Brownian motion of colloids

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. 

Jean-Baptiste Perrin (1870-1942). .. was a French physicist who worked on various subjects, for instance, on cathode rays, fluorescence, sound propagation, and the decay of radium. A major part of his scientiflc life was dedicated to colloids. His investigations on the Brownian motion of colloids by means of the previously developed ultramicroscope verified Einstein s statistic explanation of this phenomenon and thereby confirmed the atomic nature of matter. Moreover, Perrin was able to closely limit the possible range of Avogadro s number and he discovered the sedimentation-diffusion equilibrium. For his work on the discontinuous structure of matter and especially for his discovery of sedimentation equilibrium he received 1926 the Nobel Prize in Physics. 

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. 

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... 

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... 

There are some very special characteristics that must be considered as regards colloidal particle behavior size and shape, surface area, and surface charge density. The Brownian motion of particles is a much-studied field. The fractal nature of surface roughness has recently been shown to be of importance (Birdi, 1993). Recent applications have been reported where nanocolloids have been employed. Therefore, some terms are needed to be defined at this stage. The definitions generally employed are as follows. Surface is a term used when one considers the dividing phase between... 

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... 

In general, the Brownian motions of two neighboring colloids will induce a correlation between their displacements that is not zero and D will exhibit a crosscoupling term in addition to the diffusion coefficients of the two colloids when widely separated. For a detailed discussion of D, see Section 4.1.2 in Th. G. M. van de Ven, Colloidal Hydrodynamics, Academic Press, London, 1989. 

Attempts to describe the unlimited increase of the viscosity of dispersions and emulsions observed when their concentrations approach the maximum values (tPmax) meet great theoretical difficulties. Various approaches were developed to overcome these difficulties. Thus, for example, Russel et al. [58] suggested that account should be taken of the Brownian motion of particles in colloidal dispersions in the form of a hydrodynamic contribution. They showed that this contribution which is to be taken into account in considering a slow flow (with slow shear rates y), increases considerably with increasing dispersion concentration. For a description of the dependence of viscosity on concentration the above authors obtained an exact equation only in the integral form. At low shear rates it gives the following power series ... 

The random motion of colloidal dispersions due to molecular collisions is called Brownian motion. 

At low ionic strength (kR 1), other effects connected with the finite diffusivity of the small ions in the EDL surrounding the particle are present. The noninstantaneous diffusion of the small ions (with respect to the Brownian motion of the colloid particle) could lead to detectable reduction of the single particle diffusion coefficient, Dq, from the value predicted by the Stokes-Ein-stein relation. Equation 5.447. For spherical particles, the relative decrease in the value of Dq is largest at k/ 1 and could be around 10 to 15%. As shown in the normal-mode theory, the finite diffusivity of the small ions also affects the concentration dependence of the collective diffusion coefficient of the particles. Belloni et al. obtained an explicit expression for the contribution of the small ions in Ac)... 

The electrostatic interaction between diffuse layers of ions surrounding particles is one of the most thoroughly theoretically developed factors of colloid stability. The theory of electrostatic factor is, essentially, the basis for the quantitative description of coagulation by electrolytes. This theory was developed in the Soviet Union by B.V. Derjaguin and L.D. Landau in 1935 -1941, and independently by the Dutch scientists E.Verwey and T. Overbeek, and is presently known by the initial letters of their names as the DL VO theory [44,45]. The DLVO theory is based on comparison of molecular interaction between the dispersed particles in dispersion medium and the electrostatic interaction between diffuse layers of ions, with Brownian motion of particles taken into account (in the simplest version of theory this is done on a qualitative level). 

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