S16_EPR

Studying the Rotational Correlation Time of Nitroxide at Different Viscosity Levels using EPR

Samuel Iverson & Kalkidan Alemayehu Molla

School of Physics and Astronomy,

University of Minnesota - Twin Cities

Minneapolis 55455

Abstract

Rotational Correlation times of a spin probe placed in a series of mixtures of water and glycerol under varying concentration and temperature were measured using electron paramagnetic resonance (EPR) spectrometry. The rotational correlation time was used to make characteristic assumptions about the viscosities of the solutions used.

Introduction

Electron Paramagnetic Resonance (EPR) is a technique that is used to study materials consisting of molecules with a free electron, known as free radicals [1]. EPR is a spectroscopy technique that measures the absorption of energy from a microwave source by a sample of free radicals under the influence of a strong magnetic field. The energy absorption that gives rise to an EPR signal is a result of the Zeeman effect, which is the interaction between the spin of the free electron and the external magnetic field. Under the influence of this magnetic field, the magnetic moment of an electron can take one of two orientations, either parallel or antiparallel to the direction of the field. These spin states correspond to two possible energy levels for the electron. The measured EPR signal arises from the reorientation of this spin, as the electron will absorb energy in order to transition from the low to the high energy state [2].

An EPR spectrum can provide a variety of useful information about the particular free radical being studied, as well as the environment in which it resides. In this experiment, we produced a variety of EPR spectra for a particular nitroxide molecule mixed with various concentrations of a glycerol/water mixture. Using the produced spectra, we obtained the rotational correlation time, a measurement which can be used to characterize the microviscosity of our mixture and will be explained in greater detail in the Theory. Using this, we can analyze how the viscosity is related to the concentration of glycerol in the sample. Additionally, by collecting EPR spectra at different temperatures, we will also explore the temperature dependence of the viscosity of different mixtures.

Theory

As introduced, an EPR signal arises due to the absorption of energy by unpaired electrons. The energy differences studied in EPR spectroscopy is primarily due to the interaction between the unpaired electrons and an external magnetic field, known as the Zeeman effect [1]. Due to its spin, an electron has a magnetic moment which, under the influence of a magnetic field, will either align itself parallel or antiparallel to the direction of the applied field, as illustrated in figure 1. These orientations correspond to the two spin states of an electron, designated by the quantum number Ms, and have different energies associated with them.

The energy levels according to these alignments are described by Zeeman effect, where the energy for a state is given as:

(1)

where g is the g-factor of the sample (roughly equal to 2 for our free radical), and Bis the Bohr magneton. The energy difference between the two spin states is then:

(2)

In order to transition from the lower energy state to the higher energy state, the electron must absorb a photon with energy equal to this energy difference. According to Planck’s law, a photon will be absorbed if:

(3)

where h is Planck’s constant and 𝜈 is the frequency of the radiation.

Combining equations (2) and (3) provide the fundamental equation of EPR spectroscopy:

(4)

This equation provides the resonance condition that must be satisfied by the radiation supplied to the sample and by the strength of the produced magnetic field in order for absorption to occur. In typical EPR spectroscopy, electromagnetic radiation at a constant frequency is provided to the sample (in the microwave range) and the magnetic field strength is swept. When the resonance condition is met, there will be a peak in absorption that will be detected by the spectrometer, as shown in figure 2.

Figure 2. Shows the variation of spin state energies as it is sweeped by the external magnetic field of strength B0.

By taking account the modulation of the supplied magnetic field through the use of phase sensitive detection, the EPR signal we actually observe using the spectrometer is in fact the first derivative of this absorption spectrum, as illustrated in figure 3.

Figure 3. Overall depiction of the observed signal; the absorption peak is a result of the resonance condition, and the spectrum that will see is first derivative of this absorption peak. Figure obtained from source [2].

Many EPR signals have more than one absorption spectral line. This is due to the interaction between the free electron and the nuclei in our paramagnetic molecule. The nucleus of an atom has a magnetic moment which will create a local magnetic field. This interaction of electrons with the nuclei is called the hyperfine interaction. It gives us a wide variety of information about our sample such as identity and number of atoms which makes up a molecule and their distances from the unpaired electrons[3]. An illustrated example of the hyperfine splitting of a single absorbance peak is shown in figure 4.

• 1. b.

Fig. 4. (a) The nucleus of an atom creating a local magnetic field. (b) The splitting of an absorption peak as a result of hyperfine interaction.

The Rotational Correlation Time

The rotational correlation time is defined the time taken by a free radical to rotate 1 radian around its axis[4]. It is proportional to the viscosity of the solution containing the free radical. The empirical equation for the rotational correlation time, in the case that the medium has only weakly immobilized the rotation of the probe, is given as:

[1] (5)

Where the values for the linewidth H0, and the line heights h0and h1are shown in figure 5, using a collected spectrum as an example.

Fig. 5. EPR spectrum of a quickly rotating (weakly immobilized) free radical in water, with linewidth and lineheights detailed.

Through observation of a spectrum, it can be determined whether the free radical under study is being either weakly or strongly immobilized. Weak immobilization is characterized by easily discernable peaks, which are fairly similar in height, as the solution is not viscous enough to slow the probe enough to produce significant broadening effects, which are easily observed in a spectrum of a probe experiencing strong immobilization (can be observed in the plot titled “EPR Spectrum 0.5 Mole fraction Glycerol 260K” in the appendix.)

Physically, the rotational correlation time relates with rotation of the molecule under study, which in turn is affected by the direction of the rotation. The high-field line or the 3rd spectral line is the one that has more magnetic anisotropy (directionally dependent). Therefore, it is the main part of our spectrum that mainly determines the characteristics of the rotational correlation time.

Results

A series of EPR spectra were obtained using 6 mixtures of glycerol and water at 0.0, 0.1, 0.2, 0.3, 0.4, and 0.5 mole fractions of glycerol, each containing a concentration of TEMPOL at 100uM. The spectrum obtained for each mixture is presented below.

100uM of TEMPOL at constant temp (298K)

Microwave frequency =9.5GHz for each spectrum.

Temperature Dependence Data

References:

• 1. Campbell, Iain D., and Raymond A. Dwek. Biological spectroscopy. Benjamin/Cummings Pub. Co., 1984.

  2. E. Duin “Electron Paramagnetic Resonance Theory.” Auburn University- Lecture Note (https://www.auburn.edu/~duinedu/epr/1_theory.pdf)

  3. Jiang, J., and R. T. Weber. "Elexsys E 500 user manual: basic operations." (2001).

  4. GEBRE‐MARIAM, T. S. I. G. E., et al. "The use of electron spin resonance to measure micro viscosity." Journal of pharmacy and pharmacology 43.7 (1991): 510-512.