Collapse globule

The parameter /r tunes the stiffness of the potential. It is chosen such that the repulsive part of the Leimard-Jones potential makes a crossing of bonds highly improbable (e.g., k= 30). This off-lattice model has a rather realistic equation of state and reproduces many experimental features of polymer solutions. Due to the attractive interactions the model exhibits a liquid-vapour coexistence, and an isolated chain undergoes a transition from a self-avoiding walk at high temperatures to a collapsed globule at low temperatures. Since all interactions are continuous, the model is tractable by Monte Carlo simulations as well as by molecular dynamics. Generalizations of the Leimard-Jones potential to anisotropic pair interactions are available e.g., the Gay-Beme potential [29]. This latter potential has been employed to study non-spherical particles that possibly fomi liquid crystalline phases. 

The second possible geometry will arise if the micellization proceeds by aggregation of copolymer chains that already have a glassy head. Although little is known about the structure of individual glassy chains in solution, the characteristic relaxation time ofthe chain is likely to depend on the amount of solvent actually present in the collapsed globule. In the extreme case of zero solvent... 

In this review, hydrophilically and hydrophobically modified poly(N-iso-propylacrylamide) (PNIPAM) copolymers are mainly used to illustrate how amphiphilic copolymer chains can fold from an extended random coil to a collapsed globule in extremely dilute solutions and associate to form a stable mesoglobular phase which exists between single-chain globules and macroscopic precipitation. The copolymers used can be prepared by free-radical reaction. 

Fig. 2 Schematic of four thermodynamically stable states (random coil, crumpet coil, molten globule and collapsed globule) of a homopolymer chain in the coil-to-globule and the globule-to-coil transitions. There exists a hysteresis between the two transitions around the 0-temperature ( 30.6 °C) of the PNIPAM solution [37]...

The comonomer distribution can be alternated by controlling the synthesis conditions, such as the copolymerization at different reaction temperatures at which the thermally sensitive chain backbone has different conformations (extended coil or collapsed globule). In this way, hydrophilic comonomers can be incorporated into the thermally sensitive chain backbone in a more random or more segmented (protein-like) fashion. On the other hand, short segments made of hydrophobic comonomers can be inserted into a hydrophilic chain backbone by micelle polymerization. One of the most convenient ways to control and alternate the degree of amphiphilicity of a copolymer chain, i.e., the solubility difference of different comonomers in a selective solvent, is to use a thermally sensitive polymer as the chain backbone, such as poly(N-isopropylacrylamidc) (PNIPAM) and Poly(N,N-diethylacrylamide) (PDEA). In this way, the incorporation of a hydrophilic or hydrophobic comonomer into a thermally sensitive chain backbone allows us to adjust the degree of amphiphilicity by a temperature variation. 

Some decades ago Stockmayer [63] first suggested that a flexible polymer chain can transit its conformation from an expanded coil to a collapsed globule on the basis of Flory s mean - field theory [11], Since his prediction, theoretical and experimental studies of this coil - to -globule transition have been extensively conducted [31,64-68],... 

A neutral collapsed polymer chain can be considered in a first approximation as a liquid drop which undergoes the Rayleigh instability when it becomes charged [64, 66]. The various daughter drops are however linked into a chain and the daughter drops cannot separate from each other. They remain linked by stretched polymer strands. The picture that is obtained for a polymer chain in a poor solvent is thus that of a necklace of collapsed globules, the pearls, connected by the strands that are stretched by the electrostatic interactions between the pearls. 

The pearls are just at the Rayleigh instability threshold, their density is that of a collapsed globule and their size is obtained from the Rayleigh charge. It is the so-called electrostatic blob size... 

The important feature of qc p is that when a chain possesses one thermodynamically stable fold (or global minimum conformation), q p = 1 for all a and P while for a homopolymerlike collapsed globule, qap —> 1/N (indicating no stable folds or conformers). A third possibility can exist as well which typifies the spin-glass phase. The chain has numerous stable folds (or many low energy conformers). In this case, there exists a set of thermodynamically definite folds with coordinates, r, and q c = 1 when = f and q 1/N when. ... 

The conformation of a single chain in a good solvent (left side) is a self-avoiding walk of thermal blobs while the conformation in a poor solvent (right side) is a collapsed globule of thermal blobs. 

Derive an equation for the second virial coefficient in a solution of collapsed globules below their 0-temperature, in terms of the number of Kuhn monomers per chain N, the Kuhn monomer size b and the reduced temperature (0- T)jT. Can this second virial coefficient be related to the chain interaction parameter of Eq. (3.97) ... 

The froth model described earlier, and shown in Figure 18, produces collapsed globules, composed of a water (and solids) droplet surrounded by a membranous layer made up of asphaltenes and biwetted solids. When such froth is contacted with naphtha, the time required to penetrate the bitumen membrane coating is on the order of 30 min, whereas in a commercial process the elapsed time between naphtha addition and introduction into a settling vessel is less than 1 min. Thus, the diluted froth process stream can contain these globules, probably in floes, which would have a bulk density intermediate between diluted bitumen and water. Such floes would then accumulate in the separation vessel and form an interface layer (sometimes called rag-layer) emulsion, and could potentially form an effective barrier to gravity separation (68). 

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