Langmuir 2004, 20, 4779-4781
Determination of the Size of a Polystyrene Nanosphere by the Pulsed Field Gradient Nuclear Magnetic Resonance Method Takeshi Saito,* Kayori Shimada, and Shinichi Kinugasa National Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology (AIST), AIST Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8568, Japan Received December 19, 2003. In Final Form: March 8, 2004
Introduction The determination of particle size is important for understanding the nature of particles. Many techniques have been used for particle size determination. For the determination of small particle sizes, there are two major approaches. The first one is to obtain the size from imaging techniques such as scanning electron microscopy and transmission electron spectroscopy. These techniques can measure not only the size of particles but also the full distribution. To obtain an accurate particle size, the instrument has to be calibrated by using a particle with a known size. Therefore, calibration with a standard particle is essential for particle size determination with such techniques. The second approach is to determine particle size from a self-diffusion coefficient of a particle dispersed in a liquid where an average particle size can be obtained. For such an approach, dynamic light scattering (DLS)1-3 is well-known and widely used. Since the Stokes-Einstein equation shows a direct relationship between the diffusion coefficient and the hydrodynamic radius of particles, no reference is necessary for obtaining an accurate particle size. For particles in low viscosity or Newtonian solvents, they obey the Stokes-Einstein equation.4 The pulsed field gradient nuclear magnetic resonance (PFG-NMR) technique can also give the self-diffusion coefficient of a molecule. Therefore, the PFG-NMR method can also be applied for the determination of particle size. One advantage of using the PFG-NMR method is that different chemical species resonate at different chemical shifts; thus, it has the potential to distinguish the individual diffusion coefficients for all the species from a mixture at a given time. Therefore, particles must have a spherical shape. Polymer latex is one of the ideal materials for particle size estimation from diffusion coefficient measurement. The PFG-NMR technique has been used to determine the diffusion coefficients of solvents in swollen latex molecules,5 polystyrene microgels,6 and polymers associated with polystyrene latex.7 Interaction of star polymers * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Chu, B. Laser Light Scattering, 2nd ed.; Academic Press: San Diego, CA, 1991; Chapter 8. (2) Brown, W.; Nicolai, T. In Dynamic Light Scattering; Brown, W., Ed.; Clarendon Press: Oxford, U.K., 1993; Chapter 6. (3) Duke, S. D.; Brown, R. E.; Layendecker, E. B. Part. Sci. Technol. 1989, 7, 223. (4) Dunstan, D. E.; Stokes, J. Macromolecules 2000, 33, 193. (5) Piton, M. C.; Lennon, A. J.; Chapman, B. E.; Kuchel, P. W. J. Colloid Interface Sci. 1994, 166, 437. (6) Fleischer, G.; Sillescu, H.; Skirda, V. D. Polymer 1994, 35, 1936. (7) Uemura, Y.; Macdonald, P. M. Macromolecules 1996, 29, 63.
4779
with surfactants8 and between surfactants and waterbased latex9 was also determined. Furthermore, the diffusion coefficient of charged polybutadiene latex was measured10 where the molecular motion of the latex was sufficiently high. The mean displacement of a probe particle was often estimated for the determination of pore size.11 On the other hand, the PFG-NMR technique has not widely been used for the determination of particle size because local reorientational mobility of the polymer segment is very low for such particles. This makes the PFG-NMR measurement on these systems impossible.10 In this study, we succeeded in measuring the diffusion coefficient of a polystyrene sphere in aqueous solution and obtained its particle size with the PFG-NMR method at 600 MHz. Experimental Section An aqueous suspension of a polystyrene (PS) nanosphere was purchased from Duke Scientific Corporation (3020A, nominal 20 nm in size) and used as it was. The National Institute of Standards and Technology (NIST) traceable certified particle size of the sample was 21 ( 1.5 nm. The approximate sample concentration is 1% solid. The solution was transferred in a 5 mm o.d. Shigemi microcell NMR sample tube (BMS-005V, Shigemi Co., Ltd.) at a 5 mm sample height. NMR measurements were carried out on a Varian UNITYINOVA 600A (14.1 T) spectrometer equipped with a H-F{X} diffusion probe (DSI-V218, Doty Scientific) and a diffusion package. NMR lock was not used for all experiments. The temperature was controlled at 25 °C. The chemical shifts of all the spectra were referenced to the HDO in D2O (minimum deuteration degree of 99.95%, Merck Co. & Inc.) resonance of 4.7 ppm. The PFG spin-echo (SE) sequence12 for HDO was performed for the calibration of the gradient strength. HDO and poly(ethylene glycol) 1540 (3.3 × 10-3 g g-1 D2O solution, Wako Pure Chemical Industries, Ltd.) were used to ensure the linearity of the gradient strength outcome from the gradient amplifier. The diffusion coefficient of the HDO in D2O used in this study is 1.902 m2 s-1.13 The PFG stimulated echo (STE) sequence14 [(π/2)-τ1-(π/2)-τ2(π/2)-τ1-acquisition] was used for obtaining the self-diffusion coefficient of the sample. The conditions for our study were as follows: π/2 pulse widths of 12.8 µs, a 12 s relaxation delay, a 2 s acquisition time, and 32 transients were averaged for obtaining each spectrum. The delays τ1 and τ2 were 2 and 48 ms, respectively; the interval between the gradient pulses (∆) was 50 ms; when the duration of the gradient pulse (δ) was kept constant at 1 ms, the gradient strength (g) was varied up to 5.1 Tm-1. On the contrary, when g was kept constant at 5.1 Tm-1, δ was varied up to 1 ms. The echo obtained from the PFG-STE sequence is attenuated according to the following equation:
I ) I0 exp(-γ2g2δ2(∆ - δ/3)D)
(1)
where I is the area of the echo signal, I0 is the maximum area amplitude of the echo signal, γ is the gyro magnetic ratio of the nucleus, and D is the self-diffusion coefficient of the molecule. (8) Wesley, R. D.; Cosgrove, T.; Thompson, L. Langmuir 1999, 15, 8376. (9) Boissier, C.; Lofro¨th, J.-E.; Nyde´n, M. J. Phys. Chem. B 2003, 107, 7064. (10) Blees, M. H.; Geurts, J. M.; Leyte, J. C. Langmuir 1996, 12, 1947. (11) Seymour, J. D.; Callaghan, P. T. AIChE J. 1997, 43, 2096. (12) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288. (13) Weinga¨rtner, H. Z. Phys. Chem. Neue Folge, Bd. 1982, 132, 129. (14) Tanner, J. E. J. Chem. Phys. 1970, 52, 2523.
10.1021/la036406h CCC: $27.50 © 2004 American Chemical Society Published on Web 05/01/2004
4780
Langmuir, Vol. 20, No. 11, 2004
Figure 1. 1D 1H NMR spectrum of the PS nanosphere. The cutoff resonance at 4.7 ppm is a signal originating from H2O of the solution. Assignments of the resonances are as follows: terminal group of the PS at 0.65 ppm, CH2 of the PS at 1.11 ppm, CH of the PS between 1.3 and 1.5 ppm, and resonances from surfactant substance(s) shown between 3.2 and 4.0 ppm. No assignment was given for the low field resonances.
Notes
Figure 2. Spectrum of the PS sphere obtained with the PFGSTE pulse sequence. Only the aliphatic region is represented. The number shown on the right side of each spectrum indicates the gradient strength (g) in Tm-1 in the STE experiment.
Therefore, the diffusion coefficient can be obtained from the slope of a plot of the logarithm of the signal area as a function of g2δ2(∆ - δ/3).
Results and Discussion Figure 1 shows the 1D 1H spectrum of the PS sphere sample. Since we used the PS sample as we obtained it, it is an aqueous solution. As a result, a huge resonance originating from the H2O signal can be found. Furthermore, the lines are broad because of the limited mobility of the sample. The aromatic resonances of the PS sphere show almost no information because local reorientational mobility of the aromatic ring is very low. However, the aliphatic resonances showed sufficient peak shape, which indicated the possibility of diffusion measurement with NMR spectroscopy. The relative intensities obtained from the backbone aliphatic resonance to the terminal resonance are smaller than they should be; this indicated that only part of the aliphatic protons has sufficient mobility. Also, this spectrum indicates the existence of surfactant in the sample because of the 1H NMR resonances shown between 3.2 and 4.0 ppm. When the transverse relaxation time (T2) of the sample is short, the SE sequence is not applicable for the measurement of a self-diffusion coefficient of a molecule because the signal originating from the sample completely decays during the SE time. The T2 value for many polymer materials is too short for the SE sequence; in contrast, the longitudinal relaxation time (T1) is often sufficiently long for these materials. For such cases, the STE sequence is an ideal pulse sequence for obtaining the self-diffusion coefficient. Furthermore, T2 relaxation becomes longer for a molecule when the resonance frequency becomes higher.15 Therefore, the measurement of diffusion coef(15) Sanders, J. M.; Hunter, B. K. Modern NMR Spectroscopy; Oxford University Press: Oxford, U.K., 1987; Chapter 6.
Figure 3. The plot obtained from the STE attenuation of the PS sphere when δ (circle) and g (rectangle) were kept constant. The dotted line is a linear regression of the rectangles.
ficients with the PFG-NMR method at 600 MHz is preferred to the measurement at lower resonance frequencies that are often used for diffusion measurements with the PFG-NMR method. The self-diffusion coefficient of the sphere sample was obtained with the PFG-STE sequence. Figure 2 shows the aliphatic region of the spectra obtained with the PFG-STE pulse sequence. When no gradient pulse was applied to the PFG-STE sequence, the water signal distorted the spectrum. Since the water signal decays rapidly, no signal distortion due to the water signal was found for such strength of gradient pulses. Furthermore, the signals from surfactant completely disappeared. The resonance peaks of the terminal and backbone CH2 showed similar decay profiles. Figure 3 shows the echo signal attenuation curve obtained from eq 1 where the area of the signals from the terminal and backbone CH2 resonances was taken into account. Good agreement can be found between the data obtained with conditions of varying δ values at a constant g value and vice versa. The observed diffusion coefficient of the PS nanosphere was 2.54 × 10-11 m2 s-1. When each resonance was considered separately, the diffusion coefficient observed from the decay of each resonance was identical to that observed with both resonances at a time,
Notes
Langmuir, Vol. 20, No. 11, 2004 4781
which confirmed that no local diffusion mode existed in the particle. According to the Stokes-Einstein equation, D was given by the following equation:
D)
kT 6πηRh
(2)
where k is Boltzmann’s constant, T is the absolute temperature, η is the viscosity of the solvent, and Rh is the hydrodynamic radius of the particle. From eq 2, the particle size or the diameter of this PS sphere was estimated to be 19.3 nm. Since the particle had no local diffusion mode, the size observed here was comparable to the particle size certified by DLS. However, the NIST traceable certified particle size is 21 ( 1.5 nm and the particle size we obtained was slightly smaller than the certified value. The major factor that possibly caused the difference in the particle size from the certified value is the particle size distribution. If the echo signal attenuation curves in Figure 3 show a straight line, there is no distribution of the particle size. However, both curves in Figure 3 are slightly concave, indicating some particle size distribution.16-18 Since the diffusion coefficient of the particle was estimated with the slope of a linear regression of these curves, the diffusion coefficient of larger particles may not be fully estimated. Additionally, it is well-known that the diffusion coefficient observed with DLS is obtained from the time correlation of the scattered light from the particles. The scattered light is nearly proportional to the square of the molecular weight of the particle.2 Since weight is proportional to the cubic power of the radius when assuming the uniform density of the particle, the diffusion coefficient obtained with DLS is a z-averaged value; on the other hand, the diffusion coefficient obtained with the PFG-NMR method is a number-averaged one. Therefore, the response of the diffusion coefficient for (16) von Meerwall, E. D. J. Magn. Reson. 1982, 50, 409. (17) Callaghan, P. T.; Pinder, D. N. Macromolecules 1983, 16, 968. (18) Callaghan, P. T.; Pinder, D. N. Macromolecules 1985, 18, 373.
particles with particle size distribution is different between these techniques. As a result, the diffusion coefficient obtained with DLS should be larger than the coefficient obtained with the PFG-NMR method when particle size distribution exists. In other words, for such cases, the mean particle size obtained with the PFG-NMR method is smaller than the size obtained with DLS. Therefore, the result obtained here was consistent. With consideration of such factors, the PFG-NMR method can provide large particle sizes accurately. Conclusions We demonstrated the feasibility of the PFG-NMR technique for the particle size determination of a sphere molecule. We also showed that the mean particle size obtained with the PFG-NMR method should show a slightly smaller value than that observed with DLS because of particle size distribution. Although particle size determination with the PFG-NMR method should be able to apply for the particle whose diffusion coefficient is as slow as an order of 10-13 m2 s-1, a hard-core material is not preferable for NMR spectroscopy to determine the diffusion coefficient due to its short T2 relaxation time. When NMR spectroscopy at higher resonance frequencies is used, the chance to observe the diffusion coefficient is larger because of the resonance frequency dependency of T2. We took advantage of our capability to perform the PFG-NMR experiment at 600 MHz. One advantage of the PFG-NMR method is that the NMR active nucleus is not only 1H but also many other nuclei such as 19F, 31P, and 13C. Additionally, even if looking at one nucleus, target resonances may be spread along a chemical shift axis. From this feature of NMR spectroscopy, the diffusion coefficients for all the species in a mixture can be estimated individually. Using these features, chemical or structural site-specific motion can be monitored individually. Such information cannot be observed with other techniques. Since particle size measurement with DLS becomes more difficult for smaller particles, the PFG-NMR method can be a powerful tool for the determination of particle size. LA036406H
