# Correcting the Stokes-einstein-sutherland Equation

Open Access

- Area of Honors:
- Bioengineering
- Degree:
- Bachelor of Science
- Document Type:
- Thesis
- Thesis Supervisors:
- Erwin A Vogler, Thesis Supervisor
- Keefe B Manning, Honors Advisor
- William O Hancock, Faculty Reader
- Peter J Butler, Faculty Reader

- Keywords:
- Protein Adsorption
- Stokes-Einstein-Sutherland Equation
- adsorption kinetics
- viscosity ratio

- Abstract:
- Implanting prosthetic devices or any device into the human body results in protein adsorption onto the surface of the material. This adsorption is one of the factors that determines whether or the body rejects the implanted device. Thus understanding protein adsorption kinetics is vital in the field of Biomaterials. When a single protein solution comes into contact with a physical surface, an interphase layer is formed. The interphase layer expands due to the influx of protein molecules and then shrinks due to the efflux of water molecules. Eventually, the interphase comes to steady state with a finite volume. A similar set of events occur when a binary protein solution comes into contact with a surface but it is of interest to know which protein dominates the interaction. In Barnthip and Vogler’s Biomaterials publication Volumetric Interpretation of Protein Adsorption: Protein Adsorption Competition in a Binary Solution, solution depletion and tensiometric experiments were conducted using various combinations of binary solutions. It was found that the selectivity follows a similar trend predicted by taking the diffusion coefficient ratio governed by the Stokes-Einstein-Sutherland (SES) equation. When taking the diffusion coefficient ratio, it was assumed that the viscosity ratio is constant and can therefore be neglected in the SES equation. The resulting equation over predicted the selectivity for low molecular weight ratios and under predicted it for high molecular weight ratios. The goal of the project is to eliminate the discrepancy shown in the Barnthip publication by generating a modified form of the SES equation that is a good fit to the experimental data. To generate an alternative form of the SES equation, an initial assumption was that the viscosity ratio is not constant due to the crowding effect near the interphase. This allows one to generate equations to model the viscosity ratio. Since the ratio is unknown, different models were considered. To analyze the models, the curve fitting feature in SigmaPlot was utilized. Initially, an equation was generated and then coded into SigmaPlot. Then using the dynamic fit feature, the equation was fitted to the selectivity data. The obtained r-squared value and a qualitative inspection of the fit were used to determine the success of the model. The viscosity ratio was modeled using the Einstein, Hatschek, and Cokelet viscosity models. But due to the poor correlation between the predicted selectivity values and the experimental data, these models were not further pursued. The ratio was then predicted using standard functions such as: y = a*x + b and y = a*exp(x), where y is the viscosity ratio and x is the molecular weight ratio. After the exponential form, y = a*x + b was substituted into the SES equation, the resulting equation wasC_j/C_i =ae^(-x) x^(-1/3)+b. This equation yielded an r-squared value of 0.7376 and qualitatively followed the experimental data’s trend. Thus it can be concluded that this equation modifies the SES equation to better fit the data. The new equation can be validated through the use of a cone and plate viscometer to measure the viscosity of the ith and jth protein at different concentrations in the future. Upon validation, the adsorption kinetics of a binary solution consisting of two dissimilar proteins can be predicted.