除去氣體對於奈米碳管與水混和物之影響

全文

(1)國. 立. 臺. 灣. 師. 範. 大. 物理學系碩士班碩士論文. Effects of Degassing on Carbon Nanotubes/Water Mixture. 研究生 : 陳駿仁指導教授 : 黃仲仁博士共同指導: 陳志強博士. 中華民國一百零五年二月. 學.

(2) 中文摘要疏水交互作用（hydrophobic interaction）被認為是非極性物質在水中會聚集的主要原因。已知水中的氣體是可以對該作用有增益的效果。若將疏水顆粒混合於水中，則除去氣體的混合物較富含空氣的混合物有較長的生命期。本研究以單層及多層奈米碳管的水混合物為材料，實驗除去氣體對於碳管與水混合物的影響。碳管於水中的生命期與所形成之結構是以攝影與動態光散射進行觀測。實驗中發現：除去氣體後，單層碳管於水中聚集的速率較未除氣的混合物中慢，且形成較緻密的碳管團塊。多曾碳管若未進行除氣，則碳管於水中形成類凝膠(gel-like)結構；此結構在除去氣體的碳管與水混合物中較未除氣者不明顯。實驗中所觀察到，除去氣體對單層與多層碳管的水混合物所產生之影響，是可以被石墨基板上所發現的表面奈米氣泡（surface nanobubble）解釋的。. 關鍵詞：疏水交互作用、無介面活性劑膠體溶液、奈米碳管、奈米氣泡、動態光散射。. i.

(3)

(4) Abstract The hydrophobic interaction causes the aggregation of non-polar materials in water. This interaction can be enhanced by the existence of gas in water; the dispersion of hydrophobic particles have longer lifetime in degassed water than in air-rich water. We study the gas-enhanced hydrophobic interaction in both single-walled and multi-walled carbon nanotubes/water mixture with and without degassing. The lifetime and structure in carbon nanotube aggregates observed by photography and multi-angle dynamic light scattering. The single-walled carbon nanotubes (SWNTs) aggregate slower and form more compact clumps in water with degassing than without degassing. The multi-walled carbon nanotubes (MWNTs) form gel-like structure in the air-containing MWNT/water mixture; this gel-like structure is less significant in degassed MWNT/water mixture. The observation can be explained with the presence of the surface nanobubbles on graphene substrates, which is similar to the walls of the carbon nanotubes, when the water is not degassed.. Keywords: Hydrophobic interaction, Surfactant-free emulsions, Carbon nanotubes, Nanobubbles, Dynamic Light Scattering.. iii.

(5)

(6) Acknowledgements The author would like to thank Prof. Jung-Ren Huang (黃仲仁) and ChiKeung Chan (陳志強) for all the help and guidance on the research. Most experiments in this work were performed in Chi-Keung Chan’s lab in Institute of Physics, Academia Sinica. I appreciate Prof. Chi-Keung Chan’s support on instruments and techniques and the frequently discussion right after any progress of my experiments. The feedbacks and predictions from Prof. Jung-Ren Huang were also very helpful and usually made breakthroughs. I especially thank Prof. Jung-Ren Huang for all the discussions during the thesis writing period in which I tried to re-organize the experiment results and all information together. A very special acknowledgment is for Master Jang-Jiunn Jeng (鄭璋駿), who was formerly working on the same topic with me before his graduation from National Taiwan Normal University. This study is inspired and founded by the Nanobubble Project in Institute of Physics, Academia Sinica. I thank the principal investigator Ing-Shouh Hwang (黃英碩) and every research fellow and assistant participating the project for helpful advice and financial support. I also thank Prof. Hyoung Jin Choi (崔瑩鎭) of Inha University for the encouragement and material support of our multi-walled carbon nanotube (Hanwha CM-95) experiments.. v.

(7)

(8) Contents 中文摘要................................................................................................................ i. Abstract................................................................................................................ iii Acknowledgements ................................................................................................ v Contents ............................................................................................................... vii Page Chapter 1. Introduction .................................................................................... 1. 1.1. Hydrophobic Interaction . . . . . . . . . . . . . . . . . . . . . .. 1. 1.2. Surfactant-free Emulsions . . . . . . . . . . . . . . . . . . . . . .. 2. 1.3. Surface Nanobubbles . . . . . . . . . . . . . . . . . . . . . . . .. 4. 1.4. Carbon Nanotubes as Probes for Hydrophobic Interaction . . . .. 4. Chapter 2 2.1. Method and Experimental Setup .................................................... 9 Dynamic Light Scattering . . . . . . . . . . . . . . . . . . . . . . 10. 2.1.1. The light scattering theory . . . . . . . . . . . . . . . . . . . . . 11. 2.1.2. Time-correlation function: measuring fluctuations in time . . . . 14. 2.1.3. The light scattering experiment . . . . . . . . . . . . . . . . . . 16. 2.1.4. Particle size measurement of spherical Brownian particles . . . . 19. 2.2. The Degassing Methods for Liquid . . . . . . . . . . . . . . . . . 22. 2.2.1. The ultrasonic degassing method . . . . . . . . . . . . . . . . . . 22. 2.2.2. The boiling degassing method . . . . . . . . . . . . . . . . . . . 23. 2.2.3. The freeze-pump-thaw cycles . . . . . . . . . . . . . . . . . . . . 23. 2.3. Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . 23. 2.3.1. Water and glass flask cleaning . . . . . . . . . . . . . . . . . . . 23. 2.3.2. Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . 24. 2.3.3. Stock solution preparation and sampling . . . . . . . . . . . . . 24. 2.3.4. Treatments applied to degassed and controlled samples . . . . . 25. 2.4. Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 vii.

(9) Chapter 3. Experimental Results...................................................................... 31. 3.1. SWNT/water Mixtures . . . . . . . . . . . . . . . . . . . . . . . 31. 3.2. MWNT/water Mixtures. 3.3. Summary over Experimental Results . . . . . . . . . . . . . . . . 34. Chapter 4. . . . . . . . . . . . . . . . . . . . . . . 32. Discussion and Conclusion .............................................................. 45. References ............................................................................................................. 49. viii.

(10) Chapter 1 Introduction The concept of “hydrophobic interaction” arises as the interpretation of the strong attraction between non-polar materials in water, causing low solubility, aggregation, self-assembly behaviors; the concept is hence related to multiple phenomena such as the phase separation in oil/water mixtures, the formation of detergent micelles, the various geometric configurations of lipid bilayers, protein folding, just to name a few. Despite the importance in chemical, physical and biological systems, the understanding of hydrophobic interaction is incomplete, especially for its unusual strong strength and long effective distance [1]. Series of experiments investigating the behaviors of hydrophobic material/water dispersions were performed by Pashley, R. et. al. during 2003 - 2008[2] [3] [4] [5] [6] [7]; these works implicate that the presence of some non-polar gas, eg. nitrogen, increases the rate of aggregation or phase separation in the dispersion. To further discuss the effects of gas on the stability of hydrophobic material/water dispersions, we study carbon nanotubes (CNTs) in water. CNTs, like graphene, are super-hydrophobic. Graphene surfaces absorb gas in water and form surface nanobubbles.[9] The same phenomena should also happen on the CNT/wate interfaces. The We present the differences in stability, appearance of aggregates and the structures of CNTs in the water mixtures with and without degassing and give a simple picture of the role of gas in our experiments.. 1.1. Hydrophobic Interaction. The hydrophobic interaction describes the attraction between the non-polar materials in water. However, there are no fundamental forces directly related to the aggregation of non-polar materials in water. The hydrophobic interaction is recognized as an entropic effect: water molecules rearrange to maintain hydrogen bons (H-bons) in between.[8] The “common knowledge” in our everyday life tells us that oil and water do not mix.[3] Usually, oil molecules are non-polar and hence very different from water molecules, which are well-known for their strong polarization. The empirical concept 1.

(11) that “like dissolves like” claims the higher free energy of water-oil solution compared with that of the separated water-rich and oil-rich phases. The poor solubility of non-polar molecules in water is described as the effects of “hydrophobic interaction” between non-polar molecules. Similarly, interfacial tensions between most hydrocarbon oil and water are within the range 40 - 50 mJm−2 while the surface tensions (interfacial tension with air) are within 15 - 30 mJm−2 .[8] The relatively high interfacial tensions indicate the degree of difficulty to mix oil in water. These non-polar materials are hence called hydrophobic materials. Israelachvili, J.[1] measured the unsual strong hydrophobic interaction with the total force between two cylindrical mica surfaces in water. The attractive force as the function of the inter-mica surface distance shows that the interaction has the same range in distance, but one order magnitude greater in strength than the van der Waals-dispersion force. The strength of hydrophobic interaction led to the belief of “hydrophobic bond” responsible for the attraction between non-polar materials. Scientists now recognize that the interaction between two hydrophobic surfaces involves the configuration of water molecules inside the gap of the two surfaces.[8] Water molecules are believed to form structures with H-bonds that decrease the free energy. Non-polar materials cannot participate the formation of H-bonds, so water molecules near the interfaces form cage-like structures enclosing the materials. With the less interfacial area of water and the enclosed materials, the lower free energy is obtained in the mixture. From the thermodynamic point of view, water molecules would reduce the interfacial area with the non-polar materials by the rearrangement of water and the nearby materials, leading to the aggregation. The concept that hydrophobic interaction is due to the structures of water molecules explains why its effective range in distant is longer than usual chemical bonds. The strong interactions between water molecules suggest the greater strength comparing with the van der Waals interaction between non-polar molecules.[1]. 1.2. Surfactant-free Emulsions. The surfactant-free emulsion (SFE), as the name implies, is a liquid-in-liquid colloidal dispersion without any surface active material acting like a stabilizer. The formation of SFE for hydrophobic droplets, say oil droplets, in water is not energetically preferred due to the high interfacial tension between the continuous phase (water) and the dispersed phase (oil). The minimization of free energy indicates the 2.

(12) phase separation of oil and water, which is consistent with our “common knowledge” that oil and water do not mix. However Pashley, R. et. al. [3] presented the SFE of dodecane and squalane in water that remained stable for hours. This stable oilin-water SFEs are produced with gas (mostly nitrogen in the case) removed from the mixture. Here the term "stable" does not represent the thermodynamical stable state. Instead, it describes the meta-stable configuration of system that stands for the whole observation period or the time scale we are interested in. The same definition is also applied to all following chapters in this thesis if not noted. Despite the poor solubility of hydrophobic materials in water, the homogeneous mixing of the macroscopic scale is still possible though formation of colloidal dispersion. Unlike the solution in which all solute molecules disperse down to the molecular scale, colloids are tiny gas bubbles, liquid droplets, or solid particles (called the “dispersed phase”) suspending inside the continuous phase material. The emulsion is another name for liquid-in-liquid colloids. For example, the oil-in-water emulsions usually appear when we wash the dishes with soap, where water is the continuous phase and the ruptured oil droplets enclosed by the soap molecules are the dispersed phase. The high interfacial tensions between oil and water (see Section 1.1) imply that the thermodynamically stable state of the oil/water mixture is the separated two phases, which is usually the case. The oil-in-water dispersion is unstable. The usual way to enhance the lifetime of a hydrophobic material/water dispersion is to add stabilizer like surfactants and polymers. The stabilizers increase the potential barrier to prevent particles from aggregation. However, the addition of stabilizer is not allowed in many applications. The SFEs of hydrophobic oil in water prepared with degassed oil/water mixture by Pashley, R. et. al. during 2003 - 2008 [2] [3] [4] [5] are reported to be stable within one and a half hours. We repeated the experiment with dodecane in water, and observed the SEFs to be stable for days; this is obtained by the dynamic light scattering (DLS) shown in Fig. 1.1. Dispersion with solid hydrophobic powder is also possible. Pashley, R. 2003[3] reported enhanced stability of degassed Teflon powder/water dispersion. The stable SFE in degassed water implies that attraction between hydrophobic materials in water might be enhanced by the gas in water. The gas solubility in water is usually low, making a good excuse for researchers to ignore the effect of gas both 3.

(13) in experiments and theoretical modeling. Our work is to examine whether it is acceptable to ignore gas in water while studying hydrophobic materials in aqueous environments.. 1.3. Surface Nanobubbles. Gas is not stable in water. The low solubility of the non-polar gases in water leads to the recognition that gases are generally hydrophobic. If bubbles are formed, the buoyancy pushes bubbles towards the water surface. For microscopic bubbles, say bubbles with the diameter ∼ µm, the buoyancy is weak compared with thermal fluctuations and flow in water. However, the high interfacial energy alone with the large curvature of the interfaces implies that the pressure is high inside the micron or sub-micron size gas bubbles. The high pressure leads to the prediction: gas in such bubbles should diffuse into water quickly according to the above concepts. It seems that no gas bubble alone can possibly be stable in pure water. However, observations on sub-micron bubbles attached on HOPG substrates have been reported since around 2000[9]. The detailed mechanism that stabilizes such small gas bubbles on graphite surface is still controversial at the moment.. 1.4 Carbon Nanotubes as Probes for Hydrophobic Interaction The discussion in Section 1.2 and 1.3 imply that small graphene particles dispersed in water can be sensitive to the presence of gas if gas affects hydrophobic interactions. The carbon nanotubes (CNTs), which are tube-shape graphene particles with physical dimensions > 10µm, may be proper for our study. We find that graphite or graphene might be a proper and sensitive material for studying the effects of gas on the attraction between hydrophobic particles in water. The reports of surface nanobubbles on graphite (see Section 1.3) show that gas molecules adhere to the graphite surface. If gas participates in the interaction between graphene surfaces, we should also observe significant differences in the aggregations between water/graphene crumb mixtures with higher and lower gas concentration. The role of gas in the aggregation of hydrophobic particles is also discussed in Pashley, R. 2002[2]. The nature of gas adhering hydrophobic particles makes gas the medium for particle aggregation. This is shown schematicly in Fig. 1.2. The 4.

(14) picture is consistent with the discovery of surface nanobubbles which is the evident of gas adherence on hydrophobic surfaces. The carbon nanotubes (CNTs) are graphene in tube shape with the crosssection diameters ranged from 0.4 to 100 nm and the length of the micrometer range typically, or even possibly up to millimeters.[10] Different production methods give the CNTs various properties from the geometry configurations, such as length, diameter, number of branches, spontaneous curvatures, and the number of layers in one tube. Single-walled (carbon) nanotube (SWNT) discribes a CNT composed with only single layer of graphene; on the contrary, multi-walled nanotubes (MWNTs) are the CNTs with more than one layer. The number of layers in CNT walls determines not only the molecule weight, diameter and elasticity of the tubes, but also the shielding effects to the material inside the CNTs interacting with the outside environments, or vice versa. The Fig. 1.3 show the schematic of both SWNTs and MWNTs. CNTs are considered as a super-hydrophobic material[10], similar to graphene or HOPG substrate. The solubility of SWNTs is low in many of the common organic solvents.[11] Mixing CNTs in liquid, especially water, is an important topic in engineering and industrial studies; however, the nature, solution or dispersion, etc, of the reported CNT/liquid mixture, is not carefully studied.[10] CNTs are the small particles with graphene surfaces. Comercial products of powder form CNTs can be dispersed in water through ultra-sonication mixing; without degassing or addition of stabilizers, the life time of these CNT/water dispersion should be short, eg. within an hour or even shouter. We observe the lifetime, visual appearances and perform dynamic light scattering measurements of the CNT/water dispersion with and without degassing; the differences between degassed and nondegassed samples can be evidences of the changes in interactions between hydrophobic surfaces due to gas in water.. 5.

(15) 350. Hydrodynamic Radius (nm). Normailized Correlation Function. 1.0. 0.8. 0.6. 0.4. 0.2. 0.0. 300 250 200 150 100 50 0. 0. 24. 72. 96 120 144 168. Resting Time (hr.). Day 0 Day 2 Day 3 Day 4 Day 6 Day 7 0.1. 48. 1. 10. 100. Delay Time, τ (msec.). Figure 1.1: The normalized auto-correlation function and hydrodynamic radius of degassed dodecane/water SFE measured by dynamic light scattering (DLS). The correlation functions are measured at scattering angle θ = 90 deg and normalized to decay from 1.0 to 0.0 for better comparison; if multiple measurements are preformed sequentially on the same day, the correlation data are averaged. The inset shows the hydrodynamic radius of dodecane droplets. (For detail on DLS, please see Section 2.1.1-2.1.4) The figure shows that the SFE remain meta-stable for days. The SFE sample is prepared with non-treated dodecane and boiling degassed Milli-Q water. The dodecane/water mixture is loaded to a test tube for ultra-sonication. The sample preparation only obtain partial degassed SFE.. 6.

(16) Figure 1.2: The model of hydrophobic particles interacting with non-polar gas in water. The particles absorb non-polar gas in water. The gas between a clump of particles adhere to the clump while the particles also entrap the gas. The figure is a replica of the schematic (Figure 12.) in Pashley, R. 2002[2].. Cross-section. Cross-section. Figure 1.3: The schematics of (a) sigle-walled carbon nanotube (SWNT) and (b) multi-walled carbon nanotubes (MWNT). Each of the layers in the figure represents a sheet of graphene. For the materials inside the MWNT, interactions with the environments outside is blocked by the extra layers compared with that inside the SWNT.. 7.

(17) 8.

(18) Chapter 2 Method and Experimental Setup Both the stability and particle size of dispersed phase (if dispersion is formed) of the CNT/water ultra-sonicated mixture is recorded by photography and measured by dynamic light scattering respectively. The lifetime of a solution is a factor indicating how good (or bad) is the solvent for the solute. Similarly, in the case of dispersion, if the free energy cost in the formation of dispersion is much higher than of two separated phases, the dispersed phase aggregates. On the contrary, the dispersion remains in meta-stable longer when the energy difference with phase separation is small. In our experiments, a sample with CNTs still dispersed in water after resting for several days would be described as a "stable" dispersion. All samples in this study are of CNT (MWNT or SWNT) and water (degassed or air-containing) only; no surfactants are added to stabilize dispersed particles. With the presence of hydrophobic interaction between CNT surfaces in water, the particles would attach to each other, reducing the interfacial area with water. The preference of smaller interfacial area is the result of the minimization of free energy (discussed in Section 1.1). This "hydrophobisity" induced aggregation enable us to probe how strong the interaction is in our system by simply monitoring the stability of the dispersion. The following two sections introduce the methods of dynamic light scattering for monitoring microscopic status, eg. particle size or structure of CNT/water samples, freeze-pump-thaw degassing method that we applied for sample preparation. After the technical parts, there are descriptions of the step-by-step experiment procedure including sample preparation and measurements. 9.

(19) 2.1. Dynamic Light Scattering. The Dynamic Light Scattering (DLS, or Photon Correlation Spectrum, PCS) technique measures dielectric property variations of the sample from the intensity fluctuations in a scattering speckle. In most cases of suspensions and emulsions, these dielectric property variations are due to the Brownian motion of solid particles or droplets. The autocorrelation function of a DLS measurement gives an exponential decay with the decay rate proportional to the diffusion coefficient of the Brownian particles. Hence, the diameters* of the Brownian particles can be calculated using Stokes’ law with the assumption that the Brownian objects are spherical.. Figure 2.1: The schematic of the typical light scattering setup. The laser light inserts from the left-hand side and illuminates the scattering medium in the light path. Only the scattered light with scattering angle θ coming from the small area called the scattering volume, Vs impinges the detector. Hence one can measure the → − → − − scattered light intensity as a function of the scattering vector → q = ki − kf . The − − inset shows the definition of scattering vector → q and how the value q = |→ q| = → − → − → − 2| ki | sin(θ/2) can be obtained in elastic scattering, where ki = kf . *The Diameter evaluated from the diffusion coefficient of a Brownian particle is not necessarily to be the diameter of an actual spherical object. This radius (one half of the diameter) extracted from Stokes’ law is often called “Stokes’ radius” or hydrodynamic radius, RH . RH is strongly connected to the mobility of the Brownian particle in the suspension. We have further discussion in the following sections.. 10.

(20) As a long developed technique of size measurement for particles smaller or near the optical diffraction limitation, DLS setups can be seen in many commercialized instruments. The basic design can be shown with the scattering geometry in Fig. 2.1. A coherent monochromatic light beam with specific polarization, usually a laser, illuminates a narrow path in the sample suspension. A photon counting device is placed to collect scattered light from a small region in the illuminated path at a scattering angle θ between the outgoing transmitting light; the propagating direction of the measured scattered light is selected by the optical components like a sets of pin holes and lenses. Sometimes an analyzer is also placed in front of the detector for the selection of polarization. The photon counting device would record the photon count rates. These count rate data can be processed by either a hardware or software correlator for the autocorrelation function of the light intensity fluctuations. In the following sub-sections from Section 2.1.1 to Section 2.1.4, we follow the text book by Berne, B. J. et. al. (1976)[13].. 2.1.1. The light scattering theory. In the classical theory of light scattering, the incident light beam is an electromagnetic field (EM field, in short) with the form of a plan wave, → − − − →− Ei (→ r , t) = ni E0 exp[i( ki · → r − ωi t)]. (2.1). The incident field polarizes atoms in the scattering media. The polarized atoms then interact with the field and oscillate, making the atoms themselves the sources of the scattered field. As shown in Fig. 2.1, the DLS experiment collects the scattered light of a certain angle. The intersection between the incident light beam and the collected scattered beam defines the scattering volume, Vs . Only particles or any other kind of scatterers inside this Vs contributes to the EM field on the detector. The scatterers in Vs can be moving particles, vibrating membranes, oscillating units in gel, or any other objects with time-dependency in its local dielectric property. To determine the time-dependency of the local dielectric property, we can first divide Vs into small sub-regions with the dimensions much smaller than the wavelength of the incident light. Thus, atoms in each sub-region interact with essentially the same incident field. If many sub-regions of equal size are considered, the total scattered field is just the superposition of fields from all sub-regions. For a − sub-region at position → r , we can write down the dielectric tensor as the combination of the average (time-independent) dielectric constant and the perturbation term like 11.

(21) − − (→ r , t) = 0 1 + δ(→ r , t). (2.2). We can calculate the scattered EM field for a sub-region with the local dielectric tensor known. For an incident field Ei shown in Eq. (2.1), the scattered field with polarization nf , propagating vector kf , and frequency ωf is − →→ − Es ( R , t) =. E0 exp(ikf R)× 4πR Z 0 − → − − − → · [→ − − d3 r {exp(i→ q ·→ r − iωi t)[− n kf × (kf × (δ(→ r , t) · → ni ))]]} (2.3) f. The position and displacement vectors denoted in Eq. (2.3) are defined as in. Figure 2.2: The vector notations for displacements in scattering theory. → − → − − Fig. 2.2. This formalism includes the scattering vector → q = ki − kf , which can also be defined by the scattering geometry (shown in Fig. 2.1). In most cases of light scattering experiments within our discussion, the wavelength of the incident light changes small enough to be discard during the scattering process. So we have → − → − → − → − ωi = ωf or | ki | = |kf |. The angle between ki and kf is θ alone with the fact that → − → − − − the k -k -→ q is an isosceles triangle allow us to calculate the magnitute of → q with i. f. simple geometric works in the coneer of Fig. 2.1, θ 4πn θ − |→ q | = 2ki sin( ) = sin( ) 2 λi 2 12. (2.4).

(22) The right-most part of Eq. (2.4) is actually the Bragg condition. Meanwhile, the − scattering vector → q in Eq. (2.3) is the wave vector component in the integration − with the dielectric constant fluctuation, δ(→ r , t) as the amplitude of the wave-like exponential formalism. We can rewrite the right-hand-side of Eq. (2.3) by intro− ducing the special Fourier coefficient expanding δ(→ r , t) defined by − δ(→ q , t) =. Z. Vs. − − − d3 r exp[i→ q ·→ r ]δ(→ r , t). (2.5). as − →→ − Es ( R , t) =. E0 exp[i(kf R − ωi t)]× 4πR0 − → − → · [→ − − {− n k × (k × (δ(→ q , t) · → n ))]} f. f. f. i. =. −kf2 E0 4πR0. − exp[i(kf R − ωi t)]δif (→ q , t) (2.6). − → · δ(→ − − where δif (→ q , t) = − n q , t) · → ni . f The scattered EM field described in Eq. (2.6) is the result evaluated with a mean-field approach for the electric field interacting with molecules composing the scattering medium. The specific scattered field from each of the scatterers contain more information about the polarization of light than in Eq. (2.6). We can obtain these details from the molecular approach. The molecular approach starts from the polarization of molecules in Vs to − → have dipole moments in respond to the incident field Ei . The dipole moment for a − particular molecule, say the jth molecule, at position → r and time t can be written j. as − →− µj (t) = α(j) (t)Ei (→ rj , t). (2.7). where α(j) (t) is the electric polarizability tensor for the jth molecule at the same time t. It is obvious that the dipole moment for the jth molecule µj (t) is a function of time. In classical electrodynamics, a time varying dipole emits radiations. The radiated field, which is just the scattered field, from the jth dipole (originally the − → jth molecule) induced by Ei and pasted an analyzer before the detector have the − field strength → r and time t can be written as j. − → (j) − − Es (j) (t) ∝ αif (t) exp[i→ q ·→ rj (t)] (j). (2.8). where αif = nf · α(j) (t) · ni ; rj (t) is the position of the mass center of the jth − molecule; → q is the usual scattering vector. The total scattered field can be written 13.

(23) down as the superposition of all the individual scattered fields from every single molecule in Vs , Es (t) ∝. X. (j) − − αif (t) exp[i→ q ·→ rj (t)]. (2.9). j. The superposition is valid when {α(j) (t)} is not perturb very much by the neighboring molecules. Eq. (2.9) shows the way we can analyze the polarization direction from the nature of αif (t) of molecules in our sample.. 2.1.2 Time-correlation function: measuring fluctuations in time − The Scattered EM field demonstrated in Eq. (2.6) contains the δ(→ q , t) term which fully determines the time and scattering geometry dependency in the scat− tered field. To study E with a given → q means to study the nature of the fluctuation s. − δ(→ q , t). In the theory of noise and stochastic processes, time-correlations are useful tools for resolving characteristics from the fluctuations. Correlation functions provide a concise method for expressing the degree to which two dynamical properties correlated over a period. A correlation function is called autocorrelation function if the two dynamical properties are the same propertie. Hance an autocorrelation function for a measured physical property A(t) is defined as Z 1 T GA (τ ) = hA(t)A(t + τ )it = lim dtA(t)A(t + τ ) (2.10) T→∞ T 0 where T is the time over which it is averaged. It is a fact that the autocorrelation function represents the nature of A(t) better if T is closer to infinity. In the reality, a real measurement consumes time for cumulating a signal at time t. This makes the measured property A(t) discrete in the time axis. Suppose that the time axis t is divided into discrete intervals ∆t, making t = j∆t; τ = n∆t; T = N ∆t. If ∆t is short enough that property A(t) changes little during each ∆t, therefor we can define Aj = A(t = j∆t), which is the value of the property A(t) at the jth interval. Now we can approximate Eq. (2.10) by N 1 X Aj Aj+n N →∞ N j=1. GA (τ ) = hA(t)A(t + τ )it ' lim. (2.11). while the number of samples measuring property A(t) is large. The same approximation works on the time average of property A(t), N 1 X Aj N →∞ N j=1. hA(t)it ' lim. 14. (2.12).

(24) or the mean square of property A N 1 X 2 hA(t) it ' lim Aj N →∞ N j=1 2. (2.13). The value of an autocorrelation function is usually within hA(t)i2 and hA(t)2 i which we’ll discuss later in this section.. Figure 2.3: The time autocorrelation function for random variable A(t). The upper plot is linear scaled in both axis while the horizontal axis (τ -axis) in the lower plot is in log scale. The function hA(t)A(t + τ )it decays from hA2 i to hAi2 and is of the from exp(−Γτ ) in many cases. The autocorrelation function decays exponentially in many cases, or is the superposition of multiple exponential decades. This decade is easy to predict since a property at certain time A(t = t0 ) is surely most correlated with A(t = t0 ) comparing to that at all other moments. At infinite time lag, limτ →∞ A(t = t0 +tau) is supposed to be uncorrelated with A(t = t0 ), which means the two values are independent. We then obtain the value of autocorrelation function of A(t) at time lag τ is large as A(t) and A(t + τ ) are independent as lim hA(t)A(t + τ )it = lim (hA(t)it hA(t + τ )it ) = hA(t)i2t. τ →∞. τ →∞. (2.14). Now we have GA (τ = 0) and limτ →∞ GA (τ ). The general form of time-correlation 15.

(25) function can be described in the example in Fig. 2.3, or in a combination of Fig. 2.3 with different decade rate.. 2.1.3. The light scattering experiment. We now can get back to our scattering experiment. A monochromatic coherent incident light of frequency ωi impinges into the scattering medium. The incident EM wave is scattered due to the special inhomogeneity of dielectric prosperity. The dielectric prosperity can be time-dependent, making the strength of the scattered field varies in time. The scattered EM field interacting with a detector at scattered angle theta can be described by Eq. (2.6). The strength of Es fluctuates with − − δ(→ q , t). We can apply the time-correlation function to E in order to study δ(→ q , t). s. With the definition shown in Eq. (2.10), the substitution gives the result → − → − hEs∗ ( R , t)Es ( R , t + τ )i kf4 |E0 |2 − − = hδif (→ q , t)δif (→ q , t + τ )i exp(−iωi τ ) (2.15) 2 2 2 16π R 0 In the reality, the scattered EM field Es is not directly measured. Light detectors count photons, which is the energy quanta of light. The detectors are in fact detecting the square of the field, |Es |2 , not Es itself. The correlation function of light intensity is called the second-order auto-correlation function G(2) = hE ∗ (t)E(t)E ∗ (t + τ )E(t + τ )it instead of the first-order auto-correlation function G(1) = hE ∗ (t)E(t + τ )it . We evaluated the scattered field Es in Eq. (2.6) by dividing the scattering volume Vs into sub-regions of volume small compared to the wavelength of the incident light. The local dielectric constant fluctuation of a sub-region is in response to the motions of the scatterers in the same sub-region. If this sub-regions are also large enough to permit the motions of scatterers in one region to be independent of motions in all other sub-regions, we can regard Es as a sum of a set of independent random variables representing the fields from each of the sub-regions, so that Es =. X. Es(n). (2.16). n (n). where Es. is the field from the nth sub-region as well as a random variable inde-. pendent of any other sub-region. In this case, the central limit theorem implies that Es must be a random variable under Gaussian distribution. 16.

(26) If the we know the joint probability P (EO , Eτ , tau) of a random variable E(q, t) that EO ≤ E(q, 0) ≤ EO + dEO Eτ ≤ E(q, τ ) ≤ Eτ + dEτ. (2.17). where EO and Eτ are the certain values of E(q, t) ,we can easily write down the first- and second-order autocorrelation function as R R G(1) (q, τ ) = dEO dEτ (EO P (EO , Eτ , τ )Eτ ) R R G(2) (q, τ ) = dEO dEτ (|EO |2 P (EO , Eτ , τ )|Eτ |2 ). (2.18). This P (EO , Eτ , τ ) for a Gaussian stochastic E(q, t) is know as ˆ (1) (r, τ )](−1/2) × P (EO , Eτ , τ ) = [2πh|Eτ |2 i]−1 [1 − G exp(. ˆ (1) (q, τ ))2 (Eτ − EO G −EO2 ) exp[ ] (2.19) ˆ (1) (g, τ ))2 ] 2h|Eτ |2 i 2h|Eτ |2 i[1 − (G. ˆ (1) (r, τ ) = G(1) (q, τ )/G(1) (q, 0). Substitute Eq. (2.19) to Eq. (2.18) and where G carry out the integration, we obtain G(2) (q, τ ) = |G(1) (q, 0)|2 + |G(1) (q, τ )|2. (2.20). With the field autorrelation function in Eq. (2.15) as the first-order correlation G(1) (q, τ ) , we obtain the intensity autocorrelation function as the second-order autocorrelation G(2) (q, τ ) by using Eq. (2.20) and get kf4 |E0 |2 2 G (q, τ ) = ( )× 16π 2 R2 20 (2). − − − (hδif (→ q , t)i2 + hδif (→ q , t)δif (→ q , t + τ )i2 ) (2.21) − The fact that |G(1) (→ q , 0)|2 = hEs∗ (q, t)Es (q, t)it = h|Es |2 it enables us to rewrite Eq. (2.21) as ¯ (2) (q, τ ) = (h|Es |2 i + ( G. kf4 |E0 |2 2 − − ) hδif (→ q , t)δif (→ q , t + τ )i2 ) 16π 2 R2 20. (2.22). It is reasonable to generalize Eq. (2.22) by langle|Es |2 i since we are mainly interested in the time correlation part, not the time average part of barG(2) (q, τ ). The ˆ (2) (q, τ ) can be written as generalized second-order autocorrelation G − − ˆ (2) (q, τ ) = 1 + Bhδif (→ G q , t)δif (→ q , t + τ )i2 ). (2.23). where the proportional constant B = (h|Es |2 i)−1 . The value of B in a real light scattering experiment can be lower then (h|Es |2 i)− 1. The reduced value B is due 17.

(27) to the contribution of measurement noisy. Following the discussion in Section ˆ (2) (q, τ = 0) = 2 if no noisy is concerned. On the other hand, h|Es |2 i 2.1.2, G → − − q , t)δ (→ q , t + τ )i when the noisy is large compared with the signal, making the if. ˆ (2) (q, τ = 0) ' 1. Hence, the zero-tau second-order autocorrevalue B small and G ˆ (2) (q, τ = 0) is often taken as a factor of the signal to noise ratio in lation value G DLS experiments. The direct measurement of G(2) (q, τ )] is though measuring the light intensity I(t) by time. The detector gives Ij which corresponds to I(tj ) within the sampling time period (j − 0.5)∆t < tj < (j + 0.5)∆t . The discrete intensity series {Ij } can be analyzed by either a hardware or software correlater for a intensity timeautocorrelation function, which is just the measured data of Eq. (2.21). (Some correlators have the generalization function. For these correlators, the measured data of Eq. (2.23) may be given.) This strategy of measuring the scattered light alone is called “Homodyne method”. In the previous discussions (the beginning of Section 2.1.3 and Section 2.1.1), we introduced the sub-regions in Vs to help us dealing with local dielectric property. The size of the sub-regions have to be small compared with the wavelength of the impinging light but big-enough to keep the motions inside each of the sub-regions independent. The fact that motions observed by DLS should also be small compared with the impinging light indicates that these motions are usually rapid, eg. for spheres with the diameter d = 1um (The d = 1um of course is at the limit of typical DLS measurements since the wavelength commonly used is below the dimension. Here we just take an example.) undergoing diffusive motions, or Brownian motions, at room temperature in water, the characteristic time scale is about 3.3ms when a typical q with θ = 90 deg; λ = 633nm is applied. (The detail will be discussed in Section 2.1.4) The shortest sampling time, as well as the first delay time in autocorrelation function, should be shorter than this 3.3ms chracteristic time for one studying the system with DLS. If the detector cannot operate in such a high sampling rate, than the “Homodyne method” is not a proper technique for the case. An optical mixing method in which we guide a portion of unscattered light into the detector with the scattered light. The unscattered light work as a local oscillator and thus the beating effect enables you to observe the high frequency fluctuations with a slower-reacting-time detector. The technique involving the unscattered light is the “Heterodyne method”. In the further discussion and through this study, we are using the Homodyne method 18.

(28) and the Heterodyne method will not be discussed.. 2.1.4 Particle size measurement of spherical Brownian particles One of the commonly-seen application of DLS is the measurement of particle sizes in colloidal dispersion. The main idea is to observe the diffusive nature of particles undergoing Brownian motions. The thermal motions of spheres in dispersion determine the diffusion coefficient D in Stoke-Einstein Equation, D=. kB T 6πηa. (2.24). where kB is the usual Boltzmann Constant; T is the absolute temperature; η is the dynamic viscosity; a is the radius of the spheres, or the hydrodynamic radius (RH), which is the effective radius calculated with Eq. (2.24) for the hard sphere with the same diffusion coefficient. The fact that we can usually estimate the particles as spheres makes Eq. (2.24) powerful for particle size analysis. The model system for dilute spherical particles hence is often used in DLS experiments. We start our discussion from the polarization of the scattered light from spheres in a dilute dispersion that no collision is concerned. The polarizability of a uniform particle is determined by its geometric configuration. For a sphere, the three-bythree tensor of second-rank representing the polarizability (αsphere )αβ is diagonal, and moreover, (αsphere )xx = (αsphere )yy = (αsphere )zz = α. That is αsphere = α1 or (αsphere )αβ = α∆αβ. (2.25). This is expected for the symmetric property of a sphere in geometry. The dipole moment from a sphere µsphere is then − → − → µsphere = αsphere Ei = αEi. (2.26). − → The dipole moment in Eq. (2.26) is proportional to the incident field Ei with the factor alpha. Hence, the scattered field from the sphere is also directly proportional − → to Ei . For the study of scattered field at the detector in Fig. 2.1, The selection of → − → contributes to the scattered field as shown in Eq. (2.9). Substitute Eq. n and − n i. f. (2.26) to Eq. (2.9), we find − − →) Es (→ q , t) ∝ (→ ni · − n f. X j. 19. − − exp[i→ q ·→ rj (t)]. (2.27).

(29) − → in Eq. (2.27) indicates no The scattered field strength Es is proportional to → ni · − n f − → polarization of Es comes from the scattering. The intensity autocorrelation function for spherical particles in a light scattering experiment is the product of two components, one is the correlation of particles going in and out the scattering volume Vs ; the other is the intensity correlation due to the fluctuation of dielectric property. The former one corresponds to the time scale in how long a particle can go across Vs , τv =. (Vs )2/3 D. (2.28). − The later one corresponds to the wave number component in Es , which is |→ q | = q. The characteristic length q −1 represents the scale seen by the scattering. The time scale for intensity fluctuations from the diffusive thermal motions is hence τq =. q −2 D. (2.29). The comparison of the two time scale is τv = (qVs1/3 )2 τq 1/3. In common cases, q ∼ 0.1um and Vs. (2.30). ∼ 100um, making τv /τq ∼ 106 . It is reason-. able to discard the correlation of particle entering and exiting Vs if we choose the time scale to observe the diffusive motions of the particles. Now we can focus on the Brownian motion part of the intensity correlation function. We start from the results obtained in Section 2.1.3. The generalized inten− − sity autocorrelation function in Eq. (2.23) shows that the term hδ (→ q , t)δ (→ q , t+ if. if. − τ )it fully determines the τ dependency of the correlation function. δif (→ q , t) comes − from the integration inside V of δ (→ r , t), which represents the dielectric constant s. if. − fluctuation in sub-region centered at → r . Each of the sub-regions are to be small to contain only one spherical particle. This constrain arises for the assumption that each sub-region is large-enough to isolate the movements of the scatterer inside. The other assumption that the sub-regions are small compared with the wavelength of − incident light indicates that all molecules inside the j th sub-region at position → rj − →→ rj , t). So all the molecules composing the spherical and time t interact with Ei (− − →− − particle in sub-region at position → r and time t also interact with E (→ r , t). The j. i. j. scattered field from the spherical particle can be described with Eq. (2.27). On − the other hand, if the sub-region contains no particle at position → rj and time t, 20.

(30) − δif (→ r , t) = 0. Only the sub-regions with particles inside contributes to the scattered field, and each sub-region with a particle inside represents the position and the incident field interacts with the particle inside. If all spherical particles are uniform in material and size, we find the relationship between particle positions and the term of dielectric constant fluctuation autocorrelation in Eq. (2.6) as − − hδif (→ q , t)δif (→ q , t + τ )i X − →)h [exp[i→ − − − − ∝ (→ n ·− n q ·→ r (t + τ )] exp[−i→ q ·→ r (t)]] i. f. j. j. j. X − − − ∝ h [exp[i→ q · (→ rj (t + τ ) − → rj (t))]]i (2.31) j. − where the position → rj is confined to the positions of sub-regions with a sphere. In the right-most part of Eq. (2.31), the polarization components are discarded as the − → − → polarization of Ei and Ef is in the same direction. The analyzer at the near end to the detector only take effect as a neutral density filter. The quantity (j) − − q · ∆→ rj (τ )]i FD ≡ hexp[i→. (2.32). − → − is named the “self-intermediate scattering function”, where ∆→ rj (τ )] ≡ Rj (t + τ ) − − → − Rj (t) . There is no t dependency left in ∆→ rj (τ ) because no particular t should be (j). unique statistically. For all identical spherical particles in our model, FD should be the same since the number j is arbitrarily marked. The summation in Eq. (2.31) becomes a multiple by the number of sphere in Vs . The term with τ dependency in − − − hδ (→ q , t)δ (→ q , t + τ )i is now ∆→ r (τ ). if. if. t. j. If we take the self-intermediate scattering function as the special Fourier trans→ − form of a function GD ( R , t), that is Z → − → − (j) → − − FD ( q , τ ) d3 R[exp(i→ q · R )GD ( R , t)] (2.33) → − where it is not difficult to find the formalism of GD ( R , t) → − → − − GD ( R , τ ) = hδ( R − ∆→ rj )i. (2.34). The statistical meaning for Eq. (2.34) is the probability distribution of a particle → − traveled the displacement R time τ . In our model, the spherical particles are undergoing Brownian motions that causes the self-diffusion behavior. We can apply the diffusion equation → − → − ∂ GD ( R , τ ) = D∇2 GD ( R , τ ) ∂t 21. (2.35).

(31) (j). to Eq. (2.33), and obtain the partial differential equation describing FD as − ∂ (j) (j) → FD = −q 2 D∇2 FD ( R , τ ) ∂t. (2.36). (j). We can now solve FD , getting (j). FD = exp(−q 2 Dτ ). (2.37). Substituting Eq. (2.37) with Eq. (2.32) back to Eq. (2.31), we now can predict − − hδif (→ q , t)δif (→ q , t + τ )i ∝ exp(−q 2 Dτ ). (2.38). That is with Eq. (2.24), the generalized intensity autocorrelation function for spherical particles is ¯ (2) (τ ) = 1 + B ˜ exp(−2q 2 Dτ ) G. (2.39). We can use this result in Eq. (2.39) with Eq. (2.24) to analyze our DLS data for particle size or RH .. 2.2. The Degassing Methods for Liquid. Removing gaseous molecules from liquid can be done with several methods, but how much gas can really be separated from the the liquid phase is not thoroughly. studied. T hemeasuredsolubilityof gasinliquidmaybecontroversialif thevalueisobtainedbymeasurin We have tried some common procedures like the ultrasonic degassing, boiling degassing and freeze-pump-thaw degassing. These three mentioned methods are shown schematically as in Fig. 2.4. The method of freeze-pump-thaw degassing (FPT cycles) results in dramatic differences with the non-treated samples (shown in Fig. 2.5).. 2.2.1. The ultrasonic degassing method. The ultrasonic degassing introduces ultra-sonication to the liquid alone with an air pump removing the gas escaping to the empty space upon the liquid surface. The cavitation induced by high intensity ultrasonic waves produces near-vacuum cavities inside. The dissolved gas diffuses to the low pressure cavities and aggregates to larger bubbles in this process. A large bubble rises to the liquid surface easier than small ones. The air pump removes the gas released from the risen bubbles, maintaining a pressure gradient pulling bubbles to rise faster. 22.

(32) 2.2.2. The boiling degassing method. The boiling degassing method is based on the concept that gas solubility lower as temperature rising. When the boiling point of the solvent liquid is reached, gas are forced out of the liquid since the vapor pressure of the liquid is the same as the air pressure upon. When using a container with shrinking open-end, eg. A cone flask, vapor from the boiling liquid occupies most empty space in the container. Sealing the container while boiling can possibly produce an environment with low partial pressure of gases other than vapor of the degassed solvent. After cooling down the sealed container, degassed liquid stored in low gas pressure for preventing the re-entrance of gas is obtained simultaneously.. 2.2.3. The freeze-pump-thaw cycles. Both of the ultrasonic and boiling degassing strategies do not guarantee the complete phase separation of solvent and gas. The freeze-pump-thaw method start from the concept that materials of different freezing points undergo phase separation when the freezing point of one material is reached while the other is not. The fact that the crystalline structure of solvent cannot contain the gaseous molecules originally dissolved in liquid state solvent ensure the phase separation of the two materials. The complete procedure of the freeze-pump-thaw method include several cycles of freezing sample (freeze phase), pumping out escaped gas as the sample still frozen (pump phase), and heating up the sample for melting without pumping out gas (thaw phase). The method is hence called freeze-pump-thaw cycles (FPT cycles). The pump is only connected to the flask in the pump phase of the FPT procedure in order to prevent the solvent vapor from escaping, reducing the solute concentration of the sample. Also the freezing rate should be controlled to force the dissolved gas to aggregate toward the liquid surface. If the gas bubble is frozen in solvent, it is possible for the gas to mix again with the solvent during melting.. 2.3 2.3.1. Sample Preparation Water and glass flask cleaning. The Milli-Q deionized water with the electric resistance 18.2M Ω is used in this study. The glass flasks holding the samples (as shown in Fig. 2.6) are well cleaned with base bath procedure. The flasks are first cleaned with ethanol alcohol (C2 H5 OH) in a ultrasonic tank for 15 mins and rinsed again before base 23.

(33) bathing. The base bath solution is a 0.25% vol. 4M KOH(aq) in isopropanol alcohol (C3 H7 OH). The alcohol pre-cleaned flasks are then filled with the base bath solution for 4hr.s before cleaning with commercial reverse osmosis treated water. The flasks are immediately washed again with Milli-Q 18.2M Ω deionized water after flushing under large amount of reverse osmosis treated water. The cleaned flasks are filled with Milli-Q 18.2M Ω deionized water and sealed; These flasks are only to be unsealed before sampling. The last cleaning up is a double rinse with Milli-Q 18.2M Ω deionized water right before sampling.. 2.3.2. Carbon Nanotubes. Both SWNTs and MWNTs used in this study are commercial products with the aspect ratio AR ∼ 1000. The SWNTs are Sigma-aldrich cat. 773735; these SWNTs are manufactured by SouthWest NanoTechnologies, U.S. and with the cross-section diameter ' 0.78nm (with fluorescence microscopy), and AR ∼ 1000 (with atomic force microscope, AFM). The MWNTs are Hanwha CM-95, provided by Hanwha Chemical, Korea. The number of layers in a wall ' 10 and the cross-section diameter ' 12nm for the MWNTs are measured with transmission electron microscopy, TEM, (JEOL JEM2100F) images in Fig. 2.7. The AR ∼ 2000 from the MWNT manufacturer is not examined from the TEM images because of the entanglement and overlapping of the MWNTs. Due to the similar AR of our SWNTs and MWNTs, the SWNTs are like the 1 : 15 miniatures of the MWNTs if not considering the thickness of the CNT walls.. 2.3.3. Stock solution preparation and sampling. Both single-walled carbon nanotubes (SWNTs) and multi-walled carbon nanotubes (MWNTs) samples are prepared following similar procedure. The carbon nanotube (CNT) powder is weighted directly inside the glass container used for preparing the stock dispersion. The CNT powder is easy to split or self-eject the any plastic surface nearby, increasing the difficulty of precise weighting. Milli-Q 18.2M Ω deionized water is then added to the same container and weighted. The stock dispersion is pre-mixed using bath sonicator for 15 mins to prevent the difference in CNT concentration between samples. For MWNT samples, the pre24.

(34) mixing produces homogeneous CNT/water mixture (as shown in Fig. 3.6 (a), (b)). While for SWNT samples such homogeneous CNT/water mixture can only exist under sonication operation. Once the SWNT/water mixture leaves the ultrasonic tank, aggregates of centimeter scale form within seconds. These SWNT in water are weakly bounded to each other, so the aggregates can be destructed with flow induced by shaking the container. The sampling of SWNT samples from the stock dispersion is to take out the portion of stock dispersion with micropipette rapidly after shaking the stock dispersion. The flow under shaking temperately mixed SWNT in water. The variation of SWNT concentration in each sample is unpreventable at the moment. The MWNT samples are easily sampled with the homogeneous mixture after pre-mixing. No additional steps or treatments are applied while sampling MWNT/water mixture. The stock dispersion is directly taken with micropipette. The visual observation samples are sampled to Schlenk tubes as in Fig. 2.6 (a) for a better sealing with the Teflon stoppers on top. For samples put to the centrifugation, the samples are loaded to test tubes with rubber stops to achieve the sealing. The rubber stops sealing the test tubes are supposed to keep the sealing when a needle impinges or exits. The configuration of test tube with rubber stop and needle for pumping out gas is shown in Fig. 2.6 (c).. 2.3.4 Treatments applied to degassed and controlled samples The degassed samples are treated with freeze-pump-thaw cycles (FPT cycles) described in Section 2.2.3 The freezing phase is achieved with liquid nitrogen. The samples are slowly submerged into the liquid nitrogen trap and stay at a certain level until the liquid nitrogen starts to boil violently. The sudden increment of liquid nitrogen evaporation is due to the phase transition of the liquid inside sample. The sample is lower to deeper in the liquid nitrogen trap after the violently boiling is finished, meaning that the liquid under the liquid nitrogen level is frozen. At the pump phase, a valve connected to a mechanical pump is open. The pump removes the gas in the empty space upon the sample; this phase typically last for three to five minutes. The thaw phase for the liquid to melt and release bubbles trapped in ice is carried out with a infrared heating lamp. This phase last until all ice is melted. 25.

(35) Usually four to seven FPT cycles is applied to the samples depending on the amount of bubbles escaping in the thaw phase. The controlled samples undergo freeze-thaw cycles (FT cycles) with the degassed samples. The FT cycles produces similar initial condition for both degassed and controlled samples. Due to the freezing process, it is reasonable to take concern about the partial degassing on FT cycle samples. The controlled samples are shaken by human hand for approximately 5 mins after FT cycles for re-inducing gas to controlled samples. The ultra-sonication mixing for both degassed and controlled samples is operated simultaneously in the same ultrasonic tank. The degassed samples are sealed after last FPT cycle and is kept in low pressure. The controlled samples are covered but not sealed and hence are open to air. The pressure difference inside the tubes between degassed and controlled samples may very possibly take effects on the efficiency of ultra-sonication mixing. However this problem of different initial condition is not resolved at the moment. For the centrifugation before DLS measurements, the samples are loaded in 13mm (diameter) test tubes and placed inside the Eppendorf Centrifuge 5702 R with the A-4-38 round buckets and 4x4-10ml adapters. The rotating speed is 4400RPM, providing approximately 2850G in maximum to the samples.. 2.4. Measurements. The observations for examing the stability of CNT/water samples are the visual appearance for large aggregates and DLS measurements for microscopic configurations of CNTs. The appearance of CNT samples are recorded by a Pentax k-m digital SLR camera with the typical SMC Pentax-DA 18-55mm lens, capable of auto-focusing. The multi-angle DLS measurements are performed with the Brookhaven Instruments BI-200SM goniometer System and the associated Thorn EMI photon multiplier tube. The hardware correlator is the Brookhaven Instruments BI-9000AT digital correlator. The light source for DLS system is a 637nm solid state laser with the output power up to 30mW provided by Brookhaven Instruments as an accessory with the BI-200SM system. All DLS measurements start after a 15 mins left-to-stand treatment in the measurement system. The duration for each DLS measurement is 15 mins, which is tested to be enough for a good statistical result in our experiment.. 26.

(36) To Pump. Ultra-sonication and Pumping. Heating Pad. Heating Pad. Boiling. Sealing while Boiling. Cooling. To Pump. Cycling. Liquid sample. Liquid N2. Frozen sample. Freeze. Melting sample. Pump. Thaw. Figure 2.4: The three degassing methods: (a) ultrasonic, (b) boiling and (c) Freezepump-thaw. The The tubes in use are shown in Fig. 2.6. 27.

(37) Ultra-sonic. 10 mm. 10 mm. Before Treatments. Degassed and Sonicated. 10 mm. 10 mm. 10 mm. Boiling Before Treatments. Degassed. FPT Cycles. 10 mm. Before Treatments. Sonicated. 10 mm. 10 mm. Degassed. Sonicated. Figure 2.5: The comparison of MWNT/water samples degassed with (a) ultrasonic, (b) boiling and (c) Freeze-pump-thaw method. The procedures of the three different degassing methods are shown in Fig. 2.4. The differences made by ultrasonic and boiling degassing are not so significant compared with samples treated with FPC cycles.. 28.

(38) 10mm. 10mm. 10mm Teflon Stopper Side Opening (To Pump) 13mm Tube Body. Needle (To Pump). Rubber Stopper. Rubber Stopper 13mm Test Tube. 13mm Test Tube. Figure 2.6: Photographs and corresponding schematics of the glass tubes holding CNT/water samples, where (a) is the Schlenk tube, (b) is the sealed test tube proper for the centrifuge, (c) is the sealed test tube with a needle inserted for pumpping out gas. 29.

(39) Figure 2.7: The TEM images of Hanwha CM-95 MWNTs. These images of MWNT/water sample dried on a copper grid are taken with JEOL JEM-2100F TEM; the energy of the electron beam is 1.0x105 eV. The length of the CM-95 MWNTs are typically longer than 1.0 micron in (a) and (b). The MWNTs entangle with each other or lie across the field of view. The number of layers in a wall ' 10 and cross-section diameter ' 12nm are shown in (c), (d).. 30.

(40) Chapter 3 Experimental Results Experimental results on CNT/water (both SWNT and MWNT) dispersion show significant differences between samples with and without degassing. The results show that degassing prevents CNT in water from forming macroscopic structures; this result implies the enhancement of attraction between hydrophobic particles in air-rich CNT/water dispersion comparing with the degassed dispersion.. 3.1. SWNT/water Mixtures. The SWNT in water mixture is less stable compared with the MWNT/water mixture from visual appearance. The large scale aggregates (∼ cm) appears right after the ultra-sonication treatment in sample preparation. It is only possible to proceed with the SWNT experiments when the mixture is dilute. As it is difficult to disperse SWNT in water, the mixture after the sample preparation is highly affected by the ultra-sonication condition; some of the leading factors are the differences between each individual Schlenk tube, eg the wall thickness and the diameters. Since that we are only interesting in the stability (lifetime) of our samples, the differences in initial conditions may be discarded; we wil discuss about the reason further in this section. The very dilute sample pair, one degassed with FPT cycles and the other nontreated, with SWNT concentration < 0.001% wt. with similar visual appearances is placed for about four days. The two samples after the four-day resting are shown in Fig. 3.1 (a). The non-treated sample is open to the atmosphere (∼ 1atm) with the Teflon valve on the top opened to the side opening; while the degassed sample stays sealed. A laser light impinges from the right-hand-side outside the photos, illuminating particles in the path. The clear beam-like scattered light in the degassed sample indicates the existence of suspended SWNT particles. The degassed SWNT/water mixture holds the dispersed phase of SWNT longer in time. It is also interesting to notice the difference of precipitated aggregates lying on the bottom of the tubes. The details about the forms of aggregates will be described 31.

(41) later. The weak scattered light is collected by the camera with a sampling rate much lower than required by DLS. The low concentration of SWNT in water makes is hard for precise DLS measurement and hence no light scattering experiments are performed. To prevent the different ultra-sonication conditions introduced by individual containers, we exchanged the Schlenk tubes for the degassed and controlled samples in the following experiment. And also in case of the possible effects arising form the frequent freeze and thaw during FPT cycles on the SWNT/water mixtures, we applied the FT cycles to the controlled sample as mentioned in Section 2.3.4. Figure 3.1 (b), (c) shows the experiment with the SWNT concentration ∼ 0.001% wt. The initial dispersing conditions of the sample pair are significantly different in Fig. 3.1 (b), (c). If compared with the results in Fig. 3.1 (a), we find that a particulate Schlenk tube obtain higher efficiency in ultra-sonication mixing. Despite the different initial dispersing conditions, the lifetime of the samples in Fig. 3.1 (b), (c) are consistent with the samples in Fig. 3.1 (a). The degassed samples change less in appearances compared with the controlled samples. Fluffyedged aggregates are observed only in the samples without degassing. Zome-in on the aggregated precipitation lying on the bottom of the tubes we observe the different structures of SWNTs in Fig. 3.2. Note that the two tubes set on the same focal plane during the photographic. The degassed sample on the right-hand side contains sharp-edged precipitates. The controlled sample contains poor-contrast aggregates; the lost of contrast can be referred to a three-dimensional structure that cannot be well-represented by the two-dimensional photograph or to a more loose structure by which the well-defined boundaries cannot be obtained.. 3.2. MWNT/water Mixtures. Experiments with MWNT/water mixtures are more complicated to understand. The stock mixtures, even with no additional treatments and no degassing, are homogeneous within the scale of naked eye observation. The mixtures evolve little in days or even a month, hence are stable during our experiments. The absorption spectra of the stock dispersion is performed to insure that the chemical structure of our sample does not variate significantly; we also investigate how stable the MWNT/water mixture is with the absorption data. Figure 3.3 presents 32.

(42) the spectrometric data. The peak in Fig. 3.3 (a) at λ ∼ 290nm is similar to the literature value obtain by reduced graphene oxide in water.[12] The MWNT/water mixture is in metastable for at least ten days with the absorption never lowered to below half of the reading measured right after the ultra-sonication mixing (See Fig. 3.3 (b)). It is until the DLS measurement of both degassed and controlled samples are compared, that we can finally explain the phenomenon in consistent with the SWNT experiments. The multi-q, or multi-angle in our experiments, DLS measurements indicates a non-linear relationship between the decade rate in correlation function, Γ and the squared value of scattering vector q 2 . For example, the DLS measurements for diameter φ = 210mm size standards spheres in Fig. 3.4. The behavior is very different from duffusive particles. The comparison is shown in Fig. 3.5. The log to log plot of Γ to q 2 suggest the new dependency Γ ∝ q 3 ; this is the characteristic of microgel [14] [15]. The microgel as all the gels and gel-like configurations are in need of attractive interactions to hold the structure. In our case with CNTs, one of the possible interactions is the hydrophobic interaction. The pair of FPT-cycles-degassed and FT-cycles-treated controlled samples shows obvious differences in visual appearance. The samples with the MWNT concentration ∼ 0.0025% wt. in Fig. 3.6 is a typical example. The controlled sample (in Fig. 3.6 (a), (c), (e), (g), (i)) has a similar appearance, except right after the FT cycles, even after suffering a centrifugation treatment. The degassed sample also evolves little after the sample preparation (as in Fig. 3.6 (f), (h)), but is different from the stock dispersion (in Fig. 3.6 (b)). The centrifugation for the degassed sample induces significant amount of aggregation (in Fig. 3.6 (j)). The DLS measurements show us the complexity of particle size in degassed MWNT/water dispersion. However the major population of the size distribution gives a leading decade rate, and these decade rates measured in multi-q obtain the Γ ∝ q m relationship, where m is more closer to 2 rather than 3 (shown in Fig. 3.7, red circles). On the other hand, the multi-q DLS measurements for the controlled sample (in Fig. 3.7, blue squares) is like the non-treated one in Fig. 3.5, obeying Γ ∝ q 3 . This Γ ∝ q 3 relationship remains even after the centrifugation (also shown in in Fig. 3.7, blue diamonds). A different concentration ∼ 0.0006% wt. is applied to the sample pair in Fig. 3.8. The degassed sample in Fig. 3.8 (b), (d), (f), (h), (j) and controlled sample in 33.

(43) Fig. 3.8 (a), (c), (e), (g), (i) show similar behaviors as in the higher concentration ∼ 0.0025% wt. samples. The DLS measurements (shown in in Fig. 3.9) of the concentration ∼ 0.0006% wt. samples also show similar results with the ∼ 0.0025% wt. samples, except that the controlled sample behaves more closer to Γ ∝ q 3 and the degassed sample more like Γ ∝ q 2 ; the differences are not significant though.. 3.3. Summary over Experimental Results. In general, the degassed SWNT and MWNT in water samples are more stable as dispersion compared with controlled samples. Fluffy, possibly fractal, aggregates appear in a shorter time in controlled SWNT/water samples (appear within 2hrs) than degassed samples (never observed in our experiment period ≈ 5 days); MWNTs in controlled water mixture samples form gel-like structure as soon as the samples complete the preparation procedure while the degassed MWNT/water samples show, relatively, particle-like behaviors, eg. precipitation after centrifugation, Γ closer to Γ ∝ q 2 instead of Γ ∝ q 3 . Even with the more homogeneously dispersed controlled SWNT/water sample compared with the degassed sample, the experiment show similar result as above: the aggregation of SWNT is mainly observed in the controlled sample; the amount of SWNTs separating out from the dispersion is relatively small in the degassed sample.. 34.

(44) Controlled. Degassed. Degassed. Controlled. ~4 days after preparation. 964 min. S after. 964 min. S after. Figure 3.1: Photographic records of SWNT/water samples, where (a) shows the degassed and controlled samples placed to set for about four days; (b) shows the degassed and controlled samples right after the ultra-sonication and the same samples after around 15hrs. Even with a better mixed appearance in the controlled sample than in the degassed sample at initial time, the aggregates appeaser faster in the controlled than degassed sample.. 35.

(45) Controlled. Degassed. Figure 3.2: The closeup photograph of Fig. 3.1 (b), (c). The fluffy aggregates appear in the controlled sample. Meanwhile the precipitated SWNT in degassed sample has well defined edges down to the pixel resolution of the photograph. The aggregates in degassed sample seams to be more compact compared with that in the controlled sample.. 36.

(46) Figure 3.3: The absorption spectrometric data on MWNT/water stock dispersion. Subset (a) is the spectrum with the wavelength λ within 200-1200nm; the three marked regions in (a), from left to right, represents the λ = 290 ± 5nm region (pink) similar to the signature of reduced graphene oxide in water[12], the 400 ≤ λ ≥ 700nm region (green) that we defined as the visible region (VIS) comparable to observation with naked eye, and the 800 ≤ λ ≥ 1100nm region (violet) of the plateau on spectrum. Subset (b) shows the evolution of the absorption as the sample lies inside the cuvette; the green circles, pink diamonds and violet squares represent the defferent range, VIS, peak and plateau defined in (b) respectively. We believe that from the literature, the λ ∼ 290nm "peak" region is directly related to MWNTs in cuvette. That absorption in all three λ regions undergo similar decay implies the spectra is mainly determined by the concentration of MWNTs. 37.

(47) 0. 10. Slope = 2.06. 2.5. -2. 10. Γ (1/msec.). Γ (1/msec.). -1. 10. 0.0 0.0. -4. 2.0x10 4.0x10 q^2 (1/nm)^2. -4. -3. 10 1E-3. 0.01. q (1/nm). Figure 3.4: The multi-q DLS results for diameter φ = 210nm size standard spheres. The figure shows the decay rates Γ, defined in Fig. 2.3, measured with different q (determined by different θ). The slope = 2 in log-log plot agrees with Γ = Dq 2 obtained in Section 2.1.4. The inset is the Γ to q 2 plot with both horizontal and vertical axis are linear. The data in the inset are also consistent with Γ = Dq 2 .. 38.

(48) 0.0 2. 0. Γ (1/msec.). -1. 10. Γ (1/msec.). 10. 0 0.0. q^2 (1/nm)^2 -4 -4 2.0x10 4.0x10. 6.0x10. -4. Γ to q square Γ to q cube. -6. -6. 4.0x10 8.0x10 1.2x10 q^3 (1/nm)^3. -5. Slope = 2.89. -2. 10. -3. 10 1E-3. 0.01. q (1/nm). Figure 3.5: The multi-q DLS results for MWNT/water stock dispersion (MWNT concentration ∼ 0.0025% wt.). The log-log plot reveals the slope ≈ 3.0 nature of the MWNT/water mixture (without degassing). The inset shows both Γ-q 2 (red circles) and Γ-q 3 (blue diamonds) of the MWNT/water stock dispersion. The red circles represent linearity in the higher-q region (say, q 2 > 2E − 4), but is obviously curved when q approaches to 0. If one only measures Γ at q 2 > 2E − 4, the offset ˜ 2+a ˜ is, of course, not representing appears in the Γ-q 2 fitting, Γ = Dq ˜, where the D the diffusion coefficient of Brownian partiles. The blue diamonds show slightly upbending trend (but the bias from linear relation is smaller than that in the Γ-q 2 plot), which is consistent with slope = 2.89 < 3.0 in the log-log plot.. 39.

(49) Controlled Degassed Figure 3.6: The photographs of the concentration ∼ 0.0025% wt. MWNT sample pair, where (a), (c), (e), (g), (i) are the controlled sample; (b), (d), (f), (h), (j) are the degassed sample. The photographs present the samples after (a) and (b) loading the stock dispersion, (c) and (d) five FT (for the controlled sample) or FPT (for the degassed sample) cycles, (e) and (f) ultra-sonication mixing, (g) and (h) centrifugation at 4400 RPM for two minutes, (i) and (j) centrifugation at 4400 RPM for another two minutes, four minutes in total. The right-hand side in (i) and (j) shows a laser beam impinges from the left-hand side into the centrifuged sample.. 40.

(50) Controlled Sample Controlled Sample (Centrigutation) Degassed Sample. Γ (1/msec.). 1. Slope = 2.84 0.1. Slope = 2.34 0.01 1E-3. 0.01. q (1/nm). Figure 3.7: The multi-q DLS results for concentration ∼ 0.0025% wt. MWNT samples, degassed (red circles) as shown in Fig. 3.6 (f), controlled before (blue squares) and after (blue diamonds) centrifugation as shown in Fig. 3.6 (e) and in Fig. 3.6 (i) respectively. The linear fitting for the controlled sample uses measured data from both before and after centrifugation since the difference introduced by centrifugation to the controlled sample is not significant.. 41.

(51) Controlled Degassed Figure 3.8: The photographs of concentration ∼ 0.0006% wt. MWNT samples, where (a), (c), (e), (g), (i) are the controlled sample; (b), (d), (f), (h), (j) are the degassed sample. The subsets in the figure are arranged in the same order as in Fig. 3.6: the photographs presents the samples after (a) and (b) loading the stock dispersion, (c) and (d) five FT (for the controlled sample) or FPT (for the degassed sample) cycles, (e) and (f) ultra-sonication mixing, (g) and (h) centrifugation at 4400 RPM for two minutes, (i) and (j) centrifugation at 4400 RPM for another two minutes, four minutes in total. The right-hand side in (i) and (j) shows a laser beam impinges from the left-hand side into the centrifuged sample.. 42.