Solvent models polydispersity

Materials. GMC and PCLS were synthesized by free radical solution polymerization initiated by benzoyl peroxide as described previously (5,6). Nearly mono and polydisperse polystyrenes were obtained from Pressure Chemical Co. and the National Bureau of Standards respectively. Molecular weight and polydispersity were determined by gel permeation chromatography (GPC) using a Water Model 244 GPC, equipped with a set (102-106 A) of —Styragel columns using THF as the elution solvent. The molecular parameters of the above three polymers are listed in Table I. The copolymer, poly(GMA-co-3-CLS), contained 53.5 mole % 3-CLS and 46.5 mole % GMA, as determined by chlorine elemental analysis. The structure of the copolymer is shown in Figure 1. 

Among other approaches, a theory for intermolecular interactions in dilute block copolymer solutions was presented by Kimura and Kurata (1981). They considered the association of diblock and triblock copolymers in solvents of varying quality. The second and third virial coefficients were determined using a mean field potential based on the segmental distribution function for a polymer chain in solution. A model for micellization of block copolymers in solution, based on the thermodynamics of associating multicomponent mixtures, was presented by Gao and Eisenberg (1993). The polydispersity of the block copolymer and its influence on micellization was a particular focus of this work. For block copolymers below the cmc, a collapsed spherical conformation was assumed. Interactions of the collapsed spheres were then described by the Hamaker equation, with an interaction energy proportional to the radius of the spheres. 

In contrast to the crown ether 28, the cryptand K211 (33) is very beneficial to the control of MMA polymerization initiated by diphenyhnethyllithium in THF at —78 °C. As a result, PMMA with a very low polydispersity index (1.01) was obtained" . The effect of this ligand on the unimeric model, e.g. MiBLi, was studied by NMR spectroscopy. The equilibrium commonly observed in THF between tetramers and dimers is actually shifted towards a monomeric complexed species" . Both the E/Z molar ratio (90/10 instead of 0/100) and the chain tacticity (Table 5) are affected by the cryptand K211 (33) whatever the solvent used ". ... 

All the previous systems were polydisperse in nature, so that the coil-stretch transition was broad (because the relaxation time depends upon molecular weight). Also, only a part of the molecular weight distribution (the longest molecules) becomes stretched by the flow. It therefore proved impossible to determine the dependence of the coil-stretch or interaction behavior upon molecular weight. For these reasons, we examine the behavior of a model system, monodisperse atactic polystyrene (a-PS) in the 0 solvent decahydronaphthalene. We will explore separately, both by assessment of molecular strain and macrorheology, the onset of interaction behavior, particularly as a function of molecular weight, and the associated flow-induced degradation. 

As mentioned earlier, studies of simple linear surfactants in a solvent (i.e, those without any third component) allow one to examine the sufficiency of coarse-grained lattice models for predicting the aggregation behavior of micelles and to examine the limits of applicability of analytical lattice approximations such as quasi-chemical theory or self-consistent field theory (in the case of polymers). The results available from the simulations for the structure and shapes of micelles, the polydispersity, and the cmc show that the lattice approach can be used reliably to obtain such information qualitatively as well as quantitatively. The results are generally consistent with what one would expect from mass-action models and other theoretical techniques as well as from experiments. For example. Desplat and Care [31] report micellization results (the cmc and micellar size) for the surfactant h ti (for a temperature of = ksT/tts = /(-ts = 1-18 and... 

Nowadays, many polymerization reactions lead to products having very narrow molar-mass distributions, but such product samples still differ in average molar-mass values. Also, fractionation [2] can narrow the distribution function, but never produces a monodisperse polymer. As a hypothetical case, we consider a monodisperse polymer dissolved in one solvent as quasi-binary. In this chapter, first the thermodynamic models (g -models and equations of state (EOS)) for a quasi-binary system, consisting of a monodisperse polymer and a solvent, will be introduced, and later the influence of polydispersity on the phase behavior... 

Polystyrene (PS) polymer is one of the well-characterized random coil polymers used in combination with PMMA spheres. PS can be synthesized with polydispersities as small as Mw/M 1.02. The physical properties of PS in solution have been characterized in a wide range of solvents [13]. Optical tweezer experiments [14] on a pair of PMMA spheres in a PS solution were consistent with the presence of depletion layers of PS surroimding the spheres. Also DLS measurements showed that adsorption does not occur [3]. Hence, the model system of... 

Here hence denotes the position of monomer with label i (i= 1,..., N) in the feth chain molecule (fe = 1,..., N ). For simplicity, we have specialized here to a monodisp>erse system of linear homopolymers hut the generalization to polydisperse systems or to heteropolymers or to branched architecture is straightforward, as well as to multicomponent systems (including solvent molecule coordinates, for instance). Typically, the volume in which the S3 tem is considered is a cubic LxLxL box (in d = 3 dimensions, or a square LxL box in d = 2 dimensions), and one chooses periodic boundary conditions to avoid surface effects but if the latter are of interest, the corresponding change of boundary conditions is straightforward. All of what has been said so far applies to lattice models as well as to models in the continuum. 

---