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Angle of Twist: Problem Solving01:13

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An electric motor applies a torque of 700 N·m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N·m and 400 N·m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the torque...
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Pure bending is a fundamental concept in structural mechanics, essential for understanding how materials deform under symmetrical loads without direct forces. Pure bending occurs when prismatic members, such as beams, are subjected to equal and opposite moments that induce bending. The phenomenon is crucial as it allows for predicting stress distributions without the influence of axial or shear forces.
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Symmetric Member in Bending01:07

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In the study of the mechanics of materials, analyzing the behavior of prismatic members under opposing couples is crucial for understanding internal stress distributions, which are essential for structural design. When subjected to couples, a prismatic member experiences internal forces that maintain equilibrium. A couple, characterized by two equal and opposite forces, creates a moment but no resultant force. The internal forces at any section cut of the member must balance these external...
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Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The...
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Updated: Feb 4, 2026

High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal
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Nematic twist-bend phase in an external field.

Grzegorz Pająk1,2, Lech Longa1, Agnieszka Chrzanowska3

  • 1Marian Smoluchowski Institute of Physics, Department of Statistical Physics, Jagiellonian University, 30-348 Kraków, Poland; grzegorz@th.if.uj.edu.pl lech.longa@uj.edu.pl achrzano@usk.pk.edu.pl.

Proceedings of the National Academy of Sciences of the United States of America
|October 13, 2018
PubMed
Summary

Applied fields induce rich structural changes in the nematic twist-bend phase. Depending on permittivity, this liquid crystal can transition to uniaxial, elliptical, or splay-bend nematic phases, eventually forming polar structures.

Keywords:
chiralitynematicspolaritysplay–bendtwist–bend

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Area of Science:

  • Liquid crystal physics
  • Soft matter theory
  • Materials science

Background:

  • The nematic twist-bend phase exhibits unique structural properties relevant to mirror symmetry breaking.
  • Understanding its response to external fields is crucial for fundamental insights into liquid crystal behavior.

Purpose of the Study:

  • To theoretically investigate the structural transformations and stability of the nematic twist-bend phase under an applied uniform electric field.
  • To elucidate the mechanisms driving these field-induced phase transitions.

Main Methods:

  • Utilized Landau-de Gennes theory to model the nematic twist-bend phase.
  • Analyzed the effects of varying electric field strengths on the phase's structural properties and stability.
  • Considered systems with both positive and negative dielectric anisotropy.

Main Results:

  • For positive dielectric anisotropy, the phase transitions to a prolate uniaxial nematic phase, developing perpendicular polarization at high fields.
  • For negative dielectric anisotropy, new modulated structures emerge, including elliptical and splay-bend nematic phases.
  • Increasing fields lead to phase transitions into globally polar structures, including a chiral modification and a polar nematic phase.

Conclusions:

  • The nematic twist-bend phase exhibits complex field-dependent structural polymorphism.
  • Applied fields can induce transitions from nonpolar to polar states, offering insights into chirality and symmetry breaking in achiral systems.
  • The theoretical framework provides a basis for understanding and potentially controlling liquid crystal phases with external stimuli.