Monomer concentration profile

Figure 4. Monomer concentration profiles of a single monomer in the feed stream entering the reactor as a function of time for the three-tank arrangement...

Using a self-consistent field theory, Misra et al. [10] examined the effect of the brush charge, electrolyte concentration, and surface charge density on the brush thickness. They extended the self-consistent field polymer brush theory suggested by Milner et al. [11] to the case of a polyelectrolyte brush. The theory involves a parabolic monomer concentration profile rather than the step-function suggested by Alexander [12] and de Gennes [13,14], The repulsion force... 

First, the monomer concentration profile in the macrograin (Afa[rmac,t]) can be calculated based on d[M ] 1... 

Evanescent wave induced fluorescence (EWIF) and small angle neutron scattering (SANS) experiments have been performed at the polymer solution-solid interface, in the case of adsorption. The interfacial layer is characterized by its total surface excess T and by the monomer concentration profile (2) in the direction normal to the interface. 

The experimental system used consists of a dilute solution of poly(methylmethacrylate) (PMMA) in toluene (ri2 = 1.494) in contact with a solid surface of sapphire y-alumina, = 1.79). Molecular weight of the polymer chain was 120,000 with a polydispersity index of 1.15. A small percentage of the chains were labelled with anthracene chromophores at a 1J mole concentration. The chromophores served as the fluorescent markers. Since they are located randomly along the chain, it was assumed that their distribution faithfully reflects the monomer concentration profile. PMMA of higher molecular weight was also used in some instances (Af = 600,000). The reference solutions were anthracene molecules in pure toluene. 

The SANS data presented here give strong support to the de Gennes main predictions for adsorbed polymer layers the monomer concentration profile is self-similar and scales as (z) for polymer chains in good... 

Fluctuations of the local monomer concentration are of importance to the description of polymers at surfaces owing to the many possible chain conformations. These fluctuations are treated theoretically using field-theoretical or transfer-matrix techniques. In a field-theoretical formalism, the problem of accounting for different polymer conformations is converted into a functional integral over different monomer-concentration profiles [12]. Within transfer-matrix techniques, the Markov-chain property of ideal polymers is exploited to re-express the conformational polymer fluctuations as a product of matrices [22]. 

HDH/DHD interface. If the motion of the polymer was the same for each portion of the molecule, i.e., isotropic, the concentration of deuterium across the interface would remain constant. However, if the monomer motion is anisotropic, such as with reptation, where the chain ends lead the centers, a high amplitude ripple in the concentration profile, as described below will be displayed. For a reptating chain, lateral motion of the central segment of the chain is permitted up to depths approximating the tube diameter, after which the central segments must follow the chain ends in a snake-like fashion. 

The Alexander model is based on two assumptions that enable simple expressions for these two terms (1) The concentration profile of the layer is step-like. That is, the monomer volume fraction within the layer, (p Na3/d2L, is constant, independent of position (2) The chains are uniformly stretched. That is, all chain ends are positioned on a single plane at a distance L from the surface. [In this paper, we use the symbol to mean approximately equal to or equal to within a numerical factor of order one we use to mean proportional to .] The first assumption simplifies the calculation of Fin, while the second yields a simple expression for Fel. 

The average thickness of the spherical grafted layer is determined by the requirement that the integral over the segment concentration profile must account for all the monomers in the layer ... 

Fouling is only one result stemming from the influence of mixing on establishing local concentration profiles and their impact on the course of reaction [125]. Hence, in a more comprehensive view, micro mixing can affect the local concentration of initiator, monomer and additives. This should have an impact on the molecular weight distribution of the polymer formed. 

The second major difference found in vapor-liquid extraction of polymeric solutions is related to the low values of the diffusion coefficients and the strong dependence of these coefficients on the concentration of solvent or monomer in a polymeric solution or melt. Figure 2, which illustrates how the diffusion coefficient can vary with concentration for a polymeric solution, shows a variation of more than three orders of magnitude in the diffusion coefficient when the concentration varies from about 10% to less than 1%. From a mathematical viewpoint the dependence of the diffusion coefficient on concentration can introduce complications in solving the diffusion equations to obtain concentration profiles, particularly when this dependence is nonlinear. On a physiced basis, the low diffiisivities result in low mass-transfer rates, which means larger extraction equipment. 

Monomer concentrations as a function of total surfactant concentration. Experimental CMC s are marked by arrows. At 0.01 o total surfactant levels, the monomer concentrations will be approximately given by the CMC values except for Cj E g whose CMC is 0.06.. Inset shows absorption profile if values of partition coefficient (P) shown apply. From Florence (1982). 

Whereas the two-tank arrangement permits monomer feed profiles which vary smoothly in one direction, the three-tank scheme leads to inflections and concentration reversals as illustrated in Figure 4. Such reversals are useful in preparing hard-soft-hard, hydrophilic-hydrophobic-hydrophilic polymer variations and the like. In addition, three tank power feed has been useful as a means of calculating monomer inventory in copolymerization experiments (4). 

Fig. 5. Concentration profile inside a grafted PDMS layer swollen by a good solvent (octane). The molecular weight of the grafted chains is 92 kg mol-1 and the surface density in the layer is a=0.011. The full line is the profile determined by neutrons reflectivity. The dotted line is the SCF result of Zhulina et al. [52] calculated for a surface density o=0.011 and an excluded volume parameter v=0.8 a3 (a is the size of the monomer, determined to be a 0.5 nm by the slope of the scaling line in Fig. 2).

In order to get an estimate of the adhesion energy between a pseudo-brush and an elastomer (cross-linked in the dry state), we can use the concentration profile calculated [65] for the case of a pseudo-brush exposed to a melt (Nc monomers per chain)... 

In this paper, a tube of size 1/4" in diameter was considered with styrene monomer preheated to 135 C. The radial variations in temperature are minimal and good control over the concentration profile was possible. Some typical variations in conversion with radial position are shown in Figure 10. The zone temperatures for this example represent a sub-optimal case. However, it is readily seen that as we approach the optimal solution, the first zone temperature converges to an upper limit, while the second zone temperature goes to absolute zero. Figure 11 shows this trend. We also note that as the optimal temperatures are approached, there is a steady drop in the... 

Fig. 2 Left . Simulated monomer density profile (distribution of intrastar density around the center of mass) for a melt of stars of varying arm number f (from left star to right open square . 2 (linear chain), 4, 8, 16, 24, 36, 48, 64) [41]. The low intrastar density at low functionalities indicates penetrability by other stars (to satisfy incompressibility condition), whereas at high functionality the star core is formed with constant density. Inset . Cartoon illustration of a multiarm star with the three areas in different colors melt-like inner black core, theta-like intermediate blue unswollen and excluded-volume outer red swollen region. Right . The predicted Daoud-Cotton [28] monomer density distribution. The horizontal dashed line indicates the average solution concentration...

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