Segment distribution

Most important macroscopic transport properties (i.e., permeabilities, solubilities, constants of diffusion) of polymer-based membranes have their foundation in microscopic features (e.g., free-volume distribution, segmental dynamics, distribution of polar groups, etc.) which are not sufficiently accessible to experimental characterization. Here, the simulation of reasonably equilibrated and validated atomistic models provides great opportunities to gain a deeper insight into these microscopic features that in turn will help to develop more knowledge-based approaches in membrane development. 

Early theory propounded the existence of holes in a liquid that accommodated flow, as molecules jumped from hole to hole (Eyring, 1936). Modern theory perceives spaces in a polymer melt originating from randomly distributed segments of the primary structure, whose cooperative bond rotation (crankshaft motion) creates free volume (vp), thus enabling the polymer chain eventually to achieve new positions. For a gram of dispersed solute, ty is the difference between the specific volume of solute (vsp) and vex ... 

Owing to the orientation dependence that it imparts to the NMR frequency, the chemical-shift anisotropy (CSA) has proven useful not only in studies of slow dynamics but also for characterizing segmental orientation distributions and fast segmental reorientations. While static powder patterns provide this CSA information in the most accessible form, site resolution by MAS is indispensable in all but the simplest unlabeled systems. The two requirements can be combined in two-dimensional (2D) separation experiments. Recently, a robust sequence, termed separation of undistorted powder-patterns by effortless recoupling (SUPER), was introduced that makes CSA measurements under standard MAS conditions routine.28 It enables identification of functional groups and measurements of orientation distributions, segmental dynamics, and conformations. 

The freely rotating chain is formed by randomly distributed segments around some reference origin F = 0. The segment distribution density is given by the... 

Fig. XI-4. Schematic diagram of the structure of an adsorbed polymer chain. Segments are distributed into trains directly attached to the surface and loops and tails extending into solution.

Plot the number distribution of segments in loops and trains against segment number s from Eqs. XI-21 and 22. How do these profiles differ ... 

More fundamental treatments of polymer solubihty go back to the lattice theory developed independentiy and almost simultaneously by Flory (13) and Huggins (14) in 1942. By imagining the solvent molecules and polymer chain segments to be distributed on a lattice, they statistically evaluated the entropy of solution. The enthalpy of solution was characterized by the Flory-Huggins interaction parameter, which is related to solubihty parameters by equation 5. For high molecular weight polymers in monomeric solvents, the Flory-Huggins solubihty criterion is X A 0.5. 

Scale-Up Principles. Key factors affecting scale-up of reactor performance are nature of reaction zones, specific reaction rates, and mass- and heat-transport rates to and from reaction sites. Where considerable uncertainties exist or large quantities of products are needed for market evaluations, intermediate-sized demonstration units between pilot and industrial plants are usehil. Matching overall fluid flow characteristics within the reactor might determine the operative criteria. Ideally, the smaller reactor acts as a volume segment of the larger one. Elow distributions are not markedly influenced by... 

When straight or serrated segmental weirs are used in a column of circiilar cross secdion, a correction may be needed for the distorted pattern of flow at the ends of the weirs, depending on liquid flow rate. The correction factor F from Fig. 14-33 is used direcdly in Eq. (14-112) or Eq. (14-119). Even when circular downcomers are utilized, they are often fed by the overflow from a segmental weir. When the weir crest over a straight segmental weir is less than 6 mm V in), it is desirable to use a serrated (notched) weir to provide good liquid distribution. Inasmuch as fabrication standards permit the tray to be 3 mm Vh in) out of level, weir crests less than 6 mm V in) can result in maldistribution of hquid flow. 

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