of the crystal structure of benzene at atmospheric pressure is also in better agreement with experimental data if the SF model is used, while positional correlations in the liquid are better described by the GBQIII potential. The S-function potential is also computationally more convenient. These results could be useful in the semirealistic modeling of more complex molecules.

Chiral self-assembly of helical particles

The shape of the building blocks plays a crucial role in directing self-assembly towards desired architectures. Out of the many different shapes, the helix has a unique position. Helical structures are ubiquitous in nature and a helical shape is exhibited by the most important biopolymers like polynucleotides, polypeptides and polysaccharides as well as by cellular organelles like flagella. Helical particles can self-assemble into chiral superstructures, which may have a variety of applications, e.g. as photonic (meta)materials. However, a clear and definite understanding of these structures has not been entirely achieved yet. We have recently undertaken an extensive investigation on the phase behaviour of hard helical particles, using numerical simulations and classical density functional theory. Here we present a detailed study of the phase diagram of hard helices as a function of their morphology. This includes a variety of liquid-crystal phases, with different degrees of orientational and positional ordering. We show how, by tuning the helix parameters, it is possible to control the organization of the system. Starting from slender helices, whose phase behaviour is similar to that of rodlike particles, an increase in curliness leads to the onset of azimuthal correlations between the particles and the formation of phases specific to helices. These phases feature a new kind of screw order, of which there is experimental evidence in colloidal suspensions of helical flagella.

Hard convex lens-shaped particles: Densest-known packings and phase behavior

By using theoretical methods and Monte Carlo simulations, this work investigates dense ordered packings and equilibrium phase behavior (from the low-density isotropic fluid regime to the high-density crystalline solid regime) of monodisperse systems of hard convex lens-shaped particles as defined by the volume common to two intersecting congruent spheres. We show that, while the overall similarity of their shape to that of hard oblate ellipsoids is reflected in a qualitatively similar phase diagram, differences are more pronounced in the high-density crystal phase up to the densest-known packings determined here. In contrast to those non-(Bravais)-lattice two-particle basis crystals that are the densest-known packings of hard (oblate) ellipsoids, hard convex lens-shaped particles pack more densely in two types of degenerate crystalline structures: (i) non-(Bravais)-lattice two-particle basis body-centered-orthorhombic-like crystals and (ii) (Bravais) lattice monoclinic crystals. By stacking at will, regularly or irregularly, laminae of these two crystals, infinitely degenerate, generally non-periodic in the stacking direction, dense packings can be constructed that are consistent with recent organizing principles. While deferring the assessment of which of these dense ordered structures is thermodynamically stable in the high-density crystalline solid regime, the degeneracy of their densest-known packings strongly suggests that colloidal convex lens-shaped particles could be better glass formers than colloidal spheres because of the additional rotational degrees of freedom.

Smectic order parameters via liquid crystal NMR spectroscopy: Application to a partial bilayer smectic A phase

AbstractSolute molecules were dissolved in the liquid crystal 4-cyano-4′-n-octyloxybiphenyl (8OCB), known to form a partial bilayer smectic-A phase. Through measurement of solutes’ and solvent’s orientational order parameters via nuclear magnetic resonance spectroscopy, and their analysis via a statistical thermodynamic density functional theory, values of the solvent’s positional order parameters and solutes’ positional-orientational distribution functions were obtained. Near to the transition to the nematic phase, the main positional order parameter of the smectic liquid crystal turned out to be comprised in the interval 0.4–0.6, though the quality of the fittings assuming the phase as nematic all across the temperature range investigated was only slightly worse. This may be ascribed to the looseness of the partial bilayer smectic structure. Solutes were found to preferentially lie in those regions where liquid crystal molecule terminal chains are located.n

The isotropic-nematic phase transition in hard, slightly curved, lens-like particles.

Monte Carlo numerical simulations are used to study in detail how the characteristics of the isotropic-nematic phase transition change as infinitely thin hard platelets are bent into shallow lens-like particles. First, this phase transition in the former reference model system is re-examined and more accurately located. Then, it is shown quantitatively that this already quite weak but distinctly first-order phase transition weakens further upon curving the platelets to such an extent that, thanks to the thinness of these particles that does not favor its pre-emptying by a transition to a (partially) positionally ordered phase, an isotropic-nematic tricritical point limit can be arbitrarily closely approached.

Hard convex lens-shaped particles: metastable, glassy and jammed states

We generate and study dense positionally and/or orientationally disordered, including jammed, monodisperse packings of hard convex lens-shaped particles (lenses). Relatively dense isotropic fluid configurations of lenses of various aspect ratios are slowly compressed via a Monte Carlo method based procedure. Under this compression protocol, while flat lenses form a nematic fluid phase (where particles are positionally disordered but orientationally ordered) and globular lenses form a plastic solid phase (where particles are positionally ordered but orientationally disordered), intermediate, neither flat nor globular, lenses do not form either mesophase. In general, a crystal solid phase (where particles are both positionally and orientationally ordered) does not spontaneously form during lengthy numerical simulation runs. In correspondence to those volume fractions at which a transition to the crystal solid phase would occur in equilibrium, a downturn is observed in the inverse compressibility factor versus volume fraction curve beyond which this curve behaves essentially linearly. This allows us to estimate the volume fraction at jamming of the dense non-crystalline packings so generated. These packings are nematic for flat lenses and plastic for globular lenses, while they are robustly isotropic for intermediate lenses, as confirmed by the calculation of the τ order metric, among other quantities. The structure factors S(k) of the corresponding jammed states tend to zero as the wavenumber k goes to zero, indicating they are effectively hyperuniform (i.e., their infinite-wavelength density fluctuations are anomalously suppressed). Among all possible lens shapes, intermediate lenses with aspect ratio around 2/3 are special because they are those that reach the highest volume fractions at jamming while being positionally and orientationally disordered and these volume fractions are as high as those reached by nematic jammed states of flat lenses and plastic jammed states of globular lenses. All of their attributes, taken together, make such intermediate lens packings particularly good glass-forming materials.

Cholesteric and screw-like nematic phases in systems of helical particles

Recent numerical simulations of hard helical particle systems unveiled the existence of a novel chiral nematic phase, termed screw-like, characterised by the helical organization of the particle C2 symmetry axes round the nematic director with periodicity equal to the particle pitch. This phase forms at high density and can follow a less dense uniform nematic phase, with relative occurrence of the two phases depending on the helix morphology. Since these numerical simulations were conducted under three-dimensional periodic boundary conditions, two questions could remain open. First, the real nature of the lower density nematic phase, expected to be cholesteric. Second, the influence that the latter, once allowed to form, may have on the existence and stability of the screw-like nematic phase. To address these questions, we have performed Monte Carlo and molecular dynamics numerical simulations of helical particle systems confined between two parallel repulsive walls. We have found that the removal of the periodicity constraint along one direction allows a relatively-long-pitch cholesteric phase to form, in lieu of the uniform nematic phase, with helical axis perpendicular to the walls while the existence and stability of the screw-like nematic phase are not appreciably affected by this change of boundary conditions.

Detection of Significant Aprotic Solvent Effects on the Conformational Distribution of Methyl 4‐Nitrophenyl Sulfoxide: From Gas‐Phase Rotational to Liquid‐Crystal NMR Spectroscopy

The conformational equilibrium of methyl 4-nitrophenyl sulfoxide (MNPSO) was experimentally investigated in the gas phase by using microwave spectroscopy and in isotropic and nematic liquid-crystal solutions, in which the solvents are nonaqueous and aprotic, by using NMR spectroscopy; moreover, it was theoretically studied in vacuo and in solution at different levels of theory. The overall set of results indicates a significant dependence of the solute conformational distribution on the solvent dielectric permittivity constant: when dissolved in low-polarity media, the most stable conformation of MNPSO proved to be strongly twisted with respect to that in more polar solvents, in which the conformational distribution maximum essentially coincides with that obtained in the gas phase. We discuss a possible explanation of this behavior, which rests on electrostatic solute-solvent interactions and is supported by calculations of the solute electric dipole moment as a function of the torsional angle. This function shows that the least polar conformation of MNPSO is located at a twist angle close to that of the conformational distribution maximum found in less-polar solvents. This fact, associated with a relatively flat torsional potential, can justify the stabilization of the twisted conformation by the less-polar solvents.