Solute-solvent coupling

Retention Rejection and Reflection Retention and rejection are used almost interchangeably. A third term, reflection, includes a measure of solute-solvent coupling, and is the term used in irreversible thermodynamic descriptions of membrane separations. It is important in only a few practical cases. Rejection is the term of trade in reverse osmosis (RO) and NF, and retention is usually used in UF and MF. 

First, consider the solvent. The characterization of the solute-solvent coupling by a relaxation time is based on analogy to Brownian motion, and the relaxation time is called the frictional relaxational time Xp. It is the relaxation time for momentum decay of a Brownian motion in the solute coordinate of interest when it interacts with the solvent under consideration. If we call the subject solute coordinate s, then the component of frictional force along this coordinate may be written as... 

Another limit of interest is that when only short times are of importance. In this case, the time dependence of the solvent coordinate tcf At(t) can be ignored. Then one has (t) = (t=0), which by (3.12), is a measure of the solute-solvent coupling frequency. This is particularly relevant for the nonadiabatic limit (2.8), where it is only the initial friction value that is relevant for the reaction. 

Typical chemical reactions are characterized by sharp reaction barriers, often arising in part from the existence of a reaction barrier in the gas phase. Thus, even though the magnitude ofthe reactive solute-solvent coupling is strong [large (t=0)], the intrinsic barrier is of such high frequency that the nonadiabatic solvation limit... 

Note that dra(t)/dt = [H,ra]=(l/ma)[pa-qaA(ra)] and, consequently, the first term in (69) represents the kinetic energy of the system of particles in the presence of the transverse electromagnetic field. Note the analogy between this representation and the dynamical solute-solvent coupling of section 2.6 where the optical phonons are equivalent to electromagnetic photons of low frequency (the acoustical phonons are related to sound waves). 

D. J. Tannor One would think that as one adds more and more layers of solvent one is introducing irreversible decay of the correlation function of the solute-solvent coupling. The main physical content of the Grote-Hynes expression for the rate constant is that contributions from this correlation function that are slow compared with the time scale for reaction do not really contribute to the reaction rate. This suggests that by starting with a description of only the first solvent shell and introducing shorter and shorter solvent memory, one will see a transition that resembles that of adding more and more solvent shells. 

We first describe an appropriate model for the isolated CC (neglect of solute solvent coupling, see also Fig. 4). Afterwards, the electrostatic couplings within the CC and between the solvent and the CC are incorporated. 

When the density of bath modes becomes high, as in the case of a DC, counterparts of the discrete-mode expressions (Equations (3.73)-(3.80)) are readily available, based on the assumption that the solute-solvent coupling can be expressed as a linear functional of solute charge densities (p) [12]. Models for defining or calculating p are discussed in later sections. 

Anharmonic higher order terms gain importance for stronger solute-solvent couplings requiring 0 in Eq. [121]. The nonequilibrium solvent polarization can be considered as an ET reaction coordinate. The curvature of the corresponding free energy surface is... 

The solute-solvent coupling < ) xj(l ) (D p or s) which was left unspecified in Eq. (17) can be identified as the solute-solvent direct correlation functions from the requirement such that... 

In another word, the solute-solvent coupling so defined satisfies proper boundary conditions at the initial and filial equilibrium states. 

The different behavior in lnZ(t) between the Q—>Q and Na— >Na+ suggests that the multi-exponential behavior is caused not only by the solvent dynamics itself (Fjj (k,t)) but also by the solute-solvent coupling represented by Bjj (k) in Eq. (20). 

The MC simulations also provided details on the structural changes that accompany the reaction. The key observation is that the hydration-induced activation barrier is caused by a reduction in strength rather than in the number of solute-water hydrogen bonds that accompany charge delocalization in proceeding to the transition state. The recent dynamics results for the reaction in water are also nicely complementary a transmission coefficient near 0.5 was obtained and carefully analyzed. The deviation from TST for such a sharp barrier attests to the strong solute-solvent coupling. 

---