Self-Assembly and Electrical Conductivity of Colloids

University of Uppsala

Self-Assembly and Electrical Conductivity of Colloids

Supervisor:

Dr. Max Wolff Apurve Saini

Author:

Pier Silvio Tibaldi

September 2, 2015

Contents

1 Introduction 3

2 Theory 3

2.1 Dipoles . . . . 3

2.2 Superparamagnetism . . . . 4

2.3 Susceptibility . . . . 4

3 Experiment 5 3.1 Sample . . . . 5

3.2 Setup . . . . 5

3.2.1 Microscope cell . . . . 5

3.2.2 Conductivity cell . . . . 6

4 Results 7 4.1 Electric Potential . . . . 7

4.2 DC Magnetic Fields . . . . 11

4.3 AC Magnetic Field . . . . 15

5 Discussion 17 5.1 Breakdown . . . . 17

5.2 Magnetic Field Strength Effect . . . . 17

5.3 Memory Effect . . . . 18

6 Conclusions 18

Abstract

Self-assembly is an astonishing phenomenon at the base of organized structures’ formation from disordered systems. It occurs in nature from atomic and molecular lengths to galactic distances. Nowadays self-assembly of colloidal solutions can be used to fabricate photonic crystals and meta- materials.

This paper analyses the self-assembly and its effect on the electric conduc-

tivity of a colloid made up of carbon nanotubes and magnetite microparti-

cles controlled by electrostatic potentials and magnetic fields. Alignment

of the carbon nanotubes and creation of sparks and short-circuits are ob-

served when the electrostatic field is applied. The magnetic field induces

time-dependent and memory effects in the sample’s structure and con-

ductivity. At constant potential, the electric current through the sample

is reported to increase four times during and after the application of the

magnetic fields.

1 Introduction

Nanomaterials have fascinating properties that have been explored since the an- cient times in art and manufacturing. The Lycurgus Cup from the 4th century, and the stained glasses of medieval cathedrals are notable examples of brilliant colours arising from noble metal nanoparticles dispersed in the glass material.

Colloids are nanomaterials composed of micrometric and nanometric scale in- soluble particles suspended in a liquid matrix.

Novel applications include fabrication of metamaterials and photonic crystals exploiting the self-assembly properties of metallic colloids[1] [2].

In this paper the self-assembly capabilities and the changes in electrical conduc- tivity of a colloidal solution composed of iron-oxide microparticles and multi- walled carbon nanotubes (MWNT) are investigated with electric potential and magnetic fields.

Microscopy observations show the nanotubes arranging in chains perpendicular to the electrodes when subjected to electrical potential, increasing the conduc- tivity as a result.

The magnetic field can enhance the self-assembly process and the conductivity, or break the chains, depending on the field strength and the timescale. Its effect is studied through the changes in conductivity of the sample.

2 Theory

2.1 Dipoles

Conducting particles placed in an electric field become polarized due to charge separation and acquire a dipole moment.

The interaction energy between two dipoles of moment p which make angles θ

and θ

with the vector r that connects them and whose planes intersect along r at an angle ψ, as seen in figure (1), is given by[3]:

W = p

4πr

(sinθ

sinθ

cosψ − 2cosθ

cosθ

)

Figure 1: Geometry of two interacting dipoles of moment p.

2.2 Superparamagnetism

Materials can be classified depending on their magnetic properties, such as susceptibility and coercivity. For example ferromagnetic materials in an external magnetic field present a strong magnetization that, due to high coercivity, is maintained when the external field is removed. Paramagnetic materials also form induced magnetic moments, but they are weaker and not retained when the external field is removed.

This macroscopic magnetic behavior relies on domains. The magnetic moments of atoms or molecules within a certain domain are directed in the same direction.

Ferromagnetic materials have aligned domains producing a strong macroscopic field, while in paramagnetic materials without an external magnetic field the domains are not aligned and the resulting field is small.

Tiny magnetite particles in a colloid, depending on the dimension, have only one or few domains each. The thermal energy is comparable with the energy for spins to flip directions, hence the magnetic dipoles become randomized in a short period of time when the external magnetic field is turned off. This property is called superparamagnetism: Micrometer-sized magnetite particles respond strongly to an external magnetic field but they have low coercivity and do not retain a magnetic moment in absence of external fields [4].

2.3 Susceptibility

A ferrofluid is a colloidal system composed by superparamagnetic nanoparticles that alter the susceptibility of the liquid [5] yielding to a superparamagnetic substance.

If particles with micrometric size are suspended in the ferrofluid their effective

susceptibility changes with the susceptibility of the ferrofluid. Analogously to

the Archimedes principle for the weight of a body immersed in a fluid, the

effective susceptibility of particles can be turned from negative to positive values

acting on the ferrofluid in which they are suspended. Initially nonmagnetic

particles can therefore behave magnetically or anti-magnetically. The effective

susceptibility for spherical particles in a ferrofluid is

χ e

= 3 χ

− χ

χ

+ 2χ

+ 3

where χ

is the particle susceptibility and χ

is the ferrofluid susceptibility [6].

3 Experiment

3.1 Sample

The sample is a colloidal solution with mineral oil as liquid carrier. Multi-walled carbon nanotubes (MWNT) and magnetite particles are dispersed in the oil and stay suspended due to the Brownian motion [7][8].

The electrically conductive MWNT adopted were purchased from Us Research Nanomaterials. They have a nominal diameter of 10-20 nm and length of 30-100 µm.

The magnetite particles (F e

O

) have a diameter of 10 µm.

The solution is composed of 2.3 % of MWNT and 42.5 % of magnetite mi- croparticles by mass in mineral oil. It proved to be durable, maintaining the same properties after more than ten days of usage.

3.2 Setup

Two setups are employed for the study. One is used for transmission optical microscopy observations and the other for systematic measurements of conduc- tivity in the presence of electrical potentials and magnetic fields.

3.2.1 Microscope cell

A glass plate with two electrodes made of pieces of aluminium foil constitutes the thin and transparent cell used for microscopy.

The aluminium electrodes are at a distance of 1 mm from each other. The

solution is placed in the space in between the electrodes, dipping both of them,

and a cover glass is positioned on top. A clean cell and a cell with freshly

deposited solution are shown in figure (2).

(a) Clean cell with power supply cables

(b) Cell with solution and cover glass

Figure 2

3.2.2 Conductivity cell

The cell used to perform conductivity measurements is made of round gold elec-

trodes, 10 mm in diameter, kept at distances of 1 or 2 mm from each other and

sealed with O-rings, as seen in figure (3).

Figure 3: Sealable cell.

The cell is placed between electromagnets that can produce constant mag- netic fields up to 160 mT or alternate fields at tunable frequencies (fig. 4).

Figure 4: Cell between electromagnets.

4 Results

4.1 Electric Potential

The electrodes in both the conductivity cell and in the microscopy cell are put at a distance of 1 mm from each other to perform conductivity measurements without magnetic fields. The voltage is increased manually from 0 V and a breakdown usually occurs between 15 V and 25 V.

As seen in figure (5) before the critical value, in this case 20.7 V, the current

through the sample increases exponentially versus voltage from tens of thousand

Ohms to 2 KΩ. At the breakdown point the current increases sharply, the re-

sistance becoming few Ohms. The current through the system is then regulated

by the current limiter in the power supply, set at 2 A, and therefore the voltage drops down.

Figure 5: Logarithmic plot of current versus voltage through the solution between electrodes at a distance of 1 mm. The voltage is manually increased up to the breakdown (red mark), then the current sharply increases and the voltage drops down due to a limitation in the power supply (green mark).

Microscopy observations show the particles moving and clustering together

when the breaking point is approached. The sample when no voltage is applied

can be seen in figure (6a), and figure (6b) depicts the same solution just before

reaching the breaking point.

(a) Solution without electrical potential

(b) Clustered particles approaching the breaking voltage

Figure 6

When the breaking point is reached one channel appears and conducts cur-

rent. Due to high density of current it heats up and emits light becoming easily

identifiable. Figure (7) depicts a microscopic picture of the electrodes and the

channel formed between them.

Figure 7: Aligned channel of carbon nanotubes heated up at the breaking point between the electrodes.

The glow produced by the channel is intense enough to be seen by the naked eye (8).

Figure 8: Picture of the inflamed channel.

The heat provoked by the current causes the oil to evaporate drying the solution in tenths of a second.

A consequence of the heat can be seen in the glass substrate that is cracked

where the channel has formed, figure (9).

Figure 9: Crack in the glass substrate consequent to channel formation.

4.2 DC Magnetic Fields

An increased distance between the electrodes form 1 to 2 mm keeps the system in the region below the breaking point and maintain the sample in a colloidal state for voltage values up to 30 V.

To ensure stability of the sample during measurements, the solution is prepared and sealed in the cell days in advance. The cell is put at an electrical potential of 20 V for two hours before applying magnetic fields. As a result, the current flowing through the sample, that increases with logarithmic trend when the potential is applied, reaches an equilibrium.

Pulses of magnetic field are applied for tens of seconds each to the sample, that is kept at a constant electrical potential of 20 V.

The conductivity sharply decreases when the magnetic field is turned on or off.

However, in the long run, the current increases logarithmically with time when

the magnetic field is on, and increases also with the number of times it has been

switched on. Plots of the current versus time with the relative magnetic field

are shown in figure (10).

(a)

(b)

Figure 10: Current versus time at voltage of 20 V with magnetic field pulses.

The current intensity versus time for every magnetic pulse can be fitted to a logarithmic curve:

I = I

+ γ ∗ Ln(T ime) (1) The acquired values of current versus time during one magnetic pulse, and the curve fitted to the data can be seen in figure (11).

Figure 11: Experimental data and fitted curve of electric current versus time with a magnetic field of 120 mT and a potential of 20 V. In this case I

= 4.8mA and the parameter γ is 0.2

The offset parameter in equation [1] has a proportionality to the square root of the number of iterations (i.e. the number of times the magnetic field has been switched on and off):

I

= 2.96 + iterations

The offset parameter versus the number of iterations is plotted in figure (12).

Figure 12: Current offsets versus number of times the magnetic field has been switched on.

Similarly, data from pulses of different strengths of magnetic field, ranging from 10 mT to 160 mT, shows a dependence of the coefficients γ in equation [1]

upon the field strength:

γ = −1.07 + (F

)

The coefficient γ is plotted in figure (13) versus the magnetic field strength.

Figure 13: Curves’ coefficients γ versus magnetic field strength.

4.3 AC Magnetic Field

The electromagnnets can be powered with an alternating current to generate an alternate magnetic field. A square waveform is used for the current and the field intensity is 80 mT.

Figure (14) depicts the plot of electric current versus time. Every peak cor-

responds to the application of an alternate magnetic field. The magnification

of the peak corresponding to a 2.0 Hz alternating magnetic field and the fit to

equation 1 can be seen in figure (15).

Figure 14: Current versus time at 20 V when pulses of alternate magnetic fields are applied (red rectangles). From the left the frequencies are: 1.0 Hz; 1.5 Hz;

2.0 Hz; 4.0 Hz; 8.1 Hz; 1.0 Hz; 0.2 Hz; 1.0 Hz.

Figure 15: Magnification of the peak relative to 2.0 Hz magnetic field. The parameter γ of the fitting curve is 1.0

Similarly to the case of constant field, the peaks can be fitted to the loga- rithmic curve [1]. The coefficients of the logarithms are not dependent on the frequency of the field in the range between 1 and 8 Hz, but in the last peak the system is approaching a top value of conductivity.

These coefficients are two to three times greater than the values obtained for constant fields of the same strength.

5 Discussion

5.1 Breakdown

The clustering of the carbon nanotubes under an electric potential and the channel formation at the breakdown voltage are self-assembly effects produced by dipole-dipole interaction of nanotubes. The field polarizes the nanotubes that consequently align and dispose themselves in chains perpendicular to the electrodes, improving the conductivity. The breakdown is the ultimate result of this process, with one chain becoming dominant on the others in conducting current, causing a short circuit.

5.2 Magnetic Field Strength Effect

The magnetic field acts on the ferrofluid shaking the sample when applied. It

therefore breaks some of the carbon nanotubes chains formed by the electrical

potential, reducing the conductivity for a short transient. The strength of the magnetic field is at the base of the shaking intensity and the probability to brake chains, hence it drives the drop in current.

Moreover the magnetization of the magnetite particles can affect the effective susceptibility of the carbon nanotubes. Although the knowledge of this process needs to be deepened for the case in which the non-magnetic particles have size comparable to the superparamagnetic ones, an effective ant-magnetic behaviour is supposed to be at the base of the fast increase in conductivity when the magnetic field is applied. The carbon nanotubes would respond to the field acting as both electric and magnetic dipoles. The result is a speed-up in the formation of the chains that conduct current.

5.3 Memory Effect

The magnetic field plays a role in making new carbon nanotubes channels be- tween the electrodes. Successive applications of constant magnetic fields to the sample result in an increase in conductivity, that is maintained when the magnetic fields are switched off. The increase is up to 150 % compared to the maximum conductivity obtainable with only electrical potential.

This effect can be a consequence of the chain breaking due to the magnetic field:

The pieces of broken chains, each of them composed of many nanotubes, have a greater electric dipole moment than single nanotubes. Hence, they can reassem- ble faster and more efficiently under the combination of electric and magnetic potentials, making a larger number of channels. This logarithmically increases the conductivity of the solution.

This effect is even more remarkable for alternate magnetic fields, corresponding to multiple switches that shake the sample, with the current increasing three to four fold, as can be seen comparing the γ parameters of the fitting curves in figures (11) and (15).

6 Conclusions

In the present paper the behaviour of a colloidal system of conductive carbon nanotubes and magnetic iron oxide particles, in magnetic fields and electrical potentials, is described. By applying an electrical potential the nanotubes are lead to self-assembly in chains that eventually form conductive channels between the electrodes. This produces a logarithmic increase in the conductivity of the sample.

Furthermore the state of the sample can be controlled by the magnetic fields through two distinct and counterpoised effects: The breakage of some of the channels and the enhanced creation of new ones. The former prevails in a short transient after the application of the field. The latter can cause the conductivity to increase four times in the long term and is persisting after the magnetic field is shut down, generating a memory effect.

The connection between chain frustration by the magnetic field and the the

memory effect could be examined in future studies.

Beside the ability of tuning electrical currents, the study of self-assembly capa- bilities of colloids and their manipulation can result in advancements in fabri- cation processes of photonic crystals and metamaterials, and possibly leading to materials with attractive novel properties [9].

References

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[2] J.A.Fan et al., “Self-assembled plasmonic nanoparticle clusters,” Science, 2010.

[3] G. Dwight, ed., American Institute of Physics Handbook. McGraw-Hill, 1957.

[4] U.Jeong et al., “Superparamagnetic colloids: Controlled synthesis and niche applications,” Advanced Materials, 2007.

[5] P. Stephen, “Low viscosity magnetic fluid obtained by the colloidal suspen- sion of magnetic particles,” Nov. 2 1965. US Patent 3,215,572.

[6] H.Carstensen et al., “Phase formation in colloidal systems with tunable in- teraction,” Physical Review E, 2015.

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