Brownian motion of colloidal particles

Equation (31) describes phenomena (Chandrasekhar, 1943 Weiss and Rubin, 1983) ranging from the Brownian motion of colloidal particles to stellar... 

The random Brownian motion of colloidal particles creates temporal fluctuations in the intensity of the scattered light. The fluctuating intensity signal cannot be readily interpreted because it contains too much detail. Instead, the fluctuations are commonly quantified by constructing an intensity autocorrelation function (ACF) [41J. For this reason, DLS often goes by the name photon correlation spectroscopy (PCS). 

Svedberg s primary focus as a physical chemist was the field of colloid chemistry. Colloids are mixtures of very small particles that when dispersed in solvents are not dissolved, but are held in suspension by various actions of the solvent. Svedberg and his collaborators studied the interaction of colloid suspensions with light and their sedimentation processes. These studies showed that the gas laws could be applied to colloidal systems. Svedberg s Ph.D. thesis on the diffusion of platinum colloidal particles elicited a response from Albert Einstein, since it supported Einstein s theory concerning the Brownian motions of colloidal particles. 

All of the molecules in a solution are subjected to agitation forces, known as Brownian motion, that tend to make them occupy the maximum amount of available space. A solid that dissolves in a liquid is dispersed throughout the entire volume and is thus uniformly distributed. The Brownian motion of colloidal particles is slower. If they are put into the bottom of a container, they diffuse very slowly through the mass of the liquid. 

We now provide an example of such an inversion from the work of Wright et al (1992) in which spatial computer simulations were used to generate data on the aggregation of fractal clusters formed by Brownian motion of colloidal particles. We consider three-dimensional diffusion under two circumstances (i) that in which the diffusion coefficient of the cluster is independent of its mass and (ii) that in which the diffusion coefficient, decreases with increasing mass. The simulated process automatically produces noisy data and the number density in cluster mass is presented in Figure 6.2.10 at three different times for both cases (i) and (ii). 

Fluctuations of macroscopic variables in thermodynamic systems at equilibrium or in steady-state conditions have long been understood (1). Fluctuations are the macroscopic manifestation of the discrete nature of matter and can be exploited to gain quantitative information about the elementary components of large systems. A classical example is the measurement by Perrin of Boltzmann s constant (and Avogadro s number) from the application of Einstein s theory of the Brownian motion of colloidal particles (2). Another equally classical example is the evaluation of the charge of the electron from the measurement of shot noise in vacuum tubes (3). 

Another aspect of ionic liquids is that the thermal movement of the colloidal nanop>artides is suppressed due to the high viscosity of the surrounding medium minimizing the probabihty of close contacts. Let us analyse this aspect in further detail. Let us assume that nanopartides with size a = 3 nm have just formed and are dispersed at room temperature (20°C) in a medium with viscosity 77 at a volume fraction q) of 0.01. To assess qualitatively their half-life time, we assume here a very simple model of rapid random coagulation, where every collision of two nanopartides immediately leads to coagulation and, in consequence, agglomeration. The number of collisions v that one nanoparticle experiences per time unit with other nanopartides can be expressed by eq. 4,( 1 which can be obtained based on the Einstein-Smoluchowski 1 7, es] formalism of Brownian motion of colloidal particles. 

The Brownian motion of colloidal particles is observed for a length of time such that the root-mean-square displacement of the particles is 0.100 cm. How must the observation time be changed so that the root-mean-square displacement of the same set of particles is 0.200 cm at the same temperature ... 

Brownian motion The ceaseless jittering motion of colloidal particles caused by the impact of solvent molecules. 

Photon correlation spectroscopy (PCS) has been used extensively for the sizing of submicrometer particles and is now the accepted technique in most sizing determinations. PCS is based on the Brownian motion that colloidal particles undergo, where they are in constant, random motion due to the bombardment of solvent (or gas) molecules surrounding them. The time dependence of the fluctuations in intensity of scattered light from particles undergoing Brownian motion is a function of the size of the particles. Smaller particles move more rapidly than larger ones and the amount of movement is defined by the diffusion coefficient or translational diffusion coefficient, which can be related to size by the Stokes-Einstein equation, as described by... 

The Peclet number compares the effect of imposed shear (known as the convective effect) with the effect of diffusion of the particles. The imposed shear has the effect of altering the local distribution of the particles, whereas the diffusion (or Brownian motion) of the particles tries to restore the equilibrium structure. In a quiescent colloidal dispersion the particles move continuously in a random manner due to Brownian motion. The thermal motion establishes an equilibrium statistical distribution that depends on the volume fraction and interparticle potentials. Using the Einstein-Smoluchowski relation for the time scale of the motion, with the Stokes-Einstein equation for the diffusion coefficient, one can write the time taken for a particle to diffuse a distance equal to its radius R, as... 

There are some very special characteristics that mnst be considered regarding colloidal particle behavior size and shape, surface area, and surface charge density. The Brownian motion of the particles is a much-studied field, and the fractal nature of surface roughness has recently been shown to be important. Recent applications have been reported employing nanocolloids. 

When dealing with the sedimentation of colloidal particles, it is principally necessary to regard the Brownian motion of the particles, which results in diffusive particle transport and, thus, acts against the migration in the gravitational or centrifugal field. The relevance of the Brownian motion can be roughly estimated by means of a Peclet-number ... 

The electrophoretic motion of colloidal particles is superposed by their Brownian motion. Ideally, both can be separated because of their different space-time correlations, in practice however, diffusion broadens the measured zeta-potential distribution. In microelectrophoresis, the Brownian contribution can be minimised by long observation times t D,/v ). For ELS, diffusion is least pronounced at small scattering angles (Xu 2008). 

Any motion of colloidal particles is driven by volume forces (e.g. gravity), stochastic Brownian forces and hydrodynamic forces. The latter act on the particles surface and can be calculated via flie hydrodynamic stress tensor II ... 

Macromolecules, colloidal particles and micelles undergo Brownian motion. This means that they are subjected to random forces from the thermal motion of the surrounding molecules. This jostling leads to a random zig-zag motion of colloidal particles, which can be described as a random walk (Fig. 1.3). Einstein analysed the statistics of a random walk and showed that the root-mean-square displacement at time t is given by... 

Another microscopy technique, which is actually based on light scattered by colloids, is dark-field or ultra-microscopy. In this technique, an ordinary optical microscope is used, but the sample is illuminated in such a way that light does not enter the objective unless scattered by the object under investigation. This technique does now allow a direct observation of, for example, a particle, but is particularly useful for detecting the presence of particles and investigating the Brownian motion of colloids. An important requirement is that the refractive index of the coUoids... 

Around 1905 Einstein devised a theory of Brownian motion, the irregular motion of colloidal particles suspended in a liquid. Einstein assumed that a colloidal particle is bombarded randomly by the molecules of the solvent and was able to show for a spherical colloidal particle that the mean-square displacement of the particle in the z direction in a time t is given by... 

Sols are dispersions of colloidal particles in a Hquid. Sol particles are typically small enough to remain suspended in a Hquid by Brownian motion. 

---