Proton spin-lattice relaxation rates R = T1−1 have been measured in powdered samples of 4-methyl-2,6-di-tertiarybutyl phenol between 77 and 170 K. Deuteration of the hydroxy proton leads to a large change in R in the vicinity of the 120-K R maximum and in the high-temperature region. The data are successfully, although probably not uniquely, fitted and the interpretation suggests that in addition to the motion of the hydroxy proton playing a significant role in the relaxation, the two pairs of t-butyl methyl groups also contributing are inequivalent. The departure, at low temperatures, from an ω−2dependence of R where ω is the nuclear Larmor angular frequency is also investigated

Beckmann, Peter A.

English

Scholarship;  Research;  and Creative Work at Bryn Mawr College

Bryn Mawr College
Scholarship, Research, and Creative Work at Bryn Mawr
College
Physics Faculty Research and Scholarship Physics
1979
Proton spin relaxation and methyl and hydroxy
group motion
Peter A. Beckmann
Bryn Mawr College, pbeckman@brynmawr.edu
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Beckmann, Peter A. 1979. "Proton spin relaxation and methyl and hydroxy group motion." Journal of Magnetic Resonance 36.2:
199-205.
Proton spin relaxation and methyl and hydroxy group motion 
 
Peter Beckmann 
 
Journal of Magnetic Resonance 36.2: 199-205. https://doi.org/10.1016/0022-2364(79)90094-5 
 
Abstract: Proton spin-lattice relaxation rates R = T1
−1 have been measured in powdered samples 
of 4-methyl-2,6-di-tertiarybutyl phenol between 77 and 170 K. Deuteration of the hydroxy 
proton leads to a large change in R in the vicinity of the 120-K R maximum and in the high-
temperature region. The data are successfully, although probably not uniquely, fitted and the 
interpretation suggests that in addition to the motion of the hydroxy proton playing a significant 
role in the relaxation, the two pairs of t-butyl methyl groups also contributing are inequivalent. 
The departure, at low temperatures, from an ω−2 dependence of Rwhere ω is the nuclear Larmor 
angular frequency is also investigated. 
 
Introduction 
 
 Proton spin-lattice relaxation measurements have yielded a great deal of information 
concerning methyl group motion in 4-methyl-2,6-di-tertiarybutyl phenol (MDBP). A schematic 
diagram of the molecule is shown in Fig. 1. At temperatures below 50 K, quantum mechanical 
tunnelling of the 4-methyl group dominates the relaxation process (1) whereas at temperatures 
above 80 K the relaxation is dominated by the motions of the t-butyl groups (2). The complicated 
motions of the t-butyl groups and their constituent methyl groups give rise to two maxima in R, 
the spin-lattice relaxation rate. The quantity R is the inverse of T1 the spin-lattice relaxation time. 
At 31 MHz, these maxima occur at 125 and 300 K. A consistent and simultaneous analysis of the 
value of R at the two maxima leads to the model whereby the 300-K maximum arises from the 
rotation of two of the six t-butyl methyls and the entire t~butyl groups and the 125-K maximum 
arises from the rotation of the other four t-butyl methyls (2). This analysis leads to a good fit of 
the data at 31 MHz between 125 and 340 K, the melting point. However, the temperature 
dependence of the relaxation in the vicinity of and below the 125-K maximum displays some 
interesting features (discussed below), and a quantitative fit was not obtained. It was assumed in 
this analysis that the hydroxy proton plays a negligible role in the relaxation process. In this 
paper, we focus our attention on the relaxation in the vicinity of the 125-K maximum and in 
particular on the role of the hydroxyl proton. We have measured the spin-lattice relaxation rate at 
21 MHz between 77 and 170 K in fully protonated MDBP and a sample in which the hydroxy 
proton has been replaced with a deuteron. The experimental values of R, shown in Fig. 2, 
indicate the effect of deuteration and suggest that the motion of the hydroxy proton plays a 
significant.role in the relaxation process. We also investigate the role of the methyls in the 
relaxation and the interesting frequency dependence of R at low temperatures. 
 
Experimental 
 
 Proton spin-lattice relaxation rates R = T1
−1 were measured using the conventional π−t− 
π/2 pulse sequence with a Spin-Lock 21-MHz spectrometer. The temperature was controlled by 
placing the sample chamber inside a copper can, the outside of which was in thermal contact 
with a heater. This copper can was placed inside another copper can the outside of which was in 
thermal contact with a liquid nitrogen bath. By appropriately adjusting the densities of the 
helium exchange gas in the two cans and the current in the heater, the temperature could be 
varied from 77 to about 180 K. Temperature was measured by placing a thermocouple m good 
thermal contact with the inner copper can well away from the heater. The cryostat is the same as 
the one employed in the low-temperature studies (1) where the nitrogen bath was replaced with a 
helium bath. 
Two powder samples were used: the first a commercially obtained sample of fully 
protonated MDBP and the second a sample grown from a deuterated solvent (ethyl alcohol) 
resulting in the deuteration of the hydroxy proton. This procedure was repeated several times. 
The author has performed R measurements on three different commercial samples of MDBP in 
three different countries using three different spectrometers, and if impurities are present, they do 
not affect the R measurements. This has been confirmed by using the commercial samples as 
they are and by recrystallizing several times from isopropyl alcohol and degassing. 
 
Analysis and Discussion 
 
 Although our prime concern is investigating the effects on the relaxation of the hydroxy 
proton we will also discuss other interesting properties of the relaxation. The hydroxy group is in 
position 1 of the benzene ring and the r-butyl groups are adjacent to it in positions 2 and 6 as 
shown in Fig. 1. The 4-methyl group plays no role in the relaxation at these temperatures. We 
refer to the fully protonated sample as sample H and the deuterated sample as sample D. Thus, 
RH and RD refer to the relaxation rates of the two samples. 
Nuclear spin-lattice relaxation caused by molecular motion modulation of the dipolar 
interaction between protons is described by the BPP function (3). 
 
The parameter C depends on the details of the molecular motion and the geometry, τ is the 
correlation time for molecular reorientation, Ea is an appropriate activation energy, and ω is the 
nuclear Larmor angular frequency which, in the present study, is 2π (21 MHz). Often, sums of 
BPP functions are employed and the reader is referred to Ref. (2) and the references cited therein 
for the details. 
Although the value of R at the maximum is adequately explained by the model 
summarized in the Introduction, the data at 16, 31, and 59 MHz (2) as well as the present data 
(sample H) at 21 MHz cannot be fitted by a single BPP function. This is clear from the broad 
asymmetric nature of the maximum. A single BPP function fit at high and low temperatures 
leads to an R ~ 75 sec−1 at the maximum whereas the observed value is 32 sec−1. More 
surprisingly, the data cannot be fit very successfully by a sum of two BPP functions. This 
suggests that either all four methyls assumed responsible for the relaxation are inequivalent 
and/or the motion of the hydroxyl group is contributing. The data in Fig. 2 show a marked 
difference in R for the two samples, which suggests that the hydroxy proton plays a significant 
role in the relaxing process. If the only role of deuteration was that of the proton dilution factor, 
one would expect R to decrease by 23/24, the ratio of the number of protons in the two samples. 
This clearly does not account for the observed difference. 
We present a consistent and logical although certainly not unique fit of the temperature 
dependence of RH and RD. We must look for more than two BPP functions to fit the RH data and 
use the RD data as a guide. In the low-temperature or long correlation time limit (ωτ »1), Eq. [1] 
predicts 
  
It is clear from the data that ln(R)∝ − T−1 This implies that if sums of BPP functions are 
contributing then they have, to within experimental uncertainty, the same activation energy Ea. In 
this case, Eq. [2] is still valid and the ratio C/τ0 is replaced by the sum of such ratios. The data 
for RH and RD, for T < 90 K (10
3T−1 > 11 K−1) are indistinguishable and a linear least-squares fit 
to Eq. [2] yields EJk = 1280 K or Ea =10.6 kJ/moIe = 2.54 kcai/mole. The fit gives a correlation 
coefficient of 0.997, which implies a small uncertainty in the slope, Ea /k. Realistic uncertainties 
were obtained by drawing straight lines through the data (T < 90 K) to obtain upper and lower 
limits to the slope. The resulting uncertainty of Ea ± 12% is certainly larger than would be 
obtained by a more complicated fitting procedure. This result of 2,54 ± 0.30 kcal/mole at 21 
MHz is to be compared with 2.48 ± 0.42 kcal/mole at 59 MHz, 2.36 ±0.07 kcal/mole at 31 MHz, 
and 2.25 ±0.08 kcal/mole at 16 MHz (2). Taking into account the uncertainties, there is no strong 
indication that the activation-energy is frequency dependent. 
In the high-temperature or short correlation time limit (ωτ « 1), Eq. [1] predicts  
  
Although the data are less precise at the higher temperatures, both the RH and RD data are 
consistent with Eq. [3] with the same activation energy obtained from the low-temperature data 
and we assume a unique value of Ea = 2.54 ±0.30 kcal/mole throughout the remainder of the 
analysis. The high-temperature Ha at 31 MHz was found to be 2.38 ± 0.04 kcal/mole, which is 
the same as the low-temperature value at this frequency (2). The high-temperature value of Ea for 
16 and 59 MHz is consistent with that for 31 MHz (2). Within the experimental uncertainties 
from this and the previous (2) work, there is no strong indication that the activation energies are 
different at temperatures above and below the temperature of the R maximum. 
The experimental values of RD can be fit quite reasonably to the sum of two BPP 
functions as indicated in Fig. 2a. We note, however, that the region at the maximum still appears 
flatter than the fitted curve. We shall return to this point. We write  
 
and the paramters τ0 and C for RA and RB are given in Table 1. The next step is very simple. A 
freehand curve is drawn through the observed RH values. The difference RΔ = RH − RD is well 
approximated by a single BPP function. Thus we write 
 
Plots of RΔ and RH (the latter agreeing with the observed values by construction) are shown in 
Fig. 2b and C and τ0 for RΔ are given in Table 1. Also given in Table 1 is the value of R at its 
maximum and the temperature at which that maximum occurs for RA, RB, and RΔ. 
 We can associate RΔ with'the relaxation caused by the motion of the hydroxyl proton. 
Steric potential calculations (2) indicate that the hydroxy proton should see a considerably higher 
barrier and therefore should not contribute to the relaxation in this temperature range. We note, 
however, that for quite a different phenomenon in the same molecule, namely, that of quantum 
mechanical tunneling at helium temperatures, deuterating the hydroxy proton has a nonnegligible 
effect both on the proton spin relaxation arising from tunneling rotation of the 4-methyl group 
(1) and on the tunneling frequency of the 4-methyl group (4). The conclusion of the present work 
that the hydroxy proton motion is significant is independent of the fitting procedure since RΔ is 
just the difference between the two sets of experiments. 
 The quantities RA and RB can be associated with the r-butyl methyls. There are four 
groups involved since the other two contribute to the relaxation at much higher temperatures. 
That more than one BPP function is required is consistent with the structural analysis and the 
detailed calculations in Ref. (2). Again, it is the hydroxyl proton or deuteron responsible for the 
fact that different methyls see different environments. Clearly, the values of C for RA and RB 
should, in principle, be the same and that one is 25 % greater than the other (see Table 1) is just 
an indication that the four methyls are inequivalent. This further manifests itself in that the 
observed relaxation in sample D in the range 8.2 < 103T−1<10K−1 (100 < T < 122 K) is 
essentially temperature independent and the sum RD = RA + RB does not really reproduce this 
very well. This very fiat plateau is washed out to some extent in sample H. The addition of RB 
with its maximum value at a higher temperature results in the observed asymmetry in the 
relaxation. 
 An interesting feature of the relaxation is the frequency dependence at low temperatures. 
The prediction of Eq. [2] that ln(R)∝ T−1 is observed at all four frequencies (the one reported 
here and three in Ref. (2)) below 95 K (103 T−1 > 10.5 K−1), whereas the prediction of Eq. [2] that 
R∝ω−2 is not observed. The previous study showed that at 103 T−1 = 11 K−1, R∝ω−n with n = 2.1  
using 21, 31, and 59 MHz. Figure 3 shows the frequency dependence of RH at 10
3 T−1 =11 K−1 
(90 K). The points ail come from the original data and do not involve any of the fits. The error 
flags were obtained by drawing extreme lines which enclosed ail the data points at low 
temperature. The uncertainties represent, therefore, much larger uncertainties than would result 
from a numerical fitting procedure. The three frequencies 21, 31, and 59 MHz give a value of n = 
2.21 ± 0.26. A good fit at one frequency would lead to a very poor fit at either of the other two 
frequencies if n were fixed at 2. The data at 16 MHz does not fall in this wide range resulting 
from the above uncertainty in n. This very liberal estimate of the uncertainty in n based on the 
higher frequencies leads to the very strong argument that the 16-MHz data is anomalous. One 
may suspect that this effect is connected with the shift of the R maximum to lower temperatures 
at lower frequencies but this is simply not consistent with the data. It is clear that measurements 
at lower frequencies are essential before detailed models of the effect are proposed. 
 
Summary 
 
 Deuterating the hydroxy proton in MDBP has a pronounced effect on the spin-lattice 
relaxation rate in the vicinity of, and at temperatures above, the temperature at which the 
relaxation for the protonated sample goes through a broad asymmetric maximum. Deuteration 
does not change the broad nature of the maximum and, if anything, enhances it. It does seem, 
however, to remove some of the asymmetry. The fits of the data, suggest the four t-butyl methyl 
groups responsible for the relaxation should be divided into at least two inequivalent pairs. The 
different environments probably result from the position of the hydroxy proton or deuteron. 
Undoubtedly, an even better fit of the data would be obtained if it were assumed that all four 
methyls were inequivalent, a situation suggested by detailed computations (2). When an OD 
group is replaced by an OH group there is an additional relaxation mechanism due to the motion 
of the hydroxy proton. This result is surprising in the light of steric potential calculations (2). 
It would be interesting to study the proton relaxation of fully deuterated MDBP with a 
protonated hydroxy group and the deuteron relaxation of fully protonated MDBP with a 
deuterated hydroxy group. In both cases the signal would be down by a factor of 24 and in 
addition there would be a further reduction in signal to noise associated with the lower deuteron 
Larmor frequency. 
It appears from the peculiar frequency dependence of the relaxation at low temperatures 
that the relaxation is even more complicated than suggested here. Further measurements at lower 
frequencies are essential. 
 
Acknowledgements 
 
The experiments reported here were performed at the University of Nottingham and were 
supported by the Science Research Council (U.K.) and the National Research Council of Canada. 
 
References 
 
 
1. P. A. BECKMANN AND S. CLOUGH, J.  Phys. C 10, L231 (1977). 
2. P. A BECKMANN, C. I. RATCLIFFE, AND B. A. DUNELL. 7.  Magn. Reson. 32, 391 
(1978). 
3. A. ABRAGAM, "The Principles of Nuclear Magnetism," Oxford Univ. Press, New 
York/London, 1961. 
4. S. CLOUGH, T. HOBSON, AND S. M. NUGENT, J. Phys. C. 8, L95 (1975). 
  
Figures 
 
 
 
  
  
Tables 
 
 


Proton spin relaxation and methyl and hydroxy group motion

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Proton spin relaxation and methyl and hydroxy group motion

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