From Figure 4.14, it is clear that hydrophilic confinement changes the spectra of the solute. Spectra as a function of solute position in the pore must now be examined. Additionally, it is useful to know if the results for the z = 0 Å cut are general or unique. To what extent the solute position in the pore influences the fluorescence energy can be seen by examining the mean fluorescence energy as a function of position, h∆Ef li(x), which is calculated as
h∆Ef li(x) =
Z
∆E If l(∆E; x) d∆E. (4.10)
This has been calculated for the hydrophilic pore (solid lines) for the cuts along z= −10 Å (black), z = 0 Å (blue), and z = +10 Å (green) and for the hydrophobic pore (dashed line) along the cut z = 0 Å. The results are presented in Figure 4.15. All profiles are qualitatively flat from the left (x < 0 Å) side of the pore through the pore interior, indicating little to no movement of the spectral peak as a function of solute position. Near the right (x > 0 Å) side of the pore, however, the mean fluorescence energy redshifts for the solute in the hydrophilic pore. In the hydrophobic system, no redshift is observed. To partly address if these shifts might manifest in the TDF signal, the most probable solute positions have been indicated with arrows for ground (g) and excited (e) solutes. A change in fluorescence signal
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Solute COM x position (Å)
210 220 230 240 250 〈∆ E 〉 (x) (kJ mol -1 )
e
e
e
e
e
g
g
g
g
*
Figure 4.15: Mean fluorescence energy as a function of solute position, h∆Ef li(x),
is shown for the 5 D / 10 D solute system in the hydrophilic (solid lines) and hydrophobic (dashed lines) pore for the cuts z = −10 Å (black), z = 0 Å (blue), and z = +10 Å (green). The most likely position for the solute in its ground (g) or excited (e) state is indicated by arrows of the corresponding line type and color. Notably, the excited state solute can sample regions near the pore interface for the cut z = +10 Å, as indicated by e∗.
in the z = 0 Å cut across the hydrophilic pore is anticipated, as the excited state solute will be in a location where the fluorescence energy is redshifted. Similarly, the excited state solute for the z = +10 Å cut can sample the region near the interface (indicated by e∗) where some redshifting of the fluorescence energy occurs. (The excited state also samples regions toward the interior of the pore, as shown in Figure 4.15.)
To what extent this is a property of the 5 D / 10 D solute system, and to what extent absorption spectra are also altered for the model solutes employed
-6 -4 -2 0 2 4 6 8 Solute COM x position (Å)
175 200 225 250 275 300 〈∆ E 〉 (kJ mol -1 ) a -6 -4 -2 0 2 4 6 8
Solute COM x position (Å) 175 200 225 250 275 300 〈∆ E 〉 (kJ mol -1 ) b
Figure 4.16: The figure shows the mean absorption (blue) and fluorescence (red) energies as a function of the solute position within the hydrophilic pore for both the 5 D / 10 D solute system (solid lines) and 5 D / 15 D solute system (dashed lines). Arrows indicate the global maxima in the respective position probability distributions in Figure 4.2 for reference.
here is addressed in Figure 4.16. Figure 4.16a shows both absorption (blue) and fluorescence (red) for the 5 D / 10 D system for the z = 0 Å cut through the hydrophilic pore. The effect of increasing the excited state dipole to 15 D (dashed lines) results in a general shift to lower energies than are seen for the 10 D solute. Additionally, the induced shift near the pore interface is more dramatic. The profiles for the absorption curves (blue) indicate that while changes to the spectrum may occur near the pore interface for both the 10 D and 15 D excited state solutes , the most probable position for the solute is in the pore interior in both cases. Accordingly, the shift in the absorption spectrum near the interface is not anticipated to contribute substantially to the total observed spectrum. In the hydrophobic pore, the mean spectral position is relatively insensitive to the solute location within the pore, as seen by the mostly flat curves in Figure 4.16b. The
dominant feature is the general shift that accompanies the change in solute dipole moment.
The spectral width—and specifically the full-width-at-half-maximum (FWHM)— is of particular interest, as it is frequently used to provide indirect information about solute environment through inhomogeneous line broadening. Figure 4.17 shows the results of calculating the FWHM for the 5 D / 10 D solute system (solid lines) and 5 D / 15 D solute system (dashed lines) for both absorption (blue) and fluorescence (red) spectra for the z = 0 Å cut across the pore. The picture is qualita- tively similar to the results for the mean spectral position, in that dramatic changes occur near the pore interface in the hydrophilic pore (Figure 4.17a), while the changes to spectral width near the pore interface in the hydrophobic pore (Figure 4.17b) are absent. On the right side (x > 0 Å) of the hydrophilic pore, the FWHM is decreased, relative to those for spectra for solutes in the pore interior. That is, the spectra for solutes near the interface are narrowed, which, within the context of inhomogeneous broadening, suggests decreased solvent fluctuations and perhaps decreased solvent access near the pore interface. However, additional study is required to confirm this.
The collective results suggest that spectra for solutes in the pore interior are generally similar, while solutes near the interface show altered spectral properties. Accordingly, to enhance sampling while investigating in more detail the ways in which spectra depend on solute position, the spectra for solutes residing near the left (x < 0 Å) pore and also in the pore interior can be averaged. The spectra for solute positions approaching the right (x > 0 Å) side of the pore are averaged over
-6 -4 -2 0 2 4 6 8 Solute COM x position (Å)
10 20 30 40 50 ∆∆ EFWHM (kJ mol -1 ) a -6 -4 -2 0 2 4 6 8
Solute COM x position (Å) 10 20 30 40 50 ∆∆ EFWHM (kJ mol -1 ) b
Figure 4.17: The full width at half maximum is presented for absorption (blue) and fluorescence (red) spectra as a function of solute position, x, across the hydrophilic pore for both the 5 D / 10 D solute system (solid line) and the 5 D / 15 D solute system (dashed line).
small intervals in x. The results for position-dependent spectra calculated this way are presented for the 5 D / 10 D solute system in the hydrophilic pore (Figure 4.18a) and hydrophobic pore (Figure 4.18b).
The resulting spectra in the hydrophobic pore overlap with one another. This result indicates that the solvent does not appreciably change the spectra. It also supports the notion that averaging over regions in the pore where the mean spectral energy is mostly constant is not problematic (i.e., does not lead to artifacts in the averaged spectra). The results for the hydrophilic pore (Figure 4.18a) indicate that stronger redshifting occurs as the solute approaches the cluster of silanol groups on the right (x > 0 Å) side of the pore. The solid lines represent the spectra averaged over the pore left side and pore interior, from −6 to +5 Å for the z = 0 Å cut. The long dashed lines represent spectra for the solute at +6.4 Å, the short- dashed lines represent spectra for the solute at +7.0 Å, and the dot-dashed lines
175 200 225 250 275 300 325 ∆E (kJ mol-1) 0 0.2 0.4 0.6 0.8 1 Intensity (a.u.) a 175 200 225 250 275 300 325 ∆E (kJ mol-1) 0 0.2 0.4 0.6 0.8 1 Intensity (a.u.) c 0 50 100 150 200 250 300 350 ∆E (kJ mol-1) 0 0.2 0.4 0.6 0.8 1 Intensity (a.u.) b 0 50 100 150 200 250 300 350 ∆E (kJ mol-1) 0 0.2 0.4 0.6 0.8 1 Intensity (a.u.) d
Figure 4.18: (a) Absorption (blue) and fluorescence (red) spectra are shown for the 5 D / 10 D solute system dissolved in the hydrophilic pore. Each spectrum is the normalized average of spectra for the solute at a range of positions within the pore. Note that both the absorption and fluorescence red shift as the solute approaches the pore wall. (b) Spectra for the 5 D / 10 D solute system dissolved in the hydrophobic pore show little to no shift. (c ) Absorption and fluorescence spectra are shown for the 5 D / 15 D solute system in the hydrophilic pore. The abscissa scale has been changed to reflect the lower energies contributed by the 15 D solute. (d) Spectra for the 5 D / 15 D solute system in the the hydrophobic pore also exhibit little to no shift.
represent spectra for the solute at +7.6 Å. Interestingly, new features can be seen that are not observed in measures such as the mean spectral energy or the full- width-at-half-maximum, such as the blue-shifted shoulders in some fluorescence spectra.
The same calculations have been performed for the 5 D / 15 D solute system. The results for the hydrophilic pore are presented in Figure 4.18c, and those for the hydrophobic pore are presented in Figure 4.18d. These results are similar to the 5 D / 10 D case, although, as anticipated, changes to the spectra are amplified for the greater difference in dipole moment, ∆µ = µex− µgr.