Dynamic Light Scattering measuring particle size from the intensityspectrum of scattered light Biophysical Measurement Physics 173 UCSD Spring 2 0 0 2 Bernhard Englitz Table of Contents 1 Introduction 2 2 Methods 2 1 Theory 2 2 Experiment 2 3 Data Analysis 2 2 3 4 3 Results 3 1 Control Measurements 3 2 Latex Bead Measurements 3 3 Albumine Measurements 3 4 Deconvolution Correction 3 5 Generalized Fitting 8 8 9 10 10 11 4 Conclusions 12 References 12 Practical Hints 13 List of Figures 1 scattering principle 2 experimental setup 3 parameter dependence of S f 4 amplifier impulse response functions time domain 5 amplifier impulse response functions frequency domain 6 powerspectra of the control media 7 powerspectra of the latex beads 8 powerspectrum of albumine 9 deconvolved powerspectra 10 generalized function fit for 0 05 m 4 4 5 6 7 8 9 10 11 12 1 Introduction Already in the 1960s it had been recognized that the innocent seeming assumption of a brownian process as the underlying process for a solution of scattering particles can be used to estimate the size of the scattering particles to an impressively high degree of accuracy 2 1 The theoretical grounds have been worked out for both the case of isotropic and the nonisotropic scattering targets and thus the inexpensive experimental setup seems to be well suited for a whole range of measurement tasks where homogenous solutions o f particles in the range of a few to hundreds of nanometers need to be characterized In the present study we merely reproduce the known results for latex spheres of known size and the protein albumine and attempt to correct our results for changes introduced by the measurement apparatus by deconvolving with the measured transfer function 2 Methods 2 1 Theory The following introduction to the theory underlying this experiment is superficial in the sense that it only highlights the main ideas and assumptions but refers the reader to the complete and very understandable treatment in the original experimental works 1 2 and the further theoretical treatises referenced therein Based on the assumption that particles in aqueous solution undergo diffusive motion as described by a threedimensional brownian motion the powerspectrum of the intensity o f the light scattered by this solution can be linked to the probability density function pdf o f the brownian process given as P r t 0 0 4pDt 3 2 exp r 2 4 Dt 1 Since this function only depends on D the diffusion constant of the system this allows to obtain a value for D if the pdf can be measured Luckily the diameter of the scattering particles can simply be computed from D and other known quantities via D k BT 6pha 2 This link between the pdf and the powerspectrum is a consequence of the translation o f relative motion of the scattering particles into phase differences of the scattered light see Fig 1 Thus spatial correlations are translated into phasecorrelations which is manifested in the usage of the Wiener Khintchine Theorem relating the powerspectrum to the autocorrelation of a process Yet phasecorrelations lead to fluctuations in the intensity o f the focussed light at a detector and thus the measured quantity Analyzing the intensity powerspectrum we can then compare the experimentally measured to the theoretically expected spectrum namely a lorentzian line S f see Eq For the following discussion it is helpful to define the roll off point of the powerspectrum which is given by the intersection of a linear constant fit to the lowfrequency portion of S f and the linear fit to the high frequency decrease for illustration see Fig 3c This definition is important since the quality of the fit depends mainly on how well the two fits can be tied and thus the roll off point can be localized also compare Fig 3a and b Consequently the minimally measurable diameter of the scattering particles corresponds to the roll off point at the highest frequency which can be well defined As we will see later this is further complicated by possibly different spectral shapes for different scattering particles as well as the noise floor and by the transfer function intrinsic to the measurement system As often in Physics theory and experimentinteract beautifully where on the one side an extended theoretical derivation leads to a measurable prediction which on the other hand Figure 1 Figure 2 2 2 Experiment As in almost every scattering experiment a coherent light source HeNe Laser l 632nm provides the light which is then passed through a converging lens onto the scattering particles Fig 2 At a variable angle q another converging lens collects the light scattered around the q and focusses it on the collecting tube of a Photo Multiplier Tube PMT The PMT is powered by a powersupply which controls the amplification of its output signal During different experiments either an aperture or no aperture in front of the PMT was used which however only amounted to scaling effects in intensity a consequence of the obstruction of light in cases in which the aperture is present Most experiments were conducted without an aperture since it is hard to position the aperture directly in front o f the actual tube of the PMT and still have the tube in the focal plane of the second converging lens For determination of the response function of the system a light pulse see Data Analysis for reasoning was sent through the measurement apparatus Using a third hand a red LED was positioned in the focal plane of the converging lens in front of the PMT Four variables determine the amplification and filter characteristics of the measurement apparatus composed of the PMT and the amplifier The following list provides the location and range of the parameters i amplifier gain g std value e9 range e4 e11 ii amplifier suppression std value e 7A range e 10 e 3 A iii amplifier rise time trise std value 0 01ms 0 01 0 03 0 1 0 3 300 ms iv PMT Voltage Supply std value 500V 0 2500 V The actual parameter value for the rise time used in the recordings are indicated in the figures which display the results from the respective recordings All shown recording were done at the indicated standard values unless indicated otherwise Th tt i di ll th d f t t h d d f ti l hi h Figure 3 rinsed carefully with the solvent before the particle containing solution was added and finally sealed with regular scotch tape We did not find differing results if the experiment were conducted directly after or days after the preparation of the solution In this