Effect of Paramagnetic Ions in Aqueous Solution for Precision Measurement of Proton Gyromagnetic Ratio

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Mervin Charles
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1 240 Bulletin f Magnetic Resnance Effect f Paramagnetic Ins in Aqueus Slutin fr Precisin Measurement f Prtn Gyrmagnetic Rati Ae Ran Lim, Chang Suk Kim Krea Research Institute f Standards and Science, Taejn , Krea and Sung H Chh Department f Physics, Krea University, Seul , Krea 1 Intrductin The measurement f prtn gyrmagnetic rati }'p' has been the bject f an intensive experimental prgram fr several decades [l]-[3]. The gyrmagnetic rati f the prtn is defined as a resnance frequency «p divided by a magnetic field B [4], when a spherical water sample at 25 C is applied by a magnetic field. The? P ' fr a defined pure water sample is smewhat difficult t measure because f the weak absrptin due t the lng relaxatin time f the prtn [5]. In rder t reduce the relaxatin time, paramagnetic ins are added t the water sample [6]. Hwever, as the cncentratin f paramagnetic ins increases, the resnance pint f *H shifts and differs accrding t the sample shapes. The purpse f present wrk is t investigate the effect f paramagnetic ins(fe 3 *, Mn 2 *, C 2 *, and Cu 2 *) n the l H NMR in paramagnetic aqueus slutins [Fe(NO3)3-9H 2 O, FeCl 3, MnCl 2-4H 2 O, CCh-2H 2 O, and CuCl 2-2H 2 O].!H NMR in aqueus slutin cntaining paramagnetic ins was measured as a functin f cncentratin fr the fixed spherical and cylindrical sample shapes, and the spinning cylindrical sample shape. The magnetic susceptibility per unit vlume f the paramagnetic slutin has als been measured as a functin f cncentratin at rm temperature. The interactin between the ' H nucleus and paramagnetic in is discussed in terms f the shift f >H resnance pint measured with tw sample shapes and the magnetic susceptibility f the slutin. Frm these experimental results, we discuss the paramagnetic slutin having a shrt relaxatin time and nearly zer shift f resnance pint t implement the precisin measurement f prtn gyrmagnetic rati in a lw magnetic field. 2 Experimental Methd *H NMR experiment was perfrmed by a Brucker mdel MSL 200 FT pulse spectrmeter. l H NMR f paramagnetic aqueus slutins in high magnetic field f 4.7 and T, and frequency f and 500 MHz was measured with tw sample shapes at rm temperature. The magnetic susceptibility has been measured using the Guy magnetic balance. 2.1 *H NMR and Relaxatin Time in Paramagnetic Aqueus Slutins The paramagnetic aqueus slutins [Fe(NO3)3-9H 2 O, FeCb, MnCl2-4H 2 O, CCl 2-2H 2 O, CuCl 2-2H 2 O] were prepared by disslving paramagnetic ins f varius cncentratin in

2 Vl. 14, N distilled water. The linewidth and the shift f 'H resnance pint were measured at rm temperature accrding t the shape f the sample tube and the paramagnetic in cncentratin f aqueus slutin. The linewidth and the resnance pint f *H NMR in pure water were als measured. The spin-lattice relaxatin time (7"i) and spin-spin relaxatin time (T2*) were determined frm the signal f l H NMR at rm temperature by the inversin recvery methd and the inverse f linewidth, respectively. 2.2 Magnetic Susceptibility f Paramagnetic Aqueus Slutin The density f paramagnetic aqueus slutin was measured with the mass and vlume, and the magnetic susceptibility per unit vlume was btained with the susceptibility per unit mass. 3 Experimental Results OO 5 > B = 4.7 T gy-;whyt-w3 Fe(NO 3)3-9H 2O FeCb T" In Cncen.(10 20 ins/cc) Figure 1. The frequency shift f 'H NMR signal as a functin f cncentratin f paramagnetic ins in aqueus slutin cntained in a fixed cylinder (* is the resnance pint f 'H in pure H2O). 3.1 Shift f!h Resnance Pint and Linewidth In case f cylindrical sample tube, the resnance pint f r H NMR was shifted t the negative directin with respect t that f pure water accrding t the cncentratin f paramagnetic in as shwn in Figure 1. It was nearly unchanged with the variatin f cncentratin f paramagnetic in in Fe(NO3>3-9H2O slutin. Hwever, the identical Fe 3+ in in FeCb shws the largest shift f the resnance pint. Since the distributin f valence electrns is influenced by the chemical bqnding f an atm, it culd be explained that the displacement f nuclear magnetic resnance frequency depends upn the chemical envirnment [7]. Figure 2 shws the linewidth f } H NMR accrding t the cncentratin f paramagnetic ins. Here we have used the Lrentzian absrptin lineshape, and the linewidth crrespnds t the full width at the half maximum. The C 2+ and Cu 2+ ins are almst ineffective t the linewidth. Whereas the paramagnetic aqueus slutins cntaining Fe 3+ in influence the linewidth as a functin f cncentratin f paramagnetic ins. The trend in aqueus slutin cntaining the Mn 2+ in differs frm thse in ther paramagnetic ins. Fr the case f spherical sample shape, the shift f resnance pint as a functin f cncentratin f paramagnetic ins is shwn in e(no3) 9H 2 O 0 In Cncen.(10 20 ins/cc) Figure 2. The linewidth f 'H NMR signal as a functin f cncentratin f paramagnetic ins in aqueus slutin cntained in a fixed cylinder (* is the linewidth f 'H in pure H2O, 0.15 khz). Figure 3. The resnance pint f 'H NMR was shifted t the psitive directin cmpared with that f pure water. The frequency shift was nearly unchanged with the variatin f the cncentratin f paramagnetic Cu 2+ in. The linewidth f *H NMR in the spherical shape is the same as that in the cylindrical ne as shwn in Figure 2, i.e. the linewidth has n difference between the cylindrical and spherical samples within the experimental errr.

3 242 Bulletin f Magnetic Resnance 00 O B = 4.7 T B" MnCl 2-4H 2 O CuCU-2H;O In Cncen.(10 20 ins/cc) Figure 3. The frequency shift f 'H NMR signal as a functin f cncentratin f paramagnetic ins in aqueus slutin cntained in a sphere (* is the resnance pint f 'H in pure H2O). Hwever, the shift f the resnance pint f l H in case f spinning cylindrical sample shws the similar trend as that f the fixed spherical sample, but with the larger shift than the fixed sphere as shwn in Figure 4. Each line in these figures was determined by the least square fit with the experimental data. 3.2 l H Relaxatin Time Figure 5 shws the *H spin-lattice relaxatin time (Ti) fr the cylindrical and spherical samples measured by the inversin recvery methd. As the cncentratin f paramagnetic ins increased, the relaxatin time was shrtened. The 'H relaxatin time f paramagnetic ins cntaining C 2 * r Cu 2+ was lnger than that f Mn 2 + r Fe 3 +. The 'H spin-lattice relaxatin time f 2.51 s measured in pure water was cnsistent with the previusly reprted value f 2.3 s at 20 C and 29 MHz [8]. Figure 6 shws the spin-spin relaxatin time (7*2 *) fr the cylindrical and spherical samples btained with the inverse linewidth f the resnance line. This result shws the similar trend as that f Ti. Hwever, the J H relaxatin time 7z* is shrter than Ti in aqueus slutins B = T /A^MnClr4H,O FeClj / Fe(NOj)j-9HzO CCl;-2H 2 O CuCl2-2H 2 O In Cnceti.(10 20 ins/cc) Figure 4. The frequency shift f *H NMR signal as a functin f cncentratin f paramagnetic ins in aqueus slutin cntained in a spinning cylinder (* is the resnance pint f 'H in pure H2O) ! c(n03)-9hzo In Cncentratin(ins/cc) Figure 5. Spin-lattice relaxatin time Ti f 'H due t the paramagnetic ins in aqueus slutin cntained in the fixed cylindrical and spherical shapes. Bth shapes have the same values within experimental errr. 3.3 Magnetic Susceptibility The magnetic susceptibility per unit vlume f the paramagnetic aqueus slutin was btained by the Guy magnetic balance as a functin f cncentratin f paramagnetic ins

4 Vl. 14, N GO "B H B = 4.7 T ESS 3SS1 The l H resnance pint in pure water differs frm that in the paramagnetic aqueus slutin. The paramagnetic aqueus slutin induced the shift f resnance pint due t the presence f paramagnetic ins. In this study, we have tried t search a suitable paramagnetic slutin, having the shrt relaxatin time and nearly zer shift f resnance pint in rder t btain the crrect prtn resnance frequency in a lw magnetic field. X 10" The Shift f 'H Resnance Pint and Interactin Factr i 'E, In Cncentratin(ins/cc) Figure 6. Spin-spin relaxatin time r 2 * f >H due t the paramagnetic ins in aqueus slutin cntained in the cylindrical and spherical shapes. Bth shapes have the same values within experimental errr. at rm temperature as shwn in Figure 7. The susceptibility was prprtinal t the cncentratin f paramagnetic ins. 4 Analysis and Discussin MnCh-4H2O FeClj «CCl 2-2H 2 O Fe(NO3)3-9H 2 O CuCU- 2HjO In Cncentratin(ins/cc) Figure 7. The magnetic susceptibility f aqueus slutin as a functin f cncentratin f paramagnetic ins. Fr a liquid, the time averaged field at a nucleus may be divided int three significant cmpnents Bav = B B' + B" (1) where B is the external magnetic field, which is the main cmpnent in Bav. B' is the magnetic shielding field at the nucleus due t the induced mtin f the electrns in the atm r mlecule. B" is the magnetizatin field due t the paramagnetic ins t shrten the spin-lattice relaxatin time T\ f the nuclear spin system. The diple interactin between the *H nucleus and paramagnetic in is given by [9] (2) The field B\ is ascribed t the induced magnetic diples n the surface f a small hypthetical sphere with its center at the nucleus. This is the s-called Lrentz r cavity field and has the value (4H/3)M, where W is the magnetizatin. The field Bz is the familiar demagnetizing field, defined by #2 = -aw, where a is the demagnetizing factr. The value f a is 47?/3 and 2n fr the spherical and infinite cylindrical sample perpendicular t the field, respectively. It might be expected that the remaining field #3 due t thse paramagnetic ins inside the hypthetical sphere wuld be exactly zer. Hwever, it is fund experimentally that #3 may differ significantly frm zer. Therefre, we define an "interactin factr" q=b 3 /M. The expressin fr B" hence becmes [10] B" = [ ( 4 B / 3 ) - a + q]m (3) The magnetizatin H was btained frm the susceptibility per unit vlume accrding t the cncentratin f paramagnetic ins. Als, the

244 Bulletin f Magnetic Resnance V ' shift f resnance pint(b") fr paramagnetic ins with respect t resnance pint f prtn in pure water was measured frm *H NMR experiment in varius paramagnetic slutins.

5 244 Bulletin f Magnetic Resnance V ' shift f resnance pint(b") fr paramagnetic ins with respect t resnance pint f prtn in pure water was measured frm *H NMR experiment in varius paramagnetic slutins. Using the magnetic field induced t the 'H nucleus and the value f magnetizatin, we calculated the interactin factr q frm eq.(3) fr the fixed spherical and cylindrical samples. A summary fr the varius paramagnetic ins is given in Table 1. The cnsistency f the Table 1. Experimental values f the interactin factr q fr the fixed spherical and cylindrical samples, btained with eq.(3). paramagnetic ins Fe 3 * Fe 3 ' Mn 2i C 2t Cu 2 ' chemical cmpund Fe(NO 3 ) 3-9HjO FeCl 3 MnCI 2-4H 2 O CCl 2-2H 2 O CuCl 2-2H 2 O Q cylinder value sphere experimental data is indicated by the agreement between the interactin factrs fr the crrespnding cylindrical and spherical cases. The amunt f disagreement can be attributed partly t the experimental errr and partly t the meniscus effect and the lack f perfect sphericity f the spherical sample. 4.2 Relaxatin Time The spin-lattice relaxatin time measured by the inversin recvery methd with a pulse sequence f 180 (2 /is) - t - 90 ( 1 us) - 5 fis(t d ) - free inductin decay. The ringing dwn delay-time Ta was used t remve the effect f the pulse and the free inductin decay was measured with time t. The spin-lattice relaxatin time btained with the inversin recvery methd decreases as the cncentratin f paramagnetic ins increases. The relaxatin time measured with the spherical sample is similar t that with the cylindrical sample. The 'H relaxatin time f paramagnetic slutin cntaining C 2 + r Cu 2 * shws lnger than that cntaining Mn 2 * r Fe 3+. The spin-lattice relaxatin time f J H in varius paramagnetic slutins is shrter than that in pure water because f the interactin between the nuclear spin and paramagnetic ins. When the number f paramagnetic ins was increased, the shrtening mechanism f the relaxatin time culd be understd as fllws. If the number f paramagnetic ins is increased, the nuclear spin is cupled mre with the magnetic field prduced by the paramagnetic ins. This magnetic interactin between the nuclear spin and magnetic field f the paramagnetic ins can cntribute t the decrease in the spin-lattice relaxatin time [11]. In case f the shrt spin-lattice relaxatin time Ti, the fllwing relatin generally hlds [12] : (V)" 1 = (4) where Tz is the "natural" spin-spin relaxatin time, and Tz' is the time due t the field inhmgeneity. The value f Tz" is measured frm the full width at half maximum f the NMR lineshape. The linewidth f 'H NMR was brdened when the cncentratin f paramagnetic ins was increased. In case f the aqueus slutin cntaining Fe 3+ in, the linewidth was remarkably increased accrding t the cncentratin f paramagnetic ins. The linewidth culd be bradened by the magnetic diple field prduced by the paramagnetic ins at the site f *H nucleus. Nrmally the diple field f the paramagnetic ins has the field strengths f several thusands times greater than that due t the magnetic mnents f the nucleus, but it is averaged ut at the site f ] H nucleus. Cnsequently nly a small effect, the linewidth bradening is ccured in the magnetic resnance [13]. 5 Cnclusin Fr the spherical and cylindrical samples, B" wuld be always zer and psitive, respectively, if q were zer. The deviatin f the shift f resnance pint between the experimental results and the theretical predictin (q = 0) culd be understd as an effect due t an additinal interactin between the paramagnetic ins and the 'H nucleus. The spin-lattice and spin-spin relaxatin times f l H NMR in paramagnetic aqueus slutin were shrtened as the cncentratin f paramagnetic ins was increased. Frm these experimental results, we fund that the paramagnetic slutin having the shrt relaxatin time and nearly zer shift f resnance pint is CUO22H2O aqueus slutin. Therefre, the aqueus slutin cntaining Cu 2+ wuld be the best candidate t implement the precise determinatin f the

6 Vl. 14, N prtn gyrmagnetic rati. Acknwledgement This wrk was supprted by the Ministry f Science f Technlgy and in part the KOSEF thrugh the SRC f Excellence Prgram ( ). References [1] E.R.Williams and P.T.Olsen, Phys. Rev. Lett. 42, 1575 (1979). [2] E.R.Williams, G.R.Jnes, J.S. Sng, W. D. Phillips, and P. T. Olsen, IEEE Trans. Instrum. Meas. IM-38(2), 233 (1989). [3] H. Nakamura, N. Kasai and H. Sasaki, IEEE Trans. Instrum. Meas. IM-36, 196 (1987). [4] N. Blembergen, Nuclear Magnetic Relaxatin (W. A. Benjamin, New Yrk, 1961), Chap. 4. [5] J. H. Simpsn and H. Y. Carr, Phys. Rev. Ill, 1201 (1958). [6] N. Blembergen, E. M. Purcell, and R. V. [7] Pund, Phys. Rev. 73, 679 (1948). J. T. Arnld, S. S. Dharmatti and M. E. Packard, J. Chem. Phys. 19, 509 (1951). [8] N. Blembergen and W. C. Dickinsn, Phys. Rev. 79, 179 (1950). [9] W. C. Dickinsn, Phys. Rev. 77, 736 [10] (1950). A. R. Lim, S. H. Chh, Saemulli 26, 381 (1986). [11] A. Abragam, The Principles f Nuclear Magnetism(Oxfrd Univ. Press, Oxfrd, 1961), Chap. 3. [12] D. Pines and C. P. Slichter, Phys. Rev. 100, 1014 (1955). [13] W. C. Dickinsn, Phys. Rev. 81, 717 (1951).

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