Graphite Resistivity and Temperature Science Project

ISEF Category: Physics and Astronomy

Subcategory: Condensed Matter and Materials  ·  Difficulty: Intermediate  ·  Setup: School Lab  ·  Time: 1 to 2 Months

The Hook

A pencil line can act like a tiny resistor. That means you can turn a school supply into a real materials experiment. If you measure it the right way, you can test how charge moves through graphite and clay as temperature changes.

What Is It?

This project studies how well pencil graphite carries current. Pencil “lead” is not lead at all. It is a graphite and clay composite. Graphite gives electrons paths to move through, while clay blocks and scatters them. Think of it like cars driving through a city with both open roads and traffic jams.

A four-point probe helps you measure resistance more accurately than a simple two-wire setup. In a two-wire setup, the meter leads add their own resistance. A four-point probe separates the current path from the voltage-sensing path, so you measure the sample more cleanly. When you vary temperature, you can see whether the graphite line conducts better or worse, and whether its behavior matches a hopping model such as Mott variable-range hopping, where electrons move by jumping between localized spots instead of gliding freely.

Why This Is a Good Topic

This is a strong science fair topic because you can build the setup yourself, change one variable at a time, and get real numbers you can plot and model. It connects to electronics, materials science, and how conductive inks, coatings, and carbon films behave in the real world. You can learn measurement design, calibration, and basic transport analysis without needing a university lab.

Research Questions

• How does graphite line thickness affect sheet resistance measured with a four-point probe?
• What is the effect of pencil hardness grade on the temperature dependence of resistivity?
• Does the resistivity of graphite-clay lines follow a linear trend with temperature over a limited range?
• To what extent does substrate roughness change the measured resistance of pencil graphite lines?
• Which graphite line width gives the most stable resistance across repeated heating and cooling cycles?
• How does repeated drawing over the same line change the apparent carrier-transport behavior?

Basic Materials

• Wooden pencils of several hardness grades.
• Plain white printer paper or cardstock.
• Smooth index cards or acetate sheets for comparison substrates.
• Ruler or digital caliper.
• Masking tape or painter’s tape.
• Digital kitchen scale for checking sample mass if needed.
• Arduino board.
• Low-cost constant-current source parts or resistor network for current control.
• Keithley-clone digital multimeter or similar high-resolution DMM.
• Breadboard and jumper wires.
• Alligator clip leads.
• Thermometer or temperature probe.
• Warm plate, heat mat, or school hot plate with temperature control.
• Fan or cool pack for returning samples toward room temperature.
• Notebook or spreadsheet for data recording.

Advanced Materials

• University-grade probe station or custom four-point probe fixture.
• Source meter or precision current source.
• High-resolution digital multimeter.
• Temperature-controlled stage or environmental chamber.
• Microscope or stereo microscope for checking line texture and width.
• Surface profilometer or optical comparator for thickness and roughness checks.
• Four-terminal sample mounts.
• Calibrated thermocouple or platinum resistance thermometer.
• Data acquisition interface.
• Current-limiting resistors and low-noise wiring.
• Reference resistors for instrument checks.
• Conductive silver paint for contact studies if needed.

Software & Tools

• Google Sheets: Organizes resistance data, temperature data, and graph fits in one place.
• Python: Fits linear and non-linear transport models and compares residuals.
• ImageJ: Measures line width and texture from photos of the drawn graphite tracks.
• NIH ImageJ macro tools: Helps batch-process repeated images so line geometry stays consistent.
• GeoGebra: Makes quick plots and trend checks before deeper analysis.

Experiment Steps

1. Define the one transport question you will test first, such as how temperature changes resistance for a fixed graphite line geometry.
2. Design the probe geometry so current and voltage paths stay separated and your sample shape stays consistent.
3. Plan a calibration check for your current source and DMM before you trust any graphite data.
4. Choose the sample variables you will hold constant, such as paper type, pencil grade, stroke count, and line width.
5. Build a data table that links each sample to its geometry, temperature, and measured voltage drop.
6. Decide ahead of time which model you will test, such as a simple thermal trend versus a hopping transport fit.

Common Pitfalls

• Using two-wire resistance instead of a four-point measurement, which folds lead resistance into the sample data.
• Letting line width vary from sample to sample, which makes resistance changes impossible to separate from geometry effects.
• Measuring on paper that warps with heat, which changes contact quality and ruins repeatability.
• Pushing too much current through the graphite line, which can warm the sample and fake a temperature effect.
• Fitting a hopping model without checking whether the sample actually shows the needed curved trend on a log plot.

What Makes This Competitive

A stronger project does more than report that resistance changes with temperature. You can push it by comparing several pencil grades, several substrates, or several line geometries, then testing which factors truly control transport. Good entries also include clean calibration, repeated trials, and a model comparison that asks which fit explains the data best, not just which line looks nicest. If you connect your results to a real materials question, such as printable carbon traces or flexible sensors, the project feels much more original.

Project Variations

• Compare graphite lines on paper, cardstock, and plastic film to see how substrate choice changes transport.
• Test several pencil hardness grades to see how graphite-to-clay ratio changes temperature dependence.
• Add a humidity comparison to see whether absorbed water shifts the apparent hopping behavior.

Learn More

• MIT OpenCourseWare, Solid-State Chemistry and Physics materials: Search MIT OpenCourseWare for courses on solid-state physics and transport in materials.
• NIST Materials Data: Use NIST to look up reference data, measurement ideas, and materials property terminology.
• NASA NTRS: Search the NASA Technical Reports Server for papers on carbon-based films, sensors, and thin-film resistivity.
• PubMed: Search review articles on carbon nanomaterials, graphite conduction, and hopping transport in disordered systems.
• Physical Review B: Search the journal for papers on variable-range hopping, disordered conductors, and carbon-based thin films.