b Instrucciones de Diseño para la Ordenanza 2.

In a spirit similar to the development of a series of solutes, a series of confining frameworks can be used to investigate which effects are due to confining framework

Figure 5.10: Several different confining systems can be used to investigate the effects of the confining framework. In the simplest form of confinement (a), a smooth potential is used to restrict molecular motion to a small cylinder. This can be expanded to an “atomically smooth” system (b), in which a cylinder of atoms is constructed. Lastly, the atomistic amorphous silica pore (c ) can be used to investigate the effects of surface roughness and chemical functionality.

size, surface roughness, and surface chemistry. Such a set of models is shown in Figure 5.10.

The simplest way to confine the solvent/solute system is to use a potential with cylindrical symmetry (Figure 5.10a) to mimic confinement in the silica pore. No atomistic features then contribute to the TDF signals associated with confinement with such a potential. The confining potential approach has the added advantage that the effective radius of the cylinder can be easily changed. This can be exploited to study the effect of increasing solvent layering, which has been shown to influence position within the confining framework for small diatomic solutes.

Smooth cylindrical confinement cannot easily address effects associated with charge. A simple cylindrical arrangement of atoms of alternating charge (Figure 5.10b) can be used to address electrostatic effects. The sizes of the atomic cylinders can be made similar to those of the smooth cylindrical confinement to determine how charge changes solvent packing and solute position. Additionally, small defects at the surface can be added (two atoms at a time to maintain charge neutrality) as a way of adding in the effects of surface roughness without specific chemistry. Because these defects are expected to change the electric field, and thus potential, across the pore, they are of particular relevance to both the solute position distribution and solute fluorescence energy.

Lastly, the solvent and solute systems can be confined within amorphous silica pores (Figure 5.10c), as has been done in this study. The pores show a large degree of surface roughness and are chemically modified such that they present silanol groups to the pore interior. While surface irregularity can be investigated using modified atomically smooth cylinders, the placement of atoms in those systems is well-ordered. In the amorphous silica pore, the atomic arrangement is glass- like, and surface roughness may lead to slightly different effects than those in the modified atomically smooth cylinders. Additionally, the silica pore presents silanol and geminal silanol groups, and both solvent and solute are both strongly affected by surface chemistry, as shown in Section 4.3.2.

These effects of both surface roughness and surface chemistry can be quantified within the context of the extended jump model, which has been modified to account for increased reorientation timescales of water. In essence, the excluded volume

effect described in Section 2.4.2 for bulk alcohols should also apply to silica atoms at the pore interface. That is, the pore itself slows solvent reorientation by reducing the number of possible hydrogen bond exchange partners. Moreover, this effect will be site-specific, since different parts of the pore interface show different geometric arrangements of pore atoms and thus preclude hydrogen bond exchange to different degrees. Accordingly, the solvent jump time contribution should increase in the pore over that of the bulk solvent according to Equation 5.3,

hτ_{con f}jumpi = ∑ Nsites i=1 ρV, iτ jump bulk N_sites = ∑N_i=1sites  1 1− fi  τ_bulkjump N_sites , (5.3)

where the sum runs over all interfacial sites, i, and V indicates that the effect is associated with excluded volume. Recall that fiis the excluded volume fraction

so ρV, iis the slowdown factor. Similarly, the distribution of silanol groups within

the pores will affect solvent reorientation dynamics through hydrogen bonding strength. This effect is absent in the alcohols, where all hydrogen bonding is roughly equivalent. In the silica pore, the dipole associated with silanol groups is different than that for the alcohols, and a solvent molecule can interact with one or several silanol groups. Moreover, the arrangement of silanol groups can vary. This reorientational slowing is anticipated to follow Equation 5.4

hτ_{con f}jumpi = ∑ Nsites i=1 ρHB, iτ jump bulk N_sites = ∑N_i=1siteseβ ∆∆G ‡ τ_bulkjump N_sites , (5.4)

where ∆∆G‡= ∆G‡_SiOH− ∆G‡_ROH. Each ∆G term is a free energy for elongating a hydrogen bond between an alcohol and the subscripted species.[23, 24] The slowdown factor ρHBtherefore reflects the relative free energy cost for hydrogen

bond exchange with the confining framework over that of the bulk liquid. These two effects—entropy and enthalpy through excluded volume and hydrogen bond strength, respectively—should combine uniquely at each site on the silica surface [145] so that hτ_{con f}jumpi =∑ Nsites i=1 ρV, iρHB, iτ jump bulk Nsites