Universal negative poisson ratio of self-avoiding fixed-connectivity membranes

Area of Science:

• Materials Science
• Condensed Matter Physics
• Polymer Physics

Background:

• Fixed-connectivity membranes are crucial in various scientific domains.
• Understanding their mechanical properties, such as Poisson's ratio, is essential for material design.
• Previous studies have explored phantom membranes, but physical membranes require further investigation.

Purpose of the Study:

• To determine the Poisson ratio of self-avoiding fixed-connectivity membranes.
• To compare the Poisson ratio of physical membranes with phantom membranes.
• To establish the universality class of fixed-connectivity membranes and explore their potential as auxetic materials.

Main Methods:

• Modeling membranes as impenetrable plaquettes.
• Utilizing statistical mechanics to determine the Poisson ratio.
• Comparing critical exponents between physical and phantom membrane models.

Main Results:

• The Poisson ratio for self-avoiding fixed-connectivity membranes was determined to be sigma = -0.37(6).
• This value is in statistical agreement with the Poisson ratio of phantom membranes (sigma = -0.32(4)).
• The equality of critical exponents supports a unique universality class for fixed-connectivity membranes.

Conclusions:

• Physical fixed-connectivity membranes are confirmed to be auxetic materials.
• These findings establish a unique universality class for fixed-connectivity membranes.
• The study highlights the significant potential of these auxetic materials in materials science applications.