📄 chemistry

Determining the Molecular Weight of Polystyrene Through Ellipsometry of Spin-Cast Thin Polymer Films: A Multi-Technique Structural and Surface-Chemical Characterization Study

This study validates spin-cast ellipsometry as an accurate, low-cost method for determining the molecular weight of atactic polystyrene by correlating film thickness with solution concentration, while further confirming the polymer's structural and surface properties through complementary DSC, FTIR, and UV/ozone surface treatment analyses.

Original authors: Alexa Q. Xiang, Alessandro Verona, Sahil Vora, Alina Wang, Andrew Wang, Camilie Wang, Lucas Wang, William Wang, Max Weiner, Eric Xie, Brian Xiong, Kaylee Xu, Brian Yang

Published 2026-07-13

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Alexa Q. Xiang, Alessandro Verona, Sahil Vora, Alina Wang, Andrew Wang, Camilie Wang, Lucas Wang, William Wang, Max Weiner, Eric Xie, Brian Xiong, Kaylee Xu, Brian Yang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a giant, invisible ball of yarn. It's not just any yarn; it's a long, tangled chain of plastic molecules called polystyrene. If you could stretch this ball out, it might be miles long, but it's all coiled up in a tiny pile. Scientists often need to know exactly how long these chains are (their "molecular weight") because that length changes how the plastic behaves. Usually, figuring this out requires giant, expensive machines that take hours to run.

But a team of high school students from around the world decided to try a different, much simpler trick. They asked: If we spin a drop of plastic soup on a record player, how thick does the dried film get?

The Spinning Top Experiment
The team took a special kind of plastic called atactic polystyrene. They dissolved it in a liquid called toluene to make six different "soups," ranging from very watery (2.61 mg/mL) to quite thick (30.43 mg/mL). They put a tiny drop of each soup onto a shiny silicon wafer (a slice of computer chip) and spun it at 2,500 revolutions per minute for 30 seconds.

Think of it like spinning a wet pizza dough. The faster you spin, the more the dough spreads out and thins. But here's the secret: thicker, heavier chains of plastic make the soup more "sticky" (viscous). A stickier soup doesn't spread out as easily, so it leaves behind a thicker film.

By measuring the thickness of these dried films with a laser tool called an ellipsometer, the students found a perfect pattern. When they plotted the data on a graph, the relationship between how much plastic was in the soup and how thick the film became was a straight line on a special log-log scale. It was so consistent that the math fit with 99.2% accuracy.

The Magic Number
Using this pattern, they didn't just measure the films; they worked backward. They calculated that to get a film exactly 300 nanometers thick (about 1/300th the width of a human hair) under their spinning conditions, they would need a specific concentration of plastic. This "magic number" allowed them to calculate the length of the plastic chains.

Their math said the chains were about 266,000 g/mol long. The bottle the plastic came from said it was 280,000 g/mol. That's a difference of only 5%. The students proved that their simple spinning method was accurate enough to guess the length of the invisible yarn chains without needing a supercomputer.

Double-Checking the Identity
Before trusting their spinning results, the team had to make sure they were actually holding pure polystyrene and not a fake or a mix. They ran two other tests:

The Heat Test (DSC): They heated the plastic. Pure polystyrene doesn't melt like ice; it just gets soft and rubbery at a specific temperature called the "glass transition." They saw this happen between 85°C and 115°C, right where pure polystyrene should be. Crucially, they saw no sharp melting spike, which ruled out the idea that the plastic was a mix with crystalline parts. It was purely amorphous (randomly tangled).
The Chemical Fingerprint (FTIR): They shone infrared light through the plastic. The light bounced off specific chemical bonds, creating a unique "fingerprint." They saw the exact peaks for the aromatic rings and carbon chains of polystyrene. They explicitly ruled out the presence of other plastics like ABS or copolymers because the "fingerprint" didn't show the missing chemical signals those other plastics would have.

The Surface Glow-Up
Finally, the team tested what happens if you zap the plastic surface with UV light and ozone (a type of smog). They watched how water droplets sat on the plastic.

Before: The water beaded up like on a waxed car, sitting at an angle of 76°.
After 3 minutes of UV/Ozone: The water flattened out completely, sitting at 20°.

This happened because the UV light punched holes in the surface and stuck polar oxygen groups onto the plastic, making it "wettable." Interestingly, the water didn't just stop getting wetter after a minute; the angle kept dropping faster and faster the longer they zapped it, suggesting the surface was getting more and more reactive the longer they exposed it.

How Sure Are They?
The students didn't just guess; they did a rigorous math check called "error propagation." They tracked every tiny wobble in their measurements—from the scale weighing the plastic (±0.1 mg) to the pipette measuring the liquid (±0.05 mL). They found that while their concentration measurements were incredibly precise (less than 1% error), the biggest source of uncertainty came from the math used to translate the film thickness back into molecular weight.

Even with these uncertainties, their result of 266,000 ± 55,000 g/mol comfortably overlaps with the manufacturer's claim of 280,000 g/mol. They didn't just suggest it might work; they measured it and showed that the method is a reliable, low-cost way to figure out how long polymer chains are, provided you have a clean, pure sample to start with.

Technical Summary: Determining the Molecular Weight of Polystyrene Through Ellipsometry of Spin-Cast Thin Polymer Films

Problem Statement
Traditional methods for determining the molecular weight ( $M_w$ ) of polymers, such as gel permeation chromatography (GPC) and viscometry, often require specialized instrumentation and extended analysis times. For applications involving recycled plastics or rapid quality control in materials recovery, there is a need for accurate, low-cost, and reproducible analytical techniques. This study addresses the challenge of determining the molecular weight of atactic polystyrene (PS) using spin-cast thin-film ellipsometry, a method that leverages the relationship between solution concentration, film thickness, and bulk molecular weight.

Methodology
The study employed a multi-technique workflow to characterize a nominally 280,000 g/mol atactic polystyrene standard (Sigma-Aldrich). The experimental design included:

Substrate Preparation: Single-crystal [100] silicon wafers were cleaved using a diamond-tip scribe to produce rectangular fragments, verified via optical microscopy to ensure the correct crystallographic orientation for consistent surface energy and film adhesion.
Solution Preparation: Six PS-toluene solutions were prepared with concentrations ranging from 2.61 to 30.43 mg/mL.
Spin Coating: Solutions were spin-coated onto the silicon wafers at 2500 rpm for 30 seconds to create uniform thin films.
Thickness Measurement: Film thicknesses were measured in triplicate using a Rudolph Research AutoEL null ellipsometer.
Complementary Characterization:
- Differential Scanning Calorimetry (DSC): Used to determine the glass transition temperature ( $T_g$ ) and confirm the amorphous nature of the sample.
- Fourier-Transform Infrared (FTIR) Spectroscopy: Performed on a compression-molded plate (180°C, 1000 lb, 4 min) to verify chemical identity and rule out copolymer contaminants.
- UV/Ozone Treatment & Contact Angle Goniometry: A PS-coated wafer was exposed to UV/ozone for 0–3 minutes, with water contact angles measured to characterize surface chemical changes.
Data Analysis: A weighted log-log linear regression was performed to relate film thickness ( $t$ ) to solution concentration ( $C$ ). The resulting equation was extrapolated to a reference thickness of 300 nm to determine a critical concentration ( $C_{crit}$ ), which was then converted to molecular weight using a pre-established calibration curve.

Key Results

Molecular Weight Determination: The log-log regression of thickness versus concentration yielded a strong linear fit ( $R^2 = 0.992$ ) described by $\log_{10}(t) = 1.121 \log_{10}(C) + 0.648$ . Extrapolating to the 300 nm reference thickness gave a critical concentration of $42.8 \pm 2.8$ mg/mL. Using the calibration relation $\log_{10}(C_{crit}) = 3.378 - 0.322 \cdot \log_{10}(M_w)$ , the experimental molecular weight was calculated as $(2.66 \pm 0.55) \times 10^5$ g/mol. This result deviates by only 5.0% from the manufacturer's nominal value of $2.80 \times 10^5$ g/mol, falling well within the propagated uncertainty ( $0.24\sigma$ ).
Thermal and Chemical Confirmation: DSC analysis revealed a glass transition between 85–115°C (inflection point $\approx 100$ °C) with no melting endotherm, confirming the sample is amorphous atactic PS. FTIR spectroscopy identified diagnostic peaks for the aromatic and aliphatic backbone (e.g., 2938, 1605, 1455, and 707 cm⁻¹) and the characteristic aromatic overtone comb (1943/1872/1804 cm⁻¹), while ruling out significant nitrile or carbonyl contaminants.
Surface Characterization: UV/ozone treatment induced a monotonic decrease in water contact angle from $76 \pm 4^\circ$ (as-cast) to $20 \pm 2^\circ$ after 3 minutes. The rate of decrease accelerated over time, suggesting a photo-oxidative implantation of polar carbonyl and hydroxyl functionalities that increased surface wettability.
Error Analysis: A comprehensive error propagation analysis identified the covariance of the regression slope and intercept, combined with the amplification factor ( $1/0.322$ ) in the calibration curve, as the dominant sources of uncertainty. Concentration preparation errors were found to be negligible ( $\le 0.63\%$ relative) compared to thickness measurement scatter.

Significance and Claims
The paper claims to validate spin-cast ellipsometry as an accurate, low-cost, and non-destructive method for determining polymer molecular weight. The study demonstrates that this technique, when combined with a calibration curve derived from multi-molecular-weight cohorts, can reproduce manufacturer-reported values within a few percent.

Furthermore, the work presents a complete, integrated characterization workflow. By combining spin-coating/ellipsometry with DSC, FTIR, and contact angle goniometry, the authors show that a single set of benchtop measurements can simultaneously:

Confirm the chemical identity and thermal behavior of the polymer.
Quantify bulk molecular weight with high accuracy.
Characterize surface-chemical responses to oxidative treatments.

The authors position this workflow as particularly valuable for recycling stream quality control and materials recovery, where rapid, inexpensive, and reliable characterization of recovered polystyrene is essential. The study modestly notes that while the method is validated for a standard PS sample, future work could extend its application to recycled or blended samples to further demonstrate its practical utility.

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