Light scattering method Introduction: The illumination of dust particles is an illustration of light scattering, not of reflection. Reflection is the deviation of incident light through one particular angle such that the angle of incidence is equal to the angle of reflection. Scattering is the radiation of light in all directions. Thus, in observing the moonbeam, the dust particle directs a beam towards you regardless of your angle in relation to the scattering particle. Light scattering is a well established technique to investigate properties of particles in solutions. Information such as size, molecular weight, diffusion and interaction strength are obtained. This method used to determine weight average molecular weight (Mw). This technique is based on the optical heterogeneity of polymer solutions and was developed by Nobel laureate Peter Debye in 1944.

The energy scattered per second depends upon size of the scattering object shape of scattering particle (either small or large particle) scattering angle. Scattering of light is all about us….the fact that the sky above us appears blue, the clouds white and the sunset is shades of red and oranges is a consequence of the scattering of light from air molecules, water droplets, and dust particles. Other sources of energies, such as x-rays and laser beams, may be used in place of visible light sources. Modern instrument use lasers as the radiation source because they provide a monochromatic, intense and well defined light source. Principle: The basic principle is that a laser beam impinges on a sample and the scattered intensity is probed at a certain angle θ by a detector. The sample is illuminated by a laser beam and the fluctuations of the scattered light are detected at a known scattering angle θ by a fast photon detector.

Rayleigh Theory: For small molecules, at low concentrarions this scattering is described in terms of Rayleigh ratio. In 1871, Rayleigh showed when light passed through gases induced oscillatory dipoles were developed which shows the amount (intensity) of scattered light ( Ʈ ) or turbidity was inversely proportional to the fourth power of the wavelength of light. This investigation was extended to liquids by Einstein and Smoluchowski in These radiations reradiate the light energy producing turbidity, i.e., Tyndall effect. Equation (1) given below

H= and = k ´ n= index of refraction of solvent n = index of refraction of solution c = polymer concentration B, С = virial constant (related to interaction of solvent) P = partical scattering factor N = Avogadro’s number The expression dn/dc is the specific refractive increment and is determined by taking the slope of the refractive index readings as a function of polymer concentration. For small particles: In the determination of w, one measure the intensity of scattered light at different concentrations and at different angles (. For polymer solutions containing polymers of moderate to low molecular weight P is 1 and equation can be written as ;

= x When Н c/ (kc/R) is plotted against concentration, the intercept of extrapolated line is reciprocal of and the slope against the virial constant B. For large particles: As the size of scattering particle, the individual polymer chain, approaches about one-twentieth the wavelength of incident light scattering interference occurs giving a scattering envelope that is no longer symmetrical.Here the scattering dependence on molecular weight is shown by a relationship given in equation(1).

Working: The light scattered by a polymer solution or dispersion contains information about the static and dynamic properties of the molecules or particles. Static light scattering measures the average scattered intensity of a population of particles in solution by integrating the scattered signal over a period of time. This output is then used to determine particle size and if the system is appropriately calibrated, molecular weight of the particles.

Dynamic light scattering monitors the fluctuations of the scattered photons over very short time intervals from the sample. This output is a direct indication of the Brownian movement of the particles and their diffusion characteristics which can then be used to determine particle size. Dynamic light scattering (DLS) is similar in principle to typical light scattering. When several particles are hit by oncoming laser light, a spotted pattern appears with the spots originating from the interference between the scattered light from each particle giving a collection dark (from destructive interference) and light (from constructive interference) spots. This pattern of spots varies with time because of the Brownian motion of the individual scattering particles. The rate of change in the pattern of spots is dependent on a number of features including particle size. The larger the particle, the slower the Brownian motion, and consequently, the slower the change in the pattern. The measurement of these intensity fluctuations with time allows the calculation of the translational diffusion constant of the scattering particles.

The technique for making these measurements is given several names including DLS (difference in the scattered light with time), PCS (mathematical technique employed to analyze light scattering data) and QELS (no energy is lost between collision between the particle and the light photon) (1). An attenuator is an electronic dice that reduces the power of a signal without appreciably distorting its waveform.

dynamic light scattering (DLS): What can be measured by dynamic light scattering? 1. Range: 1 nm – 1000 nm Static light scattering (SLS): What can be measured by static light scattering? 1. Molecular weight. Range: 1000 g/mol – 109 g/mol 2. Size. Range: 10 nm – 1000 nm Measuring Polymer Molecular Size and Weight: Even thought absolute molecular weight measurements are obtained using static light scattering, molecular weight can sometimes be inferred from DLS measurements by exploiting the Mark-Houwinck relationship that defines the intrinsic viscosity of a polymer solution in terms of the molecular weight of the solute(2). This turns out to be closely related to the translational diffusion coefficient (D) of the molecules in the following equation:

D = k Where k is a constant for a particular polymer in a solvent, M is the molecular weight of the solute and á is a conformational parameter describing the compactness of the molecule in solution. A measured value for á of 1 suggests that the solute molecules are rigid rods; a value of 0.5 to 0.67 is obtained with random coils and a value of 0.3 occurs for spheres(1). Therefore, it is possible to obtain information regarding the conformation of a solute molecule in a particular solvent from DLS measurements. Taking logs of the equation D = kM, the following expression is obtained; Log D = Log k - α Log M Therefore a graph of Log D versus Log M will give a plot whose slope is á. The translational diffusion coefficient, D, is related to particle size through the Stoke-Einstein equation (2). Therefore, a plot of Log particle size versus Log M also allows determination of the valu e of á.