• unlimited access with print and download
    $ 37 00
  • read full document, no print or download, expires after 72 hours
    $ 4 99
More info
Unlimited access including download and printing, plus availability for reading and annotating in your in your Udini library.
  • Access to this article in your Udini library for 72 hours from purchase.
  • The article will not be available for download or print.
  • Upgrade to the full version of this document at a reduced price.
  • Your trial access payment is credited when purchasing the full version.
Buy
Continue searching

Raman correlation spectroscopy: A feasibility study of a new optical correlation technique and development of multi-component nanoparticles using the reprecipitation method

ProQuest Dissertations and Theses, 2011
Dissertation
Author: Maki Nishida
Abstract:
The feasibility of Raman correlation spectroscopy (RCS) is investigated as a new temporal optical fluctuation spectroscopy in this dissertation. RCS analyzes the correlations of the intensity fluctuations of Raman scattering from particles in a suspension that undergo Brownian motion. Because each Raman emission line arises from a specific molecular bond, the RCS method could yield diffusion behavior of specific chemical species within a dispersion. Due to the nature of Raman scattering as a coherent process, RCS could provide similar information as acquired in dynamic light scattering (DLS) and be practical for various applications that requires the chemical specificity in dynamical information. The theoretical development is discussed, and four experimental implementations of this technique are explained. The autocorrelation of the intensity fluctuations from a β-carotene solution is obtained using the some configurations; however, the difficulty in precise alignment and weak nature of Raman scattering prevented the achievement of high sensitivity and resolution. Possible fluctuations of the phase of Raman scattering could also be affecting the results. A possible explanation of the observed autocorrelation in terms of number fluctuations of particles is also examined to test the feasibility of RCS as a new optical characterization method. In order to investigate the complex systems for which RCS would be useful, strategies for the creation of a multicomponent nanoparticle system are also explored. Using regular solution theory along with the concept of Hansen solubility parameters, an analytical model is developed to predict whether two or more components will form single nanoparticles, and what effect various processing conditions would have. The reprecipitation method was used to demonstrate the formation of the multi-component system of the charge transfer complex perylene:TCNQ (tetracyanoquinodimethane) and the active pharmaceutical ingredient cocrystal of CBZ:NCT (carbamazepine:nicotinamide). The experimental results with various characterization methods including DLS, absorption spectroscopy, powder x-ray diffraction, and SEM imaging, verify formation of the multicomponent cocrystals. The observation of the self-assembly of TCNQ crystals is also discussed.

Table of Contents I Raman Correlation Spectroscopy:A Feasibility Study of a New Optical Correlation Technique 1 1 Introduction 1 2 Motivation and Applications 5 2.1 Complex Mixture Characterization...................5 2.2 Polymer Self-assembly Analysis.....................6 3 Light Scattering from Nanoparticles 7 3.1 Dynamic Light Scattering........................7 3.2 Raman Scattering.............................17 3.3 Raman Correlation Spectroscopy....................20 4 Theoretical Development of RCS 22 4.1 Derivation of Intensity Correlation Analysis in RCS..........22 4.2 Resolution and Sensitivity of RCS....................29 5 Experimental Implementation 33 5.1 Instruments................................34 5.2 Materials.................................38 5.3 Optical Configuration...........................41 5.4 Challenges in Constructing the RCS Setup...............42 5.5 Preliminary Experiment.........................46 6 Experimental Results and Discussion 51 6.1 Free Space Optics RCS Setup......................51 6.2 Fused Fiber Coupler RCS Setup.....................53 6.3 Fiber-to-Fiber Optics RCS Setup....................55 6.4 Modified Fiber Optics RCS Setup....................60 7 Feasibility of RCS 64 7.1 Analysis of RCS Theory Using Experimental Data...........64 7.2 Fiber Backscattering Optics RCS Setup.................68 vi

7.3 Data Analysis in Terms of Number Fluctuations............69 8 Conclusions and Future Research 74 II Development of Multi-component Nanoparticles Using the Reprecipitation Method 78 9 Introduction 78 10 Background on Nanoparticle Formation 80 10.1 Nanomaterial Synthesis..........................80 10.2 Reprecipitation Method.........................81 10.3 Classical Nucleation Theory.......................82 10.4 Co-crystallization and Solubility.....................83 10.5 Derivation of Three Solvent Spheres Model...............89 11 Experimental Methods 96 11.1 Sample Material..............................96 11.2 Sample Preparation............................98 11.3 Characterization Methods........................99 12 Experimental Results 104 12.1 Optical Characterization Results for Charge Transfer Crystals....104 12.2 Optical Characterization Results for API Cocrystals..........115 13 Formation and Progression in the self-assembly of TCNQ crystals 119 13.1 Background................................119 13.2 Experimental Methods..........................121 13.3 Characterization and Results.......................122 13.4 SEM Observations and Results.....................123 14 Conclusions and Future Research 129 Appendices 132 vii

A MATLAB Codes for Intensity Fluctuation Analysis in RCS 132 A.1 Main Routine:RCSascfit.m.......................132 A.2 Subroutine:fun2.m............................138 B Geometric Method of the Three Solvent Spheres Model 139 C MATLAB Codes for Three Solvent Spheres Model 144 C.1 Main Routine:TSSmodel.m.......................144 C.2 Subroutine:intersect3sphere.m.....................147 C.3 Subroutine:plotsphere.m.........................148 C.4 Subroutine:calcintlength.m.......................149 C.5 Subroutine:checkintersectibility.m...................149 References 151 viii

List of Figures 3.1 Scattering geometry............................8 3.2 Particle diffusion.............................15 3.3 Intensity fluctuations and ACF graphs of different sized particles...16 3.4 Energy transitions of scattering.....................19 5.1 Transmission spectrum of the 514.5 nm edge filter...........35 5.2 Beam spot size on a grating mirror of a monochromator........36 5.3 Raman spectrum of β-carotene measured by the Raman microscope.39 5.4 Schematic of the preliminary FORCS setup...............47 5.5 Raman spectrum of β-carotene measured by the preliminary FORCS setup....................................48 5.6 ACFs of β-carotene at different Raman lines obtained by the prelimi- nary FORCS setup............................48 5.7 ACF analysis of Raman line at 558.2 nm(ν C=C ) of β-carotene obtained by the preliminary FORCS setup....................49 6.1 Schematic of the free space optics RCS setup..............51 6.2 Raman spectra measured by the free space optics RCS setup.....53 6.3 Schematic of the fused fiber coupler RCS setup............54 6.4 Raman spectra measured by the fused fiber coupler RCS setup....55 6.5 Schematic of the FTFORCS setup....................56 6.6 Raman spectrum of β-carotene measured by the FTFORCS setup..59 6.7 ACFs of Raman line at 558.2 nm (ν C=C ) of β-carotene obtained by the FTFORCS setup.............................59 6.8 Schematic of the modified FORCS setup................60 7.1 ACF analysis of Raman line at 558.2 nm(ν C=C ) of β-carotene obtained by the preliminary FTFORCS setup...................65 7.2 ACFs of a 0.5 wt % β-carotene solution by the FTFORCS setup for RCS and DLS measurements.......................66 7.3 ACF of the Ar laser beam........................67 7.4 Calculated values of Γ for RCS and DLS................67 7.5 Schematic of the fiber backscattering setup...............68 7.6 Number fluctuation analysis of β-carotene at the 558.2nm Raman line (ν C=C ) obtained with the FTFORCS setup...............72 10.1 Illustration of the reprecipitation method for a single component ma- terial in a Hansen space.........................88 10.2 Illustration of the reprecipitation method for multi-component mate- rials in a Hansen space..........................89 10.3 Solubility of naphthalene in various solvents in terms of the interaction radius...................................93 10.4 Result from the TSS model simulation.................95 11.1 Molecular structures of perylene and TCNQ..............96 ix

11.2 Molecular structures of CBZ and NCT.................97 11.3 Crystal packings of CBZ:NCT......................97 11.4 Schematic diagram of the reprecipitation method...........98 12.1 Particle growth of reprecipitated perylene:TCNQ and perylene mea- sured by DLS...............................104 12.2 Absorption spectra of reprecipitated charge transfer crystals......105 12.3 Raman spectra of reprecipitated charge transfer crystals.......106 12.4 SEM image of reprecipitated perylene:TCNQ nanocrystals......108 12.5 SEM image of reprecipitated perylene nanocrystals..........108 12.6 SEM images of reprecipitated TCNQ crystals.............109 12.7 EDS results of reprecipitated charge transfer crystals.........110 12.8 PXRD patterns of reprecipitated charge transfer crystals.......111 12.9 Absorption spectra of reprecipitated perylene:TCNQat different molar ratios....................................112 12.10Absorption spectra of reprecipitated perylene:TCNQ at different tem- peratures.................................114 12.11DLS results of reprecipitated perylene:TCNQ at different temperature 114 12.12Raman spectrum of reprecipitated CBZ:NCT compared with that of CBZ and NCT powder..........................117 12.13DSC of reprecipitated CBZ:NCT compared with CBZ and NCT powder118 13.1 Schematic diagramof the crystallization transition following Ostwald’s rule.....................................120 13.2 Absorption spectra of TCNQ......................123 13.3 PXRD pattern of reprecipitated TCNQ.................123 13.4 SEM images of various shapes of reprecipitated TCNQ........124 13.5 SEM images of progression in self-assembly of reprecipitated TCNQ.127 13.6 SEM images of reprecipitated TCNQ at a high concentration.....128 13.7 SEM images of reprecipitated TCNQ at different temperatures....128 B.1 Schematic of three solvent spheres in a Hansen space.........139 B.2 Diagrams of the intersections of spheres.................140 List of Tables 5.1 Relative differential Raman cross sections................43 5.2 Experimental analysis results of the preliminary FORCS.......49 6.1 Estimated Raman signals for the modified FORCS setup for different materials..................................62 7.1 Experimental analysis results of the FTFORCS setup.........65 7.2 Estimated Raman signals for the fiber backscattering optics RCS setup for different materials...........................69 7.3 Results from the number fluctuation analysis for the β-carotene data obtained with the FTFORCS setup...................72 x

10.1 Results of Three Solvent Spheres Model.................95 12.1 Major Raman shifts observed in reprecipitated perylene:TCNQ com- pared with reprecipitated perylene and TCNQ.............107 12.2 Solubility check for CBZ and NCT in different solvents........116 12.3 Raman band shifts of reprecipitated CBZ:NCT compared to CBZ powder117 xi

Part I Raman Correlation Spectroscopy: A Feasibility Study of a New Optical Correlation Technique 1 Introduction In the past decade,research and development in nanoscience has significantly contributed in a wide range of innovative applications and fields.Due to the novel phe- nomena and functionalities arising from the influence of their dimensions,nanoscale objects continue to see interest for further advancement of current technology.Nanopar- ticle based systems,such as colloids,are one group of nanomaterials that demonstrate remarkable potential and properties that have been used and studied for various ap- plications from commercial products to biomedicine. Colloids consist of a dispersed phase that is distributed uniformly in a dis- persion medium.Both the disperse phase and the dispersion medium of a colloidal system could be any state - gas,liquid,and/or solid.They have always existed in nature.Fogs,mists,and smokes are the dispersion of liquid droplets in air or gas. Biological structures,such as proteins,blood cells,and bacteria,also have colloidal nature.Since ancient times,man has observed and used colloids for daily life.Milk, for example,is a colloidal dispersion of fat droplets in a liquid (aqueous phase).It is not,however,only natural phenomena or commodities of colloids that man has been familiar with.Although it was not until the mid 19th century when Michael Faraday made the first systematic study of gold colloids,the synthesis of this colloid had already been used for creating stained glass 1 and the Lycurgus Cup in Ancient 1

Rome. 2 With the development of colloid science at the beginning of the 20th century, colloids have become indispensable tools in modern living as major components of industrial products.Colloids are often used in food products,paints,cosmetics,and many commercial products. 3 In biomedical fields,there has been a surge of interest in colloidal drug carrier systems for forming aqueous formulations of water-insoluble drugs. 4 Among all the classes of colloidal systems,this research focuses on colloidal dispersions where fine solid particles are dispersed in a liquid medium so,unlike in the case of suspensions,they are evenly distributed and long-term stable.Therefore, the term colloids in this dissertation is used to describe dispersed nanoparticles. In terms of physical chemistry,colloids are molecules or polymoleculer particles that are large compared to the solvent molecule but small enough to exhibit thermal motion,known as Brownian motion.This motion is the seemingly random movement of particles suspended in a dispersion medium resulting from the bombardment by the neighboring solvent molecules.The general size range for colloidal particles is 10 nm to 10 µm.When a beam of light passes through the dispersion system,strong light scattering can be observed due to the presence of colloids and hence the path of the light can be clearly observed.The effect is known as the Tyndall effect. 5 The surface area of colloids contributes to their importance as well as their definition.The small particle size of colloids leads to a large surface area per unit vol- ume or mass and high energy from the surface electric charges.Since intermolecular forces act on particle surfaces,unlike the gravitational force that acts on the mass, the high surface-to-volume (or surface-to-mass) ratio prevents the gravitational effect from causing colloids to precipitate.With the effect of Brownian motion,where sur- rounding solvent molecules hit the colloidal particles from all directions,the colloids stay buoyant for several months up to years.Also,to maintain the colloidal stability 2

of dispersions,the repulsive forces are required to counterbalance the attractive forces such as van der Waals force.Intermolecular forces from the electrostatic effect and steric effect prevent colloids from aggregation,resulting in sustaining their particle size. From imaging of a nanoscale object to determining its elemental composition or other properties,a wide range of characterization techniques for such systems has been developed to establish understanding and control of their properties.For ex- ample,electron microscopies,such as transmission electron microscopy (TEM) and scanning electrons microscopy (SEM),create an image of species by using electrons. Laser-induced breakdown spectroscopy (LIBS) determines the elemental composi- tion or concentrations by analyzing the laser induced plasma with a spectrometer. Ultraviolet-visible spectroscopy (UV/VIS) analyzes absorbance of the species from electronic transitions to obtain information on their concentration. To characterize the nanoparticle size,techniques using optical scattering have the advantage of noninvasiveness and simple sample preparation.In particular,op- tical time correlation spectroscopy methods such as dynamic light scattering (DLS) have long been used for characterization of dynamics of particles in the size range from 10 nm to 1 µm and hence frequently used for studies of colloidal suspensions. A technique that determines the chemical compositions of materials is also useful in material science.Raman spectroscopy provides a fingerprint of a species by analyzing Raman scattering.When an electromagnetic wave impinges on a material and quasi-elastic light is scattered,simultaneously molecular bonds vibrate and/or molecules rotate,resulting in inelastic scattering.This inelastic scattering has differ- ent frequencies depending on the molecular bonds and the motion of vibrations or rotations.Because each band of this scattering identifies the specific chemical bonds and symmetry of the molecules,Raman scattering can be used as an identifier of 3

molecules.This qualitative identification of the Raman emission line allows one to detect the change in the chemical bonds and hence the chemical composition of the species,including colloidal particles. If the above two concepts were to be combined,one could make the measure- ment of the diffusion coefficient of a specific component in a colloidal dispersion sys- tem.If this new characterization technique,named Raman correlation spectroscopy (RCS),is successfully developed,it would work as a variation of DLS to provide the chemical specificity in the measurements by analyzing Raman scattering and can be widely used to investigate multicomponent colloidal systems as exemplified in the next chapter (Chapter 2).Therefore,RCS could expand possibilities in colloidal sci- ence. ∗ As a novel characterization method for colloidal dispersion,the possibility of RCS is investigated in this part of the dissertation.The theory of RCS is developed and discussed in chapter 4.Several implementations were constructed and tested in chapter 5 and 6.Finally,the results are analyzed to investigate the validity of RCS in chapter 7. ∗ Some of the contents in this part of the dissertation is currently under preparation as a manuscript to be submitted to Optics Letters. 4

2 Motivation and Applications Since each molecular bond has a unique Raman spectrum,RCS could selec- tively characterize a specific component within a complex mixture.If the possibility of RCS as a variation of DLS can be demonstrated,it has potential to be used in numerous applications in research and development. 2.1 Complex Mixture Characterization The potential of RCS lies in its specificity that can be used for complex mixture characterization.For example,Van Keuren’s group has been working on the study of the formation of charge transfer nanocrystals,which will be discussed in part II of this dissertation.When a single molecular solution is added to a miscible nonsolvent, nanocrystals can be formed.If the solution is multi-component,phase separation may occur causing different nanocrystals consisting of individual components in the mixture to be formed rather than larger nanocrystals combining both components in the mixture.However,we are interested in the formation of multi-component nanocrystals rather than the single component nanocrystals.RCS could be a great tool for the investigation of the nanocrystal formation because it could distinguish each type of nanocrystals in the complex mixture by analyzing the Raman emission line of each component in the mixture.For instance,if the diffusion coefficient from each species is the same as the other,it would indicate that the multi-component nanocrystals are successfully formed.If the diffusion coefficients were not the same, RCS would confirm that nanocrystals of single species were formed instead;thus,the formation conditions would need to be adjusted to prevent the phase separation. 5

2.2 Polymer Self-assembly Analysis RCS would also be a useful tool to study the self-assembly process of polymers. There are two primary kinds of polymerizations:one is addition polymerization that simply adds up monomers without forming byproducts,and the other is condensa- tion polymerization that eliminates some molecules to form a bond with the other monomer or polymer.During polymerization,due to the structural changes,Raman bands observed in monomers may disappear or become shifted in polymer structures, and new Raman bands may arise in polymers.By analyzing Raman bands during the assembly process,RCS would determine the size of the specific polymers so that information of dynamic behaviors and interactions between monomers and polymers during the process can be examined in detail. 6

3 Light Scattering from Nanoparticles 3.1 Dynamic Light Scattering DLS is one of the intensity-fluctuation spectroscopies employed to characterize colloidal systems.It is also known as photon correlation spectroscopy (PCS) or quasi- elastic light scattering (QELS).For its simple apparatus and non-invasiveness,this technique has been utilized in structural and dynamical analysis of samples in a wide range of fields.For example,it is often used for quality control of industrial and commercial products,such as pigments,inks,detergents,latexes,agrichemical emulsions,and food products.It also serves in biomedical fields,such as in the study of viruses and the analysis of proteins.The DLS theory is fundamental to RCS.This chapter,therefore,discusses the theory of this technique. 3.1.1 Light Scattering When electromagnetic radiation impinges on matter,the electric field of the radiation induces an oscillating electric dipole moment in its molecules.Classically, the polarized electrons radiate light,or scatter,at the frequency of their oscillation. This scattered light at the detector at a given time is the superposition of the electric fields radiated from all of the scatterers and so depends on their positions. The phase of the scattered light at a point with radius vector r relative to the phase of the scattered light at the origin is q · r where q is the scattering vector as shown in Figure 3.1: q = k i −k f (3.1) 7

Figure 3.1:Scattering geometry.The diagram illustrates the scat- tering vector q for nanoparticles in a dispersion. where the wave vectors k i and k f point in the directions of propagation of the incident light and the scattered light reaching the detector respectively. 6,7 Thus,the phase difference of the scattered light is ϕ = q · r = (k i − k f ) · r.The magnitudes of k i and k f are 2πn/λ i and 2πn/λ f respectively,where n is the refractive index of the scattering medium and λ i and λ f are the wavelengths of the incident and the scattered light.The angle between k i and k f is the scattering angle θ. The electric field resulting from scattering by a particle located at position r is E s = A j E o e i(q·r−ω o t) (3.2) where E o is the field amplitude,ω o is the angular frequency,and t is time.A term A j in the above equation contains factors such as the polarizability,the distance R to the detector,and other parameters. 7 8

Most of the scattered photons are due to quasi-elastic collisions between the incident photons and molecules of the system,hence the radiation is at almost the same frequency as the incident radiation.Such scattering are described by two mod- els:Rayleigh scattering and Mie scattering.In Rayleigh scattering,the light is scat- tered by a particle of size much smaller than the light wavelength.The upper limit of the diameter of such a particle is less than 20 to 30 nm or about 1/10 of the wavelength. 8 The refractive index in Rayleigh scattering is close to 1,so that the electric field penetrates through the particle.Hence the scattered photons interfere constructively and the radiation is uniform in all directions. 9 This scattering explains the blue sky.Air molecules undergo Rayleigh scattering with an intensity that has a strong wavelength dependence of 1/λ 4 ,so the shorter blue wavelengths are scattered stronger than red at large angles with respect to the direction of the sunlight.The intensity of Rayleigh scattering strongly depends on both the particle size and wave- length.When the particles become comparable to the size on the order of the light wavelength and if they are spherical,the scattered photons are described as Mie scat- tering.Unlike Rayleigh scattering,Mie scattering has a complicated dependence on angle and its intensity is larger in the forward direction than in the reverse direction. The larger the particle size is,the more intense the light is in the forward direction, and because Mie scattering is not strongly wavelength dependent,the white glare observed around the sun is explained by this type of scattering.The white light from mists and fogs where the light passes through clouds of particulate matters is also due to Mie scattering.As the exact solution to Maxwell’s equation,this scattering theory works well with spheres,and although solutions for some other simple shapes like ellipsoids exist,no general solution is known for arbitrary shapes. 9

3.1.2 Particle Diffusion During the scattering process,dispersed particles undergo random Brownian motion as a result of bombardment by surrounding solvent molecules due to their thermal energy.The rate of diffusion of the particles is related to their size;small par- ticles move faster than larger particles.Although the particle motion is in a random manner,more particles move from a high concentration region to a low concentration region in a unit time.Diffusion of particles is thus caused by Brownian motion.In diffusion theory,the mean square of the displacement of a particle along a given axis is ∆x 2 = 2D∆t.The phase of the scattered wave is significantly affected when the particle moves over a distance x ≈ q −1 .The correlation time τ c ,representing the characteristics decay time of the particle diffusion,is τ c ∼ 1 Dq 2 (3.3) where D is the diffusion coefficient and q is the length of the scattering wave vector q. Due to the translational diffusion of the particle,the sum of the scattered light from particles at the detector fluctuates in time.If the radiation source,such as a laser,emits monochromatic and coherent light,the coherent scattered photons interfere with each other,and consequently,the interference pattern fluctuates in time. By measuring such fluctuations of scattering,one can obtain dynamical information of the system. 10

3.1.3 Intensity Autocorrelation Analysis The time average of the signal is defined by

f

= lim T→∞ 1 T

T 0 dt f(t).(3.4) When the system is ergodic,this time average equals the ensemble average.Thus,a measure of the correlation of a fluctuating signal is the autocorrelation function of f as

f(0)f(τ)

= lim T→∞ 1 T

T 0 dt f(t)f(t +τ) =

f

2 +{

f 2

f

2 }e −τ/τ r (3.5) where τ r is the correlation time of the signal.In many cases,because for a long time τ,the signal fluctuation would be totally uncorrelated,the autocorrelation function typically illustrates a single exponential. The scattering fluctuations from a particle in diffusion take place also in a random manner as explained in the previous section.The autocorrelation of these signals is characterized in DLS to determine the diffusion coefficient of the particle. The autocorrelation function,a measure of the temporal correlation of the electric field of the scattered wave,is defined as: G 1 (τ) = E ∗ (t)E(t +τ) (3.6) where E(t) and E(t+τ) are the electric fields of the scattered light at time t and t+τ (τ is delayed time).In practice,the homodyne method,where only the scattered light impinges on the detector,is usually employed,and the autocorrelation function of the 11

scattered wave is obtained by measuring the temporal fluctuation of light intensity I(t) at the scattering angle. The intensity I,or the average energy per unit area per unit time,of the scattered light is proportional to the square of the amplitude of the electric field,or I ∝ |E| 2 .The time dependent intensity fluctuation is analyzed using the second order autocorrelation function,or in this case the intensity autocorrelation function that is defined as: G 2 (τ) = I(t)I(t +τ) (3.7) where I (t) and I (t+τ) are the intensities of the scattered light at time t and t+τ. In experiments,the scattered light intensity is collected and measured by a digital detector and correlator for a long period of time in order to get good photon statistics, which allow an accurate determination of the average in equation (3.7).The com- parison of the pairs of all and any data that are separated by the time delay interval τ is done by using equation (3.7).As τ increases,the signals become less correlated, hence G 2 decreases with τ. Since the detected signal is the sum of light scattered by many independent particles,it exhibits Gaussian statistics.In this case,a relation between the inten- sity correlation function G 2 (τ) and the field correlation function G 1 (τ) can be well approximated by the Siegert relation: g 2 (τ) = 1 +γ|g 1 (τ)| 2 (3.8) where γ is a coherence factor,which depends on the number of coherence areas observed and the sampling time interval,and is unity in the ideal case. 6 This equation only holds if the scattering field is a Gaussian process.The coherence factor γ is an 12

important variable for a good signal to noise ratio and will be explained in section 4.2.1 in detail. In equation (3.8),g 1 (τ) is the normalized field autocorrelation function,g 1 (τ) = G 1 (τ)/G 1 (0).In a monodisperse particle system where particles are in Brownian motion,the autocorrelation function decays exponentially, 6 g 1 (τ) = e −Γt .(3.9) Γ in the above equation is the diffusion rate,which is the inverse of the correlation time τ c (equation (3.3)) of the particle diffusion;thereby, Γ = Dq 2 (3.10) where,from equation (3.1), q 2 =| k f −k i | 2 = k f 2 +k i 2 −2k f k i cos(θ).(3.11) For quasi-elastic scattering,|k i | ∼ = |k f |.The length of the vector can then be written as q = 4πn λ sin θ 2 (3.12) where n is the refractive index of the sample,λ is the excitation wavelength,and θ is the scattering angle. In DLS experiments,the intensity fluctuation data is characterized by the normalized autocorrelation function (ACF) of intensity,and then a nonlinear fit al- gorithm is applied to the ACF obtained.The ideal monodispersed sample yields the single exponential decay of the ACF,but if the data is more complicated,polydisper- 13

sity of the sample can be analyzed in DLS. To analyze the data,the cumulants analysis,introduced by Koppel,is often employed in modern DLS instruments. 10 This method defines the expression for the ACFs by calculating the moments or cumulants of the distribution.However,if differ- ent numbers of data points are fitted,this traditional cumulant method can produce inconsistent results within the same data.To obtain more robust and satisfactory fits,Frisken reformulated the cumulants method and took into account an arbitrary background signal in the following moment-based expression for the normalized time autocorrelation function of the intensity of scattering g 2 (τ),which is given by 11 g 2 (τ) = γ · exp(−2Γτ) ×(1 + µ 2 2! τ 2 − µ 3 3! τ 3 +...) 2 +B (3.13) where B is a baseline,which is the long time value of g 2 (τ),and µ 2 and µ 3 are the second and third moments that are associated with the probability distribution of the diffusion rates.The second moment µ 2 is a measure of the variance of the distribution, and the third moment µ 3 is a measure of the skewness of the distribution.Since no correlation should be observed at long times,B is ideally 1.However,experimental noise can cause the value to deviate from unity.If the obtained data has a value of B that is too far from unity,it indicates a problem in the data for fitting.It could also indicate the presence of larger particles or bad normalization or scaling of data. Figure 3.2 displays the concept of the ACF.At the delay times τ 1 ,τ 2 ,and τ 3 with respect to the reference time t=τ 0 =0,a particle moves away in a randommanner so the degree of the displacement changes.Hence,at a longer time,the particle has deviated from the original position,and so the correlation decreases. 14

Full document contains 171 pages
Abstract: The feasibility of Raman correlation spectroscopy (RCS) is investigated as a new temporal optical fluctuation spectroscopy in this dissertation. RCS analyzes the correlations of the intensity fluctuations of Raman scattering from particles in a suspension that undergo Brownian motion. Because each Raman emission line arises from a specific molecular bond, the RCS method could yield diffusion behavior of specific chemical species within a dispersion. Due to the nature of Raman scattering as a coherent process, RCS could provide similar information as acquired in dynamic light scattering (DLS) and be practical for various applications that requires the chemical specificity in dynamical information. The theoretical development is discussed, and four experimental implementations of this technique are explained. The autocorrelation of the intensity fluctuations from a β-carotene solution is obtained using the some configurations; however, the difficulty in precise alignment and weak nature of Raman scattering prevented the achievement of high sensitivity and resolution. Possible fluctuations of the phase of Raman scattering could also be affecting the results. A possible explanation of the observed autocorrelation in terms of number fluctuations of particles is also examined to test the feasibility of RCS as a new optical characterization method. In order to investigate the complex systems for which RCS would be useful, strategies for the creation of a multicomponent nanoparticle system are also explored. Using regular solution theory along with the concept of Hansen solubility parameters, an analytical model is developed to predict whether two or more components will form single nanoparticles, and what effect various processing conditions would have. The reprecipitation method was used to demonstrate the formation of the multi-component system of the charge transfer complex perylene:TCNQ (tetracyanoquinodimethane) and the active pharmaceutical ingredient cocrystal of CBZ:NCT (carbamazepine:nicotinamide). The experimental results with various characterization methods including DLS, absorption spectroscopy, powder x-ray diffraction, and SEM imaging, verify formation of the multicomponent cocrystals. The observation of the self-assembly of TCNQ crystals is also discussed.