Neutron concentration profiles

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]. 

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. 

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. 

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... 

Fig. 4.8 Micelle volume fraction () versus polymer concentration at different temperatures for solutions of PEO26PPO39PEO26 in D20 (Mortensen 1993a). 4> was obtained from fits of the hard sphere Percus-Yevick model to neutron scattering profiles (see Fig. 3.9). At high concentration the asymptote = for hard sphere crystallization is reached.

Concentration profiles of PS graft chains were studied by a neutron reflection method [101]. Graft chains consisted of end-functionalized deuterated polystyrene. Although the measurement was not performed under the true equilibrium conformation, the observed metastable state was in good agreement with that predicted from the SCF theory. The kinetics of the penetration of graft chains into the polymer matrix was also investigated. 

The specular reflectivity of neutrons, like the analogous light or X-ray reflectivity, from a surface or interface provides information about the neutron refractive index gradient or distribution in the surface region and in a direction orthogonal to the plane. This can often be simply related to a composition or concentration profile in the direction orthogonal to the surface, to provide directly information about adsorption and the structure of the adsorbed layer. 

Fig. 5. Concentration profile inside a grafted PDMS layer swollen by a good solvent (octane). The molecular weight of the grafted chains is 92 kg mol-1 and the surface density in the layer is a=0.011. The full line is the profile determined by neutrons reflectivity. The dotted line is the SCF result of Zhulina et al. [52] calculated for a surface density o=0.011 and an excluded volume parameter v=0.8 a3 (a is the size of the monomer, determined to be a 0.5 nm by the slope of the scaling line in Fig. 2).

Fig. 9. Concentration profiles determined by neutron reflectivity for three end grafted PDMS layers in contact with PDMS melts. The molecular weight of the grafted chains is mN= 92 kg mol-1 for all the layers. Curve a surface density in the layer o= 0.011, molecular weight of the melt mP=90 kg mol-1 curve b o=0.01, mP=360 kg mol-1 curve c o= 0.015, mP= 17 kg mol-1. The layer contracts more and more when exposed to a melt of larger molecular weight. In all cases the melt chains penetrate down to the surface, as demonstrated by the volume fraction of end grafted chains which always remains much lower than one...

Fig. 10. Concentration profile as determined by neutron reflectivity for two irreversibly adsorbed layers in contact with a PDMS melt. The molecular weight of the surface chains is 92 kg mol-1 and is identical to that of the melt. In both cases <7=0.02. The full line corresponds to an adsorbed layer made with deuterated chains, in contact with a hydrogenated melt, while the dotted line corresponds to the reverse situation (hydrogenated surface chains, deuterated melt). The clear difference between the two profiles is a demonstration of a preferential interaction of the hydrogenated chains with the surface compared to the deuterated one...

Neutron depth profiling has been applied in many areas of electronic materials research, as discussed here and in the references. The simplicity of the method and the interpretation of data are described. Major points to be made for NDP as an analytical technique include i) it is nondestructive il) isotopic concentrations are determined quantitatively iii) profiling measurements can be performed in essentially all solid materials, however depth resolution and depth of analysis are material dependent iv) NDP is capable of profiling across interfacial boundaries and v) there are few interferences. 

NMR spectroscopy shares its ability to provide information about the elementary steps of diffusion and the resulting concentration profiles with other spectroscopic techniques like IR [45,46], neutron [47-49] and dielectric [50, 51] spectroscopy. With respect to its ability to follow molecular diffusion paths between himdreds of nanometers up to hundreds of micrometers, however, it is unique. Measurements of this type are based on the apphcation of an inhomogeneous magnetic field. In the technique, being so far the most... 

If the thermal neutron capture takes place beneath the sample surface, the energy loss of charged particle stopping in the sample can be used to obtain information about the Li or B concentration profile (Fig. 13.3). The amount of energy loss is related to the distance that the charged particle has travelled within the specimen. 

We remarked above that the force-distance curves do not appear to be particularly sensitive to the shape of the concentration profile normal to the surface used in the theoretical calculations. Evidently, it would be of value to obtain the concentration profile simultaneously with determination of the force-distance data. Cosgrove et al. (1995) have described a modified surface force apparatus that allows neutron reflectometry data to be collected figure 3.32 is a schematic diagram of the apparatus. 

The self-consistent field theory also allows one to calculate the segment density profiles of each homopol)maer and each block of the copolymer. Forward recoil spectrometry is unable to resolve the details of these concentration profiles — the apparent finite width of the copolymer layer shown in figure 6.6 is entirely due to the instrumental resolution - but from neutron reflectivity measurements on a series of differently labelled samples one is able to extract all four segment density profiles. Figure 6.20 shows an example of this, for a styrene/methyl methacrylate copolymer at an interface between polystyrene and poly(methyl methacrylate). 

The reptation dynamics and the interface structure relations in Table 2 have been demonstrated experimentally by a series of interdiffusion experiments with selectively deuterated HDH/DHD polymer interfaces using dynamic secondary ion mass spectroscopy (DSIMS - see Secondary ion mass spectrometry) and neutron reflectivity. The scaling laws for interdigitation and the complete concentration profiles for Rouse and reptation dynamics have also been calculated. ... 

Fig. 5.25. Neutron scattering profiles for L3 samples at different concentrations, with reduced units (j)I[q) is given as a function of q/(j). The identity of the profiles confirms the idea of scale invariance...

In addition to NAA, neutrons are widely used in prompt radiation analysis for the determination of concentration and spatial distribution of elements in different matrices. For example, a track-etched detector (LR-115, Makrofol KG, CR 39, mica) placed on the polished surface of a sample is irradiated with fast or thermal neutrons then etched with a suitable chemical to deduce the concentration profiles from the track distributions. This method can also be used for the detection of suspended and dissolved U, Th, and Pu in water by (n,f) reactions N in polymers by the N(n,p) C reaction B and Li in semiconductors or glasses by the B(n,a) Li and Li(n,ot) H reactions, respectively. For the detection of fission fragments the use of mica is recommended. 

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