Functional Dependence of Viscosity on Molecular Weight of Polyethylene Glycol Mixtures

Background

The purpose of this project was to quantify the relationship between molecular weight and dynamic viscosity in polyethylene glycol systems, an important factor in fluid transport, heat exchange, and industrial processing. Since viscosity governs flow behavior and energy requirements in fluid systems, understanding its correlation with molecular structure is essential for optimizing chemical process design and materials formulation.

Action

Our experiment combined controlled laboratory testing, data modeling, and statistical analysis to determine the viscosity behavior of pure and mixed PEG samples:

Experimental Setup:

Utilized a Cannon-Fenske viscometer submerged in a temperature-controlled heated water bath to measure flow times for PEG samples of varying molecular weights.

Ensured precise temperature control and calibration using the manufacturer’s viscometer manual and calibration sheets to maintain repeatable measurements.

Experimental Procedure:

Measured dynamic viscosities for pure PEG samples and binary mixtures of known molecular weights.

Determined molar ratios for a two-component mixture and compared the measured viscosity to preliminary theoretical predictions.

Recorded density data for each mixture to support accurate viscosity conversion and analysis.

Mathematical Modeling:

Applied fluid mechanics and polymer solution theory to establish a model correlating viscosity with molecular weight.

Performed linear regression on experimental data to determine empirical constants (“a” and “K”) in the relationship:

𝜇 = 𝐾𝑀^𝑎

where μ = viscosity, M = molecular weight, K and a = regression constants.

Conducted statistical validation to calculate 95% confidence intervals, standard deviations, and R² = 0.939, indicating a strong linear correlation between molecular weight and dynamic viscosity.

Data Analysis:

Compared preliminary theoretical calculations with experimental results to assess model accuracy.

Analyzed deviations and potential sources of error (temperature fluctuations, calibration drift, and mixing inconsistencies).

Result

The results confirmed a direct and approximately linear relationship between viscosity and molecular weight for polyethylene glycol mixtures. The regression analysis supported the empirical model, with an R² value of 0.939, demonstrating strong predictive reliability.

This outcome validated the theoretical assumption that increasing molecular weight increases fluid resistance to flow, consistent with established polymer behavior.

Through this project, I developed proficiency in viscometry operation, polymer fluid analysis, data regression, and statistical model validation, enhancing my ability to translate experimental data into quantitative engineering insights relevant to chemical process design and materials engineering.