Problem #1 Biocompatibility.

Halperin, Polymer brushes that resist adsorption of model proteins: design parameters. Langmuir, 1999, 15, 2525- 2533.

a) Please explain the physical meanings of the term defined in Halperin, Ueff, Ubrush, Ubare, U*, Uin, and Uout.

b) Please identify whether the brush formed by the following polymers will provide the potential profile as suggested in curve (a) of Fig. 1 in vivo. Explain your reasons. (i) poly(ethylene oxide) (PEO) (ii) poly(methyl methacrylate) (PMMA) (iii) chondroitin-sulfate glycosaminoglycan (CS-GAG, from cartilage) (iv) poly(2-hydroxyethyl methacrylate) (pHEMA)

c) For a polymer brush with equilibrium height L0 = 8 nm, if a protein with radius R ~ 20 nm is adsorbing to the brush, which mechanism in Halperin determines the energy barrier for the primary adsorption? What are the physical origins for the energy barrier? How does the magnitude compare to the other mechanism for primary adsorption?

d) Plot the Ubrush, Ubare and Ueff in the units of kBT as a function distance to the substrate L up to 30 nm, assuming the monomer size for the polymer brush is a = 1 nm, N = 20 monomers per polymer chain, at a grafting density -1 = 0.25 nm-2, and Hamaker constant A = 0.5 10-19 J. Explain your choice of equations used from Halperin.

Halperin, Polymer brushes that resist adsorption of model proteins: design parameters. Langmuir, 1999, 15, 25252533. a) Please explain the physical meanings of the term defined in Halperin, Ueff,Ubrush,Ubare,U,Uin, and Uout.. b) Please identify whether the brush formed by the following polymers will provide the potential profile as suggested in curve (a) of Fig. 1 in vivo. Explain your reasons. (i) poly(ethylene oxide) (PEO) (ii) poly(methyl methacrylate) (PMMA) (iii) chondroitin-sulfate glycosaminoglycan (CS-GAG, from cartilage) (iv) poly(2-hydroxyethyl methacrylate) (pHEMA) c) For a polymer brush with equilibrium height L0=8nm, if a protein with radius R20nm is adsorbing to the brush, which mechanism in Halperin determines the energy barrier for the primary adsorption? What are the physical origins for the energy barrier? How does the magnitude compare to the other mechanism for primary adsorption? d) Plot the Ubrush,Ubare and Ueff in the units of kBT as a function distance to the substrate L up to 30nm, assuming the monomer size for the polymer brush is a=1nm,N=20 monomers per polymer chain, at a grafting density 1 =0.25nm2, and Hamaker constant A=0.51019J. Explain your choice of equations used from Halperin