UCLA UCLA Electronic Theses and Dissertations
Title Quantitative Video-Tracking Electrophoresis and Refractometry of Nanoemulsions
Permalink https://escholarship.org/uc/item/6gt035zv
Author Zhu, Xiaoming
Publication Date 2013
Peer reviewed|Thesis/dissertation
eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA
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Quantitative Video-Tracking Electrophoresis
and Refractometry of Nanoemulsions
A dissertation submitted in partial satisfaction
of the requirements for the degree
Doctor of Philosophy in Chemistry
by
Xiaoming Zhu
2013
© Copyright by
Xiaoming Zhu
2013 ABSTRACT OF THE DISSERTATION
Quantitative Video-Tracking Electrophoresis
and Refractometry of Nanoemulsions
by
Xiaoming Zhu
Doctor of Philosophy in Chemistry
University of California, Los Angeles, 2013
Professor Thomas G. Mason, Chair
New kinds of nano-scale objects have led to immense advancements in fundamental science, medicine, and industry. As the development and application of novel nano-materials accelerates, it is vital to create effective, widely applicable, and inexpensive techniques for separating, purifying and characterizing nanoparticles and nanodroplets. In this thesis, we make two advances that rely on optical properties, specifically refractive index and scattering, of nanoparticles and nanoemulsions. We show that the droplet volume fraction φ and surfactant concentration C of a silicone oil-in-water nanoemulsion can be simultaneously determined by diluting the nanoemulsion with pure water, measuring its refractive index n using an Abbé refractometer, and fitting the result using a prediction for n that treats the nanoemulsion as an effective medium. This method can be used for accurate, non-destructive, and rapid determination of nanoemulsion compositions over a relatively wide range. Additionally, we demonstrate a quantitative method for performing real-time optical video tracking gel electrophoresis of nanoparticles and nanoemulsions in a passivated agarose gel. We use this
ii method to separate nanodroplets having different sizes and to measure the size distribution of a nanoemulsion. We have made several improvements in the experimental electrophoresis technique (e.g. gel passivation, well narrowing using a customized sample comb, and digital image background subtraction). We have also written software based on a deconvolution algorithm that involves a point-spread function that changes shape (e.g. width and skew of a modified log-normal function). This enables us to perform accurate and reliable measurements of particle and droplet size distributions having the following attributes: monodisperse containing one monomodal sharp peak, multimodal mixtures of monodisperse containing two or more sharp peaks, and broadly polydisperse (e.g. raw, unfractionated nanoemulsions). These results are significant because the latter two types of size distributions are very difficult to measure using other traditional particle-sizing methods. Beyond this, we have successfully separated different nanospheres that have the same radii but different surface charge groups by adjusting the pH of the buffer used during electrophoresis. This result shows that pH-controlled gel electrophoresis is potentially a useful method for separating and characterizing dispersions based on the total surface charge and the types of surface charge groups of charged nano-objects.
iii The dissertation of Xiaoming Zhu is approved.
Dolores Bozovic
William M. Gelbart
Thomas G. Mason, Committee Chair
University of California, Los Angeles
2013
iv
To my parents, brother, and Guojie
v TABLE OF CONTENTS
Chapter 1 Introduction 1
1.1 Nanotechnology 1
1.2 Nanoemulsion 1
1.3 Gel Electrophoresis 4
Chapter 2 Optically Probing Nanoemulsion Compositions 9
2.1 Abstract 9
2.2 Introduction 9
2.3 Experimental Methods 13
2.3.1 Materials 13
2.3.2 Nanoemulsion Preparation 13
2.3.3 Volume Fraction Measurements by Gravimetric Evaporation Method 14
2.3.4 Refractive Index Measurements 15
2.3.5 Droplet Size Characterization 16
2.3.6 Relation Between Nanoemulsion Refractive Index and Average Droplet
Radius 17
2.4 Results and Discussion 18
2.5 Conclusion 28
Chapter 3 Quantitative Video-Tracking Gel Electrophoresis of Uniformly Charged
Nanoparticles 29
3.1 Abstract 29
3.2 Introduction 30
vi 3.3 Experimental Methods 36
3.3.1 Materials 36
3.3.2 Apparatus 37
3.3.3 Preparation of Agarose Gel 40
3.3.4 Loading a Well with a Dispersion of Particles 41
3.3.5 Video Band-tracking during Gel Electrophoresis 41
3.3.6 Image Analysis 43
3.4 Results and Discussion 43
3.5 Conclusion 58
Chapter 4 Particle Size Distribution Measurements of Particles and Droplets Using Optical
Gel Electrophoresis 59
4.1 Abstract 59
4.2 Introduction 60
4.3 Experimental Methods 62
4.3.1 Materials 62
4.3.2 Preparation of Nanoemulsion 63
4.3.3 Agarose Gel Electrophoresis and Image Analysis 63
4.3.4 Deconvolution 63
4.4 Results and Discussion 65
4.5 Conclusion 75
Chapter 5 Separation of Particles by pH-Dependent Surface Charge 77
5.1 Abstract 77
5.2 Introduction 77
vii 5.3 Experimental Methods 78
5.3.1 Materials 78
5.3.2 Preparation of Buffer and Agarose Gel 79
5.3.3 Agarose Gel Electrophoresis and Image Analysis 80
5.4 Results and Discussion 80
5.5 Conclusion 84
Chapter 6 Conclusion and Future Directions 85
References 88
viii LIST OF FIGURES
Chapter 1
Figure 1.1 Schematic of the formation of nanoemulsion through extreme emulsification 2
Figure 1.2 Photograph of a Microfluidics M-110P high-shear liquid homogenizer used to
produce nanoemulsions 2
Figure 1.3 Schematic diagram of the interaction chamber in the M-110P 3
Chapter 2
Figure 2.1 Average droplet radius of nanoemulsions as a function of surfactant
concentration C 17
Figure 2.2 Normalized dimensionless refractive index difference c as a function of at
different oil volume fraction φ 18
Figure 2.3 Linear dependence of χ on φ and C for PDMS/SDS/H2O nanoemulsions 19
Figure 2.4 Schematic of evolution of an oil-in-water nanoemulsion sample during dilution with
pure water 20
Figure 2.5 Measurements of χ for a PDMS/SDS/H2O oil-in-water nanoemulsion having Vi = 0.5
mL as a function of mass of added water mw used to dilute the nanoemulsion 21
Figure 2.6 Experimental percentage uncertainty in measurements of oil volume fraction, Δφ (%),
and SDS concentration in the aqueous phase, ΔC (%), as a function of different φi and
Ci for PDMS/SDS/H2O nanoemulsions 23
Figure 2.7 Measured χ(φ,C) for oil-in-water nanoemulsion having three different oil types:
hexadecane/SDS/H2O, PPMS/SDS/H2O, and squalene/SDS/H2O 24
Chapter 3
Figure 3.1 Molecular structure of agarose 32
ix Figure 3.2 Schematic of polymer structural changes during gelation of agarose when the
temperature T decreases 33
Figure 3.3 Schematic of particle separation during agarose gel electrophoresis 34
Figure 3.4 Photograph of an optical video band-tracking electrophoresis apparatus 38
Figure 3.5 Schematic of an optical video band-tracking electrophoresis apparatus for separating
and measuring size distributions of nanoparticles using scattered light 39
Figure 3.6 Optical video band-tracking analysis of sulfate stabilized polystyrene (SSPS)
nanospheres undergoing electrophoresis in 0.195% (w/w) agarose gel for different
sphere radii a 45
Figure 3.7 Fitting parameters extracted from Fig. 3.6, plateau velocity vp and rise time τ required
for the particles to accelerate to vp, as a function of sphere radius a 46
Figure 3.8 Dependence of measured intensity I of SSPS nanospheres in agarose gel on sphere
radius a and volume fraction φ 47
Figure 3.9 Dependence of nanosphere propagation velocity v on passivation agent type and
concentration 49
Figure 3.10 Steady-state plateau propagation velocity vp is plotted as a function of agarose gel
concentration Cgel for SSPS nanospheres having different radii a 53
Figure 3.11 Video bank-tracking analysis of SSPS nanosphere electrophoresis in the absence of
agarose gel 54
Figure 3.12 Relationship between the applied field strength E and the plateau velocity vp for
agarose gel electrophoresis of SSPS nanospheres having different radii a 57
x Chapter 4
Figure 4.1 Measured average scattered light intensity I versus distance of propagation L of a
mixture of sulfate-stabilized polystyrene nanospheres at a time t = 1.5 x 104 s after
turning on the voltage of the electrophoresis apparatus 66
Figure 4.2 Representative shapes of modified lognormal point-spread functions (lines) having
different widths as a function of propagation distance L and time t for different
nanoparticle radii a 68
Figure 4.3 Convolved scattered light intensity Ic versus distance of propagation L 70
Figure 4.4 Multimodal deconvolved size distribution pφ(a) as a result of applying a
deconvolution algorithm to the passivated gel electrophoresis data for I(L) of a
mixture of four different monodisperse spheres 72
Figure 4.5 Measured I(L) for a silicone oil-in-water (1,1,5,5-Tetraphenyl-1,3,3,5-
tetramethyltrisiloxane/SDS/H2O) nanoemulsion using gel electrophoresis 73
Figure 4.6 Deconvolved size distribution pφ(a) of 1,1,5,5-Tetraphenyl-1,3,3,5-
tetramethyltrisiloxane/SDS/H2O nanoemulsion, corresponding to I(L) shown in
Figure 4.5, resulting from the application of a deconvolution algorithm 74
Chapter 5
Figure 5.1 pH dependence of the plateau velocity vp during electrophoresis for polystyrene (PS)
nanospheres having similar radius a stabilized by different surface charge groups:
sulfate (a = 42 nm) and carboxyl (a = 41 nm) 81
Figure 5.2 Gel electrophoresis images at t = 3.2 x 104 s showing separation of PS nanospheres
having the same radius and stabilized by carboxyl (C) and sulfate (S) surface charge
groups at different pH: pH = 4.76 and pH = 6.12 84
xi LIST OF TABLES
Chapter 2
Table 2.1 Refractive index and calculated and measured χφ of different oils 25
Chapter 3
Table 3.1 Average radius and standard deviation of radius of sulfate stabilized polystyrene
(SSPS) nanospheres δa 36
Chapter 4
Table 4.1 Parameters of some example point spread functions 69
Table 4.2 Average measured DLS radius of nanodroplets recovered from cut-out gel slices
after GE 75
Chapter 5
Table 5.1 Average radius and standard deviation σ of PS nanospheres having different
surface charge groups 79
Table 5.2 Buffer solution used in electrophoresis of nanoparticles to set pH 79
Table 5.3 Measured and literature pKa value of carboxyl and sulfate surface charged groups on
PS nanospheres 83
xii ACKNOWLEDGEMENTS
I am very grateful to have had the great opportunity to work with many exceptional professors, graduate students, postdoctoral researchers, undergraduate students, and supporting staff during my graduate study here at UCLA.
First of all, I would like to thank my advisor Tom Mason for his excellent mentorship for my development as a scientist throughout the last 6 years. I have been deeply influenced by his passion and curiosity toward scientific research. He has taught me how to think creatively about science and at the same time remain critical about our own work. His vast knowledge in science and mathematics as well as his attention to details has been tremendously beneficial for improvements in my ability to conduct research, in addition to my work. I am also sincerely indebted for his enormous patience and understanding toward all the difficulties that I have had due to family and health problems.
Additionally, I would like to expresses my gratitude to many other professors who have also been influential for my graduate school career, including Bill Gelbart, Chuck Knobler,
Dolores Bozovic, and Alex Levine.
Graduate students and postdoctoral researchers of the Mason group have always provided a stimulating intellectually environment in addition to mental support for me. Mike and Kenny have spent a lot time with me both doing lab experiments and discussing ideas and problems we encounter in research. Their creativity, extensive scientific knowledge and hands-on experimental or programming skills have benefitted me greatly. Jung-Ren, Kun, Clayton, KI,
Jim, Connie, Sara, and Kieche have all been friendly and helpful to work with.
I am also lucky to have many friends outside the Mason group who have been fun to fun to hang out with. Some of them, including Jenny, Mauricio, Yuewei, and Cathy, also helped with xiii my writing or gave me precious advice in their own area of expertise.
Last but not least, I would like to thank my mom, dad, brother, and Guojie for standing by me and encouraging me through all the difficulties and challenges that I have encountered.
Even though some of them are gone now but I am always grateful for all that they have done.
The foundation of four chapters as a whole in the dissertation comes directly from the following publications: Chapter 2: Zhu, X.; Fryd, M. M.; Huang, J. R.; Mason, T. G. Optically
Probing Nanoemulsion Compositions. Phys. Chem. Chem. Phys. 2012, 14, 2455-2461. Chapter 3 and 4: Zhu, X.; Mason T. G. Size Distribution Measurements of Nanoscale Particles and
Droplets Using Optical Video-Tracking Gel Electrophoresis, 2013, in preparation. Chapter 5:
Zhu, X.; Mason T. G. Separation of Nanoscale Particles by Charge Groups via Gel
Electrophoresis under Controlled pH Conditions, 2013, in preparation. Portions of the herein thesis have been copyrighted previously by the authors of these listed works and are used with permission. Anyone wishing to reproduce material herein that is also found in these works should contact the respective authors and journals to obtain appropriate permission.
xiv VITA
Education
• M.S. Chemistry: University of California, Los Angeles (June, 2010)
• B.S. Chemistry with Honors: Peking University, Beijing, China (June, 2007)
Employment
• 2013 Graduate Student Researcher
Department of Chemistry and Biochemistry
University of California, Los Angeles
• 2011-2013 Teaching Fellow
Department of Chemistry and Biochemistry
University of California, Los Angeles
• 2009-2011 Teaching Associate
Department of Chemistry and Biochemistry
University of California, Los Angeles
• 2007-2009 Teaching Fellow
Department of Chemistry and Biochemistry
University of California, Los Angeles
Publications
• Xiaoming Zhu, Michael M. Fryd, Jung-Ren Huang, Thomas G. Mason, Optically Probing
Nanoemulsion Compositions, Phys. Chem. Chem. Phys. 2012, 14, 2455-2461.
• Kenny Mayoral, Terry P. Kennair, Xiaoming Zhu, and Thomas G. Mason, Rotational Fourier
Tracking of Diffusing Polygons, Phys. Rev. E 2011, 84, 051405.
xv • Haiming Fan, Xiaoming Zhu, Lining Gao, Zichen Li, and Jianbin Huang, The
Photodimerization of a Cinnamoyl Moiety Derivative in Dilute Solution Based on the
Intramolecular Chain Interaction of Gemini Surfactant, J. Phys. Chem. B 2008, 112, 10165-
10170.
• Haiming Fan, Xiaoming Zhu, Zichen Li, Feng Han, Zhuang Liu, and Jianbin Huang,
Synthesis and Characterization of Cystine Based Gemini Surfactants, Acta Phys.-Chim Sin
2007, 23, 969-972.
Honors and Awards
• 2011: Hanson-Dow Excellence in Teaching (University of California, Los Angeles)
• 2009: Excellence in Second Year Academics and Research Award (University of California,
Los Angeles)
xvi Chapter 1
Introduction
1.1 Nanotechnology
Nanotechnology is based on science and engineering conducted at the nanoscale, which ranges from about 1 to 100 nm, according to the National Nanotechnology Initiative. It is currently a frontier in many vastly different fields of research, including fundamental science1, medicine2-4, electronics5-7, and energy production8-10. Because of its enormous potential in a variety of applications, there is increasing interest and investment in advancing nanotechnology from government, academia, and industry. Such fast development in nanotechnology has created a demand for reliable, efficient, quick, and inexpensive methods for separating and characterizing nanoscale objects.
1.2 Nanoemulsions
Nanoemulsions11,12 are multiphase colloidal dispersions of nanoscale liquid droplets.
They are typically created by extreme emulsification13-15 of one liquid into another immiscible liquid in the presence of surfactant, which inhibits subsequent coalescence between droplets via and interfacial repulsion. This repulsion can be electrostatic (in the case of ionic surfactant) or steric (in the case of non-ionic surfactant)16. This interfacial repulsion, which is provided by surfactant molecules adsorbed on the surfaces of nanodroplets, can keep the nanoemulsions kinetically stable for long periods of time. A typical procedure for forming a nanoemulsion
(NEM) through extreme emulsification is shown in Fig. 1.1. For the nanoscale emulsions we
1 make herein, a Microfluidics M-110P high-shear liquid homogenizer is used to carry out the extreme emulsification process, as shown in Fig. 1.2 and 1.3.
Figure 1.1. Schematic diagram of the formation of oil-in-water nanoemulsion through extreme emulsification. The yellow circles represent oil droplets. The oil phase is slowly added to water in the presence of surfactant molecules (not shown here) under low flow created by a rotary mixer to form microscale emulsions (premix). The premix is then passed through a high low rate homogenizer, which ruptures the large oil droplets into nanoscale droplets. The objects are not drawn to scale.
Figure 1.2. Photograph of a Microfluidics M-110P high-shear liquid homogenizer used to produce nanoemulsions. The M-110P is an electric-hydraulic pulse-action device that forces liquids at amplified pressures up to 30,000 psi though an interaction chamber (see Fig. 1.3), creating high flow rates that rupture emulsion droplets down to nanoscale. A cooling bath (not shown here) is used to counteract viscous heating due to the high shear if the sample is volatile or temperature-sensitive. Photograph used with permission from the Microfluidics Corporation. 2
Figure 1.3. Schematic diagram of the interaction chamber in the M-110P. A pre-mixed microscale emulsion is driven though the interaction chamber by a reciprocating intensifier pump. The liquid stream is split into separate micro-channels and accelerated to high velocity. The two streams both flow into the high impact zone and impinges on each other and/or on wear- resistant surface (e.g. diamond), creating high-shear and impact forces to rupture liquid droplets down to nanoscale. Picture used with permission from the Microfluidics Corporation.
Other ways to create nanoemulsions include11: phase inversion temperature, phase inversion composition, micro/nanofluidic flow focusing, satellite droplets, membrane emulsification, and liquid-liquid nucleation (Ouzo effect).
By varying the composition of the dispersed and continuous phases prior to emulsification and flow conditions during emulsification, it is possible to form many different kinds of nanoemulsions that have controlled droplet radii distributions12,13, structures17-19 and physical properties20,21. This control makes nanoemulsions advantageous for certain industrial products, such as foods and cosmetics14,22. Since the composition of a nanoemulsion, which is specified in part by the nanodroplet volume fraction φ and surfactant concentration C, can greatly affect the physical characteristics of nanoemulsions (e.g. their visual appearance, stability, and
3 rheology12,13), it would be very desirable to determine φ and C non-destructively. In Chapter 2, we present an optical method based on refractometry that does exactly this.
1.3 Gel Electrophoresis
Gel electrophoresis (GE)23-27 is a classic method of identifying and separating highly charged biopolymers having different lengths, such as strands of RNA and DNA. Various existing forms of gel electrophoresis have been developed28 following the same general principle: charged molecules or particles are forced to propagate through a porous gel network by an electric field and are separated based on their size and charge. After separation, the biological molecules can also be recovered and purified from the gels29-31, albeit in small quantities. The migration of charged biological molecules are determined by the following factors: the gel concentration, the electric field strength, the ionic strength of the buffer, the concentration of intercalating dyes used during electrophoresis, and the size, shape and net charge of the species being separated32. The effective pore size of the gel is set primarily through the gel concentration. This pore size plays an important role in determining whether or not (and if so, how fast) a charged object can propagate through the gel when an electric field is applied.
Extensible and flexible objects (e.g. semi-flexible biopolymers) could propagate through gels in a different manner than compact and rigid objects such as spherical nanoparticles and liquid nanodroplets33.
In a simple form, electrophoresis can be explained by considering the steady propagation of a charged object through a viscose medium by an electric field. When charged object reaches its terminal velocity (at steady state), the force exerted by the electric field balances out the drag force (frictional resistance) exerted by the viscous medium on the moving object: 4 E⋅ q v = (1.1) Fd where v is the velocity of propagation, E is the electric field strength, q is the net charge on the € object, and Fd is the drag force. The dielectric effects of water are ignored in this simple model.
The drag force is influenced by factors such as the viscosity of the medium, and the velocity, size, and shape of the object. In GE, the porosity of the gel network also affects the frictional resistance. Due to the complex nature of the migration of biomolecules during GE, the
34,35 relationship between v and Mw for biopolymers is not linear . Thus, it is not a simple task to derive the size of biomolecules directly from their migration during GE. In practice, molecular weight markers (a set of DNA fragments or proteins of known molecular sizes, i.e. size standards) are run in the same gel as the unknown samples. The size of an unknown molecule is determined by comparing the distance traveled with those of the markers.
Performing electrophoresis using PA gels and SDS-adsorption onto biomolecules is known as SDS-PAGE. GE methods have been adapted for proteins that do not have high charge densities by causing amphiphilic molecules, such as anionic surfactants like sodium dodecyl sulfate (SDS), to adsorb onto and thereby increase the degree of charging of the proteins. Two of the most common gel materials that are readily cross-linked are agarose and poly-acrylamide
(PA). Both classic GE and SDS-PAGE are common and important tools in rapidly determining the number of base pairs of DNA as well as the molecular weights of proteins32.
Because most biological molecules are not visible to human eyes or cameras, these molecules must be labeled for detection. Different absorbing dyes (e.g. Coomassie brilliant blue36-41, silver29, 30, Ponceau S, Amido black, zinc, and copper), fluorescent dyes (e.g. ethidium bromide, Nile red, Fluorescamine, SYBR, and SYPRO), and radioactive isotopes42,43 enable the
5 visualization of the locations of biological molecules in GE. Some of the aforementioned staining dyes bind to the biopolymers reversibly and can be removed by rinsing the gel repeatedly. Besides these staining dyes, a tracking dye (e.g. bromophenol blue and xylene cyanole FF) is routinely added to the sample solution to determine the duration of an electrophoresis experiment. A tracking dye molecule migrates faster than most biopolymers because of its small size. To prevent the biopolymers from elctrophoresing out of the gel, the power supply is turned of before the tracking dye front reaches the edge of the gel.
It is important to use a buffer solution when performing electrophoresis26,44,45 to achieve effective separation. First of all, the buffer helps prevent the pH from changing drastically due to electrolysis of water, as well as provides a medium for heat dissipation, during electrophoresis.
Furthermore, it provides ions, which carry a current necessary for the electrophoresis process44.
In the absence of ionic species from the buffer system, electrical conductance is minimal and the charged biological molecules barely move. Some common buffer systems used include:
Tris/Acetate/EDTA (TAE), Tris/Borate/EDTA (TBE), and Tris/Phosphate/EDTA (TPE). In most cases, the same type and concentration of buffer is used in both the gel and the tank (continuous buffer systems). But in polyacrylamide gel electrophoresis, discontinuous (multiphasic) buffer systems, i.e. different buffers are used for the tank and the gel, to improve the sharpness and resolution of the band. It is very important to choose the proper buffer system based on the nature of the species being separated.
A variety of instruments exist for conducting GE. Conventional slab GE is the most common and least expensive option. A slab GE apparatus typically can be obtained in two different configurations: a vertical unit is suitable for running polyacrylamide gels, and a horizontal “submarine” chamber is used for agarose gels. Some other specialized systems are
6 also used to perform GE. These include ultrathin-layer slab46,47, and capillary48-50, and microchip
GE51-53. These different GE devices offer high resolving power or fast separation but are more expensive.
GE is also a powerful tool for molecular purification if an appropriate recovery method is applied29-31,54-62 after the separating the molecules. The most straightforward method is electroelution58-61: slice a block of gel and place it in a piece of sealed dialysis tubing with a small amount of fresh electrophoresis buffer; then apply a voltage to drive the molecules out of the gel into the buffer. Another method is to incubate and melt the agarose gel in small quantities of buffer at 65 °C and extract the biomolecules by precipitation or binding to glass or silica particles. Alternatively, agarase or chaotropic salt (e.g. sodium iodide) can be used to help digest the agarose gel. For polyacrylamide gels, a “crush and soak” method is sometimes used: crush a piece of polyacrylamide gel in a microcentrifuge tube, incubate with constant shaking at 37 °C, and then eliminate the gel piece via centrifugation or filtration.
To a much more limited degree, GE has been used with charged objects, such as viruses48,63-66 and carbon nanotubes67-69. In some cases, a charged surfactant, such as SDS, has been added to the buffer. The role of SDS is similar to that in SDS-PAGE: to adsorb onto the species to be separated and provide adequate charge for them to move through the gel when an electric field is applied. The SDS is not used to alter the gel itself.
The propagation of charged nanoparticles in electrophoresis is influenced by a number of factors including the buffer’s viscosity, the temperature, and the net charge, size and shape of the particles. If spherical particles propagate relatively slowly through the medium, then there is no turbulence (low Reynolds number Re << 1) and Stokes’ drag describes the viscous drag force:
Fd = −6πηav , (1.2)
7 € where η is the viscosity of the medium, a is the radius of the spheres. In a simple model for the
GE of nanospheres, we treat the hydrogel matrix as an effective medium and introduce an effective viscosity ηeff, which accounts for the friction resistance exerted by both the gel network and the buffer solution. Combining Eq. 1.1 and 1.2, we get the following equation:
E⋅ q v = , (1.3) 6πηeffa which gives a qualitative description of the propagation of nanospheres in GE. € This thesis demonstrates that gel electrophoresis has great potential in characterizing the size distributions and electrophoretic mobilities of nanoparticles and nanoemulsion droplets. In
Chapter 3, we demonstrate a quantitative study of GE of charged nanospheres using optical video-tracking analysis. Through a combination of enhancements to both experimental techniques and data analysis methods to standard GE, we investigate the effect of various factors on the electrophoretic motion of charged nanoparticles in a reproducible manner. These improvements make GE a viable technique for measuring the size distribution of dispersions of nanoscale objects, as described in Chapter 4. Utilizing the separating power of GE, this new method overcomes the limitations of traditional techniques such as DLS and SLS and is particularly useful for multimodal or polydisperse size distributions. In Chapter 5, we show that nanoparticles stabilized by different charge groups but having the same size, shape, and charge group density can be readily separated via GE by adjusting the pH of the running buffer.
8 Chapter 2
Optically Probing Nanoemulsion Compositions
2.1 Abstract
Many types of colloids, including nanoemulsions that contain sub-100 nm droplets, are dispersed in molecular and micellar solutions, especially surfactant solutions that confer stability against droplet coalescence. Since it would be desirable to measure the droplet volume fraction φ and surfactant concentration C of a nanoemulsion non-destructively, and since the droplet and surfactant structures are much smaller than wavelengths of visible light, optical refractometry could provide a simple and potentially useful approach. By diluting a silicone oil-in-water nanoemulsion having an unknown φ and C with pure water, measuring its refractive index n using an Abbé refractometer, and fitting the result using a prediction for n that treats the nanoemulsion as an effective medium, we show that the φ and C can be accurately determined over a relatively wide range of compositions. Moreover, we generalize this approach to other types of nanoemulsions in which a molecular constituent partitions in varying degrees between the dispersed and the continuous phases.
2.2 Introduction
Nanoemulsions12 are multiphase colloidal dispersions of nanoscale liquid droplets, typically created by extreme emulsification13-15 of one liquid into another immiscible liquid in the presence of surfactant. The dispersed droplets are kinetically inhibited against coalescence for long periods of time by the repulsion of surfactant molecules that populate the droplet
9 interfaces16. By varying the composition of the dispersed and continuous phases prior to emulsification and flow conditions during emulsification, it is possible to form many different kinds of nanoemulsions that have controlled droplet radii distributions12,13, structures17-19 and physical properties20,21, making them advantageous for certain industrial products, such as foods and cosmetics14,22.
Although optical scattering from colloidal dispersions have been extensively studied, both experimentally and theoretically70,71, simple optical refractometry of colloidal systems in the visible spectrum has attracted much less attention, perhaps because the information content of refractometry is reduced by spatial averaging. In the simplest case, the refractive index of molecular solutions in the visible spectrum is well understood by basic optical polarizability. The non-absorbing solvent and solute molecules can both be regarded as polarizable dielectric elements that typically have radii that are much smaller than the wavelength of visible light λ
(i.e. droplet radii below the range from about 400 nm to about 780 nm) Effective medium
72,73 theory yields a linear dependence of the refractive index difference, n - n0, where n and n0 are the refractive index of the complex fluid (i.e. solution) and the bare solvent, respectively, on the molecular concentration C. For a fixed λ, this can be captured in the following simple relationship for the normalized dimensionless refractive index difference χ :
, (2.1)
where χC° of the solution is χ at a certain fixed reference concentration C°. As any dielectric elements increase in radius towards and beyond visible wavelengths, scattering can become appreciable, and this simple theory is no longer applicable. For many types of molecular surfactants, which can form nanoscale micelles at higher concentrations, Eq. (2.1) can still remain valid far above the critical micelle concentration C*. 10 Beyond molecular solutions, measurements of n have been made on simple single- component colloidal dispersions that are not index-matched with the continuous phase. In particular, a significant body of work exists for dispersions of non-absorbing particles70,74-82 for which n is influenced by particle volume fraction77, radius70,74,80,83, shape74,76,84 and polydispersity81,85. For spherical submicron particles having diameters between about 0.1 µm and
0.5 µm, it has been found semi-empirically that a linear relationship of n - n0 with respect to particle volume fraction φ exists up to about φ ≈ 0.570,74-79. This linear dependence effectively expresses the mean-field limit for the refractive index difference corresponding to Eq. (2.1). For dispersions containing sub-micron and microscale particles, the increased turbidity can sometimes lead to difficulties in making accurate measurements of n using standard Abbé refractometry, since the light-dark boundary (i.e. "cut-off edge") becomes blurred due to strong scattering of visible light. However, more advanced optical methods, such as differential refractometry, can measure refractive index of more turbid dispersed media where the particle sizes can be well above the nanoscale81.
Since the refractive index of a complex fluid contains important and useful information related to its composition, including both molecular and colloidal components, measuring n can potentially be used to determine unknown compositions of non-absorbing nanoscale objects dispersed in a molecular solution. Among this general class of materials, nanoemulsions are a natural sub-category, since a molecular surfactant is typically necessary to stabilize the dispersed colloidal droplets against coalescence and aggregation. Typically, the surfactant resides in the continuous phase and on droplet interfaces, but this is not always the case. Both φ and C can greatly affect the physical characteristics of nanoemulsions, such as their visual appearance, stability, and rheology12,13.
11 By measuring n(φ,C) for a model silicone oil-in-water nanoemulsion system, we verify that the Biot-Arago equation86 accurately describes the compositional dependence of the refractive index:
, (2.2)
where nd,eff and nc,eff are the effective refractive indexes of the dispersed phase and the continuous phases, respectively. This relation is the limiting form of the more general Lorentz-
Lorenz equation87,88 if the dispersion is dilute and if the refractive index difference is small between the continuous and the dispersed phases80,89. However, based on this simple equation, it becomes apparent that a single refractometry measurement of n cannot be used to deduce both unknown φ and unknown C of a nanoemulsion simultaneously. Thus, to obtain accurate values for both φ and C of a nanoemulsion by refractometry, measuring n more than once is necessary.
Here, we present a method of using optical refractometry to determine φ and C of a nanoemulsion that is systematically diluted by the solvent, the dominant component of the continuous phase. We demonstrate that this method is effective for nanoemulsions made using several different oil types. This optical refractometry - dilution approach provides a significant advantage over destructive evaporative methods for determining φ, which typically require that the oil must be non-volatile and that the surfactant concentration in the continuous phase must be known. Furthermore, we develop effective medium equations that predict the refractive index of nanoemulsions in which the surfactant resides in the dispersed phase or in a combination of the dispersed and continuous phases, rather than only in the continuous phase. Because a nanoemulsion's refractive index is sensitive to its composition, an in-line optical refractometry approach could potentially be developed and used for automated monitoring and quality-control
12 of a nanoemulsion's composition in industrial applications77.
2.3 Experimental Methods
2.3.1 Materials
Each nanoemulsion is made using one of the following non-volatile oils: 10 cSt polydimethylsiloxane (PDMS, molecular weight: ≈ 1000 to 1500 g/mol), 20 cSt polyphenylmethylsiloxane (PPMS), hexadecane, or squalene. Anionic sodium dodecyl sulfate
(SDS) is used as the surfactant at one of the following concentrations C (mM) = 25, 75, 100,
200, 400, 500, 600, 700, and 800. The critical micelle concentration of SDS is C* = 8.1 mM90.
We have measured the densities of SDS solution ρC at different concentrations gravimetrically using a volumetric flask. We find that the solution's density, relative to that of pure water, where
ρw = 0.99799 g/mL is the density of water at 1 atm and 21 °C, is proportional to C:
. (2.3)
-4 For SDS, we have measured qc = 3.23 ± 0.08 × 10 , as obtained from a least squares fit to our data.
2.3.2 Nanoemulsion Preparation
Nanoemulsions having different SDS concentrations and volume fractions are created by the following two-step procedure91. We first create a polydisperse microscale “premix” oil-in- water emulsion from an oil and surfactant of our choice using a rotary mixer. Here we fix φ and
C by the quantities of oil and surfactant added. To further rupture the microscale emulsion
13 droplets down to the nanoscale, the premix is passed through a high-pressure homogenizer
(Microfluidizer 110S, inlet air pressure ≈ 5 atm corresponding to a liquid pressure ≈ 1300 atm,
75 µm channel size). Since the flow in the high-pressure homogenizer is spatially and temporally inhomogeneous, the emulsion is cycled through the homogenizer six times to decrease and to reduce the size polydispersity13. In order to minimize any loss of water due to evaporation after the emulsification process, the microfluidic interaction chamber and outlet cooling coil are immersed in an ice bath to remove the significant heat generated due to the strong flow of the emulsion created by the homogenizer.
2.3.3 Volume Fraction Measurements by Gravimetric Evaporation Method
After emulsification, we have confirmed that the nanoemulsion’s original φ has not changed using conventional destructive evaporation according to the following procedure. To obtain 0.3% uncertainty in φ, we choose to use approximately 3 grams of a nanoemulsion for each volume fraction measurement. The accuracy of the evaporative method is determined primarily by the accuracy of our balance (±0.2 mg), since we measure the mass over time to ensure that we have reached a steady state in which no further solvent evaporates. The initial mass and the final weight of a sample, after about 12 hours of evaporation in a crystallizing dish in a fume hood, are recorded. We select a silicone oil that is non-volatile, as verified by control experiments, so the difference between the initial mass mi and the final mass mf is the mass of water in the original nanoemulsion sample, because only the oil and surfactant remain when the evaporation is complete. Therefore, if C is already known, φ can be calculated using the following equation:
14 , (2.4)
where MS is the molecular weight of the surfactant (e.g. SDS), VC = (mi - mf)/(ρC - CMS) is the continuous phase volume, and ρoil is the density of the oil.
2.3.4. Refractive Index Measurements
Refractive index measurements of PDMS/SDS/H2O oil-in-water nanoemulsions as a function of φ at a given C are obtained by diluting φ in increments of 0.05 for an original nanoemulsion at higher φ (e.g. φ ≈ 0.3) with an SDS solution having the same concentration as that used in the continuous phase of the original nanoemulsion sample. Repeating this process for different C, refractive index curves as a function of C at a given φ are measured.
Refractive index measurements are made using a Reichert Abbé Mark II Refractometer having a monochromatic light source of the sodium D line at 589 nm, a slit width of 1 mm into which the sample is loaded, and a stated precision in n of ±0.0002. The refractometer is calibrated at a temperature T = 21.0 °C using pure water, which has a refractive index of n0 =
1.3329. We find that n decreases by approximately 0.0008 when T is increased from 21.0 °C to
25.0 °C. Thus, temperature control is necessary to obtain measurements of n that have sufficient accuracy and precision for our studies. Therefore, we fix T = 21.0 ± 0.5 °C using a thermal circulator for all of our measurements. Approximately 0.2 mL of sample is loaded onto the refractometer for each measurement of n. The average value is recorded based on three independent n measurements of the same sample. The standard deviation of our three measurements of n is typically found to be ±0.0001, which is close to but slightly smaller than
15 the stated precision of the refractometer. For the nanoemulsions we have studied, the scattering mean free path of the light is comparable to or larger than the refractometer's slit width, so the light-dark boundary is quite sharp (i.e. the turbidity of the sample is not extreme).
We have investigated the dependence of n on the droplet radius and the polydispersity of several nanoemulsions. We find that when < 100 nm, n is independent of the droplet radius and polydispersity, consistent with measurements of other nanoscale dispersions80. This result ensures that n only depends on the oil type, oil droplet volume fraction, surfactant type, and surfactant concentration in our experiments. We have also made control measurements, which show that only the composition, not the history of the formation, of the nanoemulsion affects its refractive index. To check this, we have compared n of nanoemulsions created directly at a certain oil volume fractions or SDS concentration with n of nanoemulsions prepared by diluting from an originally higher oil volume fraction or higher SDS concentration, and we did not find any difference. These measurements have been made in the regime where the surfactant concentration is significantly larger than the surfactant's critical micelle concentration.
2.3.5 Droplet Size Characterization
We use dynamic light scattering (DLS) with a helium – neon laser at 90 degrees to characterize the volume weighted droplet radial distribution of the 10 cSt PDMS/SDS/H2O oil- in-water nanoemulsions used in our experiments. All nanoemulsions are made according to the two-step process described in the manuscript. The samples are all created at an initial oil volume
-5 fraction of ϕi = 0.30 and diluted to ϕ ≈ 10 for DLS measurements. From this distribution, we extract the volume-averaged radius and the polydispersity of the droplets in our nanoemulsion samples. As C varies between 25 mM and 800 mM, ranges from 20 nm to 80 16 nm, and the polydispersity index is approximately 0.3 for all samples measured.
Figure 2.1. For 10 cSt PDMS/SDS/H2O oil-in-water nanoemulsions, is plotted as a function of C at fixed ϕi = 0.30 and inlet air pressure ≈ 5 atm for the high-pressure homogenizer. The solid line is an empirical fit to ∼ C -1/3. All measurements are made at a temperature of T = 21.0 °C.
2.3.6 Relation Between Nanoemulsion Refractive Index and Average Droplet Radius
The normalized refractive index difference χ is plotted against for a series of 10 cSt
PDMS/SDS/H2O oil-in-water nanoemulsions at different ϕ. We extract a small amount of sample after each time the premixed PDMS/SDS/H2O emulsion passes through the high-pressure homogenizer for refractive index measurements. Thus each group of these samples has the same composition (ϕ and C) but different and polydispersity. In all samples plotted here, we fix C
= 100 mM. As shown in Fig. 2.2, χ is nearly independent of and polydispersity, provided
17
Figure 2.2. For 10 cSt PDMS/SDS/H2O oil-in-water nanoemulsions, χ is plotted against for a series of different ϕ as they appear from bottom to top: ϕ = 0.05(), 0.1(), 0.15(), 0.2(). In all samples, C = 100 mM. All measurements are made at T = 21.0 °C.
2.4 Results and Discussion
We have measured n(φ,C) of a PDMS oil-in-water nanoemulsion stabilized using SDS, all having 40 nm < < 100 nm, as shown in Fig. 2.3(a). For a fixed value of C, we find a linear relationship between n and φ. Similarly, we find that n depends linearly on C at constant φ, as shown in Fig. 2.3(b). These simple linear relationships reflect the applicability of the Biot-
Arago equation86 to nanoemulsion systems:
,C C /C∗ 1 , (2.5) χ(φ ) = χC ∗ ( )( − φ) + χφφ
where χC* and χφ are positive coefficients influenced by the type of surfactant in the continuous € phase and the type of oil in the dispersed phase, respectively. The first term in Eq. (2.5) effectively generates a cross-term proportional to φC having a negative coefficient. Here, χC*
* effectively describes χ of the surfactant solution at C , and we have measured χC * = (2.02 ±
-4 0.08) × 10 for SDS in water. In the second term, χφ is proportional to the refractive index
18 difference between the oil and pure water. For 10 cSt PDMS oil-in-water nanoemulsions, χφ =
-2 (5.11 ± 0.04) × 10 and is much larger than χC*, indicating that the dominant influence on the refractive index is typically through the oil volume fraction, except at very low φ.
Figure 2.3. For PDMS/SDS/H2O oil-in-water nanoemulsions, the normalized refractive index difference χ is plotted as a function of: (a) φ for a series of different C as they appear from bottom to top: C (mM) = 25 (), 75 (), 100 (), 200 (), 400 (◆), 500 (), 600 (), 700 (), and 800 (). Solid lines represent linear fits. As an example, a dilution curve of an unknown nanoemulsion sample is measured () and fit using Eq. (2.5) (dashed line- see text for description). (b) C/C* at a series of different φ as they appear from bottom to top: φ = 0 (), 0.05 (), 0.10 (◆), 0.15 (), 0.20 (), 0.25 (), and 0.30 (). Solid lines are linear fits.
By measuring the refractive index of a PDMS/SDS/H2O oil-in-water nanoemulsion as a function of increasing dilution with pure water (see Fig. 2.4), we deduce the nanoemulsion's φ and C. This enables us to assess the accuracy of the optical approach in determining a nanoemulsion's composition, as compared to its composition measured destructively by gravimetric analysis. Because diluting with a pure solvent effectively varies both φ and C, the dilution curve cuts through a series of standard curves (see dashed line in Fig. 2.3(a)).
19
Figure 2.4. Schematic of evolution of an oil-in-water nanoemulsion sample during dilution with pure water. Light blue represents aqueous continuous phase, yellow circles represent surfactant coated nanoemulsion droplets, and purple circles with tails represents surfactant molecules. The objects are not drawn to scale.
After taking into account the density change of the continuous aqueous phase SDS solution using Eq. (2.3), the results of our optical refractometry measurements as a function of diluting water mass mw are shown in Fig. 2.5. We appropriately parameterize the equations for φ and C in terms of mw, an initial volume of nanoemulsion Vi, an initial volume fraction φi, and an initial surfactant concentration Ci prior to dilution:
, and (2.6)
. (2.7)
Then, substituting these expressions into Eq. (2.5), we obtain c(mw):
. (2.8)
Thus, if χ(mw) is accurately measured for a sufficient number of dilution steps over a sufficiently wide range of mw, then a least squares fit using Eq. (2.8) will yield both φi and Ci. Although
20 nanoemulsion sample is altered by dilution, the refractometry-dilution approach is non- destructive in the sense of avoiding droplet coalescence, in contrast to the evaporation method, which destroys the emulsion through droplet coalescence.
Figure 2.5. Measurements of χ for a PDMS/SDS/H2O oil-in-water nanoemulsion having Vi = 0.5 mL as a function of mass of added water mw used to dilute the nanoemulsion. The nanoemulsion's composition is known to be Ci = 400 ± 1 mM and φi = 0.291 ± 0.001. By fitting the refractometry data for χ(mw) to Eq. (2.8) (solid line), we obtain Ci = 400 ± 15 mM and φi = 0.28 ± 0.02, in good agreement.
Next, we evaluate the accuracy of the refractive index-dilution approach for measuring droplet volume fraction and surfactant concentration. We calculate the experimental absolute percentage error in volume fraction,
, (2.9)
by comparing the volume fraction determined by refractometry φRI with that obtained by evaporation φE. Similarly, we calculate the experimental absolute percentage error in surfactant concentration,
21 . (2.10)
by comparing the concentration determined by refractometry CRI with the initial known composition of the SDS solution CE. In Figs. 3(a) and 3(b), we plot Δφ (%) and ΔC (%) as a function of φi and Ci for many nanoemulsion samples having different φi and Ci; these plots summarize the results of many sets of dilution-refractometry measurements.
From Fig. 2.3, a nanoemulsion's composition can be measured accurately over a wide range of φi and Ci provided that φi > 0.05, and C can be measured within 10% uncertainty if φi <
0.35 and 150 mM < Ci < 800 mM. The lower limits of φi and Ci that can be accurately measured by dilution-refractometry is determined primarily by the number of dilution points obtained, the range of mw over which they are obtained, and the resolution of the refractometer. Using only about 0.5 g of nanoemulsion, the absolute experimental uncertainties in φ and C are typically
±0.03 and ±10 mM, respectively. Another factor determining the lower Ci is the fact that significant amount of surfactant is distributed at the droplet interface in a nanoemulsion system.
For example, if we assume the equilibrium surface concentration is ρs = 1 surfactant molecule /
0.2 nm2, droplet radius = 50 nm and φ = 0.1, we could roughly estimate the total concentration of surfactant on the droplet interface to be about 20 mM. If > 100 nm, measuring n accurately is difficult because such larger oil droplets scatter light strongly, obscuring the total internal reflection boundary on the Abbé refractometer. Moreover, if φi >
0.35, any small error in dilution, which could cause a change in φ, would potentially conceal the dependence of n on C and decrease the accuracy in measuring C, in the typical case when χφ >>
χC. Unless a different emulsification procedure would yield significantly smaller , it is difficult to accurately obtain φi for φi > 0.4 for the nanoemulsions used in this study, because the 22 multiple light scattering by the oil droplets becomes significant and blurs the Abbé boundary, making it difficult to precisely identify. For Ci ≥ 800 mM, the relationship between n, φ, and C deviates from Eq. (2.8) since non-ideal solution effects occur related to the SDS concentration being near its solubility limit92, 93. The accuracy in determining φ typically improves if the refractive index difference between the oil and water is larger. To measure φi and Ci more accurately (at less than 5 % uncertainty), our approach is still applicable to a wide range of compositions: 0.10 < φi < 0.30 and 250 mM < Ci < 700 mM.
Figure 2.6. Experimental percentage uncertainty in measurements of: (a) oil volume fraction, Δφ (%); (b) SDS concentration in the aqueous phase, ΔC (%), as a function of different φi and Ci for many PDMS/SDS/H2O nanoemulsion samples, as determined by the optical refractometry- dilution fitting method demonstrated in Fig. 2.5.
23 We have also investigated how the oil's refractive index affects χφ. For hexadecane, 20 cSt PPMS, and squalene oil-in-water nanoemulsions stabilized by SDS, n exhibits similar dependences on both φ and C as we have already shown with PDMS, as shown for a more limited range of C in Fig. 2.7. Dilution curves for nanoemulsions having these different oils all cut through their respective series of standard curves.
Figure 2.7. Measured χ(φ,C) for oil-in-water nanoemulsion having three different oil types (values for PPMS/SDS/H2O and squalene/SDS/H2O are shifted up by 0.010 and 0.020, respectively), from bottom to top: hexadecane/SDS/H2O, C (mM) = 25 (), 75 (), 200 () and a dilution curve (and dashed line); PPMS/SDS/H2O, C (mM) = 25 (), 75 (◆), 200 () and a dilution curve (+ and dashed line); squalene/SDS/H2O, C (mM) = 25 (), 75 (), 200 () and a dilution curve (× and dashed line). Solid lines are linear fits.
By measuring the refractive index of nanoemulsions having several different oil types, we have verified that χφ = (noil - n0)/n0, where noil is the refractive index of the pure oil, as shown in Table 1. Likewise, we would expect χC* = (nC* - n0)/n0, where nC* is the refractive index of the
24 surfactant solution at some concentration C*, although we have not verified this for other surfactant types that are readily soluble in molecular or micellar form in the continuous phase.
These simple relationships for χφ and χC* can be used to generalize the equations we have presented to other compositions of nanoemulsions involving a variety of surfactants, dispersed phases, and continuous phases. The measured dilution curves shown in Fig. 2.7 illustrate how this generalization can be used to optically measure compositions of a wide range of nanoemulsion formulations.
Table 2.1. Refractive index and calculated and measured χφ of different oils
Oil Type noil Predicted Measured
10 cSt PDMS 1.3995 5.00 5.11 ± 0.04
Hexadecane 1.4346 7.63 7.66 ± 0.03
20 cSt PPMS 1.4418 8.17 8.17 ± 0.02
Squalene 1.4959 12.23 12.26 ± 0.03
Compared to nanoscale particulate dispersions in which molecular additives are typically present only in the continuous phase, emulsions offer a wider variety of interesting possibilities, such as surfactant partitioning between continuous and dispersed phases, since a surfactant may be soluble to a significant degree not only in the continuous phase but also in the dispersed phase. For nanoemulsions in which the surfactant does not remain overwhelmingly in the continuous phase, we would not expect Eqs. (2.5) or (2.8) to be valid. For instance, suppose an inverse water-in-oil nanoemulsion is stabilized by a surfactant that is only soluble in the aqueous dispersed phase and is insoluble in the continuous oil phase. In this case, the equation describing the dimensionless refractive index difference would change to: χ(φ,C) = χC*(C/C*)φ, where here
25 φ would represent the water droplet volume fraction and n0 would represent the refractive index of the continuous oil phase.
More generally, if a molecular additive in an emulsion, such as a surfactant or co- surfactant, has significant solubility in both the continuous and the dispersed phases, partitioning of the molecular additive in different amounts to the continuous and dispersed phases could occur in some types of emulsions. To handle this interesting and more complex case, we predict the appropriate form of the refractive index using the knowledge gained from our study of the simpler case. After surfactant partitioning, the equilibrium surfactant concentrations in the dispersed and continuous phases, Cd and Cc, respectively, multiply terms proportional to φ and to
(1-φ), respectively:
, (2.11)
where nc and nd are the refractive index of the pure continuous and pure dispersed phase solvents, respectively, and α and β are determined from linear fits to the refractive index of the solutions of the molecular species in the respective solvents, nsc = nc + αCc for the continuous phase and nsd = nd + βCd for the dispersed phase. At equilibrium, the relative partitioning of the surfactant can be represented by the dimensionless ratio of the concentrations of the molecular species in the dispersed and continuous phases: K = Cd/Cc. For a total surfactant concentration of the entire system:
(2.12) present in the combined continuous and dispersed phases, the effective medium prediction for the refractive index of the emulsion (i.e. Eq. (2.11)) can be re-expressed as:
26 n = nc + (nd − nc)φ +{[α(1− φ) + βφK]/[(1− φ) + φK]}C . (2.13)
This formula effectively reduces to Eq. (2.5) in the limit as K approaches zero and no € surfactant is present in the dispersed phase (i.e. when C = (1-φ)Cc). The Laplace pressure difference resulting from the curvature of nanoscale droplets having a significant surface tension could potentially affect the partitioning and therefore K, but Eq. (2.13) will hold provided K refers to the equilibrium concentrations in the emulsion.
While showing the limits of compositional determination of typical oil-in-water nanoemulsions using a standard refractometer, our study has also led to the prediction of the refractive index for small-scale emulsions in which molecular partitioning to both the continuous and the dispersed phases can occur. This type of partitioning would not be found in most types of dispersions of solid particles, because the molecular species typically cannot penetrate into non- porous solid particles. However, this prediction is likely to be important for some types of nanoemulsions, especially for certain molecular species, such as alcohol surfactants or co- surfactants, that can have significant solubility in many types of oils as well as water. It is conceivable that an additional term, related to partitioning of the surfactant to the large surface area of oil-water interfaces in a nanoemulsion, could play a role in modifying the refractive index, but the relative importance of possible interfacial terms involving a surface concentration on the droplet interfaces may be below easily measureable limits for standard optical refractometry. Experimentally, using differential refractometry80,94 or other more advanced methods than simple Abbé refractometry would extend our approach to more turbid dispersions, such as emulsions that contain submicron and even microscale droplets well above the nanoscale.
27 2.5 Conclusion
Since the droplets in nanoemulsions are significantly smaller than the lower limit of the visible spectrum, multiple scattering of light is small enough that optical refractometry using visible wavelengths can provide an effective means of characterizing a nanoemulsion's composition. If the oil and surfactant types are known, an optical refractometry-dilution method can be used to simultaneously determine both the surfactant concentration and droplet volume fraction over a wide range, because the normalized refractive index difference of oil-in-water nanoemulsions follows the Biot-Arago equation. We anticipate that this refractometry-dilution method will be useful for characterizing nanoemulsions non-destructively, since it is rapid, requires very small volumes, and does not cause droplet coalescence. Given the potential in nanoemulsions for partitioning of molecular components to both the continuous and dispersed phases, we have developed predictions for the refractive index of more complex nanoemulsion systems, beyond those in which a molecular additive is soluble only in the continuous phase.
28 Chapter 3
Quantitative Video-Tracking Gel Electrophoresis of
Uniformly Charged Nanoparticles
3.1 Abstract
Novel nanomaterials are now fabricated and used in all areas of fundamental scientific research, medicine, and industry. Consequently, there is significant demand for rapid, efficient, reliable and cost-effective analytical methods for quality control of nanoparticles and nanodroplets, because standard synthesis techniques produce nano-objects having size distributions that possess at least some size polydispersity. Gel electrophoresis has great potential for separating and purifying charged nanoparticles based on their sizes, shapes and net charges, all of which are very important characteristics. Although significant advances are being made, the lack of a quantitative understanding of how nanoparticles and nanodroplets propagate in a gel during electrophoresis remains a major challenge in this relatively new field. To address this need, we have developed a quantitative method for performing real-time video tracking gel electrophoresis of charged nanoparticles. We show that treating the gel with a passivation agent such as poly-(ethylene glycol), is necessary to a passivate the gel, thereby enabling charged nanoparticles to propagate through the passivated gel in a reproducible manner. This passivation approach allows us to measure the dependence of the propagation distance and velocity as a function of time at different field strengths and gel concentrations for different radii of charged monodisperse nanospheres. We use these measurements to predict the propagation distance and
29 integrated average intensity scattered light from bands of particles for different particle sizes and volume fractions.
3.2 Introduction
Gel electrophoresis (GE) is a common technique used for separating, identifying, and purifying highly charged biopolymers (e.g. DNA27,44,95-99, RNA100, and proteins49,101-110).
Electrophoresis has been applied to a wide variety of discrete objects: organelles,
111-113 64-66 114-121 microorganisms (e.g. bacteria and viruses ), and nanoparticles . In the 1940s and
1950s, scientists used filter paper or gel as supporting media to conduct electrophoresis (i.e. zone electrophoresis). In the 1960s, more sophisticated gel electrophoresis methods were developed and applied to the separation of biological molecules; thus GE was an important component of early molecular biology. However, in the area of biological particles (for example organelle, bacteria, and virus) capillary electrophoresis48,63,122 (i.e. electrophoresis carried out in free solution in a capillary channel) is more suitable than classical gel electrophoresis, because most biological particles are larger than the pores in polyacrylamide or agarose gels.
The most commonly used gel electrophoresis methods include polyacrylamide gel electrophoresis123 (PAGE) and agarose gel electrophoresis. Polyacrylamide gels are formed when monomers (acrylamide, CH2=CH-CO-NH2) are polymerized and chemically cross-linked with a cross-linking agent (e.g. N,N’-methylenebisacrylamide, CH2=CH-CO-NH-CH2-NH-CO-CH=CH2).
This free radical polymerization process is usually initiated with ammonium persulfate
((NH4)2S2O8) and catalyzed by N,N,N’,N’-tetramethylethylendiamine (TEMED,
(CH3)2NCH2CH2N(CH3)2). PAGE is commonly used to separate biological molecules having low molecular weight, such as protein molecules, because the average pore size is small in a 30 polyacrylamide gel. In most PAGE experiments, SDS is added to adsorb onto and charge proteins, thereby enabling proteins to move in the gel when a field is applied. As a consequence of adding SDS, many proteins denature and unfold. PAGE has higher resolving power because the pore sizes can be well controlled by manipulating the relative concentration of various components, the temperature, and the time of the gelation process. The effective range of resolution goes from a few base pairs (bp) to 2000 bp as the acrylamide gel concentration is varied from 20% to 3.5% (w/w). For the same reason, biological molecules separated using
PAGE are extremely pure124. However, SDS-PAGE is not a good option if one needs to recover functional protein, because SDS denatures proteins. In this case, a special apparatus should be used to run native tube gels (Native-PAGE). PAGE has also very limited application in separation of high molecular weight molecules. Another downside of PAGE is its difficult and tedious gelation process (e.g. the oxygen content and the gelation time need to be well controlled). Furthermore, acrylamide is a neurotoxin so it needs to be handled with great caution.
On the other hand, agarose gel electrophoresis125,126 is more useful for separating larger biological molecules but has less resolving power because the pore sizes are larger and more polydisperse. Between 3.0% to 0.3% (w/w) agarose gel concentration, the effective range of separation changes from 100 bp to 60,000 bp. Casting agarose gels is an easy, quick, and nontoxic process. Thus, using agarose gels is a more facile and versatile option in common lab applications, although the cost of high quality agarose is greater than that of polyacrylamide.
Because the purpose of our research is to study the separation of nanoparticles, corresponding to large pore sizes, we focus on using agarose gel electrophoresis.
Agarose, commonly extracted from seaweed, is a linear polysaccharide polymer having a molecular weight of about 120,000 g/mol. The repeating unit is a disaccharide composed of 1,3-
31 linked β-D-galactopyranose and 1,4-linked 3,6-anhydro-α-L-galactopyranose (see Fig. 3.1).
Small amounts of methyl, sulfate, and pyruvate groups are found substituting the free hydroxyl groups in the polymer; consequently, at neutral pH the gel is populated with negative charges resulting from these substituents27,127.
Figure 3.1. Molecular structure of agarose: linear polysaccharides consist of approximately 400 agarobiose repeating units (n ≈ 400). This disaccharide is composed of 1, 3-linked β-D- galactopyranose and 1,4-linked 3, 6-anhydro-α-L-galactopyranose. In agarose purified from algae, methyl, sulfate, and pyruvate groups can replace small numbers of H-atoms in the free hydroxyl groups. These substitution groups can affect properties of the agarose gel, namely H- bonding and charge.
Agarose in the form of a white powder dissolves in water at high temperature (near
100°C) and solidifies into a gel (now called a hydrogel) when it is cooled to room temperature128.
During the gelation of agarose, the molecules change from random coils in the solution to double helices, which bundle together to form a rigid gel network129-132, as shown in Fig. 3.2. The average pore size depends on various gelation conditions133-135: the agarose type, concentration, ionic strength134,136, and thermal history137 (e.g. quenching temperature) during gelation. In general, to increase in agarose gel pore size, one should lower the agarose concentration, increase the ionic strength, and slow down the cooling rate. Scientists have studied agarose structure and pore size distribution by microscopy (e.g. transmission electron microscopy
(TEM138-140), atomic force microscopy (AFM136,141), scanning electron microscopy (SEM)),
SANS142,143, SAXS144, absorbance145, nuclear magnet resonance (NMR146), chromatography (e.g.
32 size-exclusion chromatography147, inverse size exclusion chromatography148,149), templated electrodeposition150, and thermoporosimetry151. We use these results as guidelines to decide the agarose concentrations to prepare gels having the desired pore sizes. Moreover, we compare the pore size derived from our data to these literature values for consistency.
The agarose gels used in our experiment are predicted to have average pore radii of around 300 nm, depending on gel type, concentration, and method of preparation. This average pore radius of the gel roughly sets an upper limit on the largest sizes of molecules or particles that can propagate through the gel during electrophoresis.
Figure 3.2. Schematic of polymer structural changes during gelation of agarose when the temperature T decreases. For T ≥ 65℃, agarose molecules form random coils in solution. In the initial stage of gelation, intramolecular H-bonds increase rigidity of each agarose molecule, which transforms to a more ordered and rod-like structure. When T further decreases, intermolecular H-bonds cause the transition from rod-like structures to double helices. This same intermolecular H-bonding also causes a large number of double helices to aggregate into bundles (supercoiled structure). Finally, the intermolecular H-bonds link the bundles together into a 3- dimensional network. Water molecules (illustrated by the grey background) are also attracted to the network via H-bonding, thus the agarose solution solidifies into a hydrogel. Light blue wavy lines represent agarose molecules and blue rods represent bundles of agarose double helices.
33 The visualization of biological molecules is achieved by a number of different staining methods and agents. For example, DNA molecules can be seen under a UV lamp if they have been fluorescently labeled using ethidium bromide, either during or after electrophoresis. Other fluorescent dyes, such as SYBR gold and SYBR green, are also used. Radioactive isotopes42,43 are sometimes used to label biological macromolecules. Autoradiographs of gels are taken for visualization and detection in this case. Additionally, colorimetric dyes (e.g. Coomassie brilliant blue36-41, silver152,153, and copper) and fluorescent dyes (e.g. Nile red, SYPRO) are used to visualize protein molecules.
Figure 3.3. Schematic of anionic nanospheres separation during agarose gel electrophoresis. Negatively charged nanoparticles of different sizes are mixed and loaded into the wells in a gel slab (left). When a voltage is applied, the nanoparticles migrate toward the cathode. Different sized particles travel at different velocity and are separated due to the size-dependent drag force of the porous gel matrix (right). Light blue lines represent the agarose gel network and blue spheres represent nanoparticles. 34 During electrophoresis, an electric field is applied across an electrophoresis chamber. For negatively charged biomolecules such as DNA and RNA, they migrate through the gel toward the positive side, i.e. the cathode. At the same time, the gel matrix applies a drag force Fd on the molecules or particles as they propagate through the matrix. The drag force slows the propagation of larger nanoparticles more than smaller ones. The cartoon in Fig. 3.2 shows how spherical particles propagate and separate during a gel electrophoresis experiment. The electrophoretic mobility µ of molecules or nanoparticles is determined by the charge, size142, shape33,119 of the molecule or nanoparticle, as well as the electrophoresis conditions, such as the type, concentration, and structure of the gel, type and strength of electrophoresis buffer44,45, pH, ionic strength, temperature, and electric field strength32 E.
Even though gel electrophoresis is widely used in the quantitative identification and separation of biological molecules, how to apply and optimize this method to charged nanoparticles has only been studied to a much more limited degree. The electrophoretic mobility of a spherical particle can be significantly different from that of a biopolymer33,119. Extended and flexible linear objects (e.g. polymers or unfolded proteins) can propagate through gels in a different manner than compact objects such as spherical nanoparticles and nanodroplets. In addition, a systematic and quantitative description of how spherical nanoparticles of different size propagate through a pores gel during electrophoresis in real-time is still lacking, to the best of our knowledge.
Here, we quantitatively study gel electrophoresis of nanoparticles using video-tracking analysis. We extensively explore various conditions that affect the electrophoretic motion of the nanoparticles in a highly reproducible manner. We also show that a combination of several enhancements of standard gel electrophoresis can be made to provide accurate and precise
35 quantitative measurements of the propagation of charged nanoparticles though an agarose gel during gel electrophoresis. This combined approach involves passivation of the gel using a passivation agent that can be either uncharged or charged, so that particles do not attractively bind to the gel and can therefore propagate through it, even if the pore sizes in the gel are physically large enough to enable propagation. Moreover, our quantitative approach involves recording movies of white bands of the particles (resulting from incoherent white light scattered from the nanoparticles) during real-time electrophoresis in a passivated gel using a CCD camera.
3.3 Experimental Methods
3.3.1 Materials
Agarose (Type I-A, Low EEO) and sodium dodecyl sulfate (SDS) are purchased from
Sigma-Aldrich. Sodium borate decahydrate (Na2B4O7·10H2O) is obtained from Fisher Scientific.
Polyethylene glycol, nominal molecular weight Mw (g/mol) = 300 (PEG300), 1000 (PEG1000), and 10000 (PEG10000), are manufactured by Scientific Polymer Products, Inc. All chemicals are used without further purification. All sulfate-stabilized polystyrene (SSPS) nanospheres used are surfactant free and manufactured by Invitrogen. The radii and polydispersities have been measured using electron microscopy (see Table 3.1). The polydispersities are all very small.
Table 3.1. Average radius and standard deviation of radius δa of SSPS nanospheres
δa (nm) 2.5 2.5 1.5 5.5 4.5 NA
36 3.3.2 Apparatus
All electrophoresis experiments are carried out using a Neo SCI Double-Gel
Electrophoresis Apparatus #55-1094 (transparent Plexiglass chamber equipped with platinum wire electrodes) and Whatman/Biometra Electrophoresis DC Power Supply #125 (capable of generating voltages up to about 125 V). We typically apply 50V for most experiments described herein. This apparatus is ideal for imaging the gel because both the bottom and sides of the electrophoresis chamber and the gel-casting tray are transparent. Approximate dimensions of the electrophoresis chamber are: 20 cm x 10 cm x 9 cm.
We use a point Grey IEEE-1394 Camera Flea2 (FL2-08S2C, 8 bit, 1024 x 768) equipped with a lens suitable for imaging the gel. The maximum frame rate used is 30 frames per second, and this can be adjusted downward for time-lapse acquisition. The Flea camera is equipped with a digital shutter. The camera and lens are mounted rigidly so that the illuminated particles moving in the gel are imaged over the entire pixel range, leading to high-resolution images of spatial differences in scattered light caused by the propagating particles.
To image the particles propagating in the gel, we illuminate the electrophoresis apparatus from the side using a large light box (GLOW BOX, Instrument for Research and Industry,
Cheltenham Penna, Model No. GB11-17, 30 Watts). This light box provides very uniform lighting over a large spatial area, which is advantageous for imaging the particles as they undergo electrophoresis. Approximate dimensions of the light box are: 53 cm x 30 cm x 10 cm.
A lint-free cloth is used to prevent gas bubbles from entering the region of the gel where particles are propagating: 15 cm x 11 cm, Fisher Scientific, Catalog No. 06-667-14. Gases generated during electrophoresis near the platinum electrodes create bubbles, which can be stabilized by molecules present in the buffer solution. We place a piece of lint-free cloth near 37 each electrode in the electrophoresis chamber to prevent bubbles from entering the viewing region of interest.
We make a non-standard fine-width comb out of thin non-stick Teflon tape to reduce the thickness of the wells to 50 µm. Typical dimensions of a well that we make in a gel slab are about 5 mm length x 50 µm thickness x 2.5 mm height. Propagating bands of monodisperse particles in the gel are less smeared when the thickness of the well that originally holds the particles (i.e. before the electric field is turned on) is narrower.
Figure 3.4. Photograph of an optical video band-tracking electrophoresis apparatus. This is the actual experimental implementation of the schematic shown in Fig. 3.5. The computer controlling the digital camera is not shown. 38
Figure 3.5. Schematic of an optical video band-tracking electrophoresis apparatus for separating and measuring size distributions of nanoparticles using scattered light. Nanoparticles (e.g. nanospheres, nanodroplets, and nano-objects) are loaded into wells in a slab of gel, such as an agarose gel, that is immersed in an aqueous solution. The gel is supported by a transparent solid support (e.g. plastic base-plate) that is part of the electrophoresis chamber. The aqueous solution is typically a buffer solution at a fixed pH, and the aqueous solution typically contains a passivation agent that passivates the gel, enabling propagation of the loaded species. A voltage, produced by an electric power supply (not shown), is applied between two electrodes, designated as + electrode and - electrode, which are typically made of platinum wire and are mounted at opposite ends of the electrophoresis chamber beyond the ends of the gel slab. This applied voltage produces an electric field E that predominantly lies in the plane of the slab. Nanoparticles propagate through the gel along the direction of the electric field at different speeds that depend on their sizes, shapes, and charges. In the image shown, nanoparticles have anionic charge, so they propagate towards the + electrode. The positions of the nanoparticles, which were loaded into one or more wells, are detected using a camera and lens having an optical axis normal to the plane of the gel slab. The gel and particles are illuminated from the side by a light box that creates uniform diffuse light (which has a range of wavelengths suitable for detection by the camera); the camera detects light scattered from the nanoparticles. The scattered light appears as narrow bands, identifying the locations of the nanoparticles, if all of the nanoparticles loaded into a particular well are highly uniform in size, shape, and charge. The camera is connected to a digital computer equipped with a suitable digital camera interface. Not shown: a first piece of lint-free cloth is immersed in the buffer solution between the gel and the + electrode, and a second piece of lint-free cloth is immersed in the buffer solution between the gel and the - electrode. These pieces of cloth prevent gas bubbles generated near the electrodes from moving into the viewing region and obscuring the imaging by the digital camera. 39 A Dell Precision 490 Workstation is loaded with LabVIEW software and Image acquisition and analysis virtual instruments. We have written a customized virtual instrument
(i.e. software) in LabVIEW to acquire movies at different capture rates and shutter times. Movies of the bands of propagating nanoparticles are stored on the computer’s hard drive.
We fix the electrophoresis chamber, the light box and the camera rigidly on an optical table to prevent changes in the position of the electrophoresis chamber, illuminating light box, and detecting camera from changing over time, since these could affect the background subtraction of imaged intensities. To ensure maximum contrast, we have built a small darkroom for the apparatus. A photo and a schematic diagram of this optical video band-tracking electrophoresis apparatus are shown above in Fig. 3.4 and Fig. 3.5, respectively.
3.3.3 Preparation of Agarose Gel
We add 30 mL of 5 mM sodium borate buffer (SBB) to agarose powder and passivation agent, PEG1000 or SDS, in a flask. We heat the solution for several short intervals (15-30 seconds) using a microwave oven and swirl the flask to prevent the solution from boiling out of the flask. We repeat this heating and swirling process until all of the agarose dissolves completely and the solution becomes clear. We let the solution cool to about 50-55°C in a hot water bath. We seal both ends of the gel-casting tray with tape. We pour the melted agarose solution into the sealed tray (used as a mould) to produce a slab of gel. We place a comb in a pre- designed set of slots on the side-walls of the tray near one end of the agarose slab, so that the comb is inserted normal to the plane of the agarose slab, typically near one end of the slab. We allow the gel to cool to room temperature (about 20 °C) until it solidifies. In our experiment, a
40 gel slab is 10 cm length x 7 cm width x 0.4 cm height. We pull out the combs and remove the tape. Then we place the gel and the tray into the electrophoresis chamber, which contains 400 mL of 5 mM SBB (running buffer). If SDS is used as passivation agent in the gel, the running buffer should contain the same [SDS]. We take great care to avoid trapping any bubbles between the tray and the bottom of the chamber. Finally, we place a piece of lint-free cloth near each electrode in the electrophoresis chamber to prevent bubbles from entering the viewing region of interest.
3.3.4 Loading a Well in a Gel with Dispersion of Particles:
We pipette about 4 µL of a dispersion containing at least one of particles, droplets, macromolecules, and other small-scale objects at approximately a few percent volume fraction into a well. All particles are diluted to a desired volume fraction using D2O to increase the density of the dispersion. This increased density prevents particles from leaving the gel region.
We load steadily and slowly, avoiding overflow of the dispersion onto the surface of the gel.
3.3.5 Video Band-tracking during Gel Electrophoresis
The electrophoresis chamber is illuminated from the side using a light box (which emits white light towards the chamber) and scattered light from the particles in the gel is spatially imaged in two-dimensions in real-time using a digital camera connected to a computer. Custom- made software, which we have written in LabVIEW, enables us to control the shutter speed and frame capture rate of the camera. All experiments are conducted at T = 20 ℃ in 5 mM SBB (pH
= 9.00).
41 We vary the camera shutter speed for PS spheres of radius to avoid the saturation of the
Flea2 CCD camera and to expand the dynamic range in our measurements. A longer shutter time
(e.g. 67 ms) is used for small and dilute particle samples that scatter relatively little light, and a shorter shutter time (e.g. 1 ms) is used for large and concentrated dispersions. This adjustment eliminates saturation and yet keeps a high signal-to-background intensity.
The time between consecutive frames of the recorded time-lapse movie is typically t0 =
15 seconds. In our customized software package, we increase t0 if the bands move slowly (i.e. if we use high agarose concentration or lower applied field strength) and we decrease t0 if the bands move very rapidly. We run the gel electrophoresis experiment and record images of the particles propagating in the gel until the particles of different sizes are completely separated. The duration of each electrophoresis experiment is determined by the agarose concentration
[Agarose], the applied field strength E, and many other factors including the particle sizes. If the observation time is too short, then not enough separation of different particle sizes occurs.
However, if the observation time is too long, then the scattered light intensity from any bands containing smaller particles can become too low to be captured by the camera, or smaller particles can even migrate beyond the observation region or total length of the gel.
The gel scatters some light by itself. Therefore, an image of the gel is taken as a background image after loading all samples but before applying the voltage. This image of the gel is used for the purposes of background subtraction of subsequent images recorded after applying the voltage in order to enhance image contrast. The average background scattering intensity from a gel slab having 0.1 - 0.6 % agarose concentration in a typical illumination and detection configuration that provides adequate contrast for measuring a size distribution is in the
42 range between about 15 and 30 intensity units on a scale from 0 to 255 intensity units. Thus, the background scattering, while small, is not negligible.
3.3.6 Image Analysis
To eliminate background scattering and enhance contrast, we use ImageJ software in batch-process mode to subtract each frame by a background image taken before applying a voltage in an electrophoresis experiment. We write an automated program in LabVIEW to extract the intensity profile along lines parallel to the direction of propagation of particles within the width of each band for each pre-processed image. We measure intensity I as a function of distance L from a well along the axis corresponding to the direction of the electric field for a variety of conditions and times of observation t. A peak detection routine is used to analyze the intensity profile to calculate the location of the peak along each line. The program then averages all peak locations detected within the width of each band to generate the location of the band. For each frame, the difference between the location of the band and the well is defined as the propagation distance L(t) of this band at certain time point t, which is calculated by multiplying the frame number N by the time interval t0 between consecutive frames. The area under each peak is integrated for each frame to generate the total scattering intensity I(t) from all particles in each corresponding band.
3.4 Results and Discussion
We show that the propagation of nanoparticles through the gel can be imaged in real-time using visible light scattering. Separate dispersions of highly monodisperse SSPS nanospheres
43 having different radii in the range from about 10 nm up to about 150 nm and very small coefficients of variation (typically about 2-3%) are placed in separate wells in a passivated agarose gel in a suitable buffer solution (e.g. SBB). White bands of particles can easily be seen with the eye and imaged with the camera if the samples meet the following criteria: the particles have significantly different refractive index than the solution and are at large enough volume fractions φ. In our experiments, the refractive index is n ≈ 1.59 at 590 nm for polystyrene nanospheres. Thus, the refractive index difference is Δn ≈ 0.26 for PS nanospheres. A volume fraction of, for instance 0.2 - 0.4 %, is used for most dispersion samples having average radius
40 nm < a < 200 nm. Higher volume fractions (e.g. 2 %) are more optimal for smaller particles having a < 40 nm in order to generate enough scattering intensity from the particles (relative to scattered intensity from the gel) for facile detection by the camera.
We record and analyze time-lapse videos of bands of scattered light from monodisperse
SSPS nanospheres propagating in agarose gels during electrophoresis. Using band tracking video analysis, we obtain the distance of propagation L of different discrete bands of nanospheres, each having a different radius a, as a function of time t, as displayed in Fig. 3.6(a). Nanospheres having smaller radii propagate more rapidly than nanospheres having larger radii; if a ≥ 180 nm, we do not observe propagation of a band at this particular choice of gel concentration, passivation agent concentration, and electric field strength. A snapshot of a scattering image from the bands in the gel at a time t = 4.8 x 103 s after application of the electric field is shown in the inset of Fig. 3.6(a). From L(t), we calculate the instantaneous velocity of the band v(t) by taking a smoothed derivative, shown in Fig. 3.6(b). A rapid initial rise in v(t) is followed by a plateau in the velocity, which effectively corresponds to the steady-state propagation velocity ranging up to several microns per second, and there is a small upward drift, corresponding to an
44 acceleration that introduces a minor correction to the velocity as the experiment proceeds over long times.
Figure 3.6. Video band-tracking analysis of SSPS nanospheres undergoing electrophoresis in 0.195% (w/w) agarose gel for different sphere radii a (nm) = 17.5 (), 42 (), 70 (), 105 (), 124 (), 135 (), and 180 ( ): (a) propagation distance L of a band and (b) the instantaneous band propagation velocity v = dL/dt are plotted as functions of time t after initiating electrophoresis. Lines are fits to the data using equations in the text. The inset in (a) is an example of a gel image at t = 4.8 x 103 s, after scattering from the gel (measured in an image from the digital camera taken before the voltage is applied) has been removed through background subtraction to enhance contrast. The lower edge of the inset represents the initial location of the bands before the electric field is applied (i.e. L = 0 and t = 0). Conditions: temperature is 20 ℃, 5 mM SBB, pH = 9.00, [Agarose] = 0.195 % (w/w), [PEG1000] = 3.25 mM, and E = 1.6 x 10-4 statV/cm. 45 The measured v(t) can be fit to a simple model of propagation of charged nanospheres in a passivated gel medium. By analogy to sedimentation in a simple liquid, there is an initial
exponential rise having a time-scale τ to a plateau velocity vp; a term involving a long-term
acceleration ap is added to account for the slow upward drift. Thus, fits to the velocity are of the form:
v(t) = vp[1-exp(-t/τ)] + apt (3.1) are shown by lines in Fig. 3.6(b), and corresponding integration of v(t) yields fits to L(t) that have the same fit parameters for each radius, as shown by lines in Fig. 3.6(a). From these fits, we
extract vp(a) and τ(a), as shown in Fig. 3.7(a) and 3.7(b), respectively. A linear fit to vp(a)
exhibits quite good agreement, yielding a slope dvp/da = 22.3 1/s and a critical radius a* = 180 nm, beyond which the SSPS nanospheres do not readily propagate in the gel at the particular
composition and field strength used. By contrast to vp and τ, values of ap are quite small, vary from run-to-run, do not show a systematic trend, and are at a characteristic magnitude of about
10-5 µm/s2.
Figure 3.7. Fitting parameters extracted from Fig. 3.6 as a function of sphere radius a: (a) plateau velocity vp and (b) rise time τ required for the particles to accelerate to vp. The parameter -5 2 corresponding to acceleration in the plateau region is very small ap ≅ 10 µm/s and is independent of radius a within experimental uncertainty. 46
Figure 3.8. Dependence of measured intensity I of SSPS nanospheres in agarose gel on sphere radius a and volume fraction φ. (a) Averaged and integrated intensity of scattered light from a band is plotted as a function of φ for SSPS nanospheres having different radii a (nm) = 17.5 (), 42 (), 70 (), 105 (), and 124 (). Lines are linear fits to the data. I(φ) becomes non-linear at larger φ; at least in part arising from multiple scattering. (b) The slopes dI/dφ at small φ in (a) depend linearly on a (the slope in (b) is 0.062 arb. units/%). Conditions: 20 ℃, 5 mM SBB, pH = 9.00, [Agarose] = 0.195 % (w/w), [PEG1000] = 3.25 mM, and E = 1.6 x 10-4 statV/cm. Although I and dI are reported in arbitrary units, to calibrate the intensity to the volume fraction of particles of a particular size originally loaded into the well, it is necessary to keep all illumination and detection geometries and parameters fixed to be the same as this calibration during experiments.
In Fig. 3.8, we report the results of calibration measurements on SSPS nanospheres that relate the integrated intensity I of bands in the background-subtracted images to the particle
47 volume fraction φ and the particle radius a. In Fig. 3.8(a), we show a series of data for I(φ) at different a. At a given a, for small φ, there is a linear region in which I is proportional to φ, and the response becomes non-linear for larger φ. The relationship between I and φ deviates from linearity because multiple scattering emerges at high volume fractions. In Fig. 3.8(b), we plot the dependence of the slope of the linear region, dI/dφ, at low φ as a function of a. This slope function dI/dφ shows a linear dependence on a. These results provide the necessary information to calibrate the measured intensities I(L) into absolute volume fractions of particles of different sizes that are originally loaded into a well when determining the size distribution of an unknown dispersion.
Fig. 3.8 can also be used to determine the optimum volume fraction for certain particle sizes. To get the best signal to noise ratio, we need adequate light scattering intensity from the particles, i.e. we need to use a large enough φ. On the other hand, we have to conduct the experiment in the linear response region, in order to use the light scattering intensity to quantitatively study the size distribution of nanoparticles. This determines the upper limit of φ. In addition, if the particle sizes are too small (a < 10 nm), the light scattering intensity is too low to be observed under white light in agarose gel. This is because the light scattering from the gel
(background noise) washes out the useful signal from scattering by the particles.
It is necessary to passivate the gel using a passivation agent that can be either uncharged or charged, so that particles do not attractively bind to the gel. Gel passivation enables particles to propagate in a reproducible manner, providing that the characteristic pore size of the gel is physically large enough to allow particle propagation during electrophoresis.
48
Figure 3.9. Dependence of nanosphere propagation velocity on passivation agent type and concentration. The plateau propagation velocity vp of SSPS nanospheres is plotted as a function of the concentration of passivation agent: (a) sodium dodecyl sulfate CSDS and (b) poly(ethylene glycol) having an average molecular weight of 1000 g/mol CPEG1000, for particle radii a (nm) = 17.5 (), 42 (), 70 (), and 124 (). The inset in (a) is the same plot in a linear-log format showing the non-linear region at higher CSDS. Conditions: 20 ℃, 5 mM SBB, pH = 9.00, [Agarose] = 0.600 % (w/w), and E = 1.6 x 10-4 statV/cm.
49 We show that two different types of molecules, poly-(ethylene glycol) (PEG1000, Mw =
1000 g/mol), a charge-neutral polymer, and sodium dodecyl sulfate (SDS), an anionic surfactant, can serve well as passivation agents for agarose gels. In particular, as a passivation agent, short- chain PEG offers the distinct advantage of being charge-neutral, so that it does not affect the charge on any particle and therefore the particle's electrophoretic mobility, yet PEG1000 still passivates the gel. The use of such passivation agents at adequate concentrations enables nanoparticle propagation, whether it is positively or negatively charged, in the gel. Since SDS could influence the charge on the nanoparticles, thereby complicating the interpretation of the electrophoresis, we focus mainly on short-chain length PEG-passivated gels because PEG is a charge-neutral. SDS is used only for negatively charged particles, but PEG works for both positively and negatively charged particles.
At fixed conditions, we show vp(CSDS) and vp(CPEG) for different a in Fig. 3.9(a) and
3.9(b), respectively. Interestingly, for SDS, a linear response in vp(CSDS) is observed below the critical micelle concentration at around 8 mM; the response becomes non-linear and the velocity
decreases for larger CSDS. By contrast, for PEG1000, the response is not uniformly linear for all a, and the smallest nanospheres propagate readily when only very small quantities of PEG1000
are present. Strikingly, in the range 1 mM ≤ CPEG ≤ 10 mM, the plateau velocity is nearly independent of PEG1000 concentration [PEG1000], and this appears to be an ideal range in
which to perform physical electrophoresis experiments. Even at very high CPEG, approaching 100 mM, the plateau velocity does not decrease as significantly and uniformly as it does for SDS. In
either case, in the absence of any passivation agent, i.e. when CSDS = 0 mM and CPEG = 0 mM, none of the nanospheres propagate, regardless of a; the bands appear to be fixed at the point
50 where the nanospheres just begin to enter the gel. Thus, adequate gel passivation is essential in performing nanoparticle electrophoresis experiments successfully.
We also conduct control experiments in which we replace PEG1000 and SDS with same
concentrations of sodium borate, sodium sulfate (Na2SO4), PEG300, PEG10000, or pure water.
All other conditions ([agarose], T, E, and t) being the same, the particles do not propagate through the gel in any of the control groups except for PEG10000. We speculate that PEG300 fails to passivate the gel for particle propagation because of its shorter chain length. When the molecular weight of PEGs increases, their hydroscopic power and solubility in water deceases
(e.g. PEGs having Mw ≤ 800 g/mol are completely miscible with water while the water solubility of PEG1000 is 80% by weight), indicating a decreased interaction with water molecules. It is possible that the interaction between PEG300 and water molecules is stronger than between
PEG300 and the agarose molecules. We use PEG1000 rather than PEG10000 because of its lower molecular weight and we need less PEG1000 than PEG10000 to achieve the same passivation effect.
Next, in Fig. 3.10, we show how the gel concentration influences the plateau propagation
velocities of bands of uniform nanospheres having different radii, vp(Cgel,a). For a given gel concentration, nanospheres below a certain radius do propagate, but larger nanospheres do not propagate. The concentration of the gel affects the effective pore size distribution of the gel network, and as the gel becomes denser, the average of the pore size distribution shifts towards
smaller sizes. In the a-Cgel plane, we show a dotted line Cgel*(a) that captures the observed trend of the zero propagation velocity of nanospheres that are larger than a certain radius a. The trend can be fitted nicely to a simple reciprocal function empirically:
Cgel*(a) = m/ξ* = m/(2a), (3.2) 51 where ξ* is defined as the effective minimum pore size of a gel of concentration Cgel* and the
fitting parameter m = 0.63 nm. For a gel having concentration Cgel*, ξ* is equivalent to the diameter of the largest nanosphere which can propagate through this gel. We can use Eq. 3.2 to
predict the maximum gel concentration in which propagation is still observed (i.e. vp > 0) for nanosphere having radius a under the present conditions (see the figure caption of Fig. 3.10 for details). The value of ξ* is slightly smaller than the average pore size measured by other methods141,142,145,146. We believe that this difference exists because we directly measure the pore size distribution, which is relevant to the physical process of propagation of particles through the gel, i.e. only pores that can be utilized in particle migration is taken into account. On the contrary, the other techniques (microscopy, scattering, and NMR, etc.) average over all the pores in the gel, including closed pores, which are irrelevant for the problem at hand. In other words,
ξ* is a more accurate measure of gel pore size distribution when studying gel electrophoresis of mobile nanoparticles.
In addition, for each fixed a, we can fit vp(Cgel) to a quadratic form for Cgel ≤ Cgel*, as shown by the solid lines. All quadratic curves are also required to reach their minimum when
intercepting with a-Cgel plane. The intercept of each curve agrees well with the values of corresponding Cgel*(a) (discussed in the previous paragraph). Extrapolation of these quadratic fits in the limit as Cgel vanishes yields estimated values for the propagation velocity of the spheres in the absence of gel (open symbols) which show the same a-independent trend and are
close to yet somewhat smaller than v0(a) (described below in Fig. 3.11).
52
Figure 3.10. Steady-state plateau propagation velocity vp is plotted as a function of Cgel (% w/w) for SSPS nanospheres having different radii a (nm): 17.5 (), 42 (), 70 (), 105 (), 124
(), and 135 (). Open symbols represent the extrapolated velocity at Cgel = 0. The dotted curve in the a - Cgel plane is a fit to the critical Cgel* (at which the velocity is zero) as a function of a: -4 Cgel* ~ 1/a. Conditions: 20 ℃, 5 mM SBB, pH = 9.00, and E = 1.6 x 10 statV/cm. The concentration ratio PEG1000 : agarose is fixed as 10 mM PEG1000 : 0.6 % (w/w) agarose.
We can use Fig. 3.10 to determine the bounds on utility of this technique. Generally, high
[agarose] gives better resolution power but prohibits large particles from propagating through the gel. One important factor that determines the lower limit in resolution power of particle size is the light scattering intensity of the gel. At high [agarose], the background scattering from the gel network increases substantially. The noise in scattering signal makes the visualization and quantification of the light scattering bands of particles more difficult. If [agarose] > 3.5%, it is almost impossible to distinguish the light scattered by particles from that scattered by the gel (i.e. background scattering becomes too high). On the other hand, if [agarose] is low, large particles can be separated but the difference in electrophoretic mobility of particles of different sizes decreases. The average pore radius of the gel roughly sets an upper limit on the largest sizes of 53 particles that can propagate through the gel during electrophoresis. In addition, it is also problematic to manipulate the gel at very low [agarose], because if [agarose] < 0.15%, the gel becomes too weak and breaks easily. Casting and placing the gel in the electrophoresis chamber requires a certain minimum elasticity and rigidity. This limits the largest nanoparticle radius to be 135 nm in the gel electrophoresis conducted under the current conditions. This figure can be used as a guideline when determining the optimum [agarose] for separation of certain particle sizes.
Figure 3.11. Nanosphere electrophoresis in the absence of agarose gel in aqueous buffer solution. Video tracking analysis of sulfate-stabilized polystyrene (SSPS) nanospheres yields the following as a function of sphere radius a: (a) stead-state particle propagation velocity v0 (at zero gel concentration), (b) effective particle charge qeff determined using v0, and (c) effective particle surface charge density σeff calculated from qeff. Conditions: 20 ℃, 0.5 mM SBB, pH = 9.00, and E = 1.6 x 10-4 statV/cm.
54 In order to characterize the surface charges on the nanospheres, we have measured the plateau velocity of nanospheres in the absence of any gel, yet in the same aqueous environment and driving field as when the gel is present. Measurements of the propagation velocities of small regions of uniform nanospheres, deposited in the buffer using a micropipette, after turning on the
electric field, yield the measured propagation velocities v0 (where 0 stands for zero gel concentration) shown in Fig. 3.11(a). As expected, these velocities are larger than velocities
when the gel is present, and the measured v0(a) is nearly independent of radius. Knowing the radius a, the viscosity of water ηw ≈ 1 cP, and the electric field strength E, we calculate the effective charge
qeff(a) = 6πηwav0(a)/E (3.3) related to nanosphere mobility, which happens to rise linearly, as shown in Fig. 3.11(b).
Reported values of E take into account the dielectric constant of water (calculated using E = D/ε
= (U/d)/ε, where U and d are the voltage and distance between the two electrodes, respectively; and ε = 80.1 is the relative permittivity of water). From this we also report the effective surface charge density
2 σeff(a) = qeff(a)/(4πa ), (3.4)
as displayed in Fig. 3.11(c). These values of qeff and σeff are similar in magnitude to what are reported by the nanosphere manufacturer using a charge-titration method in a different aqueous environment; the electrophoretically measured mobility values in our aqueous environment are more relevant for interpreting our gel electrophoresis experiments.
In Fig. 3.12(a), we show how the propagation velocity vp depends on the electric field strength E for SSPS nanospheres having different radii a. We find that using very high field
55 strength can actually inhibit propagation of particles that have larger radii. By contrast, the
smallest particles propagate in a response of vp(E) that is super-linear. The data can all be fit by the following function:
qE $1 2 vp = exp[$% (qE) /(kBT)] 6"#effa (3.5)
where q is the charge on a sphere, kB is Boltzmann's constant, ηeff is an effective viscosity that is
! -1 comparable in magnitude to the viscosity of water η0 = 1 cP, and κ is a microscopic effective compliance reflecting properties of the gel-particle interaction. The size-dependence of the fitting
-1 parameters ηeff(a)/η0 and κ (a) are shown in Fig. 3.12(b) and 3.12(c), respectively. The mobility of nanoparticles in the gel matrix is primarily dictated by the particle size with respect to the gel mesh size. Thus effective viscosity increases linearly with radius; larger particles experience increasing dissipative resistance. By contrast, the effective compliance changes from positive and large for the largest radii (i.e. strongly inhibiting propagation of the particles), decreases through zero, and it actually becomes negative for smaller radii (i.e. suggesting that the network actually allows particles to propagate more easily at higher field strength). Because the response of the velocity to applied field strength at values of E > 2 x 10-4 statV/cm is nonlinear, we choose the applied voltage and therefore E for most experiments to be about 1.6 x 10-4 statV/cm, near the end of the linear region. This provides more rapid separations and determinations of particle size
distributions since vp is larger, yet maintaining the linearity of the response vp(E) at that value of
E ensures that the distances propagated by particles having different radii is also effectively linear, too. Thus, if one might wish to determine size distributions, staying at E that is near this optimum can be advantageous for simplifying the mapping of propagation distance L into particle radius a yet obtaining the size distribution in a shorter amount of time.
56
Figure 3.12. The relationship between the applied field strength E and the plateau velocity vp is shown in part (a) for agarose gel electrophoresis of SSPS nanospheres having different radii a (nm) = 17.5 (), 42 (), 70 (), 105 (), 124 (), 135 (), and 180 ( ). Lines are fits to data (see text). The fitting parameters are plotted as functions of a in part (b) (the reduced effective viscosity ηeff/η0) and (c) (1/κ). These gel electrophoresis experiments have been carried out at 20 ℃ in 5 mM aqueous sodium borate buffer at pH = 9.00. The gel is made of 0.195 % (w/w) agarose and passivated by 3.25 mM PEG1000.
57
3.5 Conclusion
We have developed a real-time video-tracking gel electrophoresis apparatus in order to conduct a quantitative and systematic study of the separation of monodispersed sulfate stabilized polystyrene nanospheres by imaging scattering incoherent white light from bands of nanoparticles. We have demonstrated how the gel concentration, passivation agent type and concentration, electric field strength, and particle size affects the electrophoretic mobility of nanoparticles during gel electrophoresis. Our results provide a means of optimizing any passivated agarose gel electrophoresis experiments for separating spherical charged nanoparticles in the size range from about 15 nm to 150 nm. We have also shown the quantitative dependence of the integrated average light scattering intensity of bands of particles on the size and volume fraction of particles, which, in principle, can be used to extract particle size distributions.
58 Chapter 4
Particle Size Distribution Measurements of Nanoscale
Particles and Droplets Using Optical Gel Electrophoresis
4.1 Abstract
In this chapter, we image simple optical scattering from charged nanospheres propagating through an agarose gel during electrophoresis (described in Chapter 3) to measure the size distribution of the nanospheres. Using several monodisperse nanospheres, each having different sizes, we calibrate the propagation distance and integrated average intensity of bands of particles, correlating these to the particle radius and loaded volume fraction. In addition, we employ a special form of iterative deconvolution, which involves a point-spread function that changes shape (e.g. width and skew of a modified log-normal function) progressively for different propagation conditions. This analysis enables us to sharpen what would otherwise be a smeared size distribution according to a variable point-spread function that removes different amounts of smearing for different propagation distances corresponding to different particle sizes. To demonstrate the broad utility of this approach, we measure a size distribution of a multimodal mixture containing several different monodisperse sizes of spherical nanoparticles each having different volume fractions as well as a broad size distribution of nanoscale droplets in a nanoemulsion. Thus, the combined approach of using passivated gels and specialized deconvolution enables us to perform accurate measurements of particle size distributions, including size distributions that contain at least one of the following characteristics: broadly
59 polydisperse, monodisperse containing one monomodal sharp peak, and multimodal mixtures of monodisperse spheres containing two or more sharp peaks.
4.2 Introduction
An important characteristic of a dispersion is its particle size distribution (PSD). The PSD affects many properties, such as the rheology and optical scattering, of the dispersion. Measuring the particle size distribution of dispersions is also crucial for the characterization of many industrial materials because it greatly influences the development, processing (e.g. sintering154, flow, mixing and packaging) and physical properties of the final product (e.g. performance, appearance, and stability). Some standard techniques used to measure size distributions of nanoparticles include155-158: dynamic light scattering (DLS, also known as photo correlation spectroscopy or quasi-elastic light scattering), static light scattering (SLS, also called laser diffraction), and electron microscopy (e.g. transmission electron microscopy (TEM) and scanning electron microscopy (SEM)). Different techniques can yield different particle size distributions for the same sample because each method relies on different physical phenomena and theories of interpretation. It is important to choose a suitable technique based on particle shape, estimated size range, concentration, the nature of the material, detection limits of the instrument and cost. It is also common to corroborate results from more than one technique.
However, many techniques are not able to accurately measure the PSD of a dispersion that is a multimodal mixture of several different highly monodispersed particles or that is very polydisperse.
Despite the variety of methods available for characterization of particle size distributions, each technique suffers from some inherent limitations. DLS measures the fluctuation of intensity
60 of the scattering light over very short time scales. This fluctuation depends on the size of the particles undergoing Brownian motion. The Stokes-Einstein relationship is used to calculate the hydrodynamic radius, assuming that all particles are spherical159,160. Large particles could mask the presence of small ones since DLS measures the intensity-weighted PSD. Thus, DLS offers reliable results for dispersions of monomondal spherical particles161. SLS relies on the Mie theory of coherent light scattering to analyze the angular variation in intensity of light scattering as a laser beam passes through a dilute dispersion162,163. If accurate optical parameters are known,
SLS can generate accurate particles size distribution results for spherical particles. However, the reported distribution can be skewed towards particles of smaller sizes if the distribution is wide164. The accuracy of SLS also strongly depends on knowing in advance the optical parameters of the particles, such as refractive index and light absorption characteristics. The high cost of both DLS and SLS instruments is another disadvantage. By contrast, transmission electron microscopy (TEM) is not limited to only spherical particles because real-space images of particles are captured and analyzed. It detects both the shape and size distribution of particles165. However, this method also has some downsides: high cost of TEM instrumentation, time-consuming sample preparation, laborious image analysis processing, and low sample throughput.
The real-time video tracking of optical scattering from charged nanoparticles or nanodroplets during agarose gel electrophoresis, presented in Chapter 3, is potentially a very advantageous technique for measuring the size distribution of aqueous dispersions of charged nanoscale spheres. In a simple implementation, the index of refraction of the spheres is known and significantly different than that of the buffer solution, so particle propagation can be easily detected during gel electrophoresis, as shown in Chapter 3. The evolution of the scattered light
61 intensity as a function of distance along the field direction, I(L,t), in a lane corresponding to a well at different observation times t (after turning on the electric field) is measured, recorded, and converted into a size distribution. The raw data is further refined by applying a deconvolution algorithm that removes smearing of the size distribution that is a consequence of the complex transport process of the particles moving through the passivated gel in the presence of an applied electric field. Because of the separating power of gel electrophoresis, this method is especially useful for dispersions that are multimodal mixtures containing several different monodispersed spherical nanoparticles each having different volume fractions. The method is versatile and likewise can be used to measure the broad size distribution of nanoscale droplets in nanoemulsions.
4.3 Experimental Methods
4.3.1 Materials
A silicone oil of the type 1,1,5,5-Tetraphenyl-1,3,3,5-tetramethyltrisiloxane (TPTMS,
C28H32O2Si3, Mw = 484.82 g/mol) is purchased from Gelest and used without further purification.
We choose this oil for two main reasons. First, the refractive index of TPTMS (n ≈ 1.56) is very close to that of polystyrene nanospheres (n ≈ 1.56) used for calibration purposes. This ensures the I(φ,a) relation that we have measured is applicable to deduce the size distribution of nanoemulsion droplets. In addition, TPTMS/SDS/H2O nanoemulsion droplets are stable against coarsening via Ostwald ripening166-168 because the solubility of TPTMS in water is extremely low. Details of all other materials have been previously described in Chapter 3.
62 4.3.2 Preparation of Nanoemulsions
Nanoemulsions are created by the same procedure described in Chapter 2. We first create a polydisperse microscale “premix” oil-in-water emulsion by mixing TPTMS and aqueous SDS solution using a rotary mixer. The premix is passed 9 times through a high-pressure homogenizer
(Microfluidizer 110P, 30,000 psi liquid pressure, 75 µm channel size) to rupture the microscale emulsion droplets down to nanoscale and reduce the size polydispersity12,13,169.
4.3.3 Agarose Gel Electrophoresis and Image Analysis
Dispersions of sulfate-stabilized monodisperse nanospheres having different radii (a =
18, 42, 70, and 105 nm), a mixture of these nanospheres, and a nanoemulsion are loaded into separate wells in an agarose gel that has been treated with an adequate quantity of a passivation agent PEG1000 in 5 mM sodium borate buffer solution at pH = 9. The electrophoresis experiments are conducted in similar conditions as described in Chapter 3. Images of the gels are taken in real-time until the band propagation has reached a steady state. After performing background subtraction, we extract the scattered light intensity as a function of distance along the field direction, I(L,t), in each lane corresponding to a well at different observation times t
(after turning on the electric field).
4.3.4 Deconvolution
We first measure calibration curves from GE experiments conducted under similar conditions (e.g. applied electric field strength E, observation time t, buffer, passivation agent, and gel concentrations) on monodisperse PS nanoparticles having known sizes a, same charge
63 density characteristics, and same refractive index difference Δn. Then, we use peak detection
routine in LabVIEW to determine the number of peaks Npeak, and the centers Li, heights Hi, and
4 widths dLi of peaks in I(L) at a near-optimal observation time (t = 1.5 x 10 s after turning on the voltage of the electrophoresis apparatus). We choose this time because it is long enough so that adequate separation of different particle sizes has occurred. In addition, this time is not too long, otherwise the scattered light intensity from smaller particles would have become too small to be captured by the camera, or smaller particles would have migrated beyond the observation region
or total length of the gel. Using the obtained Npeak, Li, Hi, and dLi, along with a calibration of the scattered light intensity to φ, the software program then establishes an approximate initial starting point for the function Id(L), the deconvolved intensity profile.
This starting point is updated in the following manner. We convolve a normalized point-
spread function Ipsf(L,δL) that has a variable width δL, which depends on distance of propagation
L, with the current deconvolved intensity profile Id(L), based on the peak detection results and a prior GE experiment of the characteristics of the widths and heights of point-spread functions for different L values. Using a direct method that is not based on Fourier transforms, we then obtain a convolved intensity profile Ic(L):
Lmax c d d I (L) = Ipsf (L,δL)∗I (L) = ∑Ipsf (L − b,δL)⋅ I (b), (4.1) b=−Lmax
where Lmax is the largest propagation distance of particles in the gel electrophoresis experiment € and b is an index of summation. Next, we compare Ic(L) to the measured I(L). If the total mean square error, given by chi-square:
2 2 c χ = ∑(I (Li ) − I(Li )) , (4.2) i 64
€ between these two functions is less than a certain acceptable error value, then we stop and report
Id(L) as the final deconvolved size distribution. If not, then we decrease values of Id(L) at a particular L if Ic(L) > I(L) and increase values of Id(L) at a particular L if Ic(L) < I(L) to obtain an
d updated I (L) that could reduce χ2 further. We repeat the direct convolution and comparison steps until χ2 is reduced below a certain acceptable error value and report the deconvolved intensity profile Id(L). For multimodal distributions, this general algorithm for obtaining the deconvolved Id(L) can be converted into a simpler algorithm involving a set of Gaussian peaks
c having center positions, standard deviations, and heights that are adjusted until χ2 of I (L) and
I(L) is minimized. Afterwards, we turn the deconvolved Id(L) to Id(a) for an unknown dispersion
at an observation time topt that is near-optimal spatial separation using a known calibration L(a)
d d (see Fig. 3.6). Finally, we convert I (a) to a deconvolved probability density p φ(a) as a function of radius a using a known calibration I(φ,a) (see Fig. 3.8).
4.4 Results and Discussion
The measured I(L) for a mixture of polystyrene nanospheres of different a at a near- optimal observation time is shown in Fig. 4.1. When measuring size distributions, we use prior results in Chapter 3 to determine the optimum GE conditions (e.g. E and gel concentration) to simplify the mapping of propagation distance L into particle radius a yet obtaining the size distribution in a shorter amount of time. We run the gel electrophoresis experiment and record images of the particles propagating in the gel for approximately 4 hours until the particles of different sizes are completely separated. The duration of each electrophoresis experiment is 65 determined by the agarose concentration [Agarose], the applied field strength E, and the particle sizes.
Figure 4.1. Measured average scattered light intensity I versus distance of propagation L of a mixture of sulfate-stabilized polystyrene nanospheres at a time t = 1.5 x 104 s after turning on the voltage of the electrophoresis apparatus. This one-dimensional average intensity is obtained through spatially averaging the intensity across the band (i.e. perpendicular to the direction of propagation) in a two-dimensional using digital image analysis of a two-dimensional image captured by the digital camera. The background scattering intensity from the gel has been eliminated by subtraction to enhance contrast and provide the scattered intensity from bands of particles within the gel. The inset shows the measured intensity of bands of monodisperse particles individually (four leftmost lanes) and the rightmost lane in the inset shows the separated multimodal mixture of particles during gel electrophoresis from which I(L) shown in this figure is calculated. In the inset, the direction of the electric field is along the vertical direction. Likewise, L = 0 corresponds to the bottom of the inset, and L is measured in the vertical direction. Conditions: 20 ℃, 5 mM SBB, pH = 9.00, [Agarose] = 0.45 % (w/w), [PEG] = 7.5 mM, and E = 1.6 x 10-4 statV/cm.
If the observation time is too short (i.e. very soon after the electric field has been turned on), not enough separation of different particle sizes has occurred, and the extracted size
66 distribution may contain features that do not accurately reflect the true size distribution.
However, if the observation time is too long, the scattered light intensity from any bands containing smaller particles can become too small to be captured by the camera, or smaller particles can even migrate beyond the observation region or total length of the gel. Thus, a near- optimal time of observation is an observation time between these two limits and around which the extracted deconvolved size distribution of particles remains substantially the same.
We use modified log-normal point-spread functions, which have shapes that capture smearing inherent in I(L), to carry out the deconvolution process. Example point-spread functions used for the deconvolution of the data in Fig. 4.1 are shown below in Fig. 4.2. Using standard polystyrene nanosphere samples of known a and φ, we obtain point-spread functions for the integrated band intensity as a function of distance I(L) that depend on the distance L along the electric field direction and time t for particles to propagate through a gel at a specific applied electric field strength, in a certain buffer solution containing a passivation agent, and at a certain gel concentration. Thus, the point-spread function for spherical particles effectively corrects for different amounts of smearing of the intensities of bands of scattering from particles that can occur as a result of the complex transport process of the differently-sized particles moving through the gel over time (and for different amounts of time). The widths of the point spread functions are obtained by performing passivated gel electrophoresis on highly monodisperse PS nanospheres having different a propagating in individual lanes, as shown in the leftmost lanes of the inset of Fig. 4.1. Modified log-normal point-spread functions, such as those shown below, are used in a software algorithm to obtain a deconvolved size distribution of particles.
67
Figure 4.2. Representative shapes of modified log-normal point-spread functions (lines) having different widths as a function of propagation distance L and time t for different nanoparticle radii a. Such point-spread functions are asymmetric and capture the feature of a tail that is characteristic of peaks in I(L) (points). This asymmetric tail can result from the complex transport of the particles through the gel, including random scattering of particles by the gel; this random scattering can slow down the propagation of some particles more than others even if the particles have identical sizes. Plots (a) through (d) correspond to the four peaks in Fig. 4.1 from left to right. Electrophoresis conditions are the same as those in Fig. 4.1. The data is obtained at a time t = 1.5 x 104 s after turning on the voltage of the electrophoresis apparatus.
68 The modified log-normal functions shown above have the form:
⎛ 2 2 ⎞ 1 ⎜ ln(Lp + Lm − L) − lnLm ⎟ I (L) = exp − , L < L + L psf ⎜ 2σ 2 ⎟ ( p m) 2π (Lp + Lm − L)σ (4.3) ⎝ ⎠ .
In this equation, Lp is the peak location of the band, Lm is the median, and σ is the standard € deviation of the log-normal distribution. To modify a regular log-normal function, we first flip it
horizontally, as indicated by the negative sign before the variable L. Afterwards, this function is
shifted horizontally by (Lp + Lm) so this becomes the new zero of the modified log-normal
function. The value of these parameters for each example point spread function are listed in
Table 4.1.
Table 4.1. Parameters of the example point spread functions shown in Fig. 4.2
Peak Itot (arb. units) Lp (mm) Lm (mm) σ a 14 19.4 3.7 0.33 b 72 15.2 2.7 0.28 c 107 7.6 1.8 0.25 d 85 2.0 1.3 0.12
Afterwards, we deconvolve the measured I(L) with the point-spread function Ipsf(L, δL)
via the algorithm described in section 4.3.4 to obtain the deconvolved intensity profile Id(L). The
d software convolves Ipsf(L, δL) with an approximate initial starting point for I (L) to generate the
convolved intensity profile Ic(L), which is compared against I(L) in each iteration to update Id(L).
d We use the deconvolved I (L) to calculate and report pφ(a), if chi-square is below a certain
acceptable error value. The final form of Ic(L) is displayed below in Fig. 4.3.
69
Figure 4.3. Convolved scattered light intensity Ic versus distance of propagation L. This function is calculated based on the measured I(L) shown in Fig. 4.1 using the deconvolution algorithm described in section 4.3.4.
Lastly, we utilize the calibration data to convert the deconvolved Id(L) to the size distribution pφ(a), which is shown in Fig. 4.4. The curve shows four narrow peaks corresponding to the different particle sizes in the mixture. By combining the deconvolution analysis with calibrations of the intensity of a band of light scattered from particles as a function of volume fraction of particles originally loaded into the well (I(φ,a), see Fig. 3.8), we obtain size distributions that are sharpened and also accurately reflect the absolute volume fractions of different sizes of particles in an unknown sample that has been loaded into the electrophoresis well. For spherical particles or droplets, we report these distributions as pφ(a) (which has units
. of inverse length), where the integral of pφ(a) da, where da is a differential in radius, from radius a to a larger radius a + da gives the volume fraction of spheres in that size range originally
70 loaded into the well prior to turning on the voltage of the electrophoresis apparatus. Provided the observation time is long enough that initial transients can be ignored and peaks become well resolved (here this time is 1.5 x 104 s after starting GE), the size distributions obtained by deconvolution at different observation times are effectively independent of observation time.
Therefore, a true a steady-state deconvolved size distribution remains essentially constant over a range of times after initial transients have died away. The result matches well with the actual particle size and volume fraction in the mixture of polystyrene nanospheres that we have created and loaded into the well.
In order to reduce smearing of the bands due to factors besides the inherent polydispersity of nanoparticles, we make a non-standard thin comb out of non-stick Teflon tape to reduce the thickness of the wells to 50 µm. Propagating bands of monodisperse particles in the gel are less smeared when the thickness of the well that originally holds the particles (i.e. before the electric field is turned on) is narrower. The thickness of the wells that we make using our customized
Teflon comb is about 4 times smaller than the standard comb provided by the manufacturer of the electrophoresis device. This makes an important difference when measuring particle size distributions, because wells that have larger thickness exhibit a higher degree of smearing of peaks in I(L), and this smearing is not indicative of the true polydispersity in the size of the particles. The smearing of I(L) caused by using a well that is not so fine cannot easily be distinguished from the smearing of I(L) caused by propagation of particles through the gel during electrophoresis, so it is usually advantageous to use a very fine thickness, such as 50 µm, such as that given by our custom comb, when making wells in the gel.
71
Figure 4.4. Resulting multimodal deconvolved size distribution pφ(a), where a is the nanoparticle radius and φ is the nanoparticle volume fraction, as a result of applying a deconvolution algorithm to the passivated gel electrophoresis data for I(L) of a mixture of 4 different monodisperse spheres, shown in Figure 4.1, using the modified log-normal point-spread functions to model smearing of the distribution into I(L). The volume fractions, sizes, and polydispersities of the four peaks shown in this pφ(a) correspond well with the particle manufacturer's data and the total particle volumes of each dispersion added together to make the mixture.
We also measure the size distribution of a broadly polydisperse silicone oil-in-water nanoemulsion using this method. We can rely on a known intensity calibration I(φ,a) because the refractive index difference Δn between the nanodroplets and the buffer solution is nearly the same as a prior calibration with polystyrene nanospheres. Otherwise, if Δn for nanodroplets or nanoparticles is not known, one must perform additional calibration measurements of intensities prior to determining the size distribution by measuring band intensity. This calibration can involve measuring scattering intensities for a series of dilutions of the unknown nanoparticles that are moving through a gel electrophoretically, because Δn affects the intensity of scattered
72 light. In our experiments, the refractive index is n ≈ 1.59 at 590 nm for polystyrene nanospheres, and n ≈ 1.56 for the particular nanoemulsion droplets of TPTMS stabilized by SDS in water
(water has n = 1.33). Thus, the refractive index differences are: Δn ≈ 0.26 for PS nanospheres and Δn ≈ 0.23 for the silicone oil nanodroplets. The two values of Δn are very similar, so we can use the prior calibration data for PS nanospheres, assuming that the surface charge density of the nanoemulsions is the same as that of the PS spheres. We perform PEG-passivated agarose GE with a dispersion of nanoscale droplets in a silicone oil-in-water nanoemulsion under the same conditions as the previous calibration experiments. The measured I(L) for the nanoemulsion at a near-optimal observation time is shown in Fig. 4.5.
Figure 4.5. Measured I(L) for a silicone oil-in-water nanoemulsion using passivated gel electrophoresis under the following conditions: 20 ℃, 5 mM SBB, pH = 9.00, [Agarose] = 0.45 % (w/w), [PEG] = 7.5 mM, and E = 1.6 x 10-4 statV/cm. The image in the inset, yielding I(L) is taken at an observation time of t = 1.8 x 104 s, after turning on the voltage. The nanoemulsion is composed of 1,1,5,5-Tetraphenyl-1,3,3,5-tetramethyltrisiloxane/5mM SDS/H2O. The absence of narrow peaks in I(L) after longer observation times indicates that the distribution of droplet radii is broad, polydisperse, and monomodal. The vertical dashed lines refer to where the gel is sliced after electrophoresis. Nanoemulsion droplets in each gel slice are recovered and their average radii measured using DLS. Inset: the measured scattered light intensity detected by the camera in the lane corresponding to the nanoemulsion at that observation time. 73 The resulting deconvolved nanodroplet size distribution pφ(a), obtained by the deconvolution algorithm, is shown in Fig. 4.6; the distribution is broad and monomodal.
Figure 4.6. Deconvolved size distribution pφ(a), where a is the droplet radius and φ is the droplet volume fraction, of a silicone oil-in-water nanoemulsion, corresponding to I(L) shown in Figure 4.5, resulting from the application of a deconvolution algorithm. The dashed lines indicate where the gel is sliced after electrophoresis. Nanoemulsion droplets in each gel slice are recovered and their average radii measured using DLS. The average droplet radius of the deconvolved size distribution is the same, within experimental uncertainty, as a measured average droplet radius that we have measured using a traditional dynamic light scattering method.
To verify the measured size distribution, we slice the gel perpendicular to the direction propagation after electrophoresis into pieces having 3 mm width. The nanodroplets in each slice of gel are recovered by electrophoretically elute the nanodroplets from the gel into buffer solution in a mini-gel electrophoresis system. Then, we collect the nanodroplets recovered from each slice and use DLS to measure their average radius , which are shown below in Table
74 4.2. The DLS results are slightly larger than the size measured using gel electrophoresis, which is shown in Fig. 4.6 after deconvolution. But this difference is still within the uncertainty of our experimental method and caused by the intrinsic difference between DLS and TEM: DLS measures the hydrodynamic radius, which is slightly larger than the core radius (measured by
TEM). Moreover, we assume the surface charge density on the nanoemulsion droplets is the same as that on the monodisperse PS nanospheres used in calibration, which may introduce some error in our data analysis. All things considered, the size distribution we measured using gel electrophoresis agrees with the DLS results. This experiment also shows that gel electrophoresis using passivated agarose gel has great potential in separating and recovering size-separated nanoparticles and nanodroplets based on electrophoretic mobility differences.
Table 4.2. Average measured DLS radius of nanodroplets recovered from cut-out slices after GE
Gel Slice No. 1 2 3 4 5
4.5 Conclusion
Several enhancements are made of standard gel electrophoresis to provide accurate and precise quantitative measurements of the size distributions of dispersions of small-scale objects, such as charged nanoparticles and charged nanodroplets. By contrast to standard deconvolution analysis methods that employ a single point-spread function (PSF) that has the same shape over an entire 1D dataset, we have created a specialized 1D deconvolution method that is specifically tailored for the problem of extracting size distributions from measurements of intensity versus distance obtained through our scattering imaging method of passivated gel electrophoresis. The combination of the experimental equipment, arrangement, materials, procedure, and analysis have been optimized to provide highly accurate size distributions of sub-micron particles, 75 including particle size distributions that have features which cannot be easily measured using techniques such as dynamic light scattering. This technique is useful in analyzing the particle size distribution of dispersions that are multimodal mixture containing several different monodispersed spherical nanoparticles each having different volume fractions as well as a broad size distribution of nanoscale droplets in nanoemulsions. Lastly, the asymmetric tail that we observe in the measured I(L) is most likely due to the propagation of nanospheres through a passivated gel during electrophoresis. It would be useful to improve theories for particle transport during gel electrophoresis to predict this asymmetric tail.
76 Chapter 5
Separation of Particles by pH-Dependent Surface Charge
5.1 Abstract
The electrophoretic mobility of nanoparticles in gel electrophoresis depends on both the size and total charge on the nanoparticles. We successfully separate different nanospheres that have the same radii but different surface charge groups by adjusting the pH of the running buffer used in electrophoresis. Separation of particles can result because pKa’s of their charge groups differ. Thus, pH controls the effective charge of the surface charge groups on the nanoparticles.
Here, we demonstrate that pH-controlled gel electrophoresis of dispersions of nanoparticles, nanodroplets, and other charged nanostructures can be a useful method for separating and characterizing these dispersions.
5.2 Introduction
The propagation velocity of a charged particle in a gel during electrophoresis is determined by a combination of factors, including the electric field strength E, the size (the average radius a), and the net charge q on the particle32,170,171. It is possible to utilize gel electrophoresis to separate particles of different net charge, even if their sizes are the same.
Polystyrene nanospheres are hydrophobic in nature and will undergo aggregation in aqueous dispersions unless the particles are stabilized by covalently linked charge groups, such as sulfate, carboxyl, and amidine. The electrostatic repulsion between the same types of charge prevents the particles from aggregating with each other172-175. The net charge on the
77 nanoparticles depends on the total number, signs, magnitudes, and the percentage of ionization of charge groups on each particle176. By adjusting the manufacturing conditions, the surface density of charge functional groups on particles can be varied177. Moreover, tuning the percentage of ionization of charge groups, after particle production can ultimately change the net charge on the particles177-179. The pKa of acidic groups on the surfaces of polystyrene nanospheres is larger
(i.e. less acidic) than that in bulk aqueous solution. This can be attributed to a higher surface free energy of the charged particle-liquid interface178. The pKa value of the sulfate moiety on the surface of polystyrene nanospheres is around 2 and that of the carboxyl moiety is around 5. The difference in pKa values makes it possible for the two types of particles to have different surface charge densities at the same pH condition even for the same surface coverage. A number of different buffer systems44,45 can be used in gel electrophoresis to control the pH value of a dispersion and change the degree of ionization of the surface charge groups, which affects the net charge of each particle. This enables the separation of nanoparticles stabilized by different charge groups but having the same size, shape, and charge group density by gel electrophoresis.
5.3 Experimental and Methods
5.3.1 Materials
All chemicals (see Table 5.2) used to prepare buffer solutions are purchased from Sigma
Aldrich and used without further purification. All polystyrene nanospheres used are surfactant free and manufactured by Invitrogen. The radii and polydispersities have been measured using electron microscopy (see Table 5.1).
78 Table 5.1. Average radius and standard deviation δa of PS nanospheres having different surface charge groups
Surface Charge Group Carboxyl Sulfate
δa (nm) 8.6 2.5
5.3.2 Preparation of Buffer and Agarose Gel
We set the pH of the electrophoresis experiment by choosing a buffer that has a pKa close to the desired pH values. We first prepare different types of 5 mM aqueous buffer solutions at their corresponding optimum buffer capacity, i.e. when the pH is equal to the pKa of the acid
HA: pH = pKa(HA). We prepare all gels in exactly the same way as described in Chapter 3. Then we soak the gel in different buffer solutions (which also contains the same PEG1000 concentration [PEG1000] as in the gel initially) for 48 hours to ensure complete buffer exchange.
By preparing the gels this way, pH is the only variable, since we maintain the same gel structure and pore size distribution throughout this set of experiments. The various buffers and corresponding pH values are given in Table 5.2.
Table 5.2. Buffer solution used in electrophoresis of nanoparticles to set pH
pH (measured) Buffer Species pKa* 2.87 Chloroacetic acid 2.87 3.78 Formic acid 3.76 4.78 Acetic acid 4.78 6.12 2-(N-morpholino)ethanesulfonic acid (MES) 6.12 7.20 3-(N-morpholino)propanesulfonic acid (MOPS) 7.20 8.00 3-[4-(2-Hydroxyethyl)-1-piperazinyl]propanesulfonic acid (HEPPS) 8.00 9.31 N-Cyclohexyl-2-aminoethanesulfonic acid (CHES) 9.30 *The pKa values are obtained from the manufacturer Sigma-Aldrich.
79 5.3.3 Agarose Gel Electrophoresis and Image Analysis
We record time-lapse videos of bands of scattered light from monodisperse sulfate- and carboxyl-stabilized polystyrene nanospheres propagating in passivated agarose gels in buffer solutions at different pH values. The electrophoresis experiments are conducted in similar conditions as described in Chapter 3. Images of the gels are taken in real-time until the band propagation has reached a steady state. Digital band-tracking analysis by our software provides the distance of propagation of bands of monodisperse particles from the starting well locations as a function of time, and fits of these band trajectories yield the connection between the particle propagation velocity v and pH.
5.4 Results and Discussion
We change the pH of the buffer to study the dependence of particles propagation on degree of protonation of charge groups on their surfaces. Fig. 5.1 demonstrates that we measure pH-dependent mobility distributions of particles, not just size distributions. In Fig. 5.1(a) and
5.1(b), we show the pH dependence of the velocity of propagation of nanoparticles stabilized by sulfate and carboxyl surface charge groups, respectively. The measured propagation velocity of either type of particle as a function of pH satisfies the following equation:
v pH = v 10pH−pK a /(1+10pH−pK a ) p( ) h[ ] (5.1)
where the pKa is known for sulfate and carboxyl surface charge groups and vh is a saturation € velocity in the limit of high pH. This equation reflects the equilibrium protonation and deprotonation reactions from surface charge groups on the nanospheres at a given pH. This, in turn, affects the total charge on the nanospheres and thus their electrophoretic mobility in the
80 passivated agarose gel. The mobility, defined as the velocity divided by the applied force, reflects a combination of the surface charge on a particle as well as its size and shape. In our experiments, the propagation velocities are about the same at high pH values (pH > 7) for both sulfate and carboxyl-stabilized polystyrene nanospheres. This indicates that these two types of polystyrene nanospheres have very similar surface charge density when all surface charge groups are deprotonated.
Figure 5.1. pH dependence of the plateau velocity vp during electrophoresis for polystyrene nanospheres (PSNS) having similar radius a stabilized by different surface charge groups: (a) sulfate (a = 42 nm) and (b) carboxyl (a = 41 nm). Solid lines: fits based on protonation of surface charge groups, yielding good agreement with established pKa's of each group. Conditions: 20 ℃, E = 1.6 x 10-4 statV/cm, 5 mM aqueous buffer solutions (see Table 5.2) at optimum buffering capacities. Gels (0.6 %wt agarose and 10 mM PEG1000) are soaked in buffers for 2 days after casting before performing gel electrophoresis. The dashed vertical lines indicate the pH values used in measurements of Fig. 5.2: left corresponds to pH = 4.76 and right corresponds pH = 6.12.
81 To fully understand the trend shown in Fig. 5.1, we consider the acid-base chemical equilibrium of carboxyl and sulfate groups on the surface of polystyrene nanospheres. The following equations can be used to describe this equilibrium:
- + For the carboxyl moiety: -COOH + H2O -COO + H3O ; (5.2)
- + For the sulfate moiety: -OSO3H + H2O -OSO3 + H3O ; (5.3)
- + In general we can write: HA + H2O A + H3O (5.4)
If we consider the general chemical equation, the equilibrium constant Ka can be written as:
A- H O+ [ ]eq[ 3 ]eq Ka = , (5.5) [HA]eq in which the square brackets represent the concentration when the system reaches equilibrium. € By some simple algebraic manipulations, we can derive the ratio between deprotonated [A-] and total concentration of the weak acid species ([A-] + [HA]), i.e. the percentage ionization:
- A pH-pK a [ ]eq Ka 10 PI = = = pH-pK . (5.6) [HA] + A- H O+ + K 1+10 a eq [ ]eq [ 3 ]eq a
If we assume that the propagation velocity of a charged nanosphere is directly proportional to its € net charge, we derive the ratio between the velocity at a low pH < pKa (i.e. vp(pH)) and at a pH high enough so that all the acid moieties is deprotonated (i.e. the saturated velocity vh):
pH-pK a vp(pH) q(pH) qtot ⋅ PI 10 = = = . (5.7) pH-pK a vh qtot qtot 1+10
This equation corroborates exactly with the fitting formula we obtained have used to fit our € experimental data.
82 The fitting formula expressed in Eq. 5.1 is derived based on the protonation of surface charge groups. The fitting results yield good agreement with established pKa’s of each surface charge groups as shown below in Table 5.3.
Table 5.3. Measured and literature pKa value of carboxyl (C) and sulfate (S) surface charge groups on PSNS
Surface Charge Group pKaC pKaS
Measured 4.59 2.93
Literature* ~ 5 ~ 2 *The literature pKa values are obtained from the manufacturer Invitrogen.
To experimentally demonstrate separation of a mixture of particles having two different surface charge groups, we present an image of bands of monodisperse spherical polystyrene nanoparticles that are stabilized by two different anionic surface charge groups: sulfate and carboxyl, in Figure 5.2. If we reduce the pH to 4.76 using a buffer, so that the pH is fixed between the two different pKa's of the sulfate and carboxyl surface charge groups, then we separate a mixture of spheres having nearly identical radii into two different bands based on differences in surface charge groups (see the rightmost lane in Fig. 5.2(a)). On the other hand, if we increase the pH of the buffer to 6.12, which is above the pKa’s of both charge groups, we cannot separate the two types of spheres (see Fig. 5.2(b)). Thus, to achieve separation based on charge group type using passivated GE, it is important to select a pH between the two different pKa’s of the surface charge groups. Even if surface charge groups are unknown, it is possible to perform gel electrophoresis at several different pH values to extract differently stabilized nano- objects that have different surface chemistries (i.e. charge groups).
83
Figure 5.2. Gel electrophoresis images at t = 3.2 x 104 s showing separation of PSNS having the same radius and stabilized by carboxyl (C) and sulfate (S) surface charge groups at different pH:
(a) pH = 4.76, between the pKa's of C and S groups, where separation of a mixture of C and S is observed since C propagates more slowly; (b) pH = 6.12, above the pKa's of both groups, so C and S propagate at the same velocity and no separation of C from S occurs. Bands are labeled C (a = 41 nm), S (a = 42 nm), and C/S for a 1:1 mixture of C and S. Lowest edges of the images in (a) and (b) represent the starting locations of bands before the electric field is applied. Conditions: 20 ℃, E = 1.6 x 10-4 statV/cm, 5 mM aqueous buffer solutions at their optimum buffering capacity. Gels (0.6 %wt agarose and 10 mM PEG1000) are soaked in buffers for 2 days after casting to ensure complete buffer exchange and a uniform pH everywhere in the gels.
5.5 Conclusion
In gel electrophoresis, the propagation velocity of particles depends on both particle size and charge. Changing the buffer’s pH can influence the charge on the surface of nanoparticles, thereby enabling us to separate different types of nanospheres that have the same radii but different pKa's of their surface charge groups. We anticipate that pH-dependant gel electrophoresis can be useful in purifying and selecting specific nano-objects having a desired charge group type and/or surface charge density at a particular pH.
84 Chapter 6
Conclusions and Future Directions
Colloidal dispersions, such as nanoparticles or nanodroplets in water, have attracted great interest in all areas of basic research and industrial production. Since most physical properties of a dispersion depend on the size, shape, charge, and volume fraction of the nano-objects in it, developing new techniques to characterize nano-objects is very important and will enable further advancements in this field. We have successfully applied two classical analytical methods, optical refractometry and gel electrophoresis, to characterize the composition and particle size distributions of colloidal dispersions, particularly nanoemulsions.
In Chapter 2, we have developed a refractometry-dilution method to determine a nanoemulsion’s composition over a wide range. Since the nanodroplets are significantly smaller than the lower wavelength limit of the visible spectrum, multiple light scattering is often negligible for thin layers of nanoemulsions loaded into an Abbé refractometer. We have shown that the refractive index depends linearly on both the surfactant concentration and the nanodroplet volume fraction, following the Biot-Arago equation. This refractometry-dilution method provides a means of characterizing the compositions of nanoemulsions non- destructively, since it is rapid, requires very small volumes, and does not cause droplet coalescence.
In Chapter 3 and 4, we have developed a real-time video-tracking gel electrophoresis experiment in order to conduct a quantitative and systematic study of the separation of monodispersed sulfate stabilized polystyrene nanospheres using light scattering detection.
Blindly using GE for biomolecules does not work for most nanoparticles and nanoemulsions. 85 The passivation of the gel is necessary, not just an improvement, for applying GE to nanoparticles and nanoemulsions. We have fundamentally altered the standard gel electrophoresis procedure to obtain accurate size distributions of dispersions of small-scale objects such as charged nanoparticles and charged nanodroplets. These alterations include: passivating an agarose gel using a PEG1000 passivation agent; creating wells in a gel that have very thin design (e.g. about 50 µm) using a customized comb; recording real-time images of light scattered from propagating nanoparticles in a gel; and analyzing images of background- subtracted movies to obtain the size distribution of small-scale objects via specialized deconvolution. We have demonstrated the effect of gel concentration, passivation agent type and concentration, electric field strength, and particle size on the electrophoretic mobility and separation of nanoparticles in the size range from about 15 nm to 150 nm during gel electrophoresis. We have also shown the quantitative dependence of the integrated average light scattering intensity of bands of particles on the size and volume fraction of particles, which is used to extract important particle size distribution information. Using the calibration data, we have created a specialized deconvolution method to extract size distributions from measurements of intensity versus distance obtained through our scattering imaging method during passivated
GE. We have successfully demonstrated this quantitative video-tracking gel electrophoresis technique by measuring the particle size distributions of two very different types of polydisperse dispersions: (1) a multimodal mixture containing several different monodispersed spherical nanoparticles each having different volume fractions and (2) a broad size distribution of nanoscale droplets in nanoemulsions. Our passivated GE deconvolution method has great potentially because it overcomes limitations of other traditional particle-sizing technique, such as
DLS and SLS, and it is also low-cost.
86 Furthermore, we have successfully separated nanoparticles based on their surface charge groups, even when they are similar in size (Chapter 5). We have controlled the buffer’s pH values to change the charge on the surface of nanoparticles, thereby enabling us to separate different types of nanospheres that have the same radii but different pKa's of their surface charge groups. This pH-dependant gel electrophoresis method can be useful in purifying and selecting specific nano-objects based on their surface charge density and the type of surface charge group.
We foresee that the simple optical band-imaging measurements of particles propagating in real-time in passivated gels can be extended to other methods of imaging and detection. These methods might improve the accuracy as well as the detection limits (range of sizes and volume fractions) of this technique. These include, using monochromatic illumination (such as laser illumination: a scanned laser beam or a laser light sheet created by a cylindrical lens), absorption of illuminating light by strongly absorbing particles, longer-wavelength fluorescent light emitted from fluorescent particles and fluorescently labeled molecules that are illuminated by shorter- wavelength incident light where the shorter wavelength illuminating light is filtered out by a filter placed in front of the optical detector that permits the passage of fluorescent emitted light, x-rays, and emitted elementary particles (e.g. neutrons, beta particles, and alpha particles) if nanoparticles or labeled molecules contain certain radio-isotopes that emit such x-rays and emitted particles.
In addition to characterizing the size distribution of nanoparticle dispersions, we also see the potential of pH-controlled passivated gel electrophoresis in separating nanoparticles based on their size, shape, surface charge density, and surface charge group type.
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