Molecular Diffusive Dynamics in Complex Liquids

This document is downloaded from Outstanding Academic Papers by Students

(OAPS), Run Run Shaw Library, City University of Hong Kong.

Title Molecular diffusive dynamics in complex liquids

Author(s) Tsang, Yuk Wai (曾郁惠 )

Tsang, Y. W. (2018). Molecular diffusive dynamics in complex liquids Citation (Outstanding Academic Papers by Students (OAPS), City University of Hong Kong).

Issue Date 2018

URL http://dspace.cityu.edu.hk/handle/2031/9126

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CITY UNIVERSITY OF HONG KONG

DEPARTMENT OF

PHYSICS AND MATERIALS SCIENCE

BACHELOR OF SCIENCE (HONS) IN APPLIED PHYSICS 2017-2018

DISSERTATION

Molecular diffusive dynamics in complex liquids

TSANG Yuk Wai

April 2018

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. Molecular diffusive dynamics in complex liquids

TSANG Yuk Wai

Submitted in partial fulfilment of the

requirements for the degree of

BACHELOR OF SCIENCE (HONS)

APPLIED PHYSICS

from

City University of Hong Kong

April 2018

Project Supervisor : Dr. Mavila C Suresh

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. Table of Contents List of Figures ...... v

List of tables ...... vi

List of equations...... vii

Acknowledgement ...... 1

Abstract ...... 2

1. Introduction ...... 3

2. Objective ...... 5

3. Literature Review ...... 6

3.1. Dynamics in Liquids ...... 6

3.2. Glass-Forming Liquids...... 6

3.2.1. Salol (Phenyl Salicylate) ...... 7

3.2.2. Acetone ...... 8

3.3. Other Studies ...... 8

3.5.1. Study of Dendrimers ...... 8

3.5.2. Study of Colloidal Microgels ...... 9

4. Dynamic Light Scattering ...... 10

4.1. Three Components of DLS ...... 10

4.1.1. LASER ...... 11

4.1.2. Sample Container ...... 12

4.1.3. Light Detector ...... 12

4.2. Experimentation ...... 13

5. Dynamics of Salol in Acetone ...... 15

5.1 Sample Preparation ...... 15

5.1.1. Molecular Weight of the Samples ...... 15

5.1.2. 10:1 Sample ...... 16

iii

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 5.1.3. 20:1 Sample ...... 16

5.1.4. Pure Salol ...... 16

5.2. X-ray Diffraction Study...... 17

5.2.1. Parameters ...... 18

5.3 Dynamic Light Scattering Experiment ...... 19

5.4. Data Analysis of DLS...... 20

5.4.1. Relaxation Time 흉 from Linux ...... 20

5.4.3. Wave Vector q ...... 22

5.4.4. Origin 8 ...... 22

5.4.5. Diffusion Coefficient D ...... 24

6. Results and Discussion ...... 25

6.1 Results from X-ray Diffraction ...... 25

6.2. Results of DLS Experiments ...... 27

6.2.1. 1/τ VS q2 ...... 27

6.2.2. lnD VS 1000/T ...... 32

7. Limitations ...... 37

8. Improvements ...... 38

9. Recommendations ...... 39

10. Conclusion ...... 40

References ...... 41

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. List of Figures

Figure 1. Two-time relaxation process of materials ...... 4 Figure 2. Esterification of salicylic acid and phenol to produce salol (Sharma & Rani, 2015) ...... 7 Figure 3. The chemical structure of phenyl salicylate (SIGMA-ALDRICH, n.d.) ...... 7 Figure 4. The chemical structure of acetone (BIOMEDICALS, n.d.) ...... 8 Figure 5. A phase diagram showing the concentration dependence phase separation temperature of PNIPAM ...... 9 Figure 6. The model of Photon Correlation Spectrometer ...... 10 Figure 7. Real DLS setup ...... 11 Figure 8. The illustration of scattered light in air ...... 11 Figure 9. The sample container ...... 12 Figure 10. Light scattering with thickness x ...... 13 Figure 11. Weighing the bottle with an electronic balance ...... 17 Figure 12. Setup of D2-phaser ...... 18 Figure 13. A working interface of DynaLS software ...... 19 Figure 14. A working interface of Linux ...... 21 Figure 15. A fitted curve in Linux ...... 21 Figure 16. Final values in Linux ...... 21 Figure 17. A fitted linear curve of 1/τ vs q2 under 20 degree Celsius (10:1)...... 22 Figure 18. 1/τ against q2 of different angles under different temperatures ...... 23 Figure 19. A graph of lnD against 1000/T ...... 24 Figure 20. XRD results (20:1 and 10:1)...... 25 Figure 21. XRD result of bulk salol and deuterated acetone ...... 26 Figure 22. 1/τ vs q2 at 20℃-50℃ Figure 23. 1/τ vs q2 at 20℃-50℃ ...... 29 Figure 24. 1/τ vs q2 at 20℃ (10:1) Figure 25. 1/τ vs q2 at 30℃ (10:1) ...... 30 Figure 26. 1/τ vs q2 at 20℃ (20:1) Figure 27. 1/τ vs q2 at 30℃(20:1) ...... 30 Figure 28. 1/τ vs q2 at 30℃ (10:1 and 20:1) ...... 31 Figure 29. lnD vs 1000/T at 20℃-50℃ (10:1 and 20:1) ...... 33 Figure 30. The linear fit of the curve under lnD versus 1000/T in 10:1 sample ...... 33 Figure 31. The non-linear fit of the curve under lnD versus 1000/T in 20:1 sample ...... 34

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. List of tables

Table 1. 1/τ and q2 for different angles and temperatures (10:1) ...... 27 Table 2. Slopes at 20℃-50℃ (10:1) ...... 28 Table 3. 1/τ and q2 for different angles and temperatures (20:1) ...... 28 Table 4. Slopes at 20℃-50℃ (20:1) ...... 28 Table 5. lnD at 20℃-50℃ (10:1) ...... 32 Table 6. lnD at 20℃-50℃ (20:1) ...... 32

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. List of equations

Equation 1. The attenuation of intensity ...... 13 Equation 2. Molecular weights of samples ...... 15 Equation 3. Bragg's Law ...... 17 Equation 4. Kohlrausch-Williams-Watts Function (KWW) ...... 20 Equation 5. Wave vector ...... 22 Equation 6. Diffusion coefficient ...... 24 Equation 7. Stokes-Einstein equation ...... 24 Equation 8. Arrhenius equation ...... 34 Equation 9. Vogel-Fulcher Tammann equation (Chen, Wong, Krishnan, Embs, & Chathoth, 2018) 34 Equation 10. Natural log of equation 9 ...... 35 Equation 11. Expression of Vogel-Fulcher-Tammann equation ...... 35

vii

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. Acknowledgement

This study cannot be finished without the great help from my supervisor and his PhD assistant. I would

like to thank my supervisor Professor Suresh who gave me step-by-step instructions, and guidance to

finish the whole experiment. Moreover, he shared some of his research papers for me to get a clearer

concept about the whole project. He does not put pressure on me or push me hard. I am happy that he

always drops by the laboratory and sees if I have any questions about the experiment. I have no Physics

background when I was in secondary school and I was not interested in Physics at the beginning. I

always encounter difficulties about Physics theories in my university life. I am not confident enough

to finish the whole project by myself before receiving the help from my supervisor, but now I have a

positive mind to pursue my study in the future. My second assessor Professor Zhang has been a great

assistance as well. His valuable opinions on the project are helpful for my research.

Mr. Rithin Pachan Krishnan is a PhD student of Professor Suresh, who also helped me during the

whole experiment. He taught me a lot, and showed me how to prepare the samples and carry out

dynamic light scattering (DLS). When we came across some difficulties, he would help me find out

the reason together instead of asking me to check by myself especially when he was always available

in the laboratory. He also encouraged and gave me a relaxing working station to finish my research

especially when I was doing the fitting of the Kohlrausch’s function in Linux. I did not know how to

fit the graph well, and he would help me adjust the values every time. I really appreciate his helpfulness

and support towards his work. I hope that we can work together in the future.

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. Abstract

In simple expanded liquids, atoms/molecules show a two relaxation process, namely vibrations and

long range diffusion process, also known as α-process. However, in viscous liquids the

atoms/molecules undergo an additional relaxation process and is called fast β-relaxation (Angelani,

Cavagna, Giardina, Leuzzi, & Scala, 2008). In this case atoms/molecules rattle around the cage formed

by its neighbouring atoms/molecules before the long range diffusion process. Theoretically, Mode-

Coupling Theory (MCT) has been very successful in describing the fast β-relaxation process in dense

liquids (Würger, March 1994). Experimentally, the fast β-relaxation process has been observed in a

variety of molecular liquids by light scattering, neutron scattering and dielectric spectroscopy, etc. In

most liquids, the fast β-relaxation process exhibits a simple exponential decay (Han, Akcasu, & A,

2011).

Recently, logarithmic decay of correlations for the fast β-relaxation has been observed in ortho-

terphenyl (OTP), benzophenone (BZP), 2-biphenylmethanol (BPM) and in Salol, in their supercooled

state by Optical-Kerr-Effect experiments and in DNA, tRNA and proteins by QENS. One of the

striking features of the liquids that show the logarithmic relaxation process is their molecular structure.

For example, the molecular structure of Salol, OTP, BZP or BPM shows two benzene rings either end

of a chain. Studied have suggested that the unique inter molecular potential is the origin of exotic

logarithmic relaxation process in molecular liquids. In this project we have studied the long range

diffusion dynamics in one of the molecular liquids, phenyl-salicylate (Salol), that show the logarithmic

decay. We have altered the inter-molecular potential of the Salol by dissolving it in Acetone and

studied the self-diffusion dynamics by dynamic light scattering. We found that the a-relaxation

dynamics of the Salol do not change appreciably in the Acetone even at high diluted state. However,

temperature dependence of diffusion coefficient changes from an Arrhenius to non-Arrhenius form.

At high dilution the system changes from a strong liquid to a fragile liquid.

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 1. Introduction

Simple liquids are commonly known for their molecular dynamics, atomic structures and physical

properties. However scientifically, liquids can become complex in terms of their relaxation processes.

Throughout the years, countless studies have investigated towards the direction of when the liquids

develop into an amorphous state. An amorphous material is defined as a crystal which lacks a closely

packed order of atomic arrangement, it is acknowledged as a liquid that does not flow (Angell, Ngai,

Mckenna, McMillan, & Martin, 2000). Common amorphous materials are polymers, gels, colloids and

nanostructure substances. Interestingly, their exclusive molecular properties raise questions about the

factors affecting the moment of materials becoming amorphous, known as the glass transition.

A glass-forming liquid generally is divided into strong and fragile. The key determination of whether

a material is strong or fragile is the viscosity. Viscosity affects the molecular diffusion of a material.

A molecular diffusion is the tendency for substances to move from one space to another in a random

manner which obeys the laws of Brownian motion. Brownian motion is present within the particles

that oscillate with an unpredicted direction and vibrate continuously (Britannica, 2016). Concentration

and temperature are the main conditions for diffusion to happen.

Apart from concentration and temperature, the relaxation time between particles in a glass-forming

liquid is also important for properties analysis. The relaxation time of glass-forming liquid can be

explained by the two-time relaxation processes as mentioned in the abstract. α-process represents the

vibrations and long range diffusion process; β-process is an additional relaxation process of amorphous

materials, it usually undergoes an exponential decay, mathematically expressed in the Vogel-Fulcher-

Tammann equation. The exponential decay can be observed under the techniques like light scattering,

neutron scattering and dielectric spectroscopy.

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. Therefore, in this dissertation, the technique of dynamic light scattering (DLS) is used to study the

diffusive behavior of the salol-acetone mixture under different concentrations, temperatures and

scattering angles.

Figure 1. Two-time relaxation process of materials

In figure 1, it explains α and β relaxations of different liquid types. The middle curve depicts the glass-

forming liquid which is amorphous.

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 2. Objective

This project mainly focuses on how the diffusion coefficients of the samples vary under different

parameters. This can be achieved by following few steps.

 To derive the relationship between diffusion coefficient and sample concentration (salol to

acetone).

 To obtain the relaxation time (tau) for each sample.

 To determine the temperature dependence of diffusion coefficient

 To determine the concentration dependence of diffusion coefficient

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 3. Literature Review

3.1. Dynamics in Liquids

In fluid dynamics, it is the study of random movements and interactions between molecules in liquids.

It is mainly divided into two categories, fluid mechanics and fluid statics. Fluid mechanics deals with

moving molecules while fluid statics deals with molecules at rest (Jones, 2017). In this dissertation,

the concept of fluid statics is understood since the samples are not moving macroscopically. They

interact with each other in a microscopic dimension.

Analysis of different properties of a material can be performed under experimentation, mostly, the

viscosity, diffusive behavior, time of interaction and temperature/concentration dependence are

investigated under specific parameters. The investigation of molecular behavior in a liquid can be done

using dynamic light scattering.

3.2. Glass-Forming Liquids

In recent studies, glass forming liquids are commonly used for investigation. This is because it has

some unique properties which are valuable for comparison with other simple liquids. When a glass

forming liquid encounters increasing temperature, its dynamics greatly slows down, as well as

heterogeneous when approaching the glass-transition temperature (i.e. 푇푔 ) (Tanaka, Kawasaki,

Shintani, & Watanabe, 2010).

This study serves the purpose of finding the glass-transition temperature of the samples at certain

conditions such as temperatures and scattering angles. In addition, the fragility parameter can be 6

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. determined once 푇푔 is found. During the transition, the viscosity of the glass-forming liquid will

increase dramatically, while the temperature increases within a few degrees. The sample used in this

project is a selected mixture of salol and acetone, which is a glass-forming liquid.

3.2.1. Salol (Phenyl Salicylate)

Salol is presented in white crystalline powder form naturally. It can be solidified without going through

crystallization (Sidebottom & Sorensen, 1989). Its IUPAC name and molecular formula are phenyl 2-

hydroxybenzoate and C13H10O3 respectively. Its molecular weight is 214.22 grams per mole (SIGMA-

ALDRICH, n.d.). The complexity of salol is 233. It is insoluble in water and has a high boiling point

which is around 172 degree Celsius and the melting point is 43 degree Celsius. Its viscosity fluctuates

with temperature (Chem, 2005). It is produced by esterification of salicylic acid and phenol together

with acid catalyst (as in figure 2) (Kuriakose & Nagaraju, 2004). Conventionally, salol has medical

applications such as pain relieving and acts as antiseptic.

Figure 2. Esterification of salicylic acid and phenol to produce salol (Sharma & Rani, 2015)

Figure 3. The chemical structure of phenyl salicylate (SIGMA-ALDRICH, n.d.)

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 3.2.2. Acetone

Acetone is a well-known chemical and has many properties. It is an organic compound and is used for

the cleansing of laboratory apparatus. When the temperature is above 56.05 degree Celsius, acetone

changes from liquid to gas (i.e. vaporization). The molecular weight of acetone is 58.08 grams per

mole. It is inflammable and soluble in water. This colorless liquid is corrosive and can irritate human

skin when in contact. Its complexity is 26.3. It is usually used as a solvent when mixing with other

chemicals (Database, 2018).

Figure 4. The chemical structure of acetone (BIOMEDICALS, n.d.)

3.3. Other Studies

There are many study using dynamic light scattering techniques to study different kinds of sample,

such as gold nanoparticles, dendrimers, and microgels, etc.

3.5.1. Study of Dendrimers

A paper about the study of dendrimers in 2016, which has similar chemical structure to salol. Besides,

dendrimers and salol are both complex liquids. In the study of the dendrimer, dynamic light scattering

is used to study the relationship between translational diffusion and chemical structure, concentration

of dendrimer (Wong, Wu, Lam, & Chathoth, 2016). On the other hand, this experiment mainly focuses

on how the concentration and temperature affect the diffusive properties of the salol being mixed with

acetone. 8

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 3.5.2. Study of Colloidal Microgels

The dimensions of colloidal systems can be examined by techniques like dynamic light scattering

(DLS) and optical microscopy. The normally controlled parameters of a colloidal system contain

packing fraction, waiting time and ionic strength. Under different conditions, the microgel can give

rise to distinguished arrested states, such as gels, glasses, etc. Microgel is being widely used because

of its versatility and sensitivity to stimuli such as pH, temperature, electric field, ionic strength, solvent,

light, etc. One of the most studied responsive microgels is based on the polymer (N-

isopropylacrylamide), also known as PNIPAM, a thermo-sensitive polymer (as in figure 5) (Nigro, et

al., 2014).

Figure 5. A phase diagram showing the concentration dependence phase separation temperature of PNIPAM

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 4. Dynamic Light Scattering

Dynamic light scattering (DLS) is a technique which detects the decaying process of molecules by

using laser beam and detector. It observes the scattered light intensity from the laser and size

distribution of molecules. A wide range of angles and temperatures can be set within the device for

many different applications, like the imaging of living tissues, size establishment of micelles, and

estimation of particles’ molecular weights.

4.1. Three Components of DLS

There are three components of DLS, which are the laser source, the container that contains the sample,

and the light detector (as in figure 6). Besides, the DLS system is connected to an analog-to-digital

analyzer, a computer and a temperature controller. The name of this DLS system is Photocor Complex

and produced from Photocor Instruments Inc (Instruments, 2018). The approximate area of the whole

setup is 75x30 cm2.

Figure 6. The model of Photon Correlation Spectrometer

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong.

Figure 7. Real DLS setup

4.1.1. LASER

The laser source emits a monochromatic light beam which is red in color and concentrated at the center,

so the diameter of the cross section of the light beam is short. The wavelength of the laser beam is 777

nanometers. The laser beam is emitted in a straightforward direction. It is to provide a light source and

allow the detector to detect the light after being scattered within the sample. The sample is stored inside

a transparent glass bottle, therefore, the light beam is transmitted to the sample without interruptions.

Laser is harmful to human’s eyes even if the beam does not irradiate the eyes directly, since some of

the light is scattered by air particles and to our eyes. Under normal circumstances, we cannot see laser

beam. However, dust particles in air can scatter the beam and eventually enter our eyes (as in figure

8). It is impossible for us to observe laser beam if there are no dust particles in air (Ogendal, 2016).

Figure 8. The illustration of scattered light in air

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 4.1.2. Sample Container

The container is cylindrical in shape with a lid atop. At the half of its height, there is a gap circling the

container, in a sense that the scattered laser beam can reach the detector. The container is made of heat

insulating materials in order to raise the temperature without any heat loss. According to the pre-set

value of the temperature in the computer, the container will continuously heat up until the temperature

inside reaches the targeted level. As shown in figure 9, the cover inside the container helps decrease

the chance of dust gathering around the sample when we open the lid. The sample is put at the middle

of the container.

Figure 9. The sample container

4.1.3. Light Detector

The detector can be set to different angles in order to record the scattered light intensity. Due to the

detector’s high sensitivity to the light source, it can be damaged by the laser beam easily.

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 4.2. Experimentation

In this experiment, we used this method to provide the intensity of the scattered light in order to find

out the relaxation τ and diffusion coefficient D of the samples. The particles observed scatter the light

and indicate the information about their motion (i.e. geometric Brownian motion).

When light passes through the sample which contains the randomly arranged particles, the intensity of

the light beam will be attenuated due to scattering. In this experiment, the intensity of the laser beam

is attenuated by the small particles of the solution.

The following equation describes how the intensity is being attenuated,

−휏푥 I = 퐼0푒

Equation 1. The attenuation of intensity

where I is the transmitted intensity, I0is the initial intensity of the laser beam, 훕 is the relaxation time

and x is the thickness of the sample through where the light passes. The transmissivity of light will

decrease in an exponential relationship with increasing thickness of the sample (Ogendal, 2016, pp. 3-

10). Figure 10 shows a schematic illustration of intensity attenuation.

Figure 10. Light scattering with thickness x

The main purpose of using this method is to determine the velocity of particles inside the sample by

the fluctuation of scattered light intensity. The particle velocity is dependent on the temperature since

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. the kinetic energy of particles increases with increasing temperature. As a result of their difference in

velocity, the time required of two successive collisions between the particles are different, and the time

required is the relaxation time (NASA, 2015). By that logic, a constant relaxation time can be achieved

under constant temperature. The intensity fluctuations can be obtained by calculating the intensity

correlation function, which leads to the autocorrelation function (ACF). To add, the diffusion

coefficient can be derived from the correlation function.

Since the particles have different concentrations from point to point. Therefore, the amount of laser

beam being scattered at each point is different and the refractive index n of the whole sample is not

constant.

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 5. Dynamics of Salol in Acetone

5.1 Sample Preparation

First of all, a new glass bottle of 10 ml was prepared, its volume is around 10 ml. the glass and lid were

weighted separately in order to calculate the molecular ratio for salol and acetone in order to get 20-1

and 10-1 ratios.

The concentrations of the sample of salol to acetone are 10:1 and 20:1 because the interaction between

two types of particles can be shown easily under higher concentration of salol. Since salol is much

smaller than acetone, a much larger amount of salol is needed to interact with all acetone molecules.

If a smaller amount of salol (e.g. 4:1) is used, the interaction between molecules is not obvious.

5.1.1. Molecular Weight of the Samples

The formula of calculating the molecular weights of the samples is as the following, 푚 푥 1 1 × 5 푔 푚1푥1 + 푚2푥2 Equation 2. Molecular weights of samples

where 푚1 is the molecular weight of salol, 푚2 is the molecular weight of acetone, 푥1 is the molar

ratio of salol, 푥2 is the molar ratio of acetone.

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 5.1.2. 10:1 Sample

By calculating the molecular ratio of salol and acetone, the resulting solution should be in total of 5

grams. The weight of salol in liquid form should be 10 to 1 when it is compared to that of acetone.

4.8616 grams of salol and 0.1329 grams of acetone were used so as to obtain a 10:1 sample.

5.1.3. 20:1 Sample

By calculating the molecular ratio of salol and acetone, we need to mix a solution in total of 5 grams.

The weight of salol in liquid form should be 20:1 when it is compared to the weight of acetone.

Therefore, 4.93 grams of salol and 0.066 grams of acetone should be mixed together.

5.1.4. Pure Salol

An empty bottle was prepared for melting salol. The weight of this empty bottle was 18.3948 grams,

and 5.2497 grams then add solid salol with. The total weight is 23.6445 grams. After melting the salol

under 100 degree Celsius, the weight of the bottle mentioned before and liquid salol form is 23.5908

grams. Since the weight after the melting of salol is lower than before, so we know that the salol used

in the experiment is pure.

The salol is melted at around 100 degree Celsius to make it changes from white solid powder to

transparent liquid. According to the molecular ratio, the bottle containing the melted salol is weighted

and acetone is added into it. The mixture should be 5 grams. After closing the lid tightly, the bottle is

washed with acetone. To make sure there is no dust or fingerprint on the glass bottle, it is cleaned by

Kimwipes.

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong.

Figure 11. Weighing the bottle with an electronic balance

5.2. X-ray Diffraction Study

Another effective way to study the atomic structures and properties of the samples is the X-ray

diffraction (XRD). XRD is based on using a monochromatic X-ray source which is ejected by a

cathode tube (IRAMIS, 2013 ). The ejected X-ray is collimated like a laser and concentrated on the

sample. It produces a constructive interference with the sample under the Bragg’s Law,

푛휆 = 2푑 sin 휃

Equation 3. Bragg's Law

where n is the order of diffraction, 휆 is the incident wavelength, 휃 is the scattering angle and d is

the interplanar distance of the sample. In this experiment, a device called the D2 Phaser is used to

undergo XRD of the samples. Within the device, a detector detects the X-ray signal and converts it

into count rate (later referred as intensity of the samples) (Bruker). The intensities of scattered X-ray

are compared between samples.

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 5.2.1. Parameters

This Phaser consists of the X-Ray source, a sample holder and a X-Ray detector.

After each sample (i.e. 10-1 or 20-1 concentrations of salol and acetone) is placed inside the sample

holder, two different parameters of time and angle are set on the Phaser’s monitor. The angle parameter

appeared as “2Theta” on the screen. Time is set as 0.5 seconds, and the angle is set as the range from

5 degrees to 85 degrees. The angle increment is set as 0.02 degrees, which means the angle increases

by 0.02 degrees for each 0.5 seconds.

Once the parameters are completely established, the Phaser can be turned on. For each sample, around

30 minutes are required for undergoing the experiment after the X-Ray has been released. Hence, a

graph is obtained with counts against angles (degrees).

Figure 12. Setup of D2-phaser

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 5.3 Dynamic Light Scattering Experiment

After preparing the samples, we need to turn on the device which is called the "Photocor CS" or photo-

correlator (Photocor, 2018). It is used for processing and recording all entire data sets obtained from

the instrument.

Before the data collection, the preferred angle and temperature were run in the computer. The

parameters are 293K, 303K, 313K, 323K, 45°, 65°, 90°. In total, there should be 24 distinct data sets.

Wait for around 5 minutes to ensure the temperature becomes constant. Next, insulate the experimental

setup from light with a black blanket. Turn on the laser source and start collecting the data. After data

collecting, a software which is called DynaLS software is used for presenting the data. (as in figure 13)

A graph of correlation function vs channel is presented by a window which is called “Accumulation”.

When the program is running, the dots start to appear on the graph of correlation function VS channel

and wait for around two hours until the dots become stable and do not fluctuate anymore. It is important

to select a suitable range of channels as under different conditions, the desirable channels are different.

A suitable range of channels should be the fluctuating part of the graph (e.g. 75-200, 100-220).

Figure 13. A working interface of DynaLS software

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 5.4. Data Analysis of DLS

5.4.1. Relaxation Time 휏 from Linux

After getting the graph of desirable channels, the data can be transferred to a computer software called

the Linux. The main purpose of using Linux is to obtain the relaxation time 휏 of each sample, the

calculation is done inside the software incorporating the installed KWW function.

The KWW function, which is called the function 85 inside the software, calculates the relaxation time.

It is not only used to calculate one specific variable but any variables we want in an equation. In this

case, all the variables other than the relaxation time are known, hence, a resultant τ is calculated. 푡 퐼 = 푏 + 푓 푒푥푝[−( )]훽 푔 푔 휏 Equation 4. Kohlrausch-Williams-Watts Function (KWW)

where I being the intensity;

푏푔 being the background;

푓푔 being the height of the curve at the beginning;

t being the time;

훽 being the stretching exponent, a fixed value between 0 and 1.

Inside Linux, read the curve of the graph and input the values: background, a (i.e. the height of the

curve at the beginning), τ (i.e. relaxation time) and fixed β (i.e. fixed between 0-1). (as in figure 14)

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Figure 14. A working interface of Linux

According to the above values, the line is fitted corresponding to the curve. (as in figure 15)

Ideally speaking, the decreasing part of the curve should be fitted perfectly in order to get an accurate

τ value. Apart from that, β should change from time-to-time. In figure 14, the third row of data is the

τ.

Figure 15. A fitted curve in Linux

With y-axis being the intensity in unit (a.u.) and x-axis being the time in unit (ms).

After fitting the curve, the values will fluctuate besides β.

Obtaining the final relaxation time of the fitted curve,

Figure 16. Final values in Linux

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 5.4.3. Wave Vector q

In order to further understand the diffusive properties of salol-acetone, the wave vector is necessary as

well. 4π푛 휃 q = 0 sin ( ) 휆 2 Equation 5. Wave vector

where q is the wave vector, 푛0 is the refractive index of the sample, 휆 is the wavelength of the

incident laser and 휃 is the angle between the detector and the axis of the sample (Sidebottom &

Sorensen, 1989). q represents the momentum transfer. Energy is being transferred if two particles

collide with each other. q is the measure of this energy.

5.4.4. Origin 8

For the purpose of finding the diffusion coefficient D of each sample, graphs of 1/τ VS q2 under each

temperature are needed (as in figure 17). Graphs are plotted using another software called the Origin

8. The Origin 8 serves a similar function as Microsoft Excel.

Fit a linear curve to represent the relationship between 1/τ and q2, then obtain the slope.

Figure 17. A fitted linear curve of 1/τ vs q2 under 20 degree Celsius (10:1) 22

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. Before obtaining the slope, we established a boundary condition in which the temperature should not

be 60℃ or higher. The relaxation time (τ) under 60℃ is higher than that of 50℃ (as in figure 18).

Figure 18. 1/τ against q2 of different angles under different temperatures

It is an abnormal phenomenon because the particles should move faster under higher temperature, so

the relaxation time should be shorter within the particles. The contradiction appears because the sample

is a mixture of salol and acetone, of which the boiling point of acetone is 56.05℃. When the

temperature of the sample increases to 60℃, the acetone in the sample evaporates. Gas molecules are

different from the liquid molecules, and they scatter light in a different speed, so the result is not

reasonable.

We also set the temperature to 10℃. When the temperature is almost 10℃, most of the salol molecules

will be crystallized into white solid form. This is not the state we want, so we set the temperature

starting from 20℃.

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 5.4.5. Diffusion Coefficient D

The slope of 1/τ VS q2 represents the diffusion coefficient D. Therefore, in figure 19, its slope is the

D of 10:1 sample under 20 degree Celsius.

1 퐷 = . 휏푞2

Equation 6. Diffusion coefficient

Besides, plot another graph of lnD vs 1000/Temp (K).

Figure 19. A graph of lnD against 1000/T

Compare the results among different temperatures.

Apart from the experimental calculation above, D can be calculated from the famous Stokes-Einstein

equation (Ogendal, 2016, p. 30), 푘 푇 퐷 = 퐵 6휋휂푟 Equation 7. Stokes-Einstein equation

-23 with 푘퐵 is the Boltzmann’s constant which is 1.38x10 , T is the absolute temperature, 휂 is the

dynamic viscosity and r is the radius of the spherical particle.

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 6. Results and Discussion

In this section, the relationships between diffusion coefficient, temperature and scattering angle are

analyzed by different graphs. Such as the graph of 1/τ vs q2, lnD vs 1000/T and intensity vs 2Theta

from X-Ray diffraction.

6.1 Results from X-ray Diffraction

10000

10:1

20:1

intensity(a.u)

0 20 40 60 80 100 2 theta(in degrees) Figure 20. XRD results (20:1 and 10:1)

From figure 20, both samples have only one peak after being diffracted by X-ray. Each peak has

specific intensity and no other peaks can have the same intensity. Therefore, it proves that the mixture

of salol and acetone is not phase separated, instead, it is almost homogeneous. Two or more peaks can

appear if the materials are immiscible to each other, like oil and water. Oil and water cannot be mixed

together, as a result, two different peaks are detected.

The intensity of 20:1 sample is lower than that of the 10:1 sample, meaning that at the same scattering

angle (20 degrees), the scattered X-ray intensity of a higher concentration is lower.

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Figure 21. XRD result of bulk salol and deuterated acetone

Figure 21 is obtained from the database, it is commonly used for comparison with the experimental

results. The top line represents bulk salol, the bottom line represents deuterated acetone, and the middle

line is the mixture of both like the sample we used. Either 20:1 or 10:1 sample can replace the middle

line as the intensity of scattered X-ray. For the mixture, it shares the same peak with pure salol and

acetone, which indicates the mixture becomes homogeneous at 20 degrees. The usefulness of XRD is

to determine when the sample becomes amorphous or glassy, in this case, the mixture becomes

amorphous at 20 degrees.

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6.2.1. 1/τ VS q2

At the first part of comparison, the graphs of 1/τ VS q2 under 10:1 and 20:1 concentrations are

examined (Han, Akcasu, & A, 2011). The slopes of the graphs, which represent the D value, are also

obtained.

6.2.1.1. 10:1 Sample (1/τ VS q2)

By applying the equation 5, q value can be obtained.

q2 1/τ

20℃ 30℃ 40℃ 50℃

45° 1.3078 14.1422 22.3679 36.2755 53.86

65° 2.1484 23.485 37.7606 71.499 107.8109

90° 2.6200 28.5442 47.6 89.6346 141.02

Table 1. 1/τ and q2 for different angles and temperatures (10:1)

The q2 value remains unchanged for the same angle no matter which temperature. From the above

results, we observe that the values of q2 is increasing with the angle of the light detector. This is because

of the equation of q, q and scattering angle have a proportional relationship. Since an inverse

relationship exists between τ and 1/τ, the largest value of τ in this sample of 10:1 concentration is in

20 degree Celsius at 45 degrees of the detector. On the contrary, the lowest value of τ is under 50

degree Celsius at 90 degrees.

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The slopes can be obtained from the graphs.

20℃ 30℃ 40℃ 50℃ Slope (D) 10.89706 17.82283 33.20663 50.91076 Table 2. Slopes at 20℃-50℃ (10:1)

From table 2, we observe that the slope of the line increases with increasing temperature. With higher

temperature, the 1/τ value increases at a higher rate with a smaller change of q2. Since the value of y-

axis increases with increasing temperature, so temperature slope is steeper. (as in figure 22)

On the other hand, the slope increases with increasing temperature, so this is reasonable to the Stokes-

Einstein equation. Both of them have a linear relationship.

6.2.1.2. 20:1 Sample (1/τ VS q2)

Use the same method in section 6.2.1.1 to calculate q, the q value is the same no matter what the

concentration is.

q2 1/τ

20℃ 30℃ 40℃ 50℃

45° 1.3078 9.8698 18.5313 29.1357 38.46

65° 2.1484 19.807 33.6946 48.9795 68.14

90° 2.6200 24.4 41.66 60.9525 82

Table 3. 1/τ and q2 for different angles and temperatures (20:1)

In this sample, the trend of 1/τ values under different angles is similar to that of 10:1 sample. Similarly, the slope can be obtained. 20℃ 30℃ 40℃ 50℃ Slope (D) 9.0595 15.61471 22.99468 31.22848 Table 4. Slopes at 20℃-50℃ (20:1)

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. In the 20:1 sample, the slope still increases with increasing temperature.

6.2.1.3. Comparison under Different Temperatures

By comparing the sample at 20℃ and 50℃, τ values decrease with increasing temperature (as in figure

22). For example, when the detector is in 45 degrees with respect to the axis of the laser beam source,

the 1/τ value increases from 14.1422 under 20℃ to 53.86 under 50℃ (as in table 1). Since the tau

value has the inverse relationship with the temperature, τ value decreases.

Temperature is a measure of the mean kinetic energy of molecules. When temperature increases, the

average kinetic energy of each particle inside the sample will also increase. They exhibit a positive

correlation in relationship. Moreover, with higher kinetic energy, the particles’ molecular velocity

becomes higher. Under this condition, the chance of one particle bombarding with another one is

higher and the time between two successful collisions is lower. Therefore, the relaxation time is lower

at higher temperature.

Figure 22. 1/τ vs q2 at 20℃-50℃ Figure 23. 1/τ vs q2 at 20℃-50℃

The trend of τ values under different temperatures in 20:1 sample is similar to that of 10:1 sample.

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Since the inverse of τ is calculated under each temperature and it increases with the increasing angle

of detector, the value of τ decreases with the increasing angle of detector. When the temperature is

40 degree Celsius, 1/τ increases from 36.2755 under 45 ° to 89.6346 under 90 ° (as in table 1). The tau

value decreases with increasing angle.

When θ increases, the sin(θ) and q values also increases. With the expressions Γ=1/τ and Γ=q2D

(Instruments, 2018), when q increases, the decay rate (Γ) increases. Owing to the fact that Γ is inversely

proportional to τ, so τ will decrease with increasing Γ.

The values obtained from table 1 are represented under each temperature,

Figure 24. 1/τ vs q2 at 20℃ (10:1) Figure 25. 1/τ vs q2 at 30℃ (10:1)

Figure 26. 1/τ vs q2 at 20℃ (20:1) Figure 27. 1/τ vs q2 at 30℃(20:1)

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. From figures 24-27, under the same temperature, it is observed that the τ behavior (decreases with

increasing angle) of 10:1 and 20:1 is similar.

6.2.1.4. Comparison under Different Concentrations

In the 20:1 sample, every 1/τ value under each temperature and angle is lower than that of the sample

10:1 when both values are under the same conditions. This represents that τ in 20:1 sample are higher

than that of the 10:1 sample generally. Also, the slopes of the 20:1 sample are much smaller than that

of the 10:1 sample.

For example, two samples of different concentrations can be compared under 30 degree Celsius. The

1/τ value of the 20:1 sample is lower than that of the 10:1 sample, which means that τ of 20:1 is larger

than that of 10:1.

Figure 28. 1/τ vs q2 at 30℃ (10:1 and 20:1)

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The slopes D obtained from sections 6.2.1.1 and 6.2.1.2 can be taken natural logarithm, and plot a

graph of lnD vs 1000/Temperature. The temperature scale should change from degree Celsius to

Kelvin. In this section, the graph of lnD against 1000/T is shown under different concentrations.

lnD T(K) 1000/T(K)

20℃ 2.388493 293 3.412969

30℃ 2.88048 303 3.30033

40℃ 3.50275 313 3.194888

50℃ 3.930074 323 3.095975

Table 5. lnD at 20℃-50℃ (10:1)

lnD T(K) 1000/T(K)

20℃ 2.203814 293 3.412969

30℃ 2.748213 303 3.30033

40℃ 3.135263 313 3.194888

50℃ 3.44133 323 3.095975

Table 6. lnD at 20℃-50℃ (20:1)

Similar trend is found under different concentrations (as in table 5 and 6). The value of lnD decreases

with decreasing temperature.

lnD and 1000/T is plotted in a graph with different concentrations (as in figure 29). Since the

temperatures used for the two samples are the same, so the values of 1000/T are the same. It is found

that 10:1 sample has a higher average value of lnD than that of 20:1.

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Figure 29. lnD vs 1000/T at 20℃-50℃ (10:1 and 20:1)

Besides, an important observation is shown. The dots in 10:1 sample are linear, which means the slope

is constant throughout different temperatures. In contrast, the values of lnD in 20:1 show a non-linear

relationship. The slope of 20:1 sample changes with different temperatures. The Arrhenius equation

and Vogel-Fulcher Tammann equation (Chen, Wong, Krishnan, Embs, & Chathoth, 2018) are used to

explain the discrepancy of the slopes of two samples.

6.2.2.1. Arrhenius Relation (10:1)

Figure 30. The linear fit of the curve under lnD versus 1000/T in 10:1 sample

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. The relationship between lnD and 1000/T can be found out by using the Arrhenius equation (Lagzi,

Mészáros, Gelybó, & Leelőssy, n.d.),

−퐸 1 푙푛(푘) = 푎 ( ) + 푙푛(퐴). 푅 푇

Equation 8. Arrhenius equation

From figure 30, the slope of 10:1 sample is obtained, and it is -4.966. The slope is negative since lnD

−퐸 values are decreasing. According to equation 8, 푎 is equal to -4.966 where R is the universal gas 푅

-1 -1 constant (8.3144598 JK mol ). As a result, 퐸푎 = -41.29 J which is the activation energy of the

particles.

6.2.2.2. Non-Arrhenius Relation (20:1)

Figure 31. The non-linear fit of the curve under lnD versus 1000/T in 20:1 sample

Equation 9 is used to explained the curve under 20:1 sample for its non-linearity.

퐷푓푇0 [− ] 푇−푇 퐷 = 퐷0푒 0

Equation 9. Vogel-Fulcher Tammann equation (Chen, Wong, Krishnan, Embs, & Chathoth, 2018)

with 퐷0 is the diffusion coefficient at infinite temperature; 퐷푓 is the fragility parameter, T is the

temperature, 푇0 is the ideal glass transition temperature (Sidebottom & Sorensen, 1989). The

variables in equation 9 are obtained from the table of figure 31. 34

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Equation 9 is taken natural logarithm, the equation becomes

퐷푓푇0 푙푛퐷 = 푙푛퐷0 − 푇 − 푇0 Equation 10. Natural log of equation 9

with lnD equals to y, 푙푛퐷0 equals to D, 퐷푓푇0 equals to B, 푇0 equals to T. Therefore, the

relationship is shown by 퐵 푦 = 퐷 + 푥 − 푇 Equation 11. Expression of Vogel-Fulcher-Tammann equation

From the table of figure 31, the values of D, B and T can be substituted into equation 11. Then we get

퐷푓푇0 = 3.251, T= 4.181, and 퐷푓 is 0.777. To compute 푇0, we calculate x by dividing 1000 by T.

Therefore, 푇0=239.1715 K.

6.2.2.3. Comparison in terms of Linearity

The value of 퐷푓 indicates that the 20:1 sample is highly fragile. Smaller value of fragility relates to a

more fragile liquid (Chen, Wong, Krishnan, Embs, & Chathoth, 2018). The experimental result (0.777)

is small enough to conclude that the 20:1 sample is a fragile liquid. In figure 31, theoretically, the

fragile 20:1 sample exhibits an exponential decay of α-relaxation process, which conforms to its non-

linearity. Refer to equation 7, D has an inverse relationship with 휂. At the glass transition temperature,

휂 increases drastically and D decreases exponentially. On the other hand, the 10:1 sample exhibits

linearity which indicates it is a strong liquid.

Aside from comparing the slopes of D and T, the fragility of samples can be tracked back from the

Linux working interface. Recall equation 4, one of the variables of KWW function is β and it is fixed

between 0 and 1. The β values require alteration until the line is well fitted according to the curve. A

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. smaller β value pinpoints a higher fragility, a greater β value pinpoints a lower fragility. Hence, the β

value used in 20:1 sample is smaller and the β value in 10:1 sample is higher, because 20:1 sample is

highly fragile at the glass-transition temperature. For example, under 40 and 50 degree Celsius, β value

of 20:1 is 0.7 and β value of 10:1 is 0.8 at 65 degrees of scattering angle.

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 7. Limitations

Although all experiments were carried out under vigilance, limitations exist in the following ways.

Temperature fluctuation: The thermostat of the spectrometer is not constant enough, it keeps

fluctuating within three degree Celsius and the scattering result could be affected by this.

Background interference: Background light can enter the setup even though it is covered by a large

black blanket. To add, any vibration on the setup table can affect the scattering result as well.

Sample preparation: Acetone is highly volatile and can react with air when it is inappropriately

handled, and the resulting concentration may be different.

Manmade error: There are some bias by our fitting technique which is used to determine whether the

solid line is fitted on the dots in Linux (KWW function). Thus, different handlers obtain different

results.

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In section 6.8, the limitations cannot be completely prevented, but there are certain actions can be

taken in order to improve the productivity.

 A constant temperature needs to be achieved before taking any measurement.

 To make sure the data collected is at constant temperature, wait until the temperature stops

fluctuating and is ready for measurement.

 Cover the DLS setup wholly to make sure no external light can enter the setup.

 Avoid the blanket from blocking the laser outlet.

 After the sample was mixed, we should close the lid as soon as possible in order to prevent

acetone from evaporating.

 The line fitting in Linux should be checked more frequently and we should ask the technician

for a second check.

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Other than the above actions, some general advice of performing the experiments are as follows.

 Wear safety goggles to prevent laser from entering our eyes.

 Wear protective gloves to prevent imprinting onto the sample bottle.

 Put the sample in the container before turning on the laser to avoid damage to the detector.

 The lid of the container should be closed tightly under high temperature to avoid explosion of

gas in the bottle.

 Clean the bottles with acetone and Kimwipes to prevent the dirt from scattering the light.

 The mixture should be transparent and does not absorb light with specific wavelengths.

 Two substances should not have any structural change after a long period of time.

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. 10. Conclusion

The molecular diffusive dynamics of glass-forming liquids (complex liquids) are difficult to

investigate. However, with proper techniques like the dynamic light scattering and X-ray diffraction,

we can deeply explore the mechanism of glass transition as well as the factors affecting the glass

transition.

By using Linux and Origin 8, the results obtained from DLS setup are plotted against various factors

such as concentration, temperature and scattering angle. During experimentation, two primary

relationships which are relaxation time (τ) VS wave vector (q) (Han, Akcasu, & A, 2011)and diffusion

coefficient (D) VS temperature (T), are analyzed. From the relationship of τ and q, τ values decrease

with increasing temperature and scattering angle. It has the similar trend for 10:1 and 20:1

concentrations. Generally, τ values of 20:1 is larger than that of 10:1 under different scattering angles.

Besides, the Arrhenius equation used is to explain the linear relationship of D and T in 10:1 sample,

thus, its activation energy is obtained. Since 20:1 sample is a fragile liquid, the relationship cannot be

explained by the Arrhenius equation, instead, the Vogel-Fulcher-Tammann equation is applied to

explain the non-linearity and derive its glass transition temperature. Additionally, the β values of

KWW function set in the Linux implicitly indicate the fragility of the two samples. The stretching

exponent (β) of 20:1 should be smaller than that of 10:1 as 20:1 is highly fragile while 10:1 is a strong

liquid.

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This document is downloaded from Outstanding Academic Papers by Students (OAPS), Run Run Shaw Library, City University of Hong Kong. References

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