Bead size

Mesoscale simulations model a material as a collection of units, called beads. Each bead might represent a substructure, molecule, monomer, micelle, micro-crystalline domain, solid particle, or an arbitrary region of a fluid. Multiple beads might be connected, typically by a harmonic potential, in order to model a polymer. A simulation is then conducted in which there is an interaction potential between beads and sometimes dynamical equations of motion. This is very hard to do with extremely large molecular dynamics calculations because they would have to be very accurate to correctly reflect the small free energy differences between microstates. There are algorithms for determining an appropriate bead size from molecular dynamics and Monte Carlo simulations. 

Polymer simulations can be mapped onto the Flory-Huggins lattice model. For this purpose, DPD can be considered an off-lattice version of the Flory-Huggins simulation. It uses a Flory-Huggins x (chi) parameter. The best way to obtain % is from vapor pressure data. Molecular modeling can be used to determine x, but it is less reliable. In order to run a simulation, a bead size for each bead type and a x parameter for each pair of beads must be known. 

Of all the topics discussed in this text, mesoscale simulations are probably at the most infantile stage of development. The idea of the mesoscale calculations is very attractive and physically reasonable. However, it is not as simple as one might expect. The choice of bead sizes and parameters is crucial to obtaining physically relevant results. More complex bead shapes are expected to be incorporated in future versions of these techniques. When using one simulation technique to derive parameters for another simulation, very small errors in a low-level calculation could result in large errors in the final stages. 

Sephadex. Other carbohydrate matrices such as Sephadex (based on dextran) have more uniform particle sizes. Their advantages over the celluloses include faster and more reproducible flow rates and they can be used directly without removal of fines . Sephadex, which can also be obtained in a variety of ion-exchange forms (see Table 15) consists of beads of a cross-linked dextran gel which swells in water and aqueous salt solutions. The smaller the bead size, the higher the resolution that is possible but the slower the flow rate. Typical applications of Sephadex gels are the fractionation of mixtures of polypeptides, proteins, nucleic acids, polysaccharides and for desalting solutions. 

Bead Size - The resins must be in the form of spherical granules of maximum homogeneity and dimensions so that they do not pack too much, the void volume among their interstices is constant for a given type, and the liquid head loss in percolation remains acceptable. Most ion-exchange resins occur as small beads or granules usually between 16 and 50 mesh in size. 

Type Bead size djo (/xm) Size exclusion pore dimension (nm) Exclusion limit protein (M,) Fractionation range protein (/V ,) pH stability (long term/ short term)... 

Bead size dso (/im) Size exclusion Exclusion Fractionation range pH stability... 

Superose gel material of Pharmacia Biotech is a highly epichloro-hydrine cross-linked agarose matrix that has a pH range of 3-12 (short term 1-14). Hydrophilic interactions may be noticeable for lipids, peptides, and small aromatic compounds, but such interactions might even improve resolution. Superose medium is available in two different porosities Superose 6 HR 10/ 30 (bead size 13 2 /um maximum pressure 1.5 MPa) and Superose 12 HR 10/30 (bead size 10 2 /um maximum pressure 3.0 MPa). 

Effects of agitator size and speed on bead size (microns). 

Many factors affect gas holdup in three-phase fluidized systems, including bead size and density, liquid physical properties, temperature, sparger type, and fluid superficial velocities (Bly and Worden, 1990). System parameters such as reactor and gas distributor design can have... 

Size measurements have also been collected for film thicknesses and bead sizes on the electron microscope [79-81]. One example is the study of the relationship between film thickness and the size and mass of a bead in a fluidized-bed unit [79]. The bead diameter and film thickness were determined by SEM and correlated to dissolution data. It was found that larger beads received thicker coatings and exhibited slower release rates than the smaller beads. 

Since the general concept in CEC is to use packing materials with a beads size as small as possible, the viscosity of the liquid used for slurring the beads is critical. Equation (2) rearranged to... 

Fig. 3.26 Simulated single chain dynamic structure factor Schain(Q>0 for different chain lengths AT=350 (pluses) 700 (crosses) and 10,000 (filled squares) for various Q-values [79] (Q is given in terms of bead size a). Solid lines are fits to Eq. 3.39 and Eq. 3.42. For equal Q-values the plateaus show a strong N-dependence. (Reprinted with permission from [79]. Copyright 2000 EDP Sciences)...

The bromination reaction (Scheme 12.3) was also carried out on resins (1) of three different sizes (Fig. 12.5). Single bead FTIR study and the kinetics analysis were carried out as in the esterification reaction studies. Rate constants are hsted in Tab. 12.2. The relationship between the rate constants and the bead size is shown in Fig. 12.7b. 

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