Necklace chains

Micka, U. and Kremer, K. (2000) Strongly charged flexible polyelectrolytes in poor solvents—from stable spheres to necklace chains. Europhys. Lett., 49, 189-195. 

The qnD values of cellulose and its derivatives lie between 3 and 25 nm and are larger than those of typical vinyltype polymer ( 1 nm), but markedly smaller than those of typical stiff chain polymers, such as DNA (Table 14)67). Thus, the chains of cellulose and its derivatives can be considered as semi-flexible. It may be concluded that both the pearl-necklace chain and the wormlike chain models are adequately applicable to these polymers. 

Micka U, Kremer K. From microgel to necklace chains—strongly charged polyelectrolytes in poor solvents. Europhys. Lett., 2000 49 189. 

We have studied the effects of mixture composition on droplet microstructure (5), and summarized these results in the form of a rich morphology diagram (Figure 3) in the parameter space of mass fraction and shear rate. Formation of strings of the suspended phase was observed over a broad composition window. At each composition, experiments were stopped when strings were formed. We also found a non-transient moiphology where we saw arrangement of the droplets in ordered pearl-necklace chain structures. 

It turns out that there is a simple rescaling possible, by which all curves superimpose (at least approximately) on a master curve (Fig. 13b) A b is rescaled by Sbiob. the number of monomers per blob, motivated by the idea that the bottlebmsh polymer is viewed as a pearl-necklace chain of blobs, the blob radius being the cross-sectional radius of the cylindrical brush. From this condition, biob is easily derived numerically from the simulation data. 

Several studies have demonstrated the successful incoriDoration of [60]fullerene into polymeric stmctures by following two general concepts (i) in-chain addition, so called pearl necklace type polymers or (ii) on-chain addition pendant polymers. Pendant copolymers emerge predominantly from the controlled mono- and multiple functionalization of the fullerene core with different amine-, azide-, ethylene propylene terjDolymer, polystyrene, poly(oxyethylene) and poly(oxypropylene) precursors [63,64,65,66,62 and 66]. On the other hand, (-CggPd-) polymers of the pearl necklace type were fonned via the periodic linkage of [60]fullerene and Pd monomer units after their initial reaction with thep-xy y ene diradical [69,70 and 71]. 

Anionic Surfactants. PVP also interacts with anionic detergents, another class of large anions (108). This interaction has generated considerable interest because addition of PVP results in the formation of micelles at lower concentration than the critical micelle concentration (CMC) of the free surfactant the mechanism is described as a "necklace" of hemimicelles along the polymer chain, the hemimicelles being surrounded to some extent with PVP (109). The effective lowering of the CMC increases the surfactant s apparent activity at interfaces. PVP will increase foaming of anionic surfactants for this reason. 

Harada et al. were the first to synthesize a polyrotaxane. Using the process shown in Scheme 1, they obtained an inclusion compound in which many a-CDs are threaded by a PEG chain and named it molecular necklace . Wenz et al. [132] reported polyrotaxanes containing polyamines and a-CDs. Because of its significance and interest, the approach used by Harada et al. to obtain the molecular necklace is worth reproducing here in some detail. 

The focus of this chapter is on an intermediate class of models, a picture of which is shown in Fig. 1. The polymer molecule is a string of beads that interact via simple site-site interaction potentials. The simplest model is the freely jointed hard-sphere chain model where each molecule consists of a pearl necklace of tangent hard spheres of diameter a. There are no additional bending or torsional potentials. The next level of complexity is when a stiffness is introduced that is a function of the bond angle. In the semiflexible chain model, each molecule consists of a string of hard spheres with an additional bending potential, EB = kBTe( 1 + cos 0), where kB is Boltzmann s constant, T is... 

To make the idea more nearly concrete, here is a specific example, anticipating what follows in chapters 9 and 10. Think about creating a necklace by threading 100 beads on a chain. Let s suppose that there are 20 different beads, distinguished by color and shape. It should be clear that there are a great many different necklaces that you could produce, depending on the order in which you thread the different beads. 

A protein molecule is a precisely ordered chain of units called amino acids. There are twenty amino acids that occur commonly. A modestly sized protein would contain a chain of 100 or more of these units. So a protein is analogous to the specific necklace cited above. The job of a living organism is to sort out one specific state from the wealth of possibilities each time it makes a protein molecule. The creation of this order comes at the expense of order in the surrounding environment. 

The affinity of Cgo towards carbon nucleophiles has been used to synthesize polymer-bound Cgo [120] as well as surface-bound Cjq [121]. Polymers involving G q [54, 68, 69] are of considerable interest as (1) the fullerene properties can be combined with those of specific polymers, (2) suitable fullerene polymers should be spin-coatable, solvent-castable or melt-extrudable and (3) fullerene-containing polymers as well as surface-bound Cgo layers are expected to have remarkable electronic, magnetic, mechanical, optical or catalytic properties [54]. Some prototypes of polymers or solids containing the covalently bound Cjq moiety are possible (Figure 3.11) [68,122] fullerene pendant systems la with Cjq on the side chain of a polymer (on-chain type or charm bracelet ) [123] or on the surface of a solid Ib [121], in-chain polymers II with the fullerene as a part of the main chain ( pearl necklace ) [123], dendritic systems III, starburst or cross-link type IV or end-chain type polymers V that are terminated by a fullerene unit For III and IV, one-, two-and three-dimensional variants can be considered. In addition, combinations of all of these types are possible. 

The molecular necklace 12 of a-cyclodextrin 13 beads threaded on a polyether chain (Figure 1.5) forms spontaneously in solution [17]. This is an example of a so-called one-pot reaction in which complicated structures are... 

Necklace models represent the chain as a connected sequence ctf segments, preserving in some sense the correlation between the spatial relationships among segments and their positions along the chain contour. Simplified versions laid the basis for the kinetic theory of rubber elasticity and were used to evaluate configurational entropy in concentrated polymer solutions. A refined version, the rotational isomeric model, is used to calculate the equilibrium configurational... 

At sufficiently high temperature, i.e., in the weak coupling regime, the chains have extended coil-like or necklace-like conformations and are distributed more or less uniformly in the solution. Such a behavior is typical for single-chain HPEs [164]. 

Mixtures of poly (ethylene oxide) (PEO) of various molecular weights with a -CD have given stoichiometric complexes in high yields [17]. It is important to consider that the formation of the complexes involved the threading of the a-CD along the polymer chain into a necklace-like structure [26], This process is driven... 

The next subsections describe the properties of the pearl-necklace structure and the elongation of the pearl-necklace polymer chain by an external force. We will then present numerical simulations of single polyelectrolyte chains in a poor solvent. 

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. 

It decreases with the solvent quality and crosses over to the radius of a Gaussian polyelectrolyte for T (f-ls/b)1/3. In the pearl-necklace structure most of the polymer mass and charge belongs to the pearls but the size of the chain is dominated by the stretched strands. 

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