Related Experiment Video
Updated: Jun 22, 2026
06:24
High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal
Published on: October 31, 2019
Crumpling transition and flat phase of polymerized phantom membranes
1LPTM, CNRS UMR 8089, Université de Cergy-Pontoise, 2 Avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France. kownacki@u-cergy.fr
Summary
This study revisits polymerized phantom membranes using a nonperturbative renormalization-group approach. The research determines the lower critical dimension and finds the crumpling phase transition to be second-order, though a weak first-order behavior isn't excluded.
Area of Science:
- Polymer Physics
- Statistical Mechanics
- Condensed Matter Physics
Background:
- Polymerized phantom membranes exhibit complex phases, including a crumpled state and a low-temperature flat phase.
- Understanding their phase transitions and critical behavior is crucial in polymer physics.
Purpose of the Study:
- To re-examine polymerized phantom membranes using a nonperturbative renormalization-group (RG) approach.
- To investigate the crumpling transition and the low-temperature flat phase across various dimensions.
- To determine the lower critical dimension for these membrane systems.
Main Methods:
- Application of a nonperturbative renormalization-group (RG) approach.
- Analysis of membrane behavior in arbitrary internal dimension (D) and embedding dimension (d).
- Determination of critical exponents and phase transition orders.
Main Results:
- The crumpling phase transition for physical membranes is identified as second-order within the employed approximation.
- The lower critical dimension for polymerized phantom membranes is determined.
- A weak first-order behavior, consistent with some Monte Carlo simulations, remains a possibility.
Conclusions:
- The nonperturbative RG approach provides a robust framework for studying membrane phase transitions.
- The study clarifies the nature of the crumpling transition, favoring a second-order transition.
- Further investigation may be needed to fully reconcile theoretical findings with experimental or simulation results suggesting weak first-order behavior.
More Related Videos
06:26Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets
Published on: May 15, 2017
10:08Phase Behavior of Charged Vesicles Under Symmetric and Asymmetric Solution Conditions Monitored with Fluorescence Microscopy
Published on: October 24, 2017
Related Concept Videos
01:21Polymer Classification: Crystallinity
Unlike ionic or small covalent molecules, polymers do not form crystalline solids due to the diffusion limitations of their long-chain structures. However, polymers contain microscopic crystalline domains separated by amorphous domains.
Crystalline domains are the regions where polymer chains are aligned in an orderly manner and held together in proximity by intermolecular forces. For example, chains in the crystalline domains of polyethylene and nylon are bound together by van der Waals...
Crystalline domains are the regions where polymer chains are aligned in an orderly manner and held together in proximity by intermolecular forces. For example, chains in the crystalline domains of polyethylene and nylon are bound together by van der Waals...
01:26Membrane Fluidity
Membrane fluidity is explained by the fluid mosaic model of the cell membrane, which describes the plasma membrane structure as a mosaic of components—including phospholipids, cholesterol, proteins, and carbohydrates—that gives the membrane a fluid character.
Mosaic nature of the membrane
The mosaic characteristic of the membrane helps the plasma membrane remain fluid. The integral proteins and lipids exist as separate but loosely-attached molecules in the membrane. The membrane is a relatively...
Mosaic nature of the membrane
The mosaic characteristic of the membrane helps the plasma membrane remain fluid. The integral proteins and lipids exist as separate but loosely-attached molecules in the membrane. The membrane is a relatively...
01:23Membrane Fluidity
Cell membranes are composed of phospholipids, proteins, and carbohydrates loosely attached to one another through chemical interactions. Molecules are generally able to move about in the plane of the membrane, giving the membrane its flexible nature called fluidity. Two other features of the membrane contribute to membrane fluidity: the chemical structure of the phospholipids and the presence of cholesterol in the membrane.Fatty acids tails of phospholipids can be either saturated or...
01:28Classification and Mechanical Properties of Synthetic Polymers
Synthetic polymers are classified as elastomers, fibers, or plastics based on their crystallinity. Crystallinity, the degree of long-range order in the solid state, influences the mechanical properties (stretching or contracting) of elastomers. Elastomers are flexible polymers that can expand or contract easily upon the application of an external force. They have numerous crosslinks that pull them back into their original shape when stress is removed. Silicones, for instance, are highly elastic...
01:19Fluid Mosaic Model
Scientists identified the plasma membrane in the 1890s and its principal chemical components (lipids and proteins) by 1915. The model for plasma membrane structure, proposed in 1935 by Hugh Davson and James Danielli, was the first model to be widely accepted in the scientific community. The model was based on the plasma membrane's "railroad track" appearance in early electron micrographs. Davson and Danielli theorized that the plasma membrane's structure resembled a sandwich with the analogy of...
02:39Phase Transitions: Melting and Freezing
Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...