Proton Activity in Nanochannels Revealed by EPR of Ionizable

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C: Physical Processes in Nanomaterials and Nanostructures

Proton Activity in Nanochannels Revealed by EPR of Ionizable Nitroxides: a Test of the Poisson –Boltzmann Double Layer Theory Elena G. Kovaleva, Leonid S. Molochnikov, Denis O. Antonov, Darya P. Tambasova (Stepanova), Martin Hartmann, Anton N Tsmokalyuk, Antonin Marek, and Alex I Smirnov J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b04938 • Publication Date (Web): 13 Aug 2018 Downloaded from http://pubs.acs.org on August 17, 2018

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The Journal of Physical Chemistry

Proton Activity in Nanochannels Revealed by EPR of Ionizable Nitroxides: a Test of the Poisson – Boltzmann Double Layer Theory Elena G. Kovaleva,*,† Leonid S. Molochnikov, ‡ Denis O. Antonov,†,‡ Darya P. Tambasova (Stepanova), † Martin Hartmann,§ Anton N. Tsmokalyuk, † Antonin Marek,¶ Alex I. Smirnov*,¶ †

Institute of Chemical Engineering, Ural Federal University, Mira St., 19, 620002,

Yekaterinburg, Russia ‡

Department of Chemistry, Ural State Forest Engineering University, Siberian Highway, 37,

620100 Yekaterinburg, Russia §

Erlangen Catalysis Resource Center (ECRC), Fridrich-Alexander Universität Erlangen-

Nürnberg, Egerlandstraße 3, 91058 Erlangen, Germany ¶

Department of Chemistry, North Carolina State University, 2620 Yarbrough Drive, Raleigh,

North Carolina, 27695-8204, USA

ACS Paragon Plus Environment

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ABSTRACT

Chemical and physical processes occurring within the nanochannels of mesoporous materials are known to be determined by both chemical nature of the solution inside the pores/channels as well as the channel surface properties, including surface electrostatic potential. Such properties are important for numerous practical applications such as heterogeneous catalysis and chemical adsorption including chromatography. However, for solute molecules diffusing inside the pores the surface potential is expected to be effectively screened by counter ions for the distances exceeding the Debye length. Here we employed EPR spectroscopy of ionizable nitroxide spin probes to experimentally examine the conditions for the efficient electrostatic surface potential screening inside the nanochannels of chemically similar silica-based mesoporous molecular sieves (MMS) filled with water at ambient conditions and a moderate ionic strength of 0.1 M. Three silica MMS having average channel diameters of D=2.3, 3.2 and 8.1 nm (C12MCM-41, C16MCM-14, and SBA-15, respectively) were chosen to investigate effects of the pore diameter at the nanoscale. The results are compared with the classical Poisson–Boltzmann (PB) double layer theory developed for diluted electrolytes and applied to a cylindrical capillary of infinite extent. While the surface electrostatic potential was effectively screened by the counter ions inside the largest channels of 8.1 nm in diameter (SBA-15) the effect of the surface electrostatic potential on local effective pH was significant for the 3.2 nm channels (C16MCM-14). The smaller pores of С12MCM-41 (2.3 nm in diameter) provided the most critical test for the PB equation that is based on a continuum electrostatic model and demonstrated its inapplicability likely due to discrete nature of molecular systems at the nanoscale and nanoconfinement effects leading to larger spatial heterogeneity.


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1. INTRODUCTION

Acid-base properties of organic and inorganic porous materials are of a great interest from perspectives of fundamental understanding of molecular processes in heterogeneous catalysis and chemical adsorption as well as numerous practical applications including chromatography.1-5 These processes occur at the channel surfaces and are known to be affected by both chemical nature of solutions and surface properties of these materials. In the past, the classic method of acid strength measurements based on monitoring the color changes of adsorbed dye indicators (Hammett indicators) upon titration as well as microcalorimetry and thermal programmed desorption (TPD) measurements of other basic and/or acidic probes of different strength absorbed on catalysts were employed to determine the concentration and strength of the acid sites.6-10 A number of spectroscopic methods including FTIR, magic angle spinning (MAS) NMR, IR, photoluminescence, Raman, UV–Vis, XPS, and EPR have been also successfully applied to some of catalytic mesoporous materials in order to identify and characterize acid–base properties of the surface sites.11-16 While each of these spectroscopic methods has its own pros and cons, EPR spectroscopy of ionizable nitroxides14-20 has the benefits of being applicable to non-transparent /turbid materials. Also, spin-probe EPR generally exhibits better concentration sensitivity than solid state NMR.

The EPR method is based on a spectroscopic observation of reversible protonation of stable free radicals such as, for example, pH-sensitive nitroxide radicals (NRs)14-20 or triarylmethyl radical derivatives.21 Such probes provide measurements of local pH (p𝐻 𝑙𝑜𝑐 ) when either absorbed by the surfaces or being dissolved in a liquid phase trapped by the pores.


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For example, by using pH-sensitive nitroxides it was shown that pH values in volumes confined inside solid mesopores could differ from the bulk pH by 0.8-2.1 units.14,15 A number of porous materials of organic (e.g., cation and anion exchange resins and films based on cross-linked polymers), inorganic (e.g., zeolites, kaolin, alumina, silica gel, titanium oxide) and composites (SiO2, TiO2, ZrO2, and cellulose powder) have been examined in the past by the spin probe EPR method to determine p𝐻 𝑙𝑜𝑐 and surface electrical potential (SEP).14-16,22-24

Acid-base and sorption properties of mesoporous silica have been also examined by spin probe EPR in the past.

Specifically, continuous wave (CW) EPR spectra of pH-sensitive

nitroxides were analyzed to reveal rotational dynamics of such probes in aqueous phase confined in nanochannels and upon adsorption on the pore surfaces for the two most common types of mesoporous silica nanoparticles, MCM-41 and SBA-15.25,26 Furthermore, an EPR-based method for measurements of the near-surface (Stern) potential of nanosized hydrated channels has been described and tested for these mesoporous molecular sieves (MMS).26 These studies have shown that depending on pH, the surfaces of nanochanneles could acquire a surface potential ranging from small positive (e.g., φ=19±6 mV for SBA-15 at acidic pH) to large negative values (e.g., φ =-179±6 mV for C16MCM-41 at basic pH).26 The observed trend and φ values are in general agreement with results reported recently for the aqueous electrolyte-silica nanoparticle interface.27

For nanochannels of just a few nm in diameter such as those formed in MCM-41 and SBA-15 the large negative surface electrostatic potential developed on the silica surface at basic pH cannot be effectively screened by the counter ions and are expected to affect proton activity


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and the observed p𝐻 𝑙𝑜𝑐 in the nanochannels. Indeed, the diameter of the smallest pores in these MMS is not sufficient for the surface double layer to form at typical experimental conditions, such as room temperature and an aqueous solution of single-charged ions at 0.1 M ionic strength, because the Debye length -1≈0.96 nm is comparable to the average pore radius (e.g., r≈1.15 nm for C12MCM-41). Furthermore, the properties of water at nanoscale could be affected by the channel surfaces and the effects of nanoconfinement.28 Here we report on investigating effects of the channel surface charge on the effective p𝐻 𝑙𝑜𝑐 of the aqueous phase confined in the pores by using spin probe EPR method. Three silica MMS having average channel diameters of D=2.3, 3.2 and 8.1 nm (C12MCM-41, C16MCM-14, and SBA-15, respectively) were chosen to investigate effects of the pore diameter. The results are compared with the classical Poisson– Boltzmann double layer continuum electrostatic theory developed for diluted electrolytes and applied to cylindrical capillary of infinite extent.29-33

2. EXPERIMENTAL SECTION

2.1 Materials and EPR pH-sensitive Probes

Similar to the preceding reports25,26 two pH-sensitive NRs of the imidazoline type, 4dimethylamine-2-ethyl-5,5-dimethyl-2-pyridine-4-yl-2,5-dihydro-1H-imidazole-1-oxyl (R1) and 4-dimethylamine-2-ethyl-5,5-dimethyl-2-phenyl-4-yl-2,5-dihydro-1H-imidazole-1-oxyl

(R2)

(large-size NRs), and of the imidazole type, 4-amino-2,2,5,5-tetramethyl-2,5-dihydro-1Himidazole-1-oxyl (R3) (small-size NR) (Table 1) were employed. These water-soluble NRs exhibiting pH-sensitivity in the range from ca. 2 to 7 of pH units were synthesized at the Institute


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of Organic Chemistry, Siberian Branch of the Russian Academy of Sciences (Novosibirsk) using procedures described earlier.34,35

TABLE 1. Molecular structures, approximate dimensions, p𝐾𝑎 , and isotropic nitrogen hyperfine coupling constants, Aiso, of pH-sensitive nitroxide radicals employed in this study.25 Radical Structural formula

R1

Approximate molecular dimensions,a length × height × width, Å3 7.1×6.7×7.1

рКa, ±0.04

Aiso, ± 0.05, G

𝑝𝐾𝑎1 =2.92

13.94 (𝑅 • 𝐻 + 𝐻 +)

𝑝𝐾𝑎2 =5.06

14.570 (𝑅 • 𝐻 + ) 15.20 (𝑅 •)

R2

7.1×6.6×7.2

N

𝑝𝐾𝑎 =5.90

N

14.62(𝑅 • 𝐻 + ) 15.46 (𝑅 •)

N O

R3

H2N

6.2×5.4×4.4 N

𝑝𝐾𝑎 =6.10

15.76 (𝑅 •)

N O a

14.96(𝑅 • 𝐻 + )

Approximate molecular dimensions were determined by the molecular mechanics method using

HiperChem Pro 6.03 (Hypercube Inc., Gainesville, FL).

All-silica MCM-41 materials were synthesized using dodecyltrimethylammonium bromide (C12MCM-41) and hexadecyl trimethylammonium bromide (C16MCM-41) and exhibited average pore diameters of 2.3 and 3.2 nm, respectively, as reported earlier.36,37 SBA-


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15 with average pore diameter 8.1 nm was prepared using literature methods starting from tribloc copolymer poly(ethylene glycol)-bloc-poly(propylene glycol)-bloc-poly(ethylene glycol) (Pluronic

P123,

molecular

weight

5800,

HO(CH2CH2O)20(CH2CH(CH3)O)70(CH2CH2O)20H).38

nominal

chemical

formula

These MMS were characterized using

nitrogen adsorption and desorption isotherms (Table 2). NR solutions and MMS samples for EPR experiments were prepared as described earlier.25

TABLE 2. Properties mesoporous molecular sieves (MMS).25 MMS

Pore channel diameter, D, ± 0.1, nm

Specific surface area (АВЕТ), ±10, m2/g

Specific pore volume, ± 0.01, cm3/g

С12MCM-41

2.3

1210

0.70

С16MCM-41

3.2

1080

0.86

SBA-15

8.1

550

1.17

2.2. EPR Experimental Procedures

Continuous wave (CW) X-band (9 GHz) CW EPR spectra of nitroxide radicals in bulk aqueous solution and upon incorporation into the channels of solid MMS samples were recorded at room temperature (≈293 K) using either a Bruker ElexSys 500 (Bruker Biospin, Karlsruhe, Germany) spectrometer or an automatic ADANI PS-100.X spectrometer (ADANI Inc., Minsk, Belarus).


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EPR spectra of aqueous solutions were measured by filling a quartz capillary (i.d.=0.7 mm) and then placing the capillary into a quartz EPR tube (i.d.=3.5 mm, o.d.=4.5 mm) sealed from one end. The tube was consequently inserted into EPR resonator. For measurements with MMS, the powder was first soaked with an aqueous solution of NRs for at least 24 hr and pH was adjusted till no changes were observed for at least 30 min. Consequently, the powder was separated from the solution by a filtration. Remaining solvent from the particle surface was removed with a filter paper and the powder was placed into the EPR tube immediately before recording the EPR spectrum to prevent the sample from drying. For longer measurements the tube was capped to maintain the humidity sufficient for keeping water condensed in the nanochannels. In an alternative procedure the powder was separated from the solution by a centrifugation. Both sample preparation procedures yielded identical EPR spectra.

pH of bulk aqueous solutions of NRs and those employed for impregnating MMS powder (i.e., “external” solutions) were measured by a “1-in-3” combination electrode connected to a Symphony S20-K pH-meter (VWR International, Radnor, PA), which has accuracy of ± 0.02 pH units. The concentrations of the nitroxide radicals were kept below 0.5 mM in order to avoid broadening of EPR spectra.25 The ionic strength, I, was adjusted to 0.1 with KCl.

2.3 Analysis of CW EPR Spectra by Multiple Component Simulations and pKa Determination

Analysis of multicomponent EPR spectra and pKa determination from pH-dependent EPR spectra were carried out using the methods described earlier. Specifically, experimental EPR


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spectra were double-integral normalized using Microcal Origin 7.0 software. Spectral simulations were carried out using methods and computer software developed by Freed and coworkers39 assuming up to three different nitroxide motion components. Figure 1 shows an example of a decomposition of an experimental spectrum (A) of the nitroxide R2 incorporated into aqueous nanochannels of SBA-15 into two slow (B and C) and one fast (D) motion components. The simulations assumed that the chemical exchange between all these three nitroxide forms is slow on the EPR time scale. The slow motion components were assigned to the spin probes adsorbed on the pore surfaces and corresponding to two protonation stages while the fast motion component was originating from the nitroxide remaining in the aqueous phase and undergoing a fast chemical exchange between the two protonation states. Parameters of this slow on the EPR timescale rotational diffusion were reported elsewhere.26 Here we focus on the fast motion component that reports on p𝐻 𝑙𝑜𝑐 of the nanochannel aqueous phase and compare the results with those reported by the probes immobilized on the channel surfaces.

Nitroxide radicals employed in this work contain one or two functional groups capable of reversible ionization (protonation, in particular) in the immediate proximity to an EPR-active N– O• reporter group (cf. Table 1). Specifically, each R2 and R3 contains only one functional group undergoing protonation in accessible pH range:

𝑅•𝐻+ ⇄ 𝑅• + 𝐻+

(1)


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where R• is nonprotonated nitroxide radical. Spin probe R1 contains two functional groups capable of reversible ionization with pKa1=2.92±0.04 and pKa2=5.06±0.04.25 One can assume that the protonation occurs as two consequent reactions:

𝑅•𝐻+ ⇄ 𝑅• + 𝐻+

(2a)

𝑅•𝐻+ 𝐻+ ⇄ 𝑅• 𝐻+ + 𝐻+

(2b)

Protonation of a functional group in the immediate proximity to an EPR-active N–O• reporter moiety produces large internal electric field that changes magnetic parameters (Aiso, giso) of spin probe.40 The latter are readily observed from the fast motion EPR spectra. Typically, protonation reactions for nitroxide spin probes are diffusion-controlled with a rate constant k1≈1010 M-1 s-1 and the changes in the line magnetic field positions for NRs freely tumbling in a solution do not exceed 1-1.4 G.41 Under such conditions the EPR spectra are expected to fall into a fast exchange regime with magnetic parameters Aiso and giso proportional to the fractions of the nonprotonated and protonated species:41,42

𝐴𝑖𝑠𝑜 = 𝑓 ∙ 𝐴𝑖𝑠𝑜 (𝑅 • ) + ∑𝑛 𝑓 𝑛 ∙ 𝐴𝑖𝑠𝑜 (𝑅 • 𝐻 𝑛 )

(3)

Here, 𝑓 and 𝑓 𝑛 are the fractions of NR in nonprotonated and protonated forms, respectively, and summation takes over all the protonation levels n=+ or n=++. Then, from eq.(2) and assuming that the protonation reaction eq.(2a) of a NR containing single ionizable functionality (such as


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R2 and R3) is at equilibrium, the observed Aiso follows a modified Henderson-Hasselbalch equation:43

𝐴𝑖𝑠𝑜 =

𝐴𝑖𝑠𝑜 (𝑅 • )∙10(p𝐻−p𝐾𝑎 ) +𝐴𝑖𝑠𝑜 (𝑅 • 𝐻 + ) 1+10(p𝐻−p𝐾𝑎 )

(4)

Similarly, for NR with two ionizable groups exhibiting pKa1 0 contribution to p𝐾𝑎𝑙𝑜𝑐 in eq. (6) that is likely originating from changes in properties of water molecules confined by the nanopores. For example, additional ordering of water molecules in the nanochannels is expected to increase effective local dielectric permittivity constant ε and, thus, p𝐾𝑎𝑙𝑜𝑐 observed by NR pH-probes as was demonstrated experimentally by varying the dielectric constant of bulk solvents.43 We speculate that another possible reason could be related to transient structural distortion of the intraporous water causing a change in the hydrogen ions activity. Thus, for water confined within SBA-15 channels we tentatively assign Δp𝐾𝑎𝑒𝑙 ≈ 0 and Δp𝐾𝑎𝑐ℎ = 0.2 − 0.3 pH units.


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EPR titration curves for two other MMS studied, С12МСМ-41 and С16МСМ-41 were shifted to higher pH by more than Δp𝐾𝑎𝑐ℎ = 0.2 − 0.3 pH units (data for С16МСМ-41 are shown as filled squares and stars in Fig.2).

Such larger Δp𝐻 shifts are indicative of a negative

electrostatic surface potential (𝜑 < 0) at the location of the probe (see eqs. (6-7)). Indeed, the magnitude of the absolute surface potential at the silica-electrolyte interface has been shown to increase with pH (e.g., see the data for silica nanoparticles27) and this surface potential is not expected to be effectively screened by the counter ions across the nanochannels of just a few nm in diameter such as found in С12МСМ-41 and С16МСМ-41. Similar shifts of the titration curves were previously observed for nanostructured organic sorbents14 and inorganic materials with negatively charged surfaces.15,16

In addition to a shift to higher p𝐻 𝑒𝑥𝑡 values, the EPR titration curves for nitroxides incorporated into MMS channels exhibit sloping plateaus from ca. p𝐻 𝑒𝑥𝑡 =5.5 to 7.5 depending on the nitroxide and the material studied (cf. Fig. 2). Such sloping plateaus are clearly absent to the titration curves measured for the bulk aqueous phase. The appearance of such plateaus is an indication that the ionization equilibrium of nitroxide probes in the aqueous phase confined to the pores and, therefore, pH loc , being largely unaffected by changes in pH ext . Previously, the appearance of the plateaus was related to a reversible ionization of functional groups typically found on the pores’ surfaces.14,15

29

Si NMR and FTIR studies of MCM-41 identified some of

such groups as silanol Q3 (Si(O-Si)3-OH) and silanediol Q2 (Si(O- Si)2-(OH)2).46-48 The total density of these hydrophilic sorption centers located on MMS channel surfaces was found to be as high as 3 groups/nm2 or 45 mmol/g with the silanol groups considerably outnumbering silanediols.46-48 Once titration of the silanol and silanediol groups is completed, the experimental


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titration curves appear to be approximately parallel to the calibration curves measured for the bulk aqueous phase (Figure 2), suggesting that the electric potential φ at the location of the EPR probe remains largely unchanged within the corresponding pH range.

Approximate p𝐾𝑎 of the nanochannel surface functional groups was determined from EPR titration curves by projecting the midpoint of the observed plateau onto the calibration curve obtained for the same NR but in the bulk aqueous phase and then onto the horizontal axis. An example of such a procedure for С16МСМ-41, illustrated in Fig.2a by dashed lines, yields 𝑙𝑜𝑐 p𝐾𝑎1 = 5.58 ± 0.12. The same procedure was applied to other plateaus appeared in Fig.2. We

note that while similar plateaus have been previously observed in EPR spectra of pH-sensitive NR immobilized on the nanochannel surfaces,26 the corresponding p𝐾𝑎𝑙𝑜𝑐 have not been reported. Here, we have analyzed the previously published data26 for these immobilized NRs and summarized all the results in Table 3. It should be noted that the general procedure outlined here allows one to derive p𝐾𝑎𝑙𝑜𝑐 without separating the individual contributions of 𝛥p𝐾𝑎𝑐ℎ and 𝛥p𝐾𝑎𝑒𝑙 terms in the eq.(7).

We note that midpoints of the titration plateaus observed for C12MCM-41 from EPR titration curves measured from fast motion spectra of either R1 or R2 (Fig.2a and b) correspond 𝑙𝑜𝑐 to approximately the same p𝐾𝑎 ≈ 5.5 attributed to the surface silanol groups (p𝐾𝑎1 , Table 3).

Such a plateau is not observed upon R3 titration because p𝐾𝑎 ≈ 5.5 falls outside the pHreporting range of this molecular probe.25 The plateau observed for С16MCM-41 is indicative of 𝑙𝑜𝑐 𝑙𝑜𝑐 p𝐾𝑎1 = 5.58 ± 0.12, which is essentially the same as p𝐾𝑎1 for C12MCM-41 (Table 3). These 𝑙𝑜𝑐 p𝐾𝑎1 values are in general agreement with the values derived from the analysis of slow motion


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𝑙𝑜𝑐 EPR spectra measured previously:26 p𝐾𝑎1 = 5.62 ± 0.12 for either C12MCM-41 or С16MCM𝑙𝑜𝑐 = 5.25 ± 0.12 for SBA-15 (Table 3). All these p𝐾𝑎 values are higher than p𝐾𝑎 = 41 and p𝐾𝑎1

3.5–4.7 range reported for the surface silanol groups of silica microparticles employed as a support for several commercial liquid chromatography columns.5 These differences are likely associated with a higher negative electric surface charge of MCM-41 channels vs. that of silica microparticles at the same p𝐻 𝑒𝑥𝑡 (see also eqs.(7) and (8)). Indeed, as was shown in preceding report using nitroxides immobilized on the channel surfaces, the channel surface acquires a 𝑙𝑜𝑐 negative charge above p𝐻 ≈ 5.5.26 Essentially the same p𝐾𝑎1 observed for the two types of

MCM-41 (Table 3) is a clear indication of similarities in the surface charge and the silanol groups involved.

The midpoints of the second plateaus observed for C12MCM-41 and SBA-15 (Fig.2b and 𝑙𝑜𝑐 𝑙𝑜𝑐 2c; p𝐾𝑎2 = 6.75 ± 0.13 and p𝐾𝑎2 = 6.80 ± 0.13, measured from fast motion EPR spectra of

R2 and R3, respectively) are identical within the experimental error and are attributed to the silanediol surface groups in a good agreement with available data for silica microparticles (cf. 𝑙𝑜𝑐 values of those groups for C16MCM-41 were not measured. The Table 3). Note that p𝐾𝑎2

absence of the second plateaus in EPR titration curves derived from slow motion spectra studied 𝑙𝑜𝑐 previously26 also prevented determination of p𝐾𝑎2 .

We note that no plateaus attributed to protonation of silanol groups were observed for SBA-15 from EPR titration of fast motion nitroxides (Fig.2, open circles) even though the SBA15 surface is expected to contain such functional groups. We speculate that the absence of the plateaus is related to an effective screening of the surface electrostatic potential by the counter


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ions for molecular probes that are located (on average) further away from the surface due to a larger channel diameter. A small plateau observed at alkaline pH is attributed to the protonation of silandiols. At this pH range the channel surface is acquiring the total electrostatic potential as high as 𝜑 = −141 ± 6 𝑚𝑉 pH26 and such a high potential is no longer effectively screened by the counter ions.

𝑙𝑜𝑐 𝑙𝑜𝑐 TABLE 3. 𝑝𝐾𝑎 values of surface silanol (p𝐾𝑎1 ) and silanediol (p𝐾𝑎2 ) functional groups as

reported by fast motion nitroxide EPR spectra of the probes dissolved in MMS channel aqueous phasea and slow motion spectra of the probes immobilized near the channel surfaces,b literature data for 𝑝𝐾𝑎 values of surface groups of silica microparticles,c

MMS

𝑙𝑜𝑐 p𝐾𝑎1 ,  0.12

𝑙𝑜𝑐 p𝐾𝑎2 ,  0.13

5.50a 5.62b С16MCM-41 5.58a 5.62b SBA-15 n/aa 5.25b Silicatesc 3.5–4.7 b EPR titration data were reported by Kovaleva et al.26 С12MCM-41

c

Data for silica microparticles reported by Mendez et al.5

d e

6.75a n/ab n/aa n/ab 6.80a n/ab 6.2–6.8

𝑒𝑙 Note that for SBA-15 𝛥p𝐾𝑎1 ≈0.

Intrinsic p𝐾𝑎0 values for R1, R2 and R3 in aqueous solutions with I =0.1 are given in the Table

1. Overall, these data demonstrate a good agreement between p𝐾𝑎 values of the surface groups determined from analysis of fast motion EPR spectra corresponding to the nitroxides diffusing within the nanochannel aqueous phase vs. those obtained from nitroxides immobilized on the channel surfaces26 (cf. Table 3). We speculate that a larger pH interval corresponding to a


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plateau of the slow motion NR EPR titration curve reported previously by Kovaleva et al.26 as compared to that derived here from fast motion EPR spectra (Fig.2) is conditioned by higher sensitivity of molecular probe absorbed on the channel surface to the ionization of surface functional groups.

The fast motion nitroxide method introduced in this work could be advantageous in some cases because of (i) a simpler data analysis (no computationally demanding simulations of slow motion EPR components is required because the fast motion spectrum could be readily extracted by available methods49), (ii) better concentration sensitivity for nitroxides exhibiting narrow fast motion spectra vs. broad immobilized one, and (iii) applicability to molecular probes that do not absorb on the pore surface and, therefore, do not change surface properties. For example the method is fully applicable to small molecular probe R3 radical which in MMS yields fast motion EPR spectra but no measurable immobilized components.25 The method described here is also expected to be fully applicable to new pH-sensitive EPR probes based on triarylmethyl radical derivatives.21 The main disadvantage of the method would be its inapplicability to the channels with diameters much larger than the Debye length because the surface electrostatic potentials will be effectively screened by the electrolytes present. Thus, we turn our attention to the analysis of the electric potential across cylindrical pores and a comparison of the experimental results with the classical Poisson–Boltzmann double layer theory.29-33


23


3.2

Page 24 of 43

Comparison of EPR titrations data with Poisson–Boltzmann double layer

theory for cylindrical capillaries of infinite extent.

The shifts in EPR titration curves were used to calculate Δp𝐾𝑎𝑒𝑙 using the procedure outlined previously.26 In brief, a shift between the EPR titration curves for NR in nanopores and bulk aqueous solutions is measured at pH values when the surface is uncharged (i.e., at the isopotential point) to yield Δp𝐾𝑎𝑐ℎ . We note that for R1 the EPR titration curves in nanopores deviate from the bulk phase calibration curve even at low pH when the silica surface is expected to be uncharged27 and the R1 titration curves for both С12MCM-41 and С16MCM-41 coincide and run approximately parallel to the calibration curve for the bulk phase up to appearance of plateaus at p𝐻𝑒𝑥𝑡 > 5.5 (Fig. 2a). We measured this shift before the plateau (see lower red arrow in Fig. 2a) and used its value an estimate for Δp𝐾𝑎𝑐ℎ ≈ 0.83 (Table 4). This value is greater than Δp𝐾𝑎𝑐ℎ ≈ 0.2 − 0.3 estimated for SNA-15 but both С12MCM-41 and С16MCM-41 exhibit channels with much smaller diameters. Then a shift in the titration curves is measured above the plateau (upper red arrow in Fig. 2a) to yield 𝛥𝑝𝐾𝑎𝑐ℎ + 𝛥𝑝𝐾𝑎𝑒𝑙 allowing for estimating 𝛥𝑝𝐾𝑎𝑒𝑙 and calculating an average potential, 𝜑𝑎 , experienced by NR radical diffusing in in accessible aqueous volume of the channels, from eq. (8). The results of such measurements are summarized in Table 4 and compared with data measured by NR absorbed on the channel surfaces using calculations summarized below.

As synthesized the pores of MCM-41 are known to exhibit hexagonal50 or rounded hexagonal cross sections that become round upon calcination.51 Thus, the round cross section appears as a good geometrical model for the pores studied here. The pore length is typically


24

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assumed to be equal to the length of the particles along their pore channels.52 Then for MMS particles of at least 10 µm in size, the length of the pores will exceed the diameter by 1,000-fold or more even for the largest of the pores studied here (D=8.1±0.1 nm for SBA-15). For such pores the boundary effects could be neglected and the pores can be approximated as being infinitely long. The problem of a dilute electrolyte in the infinitely long cylindrical pores with charged surfaces has been considered by several authors who applied the classical Poisson– Boltzmann double layer theory.29-33 Based on these preceding studies the Poisson-Boltzman (PB) equation for monovalent ions can be written in polar coordinates as a function of the distance r from the pore center:

𝑑2 𝜑(𝑟) 𝑑𝑟 2

1 𝑑𝜑(𝑟)

+𝑟

𝑑𝑟

=

2𝑐0 𝐹

𝐹𝜑(𝑟)

sinh (

𝜀0 𝜀𝑟

𝑅𝑇

),

(9)

where 𝜑(𝑟) is the electrostatic potential with respect to radial distance, 𝜀0 - permittivity of vacuum, 𝜀𝑟 - relative permittivity, 𝐹 - Faraday constant, 𝑅 – universal gas constant, 𝑇 thermodynamic temperature, and 𝑐0 is molar monovalent salt concentration.

The second order differential equation (9) can be solved numerically if two boundary conditions are given. One is coming from the axial symmetry of the pore that is imposing the following requirement for the pore center:

𝑑𝜑(𝑟) 𝑑𝑟

|

𝑟=0

= 0. The second boundary condition is

typically provided in a form of a known electrostatic potential value 𝜑(𝑟) or its derivative 𝑑𝜑⁄𝑑𝑟, for example, at the pore extremes such the pore axis or the wall or any other defined location inside the pore channel.


25


Page 26 of 43

EPR experiments described in the preceding report26 provide for such boundary conditions by employing nitroxide probes which become immobilized on the channel surfaces. Indeed, EPR titration experiments of such probes report on surface electrostatic potential 𝜑(𝑟) at about the minimal nitroxide approach distance d to the wall.26 On the other hand, the niroxide probes remaining in the pore aqueous phase (i.e., fast motion component observed and analyzed in this study), report on the electrostatic potential 〈𝜑(𝑟)〉 averaged over the inner pore region up to the collision distance where the nitroxide gets immobilized. Although not located at the pore extremes, each of the experimental values uniquely determines the solution of the PB equation. Since one could have two boundary conditions from the “mobile” and the “immobilized” NR probe components and then the third

𝑑𝜑(𝑟) 𝑑𝑟

|

𝑟=0

= 0 boundary condition for the center of the pore,

the problem becomes overdetermined, thus, allowing for a critical examination of the PB model applicability to the nanoscale pores.

In order to carry out numerical integration of the PB equation Matlab ODE solver has been employed. The procedure involves transforming eq.(9) into the following dimensionless units:

𝐹

𝑐 2𝐹2

𝑦 = 𝑅𝑇 𝜑, 𝑥 = 𝜒𝑟, where 𝜒 = √𝜀 0𝜀

0 𝑟 𝑅𝑇

.

(10)

In these dimensionless units the PB equation has a particularly simple form suitable for a numerical integration:


26

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𝑑2 𝑦 𝑑𝑥 2

1 𝑑𝑦

+ 𝑥 𝑑𝑥 = sinh(𝑦).

(11)

In the next step the Matlab ODE solver requires transferring eq. (11) into a set of two first order 𝑑𝑦

equations. By substituting 𝑌[1] = 𝑦 and 𝑌[2] = 𝑑𝑥 , eq.(10) converts into the required form 𝑌′ = 𝑓(𝑥, 𝑌):

𝑌 ′ [1] = 𝑌(2), 𝑌 ′ [2] = sinh(𝑌[1]) − 𝑌[2]/𝑥.

(12)

Within the Matlab ODE toolbox eq.(11) is the best solved by using function ‘bvp4c’, which is designed for solving boundary value problems. Supplementing ‘bvp4c’ with a function prescribing specific values at integration limits, eq.(11) is readily solved.

Numerical values for the electrostatic potential 𝜑(𝑟) reported in the preceding report26 were measured from EPR titrations of a nitroxide probe immobilized on the surface of the pore channel. Such a probe reports 𝜑𝑑 at a distance d from channel wall towards the center of the channel. For the “mobile” probe rapidly diffusing across the pore, the reported electrostatic potential is an average 〈𝜑(𝑟)〉 over the volume accessible to this molecular probe (we assume that the fast exchange conditions for EPR spectra are satisfied). Thus, we calculate 𝜑𝑎 = 〈𝜑(𝑟)〉 as a mean value of the potential 𝜑(𝑟) weighed by the radial probe concentration distribution function. For a homogeneous probe density across the channel, the radial distribution function is given by:

𝑃(𝑟) = 2𝑟/(𝐷⁄2 − 𝑑 − 𝑙)2 ,

(13)


27


Page 28 of 43

where P(r) is the probability of finding the probe at the distance r from pore axis, r=0, D is the pore diameter, and l is the distance of the closest approach of the “mobile” probe to the immobilized approach distance (specified by the distance d). Note that 𝜑𝑎 is not one of the normal boundary conditions for the PB equation, such as, for example, the value of 𝜑(𝑟) at a specific location, but rather an average value 𝜑𝑎 = 〈𝜑(𝑟)〉 calculated over the volume accessible to the NR probe diffusing within the MMS channel.

Integration limits specified by values d and l can be estimated from the following considerations. While the exact mechanism for NR immobilization of the channel surface is unclear, we speculate that multiple non-covalent interactions including Van der Waals forces have to be involved. The nitroxide NO moiety is also known to readily form hydrogen bonds of ca. 1.74 Å in length with different H donors;53 however, the single hydrogen bond between the nitroxide NO moiety and the silanol OH group would be insufficient for the NR immobilization on the EPR time scale. Thus, the nitroxide ring is most likely to adapt a planar docking conformation on the surface. By taking into account the typical bond lengths and molecular dimensions of the NR radicals we estimate that the immobilized molecular probes report at a distance d ≈ 0.3 nm from the surface. Then, the pore volume accessible to the mobile probe must be smaller by at least this distance d. Furthermore, because of the essentially free rotation observed for mobile probe from the EPR spectra the average closest approach distance is further shortened by half of its diameter. The typical dimensions of the NR radicals employed are estimated to be about 0.9 nm and, therefore, we set the distance to l = 0.45 nm.


28

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Table 4. Δp𝐾𝑎𝑐ℎ and Δp𝐾𝑎𝑒𝑙 measured from the shifts of EPR titration curves derived from fast motion nitroxide spectra (cf. Fig. 2), corresponding experimental electrostatic potentials derived from EPR titrations of mobile probes reporting on an average potential, 𝜑𝑎 = 〈𝜑(𝑟)〉 over the accessible pore volume and associated near-surface potential, 𝜑𝑑 ,

reported by surface-

immobilized probes for the MMS studied. MMS С12MCM-41 С16MCM-41

R1

Sensitivity range, pH units 2.0-6.5

Δp𝐾𝑎𝑐ℎ ,  0.1 Δp𝐾𝑎𝑒𝑙 ,  0.1 𝜑𝑎 = 〈𝜑(𝑟)〉, 𝜑𝑑,  6,  6, mV mVa 0.83 0.60 -35 -171

R2

4.5-7

0.40

0.98

-57

-150

R1

2.0-6.5

0.83

0.93

-54

-179

R1

2.0-6.5

0.2-0.3

0

0

-110

R2

4.5-7

0.2-0.3

0

0

-141

NR

SBA-15 a

Values of 𝜑𝑑 were determined in ref.26


29


Page 30 of 43

a) С16MCM-41/R1

b) С12MCM-41/R2

c)

С12MCM-41/R1

Figure 4. Radial profiles of electrostatic potential 𝜑(𝑟) obtained from numerical solutions of the Poisson-Boltzmann equation using different boundary conditions. Vertical lines denote integration limits inside the channel: solid black corresponds to the channel wall, dashed black to the distance of the immobilized probe to the wall, d=0.3 nm, and dashed green delimits the mobile probe region (up to the radius of nitroxide probes, l=0.45 nm, away from the immobilized distance. For three channel /probe combinations a) С16MCM-41/R1, b) С12MCM-41/R2, and c) С12MCM-41/R1 (see Table 4: MMS/NR), two sets of profiles are calculated. The first (blue


30

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curves) is calculated using the experimental boundary condition given by 𝜑𝑎 = 〈𝜑(𝑟)〉- an average potential over the mobile probe region (i.e., from the channel center to the distance indicated by vertical green dashed lines). The second set (red curves) is calculated using the experimental boundary condition, φd, the electrostatic potential measured by an immobilized NR at a distance d from the channel wall. The corresponding numerical values are indicated in the graph. Averaging of the electrostatic potential over the pore region accessible to the mobile NR probe has been carried out assuming a homogeneous distribution inside the pore and the corresponding values are indicated by horizontal blue and red dashed lines. See text for details.

Table 4 summarizes the experimental values of 𝜑𝑎 = 〈𝜑(𝑟)〉 and 𝜑𝑑 employed as the boundary conditions for solving the PB equation. For each of the pore diameter / EPR probe combinations two sets of 𝜑(𝑟) radial profiles were calculated – one using 𝜑𝑎 and another 𝜑𝑑 (cf. Fig. 4). Ideally both curves coincide if the theory matches the experiment.

An examination of blue and red curves in Fig.4 demonstrates that taking 𝜑𝑎 and 𝜑𝑑 as one of the boundary conditions of the PB equation (the second one is always given by 𝑑𝜑(𝑟) 𝑑𝑟

|

𝑟=0

= 0) results in different 𝜑(𝑟) profiles across the pores although for some of the

combinations the disagreement is larger than for others. The data for С16MCM-41 (pore D=3.2± 0.1 nm) obtained using molecular R1 probe demonstrate the closest agreement. Specifically, by taking 𝜑𝑑 = − 179 𝑚𝑉 the PB solution yields 𝜑𝑎 = − 65 𝑚𝑉, which is very close to 𝜑𝑎 = − 54 ± 6 𝑚𝑉. It is worthwhile to note here that if we use 𝜑𝑎 = − 54 𝑚𝑉 as a boundary


31


Page 32 of 43

condition, the absolute value of calculated 𝜑𝑑 = − 103 𝑚𝑉 will be by ca. 40% smaller that the experimental 𝜑𝑑 = − 179 ± 6 𝑚𝑉. This is expected as the solution of the PB equation at high potential values (>100 mV) grows quickly with distance as 𝜑(𝑟) approaches the electrically charged walls of the pore. In other words, some experimental errors in 𝜑𝑑 would result in only minimal errors in calculated 𝜑𝑎 . In a contrast, a decrease in the magnitude of 𝜑𝑎 by only 18% results in a 43% decrease in |𝜑𝑑 | (compare red and blue curves in Fig. 4a). In general, the agreement between red and blue PB profiles improves by choosing parameters corresponding to a more efficient screening of the surface electrostatic potential. For example, one could achieve a better agreement by choosing a larger pore diameter D, smaller d, and larger l, and/or those media constants that would yield a better screening: specifically, a higher ion concentration c and a lower relative permittivity εr. For example, a perfect match between the red and blue profiles can be easily achieved by only minor alterations of just a few parameters such as by taking: c=0.120 M, d=0.2 nm, and l=1.2 nm. Overall, the experimental data for 𝜑𝑎 and 𝜑𝑑 measured for С16MCM-41 with the average pore diameter D=3.2± 0.1 nm appear to be in a reasonable agreement with the classical PB theory that is based on a continuum electrostatic model.

As the pore diameter increases, the screening of the surface electrostatic potential by electrolyte ions becomes more efficient and 𝜑𝑎 should approach zero regardless 𝜑𝑑 values. 1

1

Typically, this condition is satisfied when 2 𝐷−1 > 4, where 2 𝐷 is the pore radius and 𝜒 −1 is the Debye length.47 This condition is fully satisfied for SBA-15, (𝜒 −1 =0.98nm from eq. (9), D=8.1± 0.1 nm). Indeed, experimentally measured 𝜑𝑎 ≈ 0 𝑚𝑉 is in the full accord with the PB theory (Table 4, no radial 𝜑(𝑟) profiles are shown).


32

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Pores with smaller diameters such as С12MCM-41 (D=2.3± 0.1) provide the most critical test for the classical PB equation because the effect of 𝜑𝑑 on 𝜑𝑎 should decrease with D. Figures 4b and 4c show the sets of radial 𝜑(𝑟) profiles calculated from the experimental data available for two molecular probes, R1 and R2, respectively. Either sets of curves demonstrate large deviations that cannot be reconciled by considering experimental errors in 𝜑𝑑 and 𝜑𝑎 . For example, by taking the experimental value 𝜑𝑑 = − 171 𝑚𝑉 measured from the R1 EPR titration, the absolute value of calculated 𝜑𝑎 = −80 𝑚𝑉 is significantly higher than the experimentally measured 𝜑𝑎 = −35 ± 6 𝑚𝑉 (cf. Fig. 4c and Table 4).

This discrepancy is

particularly striking because the experimental 𝜑𝑑 and 𝜑𝑎 values measured for С16MCM-41 with similar surface chemistry are in a close agreement with the PB equation. The main difference between С12MCM-41 vs. С16MCM-41 is about 30% smaller pore diameter and this must be the critical factor. Indeed, as previously discussed in the literature,32 when

1 2

3

𝐷−1 ≤ 2

(13)

the pore has insufficient space for the near-surface double electric layer (DEL) to form. For C12 МCM-41 parameter

1 2

𝐷 −1 = 1.1271/2𝐷−1=1.127 while for С16MCM-41

1 2

𝐷−1 = 1.568.

Under such conditions DEL is subject to deformations due to a mutual electrostatic repulsion between identically charged ions in the diffuse areas. Under these conditions the concentration of counter ions in the diffuse area of DEL is expected to be higher as compared to the completely formed DEL at the same electrolyte concentration. Another possible explanation could be in a significantly further altered water structure upon confinement in the nanochannels as speculated in the literature.28 If the latter is indeed the case, then one would expect to observe some changes


33


Page 34 of 43

in rotational diffusion of small molecular probes and/or changes in the nitroxide nitrogen hyperfine coupling parameters, such as Aiso, which is primarily affected by the hydrogen bonding to water molecules.53,54 However, neither of these effects was observed in the experimental EPR spectra (not shown). It is worthwhile to note here that while the hydrogen bonding increases Aiso, a lower effective solvent polarity has an opposite effect and, therefore, potentially, such changes in Aiso could be mutually canceled. Furthermore, if the properties of water in the nanopores are indeed perturbed (as suggested by our data for SBA-15), such perturbations are expected to be highly heterogeneous across the pore diameter with stronger perturbations occurring closer to the pore surface. In particular, according to the classical Booth theory the bulk dielectric constant of water is reduced at high electrical fields,55 such as those measured at alkaline p𝐻 𝑒𝑥𝑡 by the EPR probes immobilized probes. Such fields are not only spatially heterogeneous but are also determined by the surface charge that is changing with p𝐻 𝑒𝑥𝑡 .

Other potential problems could be steaming from the continuum electrostatic model on which the PB equation is based. Indeed, when the pore diameter is becoming comparable with the size of the ions, the point charge approximation becomes inaccurate. The efforts to implement corrections for the finite charge sizes in both the diffuse layer and the surface charging have been described in the literature.56,57 Based on the arguments presented in the latter studies, we expect that such corrections would improve the overall agreement of our data with the PB model. However, we speculate that at least for the smallest channels studied the ever increasing system heterogeneity and the discrete character of the ions and molecular probes in the nanochannels would render the continuum electrostatic model impractical. Then one would


34

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have to resort to rigorous molecular dynamics simulations; however, such simulations appear to be outside the scope of the current study.

4. CONCLUSIONS

EPR experiments with water-soluble ionizable pH-sensitive nitroxides describe here provide the means to determine an average effective local p𝐻 𝑙𝑜𝑐 experienced by such molecules confined but diffusing in aqueous volume inside the nanopores of the mesoporous molecular sieves. On example of SBA-15 channels filled with aqueous solutions at ambient temperature and 0.1 M ionic strength, i.e., when the pore radius is about fourfold larger than the Debye radius, we show that p𝐻 𝑙𝑜𝑐 averaged over the central section of the nanochannel accessible to the pore is still higher by 0.2-0.3 pH units than p𝐻 𝑒𝑥𝑡 . This pH shit cannot be explained by the electrostatic potential of the pore surface in the essentially electroneutral for silica acidic region. Furthermore, when at alkaline p𝐻 𝑒𝑥𝑡 the surface of SBA-15 channels becomes electrically charged, the EPR spectra of the mobile probe are still essentially insensitive to the surface charges due to the effective screening of the surface charge by the counter ions over the distance of several Debye radii. A likely explanation of such small but measurable pH shift is an additional ordering of water molecules in the nanochannels. In a contrast, for the pores with the radii comparable with the Debye length, such as for С12MCM-41 and С16MCM-41 sieves, the fast motion EPR spectra of ionizable nitroxides become sensitive to the protonation of the surface groups. A good agreement between p𝐾𝑎 values of the surface groups determined from


35


Page 36 of 43

analysis of such fast motion EPR spectra vs. those obtained from nitroxides immobilized on the pore surfaces demonstrates the applicability of this new method described here. The method could be particularly advantageous when utilized together with molecular probes that do not absorb on the pore surface and, thus, do not change the surface properties.

With data on the average electrostatic potential over the central volume of the nanochannels measured by “mobile” EPR probes and the surface potential at the channel surface determined from EPR titrations of immobilized nitroxides, we have examined the applicability of the classical Poisson–Boltzmann double layer theory to the channels of the nanoscale diameter. This theory has been initially developed for diluted electrolytes in cylindrical capillaries of infinite extent. The experimental data were found to be in a good agreement with the theory for the channels down to 3.2±0.1 nm in diameter but deviated significantly for the 2.3±0.1 nm pores such as found in С12MCM-41. We attribute the later discrepancy to the insufficient space in the 2.3±0.1 nm pores leading to a large spatial heterogeneity and, most likely, the failure of the continuum electrostatics/point charge model to account for the finite dimensions of the ions and the molecules involved in such small nanopores.


36

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AUTHOR INFORMATION

Corresponding Authors *E-mail: [email protected] or [email protected] ORCID

Alex I. Smirnov: 0000-0002-0037-2555

Author Contributions The manuscript was written through contributions of all the authors. All authors have given approval to the final version of the manuscript. Funding E.G.K., L.S.M., D.O.A., D.P.T., and A.N.T. acknowledge the financial support of the Program 211 of the Government of the Russian Federation № 02.A03.21.0006, RFBR grant 17-03-00641 and the State Task from the Ministry of the Education and Science of the Russian Federation №

4.9514.2017/8.9 and № 4.7772.2017/8.9. A.M. and A.I.S. acknowledge the financial support of the U.S. DOE Contract DE-FG02-02ER15354 (modelling of electrostatic phenomena in the nanochannels and the final preparation of the manuscript). Notes The authors declare no competing financial interest. ACKNOWLEDGEMENTS

The authors are thankful to Prof. Igor A. Grigor’ev and Dr. Igor. A. Kirilyuk (Institute of Organic Chemistry of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk,


37


Page 38 of 43

Russia) for synthesis of pH-sensitive nitroxide radicals. We also acknowledge productive discussions with Prof. Maxim A. Voynov (NCSU) and his assistance with graphical software.

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Proton Activity in Nanochannels Revealed by EPR of Ionizable

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