Monomer volume fraction

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 theory of Broseta and Fredrickson (1990) was primarily for blends containing AB random copolymer. However, they also found a region of validity of this approach for block copolymers at high temperatures. Using the random phase approximation (RPA), the structure factor associated with fluctuations of the total A monomer volume fraction was found to be (Broseta and Fredrickson 1990)... 

Figure 6. Monomer volume fraction () vs. conversion (1) batch (2) corrected batch...

The present model is based on several assumptions (i) the possible configurations of the grafted chain are described by a random walk (ii) their free energy densities are expressed as functions of the local monomer volume fraction alone (iii) the configurations of minimum energy dominate the partition function of the system (iv) only the configurations with monomers distributed between the surface and the position of the last monomer of the chain, assumed to be the farthest one, are taken into account. The latter assumption basically implies that the probability that the most distant monomer from the surface reaches the distance z is equal to the probability that the last monomer of the chain reaches this distance this approximation clearly fails when z is in the vicinity of the surface. However, in swollen brushes the behavior of the monomers in the vicinity of the surface is less important than the behavior of the distant monomers, which are primarily responsible for the brush thickness and for the interactions between brushes. 

B. Poor Solvents. When the exponential tails of two brushes immersed in a poor solvent overlap, one might expect the local increase in the monomer volume fraction to lead to a more negative Elory—Huggins free energy and therefore to a lower total free energy of the system, which corresponds to an attraction between surfaces. However, as will be shown below, this is not always true. 

Figure 18, which plots conversion vs monomer volume fraction, exhibits a maximum at about during polymerization, some cells of the gel coalesce and form a bulk phase in which the conversion is smaller. Visual observations indeed indicated a separated thin layer at the upper part of the tube after polymerization. Since no appreciable separated liquid phase was observed before polymerization, it is likely that during polymerization some cells did coalesce. Molecular weight distribution curves have been determined for various values of (j>. The GPC curves (see Fig. 19) have a tail which is consistent with the molecular weight distribution of the polymer prepared by bulk polymerization. Therefore it is likely that this tail is due to the polymerization in bulk. The greater amount of bulk phase formed for values of < ) greater than 0.9 is probably due to the decreased stability of the concentrated emulsion in such cases. 

Fig. 18. Plot of conversion against the monomer volume fraction (SDS 0.15 g, styrene 17 ml, 40 °C, 24 h)...

Fig. 8 Monomer chemical potential in a droplet comprising monomer and hydrophobe as a function of the monomer volume fraction (top) and droplet radius (bottom). The global potential (as given by Ugelstad s equation) is given, as well as the entropic term due to mixing and the Laplace term due to surface tension. Parameters m Y=l Vm,h=0 y=25 mN/m Vjn=l-1 10 m mol T=298.15 K (p =0,96 r =100 nm...

Consider a semidilute polymer solution of chains with A b monomers, volume fraction

excluded volume v. A trace amount of longer chemically identical chains with Aa monomers is added to the solution. What is the size Ra of these A-chains, if they are assumed not to overlap with each other and not to change the overall volume fraction (pi Derive Eqs (5.23) and (5.26) for good solvents with 0 < v < from Eqs (5.38) and (5.39) for athermal solvents. Hint Renormalize the monomer to the thermal blob. 

Fig. 5. SANS measurements of monomer volume fraction in polymer particles over the course of styrene microemulsion polymerizations at 60°C [30]. Micro emulsions consist of 12 wt% dodecyltrimethylammonium bromide surfactant in D2O and (circles) 3 wt%, (squares) 5 wt%, and (triangles) 7.5 wt% monomer on a surfactant-free basis...

In the studies of dependence of [M]e on [M in the cationic polymerization of THF, the linear dependence of polymer volume fraction ([Pg.8]

Fitting the data shown in Figure 3 reveals a dry polymer thickness of 2.6 nm, which corresponds to an adsorbed mass of 290 100 ng/cm. This implies an average distance of grafting points of about = 3.5 nm and an average PEG monomer volume fraction of 4> = 0.17 of the uncompressed, solvated polymer layer. 

Fig. 15. Change of monomer volume fraction in latex particles during batch styrene emulsion polymerization with SDS as emulsifier. A Initiator potassium peroxodisulfate (117) Initiator 2,2 -azobisisobutyronitrile (118) O Initiator 2,2 -azobisisobut5rronitrile(115).

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