Chains collapsed

The preparation of monoliths with polyNIPAAm chains grafted to the internal pore surface was discussed previously. The extended solvated polyNIPAAm-chains that are present below the lower critical solution temperature of this particular polymer are more hydrophilic, while the collapsed chains that prevail above the lower critical solution temperature are more hydrophobic. In contrast to isothermal separations in which the surface polarity remains constant throughout the run [ 136], HIC separation of proteins can be achieved at constant salt concentrations (isocratically) while utilizing the hydrophobic-hydrophilic... 

As discussed before, the lower value of Rg)/ Rh) confirms that the collapsed chain has a core-shell nanostructure and the collapsed PNIPAM core is denser than the swollen PEO shell. In comparison with a uniform sphere with the same (R ), the denser core leads to a smaller (Rg). The increase of (Rg)/ (J h) in the range 35-40 °C reflects the core-shell structure and becomes more uniform in density because the PEO chains in the shell are forced to overlap each other when the PNIPAM core continues to shrink (Fig. 14c). In Fig. 15, it is the further increase of (Rg)/(Rh) in the range 40-50 °C that differentiates the two scenarios. Namely, if the first one was correct, (Rg)/(Rh) should decrease because the core becomes denser. On the other hand, in the second scenario, the collapse of the PEO chains increases the chain density of the shell so that the core-shell nanostructure becomes more uniform, as... 

The impact of the type of earth alkaline cation on the shrinking mechanism is an interesting question by itself. Moreover, knowledge in this field is relevant for SAXS measurements. The earth alkaline cations with higher electron density might reflect the shape of the collapsing chains if they are bound to the very chains [77]. 

In conclusion, we would like to state our hypothesis concerning the possibility of reformulation of some topological problems for strongly collapsed chains in terms of integration over the set of trajectories with a fixed fractal dimension but without any topological constraints. 

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

The result decreases with k less quickly than S contrary to the unperturbed and the collapsed chain [see Eqs. (2.1.73) and (2.2.14), respectively] as a consequence, the sum of the long-range bond correlation contributions diverges and the mean-square chain size increases more quickly than N -. In particular, the central-limit theorem cannot be applied and the Gaussian distribution for W(k, r) is incorrect. Actually, it has been determined that for /c > 1 this function obeys the generalized Domb-Gillis-Wilmers form [71, 72]... 

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,...

The last result is in agreement with the general scaling law of Eqn. (3.1.32), y = j. The same conclusion was arrived at for the collapsed chain limited to sufficiently short times. 

The adsorption of proteins at interfaces is a key step in the stabilization of numerous food and non-food foams and emulsions. Our goal is to improve our understanding of the relationships between the sequence of proteins and their surface properties. A theoretical approach has been developed to model the structure and properties of protein adsorption layers using the analogy between proteins and multiblock copolymers. This model seems to be particularly well suited to /5-casein. However, the exponent relating surface pressure to surface concentration is indicative of a polymer structure intermediate between that of a two-dimensional excluded volume chain and a partially collapsed chain. For the protein structure, this would correspond to attractive interactions between some amino acids (hydrogen bonds, for instance). To test this possibility, guanidine hydrochloride was added to the buffer. A transition in the structure and properties of the layer is noticed for a 1.5 molar concentration of the denaturant. Beyond the transition, the properties of the layer are those of a two-dimensional excluded volume chain, a situation expected when there are no attractive interac-... 

Thus, let us consider a collapsed chain filling completely the volume of a sphere of radius R0. We can admit that the end points are located at random in the sphere whose centre is assumed to coincide with the origin. Consequently, we have... 

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