Renormalized solute-solvent interactions

The surrogate Hamiltonian is expressed in terms of renormalized solute-solvent interactions, a feature that leads to a simple and natural linear response description of the solvent dynamics in the vicinity of the solute. In addition to the measurable solvation time correlation function (tcf), we can also calculate observables needed to elucidate the detailed mechanism of solvation response, such as the evolution of the solvent polarization charge density around the solute. 

The difference between and is that the former is defined in terms of renormalized solute-solvent interactions which need to be specified. 

While there is no unique criterion for choosing 4 E, the selection must lead to an accurate theory of solvation dynamics without invoking two-time many-point correlation functions. We have found that this goal can be achieved with a new theory for the nonequilibrium distribution function in which the renormalized solute-solvent interactions enter linearly. In this theory and are chosen such that the renormalized linear response theory accurately describes the essential solute-solvent static correlations that rule the equilibrium solvation both at t = 0 (when solvent is in equilibrium with the initial charge distribution of the solute) and at 1 = oc (when the solvent has reached equilibrium with the new solute charge distribution). ... 

It is a statistical-mechanical theory of solutions to express the solvation free energy as a functional of distribution functions. Traditionally, the theory of solutions is formulated with a diagrammatic approach [13], in which an approximation is provided in a two-step procedure. In the first step, the free energy and/or distribution function is expanded with respect to the solute-solvent interaction potential function or its related function as an infinite, perturbation series. In the second step, a renormalization scheme is applied a set of functions are defined through partial summation of the series and are employed for substitution to make the infinite series more tractable. An approximation is typically introduced by neglecting diagrams of ill character. 

A comparison with Burchard s first cumulant calculations shows qualitative agreement, in particular with respect to the position of the minimum. Quantitatively, however, important differences are obvious. Both the sharpness as well as the amplitude of the phenomenon are underestimated. These deviations may originate from an overestimation of the hydrodynamic interaction between segments. Since a star of high f internally compromises a semi-dilute solution, the back-flow field of solvent molecules will be partly screened [40,117]. Thus, the effects of hydrodynamic interaction, which in general eases the renormalization effects owing to S(Q) [152], are expected to be weaker than assumed in the cumulant calculations and thus the minimum should be more pronounced than calculated. Furthermore, since for Gaussian chains the relaxation rate decreases... 

Relatively few theoretical studies have been devoted to the conformational characteristics of asymmetric star polymers in solution. Vlahos et al. [63] studied the conformational properties of AnBm miktoarm copolymers in different solvents. Analytical expressions of various conformational averages were obtained from renormalization group calculations at the critical dimensionality d=4 up to the first order of the interaction parameters uA> uB> and uAB between segments of the same or different kind, among them the radii of gyration of the two homopolymer parts < S > (k=An or Bm) and the whole miktoarm chain < /im > > the mean square distance between the centers of mass of the two homopolymer parts A and B < > and the mean square distance between the center of... 

Note that the dimensionless units defined in Table I are used, so that the curvature along the X direction is renormalized to 1. Here Uq is the two-body interaction potential defined in Eq. (2.13). The two terms linear in X are the dipolar interaction energy (with Uj and U2 two unit vectors, respectively, along the z-axis of the fixed frame for the solute and the solvent body, cf. Fig. 1). Finally a quadratic term in X has been added in order to confine the fluctuations of the stochastic field. 

We shall assume that this expression remains valid when it is extrapolated to the poor solvent domain. Thus, b 0 for T = TF (34.0 °C) and b < 0 for T < TF. This does not really mean that the true two-body interactions vanish for T = TF and that at T = TF there are only three-body interactions. Actually, the interaction b is a bare interaction but is nevertheless an interaction which is additively renormalized (see Chapter 14, Section 6) and its value depends partly on the true three-body interactions. Incidentally, this remark also applies to good solutions for this reason, if b is measured in good solvent, it is legitimate to extrapolate the result thus obtained to determine the value of b in poor solvent. Thus, in perturbation theory, when the diagram contributions are calculated by dimensional regularization, we may say that b = 0 for T = TF ... 

Relatively few theoretical studies have been devoted to the conformational characteristics of asymmetric star polymers in solution. The conformational properties of A B miktoarm star copolymers in different solvents were studied by renormalization group calculations. Analytical expressions of various conformational averages were obtained at the critical dimensionality d = 4 up to the first order of the interaction parameters... 

In a dilute solution in a common good solvent for both blocks, the interactions between. different copolymers may be studied using the same direct renormalization procedures as the interactions between two homopolymers A and B equivalent to the two blocks.As for blends, in the asymptotic limit of infinite molecular masses, the chemical difference between the two blocks is irrelevant and the dimensionless virial coefficient gc between block copolymers defined by Eq. (10) is equal to the same value g as for homopolymers. The interactions which may provoke the formation of mesophases are here again due to the corrections to the scaling behavior ... 

In recent years, studies of solutions of polymer blends and of copolymers have aroused a substantial theoretical and experimental interest. This is motivated by both numerous applications and more fundamental issues concerning the usefulness of the scaling and universality concepts to describe the thermodynamic properties and the phase transitions in these systems. In this lecture, chain interactions in dilute and semidilute solutions are reviewed and it is discussed how and when the interactions between chemically different monomers lead to a macroscopic phase separation in the case of ternary polymer A-polymer B- solvent systems and to a mesophase formation in diblock-copolymer solutions. The important conclusion is that due to both the overall monomer concentration fluctuations (excluded volume effects) and the composition fluctuations, the classical Flory theory often fails. This requires the use of the renormalization method and of scaling concepts to give a correct description of the phase diagrams and the critical phenomena observed in these complex systems. We give only here a brief outline, a complete review has been published elsewhere, ... 

Another important implication of the screening of the hydrodynamic interactions is that the effective friction of the monomers on the solvent is concentration dependent in a semi-dilute solution. The finite concentration of the surrounding monomers renormalizes the friction constant... 

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