Biological Physics: Energy, Information, Life
7.3. Beyond equilibrium: Osmotic flow[[Student version, January 17, 2003]] 225 bonuswewill also learn about nonequilibrium flow, ...
226 Chapter 7. Entropic forces at work[[Student version, January 17, 2003]] r F(r)dxdydz p(z)dxdz p(z)dxdz p(z−^12 dz)dxdy p(z+^ ...
7.3. Beyond equilibrium: Osmotic flow[[Student version, January 17, 2003]] 227 c=0 c=c 0 U (z ) p (z ) p (z ) z z a z z ∆p=c 0 k ...
228 Chapter 7. Entropic forces at work[[Student version, January 17, 2003]] the membrane is obliged to supply a kick to the righ ...
7.4. A repulsive interlude[[Student version, January 17, 2003]] 229 have pure water on both sides of the membrane, there will be ...
230 Chapter 7. Entropic forces at work[[Student version, January 17, 2003]] the electrostatic potential energy of such a shell ( ...
7.4. A repulsive interlude[[Student version, January 17, 2003]] 231 off with distance at all! In short, Even though the electros ...
232 Chapter 7. Entropic forces at work[[Student version, January 17, 2003]] positive layer negative surface E(x 1 ) E(x 2 ) −σqd ...
7.4. A repulsive interlude[[Student version, January 17, 2003]] 233 a σq bc x x 2 D Figure 7.8:(Schematics.) (a)Counterion clo ...
234 Chapter 7. Entropic forces at work[[Student version, January 17, 2003]] solve Poisson equation Boltzmann distribution charge ...
7.4. A repulsive interlude[[Student version, January 17, 2003]] 235 Your Turn 7e Now combine the Poisson equation with the Boltz ...
236 Chapter 7. Entropic forces at work[[Student version, January 17, 2003]] This expression has the feature thatV(0) = 0, so we ...
7.4. A repulsive interlude[[Student version, January 17, 2003]] 237 free energy≈ 4 π(10μm)^2 ×(0. 7 /nm^2 )kBTr≈ 109 kBT. It’s a ...
238 Chapter 7. Entropic forces at work[[Student version, January 17, 2003]] tan(Dβ), largeD smallD 2 πBσq εβ tan(Dβ), β 1 β 2 β ...
7.4. A repulsive interlude[[Student version, January 17, 2003]] 239 104 105 106 107 0 2 4 6 8 10 separation, nm pressure, Pa Fig ...
240 Chapter 7. Entropic forces at work[[Student version, January 17, 2003]] shape can be very strong.^9 7.5 Special properties o ...
7.5. Special properties of water[[Student version, January 17, 2003]] 241 H a H H 0.27 nm O O Figure 7.12:(Sketch; metaphor.) (a ...
242 Chapter 7. Entropic forces at work[[Student version, January 17, 2003]] awater molecule. Get a few dozen friends to assume t ...
7.5. Special properties of water[[Student version, January 17, 2003]] 243 asingle H-bond in water is generally only about 1–2kBT ...
244 Chapter 7. Entropic forces at work[[Student version, January 17, 2003]] Figure 7.13:(Sketch.) Clathrate cage of H-bonded wat ...
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