Comparing Rotational and Translational Diffusion to Evaluate

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B: Liquids, Chemical and Dynamical Processes in Solution, Spectroscopy in Solution

Comparing Rotational and Translational Diffusion to Evaluate Heterogeneity in Binary Solvent Systems Stephen M. Baumler, Jillian M. Mutchler, and Gary J Blanchard J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b09181 • Publication Date (Web): 11 Dec 2018 Downloaded from http://pubs.acs.org on December 17, 2018

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The Journal of Physical Chemistry

Comparing Rotational and Translational Diffusion to Evaluate Heterogeneity in Binary Solvent Systems Stephen M. Baumler*, Jillian M. Mutchler, and G. J. Blanchard* Michigan State University Department of Chemistry 578 S. Shaw Lane East Lansing, Michigan 48824

Abstract We report on the rotational and translational diffusion dynamics of two monovalent fluorescent probe molecules, cationic oxazine 118 and anionic resorufin in the glycerolwater solvent system using time-resolved fluorescence anisotropy (TRFA) and fluorescence recovery after photobleaching (FRAP) measurements.

Experimental

measurements of the chromophores are compared to well-established hydrodynamic models of rotational diffusion by the modified Debye-Stokes-Einstein (DSE) equation and of translational diffusion by Stokes-Einstein-Sutherland (SES) equation. Other quasihydrodynamic models by Geirer–Wirtz (GW) and Dote–Kivelson–Schwartz (DKS) are compared to the modified DSE and SES models to better understand their utility to these systems. Deviations from the theoretically predicted diffusion constants are attributed to local solvation differences between the cationic and anionic chromophores and heterogeneity within the glycerol-water solvent system. Direct comparison between the modified DSE and SES models allow for empirical determination of the solvent-solute frictional interaction factor.



Present address: Department of Chemistry, Ohio State University. Email: [email protected] Authors to whom correspondence should be addressed. Email addresses: [email protected] and [email protected]

*

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Introduction Understanding diffusional motion that depends on ionic charge in heterogeneous liquid-phase environments is of fundamental importance to areas ranging from cellular biophysics to material science and drug delivery. Intermolecular interaction dynamics in these systems play an important role in governing the bulk physicochemical properties of binary solvent systems. To better understand these molecular processes, we focus on understanding the molecular interactions between solute and solvent. Well-established models can provide substantial insight into the solvent-mediation of molecular motion in neat solvents. The modified Debye-Stokes-Einstein,1-4 Geirer–Wirtz (GW),5 and Dote– Kivelson–Schwartz (DKS)6 models each provide insight into the factors governing solute rotational diffusion behavior in simple solvent systems. Similarly, the Stokes-EinsteinSutherland (SES) equation is commonly employed to model molecular translational diffusion in homogeneous systems.2-4, 7 In more complex systems, such as binary solvent systems, these models do not account for short-range heterogeneity and possible strong interactions between the solvent molecules, which can lead to significant deviations between experimentally measured diffusion constants and those predicted by the several models in use.1-11 The glycerol-water binary solvent system is of great interest due to its use in cryopreservation,12 industrial formulations,13 and as an environmentally friendly “green” solvent system.14 In addition, glycerol-water serves as excellent model system because of its inherently high viscosity, molecular-scale heterogeneity,15-16 and potential relevance to many systems of interest, such as ionic liquids,17-18 deep eutectic solvents,19 solvents in the glassy state,20-22 and confined solvation environments.23-24 Theoretical, computational, and


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experimental approaches have been utilized to better understand dynamics and heterogeneity in binary solvent systems.25-27

Previous studies have examined

computationally the temperature dependent rotational or translational diffusion behavior of molecular species in binary solvents, focusing on changes in interaction energies at the solute-solvent “boundary”.27-28 Unfortunately, changes in temperature likely result in transformation(s) to the molecular-scale organization of the solvating environment.20, 29 Recent work by our group has utilized the relationship between rotational and translational diffusion as expressed through DSE and SES models to determine the interaction energy of a tethered chromophore at the solid-liquid interface.30 In this study, we utilize the relationship between rotational and translational diffusion to evaluate the solute-solvent system interfacial boundary behavior at constant temperature to minimize thermal perturbation of the micro-scale heterogeneous environment that characterizes the glycerolwater binary solvent system. A primary purpose of this work was two examine the relationship between the modified Stokes-Einstein-Sutherland (SES) (Eq. 1) and Debye-Stokes-Einstein (DSE) (Eq. 2) models by examining the diffusional characteristics of two structurally similar, isoelectronic molecular species of opposite charge in the glycerol-water binary system. DT is the translational diffusion constant, DROT is the rotational diffusion constant, kBT is the thermal energy term, η is the bulk viscosity of the surrounding medium, r is the radius of the spherical diffusing molecule, and V is the hydrodynamic volume of the rotating species.31 The DSE and SES models originally treated the rotational diffusion of a spherical rotor in a homogeneous medium. Correction factors to account for ellipsoidal rotor shape have been added to the modified DSE and SES models (Eqs. 1-2).8-10 The



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geometric shape factor S was first derived analytically by Perrin and is used to account for the ellipsoidal shape of the diffusing molecules.9-10 First described by Hu and Zwanzig, an additional correction factor f to the DSE equation is added to account for rotational torque induced by solute-solvent frictional interactions.8

DT  k BTS 6 r

(1)

DROT  k BTS 6V  f

(2)

Addition of the frictional correction term to the DSE equation provides an upper and lower limit to an expected rotational diffusion constant where f = 1 under “stick” conditions and f < 1 under “slip” conditions. Geirer–Wirtz (GW),5 and Dote–Kivelson–Schwartz (DKS)6 models each provide supplemental insight into the frictional correction factor governing solute rotational diffusion in simple solvent systems. Ideally, comparison between rotational and translational diffusion constants should allow for experimental determination of the frictional coefficient term. Time-resolved fluorescence anisotropy decay measurements are used to measure rotational correlation times and diffusion constants, which sense the solute immediate environment in a series of solutions of high glycerol concentration (90-100%). Fluorescence recovery after photobleaching (FRAP) measurements provide translational diffusion information on a macroscopic-scale (μm-mm), and report on heterogeneity within the binary solvent system that may exist on length scales greater than the molecular level. The two time-resolved fluorescence techniques were chosen due to their complementary nature. There is a relationship between DT (Eq. 1) and DROT (Eq. 2) that can be determined using the modified DSE and SES models (Eq. 3), yielding the frictional coefficient term.

f  3DT 4DROT r 2 -4ACS Paragon Plus Environment

(3)

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By acquiring both DROT and DT experimentally, composition-dependent variations in the solute-solvent frictional interactions can be determined directly. Such information is expected to depend on the ionic charge of the diffusing entity because of solvent local organization. Examination of the length-scale dependence of the DT data also provides insight into the heterogeneity that characterizes this binary solvent system.

Experimental Section Sample preparation. Glycerol (Sigma Aldrich), resorufin (Sigma Aldrich, sodium salt), and oxazine 118 (Exciton, chloride) were used as received, without further purification. Chemical structures for the two dyes are shown in Fig. 1. Water (18 MΩ) was obtained from a Milli-Q Plus water purification system and used for all experiments. Both oxazine 118 and resorufin were first dissolved in pure glycerol by stirring for 24 hours and serially diluted to a concentration of 20μM. All glycerol-water binary solvent systems reported here are measured in wt.%. The comparison between weight, volume, and molar percent for the glycerol-water binary system is presented in Table S1. All solutions were mixed in closed containers for a minimum of 12 hours before measurements were made. FIGURE 1 HERE.



Oxazine 118

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y z

x

Resorufin Figure 1: Chemical structures of the isoelectronic dyes oxazine 118 and resorufin. Both chromophores are observed to rotate as prolate ellipsoids and with the dominant axis of rotation being the x-axis. Steady State Absorbance and Fluorescence Measurements. Absorbance spectra of the oxazine 118 were measured using an Ocean Optics USB4000-UV-VIS spectrometer equipped with a US-ISS-UV/VIS illuminated cuvette holder. Emission spectra for oxazine 118 were collected using a Jobin Yvon Spex Fluorolog-3 spectrometer.

Resorufin

absorbance was measured using a Perkin Elmer Lambda 950 and emission on a Varian Cary Eclipse. Excitation was set to 580 nm for all emission measurements. Fluorescence Recovery After Photobleaching (FRAP) Measurements.

FRAP

measurements were conducted on a Nikon C2+ confocal laser scanning microscopy system. A Nikon Eclipse Ti-E inverted microscope with a confocal scanning system (Nikon Ti-SCON) used the 561 nm line of a DPSS laser (Nikon Lu-N4) for excitation. Excitation light was filtered using an excitation filter (Nikon EX560/40) and dichroic filter centered at 595


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nm (Nikon DM595). Emission was collected from 600-660 nm (Nikon BA630/60) using a standard PMT detector (Nikon C2-DU3). A 20x objective lens (N.A. 0.75) was used for imaging. The sample format for the FRAP measurements was in the form of a thin film sandwiched between a borosilicate microscope slide and coverslip using a silicone gasket spacer (20 mm diameter, ca. 0.5 mm thickness, ThermoFisher). Initial intensities I(t

Comparing Rotational and Translational Diffusion to Evaluate

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