Keywords

15.1 SAS Data Analysis

There are many methods of modeling and interpreting SAS data. Figure 15.1 shows an overview of the most common techniques used ab initio to interpret the data gathered in structural studies. Starting from the common Porod (log-log) plot most often encountered from reduced data, the first of the model-free analyses is the Guinier approximation used to estimate the radius of gyration, R g , and generalized particle form. This is a common first step for data on drug delivery carriers in the 50–200 nm size range. The Guinier range is the region of q such that qR g <1.3 and the q n dependency of the form factor in this range of the log-log plot describes in general the morphology of the scattering body with n = 0, 1, and 2 representing globular (spherical), rod-like, and lamellar (flat) morphologies, respectively (Schnablegger and Singh 2013). It is important to note that several assumptions of ideality must be taken in this analysis. First, since the intensity of scattering I as a function of the scattering vector q is a product of two factors, following Eq. 15.1,

$$ I(q)=P(q)\ S(q) $$
(15.1)

where P(q) and S(q) are the form and structure factors, respectively, sufficient dilution must be achieved such that the form factor can be analyzed independently of the contribution from the structure factor. The reason for this is that the scattering contribution from the structure factor due to interparticle interactions and arrangement in diluted systems is minimal such that it tends to approach unity and the intensity therefore becomes equal to the form factor (Guinier and Fournet 1955). Guinier’s approximation is made in reference to the form factor with sufficient dilution being assumed. This is a particularly important consideration for drug delivery carriers that exist as insoluble suspensions. Secondly, monodispersity of the particles is a requirement for the most accurate approximation, as small polydispersities affect the slope of the scattering curve significantly at very small q. With these assumptions fulfilled, an expansion of Guinier’s original theory (Glatter and Kratky 1982) takes the form of

$$ I=I(0)\exp \left(\frac{-{R}_g^2{q}^2}{3}\right) $$
(15.2)

where I is the scattering intensity. Plotting ln(I) vs q 2 therefore gives the R g from the slope of the fit line once it is extrapolated to the intercept I(0).

Fig. 15.1
figure 1

Different regimes in scattering curves with the relevant structural information defined for each method of analysis

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The next region in the log-log plot encompasses the intermediate values of q between the Guinier range and Porod range (qR g >3). Indirect Fourier Transform (IFT) and Kratky analyses both produce useful plots from this region with the IFT providing a Pair Distance Distribution Function (PDDF). The PDDF represents a distribution of the intraparticle distances elucidated by the scattered radiation. The shapes produced by this plot are characteristic of specific form factors and again present model-free approximations as well as another representation of the particle size with the largest intraparticle distance(s) being the distance from one terminal edge of the particle to another (Schnablegger and Singh 2013). This distance is found at the end of the rightmost shoulder for spherical particles and other shapes have multiple points at which critical dimensions are represented. Figure 15.2 shows a representation of various PDDF plot shapes with their corresponding morphologies and size indications.

Fig. 15.2
figure 2

Determination of critical dimension and shape from PDDF plots (Schnablegger and Singh 2013) (Reprinted with permission from Anton Paar GmbH)

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Flowing from the same region of q is the Kratky plot of Iq 2 vs q which gives insight into the conformation of polymers in solution from their mid to high q scattering. At the higher part of this q range, Gaussian coiled polymers result in scattering that follows 1/q 2 behavior and so tend to produce curves that level out in the Kratky plot. Deviation from this line-shape indicates non-Gaussian conformations, the source of which is usually interpreted by the researcher based on the sample composition. The shape of the curve in a Kratky plot can therefore be used to distinguish between stretched Gaussian coil polymers or non-ideal conformations due to attractive/repulsive forces that result in excluded volume (Hammouda 2016). For drug delivery applications involving self-assembled systems, polymer conformation can be an important piece of information.

Deeper application of this analysis in drug delivery vehicle structural research will be clear when the following is considered: if Gaussian chains result in a curve with a slow rise that levels into a plateau, self-associative forces that lead to precipitation and the formation of nano-objects are characterized by a peak in the initial region of the Kratky plot. The position of this peak is inversely proportional to the Rg (Filippov et al. 2012). Especially in systems of complex multi-component structure, such as drug-conjugated copolymers, this analysis provides detail of the solvated or structural morphology that can be focused using contrast variation techniques.

The Kratky and PDDF analysis techniques were used to probe constructs of 2-hydroxypropylmethacrylamide (HPMA) copolymers containing cholesterol moieties and doxorubicin in elegant characterizations that revealed the conformation of polymers within the nanoparticle structures as rounded cylinders (Filippov et al. 2012, 2013). Kratky analysis and cross-sectional PDDF in this case showed that the nanoparticle structure changed from Gaussian coiled coronas to more compact objects with higher excluded volume as a function of the concentration of cholesterol moieties (0–3.0 mol%) in the chain (Filippov et al. 2012). The power of modeling software and the true richness contained within scattering data can be seen in Fig. 15.3 (Kratky and PDDF) from the same study in which computational analysis yielded hypothetical shapes of the nanoparticles from cross-sectional PDDF as ellipsoids with lengths of 12.1 nm and widths of 4.6 nm.

Fig. 15.3
figure 3

Kratky (a) and cross-sectional PDDF (b) plots showing morphology and cross-sectional distances of conjugates used to compute the hypothetical structure (c) (Reprinted with permission from Filippov et al. 2012, copyright American Chemical Society)

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After the Guinier and Kratky analyses, the final type of model-free data to be obtained comes from the region of the standard scattering plot known as the Porod range where q R g >3. The slope of the q −m dependency in this region is dependent on the surface per volume according to Porod’s law and the value of m can speak about the physical properties of the surface scattered at large angles. An m value of 4 at high q is indicative of a smooth surface for spherical objects while 2 < m <4 represents scattering due to a rougher adsorbed layer (Estrela-Lopis et al. 2009). Extensive multi-slope plots, their q −m laws, and their shape implications can be found in the works of Boualem Hammouda (2010a, b, 2016). Plots built from combined concepts such as Kratky-Porod reveal even greater detail from advanced methods and will be discussed later in the chapter.

Outside of these model-free techniques there are a multitude of model-intensive approaches often used within analysis environments such as SASview, PRIMUS, and others that can fit scattering curves to relevant physical parameters. However, since scattering curves are not fingerprints, the models must be informed to avoid unreasonable parameter definitions. This is an important point for characterization of drug delivery vehicles and is one of the predominate reasons that supplementary characterizations are often performed alongside SAS. The fewer parameters that are left to float during model fitting routines, the more accurate the remaining parameters can describe the scattering curve and the better the picture that can be obtained with SAS. Modeled approaches are often used if the shape or form of the particle is known a priori; therefore data fitting approaches should start from model-free analysis before moving into precise characterization with fitting models. The workings of model fitting are not discussed in detail due to their highly specific and customizable nature. However, model analysis is still present in nearly every SAS study, as the parameters are highly relevant especially in terms of the properties of drug delivery devices. This will be seen in the following sections.

15.2 Structural Characteristics of Drugs and Drug Delivery Vehicles

15.2.1 Delivery Vehicles

15.2.1.1 Nanoparticles

Nanoparticles can be defined as nanometer-sized clusters of atoms or molecules. Nanoparticles come in many shapes and have been gaining popularity as drug delivery vehicles (Urbina et al. 2008; Mattingly et al. 2015). Owing to their small size (1–100 nm), tunable composition, and potential inclusion of metals to imbue them with fluorescent/IR/magnetic sensitivities they often have unique properties in terms of cellular uptake, bio-distribution, and reactivity to stimuli (Remant Bahadur et al. 2012). These properties also make them common candidates for SAS studies because, while other techniques can give size information, they fall short in characterizing the internal structures and interparticle interactions that make nanoparticles unique and useful for drug delivery.

15.2.1.2 Micelles

Micelles are single or dual-component nanometer-sized formations of amphiphilic molecules dispersed in a solvent, often water, that generally have spherical morphology but are not strictly limited to spheres (Biggs et al. 2007). Micelles have a core-corona architecture featuring hydrophobic cores and hydrophilic coronas when used in aqueous environments. Micelles often self-assemble in water to stabilize the interactions of the two portions of the molecule with the solvent, with reverse micelles possible in the case of hydrophobic solvents (Nunes and Car 2013; Correa et al. 2012). Block copolymers are widely utilized as micelle forming delivery devices and often include PEG paired with a less hydrophilic polymer such as poly(lactic acid) or polystyrene (Cho et al. 2006; Bae et al. 2009). SAS studies with micelles often utilize contrast variation techniques and/or selective deuteration of components to isolate them from the overall scattering in efforts to characterize their structural components (Almgren et al. 2007; Naruse et al. 2009; Smith et al. 2014).

15.2.1.3 Vesicles

Polymeric vesicles are multi-component nanometer- or micrometer-sized assemblies of amphiphilic molecules dispersed in a solvent. Vesicles are similar to micelles in terms of their components, but in contrast, form hollow spherical or worm-shaped structures with solvent trapped in the inner cavity and a hydrophobic bilayer between the core cavity and hydrophilic corona (Srinivas et al. 2013; Sauer and Meier 2004). Vesicle applications within drug delivery are often similar to those of micelles, with some systems able to switch from one morphology to the other in response to stimuli (Lagzi et al. 2010).

15.2.1.4 Multilayer Capsules

Multilayer capsules are nanometer to micron-sized polymer constructs made of ionic, hydrogen-bonded, or covalently bonded layers of polymers or other constituents (Kharlampieva et al. 2009; Kozlovskaya et al. 2009, 2012a, b; Erel-Unal and Sukhishvili 2008). Hollow hydrogel microcapsules are formed by layer-by-layer (LbL) assembly of polyelectrolytes on sacrificial particulate templates, followed by chemical cross-linking of the assembled polyelectrolyte multilayer and template dissolution (Sukhorukov and Möhwald 2007; Wang et al. 2008; Skirtach et al. 2011). LbL technology offers unique opportunities to fabricate capsules of any size, geometry, composition and thickness controlled at the nanoscale (Lvov et al. 1993; Decher 2002; Kharlampieva and Sukhishvili 2006; Lutkenhaus and Hammond 2007; Hammond 2011; Mjahed et al. 2008; Tang et al. 2006). The technique can synthetically recreate shapes and easily impart a desired elasticity and responsiveness to the thin capsule wall (Elsner et al. 2006; Lisunova et al. 2011). The capsule's wall can be easily functionalized, with an internal cavity which can be used for loading functional compounds. Unlike other competing delivery systems such as nanoparticles, liposomes, dendrimers, and block copolymer vesicles and micelles, nanothin capsules have a high loading capacity and can deliver cargo on demand in response to a stimulus (Donath et al. 1998; Caruso et al. 1998; Becker et al. 2010; Matsusaki and Akashi 2009; Tong and Gao 2008). Because of their templated construction and multilayer or hydrogel architecture, capsules have greater structural stability compared to vesicles and micelles (Liu et al. 2014; Kozlovskaya et al. 2012a, b). Their core-shell structure and potential for selective deuteration both make polymer capsules interesting candidates for SAS studies where characterization of the shell thickness, capsule morphology, or cargo in the cavity can only be determined through precise methods.

While efforts are being directed toward making drugs more selective by their structural design, at least as many efforts are aimed at developing smart carriers that can chaperone drugs that have high efficacy but limited selectivity to their intended target in the body, thus minimizing collateral damage from rogue drug molecules by releasing them in a controlled manner via biologically relevant triggers such as pH, temperature, and presence of cellular peptides (Xue et al. 2015; Liu et al. 2015; Kozlovskaya et al. 2014).

The structures of these drug carriers range from micelles and vesicles between 5 and 200 nm in diameter (Fig. 15.4) to larger constructs including capsules and gel particles in the 1–10 μm range and, although they function according to their intended purpose, researchers are often left hypothesizing about exactly what happens during response to the stimulus, release of the drugs, or sometimes even exactly what size or shape the carriers are. Due to their extremely diminutive nature, characterizing the shape and structure of a drug carrier such as a nanoparticle can be challenging without advanced techniques (Mariani et al. 2016). SANS and SAXS are among these techniques: they can probe the structures of these innovative materials to evaluate carrier’s shape and size, interior and exterior dimensions, layer spacing and stratification, interparticle spacing and interaction behaviors, and dynamic assembly with the proper experimental design and material construction (Lu et al. 2016; Fong et al. 2010; Yin et al. 2016). For instance, consider an amphiphilic molecule or polymer in D2O (Fig. 15.4). Since the scattering length density (SLD) values for the protium and deuterium isotopes of hydrogen lie on opposite sides of a spectrum of values, hydrogen-containing molecules in D2O will have an SLD that lies somewhere within this spectrum depending on the extent of solvation. A simple experimental setup such as this allows for core-corona dimensions to be modeled since the hydrophobic core will have a different extent of solvation compared to the hydrophilic corona. Selective deuteration opens many possibilities for structural characterization and methods of determining dynamic solution behaviors, fine examples of which can be seen in the works of the Lodge group (Lu et al. 2012, 2015, 2016).

Fig. 15.4
figure 4

Schematic of the internal structure of micelles (a) and vesicles (b) where hydrophobic portions of the molecule are shown as yellow and the hydrophilic portions are colored blue

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15.2.2 Pharmaceutically Relevant Structural Considerations of Self-Assembled Carriers

Besides effective delivery of drugs, there are aspects of drug behavior on the nanoscale that are important to the pharmaceutical researcher. For example, while it can be easily observed that a chemical entity once PEGylated gains water solubility (Harris et al. 2012; Veronese and Mero 2012), the conformation that clusters of the amphiphilic molecule adopt in solution has implications on how the drug will exist and act in the body.

For example, it has been shown in computational analyses that each PEG repeat unit can bind at least two water molecules which end up forming a hydrated corona around the molecule (Rissanen et al. 2014). Increased hydration due to PEG chains, however, leads to an increased entropic barrier for entering a lipid bilayer. Furthermore, this hydration increases association of Na+ ions which compounds repulsive forces between drug conjugates and cellular membranes as demonstrated by modeled computations of distance between PEGylated (~2000 Da PEG) biochanin and tetrahydroxyphenylporphyrin (THPP) drug conjugates and a modeled 1-palmitoyl-2-oleoylphosphatidylcholine (POPC) lipid bilayer (Rissanen et al. 2014). The results from these studies demonstrated that exposed hydrophobic portions of the PEG-THPP conjugates had solvent accessible surface areas (SASA) of 54–57% depending on the presence or absence of 140 mM NaCl while the PEG-biochanin conjugates had SASAs of only 41–45% in the same conditions. Higher SASA helped to locate the PEG-THPP conjugates on or near the modeled membrane, with typical distances of 0.8–1 nm from the membrane center, while PEG-biochanin conjugates more extensively wrapped with a PEG corona (lower SASA) associated more Na+ ions which prevented any association with the POPC membrane.

Stopped-flow SANS was used in a related kinetic study of the interaction of amphotericin B-sodium cholesteryl sulfate (AmB-SCS) ellipsoidal micelles (45 × 2.5 nm) with 100 nm POPC-cholesterol vesicles as model 3D membranes (Foglia et al. 2015). Incorporation of SCS into the micelle decreased the time to swell the POPC-cholesterol vesicles by 0.5 nm (indication of the interaction) to 5 s vs 25 min for SCS-free micelles. It should be clear from these illustrations how information on the sizes of the core and corona in drug conjugates and the creative use of powerful SAS techniques can significantly enhance the quality of results obtained from development research.

Size characterizations such as dynamic light scattering (DLS) can give information on the size of assemblies, but with proper sample preparation, SAS studies enable “visualization” of the core and corona with nanometer accuracy and therefore give much deeper insight into the adopted conformation of the vehicle. In fact, the interior structure of an intricate self-assembled poly-ion complex system was precisely characterized using contrast variation (CV) SAXS in a study that depicted the particle morphology as a function of the ratio of cationic to neutral repeat units in a copolymer (Sakamoto et al. 2014). This investigation elegantly used form factor analysis of SAXS curves of the copolymer dispersion in water to elucidate the morphology as micelle- or vesicle-like. In addition, CV SAXS performed in a series of 5–20% PEG/H2O solvent systems yielded electron density profiles of the vesicular structures from simultaneous model fitting of the scattering curves at different solvent contrasts. The model fitting allowed extremely precise analysis of the vesicle structure: a compact 18 nm diameter core with a 4 nm thick coronal layer and 100 nm thick hydrated shell. One of the interesting features of SAS studies such as this is the exposition of radial electron density that shows gradients of hydration. Micelles, for example, are often depicted with a strictly hydrophobic and hydrophilic region, and techniques such as DLS that reveal only size distribution cannot resolve the picture any further. However, CV SAXS and CV SANS reveal a clearer picture of the non-uniform nature of each structural component, with micelles that have interpenetrating hydrophilic polymers in the core and a shell that slowly becomes more hydrated as the polymers stretch out into the solvent.

While DLS and SAS are often complementary techniques, going from DLS to SANS characterization of the same drug-loaded micelle means going from knowing the size distribution and polydispersity of the particle to knowing such details as the intermixing of hydrophobic and hydrophilic sections when drugs are present and absent. For example, two SAXS studies on the partially benzyl esterified poly(aspartic acid)-PEG block copolymer PEG-P(Asp(Bzl)) found differing behaviors of the hydrophobic core upon loading of drug mimics of various hydrophobicities (Akiba et al. 2010; Sanada et al. 2013). Model fitting of scattering curves showed that the more hydrophobic retinoid LE540 was shown to increase the radius of the core from 5.9 to 6.9 nm when the weight % of the drug mimic in the micelle was increased from 0 to 8.3%. In analysis of a linear-linear scattering curve at high q (Fig. 15.5), the decrease of a characteristic ordering peak prompted the discovery that a decrease in ordering of the core occurred as the LE540 concentration increased (Sanada et al. 2013). This result was taken to be indicative that the drug mimic was uniformly dispersed throughout the core which interrupted the interchain ordering from the aspartate groups.

Fig. 15.5
figure 5

Linear-linear plot of decreasing ordering from LE540 displacing hexagonal chain arrangement (Reprinted with permission from Akiba et al. 2010, copyright American Chemical Society)

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In contrast, using the less hydrophobic cargo molecule tetrabromocatechol (TBC) caused no appreciable growth of the core, but anomalous SAXS showed that the TBC concentration sphere extended slightly into the hydrophilic PEG region (Akiba et al. 2010). The highly precise characterizations from both of these studies, which are uniquely available through SAS, led to the significant conclusion that the relative hydrophobicity of the cargo plays a critical role in influencing the micelle morphology, even revealing that cargo molecules may exist in both micellar regions to a small extent based on the relative hydrophobicity.

The architecture of micelles in different backbone-selective solvents is also an interesting topic that has been addressed with SANS (Alexander et al. 2014). In the investigation of grafted polyisoprene(PIP)-g-Pluronic polymers (where Pluronic is a trade name for PEO-poly(propylene oxide)-PEO triblock copolymers), the micelle architecture in solvent systems of mixed polymer selectivity (ethanol: Pluronic-selective, hexane: backbone-selective, THF: good solvent for both) was characterized to gain understanding on the solution behavior of the micelles. The contrast between deuterated solvents and hydrogenated polymers was used in model fitting to elucidate the structures. For PIP-g-P123 in 100% EtOH, fuzzy micelles with 16.5 nm PIP cores and 7.3 nm thick P123 chain coronas were formed. One hundred percent hexane did not produce stable particles, and after iterative solvent trials it was found that 40% THF/hexane was able to produce stable flower-like micelles with 6.4 nm P123 cores and 15.5 nm thick PIP loops in the corona. Although CV techniques are powerful as addressed above, intensive model analysis can sometimes provide similar results. In the case of the PIP-g-Pluronic micelles, the core and coronas were separated by their solvation densities from within model fitting analysis to provide the thicknesses.

15.2.3 Drugs

The solubility of drugs plays a key role in their behavior in and out of the body as well as in their bioavailability. For example, the loading of hydrophobic drugs into drug delivery nano-carriers is a common way to increase their water solubility but the mechanism of drug entrapment is often assumed because it is not easily characterized without precise information on the drug’s localization in the nanocarrier (Yokoyama et al. 1996).

It is clear that SAS can help illuminate the answers to these questions, but it is also used for more complex characterizations. SAS studies have been used to find the kinetics of drug release from conjugates, drug/polymer co-crystallization and association characteristics, and the relationship between conformation of formulations and their respective efficacy (Zhu et al. 2011; Paul et al. 2007; Vicent et al. 2005). For instance, time-resolved SAXS showed that the lamellar long period of 3300 Da PEG increased by 5 nm when co-crystallized with 20% benzocaine, visualized by a low q peak around 0.04 nm−1 that increased in size over 30 min (Zhu et al. 2011). After 24 h, this peak reduced to nothing as benzocaine was expelled from the PEG and the long period returned to 11.6 nm, close to the value of pure PEG of 11.4 nm. Ibuprofen at the same concentration was found to increase the PEG long period by 4.9 nm but as the drug crystallized separately, it was rapidly excluded from the PEG lamellae after 100 min.

In a separate study, the inclusion of a targeting ligand, galactosamine, on a polymer-drug conjugate was shown to drastically change its maximum tolerated dose (MTD). To evaluate the effect of the ligand on the in-solution conformation, solutions of 30 kDa 2-hydroxypropylmethacrylamide (HPMA)-doxorubicin (DOX) and HPMA-DOX-galactosamine in D2O were analyzed with USANS (Vicent et al. 2005). Fitting of Gaussian coil models to the scattering data showed that the formulation containing galactosamine had a larger Rg of 9.0 nm compared to that of the standard HPMA-DOX conjugate of 7.8 nm. While both conjugates showed the same overall antitumor activity and total release of DOX, the larger Rg of the targeted conjugate was hypothesized to be responsible for the lower MTD as it indicated a more open solution geometry which allowed greater exposure of the drug to the biological locale.

15.3 SAS Studies of Drugs and Drug Delivery Vehicles

15.3.1 Nanoparticles and Micelles

One of the caveats of inorganic and drug nanoparticle preparation is the need to stabilize the particles by attaching organic molecules or polymers to their surfaces. The choice of stabilizer obviously has significant effects on the morphology and efficacy of the drug nanoparticle agent and several studies have therefore identified relevant drug-stabilizer interactions to develop rational design approaches (Choi et al. 2013; Ghosh Chaudhuri and Paria 2012).

Detailed structural analysis of the adsorption of polymers on nanoparticles is therefore an important endeavor but is only feasible through SAS. To address this, hydroxypropylcellulose (HPC)-coated nabumetone and halofantrine particles 300 nm in size were prepared and analyzed in a CV SANS experiment to gain further understanding of polymer-drug adsorption parameters (Goodwin et al. 2013). Tabulated nabumetone and halofantrine SLDs were used to initiate CV calibration and the respective D2O/H2O ratios of 31.3 and 33.8% were found to match the drug suspensions and agree with the tabulated values. CV SANS studies in these solvent ratios therefore eliminated scattering due to the drug core from the form factor P(q) and enabled strict characterization of the adsorbed HPC corona. First, a relationship between the known Rg of free HPC of molecular weights ranging from 47 to 110 kDa and the thickness of the respective coronas was established which showed that adsorbed layers may approach thicknesses nearing the Rg (Goodwin et al. 2013). However, the adsorbed layers were found to have thicknesses below the Rg which implied that the polymers were attaching to the surface in a compacted state. For example, the Rg of 110 kDa HPC was measured to be 23.9 nm while the thickness of its nanoparticle corona layer was only 15.4 nm.

Interestingly, the molecular weight was not found to proportionally affect the layer thickness, as polymer Rg values between 16 and 24 nm (MW 47–110 kDa) resulted in layer thicknesses that varied randomly between 11.2 and 15.4 nm. This indicated that some of the lower molecular weight HPC adopted a less condensed conformation at the nanoparticle surface. This example shows how model fitting analysis can be effectively used to characterize the polymer-stabilized surface of micellar structures, but model-free analysis is a more concrete tool for analyzing scattering curves. Its use in conjunction with model fitting will be discussed in the next example.

In an investigation of DNA-coated gold nanoparticles (NPs), the effect of ionic strength on the architecture of 15-mer polythymine coated NPs (named T15) and 15-mer mixed sequence of 7 polythymine-CTCATGAG coated NPs (named T7–8) was characterized with SAXS/SANS (Yang et al. 2015b). This approach demonstrates intelligent solutions to some of the considerations of using both X-rays and neutrons. First, the X-ray scattering of coated metal NPs is dominated by the scattering due to the metal because of its much higher electron density in comparison to the organic molecules, which makes elucidation of coronal parameters such as thickness and chain conformation difficult (Von White et al. 2011). Therefore, SAXS was used to evaluate core parameters such as size and polydispersity independently; finding these values allowed fixing of those particular parameters during model fitting of SANS data, where, since neutron SLD values are not dependent on the size of the nucleus, core and corona scattering would not be highly differentiated between gold and DNA.

Guinier analysis of SANS curves at minimum q was used to find the Rg of the particles with T15 and T7–8 equaling 9.06 and 9.03 nm, respectively. These values were slightly higher than those found with DLS; this is a good place to note that the Guinier approximation, being made in the assumption of sufficient dilution (S(q) ~ 1 so I(q)=P(q)), is sensitive to interparticle interactions that give rise to structure factor S(q) scattering. In light of this, indirect Fourier transform (IFT) analysis was used to populate a pair distance distribution function (PDDF), from which the Rg values of 8.80 and 8.79 nm for the T15 and T7–8 NPs, respectively, agreed with DLS measurements.

After the addition of 0.5 M NaCl, the PDDF of T15 retained a bell shape indicative of spherical geometry but shifted to reveal an Rg value of 8.34 nm. The T7–8 sample was found to increase in size to 13.21 nm at the same salt concentration. Interestingly, at 1 M NaCl, the Rg of T15 decreased to 8.21 nm but T7–8 aggregated which resulted in separate peaks in the PDDF. DLS data confirmed the IFT indication of aggregates.

Finally, model fitting revealed a decrease in coronal thickness for T15 from 6.58 to 5.91 nm after addition of 1 M NaCl. The most interesting analysis came from this result, where the difference between the SLD of the solvated corona and solvent was found to be 3.4 × 10–7 Å−2 at both 0.5 and 1 M salt concentrations. Since the shell decreased in size, the contrast difference would be expected to increase as solvent was excluded from the DNA chain. However, a constant SLD indicated that the material density of the corona increased; in other words, the solvent density was higher in the corona than in the bulk solvent. This study is an excellent example of the extremely interesting nanoscale results that can be illuminated by well-designed SAXS/SANS experiments and model-free/modeled scattering analyses.

A final example of model-free nanoparticle analysis is the SANS study of single chain nanoparticles (SCNP) in which the gap between current efforts and the goal of synthetic, globule-state, protein-like nanomachines is demonstrated (Pomposo et al. 2014). In general, the goal of SCNP research is to produce a synthetic polymer that, by carrying out the crosslinking in such a way as to eliminate interchain crosslinks in favor of purely intrachain linkages, can adopt a compact globular state. Computer simulations and SAXS/SANS data of poly(methyl methacrylate) (PMMA) SCNPs with 20 mol% reactive groups pointed to particles in an open state. The clearest presentation of the difference between SCNPs and true compact globules is presented in a Kratky plot from this study (Fig. 15.6) which shows the PMMA SCNP curve resembling those of intrinsically disordered proteins and lacking the characteristic sharp curve of globular scattering objects. This should serve as a good example for why Kratky plots are so useful in SAS research: the Kratky plot provides quick, model-free, clear presentation of chain/particle conformation.

Fig. 15.6
figure 6

Kratky plot of the SCNPs compared to a true globular protein and various intrinsically disordered proteins (IDPs) with open solution geometries (Reprinted with permission from Pomposo et al. 2014 copyright (2014) the American Chemical Society)

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Although micelles are well established delivery candidates, structural studies are being carried out on even classic examples like poly(lactic acid)-poly(ethylene glycol) (PLA-PEG) micelles (Riley et al. 2003) and the poly(lactic-co-glycolide)-poly(ethylene glycol) (PLGA-PEG) system employed in one study to create micelle-like nanoparticles (Yang et al. 2015a). While the diameter of the particles was in the range of 186 nm from nanoprecipitation in THF/H2O as observed using DLS, information on the internal particle structure was only obtainable through CV SANS which was collected using 70 and 100% D2O in simultaneous fits (Yang et al. 2015a).

The characterization of the hydrophobic core was separated from the overall particle dimension via CV SANS which elucidated the core as a 7–9 nm PLGA sphere. The DLS and CV SANS R g values were in good agreement averaging ~98 nm for particles prepared in THF/H2O. The size results provided validation for the use of SANS to characterize these particles. A total particle R g of ~98 nm with a core sized at only 7 nm in radius would seem to suggest a micelle with a giant corona in comparison to the core. A detailed and advanced modeling of the CV SANS data was able to reveal the large 180 nm diameter particle as a hydrophilic PEG/water environment with a fractal arrangement of multiple PLGA/PEG micelles (Fig. 15.7). It should be noted that this eventual conclusion was drawn through multiple-trial fitting routines of different models when describing the assemblies as simple spherical core-shells or solid multicomponent particles did not give reasonable conclusions.

Fig. 15.7
figure 7

CV SANS on PLGA-PEG nanoparticles used to elucidate the structure as fractal micelles forming a nanoparticle (Reprinted with permission from Yang et al. 2015a, copyright American Chemical Society)

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As is often the case in SAS studies, detailed modeling is complex and iterative. For example, in one study of hexaethylene glycol monododecyl ether (C12E6) micelles prepared by simply mixing the surfactant in D2O, four separate models including rounded elliptical rod, 3-axial ellipsoid, polydisperse sphere, and ellipsoid of revolution were fit to the scattering data and all showed reasonable agreement (Gapiński et al. 2010). For each model, the calculated diffusion coefficients from the dimensions were compared to DLS and fluorescence correlation spectroscopy (FCS) results before finally agreeing on the morphology of a rounded rod with elliptical cross-section resulting in the dimensions of L = 6.8 nm, a = 2.55 nm, b = 1.95 nm.

While other characterization techniques are often used to support SAS studies, as demonstrated above, SAS is equally used to validate the results from physical characterizations such as transmission electron microscopy (TEM). For example, pixel analysis of cryo-TEM images was used to determine the coronal dimension of micelles formed from pincer-ligand end-functionalized poly(N-isopropylacrylamide) (PNIPAM) of 20 kDa in water (Patterson et al. 2013). However, to validate this method and extend the characterization, SANS curves from mixing the polymer in D2O were fit with core-shell models including a corona of radially decreasing hydration. The cryo-TEM image analysis identified the micelles as ~20 nm spheres, which agreed with DLS results. The SANS results extended this characterization to a 1–2 nm core with 18–20 nm corona. Interestingly, the core size from SANS was indicative of a fully extended C12 chain, which was consistent with the size of the end-functional pincer ligand. It should be noted that SANS is an ensemble technique; scattering from a sample represents an average of all the constituents of that sample. It therefore gives a representative picture of the size and shape of all the particles in solution, in contrast to techniques like cryo-TEM which offer direct imaging of a very localized scope. Using both techniques in parallel offers the best range of size scales and the most complete level of precision.

In a characterization of simpler PLA/PEG micelles, the PLA core could be modeled as homogenous with a constant SLD (Riley et al. 2003). However, the PEG shell was better modeled by an SLD that decreased radially from the core as the polymer became hydrated to the point of equaling the solvent in SLD. This accurate model based on contrast variation was used to show that the micelle radius increased from 16 to 54.5 nm as the ratio of PLA:PEG repeat units increased from 3:5 to 45:5 and that the thickness, structure, and density of the PEG layer depended on the same parameter. CV SANS was used to isolate the core parameters from the overall scattering by subtracting the shell from the overall size. In the case of the PLA/PEG micelles, different solvent ratios and pure polymers were scanned as building blocks for the CV analysis (Fig. 15.8).

Fig. 15.8
figure 8

CV SANS on mixed solvents showing the range of SLDs obtainable and the scattering due to PLA(D)-PEG 15:5 micelles at (a) 100% D2O, (b) 80% D2O, (c) 65% D2O (Reprinted with permission from Riley et al. 2003, copyright American Chemical Society)

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It should be noted, however, especially considering these successful characterizations through CV SANS, that the actual experimental case of contrast management is slightly more complicated than the usual diagram depictions and results sections may appear. What would be expected to be acutely disparate contrast differences (i.e. hydrophobic core/hydrophilic shell) are in reality blurred by factors like chain exchange, core interpenetration, and partial hydration (Patterson et al. 2013; Lu et al. 2016). Thus, in an effort to clarify the properties affecting chain exchange, polystyrene (PS)- poly(ethylene-alt-propylene) (PEP) block copolymers were assembled into micelles in the PEP-selective solvent squalane in thoughtfully designed CV SANS studies which monitored dynamic contrast over time to evaluate the kinetics of chain exchange (Lu et al. 2015, 2016). The experimental design in these studies is a wonderful example of inventive CV SANS use. Firstly, PS-PEP-PS and PEP-PS-PEP triblock copolymers with comparable solvophilic PEP blocks form micelles in squalane, with the former resulting in flower-like micelles with PEP loops extending from the core and the latter forming the classic fuzzy micelles with PEP chains extending from the core. The molecular weight of the copolymers was ~230 kDa, with PEP blocks of ~140 kDa. Standard copolymers and identical versions with perdeuterated PS blocks were prepared as micelles in the solvent and dried before being mixed in equal ratios. The inventive concept was as follows: when the dried, pure-core micelles, half containing hydrogenated PS and half containing deuterated PS, were suspended in a 58% D-squalane/H-squalane solvent mixture which has an SLD matching that of a perfectly mixed PS core, the initial contrast from the pure micelle cores, which is given by the contrast factor I~(SLDd,core-SLDh,core)2 would be at a maximum value and would decay to zero as the chains exchanged and eventually cause evenly mixed cores (Lu et al. 2012). From time resolved (TR) SANS studies on these micelles it was found that the exchange rate of PS-PEP-PS micelles was nine orders of magnitude greater than the PEP-PS-PEP micelles which resulted in the conclusion that the rate limiting mechanism was the extraction of PS block cores into the solvent.

15.3.2 Vesicles

The ability of delivery vehicles to entrap and release drugs of various hydrophobicities is correlated to the carrier structure (Chemelli et al. 2012; Nguyen et al. 2011). In this regard, stimuli responsive shape change in a drug carrier offers a viable mechanism for controlled delivery. However, detailed characterization of these shape changes is crucial for understanding and optimizing the mechanism of delivery.

Using pH change as a stimulus, nicergoline/glycerol monooleate (GMO) colloids prepared by sonication of both solids (5 w/w% total, nicergoline varied between 10 and 30 wt%) in 1% Pluronic F108/water were found to have pH-dependent morphology, switching from vesicles to inverse micelles during a change from below pH = 5.1 to above pH = 6.6 (Salentinig et al. 2014). GMO bearing a relatively small C17 chain resulted in micelles 4 nm in diameter when the nicergoline concentration was >20% at pH >6.6, with the nicergoline entrapped in the center.

However, nicergoline has multiple lone-pair nitrogens that can be protonated at different pH values and is responsible for the pH-driven shape change. Using crystallographic parameters outside the scope of this description allowed the determination of the apparent pKa of the nicergoline-GMO system. Generalized IFT from q >0.09 Å−1 was used to provide a PDDF that characterized the size and shape of the nano-objects and revealed that the monooleate bilayer of the vesicle resulting from shifting the pH <5.1 was 5 nm in thickness.

This type of analysis for vesicle bilayers, or generically, locally flat sheets with respect to the scattering range of q, from thickness PDDF plots is an analysis shown in early SAXS works by Glatter (Glatter 1980; Glatter and Hainisch 1984). In these crystallographic studies, Glatter worked with simulated scattering data to develop mathematical analysis techniques for interpreting physical parameters of solid objects. It was shown that deconvolution using a function he derived allows radial electron density profiles to be calculated. Electron densities within the particle radius can thusly reveal the thickness of interlayers and their molecular ordering (crystallographic unit cell packing parameters) in addition to providing information on the location of drug molecules as shown in this study. For example, the packing of GMO was found from Bragg reflections in the scattering data to be indicative of Pn3m cubosomes and hexosomes, which shifted to an Im3m bicontinuous cubic phase as pH went from >8.0 to <7.0.

Further, radially dependent electron density moving outward from the micellar monooleate core was also used to evaluate the water hydration sphere in the glycerol corona. From the examples in this study, along with the chain exchange, solvent selective morphology, and drug effect on micelle conformation studies discussed in the previous section it can be seen that questions concerning self-assembly are being addressed very quantitatively with SAS techniques.

Vesicles, owing to their unique architecture and larger size compared to micelles, are often the focus of studies aiming to uncover details about the hydrophobic layer or bilayer. The first important consideration for vesicles is that their size can easily exceed 1 μm and, therefore, the range of q in scattering studies is not low enough to encompass the Guinier region (Borchert et al. 2006). Instead, the scattering intensity in the reasonable q range of the instrument is best approximated by that due to a flat sheet. For vesicles this enables detailed analysis of the hydrophobic interlayer when CV conditions or modeling analyses are used.

For example, the bilayer thickness of poly(2-vinylpyridine-b-ethylene oxide) (PVP-PEO) block copolymer vesicles 1–10 μm in diameter formed from nanoprecipitation in CHCl3/H2O was evaluated with SANS in D2O (Rubner and Cohen n.d.). The PVP polymer contains ionizable nitrogens that render the polymer insoluble above the pKa and result in the formation of vesicles. By fitting scattering data in the q range of 0.005–0.05 Å−1, the PVP bilayer thickness of vesicles formed from PVP-PEO copolymers with ~30, 40, and 70 PVP units at pH >5 was found to be 10.7, 13.6, and 13.5 nm, respectively.

Similarly, in an investigation of polydimethylsiloxane-g-poly(ethylene oxide) (PDMS-g-PEO) graft polymers and PEO-PDMS-PEO triblock copolymers, the hydrophobic bilayer was characterized using SANS in D2O (Salva et al. 2013). The vesicles were prepared by mixing the polymers in water and extruding 19 times through 0.1 μm filters. However, cryo-TEM still revealed large, polydisperse vesicles which caused oscillations at low q such that quantification in that range was not possible. However, modeling of the scattering curves revealed an average of 33 nm PEO cores with 5.75 nm PDMS bilayer membranes and 15 nm outer shells. An interesting use of a log-log scaled Kratky plot was also utilized for intermediate q in which π/qmax (the local maximum of intermediate q) provided the characteristic length of the membrane, 6.0 nm, which agreed well with the model fitting analysis.

For the PEO-PDMS-PEO triblock copolymers, high polydispersity disrupted higher q such that the log scaled Kratky plot was not useful. However, the slope of the fit line from a Kratky-Porod plot of ln(Iq 2) vs q 2 provided the membrane thickness as 11 nm which agreed with cryo-TEM images. Model fitting of the entire curve gave a core of 14.9 nm with a PDMS interlayer membrane of 11.4 nm and a 26.5 nm hydrated PEO outer corona, giving a final agreement for multiple analyses.

While the two studies discussed above focused on the characteristics of the vesicle membrane as a homogenous entity, there are a number of works focused on investigating small nano-domains within vesicle walls. The nanodomains have completely different form factors compared to the assumed flat sheet of the vesicle surfaces which make them difficult to analyze without SAS. Similar principles to those in the studies above apply: that in a polydisperse system of large spheres, surface curvature can be neglected and the scattering is treated as coming from randomly dispersed flat surfaces (Vogtt et al. 2010).

In a study of vesicles formed from multiple extrusions of a mixed lipid system (molar ratio of 45:27:28 DOPC:DPPC-d62:cholesterol) through 30-nm filters in water, CV SANS in D2O/H2O was used to characterize the vesicles as 14.5 nm spheres with 2.5 nm bilayers. Selection of a single deuterated component and a contrast matched D2O/H2O solvent system also allowed characterization of small nanodomains in the disordered liquid phase as flat cylinders 2.5 nm long with a radius of 14.5 nm. This general flattened shape was confirmed from the low q behavior of the log-log scattering curve in the region of 0.1 < q < 1.5 nm−1 where the scattering curve displayed q −2 dependence indicative of flat objects.

The formation of nanodomains is not limited to vesicles composed purely of lipids, as demonstrated by the study of grafted PDMS-g-PEG mixed with DPPC/POPC (50:50) ratio to form 80:20 polymer:lipid vesicles (Dao et al. 2015). In this work, thin film rehydration/extrusion through 100-nm pores was used to create vesicles 52 nm in diameter. CV SANS in 10% D2O/H2O provided PDMS-matched conditions in which independent observation of the lipids was possible, while 80% D2O/H2O matched the SLD of the lipids and allowed polymer “visualization” in the SANS curve. From Kratky-Porod plots the vesicle membrane thickness was found to be 5.8 nm, but the vesicle model was found to be insufficient for the lipid-matched polymer scattering curves. Instead, the polydisperse flat cylinder model was found to describe the polymer nanodomains as 30 nm radius, 5.1 nm length cylinders. It should be noted that the apparent size of the flat cylinders from the model does not seem reasonable considering the diameter of the overall vesicles (~52 nm). A major consideration in this case was the polydispersity and variable content of the nanodomains and the ever-present fact that SAS curves can be acceptably fit with multiple models.

Without information from other characterization techniques it can be difficult to pinpoint some structural features in SAS modeling due to the number of uninformed floating parameters. While characterization of the vesicle’s overall structure was confirmable with DLS and shown to be reliable from several modeled approaches, characterization of the nanodomains suffered from being necessarily independent from other techniques. Both the immense strength and characteristic weaknesses of SAS can be seen in these studies.

15.3.3 Capsules

Hollow polymer capsules present one of the most interesting subjects of SAS drug delivery subjects. Firstly, they have an extremely wide range of compositional aspects that can be varied quite easily, including polymer composition, molecular weight, interlayer interaction, and size (Li et al. 2011; Shutava and Lvov 2006; Shutova et al. 2007; Zavgorodnya et al. 2015). Small nm-range sizes of capsules can be studied encompassingly with SANS which provides very interesting details on their morphology before and after template dissolution (Estrela-Lopis et al. 2002). Since polymer capsules can also exist as large particles >1 μm, very low q ranges can be needed to fully characterize their size and shape in SAS. However, when this information is gathered in other more facile ways these parameters can be included in fitting models. Following this, the ratio of shell thickness to overall particle diameter is very small, which makes characterizing the thickness accurately impossible without SAS techniques. Additionally, specific modeling and analyses such as those stemming from Kratky-Porod plots are able to shed light on this topic (Balgavy et al. 2001; Richter et al. 2011). In this regard the smallest of small angles can be fully utilized and scattering instruments can be pushed to their physical limits. For perspective, the D11 SANS instrument at Institut Laue-Langevin uses a 39 m sample-to-detector distance to separate low q range scattering measurements from the main beam.

Capsules also have the potential to be extremely monodisperse due to their templated assembly which provides highly uniform scattering in contrast to self-assembled structures that can be quite polydisperse. Common goals for SAS research on hollow capsules are finding the capsule wall thickness in solution and characterizing the interior environment (Estrela-Lopis et al. 2007). The hollow morphology of these particles means that the solvent-filled core can be modeled as equal to the bulk solvent in SLD and scattering due to the polymeric shell can be analyzed separately.

It is important to remember that scattering data may look somewhat similar and that the important conclusions come from careful modeling. For acquisitions leading to information on capsule shell thickness, fewer parameters left floating during data fitting such as particle radius, SLD of the core/shell, interparticle factors, and polydispersity lead to more accurate results when the models are being pushed. This is born from the fact that the q range of most instruments falls short of fully wrapping the scale of such objects. Polydispersity and size can be measured with DLS (Rube et al. 2005), or confocal laser scanning microscopy (Kozlovskaya et al. 2014) while the SLD value of polymeric material can be closely approximated to known values. Since polydispersity smoothens scattering profiles quite effectively, having guidelines for these parameters can enhance model accuracy for other parameters such as core size which can be independently measured by scanning electron microscopy (Chen et al. 2013) and shell thickness which can be determined by atomic force microscopy (AFM) (Liu et al. 2014; Espinosa-Dzib et al. 2015). Outside of some of the more advanced modeling routines, a good example of model-free analysis is the modified Guinier plot which can give bilayer thickness of vesicles (Kim et al. 2014) from the slope of ln(Iq 2) vs q 2 in the Guinier thickness range (Fig. 15.9).

Fig. 15.9
figure 9

Modified Guinier plot with linear fits giving R g which can be used to calculate shell thickness (Reprinted with permission from Kim et al. 2014, copyright American Chemical Society)

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Analyses such as these have also been conducted on polyelectrolyte multilayer capsules made via ionic pairing of poly(styrene sulfonate) with poly(allylamine hydrochloride) (PSS/PAH) and ranging from 130 nm to 3 μm in size for separate samples with successful modeling of capsule wall thicknesses (Estrela-Lopis et al. 2009). The capsules in this study were modeled as core-shell particles, and removal of interparticle structure factors (by sufficient dilution) allowed isolation of the form factors representing scattering from the core, core-shell interface, and shell polymers.

As mentioned, for hollow capsules a core-shell model where the core matches the solvent in SLD can be used to isolate scattering from the polymer shell. However, analysis of scattering from separate samples with reserved core templates enabled the conclusion that supported shell layers, i.e., those still standing on the templates, are 25% thinner than free capsule shells, i.e., those with templates having been dissolved (Balgavý et al. 2001). While this result may seem intuitive, it is quite significant in that SANS is one of the only ways to characterize detailed shell swelling and prove this reasonable hypothesis.

Moreover, the hydration of the (PSS/PAH)8,12,16 shells where the subscript denotes the number of PSS/PAH polymer bilayers within the capsule shell was determined to be higher in freestanding layers (52%) compared to template-bound layers (42%) from the difference in SLD of hydrated polymers compared to pure solvent (Balgavý et al. 2001). The thickness of PSS/PAH capsule shells in solution, found from SANS analysis to be ~2 nm per PSS/PAH bilayer, was found to be in agreement with the thickness of collapsed capsules in the dry state found using AFM.

However, AFM thickness data cannot always accurately approximate thicknesses of hydrated layers. For example, in a study of PSS/PAH multilayer capsules formed on red blood cells, AFM measurements revealed capsule wall thickness that were artificially higher than the thickness measured with SANS (Estrela-Lopis et al. 2007). In this work, six bilayers of PSS/PAH were found from modeled SANS data to have a total thickness of only 4.5 nm, while AFM results were much higher. The difference stems from the removal of up to 90% of the PSS during core removal, which was shown to be trapped within the core with SANS. However, when drying the capsule suspension for AFM it was hypothesized that the PSS trapped in the core contributed to the height found from the AFM probe. These results are a significant example of how SANS can validate results brought to hypothesis from other techniques, while also shedding light on the intrinsic weakness of other techniques that can lead to inaccurate conclusions.

Investigating the core environment of capsules is another useful application for SAS techniques where in-solution techniques like DLS are not sensitive to scattering from the object’s interior (Lof et al. 2007). For encapsulated biological macromolecules that contain metals, SAXS is particularly helpful due to the disparate contrast from the electron density of metals compared to organic molecules as shown in the characterization of hemoglobin inside (chitosan/alginate)10 capsules (Mandal et al. 2012). In this study, the aggregation of hemoglobin inside the capsules compared to free hemoglobin in solution was compared to evaluate the effect of encapsulation on redox response found from cyclic voltammetry of the hemoglobin. Porod analysis was used heavily with a focus being the Porod exponent aggregation behavior.

First, a theoretical R g for hemoglobin was established by a simulation and found to be 22.37 Å. This value was compared to the value determined from SAXS of the polymer-encapsulated hemoglobin (26.6 Å) and found to be in agreement. The more interesting result came from the experimentally determined polydispersity figure for encapsulated hemoglobin of 0.11, which was much lower than the free hemoglobin value of 0.71. This implied that the hemoglobin was highly monodisperse when encapsulated which is indicative of non-aggregation. This study is a good example of how SAXS can be used to take advantage of the increased scattering from biological macromolecules that contain or incorporate metals to evaluate their properties independently of the system in which they are being studied.

15.3.4 Drug Modeling, Behaviors, Interactions

The constant development of new drugs that are very often hydrophobic comes with the parallel development of methods to increase the solubility of these drugs. Characterizing the solubility of drugs is an effort being pursued by medicinal laboratories but often the acquisition timescale is slower than the drug dissolution species change. Powder X-ray diffraction is often used to characterize solids but available instruments typically have measurement timescales around 10 min. Efforts to elucidate more detail in shorter time intervals for rapidly solubilizing or crystallizing drugs are being supported by the speed and resolution of SAXS (Boetker et al. 2012), with intermediate species and kinetics being discovered from this technique. Both anhydrous and monohydrate forms of theophylline were characterized kinetically during dissolution and recrystallization using SAXS at complete experimental timescales under 100 s.

At the other end of the spectrum, encapsulating protein drugs is an application that has potential for drug delivery (Besanger et al. 2004; Ciriminna et al. 2013; Zeno et al. 2014). However, characterizing the encapsulated proteins is not simple using optical techniques. Instead, CV SANS and deuterated proteins were used in a study of green fluorescent protein in silica sol-gels to evaluate the conformation of the protein and its effects on the structure of the gel (Luo et al. 2009). The mixed solvent system of 60% D2O/H2O was found to match silica which allowed direct access to scattering from the protein, while 42% D2O was used to match hydrogenated protein and evaluate scattering from the silica matrix. From simultaneous fits of SANS data at 0, 30, and 100% D2O the typical particle size in the silica sol-gel was found to have a radius of 13.73 Å with pores having a radius of 33.69 Å. Entrapment of the protein did not significantly change the particle size (12.24 Å) but was shown to increase the pore size significantly to 66.01 Å. A Fourier transform approach from the silica-matched SANS curve with deuterated protein to increase the contrast without having to significantly increase protein concentration allowed the elucidation of protein quaternary structure to be an end-to-end dimer.

15.4 Conclusions and Practical Tips

SAS techniques are powerful tools to the researchers looking to discover the most fundamental details of drug delivery systems. The elucidation of these details has rapidly increased the knowledge available to polymer, material, and pharmaceutical researchers over the last decade. While other techniques have allowed discovery of information about the size and dispersity of nanometer sized particles, SAS has helped answer questions that will likely increase the efficiency of drug delivery systems moving forward. However, as the subjects of SAS studies continue to increase in complexity, the instrumental techniques are also increasing in power, resolution, etc. The proliferation of USANS and USAXS instruments is heralding the characterization of larger particles while increased flux in both types of scattering sources is increasing throughput of samples and the speed of information being gained on both novel and fundamental systems.

Practical tips:

  • When using model-free data analysis of the Guinier region, keep in mind that particle aggregation has a significant effect on the line slope and apparent Rg: this may provide estimates that are different than would be expected. Aggregation of particles also effects parameters in model fitting in ways that are not always apparent. For instance, aggregation increases polydispersity which intuitively affects the apparent particle size, but can decrease the apparent shell thickness for core-shell models.

  • SAS characterizations of drug delivery particles and systems provide the most reliable data only when supplemented with as many other techniques as possible. Model parameters that can be fixed due to prior knowledge make the model fit more accurate. Model-free analyses give the best results when they are informed by relevant physical characterizations. The same scattering data can be fit equally well by many completely unrelated models.

  • Always keep the size frame of reference for SAS scattering in mind when looking at data: Porod slopes describe surfaces or fractals; Guinier region slopes describe particle shape if the particle size is measurable at that q; remember also that non-dilute samples show interparticle peaks and/or structure factor scattering.

  • Conclusions drawn from SAS techniques are often the result of an iterative approach with a sizable amount of trial and error where good intuition can help clarify the results; particle scattering could be fit equally well by a fractal micelle model or one that indicates a micelle with unreasonable dimensions, such as a 2 nm core and 100 nm corona. It is left to the user to distinguish whether the conclusion is reasonable or not and to interpret the model from an informed standpoint to give reasonable results.

  • Polymers, drug molecules, and polymeric materials do not always have the same behavior in D2O and H2O. It is best to check simple things like the solubility, R g , and dispersity before beginning scattering experiments.