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Quantitative Analysis of Polymer Colloids by Cryo-Transmission Electron Microscopy J. J. Crassous, C. N. Rochette, A. Wittemann, M. Schrinner, and M. Ballauff* Physikalische Chemie I, University of Bayreuth, 95440 Bayreuth, Germany
M. Drechsler Makromolekulare Chemie II, University of Bayreuth, 95440 Bayreuth, Germany Received February 4, 2009 The structure of colloidal latex particles in dilute suspension at room temperature is investigated by cryogenic transmission electron microscopy (cryo-TEM). Two types of particles are analyzed: (i) core particles made of polystyrene with a thin layer of poly(N-isopropylacrylamide) (PNIPAM) and (ii) core-shell particles consisting of core particles onto which a network of cross-linked PNIPAM is affixed. Both systems are also studied by small-angle X-ray scattering (SAXS). The radial density profile of both types of particles have been derived from the cryo-TEM micrographs by image processing and compared to the results obtained by SAXS. Full agreement is found for the core particles. There is a discrepancy between the two methods in case of the core-shell particles. The discrepancy is due to the buckling of the network affixed to the surface. The buckling is clearly visible in the cryo-TEM pictures. The overall dimensions derived from cryo-TEM agree well with the hydrodynamic radius of the particles. The comparison of these data with the analysis by SAXS shows that SAXS is only sensitive to the average radial structure as expected. All data show that cryo-TEM micrographs can be evaluated to yield quantitative information about the structure of colloidal particles.
I. Introduction For many decades, transmission electron microscopy (TEM) has been one of the most important techniques for the study of nanostructured materials. In recent years, cryogenic TEM (cryoTEM) has greatly enlarged the scope of this technique and has thus become an indispensable tool of biological research.1-4 Aqueous solutions containing, for example, viruses are vitrified by shock-freezing in liquid ethane. Thus, thin films of vitrified solutions result which can be analyzed by TEM. Evidently, cryoTEM allows us to study sensitive biological and colloidal5-12 structures in situ, that is, in aqueous solution. Thus, there is no need for any further preparatory step. Up to now, there is a large *Corresponding author. E-mail:
[email protected]. (1) Adrian, M.; Dubochet, J.; Lepault, J.; McDowall, A. W. Nature 1984, 308, 32. (2) Dryden, K. A.; Farsetta, D. L.; Wang, G. J.; Keegan, J. M.; Fields, B. N.; Baker, T. S.; Nibert, M. L. Virology 1998, 245, 33. (3) Grimm, R.; Singh, H.; Rachel, R.; Typke, D.; Zillig, W.; Baumeister, W. Biophys. J. 1998, 74, 1031. (4) Hill, C. L.; Booth, T. F.; Prasad, B. V.; Grimes, J. M.; Mertens, P. P.; Sutton, G. C.; Stuart, D. I. Nat. Struct. Biol. 1999, 6, 565. (5) Toyoshima, C.; Unwin, N. Ultramicroscopy 1988, 25, 279. (6) Toyoshima, C.; Unwin, N. J. Cell Biol. 1991, 111, 2623. (7) Langmore, J. P.; Smith, M. F. Ultramicroscopy 1992, 46, 349. (8) Smith, M. F.; Langmore, J. P. J. Mol. Biol. 1992, 226, 763. (9) Zheng, Y.; Won, Y. Y.; Bates, F. S.; Davis, H. T.; Scriven, L. E.; Talmon, Y. J. Chem. Phys. B 1999, 103, 10331. (10) Li, Z. B.; Kesselman, E.; Talmon, Y.; Hillmyer, M. A.; Lodge, T. P. Science 2004, 306, 98. (11) Pochan, D. J.; Chen, Z. Y.; Cui, H. G.; Hales, K.; Qi, K.; Wooley, K. L. Science 2004, 306, 94. (12) Klookenburg, M.; Dullens, R. P. A.; Kegel, W. K.; Erne, B. H.; Philipse, A. Phys. Rev. Lett. 2006, 96, 037203. :: (13) Erhardt, R.; Zhang, M. F.; Boker, A.; Zettl, H.; Abetz, C.; Frederik, P.; :: Krausch, G.; Abetz, V.; Muller, A. H. E. J. Am. Chem. Soc. 2003, 125, 3260. (14) Wittemann, A.; Drechsler, M.; Talmon, Y.; Ballauff, M. J. Am. Chem. Soc. 2005, 127, 9688. (15) Crassous, J. J.; Ballauff, M.; Drechsler, M.; Schmidt, J.; Talmon, Y. Langmuir 2006, 22, 2403. :: (16) Crassous, J. J.; Wittemann, A.; Siebenburger, M.; Schrinner, M.; Drechsler, M.; Ballauff, M. Colloid Polym. Sci. 2008, 286, 805.
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number of morphological studies using cryo-TEM.13-19 However, there are only few investigations which evaluate the cryoTEM micrographs in a quantitative manner.2,3,5-9 In a similar fashion, small-angle X-ray scattering (SAXS)19-21 and small-angle neutron scattering (SANS)22 present well-established tools for the analysis of nanostructures. There is a huge number of publications in which one of these methods has been used to analyze particulate structures in solution, and the literature in this field is hard to overlook. Both SAXS and cryo-TEM are sensitive toward the local electron density in the object and thus lead to similar information about the sample under scrutiny. In principle, the gray scale of TEM micrographs could be evaluated to yield the electron density of the sample. This in turn will lead directly to the SAXS intensities and vice versa. To the authors’ best knowledge, this obvious relation between SAXS and TEM has hardly been exploited yet. The reasons for this are given by the fact that the quantitative evaluation of TEM micrographs presents a difficult task because of the multiple scattering of the electrons in thick samples.3,23-26 Moreover, any staining procedure or other preparation of the sample will lead to irreversible changes and render a quantitative comparison between TEM and SAXS impossible. (17) Lu, Y.; Mei, Y.; Drechsler, M.; Ballauff, M. Angew. Chem., Int. Ed. 2006, 45, 813. (18) Cui, H.; Hodgon, T. K.; Kaler, E. W.; Abegauz, L.; Danino, D.; Lubovsky, M.; Talmon, Y.; Pochan, D. J. Soft Matter 2007, 3, 945. (19) Bang, J.; Jain, S. M.; Li, Z. B.; Lodge, T. P.; Pedersen, J. S.; Kesselman, E.; Talmon, Y. Macromolecules 2006, 39, 1199. (20) Guinier, A.; Fournier, G. Small-Angle Xray Scattering. :: (21) Dingenouts, N.; Bolze, J.; Potschke, D.; Ballauff, M. Adv. Polym. Sci. 1999, 144, 1. (22) Higgins, J. S.; Benoit, H. C. (23) Goudsmit, S.; Saunderson, J. L. Phys. Rev. 1940, 57, 24; 1940, 58, 36. (24) Moliere, G. Z. Naturforsch. 1948, 3a, 78. (25) Crewe, A. V.; Groves, T. J. Appl. Phys. 1974, 45, 3662. (26) Reimer, L. Transmission Electron Microscopy: Physics of Image Formation and Microanalysis, 4th ed.; Springer Series in Optical Sciences 36; 1997.
Published on Web 03/24/2009
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Here, we present a quantitative comparison between the analysis of colloidal systems by cryo-TEM and by SAXS. Following previous work by Langmore and Smith,7,8 we evaluate the local excess electron density from the gray scale of the cryoTEM micrographs. In particular, we calculate the SAXS intensity directly from the cryo-TEM micrograph and compare these results to measured intensities. As an example for this analysis, we chose aqueous dispersions of latex particles: The first system consists of homogeneous polystyrene particles covered with a thin layer of poly(N-isopropylacrylamide) (PNIPAM) and serves as a simple model for particles with a well-known structure. The second system is core-shell particles consisting of core particles onto which a dense network of PNIPAM is affixed. The diameter of the core particles is of the order of 100 nm. Immersed in cold water, the shells of these composite particles will swell. Heating a suspension of the particles to temperatures above 32 C will lead to a volume transition within the shell in which most of the water will be expelled. Macroscopic PNIPAM gels were introduced many years ago in the now classical work of Tanaka and co-workers27 and have been intensively studied by many workers since. Based on this work, thermosensitive microgels have become an important class of colloids in the past few years because of their versatile applications28 and as model systems in colloid physics.29-32 The reason for the choice of this system for the present purpose is given by the fact that core-shell microgels polystyrene (PS)/ PNIPAM have already been the subject of a number of studies employing SAXS and SANS.33-40 More recently, it has been demonstrated that cryo-TEM is well-suited to investigate the volume transition and the structure of the composite PS/PNIPAM core-shell.15,16 Hence, this system is the obvious choice for a quantitative comparison of SAXS and cryo-TEM. The paper is organized as follows: In section II, the particles used in this studied are presented, while section III gives the theoretical background of contrast in electron microscopy. In section IV, the analysis of the cryo-TEM micrographs is first validated using homogeneous polystyrene particles carrying a thin layer of PNIPAM. Moreover, the effect of the focusing, dose, sample thickness, and energy filtering will be discussed. Finally, quantitative comparison between the cryo-TEM micrographs of the core-shell system with the respective SAXS data will be given.
II. Experimental Section A. Materials. All particles used herein have been synthesized and purified as described in ref 33. The core particles result (27) Shibayama, M. See the review of this work in Macromol. Chem. Phys. 1998, 199, 1. (28) Nayak, S.; Lyon, L. A. Angew. Chem., Int. Ed. 2005, 44, 7686. (29) Wu, J. Z.; Huang, G.; Hu, Z. B. Macromolecules 2003, 36, 440. (30) Wu, J. Z.; Zhou, B.; Hu, Z. B. Phys. Rev. Lett. 2003, 90, 048304. :: (31) Crassous, J. J.; Siebenburger, M.; Ballauff, M.; Drechsler, M.; Henrich, O.; Fuchs, M. J. Chem. Phys. 2006, 125, 204906. :: (32) Crassous, J. J.; Siebenburger, M.; Ballauff, M.; Drechsler, M.; Hajnal, D; Henrich, O.; Fuchs, M. J. Chem. Phys. 2008, 128, 204902. (33) Dingenouts, N.; Norhausen, Ch.; Ballauff, M. Macromolecules 1998, 31, 8912. (34) Seelenmeyer, S.; Deike, I.; Rosenfeldt, S.; Norhausen, Ch.; Dingenouts, N.; Ballauff, M.; Narayanan, T. J. Chem. Phys. 2001, 114, 10471. (35) Dingenouts, N.; Seelenmeyer, S.; Deike, I.; Rosenfeldt, S.; Ballauff, M.; Lindner, P.; Narayanan, T. Phys. Chem. Chem. Phys. 2001, 3, 1169. (36) Stieger, M.; Richtering, W.; Pedersen, J. S.; Linder, P. J. Chem. Phys. 2004, 120, 6197. (37) Mason, T. G.; Lin, M. Y. Phys. Rev. E 2005, 71, 040801. (38) Berndt, I.; Pedersen, J. S.; Richtering, W. J. Am. Chem. Soc. 2005, 127, 9372. (39) Berndt, I.; Pedersen, J. S.; Richtering, W. Angew. Chem., Int. Ed. 2006, 45, 1737. (40) Berndt, I.; Pedersen, J. S.; Linder, P.; Richtering, W. Langmuir 2006, 22, 459.
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from the copolymerization of polystyrene with 5 wt % PNIPAM in emulsion; after dialysis, these particles have been used as seeds for the polymerization of the PNIPAM shell. A concentration of 2.5 mol % N,N0 -methylenebisacrylamide (BIS) was used as a cross-linker. The number average radius of the core particles has been determined directly from the cryo-TEM images. The mass ratio between the core and the shell was found to be 1.15 as determined by gravimetry. B. Methods. Samples for TEM were prepared by placing a drop of the 0.2 wt% solution on a carbon-coated copper grid. After a few seconds, excess solution was removed by blotting with filter paper. The cryo-TEM preparation was done on dilute samples (0.2 wt %). The sample was kept at room temperature and vitrified rapidly by the method described previously.14 A few microliters of diluted emulsion were placed on a bare copper TEM grid (Plano, 600 mesh). The dimensions of the holes where the sample is absorbed and vitrified are 35 35 10 μm3. The excess liquid was removed with filter paper. This sample was cryo-fixed by rapid immersing into liquid ethane at -170 to -180 C in a cryo-box (Carl Zeiss NTS GmbH). Typically, the film thickness where the particles are investigated ranges between 1 μm and the diameter of the particles. The specimen was inserted into a cryo-transfer holder (CT 3500, Gatan, Munich, Germany) and transferred to a Zeiss EM 922 EFTEM instrument (Zeiss NTS GmbH, Oberkochen, Germany). Examinations were carried out at temperatures around 90 K. The transmission electron microscope was operated at an acceleration voltage of 200 kV. Zero-loss filtered images were taken under reduced dose conditions ( R0), and f(R) is the molecular scattering amplitude. The Broglie wavelength λ can be calculated relativistically in the case where the kinetic energy E used for the measurement is close to the rest energy: -1=2 λ ¼ h 2m0 Eð1 þ e=2E0 Þ
ð2Þ
with E being the acceleration voltage (here 200 keV) and E0 being the rest energy electron (E0 = m0c2 = 511 keV, with m0 = 9.10912 10-31 kg being the rest mass and c = 2.9979 108 m s-1 being the speed of light). Given the above approximations, the contrast transfer function CTF(R) can be expressed through CTFðRÞ ¼ sin χðRÞ þ QðRÞ cos χðRÞ
ð3Þ
with χ(R) = 2π/λ(-CsR4 + ΔfR2/2) where Cs is the coefficient of spherical aberration and Δf is the defocus. The function sin χ(R) is the phase contrast transfer function. Q(R) refers to the amplitude contrast transfer function. It represents the maximum contribution from amplitude contrast relative to that deriving from phase contrast. At low resolutions, f(R) and Q(R) can be considered constant and the effects of spatial and temporal coherence are ignored, because they are expected to be negligible.44,45 The ratios of the Fourier transformations of the core particles at different defoci have been compared to the ratio of the theoretical values (eq 3) with Q as an adjustable parameter (see Figure 1). We determined the value of Q that best describes changes in the images due to defocus as described by Langmore and Smith.7 An empirical value of Q = 0.14 was found. Figure 1 presents the different CTF(R) values obtained for different defoci. For a defocus Δf = 0 nm, the CTF(R) is almost constant up to approximately 0.5 nm-1. Considering the good contrast of :: (42) Ballauff, M.; Bolze, J.; Dingenouts, N.; Hickl, P.; Potschke, D. Macromol. Chem. Phys. 1996, 197, 3043. (43) Erickson, H.; Klug, A. Philos. Trans. R. Soc. London, Ser. B 1971, 261, 105. (44) Frank, J. Optik 1973, 38, 519. (45) Scherzer, O. J. Appl. Phys. 1949, 20, 20.
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Figure 1. Calculated contrast transfer function for different defoci. Values are plotted assuming the instrumental parameters of the Zeiss EM922 instrument (λ = 0.0025 nm, aberration coefficient Cs = 1.2 mm).26
our pictures, there was no need to go out of focus. Hence, a compensation of the CTF(R) was not required in the following study. Thus, phase contrast can be neglected if the images are taken in focus, that is, Δf = 0 nm. Moreover, the following analysis will be restricted to the region of low spatial resolution. From the above discussion of CTF(R), it is evident that the range of spatial frequencies must hence be smaller than ∼0.5 nm-1. This leads to ∼2 nm minimal spatial resolution which is smaller than the smallest object which can be seen on the micrographs presented in this study. Hence, it suffices to discuss the evaluation of the images solely in terms of amplitude contrast. B. Amplitude Contrast. Amplitude contrast is brought about by scattering processes that can be elastic or inelastic. The total electron scattering cross section σT(R0) is therefore expressed as the sum of the elastic and inelastic cross sections.7,8,26 σT ðR0 Þ ¼ σel ðR0 Þ þ σ inel ðR0 Þ
ð4Þ
Elastically scattered electrons are usually scattered through large angles and thus largely contribute to the contrast.26 The transmission depends on the objective aperture R0, the electron energy E, the mass thickness x = Ft (F = density, t = thickness), and the material composition (atomic weight A, and atomic number Z). The inelastic scattered electrons are mainly transmitted through the objective aperture. In the case of an energy filtered electron microscope, the inelastic part will be removed nearly totally. This will enhance the amplitude contrast considerably. Hence, both elastic and inelastic processes must therefore be taken into account when calculating the gray scale of the images.7,8 The differential elastic cross sections dσ/dΩ were calculated using the Dirac partial-wave analysis described by Walker.46 The scattering potential was obtained from the self-consistent Dirac-Hartree-Fock (DHF) charge density for free atoms47,48 with the local exchange potential of Furness and McCarthy.49 The numerical calculations were performed with the algorithm described by Salvat and Mayol.50 Further details have been given by Jablonski et al.51-53 The calculation was done using the NIST electron elastic-scattering cross section database (SRD 64) (version 3.1) for an energy of 200 keV (see Table 1).52 Given the (46) Walker, D. W. Adv. Phys. 1971, 20, 257. (47) Desclaux, J. P. Comput. Phys. Commun. 1977, 9, 31. (48) Desclaux, J. P. Comput. Phys. Commun. 1977, 13, 7. (49) Furness, J. B.; McCarthy, I. E. J. Phys. B: At., Mol. Opt. Phys. 1973, 6, 2280. (50) Salvat, F.; Mayol, R. Comput. Phys. Commun. 1993, 74, 358. (51) Jablonski, A.; Salvat, F.; Powell, C. J. J. Phys. Chem. Ref. Data 2004, 33, 409. (52) Jablonski, A.; Salvat, F.; Powell, C. J. NIST Electron Elastic-Scattering Cross-Section Database, version 3.1; National Institute of Standards and Technology: Gaithersburg, MD, 2003. (53) Tanuma, S.; Powell, C. J.; Penn, D. R. Surf. Interface Anal. 1994, 21, 165.
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differential cross sections dσ/dΩ, the number of electrons elastically passing through an aperture R0 can be expressed through the partial elastic cross section σel(R0): Z σ el ðR0 Þ ¼
π R0
dσ 2π sin R dR dΩ
ð5Þ
Table 1 gathers all partial elastic cross sections σel,PW. An estimate of the total elastic cross section given by the integral over the entire solid angle was proposed by Langmore and Smith.7 It can be expressed by σ el ¼
1:4 10 -6 Z 3=2 β2
½1 - 0:26Z=ð137βÞ
ð6Þ
Table 1. Quantitative Analysis of the Gray Scalea Z 1 6 7 8
σel 2.26 50.48 54.12 56.89
σel(R0) 1.18 27.85 34.23 39.57
σin b
32.41 and 11.22c 79.38 85.74 91.66
a Total elastic cross sections (σel) and partial elastic cross sections σel(R0) calculated from the Dirac partial-wave analysis using the NIST electron elastic-scattering cross section database.52 The inelastic cross sections σin have been calculated from eq 9 with the expression given by Wall et al.55 Z denotes the ordinary number of the respective element. All cross sections have been derived in pm2 for an acceleration voltage of 200 kV for an aperture R0 = 10 mrad. b Equation 9. c Empirical.
where β is the ratio of the speed of the electrons to that of the light (β2 = 1 - [E0/(E + E0)2]). Furthermore, σel can be calculated for small angles to a good approximation: σ el ðR0 Þ ¼ σel ηel ðR0 Þ ¼ σ el ½1 - s0 =10
ð7Þ
where ηel defines the number of electrons scattered outside the aperture and is called the elastic efficiency expressed as function of the maximum spatial frequency s0 s0 ¼ 2sinðR0 =2Þ=λ
ð8Þ
with the objective aperture half-angle R0 = 10 mrad, the maximum spatial frequency s0 = 4 nm-1, and the electron wavelength λ = 2.5 10-3 nm. For the calculation of the inelastic scattering cross sections, we used the expression derived by Wall et al:55 σ in ¼
1:5 10 -6 Z 1=2 β2
lnð2=ϑe Þ
ð9Þ
where ϑe = E/[β2/(V0 + mc2)] and E is the average energy loss, assumed to be 20 eV from the calculation of Wall et al. for organic materials.55 Equation 9 is not valid for hydrogen.55 Here, we use an estimate of the cross section given by 11.2 pm2 at 200 kV. This value was obtained from the apparent inelastic mean free path of ice, the calculated inelastic scattering from oxygen, and the density for hyperquenched glassy water (0.92 g/cm3).57,58 We took the inelastic mean free path length of ice from the work of Langmore measured to 180 nm at 80 kV. The inelastic mean free path length of ice then results to 284.6 nm at 200 kV if we consider its dependence on the acceleration voltage given by U1/2.56 Table 1 gathers the inelastic scattering cross sections thus obtained for the elements of interest. C. Contrast in TEM and Cryo-TEM. In the present approximation, the gray value obtained at a given point in an image is solely related to the amplitude contrast, that is, to the weakening of the intensity I of the electron beam by scattering processes. Thus, one may treat this weakening in terms of the difference ΔI between the rays passing through the sample and through the aqueous phase.7 Here, we use a different approach. (54) Gries, W. H. Surf. Interface Anal. 1996, 24, 38. (55) Wall, J.; Isaacson, M.; Langmore, J. P. Optik 1974, 39, 359. (56) Grimm, R.; Typke, D.; Barmann, M.; Baumeister, W. Ultramicroscopy 1996, 63, 169. (57) Sceats, M. G.; Rice, S. A. Water; Plenum Press: New York, 1982; Vol. 7. (58) Sciortino, F.; Poole, P. H.; Essmann, U.; Stanley, H. E. Phys. Rev. E 1997, 55, 727.
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Figure 2. (A) TEM evaluation of the gray scale G(r) of a homogeneous spherical particle dried on a thin carbon film. Application of the Lambert-Beer law to the ratio G(r)/G0 leads to eq 13. (B) Cryo-TEM evaluation of the gray scale of a homogeneous spherical particle embedded in a thin film of hyperquenched glassy water (HGW). Application of the Lambert-Beer law leads in the same way to eq 14. See text for further explanation.
Figure 2 demonstrates the central idea in a schematic fashion: The weakening of the intensity I of the electron beam passing through the sample can be treated within the frame of the Lambert-Beer law. Therefore, the ratio I/I0 of the rays passing through the particle and through the aqueous phase or through vacuo in the case of TEM (marked in Figure 2) is only related to the contrast within the particle. Other factors such as, for example, multiple scattering will weaken both rays outside the particle in the same way. Their ratio is thus not affected by these effects. On the other hand, the colloidal objects under consideration here have dimensions of the order of a few 100 nm only. Hence, the prerequisites of theory, most notable the assumption that multiple scattering within the particle can be neglected, are fully justified. When the inelastic scattered electrons are filtered off, the resulting images, that is, the local gray scale G(r), result from a weakening of the primary beam through the elastic as well as the inelastic scattering of the electrons. Hence, both the elastic and the inelastic cross sections must be used to calculate the gray scale of the images. Without energy filtering, only the elastic cross sections are taken into account. This can be argued from the fact that inelastic scattering is only significant at small scattering angles. Hence, the inelastically scattered electrons will go through the diaphragm and will not contribute to the measured gray values of the image (see below). DOI: 10.1021/la900442x
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In the following, we shall calculate the resulting contrast in TEM and cryo-TEM. In the absence of chemical shifts, we can assume that the scattering cross section of a molecule composed of nk elements is the sum of the cross sections of the atoms (σT,i) weighted by their proportion in mass Mi in the molecule.7 Thus, the relative decrease dI/I of the intensity when the path t through the respective material is enlarged by dt can be expressed by nk X dI N A νi ¼ -F σ T, i ðR0 Þ dt I Mi i ¼1
ð10Þ
The image intensity I can be obtained by integration I Ft ¼ exp I0 xk ðR0 Þ
ð11Þ
ð12Þ
where I0 is the intensity of the incident electron beam. The quantity (F/xk(R0))-1 is therefore the total mean free path length of the respective material through which the electron beam is passing (see Table 2). Equation 12 is the base of the following analysis. It demonstrates that the weakening of the primary beam is directly related to (F/xk(R0))-1 which may be calculated for all materials under consideration. We now derive the contrast of the images following from eq 12 by considering two essential cases: (i) In the case of TEM, the objects, as for example, a homogeneous sphere with a radius R, are lying on a thin carbon film for example (see Figure 2A). The gray values G(r) in the image are proportional to the respective intensities I(r). The path t(r) = 2(R2 - r2)1/2 of the electron beam going through the particles is characterized by the gray value G(r) which depends on the distance to the center of the particle r. For r > R, the gray value is constant because it is related to the scattering cross section of the surrounding medium. For TEM, the medium is vacuum and the intensity is the one transmitted through the carbon grid. This defines the contribution of the surrounding medium G0. It is now expedient to consider only the ratio G(r)/G0. From the Lambert-Beer law, it follows for a homogeneous sphere: 0 !1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fp GðrÞ A ð13Þ ¼ exp@ - 2 R2 - r2 G0 xk, p From this analysis, the radial density profile is obtained by an azimuthal average of the gray values of one isolated particle. (ii) In the case of cryo-TEM analysis, we have to consider a thin layer of vitrified water in which spherical particles are embedded (see Figure 2B). However, the thickness of this layer must exceed the largest dimensions of the particles; that is, the particles must be fully immersed in the layer of glassy water. For r > R, the ray passes only through vitrified water. Hence, it corresponds to the contribution of the vitrified water only and is characterized by the gray value G0 I0 exp(-Fwt/xk,w). Inside the objects, the material may be homogeneous or may have taken up a certain amount of water. In the latter case, the volume fraction of the material φ within the particle must be taken into account. For systems impenetrable by the solvent 7866 DOI: 10.1021/la900442x
molecules
F
HGW polystyrene PNIPAM+BIS
0.92 1.0525 1.1492
(Fp/xk,p)
(Fp/xk,p - Fw/xk,w)
filter 4.803 10-3 5.828 10-3 6.305 10-3
0 1.025 10-3 1.503 10-3
no filter
where vi is the stoichiometric coefficient of the ith element in the compound and F is the mass density of the compound (g/cm3). We can then define the contrast parameter xk of the material as follows: nk X 1 NA νi ¼ σT, i ðR0 Þ xk ðR0 Þ i ¼1 M
Table 2. Densities (in g/cm3) and TEM Contrasts (Gp/xk,p) (in nm-1) for the Hyperquenched Glassy Water (HGW),57,58 the Polystyrene Core, and the Cross-Linked PNIPAM Shella
HGW polystyrene PNIPAM+BIS
0.92 1.0525 1.1492
1.546 10-3 1.702 10-3 1.869 10-3
0 1.57 10-3 -3 3.22 10
a The quantity (Fp/xk,p - Fw/xk,w) is the contrast in cryo-TEM calculated in nm-1. Both contrasts are calculated for an acceleration voltage U = 200 kV and an aperture R0 = 10 mrad with or without filtering of the inelastic contribution.
water, φ = 1. Thus, for spheres embedded in glassy water, we obtain from eq 13: 0 !1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fp GðrÞ F ¼ exp@ -2φ R2 - r2 - w A ð14Þ G0 xk, p xk, w Equation 14 is the central result of the present analysis. It demonstrates that we can define the contrast in cryo-TEM by the difference of the reciprocal mean free path length in the material and in glassy water, respectively (Fp/xk,w - Fw/xk,w). By considering the ratio G(r)/G0 in terms of the Lambert-Beer law, no absolute intensities need be measured, and no knowledge about the absolute thickness of the water layer is needed. As mentioned above, multiple scattering of the electrons is of no concern, since the probability that the secondary radiation goes through the diaphragm is small, at least for the conditions under which cryo-TEM pictures are taken. Hence, G(r)/G0 may be used to derive directly the radial mass density of objects embedded in glassy water. For the sake of simplicity, eq 14 has been developed for the case of spheres. For elongated objects, the calculation of the length t may become a more involved task, since it depends on the orientation of the object with regard to the direction of the primary beam. The main point of the analysis, however, remains valid. Table 2 provides values of the TEM and cryo-TEM contrasts obtained from the partial-wave calculation of the elastic cross section and from eq 9 as described above for hyperquenched glassy water, polystyrene, and the PNIPAM cross-linked shell with or without energy filtering. The table clearly shows the difference of contrast between the different experiments. If we take as a reference the polystyrene with energy filter, TEM experiments have a contrast approximately 5.7 times higher than that for cryo-TEM. The same comparison without filter gives a factor around 10.8. Comparing now the contrasts with and without filter gives a factor of 3.4 for TEM and 6.5 for cryoTEM. This clearly indicates the great advantage of energyfiltered microscopy. D. Small Angle X-ray Scattering. The scattering intensity I (q) measured for a suspension of particles with spherical symmetry may be rendered as the product of I0(q), the scattering intensity of an isolated particle, and S(q), the structure factor that takes into account the mutual interaction of the particles: IðqÞ ¼ ðN=VÞ I0 ðqÞ SðqÞ
ð15Þ
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where N/V denotes the number density of the scattering objects. A previous discussion of S(q) for systems of spherical particles has demonstrated that the influence of the structure factor is restricted to the region of smallest q values when the concentration of the particles is small. Its influence onto the measured scattering intensity can therefore be disregarded in the present analysis. Hence, S(q) = 1 will be assumed in the following.21 The scattering intensity of one single particle can be decomposed in principle in three terms:21,33-35 I0 ðqÞ ¼ Ipart ðqÞ þ Ifluc;PS ðqÞ þ Ifluc;shell ðqÞ
ð16Þ
Ipart(q) is the part of I0(q) due to the core-shell structure of the particles (i.e., the scattering intensity caused by composite particles having a homogeneous core and shell).34,35 The core and the shell are characterized by different electron densities. Ifluc,PS(q) and Ifluc,shell(q) refer to the thermal fluctuation of the PS core and the PNIPAM shell, respectively. The shell, however, does not consist of a solid material but of a polymeric network which exhibits static inhomogeneities and thermal fluctuations, and for this reason we neglected the contribution of the fluctuation of the PS core and we only take into account Ifluc,shell(q). For spherical symmetric particles with radius R, Ipart(q) is equal to B2(q) where the scattering amplitude B(q) is given by Z R sinðqrÞ ð17Þ dr BðqÞ ¼ 4π φðrÞ½Fe, p ðrÞ -Fe, w r2 qr 0 The scattering contrast is the difference of the scattering length density of the polymer and the surrounding solvent ΔFe(r) = Fe,p(r) - Fe,w. By multiplying the polymer fraction φ(r) profile by the scattering contrast of the polystyrene for the core (ΔFe,PS = 7.5 e.u/nm3) and of the cross-linked PNIPAM for the shell (ΔFe,PNIPAM = 45.5 e.u/nm3; see the Methods subsection), we obtained the electron density profile necessary for the calculation of the scattering intensity. The polydispersity can be described by a normalized Gaussian number distribution:21,33 " # 1 ðR - ÆRæÞ2 DðR, σÞ ¼ pffiffiffiffiffiffi exp 2σ2 σ 2π
ð18Þ
with ÆRæ being the average radius and σ being the standard deviation. Here, it suffices to mention that the polydispersity smears out the deep minima of Ipart(q) to a certain extent.34,35 For the evaluation of the part of the scattering caused by the thermal density fluctuations within the shell Ifluc(q), it is appropriate to use the empirical formula:34,35 Ifluc ¼
Ifluc ð0Þ 1 þ ξ2 q2
ð19Þ
where the average correlation length in the network is described by ξ. Ifluc contributes significantly only in the high q regime.
IV. Results and Discussion A. Core Particles. 1. TEM Analysis. A dilute solution of core particles was analyzed first. The particles thus consist of a polystyrene core of constant density with a thin layer of PNIPAM.33 The dispersion was first investigated by transmission electron microscopy. Figure 3A presents the TEM micrograph obtained from this analysis and the normalized distribution of the radius obtained on a population of more Langmuir 2009, 25(14), 7862–7871
Figure 3. (A) TEM micrographs of the core particles and the corresponding normalized size distribution. (B) Relative gray values G(r)/G0 obtained by azimuthal average of 200 particles (circles). Full line refers to the theoretical calculation considering the contrast of pure polystyrene (see Table 2) and a radius of 51.5 nm from the statistic. Inset displays the sample thickness derived from this analysis (circles) and its comparison to the thickness of a spherical particle (full line).
than 200 particles. All the micrographs were taken as close as possible to the focus with the same dose conditions. The particles appear spherical and monodisperse. The average radius was found equal to 51.3 ( 2.6 nm. The distribution can be described by a Gaussian considering an average radius of 51.5 nm and a standard deviation of 2 nm (see inset of Figure 3A). The variation between the measurement represented by the size of the error bars is rather small, which attests to the reproducibility of the measurement from one picture to another. The experimental result has been directly compared to the theory developed for spheres. The average radius of 51.5 nm was determined assuming a Gaussian distribution. Moreover, the contrast of pure polystyrene particles was used. The theory described relatively well the experimental results (see Figure 3B). However, the average height of the dried particles is slightly smaller in the center of the particles (see inset of Figure 3B). We ascribe this small discrepancy to a slight distortion of the spherical form of the particles during drying. 2. Cryo-TEM Analysis. Cryogenic electron microscopy was then performed on the same system. Figure 4A displays the micrographs obtained and the resulting normalized distribution of the radius of the particles. The same feature as in the TEM analysis can be observed. The particles appears as spheres with a narrow size distribution. The average radius from this analysis also over more than 200 particles is equal to 51.4 ( 3.2 nm. The distribution can be described by a Gaussian centered at 52 nm with a standard deviation of 2 nm, which is in good agreement with the TEM results and with the SAXS analysis of the core (50 nm) and the dynamic light scattering (55 nm). The residual differences are due to the finite polydispersity of the particles that will be weighted differently by these methods. The contrast between the particles and the background is less pronounced than that in TEM as expected from the above calculation. Now, the contrast is given by the difference between the contrast of the polystyrene and water (Fp/xk,p - Fw/xk,w). This quantity is approximately six times smaller than the one of polystyrene in vacuo Fp/xk,p (see Table 2). Moreover, the background is not constant on the whole micrographs, which is directly related to the variation of the thickness of the film. A simple method has been applied to estimate the thickness of the vitrified water film (see Figure 4).7 First, the micrographs were obtained as close as possible to the focus (Figure 4A). Then, in an area close to the particles, a hole was burned in the film by excessive irradiation. A picture of the hole was taken in the same conditions as the particles before, and the gray value inside the DOI: 10.1021/la900442x
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Figure 4. (A) Cryo-TEM micrograph of the core particles and the corresponding size distribution (B) Micrograph of a hole performed in the film by electronic irradiation in the vicinity of (A). The picture is taken under the same condition as in (A), and the average gray values in the hole are defined by G0. (C) Color representation of the thickness of the HGW film (only the points outside of the particles can be considered) deriving from G0, the contrast of glassy water (see Table 2 and eq 13). Color bar is a linear scale of the height between 250 and 450 nm.
hole then defines G0 (see Figure 4B). Using the known contrast of the HGW film Fw/xk,w, it is possible to determine its thickness in all the points outside of the particles in the first picture following the same approach as described for the TEM analysis. Figure 4C presents a representation of the film thickness following eq 13. Here, the thickness of the frozen water film is encoded by coloration. Only the values besides the particles were taken into account. A variation of the thickness from approximately 250 to 450 nm within 1.7 μm was observed in this example. Considering the average size of the particles of 100 nm, this thickness should be sufficient in order to perform a correct analysis. The effect of the focusing has been investigated by taking different pictures for different defocusing. If taken in focus, the micrographs exhibit a sharp interface with the surrounding solvent. With increasing defocus, diffraction phenomena occur at the edge of the particles under the form of Fresnels fringes as expected. Evidently, these micrographs would need a correction through the CTF(R) before doing a qualitative evaluation. Figure 4 demonstrates, however, that the contrast between the particles and the vitrified water is sufficient. As mentioned above, no defocusing is needed to enhance the contrast, and the evaluation of the gray scale proceeds from micrographs taken in focus. The relative gray values G(r)/G0 shown in Figure 5 have been obtained by averaging over 100 particles. The symbols display the mean values while the error bars give the standard deviation in each point. The average size was found to 52 nm from cryoTEM micrographs using the contrast (Fp/xk,p - Fw/xk,w) of pure polystyrene in HGW. The obtained values presented by the solid line described the experimental results very well. There is a slight discrepancy near the surface of the particles, most probably due to the effect of polydispersity. The dashed line displays the respective average of the radial gray values if a core-shell structure has been assigned to the particles with the following data: A polystyrene core with a radius of 50 nm is surrounded by a thin shell (2 nm) of PNIPAM with a volume fraction of 50 %. As expected, the small difference is within the limits of experimental error and the contrast between the shell and core is too small to be detected by cryo-TEM. The effect of the energy filtering has also been considered. Figure 6 presents cryo-TEM micrographs of one single particle taken with (Figure 6A) and without (Figure 6B) an energy filter. The relative gray values G(r)/G0 have been derived for the two micrographs and fitted using eq 14. Here, the respective contrasts given in Table 2 have been used. (Figure 6C). Equation 14 describes the radial absorbance in the two cases. However, the 7868 DOI: 10.1021/la900442x
Figure 5. Average of the radial electron absorbance A(r) of the core particles analyzed by cryo-TEM (circles). Experimental data have been derived by taking the average over 100 particles. Full line refers to the theoretical calculation considering the contrast of pure polystyrene particles (see Table 2) and a radius of 52 nm. Dashed line is the calculation for a core-shell system with a 50 nm polystyrene core and a swollen 2 nm thin PNIPAM shell (φ = 0.5).
Figure 6. Cryo-TEM micrographs of one core particle with (A) and without (B) filter of the inelastic scattered electrons. Relative gray values G(r)/G0 have been calculated in the two cases (with filter (hollow circles), without filter (hollow squares)) and fitted following eq 14 and the contrast values of Table 2 (full and dotted lines) assuming a pure polystyrene core of 55 nm.
contrast is much better in case of the energy-filtered images as expected. In what is to follow, only energy-filtered images will be analyzed. However, Figure 6 demonstrates that the analysis can be done for both cases in terms of eq 14 in good accuracy. 3. SAXS. Figure 7 presents the scattering intensity obtained for the monodisperse core particles. The scattering intensity has been calculated for one single particle by normalizing through Langmuir 2009, 25(14), 7862–7871
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Figure 7. Scattering intensity of an isolated particle, I0(q) = I(q)/ (N/V), obtained for the core particles (circles). Dashed line presents the scattering intensity profile of a pure 52 nm polystyrene particle. Solid line is the best fit obtained for a core-shell system with a 48 nm polystyrene core and a 2 nm thin PNIPAM shell with an electronic density of 23 e-/nm3.
the number density N/V of the dispersion. This was obtained from the weight percentage of latex, the density of the core, and the radius of the core from cryo-TEM (= 52 nm). The best fit was obtained for a core-shell profile with a dense polystyrene core of 48 nm. The SAXS analysis of the core particles demonstrates furthermore that a small fraction of PNIPAM is located in a thin 2 nm shell at the surface of the particles. Thus, the overall diameter is given by 50 nm. Considering the various sources of error, both SAXS (50 nm) and cryo-TEM (52 nm) come to the same result. The electron density of the shell (26.0 e-/nm3) is considerably higher than the one of the core (7.5 e-/nm3). Hence, there is sufficient SAXS contrast, and the shell contributes considerably to the scattering intensity (see inset Figure 7). The sensitivity of SAXS to detect a thin polymer layer at the solid core interface has already been found in former studies for similar systems35 and also in the adsorption of surfactant on core latices.59-61 The fit procedure also shows that the size distribution of the core particles is rather small with a polydispersity of 5.0%. This results is in good agreement with the overall size and polydispersity of 4% determined from TEM analysis. The profile deriving from SAXS can now be compared directly to the profile obtained by cryogenic electron microscopy. The dashed line in Figure 7 was calculated for solid polystyrene spheres of 52 nm and a polydispersity of 5.0% with the same number density N/V. Good agreement has been found for the positions of the side maximum. At higher q values, the measured scattering is considerably higher than the one calculated for a homogeneous sphere. This discrepancy is due to the presence of a thin PNIPAM layer at the interface. As mentioned above, the contrast in cryo-TEM is too small to discern this detail. B. Core-Shell Particles. Figure 8 displays the micrograph of the core-shell microgel obtained by cryo-TEM in pure water. The sample was kept at 23 C prior to cryogenization.15 The thermosensitive shell is clearly visible in these pictures because of sufficient contrast between the shell and the core. Moreover, the micrograph shows directly the thermal fluctuations and inhomogeneous cross-linking which lead to a further contribution to the scattering intensity.27,34,35 This is directly obvious from
(59) Weiss, A.; Hartenstein, M.; Dingenouts, N.; Ballauff, M. Colloid Polym. Sci. 1998, 276, 794. :: (60) Ballauff, M.; Bolze, J.; Dingenouts, N.; Hickl, P.; Potschke, D. Macromol. Chem. Phys. 1996, 197, 3043. (61) Wu, X.; Pelton, R. H.; Hamielec, A. E.; Woods, D. R.; McPhee, W. Colloid Polym. Sci. 1994, 272, 467.
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Figure 8A, which presents a zoom-in on a particle to evidence the inhomogeneities of the shell. As discussed in previous investigations,15,16 a feature directly visible in the cryo-TEM images is the buckling of the shell (see Figure 8). This finding can be related to the instabilities of swelling or deswelling gels occurring at the surface of swollen gels affixed to solid substrates.62-68 A review of the studies of this effect related :: to macroscopic systems was given by Boudaoud and Chaieb.62 This result corroborates recent small-angle neutron scattering analysis performed on core-shell PNIPAM/ PNIPMAM also synthesized via seed emulsion polymerization, which pointed out the presence of a depletion zone at the interface core-shell.39 As a consequence, the core-shell particles deviate from an ideal spherical symmetry. In order to demonstrate this, we have evaluated the relative gray scale G(r)/G0 along the lines indicated in Figure 8A. Figure 8B shows that the size along these lines may differ appreciably. As already discussed above, this difference is mainly due to the buckling of the shell. Figure 8C then displays the polymer volume fractions that have been evaluated using eq 14 together with the contrasts of polystyrene (core) and PNIPAM (shell). For specimens embedded in HGW, the calculated ratio of the contrast between polystyrene and PNIPAM is 0.682 (see Table 2) and the profile of the shell can be derived without problems. (Note that the ratio calculated with the approximation given by Langmore and Smith for the elastic cross section (eqs 6 and 7)7 would give a ratio of 0.650.) Figure 8C demonstrates the strong fluctuations of the shell leading to strong local variations. This fact must be kept in mind when considering the comparison with SAXS data discussed further below. In order to arrive at an average profile that can be compared to a profile deriving from SAXS measurements, analysis of the particles has been performed on 45 particles shown in the micrograph in Figure 8. Only isolated particles were analyzed in this way. Prior to taking the gray values, a rotational average was performed as shown in Figure 2C. The average relative gray values resulting from this analysis are displayed in the inset of Figure 9A. G(r)/G0 can be decomposed in two parts: the contribution of the core and the contribution of the shell. The average result has been fitted considering a dense polystyrene core and a parabolic density profile for the shell. This parabolic profile that takes into account the fuzziness of the shell was proposed recently by Berndt and co-workers.38-40 The following relation has been used to describe the polymer volume fraction profile for the cross-linked shell:
KφðrÞ ¼
8 > 1 : > > > > 2 > > > 1 -ðRhw - r þ σÞ : > > < ð2σ 2 Þ > ðr - Rhw þ σÞ2 > > > > > ð2σ 2 Þ > > > > : 0
r e Rc Rc
