Collapse chain dynamics

The Bead-and-Spring Model in Bad and Good Solvents Dynamics of the Collapsed Chain... 

Dynamics of the Collapsed Chain. As done with the unperturbed chain, we shall treat the Rouse and the Zimm limits in order. 

The correlation function B(k, t) cannot be evaluated in closed form in the present case. However, for t comprised between T ,j and numerical calculations [54] show that B(0, t) cc whereas, for t x q), B(0, t) oc t due to globule diffusion. Consequently, the exponent of the relationship hiiQ = const has values 3 and 2 in the two respective regimes, as with the unperturbed chain [see Eqs. (3.2.15 ) and (3.2.16)]. We do not obtain any plateau of B 0,t) in this case, unlike the Rouse limit. Figure 7 shows the coherent dynamic structure factor S Q, t) as a function of t for two different Q values both for the unperturbed and for the collapsed chain. The two Q s correspond to observation distances /Q [ref. 15, note 6] just below and... 

Figure 7. Coherent dynamic structure factor S(Q,t)/S(Q,0) vs. t/to (to = U / bT) for atactic poiystyrene in collapsed state (continuous lines) and in unperturbed state (dashed lines). The Q values correspond to observation distances just below (Q = 0,0lA ) and above (Q = 0.003 A ) radius of gyration of collapsed chain (2 is 2.5 and 0.75, respectively). [Parameters JV = 5 x 10 chain atoms, J = 5 x 10, = 1450A, a, = 0.17,...

Key words Coil-globule transition -collapsed transition - self-organized nano-structure - single chain dynamics - hierarchical system... 

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 structure of these globular aggregates is characterized by a micellar core formed by the hydrophilic heads of the surfactant molecules and a surrounding hydrophobic layer constituted by their opportunely arranged alkyl chains whereas their dynamics are characterized by conformational motions of heads and alkyl chains, frequent exchange of surfactant monomers between bulk solvent and micelle, and structural collapse of the aggregate leading to its dissolution, and vice versa [2-7]. 

The effect of copolymer sequence on coil-to-globule transition was also studied using Langevin molecular dynamics [103]. The method for estimation of the quality of reconstruction of core-shell globular structure after chain collapse was proposed. It was found that protein-like sequences exhibit better reconstruction of initial globular structure after the cooling procedure, as compared to purely random sequences. 

In the solution with a higher concentration, interchain association accompanies intrachain contraction. When interchain association is dominant, (Rh) increases as the temperature increases, leading to a peak in the temperature range of 32-35 °C. At higher temperatures, Rvv(q)/KC stops to increase at 34 °C, as shown in Fig. 27, and reflects the end of interchain association. Therefore, the decrease of (Rh) at temperatures higher than 34 °C is related to further collapse of the PNIPAM chain backbones inside each aggregate. Besides (Rg) and (Rh), a combination of static and dynamic LLS results can also lead to other microscopic parameters of these stable interchain aggre-... 

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