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Strain and Elastic Modulus01:15

Strain and Elastic Modulus

The quantity that describes the deformation of a body under stress is known as strain. Strain is given as a fractional change in either length, volume, or geometry under tensile, volume (also known as bulk), or shear stress, respectively, and is a dimensionless quantity. The strain experienced by a body under tensile or compressive stress is called tensile or compressive strain, respectively. In contrast, the strain experienced under bulk stress and shear stress is known as volume and shear...
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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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Related Experiment Video

Updated: May 21, 2026

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

Nanoscale elastic modulus variation in loaded polymeric micelle reactors.

Alim Solmaz1, Taner Aytun, Julia K Deuschle

  • 1Materials Science and Engineering Program, Sabanci University, Orhanli, Tuzla, 34956 Istanbul, Turkey.

Langmuir : the ACS Journal of Surfaces and Colloids
|June 15, 2012
PubMed
Summary

This study used tapping mode atomic force microscopy to map mechanical differences in polymer micelles. The researchers found that phase contrast in images reflects elastic modulus variation between loaded and unloaded micelles. They used a polystyrene support film to eliminate substrate effects and calibrate the cantilever tip geometry. Force-indentation curves were measured using standard tapping mode probes. The Hertz model extracted modulus values of 8.26 GPa for loaded micelles and 4.17 GPa for unloaded ones. This suggests that phase contrast images can map nanoscale mechanical and chemical differences. The team used the same cantilevers for imaging and indentation, improving measurement accuracy. Their findings support using TM-AFM for nanoscale material characterization.

Keywords:
atomic force microscopypolymeric micelleselastic modulus measurementnanoscale imagingmaterials characterization

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Last Updated: May 21, 2026

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Atomic Force Microscopy Cantilever-Based Nanoindentation: Mechanical Property Measurements at the Nanoscale in Air and Fluid
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Published on: March 25, 2015

Area of Science:

  • Polymer science and nanomechanics
  • Atomic force microscopy in materials analysis
  • Nanoparticle drug delivery systems

Background:

Understanding mechanical properties at the nanoscale is essential for optimizing polymer-based systems. Prior research has shown that atomic force microscopy can detect surface variations. However, the connection between phase contrast and elastic modulus remains unclear. This gap motivated the need for precise measurement techniques. No prior work had resolved how to map chemical composition through mechanical data. Standard methods often fail to distinguish soft and hard regions within small structures. This uncertainty drove the development of new calibration approaches. By linking phase shifts to mechanical properties, researchers aim to improve material characterization accuracy.

Purpose Of The Study:

This study aimed to demonstrate how phase contrast in tapping mode atomic force microscopy can reflect elastic modulus variation. The specific problem involved interpreting phase shifts in loaded micelles. The motivation was to improve nanoscale imaging accuracy for polymer systems. Researchers focused on reverse PS-b-P2VP micelles loaded with zinc acetate. The goal was to confirm that phase contrast maps mechanical differences. By using a known soft material for calibration, the team sought to standardize measurement tools. This approach allows using the same cantilevers for imaging and indentation. The study also aimed to validate the Hertz model for modulus extraction.

Main Methods:

The team used tapping mode atomic force microscopy to map elastic modulus variations. Three sample configurations were analyzed: a PS support film, an unfilled micelle, and a loaded micelle. Force-indentation curves were measured using standard tapping mode probes. Three different spring constants were tested to assess mechanical response. The same cantilevers were used for imaging and indentation measurements. Nanoindentation was performed on the PS film for tip geometry calibration. The Hertz model was applied to extract elastic modulus values. This method enabled comparison between loaded and unloaded micelles.

Main Results:

Elastic modulus values were extracted using the Hertz model from indentation data. Loaded micelles showed a modulus of 8.26 ± 3.43 GPa compared to 4.17 ± 1.65 GPa for unloaded ones. These results suggest that phase contrast reflects mechanical differences. The PS support film helped eliminate substrate effects. Calibration using the PS film allowed accurate modulus extraction. The same cantilevers were used before and after loading. Phase contrast images of loaded micelles represent chemical and mechanical maps. This confirms that TM-AFM can detect nanoscale modulus variation.

Conclusions:

The authors propose that phase contrast in TM-AFM images reflects elastic modulus variation. They suggest that this method can map chemical and mechanical differences at the nanoscale. Their findings support using standard tapping mode cantilevers for both imaging and indentation. Calibration using a known soft material improves measurement accuracy. The study confirms that loaded micelles have higher modulus than unloaded ones. This approach avoids the need for specialized probes or complex setups. The results align with the Hertz model for modulus extraction. The authors emphasize that this technique enhances nanoscale material characterization.

According to the authors, phase contrast in TM-AFM images suggests variation in elastic modulus between loaded and unloaded micelles.

The PS support film was used to eliminate substrate effects and calibrate tip geometry for accurate modulus extraction.

The team performed nanoindentation on a known soft material, the PS film, to calibrate the tip geometry indirectly.

The Hertz model was used to extract elastic modulus values from force-indentation curves measured on micelles.

Loaded micelles had a modulus of 8.26 ± 3.43 GPa versus 4.17 ± 1.65 GPa for unloaded ones.

The authors propose that phase contrast in TM-AFM images represents nanoscale chemical and mechanical variation.