Depth resolved grazing incidence scattering from the solid-liquid interface
Max Wolff, Peter Kuhns, Andrew J C Dennison, Georg Liesche, Philipp Gutfreund, Sarah Rogers
DDepth resolved grazing incidence time of flight neutron scattering from thesolid-liquid interface
M. Wolff, a) J. Herbel, F. Adlmann, A. J. C. Dennison,
1, 2
G. Liesche,
3, 2
P. Gutfreund, and S. Rogers Division for Materials Physics, Department of Physics and Astronomy,Uppsala University, Box 516, 751 20, Uppsala, Sweden Institut Laue Langevin, BP 156, 38042, Grenoble, France Hochschule Bremerhaven, Bremerhaven, Germany ISIS-STFC, Rutherford Appleton Laboratory, Chilton, Oxon OX11 0QX,United Kingdom (Dated: 18 August 2018)
We have applied small angle scattering in grazing incidence beam geometry on a time-of-flight neutron instrument. Due to the broad wavelength distribution provided fora specific incident beam angle the penetration depth of the neutron beam is variedover a broad range in a single measurement. The near surface structure of block co-polymer micelles close to silicon substrates with distinct surface energies are resolved.It is observed that the very near-surface structure strongly depends on the surfacecoating whereas further away from the surface bulk like ordering is found. a) max.wolff@physics.uu.se a r X i v : . [ c ond - m a t . s o f t ] S e p . INTRODUCTION Neutrons have properties which enable them to be used as an unique probe in materialresearch. Their spin and low energy makes them sensitive to the magnetic induction insolids and suitable to investigate lattice vibrations and diffusive processes. Most importantin this context for the present study is that neutrons interact with the nuclei via the weakinteraction. As a consequence they are characterized by a weak absorption, resulting ina high penetration power, for many engineering materials like, e.g. silicon, aluminum orsapphire. In addition the neutron is sensitive to different isotopes of the same element,which allows contrast variation experiments and highlighting of specific parts of a sample.The two points just mentioned make neutrons an ideal probe for the study of buried liquidinterfaces and surfaces by extracting the density profile in a reflectivity measurement. Inaddition to the density profile along the surface normal, in-plane correlations are accessiblevia diffuse and small angle scattering. As an example the ordering of micelles at the solid-liquid interface was studied using off-specular neutron scattering . Grazing incidence smallangle neutron scattering (GISANS) expands on this technique by offering resolution forthe scattering in all three dimensions thus providing a unique insight into the interfacialstructure.Following along this line recent developments in instrumentation have provided an optimizedbeam geometry and high neutron flux as required for GISANS studies . In this contextexperiments showed that the signal from the bulk of a sample might be separated from thesurface scattering or that time-of-flight TOF-GISANS can be used to probe a large rangeof momentum transfers for a single incident beam angle .One interesting class of materials to fully exploit the capabilities of this technique are blockco-polymers since they have self-assembling properties on the molecular scale making themone promising way for the fabrication of nano-devices . In particular; close to a solidboundary one expects surface enrichment in case of an attractive interaction between theinterface and one of the building blocks, or depletion in case of a repulsive interaction. Thismay lead to lamellar phases with different orientations with respect to the interface .In aqueous solution block co-polymers may form micelles since the hydrophobicity of thebuilding blocks may differ from each other resulting in the association with or exclusion ofwater molecules. As the properties of different blocks may change with e.g. temperature2r pressure, block co-polymers offer a model system for the study of gelation, percolation,crystallization or the glass transition . To become more specific for the system, consistingof polypropylene (PPO) and polyethylene (PEO) building blocks, presented here, increasingtemperature results in a conformational change of the PPO towards lower polarity resultingin a loss of hydration of the polymer chains in water , whereas PEO blocks remain solvatedacross a broad range of temperatures. At sufficiently high polymer concentrations thiseffect drives the macromolecules to aggregate into micelles with a hydrophobic core (PPO)surrounded by a more hydrophilic shell (PEO) .In this article we describe a scattering experiment probing the near surface structure of amicellar polymer solution, which is in its cubic (fcc) phase, in contact to a solid boundary.Our experiments go beyond previous studies, where depth sensitivity was shown for anair-sample interface with a thin layer deposited on the surface. The present study is onlypossible since first D O has a smaller refractive index than silicon for neutrons and secondsilicon is nearly transparent for them. This allows the investigation of the interface betweentwo bulk materials in contact to each other. We demonstrate that by combining a broadneutron wavelength spectrum with a grazing incidence beam geometry on a TOF-SANSinstrument, the structure of polymer micelles can be resolved close to the solid surface aswell as in the bulk in a single measurement. II. EXPERIMENTAL DETAILS
Two functionalized single crystalline silicon (100) crystals (70*70*10 mm , polished,obtained from CrysTec, Germany) were used as solid substrates. The roughness of thesubstrates was verified by x-ray reflectivity measurements and is below 0.5 nm. One waferwas chemically cleaned in freshly prepared piranha solution (50/50 v/v H SO (concen-trated) and H O (30 % aqueous)) for 30 minutes and rinsed with Millipore water. Thisprocedure leads to an surface energy of approx. γ = 72 mJm at room temperature . Thesecond wafer was cleaned in the same way and subsequently chemically covered with aself-assembled monolayer of octadecyltrichlorosilane OTS. The resulting surface energy isabout γ = 19 mJm at room temperature. A detailed discussion of the roughness and surfaceenergy measurements of the substrates used in the present study can be found in ref. .The sample is a 18.5 % (in weight, corresponding to 20 % in H O ) solution of Pluronic3 SampleSilicon Position − SensitiveDetectork z xy
31 2 P e n . d e p t h [ n m ] Q [Q/Q C ] FIG. 1. Schematics of the scattering geometry used for grazing incidence neutron scattering at thesolid-liquid interface (left panel) . The right panel depicts the penetration depth of the neutronbeam plotted over the transfer of momentum, normalized to the critical transfer of momentum fortotal external reflection. The regions 1, 2 and 3 mark the Q intervals at which the GISANS datawere taken. F127 ((ethylene oxide) -(propylene oxide) -(ethylene oxide) ) in D O . The bulk proper-ties of this material have been reported in literature in great detail . The polymer waspurchased from Sigma-Aldrich and used without further purification. The molecules weresolved in D O (for better contrast) at a low temperature under constant stirring until ahomogeneous solution was formed. The sample cell was then filled with the sample in itsliquid state at 5 ◦ C. All measurements were performed at 25 ◦ C with the polymer solutionin the crystalline phase.Figure 1 (left panel) depicts the scattering geometry for the neutron scattering experiments.Neutrons penetrate a single crystalline block of silicon from the narrow side and are scat-tered at the solid-liquid interface. A detailed discussion of the scattering geometry can befound in . Note, measurements of solid-liquid interfaces are much easier using neutronsthan x-rays, since the neutron has a high penetration power for many engineering materials,for example silicon, aluminum and steel. This property is combined with a large scatteringpotential of light elements and in particular of deuterium, resulting in a finite angle of totalexternal reflection at the silicon D O interface.Table I summarizes the scattering length density and electron density for silicon and thesample. For x-rays no critical angle of total external reflection exists at the silicon-liquidinterface. On the other hand neutrons are totally reflected for a momentum transfer smallerthan Q c = 0 .
124 nm − . This implies that for an incident angle of 0.3 ◦ the critical wavelengthfor total external reflection is λ c = 0 .
53 nm. Wavelengths longer than λ c are totally reflected4 LD Neutron SLD x-raySilicon 2.08*10 − ˚A − − ˚A − Sample 5.17*10 − ˚A − − ˚A − TABLE I. Neutron scattering length densities and electron densities for the interface studied inthe present work. with only the evanescent wave penetrating the sample, whereas shorter wavelength neutronsare refracted and transmitted into the liquid.The TOF-GISANS experiments were performed on the instrument SANS-2D at ISIS(Rutherford-Appleton Laboratory, Didcot, England). The choppers were set to allow awavelength band of 0.175 - 1.56 nm which prevents frame overlap of preceding and subse-quent pulses at the repetition rate of 10 Hz generated at TS2 at ISIS. In order to probedifferent penetration depths the intensities were integrated for one incident beam angle overwavelength intervals of 0.175-0.5 nm, 0.5-0.6 nm, 0.6-1.56 nm, corresponding to wavelengthresolutions of ∆ λλ of 48 %, 9 % and 44%, respectively. In addition; the lattice parameter ofthe crystalline structure is evaluated for more narrow wavelength bands. The incident beamwas collimated over a distance of 6 m and had a horizontal and vertical divergence of 0.29 ◦ and 0.04 ◦ (base width of a triangular). The source and sample slits were set to 20*4 mm and 10*0.2 mm , respectively. The footprint of the sample for the incident beam angle of0.3 ◦ was about 0.25 mm to avoid over illumination and air scattering, which would resultin additional background. The detector with a pixel resolution of 5*5 mm was set to adistance of 6 m. III. RESULTS AND DISCUSSIONA. Result
Figure 2 depicts the patterns of intensity measured on SANS-2D for an 18.5 % (byweight) solution of the polymer F127 solved in D O . The three pictures for the siliconsurface treated with piranha solution (top panels) and OTS (lower panels) were measured5 [ n m - ] Q [ n m - ] Q [nm -1 ] I n t e n s i t y [ a r b . un i t s ] I n t e n s i t y [ a r b . un i t s ] OTS ~ 10 nm (< 1 µm) ~ 10 µm > 30 µm
Piranha (111) (111)(111) (111)(111)(111) (222) (222)(222)(222) (200)’(-111)(-311)(022)(311)’(-111)’(200)(022)’(311)(3-11)(-220) (2-20)
FIG. 2. GISANS data taken for an 18.5 % (by weight) solution of the polymer F127 solved in D O in contact with a silicon surface treated with piranha solution (top panels) and OTS (lowerpanels). The different penetration depths, noted at top and increasing from left to right, resultfrom the different wavelengths in the incoming beam. Crystalline ordering is clearly preferred inthe vicinity of the piranha solution treated surface. simultaneously for the incident beam angle of 0.3 degree with a fixed detector angle. Thedirect as well as the reflected beam were masked by the beam stop in order to avoid detectorsaturation and reduce the background. The left panels correspond to the integration of thedetector images for wavelengths ranging from 0.6-1.56 nm resulting in a penetration depthof the neutron beam into the polymer solution of approximately 10 nm (region 1 in figure 1)or 1 µ m taking into account the tail in divergence of the incident beam and marked by thegrey dashed line in figure 1. The intensity integrated for short wavelengths of 0.175-0.5 nmwhich have a large penetration depth of about 30 µ m are shown in the right panels. Thecentral column summarizes the intensities for wavelengths integrated around the criticalwavelength, 0.5-0.6 nm, resulting in an intermediate penetration depth of about 10 µ m.For the smallest penetration depth of about 10 nm a ring of scattered intensity is visiblearound the direct beam (Q=0) for the OTS substrate. This ring is absent for the micellesin contact with the surface treated with piranha solution. It should be pointed out thatdue to the divergence of the incident beam the angular spread of the incident beam results6n probing a range of penetration depths; this varies from 10 nm to around 1 µ m for thosewavelength with a nominal penetration depth of 10 nm. The presence of Bragg reflectionsat Q z ≈ . µ m. 10 well resolved Bragg peaks, together with 4 weakerpeaks are observed for the sample close to the piranha treated surface, whereas for the OTSsurface peaks of a lower intensity together with a Debye-Scherrer ring at Q = 0.4 nm − areobserved. The insert between the left and middle panels depicts a zoom into the low Q-region and with a narrow wavelength band around 0.56 nm, which is slightly larger than thecritical wavelength. On the two panels the difference in structure between both interfaces ismost striking. For the piranha cleaned surface clear Bragg reflections are visible even withan asymmetry in the reflection found at positive and negative Q y values, respectively. Thisimplies a highly textured well ordered crystalline structure in the vicinity of the interface.On the other hand for the OTS surface a ring of increased intensity is found corresponding toa powder or amorphous surface layer. For the largest penetration depth (right panels) bothdetector images become more similar; for the piranha solution treated surface the diffusescattering becomes increased, whereas for the OTS one the reflections are separated moreclearly. B. Reciprocal space
In order to understand the crystalline structure formed at the different distances fromthe solid substrate and to relate those to the scattering patterns presented in Figure 2 itis important to have a closer look at the scattering geometry and to understand how theinstrumental settings affect our observations. Figure 3 depicts intensities for the same kindof cubic structure formed by F127 micelles solved in D O taken on the instrument ADAM atthe Institute Laue-Langevin (Grenoble, France) . This instrument uses a monochromaticneutron beam of 4.41 ˚A. The incident beam was collimated in order to well resolve the Braggreflections. Figure 3 shows the scattering pattern at a single point near the critical reflectionof the surface on the Ewald sphere. The logarithm of the scattered intensity is plotted as acolor map (high and low intensity in red and blue, respectively). The coordinate system x,7 y [nm -1 ]Q z [nm -1 ] Q x [nm -1 ] Direct beamSpecular reflectivityBragg reflection (111) Sample horizon1-0.50.50 -0.50.5 0 -1 -0.1 -0.05 0 0.05-11 Debye Scherrer 2DDebye Scherrer 2D
FIG. 3. Detector image for a fcc crystalline structure plotted as color map on the surface of theEwald sphere. y and z is defined with respect to the sample surface as shown in Figure 1. A more detaileddiscussion of the length-scales probed along the different directions can be found in . It isclear that the detector plane represents a curved surface with Q=0 at the position of thedirect beam. The second and only other point where the in-plane coordinates Q x and Q y are zero is the point where the specular scattered intensity is detected. All other points onthe detector have none-zero Q x and/or Q y components.Considering a densely packed cubic structure at the interface, the (111) lattice planes wouldbe parallel to the solid-liquid boundary and the Bragg reflections resulting from them shouldhave no in-plane component ( Q x = Q y = 0). This implies that the (111) reflection can onlybe detected if it has a certain rocking width along Q x . The values probed along the Q x direction are much smaller than those probed along Q y and Q z and for a crystal coherenceon the order of µ m a finite intensity is detected in the detector plane. Moreover with de-creasing wavelength the momentum transfer along the x direction decreases at the positionof the Bragg refelection for small Q . This implies that for a specific crystal coherence theintensity scattered into the detector plane should increase with decreasing wavelength. Allother four Bragg reflections are only visible if the crystalline structure is a two dimensionalpowder with respect to the sample interface , since the Q y values are much larger thanthe Q x values and the probability of a crystal orientation with the Bragg reflection on theEwald sphere is unlikely. Moreover, for a single crystal arrangement the reflections with andwithout prime visible in figure 2 can never be detected on the Ewald sphere at the sametime, since they would be separated by an angle of 180 ◦ on the Debye-Scherrer ring, which8 I n - p l a n e c o rr e l a t i o n l e n g t h [ n m ] FIG. 4. In-plane correlation length probed for the different wavelength at the position of the (111)Bragg reflection. is not possible for the symmetry of the crystal.
C. In-plane correlations
As mentioned in the previous section the (111) reflection can only be detected if it hasa certain rocking width along Q x . This rocking width along Q x transfers directly into ain-plane correlation length by taking the Fourier transform from reciprocal to real space.Figure 4 shows how the correlation length varies as a function of wavelength at the (111)peak position. The solid line represents a full width half maximum of the diffuse scatteringcorresponding to the Q x values probed in the detector plane. The dashed line represents aline width which is five times larger. A strong Bragg reflection is only expected in the areabetween the two lines.Considering the scattering geometry the intensity distribution visible in Figure 2 is explainedby the following model. The crystal has a larger coherence and better epitaxy close to thesurface cleaned with piranha solution. For the smallest penetration depth (left panels) andthe largest wavelength a relatively large Q x is probed. Considering the large coherence ofthe crystal it becomes clear why almost no intensity is visible in the upper left panel. On theother hand for the more powder like structure with small coherence close to the OTS surfacethe ring of intensity visible in the lower panel on the left hand side becomes understandable.For decreasing wavelength and increasing penetration depth the component of Q x at theBragg peak becomes smaller. The good crystallinity next to the piranha solution cleanedsurface is well reflected by the significantly increased intensity of the (111) reflection and the9 L a tt i c e p a r a m e t e r [ n m ] nm] Piranha OTS (111)(-111)(022) FIG. 5. d-spacing extracted for different Bragg reflections and plotted versus penetration depth.For clarity, the data for the (-111) and (022) reflection are shifted by 10 and 20 nm, respectively. large number of visible reflections in this case. For the OTS interface the intensity increasesless and a lot of diffuse scattering is visible. For the largest penetration depth (right panels)the two scattering patterns, top and bottom, become more similar resembling a more bulklike ordering in the sample. In addition all reflections become more smeared out since theintensity is integrated over a large wavelength band.
D. Lattice parameter
One parameter which is relatively easy to extract from the data is the position of thedifferent Bragg reflections. As a result of this evaluation the lattice parameter of the fcccrystal structure is depicted in fig. 5 for both samples. For the data evaluation the intensitywas integrated over a narrow wavelength band of typically 0.1 - 5 pm. Subsequently, theintensity map is fitted by a two dimensional Gauss function and Q is extracted from the po-sition of the peak maximum. The error bars shown in the figure represent the mathematicaluncertainty of the fitting routine. The missing points are due to the low intensity and a notconverging fit for some wavelength. The data points extracted from the (-111) and (022)reflections are shifted by 10 and 20 nm, respectively, for reasons of clarity. As seen fromthe figure no change in lattice parameter with depth as well as no tetragonal distortion isfound, even though the correlation length and epitaxy of the structures formed at the twointerfaces differs largely. However, for the very low penetration depth the position of theBragg reflections is difficult to measure since the scattered intensity is extremely low andthe resolution, as discussed in the next section, is determined by the angular divergence of10he incident beam. Regarding the uncertainty in the determination of the lattice parameterand the fact that the Q value at the position of the Bragg reflections is more than threetimes the critical momentum transfer we have not corrected the data for refraction effects.
E. Resolution
From figure 1, right panel, it is seen that the penetration depth into the liquid changesby three orders of magnitude within 10 % above and below Q c . This implies that in order toreach a good depth resolution an excellent ∆ QQ c is needed. ∆ QQ is calculated by the followingequation taking into account the wavelength distribution ∆ λ and a angular divergence ∆ θ :∆ QQ = (cid:118)(cid:117)(cid:117)(cid:116)(cid:32) ∆ λλ (cid:33) + (∆ θ cot θ ) (1)For small angles θ this can be simplified:∆ QQ = (cid:118)(cid:117)(cid:117)(cid:116)(cid:32) ∆ λλ (cid:33) + (cid:32) ∆ θθ (cid:33) (2)For a time of flight instrument the wavelength resolution is given by the length of theinstrument and the time resolution of the detector. If the acquisition is run in event modethe wavelength resolution can be chosen after the experiment and be optimized to the signal.However, the lower limit in the wavelength resolution is given by the length of the neutronpulse ∆ t and the flight time from the source to the detector and can be calculated from:∆ λ = h ∆ tm n L (3)with h , m n and L being Plancks number, the mass of the neutron and the distance fromthe source, which is the cold source at TS2 at ISIS for the present case, to the detector,respectively. Plugging in the numbers for L = 25 m and ∆ t , which is between 0.3 and0.6 ms, results in an intrinsic wavelength resolution of about 1 % or 5 pm at the criticalwavelength which is close to 0.53 nm for the angular settings chosen here. On the otherhand the resolution in angular divergence is given by the settings of the collimation slitsand was 0.04 ◦ in the present study. The incident beam angle was 0.3 ◦ resulting in a rela-tive uncertainty of 13.3 %. However, even though the angular resolution was relaxed theintensity for wavelengths larger than the critical wavelength were not sufficient to extract asignal from the very near surface layer. To allow such studies much longer counting times11r stronger pulsed neutron sources are needed. IV. CONCLUSION
In this paper we present a TOF-GISANS experiment to resolve the near surface structureof micellar systems. By use of TOF neutron reflectometry and small angle scattering depthsensitive information is extracted in one single measurement. It turns out that with increas-ing distance from the interface the crystallographic structure approaches the bulk structure.Our experiments open new possibilities for the investigation of near-surface structures overseveral orders in length scale not only of micellar systems but also of colloids.
V. ACKNOWLEDGEMENT
The authors thank Katharina Theis-Br¨ohl for sending Georg Liesche for a project basedat the Institute Laue-Langevin and Peter Kuhns for help with the measurements at ISIS.In addition we acknowledge financial support from the Swedish research council VR undercontract number A0505501 and the European Union NMI-3 initiative for financial assistancefor travel as well as the STFC for the beam time, RB1120261.
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