Neutron reflectivity

Fundamentals. A collimated beam of neutrons generated in a nuclear reactor or a spallation source with wavelength X impinges onto an interface at an angle 0 (close to glancing angle). The reflected intensity R is measured as a function of momentum transfer Q 

Instrumentation. Films to be investigated are deposited on a material (e.g. single crystal quartz) that is transparent for thermal neutrons (0.1 nm A. 0.6 nm). A typical cell is displayed in Fig. 5.156. The electrochemically inert metal used as 

This may be different in kinetic studies, where the kinetic isotope effect might come into play. 

Investigated examples include the determination of the spatial distribution of a polymer, solvent and mobile species in poly( -toluidine) [983, 984] and polybithiophene [989] films, film swelling and solvent content in electroactive films containing transition metal complexes [988, 985], postdeposition modified electroactive polymers [986] and organic adsorbate layers [987]. The method allows also the investigation of buried interfaces in bilayer systems of various polymers [988]. 

Other technique—for example, dynamic secondary ion mass spectrometry or forward recoil spectrometry—that rely on mass differences can use the same type of substitution to provide contrast. However, for hydrocarbon materials these methods attain a depth resolution of approximately 13 nm and 80 nm, respectively. For many problems in complex fluids and in polymers this resolution is too poor to extract critical information. Consequently, neutron reflectivity substantially extends the depth resolution capabilities of these methods and has led, in recent years, to key information not accessible by the other techniques. 

An additional advantage to neutron reflectivity is that high-vacuum conditions are not required. Thus, while studies on solid films can easily be pursued by several techniques, studies involving solvents or other volatile fluids are amenable only to reflectivity techniques. Neutrons penetrate deeply into a medium without substantial losses due to absorption. For example, a hydrocarbon film with a density of Ig cm havii a thickness of 2 mm attenuates the neutron beam by only 50%. Consequently, films several pm in thickness can be studied by neutron reflecdvity. Thus, one has the ability to probe concentration gradients at interfaces that are buried deep within a specimen while maintaining the high spatial resolution. Materials like quartz, sapphire, or aluminum are transparent to neutrons. Thus, concentration profiles at solid interfaces can be studied with neutrons, which simply is not possible with other techniques. 

The single most severe drawback to reflectivity techniques in general is that the concentration profile in a specimen is not measured directly. Reflectivity is the optical transform of the concentration profile in the specimen. Since the reflectivity measured is an intensity of reflected neutrons, phase information is lost and one encounters the e-old inverse problem. However, the use of reflectivity with other techniques that place constraints on the concentration profiles circumvents this problem. 

The high depth resolution, nondestructive nature of thermal neutrons, and availability of deuterium substituted materials has brought about a proliferation in the use of neutron reflectivity in material, polymer, and biological sciences. In response to this high demand, reflectivity equipment is now available at all major neutron facilities throughout the country, be they reactor or spallation sources. 

The im inary component of the refractive index is associated with absorption. In general, the absorption for thin films is not significant and, consequently, P can be ignored. However, for materials containing the elements Li, B, Cd, Sm, or Gd, where the absorption coefficient is large, P must be taken into account and the refiacdve index is im inary. 

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The ability to contrast match the air with a mixture of water and heavy water makes neutron reflectivity an attractive technique [180,181], Under these contrast conditions the scattering arises from the monolayer alone and combining... 

The polymer concentration profile has been measured by small-angle neutron scattering from polymers adsorbed onto colloidal particles [70,71] or porous media [72] and from flat surfaces with neutron reflectivity [73] and optical reflectometry [74]. The fraction of segments bound to the solid surface is nicely revealed in NMR studies [75], infrared spectroscopy [76], and electron spin resonance [77]. An example of the concentration profile obtained by inverting neutron scattering measurements appears in Fig. XI-7, showing a typical surface volume fraction of 0.25 and layer thickness of 10-15 nm. The profile decays rapidly and monotonically but does not exhibit power-law scaling [70]. 

Fig. XV-4. Schematic drawing of four streptavidin molecules bound to biotinylated lipid in a monolayer above heavy water. The scattering length density for neutron reflectivity is shown at the side. (From Ref. 30.)...

A unique but widely studied polymeric LB system are the polyglutamates or hairy rod polymers. These polymers have a hydrophilic rod of helical polyglutamate with hydrophobic alkyl side chains. Their rigidity and amphiphilic-ity imparts order (lyotropic and thermotropic) in LB films and they take on a F-type stmcture such as that illustrated in Fig. XV-16 [182]. These LB films are useful for waveguides, photoresists, and chemical sensors. LB films of these polymers are very thermally stable, as was indicated by the lack of interdiffusion up to 414 K shown by neutron reflectivity of alternating hydrogenated and deuterated layers [183]. AFM measurements have shown that these films take on different stmctures if directly deposited onto silicon or onto LB films of cadmium arachidate [184]. 

In neutron reflectivity, neutrons strike the surface of a specimen at small angles and the percentage of neutrons reflected at the corresponding angle are measured. The an jular dependence of the reflectivity is related to the variation in concentration of a labeled component as a function of distance from the surface. Typically the component of interest is labeled with deuterium to provide mass contrast against hydrogen. Use of polarized neutrons permits the determination of the variation in the magnetic moment as a function of depth. In all cases the optical transform of the concentration profiles is obtained experimentally. 

All the techniques discussed here involve the atomic nucleus. Three use neutrons, generated either in nuclear reactors or very high energy proton ajccelerators (spallation sources), as the probe beam. They are Neutron Diffraction, Neutron Reflectivity, NR, and Neutron Activation Analysis, NAA. The fourth. Nuclear Reaction Analysis, NRA, uses charged particles from an ion accelerator to produce nuclear reactions. The nature and energy of the resulting products identify the atoms present. Since NRA is performed in RBS apparatus, it could have been included in Chapter 9. We include it here instead because nuclear reactions are involved. 

Though a powerfiil technique, Neutron Reflectivity has a number of drawbacks. Two are experimental the necessity to go to a neutron source and, because of the extreme grazing angles, a requirement that the sample be optically flat over at least a 5-cm diameter. Two drawbacks are concerned with data interpretation the reflec-tivity-versus-angle data does not directly give a a depth profile this must be obtained by calculation for an assumed model where layer thickness and interface width are parameters (cf., XRF and VASE determination of film thicknesses. Chapters 6 and 7). The second problem is that roughness at an interface produces the same effect on specular reflection as true interdiffiision. 

Figure 1 Schematic diagram of the neutron reflectivity measurement with the neutrons incident on the surface and refiected at an angle 6 with respect to the surface. The angie 62 is the angle of refraction. The specimen in this case is a uniform film with thickness d, on a substrate.

Important neutron reflection parameters for some common materials. 

The measurements of concentration gradients at surfaces or in multilayer specimens by neutron reflectivity requires contrast in the reflectivity fiDr the neutrons. Under most circumstances this means that one of the components must be labeled. Normally this is done is by isotopic substitution of protons with deuterons. This means that reflectivity studies are usually performed on model systems that are designed to behave identically to systems of more practical interest. In a few cases, however (for organic compounds containing fluorine, for example) sufficient contrast is present without labeling. 

Neutron reflectivity measures the variation in concentration normal to the surface of the specimen. This concentration at any depth is averaged over the coherence length of the neutrons (on the order of 1 pm) parallel to the sur ce. Consequendy, no information can be obtained on concentration variadons parallel to the sample surface when measuring reflectivity under specular conditions. More imponantly, however, this mandates that the specimens be as smooth as possible to avoid smearing the concentration profiles. 

Neutron reflectivity is ideally suited to this problem, since concentration profiles can be resolved on the nanometer level and since, for an infinitely sharp interface, Rkjf will approach asymptotically a constant value. In addition, neutron reflectivity is nondestructive and multiple experiments can be performed on the same specimen. Figure 4 shows a plot of Rk Q as a function of bilayer of protonated... 

Neutron reflectivity provides a depth resolution of 1 nm and fills an important gap in the resolution between X-ray photoelectron spectroscopy and ion-beam techniques. In this regard, neutron reflectivity promises to play a decisive role in the investigation of solid materials. Equally important is the fact that reflectivity meas-... 

The toughness of interfaces between immiscible amorphous polymers without any coupling agent has been the subject of a number of recent studies [15-18]. The width of a polymer/polymer interface is known to be controlled by the Flory-Huggins interaction parameter x between the two polymers. The value of x between a random copolymer and a homopolymer can be adjusted by changing the copolymer composition, so the main experimental protocol has been to measure the interface toughness between a copolymer and a homopolymer as a function of copolymer composition. In addition, the interface width has been measured by neutron reflection. Four different experimental systems have been used, all containing styrene. Schnell et al. studied PS joined to random copolymers of styrene with bromostyrene and styrene with paramethyl styrene [17,18]. Benkoski et al. joined polystyrene to a random copolymer of styrene with vinyl pyridine (PS/PS-r-PVP) [16], whilst Brown joined PMMA to a random copolymer of styrene with methacrylate (PMMA/PS-r-PMMA) [15]. The results of the latter study are shown in Fig. 9. 

The interface properties can usually be independently measured by a number of spectroscopic and surface analysis techniques such as secondary ion mass spectroscopy (SIMS), X-ray photoelectron spectroscopy (XPS), specular neutron reflection (SNR), forward recoil spectroscopy (FRES), scanning electron microscopy (SEM) and transmission electron microscopy (TEM), infrared (IR) and several other methods. Theoretical and computer simulation methods can also be used to evaluate H t). Thus, we assume for each interface that we have the ability to measure H t) at different times and that the function is well defined in terms of microscopic properties. 

Significant experimental support for these relations and the minor chain repta-tion model has been obtained from neutron reflection and SIMS experiments using specially deuterated polymers... 

Figs. 7 and 8 respectively show the ripples obtained by SIMS and neutron reflection during welding of HDH/DHD interfaces. Its interesting to note that all dynamics models predict ripples since in general, the chain ends move faster than the chain centers. However, their shape, amplitude and time dependence provide a... 

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