Light Scattering Biophysics https://www.youtube.com/watch?v=4CtnUETLIFs

Review of EM Wave The electric field must be perpendicular to the wave direction The magnetic field is perpendicular to both of them Recall: E  B is in direction of motion

Exercise Light that is polarized along the z-axis is traveling along the y-axis. Write the equations describing the electric and magnetic fields as a function of position and time.

Exponential Description Why use exponential form Easier for interference

Exercise Two waves described by E1 and E2 have the same polarization and amplitude and differ only by a phase factor, f. Describe their interference when f = 0,p, 2p Consider a wave . Write the electric and magnetic field in exponential form.

Single Particle Rough Treatment Sample - dipole Light Source k0 q The scattering angle, q, is defined w/r transmitted light in the scattering plane. The scattering plane is defined by the vectors k and k0. P is the polarization which is the total dipole moment/volume. a is the polarizability. Go over description of light in terms of 3d exponential function (board).

Example Circularly polarized light (where the y and z components are 90 degrees out of phase) is travelling in the x-direction and is incident on a particle with a polarizability given by . (a) Write an electric field vector for the incident light. (b) Calculate .

Single Particle Rough Treatment Bottom line Light can be described by electric field For Horizontally polarized light intensity the |E|2 given by For vertically polarized light For unpolarized light Why is there angular dependence for one but not the other? Why does the sky usually appear blue?

Why is sunset red?

Why are Blue Ridge mountains blue? But you asked why our mountains-which are made up of many colors-appear blue. The blue-sky principle still holds: when you view a dark, solid object, such as a mountain, from a distance, the scattered light makes it appear blue. Yet the distinct blue haze of the Appalachians can also be attributed to the thick vegetation that blankets the slopes. Tiny hydrocarbon particles, including terpenes from pine trees, are released by plants. The particles react with natural ozone molecules to produce a hazy effect over the mountains. Again, the small size of the particles means that the light scatters blue. The Blue Ridge is not unique in this respect. This effect occurs in other mountain ranges around the world, including the Blue Mountains in Australia. http://www.blueridgeoutdoors.com/magazine/august-2004/why-is-the-blue-ridge-blue/

Dilute gas of small particles Use Classius-Mosotti relation to express polarizability a in terms of index of refraction, n. n2 – 1 = 4pNa, Scattered light per unit volume goes as molecular weight

Macromolecules in solution n2 – 1  n2 – no2, where no is the index of refraction of the medium. Rq = KcM, with Rq = Rayleigh ratio = This is true for dilute solutions

Examples of plots Dilute smaller molecules Get Molecular weight

Example You are doing light scattering with unpolarized light with l = 633 nm on a dlute solution of deoxygenated normal adult hemoglobin (tetramers have diameter of 5.5 nm). Where is the scattering highest and lowest (q = 0, 90, 180, other?) Where is Rq lowest? You oxygenate and notice Rq decreases. Why?

More concentrated solutions of small molecules With small interaction get Kc/ Rq = 1/M + 2Bc where B = 2nd virial coefficient – fudge factor. Like ideal vs real gas. As sample gets more concentrated have interactions between molecules Practically, do scattering at different concentrations and see if get different results for M.

Large macromolecules Mostly Forward Scattering Get molecular weight and size Zimm plot http://www.bic.com/pict/ZP.png

Zimm Plotting When q = 0 When c = 0 Can’t really do at q = 0 or c = 0 Vary angle at constant c and extrapolate to q = 0. Do at different c and get line for q = 0 Vary c and constant angle and extrapolate to c = 0. Do at different angles and get line for c = 0

Nephelometer

Raw Data Why plot as Log(sin(angle)? Why buffer give more noise? What do you notice about angular dependence?

Data from Chen et al BJ 2004