Photon correlation, theory

A very similar effect of the surface concentration on the conformation of adsorbed macromolecules was observed by Cohen Stuart et al. [25] who studied the diffusion of the polystyrene latex particles in aqueous solutions of PEO by photon-correlation spectroscopy. The thickness of the hydrodynamic layer 8 (nm) calculated from the loss of the particle diffusivity was low at low coverage but showed a steep increase as the adsorbed amount exceeded a certain threshold. Concretely, 8 increased from 40 to 170 nm when the surface concentration of PEO rose from 1.0 to 1.5 mg/m2. This character of the dependence is consistent with the calculations made by the authors [25] according to the theory developed by Scheutjens and Fleer [10,12] which predicts a similar variation of the hydrodynamic layer thickness of adsorbed polymer with coverage. The dominant contribution to this thickness comes from long tails which extend far into the solution. 

The use of photon correlation spectroscopy to study the dynamics of concentration fluctuations in polymer solutions and gels is now well established. In bulk polymers near the glass transition there will be slowly relaxing fluctuations in density and optical anisotropy which can also be studied by this technique. In this article we review the development of the field of photon correlation spectroscopy from bulk polymers. The theory of dynamic light scattering from pure liquids is presented and applied to polymers. The important experimented considerations involved in the collection and analysis of this type of data are discussed. Most of the article focuses on the dynamics of fluctuations near the glass transition in polymers. All the published work in this area is reviewed and the results are critically discussed. The current state of the field is summarized and many suggestions for further work are presented. 

This section contains a general description of the principles by which the Coulter Model N4 Sub-Micron Particle Analyzer, used in this study to characterize artificial gas-in-water emulsions (see Section 10.4), determines sample particle size. The measuring principles are based on the theory of Brownian motion and photon correlation spectroscopy (ref. 464,465 see also Sections 10.2 and 10.4). 

Beside of the progress in the theory of a particle movement in the zetameter measurement cell, there was progress in particle measurement techniques. New models of zetameters enable automatic measurement of electrophoretic mobility on the basis of the shift of light wave scattered on the particle that moves in the electric field [82]. This technique is called photon correlation spectroscopy (PCS). To increase the sensitivity of the measurement, it is supported by multiangle electrophoretic light scattering (ELS). This combination, allows one also to measure the particle size distribution of the dispersed phase [83]. 

Malvern System 4700 comprises a variable angle spectrometer with computer controlled automatic operation, combining photon correlation spectroscopy and angular intensity measurements with full Mie theory calculations to give accurate size distributions in the 1 nm to 5 pm size range. 

The general experimental fact of constant frequency dispersion (or time dependence of the correlation function) of the a-relaxation at constant Ta for different combinations of T and P has an immense impact on glass transition. Although the data were mostly obtained by dielectric relaxation, the same effect was found in some glass-formers by photon correlation spectroscopy. The primary concern of most theories, including those mentioned in the NY Times article, is to explain the temperature and pressure dependences of the structural relaxation time Tq.. In these theories, the dispersion of the structural relaxation is either not addressed, or else considered separately with additional input not involved in arriving at r . Consequently, the frequency dispersion is unrelated to the relaxation time of the structural a-relaxation in these theories, and they are unlikely to be consistent with the T, / -superpositioning property by happenstance. 

In other words, two photons can never be detected at two points separated by an odd number of X/lr 2, despite the fact that one photon can be detected anywhere. The vanishing of G 2 (Ri, t R2, f2) for two photons at widely separated points Ri and R2 is an example of quantum-mechanical nonlocality, that the outcome of a detection measurement at Ri appears to be influenced by where we have chosen to locate the R2 detector. At certain positions R2 we can never detect a photon at Ri when there is a photon detected at R2, whereas at other position R2 it is possible. The photon correlation argument shows clearly that quantum theory does not in general describe an objective physical reality independent of observation [17],... 

Ford NC. Theory and practice of photon correlation spectroscopy. In Dahneke BE, editor. Measurement of Suspended Particles by Quasi-elastic Light Scattering. New York WUey-Interscience 1983. p 31. 

Rocculation kinetics can be readily measured for dilute dispersions, e.g. by particle counting (equation 6.7)), or from light-scattering data and recently by photon-correlation spectroscopy, and numerous experimental data for aqueous systems confirm that the DLVO theory is essentially correct although there are deviations in some of the fine detail. 

In photon correlation spectroscopy (PCS), light from a low-power helium-neon laser is focused on a temperature-controlled sample cell and light scattered at a known angle to the cell is detected by a photomultiplier. The random motion of particles in the laser beam causes fluctuations in the intensity of the scattered radiation that can be analyzed with a digital correlator. The smaller the particle the more rapid the fluctuations due to more rapid motion. The time dependence of the fluctuations is used to generate a correlation function, which is the sum of fluctuations caused by all particles. Autocorrelation theory can then be used to determine the diffusion coefficient, D, for the particles and hence the particle s hydrodynamic diameter, S, from the Stokes-Einstein equation ... 

N. Lu and S. Y. Zhu. Quantum theory of two-photon correlated-spontaneous-emission lasers Exact atom-field interaction Hamiltonian approach. Physical Revew A 1989 Nov 15 40(10) 5735-5752. 

As mentioned in the introduction to Parts A and B, new experimental methods have enriched and advanced the field of atomic spectroscopy to such a degree that it serves not only as a source of atomic structure data but also as a test ground for fundamental atomic theories based upon the framework of quantum mechanics and quantum electrodynamics. However, modem laser and photon correlation techniques have also been applied successfully to probe beyond the traditional quantum mechanical and quantum electrodynamical theories into nuclear stracture theories, electro-weak theories, and the growing field of local realistic theories versus quantum theories. 

While two-photon absorption spectroscopy has been widely applied for precision measurements of atomic structure, the polarization correlation of the simultaneous two-photon emission from the metastable Is state of atomic hydrogen has only been measured very recently. The emission of the coincident two photons can be described by a single state vector which determines the circular and linear two-photon polarization. Compared to the two-photon cascade experiments the polarization correlation of the simultaneous two-photon decay of metastable hydrogen is conceptually closer to the original proposals by Bell and Bohm for tests of the foundation of quantum mechanics. More than SO years have elapsed since the famous Einstein-Bohr debate on microphysical reality and quantum formalism. The present and future outcome of the hydrogen two-photon correlation experiment is considered to be a most crucial test with regard to the rivalry between quantum mechanics and local realistic theories. 

In recent years, in addition to theoretical developments, e.g., reptationW and tube theories,(i3,i4) iYiqyq have been many new analytical techniques,5) such as electron-induced X-ray fluorescence, the NMR field gradient method, forced Rayleigh scattering (FRS), forward recoil spectrometry (FRES), photon correlation spectroscopy, Rutherford back scattering. 

In a complete quantum theory of radiation several interesting phenomena regarding photon statistics are predicted. One such effect is photon anti-bunching for a two-level system. When an atom has just emitted a photon it cannot immediately radiate a second photon since it is in the lower state [4.17,18]. This behaviour is experimentally observed in photon correlation experiments. 

Forty years ago anyone interested in fineparticle characterization who had a science degree could cope with the theory of the techniques and was able to build relatively simple equipment to carry out the measurements. In the two most recent areas of fineparticle characterization — diffractometers (discussed earlier) and the method to be discussed in this section photon correlation spectroscopy (PCS), the relevant theories involve the use of concepts normally not studied until the post graduate level in an honours physics degree. The theory also involves electronic equipment and data processing concepts out of reach for people without a mathematical background. For these instruments the expensive electronic processing equipment and size evaluation equipment can truly be called a black box, from the point of view of the average operator. 

Pike ER and McNally B (1997) Theory and design of photon correlation and light-scattering experiments. Applied Optics 36 7531-7538. 

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