Dynamics of Dimethylbutanols in Plastic Crystalline Phases by Field

Subscriber access provided by UNIV OF NEW ENGLAND

B: Fluid Interfaces, Colloids, Polymers, Soft Matter, Surfactants, and Glassy Materials

Dynamics of Dimethylbutanols in Plastic Crystalline Phases by Field Cycling H NMR Relaxometry 1

Elisa Carignani, Claudia Forte, Ewa Juszy#ska-Ga##zka, Miroslaw Ga##zka, Maria Massalska-Arod#, Alessandro Mandoli, Marco Geppi, and Lucia Calucci J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b06391 • Publication Date (Web): 02 Oct 2018 Downloaded from http://pubs.acs.org on October 6, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Dynamics of Dimethylbutanols in Plastic Crystalline Phases by Field Cycling 1H NMR Relaxometry Elisa Carignani,1,2,* Claudia Forte,1 Ewa Juszyńska-Gałązka,3 Mirosław Gałązka,3 Maria Massalska-Arodź,3 Alessandro Mandoli,2 Marco Geppi,1,2 Lucia Calucci1,* 1

Istituto di Chimica dei Composti OrganoMetallici, Consiglio Nazionale delle Ricerche - CNR,

via G. Moruzzi 1, 56124 Pisa, Italy. 2

Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via G. Moruzzi 13, 56124

Pisa, Italy. 3

Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego

152, 31342 Krakow, Poland.

ACS Paragon Plus Environment

1

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 37

Abstract

2,2-dimethylbutan-1-ol

(2,2-DM-1-B),


(3,3-DM-1-B),

and

3,3-

dimethylbutan-2-ol (3,3-DM-2-B) show a rich solid-state polymorphism, which includes one or more plastic crystalline phases (also referred to as orientationally disordered crystalline (ODIC) phases) and glass of the liquid or ODIC phases. In this work, the dynamics of the three isomeric alcohols was investigated in the liquid and plastic crystalline phases by Fast Field Cycling 1H NMR relaxometry in the temperature range between 213 and 303 K. The analysis of the Nuclear Magnetic Relaxation Dispersion (NMRD) curves (i.e. longitudinal relaxation rate R1 vs 1H Larmor frequency) acquired for the different alcohols at different temperatures gave quantitative information on internal motions, overall molecular reorientations, and molecular self-diffusion. Self-diffusion coefficients were also determined in the liquid phase and in some ODIC phases of the samples from the trends of 1H R1 as a function of the frequency square root at low frequencies. Remarkable changes in the temperature trends of correlation times and selfdiffusion coefficients were found at the transition between the liquid and the ODIC phase for 2,2-DM-1-B and 3,3-DM-1-B, and between ODIC phases for 3,3-DM-2-B, the latter sample showing a markedly different dynamic and phase behavior.


2

Page 3 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Introduction Plastic crystalline phases (also referred to as orientationally disordered crystals (ODIC)) are characterized by long range positional order of the centers of mass of molecules in a highly symmetric (usually cubic) crystal lattice, but orientational disorder of the molecules.1,2 The formation of ODIC phases is favored by the globular shape of molecules, as well as by the possibility of having several conformational isomers associated to internal rotations. In these phases, the large concentration of structural defects allows translational mobility, which is at the origin of the plastic deformations observed for these systems. In fact, plastic crystals are generally soft and frequently flow under their own weight.3,4,5 Therefore, different types of dynamic processes may be present in plastic crystalline phases depending on the temperature, the molecular architecture, and the crystal lattice symmetry. Thanks to the possibility of combining T2, T1 and, especially, T1ρ relaxation times measured at different frequencies and temperatures, and for different nuclei (most commonly 1H, but also 13C and 2H), NMR relaxometry allowed internal, reorientational, and self-diffusion molecular motions to be investigated for several molecules showing plastic crystalline phases.6,7,8,9,10,11,12,13 In this context, Fast Field Cycling (FFC) 1H NMR relaxometry, a technique allowing 1H T1 values to be measured over a wide frequency range with a single instrument (0.01 - 40 MHz with commercial relaxometers, the lower limit being extended even below 100 Hz in homemade relaxometers14,15,16,17), was found to be particularly suited for investigating both reorientational and translational dynamics in these phases. In fact, 1H longitudinal relaxation results from the fluctuations of both intra- and intermolecular dipole-dipole interactions between pairs of nuclei caused by molecular reorientations and translational motions. In particular, the intramolecular contribution to relaxation is solely determined by reorientational motions, while the


3


Page 4 of 37

intermolecular one is generally associated with self-diffusion, although an additional contribution may come from the reorientation of neighboring molecules. This renders the analysis of Nuclear Magnetic Relaxation Dispersion (NMRD) curves (i.e. R1=1/T1 vs Larmor frequency curves) quite complex and, in some cases, dependent on the choice of the models devised for the description of contributions to R1 arising from internal and overall molecular reorientations, and self-diffusion motion. In spite of this, FFC 1H NMR relaxometry has been increasingly employed to investigate dynamics in condensed matter.18,19,20,21 Self-diffusion coefficients (D) and rotational correlation times were determined from the analysis of NMRD curves for molecular and ionic liquids 14,22,23,24,25,26,27,28,29,30 and for liquid crystals,31,32,33,34,35 but only for few plastic crystals.12,13 The linear dependence of R1 on the square root of the Larmor frequency (ν) at low frequencies, theoretically predicted for translational motion in three dimensions,36,37,38,39 allowed an independent determination of D for some of them.12,14,22,23,24,25,30 As far as self-diffusion is concerned, FFC NMR relaxometry makes it possible to bridge the gap between the timescale of a field gradient NMR diffusion experiment (10 ms to s when applied to plastic crystals) and that of T1 relaxation times measured with conventional high field spectrometers, which probe motions with characteristic correlation times on the order of or lower than 10-9 s.21 Indeed, self-diffusion coefficients in the range between 10-14 and 10-9 m2/s can be determined by FFC 1H NMR: the lower limit is related to the possibility of observing a slope in the NMRD curve, while the upper one is due to the restriction imposed on the maximum measurable relaxation rates by the relaxometer switching time (i.e. the time interval required to switch between different magnetic field values in a FFC NMR experiment).23 In fact, at low frequencies, 1H T1 values in viscous liquids30 or plastic crystalline phases12 may be less than a millisecond, whereas typical switching times are on the order of few milliseconds. However, it


4

Page 5 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


has been theoretically and experimentally demonstrated that, provided the changes between the different field levels are reproducible, the use of a switching interval longer than the measured T1 values brings to magnetization losses and, hence, reduces the experimental precision of relaxation rate measurements, but does not induce any systematic error.18,40 As a consequence, a lower precision is expected on self-diffusion coefficient values determined from R1 vs √ at low frequency.30 In the present work, 1H NMR relaxometry was applied to study the dynamics of a family of isomeric monohydroxy alcohols showing peculiar phase behavior,41,42,43 namely 2,2dimethylbutan-1-ol

(2,2-DM-1-B),


(3,3-DM-1-B),

and

3,3-

dimethylbutan-2-ol (3,3-DM-2-B); their molecular structures are shown in Figure 1. These alcohols differ from each other by the positions of the OH and CH3 groups, which influence both the tendency to form H-bonds and the number of conformational isomers, but all have a nearly globular shape, which promotes the formation of plastic crystals. The different molecular architecture and motional degrees of freedom give rise to a different solid state polymorphism of 2,2-DM-1-B, 3,3-DM-1-B, and 3,3-DM-2-B, which was investigated by differential scanning calorimetry (DSC), adiabatic calorimetry, and inelastic incoherent neutron scattering in previous studies.41,42,43,44,45,46,47 In particular, 2,2-DM-1-B was found to form a fully ordered crystalline phase, an ODIC phase, a conformational disordered (CONDIS) phase, and a glassy crystal of the CONDIS phase. 3,3-DM-2-B forms four ODIC phases, with the lower temperature ODIC phase forming a glassy crystal on further cooling. For 3,3-DM-1-B, the structural glass was observed on cooling, while on heating a spontaneous crystallization was observed; however, the formed phase was identified as either a CONDIS41 or an ODIC42 phase. For all three alcohols,


5


Page 6 of 37

polymorphism and phase transition temperatures markedly depend on the thermal treatment and on the rate of cooling/heating.

Figure 1. Molecular structure of 2,2-DM-1-B, 3,3-DM-1-B, and 3,3-DM-2-B. Here, the dynamics was investigated in the temperature range between 213 and 303 K, the limiting temperature values being determined by instrumental parameters (i.e. minimum temperature available, minimum T1 value measurable, maximum polarization time achievable). The NMRD curves were interpreted in terms of suitable models for internal and molecular motions in order to relate molecular structure and microscopic dynamic processes of the three alcohols with their phase behavior. Experimental Section Materials. 2,2-DM-1-B was available from previous studies.42,45 3,3-DM-1-B, and 3,3-DM-2-B were purchased from Aldrich and used without further treatment. Phase transitions, determined by adiabatic calorimetry on heating (after cooling at a rate ≥ 5 K/min), were: 2,2-DM-1-B:43 GCr2-(123 K)→sCr2-(148 K)→Cr3-(195 K)→Cr2-(209 K)→Cr1-(234 K)→L


6

Page 7 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3,3-DM-1-B:41 GL-(146 K)→sL-(188 K) →Cr1-(234 K)→L 3,3-DM-2-B:48 GCr4-(223 K)→Cr4-(239 K)→ Cr3-(256 K)→Cr2-(264 K)→Cr1-(276 K)→L where Cr, L, G, and s indicate crystalline, liquid, glass, and supercooled phases, respectively. NMR Relaxometry Measurements. 1H R1 values were measured at several frequencies between 0.01 and 35 MHz on a SpinMaster FFC-2000 (Stelar srl) relaxometer and at 400.03 MHz on an Infinity Plus 400 spectrometer (Varian). For measurements on the relaxometer, the non-prepolarized and prepolarized sequences18,49 were used above and below 12 MHz, respectively, with polarizing and detection fields of 0.70 T (30.0 MHz) and 0.50 T (21.5 MHz), respectively. The 90° pulse duration was 10 µs, the switching time 3 ms, and a single scan was acquired. All the other experimental parameters were optimized for each experiment. In all cases a monoexponential function well reproduced the magnetization trends as a function of the variable delay; errors on R1 were ≤ 2 % for R1 values ≤ 1000 s-1 and ≤ 5 % for R1 > 1000 s-1. The sample was contained in a standard 10 mm NMR tube and the temperature, stabilized for at least 10 min before each measurement, was controlled within ± 0.1 K with a Stelar VTC90 variable temperature controller. The Varian spectrometer was equipped with a 5 mm probe and the Saturation Recovery pulse sequence was used with a 90° pulse duration of 4 µs. At least 24 spectra at different recovery times were acquired to build the recovery curves at each temperature and 4 scans were acquired for each spectrum. In all cases, a monoexponential function well reproduced the recovery curves, with errors on R1 values ≤ 1 %. The temperature, controlled within ± 0.5 K, was stabilized for at least 10 min before measurement


7


Page 8 of 37

In all cases, samples were cooled to the liquid nitrogen temperature to allow the crystalline phases to form on heating and measurements were performed on heating starting from 213 K. Data Analysis. 1H NMRD profiles, obtained by combining the R1 values measured with the FFC relaxometer between 0.01 and 35 MHz and that measured with the stationary field spectrometer at 400.03 MHz, were analyzed using the least-squares minimization procedure implemented in the Fitteia environment.50,51 Theoretical background The analysis of the NMRD curves was performed by expressing R1 as the sum of contributions ( ) coming from the different relaxation mechanisms envisaged in each phase; these mechanisms were assumed independent as usually done. Considering the molecular structure of the investigated alcohols (Figure 1) and the phases they form in the examined temperature range, contributions arising from internal motions ( ) and overall molecular reorientations ( )

were expected in all phases. On the other hand, translational self-diffusion ( ) certainly contributed to relaxation in the liquid phase, as already pointed out in a previous study,66 but it might also affect relaxation in the ODIC phases, as reported in the literature for other plastic crystals.6,7,8,12,52,53 The and contributions were expressed as54,55 ( ) = [ ( ) + 4 (2 )]

(1)

where Ci is a relaxation amplitude factor, which is proportional to the square of the strength of the residual homonuclear dipolar interaction, and ( ) and (2 ) are the spectral densities of motion, which depend on both temperature and angular Larmor frequency (ω=2πν). For all


8

Page 9 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


samples in all phases, the spectral densities for internal motions in were expressed in terms of the correlation time for the motion, τIM, according to the Bloembergen-Purcell-Pound (BPP) model (or Debye model), where ( ) is a Lorentzian function.56 For the contribution from molecular reorientations ( ), the spectral densities were expressed by the Lorentzian function

in the liquid (L) phase of all samples and in the Cr1 phase of 3,3-DM-2-B, and by the HavriliakNegami (HN) function (Eq. 2), or the derived Cole-Cole and Davidson-Cole functions (vide infra), in the other crystalline phases. The HN function takes into account both a distribution of activation barriers for the motions and the presence of correlated motions,57 which could indeed be present in ODIC phases because of the dynamic disorder. In the HN function, expressed as:

( ) =

2 $%&'(,*+ , ./01- 4 3 9: 2 56$%&'(,*+ , 78.1- 4 3

∙ !"#

-

2

;'(,*+ , !?1@ 4'(,*+ , 3

B 3- 3

A

(2)

δ and ε are parameters that account for the symmetric and asymmetric broadening of the distribution of correlation times, respectively; δ, which is a measure of correlation between motions, ranges from 0 to 1, while ε goes from 0 to 1/δ, εδ being a measure of the spread of the activation barriers. The HN function reduces to the Cole-Cole, Davidson-Cole, or BPP ones if ε=1, δ=1, or δ=ε=1, respectively. In order to facilitate the comparison between correlation times for reorientational motions determined using different expressions of the spectral densities, the correlation time, C =

1⁄ ,EF , with ,EF the angular frequency at the Havriliak-Negami function maximum,

was derived from the best fit correlation time C , using Eq. 3, borrowed from dielectric relaxation data analysis58,59


9


5 2-B 4 3(56B) 21 4 3(56B)

1

C = C , H

I

Page 10 of 37

(3)

For the self-diffusion contribution ( ) two different models were used. In the liquid phase,

was expressed in terms of the commonly used force-free hard-sphere model proposed by

Hwang and Freed60 and by Ayant et al.,61 which assumes that the interacting nuclei are located in the centers of the molecules that undergo Fickian diffusion. The molecules, treated as hard spheres, are uniformly distributed outside the distance of closest approach, d, which corresponds to the molecular diameter; hence, spheres are not allowed to interpenetrate. According to this model ( ) =

J

L K

MN

Q

=

1 R 4 SM ℏ= [ ( ) + 4 (2 )] OP MN

J

(4)

where NH is the spin density, and γH is the proton gyromagnetic ratio. The spectral density is written as62,63

( ) = 72

J

_

V MN K

W3

W3 >]^

X, and on the mean time between jumps C

(the expression of d ( C ) is lengthy,38 so we refrain from showing it here). < fg= > and C

are related, in turn, to the translational diffusion constant (D) through the expression b =< fg= > /6C .

Self-diffusion coefficient values were also determined without recurring to any model for . In fact, at low frequency, where C ≪ 1, the spectral density associated to self-diffusion can

be approximated as ( ) = l −

n

P/3

√ as a result of the fact that free diffusion controls

translational motions at long times.36,37,39,60,61 Therefore, when ( ) at low frequency is dominated by the self-diffusion contribution, it can be written as ( ) = (0) −

p

P/3

√

(7)

with q=

N

(1 + 4√2)L 1 JK

QR

MN

S= ℏ4

=

(8)


11


Page 12 of 37

(0) is the value of ( ) extrapolated to zero frequency. This implies that Eq. 7 can be exploited to directly determine D values from the slope of ( ) vs √ at low frequencies.

Results and Discussion Trends of 1H relaxation rates as a function of Larmor frequency and temperature. NMRD curves acquired at different temperatures on heating 2,2-DM-1-B, 3,3-DM-1-B, and 3,3-DM-2-B samples are shown in Figure 2 (left panel). At frequencies lower than 10 MHz, sudden changes in the NMRD curves were clearly observed at temperatures corresponding to phase transitions for all samples, although with some differences. For 2,2-DM-1-B, a strong decrease in the R1 vs ν slope was observed for ν ≤ 0.2 MHz and in the MHz range going from 229 to 231 K, that is, close to the melting of the Cr1 phase, indicating the speeding up of both a low and an intermediate frequency motion. For 3,3-DM-1-B, a strong decrease of R1 occurred going from 226 to 228 K, i.e., close to the melting temperature, accompanied by a sudden shift of the dispersion to higher frequencies. This suggests an abrupt change in motional parameters, which is expected on passing from a Cr to a liquid phase. For 3,3-DM-2-B marked changes in the NMRD curves were observed between 233 and 238 K, 253 and 258 K, and 262 and 264 K, corresponding to Cr4-Cr3, Cr3-Cr2, and Cr2-Cr1 phase transitions, respectively; no appreciable discontinuities characterized the transition between the Cr1 and the L phase. For all samples at all temperatures, NMRD curves did not show a completely flat plateau at low frequencies, suggesting the contribution of translational motions to relaxation. In order to corroborate this hypothesis, the dependence of R1 on √ at low frequencies, theoretically predicted for translational motions (Eqs. 7 and 8),36,37,38,39 was verified. As shown in Figure 3, a clear linear dependence was found for all samples in the L phase, although with a very small slope at the


12

Page 13 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


higher temperatures, in the Cr1 phase for 2,2-DM-1-B and 3,3-DM-1-B, and in the Cr1, Cr2 and Cr3 phases for 3,3-DM-2-B. The slope progressively decreased in each phase by increasing the temperature, while sudden changes were observed at the Cr1 to L phase transition for 2,2-DM-1B and 3,3-DM-1-B and at the Cr3 to Cr2 and Cr2 to Cr1 phase transitions for 3,3-DM-2-B.


13


Page 14 of 37

Figure 2. NMRD curves (left panel) and NMR susceptibility curves (right panel) at the indicated temperatures for 2,2-DM-1-B, 3,3-DM-1-B, and 3,3-DM-2-B.


14

Page 15 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3. Trends of vs √ for 2,2-DM-1-B, 3,3-DM-1-B, and 3,3-DM-2-B at the indicated temperatures. Expansions of the high temperature data are shown in the insets. The presence of motions dominating relaxation in different frequency regions and the changes in motional frequencies at the phase transitions could be highlighted using the susceptibility representation of relaxation data, since in this representation such motions may give rise to ss distinct peaks.65 The NMR susceptibility values, defined as r = 2t according to the

fluctuation-dissipation theorem (r′′( ) = ( )), are plotted vs the Larmor frequency in Figure

2 (right panel) for the three samples at different temperatures. In the obtained curves, peaks were clearly observed for 3,3-DM-2-B in the ODIC phases, with maximum shifting from 0.06 to 0.7 MHz with increasing the temperature. Peaks with maxima between 1.1 and 3.5 MHz were also ss present in the r curves of 3,3-DM-1-B in the Cr1 phase. For 2,2-DM-1-B, a peak with

maximum at ~3 MHz could be clearly distinguished only at 213 K in the Cr1 phase, while a broad peak with maximum in the MHz range was found between 223 and 229 K in the Cr1 phase, and between 233 and 243 K in the L phase, which overlapped a peak at higher frequencies, clearly present although not well defined. The latter peak is ascribed to internal rotations of the methyl and/or t-butyl groups about their ternary axes with an associated ss correlation time shorter than 10-9 s. Similar features were detected in the r curves for 3,3-

DM-1-B between 228 and 243 K. For 2,2-DM-1-B, a change in the slope was observed in the ss low frequency flank (< 0.2 MHz) of the main peak for temperatures ≤ 229 K. The r values

did not show any maximum for all samples at the higher temperatures in the L phase and their increasing trends indicate that all relevant motions are in the fast regime in the whole investigated frequency range.


15


Page 16 of 37

Further details on the motions contributing to relaxation at different temperatures for the three samples can be highlighted from the trends of the T1 values as a function of the inverse temperature, shown in Figure 4. For 2,2-DM-1-B and 3,3-DM-1-B in the L phase, the T1 vs 1/T trends were quite similar to those previously observed upon heating from the supercooled liquid phase,66 indicating the presence of motions in the fast and intermediate regime. For 2,2-DM-1-B a discontinuity was found between 229 and 231 K for frequencies lower than 0.2 MHz, whereas, for 3,3-DM-1-B, a discontinuity was observed between 226 and 228 K for frequencies lower than 10 MHz. This indicates a sudden change in the lower frequency motions close to the Cr1 to L phase transition. In the case of 3,3-DM-2-B, the T1 vs 1/T trends in the Cr1 and L phases were typical of motions in the fast regime. For this sample, a discontinuity was observed between 264 and 266 K (corresponding to the Cr2 to Cr1 phase transition) for frequencies lower than 10 MHz; another one was observed at the Cr3 to Cr2 transition for frequencies lower than 0.4 MHz. For temperatures below 260 K, a minimum was observed for frequencies between 30 and 700 kHz, the minimum shifting to lower temperatures with decreasing the frequency.


16

Page 17 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. Trends of 1H T1 vs inverse temperature for 2,2-DM-1-B, 3,3-DM-1-B, and 3,3-DM-2B at the indicated Larmor frequencies.


17


Page 18 of 37

Analysis of the NMRD curves. The analysis of the NMRD curves (Figure 2) was performed by expressing R1 as the sum of contributions ( ) coming from the different relaxation mechanisms envisaged in each phase; the motional models adopted for the different contributions are reported in the Theoretical background section. A fitting procedure that minimizes the least-squares of residuals between experimental data and R1 values was applied. The criterion of employing the minimum number of contributions to R1 that well reproduced the experimental trends with physically reasonable parameter values was used in order to avoid over-interpretation of data. For all samples in the L phase and for 3,3-DM-2 in the Cr1 phase, the NMRD curves were well reproduced (examples are shown in Figure 5) considering the BPP model for and (Eq.1 with Lorentzian spectral densities) and the force-free hard-sphere model for (Eqs. 4 and 5),

in agreement with a previous study on 2,2-DM-1-B and 3,3-DM-1-B.66 In the calculations, NH was kept fixed at all temperatures at values of 6.83 1028, 6.96 1028, and 6.70 1028 spins/m3 for 2,2-DM-1-B, 3,3-DM-1-B, and 3,3-DM-2-B, respectively. These values were determined from the expression NH = nρNA/Mmol, where n is the number of hydrogen atoms per molecule, ρ is the alcohol density, NA is Avogadro's number, and Mmol the molecular weight. CIM and CMR were set at 5.1 109 s-2 and 1.4 109 s-2, 5.7 109 s-2 and 7.0 108 s-2, 5.4 109 s-2 and 7.0 108 s-2 for 2,2-DM-1-B, 3,3-DM-1-B, and 3,3-DM-2-B, respectively, on the basis of a preliminary screening. τIM, τMR, d, and D were adjustable parameters in the fitting procedure. The best fitting values of τIM and τMR are reported in Figure 6 and those of D in Figure 7 (full symbols), while the optimized values of d were 4 (± 0.2), 5 (± 0.2), and 4 (± 0.2) Å at all temperatures for 2,2-DM-1-B, 3,3-DM-1-B, and 3,3-DM-2-B, respectively.


18

Page 19 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 5. Experimental (circles) and calculated (black lines) 1H NMRD curves of 2,2-DM-1-B, 3,3-DM-1-B, and 3,3-DM-2-B at the indicated temperatures. Blue dashed, red dotted, and green dot-dashed lines indicate contributions to relaxation arising from self-diffusion (SD), molecular reorientation (MR) and internal motions (IM), respectively.


19


Page 20 of 37

Figure 6. Correlation times for internal motions (green symbols) and overall reorientational motions (red symbols) of 2,2-DM-1-B (circles), 3,3-DM-1-B (squares), and 3,3-DM-2-B (triangles). Dashed lines indicated phase transition temperatures determined by adiabatic calorimetry measurements in Refs. 41, 43, 48.

Figure 7. Self-diffusion coefficients (D) determined for 2,2-DM-1-B (circles), 3,3-DM-1-B (squares), and 3,3-DM-2-B (triangles) from the fittings of the NMRD curves (full symbols) and from the slope of ( ) vs √ (Figure 3) using Eqs. 7-8 (empty symbols).


20

Page 21 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


As far as the crystalline phases are concerned, a separate contribution for translational motions in the NMRD curves could be clearly distinguished only for the Cr1 phase of 2,2-DM-1-B at frequencies lower than 0.2 MHz (Figure 2). In this case, the NMRD curves could be satisfactorily reproduced (Figure 5) considering Eq. 1 with Lorentzian spectral densities for internal motions and with HN spectral densities (Eq. 2) for molecular reorientations, and the isotropic Torrey model for self-diffusion (Eq. 6). Being the crystal lattice parameters unknown, r = rj was assumed in the calculations in order to minimize the number of parameters. CIM, CMR, and NH were kept fixed at 5.1 109 s-2, 2.9 109 s-2, and 6.83 1028 spins/m3. The self-diffusion contribution was satisfactorily reproduced with r = 7.5 (± 0.2) Å at all temperatures and the D values reported in Figure 7 (full symbols). The best fit values of the parameters in the HN function were found to be ε = 0.25 ± 0.01 and δ =1, thus corresponding to a Davidson-Cole function, at all temperatures; the correlation times for the reorientational motions are reported in Figure 6 after scaling on the basis of Eq. 3. For the Cr1 phase of 3,3-DM-1-B and the Cr2, Cr3 and Cr4 phases of 3,3-DM-2-B a separate contribution for translational motions was not clearly observed in the NMRD curves (Figure 2); hence, a global contribution for molecular motions, , was written using Eq.1 and the HN function (Eq. 2) was employed as a phenomenological spectral density function that allows both the slope at low frequency, associated to self-diffusion, and the dispersion in the MHz range, due to reorientational motions, to be reproduced. The contribution arising from internal motions was expressed according to the BPP model (Eq.1 with Lorentzian spectral densities), as in the liquid phase. In particular, the NMRD curves acquired in the Cr1 phase of 3,3-DM-1-B could be satisfactorily reproduced with CIM and CMR kept fixed at 5.7 109 s-2 and 2.4 109 s-2, respectively (Figure 5). The best fitting parameters for the HN function were found to be ε = 1


21


Page 22 of 37

and δ = 0.97 ± 0.01 at all temperatures, thus corresponding to a Cole-Cole function only slightly deviating from the BPP one. The NMRD curves acquired in the Cr2, Cr3, and Cr4 phases of 3,3DM-2-B could be well reproduced (Figure 5) with CIM and CMR kept fixed at 5.4 109 s-2 and 1.3 109 s-2, respectively, at all temperatures, except for 223 K and 213 K where better fitting results were obtained with CMR equal to 1.0 109 s-2 and 7.2 108 s-2, respectively. The best fitting parameters for the HN function were found to be ε = 0.80 ± 0.05 and δ = 0.96 ± 0.03 at all temperatures, thus close to a Davidson-Cole function. The optimized values of the correlation times for internal and molecular motions are reported in Figure 6, those relative to the HN function being scaled according to Eq. 3. Determination of self-diffusion coefficients from vw (x) vs √x. When a linear dependence of

( ) on √ was observed at low frequencies (Figure 3), the self-diffusion coefficient D was determined from the slope on the basis of Eqs. 7 and 8, taking NH equal to the above reported values at all temperatures. As shown in Figure 7, for all samples in the L phase a very good agreement was found between the D values determined with this method (open symbols) and those determined from the NMRD curve analysis (full symbols), as previously reported for 2,2DM-1-B and 3,3-DM-1-B.66 Good agreement was also observed between the two sets of D values for the Cr1 phase of 3,3-DM-2-B and 2,2-DM-1-B, notwithstanding the crude assumptions of isotropic jumps and rj = r made for the translational motion in the Torrey model used for the latter. Dynamics in liquid and ODIC phases. Correlation times C shown in Figure 6 indicate that

internal motions are quite fast for all samples in both the liquid and crystalline phases. C

showed regularly decreasing trends within each phase by increasing the temperature, with


22

Page 23 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


discontinuities close to the Cr1 to L transition for 2,2-DM-1-B and 3,3-DM-1-B, and at the Cr2 to Cr1 transition for 3,3-DM-2-B, associated to a speeding up of internal motions, whereas no discontinuities were observed at the transitions between the lower temperature ODIC phases of 3,3-DM-2-B. The C values and temperature dependences are compatible with those reported in the literature for rotations of methyl and tert-butyl groups about their ternary symmetry axes.10,67,68 As shown in Figure 6, values of C were one or two orders of magnitude higher than those of

C in the L phase of 2,2-DM-1-B and 3,3-DM-1-B, indicating much slower overall reorientational motions with respect to internal ones. In the case of 3,3-DM-2-B in the L phase, C and C values were almost equal, most probably because of a strong correlation between

parameters for these motions in the fitting procedure. In the Cr phases, C values were two

orders of magnitude higher than C ones for 2,2-DM-1-B and 3,3-DM-1-B, and up to almost

four orders of magnitude for 3,3-DM-2-B. C decreased by increasing the temperature with a jump (by one order of magnitude) on passing from the to L to Cr1 phase for all samples. 3,3-

DM-2-B showed a remarkable discontinuity of C (by three orders of magnitude) at the Cr1 to Cr2 phase transition, and a smaller one at the Cr2 to Cr3 transition. Hence, a remarkable slowing down of reorientational motions is associated to the formation of crystalline phases. For all samples the D values determined in the liquid and crystalline phases (Figure 7) were on the same order of magnitude of those determined for other plastic crystals in the corresponding phases.3,6,7,8,9,10,11,12,69 D showed decreasing trends by decreasing the temperature in each phase, while discontinuities were observed at the melting for 2,2-DM-1-B and 3,3-DM-1-B and at the Cr1 to Cr2 transition for 3,3-DM-2-B. In the L phase, the D values were on the order of 10-12-10-


23


10

Page 24 of 37

m2/s for 2,2-DM-1-B and 3,3-DM-1-B, while for 3,3-DM-2-B, D values on the order of 10-10

m2/s were found, although with a large error due to the small slope of the ( ) vs √ curves. In the Cr1 phase of 2,2-DM-1-B, the D values were between 5 10-14 and 10-13 m2/s, indicating that the self-diffusion motion considerably slowed down on entering the plastic crystalline phase. In the case of 3,3-DM-1-B, the reduction of D on entering the Cr1 phase was smaller (D values were between 10-13 and 10-12 m2/s in the Cr1 phase). On the other hand, no large effects on the D trend were observed at the L to Cr1 phase transition for 3,3-DM-2-B, whereas a very large reduction of the self-diffusion rate was found at the Cr1 to Cr2 one, the D values being on the order of 10-11-10-10 m2/s in the Cr1 phase and 10-14-10-13 m2/s in the lower temperature Cr2 and Cr3 phases. By comparing the results obtained for the three alcohols, it can be observed that samples 2,2DM-1-B and 3,3-DM-1-B have very similar values of C and C at the same temperature (Figure 6), whereas considerable differences exist between the D values, 3,3-DM-1-B showing higher D values at all the investigated temperatures, especially in the Cr1 phase (Figure 7). The values of C , C and D here determined for these alcohols in the L phase on heating from the crystalline one are in good agreement with those previously reported on heating from the supercooled liquid phase.66 Moreover, it must be pointed out that, for 3,3-DM-1-B, the values of C and D suggest that the Cr1 phase here formed is most probably an ODIC phase, analogous to that reported by DSC measurements.42 3,3-DM-2-B exhibited a markedly different dynamic behavior that corresponds to the very different phase behavior of this alcohol with respect to its isomers. In fact, 3,3-DM-2-B showed a remarkable discontinuity of both the reorientational correlation time and the self-diffusion coefficient at the Cr1 to Cr2 phase transition, and a smaller one at the L to Cr1 phase transition. The sudden slowing down of molecular


24

Page 25 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


reorientations and translational motions can be associated to the lower capability of this alcohol to be supercooled in the liquid phase, as observed by calorimetric measurements. The values of C and D in the Cr2 and Cr3 phases of 3,3-DM-2-B are similar to those of 3,3-DM-1-B in the Cr1 phase. The peculiar dynamic and phase behavior of 3,3-DM-2-B with respect to the other alcohols here examined can be explained considering its more globular shape and the internal position of the OH group, these factors limiting the association of molecules through hydrogen bonding but favoring the formation of plastic crystalline phases. Conclusions FFC 1H NMR relaxometry allowed internal, reorientational, and self-diffusion motions to be characterized in the liquid and plastic crystalline phases of a family of dimethyl butanols showing an interesting polymorphism in the solid state. In particular, self-diffusion coefficients could be determined in the L phase and in some ODIC phases by a model independent method, which exploits the dependence of the total relaxation rate on the square root of the Larmor frequency at low frequencies. This method is in general easily applicable within limits dictated by the possibility of reliably measuring the slope of the NMRD curves and by the maximum R1 value measurable with the FFC relaxometer. For all samples in the L phase and for 2,2-DM-1-B and 3,3-DM-2-B in the Cr1 phase, self-diffusion coefficients could also be determined, together with correlation times for internal and reorientational motions, from the analysis of the NMRD curves, in which appropriate models were applied to describe the different contributions to the relaxation rate. The analysis of the NMRD curves for 3,3-DM-1-B and 3,3-DM-2-B in the ODIC phases, using a global phenomenological function to describe self-diffusion and molecular reorientations, gave correlation times for internal and reorientational motions. Phase transitions were associated to significant changes in the correlation times of motions. In particular,


25


Page 26 of 37

remarkable changes were observed at the L to Cr1 phase transition for 2,2-DM-1-B and 3,3-DM1-B for all motions. These samples showed quite similar behavior for molecular reorientations and internal motions over the whole investigated temperature range, but they differed in selfdiffusion, which was slower for 2,2-DM-1-B. On the other hand, 3,3-DM-2-B, with a more globular molecular shape and the hydroxyl group in position 2 instead of 1, showed a markedly different dynamic and phase behavior, with a more abrupt slowing down of molecular reorientations and translational motions. The results here obtained give evidence of the power of FFC 1H NMR relaxometry in the investigation of motions in plastic crystalline phases; in fact, differently from other techniques used for the investigation of dynamics (as dielectric spectroscopy and NMR diffusometry), FFC NMR yields simultaneous information on translational and reorientational motions with a single experiment.


26

Page 27 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


AUTHOR INFORMATION Corresponding Authors *Elisa Carignani, Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via G. Moruzzi 13, 56124 Pisa, Italy. Phone:+390502219284. E-mail:[email protected] *Lucia Calucci, ICCOM-CNR Sede Secondaria di Pisa, via G. Moruzzi 1, 56124 Pisa, Italy. Phone: +390505152517. E-mail: [email protected]. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT The authors would like to acknowledge the contribution of the COST Action CA15209 (Eurelax: European Network on NMR Relaxometry) and of the CNR-PAS 2014-2016 and 20172019 bilateral projects. E. C. is grateful to GIDRM for the AnnaLaura Segre fellowship. The authors thank Professor P. J. Sebastião for technical assistance with the Fitteia platform and Professor E. Rössler for helpful discussions.

ABBREVIATIONS FFC, Fast Field Cycling; NMRD, Nuclear Magnetic Relaxation Dispersion; 2,2-DM-1-B, 2,2dimethylbutan-1-ol; 3,3-DM-1-B, 3,3-dimethylbutan-1-ol; 3,3-DM-2-B, 3,3-dimethylbutan-2-ol.


27


Page 28 of 37

REFERENCES

(1) Timmermans, J. Plastic Crystals: A Historical Review. J. Phys. Chem. Solids 1961, 18, 1-8. (2) Staveley, L. A. K. Phase Transitions in Plastic Crystals. Annu. Rev. Phys. Chem. 1962, 13, 351-368. (3) Chezeau, J. M.; Strange, J. H. Diffusion in Molecular Crystals. Phys. Rep. 1979, 53, 1-92. (4) Rao, C. N. R. Molecular Motion in Plastic Crystals. Proc. Indian Acad. Sci. 1985, 94, 181199. (5) Brand, R.; Lunkenheimer, P; Loidl, A. Relaxation Dynamics in Plastic Crystals. J. Chem. Phys. 2002, 116, 10386-10401. (6) Folland, R.; Jackson, R. L.; Strange, J. H.; Chadwick, A. V. Self-Diffusion in a Series of Plastic Organic Solids Studied by NMR. J. Phys. Chem. Solids 1973, 34, 1713-1726. (7) Boden, N.; Cohen, J.; Squires, R. T. On the Interpretation and Significance of Nuclear Spin Relaxation by Translational Diffusion in Organic Plastic Crystals. Mol. Phys. 1976, 31, 18131832. (8) Britcher, A. R.; Strange, J. H. On Self-Diffusion in Plastic Crystals. Mol. Phys. 1979, 37, 181-189. (9) Szcześniak, E. Molecular Dynamics and Phase Transitions in Solid 2-Methyl-2propanethiol by 1H NMR Relaxation. Mol. Phys. 1986, 58, 551-560.


28

Page 29 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(10) Szcześniak, E. N.M.R. Study of Molecular Dynamics and Phase Transitions in Solid 2Methyl-2-propanol. Mol. Phys. 1986, 59, 679-688. (11) Eguchi, T.; Soda, G.; Chihara, H. Molecular Motion and Polimorphic Forms in Cyclohexanol as Studied by Nuclear Magnetic Resonance. J. Magn. Reson. 1975, 23, 55-65. (12) Stapf, C.; Kimmich, R. Translational versus Rotational Molecular Dynamics in Plastic Crystals Studied by NMR Relaxometry and Diffusometry. Mol. Phys. 1997, 92, 1051-1060. (13) Decressain, R.; Carpentier, L.; Cochin, E.; Amoureux, J. P. Modelling and Dynamical Processes in a Molecular Crystal by NMR. Eur. Phys. J. B 2007, 58, 223-230. (14) Meier, R.; Kruk, D.; Bourdick, A.; Schneider, E.; Rössler, E. A. Inter- and Intramolecular Relaxation in Molecular Liquids by Field Cycling 1H NMR Relaxometry. Appl. Magn. Reson. 2013, 44, 153-168. (15) Fujara, F.; Kruk, D.; Privalov, A. F. Solid State Field-Cycling NMR Relaxometry: Instrumental Improvements and New Applications. Prog. Nucl. Magn. Reson. Spectrosc. 2014, 82, 39-69. (16) Sousa, D. M.; Marques, G. D.; Sebastião, P. J.; Ribeiro, A. C. New Isolated Gate Bipolar Transistor Two-Quadrant Chopper Power Supply for a Fast Field Cycling Nuclear Magnetic Resonance Spectrometer. Rev. Sci. Instrum. 2003, 74, 4521-4528. (17) Kresse, B.; Becher, M.; Privalov, A. F.; Hofmann, M.; Rössler, E. A.; Vogel M.; Fujara, F. 1H NMR at Larmor Frequencies Down to 3Hz by Means of Field-Cycling Techniques. J. Magn. Reson. 2017, 277, 79-85.


29


Page 30 of 37

(18) Kimmich, R.; Anoardo, E. Field-Cycling NMR Relaxometry. Prog. Nucl. Magn. Reson. Spectrosc. 2004, 44, 257-320. (19) Meier, R.; Kruk, D.; Rössler, E. A. Intermolecular Spin Relaxation and Translation Diffusion in Liquids and Polymer Melts: Insight from Field-Cycling 1H NMR Relaxometry. ChemPhysChem 2013, 14, 3071-3081. (20) Kruk, D.; Herrmann, A.; Rössler, E. A. Field-Cycling NMR Relaxometry of Viscous Liquids and Polymers. Prog. Nucl. Magn. Reson. Spectrosc. 2012, 63, 33-64. (21) Kimmich, R.; Fatkullin, N. Self-Diffusion Studies by Intra- and Inter-Molecular SpinLattice Relaxometry Using Field-Cycling: Liquids, Plastic Crystals, Porous Media, and Polymer Segments. Prog. Nucl. Magn. Reson. Spectrosc. 2017, 101, 18-50. (22) Kruk, D.; Meier, R.; Rössler, E. A. Translational and Rotational Diffusion of Glycerol by Means of Field Cycling 1H NMR Relaxometry. J. Phys. Chem. B 2011, 115, 951-957. (23) Kruk, D.; Meier, R.; Rössler, E. A. Nuclear Magnetic Resonance Relaxometry as a Method of Measuring Translational Diffusion Coefficients in Liquids. Phys. Rev. E 2012, 85, 020201. (24) Meier, R.; Schneider, E.; Rössler, E. A. Change of Translational-Rotational Coupling in Liquids Revealed by Field-Cycling 1H NMR. J. Chem. Phys. 2015, 142, 034503. (25) Kruk, D.; Meier, R.; Rachocki, A.; Korpała, A.; Singh, R. K.; Rössler, E. A. Determining Diffusion Coefficients of Ionic Liquids by Means of Field Cycling Nuclear Magnetic Resonance Relaxometry. J. Chem. Phys. 2014, 140, 244509.


30

Page 31 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(26) Daniel, C. I.; Vaca Chávez, F.; Feio, G.; Portugal, C. A. M.; Crespo, J. G.; Sebastião, P. J. 1

H NMR Relaxometry, Viscometry, and PFG NMR Studies of Magnetic and Nonmagnetic Ionic

Liquids. J. Phys. Chem. B 2013, 117, 11877-11884. (27) Beira, M.; Daniel, C. I.; Almeida, P. L.; Corvo, M. C.; Rosatella, A. A.; Afonso, C. A. M.; Sebastião, P. J. 1H NMR Relaxometry and Diffusometry Study of Magnetic and Nonmagnetic Ionic Liquid-Based Solutions: Cosolvent and Temperature Effects. J. Phys. Chem. B 2017, 121, 11471-11484. (28) Wencka, M.; Apih, T.; Korosěc, R. C.; Jenczyk, J.; Jarek, M.; Szutkowski, K.; Jurga, S.; Dolinsěc, J. Molecular Dynamics of 1-Ethyl-3-methylimidazolium Triflate Ionic Liquid Studied by 1H and 19F Nuclear Magnetic Resonance. Phys. Chem. Chem. Phys. 2017, 19, 15368-15376. (29) Ordikhani Seyedlar, A.; Stapf, S.; Mattea, C. Dynamics of the Ionic Liquid 1-Butyl-3methyl-imidazolium

Bis(trifluoromethylsulphonyl)imide

Studied

by

Nuclear

Magnetic

Resonance Dispersion and Diffusion. Phys. Chem. Chem. Phys. 2015, 17, 1653-1659. (30) Ordikhani Seyedlar, A.; Stapf, S.; Mattea, C. Cation Dynamics in Supercooled and Solid Alkyl Methylimidazolium Bromide Ionic Liquids. J. Phys. Chem. B 2017, 121, 5363-5373. (31) Calucci, L.; Veracini, C.A. Liquid Crystals and Liquid Crystal Solutions Studied By NMR. In Elsevier Reference Module in Chemistry, Molecular Sciences and Chemical Engineering; J. Reedijk Ed.; Elsevier: Waltham, MA, 2014.


31


Page 32 of 37

(32) Apih, T.; Domenici, V.; Gradisěk, A.; Hamplová, V.; Kaspar, M.; Sebastião, P. J.; Vilfan, M. 1H NMR Relaxometry Study of a Rod-like Chiral Liquid Crystal in its Isotropic, Cholesteric, TGBA*, and TGBC* Phases. J. Phys. Chem. B 2010, 114, 11993-12001. (33) Sebastião, P. J.; Gradisěk, A.; Pinto, L. F. V.; Apih, T.; Godinho, M. H.; Vilfan, M. Fast Field-Cycling NMR Relaxometry Study of Chiral and Nonchiral Nematic Liquid Crystals. J. Phys. Chem. B 2011, 115, 14348-14358. (34) Cachitas, H.; Sebastião, P. J.; Feio, G.; Vaca Chávez, F. Proton NMR Relaxation Study of Molecular Dynamics of Chromonic Liquid Crystal Edicol Sunset Yellow. Liq. Cryst. 2014, 41, 1080-1089. (35) Carignani, E.; Calucci, L.; Juszyńska-Gałązka, E.; Gałązka, M.; Massalska-Arodź, M.; Forte, C.; Geppi, M. Dynamics of the Chiral Liquid Crystal 4′-Butyl-4 (S) (2methylbutoxy)azoxybenzene in the Isotropic, Cholesteric, and Solid Phases: A Fast FieldCycling NMR Relaxometry Study. J. Phys. Chem. B 2016, 120, 5083-5092. (36) Harmon, F.; Muller, B. N. Nuclear Spin Relaxation by Translational Diffusion in Liquid Ethane. Phys. Rev. 1969, 182, 400-409. (37) Belorizky, E.; Fries, P. H. Translational Diffusion in Liquids: Specific Features of the Spectral Densities for Isotropic Intermolecular Interactions. Chem. Phys. Lett. 1988, 145, 33-38. (38) Torrey, H. C. Nuclear Spin Relaxation by Translational Diffusion. Phys. Rev. 1953, 92, 962-969.


32

Page 33 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(39) Sholl, C. A. Nuclear Spin Relaxation by Translational Diffusion in Liquids and Solids: High- and Low-Frequency Limits. J. Phys. C Solid State Phys. 1981, 14, 447-464. (40) Ferrante, G.; Sykora, S. Technical aspects of fast field cycling. In Advances in Inorganic Chemistry 57: Relaxometry of Water-Metal Ion Interactions; Van Eldik, R., Bertini, I. Eds.; Elsevier: San Diego, CA, 2005; pp 405-470. (41) Massalska-Arodź, M.; Nakamoto, T.; Wasiutyński, T.; Mayer, J.; Krawczyk, J.; Sorai, M. Thermal and Relaxational Properties of Glass-Forming Material 3,3-Dimethyl-1-butanol. J. Chem. Thermodyn. 2004, 36, 877-888. (42) Juszyńska, E.; Massalska-Arodź, M.; Zieliński, P. M.; Ściesiński, J. DSC Studies of Neohexanol and its Isomers. Phase Transitions 2006, 79, 899-909. (43) Juszyńska-Gałązka, E.; Zieliński, P. M.; Massalska-Arodź, M.; Krawczyk, J. Solid State Polymorphism and Dynamics of 2,2-Dimethylbutan-1-ol as Studied by Adiabatic Calorimetry and Dielectric Spectroscopy. Acta Phys. Pol. A 2013, 124, 917-925. (44) Juszyńska, E.; Massalska-Arodź, M.; Mayer, J.; Natkaniec, I.; Krawczyk, J.; Tracz, P. Neutron Scattering in 3,3-Dimethyl-2-butanol and 2,3-Dimethyl-2-butanol. Solid State Phenom. 2006, 112, 89-92. (45) Juszyńska, E.; Hołderna-Natkaniec, K.; Massalska-Arodź, M.; Natkaniec, I.; Ściesińska, E.; Ściesiński, J. IINS, MIR, and DFT Investigations of Vibrational Spectra of 3,3-Dimethyl-1butanol and 3,3-Dimethyl-2-butanol. Acta Phys. Pol. A 2008, 113, 1131-1143.


33


Page 34 of 37

(46) Juszyńska, E.; Massalska-Arodź, M.; Natkaniec, I.; Krawczyk, J. Neutron Scattering Studies of Solid-State Polymorphism in Dimethyl Butanol Glass Formers. Physica B 2008, 403, 109-114. (47) Juszyńska, E.; Hołderna-Natkaniec, K.; Massalska-Arodź, M.; Natkaniec, I.; Ściesińska, E.; Ściesiński, J. Formation of Hydrogen Bonds; Hydroxyl and Methyl Groups Dynamics in 2,2Dimethylbutan-1-ol and 2,3-Dimethylbutan-2-ol: DFT, IINS and IR Investigations. Acta Phys. Pol. A 2012, 122, 765-775. (48) Juszyńska, E. Investigations of the Polymorphism and the Dynamics in Dimethyl Butanols. Ph. D. Dissertation, Institute of Nuclear Physics PAN, Krakow, Poland, 2008. (49) Anoardo, E.; Galli, G.; Ferrante, G. Fast-Field-Cycling NMR: Applications and Instrumentation. Appl. Magn. Reson. 2001, 20, 365-404. (50) Sebastião, P. J. Fitteia. Fitting Environment Interfaces for All. http://fitteia.org (accessed May 3, 2018). (51) Sebastião, P. J. The Art of Model Fitting to Experimental Results. Eur. J. Phys. 2014, 35, 015017. (52) Sholl, C. A. Nuclear Spin Relaxation by Translational Diffusion in Solids. J. Phys. C Solid State Phys. 1974, 7, 3378-3386. (53) Sholl, C. A. Nuclear Spin Relaxation by Translational Diffusion in Solids: II. Diffusion in BCC and SC Lattices. J. Phys. C Solid State Phys. 1975, 8, 1737-1741.


34

Page 35 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(54) Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: Oxford, 1961. (55) Redfield, A. G. In Advances in Magnetic Resonance; Waugh, J. S., Ed; Academic Press: New York, 1965; Vol. 1, pp 1-32. (56) Bloembergen, N.; Purcell, E. M.; Pound, R. V. Relaxation Effects in Nuclear Magnetic Resonance Absorption. Phys. Rev. 1948, 73, 679-712. (57) Beckmann, P. A. Spectral Densities and Nuclear Spin Relaxation in Solids. Phys. Rep. 1988, 171, 85-128. (58) Boersma, A.; van Turnhout, J.; Wübbenhorst, M. Dielectric Characterization of a Thermotropic Liquid Crystalline Copolyesteramide: 1. Relaxation Peak Assignment. Macromolecules, 1998, 31, 7453-7460. (59) Díaz-Calleja, R. Comment on the Maximum in the Loss Permittivity for the HavriliakNegami Equation. Macromolecules, 2000, 33, 8924. (60) Hwang, L. P.; Freed, J. H. Dynamic Effect of Pair Correlation Functions on Spin Relaxation by Translational Diffusion in Liquids. J. Chem. Phys. 1975, 63, 4017-4025. (61) Ayant, Y.; Belorizky, E.; Alizon, J.; Gallice, J. Calcul des Densités Spectrales Résultant d'un Mouvement Aléatoire de Translation en Relaxation par Interaction Dipolaire Magnétique dans les Liquides. J. Phys. France 1975, 36, 991-1004. (62) Kruk, D.; Nilsson, T.; Kowalewski, J. Outer-Sphere Nuclear Spin Relaxation in Paramagnetic Systems: a Low-Field Theory. Mol. Phys. 2001, 99, 1435-1445.


35


Page 36 of 37

(63) Kruk, D.; Kowalewski, J. General Treatment of Paramagnetic Relaxation Enhancement Associated with Translational Diffusion J. Chem. Phys. 2009, 130, 174104. (64) Torrey, H. C. Nuclear Spin Relaxation by Translational Diffusion. II. Diffusion in a B.C.C. Lattice. Phys. Rev. 1954, 131, 690. (65) Meier, R.; Kahlau, R.; Kruk, D.; Rössler, E. A. Comparative Studies of the Dynamics in Viscous Liquids by Means of Dielectric Spectroscopy and Field Cycling NMR. J. Phys. Chem. A 2010, 114, 7847-7855. (66) Carignani, E.; Forte, C.; Juszyńska-Gałązka, E.; Gałązka, M.; Massalska-Arodź, M.; Geppi, M.; Calucci, L. Dynamics of Two Glass Forming Monohydroxy Alcohols by Field Cycling 1H NMR Relaxometry. J. Mol. Liq. 2018, 269, 847-854. (67) Yamauchi, J.; McDowell, C. A. NMR Study of Molecular Motion in Some Molecules Containing t-Butyl Groups, J. Chem. Phys. 1981, 75, 1051-1059. (68) Popa, L. C.; Rheingold, A. L.; Beckmann, P. A. A Proton Spin-Lattice Relaxation Rate Study of Methyl and t-Butyl Group Reorientation in the Solid State, Solid State Nucl. Magn. Reson. 2010, 38, 31-35. (69) Chang, I.; Hinze, G.; Diezemann, G.; Fujura, F.; Sillescu, H. Self-Diffusion Coefficients in Plastic Crystals by Multi-Pulse NMR in Large Static Field Gradients. Phys. Rev. Lett. 1996, 76, 2523-2526.


36

Page 37 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic


37

Dynamics of Dimethylbutanols in Plastic Crystalline Phases by Field

Recommend Documents