Thermalized buckling of isotropically compressed thin sheets

Kinetoplast DNA: a polymer physicist's topological Olympic dream

All life forms are miraculous, but some are more inexplicable than others. Trypanosomes are by far one of the most puzzling organisms on Earth: their mitochondrial genome, also called kinetoplast DNA (kDNA) forms an Olympic-ring-like network of interlinked DNA circles, challenging conventional paradigms in both biology and physics. In this review, I will discuss kDNA from the astonished perspective of a polymer physicist and tell a story of how a single sub-cellular structure from a blood-dwelling parasite is inspiring generations of polymer chemists and physicists to create new catenated materials.

Narrowing of the Flexural Phonon Spectral Line in Stressed Crystalline Two-Dimensional Materials

We develop the microscopic theory for the attenuation of out-of-plane phonons in stressed flexible two-dimensional crystalline materials. We demonstrate that the presence of nonzero tension strongly reduces the relative magnitude of the attenuation and, consequently, results in parametrical narrowing of the phonon spectral line due to stress-controlled suppression of the retardation effects in the dynamically screened inter phonon interaction. We predict the specific power-law dependence of the spectral-line width on temperature and tension. We speculate that suppression of the phonon attenuation by nonzero tension might be responsible for high quality factors of mechanical nanoresonators based on flexural two-dimensional materials.

Bending rigidity exponent of a two-dimensional crystalline membrane with arbitrary number of flexural phonon modes

We investigate the elastic behavior of two-dimensional crystalline membrane embedded into real space taking into account the presence an arbitrary number of flexural phonon modes d_{c} (the number of out-of-plane deformation field components). The bending rigidity exponent η is extracted by numerical simulation via Fourier Monte Carlo technique of the system behavior in the universal regime. This universal quantity governs the correlation function of out-of-plane deformations at long wavelengths and defines the behavior of renormalized bending rigidity at small momentum ϰ∼1/q^{η}. The resulting numerical estimates of the exponent for various d_{c} are compared with the numbers obtained from the approximate analytical techniques.

Geometric control of tilt transition dynamics in single-clamped thermalized elastic sheets

We study the finite-temperature dynamics of thin elastic sheets in a single-clamped cantilever configuration. This system is known to exhibit a tilt transition at which the preferred mean plane of the sheet shifts from horizontal to a plane above or below the horizontal. The resultant thermally roughened two-state (up/down) system possesses rich dynamics on multiple timescales. In the tilted regime a finite-energy barrier separates the spontaneously chosen up state from the inversion-symmetric down state. Molecular dynamics simulations confirm that, over sufficiently long time, such thermalized elastic sheets transition between the two states, residing in each for a finite dwell time. One might expect that temperature is the primary driver for tilt inversion. We find, instead, that the primary control parameter, at fixed tilt order parameter, is the dimensionless and purely geometrical aspect ratio of the clamped width to the total length of the otherwise-free sheet. Using a combination of an effective mean-field theory and Kramers' theory, we derive the transition rate and examine its asymptotic behavior. At length scales beyond a material-dependent thermal length scale, renormalization of the elastic constants qualitatively modifies the temperature response. In particular, the transition is suppressed by thermal fluctuations, enhancing the robustness of the tilted state. We check and supplement these findings with further molecular dynamics simulations for a range of aspect ratios and temperatures.

Buckling in a rotationally invariant spin-elastic model

Scanning tunneling microscopy experiments have revealed a spontaneous rippled-to-buckled transition in heated graphene sheets, in absence of any mechanical load. Several models relying on a simplified picture of the interaction between elastic and internal, electronic, degrees of freedom have been proposed to understand this phenomenon. Nevertheless, these models are not fully consistent with the classical theory of elasticity, since they do not preserve rotational invariance. Herein, we develop and analyze an alternative classical spin-elastic model that preserves rotational invariance while giving a qualitative account of the rippled-to-buckled transition. By integrating over the internal degrees of freedom, an effective free energy for the elastic modes is derived, which only depends on the curvature. Minimization of this free energy gives rise to the emergence of different mechanical phases, whose thermodynamic stability is thoroughly analyzed, both analytically and numerically. All phases are characterized by a spatially homogeneous curvature, which plays the role of the order parameter for the rippled-to-buckled transition, in both the one- and two-dimensional cases. In the latter, our focus is put on the honeycomb lattice, which is representative of actual graphene.

Analytical model of critical buckling transition for smectic liquid crystal based on the viscoelastic scaling of coarse-grained molecular dynamics

The buckling transition of smectic liquid crystals (LCs) is important not only as fundamental physics but also for the rational design of devices to make use of their optical and mechanical properties. However, there exists a huge gap between the specific knowledge and universal analytical formulation. We have conducted coarse-grained molecular dynamics (CGMD) simulations with the force field optimized for the description of buckling phenomena including topological defects to link the molecular nature and continuum formulation. The simulations reveal the viscoelastic characteristics where the critical strain and the compression modulus highly depend on the strain rate as well as the number of layers. Therefore, we formulate the scaling model whose coupling constants depend on both strain rate and domain size. The model reproduces the CGMD results as well as experimental and theoretical values in existing literature. Furthermore, we elucidate from this model that the critical buckling behavior is determined by the competition between the suppression of compression-induced flow and the undulation fluctuation of layers. The framework consisting of the CGMD simulation and the scaling model enables us to estimate the buckling characteristics of smectic LCs reflecting their molecular structures in a wide range from the low-frequency regime that can be verified by experiments to the high-frequency regime beyond the reach of it.

Thermally fluctuating, semiflexible sheets in simple shear flow

We perform Brownian dynamics simulations of semiflexible colloidal sheets with hydrodynamic interactions and thermal fluctuations in shear flow. As a function of the ratio of bending rigidity to shear energy (a dimensionless quantity we denote S) and the ratio of bending rigidity to thermal energy, we observe a dynamical transition from stochastic flipping to crumpling and continuous tumbling. This dynamical transition is broadened by thermal fluctuations, and the value of S at which it occurs is consistent with the onset of chaotic dynamics found for athermal sheets. The effects of different dynamical conformations on rheological properties such as viscosity and normal stress differences are also quantified. Namely, the viscosity in a dilute dispersion of sheets is found to decrease with increasing shear rate (shear-thinning) up until the dynamical crumpling transition, at which point it increases again (shear-thickening), and non-zero first normal stress differences are found that exhibit a local maximum with respect to temperature at large S (small shear rate). These results shed light on the dynamical behavior of fluctuating 2D materials dispersed in fluids and should greatly inform the design of associated solution processing methods.

Spontaneous Tilt of Single-Clamped Thermal Elastic Sheets

Very thin elastic sheets, even at zero temperature, exhibit nonlinear elastic response by virtue of their dominant bending modes. Their behavior is even richer at finite temperature. Here, we use molecular dynamics to study the vibrations of a thermally fluctuating two-dimensional elastic sheet with one end clamped at its zero-temperature length. We uncover a tilted phase in which the sheet fluctuates about a mean configuration inclined with respect to the horizontal, thus breaking reflection symmetry. We determine the phase behavior as a function of the aspect ratio of the sheet and the temperature. We show that tilt may be viewed as a type of transverse buckling instability induced by clamping coupled to thermal fluctuations and develop an analytic model that predicts the tilted and untilted regions of the phase diagram. Qualitative agreement is found with the molecular dynamics simulations. Unusual response driven by control of purely geometric quantities like the aspect ratio, as opposed to external fields, offers a very rich playground for two-dimensional mechanical metamaterials.