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One problem we address in dynamic light scattering of samples of high extinction coefficient is the heating effects.  Light absorption causes localized heating and changes the scattering geometry from cylindrical to conical.  The temperature increase and degree of coning is influenced by laser power and by concentration of the absorbing species.  A study of the temperature profile of the scattering cell containing light absorbing solution shows a thermal gradient along the beam path and perpendicularly above the volume illuminated by the laser beam.  The apparent diffusion coefficient (D_app) of hard silica spheres and polystyrene dissolved in a light absorbing medium were determined using the approach developed by Seery and Sehgal. The apparent diffusion coefficient, D_app, of the hard spheres is used to calculate the ratio of temperature to viscosity, T/h, using the Stokes-Einstein equation.  This provides a thermometer from which to obtain the apparent temperature of the scattering volume illuminated by the laser. Local heating causes a decrease in both the viscosity and density of the heated volume which, in turn, results in convection and thermal diffusion. This phenomenon manifests as a thermal gradient in the sample and is accompanied by a refractive index change due to the decrease in density.  The refractive index gradient along the beam appears as a "lens".  Thermal lensing enhances beam divergence.  The high intensity of light used in laser light scattering and the presence of focusing optics makes these effects crucial even when the scattering solution has a low optical density. Absorption of 10^-3 to 10^-4 parts per centimeter is sufficient to form a thermal lens.^1,2 We have recently measured the temperature profile, the thermal gradient and the coning effect occurring during light scattering experiments where the analyte is a light absorbing solution.  The effect of both dye concentration and laser power on the temperature rise and on the coning angle was studied.  Also, we explored the use of a hard sphere scatterer in a light absorbing medium as a probe in obtaining the apparent temperature of the scattering volume.

Coning Angle.  The degree of coning was evaluated in two ways: from the coning images and from the DLS data.  Digital photographic images were taken of light absorbing solutions under illumination at varying dye concentrations. The first set consisted of solutions of boronal in toluene, the second set had 10 mg/mL PS and boronal in toluene while the third set was composed of 0.3mg/mL coated silica particles, 10 mg/mL PS and boronal in THF.  The solutions were placed in the sample cell holder and illuminated at 500 mW.  These images are depicted in Figure 1.

Local Heating and Thermal Gradient. Solutions of polystyrene and silica spheres, separately and in combination, in NMP, THF and toluene were illuminated with 500mW to 800mW laser beam. These were sufficiently transparent that there was no significant difference in temperature between the sample inside the scattering cell and the decalin bath.  This was true even in regions close to the beam path and even at high laser powers demonstrating that no light was absorbed by these solutions.  

The temperature of the light absorbing solutions of NMP was scanned at varying distances from the beam path.  The closest distance at which temperature can be taken was 0.5 mm from the laser beam, because at the center of the beam the thermometer probe absorbs light. Figure 2 shows the temperature profile of the light absorbing sample (0.10 mg/mL boronal in NMP) 0.5 mm above the laser beam. The temperature is maximum in the region closest to the entry window of the laser beam and decreases to the exit window. The decrease in temperature with the distance from the beam entry window creates a thermal gradient from left to right across the beam path. 

As shown in Figure 2, the temperature of the region that is perpendicularly above the beam decreases with increasing distance from the laser beam, creating a thermal gradient in the upward direction.  The temperature was also observed to be remarkably higher above the beam than along the side of the beam, indicating that heat flow is favored more in the upward direction rather than in lateral direction.  The illuminated region was heated by light absorption resulting in a decrease in density and an increase in buoyancy.   Consequently, the heated volume floats, dissipating heat in the upward direction.  As this volume rises, it cools, creating convective flow within the scattering volume.  Since the sample is continuously illuminated by the laser throughout the duration of the experiment, absorption, heating and convection occur continuously.

These initial measurements are being followed with modeling and further data analysis to provide for efficient use of this approach with light absorbing solutions.

Figure 1. Coning images of the laser beam in the scattering cell for various samples.

Figure 2. Profile of temperature increase inside the scattering cell

1.         Gordon, J. P.; Leite, R. C. C.; Moore, R. S.; Porto, S. P. S.; Whinnery, J. R., Journal of Applied Physics 1964, 36 (1), 3-8.

2.         Kohanzadeh, Y.; Ma, K. W.; Whinnery, J. R.,. Applied Optics 1973, 12 (7), 1584-7.