Concentration, Brownian fluctuations

In the case of solutions, concentration fluctuations only contribute to the central elastic part of the scattering spectrum. However, the Brownian movement of solute molecules creates weak frequency displacements that broaden the central peak. This phenomenon is called Rayleigh line broadening or quasielastic scattering [26-28]. This section deals with elastic scattering only. 

As a result of Brownian motion, continual fluctuations of concentration take place on a molecular or small-particle scale. For this reason, the second law of thermodynamics is only valid on the macroscopic scale. 

For non-ideal polymer solutions where there are interactions between the polymer molecules, Einstein and Debye showed independently that if the solute is uniformly distributed throughout the solution, no light is scattered by the solution because light scattered by one particle will interfere destructively with light scattered by the neighbouring particle. Random Brownian motion causes fluctuations in concentration, the extent of fluctuations is inversely proportional to the osmotic pressure developed by the concentration difference. It is found that... 

Because the random fluctuations in the positions of particles in space are often translational, the kinetics of these processes can be considered comparable to the decay of a concentration gradient by translational Brownian motion. Likewise, as the orientation of any molecule undergoes similar random fluctuations in space,... 

In the semidilute regime, the molecules cannot distribute themselves at random over the volume. The polymer concentration fluctuates with a wavelength equal to the correlation length. The system can be seen as a kind of network with mesh size comparable to The network continuously changes conformation due to Brownian motion. Over distances along the polymer chain < , which implies short time scales for molecular motion, polymer sub-chains behave as in a dilute solution interactions between two... 

Particle concentration gradient Particle diffusion, Brownian motion, Concentration fluctuations ... 

V.2.4. Brownian Motion and Fluctuations in the Concentration of Disperse Phase Particles... 

Coalescence occurs in shear as well as in quiescent systems. In the latter case the effect can be caused by molecular diffusion to regions of lower free energy, by Brownian motion, dynamics of concentration fluctuation, etc. Diffusion is the mechanism responsible for coalescence known as Ostwald ripening". The process involves diffusion from smaller drops (high interfacial... 

The diffusional or Brownian motion of molecules in a liquid or gas gives rise to fluctuations in density or concentration that can be observed by optical methods. 

In pure liquids. Brownian (i.e., thermal) motion of the molecules leads to fluctuations in time and place of the density of the liquid. In solutions, there is also a fluctuation in solute concentration. It can be assumed that fluctuations in solvent density and solute concentration are independent of each other. In this case, the intensity of scattered light is by the solute is given simply by subtracting the intensity of scattered light by the pure solvent /soiv from that by the solution soln ... 

Coalescence occurs in quiescent as well as in sheared systems. In the former it starts by molecular diffusion from smaller to larger diameter drops, caused by the difference in surface energy. This mechanism, known since 1896 as Ostwald ripening, was originally proposed for rain drop formation. Small drops may also coalesce by Brownian motion, dynamics of concentration fluctuation, and so on. Shearing enhances the coalescence [291] ... 

When multiple scattering is discarded from the measured signal, DLS can be used to study the dynamics of concentrated suspensions, in which the Brownian motion of individual particles (self-diffusion) differs from the diffusive mass transport (gradient or collective diffusion), which causes local density fluctuations, and where the diffusion on very short time-scales (r < c lD) deviates from those on large time scales (r c D lones and Pusey 1991 Banchio et al. 2000). These different diffusion coefficients depend on the microstructure of the suspension, i.e. on the particle concentration and on the interparticle forces. For an unknown suspension it is not possible to state a priori which of them is probed by a DLS experiment. For this reason, a further concentration limit must be obeyed when DLS is used for basic characterisation tasks such as particle sizing. As a rule of thumb, such concentration effects vanish below concentrations of 0.01-0.1 vol%, but certainty can only be gained by experiment. 

The DLS technique involves measurement of the Doppler broadening of the Rayleigh-scattered light as a result of Brownian motion (translational diffusion) of the particles. This thermal motion causes time fluctuations in the scattering intensity and a broadening of the Rayleigh line. The Rayleigh line has a Lorentzian line shape. In macromolecular solutions, concentration... 

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