Subscriber access provided by EMORY UNIV
Article
pH-Responsive Micelles Based on Caprylic Acid Stefan Salentinig, Stephanie Phan, Tamim A. Darwish, Nigel Kirby, Ben J. Boyd, and Elliot P. Gilbert Langmuir, Just Accepted Manuscript • DOI: 10.1021/la500835e • Publication Date (Web): 06 Jun 2014 Downloaded from http://pubs.acs.org on June 16, 2014
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
pH-Responsive Micelles Based on Caprylic Acid
Stefan Salentiniga*, Stephanie Phana, Tamim A. Darwishb,c, Nigel Kirbyd, Ben J. Boyda*, Elliot P. Gilbertb*
a
Drug Delivery, Disposition and Dynamics, Monash Institute of Pharmaceutical
Sciences, Monash University (Parkville Campus), 381 Royal Parade, Parkville, VIC 3052, Australia b
Bragg Institute, Australian Nuclear Science and Technology Organisation, Locked Bag 2001, Kirrawee DC, NSW 2232, Australia
c
National Deuteration Facility, Australian Nuclear Science and Technology Organisation, Locked Bag 2001, Kirrawee DC, NSW 2232, Australia
d
SAXS/WAXS beamline, Australian Synchrotron, 800 Blackburn Rd, Clayton, VIC 3168, Australia
Corresponding authors:
[email protected],
[email protected] and
[email protected] KEYWORDS: Lipid digestion, fatty acid, caprylic acid, SANS, SAXS, self-assembly
ACS Paragon Plus Environment
1
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 28
ABSTRACT Free fatty acids play a vital role as fuel for cells and in lipid metabolism. During lipid digestion in the gastrointestinal tract, triglycerides are hydrolyzed resulting in the amphiphilic products free fatty acids and monoglycerides. These components, together with bile salts, are responsible for the transport of lipids and poorly water soluble nutrients and xenobiotics from the intestine into the circulatory system of the body. In this study we show that the self-assembly of digestion products from medium chain triglycerides (tricaprylin) in combination with bile salt and phospholipid is highly pH responsive. Individual building blocks of caprylic acid within the mixed colloidal structures are mapped using a combination of small angle X-ray and neutron scattering combined with both solvent contrast variation and selective deuteration. Modelling of the scattering data shows transitions in size and shape of the micelles in combination with a transfer of the caprylic acid from the core of the micelles to the shell or into the bulk water upon increasing pH. The results help to understand the process of lipid digestion with a focus on colloidal structure formation and transformation for the delivery of triglyceride lipids and other hydrophobic functional molecules.
ACS Paragon Plus Environment
2
Page 3 of 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
INTRODUCTION Fatty acids are a major end product of triglyceride digestion. They are composed of a hydrophilic carboxylic acid group and an aliphatic hydrocarbon chain with carbon numbers between 4 and 28.1 Most of the naturally occurring fatty acids have an even number of carbon atoms, due to their biosynthesis with the coenzyme acetyl-CoA. In the case of unsaturated fatty acids, the dominant configuration in naturally occurring species is cis; the trans configuration is mostly the result of industrial hydrogenation processes or bacterial metabolism.2 It has been reported that diets rich in saturated fatty acids or trans-fatty acids raise cholesterol levels more than the polyunsaturated cis-fatty acids.3 Free fatty acids have important biological properties: Part of the energy for the heart muscle is fuelled by free fatty acids delivered via the plasma compartment from the adipocytes in distal sites. High concentrations have been shown to induce diabetes through the lipotoxic effect of free fatty acids on the islets of Langerhans.4 A knowledge and understanding of how major food components are treated, transported and utilized during the digestion process opens opportunities for functional food products that help to avoid, or even cure, such health issues.5 When food arrives in the small intestine, the body secretes bile including bile salts and phospholipids. These components can form mixed micelles or vesicles depending on the their ratio and dilution. Bile salt / phospholipid micelles have been reported to form globular or worm-like structures, with the phospholipid molecules oriented radially along the axis surrounded by the bile-salt at the aggregate-water interface.6 Elongation of these mixed micelles and a transition to vesicles was found to occur upon dilution or addition of phospholipids.6-12 At the end of the lipid digestion process in the small intestine, these mixed micelles are solubilizing fatty acids and monoglycerides.13-16 These assemblies then diffuse through the unstirred water layer, which separates the brush-border membrane of the enterocytes (the absorptive cells in the small intestine), from the bulk fluid phase of
ACS Paragon Plus Environment
3
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 4 of 28
the intestinal lumen.17, 18 The unstirred water layer is proposed to have a reduced pH environment compared to the bulk lumen; thus a pH gradient exists, across which, the degree of ionization of fatty acids may vary. This has been proposed as a mechanism of driving lipid absorption through increases in thermodynamic activity.19, 20
More polar, low molecular weight fatty acids such as caprylic acid have higher
rates of penetration across the intestine and gall bladder than larger, less polar compounds. This implies that in addition to passive absorption of molecules across the lipid membrane of the mucosal cell, there is also a movement of small molecules through a more polar diffusion pathway through the epithelial surface.21 This study shows that the pH response of the mixed colloidal digestion products can influence the fatty acid delivery through modification of the micelle-water interface. The aim is to systematically study the influence of pH modification on the selfassembly of caprylic acid in biologically relevant systems containing the corresponding monoglyceride monocaprylin, bile salt and phospholipid. Somewhat tangential to the low pH microclimate at the enterocytes, during the digestion process in mammals, the pH of the food bolus gradually increases as it passes along the gastrointestinal tract; the pH of gastric contents varies from 1.0– 3.0, and of duodenal contents from 4.8–8.2 (from
22
). Thus a complete understanding
of the impact of pH on such colloidal structures is imperative. With increasing pH, the polarity of the amphiphilic molecule caprylic acid increases upon deprotonation of its carboxylic group. The pH modifies the protonation state of the fatty acid with a shift in the pKa of the carboxylic group to higher values having been observed for fatty acids in self-assembled systems.23 The thermodynamic model of the transfer properties of charged and uncharged fatty acid from bulk water to the surface of the micelle, based on the Poisson-Boltzmann equation, has highlighted the major role of the dielectric discontinuity on the protonation behaviour of fatty acids.24 Calorimetric measurements during the titration of fatty acids solubilized in micelles showed that this process is endothermic at 298 K, contrary to
ACS Paragon Plus Environment
4
Page 5 of 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
fatty acids solubilised in water (∆H ≈ 0).24 This has been attributed to a dielectric interface caused by lower static permittivity in the core of the micelles compared to the surrounding water solution; the presence of a dielectric interface results in large energies for charged molecules located near the micelle-water interface.25 This study aims to identify the location of the fatty acids within the micellar structures using contrast variation from SANS in combination with SAXS and DLS, to explain the faster absorption rates of short chain fatty acids such as caprylic acid. The pH response is of relevance to this process as the fatty acid molecules change their location within the mixed micelles with changing polarity due to the modified protonation state.
EXPERIMENTAL AND METHODS Materials Deuterated caprylic acid (C8D16O2) was prepared as described below. Tris maleate (reagent grade), bile salt (sodium taurodeoxycholate >95%), monocaprylin (purity ≥ 98%) (C11H22O4), NaOH (p.a. grade) and HCl (p.a. grade) were purchased from Sigma Aldrich (St. Louis, MO, USA). Phospholipid (dioleoylphosphatidylcholine, DOPC, >94%) was from Trapeze Associates Pty Ltd. (Clayton, Victoria, Australia). Calcium chloride (> 99%) was obtained from Ajax Finechem (Seven Hills, NSW, Australia) and sodium chloride (> 99%) from Chem Supply (Gillman, SA, Australia). Ultra-pure water (resistivity > 18 MΩcm) was used for the preparation of all samples. Caprylic acid (purity ≥ 98%) was purchased from Sigma Aldrich (St. Louis, MO, USA). D2O (99.8 %) was supplied by AECL (Ontario, Canada). Thin-layer chromatography (TLC) was performed on Fluka Analytical silica gel aluminium sheets (25 F254) (product of Sigma Aldrich, St. Louis, MO, USA). Davisil® silica gel (LC60Å 40-63 micron) (product of W. R. Grace & Co.-Conn, Columbia, USA) was used for bench-top column chromatography.
ACS Paragon Plus Environment
5
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 6 of 28
Methods Deuteration of caprylic acid A mixture of caprylic acid (13 g, 90.5 mmol), Pt/activated carbon (0.48 g, 10 wt % of the substrate) and 40% w/w NaOD (9.5 g, 92.6 mmol) in D2O (120 mL) was loaded into a Parr pressure reactor (600 mL size). The contents of the reactor were degassed by purging with N2 gas, and then sealed and heated to 220°C (23 bar), with constant stirring for 3 days. The reactor was cooled to room temperature and the contents were filtered through a short plug of Celite, to remove the catalyst, which was further washed with H2O (100 mL). The aqueous filtrate was acidified to pH 2 using 1M HCl. The aqueous phase was extracted with diethyl ether (100 mL × 3) and the combined organic phases were dried over Na2SO4, filtered and concentrated in vacuo to give an oily substance of caprylic acid (12g, 92% D by MS). The aforementioned quantity of acid (12 g) was reloaded into the reactor, and the above method repeated using fresh reagents to give 10.5 g of caprylic acid (73% yield on the basis of the original amount of the protonated caprylic acid; 98% D). Thin layer chromatography was used (referenced with the protonated compound) to estimate the purity and to develop separation protocols. 1H NMR (400 MHz) and 2H NMR (61.4 MHz) spectra were recorded on a Bruker 400 MHz spectrometer at 298 K. More details on the preparation and characterisation are presented in the Supporting Information. The 1H NMR and 2H NMR spectra are shown in Figure SI-1 and 2 respectively.
Sample preparation Bile salt micelles were prepared using bile salt (BS, sodium taurodeoxycholate) and phospholipid (DOPC) concentrations at a ratio of 20 mM:5 mM in digestion buffer (50 mM Tris maleate, 150 mM NaCl). Caprylic acid (20 mM) and monocaprylin (10 mM) were added to the solution. Sonication with a tip sonicator for 30 s at 100 W was used to solubilize the components. The pH of the micellar systems was adjusted by
ACS Paragon Plus Environment
6
Page 7 of 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
the addition of 1M HCl or NaOH. pH values in this study are the direct pH meter readings in H2O and D2O using a glass electrode.26 Samples were equilibrated for a minimum of 24 h before the experiments.
Small angle neutron scattering (SANS) SANS experiments were performed on the Quokka instrument at OPAL27 at a wavelength of 5.0 Å and 10% wavelength resolution. Two instrument configurations were used with a source-to-sample distance of 8 m and sample-to-detector distances of 8 m and 2 m, the latter with a 300 mm detector offset to increase maximum q. These configurations provide a continuous q range of 0.01 to 0.5 Å -1 where q is the magnitude of the scattering vector, defined by q = 4π / λ sin(θ/2),
λ
is the
wavelength and θ the scattering angle. All samples were enclosed in Hellma cuvettes with a 1 mm path length. Samples were studied at several temperatures with control provided with a Julabo thermostatted bath. All data were corrected for blocked beam measurements, normalised and radially averaged, and placed on an absolute scale, using a package of macros in Igor software (Wavemetrics, Lake Oswego, Oregon, U.S.A.) and modified to accept HDF5 data files from Quokka.28
Small angle X-ray scattering (SAXS) SAXS measurements were performed at the SAXS/WAXS beamline at the Australian Synchrotron.29 An X-ray beam with a wavelength of 1.1271 Å (11 keV) was used. A sample to detector distance of 1015 mm gave the q-range 0.007 < q < 0.7 Å-1. The 2D SAXS patterns were acquired within 1 s using a Pilatus 1M detector with active area 169 x 179 mm2 and with a pixel size of 172 µm. All experiments were performed at T = 27°C (hutch temperature at the Beamline). All samples were degassed under vacuum and centrifuged at 3500 rpm for 5 min before the measurement in quartz capillary mounted in the beam. To avoid beam damage, the solution was pumped
ACS Paragon Plus Environment
7
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 8 of 28
continuously during the measurement. For each curve, 10 frames were recorded and averaged manually after inspection for beam damage; no beam damage was observed in the samples. Two dimensional scattering patterns were integrated into the one-dimensional scattering function I(q) using the in-house developed software package scatterBrain. Scattering curves are plotted as a function of relative (SAXS) or absolute (SANS) intensity, I, versus q.
Dynamic light scattering (DLS) DLS was used to determine the mean hydrodynamic radius (RH) and the size distribution width of the dispersed particles. Measurements were carried out on a Malvern Zetasizer NanoZS with a He-Ne laser (λ = 633 nm) and laser power of 4 mW at a back-scattering angle of 173° at 25°C. From the correlation functions, the average diffusion coefficient D was obtained by cumulant analysis.30 The hydrodynamic radius RH was deduced from the diffusion coefficient using the StokesEinstein equation: ܴு =
݇ ܶ 6ߨߟܦ
1
kB being the Boltzmann constant, T the absolute temperature (298.15 K) and η the viscosity of the solvent (η(D2O) = 1.095 cP). The polydispersity index (PDI) of the size distribution was determined from the second cumulant: ܲ= ܫܦ
ߤଶ Γത ଶ
2
where ߤଶ is the second cumulant and Γത the mean of the inverse decay time. Before the DLS measurements, all samples were centrifuged at 3500 rpm for 5 min. The samples were measured without further dilution to avoid the possible affect of dilution on the mixed-micelles.7-11 Consequently the hydrodynamic radii presented in this study are ‘apparent’ values. The total concentration of BS + DOPC + Caprylic acid + monocaprylin micelles is approximately 2 wt%.
ACS Paragon Plus Environment
8
Page 9 of 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
Evaluation of SANS and SAXS data Constant background after buffer subtraction (e.g. from the incoherent neutron scattering by
1
H) was determined with a Porod extrapolation, I(q) ∝ q-4 and
subtracted from the corresponding data set. Where applicable, Guinier analysis, from the Guinier approximation and further analysis of the Inverse Fourier Transform of the scattering data (see below), was performed to calculate the radius of gyration (Rg). Note that the Rg represents the root mean square distance of the scattering density from the centre of an object and it is thus weighted by the associated distribution of electron density (SAXS) or nuclear density (SANS) with the particle of interest. This will become apparent below when Rg values extracted from the two scattering methods are compared. The generalized indirect Fourier transformation method (GIFT) was used to analyse the scattering data.31-33 For particles of arbitrary shape with an electron density or scattering length density difference of ∆ρ(r) relative to the mean value, the pairdistance distribution function p(r) is given by p(r) = r2∆ρ̃2(r) where ∆ρ̃2(r) is the convolution square of ∆ρ̃(r) averaged for all directions in space. This averaging causes no loss of information in the case of particles with spherical symmetry. The p(r) is calculated from the scattered intensity I(q) using following equation:34 Iሺqሻ = 4π න pሺrሻ ∞
0
sinሺqrሻ dr qr
3
and enables the determination of the overall shape and size of the scattering objects.35 In the case of cylindrical micelles with sufficient length / diameter ratio (> 3), the cross section can be investigated using the cross section pair distance distribution function pc(r). The radial electron density profile ∆ρc(r) is related to the pc(r) via pc(r) = r ∆ρ̃2(r).36 The pc(r) can be calculated from I(q) with following equation:
ACS Paragon Plus Environment
9
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
ܫሺݍሻ =
2ߨ ଶ ܮஶ න ሺݎሻܬ ሺݎݍሻ݀ݎ ݍ
Page 10 of 28
4
Here, J0(qr) is the zero-order Bessel function and L the length of the cylinder. Deconvolution of p(r) for spherical particles and pc(r) for cylindrical micelles gives the radial contrast profile ∆ρ(r) or ∆ρc(r) in electron density or scattering length density, which gives information about the internal structure of the scattering particles. Most spherical micelles have a core−shell type structure, with a hydrophobic core and a hydrophilic shell also containing counter-ions and bound solvent molecules. If there is a difference in scattering length, the radius of the core and the thickness of the shell can be discerned directly from the radial contrast profile. Interparticle effects described by the structure factor S(q) can influence the scattering function at higher concentration (volume fraction). In the case of monodisperse, homogeneous and spherical particles, the scattering intensity can then be expressed by ܫሺݍሻ = ܰܵሺݍሻܲሺݍሻ
5
with N being the number of particles and P(q) the form factor describing the intraparticle interactions. The generalized indirect Fourier Transformation (GIFT) method allows the separation of form- and structure factor.31,37 This technique uses the model free approach for the p(r) described above, which corresponds only to the form factor. Simultaneously, a model for the structure factor is fitted to Eq. 5. As the colloids in this study are charged, the Ornstein-Zernike equation38 with the hypernetted-chain (HNC) approximation for the closure relation was employed.37 The radius of gyration was also calculated from the p(r) using ሺݎሻ ݎଶ ݀ݎ ܴ = ඨ 2 ሺݎሻ݀ݎ
6
RESULTS AND DISCUSSION
ACS Paragon Plus Environment
10
Page 11 of 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
SANS is a powerful method to study colloidal structures in food-relevant systems39 and benefits from the possibility to enhance scattering contrast through the replacement of hydrogen with its heavier isotope deuterium. Since neutrons scatter from the atomic nucleus, the associated isotopic dependence enables both solvent contrast variation (e.g. mixtures of H2O and D2O) and, typically more costly, selective deuteration of non-solvent molecules. Contrast variation with X-rays is typically limited to anomalous methods, which are unsuitable for low atomic number elements. In this study, mixed micelles formed by custom-synthesized fully deuterated fatty acids in combination with non-deuterated monoglyceride, bile salt and phospholipid were employed. Using D2O as a solvent resulted in the generation of scattering arising primarily from the bile salt, phospholipid and monoglyceride, whereas in H2O the scattering signal is dominated by the scattering of the deuterated fatty acid. The X-ray and neutron scattering length densities of the components are summarised in Table 1.
Component
Physical
X-ray
Neutron
Neutron
Neutron
Density
Scattering
Scattering
Contrast
Contrast
[g/cm-3]
length
length
in H2O
in D2O
density
density
∆ρ (H2O)
∆ρ (D2O)
[Å-2]
[Å-2]
D2O
1.1
9.37 10-6
6.38 10-6
H2O
1.0
9.47 10-6
-5.61 10-7
C8D16O2
0.9
7.64 10-6
5.80 10-6
6.36 10-6
-5.80 10-7
C11H22O4
0.9
8.43 10-6
3.49 10-7
9.10 10-7
-6.03 10-6
ACS Paragon Plus Environment
11
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 12 of 28
C26H44NO6SNa
0.9
8.29 10-6
6.12 10-7
1.17 10-6
-5.77 10-6
C42H82NO8P
0.9
8.47 10-6
2.38 10-7
7.99 10-7
-6.14 10-6
Table 1: Summary of chemical formulae and X-ray and neutron scattering length densities (ρ) of the individual components. Also shown is the neutron contrast ∆ρ = (ρ – ρsolvent); the highest contrast (strongest scatterers) in D2O and H2O are underlined.
The radius of gyration (Rg) from Guinier analysis for the bile salt-phospholipid micelles assembled in D2O at pH 4 is presented in Table 2. Before the addition of fatty acid and monoglyceride, the Rg was approximately 16 Å. This Rg is comparable to literature values for similar systems, i.e. 19 Å for the lecithin / sodium taurocholate at a ratio of 0.4 and 21 mM total concentration.7 On addition of fatty acid or monoglyceride, the Rg of the micelles increased to approximately 20 Å. Interestingly, the addition of a mixture of both fatty acid and monoglyceride resulted in a dramatic increase of the Rg to 60 Å. The change in the equilibrium packing geometry in this multicomponent system is thought responsible for this behavior. At this pH, the fatty acid is mostly protonated. Increasing the concentration of rather hydrophobic components in the micelles results in an increase in particle size and elongation. This effect is comparable to the dilution of phospholipid/bile-salt systems; indeed, prior studies on dilution of the lecithin / bilesalt system found particle elongation due to the leaching of bile salt from the micelles and, as a result, increasing the hydrophobic material (lecithin) / bile salt ratio within the mixed micelles.7, 10
ACS Paragon Plus Environment
12
Page 13 of 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
Sample
Rg [Å]
Bile salt micelles
16.5 ± 0.5
Bile salt micelles 20.4 ± 0.8 monoglyceride Bile salt micelles + 24.2 ± 0.5 fatty acid Bile salt micelles + monoglyceride and
59.3 ± 2.7
fatty acid Table 2: Radius of gyration calculated from the SANS data of the mixed micelles in D2O at pH = 4.0.
The influence of varying the pH on the scattering from the caprylic acid + monocaprylin micellar systems with simulated intestinal fluid in D2O and H2O is presented in Figure 1 a and b respectively. With increasing pH, a decrease in the forward scattering was observed. Increasing S(q) due to partial deprotonation of fatty acids (increase in charge) as well as decrease in the size of the micelles and a shape transition from elongated to spherical can explain this change in the I(q) in the D2O based system. This transition from elongated to approximate spherical shape with increasing pH values is clearly shown in the cross section Guinier plots of the SANS data in D2O presented in the Supporting Information in Figure SI-3. The scattering intensity for the H2O based system decreased dramatically between pH 3.8 and 6.5 showing no further changes at higher pH values. As the I(q) in the H2O based system mainly results from the scattering of the deuterated caprylic acid,
ACS Paragon Plus Environment
13
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 14 of 28
this suggests that most of the fatty acid is transferred from the interior of the mixed micelles into the bulk water phase with increasing pH. The pH-responsiveness of the system is a result of the gradual deprotonation of the caprylic acid. This leads to negatively charged carboxylic groups increasing the effective area per headgroup at the interface due to coulomb repulsion or, in the extreme case, the transport of the fatty acid into the bulk solution. A control experiment is presented in the Supporting Information (Figure SI-4) showing that the bile salt micelles in the absence of caprylic acid are not pH responsive. The release of the short-chain fatty acid at intestinal pH values observed here might provide a mechanism for the fast digestion kinetics and absorption of short-chain triglycerides in the intestine.
Figure 1: SANS curves for the bile salt micelles containing monocaprylin and deuterated caprylic acid at different pH values in D2O (a) and H2O (b). The scattering of bile salt micelles in both solvents is also presented.
The Rg values calculated from Guinier analysis of the scattering curves are presented in Figure 2. To demonstrate the consistency of the results obtained from the modeling using the generalised indirect Fourier transformations, Rg values calculated from the p(r) functions according to Eq. 6 have been included in the same figure. The systematic deviation between the values is caused by a small structure factor
ACS Paragon Plus Environment
14
Page 15 of 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
present in this system: Whereas the I(q) is a combination of form and structure factor, the p(r) is calculated from P(q) only (Eq. 5). A decrease in the Rg from around 70 to 10 Å can be observed with increasing pH from 2.2 to 7.8 in the D2O system. In the H2O-based system, focusing on the deuterated fatty acid only, a smaller Rg of ca. 35 Å for pH 2.7 and 3.8 was observed. The corresponding cross-section Rgc of the rod-like particles at low pH was calculated from a cross section Guinier plot (ln(I(q)q) vs q2). For the D2O based system a value of 17 Å (pH = 2.2) and for the H2O based system 13 Å (pH = 2.7) was found. The cross section Guinier plots and fits to the linear q-region are presented in Figure SI-5. The dimension of the largest semi-axis (c) of the elongated particles was estimated to be 151 Å in D2O and 73 Å in H2O using Eq 7.
ܴ ଶ − ܴ ଶ =
ܿଶ 5
7
This difference between the D2O and H2O based system indicates that the deuterated fatty acid is located in the core of the cylindrical micelles at low pH. Dynamic light scattering was used as a complementary method to study the micelle size and polydispersity. The hydrodynamic radii and size-polydispersity of these samples measured with DLS are summarized in Table 3. The corresponding correlation functions showing rather monomodal and uniformly distributed particles are presented in Figure SI-6. The RH follows the same trend as Rg where it decreases with increasing pH. The Rg/RH ratios, which provide further details on particle shape, are presented in the same table. The theoretical Rg/RH value for homogenuous spheres is 0.775 with elongated particles deviating to values > 1.41 With Rg calculated directly from the experimental I(q), lower Rg/RH ratios than those for homogeneous spheres were observed in some systems (e.g., as low as 0.4 for the system at pH 6.4; and 0.5 for the
bile salt - DOPC mixed micelles). As
mentioned above, a structure factor can lead to an underestimation of the Rg values
ACS Paragon Plus Environment
15
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 16 of 28
due to the excluded volume effect decreasing the forward scattering intensity. Consequently, the S(q) and P(q) were determined from the I(q) for all systems (Eq. 5). Details on the interaction parameters resulting from this calculation are presented in the Supporting Information. The resultant values, which we denote as Rg*, were then calculated with the Guinier extrapolation from the P(q). All Rg*/RH ratios are higher than the Rg/RH indicating that the structure factor was a major cause for the deviation. Yet, the Rg*/RH for system at high pH > 6.4 and the bile salt - DOPC mixed micelles still deviate to lower values < 0.775. Such lower values can result from the presence of small amounts of dust or aggregates that are not detected with SANS, as they will affect the RH obtained from DLS more than the Rg from SANS (larger particles scatter to lower q and the DLS operates at much lower q than SANS). We also note that the deviation of Rg/RH to values to around 0.6 has been reported for particles with denser core than shell in the literature.42
Figure 2: The pH-dependence of the radius of gyration calculated from SANS curves presented in Figure 1 using Gunier approximation (full symbols) and from p(r) obtained from model independent fitting with generalised indirect Fourier transformation using Eq. 6 (open symbols).
ACS Paragon Plus Environment
16
Page 17 of 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
pH
RH [Å]
PDI
Rg/RH
Rg*/RH
2.2
50
0.18
1.39
1.48
5.3
37
0.24
0.70
0.83
6.4
32
0.29
0.41
0.60
7.1
25
0.15
0.51
0.70
28
0.15
0.57
0.67
bile salt micelles Table 3: Measured hydrodynamic radii and polydispersity in D2O for the deuterated caprylic acid-based mixed micelle system at various pH values. The included Rg/RH and Rg*/RH were calculated with Rg from Guinier approximation from I(q) directly (Rg) and from P(q) (Rg*).
For further details on the change in size and shape of the micelles the I(q) profiles from SANS and SAXS were analyzed at low pH = 2.2 and elevated pH = 6.4. It is theoretically impossible to simultaneously deduce the geometrical shape and the size distribution of a polydisperse system of particles from scattering data.43 The correlation functions and polydispersity index from the dynamic light scattering measurements on the same samples indicates rather monomodal micelles within the accuracy of the method and equipment used (see table 3 and Figure SI-6). The minimum in the I(q) from SAXS provides a further indication for low sizepolydispersity in the samples used for further analysis. The I(q) profiles for the micelles at pH 2.2, in combination with the model independent fits calculated with the generalized indirect Fourier transformation method and the corresponding p(r) functions are presented in Figure 3 a and b respectively. Figure SI-7 presents a plot of SANS I(q) versus q with the fit focusing
ACS Paragon Plus Environment
17
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 18 of 28
on the low-q region and showing that the intensity follows a q-1 dependence characteristic of cylindrical structures such as elongated micelles. The shape of the calculated p(r) functions from SAXS and SANS at this pH is characteristic of ellipsoidal particles. This can easily be determined by comparing the shape of this experimental p(r) to theoretically calculated p(r) functions based on cylindrical geometry (e.g. in Ref. 40) and is in agreement with the results on the particle shape deduced from Guinier analysis before. The axial length of the cylinder is responsible for the linear decay of the p(r) with the maximum dimension of the cylinder at p(r) = 0 at large r. The p(r) from SAXS provides information on the overall system, as expected, based on contrast in electron density (Table 1). The overall length of the elongated particles, estimated from the p(r), is 300 Å. The pronounced (negative) minimum in the p(r) between 0 < r < 60 Å indicates a core-shell structure for the cross-section of the ellipsoidal particles. The cross section diameter is approximately 60 Å, determined from the pc(r) presented in Figure SI-8. With SANS in D2O, elongated micelles with a similar size (maximum dimension ~ 300 Å) are observed. The different tail in the p(r) functions in Figure 3 can be a result of the low overall contrast with SAXS compared to SANS.40 For SANS in H2O, the scattering arises primarily from the deuterated fatty acid; as a result, a smaller length of approximately 160 Å is observed for the ellipsoidal particles compared to the system in D2O. These maximum particle dimensions derived from the p(r) in both solvents are in good agreement with the estimated largest semi-axis from Guinier analysis presented before (i.e. 2c = 302 Å in D2O and 2c = 146 Å in H2O). These results further support our hypothesis that the protonated fatty acid is preferentially located in the core of the mixed micelles, away from the water,
and
that
the
mainly
non-deuterated
components
(e.g.,
bile
salt,
monoglyceride) are forming the shell between the protonated fatty acid and the bulk
ACS Paragon Plus Environment
18
Page 19 of 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
water.
Figure 3: (a) Measured SANS profiles in D2O and H2O, and SAXS profile for the deuterated caprylic acid-based mixed micelles system at pH = 2.2 (symbols) and fit (red line). (b) The corresponding p(r) profiles calculated from (a) using Eq. 3 and the structure factor model.
At elevated pH = 6.4, the SAXS and SANS curves for the fatty acid monoglyceride simulated intestinal fluid system in D2O, in combination with the model independent fits and corresponding pair distance distribution functions, are presented in Figure 4 a and b respectively. The oscillations in the I(q) from SAXS indicate a core shell structure and small size- polydispersity. The relatively symmetrical shape of the resulting p(r) is characteristic for approximate spherical symmetry of the particles. The p(r) from SANS shows an apparent maximum dimension of ~ 70 Å and SAXS of ~ 75 Å for the mixed micelles. The difference in the apparent size can result from the higher overall contrast for neutrons than for X-rays in the sample (see Table 1 for details on the contrast). The maximum overall particle dimensions from the p(r) are in agreement with the apparent RH values from DLS presented in Table 3 (i.e., 2RH = 64 Å). The smaller radius from DLS compared to that from SAXS and SANS can be a result of particle interactions (only the effective diffusion coefficient is measured with DLS) and slight deviation of the particle shape from spherical to oblate.
ACS Paragon Plus Environment
19
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 20 of 28
Deconvolution of the p(r) arising from SAXS leads to the electron density distribution profile within the micelle presented in Figure 4 c. Contrary to the definition of r as distance in the p(r) as discussed before, r it is the radius in the ∆ρ(r). The micelle radius of 35 Å from SAXS and SANS corresponds to the diameter deduced from the p(r). In contrast to the profile obtained from SANS, where no difference in scattering length within the micelles can be observed at this pH, SAXS shows a core-shell structure with different electron density providing access to information about the interfacial region. The negative electron density corresponds to the alkyl chains with a radius of approximately 11 Å, and the positive electron density to the head-groups with their associated counter-ions. The head-group area is broad as the surfactant headgroups are not fixed at a certain radius but distributed at various positions and experience temperature-dependent fluctuations.
ACS Paragon Plus Environment
20
Page 21 of 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
Figure 4: Deuterated caprylic acid + monocaprylin based mixed micelles at pH 6.4: Measured SANS and SAXS scattering in D2O (symbols) and fit calculated with Eq. 3
ACS Paragon Plus Environment
21
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 22 of 28
(red line) and the structure factor model using the generalized indirect Fourier transformation method. (b) The corresponding p(r) calculated from (a) (full lines) and the fits calculated from deconvolution (dotted red lines). (c) The radial contrast profiles calculated from (b) by deconvolution.
Conclusions SANS, SAXS and DLS were employed to study the effect of composition and pH on caprylic acid-based micelles containing bile salt, phospholipid and monocaprylin. Mixed micelles of elongated shape were found at low pH values between 2 and 4. Increasing pH was found to gradually tune the structure towards more spherical geometry. Selective deuteration of caprylic acid combined with variable contrast (neutrons and X-rays) as well as solvent contrast (SANS) enables the distribution of components within the micelles to be identified. At low pH, approximating that of the gastric compartment, the caprylic acid was found to preferentially located in the interior of the micelles, but redistribute at intestinal pH values of > 6 towards the micelle-water interface and disperse into the aqueous bulk phase. This result has important implications for fatty acid release during the digestion of lipids: The fast release of short-chain fatty acids to the aqueous bulk phase may provide a mechanism for the fast digestion kinetics observed for corresponding short chain triglyceride systems. The method of localizing individual components in complex colloidal systems presented in this work might also be of interest for studying and optimizing colloidal drug delivery systems.
ACKNOWLEDGEMENTS The authors would like to thank AINSE Ltd for providing financial assistance to enable work on the Quokka SANS instrument at ANSTO.
ACS Paragon Plus Environment
22
Page 23 of 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
ASSOCIATED CONTENT Supporting Information Available: Detailed description on the preparation of deuterated carpylic acid, control experiments additional SAXS, SANS and DLS data, the cross-sectional Guinier plots and details on the interaction parameters for the structure factor model. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author Postal Address: Monash Institute of Pharmaceutical Sciences, Monash University (Parkville Campus), 381 Royal Parade, Parkville, VIC 3052, Australia, Email:
[email protected] Funding Sources The studies were funded by the Australian Research Council through the Discovery Projects scheme (DP120104032).
REFERENCES 1.
Moss, G. P.; Smith, P. A. S.; Tavernier, D. Glossary of Class Names of
Organic-Compounds and Reactive Intermediates Based on Structure. Pure Appl. Chem. 1995, 67, 1307-1375. 2.
Voet, D.; Voet, J. G. Biochemistry. 2nd ed. New York: John Wiley & Sons:
1995. 3.
Katan, M. B. Trans Fatty Acids and Plasma Lipoproteins. Nutr. Rev. 2000, 58,
188-191. 4.
Unger, R. H.; Zhou, Y. T. Lipotoxicity of Beta-Cells in Obesity and in Other
Causes of Fatty Acid Spillover. Diabetes 2001, 50, S118–S121. 5.
Singh, H.; Ye, A.; Horne, D. Structuring Food Emulsions in the
Gastrointestinal Tract to Modify Lipid Digestion. Prog. Lipid Res. 2009, 48, 92-100. 6.
Hjelm, R.P.; Thiyagarajan, P.; Alkan-Onyuksel M.H. Organization of
ACS Paragon Plus Environment
23
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 24 of 28
Phosphatidylcholine and Bile Salt in Rodlike Mixed Micelles. J. Phys. Chem. 1992, 96, 8653-8661. 7.
Long, M. A.; Kaler, E. W.; Lee, S. P. Structural Characterization of the
Micelle-Vesicle Transition in Lecithin-Bile Salt Solutions. Biophys. J. 1994, 67, 17331742. 8.
Madenci, D.; Egelhaaf, S. Self-Assembly in Aqueous Bile Salt Solutions. Curr.
Opin. Colloid Interface Sci. 2010, 15, 109-115. 9.
Madenci, D.; Salonen, A.; Schurtenberger, P.; Pedersen, J. S.; Egelhaaf, S.
U. Simple Model for the Growth Behaviour of Mixed Lecithin-Bile Salt Micelles. Phys. Chem. Chem. Phys. 2011, 13, 3171-3178. 10.
Luk A.S.; Kaler, E.W.; Lee, S.P. Structural Mechanisms of Bile Salt-Induced
Growth of Small Unilamellar Cholesterol-Lecithin Vesicles. Biochemistry 1997, 36, 5633-5644. 11.
Hjelm R.P., Thiyagarajan, P.; Alkan H. A Small-Angle Scattering Study of the
Effects of Dilution on Particle Morphology in Mixtures of Glycocholate and Lecithin. J Appl. Cryst. 1988, 21, 858-863. 12.
Schurtenberger, P.; Mazer, N.; Kaenzig, W. Micelle to Vesicle Transition in
Aqueous Solutions of Bile Salt and Lecithin. J. Phys. Chem. 1985, 89, 1042-1049. 13.
Hernell, O.; Staggers, J. E.; Carey, M. C. Physical-Chemical Behavior of
Dietary and Biliary Lipids during Intestinal Digestion and Absorption. 2. Phase Analysis and Aggregation States of Luminal Lipids during Duodenal Fat Digestion in Healthy Adult Human Beings. Biochemistry 1990, 29, 2041-2056. 14.
Hofmann, A. F.; Borgström, B. The Intraluminal Phase of Fat Digestion in
Man: The Lipid Content of the Micellar and Oil Phases of Intestinal Content Obtained during Fat Digestion and Absorption. J. Clin. Invest. 1964, 43, 247-257. 15.
Mazer, N. A.; Benedek, G. B.; Carey, M. C. Quasielastic Light-Scattering
Studies of Aqueous Biliary Lipid Systems. Mixed Micelle Formation in Bile SaltLecithin Solutions. Biochemistry 1980, 19, 601-615.
ACS Paragon Plus Environment
24
Page 25 of 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
16.
Maldonado-Valderrama, J.; Wilde, P.; Macierzanka, A.; Mackie, A. The Role
of Bile Salts in Digestion. Adv. Colloid Interface Sci. 2011, 165, 36-46. 17.
Dietschy, J. M.; Sallee, V. L.; Wilson, F. A. Unstirred Water Layers and
Absorption Across the Intestinal Mucosa. Gastroenterology 1971, 61, 932-934. 18.
Nordskog, B. K.; Phan, C. T.; Nutting, D. F.; Tso, P. An Examination of the
Factors Affecting Intestinal Lymphatic Transport of Dietary Lipids. Adv. Drug Delivery Rev. 2001, 50, 21-44. 19.
Williams, H.; Trevaskis, N.; Yeap, Y.; Anby, M.; Pouton, C.; Porter, C. H.,
Lipid-Based Formulations and Drug Supersaturation: Harnessing the Unique Benefits of the Lipid Digestion/Absorption Pathway. Pharm. Res. 2013, 30, 2976-2992 20.
Shiau, Y., Mechanism of Intestinal Fatty Acid Uptake in the Rat: the Role of
an Acidic Microclimate. The Journal of Physiology 1990, 421, 463-474. 21.
Sallee, V. L.; Dietschy, J. M. J. Determinants of Intestinal Mucosal Uptake of
Short-Chain and Medium-Chain Fatty-Acids and Alcohols. Lipid Res. 1973, 14, 475484. 22.
Lide, D. R., CRC Handbook of Chemistry and Physics. 1992-1993.
23.
Salentinig, S.; Sagalowicz, L.; Glatter, O. Self-Assembled Structures and
pK(a) Value of Oleic Acid in Systems of Biological Relevance. Langmuir 2010, 26, 11670-11679. 24.
Soderman, O.; Jonsson, B.; Olofsson, G. Titration of Fatty Acids Solubilized
in Cationic and Anionic Micelles. Calorimetry and Thermodynamic Modeling. J. Phys. Chem. B 2006, 110, 3288-3293. 25.
da Silva, F. L. B.; Bogren, D.; Soderman, O.; Akesson, T.; Jonsson, B.
Titration of Fatty Acids Solubilized in Cationic, Nonionic, and Anionic Micelles. Theory and Experiment. J. Phys. Chem. B 2002, 106, 3515-3522. 26.
Primrose, W.U. in: G.C.K. Roberts (Ed.), NMR of Macromolecules. A Practical
Approach, Oxford University Press, Oxford, 1993, pp. 22–23.
ACS Paragon Plus Environment
25
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
27.
Page 26 of 28
Gilbert, E. P.; Schulz, J. C.; Noakes, T. 'Quokka' - the Small-Angle Neutron
Scattering Instrument at OPAL. J. Physica B 2006, 385-86, 1180-1182. 28.
Kline, S. R. Reduction and Analysis of SANS and USANS Data Using IGOR
Pro. J. Appl. Crystallogr. 2006, 39, 895-900. 29.
Kirby, N. M.; Mudie, S. T.; Hawley, A. M.; Cookson, D. J.; Mertens, H. D. T.;
Cowieson, N.; Samardzic-Boban, V. A Low Background Intensity Focusing Small Angle X-ray Scattering Undulator Beamline. J. Appl. Crystallogr. 2013, 46, 16701680. 30.
Pecora, R. (ed.) Dynamic Light Scattering (Plenum Press, New York, 1985).
31.
Brunner-Popela, J.; Glatter, O. Small-Angle Scattering of Interacting Particles.
I. Basic Principles of a Global Evaluation Technique. J. Appl. Crystallogr. 1997, 30, 431-442. 32.
Weyerich, B.; Brunner-Popela, J.; Glatter, O. Small-angle scattering of
interacting particles. II.
Generalized Indirect
Fourier
Transformation Under
Consideration of the Effective Structure Factor for Polydisperse Systems. J. Appl. Crystallogr. 1999, 32, 197-209. 33.
Fritz, G.; Glatter, O. Structure and Interaction in Dense Colloidal Systems:
Evaluation of Scattering Data by the Generalized Indirect Fourier Transformation Method. J. Phys.: Condens. Matter 2006, 18, S2403-S2419. 34.
Glatter, O. A New Method for the Evaluation of Small-Angle Scattering Data.
J. Appl. Crystallogr. 1977, 10, 415-421. 35.
Glatter, O. The Interpretation of Real-Space Information from Small-Angle
Scattering Experiments. J. Appl. Crystallogr. 1979, 12, 166-175. 36.
Glatter, O. Evaluation of Small-Angle Scattering Data from Lamellar and
Cylindrical Particles by the Indirect Transformation Method. J Appl. Crystallogr. 1980, 13, 577-584.
ACS Paragon Plus Environment
26
Page 27 of 28
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
37.
Fritz, G.; Bergmann, A.; Glatter, O. Evaluation of Small-Angle Scattering Data
of Charged Particles using the Generalized Indirect Fourier Transformation Technique. J. Chem. Phys. 2000, 113, 9733-9740. 38.
Ornstein, L.S.; Zernike, F. Proc. Sect. Sci. K. Ned. Akad. Wet. 1914, 17, 793–
806. 39.
Lopez-Rubio, A.; Gilbert, E. P. Neutron Scattering: a Natural Tool for Food
Science and Technology Research. Trends Food Sci. Technol. 2009, 20, 576-586. 40.
Iampietro, D. J.; Brasher, L. L.; Kaler, E. W.; Stradner, A.; Glatter, O. Direct
Analysis of SANS and SAXS Measurements of Catanionic Surfactant Mixtures by Fourier Transformation. J. Phys. Chem. B 1998, 102, 3105-3113. 41.
Burchard, W. Polymer characterization: Quasi-Elastic and Elastic Light
Scattering. Macromolecular Symposia 1988, 18, 1-35. 42.
Senff, H.; Richtering, W. Temperature Sensitive Microgel Suspensions:
Colloidal Phase Behavior and Rheology of Soft Spheres. The Journal of Chemical Physics 1999, 111, 1705-1711. 43.
Mittelbach, P.; Porod, G. Small Angle X-Ray Scattering of Dilute Colloids. VII.
Distribution Functions of Triaxial Ellipsoids. Acta Physica Austriaca 1962, 15, 122147.
ACS Paragon Plus Environment
27
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 28 of 28
TOC Graphic
ACS Paragon Plus Environment
28