Solution colloidal motion

Most descriptions of the dynamics of molecular or particle motion in solution require a knowledge of the frictional properties of the system. This is especially true for polymer solutions, colloidal suspensions, molecular transport processes, and biomolecular conformational changes. Particle friction also plays an important role in the calculation of diffusion-influenced reaction rates, which will be discussed later. Solvent multiparticle collision dynamics, in conjunction with molecular dynamics of solute particles, provides a means to study such systems. In this section we show how the frictional properties and hydrodynamic interactions among solute or colloidal particles can be studied using hybrid MPC-MD schemes. 

The above model assumes that both components are dynamically symmetric, that they have same viscosities and densities, and that the deformations of the phase matrix is much slower than the internal rheological time [164], However, for a large class of systems, such as polymer solutions, colloidal suspension, and so on, these assumptions are not valid. To describe the phase separation in dynamically asymmetric mixtures, the model should treat the motion of each component separately ( two-fluid models [98]). Let Vi (r, t) and v2(r, t) be the velocities of components 1 and 2, respectively. Then, the basic equations for a viscoelastic model are [164—166]... 

Lindman, B. and Bran, B. (1973) Translational motion in aqueous sodium n-octanoate solutions. /. Colloid Interface Sci., 42, 388-399. 

This section treats four approaches for calculating light scattering spectra of macromolecule solutions. Historically, the methods were primarily applied to colloid particles and protein molecules. Charged colloids are not the center of this volume, but the results clarify the meaning of measurements on polymer solutions. Furthermore, colloid motion is central to studies of optical probe diffusion. Finally, the quantitative success of the colloid calculations indicates that the nature of the forces between diffusing macromolecules in solution is well-understood. 

The most familiar type of electrokinetic experiment consists of setting up a potential gradient in a solution containing charged particles and determining their rate of motion. If the particles are small molecular ions, the phenomenon is called ionic conductance, if they are larger units, such as protein molecules, or colloidal particles, it is called electrophoresis. 

Hydrophobic colloidal particles move readily in the liqnid phase under the effect of thermal motion of the solvent molelcnles (in this case the motion is called Brownian) or under the effect of an external electric field. The surfaces of such particles as a rule are charged (for the same reasons for which the snrfaces of larger metal and insnlator particles in contact with a solution are charged). As a result, an EDL is formed and a certain valne of the zeta potential developed. 

There are several attractive features of such a mesoscopic description. Because the dynamics is simple, it is both easy and efficient to simulate. The equations of motion are easily written and the techniques of nonequilibriun statistical mechanics can be used to derive macroscopic laws and correlation function expressions for the transport properties. Accurate analytical expressions for the transport coefficient can be derived. The mesoscopic description can be combined with full molecular dynamics in order to describe the properties of solute species, such as polymers or colloids, in solution. Because all of the conservation laws are satisfied, hydrodynamic interactions, which play an important role in the dynamical properties of such systems, are automatically taken into account. 

Multiparticle collision dynamics describes the interactions in a many-body system in terms of effective collisions that occur at discrete time intervals. Although the dynamics is a simplified representation of real dynamics, it conserves mass, momentum, and energy and preserves phase space volumes. Consequently, it retains many of the basic characteristics of classical Newtonian dynamics. The statistical mechanical basis of multiparticle collision dynamics is well established. Starting with the specification of the dynamics and the collision model, one may verify its dynamical properties, derive macroscopic laws, and, perhaps most importantly, obtain expressions for the transport coefficients. These features distinguish MPC dynamics from a number of other mesoscopic schemes. In order to describe solute motion in solution, MPC dynamics may be combined with molecular dynamics to construct hybrid schemes that can be used to explore a variety of phenomena. The fact that hydrodynamic interactions are properly accounted for in hybrid MPC-MD dynamics makes it a useful tool for the investigation of polymer and colloid dynamics. Since it is a particle-based scheme it incorporates fluctuations so that the reactive and nonreactive dynamics in small systems where such effects are important can be studied. 

The rapid motion in all directions of the particles in a colloidal solution it results from the irregular bombardment of the suspended particles by the molecules of the liquid. 

For small colloidal particles, which are subject to random Brownian motion, a stochastic approach is more appropriate. These methods are based on the formulation and solution of the diffusion equation in a force field, in the presence of convection... 

An interesting problem arises when we consider solutions or colloidal sols where the diffusing component is much larger in size than the solute molecules. In dilute systems Equation (1.14) would give an adequate value of the Peclet number but not so when the system becomes concentrated, i.e. the system itself becomes a condensed phase. The interactions between the diffusing component slow the motion and, as we shall see in detail in Chapter 3, increase the viscosity. The appropriate dimensionless group should use the system viscosity and not that of the medium and now becomes... 

A colloidal solution is defined as a solution intermediate in character between a suspension and a true solution. Particles with diameters < 10 pm are usually called colloids [19,65], although the distinction based on size is arbitrary. The size of particles is a continuum and the point at which large macromolecules end and small colloids begin is subject to judgment, as is the upper end of the size continuum, where colloids and suspended particles merge. The tendency of suspended particles to settle out of solution is not really a function of size alone, rather the relative density of the particles and the motion of the water will determine what is suspended and what settles. 

Once nanoparticles have been formed, whether in an early state of growth or in a more or less final size, their fate depends on the forces between the individual particles and between particles and solid surfaces in the solution. While particles initially approach each other by transport in solution due to Brownian motion, convection, or sedimentation, when close enough, interparticle forces will determine their final state. If the dominant forces are repulsive, the particles will remain separate in colloidal form. If attractive, they will aggregate and eventually precipitate. In addition, they may adsorb onto a solid surface (the substrate or the walls of the vessel in which the reaction is carried out). For CD, both attractive particle-sur-... 

One type of colloidal system has been chosen for discussion, a system in which the solid metal phase has been shrank in three dimensions to give small solid particles in Brownian motion in a solution. Such a colloidal suspension consisting of discrete, separate particles immersed in a continuous phase is known as a sol. One can also have a case where only two dimensions (e.g., the height z and breadth y of a cube) are shrank to colloidal dimensions. The result is long spaghettihke particles dispersed in solution—macromolecular solutions. 

Colloids are particles with diameters of 1-500 nm. They are larger than molecules but too small to precipitate. They remain in solution indefinitely, suspended by the Brownian motion (random movement) of solvent molecules.2... 

Chemical parameters determine the surface characteristics of the suspended colloids, the concentration of the coagulant and its effects upon the surface properties of the destabilized particles, and the influence of other constituents of the ionic medium upon the coagulant and the colloids. The extent of the chemical and physical interactions between the colloidal phase and the solution phase determines the relative stability of the suspended colloids. One speaks of stable suspensions when all collisions between the colloids induced by Brownian motion or by velocity gradients are completely elastic the colloidal particles continue their... 

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