The equilibrium simulations presented in this Chapter indicate that the solute position in a confining framework can be a function of its charge distribution, as shown in Section 4.3. The spectral properties—fluorescence energy, absorption energy, and spectral width—associated with the solute are, in turn, a function of the solute position in hydrophilic (but not hydrophobic) pores, as shown in Section 4.4. Thus, requirements 1 and 2 are satisfied for the model solute in the hydrophilic pore. Additionally, it was shown that the satisfaction of these requirements is associated with specific chemistry at the pore interface, as indicated in Section 4.3.2.
Investigation of the extent to which the solute contributions are observable in the TDF spectrum requires non-equilibrium simulations. If the results from equilibrium
simulations presented in this Chapter are any indication of the challenges inherent in proper sampling in these systems, non-equilibrium studies will likely require alternative approaches. The initial results from non-equilibrium simulations and the development of a number of models aimed at improving physical understanding together constitute the bulk of the next Chapter.
Chapter 5
Non-Equilibrium Studies of Confined Systems
The emergent timescales observed in the time-dependent fluorescence (TDF) spec- tra of nanoconfined systems may originate with solute motions within the confining framework. As outlined in Section 4.2, this requires that the system satisfies three properties. First, the solute position must be a function of the charge distribution of the solute, and, second, the fluorescence energy must in turn be a function of the solute position within the confining framework. Using equilibrium molecular dynamics (MD) simulations and a model Stockmayer solute, it was shown in Chapter 4 that the solute position is a function of its charge distribution in both hydrophilic and hydrophobic confinement. However, only for confinement in a hydrophilic pore is the fluorescence a function of solute position. The third required property is that the contribution to the time-dependent fluorescence spectrum must be experimentally observable—that is, it must occur on an experimentally acces- sible timescale with measurable amplitude. To address this third requirement, non-equilibrium molecular dynamics (NEMD) simulations must be employed.
The results in Chapter 4 also indicate that solute position biasing and spectral properties within the pore depend strongly on surface chemistry. The importance of molecular-level effects suggests that properties of both the confining framework and solute molecule may affect the TDF signal upon nanoconfinement of the so- lution. Ideally, combinations of confining framework and solute molecule would be systematically tested to determine which effects are important in changing the spectrum. For example, are changes in the spectrum observed for the Stockmayer solute confined in an atomically smooth cylinder? Clearly, changes to the spectrum are observed when the solute is near a cluster of silanol groups in a silica pore. Do changes to the spectrum grow in linearly with the number of clustered silanol groups? How does the arrangement of silanol groups alter spectral properties? Sim- ilarly, hydrogen bonding was observed to be important. Does a change in spectral signature occur as a consequence of the specific chemistry of the dye molecule? For example, does the TDF signal change when a silanol group donates a hydrogen bond to a solute carbonyl group vs. a nitro group? Such questions are of direct chemical relevance, particularly in applications of nanoconfinement in separations, sensing, and catalysis. Addressing these questions requires the development and systematic testing of several models for both the confining framework and solute molecule.
The first part of this Chapter is dedicated to nonequilibrium simulations of time-dependent fluorescence for the Stockmayer solute. The solute biasing and spectral changes described in the equilibrium simulations of Chapter 4 are reestab- lished for the NEMD simulations, and TDF spectra are calculated and interpreted.
The second part of this Chapter is dedicated to the development of models for identification and quantification of molecular-level effects associated with TDF signals in nanoconfined systems.
5.1
Non-equilibrium Simulation Methods
To determine if the solute movement and spectral signatures occur as predicted by equilibrium simulations, the same confined system described in Section 4.1 was treated using non-equilibrium molecular dynamics (NEMD). To generate initial conditions for NEMD trajectories, an equilibrium trajectory for the 5 D solute was equilibrated for 500 ps and followed by a 60 ns collection phase. Configurations, velocities, and forces were recorded every 100 fs. From this output, 4000 starting conditions were collected at evenly spaced time intervals of 1 ps (i.e., every tenth configuration was used from the initial 4 ns of the 60 ns equilibrium trajectory). Temperature and long-range electrostatics were handled as before (see Section 4.1).
The charge distribution for the solute was switched to that of the excited state (10 D for the Stockmayer solute) in each of the 4000 prepared systems, which were equilibrated in the ground state. Thus, time-dependent quantities include effects from solvent reorganization in response to the new excited state charge distribution. For each system, a 200 ps trajectory was collected with sampling every 0.5 ps for a total of 401 configurations (including time t0). Time-dependent analyses were
0 50 100 150 200 Time (ps) 0 0.2 0.4 0.6 0.8 1 S(t)
Figure 5.1: Time-dependent fluorescence signal, S(t), for the Stockmayer solute (black) and coumarin 153 (red) dissolved in ethanol and confined in the hydrophilic pore.