Distribution of guest molecules in Pluronic micelles studied by double electron electron spin resonance and small angle X-ray scattering

Abstract

Pulse double electron–electron spin resonance (DEER) measurements were applied to characterize the distribution and average number of guest-molecules (in the form of spin-probes) in Pluronic P123 micelles. Two types of spin-probes were used, one of which is a spin-labeled P123 (P123-NO), which is similar to the micelles constituent molecules, and the other is spin-labeled Brij56 (Brij56-NO) which is significantly different. Qualitative information regarding the relative location of the spin-labels within the micelles was obtained from the isotropic hyperfine coupling and the correlation times, determined from continuous wave EPR measurements. In addition, complementary small angle X-ray scattering (SAXS) measurements on the P123 micellar solutions, with and without the spin-probes, were carried out for an independent determination of the size of the core and corona of the micelles and to ensure that the spin-probes do not alter the size or shape of the micelles. Two approaches were used for the analysis of the DEER data. The first is model free, which is based on the determination of the leveling off value of the DEER kinetics. This provided good estimates of the number of radicals per micelle (low limit) which, together with the known concentration of the P123 molecules, gave the aggregation number of the P123 micelles. In addition, it provided an average distance between radicals which is within the range expected from the micelles' size determined by SAXS. The second approach was to analyze the full kinetic form which is model dependent. This analysis showed that both spin-labels are not homogeneously distributed in either a sphere or a spherical shell, and that large distances are preferred. This analysis yielded a slightly larger occupation volume within the micelle for P123-NO than for Brij56-NO, consistent with their chemical character.

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Introduction

Water-soluble triblock copolymers of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO), often denoted as Pluronics PEO_n–PPO_x–PEO_n, are commercially available non-ionic macromolecular surface active agents.^1,2 Variation of the copolymer composition (PPO/PEO ratio) and molecular weight (PEO and PPO block length) produces molecules with optimized properties that often meet the specific requirements for various technological applications. Consequently, PEO_n–PPO_x–PEO_n block copolymers comprise an important class of surfactants that find widespread industrial applications in detergency, dispersion stabilization, foaming, emulsification, lubrication, and formulation of cosmetics.¹ Another important application of these block-copolymers is also their use as templates in the synthesis of ordered mesoporous materials.^3–6

The water solubility of the Pluronics is highly dependent on temperature. At low temperatures both the PEO and PPO blocks are significantly hydrated and, below a critical micellization temperature (CMT), the polymers are present mainly as soluble individual single chains (unimers). As the temperature increases, the PPO groups become increasingly hydrophobic and above the CMT, micelles are formed.^1,7–10 The PPO block comprises the hydrophobic core of the micelles and the PEO blocks the hydrophilic corona.

One of the most useful properties of the Pluronic micelles is their ability to take up hydrophobic guest molecules, which are otherwise only sparingly soluble in water. The micelle’s core serves as a compatible micro-environment for the water-insoluble guest molecules, thereby enhancing their solubility in water. This process, referred to as solubilization,^9,10 is important for applications such as drug delivery.^11,12 For this purpose the knowledge of physico-chemical properties of the micelles such as CMT and CMC (critical micelles concentration), micelles dimensions, the effect of the guests on these properties, and the amount and partitioning of the guests within the micelles, is required. The solubilization characteristics of the Pluronics also allow introducing various probes, such as magnetic or fluorescence probes, to explore various local properties of the micelles¹³ and follow processes such as the formation mechanism of mesoporous materials.^14,15 Several studies dealt with solubilization of hydrophobic guests in block copolymer micelles and their effect on the CMC, CMT and aggregation number using techniques such as SANS (small angle neutron scattering), SAXS (small angle X-ray scattering), dynamic light scattering (DLS), fluorescence and NMR spectroscopy.^9,13,16–19

Traditionally, micelles' properties have also been investigated by EPR of nitroxide spin-probes, focusing mainly on the dynamic characteristics determined using lineshape analysis and polarity gradients obtained from the hyperfine coupling constant.^20,21Electron spin echo envelope modulation (ESEEM) spectroscopy has also been applied to investigate structural properties of micelles such as the water penetration profile.^22,23 Double electron–electron resonance (DEER) is a pulse EPR method which is capable of recovering dipolar couplings between electron spins, and thus it can provide distances in the nm range.^24–28 Consequently, it has been applied to investigate the distribution of radicals in irradiated solids and of spin-probes in polymers for identifying and characterizing the formation of clusters.^{24–26,29,30} In a recent study we demonstrated that DEER can also be used to explore the properties of micelles of Pluronics³¹ and that it can detect variations in micelles’ dimensions during the formation of mesoporous materials prepared with Pluronic templates.³² In these early works the spin-probe used was 4-hydroxy-TEMPO-benzoate (4HTB), which is a small hydrophobic molecule localized in the hydrophobic core of the micelles.^32,33 The DEER measurements gave estimates of the number of spin-probes in the core and the volume of the core of the micelles.³¹ In the present work we employ DEER to study the distribution of guest molecules in P123 micelles using different classes of spin-labeled guest molecules; specifically comparing Brij56-NO and P123-NO (see Fig. 1) which are considerably larger than 4HTB and located in different regions of the Pluronic micelles. P123-NO is a labeled Pluronic, which is highly similar to the molecules constituting the micelles and the label is located at the corona of the micelle. Brij56-NO has a highly hydrophobic alkyl chain, expected to locate the spin-label at the core–corona interface.

Fig. 1 The spin-probes used in this study.

The DEER technique works very well for distance determination of a pair of radicals with a narrow distribution of distances. In this case, the DEER kinetics exhibits modulation at a frequency characteristic of the dipolar interaction, which can be readily translated into the distance between the radicals. However, when the distance between the radicals has a large distribution and the number of interacting radicals becomes larger than two, as encountered in clusters and micelles, the DEER kinetics becomes featureless and the extraction of the distance distribution and the number of interacting spins becomes more involved and often model dependent. This essentially limits the data analysis that aims at providing the size of the cluster and the number of radicals in the cluster.

Here we present an experimental approach which allowed us to carry out a model free analysis of the DEER data to estimate the average number of spin-probes (guest molecules) in the micelles, the volume they occupy and the aggregation number of the micelle. This is achieved by performing a series of DEER measurements as a function of microwave power and pulse duration and of the concentration of the spin-probes. In addition to the DEER experiments, we present SAXS results which shows that the spin-probes added did not affect the micelles dimensions and provide an independent measure of the size of the core and corona of the micelles to validate and complement the DEER results.

Experimental

Sample preparation

Pluronic P123 (EO₂₀PO₇₀EO₂₀, M_av = 5800) was a gift from BASF Corp. (USA). The spin-probes L62-NO, L64-NO, P123-NO, F127-NO and Brij56-NO were synthesized as described in the literature³⁴ and 4-hydroxy-TEMPO-benzoate (4HTB) was purchased from Aldrich. Fig. 1 depicts the structure of the spin-probes used. The triradical (Fig. S2b)† has been synthesized as described earlier³⁵ and has been investigated by DEER.³⁶ The biradical (Fig. S2a)† was kindly given to us by Prof. G. Jeschke.

The samples for DEER and ESEEM measurements were prepared as follows :  the spin-probe was dissolved in 4 wt% P123 solution in D₂O at 50 °C; after stirring for approximately 1 h, a sample from the solution was placed in a 3 mm od Teflon tube (for X-band measurements) or in a thin wall, 2.9 mm od quartz tubes (for Ka-band measurements). The samples were kept at 50 °C in a hot water bath for 20 min and then frozen rapidly by placing the tubes in a 2-methyl butane bath cooled by liquid nitrogen. The samples for X-band continuous wave (CW) EPR were prepared similarly, except for the freezing part, and flat cells were used. The solutions made were of Brij56-NO or P123-NO dissolved in a 4 wt% P123 solution in D₂O at three total spin concentrations, 0.3, 0.5 and 0.7 mM. The latter corresponds to a molar ratio of 10 : 1 for P123 : Brij56-NO and 20 : 1 for P123-NO.

EPR spectroscopic measurements

The EPR measurements were performed at X (∼9.4 GHz) and Ka (∼30–34 GHz)-bands. CW EPR spectra were recorded using a X-band Bruker Elexsys 500 spectrometer. The pulse X-band EPR measurements, (ESEEM and DEER) were carried out on a Bruker Elexsys E580 spectrometer and the Ka-band DEER experiments were performed with the home-built spectrometer of the University of Arizona.³⁷ The three-pulse ESEEM sequence, π/2-τ-π/2-T-π/2-τ-echo, was employed with a 4-step phase cycling.³⁸ The π/2 pulse length was 20 ns, and τ was set to 224 ns, to maximize the ²H modulation depth and the field was set to maximum echo intensity (M_I = 0 component). The modulation depth was taken as k = (a/(a + b)), where a + b is the interpolated echo intensity between the first and second maxima, and b is the echo intensity at the first minimum.¹⁴

The triradical and biradical homogeneous solutions were measured at the X-band using the constant time four-pulse DEER sequence, (π/2)(ν_obs)-τ₁-π(ν_obs)-t-π(ν_pump)-(τ₁+τ₂-t)-π(ν_obs)-τ₂-echo.³⁰ A two step phase cycle was employed on the first pulse, and averaging over 25 increments of τ₁ (τ₁ = 200 ns, Δτ₁ = 8 ns) was carried out to suppress proton and deuterium modulations. The echo was measured as a function of t (Δt = 20 ns) while τ₂ was kept constant to eliminate relaxation effects. The pump frequency, ν_pump, was set to the maximum intensity of the nitroxide spectrum, and the observer frequency, ν_obs, was 60 MHz higher. Both the π/2 and π pulses (observe and pump) had a length of 40 ns. Typical numbers of shots per point and accumulations are 30 and 10, respectively, and the measurement temperature was 50 K. The flip probability of the pump pulse was determined experimentally using a series of glassy solutions of 4HTB spin-probes in 50/50 methanol/toluene (more details are given below).

The micellar solutions were measured using the three-pulse DEER, (π/2)(ν_obs)-t-π(ν_pump)-(τ-t)-π(ν_obs)-τ-echo. This sequence was chosen because of its better sensitivity, which enables a larger acquisition time interval (at the same S/N) or a better S/N for the same time interval, as compared with the 4-pulse DEER. Due to the large distance distribution in micelles solutions, the DEER kinetics does not exhibit any features that could be lost due to the dead-time. For the X-band measurements the first value of t was 80 ns, Δt = 20 ns, τ = 1.6–2.0 μs and a two-step phase cycle on the first pulse was employed. The set up of the pump and observe frequencies were as above and so were all other experimental conditions except that pump pulse durations of 40 and 28 ns were used.

In the Ka-band DEER measurements the nominal flip angle of the pump pulse was varied between π and ∼π/6. This was achieved by variation of the pump pulse duration from ∼20 to 50 ns as well as of the pulse amplitude. The typical separation between pump and observed frequencies was ∼40–50 MHz, with the pump frequency set to the maximum intensity of the nitroxide spectrum. Here the time interval, τ, was ∼2.5 μs and the first data point collected was at time equal to the sum of the duration of the pump and observed pulses, typically ∼60–80 ns.

Because the evaluation of the magnitude of DEER kinetics becomes highly sensitive even to small background corrections when the decay is large (>e⁻³), an additional test for the presence of baseline background was made in the Ka-band measurements. This was achieved by performing the DEER measurements in absence of a signal and the trace obtained was used in final data processing to correct the DEER kinetics.

SAXS measurements

Small angle X-ray scattering (SAXS) were performed using a small angle diffractometer (The Molecular Metrology SAXS System) at the Technion-Israel Institute of Technology. Cu Kα radiation is generated by Osmic MicroMax®, an integrated microfocus sealed tube generator (powered at 45 kV and 0.9 mA) with Osmic™ Confocal Max-Flux® optics, 3 pinholes collimation. A 20 × 20 cm² 2D position-sensitive wire detector (1024 × 1024 pixels) was positioned 150 cm behind the examined samples, resulting in a q-range of 0.07 < q < 2.8 nm⁻¹. The wave vector defined as, q = (4π/λ) sin(2θ/2), where 2θ is the scattering angle and λ is wave length of Cu Kα radiation (0.1542 nm). A total of 10⁶ or more counts were collected in order to obtain a high signal to noise ratio. Conversion to absolute units was performed according a procedure described by Zemb et al.³⁹ The 2D SAXS patterns were azimuthally averaged and the background subtracted using standard methods. Data analysis was based on fitting the scattering curve to an appropriate model using a least-squares method.

DEER theoretical background

In spin echo based experiments, the evolution time of the spin echo signal for a single pair (i,k) of dipolar interacting spins is:⁴⁰

V(t) = V₀[1 −λ_k(1 − cos(ω_ikt))] (1)

where t is the appropriate variable time interval that depends on the chosen technique, and λ_k is the probability to flip one of the two spins by the appropriate pulse.⁴¹ The frequency ω_ik is:

ω_ik = ω^(ik)_dd(3 cos²θ_ik− 1) (2)

where ω^(ik)_dd is the so called dipolar evolution frequency given by:Spin i is treated as an observer spin (A spin) and spin k as a pump spin (B spin), g_i and g_k are the electron g values of the two spins, r_ik is the distance between the two spins and θ_ik is the angle between the external magnetic field, B₀, and the vector connecting the loci of the two spins. Henceforth we assume g_i = g_k = g for all i,k spins. In eqns (2)–(3) the absence of an exchange interaction is assumed. In the simple case of a radical pair with a fixed distance but a random θ, the DEER kinetics becomes:

V(t) = V₀[1 −λ_k(1 −∫cos(ω_ikt)d cos θ_ik)] (4)

This is usually superimposed on a background decay arising from inter-pair dipolar interaction. After background removal, Fourier transformation of V(t) yields a quasi-Pake doublet pattern. In such a powder pattern the singularities corresponding the θ = 90° are clearly identified, providing ω_dd and the distance is readily obtained (see eqn (3)).

In a multi-spin system, the echo intensity due to any A spin is given by:

and the total echo is the sum of the echoes from all A spins. This yields for N interacting spins:and 〈〉 denotes the relevant averaging.

For a disordered system with an isotropic homogeneous distribution of spins, the dipolar time evolution exhibits a mono-exponential decay, which depends on the spin concentration, C, according to⁴¹

V(t) = V₀ exp(−t/T_hom) (7)

and the time constant, T_hom iswhere C is given in molar units and T_hom in μs.

In a system consisting of aggregates (clusters) of radicals, where the average inter aggregate distance is larger than the average distance within the aggregate, the DEER kinetics can be described as the following product^24,26,42,43

V(t) = V_intra(t)V_inter(t) (9)

where V_intra(t) describes the decay due to spins in the same aggregate, and V_inter(t) is due to the interaction with spins in different aggregates. The determination of V_inter(t) is a complicated problem and was explicitly investigated only in a few publications.^24,26,44 The case that is most relevant to our investigation is the work of Milov et al.²⁴ on polymers sparsely labeled with radicals, which produced “clusters” of radicals with 30–45 radicals per cluster and a “cluster” size of ∼10 nm. Based on the data shown in this work V_inter(t) can be approximated as:²⁴

V_inter(t) = V₀ exp(−t/χT_hom). (10)

This is equivalent to the use of an effective concentration C_inter = C/χ (C is the bulk radical concentration) to describe the inter cluster decay. χ is a parameter which depends on the size of the cluster and, probably also on the number of radicals in a cluster. For the objects investigated in the work of Milov and coworkers²⁴χ∼ 10 was evaluated.

For a micellar solution with M_av average spins per micelle, V_intra(t) (eqn (9)) is:

Here the averaging is over all possible positions within the micelle and all possible orientations with respect to B₀. P(M, M_av) is the distribution probability for finding M spins in a micelle and M_av is the average number of spins per micelles. When there is no correlation between the radical positions, the integration can be carried out independently for each radical, yielding:^44,45P(r) is the distance distribution function. In eqn (12)r_max represents the maximum distance between spins and r_min is the minimum inter distance that can be detected by DEER or the minimum approach of the spins (the smallest of the two). In the case of spherical micelles r_max is the diameter of the sphere occupied by the spin-labels. When P(r) = r² the distribution of spins within the volume corresponds to the hard sphere model.²⁹

For long time intervals the integral over the cosine averages to zero and V_intra(t) levels off and converges to:

Using eqns (9)–(10) one obtains:Neglecting the distribution in M, V(t_long) becomes:

V(t_long) ∼V₀ exp(−t_long/χT_hom)[1 −λ]^M_av−1 (15)

and

ln(V(t_long)/V₀) + t_long/χT_hom = ln(V_intra(t_long)) ∼ (M_av− 1)ln[1 −λ]. (16)

Hence, a plot of ln(V(t_long)/V₀) as a function of ln(1 −λ) provides M_av.

The time at which the echo levels off, t_a, is related to a characteristic (average) pair distance, R_a according to:⁴⁶

The time at which the completion of leveling off is reached, t_long, depends on the shape of the distance distribution function and t_long∼ (5–10)t_a is a safe guess. Using eqn (17) and the experimentally determinedt_a it is possible to estimate R_a, even though no modulations have been observed. For example, if the characteristic size of a cluster is ∼10 nm and it contains ∼10 radicals, one can expect that the echo decay will starts to level off at t_a∼ 0.4–0.5 μsec and will reach the limit determined by eqn (13) between 2 and 5 μs.

The determination of M_av requires the knowledge of λ. It can be calculated from the EPR lineshape according to:⁴⁶

where ω₁ is the amplitude of the pump pulse, t_p is its duration, Δω_k is the offset of resonance frequency and g(Δω_k) is the EPR lineshape. When eqn (18) is used to calculate λ it is assumed that the pulse shape is rectangular and the bandwidth of resonator is large enough to avoid distortions of the pulse and changes in its duration. Furthermore, it does not take into account the B₁ inhomogeneity as well as possible leakage of mw-power while the pulse is formed at the low-power stage. Therefore, we compared the λ calculated using eqn (18) with that obtained from DEER experiments carried out on a series of samples with a random distribution of radicals (frozen isotropic solutions) and different concentration. Evidently, such samples have to be positioned in the resonator in the same way as the samples under study, having the same size, and the same pulse parameters (amplitude and duration) should be used. In all our experiments the difference between the λ values calculated using eqn (18) and those found from measurements on isotropic solutions (toluene/methanol) was 14% (See the calibration presented in Fig. S1 in the ESI).† All calculated λ values of the Ka-band measurements were corrected accordingly.

Eqns (15) and (16) show that to obtain a good evaluation of the number of guest radicals in the micelles leveling off of V_intra(t) should be reached. Limitations in S/N (due to a finite phase memory time) suggest an experimental strategy where measurements should begin with samples having a maximal radical load and a minimal number of micelles, and experimental conditions with the largest possible λ should be applied. If the DEER kinetics in such a sample shows features characteristic of radicals in a confined volume, manifested by leveling off of V_intra(t), measurements of other radicals/micelles concentrations can be gradually worked out. Results obtained using such an approach are presented in this work.

Modeling of small angle scattering intensities

The scattering intensity of a monodisperse system of particles of identical shape can be described as^47,48

I(q) = NP(q)S(q) (19)

where N is the number of particles per unit volume, S(q) is the structure factor that accounts for the interparticle interactions and P(q) is the form factor characteristic of the specific size and shape of the scaterrers.

In dilute solutions, where the interactions between the objects can be neglected, S(q) equals one. The total intensity scattered from a polydisperse system with particles having an identical shape can be described by:

where D_n(R) is a distribution function and D_n(R)dR is the number of particles, the size of which is between R and R + dR, per unit volume of sample.

A form factor for a simple spherical core-shell model where the core and the shell have a uniform electron density is given by:

where R and ρ are radius and electron density and c and s stand for core and shell respectively.

is the normalized amplitude scattered by a sphere.

A Gaussian distribution is given by:

where 〈R〉 is the average radius and σ is the root mean deviation. The polydispersity δ is defined by δ = σ/〈R〉.

Results

SAXS measurements

The scattering curves of 4 wt% P123, with and without 0.7 mM Brij56-NO, at 50 °C are presented in Fig. 2. Both curves show a broad peak at the same position. This peak reflects the form factor of the micelles’ core⁴⁹ indicating that the presence of the spin-probes does not affect the micelle’s core size. The influence of the structure factor is minor. Ideally, the scattering pattern would be fitted to a form factor of a spherical block copolymer micelle, which includes the self correlation of the PPO spherical core, the self correlation of the PEO chains, the cross term between the core and the chains and cross term between chains.⁵⁰ However, due to the low contrast between PEO and water and the high degree of solvation, the electron density of the chains is very similar to that of the solvent. Therefore, it was difficult to obtain a clear signal at the larger scattering vector range, corresponding to the contribution of the individual PEO chains form factor. An attempt to fit the data to a simpler model describing only the spherical core failed, therefore we fitted the data to a spherical core-shell model given by eqn (21), where the fine structure from which the shell is made is ignored. A Gaussian distribution was chosen to account for the polydispersity of the micelles. The best fit parameters are presented in Table 1. We note, however, that the shell thickness and electron density could not be determined accurately. The core radius, R_c, was found to be 5.2 nm and the aggregation number, N_agg was calculated according towhere N_PO is the number of PO units in one Pluronic chain and V_PO = 0.0954 nm³ is the volume of one PO unit.⁵¹ All fitted parameters are in good agreement with values reported in the literature for various P123 systems.^52–54 The difference in electron density of the cores can be attributed to the presence of the spin probes, however this did not lead to major changes in core sizes.

Fig. 2 SAXS curves of 4 wt% P123 (◆) and 0.7 mM Brij56-NO in 4 wt% P123 (▲). The solid lines are fit to a polydisperse core-shell spherical model (eqn (21)) and the best-fit parameters are summarized in Table 1. The 0.7 mM Brij56-NO in 4 wt% P123 curves is vertically shifted by a factor of 10 for clarity.

Table 1 Best fit parameters from polydisperse, core-shell spherical model (eqn (21))

	R c (nm) ±0.1	δ±0.01	ρc (e^−/nm^3)	R s (nm)±0.1	ρ s (e^−/nm^3)	ρ m (e^−/nm^3)	N agg±5	R HS (nm) ±0.1	ϕ	N ^a (nm^−3)
a Micelles density.
4 wt% P123	5.2	0.19	335.9	4	328.9	333.4	88			1.2 × 10^−4
0.7 mM Brij56-NO in 4 wt% P123	5.4	0.15	335.6	4	329.6	333.4	97			1.0 × 10^−4
6 wt% P123	5.4	0.15	336.1	3.5	329.0	333.4	99	12.7	0.077	1.57 × 10^−4
0.7 mM Brij56-NO in 6 wt% P123	5.5	0.14	336.2	3.6	329.0	333.4	104	12.7	0.077	1.54 × 10^−4

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In order to verify these results and the validity of the chosen model, we repeated the SAXS experiment with 6% P123 samples (Fig. 3). The curves were fitted to the spherical core-shell model. The structure factor cannot be neglected in this case; therefore an analysis described by Soni et al.⁵² using Percus–Yevic structure factor⁵⁵ and Gaussian polydispersity was applied. The micellar volume fraction ϕ, and the hard sphere interaction distance R_HS were variables in the S(q) calculation. The best fit parameters are presented in Table 1. As for the 4 wt% P123 systems, the fitted parameters are in good agreement with values reported in the literature and the addition of Brij56-NO did not change the size of the micelles. These results confirm that at the highest loading of spin-probe used in this work, 0.7 mM, the presence of the spin-probe does not alter the size or shape of the micelles for both 4% and 6 wt% P123 micellar solutions.

Fig. 3 SAXS curves of 6 wt% P123 (◆) and 0.7 mm Brij56-NO in 6 wt% P123 (▲). The solid lines are fits to a polydisperse core-shell spherical model (eqn (21)) and best-fit parameters are summarized in Table 1. The 0.7 mM Brij56-NO in 6 wt% P123 curves is vertically shifted by a factor of 10 for clarity.

The location of various spin-probes in Pluronic P123 micelles

DEER and ESEEM measurements are carried out at low temperatures to slow down the phase memory time such that echoes can be detected and to avoid motional averaging of dipole–dipole interactions in liquid samples. We have shown in a number of studies that upon rapid freezing the structure of the Pluronic micelles is preserved.^1,14,31 The CMT of 3–4 wt% P123 is around 35 °C^1,56 and therefore CW EPR measurements were carried out at 50 °C, which is well above the CMT, and samples for DEER and ESEEM were rapidly frozen from 50 °C.

The depth of the nitroxide spin label of several Pluronic spin-probes and 4HTB in the P123 micelle was estimated previously by their relative hyperfine coupling, a_N, and the correlation time τ_c, obtained from the CW EPR spectrum, and by the ²H modulation depth, k(²H), of three-pulse ESEEM traces of P123 micellar solutions in D₂O.^15,33k(²H) gives a qualitative measure of the amount of water around the spin-label and therefore, the lower k(²H) is, the deeper in the micelle is the nitroxide label. Similarly, the lower is a_N and the higher is τ_c, the deeper is the label. Table 2 lists the a_N, k(²H), and τ_c values for a number of spin probes in 3 wt% P123 micellar solutions at 50 °C and of L62-NO in a water solution for comparison. Fig. 4a presents the corresponding CW EPR spectra. 4HTB is the most hydrophobic spin-probe, it’s spectrum reveals the existence of two species. One is assigned to 4HTB dissolved in single chains (unimers) in solution (15%), and the other to 4HTB in the core of the micelle (85%). The nitroxide group of 4HTB is a TEMPO group (six-membered ring) as opposed the Pluronic spin-probe, which has a proxyl group (five-membered ring), therefore it’s a_N value is larger than that of the Pluronic spin-probes and cannot be compared directly.⁵⁷

Fig. 4 (a) CW-EPR spectra of 0.5 mM of various spin-probes in 3 wt% P123 at 50 °C. (b) DEER kinetics of 0.3 mM (spin concentration) of various spin-probes in 4 wt% P123 measured at 50 K and freeze quenched from 50 °C.

Table 2 a _N , k(²H), and τ_c for various spin-probes dissolved in water and 3 wt% P123 micellar solution at 50 °C

Spin-probe	a N [mT] ± 0.02 mT	k(^2H) ± 0.005	τ c 10^10 s ± 0.1
a 4HTB and L64-NO are distributed at these conditions between two different environments :  micelles and single chains. b For a solution of 4 wt% P123.
L62-NO in water	1.66	0.23	1.0
F127-NO	1.59	0.13	0.8
P123-NO	1.56	0.076	3.5
	1.56^b		3.5^b
L62-NO	1.55	0.062	2.0
L64-NO	1.52/1.59^a	0.065	3.5/1.0
Brij56-NO	1.48	0.07	3.5
	1.48^b		3.5^b
4HTB	1.55/1.72^a	0.053	2.6/0.8

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The results summarized in Table 2 show that the location of the spin-label of the Pluronic spin-probes in the micelles is mostly determined by the PEO length: F127-NO has the longest EO chain, and thus, on the average, the label is situated close to the corona-water interface. This is manifested by a large a_N, close to that of spin-labeled Pluronic dissolved in water (a_N = 1.6 mT), a large k(²H) and a low τ_c. P123-NO has lower a_N and k(²H) values than F127-NO, and a larger τ_c =3.5 × 10⁻¹⁰ s owing to its deeper location in the P123 corona. L64-NO and L62-NO were found at two regions in the corona, where most of the spin-labels, 92%, are located at the core-corona interface, with a_N = 1.52 mT and τ_c =3.5 × 10⁻¹⁰ s, and the others are closer to the corona-water interface, with a_N = 1.59 mT, and τ_c decreases to 1.0 × 10⁻¹⁰ s. The PEO block length of Brij56-NO is very similar in length to that of L64-NO, but it has a different hydrophobic part. Its k(²H) is similar to that of L62-NO, but the a_N of Brij56-NO is significantly smaller, 1.48 mT, than that of L64-NO, and also τ_c of Brij56-NO is higher than that of L64-NO. This suggests that the alkyl tail of Brij56-NO, which is more hydrophobic than the PPO block, pulls it into a pocket, where its motion is restricted and with very little water that can hydrogen bond to the NO group.⁵⁸ The k(²H) value of L64-NO, P123-NO, L62-NO and Brij56-NO are close and show that the resolution of k(²H) in terms of depth within the micelles is lower than that of a_N because of its longer range of interaction with water molecules. CWEPR measurements of 4HTB in P123 solutions with various concentrations (3–6 wt%) showed that the increase in the P123 concentration changed only the distribution of the spin-probes between unimers and micelles, where a_N and τ_c values remained constant.³¹ Similarly, measurements of P123-NO and Brij56-NO in 3% and 4 wt% P123 gave the same a_N and τ_c values (see Table 2).

Comparative DEER traces of 0.3 mM (radical concentration) spin-probe in 4 wt% P123, freeze-quenched from 50 °C, are shown in Fig. 4b. The following trend of the decay rates is observed F127-NO < 4HTB < L62-NO ∼ L64-NO ∼ P123-NO < Brij56-NO. This trend is expected because F127-NO, which is located at the corona/water, interface exhibits a slower decay as it is distributed over a larger radius within the micelle, compared to the other Pluronic spin-probes. The relatively lower decay rate of the 4HTB is attributed to its lower effective concentration within the micelles owing to the presence of 15% in solution (dissolved within unimers). Brij56-NO decays somewhat faster than L62-NO, probably because it is located in a smaller radius within the micelle, consistence with its smaller a_N and larger τ_c.

DEER experiments

Determination of χ. Before proceeding to the DEER measurements and their analysis, aiming at the determination of the number of spin-probes within the micelles and the volume they occupy, we determined the parameter χ (see eqn (10)). This parameter is essential for the determination of V_inter(t) that is required for the extraction of the contribution of the intra-micellar dipolar interaction, V_intra(t), from V(t). For this purpose, we measured the DEER kinetics of homogeneous solutions with varying concentrations of a rigid triradical with a distance of around 3.6 nm between the NO groups, and a flexible biradical with a distance of 2.2 ± 0.2 nm (shown in Fig. S2a,b). In such solutions, a rise in the spin concentration increases the contribution of V_inter(t), but V_intra(t) remains invariant (Fig. S2a,b). From eqn (10) it follows that : 

ln(V(t)/V₀) = ln(V_intra(t)) − (tλC/10⁻³χ)) (24)

Plot of ln(V(t)) at a chosen time, t, as a function of C (the total spin concentration) yields a linear relationship and χ can be evaluated from the slope once λ is known. The linear relationship obtained for the biradical and triradical solutions (shown in Fig. S1c),† yields χ∼ 1. This is quite different from χ = 10 obtained by Milov and co-workers.⁴⁴ The reasons for this difference are not clear yet, it could arise from the large difference in the number of spins within the cluster, but this requires further investigation and discussion.

Model independent approach. DEER measurements were carried out on Brij56-NO dissolved in a 4 wt% P123 solution at three total spin concentrations, 0.3, 0.5 and 0.7 mM. The solutions were prepared in D₂O to achieve longer phase memory times, T_m.⁵⁹ As a representative example, we show in Fig. 5a the DEER kinetics of the sample with the highest Brij56-NO concentration, (0.7 mM), obtained with a pump π-pulse of 32 ns for which λ = 0.20. The results are presented in a semi-logarithmic scale and show a clear deviation from a linear relationship, suggesting a significant contribution of intra-micelle dipolar interactions. The maximal calculated V_inter(t) due to inter-micelle dipolar interaction, calculated using eqn (10) and χ = 1, and V_intra(t), obtained by (ln V(t) − ln V_inter(t)) is depicted in Fig. 5a as well. The latter represents the minimal decay expected from intra-micelle dipolar interactions and shows that V_intra(t), if not completely leveled off, is close to leveling off at t = 2.5 μs. Using eqn (16) we estimated the lower limit to the average number of spin-probes in a micelle, M_av≥ 9.5. The leveling off starts at t_a∼ 500–700 ns, and using eqn (17), we evaluate the characteristic distance between the spins as R_a≥ 10 nm. This gives the order of the diameter of the volume that the spin-probes occupy.

Fig. 5 (a) The DEER kinetics of 0.7 mM Brij56-NO in 4 wt% P123: normalized raw data (V(t)), V_intra(t) and the calculated V_inter(t) as indicated on the figure. (b) The dependence of ln(V_intra(t)/V₀), for t = 2.3 μs, on ln(1 −λ). (Ka-band measurements). The solid line represents a linear best fit. The circled points represent data obtained from P123-NO in the same solution and at t = 1.7 μs measured at X-band.

For a more precise determination of M_av we performed a series of measurements at different λ values and Fig. 5b shows the dependence of ln V_intra(t = 2.3 μs) on ln(1 −λ) (eqn (16)). Here the λ-values were obtained by calculations and corrected according to the experimental calibration of λ (Fig. S1). The linear dependence yields a slope of M_av−1 = 8.9, from which we obtain M_av≥ 9.9 for 0.7 mM Brij56-NO in 4 wt% P123 at 50 °C.

A decrease in the spin-probe concentration, while keeping all other conditions constant, should lead to a decrease in M_av as well. Such a decrease, however, will increase the acquisition time interval necessary to reach leveling off of V_intra(t) for the same size of micelles (see eqn (17)). Therefore, the time interval of the measurements should preferably be increased and scaled according to radical loading. Unfortunately, this was not possible due to S/N limitation. Fig. 6a and b present the dependence of ln V_intra(t_long) on ln(1 −λ) for 0.5 mM and 0.3 mM of Brij56-NO in 4 wt% P123 and the dependence of M_av on [Brij56-NO] is summarized in Fig. 6c. A linear fit of the latter with a forced zero-intercept, yields a slop of 15.6 ± 1.1 mM⁻¹. The fit is not excellent, but reasonable and suggests that such a crude approach for estimating of M_av can be used with a high degree of confidence since all these estimates do not use any models or simulations.

Fig. 6 The dependence of ln(V_intra(t)/V₀), for t = 2.5 μs, on ln(1 −λ) for (a) 0.5 mM and (b) 0.3 Brij56-NO in 4 wt% P123 (Ka-band measurements). In (a) and (b) the circled points represent data obtained from P123-NO for t = 1.7 μs in X-band. (c) The dependence of M_av on the total spin concentration for Brij56-NO and for P123-NO. The solid lines represent the linear best fit.

For comparison, measurements were carried out with P123-NO, which is similar to the molecules constituting the micelles. Here the DEER measurements were carried out at X-band for two values of λ and the longest time interval attained was 1.7 μs. The dependence of ln V_intra(1.7 μs) on ln(1 −λ) for spin concentrations of 0.3, 0.5 and 0.7 mM were added to the plots of Brij56-NO at the same spin concentration in Fig. 5b and 6a,b. The data points (circled) fall quite close to those of Brij56-NO. The dependence of M_av on the radical concentration is depicted, together with the results of Brij56-NO in Fig. 6c, yielding a slope of 15.1 ± 1.8 mM⁻¹ which is very close to the one determined for Brij56-NO. Interestingly, in both cases M_av for the high concentration, 0.7 mM, is somewhat underestimated and could suggest a saturation effect.

The slopes obtained from Fig. 6c provide the number of micelles per unit volume, C_m, according to C_m = [radical]/M_av = 0.067 ± 0.007 mM. The average aggregation number can be derived from the known concentration of the Pluronic in the solution (6.7 mM). This yields N_agg of 95 ± 7 and 100 ± 10 for the Brij56-NO and P123-NO data, respectively, in good agreement with the N_agg value that was calculated from the SAXS results (Table 1). In our calculations we neglected the dispersion in molecular weight and did not include the weight of the spin-probes. Furthermore, we assumed that the amounts of unimers in solution is negligible.

Model dependent analysis. Because of the limitation in the acquisition time interval of the DEER kinetics, preventing an accurate determination of the leveling off values of V_intra(t) at low spin concentrations, we have also analyzed the DEER data by fitting the full kinetics using simple models. The first and simplest model we considered was of homogeneous distribution of spin-labels in a volume of a shell. According to the a_N values, for P123-NO such a shell comprises the corona, while for Brij56-NO, it will be closer to the core–corona interface, or even within the core. The calculation of V_intra(t) was obtained by considering all possible positions and orientations of the spins in the shell through Monte-Carlo calculations based on eqn (11) with a Poisson distribution. The spins were distributed between r_min (inner radius of the shell) and r_max (outer radius of the shell), and when the distance between two spins was less than 1.5 nm its contribution to the DEER kinetics was not taken into account because this is the lowest limit of r that can be detected by DEER.^43,60–62V_inter(t) was calculated using eqn (7). The fitted parameters were r_max and r_min, which are the same for all spin concentrations, and M_av that varies with concentration. Fig. 7a and 8a show the DEER kinetics (solid line) for 0.3 mM Brij56-NO and P123-NO in 4 wt% P123 for various λ values, and the best fit curve (dotted lines) obtained with parameters listed in the figure caption. The agreement between the calculated and experimental trace is unsatisfactory. Taking a Gaussian distribution within the shell, namely a radius r₀ and a width ±δr, did not improve the agreement between the experimental and calculated decays.

Fig. 7 Ka-band DEER decay of 0.3 mM Brij56-NO in 4 wt% P123, measured at various λ. The dotted line is the best fit obtained with (a) homogenous distribution in a shell with r_max = 7.0 nm, r_min = 3.0 nm, M_av = 9.0. (c) A distribution of spins in a spherical with P(r) = r², r_max = 9.0 nm, M_av = 9.0. Here r_max corresponds to the maximum distance between spins.

Fig. 8 X-band DEER decay of 0.3 mM P123-NO in 4 wt% P123, measured at various λ. The dotted line is the best fit obtained with (a) homogenous distribution in a shell with r_max = 6.2 nm, r_min = 5.2 nm, M_av = 10.0. (b) A distribution of spins in a sphere, with P(r) = r², r_max = 10.0 nm, M_av=11.0. Here r_max corresponds to the maximum distance between spins.

The disagreement between the experimental DEER kinetics and the best-fit calculated kinetics suggests that the basic assumption that the positions of the spin-probes are independent is not valid. Therefore, we refined the model and included excluded volume. Namely, once a nitroxide is situated at a particular location, there is a volume around it that cannot be occupied by any other spin-label. Inclusion of an excluded volume of a sphere with a radius of 2.5 nm improved the fit for both spin-probes, but not enough. Extending the distribution within a shell to a sphere did not improve the fit either.

In our earlier study we showed that the DEER kinetics of 4HTB in P123 micelles³¹ could be fitted with a model based on eqn (12) with P(r) = r². In this model the probability to find pairs with long distances is significantly higher than for the short distances. This implies that the excluded volume is large and that the nitroxides distribution prefers long distances. This model gave better fit than the homogeneous distribution model discussed above for both Brij56-NO and P123-NO. Here r_min was taken as 1.5 nm as well. Examples of the quality of the fit for both spin-probes are shown in Fig. 7b and 8b for the 0.3 mM samples and the best fit parameters are listed in Table 3. These were determined as follows: Initially, a least-squares fitting was done individually for each concentration (for all λ values), to find the best fit values of r_max and M_av. Then, from these r_max values, the average value was chosen and fixed and only M_av was fitted. The M_av values listed in Table 3 are averages over all DEER kinetics obtained with different λ-values.

Table 3 The parameters obtained from the model free analysis and a model of a distribution in a sphere with P(r) = r², for Brij56-NO and P123-NO in 4 wt% P123 freeze quenched at 50 °C

	Brij56-NO	P123-NO
	0.3/0.5/0.7 mM	0.3/0.5/0.7 mM
R a , model free	∼10 nm	∼11
M av, model free	(5.0/8.8/9.9) ± 0.35	(6.5/7.7/9.6) ± 0.5
N agg, model free	95 ± 7	100 ± 10
M av, P(r) = r^2	(9.0/13/15) ± 1.5	(11.0/13.0/22.0) ± 0.5
r max [nm], P(r) = r^2	9.0 ± 0.5	10.0 ± 0.2
N agg, P(r) = r^2	150 ± 15	210 ± 20

---

The r_max obtained for P123-NO is somewhat larger than for Brij56-NO as expected from the difference in a_N. Here r_max provides the largest distances between two spins, which give the diameter of the spherical volume they occupy. Comparison of the values obtained (9–10 nm, Table 3) with a core diameter of 10.4–10.8 nm and a total micelle diameter of 18.4–18.8 nm determined from the SAXS measurements, suggests that this model underestimates the diameter of the volume with spin-probes.

Fig. 9 presents a plot of M_av obtained with the model with P(r) = r², as a function of the spin-probe concentration. The M_av values are higher than those obtained from the model free analysis (see Table 3). This is expected since the model free analysis provides the lower limit of M_av due to difficulties in reaching the leveling off part of the DEER kinetics. However, the slopes obtained from Fig. 9 gave N_agg∼ 150–210 (see Table 3), which is 50–100% higher than obtained by the model free analysis and estimated from the core radius obtained by SAXS. The DEER experiments on 4HTB in 3 wt% P123, where unimers were detected also in the EPR spectrum, gave N_agg = 56 ± 4, and for 4HTB in 6 wt% P123 N_agg = 121 ± 7.²⁷ The latter is higher by ∼20% with respect to the SAXS data. For 4HTB in 3 wt% P123 r_max = 7.3 ± 0.2 nm,³¹ which is smaller than the core volume. This is not surprising because of the hydrophobic nature of 4HTB. This is also smaller than the r_max of Brij56-NO and P123-NO as expected.

Fig. 9 M _av determined by modeling the DEER kinetics using a model of an isotropic distribution of spins in a spherical cluster with P(r) = r² (eqn (12)) as a function of the total radical concentration for Brij56-NO and P123-NO.

Discussion

In this work we have used DEER to study the number and distribution of guest molecules (spin-probes) in P123 micelles, as well as the volume they occupy and the aggregation number of the micelles. The SAXS measurements have shown that the addition of the spin-probes used (up to 0.7 mM) did not affect the dimensions of the micelles. The model free analysis of the DEER kinetics of P123-NO and Brij56-NO gave reasonable estimates of the volume occupied by the spin-probes, determined via the average distance between them, R_a, and average number of spins per micelle, M_av (see Tables 1 and 3) in spite of the limited acquisition time interval (2.3–2.5 μs for the Ka-band measurements and 1.7 μs for the X-band measurements). The aggregation number of the P123 molecules in a micelle was calculated from the dependence of M_av on the spin concentration at constant P123 concentration and is in good agreement with the value predicted from the core size determined by the SAXS measurements. Comparison of the results of Brij56-NO, which has one spin-label per polymer chain, and P123-NO, that has two labels, shows that the two spin-labels in P123-NO are completely uncorrelated and behave like spin-labels on two different chains.

In the following we summarize essential points in the application of the model free approach:

1. The three-pulse sequence, as opposed to the four-pulse sequence, is recommended because it has a better S/N ratio and therefore longer acquisition times can be employed. The dead-time in this particular case is not critical because a fast decay at very short times, characteristic of pairs with short distances, is not expected.

2. Efforts to achieve long acquisition times, where the leveling off of the DEER decays can be reached, should be made. If possible, samples should be prepared in D₂O to increase phase memory time. Measurements should begin with samples with the highest possible spin concentration, and with the largest possible λ value, to reach the leveling off value of V_intra(t). This single measurement will provide estimates of the parameters involved and supply good guidelines for the choice of the experimental parameters and samples compositions needed to substantiate the single point results.

3. Measurements on a series of samples with different spin concentrations and employing different λ values should be carried out.

Attempts to analyze the full DEER kinetics using rather simple models showed that the average distance between the spins in the micelle is considerably larger than expected from a homogenous distribution in micelles (in a shell or a sphere) with sizes compatible with those obtained from the SAXS measurements. A reasonable fit of the DEER kinetics was obtained with a model with a pair distance distribution function of r². This gave the following trend for the diameter of the sphere the spin-probes occupy: 4HTB²⁷ < Brij56-NO < P123-NO. This is in agreement with the location of the spin-label within the micelle as implied by the a_N and τ_c values. However, the actual volumes occupied by the spin-probes seem to be underestimated for Brij56-NO and P123-NO in light of the SAXS results. Alternatively, these results could indicate that the spin-probes are localized within the core. While this may be possible for Brij56-NO, it is unlikely for P123-NO, based on the EPR results given in Table 2.

Remaining open questions are: What is the reason for the preferred large distances between the spin labels? Is this an inherent property of the P123 micelles, or is it a consequence of the freezing? This preference was observed for all spin-probes used, independent on their resemblance to the constituent molecules of the micelles and their sizes. Therefore this suggests that it reflects a general property of the micelles and not of the spin-probe. One possibility is that the high density of PPO chains in the core of the micelles does not allow guests such as 4HTB and the Brij56-NO to be close to one another, pushing them towards the core-corona interface. It is also possible that the freezing of the chain dynamics induces some local order and further expelling these foreign solutes outwards. Such an expulsion would be more facile for 4HTB, which is a small molecule compared to Brij56-NO. In contrast, P123-NO can be considered as a native constituent of the molecules forming the micelles and not as a solute molecule, as it differs only by the nitroxides at the ends of the PEO blocks. Therefore, its distribution should resemble that of the P123 end chains and therefore significant expulsion upon freezing is unlikely. Here one has to consider the character and size of the nitroxide, compared to the OH group. However, it is unlikely that it will be the reason for such a large excluded volume effect.

The large density in the core of the micelle was reported previously. The micelles of polystyrene/polyethylene oxide (PS/PEO) were studied by Monte Carlo simulations and SAXS.^44,63 It was shown that the polymer density profile decays from the center of the micelle as (1/r)^a, where a≥ 1 and it depends on the solvent quality. In addition, the excluded volume around each monomer in the polymer chain, named “blob size”, increases with r and decreases with an increase in the aggregation number. For instance, an average blob size diameter for a micelle with N_agg = 20 is 3.3 nm, whereas for N_agg = 100 is 1.66 nm. For N_agg = 65–80, the blob size at the corona of the micelle is 6.3 nm. Simulations for polymers in spherical volume also showed that the density at the core of the micelle is high and decreases from the center of the core.^45,64 Calculations for Pluronic block copolymers showed that the density at the core of the micelle is fairly high (0.7–0.8 g cm⁻³) and spatially uniform. The density of the shell is appreciably lower (0.15–0.25 g cm⁻³) and decreases from the core/shell interface to the micelle periphery.⁶⁵

In this work we have studied micelles of P123, which have a total diameter (core + corona) of 18 nm. Hence, relatively large intra-micelles distances between radicals are accommodated for relatively low loadings and long times are required for V_intra(t) to level off. Accordingly, we expect that the model free approach for DEER data analysis will be more easily applied to systems with smaller micelles, such as those formed by alkyl based cationic or anionic surfactants.

In this work we limited ourselves to spheroidal micelles, it is yet to be shown whether this approach can be applied to thread-like micelles as well. Because the model free approach is shape independent it cannot provide the shape of the micelles. Nonetheless, it does provide the average number radicals in a micelle and its dependence on the total spin concentration will provide the aggregation number. A transition from spherical-to thread-like micelles may be detected indirectly through the change in N_agg. Alternatively, the data could be analyzed using a model with cylinders to derive the size, however, because the exact form of P(r) is unknown such an analysis may be problematic.

Finally, we compare the information provided by the DEER experiments with that of SAXS or dynamic light scattering (DLS). While SAXS and DLS give information on size and shapes, from which the aggregation number is derived indirectly, they cannot give information regarding the local concentration and spatial distribution of guest molecules within the micelles. This, in turn can be determined by DEER measurements, which also give the aggregation number. Therefore, the techniques are complementary. When micelles properties are of interest the spin-probe concentration should be kept low to avoid changes in size or shape,³¹ but when the interest is the load of the micelles with guests and to follow their effects on the micelles properties this issue is no longer relevant. A disadvantage of the DEER technique is that it has to be carried out at low temperatures; therefore the issue of preserving the solution structure is crucial. In addition, the measurements are time consuming as series of measurements have to be carried out as a function of spin concentration and pump flip angle. When leveling off of V_intra(t) is not reached the data analysis becomes complicated and model dependent. Here an improvements in the fit of the experimental data can be obtained by introducing a more realistic model for the effect of the pump pulse as reported recently.⁶⁶ In addition, the Poisson distribution may not be the most appropriate one to describe the distribution of the number of spin-probes in the micelles as it assumes non-interacting particles. The low temperature measurements may be advantageous for time resolved applications, such as the formation of templated mesoporous materials,⁶⁷ because freeze quench measurements can be done.

Conclusions

DEER measurements were used to obtain the number of guest molecules (in the form of spin-probes), their distribution and the volume they occupy in P123 micelles and the aggregation number of the micelles. We showed that a simple model free approach for the analysis of the DEER data yields good estimates to the above properties, some we determined independently by SAXS measurements. The application of this approach, however, requires experimental efforts, namely a series of measurements as a function of microwave power and spin concentration are necessary. More importantly, it requires long acquisition times of the DEER kinetics, which are limited by the phase memory time, to reach the leveling off that is characteristic of distribution of radicals within a confined volume.

Data analysis in terms of a simple model of spins distributed in a sphere or a shell of particular dimensions showed that for both P123-NO and Brij56-NO there is a preference for large distances between the nitroxide groups, situated at the polymer ends, suggesting the presence of a large excluded volume. It also showed that the volume the spin-labels occupy in P123 micelles varies according to P123-NO > Brij56-NO > 4HTB. This trend is consistent with the nitroxide depth in the micelles, determined by the hydrophophic/hydrophylic character of the spin-probe.

For full realization of the potential of DEER as a method to characterize micelles and guest molecules in micelles the data analysis of the complete DEER kinetics needs further improvement. This requires additional experimental results on solutions with different Pluronic concentrations and different types of Pluronics and spin probes.

Acknowledgements

Acknowledgment is given to the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research. This research has been also supported by Binational USA-Israel Science Foundation (BSF) and the Ilse Katz Institute for Material Science and Magnetic Resonance Research. S.R. acknowledges the support of a grant from the Ministry of Science. D.G. holds the Erich Klieger Professorial chair in Chemical Physics. R.B. thanks the support of the Reimund Stadler Minerva Center for Mesoscale Macromolecular Engineering at Ben Gurion University. Minerva is funded through the BMBF. We thank Ciba-Geigy AG and Gunnar Jeschke (MPI for polymer research, Mainz) for providing the oligomethylene biradical and Rachel Yerushalmi-Rozen (Ben Gurion University) and Alexey Potapov (Weizmann Institute of Science) for very useful discussions.

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Footnote

† Electronic supplementary information (ESI) available: Experimental calibration of λ at Ka-band and four-pulse DEER measurements of a triradical and a biradical as a function of radical concentration. See DOI : 10.1039/b812475b

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