Helix Pitch Research Articles

Optimal milling cutter helix selection for period doubling chatter suppression

In high speed milling, interrupted cutting conditions can lead to period doubling chatter vibrations. While many studies have already confirmed that the use of helical tools can effectively shrink or remove these regions of unstable cutting, none of them has provided clear guidance to select the minimum helix that completely cancels the period doubling lobes. This study addresses this gap by introducing a novel analytical formula for a critical tool helix pitch: if the helix pitch is below the critical flip depth of cut of the straight helix cutter multiplied by π, the flip lobes will totally vanish. This rule is not only valuable for chatter-free process planning purposes, but it also establishes exact limit below which the fast and simple zeroth order stability algorithm can provide exact stability boundaries for helical tools. The effectiveness of the formula is numerically corroborated over three different milling scenarios: thin wall milling, slender tool and machine tool structure chatter cases. Finally, the findings are validated through experimental cutting tests.

Theoretical study of a tunable optical device on the base of magnetoactive cholesteric liquid crystals

We investigated the light reflection from half-space of cholesteric liquid crystal (CLC) being in external static magnetic field directed along the helix axis at normal light incidence. In this case there appear three photonic band gaps (PBGs) and these bands can be tuned in large intervals. We found the eigenpolarizations (EPs) at reflection of light from half-space and investigated their peculiarities. We have shown that in the absence both of absorption and of external magnetic field and at minimal influence of dielectric boundary (when the dielectric permittivity of isotropic half-space which borders with CLC half-space is equal to the CLC's mean dielectric permittivity) these polarizations are orthogonal. While, in the presence of external magnetic field they become quasi-orthogonal everywhere outside the main PBG (which exist also at the absence of external magnetic field), and they are significantly non-orthogonal within the main PBG. At some values of helix pitch they become significantly non-orthogonal practically everywhere. Moreover, in this case there exist some special points where the EPs degenerate. This system can apply as tunable narrow-band or broad-band filter and mirror, a highly tunable broad/narrow-band optical diode, and other devices.

Double-Helical Tiled Chain Structure of the Twist-Bend Liquid Crystal Phase in CB7CB

The twist-bend nematic liquid crystal phase is a three-dimensional fluid in which achiral bent molecules spontaneously form an orientationally ordered, macroscopically chiral, heliconical winding of a ten nanometer-scale pitch in the absence of positional ordering. Here, the structure of the twist-bend phase of the bent dimer CB7CB and its mixtures with 5CB is characterized, revealing a hidden invariance of the self-assembly of the twist-bend structure of CB7CB, such that over a wide range of concentrations and temperatures, the helix pitch and cone angle change as if the ground state for a pitch of the TB helix is an inextensible heliconical ribbon along the contour formed by following the local molecular long axis (the director). Remarkably, the distance along the length for a single turn of this helix is given by 2πRmol, where Rmol is the radius of bend curvature of a single all-trans CB7CB molecule. This relationship emerges from frustrated steric packing due to the bent molecular shape: space in the fluid that is hard to fill attracts the most flexible molecular subcomponents, a theme of nanosegregation that generates self-assembled, oligomer-like correlations of interlocking bent molecules in the form of a brickwork-like tiling of pairs of molecular strands into duplex double-helical chains. At higher temperatures in the twist-bend phase, the cone angle is small, the director contour is nearly along the helix axis z, and the duplex chains are sequences of biaxial elements formed by overlapping half-molecule pairs, with an approximately 45° rotation of the biaxis between each such element along the chain.

Cholesteric liquid crystal phase variations within nanotubes: an in-depth analysis of the influences of twist radius and molecular pitch

ABSTRACT This study investigates the self-assembly and phase transitions of cholesteric liquid crystals (CLCs) when confined in nanotubes, specifically focusing on the variations in their molecular structures. A dissipative particle dynamics method was used to investigate how the changes in helix radius ( r LC ) and pitch ( P ) affect the behaviour of the LCs. For pitches of 24, 12, and 6, the orientation order parameter ( P 2 ) showed distinct trends during cooling. Smaller helix radii resulted in isotropic to nematic to smectic phase transitions, whereas larger radii resulted in a novel smectic phase with spiral structures (Sm s ). Circumferential local-order parameters ( P 2 r and P 2 z ) were introduced to better characterise the phases, and a disordered spiral-structure phase (Sm s 2 ) with local perturbations was observed. The transitions between isotropic, nematic, and smectic phases, highlighting the influence of the pitch and helix radius, were observed from the phase diagrams. Smaller pitches and radii prevented the formation of stable structures; however, specific combinations induced characteristic spiral structures in the smectic phase. These results provide new insights into the self-assembly of confined CLCs, which have potential applications in the design of photonic devices and LC-based sensors. This study advances our understanding of phase control in quasi-one-dimensional systems and highlights the importance of molecular variations in liquid crystal behaviour.

Numerical investigation of coupled heat transfer and flow characteristics in helical coil heat exchanger for mine water waste heat recovery

To efficiently recover waste heat from mine water, this study numerically investigates the flow and heat transfer performance of a tube-shell coupled helical coil heat exchanger (HCHE), under high Reynolds number conditions. The effects of inlet water temperature, mass flow rate (m), tube diameter (d), and helix pitch (P) on the tube side, shell side, and overall performance are analyzed. Performance metrics include friction factor (f), Nusselt number (Nu), overall heat transfer coefficient (U), heat transfer rate, and the Performance Evaluation Criteria (PEC) number. Specifically, this study focuses on detailed observation and analysis of the shell-side flow and temperature fields. Findings reveal that enlarging d from 30 mm to 50 mm results in a 32.55% decrease in U, whereas increasing P from 50 mm to 200 mm boosts U by 8.02%. The highest PEC number of HCHE is 2.43, observed in conditions of P = 50 mm, d = 30 mm, and mc = 4 × 103 kg/h. Correlations for fc, Nuc, and Nush are proposed based on simulation results. This study provides a theoretical basis for the design and structural optimization of HCHE in the mine water waste heat recovery applications.

Photoinduced Transformation of the Orientational Structure of a Chiral Nematic under Planar-Conical Anchoring

The photo-induced change in the orientation structure of the chiral nematic based on LN-396 doped with chiral dopants S811 and cChD has been investigated. It is shown that the use of planar-conical boundary conditions makes it possible to realise a smooth variation of the structure twist angle by changing the helix pitch. It is shown that the twisting of the structure of the studied chiral nematic to an angle of more than 240° leads to undulations when the conical anchoring is specified by the PiBMA polymer. The PtBMA polymer, on the other hand, specifies tangential boundary conditions for the chiral nematic under study, allowing the director to rotate easily in the plane of the sample. The results presented may be promising for the development of liquid crystal systems with finely tunable polar and azimuthal angles of the director.

Thermal colour map of 4D smart microtags made by Two-Photon Lithography in cholesteric reactive mesogens

ABSTRACT The helicoidal architecture of cholesteric reactive mesogens allows for smart 4D responsive microdevices that reflect selectively the wavelength and polarisation of the incident light. Two-photon lithography is an effective 4D microprinting technology which also enables fine tuning of the Bragg reflection, as a function of the energy delivered during the manufacturing and the polymerisation degree. When CRMs objects undergo temperature variation, thermal expansion causes the elongation of the effective helix pitch and the consequent red-shift of the photonic band gap. A thermal characterisation of the optical response of CRMs microcylinders is presented, showing a tunable red-shift from 2 to 37 nm in the 30–150°C range. The red-shift is enhanced for tall structures, with high polymerisation degree. This characterisation is exploited to add a security label to a 4D cholesteric QR code.

Design and analysis of a novel magnetic helical swimmer

Magnetic helical swimmers are one type of robots that swim at low Reynolds number environments by rotating around the helix axis. Considering the importance and dramatic increase in the use of robots and microrobots in the near future, optimizing and increasing their efficiency is very important and noteworthy. Propulsion force and translational velocity are among the most important features of the magnetic helical swimmer, which improves the function of the swimmer as each of them increases. In this paper, a new design has been proposed for the magnetic helical swimmer by changing the geometry of the tail region, which has increased the propulsion force and improved its translational velocity. A suitable experimental setup has been designed and built in accordance with the required experiments to evaluate the translational velocity of the proposed swimmer. Using the experimental results, two models have been presented to express the translational velocity and propulsion force of the swimmer in terms of its angular velocity. The results of the experiments show that the propulsion force of the built swimmer is 698.89 % higher than that of the common magnetic helical swimmer with similar dimensions and the same environmental conditions in Newtonian fluid. At the end of the experiments, the motion of the proposed swimmer is simulated in the COMSOL software, and the results of the experiments are used to validate the simulation results. Finally, the effect of parameters such as the helix pitch and the number of turns of the helix on the translational velocity of the swimmer is investigated using the computer simulations.

Electromagnetic oscillations and anomalous ion scattering in the helically symmetric multiple-mirror trap

The paper presents an investigation of the plasma fluctuation in the SMOLA helical mirror, which is suspected to be responsible for anomalous scattering. The helical mirror confinement is effective when the ion mean free path is equal to the helix pitch length. This condition can be satisfied in hot collisionless plasma only by anomalous scattering. The wave, which scatters the passing ions, is considered to receive energy from the trapped ions. The oscillations of the electric field in the helically symmetric plasma were observed in experiment. The oscillations have both regular highly correlated and chaotic components. The dependency of the regular component frequency on the Alfvén velocity is linear for $V_{\rm A} < 2.8 \times 10^6\ \text {m}\ \text {s}^{-1}$ and constant for higher values. It is shown experimentally that the condition for the wave to be in phase resonance with the trapped ions is satisfied in a specific region of the plasma column for the highly correlated component. The amplitude of the chaotic component (up to $3\ \text {V}\ \text {cm}^{-1}$ ) is higher than the estimated electric field required for the ion scattering.

Positive Synergy between the Helical Poly(phenylacetylene) Backbones and the Helical L-Proline Oligopeptide Pendants for Enhanced Enantioseparation Properties.

A series of optically active helical poly(phenylacetylene)s (PPA-Pro1, PPA-Pro3, PPA-Pro6, PPA-Pro9, and PPA-Pro12) bearing different chain lengths of L-proline oligopeptide in the side chains were obtained by polymerizing the corresponding novel phenylacetylene monomers. The monomer adopted a trans-rich helix structure when the L-proline oligopeptide chain length was longer, according to the optical activities and 2D-NMR analysis. The helical structure could be maintained and significantly influenced the polymers' helical conformation by introducing the L-proline oligopeptide to the pendants. By the way, the morphology of PPA-Pro3 was observed by atomic force microscope (AFM) on highly oriented pyrolytic graphite (HOPG), and the information on the helix direction, pitch, and chain arrangement was obtained. Also, the chiral separation properties of these polymer-based chiral stationary phases (CSPs) were investigated using high-performance liquid chromatography (HPLC). The poly(phenylacetylene)s showed enhanced enantioseparation properties toward various racemates depending on the longer chain length of the L-proline oligopeptide in the pendants and the positive synergy between the helical backbone and helical side chains. Particularly, PPA-Pro9 showed comparable or even superior enantioseparation properties for racemates 2 and 9 to four commercial columns (Daicel Chiralpak or Chiralcel AD, AS, OD, and OT), indicating that these poly(phenylacetylene)-based CSPs have potential practical values. This work presented here provides inspiration for the further development of CSPs based on a new paradigm.

The influence of antiferromagnetic spin cantings on the magnetic helix pitch in cubic helimagnets

In cubic helimagnets MnSi and Cu2OSeO3 with their nearly isotropic magnetic properties, the magnetic structure undergoes helical deformation, which is almost completely determined by the helicoid wavenumber k=D/J , where magnetization field stiffness J is associated with isotropic spin exchange, and D is a pseudoscalar value characterizing the antisymmetric Dzyaloshinskii–Moriya (DM) interaction. Another magnetic feature of these crystals, also caused by the DM interactions, are antiferromagnetic spin cantings, similar to the ferromagnetic cantings responsible for the phenomenon of weak ferromagnetism. Here we show that cantings can strongly influence the helical order through the value of the parameter D . Changing the cantings in a strong magnetic field is predicted to affect the magnon spectrum of the crystals.

Amplification of Light‐Induced Helix Inversion of Intrinsically Chiral Diarylethene Molecular Switches

AbstractPhotonics and tunable optics are rapidly developing fields that require materials with programmable properties and advanced functionalities. Cholesteric liquid crystals (CLCs) are unique materials that exhibit selective light reflection and can be tuned using stimuli‐responsive small organic molecules. The challenge lies in designing molecules that can convert external signals, such as light, into dynamic and invertible chiral states, which can be transduced to the CLC supramolecular structures inducing large differences in helicity and eventually to macroscopic properties. Here, novel intrinsically chiral phenanthrene‐based diarylethenes as light‐responsive chiral dopants for controlling the supramolecular helical architectures of CLCs are introduced. The substitution pattern and light‐invertible axial chirality of these diarylethenes make them highly compatible with liquid crystals and provide high twisting power. The light‐induced cyclization and molecular chirality transformation result in a wide tunability of the cholesteric helix pitch (reflection colors) and reversible inversion of helical handedness. These findings provide a powerful tool for controlling and manipulating the macroscopic properties of CLCs, opening new avenues for a range of applications, including diffractive optics and photonics, anticounterfeiting tags, and displays.

Liquid Crystalline Electro-Optical Modulator of Submegahertz Range

A liquid crystalline (LC) electro-optical modulator providing an electro-optical response time up to 400 nanoseconds with a modulation frequency up to 500 kHz has been developed. The ferroelectric liquid crystal FLC-576 obtained by us was used as the electro-optical medium of the modulator. Its helix pitch р0 is much smaller than wavelengths of visible light (р0 < 100 nm). The liquid crystal operates in the deformed helix ferroelectric mode (DHF-effect) under the action of electric fields. The controlling electric fields are less than a critical field of helix unwinding. At high frequencies of the control voltage (over 10 kHz), the heating of electro-optical cell by repolarization currents of FLC can occur up to the temperature of phase transition from ferroelectric to paraelectric phase, which leads to the cessation of electro-optical modulation. The work experimentally and theoretically examines the self-heating issues of electro-optical modulators depending on the liquid crystal layer thickness, frequency and strength of applied electric field. The heat removal conditions from the liquid crystal cell have been determined and experimentally implemented. Under these conditions the LC is in the smectic C* ferroelectric phase temperature range, which is necessary to provide electro-optical modulation in submegaherts diapason.

Changes in the structure of potato virus A virions during limited proteolysis <i>in situ</i> according to tritium labeling data and computer simulation

The coat proteins (CP) of potato virus A virions (PVA) contain partially disordered N-terminal domains, which are necessary for performing vital functions of the virus. A comparative analysis of the structures of coat proteins (CPs) in intact PVA virions and in virus particles lacking the N-terminal 32 amino acids (PVAΔ32) was carried out in this work based on the tritium planigraphy data. Using the atomic resolution structure of the potato virus Y potyvirus (PVY) protein, which is a homolog of CP PVA, the available CP surfaces in the PVY virion were calculated and the areas of intersubunit/ interhelix contacts were determined. For this purpose, the approach of Lee and Richards (Lee, B., and Richards, F. M. (1971) J. Mol. Biol., 55, 379-400) was used. Comparison of the incorporation profiles of the tritium label in intact and trypsin-degraded PVA∆32 revealed the position of the ΔN-peptide shielding the surface domain (a.a. 66-73, 141-146) and the interhelix zone (a.a. 161-175) of the PVA CP. The presence of channels/cavities was found in the virion, which turned out to be partially permeable to tritium atoms. Upon removal of the ∆N-peptide, a decrease in the label within the virion (a.a. 184-200) was also observed, indicating a possible structural transition leading to virion compactization. Based on the data obtained, we can conclude that part of the surface ∆N-peptide is located between the coils of the virion helix, which increases the helix pitch and provides greater flexibility of the virion, which is important for the intercellular transport of the viruses in the plants.

Cholesteric Spherical Reflectors with Tunable Color from Single-Domain Cellulose Nanocrystal Microshells.

The wavelength- and polarization-selective Bragg reflection of visible light exhibited by films produced by drying cholesteric liquid crystal (CLC) suspensions of cellulose nanocrystals (CNCs) render these biosourced nanoparticles highly potent for many optical applications. While the conventionally produced films are flat, the CLC-derived helical CNC arrangement would acquire new powerful features if given spherical curvature. Drying CNC suspension droplets does not work, because the onset of kinetic arrest in droplets of anisotropic colloids leads to severe buckling and loss of spherical shape. Here, these problems are avoided by confining the CNC suspension in a spherical microshell surrounding an incompressible oil droplet. This prevents buckling, ensures strong helix pitch compression, and produces single-domain cholesteric spherical reflector particles with distinct visible color. Interestingly, the constrained shrinkage leads to spontaneous puncturing, leaving every particle with a single hole through which the inner oil phase can be extracted for recycling. By mixing two different CNC types at varying fractions, the retroreflection color is tuned throughout the visible spectrum. The new approach adds a versatile tool in the quest to utilize bioderived CLCs, enabling spherically curved particles with the same excellent optical quality and smooth surface as previously obtained only in flat films.

Changes in the Structure of Potato Virus A Virions after Limited in situ Proteolysis According to Tritium Labeling Data and Computer Simulation.

Coat proteins (CP) of the potato virus A virions (PVA) contain partially disordered N-terminal domains, which are necessary for performing vital functions of the virus. Comparative analysis of the structures of coat proteins (CPs) in the intact PVA virions and in the virus particles lacking N-terminal 32 amino acids (PVAΔ32) was carried out in this work based on the tritium planigraphy data. Using atomic-resolution structure of the potato virus Y potyvirus (PVY) protein, which is a homolog of the CP PVA, the available CP surfaces in the PVY virion were calculated and the areas of intersubunit/interhelix contacts were determined. For this purpose, the approach of Lee and Richards [Lee, B., and Richards, F. M. (1971) J. Mol. Biol., 55, 379-400] was used. Comparison of incorporation profiles of the tritium label in the intact and trypsin-degraded PVAΔ32 revealed position of the ΔN-peptide shielding the surface domain (a.a. 66-73, 141-146) and the interhelix zone (a.a. 161-175) of the PVA CP. Presence of the channels/cavities was found in the virion, which turned out to be partially permeable to tritium atoms. Upon removal of the ΔN-peptide, decrease in the label incorporation within the virion (a.a. 184-200) was also observed, indicating possible structural transition leading to the virion compactization. Based on the obtained data, we can conclude that part of the surface ΔN-peptide is inserted between the coils of the virion helix thus increasing the helix pitch and providing greater flexibility of the virion, which is important for intercellular transport of the viruses in the plants.

Instability of cholesteric bridge in isotropic environment with break-up and satellite droplet formation

ABSTRACT We investigate quasi-two-dimensional coalescence of domains of isotropic liquid in chiral liquid crystal in flat optical cells. It is demonstrated that coalescence can be accompanied by instability of the liquid crystal bridge separating the domains. We analyse the transformation of the bridge for materials in a wide range of the pitch of the cholesteric helix and different spatially modulated structures: planar cholesteric, one-dimensional stripe structure, focal conic structure and Blue Phases. The instability is followed by cascade break-up and formation of satellite cholesteric droplets. This picture differs from the standard three-dimensional coalescence scenario, where only a bridge between the droplets forms and grows. Studies of thinning dynamics in the bridge region showed that at the final stage of instability the width of the cholesteric bridge decreased linearly with time. In cholesteric with high chirality and small helical pitch the bridge thinning occurs substantially slower than in cholesteric with large helical pitch.

Thermoresponsive Helical Dendronized Poly(phenylacetylene)s: Remarkable Stabilization of Their Helicity via Photo-Dimerization of the Dendritic Pendants.

Dynamic helical polymers can change their helicity according to external stimuli due to the low helix-inversion barriers, while helicity stabilization for polymers is important for applications in chiral recognition or chiral separations. Here, we present a convenient methodology to stabilize dynamic helical conformations of polymers through intramolecular cross-linking. Thermoresponsive dendronized poly(phenylacetylene)s (PPAs) carrying 3-fold dendritic oligoethylene glycol pendants containing cinnamate moieties were synthesized. These polymers exhibit typical features of dynamic helical structures in different solvents, that is, racemic contracted conformations in less polar organic solvents and predominantly one-handed stretched helical conformations in highly polar solvents. This dynamic helicity can be enhanced through selective solvation by increasing the polarity of the organic solvents or simply via their thermally mediated dehydration in water. However, through photocycloaddition of the cinnamate moieties between the neighboring pendants via UV irradiation, these dendronized PPAs adopt stable helical conformations either below or above their phase transition temperatures in water, and their helical conformations can even be retained in less polar organic solvents. Spectroscopic and atomic force microscopy measurements demonstrate that photocycloaddition between the cinnamate moieties occurs on the individual molecular level, and this is found to be helpful in restraining the photodegradation of the PPA backbones. Molecular dynamics simulations reveal that the spatial orientation of the pendants along the rigid polyene backbone is crucial for the photodimerization of cinnamates within one helix pitch.

Short helix pitch ferroelectric liquid crystals induced in nematic matrix by chiral non-mesogenic dopants

We report the development of chiral smectic C (SmC*) ferroelectric liquid crystals (FLCs) obtained by mixing of a nematic liquid crystal (NLC) as a host and chiral non-mesogenic dopants. The NLC is a binary eutectic mixture of phenyl- and biphenyl-pyrimidines, while chiral dopants belong to homologous series of secondary dilactates with terphenyldicarboxylate core. The induction in the mixtures not only the cholesteric phase, but also the wide temperature range ferroelectric SmC* phase with the helix pitch p0≈100 nm and the spontaneous polarization Ps about 70 nC/cm2 has been confirmed by dielectric, optical, and electro-optical measurements. The developed FLC mixtures are highly efficient for the deformed helix ferroelectric liquid crystal electro-optical mode because the mixtures combine mechanical stability (or mechanical shock resistance) of NLCs and kilohertz switching frequency (due to short helix pitch) of FLCs. These FLCs can be used to create various photonic devices, such as generators of vortex light fields and field-sequential color displays.

Helical model of compression and thermal expansion

A negative linear temperature expansion and a negative linear compressibility were observed for imidazolium benzoate salt. Its strongly anisotropic strain induced by the temperature and pressure changes has been explained by the mechanism of H-bonded helices deformed in the structure. X-ray diffraction and vibrational spectroscopy were used to analyze interactions in the crystal. The Quantum Theory of Atoms in Molecules (QTAiM) approach was applied to analyze the hydrogen bonds and other interactions. In the salt under study, the interactions within the helix are substantially higher in energy than between helices. With decreasing temperature and increasing pressure, the value of the helix pitch increases while the value of the semi-major axis decreases, which results in the negative linear expansion and negative linear compression, respectively.