Partitioning polymers

The result of the interactions of some copolymer mimics of AMP with model bacterial membranes has been studied via atomistic molecular dynamics simulation (Figure 3.2). The model bacterial membrane expands homogeneously in a lateral manner in the membrane thickness profile compared with the polymer-free system. The individual polymers taken together are released into the bacterial membrane in a phased manner and the simulations propose that the most possible location of the partitioned polymers is near the l-palmitoyl-2-oleoyl-phosphatidylglycerol clusters. The partitioned polymers preferentially adopt facially amphiphilic conformations at the lipid-water interface, although lack intrinsic secondary structures, such as an a-helix or P-sheet, found in naturally occurring AMP [23]. 

The object of FFF is to find means for differentially partitioning polymers or other species between different parts of the flow profile so they will be swept along at different velocities. Since there is only one phase in the channel, ruling out the use of phase distribution forces, and since there is no packing or porous structure to generate entropic differences as in SEC, an external influence must... 

It is convenient to partition polymer solutions into three different cases according to their concentration. Dilute solutions involve only a minimum of interaction (overlap) between different polymer molecules. The Flory-Huggins theory does not represent this situation at all well due to its mean-field assumption. The semi-dilute case involves overlapping polymer molecules but still with a considerable separation of the segments of different molecules. 

Of particular interest has been the study of the polymer configurations at the solid-liquid interface. Beginning with lattice theories, early models of polymer adsorption captured most of the features of adsorption such as the loop, train, and tail structures and the influence of the surface interaction parameter (see Refs. 57, 58, 62 for reviews of older theories). These lattice models have been expanded on in recent years using modem computational methods [63,64] and have allowed the calculation of equilibrium partitioning between a poly-... 

This is better understood with a picture see figure B3.3.11. The discretized path-integral is isomorphic to the classical partition fiinction of a system of ring polymers each having P atoms. Each atom in a given ring corresponds to a different imaginary tune point p =. . . P. represents tire interatomic interactions... 

In the limit that the number of effective particles along the polymer diverges but the contour length and chain dimensions are held constant, one obtains the Edwards model of a polymer solution [9, 30]. Polymers are represented by random walks that interact via zero-ranged binary interactions of strength v. The partition frmction of an isolated chain is given by... 

Otlier expressions for tire diffusion coefficient are based on tire concept of free volume [57], i.e. tire amount of volume in tire sample tliat is not occupied by tire polymer molecules. Computer simulations have also been used to quantify tire mobility of small molecules in polymers [58]. In a first approach, tire partition functions of tire ground... 

At equilibrium, in order to achieve equality of chemical potentials, not only tire colloid but also tire polymer concentrations in tire different phases are different. We focus here on a theory tliat allows for tliis polymer partitioning [99]. Predictions for two polymer/colloid size ratios are shown in figure C2.6.10. A liquid phase is predicted to occur only when tire range of attractions is not too small compared to tire particle size, 5/a > 0.3. Under tliese conditions a phase behaviour is obtained tliat is similar to tliat of simple liquids, such as argon. Because of tire polymer partitioning, however, tliere is a tliree-phase triangle (ratlier tlian a triple point). For smaller polymer (narrower attractions), tire gas-liquid transition becomes metastable witli respect to tire fluid-crystal transition. These predictions were confinned experimentally [100]. The phase boundaries were predicted semi-quantitatively. 

This monomer polymerizes faster ia 50% water than it does ia bulk (35), an abnormaHty iaconsistent with general polymerization kinetics. This may be due to a complex with water that activates the monomer it may also be related to the impurities ia the monomer (eg, acetaldehyde, 1-methyl pyrroHdone, and 2-pyrroHdone) that are difficult to remove and that would be diluted and partitioned ia a 50% aqueous media (see Vinyl polymers, A/-VINYLAMIDE POLYPffiRS). 

Recycle and Polymer Collection. Due to the incomplete conversion of monomer to polymer, it is necessary to incorporate a system for the recovery and recycling of the unreacted monomer. Both tubular and autoclave reactors have similar recycle systems (Fig. 1). The high pressure separator partitions most of the polymers from the unreacted monomer. The separator overhead stream, composed of monomer and a trace of low molecular weight polymer, enters a series of coolers and separators where both the reaction heat and waxy polymers are removed. Subsequendy, this stream is combined with fresh as well as recycled monomers from the low pressure separator together they supply feed to the secondary compressor. 

By 1980, research and development shifted from relatively inexpensive surfactants such as petroleum sulfonates to more cosdy but more effective surfactants tailored to reservoir and cmde oil properties. Critical surfactant issues are performance in saline injection waters, adsorption on reservoir rock, partitioning into reservoir cmde oil, chemical stabiUty in the reservoir, interactions with the mobiUty control polymer, and production problems caused by resultant emulsions. Reservoir heterogeneity can also greatly reduce process effectiveness. The decline in oil prices in the early 1980s halted much of the work because of the relatively high cost of micellar processes. 

Permeant movement is a physical process that has both a thermodynamic and a kinetic component. For polymers without special surface treatments, the thermodynamic contribution is ia the solution step. The permeant partitions between the environment and the polymer according to thermodynamic rules of solution. The kinetic contribution is ia the diffusion. The net rate of movement is dependent on the speed of permeant movement and the availabiHty of new vacancies ia the polymer. 

The basis for the separation is that when two polymers, or a polymer and certain salts, are mixed together in water, they are incompatible, leading to the formation of two immiscible but predominantly aqueous phases, each rich in only one of the two components [Albertsson, op. cit. Kula, in Cooney and Humphrey (eds.), op. cit., pp. 451 71]. A phase diagram for a polyethylene glycol (PEG)-Dextran, two-phase system is shown in Fig. 22-85. Proteins are known to distribute unevenly between these phases. This uneven distribution can be used for the selective concentration and partial purification of the products. Partitioning between the two phases is controlled by the polymer molecular weight and concentration, protein net charge and... 

FIG. 22-85 Phase diagram for a PEG/Dextran, hiphasic, aqueous-polymer system used in liquid-liquid extraction operations for protein separations. Alheiisson, Partition of Cell Particles and Macromolecules, 3d ed., Copyright 1986. Reprintedhy petTTUssion of John Wiley Sons, Inc.)... 

The partition function, H, Eq. (3), can be solved only approximately, e.g., in the MFA. However, from the magnetic analog one can obtain scaling relations for the concentration of links and polymer chains p, cf. Eq. (4)... 

The last quantity that we discuss is the mean repulsive force / exerted on the wall. For a single chain this is defined taking the derivative of the logarithm of the chain partition function with respect to the position of the wall (in the —z direction). In the case of a semi-infinite system exposed to a dilute solution of polymer chains at polymer density one can equate the pressure on the wall to the pressure in the bulk which is simply given by the ideal gas law The conclusion then is that [74]... 

The analyst must remember that solubility of a polymer in the chosen eluant is a necessary, but not sufficient, requirement for ideal GPC separations. Once injected on the column, the polymer has a choice of partitioning onto the stationary phase or remaining in the solvent. It is imperative that the analyst choose solvent and column conditions such that the ideal, nonadsorptive, GPC mechanism can occur. 

When a dilute solution of a polymer (c << c ) is equilibrated with a porous medium, some polymer chains are partitioned to the pore channels. The partition coefficient K, defined as the ratio of the polymer concentration in the pore to the one in the exterior solution, decreases with increasing MW of the polymer (7). This size exclusion principle has been used successfully in SEC to characterize the MW distribution of polymer samples (8). 

The partitioning principle is different at high concentrations c > c . Strong repulsions between solvated polymer chains increase the osmotic pressure of the solution to a level much higher when compared to an ideal solution of the same concentration (5). The high osmotic pressure of the solution exterior to the pore drives polymer chains into the pore channels at a higher proportion (4,9). Thus K increases as c increases. For a solution of monodisperse polymer, K approaches unity at sufficiently high concentrations, but never exceeds unity. 

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