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- (21 pts) CoCrMo alloys form a passivating oxide on their surface that renders them useful for orthopaedic implants. Such implants remain susceptible, however, to fretting corrosion, which occurs as a consequence of repetitive rubbing of the implant against a second hard surface (e.g., another implant component or bone). To study fretting corrosion, Contu et al. ( Corrosion Sci. 2005 , 47 , 1863) employed a tribo-electrochemical cell, illustrated below, employing a CoCrMo alloy (66:28:6 wt ratio Co:Cr:Mo) as the working electrode, Pt wire as the counter electrode and a saturated calomel electrode (SCE) as the reference electrode (SCE is +0.231V on the standard hydrogen electrode (SHE) scale.) A ceramic tube in contact with the sample was rotated periodically to create a rubbing action on the surface. Dissolved oxygen was removed from electrolyte solutions by bubbling with argon gas for 24 h prior to the experiments. The figure below shows data for the open circuit potential (OCP) measured before, during and after 3 rotations of the ceramic tube in buffered solutions at pH 4 (solid) and pH 7 (dashed).
Images removed for copyright reasons.
See Fig. 1 and Fig. 2(a) in Contu, F., B. Elsener, and H. Böhni. "Corrosion Behaviour of CoCrMo Implant Alloy During Fretting in Bovine Serum." Corrosion Science 47 (2005): 1863-1875.
a) (4 pts) Why does the OCP first drop rapidly then rise rapidly and plateau following each abrasion of the alloy surface by the ceramic tube?
Stresses on the oxide layer at the alloy surface induced by rubbing cause breaks in the oxide film that expose pure metal to the electrolyte solution, increasing the magnitude of the measured OCP. Immediately upon exposure, the bare metal begins to react with water to reform an oxide layer at the surface. With increasing time, the oxide growth becomes limited by ion diffusion through the oxide and the potential plataeaus.
b) (6 pts) Write the expected anodic half-reaction(s) for this alloy at pH 4. Based on this reaction and the Nernst equation, provide an expression for the measured electrical potential across the rubbed alloy surface.
Expected anodic reactions include:
Co → Co2+^ + 2e
Cr → Cr2+^ + 2e
The Nernst equation for metal oxidation is
[ M^ n +^ ] E E^0 +
RT
= ln nF [ M ]
Noting that the SCE electrode is +0.231V from the standard hydrogen electrode
(SHE) scale, the standard electrochemical potentials ∆ E^0 for Co and Cr can be
obtained from Table 5 on pg. 432. The atomic fraction of Co and Cr are 65 and 31%, calculated from the weight fractions provided.
The resulting expressions for the measured potentials from these reactions would be:
E V ( ) = −0.511+
log [ Co^2 +^ ] = −0.506 + 0.0295 log[ Co^2 +^ ] 2 [ Co ]
E V ( ) = −0.961+ 0.0591^ log [ Cr^^2 +^ ]
2 + ]
= −0.946 + 0.0295 log[ Cr 2 [ Cr ]
c) (4 pts) What is the expected cathodic half reaction at pH 4 and pH 7 for this experiment?
Since dissolved oxygen has been removed from the electrolyte solution, the cathodic half-reactions will involve other species:
Protein molecules in serum would be expected to adsorb on the metal surface, impeding the kinetics of the cathodic reaction. This would be a favorable effect in vivo as the reduced current means a reduced corrosion rate of the alloy.
- (19 pts) Catalase is an enzyme (mol. wt.: 247kDa, diameter: 10.5 nm) found in liver cells that catalyses the conversion of hydrogen peroxide to water and oxygen. Its catalytic activity is of interest for biosensor applications. As an approach for fractionating catalase from biological solutions, Jia and coworkers ( Int. J. of Biol. Macromol. 2005 , 37 , 42) prepared chitosan microspheres coated with a covalently attached dye, Cibacron Blue F3GA, which exhibits strong binding to catalase. The figure below shows an SEM image of the chitosan particles. The wet density of the spheres was found to be 1.328 g/mL. Adsorption studies were performed to determine the amount of catalase adsorbed to the particles as a function of solution concentration. An adsorption isotherm for pH 7 is shown below.
Images removed for copyright reasons. See Fig. 1 and 4 in Shentu, Jingling, Jianmin Wu, Weihua Song, and Zhishen Jia. "Chitosan Microspheres as Immobilized Dye Affinity Support for Catalase Adsorption." International
Journal of Biological Macromolecules 37 (2005): 42-46.
a) (5pts) Assuming a Langmuir model, determine the affinity constant Ka and the maximum surface coverage Γmax for CAT adsorption on the dye-linked chitosan beads.
[CAT] (mg/mL) 1/[CAT] (mL/mg) Γ (mg/g) 1/Γ (g/mg) 0.03 33. 2.5 0. 0.13 7.7 7 0. 0.53 1.9 17.5 0. 1.13 0.89 23.5 0. 1.80 0.56 24 0. 2.50 0.40 24.5 0.
Noting that ν = Γ/Γ max , the Langmuir equation can be expressed as:
1 1 1 = + Γ [ P K ] (^) a Γ (^) max Γmax
Performing linear regression on the data gives a best-fit line of:
1// Γ = 0.011/[CAT] + 0.
from which we obtain Γ max = 25.6 mg/g and K (^) a = 3.55 mL/mg
1 /Γ
(
g/mg)
0 0 5 10 15 20 25 30 35 1/[CAT] (mL/mg)
b) (6 pts) From the obtained value for Γmax , calculate the effective area per protein, stating any assumptions you make.
The effective area per protein can be computed from:
M (^) protein Aeff = N (^) Av Γmax
e) (2 pts) The data below shows the amount of adsorbed CAT as a function of ionic strength of the solution (increasing NaCl content). Explain why a decrease in adsorption is observed with increasing salt content in solution.
Images removed for copyright reasons. See Fig. 3 in Shentu, Jingling, Jianmin Wu, Weihua Song, and Zhishen Jia. "Chitosan Microspheres as Immobilized Dye Affinity Support for Catalase Adsorption." International
Journal of Biological Macromolecules 37 (2005): 42-46.
This data suggests that the adsorption of CAT to Cibacron Blue F3GA is predominantly electrostatic in nature. As the ionic strength increases, charge shielding leads to decreased adsorption.
- (10 pts) Aliphatic polycarbonates have been gaining much attention as degradable polymers, due to biocompatibility or bioresorbability, while aromatic polycarbonates are hardly hydrolysable. Feijin and coworkers have reported in vitro and in vivo degradation of poly(trimethylene carbonate) (PTMC), an aliphatic polycarbonate with a glass transition temperature of Tg = -15C, and found interesting aspects of its degradation ( Biomaterials , 2006 , 27 , 1741).
a) (3 pts) PTMC is synthesized by ring-opening polymerization of 1,3-dioxan-2-one rather than by polycondensation of carbonic acid mono-(3-hydroxy-propyl)ester as shown in the scheme below. Why?
O O
O
O O
O
H O O OH
O
X
Synthetic scheme of PTMC
With polycondensation of the linear monomer, a by-product H 2 O has to be removed at high temperature and under vacuum conditions, and during the polymerization, the entropy of the system decreases. By comparison, ring-opening of the cyclic monomer does not produce by-products and the reaction proceeds under mild conditions. Due to ring-strain, ring-opening is enthalpically favorable and increases available conformations (and therefore entropy). The ∆ G value of most ring- opening polymerizations is negative.
b) (2 pts) Various PTMCs were implanted in the femur and tibia of rabbits. Mass losses and molecular weight (MW) changes were monitored as a function of time. Here, x of PTMCx stands for MW (kDa) of TMC. As can be seen in Figs 1 and 2, in the initial degradation stage, the mass of the polymeric materials decreased with time; however, MW values did not change significantly. Explain what happened.
Image removed for copyright reasons.
See Fig. 1 and 2 in Zhang, Zheng, Roel Kuijer, Sjoerd K. Bulstra, Dirk W. Grijpma, and
Jan Feijen. "The In vivo and In vitro Degradation Behavior of Poly(trimethylene carbonate)." Biomaterials 27 (2006): 1741-1748.
The in vivo degradation of PTMC proceeded by enzymatic hydrolysis. In the initial degradation stage, surface erosion took place, and the polymer was hydrolyzed from the surface by enzyme(s), while the bulk polymer stayed intact. Thus, molecular weights did not change much during that period.
In the in vitro and in vivo experiments, enzyme(s) played an essential role in PTMC degradation. Lipases have hydrophobic domain(s) and will adsorb to a hydrophobic surface. In the case of low MW PTMC, the more hydrophilic surface suppressed the enzyme attack, which resulted in a slower degradation.
