HISTORICAL SKETCH AND INTRODUCTION

The advent of the laser in the early 1960s provided the long awaited ideal of a narrow-band, high power light source for light-scattering experiments. In 1964, Pecora(1S) showed that the Rayleigh component of the light

scattered by a very dilute macromolecular solution would be broadened

by macromolecular translational diffusion. The mathematical formalism

used by Pecora was partially based on the earlier formalism of Van Hove(19) , developed for neutron scattering. Pecora showed that the broadening of the Rayleigh line might also be used to study rotational motion and molecular flexation.

The frequency shifts involved in the broadening of the Rayleigh line, which have their origins in the Doppler shifts associated with

macromolecular Brownian motion, are so small that conventional

interferometers can not be used to resolve the frequency distribution of

h d . h H (20 ) d . 1 . d

t e scattere l�g t. owever, Forrester ha prev�ous y po�nte out that if a narrow-band light source containing several frequency components was incident upon a photodetector, the frequency components would beat together to provide a photocurrent containing the component difference frequencies. The photocurrent could then be examined by a spectrum analyser. This process afforded a much improved resolution over interferometric methods; as was first demonstrated for a laser light

(21)

source by Javan et al. •

In 1964, Cummins, Knable and Yeh(22) used such an optical mixing technique to observe the spectrum of laser light scattered by dilute solutions of polystyrene latex spheres, and the broadening of the Rayleigh line was found to be in quantitative agreement with theory. Pecora's theories have since been validated for a wide range of very dilute, macromolecular systems.

In the early 1970s the analysis of the photocurrent was shifted from the frequency domain into the time domain. The range in time over which intensity fluctuations in the scattered light were correlated was now

determined by forming the intensity autocorrelation function . The origin of the intensity fluctuations in the light scattered by a solution of macromolecules can be seen by analogy with the scattering of X-rays

by a crystal . An ordered crystalline array scatters X-rays to give a

diffraction pattern with relatively few , but intense , maxima . In contrast , macromolecules in solution are , at any instant , randomly located . The diffraction pattern arising from the scattering of laser light by such a solution thus consists of a superposition of many randomly placed

maxima and minima of varying intensity and size . Since the macromolecules are free to diffuse through the solution , the diffraction pattern of the scattered light will fluctuate with time . A photodetector having a photosensitive area approximately equal to the extent of one diffraction maximum ( a coherence area ) will thus record a randomly fluctuating

light intensity whose time evolution is related to the diffusive displacements of the macromolecules . An estimate of the t imescale of

these fluctuations is the average time (a coherence time of the

scattered light ) taken for a diffraction minimum to replace a maximum at the detection point . A coherence time is of order of the time taken for a macromolecule to diffuse over the distance of one wavelength of light .

The time domain approach by Jakeman and Pike( 23 ) ,

( 24 25 ) made by Koppel ' •

was formalised in an extended series of papers with several important contributions also being The time domain and frequency domain data form

a Fourier-transform pair , and so the information obtained by either analysis method is equivalent . However , in practice time domain analysis is preferred since it offers freedom from errors associated with non-linearities in the analogue spectrum analysis method.

The range of systems to which the laser light scattering technique could

. ( 25 )

be appl1ed was also extended in the early 1970s , when Koppel

provided a theoretical interpretation for data collected from very

. ( 26 ) dilute , polydisperse macromolecular solutions . Brown , Pusey and D1etz

provided experimental confirmation of Koppel's work , and also provided

a more practical method of analysis which could be used to characterise the intensity autocorrelation functions obtained from studies on

polydisperse systems . This development released many interesting biological systems for study since these systems can not usually be prepared to contain a single component . (The reasons for this may

presence of complex equilibria in the solution . ) The analysis method developed for polydisperse solutions can also be used to characterise the intensity autocorrelation functions obtained from concentrated macromolecular solutions( iO ,ii ) .

The remaining contents of this chapter will be devoted to a review of the theoretical basis required for the characterisation of intensity autocorrelation functions of the type encountered in QELS studies on concentrated macromolecular solutions .

2 . 2 THEORY REVIEW

2 . 2 . a . The Laser

This section defines a laser light-scattering experiment , and introduces terminology used in discussion of the experiment .

In Figure 2 . 1 the laser light-scattering experiment is presented schematically . A narrow beam of laser light passes through the macromolecular solution of interest and the �cattered light is

intercepted by a photodetector ( a photomultiplier in the case of this work ) . The position of the photodetector relative to the emergent

unscattered beam defines the angle , e , while the intersection of the incident and scattered beams defines the scattering

Figure 2 . 1 actually defines a scattering experiment ; that is only light scattered by the macromolecular component impinges upon the photodetector . An alternative QELS experiment , the

experiment , colinearly mixes a portion of the unscattered beam with the scattered light at the photodetector .

In the following discussion it will be assumed that the light from a laser can be considered as a single frequency , constant amplitude , plane wave of coherence time long compared with any requirements for phase stability of the incident light . The photodetector is assumed to have a photosensitive area of less than a coherence area . Also , the photodetector is assumed to have a finite quantum efficiency , and it is further assumed that only one anode-pulse is emitted per detected photoevent at the photocathode . These assumptions are met by commercial lasers and photodetectors of the type employed in this thesis ( 27 ) .

Furthermore , QELS experiments are arranged so that the number of detected photoevents is well within the count-rate capacity of the photodetector .

For the geometry shown in Figure 2 . 1 , the scattering is defined by

k �s

k·

Figure 2. 1.

A

schematic representation of the laser light scattering