Partition Polymer/liquid

Estimate the polymer/liquid partition coefficient for cis-3-hexenol between a package with a LDPE material food contact layer. The package contains a food system whose partitioning characteristics can be simulated using 100 % ethanol at 25 °C. Use the UNIFAC activity coefficient estimation method and assume a dilute solution (x, = w, 0.00001). 

Since a molal activity coefficient has been calculated for the solute in the polymer phase and a molar activity coefficient calculated for the liquid phase Eq. (4-45) should be used to calculate the polymer/liquid partition coefficient ... 

Because of the lack of quantitativeness of the Regular Solution Theory and large amount of effort and computing power required for the UNIFAC method, yet another way will be taken here. This way leads to values using simple means which can adequately estimate values for the most important practical cases. The method described in this section is based on the potential already recognised in gas chromatography that the partition of a substance between a gas and a polymer liquid can be estimated based on its structural increments and these can be used as characteristic quantities for identification. 

Nose, T., A hole theory of polymer liquids and gasses I. Partition function and equation of state for polymer liquids, Polym. J., 2, 124—133 (1971). 

For polymer liquids, the partition funetion, Q, normalized per unit volume is given... 

In fact, this result is not uncommon, and the conclusion is easy to draw the process of diffusion is characterised by more than one parameter the diffusivity D coupled with the amount at equilibrium, M , without forgetting the coefficient of convection at the polymer-liquid interface and the possible partition factor. 

Simha has recently summarized a corresponding states model for one component polymer liquids which he then applies to the glass transition. Equation-of-State Models.—In the 1960 s Flory attempted to remove phenomenological parameters from previous models by relating them to molecular quantities using an approach which is formally similar to corresponding states. Starting with a simple partition function for a liquid, he obtained an equation-of-state ... 

Suppose a solute 5 partitions between a polymer liquid A having chain length Na and a polymer liquid B having length Ng. If the solute is dilute in both phases, then its concentrations in the two phases are 4>sa,4>sb ... 

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-... 

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. 

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 concept of SPME was first introduced by Belardi and Pawliszyn in 1989. A fiber (usually fused silica) which has been coated on the outside with a suitable polymer sorbent (e.g., polydimethylsiloxane) is dipped into the headspace above the sample or directly into the liquid sample. The pesticides are partitioned from the sample into the sorbent and an equilibrium between the gas or liquid and the sorbent is established. The analytes are thermally desorbed in a GC injector or liquid desorbed in a liquid chromatography (LC) injector. The autosampler has to be specially modified for SPME but otherwise the technique is simple to use, rapid, inexpensive and solvent free. Optimization of the procedure will involve the correct choice of phase, extraction time, ionic strength of the extraction step, temperature and the time and temperature of the desorption step. According to the chemical characteristics of the pesticides determined, the extraction efficiency is often influenced by the sample matrix and pH. 

The liquid-liquid partition systems discussed above are in fact very similar to various membrane-type interfaces and may serve as a model for them. A good example is, for instance, the distribution of a dissociated salt between aqueous solution and a permeable organic polymer [60]. 

The retention mechanism of organic solutes by porous polymer beads remains ambiguous [478]. At low temperatures adso tion dominates but at higher temperatures the polymer beads could behave as a highly extended liquid with solvation interactions. The evidence for a partition mechanism is not very strong and its importance, at present, remains speculative. Like other adsorbents it has proven possible to control retention and enhance efficiency by diluting porous polymers with an inert support material (479). 

Essentially, extraction of an analyte from one phase into a second phase is dependent upon two main factors solubility and equilibrium. The principle by which solvent extraction is successful is that like dissolves like . To identify which solvent performs best in which system, a number of chemical properties must be considered to determine the efficiency and success of an extraction [77]. Separation of a solute from solid, liquid or gaseous sample by using a suitable solvent is reliant upon the relationship described by Nemst s distribution or partition law. The traditional distribution or partition coefficient is defined as Kn = Cs/C, where Cs is the concentration of the solute in the solid and Ci is the species concentration in the liquid. A small Kd value stands for a more powerful solvent which is more likely to accumulate the target analyte. The shape of the partition isotherm can be used to deduce the behaviour of the solute in the extracting solvent. In theory, partitioning of the analyte between polymer and solvent prevents complete extraction. However, as the quantity of extracting solvent is much larger than that of the polymeric material, and the partition coefficients usually favour the solvent, in practice at equilibrium very low levels in the polymer will result. 

The structure of a simple mixture is dominated by the repulsive forces between the molecules [15]. Any model of a liquid mixture and, a fortiori of a polymer solution, should therefore take proper account of the configurational entropy of the mixture [16-18]. In the standard lattice model of a polymer solution, it is assumed that polymers live on a regular lattice of n sites with coordination number q. If there are n2 polymer chains, each occupying r consecutive sites, then the remaining m single sites are occupied by the solvent. The total volume of the incompressible solution is n = m + m2. In the case r = 1, the combinatorial contribution of two kinds of molecules to the partition function is... 

To see this, consider the mixing free energy expression for a polymer blend with symmetrical chain lengths and with only one crystallizable component (i.e., p = 0 for one component and Ep 0 for the other). In that case the (mean-field) partition function for the liquid mixture is... 

Model of Dissolution. Based on the results described above, a model for the dissolution of phenolic resins in aqueous alkali solutions 1s proposed. The model 1s adapted from Ueberrelter s description for polymer dissolution 1n organic solvents (.21). In Ueberrelter s model, the dissolution process takes place 1n several steps with the formation of (a) a liquid layer containing the dissolved polymer, (b) a gel layer, (c) a solid swollen layer, (d) an infiltration layer, and (e) the unattacked polymer. The critical step which controls the dissolution process is the gel layer. In adapting h1s model to our case, we need to take into account the dependence of solvation on phenolate ion formation. There 1s a partition of the cation and the hydroxide ion between the aqueous solution and the solid phase. The... 

The formation of two aqueous phases can be exploited in the recovery of proteins using liquid-liquid extraction techniques. Many factors contribute to the distribution of a protein between the two phases. Smaller solutes, such as amino acids, partition almost equally between the two phases, whereas larger proteins are more unevenly distributed. This effect becomes more pronounced as protein size increases. Increasing the polymer molecular weight in one phase decreases partitioning of the protein to that phase. The variation in surface properties between different proteins can be exploited to improve selectivity and yield. The use of more hydrophobic polymer systems, such as fatty acid esters of PEG added to the PEG phase, favors the distribution of more hydrophobic proteins to this phase. In Fig. 10.13, partition coefficients for several proteins in a dextran-PEG system are given [27]. 

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