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Microstructural characterization of polymeric materials by small angle neutron scattering.


Neutron investigations have recently become an increasingly significant probe across a wide range of disciplines, revealing important properties about materials, and components of industrial interest. The basic principles of the analysis of nanoscopic defects in solids (e.g., microphase inclusions, atomic clusters formed by precipitation) were designed in early period of X-ray and neutron small-angle scattering technique (SAXS, SANS; small angle neutron scattering) development [1-3]. The SANS peculiarity, with respect to other investigation techniques, is the possibility of giving full information down to ~[Angstrom] (0.1 nm) dimensions, in a nondestructive way for deep penetrating radiation, about the microphysical structure of the materials subsurface [4].

SANS, further to other techniques, allows the true and full characterization of various materials on the micro- and nanoscale. The small energies and the weak--but not negligible--interaction of neutrons with matter means SANS is a nondestructive technique. The sample, thus, can be studied in situ or measured any number of times after either further usage or heat treatment. SANS, averaging over a macroscopic sample volume provides information with high statistical accuracy. The considered technique allows investigating various materials such as porous media, polymers, solutions of micelles, membranes, ceramics, and metals; moreover, it consents to determine void sizes and their distributions in porous media as well as to investigate particle agglomeration and pores evolution during the sintering process. SANS is also useful for the understanding of thermodynamics of two-phase systems [5].

The investigation of the nanoscale defects by SANS seems to represent a necessary step to develop scientifically based advanced technology of industrial polymers. A SANS characterization can concern the bulk polymers structure, especially regarding nanopores, microcracks, and their arrangement (grouping) in the polymer matrix. This allows estimating the invisible total internal surface of nanopores and cracks responsible for the material fracture by mechanical loading.

The structure of macromolecules in solution, as usual, can be investigated using isotopic substitution (hydrogen [right arrow] deuterium) for polymer or solvent that provides a high contrast in scattering between polymer and surrounding medium. Such a substitution, often, is not possible for industrial polymers in the bulk (e.g., in polymeric networks). The neutron-scattering experiments, in this situation, should be performed with protonated polymers where the contrast of some structural elements (defects) is determined by the coherent scattering length density of material. For example, the bulk protonated polyurethane possesses the magnitude of coherent scattering length density [B.sub.H] = 1.7 x [10.sup.10] [cm.sup.-2] against the three times higher value of [B.sub.D] = 5.2 x [10.sup.10] [cm.sup.-2] for a fully deuterated polymer. It means that the coherent scattering from the protonated polymer will be smaller by an order than that for the deuterated analogue, and we have to eliminate carefully the incoherent background from hydrogen. The latter can be separated in total scattering intensity by using neutron-polarization analysis [6].

Various examples exist, demonstrating the usefulness of SANS in the study of polymers. Nanostructural investigations have been carried out by SANS into various polymers (polybutyl acrylate mini-emulsions of particle sizes, methacrylate/methyl-methacrylate copolymer samples, etc.), showing significant SANS peaks and confirming the feasibility of the adopted technique [7].

Several samples of ternary mixtures of d-polystyrene (PS), polymethylmethacrylate (PMMA), and the parent diblock copolymer, PS-b-PMMA, were analyzed by SANS with the aim to determine whether a microemulsion is created upon dilution and what are its properties [8].

A SANS study of aqueous solutions of a PMMA and polyethyleneoxide (PEO) symmetric block copolymer was also performed obtaining useful information on the aggregation number and solution of PEO groups [9]. Recent progress has been made, in fact, in analyzing block copolymer systems and complex polymer blends adopting SANS, which can provide insight into static phase behavior and polymer conformation [10]. A clear overview of the application of SANS to the study of multiphase polymer systems can be found in Ref. [11], while a useful review is represented by Ref. [12].

In this article, we present a short theoretical background for SANS applications to polymeric materials. We describe a typical approach and model experiment with data evaluation for the featuring of measured polyurethane material. In the last part of the article, a particularly new application is presented by investigating of changing physical properties in a microturbine polymeric material.


Theoretical Bases

The considered technique deals with elastic and coherent scattering, the scattered intensity I(q) being measured as a function of the incoming neutron flux [PHI], the instrument specific constant A, the transmission of the sample T, and the volume of the sample V:

I([lambda], Q) = [PHI][ATV.sub.sample] [[d[SIGMA]]/[d[OMEGA]]] + bg (1)

where [lambda] is the neutrons wavelength, and Q is the momentum transfer:

Q = 4[pi] sin([theta]/2)/[lambda] (2)

being [theta] the scattering angle. Finally, bg is the instrumental background and [SIGMA] is the total area of the interface per unit volume of the sample [5, 13]. d[SIGMA]/d[OMEGA] is the so-called form factor F(Q), which contains information about the scattering particles of the sample. The scattering particles are nanosized inhomogeneities in the studied material, for example, micelles, pores, nanocracks, and precipitates. The form factor, thus, can be expressed with the characteristic size of the scattering particle, and two approaches are generally used. In the low or so-called "Guinier region" (Q[R.sub.g] [less than or equal to] 1), the behavior of the scattering intensity can be written with the Guinier expression for all shapes of noninteracting scatterers:

F(Q) = [K.sup.2] [V.sub.particles.sup.2] exp(-[Q.sup.2] [R.sub.g.sup.2]/3) (3)

where [R.sub.g] is the radius of gyration of each individual scatterer and V is the total volume of the scattering particles per unit volume. K is a dependent factor of the material and it is often called the contrast between the embedding medium (or matrix) and the scattering object. An important feature of Eq. 3 is that [R.sub.g] can be determined even if I(q) is known only in arbitrary units.

A different approach can be used in large Q regions (Q[R.sub.g] [greater than or equal to] 4). The Porod law describes this behavior as follows:

F(Q) = [K.sup.2] [[2[pi]A]/[Q.sup.4]] + bg (4)

where A is the total area of the interface per unit volume of the sample [5, 13]. See Refs. [13-17] for a detailed treatment of the theoretical bases.


SANS Investigation of Monoethylene Glycol-Based Polyurethanes

A SANS investigation has been performed of various polyurethane samples changing in chemical composition and technology, obtained from a mixture of: MDI (4-4' methylene diphenil isocyanate), polyester resins (from adipic acid and glycols), MEG (monoethylene glycol), TEDA (triethylendiamine), and 1,4-diazabicyclooctane and TEA (Tri Ethanol Amine) as catalysts, Dabco DC-193 as surfactant, and water as blowing agent. Polyurethanes are polymers containing the urethane linkage in their backbone chain, and they are made by reacting di-isocyanates with di-alcohols. The di-alcohols, sometimes, are replaced with a diamine, and the obtained polymer is a polyurea, because it contains a urea linkage, rather than a urethane linkage. Since polyurethanes chains easily form hydrogen bond, these polymers can be very crystalline, so they are frequently used to compose block copolymers (having the properties of thermoplastic elastomers) with soft rubbery polymers. The same material is largely adopted in different industrial sectors (e.g., automotive, interior design, footwear, etc.). A single surfactant is generally adopted, and novel surfactants are currently under development, reducing densities while maintaining physical properties. The combination of two different surfactant chemistries, in the recent years, has improved dimensional stability, surface characteristics, and, in general, physical properties of the final product. A complicated structural organization of polyurethanes, containing crystalline and amorphous domains, meanwhile, may influence strongly on material functional properties. This leads under particular conditions (e.g., mechanical and thermal loading, aging) to the material degradation especially in the presence of some nanodefects even in fresh-prepared bulk polymer.


The SANS diffractometer of the Budapest Research Reactor (BRR) was adopted for a feasibility investigation of the considered material. This device covers a Q-range 0.004-0.5 [[Angstrom].sup.-1], which allows the density composition and magnetization fluctuations in materials to be measured on a length scale of 10-1000 [Angstrom]. The neutrons are produced by a 10 MW reactor and guided to the sample by super-mirrors. The wavelength can be varied between 3.4 and 23 [Angstrom] with the aid of a multidisc-type velocity selector. The beam intensity is monitored by a 64 x 64 pixel (each of 1 x 1 [cm.sup.2]) two-dimensional position sensitive detector filled with [BF.sub.3] gas. The measurement was carried out using a neutron wavelength of 9.14 [Angstrom]. The sample to detector distance of 5.6 m sets Q to values ranging from 0.006 to 0.04 [[Angstrom].sup.-1]. The samples (size 15 x 15 x 2 [mm.sup.3]) have been cut-off from the bulk material. Figure 1 shows a SANS pattern, and clearly represents the existence of two sharply different scattering objects. These are nanoscale entities resolved by conventional SANS having middle resolution.

Additionally, one can see the existence of large-scale objects (bubbles, size by 1-2 order in magnitude higher than this one for nanodefect), which scatter to the low-q region and have to be studied separately using very high resolution. A SANS full investigation was carried out using the double-crystal diffractometer DN-2 at NPI Rez that allows for measurements with momentum transfers magnitude Q tunable in the range 0.002-0.2 [[Angstrom].sup.-1], corresponding to the real size range of about 0.01-1 [micro]m. The resolution of the same instrument can be properly tuned by elastic bending of the monochromator and analyzer crystals.


Unwanted bubbles are created in the considered material, during the forming and the expansion of the mixture because of the chemical reaction, which are also present on the surface of the final product. The high resolution SANS [18, 19], having less Q value than small angle X-ray scattering (SAXS)--0.005 [[Angstrom].sup.-1], or less, if necessary--allows investigating larger sizes of objects than SAXS. In particular, while SANS allows to detect H inside the bubbles, SAXS detects only N and C. The bubbles sizes can be different, because of the molecular orientation of their surrounding (internal surface effect). Both techniques are, in this case, complementary and they can give useful information on the bubbles structure. The spatial distribution of the bubbles in the bulk is homogeneous as the external surface does not represent the inner material of the sample. A comparison can be done between bubbles and cracks, in particular, considering the Porod region [20], thus giving useful information on the molecular orientation around bubbles and cracks, and on their implications in mechanical properties.

In Fig. 2, a model is represented of the considered polyurethanes. The crystalline zone is based on "urethane group" formed by the reaction of MDI (methylene di-isocyanate) and MEG. More crystal zones are present, more hard is the polyurethane, and the homogeneity of such crystal zones is important to determine the mechanical characteristics of the material. The amorphous zone has a joining action between crystal zones. The bubbles, according to optical and neutron high-resolution data, having a size ranging from 1 to 100 [micro]m, can be closed or open, and they change depending on mixing procedure, catalysis, temperature, and material type. The crystal zone morphology is almost entirely ignored: a moderate irregularity of form and dimension can be imagined, however, because the crystallization phase happens very quickly and the mixing of the two components, often, is not constant for the whole volume. Also for this motive, in some cases, in the polyurethane--more often in the thermoplastic polyurethane (TPU)--some reassessment thermal treatments are tried, in which morphology changes and consequently the characteristics of the material vary. It is difficult to establish the dimensional scale (~100-5000 [Angstrom]), especially for the superior limit, while the minimum dimension (~100 [Angstrom]) is relatively certain. The number and dimensions distribution probably deals with an only Gaussian, at least for the number, and there can be perhaps more Gaussians concerning the dimension. The bubbles morphology is supposed to be rather regular regarding the form (i.e., approximately spherical). The dimension depends on many factors, and the most important being clear is the sample density. The dimension, for the analyzed samples having intermediate density, can vary indicatively in the range of 1-100 [micro]m. The distribution of the bubbles number and dimensions is supposed to be rather regular, having only Gaussian, also because opportune additive is used for the purpose.

The neutron scattering, as it will be shown in the following data treatment, enables us to visualize polymer chains in the bulk as a result of contrast between small-size ordered (quasi-crystalline) domains and amorphous matrix around. The neutron-scattering intensity distribution adheres to the model function:

I(q) = [I.sub.or] exp[??]-([r.sub.G]q)[.sup.2]/3[??]{1 + [epsilon] sin(qL)/(qL)} + [I.sub.R] exp [??]-([R.sub.G]q)[.sup.2]/3[??] + B. (5)

The first term of Eq. 5 is the contribution of small domains (gyration radius [r.sub.G]). Their spacing L ~ d is close to the diameter of such a particle d = 2[r.sub.G](5/3)[.sup.1/2] (in spherical approximation). The parameter [epsilon] shows the probability of a particle to be coupled with another one. The second term represents the large scale correlation in positions of domains, i.e., their linkage to a coil having gyration radius [R.sub.G] = n[L.sup.2]/6 (in Gaussian approximation for a polymer chain) where n is the number of "beads" in this "necklace." The third term is the incoherent background from hydrogen in polymer. These fitting parameters are listed in Table 1.

Using the gyration radius of elementary crystalline domain, we obtain its diameter (in spherical approximation) d = 6.7 nm. Really, it is close to the neighboring domains characteristic spacing L ~ 8.4 nm, and the difference (L - d) ~ 1.7 nm corresponds to the minimal length of linking chain fragment. The probability of a domain to be bonded with neighboring entity, as we found from scattering data, is close to [epsilon] ~ 2/3. The most of domains, thus, participate in the visualization of their chains being the objects with gyration radius [R.sub.G] ~ 18 nm. The chain-like character of this object is confirmed by the parameter [D.sub.F] = [ln([I.sub.R]/[epsilon][I.sub.or])]/[ln([R.sub.G]/[r.sub.G])] ~ 1.9 that shows the relationship between the object mass and size. The value of [D.sub.F] is very close to the parameter [D.sub.F] = 2 for Gaussian polymer coil composed of elementary units (size [r.sub.G]). Thus, each chain is like a sequence of dense "balls" beaded on the guiding thread (Fig. 3). The ratio [I.sub.R]/[epsilon][I.sub.or] ~ [n.sub.C] ~ 40 represents the number of units in a chain. To verify this conclusion, we calculated the gyration radius of a chain consisting of [n.sub.C] units (each length L): [R.sub.G] = [n.sub.C][L.sup.2]/6 ~ 21 nm. The estimate, indeed, is in agreement with the experimental magnitude. Therefore, we have to state the fact of visualizing the polymer chains in solid (dense) polymer matrix as a result of their local contrasting by locally ordered domains pierced by them. We observed mesoscopic objects (pores, bubbles) having a diameter ~1 [micro]m, except of these small-size and middle structural elements. The analysis of high resolution SANS data has shown the eligibility of a three-mode spherical approximation to describe the scattering from the bubbles imbedded into the polymer bulk. The patterns with fitting functions are displayed in the Porod form: [q.sup.4]I(q) vs. q (Figs. 4 and 5). In this way, we look for the structural peculiarities masked usually by a fast decrease of the particles' form factors. The following model function was applied for the intensity:


I(q) = [summation][I.sub.oi] [[PHI].sup.2](q[R.sub.i]) (6)


where i = 1, 2, 3 and the parameters [I.sub.oi] ~ [K.sup.2][C.sub.i][V.sub.i] depend on the density of polymer coherent scattering length K, bubbles volume fraction [C.sub.i], and volume [V.sub.i] = (4[pi]/3)[R.sub.i.sup.3] of a bubble with radius [R.sub.i]. Taking into account the form factor of a sphere,

[PHI](qR) = 3[sin(qR) - (qR) cos(qR)]/(qR)[.sup.3] (7)

we obtained the Porod approximation:

[q.sup.4]I(q) [approximately equal to] 2[pi] [summation][S.sub.i]{2[sin(q[R.sub.i])/(q[R.sub.i]) - cos(q[R.sub.i])][.sup.2]} (8)

where [S.sub.i] is the total area of the surface for a fraction of bubbles.

In Fig. 4, we present the most specific patterns for the first sample. The other samples' scattering curves can be observed in Fig. 5, where only the fitting functions are plotted. As we found from the scattering data, the sample 1 with saddle-like scattering picture possesses mainly large-scale bubbles. The following changes in chemical composition and technology produce a lot of small bubbles that is evident from highly increased intensity at q ~ 0.01 [nm.sup.-1]. In this series of polymers, the sample 4 is the most imperfect. We have to stress that, specifically, the interface area plays the most important role as a factor defining polymer material's strength and durability. In Fig. 6, the contributions of fractions to the total interface are given for samples of different technologies of polymer manufacturing.

Summarizing the high-resolution SANS findings, we can conclude that the variation in chemical composition and technology of polymers causes the bubbles' radii decrease, and the small fractions dominate giving a large contribution to the interface area. These results can really serve to control and predict the functional properties of polymers, which strongly depend on the size and amount of defects and especially on their total area detected by SANS. Thermal-neutron radiography and fast neutron gauging measurements techniques have been adopted, moreover, to evaluate the feasibility of detecting voids in polyurethane and determining its uniformity, concerning bigger size bubbles [21]. Concerning the investigation zones, to appraise the different crystallinity, for this case, it is useful to take into account that zones near the external skin should have smaller and more numerous bubbles, vice versa in zones away from the wall.


SANS Investigation of Organic Resin Microturbines

A particularly new application of SANS concerns the microturbine, which is a completely innovative device for the first original study of either gas or airflow using the low pressure-head features of axial-flow on the micro-scale, and it is currently being developed from both a scientific and industrial point of view [22]. A SANS study has been recently performed on microturbines produced using excimer laser fabrication with mask-dragging to profile optimally smooth airflow contours [23]. The adopted instrumentation, also in this case, has been the SANS diffractometer at BRR. The used neutron wavelength was [lambda] = 9.14 [Angstrom]. The sample to detector distance of 5.6 m has set Q to values ranging from 0.006 to 0.04 [[Angstrom].sup.-1]. The constitutive material for the microturbine preforms and hence finished microturbines is an organic resin solution that forms a negative photo resist including an epoxy resin organic solvent and [gamma]-butyrolactone. The resin constituents are epoxy resin (35-75%) and [gamma]-butyrolactone (22-60%) mixed with triarylsulfonia/hexafluroantimonate salt and propylene carbonate (1-5%). Such substrate material has been primarily exposed to UV to prepare it for oven drying and final hardening (curing/polymerization) to make the preforms for the microturbines. In the semitransparent hardened state, as for the finished microturbines, the material consists of C--C--O in the form of repeating triangles. The O occasionally forms OH when heated, which joins with other hydroxyl molecules to form water. Figure 7 shows a microturbine original rotor preform, while Fig. 8 shows a SANS curve obtained for the same sample.



The Porod model was used (Eq. 4), in which the B parameter can provide information about the total scattering surface of the sample. The p parameter had the value of 4.96 [+ or -] 0.51, and this is the case where there are no sharp interfaces, but rather a gradual transition (like a smooth composition gradient) between the phases. More distinctive graphical differences have been obtained by using a lower Q range investigating microturbine samples produced under condition of widely varying polymerization and wear (usage). The adoption of smaller values for Q in the Guinier region (Eq. 3) has also allowed the averaged sizes of the inhomogeneities to be found.


A crosslinked preform microturbine has also been tested after excessive UV exposure, and others two after differing temperatures and durations of thermal baking up to 300[degrees]C (the maximum temperature before crosslink degradation). The tests used the best curing data and constituent composition percentages of the substrate of each test turbine. Comparative investigations of new, aged material, and the material surrounding the defects, have been performed, successively, to isolate all the diverse defects measurable in the material. SANS could also be used for the detection of long-term defect orientations in the material by placing a given load on a separate piece of material (a 1 x 10 x 20 [mm.sup.3] parallelepiped) for a few days (seven days maximum), and changing the temperature from room temp to 300[degrees]C. The SANS result could help to produce the best curing times for future turbine preforms and finished turbines. This would better identify their structural strength limits and allow them to be selected for their optimum mainstream applications, e.g., airspeed conditions or the power generation requirements of handheld devices.


Industrial applications of SANS have been described, showing the usefulness of this neutron technique in the polymers field. In particular, monoethylene glycol-based polyurethanes, and epoxy resin (35-75%) and [gamma]-butyrolactone (22-60%) mixed with triarylsulfonia/hexafluroantimonate salt and propylene carbonate (1-5%) microturbines preforms were successfully investigated by SANS, obtaining valuable information either for the materials improvement or for the control and prediction of the functional properties. The main features of the nano- and microstructures in polyurethanes have been found by SANS. This enables us to conclude that a fine variation in chemical composition and technology of polymers causes the substantial bubbles' radii decrease, so that the small fractions dominate giving a large contribution to the interface area. The results really allow to control and predict the functional properties of polymers, which strongly depend on the size and amount of defects and especially on their total area detected by SANS.

Various other examples exist, concerning polymers characterization by SANS, which are reliably published in open scientific literature.


The authors acknowledge Dr. L. Incicco and Dr. L. Rosta for useful discussions.


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Massimo Rogante, (1) Vassili T. Lebedev (2)

(1) Rogante Engineering Office, NDT, Contrada San Michele, 62012 Civitanova Marche, Italy

(2) Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg, Russia

Correspondence to: Massimo Rogante; e-mail:

Contract grant sponsors: BRR and NPI Rez.
TABLE 1. Macromolecule in solid polymer matrix: fitting parameters for
the model of "necklace".

[I.sub.or] (a.u.) 6.67 [+ or -] 0.15
[r.sub.G] (nm) 2.60 [+ or -] 0.04
[epsilon] 0.61 [+ or -] 0.06
L (nm) 8.39 [+ or -] 0.24
[I.sub.R] (a.u.) 153 [+ or -] 71
[R.sub.G] (nm) 17.8 [+ or -] 1.4
B (a.u.) 2.28 [+ or -] 0.02
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Author:Rogante, Massimo; Lebedev, Vassili T.
Publication:Polymer Engineering and Science
Article Type:Technical report
Geographic Code:1USA
Date:Aug 1, 2007
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