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Related Concept Videos

Atomic Force Microscopy01:08

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Atomic force microscopy (AFM) is a type of scanning probe microscopy that can analyze topographic details of various specimens like ceramics, glass, polymers, and biological samples. AFM offers over 1000 times more resolution than the optical imaging system. Images generated from AFM are three-dimensional surface profiles, offering an advantage over the flat, two-dimensional images from other imaging techniques.
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Solving problems related to two-dimensional force systems is an essential aspect of mechanics and engineering. By applying the principles of vector analysis and force equilibrium, one can determine the effect of multiple forces acting on an object in a two-dimensional space.
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The method of joints is a commonly used technique to analyze the forces in structural trusses. The method is based on the principle of equilibrium, which assumes that the truss members are connected by frictionless pins. The forces at each joint can be determined by considering the equilibrium of the forces acting on that joint. Consider a truss structure with two forces of 20 N and 10 N acting at joints C and D, respectively. The method of joints can be used to determine the forces FCB, FDC,...
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Consider a truss structure with frictionless joints fixed to a wall and roller support. If a force of 150 N is applied to joint A, the forces in each member of the truss can be determined using the method of joints.
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Method of Sections: Problem Solving I01:27

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Consider a symmetrical roof truss structure, composed of vertical, diagonal, and horizontal members. The length of each horizontal member is 4 m. The lengths of the vertical members FB and HD are 4 m, while the length of member GC is 6 m. The loads acting at joints F, G, and H are 2 kN, while those at joints A and E are 1 kN.
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Consider a truss structure, as shown in the figure.
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Updated: Sep 20, 2025

Covalent Attachment of Single Molecules for AFM-based Force Spectroscopy
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Error analysis in calculation and interpretation of AFM tip-surface interaction forces.

Bo Feng1, Yingli Li1, Rui Li1

  • 1Chongqing Key Laboratory of Soil Multi-Scale Interfacial Processes, College of Resources and Environment, Southwest University, Chongqing 400715, PR China.

Advances in Colloid and Interface Science
|June 12, 2022
PubMed
Summary

Accurate atomic force microscopy (AFM) force measurements require precise calculations. This review identifies errors in electrostatic force formulas, tip-surface models, and tip geometry, offering solutions for reliable colloid and interface science applications.

Keywords:
DLVO theoryElectrostatic forceHalf angleTip geometryTip radius

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Area of Science:

  • Colloid and interface science
  • Surface science
  • Nanotechnology

Background:

  • Atomic Force Microscopy (AFM) is crucial for measuring tip-surface interactions.
  • Inaccurate calculations and interpretations of these forces hinder AFM applications.
  • Existing models often oversimplify complex interactions.

Purpose of the Study:

  • To identify and address common errors in calculating and interpreting AFM tip-surface interaction forces.
  • To propose improved methods for more accurate force measurements.
  • To enhance the reliability of AFM in colloid and interface science.

Main Methods:

  • Comprehensive analysis of existing literature on AFM force calculations.
  • Identification of over-approximated electrostatic force formulas and interaction models.
  • Evaluation of the impact of AFM tip geometry parameters on measurement accuracy.

Main Results:

  • Over-approximated electrostatic force formulas lead to significant errors in force fitting and surface property determination.
  • Simplified tip-surface models (spherical/flat tip-flat surface) introduce large inaccuracies in electrostatic and van der Waals forces.
  • Inaccurate AFM tip geometry parameters significantly affect fitted surface potential, charge density, and Hamaker constant.

Conclusions:

  • Employ adequate electrostatic force calculation methods (e.g., linear superposition approximation, exact numerical solutions).
  • Utilize more accurate tip-surface interaction models (conical tip with spherical/flat end) for precise force measurements.
  • Ensure accurate AFM tip geometry parameters and error assessment for reliable scientific interpretation.