Practical AFM Force Curve Analysis with Python: From Raw Data to Mechanical Properties

Why This Guide Exists

If you work with AFM force spectroscopy on soft biomaterials (collagen fibers, silk, hydrogels, cells), you have probably faced the same frustration: your instrument exports a pile of .txt or .csv files, and you spend hours manually processing them in proprietary software or Excel.

This guide gives you a complete, copy-paste-ready Python pipeline that handles everything from raw data loading to Young's modulus extraction. No commercial software required. Just numpy, scipy, and matplotlib.

1. Understanding AFM Force Curve Data

A typical AFM force curve records cantilever deflection (in volts or nanometers) as the piezo moves the tip toward and away from the sample:

Segment	What happens	What you extract
---------	-------------	-----------------
Approach	Tip approaches surface	Contact point, sample stiffness
Contact	Tip presses into sample	Elastic modulus (via fitting)
Retract	Tip pulls away	Adhesion force, unbinding events

import numpy as np
import matplotlib.pyplot as plt
from scipy import signal, optimize

2. Loading Typical AFM Data Files

Most AFM instruments export tabular data. Common formats:

• Bruker/Veeco: .txt with header lines starting with \
• JPK/Nanowizard: .txt or .jpk-force with metadata header
• Asylum/AR: .txt or .ibw (use igorpro package)
• Generic: .csv with columns: Z_piezo, Deflection

def load_afm_curve(filepath, skip_rows=0):
    data = np.loadtxt(filepath, skiprows=skip_rows)
    return data[:, 0], data[:, 1]

# Example: Bruker force curve
z_piezo, deflection = load_afm_curve("force_curve_001.txt", skip_rows=320)

Handling Bruker Headers

def load_bruker_curve(filepath):
    with open(filepath, "r") as f:
        lines = f.readlines()
    skip = 0
    for i, line in enumerate(lines):
        if line.strip().startswith("\\*") or "Ciao" in line:
            skip = i + 1
    data = np.loadtxt(filepath, skiprows=skip)
    return data[:, 0], data[:, 1]

3. Converting Deflection to Force

def deflection_to_force(deflection_V, spring_constant, sensitivity_nm_per_V):
    deflection_nm = deflection_V * sensitivity_nm_per_V
    force_N = spring_constant * deflection_nm * 1e-9
    return force_N * 1e9  # nN

k = 0.06        # N/m (Bruker MLCT)
sensitivity = 45.0  # nm/V
force = deflection_to_force(deflection, k, sensitivity)

4. Baseline Correction

def baseline_correct(z_piezo, force, contact_idx):
    baseline_region = slice(0, contact_idx)
    coeffs = np.polyfit(z_piezo[baseline_region], force[baseline_region], 1)
    baseline = np.polyval(coeffs, z_piezo)
    return force - baseline

5. Finding the Contact Point

def find_contact_point(z_piezo, force, window=50, threshold_factor=5):
    force_smooth = signal.savgol_filter(force, window_length=21, polyorder=3)
    dz = np.gradient(z_piezo)
    df = np.gradient(force_smooth)
    derivative = df / dz
    noise_region = slice(0, len(force) // 5)
    noise_std = np.std(derivative[noise_region])
    threshold = threshold_factor * noise_std
    above_threshold = np.abs(derivative) > threshold
    for i in range(len(above_threshold) - window):
        if np.all(above_threshold[i:i + window]):
            return i + window // 2
    return len(force) // 2

6. Extracting Adhesion Force

def extract_adhesion(z_piezo, force, contact_idx):
    retract_region = force[contact_idx:]
    adhesion_idx = np.argmin(retract_region)
    adhesion_force = retract_region[adhesion_idx]
    return adhesion_force if adhesion_force < 0 else 0.0

7. Hertz Model Fitting for Young's Modulus

For a spherical indenter on a flat elastic half-space:

F = (4/3) E* sqrt(R) delta^(3/2)

where E* = E / (1 - nu^2).

def hertz_sphere(indentation, E_star, R):
    return (4/3) * E_star * np.sqrt(R) * np.power(np.maximum(indentation, 0), 1.5)

def fit_youngs_modulus(z_piezo, force, contact_idx, tip_radius_nm=20.0,
                        poisson=0.5, fit_range_nm=50.0):
    indent = z_piezo[contact_idx] - z_piezo
    contact_force = force - force[contact_idx]
    fit_mask = (indent > 0) & (indent < fit_range_nm) & (contact_force > 0)
    indent_fit = indent[fit_mask]
    force_fit = contact_force[fit_mask]
    if len(indent_fit) < 50:
        return np.nan, np.nan
    def model(delta, E_star):
        return hertz_sphere(delta, E_star, tip_radius_nm)
    popt, pcov = optimize.curve_fit(model, indent_fit, force_fit,
        p0=[1000], bounds=(1, 1e9))
    E_star = popt[0]
    E = E_star * (1 - poisson**2)
    E_std = np.sqrt(pcov[0, 0]) * (1 - poisson**2)
    return E, E_std

8. Batch Processing

import glob
from pathlib import Path

def batch_process_curves(data_dir, k=0.06, sensitivity=45.0):
    results = []
    for filepath in sorted(glob.glob(f"{data_dir}/*.txt")):
        try:
            z, deflection = load_afm_curve(filepath, skip_rows=320)
            force = deflection_to_force(deflection, k, sensitivity)
            cidx = find_contact_point(z, force)
            force_corr = baseline_correct(z, force, cidx)
            adhesion = extract_adhesion(z, force_corr, cidx)
            E, _ = fit_youngs_modulus(z, force_corr, cidx)
            results.append({"file": Path(filepath).name,
                "adhesion_nN": adhesion, "E_Pa": E})
        except Exception as e:
            print(f"Failed: {filepath}: {e}")
    return results

9. Common Pitfalls

Problem	Likely Cause	Fix
---------	-------------	-----
Contact point too early	Baseline noise	Increase threshold_factor
Negative modulus	Wrong direction	Check z_piezo sign convention
Substrate effect	Too deep indentation	fit_range_nm < 10% of thickness
Zero adhesion	No retract data	Enable retract in AFM method

10. Alternative Models

• Sneddon model: for conical indenters: F = (2/pi) E* tan(alpha) delta^2
• JKR model: includes adhesion in contact mechanics
• Ting's model: for viscoelastic relaxation

def sneddon_cone(indentation, E_star, alpha_deg=18):
    alpha = np.radians(alpha_deg)
    return (2 / np.pi) * E_star * np.tan(alpha) * np.power(indentation, 2)

References

• Cappella, B. & Dietler, G. (1999). Force-distance curves by AFM. Surface Science Reports, 34(1-3), 1-104.
• Hertz, H. (1882). On the contact of elastic solids. J. Reine Angew. Math., 92, 156-171.
• Sneddon, I.N. (1965). The relation between load and penetration. Int. J. Eng. Sci., 3(1), 47-57.