Experiment No.1: Ellipsometry Room No.: 145 (Colloids and ... · The polarization change is...

CL 610 – Experimental Methods

Experiment No.1: Ellipsometry

Room No.: 145 (Colloids and Nanomaterials Lab)

Lab Manual

Department of Chemical Engineering,

Indian Institute of Technology, Bombay

Thin film formation by spin coating and thickness measurement by

Ellipsometry

Objective

To make a thin-film of polymer by spin coating and measure thickness of the polymer thin film

by Ellipsometry.

Introduction

Optical measurement techniques are normally non-invasive. These techniques do not involve any

physical contact with the surface and do not destruct the surface. This is a lucrative property of a

measurement technique on nano-scale. Several optical measurement techniques based on the

reflection or transmissions of light from a surface are interferometry, reflectometry and

ellipsometry. There are three different types of ellipsometry, namely scattering, transmission and

reflection ellipsometry. This experiment deals with the reflection ellipsometry only. One of the

applications is in the semiconductor industry, which deals with a thin layer of SiO2 on a silicon

wafer. To ensure the thickness of this film, process engineers use ellipsometry to measure the

film thickness of sample wafers. Ellipsometry is known for the high accuracy when measuring

very thin film, with a thickness in the Angström scale or below. Other applications of

ellipsometry involve determination of the refractive index, the surface roughness or the

uniformity of a sample and more.

Theory

a) Spin coating

Spin coating is one of the standard methods for obtaining uniformly thick dielectric films.

The substrate on which the desired material is to be coated is mounted on the spin coater and

held by vacuum. The polymer dissolved in a suitable volatile solvent or synthesized in solution is

poured on the substrate and it is spun at high speeds of the order of few thousand rpm. Clearly

the film thickness will increase with the increase in concentration in solution and will reduce

with the increase in spin speed. But other factors like viscosity, volatility of the solvent used,

humidity of the environment, etc. also matter [1, 3].

The mechanism of film formation can be split into 2 stages. The first stage involves the

interplay between the centrifugal and viscous forces followed by evaporation. Meyerhofer (1978)

predicted the final thickness, hf in terms several solution parameters [1, 3] as given by the

following equation:

13

2(1 )

f

eh x

x K

Where e and K are the evaporation and flow constants defined below and x is the effective solid

constant of the solution.

2

3

e C

K

Where ω is the rotation rate, ρ is the density of the solution, η is its viscosity and C is

a proportionality constant that depends on whether airflow above the surface is laminar or

turbulent and on the diffusivity of the solvent molecules in air.

Substituting e and K in the equation for hf [1, 3, 6] we can see that the thickness varies linearly

as the inverse square root of spinning speed, when other parameters remain the same.

This is the relationship which we will verify experimentally.

tconsh f

tan

b) Ellipsometry

Ellipsometry is primarily used to determine film thickness and optical constants. However, it is

also applied to characterize composition, crystallinity, roughness, doping concentration, and

other material properties associated with a change in optical response.

Light can be represented as a transverse electromagnetic wave made up of mutually

perpendicular, fluctuating electric and magnetic fields. The left side of the following diagram

shows the electric field in the xy plane, the magnetic field in the xz plane and the propagation of

the wave in the x direction. The right half shows a line tracing out the electric field vector as it

propagates. Traditionally, only the electric field vector is dealt with because the magnetic field

component is essentially the same.

Light in the form of a plane wave in space is said to be linearly polarized. If light is composed of

two plane waves of equal amplitude by differing in phase by 90°, then the light is said to be

circularly polarized. If two plane waves of differing amplitude are related in phase by 90°, or if

the relative phase is other than 90° then the light is said to be elliptically polarized.

The polarization change is represented as an amplitude ratio, Ψ, and the phase difference, Δ [2].

The measured response depends on optical properties and thickness of individual materials.

Ellipsometry measures the interaction between light and material.

When light enters a different medium the dielectric constant of the medium changes the

electrical field strength. As light is electromagnetic wave, in a different dielectric medium, it

changes it’s velocity for which it changes its trajectory and wavelength. When a polarized light

beam falls at the interface of two dielectric media, its electric vector can be separated into two

orthogonal components parallel and perpendicular to the plane of incidence (p and s components

respectively). When these components traverse through the medium and undergo reflection and

refraction, there is a change in the polarization of the light which is a function of amplitude ratio

and phase difference of these components. The change in polarization is the ellipsometry

measurement, commonly written as:

tan exp(i ) p

s

R

R

Where tanp

s

R

R

which again can be derived from Maxwell’s theory as a function of total

reflectance R, refractive index, incident angle, wavelength of the incident light and thickness of

the film. Out of these parameters except the thickness other parameters are constant for a given

system, thus calculable (or can be found in literature).

For a transparent film the Cauchy relationship [2] is typically given as:

2 4( )

B Cn A

Where, the three terms are adjusted to match the refractive index for the material.

So in the model the only unknown variable remains, is thickness for the film, as the total

reflectance is also a function of refractive index and incident angle.

The Ellipsometer experimentally measures the amplitude ratio vs. wavelength of light and phase

difference vs. wavelength of light which is the fitted with the theoretically obtained amplitude

ratio vs. wavelength of light and phase difference vs. wavelength of light, having the fitting

parameters A, B, C (Cauchy parameters) and hf. These parameters are fitted to obtain the film

thickness.

A known polarization is reflected or transmitted from the sample and the output polarization is

measured. A sample ellipsometry measurement is shown in Figure 1. The incident light is linear

with both p- and s- components. The reflected light has undergone amplitude and phase changes

for both p- and s- polarized light, and ellipsometry measures their changes.

In ellipsometry a circularly polarized light is made incident on the substrate. A part of this

incident light gets reflected and a part refracted at the interference.If n1 and n2 be the refractive

index of two media and if 1 and 2 be the angle of incidence and refraction in the

two media respectively from Snell’s law:

Instruments Used:

1. Ultra-Sonicator

2. Spin Coater

3. Ellipsometer

Figure 1 Typical ellipsometry configuration, where linearly polarized light is reflected from the

sample surface and the polarization change is measured to determine the sample response

1n sin 1 = 2n sin 2

Chemicals Used:

1. Polystyrene solution

2. Silicon wafer

3. Toluene

4. Milli-Q-water

Procedure:

1. Polystyrene solution with toluene is prepared

2. Silicon wafer is mounted on the chuck of spin coater and vacuum is on to keep the

sample in place

3. Sample is placed on the wafer and rotational speed is set in a desired value.

4. Wafer is taken out and thickness is measured in Ellipsometer

5. Thickness measuring software is initialized and then sample is loaded.

6. Then beam alignment is done and then data is taken. Depolarisation is also measured.

7. Once data is collected from spectroscopic scan, data is fitted with Cauchy model. Fitting

is continued till the MSE is less than 20%. To reduce the MSE, higher order terms in

Cauchy equation is taken into account.

8. If there is depolarisation in sample, data collected in that range (wave length range) is

removed and rest of the data are fitted with theoretical model.

References:

1. David B. Hall, Patrick Underhill and John M. Torkelson,’ Spin Coating of Thin and

Ultrathin Polymer Films’, Polymer engineering and Science, December 1998, Vol. 38,

No. 12

2. http://www.jawoollam.com/tutorial_1.html

3. Niranjan Sahu, B Parija, and S Panigrahi, ‘Fundamental understanding and modeling of

spin coating process’, Indian J.Physics, 83(4) 493-502 (2009)

4. A G Emsile, F T Bonner and L G Peek J. Appl. Phys. 29 858 (1958)

5. C J Lawrence and W Zhou Journal of Non-Newtonian Fluid Mechanics 39137 (1991)

6. http://www.cise.columbia.edu/clean/process/spintheory.pdf

http://www.jawoollam.com/tutorial_1.html


Experiment No. 2: Karl Fischer

Room No.: 227 (Organic Processing Lab)

Lab Manual



Measurement of percentage moisture using Karl Fischer volumetric titration in a sample of unknown moisture content

Aim:

Determine the percent moisture in Potassium Chloride and Glycerol samples using Karl Fischer

volumetric titration.

Introduction:

Pioneered by a German chemist, Karl Fischer titration has achieved to be established as the most

important method for determining water and humidity. With the KF titration both free and bound

water can be determined, e.g. surface water on crystals or the water contained inside them. The

method works over a wide concentration range from ppm up to 100% and supplies reproducible

and correct results. Karl Fischer titration is used in determining the water in diesel fuel and

gasoline, silicone oil, liquid ammonia etc. and for the analysis of edible fats and oils.

Apparatus and Instrument: The experiment is performed in organic process lab.

Glassware – Beakers, Titration flask with magnetic stirrer

Karl Fischer Titrator, Weighing balance

Chemicals:

Karl Fischer reagent,

Karl Fischer grade dry methanol

Di-sodium tartrate dihydrate (purified)

Samples (KCl and Glycerol)

Principle:

When developing his new analytical method Karl Fischer took into account the well known

Bunsen reaction, which is used for the determination of sulfur dioxide in aqueous solutions:

SO2 + I2 + 2 H2O → H2SO4 + 2 HI

To determine the titer of Karl Fischer reagent which is measured as mg of water per ml (mg

H2O/ml of KF reagent) of Karl Fischer reagent. In Karl Fischer volumetric titration, iodine is

added to solvent containing the sample by a burette. Moisture is calculated on the basis of the

volume of Karl Fischer reagent consumed.

Volumetric titration is recommended for determination of water content in the range of 0.1% to

100%.

Volumetric Karl-Fischer titration:

The volumetric Karl Fischer titration is based on the stoichiometric principle that 1 mole of

iodine reacts with 1 mole of water. Water and iodine are consumed in 1:1 ratio in the following

reaction

I2+ SO2 + H2O + 3Base + CH3OH → 2Base HI + Base HSO4CH3

When all the moisture present is consumed the excess iodine present is detected

voltammetrically by the titrator electrode. The system controls the current voltage detection. A

constant current of 1-30µA is applied to the two platinum electrodes. If the titration solution has

a high moisture, a polarization voltage of 300-500mV will be produced. As the titration

continues and the end point is near, the voltage suddenly drops to 10-50 mV. In volumetric

analysis the endpoint is considered to have reached after the voltage has remained at this level

for a specific period of time. In commercial titration systems, this period is 30-60 seconds.

The moisture present in the sample is then calculated on the basis of concentration of iodine in

Karl Fischer reagent and the amount of Karl Fischer reagent consumed in the titration.

Procedure:-

1. Put 50 ml KF-grade methanol in the flask which has been well dried in hot air oven

overnight.

2. Fill the desiccant tubes with silica gel and molecular sieves and place at the appropriate

positions on the titration flask.

3. Place KF dispenser and platinum electrode opposite to one another at the titration flask.

4. Carry out a neutralization step to remove all the moisture that may have been added along

with the solvent.

5. Standardization: Add a fixed amount of Millipore water into the flask to know the

concentration factor of KF reagent. The amount of water should be 25 mg to 250mg.

6. Add KCl sample containing unknown amount of moisture in the flask and titrated. The

endpoint reaches when the voltage remains at 10-20 mV for some time.

7. Repeat the titrations for each sample thrice and note the amount.

8. Wait till the end point is detected electrically by the system and titration stops.

9. Note the volume of KF reagent consumed and moisture percentage.

10. Repeat the above steps to determine the moisture of anhydrous Glycerol sample.

11. Repeat the above steps for determination of moisture with hydrated samples of KCl and

Glycerol.

12. Calculate the moisture content using the concentration factor noted by standardization.

Calculation:

Concentration factor = S

Leak rate = L

Weight of Millipore water

Used in standardization = W

Blank volume = B

The percentage of moisture can also be calculated from the given formulae

where S = Strength of KF reagent(mg/ml)

W = Weight of Sample (mg)

KF = Volume of KF consumed during titration (ml)

B = Blank volume entered(ml)

L = Leak Rate (µl/min)

Table 1 Format of observation table :

S.No Weight

of

sample

W(mg)

Volume of

KF

reagent(ml)

% moisture

(from

instrument)

%

(moisture

from

calculation)

% error in

calculation

Coefficient

of

variation

1

2

3

Sources of error:

1. For very low moisture content the low sample quantity the burette resolution is not

suitable to reproduce the results.

2. Potassium Chloride which has low solubility in methanol which is used as solvent in

this method cannot dissolve the consecutive samples, and hence calculates low

moisture.

References:

1. Eugen Scholz Reagents for Karl Fischer Titration,

Sigma-Aldrich/Riedel-de-Haën,2001

2. Peter Bruttel, Regina Schlink, Water Determination by Karl Fischer Titration


Experiment No. 3: High Performance Thin Layer Chromatography


Lab Manual



2

High Performance Thin Layer Chromatography

3.1. Aim: To measure the unknown concentration of Benzophenone and Benzhydrol in a

mixture.

3.2. Introduction

Chromatography is a technique which is mostly used for separating and identifying compounds

in a mixture. It is a very useful technique in industry where it is used for large scale separation

and purification of various products and intermediates in a chemical reaction.

All chromatographic techniques require a stationary phase and a mobile phase. The separation of

components in chromatography is based on the differential adsorption of components onto the

stationary phase or the mobile phase. There are several different types of chromatography which

are used – i.e. paper chromatography; high performance thin layer chromatography (HPTLC);

gas chromatography (GC); liquid chromatography (LC); high performance liquid

chromatography (HPLC); ion exchange chromatography; and gel permeation or gel filtration

chromatography.

Thin Layer Chromatography (TLC) is an extremely useful technique for monitoring reactions,

identify compounds given in a mixture and determine the purity of a substance. High

Performance Thin Layer Chromatography (HPTLC) is an enhanced form of thin layer

chromatography (TLC). A number of enhancements can be made to the basic method of thin

layer chromatography to automate different steps, to increase the resolution achieved and to

allow more accurate quantitative measurements. Automation allows overcoming the uncertainty

in droplet size and position when the sample is applied to the TLC plate by hand.

3

3.3. Theory

3.3.1. Stationary phase:

TLC uses a stationary phase, usually alumina or silica supported on an inert base such as glass,

aluminum foil or insoluble plastic. The mixture to be separated is ‘spotted’ at the bottom of the

TLC plate and allowed to dry. The plate is placed in a closed vessel containing solvent (the

mobile phase) so that the liquid level is below the spot.

3.3.2. Mobile phase:

The mobile phase is a solvent whose polarity is chosen according to the requirements. The

solvent ascends the plate by capillary action, the liquid filling the spaces between the solid

particles. This technique is usually done in a closed vessel to ensure that the atmosphere is

saturated with solvent vapour and that evaporation from the plate is minimised before the run is

complete. The plate is removed when the solvent front approaches the top of the plate and the

position of the solvent front recorded before it is dried (this allows the Rf value to be calculated).

3.3.3. Principle of separation:

In chromatography, the components of a mixture get differentially partitioned between the

stationary phase and the mobile phase depending on their interaction with the adsorbent. This

results in differential rates of migration of various components in a mixture. At any given time, a

particular analyte molecule is either in the mobile phase, moving along at its velocity, or in the

stationary phase and not moving at all in the downstream direction. The sorption–desorption

process occurs many times as the molecule moves through the bed. The ratio of the equilibrium

concentration of an analyte in the stationary phase to that in the mobile phase is called the

distribution constant or the partition co-efficient: Ka.

Ka = Cs/Cm

Where Cs is the equilibrium concentration of the analyte in the stationary phase and Cm is the

equilibrium concentration of the analyte in the mobile phase. As the chromatography proceeds,

it partitions itself between the two phases depending on its distribution constant. A lower

partition co-efficient means that the analyte will migrate faster and spend less time in the

stationary phase.

4

In case of TLC, the position of a spot is characterized by its retention factor (Rf). Rf is defined as

the ratio of the distance travelled by the analyte to the distance travelled by the solvent front.

The Rf value of a component is a constant for a particular solvent system and changes with the

solvent system. Thus it is important to choose a solvent system where the Rf values of individual

components in a mixture are sufficiently different so that the components have different

migration velocities.

Further, the composition of the solvent phase can also be tweaked in order to bring the the Rf to

a more desirable range. If Rf values on silica coated plates are higher than desired, the polarity of

the mobile phase is reduced. For Rf values that are too low, the polar component of the mobile

phase is increased.

In this experiment, the separation of the components is based on the polarity of the components

in the mixture. Due to difference in the polarities, different compounds will travel different

distances up the plate. More polar compounds will be retained in the polar silica stationary phase

and travel a shorter distance on the plate. Non-polar substances will have a higher affinity for the

mobile phase and thus travel a larger distance on the plate.

5

3.3.4. Description of the apparatus:

The HPTLC apparatus consists of two different equipments: a sample applicator and a TLC plate

UV scanner.

The sample applicator is connected to a nitrogen cylinder which nebulizes the sample just before

it is spotted. The syringe containing the sample is attached to the applicator and the appropriate

volume is spotted onto the TLC place. This entire step is fully automated. After the sample is

spotted, the TLC plate is placed on a developing chamber.

The UV scanner is used for visualizing and measuring the intensity of spots on the TLC plate

based on which a chromatogram is generated.

TLC Applicator Solvent chamber

TLC plate UV scanner

6

3.3.5. Apparatus used: TLC Plate, Applicator, Glass developing chamber, TLC UV Scanner,

Syringe, Beakers, Measuring cylinder, Sample bottles.

3.3.6. Chemicals used: Benzophenone, Benzhydrol, Methanol, Hexane, Toluene.

3.4. Experimental Procedure:

1. Two standard solutions of 150 ppm Benzophenone and 2500 ppm Benzhydrol each was

prepared in 5ml of methanol.

2. Mixtures of Benzophenone and Benzhydrol in unknown proportions were also prepared.

3. 30ml of developing solvent containing Hexane-Toluene in a ratio of 30:70 was prepared

and poured in the developing chamber.

4. The HPTLC instrument (applicator) was started and various parameters like Plate width,

Band width, Band pitch and start position were set. Based on these parameters the

number of tracks available on the TLC plate was calculated to be 13.

5. In the first five tracks, bands of pure Benzophenone solution, in the middle five tracks,

bands of pure Benzhydrol solution and in the last three tracks, bands of unknown samples

were loaded by entering different volumes of the samples in each track.

6. After applying the samples, the TLC plate was kept in the developing chamber containing

the solvent. The plate was removed when the solvent had covered 75% of the plate and

was dried with the help of a dryer.

7. The TLC plate was placed under a UV lamp for identification of the bands after they had

migrated.

8. The plate was then analyzed by using the TLC scanner in order to obtain the

chromatograms using the CAMAG software at 254nm wavelength. Each track was

separately analyzed and depending on the number of components present they showed

one or two peaks. By using the integration option the areas under the peaks were

obtained.

3.4.1. Preparation of standard solutions of Benzophenone and Benzhydrol:

5.94 mg of Benzophenone was dissolved in 50 ml of Methanol (density: 0.791 g/cc) to give a

solution of 150 ppm. 98.99 mg of Benzhydrol was dissolved in 50 ml of Methanol (density:

0.791 g/cc) to give a solution on 2500 ppm.

7

3.4.2. Parameters entered:

Plate width = 200 mm

Space between bands = 10 mm

Band width = 4 mm

Observations:

Start position = 10 mm

3.6. Calculations:

Determine the calibration factors for Benzophenone and Benzhydrol.

Report the unknown concentrations of these two in a mixture from the above plots (in

ppm).

Questions

1) Two compounds A and B were analysed using HPTLC and the following chromatogram

was obtained :

Peak Intensity (AU)

Distance migrated (mm)

8

What parameters will you modify so as to get two distinct peaks in the chromatogram and a

merged peak?

2) You have a mixture of 3 compounds A, B and C. The Rf values of the compounds in different

solvent systems are given below:

Compound Name Solvent systems Hexane – Toluene

(Rf) Hexane – Water

(Rf) Hexane – Acetonitrile

(Rf) A 0.30 1 0.25 B 0.25 0.90 0.65 C 0.31 0.95 0.89

Which solvent system would you choose for separating the compounds? Give reasons.

3) A polar compound – X, when analysed on a TLC plate coated with silica using a solvent

system of Hexane and Toluene in a ratio of 3:10 gave a Rf value of 1. What modifications do you

suggest to decrease the Rf value using the same solvents Hexane and Toluene?

4) The minimum detection limit (MDL) of compounds A and B using HPTLC when scanned

using a UV scanner is 0.15 ug and 3.5 ug respectively. Which property of the compound would

determine the MDL? Explain w.r.t. the compounds A and B.

5) Given below is a chromatogram when Benzophenone and Benzhydrol is analysed using

HPTLC and scanned under a UV detector. Silica was used as the stationary phase while

Peak Intensity (AU)

Distance migrated (mm)

Benzhydrol

Benzophenone

9

Ethanol is now added to the mixture of Benzophenone and Benzhydrol. Assuming that ethanol

does not interact with either BP or BH, where would you expect to find the peak of ethanol when

the TLC place is scanned under a UV detector? Give reasons for your answer.

6) A student spots an unknown sample on a TLC plate. After developing in hexanes/ethyl acetate

50:50, he/she saw a single spot with an Rf of 0.55. Does this indicate that the unknown material

is a pure compound? Give reasons for your answer.


Experiment No. 4: Rheometry

Lab Name: Fluid Mechanics Lab

Lab Manual



CL- 610 Experimental Methods

Experiment 4: Rheometer 2

4.1 Objective

To measure the viscosity of suspended silica particles and study the behaviour of the sample’s

relative viscosity as linear (Einstein equation) with volume fraction of suspended solids using

rheometer

4.2 Introduction

Rheology is the science of deformation and flow of matter under controlled testing

conditions. Flow and deformation are interdependent to each other. Rheology studies the

relationships between deformations and stresses in a material, which in general is moving or

flowing.

Viscosity, the tendency of a fluid to resist the applied stress, is one of the important properties

of fluid in the field of fluid mechanics. It is used in designing of pumps and piping, mixing

and agitation of dispersions and solutions, coatings, adhesives and other chemical processes.

The viscosity of fluid varies with introduction of dispersed phase, such as emulsions and

slurries, and also depends on physical (size and concentration) and chemical properties of

dispersed phase. Based on the response of the viscosity to the shear rate, fluids can be classified

as Newtonian and Non-Newtonian and their flow behaviour has been given in fig 1.

Figure 1: Flow behaviour of fluids

4.3 Theory

Various models exist to represent the viscosity of a suspended fluid as a function of volume

fraction of solid particles, i.e., the size and concentration of the solid particles, and viscosity

of pure fluid.



4.3.1 Einstein Model (Linear):

It may be used for extremely low concentrations of fine particles and particles are considered as spherical and there is no interaction among them.

(4.1)

Where and = Viscosity of particle suspended fluid and pure fluid respectively [Pa.s],

= Volume fraction of suspended solid particles in the fluid and = Constant

4.3.2 Rheometer Operating Principle

Common characteristic of all rheometer is the measure of two physical quantities: one is a

dynamic quantity (i.e. a force, torque) and the other is a kinematic quantity (i.e. a velocity,

shear rate, flow rate, time). One of the two quantities is directly controlled (or set) by the

instrument.

There are different geometries available as, plate-plate, cone-plate and concentric cylinders,

shown in fig 2.

Figure 2: Geometries of rheometer

The sample fluid is sheared in an annulus gap between concentric cylinders. The viscosity is

measured as the ratio of the shear stress and the shear rate by rotation mode operation. The

stress is dependent on the torque applied on the inner cylinder and the shear rate is dependent

on the angular velocity. During operation, one of these variables is selected and the other is

measured in controlled stress or controlled strain mode of operations. The following sequence

of calculation happens in rheometer:

1. Shear rate is controlled by angular velocity of inner cylinder



-------------------------(2)

2. Torque applied to shear fluid on inner cylinder is calculated is from power supplied

and angular velocity.

Torque = (power / angular velocity)

3. Shear stress on the inner cylinder

4. Viscosity = (Shear stress / shear rate)

4.4 Experimental Method

4.4.1 Chemicals

1000 cP silicone oil, 500 nm Silica particles and Distilled water

4.4.2 Apparatus

Rheometer (Anton paar Physica MCR 301), geometries (plate-cone type) available for

measurements

4.4.3 Experimental Procedure

1. Prepare the various particle volume fractioned silica in silicone oil samples.

2. Find the viscosity of the pure silicone oil ( ).

3. Find the viscosity of the other samples ( ).



4.4.4 Observations and Results

Record the observations from the system.

Table 1: Shear rate vs Shear stress data from rheometer

Pure Silicone oil ( =0) Sample 1 ( = ) Shear Rate [1/s] Shear Stress [Pa] Shear Rate [1/s] Shear Stress [Pa]

Table 2: Shear rate vs Shear stress data from rheometer

Sample 2 ( = ) Sample 3 ( = ) Shear Rate [1/s] Shear Stress [Pa] Shear Rate [1/s] Shear Stress [Pa]

Results and Analysis

1. Comment on the rheological behaviour of fluid.

2. Study the Newtonian curve fit of pure silicone oil, and various volume fractions of suspension

of silica in pure silicone oil.

3. Determine the viscosity of samples. How is the volume fraction of solid particles in

suspension affect viscosity?

4. Calculate the error bars. ( Refer Table 3)

5. Validate Einstein’s model graphically. Is the model suitable for experimental measurements?



Table 3: Error calculation for relative viscosity

Sample type

Volume fraction of particles,

Viscosity of suspended phase, [Pa.s]

lower bound From straight line fit

upper bound From straight line fit

Relative viscosity,

Lower error bar

upper

error bar

Questions

1. Derive an expression of strain for a cylindrical geometry (equation 2)

2. What are the assumptions while considering Einstein’s equation? How could you get

more accuracy so that the experimental data fit Einstein’s model?

3. What are the various geometries used to measure viscosity? Which geometry is used

when? Mention their advantages and disadvantages.

4. Suppose we add sodium dodecyl sulphate (a surfactant) instead of silica particles, what

will be the relation in viscosity and volume fraction?

5. The viscosity is measured here with varying shear rate. What could be the other

parameters to study the viscosity of suspension?

6. You have been given two particle samples, 1. = 0.0005 and silica particle diameter= 50

nm and 2. = 0.0005 and silica particle diameter = 100 nm. Which sample is more

viscous?

7. What is the effect of molecular weight distribution on rheological properties (say

viscosity)?

Reading Material

1. Transport Phenomena, Bird, Stewart, Lightfoot, II edition, Wiley Publication. (Page

40-110)


Experiment No. 5: Langmuir Blodget Trough


Lab Manual



1 Objective

To prepare Langmuir films and to study the variation of surface pressure bychanging the film area.

2 Introduction

Consider a two phase system for example water in a pond and the air. Whena substance (one molecule of which consists of two parts one of which ishydrophilic and another is hydrophobic) is placed on the interface of theconsidered system, the hydrophilic part get attached to the water phase andhydrophobic part remains in the air phase. If the interface is now seen on themacroscopic scale it can be observed that a film has formed at the interface.Only hydrophilic head get adsorbed that’s why the film is a monolayer only.This film is called a Langmuir film. Films like this when transferred on toa solid substrate are called Langmuir-Blodgett (L-B) films. L-B films havemany potential applications such as in molecular electronics, piezo-electronicorganic films, waveguides, nonlinear optics etc.

3 Theory

Surface of the water has a initial surface tension γ0 which is reduced by theadsorbed substance which forms a Langmuir film on the water-air interface.This reduction in surface tension is due to the adsorbed hydrophilic head ofthe added substance (also called amphiphile e.g. fatty acid like stearic oroleic acid) which comes in between the water molecules and reduce the totalinteraction energy. That’s why the layer consists of these molecules is saidto exert a film pressure (π) on the interface which is given by:

π = γ0 − γ

The results of this experiment clearly depict that the presence of theseadsorbed molecules reduce the surface tension of the water-air interface. Highnumber of these molecules present in a given area result in more reductionof the surface tension. Now consider a case when the area available for thesemolecules can be controlled. For a very large available area the numberdensity (molecules per unit area) of the adsorbed molecules will be very

1

Figure 1: Pressure-area isotherm of stearic acid on pure water

low. It means less number of these molecules will present among the watermolecules of that area so it will result in very low reduction of the surfacetension. As the available area for the adsorbed molecules is reduced numberdensity of these molecules increase which results in more reduction of thesurface tension. These variations can be plotted as a surface pressure vs filmarea graph. This plot suggests a phase transition of the adsorbed moleculeswhich is shown qualitatively in the figure 1.

An analogy between π and Area with pressure and volume of an idealgas for very large areas exists. The π and Area has inverse proportionalityrelation such as pressure and volume for an ideal gas. A more complex rela-tionship is required to connect these variables when the area decreases. Thetwo-dimensional equivalent of Amagat’s law of gases for the gaseous state ofadsorbed molecules can be employed as:

π(A− A ◦) = qRT

Where, A ◦ is a measure of excluded area and q is a measure of thenumber of moles in the system. It is obeyed fairly well around a π range of5-10 mN/m.

2

Figure 2: Schematic diagram of Wihelmy Plate Trough

4 Materials & Instruments

4.1 Chemicals

Acetone, Millipore water, Solution of Stearic acid in Hexane (1mg/ml).

4.2 Apparatus

Langmuir balance, volumetric flasks, beakers, hypodermic syringe, micro sy-ringe

4.3 Instrument description

Langmuir-Blodgett trough is a laboratory apparatus which is used to com-press the monolayers of molecules on the surface of a given subphase (usu-ally water) and measure the surface pressure due to this compression. Theschematic diagram of the instrument is shown in the figure 2. The troughand movable barrier are made of Teflon. The Wihelmy plate which is usedto measure the surface pressure is generally made of platinum. Workingprinciple of the Wilhelmy plate can be found in the supplementary reading.Diameter of the Wilhelmy plate is 39.24 mm and trough width is 75 mm.

5 Experimental Procedure

1. Clean the trough with acetone and wash away the acetone using dis-tilled water

3

2. Put in distilled water in the trough and remove any air bubbles present

3. click on the ‘sgserver icon to access control panel

4. Keep barriers in extreme position

5. Hang the Wilhelmy plate on its hook using tweezers

6. Set balance and barrier position to zero

7. Close in the barriers by means of switch. A positive value of surfacepressure is displayed

8. Remove the dirt from water-air interface till surface pressure is close tozero mN/m

9. Bring the barriers to extreme position and set balance and barrier po-sition to zero (use the switch/manual control unit)

10. Place the solution (givenµl) gently on the surface of the water

11. Wait 20 minutes for the solvent to evaporate

12. LB control software can be accessed by going to Experiments-LB soft-ware

13. Go .File.New Isotherm

14. Fill up the screen and then start:

15. Fill up the next screen

• Constant rate compression

• From go to target (target= mN/m)

• Rate is 10mm/min

• Zero balance

• Zero barrier position

• Go

16. Plot the graph between surface pressure vs mean molecular area

17. Stop and save the data

4

6 Results/Conclusion

1. Find out the mean molecular area of the adsorbed molecules (stearicacid) theoretically.

2. Estimate the number of moles of the adsorbed molecules in system byusing experimental data.

3. Estimate the excluded area by using experimental data.

4. As described earlier the adsorbed molecules show phase transition.Find out the values of surface pressure at which these transitions occur.

5. Perform an error analysis for your calculations.

7 Review Questions

1. What is a surfactant? Why is it often referred to as an amphiphile?

2. What are Langmuir-Blodgett films? What are the uses of LB films?

3. Why the formed Langmuir film is supposed to be monolayer only notbi-layer or multilayered?

4. What is the meaning of ”two-dimensional” phases?

5. What is the meaning of surface pressure?

6. What is the analogy between ideal gas and gaseous state of amphiphilesof the Langmuir film? Till what values of surface pressure does it hold?

7. Describe the Langmuir film balance and how it is used to measuresurface pressure?

5


Experiment No. 6: Thermo Gravimetry Differential Thermal Analysis


Lab Manual



Experiment Number 6

Analysis of Physico-Chemical Changes of a Sample on Heating by TGA-DSC Technique

Objective: To perform experiments with Thermo Gravimetric Analysis and(TGA) and Differential Scanning Calorimetric (DSC) analysis technique for obtaining information on mass and enthalpy changes of a sample undergoing physico-chemical changes on heating

Introduction: A solid substance on heating can undergo physico-chemical changes e.g. decomposition, sintering, oxidation, fusion, melting or dehydration. Its change in mass due to liberation or absorption of matter and liberation or absorption of heat can be monitored using TGA-DSC analysis. Thermo gravimetric analysis (TGA) measures the change of mass of a sample in a controlled temperature programmed environment. Measuring the change in mass, it predicts the sample purity, decomposition, dehydration, oxidation and other such properties. The Differential Scanning Calorimetry (DSC) measures the temperature difference corresponding to physic-chemical changes and finds applications in identifying the phase change, find the enthalpy of transformations, etc.

Theory: Mass change occurring on a solid or liquid sample due to liberation or absorption of matter (mainly gaseous) is detected through Thermo gravimetric Analysis. The analysis of change of mass generally can be done through step heating and ramp heating. When step heating is done the sample is subjected to uniform temperature conditions, and the mass is measured as a function of increasing time. When ramp heating is done i.e. keeping heating rate constant the mass is measured as a function of increasing temperature. In most of the cases TGA is done with ramp heating so that the physico-chemical changes taking place for a specific sample can be monitored over a certain temperature range rather than focusing on a fixed temperature.

In Differential Scanning Calorimetry the difference in heat flow into the sample and a reference material is measured as a function of temperature or time, while the substance and reference material are subjected to same controlled temperature programme in a specified atmosphere. Here sample and the reference materials are heated by separate, individual heaters and the temperature difference is kept close to zero and the electrical power needed to maintain equal temperatures is measured. During the DSC experiment, the sample is heated over a range of temperature. At some point, the material starts to undergo a chemical or physical change that releases or absorbs heat. The ordinate value at any time or temperature is related to the difference in heat flow between a reference sample and the unknown. The integration of the area under the heat flow curve gives enthalpy change associated with the thermal event of interest. Applications: TGA - Reactions involving change in mass of solid or liquid sample can be studied with TG.

Thermal or time dependent decomposition with temperature

Temperature dependant desorption of adsorbed gases

Fusion and evaporation of water associated with the sample

Combustion reactions

DSC- It is the most widely used thermal analysis technique since it gives the measure of heat flow associated with endothermic or exothermic transitions. Thus it is useful to study reaction thermodynamics as well as kinetics. The transitions usually traced by the technique are as follows:

Glass transition temperature, crystallization temperature, melting temperature and associated enthalpy changes for a polymer

Phase change

Product stability

Frequently used in industry to measure glass transition temperature and %crystallization of polymer.

Apparatus:TGA The TGA part of the TGA-DSC apparatus and has following four major components;

The electro-balance and its controller: e.g. Null point weighing mechanism.

The furnace and temperature sensors: e.g. MoSi2 based furnace with alumina refractories and a thermocouple Pt-30%Rh (+) Vs Pt-6%Rh (-) for operation to 1500 to 1700 0C.

Purge gas flow controller

The programmer or computer

The data acquisition device

Apparatus: DSC The major parts of the DSC part of the system are;

The DSC sensor plus amplifier

The furnace and its temperature sensor

The programmer or computer

The data acquisition device

Instrument Detail

Company: M/s. NETZSCH Gerabau GmbH

Model: Simultaneous TGS-DSC Apparatus STA 409/PC/4/H/LUXX

Temperature range: 25o – 16500C

Heating and cooling rate: 0.01 K/min to 50 K/min (dependent on furnace) generally operated at 10K/min.

The balance: can weigh maximum of 50 mg.

Resolution: The resolution of TG instrument is 2 μg.

Operating Atmosphere: inert, oxidizing, reducing, static, dynamic.

Simultaneous TG-DSC apparatus

Experimental Procedure:

Power unit, Furnace unit, Gas control unit, Water circulation unit were switched on in the respective order.

Pressure from the connected gas line N2/O2/air should be maintained around 1kgf/cm2 and gas lines should be turned on. Baseline correction

Reference and analysis pan was cleaned manually and the weight was taken.

Furnace unit was opened using PUSH UP+ SAFETY buttons. Pan was placed over the sensors using forks and their weights were noted down.

Baseline correction was performed in the same program which is used to generate results.

The software STA409PC was opened.

Under Measurements CORRECTION was marked.

Entered Sample ID and name.

Tare sample crucible and reference crucible mass by clicking “weigh” button.

Kept the reference mass blank.

Under PURGE GAS Gas1 (N2) flow: 40ml/min and Gas2 (N2) flow: 60ml/min were set.

After pressing continue, calibration file were selected from source NEW-DTA-CAL-N2 and sensitivity file from source SENSCAL-AL2O3-N2.ESV.

Multiple tabs got opened.

Under step conditions: The check box for STC, GAS 1 and GAS 2 were selected.

Under Category Initial Temperature Conditions were set to 260C.

ADD to END was pressed to close the TAB.

In side bar DYNAMIC was selected and Under Category End Temperature and the Heating Rate (Acquisition rate in points/K and in points/min will be taken automatically) were entered.

ADD to END was repressed to end the tab.

In the graph generated in the screen all of these got added.

In side bar FINAL was selected and the final temperature is automatically taken 100C more than the end temperature by the instrument. This is the emergency reset temperature.

In the specified path the file was saved and named. All the above settings were saved there as baseline correction.

COM1 WINDOW appeared soon after a minute.

Pressed initial condition on.

Gas flow in the rotameter was checked.

TARE tab was pressed.

Then START tab was pressed. Program got started and data acquisition started to take place.

Precautions:

1. Total mass of the sample taken should be in the range of 10-20 mg. Within this range temperature distribution remains uniform.

2. As hands contain moisture no hand contact should be made with the crucible. It might change the reading. Some moisture will add up the mass.

3. To get a stable weight in the electrobalance the instrument should be turned on an hour before the experiment.

4. Once the desired temperature rate is achieved the instrument is allowed to cool down to room temperature. Else when the heated instrument remains exposed to the open atmosphere due to the large temperature difference sensitivity of the thermocouple might be damaged.

5. After the completion of the experiment the pans should be washed properly to get rid of minute traces of residues.

References

1. Brown, M. E. (Ed.), 2007, “Introduction to Thermal Analysis: techniques and Applications”, 2nd Edition, Springer, New Delhi, 1-90. 2. Price, D. M., Hourston, D. J. and Dumont, F. 2000, “Thermogravimetry of Polymers” in “Encyclopaedia of Analytical Chemistry” edited by Meyers R.A., John Wiley &

Sons Ltd, Chichester, 8094–8105.


Experiment No. 7: Stopped Flow Reactor


Lab Manual



1. Aim:

To study the kinetics of a fast reactiondichlorophenolindophenol (DCPIP) by Ascorbic acid(AA)

2. Introduction:

The conventional methods of determining rate constants cannot be used for fast reactions. Kinetics of such fast reactions is determined by flow methods. The stopped flow reactor is one of the flow methods techniques used for kinetics determination. Two or more solutions containing reactants are mixed and then concentration of the component is measured, generally by spectrometer. Based on the absorbance by DCPIP, concentration and hence kinetics is determined.

Fig: Schematic view of stopped flow reactor

3. Theory:

In the stopped flow technique, the reagents are mixed rapidly in a cuvette by forcing the solutions from syringes through jets in the cuvette mixing chamber. The flow of reagents is stopped suddenly and the time course of the reaction is monitored spectrometrically. The limiting factor in the observation of the fast reactions is the mixing time, the halfmixing time. There is another term in this technique, dead time. It is a critical performance parameter in stopped flow technique, which is difference in time between the end of mixing point and the start of observation point.

Reaction: DCPIP + AA DCPIPH

Rate of reaction:

kinetics of a fast reaction for the reduction of 2,6-dichlorophenolindophenol (DCPIP) by Ascorbic acid(AA)

The conventional methods of determining rate constants cannot be used for fast reactions. Kinetics of such fast reactions is determined by flow methods. The stopped flow reactor is one of the flow methods techniques used for kinetics

more solutions containing reactants are mixed and then concentration of the component is measured, generally by spectrometer. Based on the absorbance by DCPIP, concentration and hence kinetics is determined.

Fig: Schematic view of stopped flow reactor

In the stopped flow technique, the reagents are mixed rapidly in a cuvette by forcing the solutions from syringes through jets in the cuvette mixing chamber. The flow of reagents is stopped suddenly and the time course of the reaction is

spectrometrically. The limiting factor in the observation of the fast reactions is the mixing time, the half-time of the reaction must be larger than the mixing time. There is another term in this technique, dead time. It is a critical

er in stopped flow technique, which is difference in time between the end of mixing point and the start of observation point.

DCPIPH2 + Dehydro-AA

The conventional methods of determining rate constants cannot be used for fast reactions. Kinetics of such fast reactions is determined by flow methods. The stopped flow reactor is one of the flow methods techniques used for kinetics

more solutions containing reactants are mixed and then concentration of the component is measured, generally by spectrometer. Based on the absorbance by DCPIP, concentration and hence kinetics is determined.

In the stopped flow technique, the reagents are mixed rapidly in a cuvette by forcing the solutions from syringes through jets in the cuvette mixing chamber. The flow of reagents is stopped suddenly and the time course of the reaction is

spectrometrically. The limiting factor in the observation of the fast time of the reaction must be larger than the

mixing time. There is another term in this technique, dead time. It is a critical er in stopped flow technique, which is difference in time

]][[2 BAA CCk

dt

dC

Here, CA-concentration of DCPIP, CB-concentration of AA, k2-rate constant of the reaction. Defining M=CBO/CAO, the rate law after integration can be written in following form,

MtkCCC

CAOBO

A

B lnln 2

Hence the slope of

A

B

C

Cln vs time gives the rate constant.

If cocncentration of one of the reactants is in excess, then the reaction can be considered to be pseudo first order, hence rate law becomes,

][ AeffA Ck

dt

dC

Here keff = k1*[CB], effective pseudo first order rate constant and k1 is second order rate constant based on keff

After integration,

tkC

Ceff

A

AO

ln

4. Materials/ Instruments:

Chemicals:

De-ionized water, ascorbic acid, DCPIP

Apparautus:

MOS-200/M, FC-15 cuvette, SFM-20 equipped with 10ml syringes, Bio-Kine software, beakers volumetric flask.

5. Procedure: Prepare stock solutions of AA and DCPIP

Take absorption readings for water

Make calibration for DCPIP-water system

Record absorbance values for DCPIP-AA system at different mixing ratios

Rinse the system with DI water

6. Applications: protein folding, enzyme reactions, redox reactions.

7. Precautions: Air bubbles should not be present in the syringe.

One of the reactants must have absorption capacity.

8. References:1. Chemical reaction engineering (2nd edition), O.Levenspeil2. Prigodich R.V. A Stopped-Flow Kinetics Experiment for the Physical

ChemistryLaboratory Using Noncorrosive Reagents. J.Chem. Educ. 2014, 91, 2200-2202.

9. Questions :i. The half life of the reaction should be greater than the dead time. If the half-

life is shorter than the dead time, what will be the effect on the results?ii. What is advantage of stopped flow method than the continuous flow method

to study kinetics?iii. Can this method be useful to study the kinetics of slow rate reactions?iv. Reversible and irreversible reactions, which type of reactions, can be studied

by this method?v. Why the initial detectable concentration of the reactant is not equal to the

feed concentration of the reactant?


Experiment No. 8: Image Analysis

Lab Name: Fluid Mechanics Lab

Lab Manual



Objective

To estimate Boltzmann constant, (kb) performing image analysis of Brownian motion of parti-cle.

Introduction

Although Jan Ingenhousz is known for the first person to make a documented observation offluctuating motion of carbon dust in alcohol in 1765, the discovery of Brownian motion iscredited to Robert Brown for his in depth observations of pollen in water in 1827. Brownianmotion is stochastic movement of small particles, (size ∼ 1µ) suspended in a solution. Solventmolecules hit the immersed particle, and the resulting force of the infinite number of collisionresults in a chaotic motion. The measurement of this motion can be done by the mean squaredisplacement, 〈(∆r)2〉 and the lag time ∆t. This motion is also characterized by the diffusioncoefficient, D which is the measure of the speed of diffusion.

Einstein published a paper in 1905 reporting the relationship between the mean square mag-nitude of displacement due to Brownian motion and the size of particles. French Physicist JeanBaptiste Perrin’s experimental evidence justified Einstein’s hypothesis and thereby confirmedthe atomic nature of the matter. For this study he has been awarded Nobel prize for Physicsin 1926. Since then, a thorough understanding of Brownian motion has find its importance notonly in polymer physics to biophysics, aerodynamics to statistical mechanics but also in stockoption pricing.

Boltzmann constant can be calculated from various experimental methods few of whichinclude

• Image analysis

• Acoustic gas thermometry

• Quasi-spherical cavity resonators

• Dielectric constant gas thermometry

• Doppler broadening thermometry

• Noise thermometry.

In this experiment, we will follow the Image Analysis technique to calculate the value of Boltz-mann constant, kb.

1

Theoretical and mathematical background

Kinetic theory suggests that any particle has the same average translational kinetic energy irre-spective to their size. In 3 dimension the value of this average translational energy is 3

2kbT i.e.

12kbT for each degrees of freedom, where T is the absolute temperature in Kelvin scale. The

velocity of particle is directly proportional to square root of T and inversely proportional tosquare root of mass. Einstein has calculated the diffusion coefficient for a spherical Brownianparticle as

D =kbT

6πηa, (1)

where η is the dynamic viscosity of the solution and a is the radius of the particle. Due toinfinite number of collisions the direction of the resulting force could be random there fore theparticle has the chaotic motion which is shown in fig. (1).

Figure 1: Trajectory of Brownian motion of a particle

The force balance equation can be written by equating inertial force to the drag force andthe stochastic force acting on it.

md2x

dt2= −6πηa

dx

dt+ f(t), (2)

where m is the mass of the particle, x is the position of particle and f(t) is the stochastic forceacting on particle. For a tiny particle with very small mass, the inertial term can be ignored.

6πηadx

dt= f(t) (3)

which is known as overdamped Langevin equation. In absence of any external potential solu-

2

tion of eq. (3) gives the position of a particle.

x(t) = x0 +

∫ t

0

f(τ)

ζdτ, (4)

where ζ = 6πηa. The ensemble average of eq. (4) gives the average position of the particle.Also the random walk model suggests the average position of a particle in stochastic motion isat its initial position.

〈x(t)〉 = x0 +

∫ t

0

〈f(τ)〉ζ

dτ = x0 (5)

The variance of a Brownian particle is calculated as

〈(x(t)− x0)2〉 =

∫ t

0

dτ1

∫ t

0

dτ2〈f(τ1)f(τ2)〉

ζ2=

2kbT

ζt (6)

because of the property of f(t) is such that it’s a delta correlated random force with the meanzero. Comparing eq. (1) and eq. (6), we get the relation among variance and diffusion coeffi-cient.

〈(x(t)− x0)2〉 = 2Dt (7)

Carrying out image analysis experiment we can identify positions of a Brownian particle atcertain time lag. Then calculating variance and using it in eq. (6) with other known variableswe can calculate Boltzmann constant, kb.

Experimental setup

Image analysis experiment requires an optical microscope the head of which is replaced with avideo head to mount a monochrome CCD, a glass slide, a cover slide and a well sonicated dilutecolloid solution of 1µ diameter polystyrene particles in water. From the images taken from themicroscope using the CCD (40X magnification) gives position of the particle in pixels whichcan be converted to micrometer scale using the calibration relationship.

Experimental procedure

Following content is the step by step procedure to carry out image analysis experiment.

1. A dilute solution of polystyrene particles of size 1µ is prepared in water.

2. Prepared solution is sonicated for 5 minutes to get an uniform solution.

3. A drop of the solution is placed on well of a glass slide. Place a cover slip gently on theslide well so that a seal is formed and no air bubbles remains inside. Existence of airbubble will cause a external force on the solution because of the molecular motion in air.

3

4. The slide is placed under microscope for observation. Illumination of the microscopeand the focus is adjusted to obtain the best image.

5. Twenty snapshots of the well focused particles in solution are captured at a certain lagtime, ∆t using IMAGE PRO software interface installed in the PC attached with thecamera.

6. Position of a particle, (values in x and y co-ordinates) at different snapshots are mea-sured using image processing software interface IMAGE J and stored in a file for furthercalculations.

7. Measured co-ordinates are converted to µ from pixels using standard calibration data.

8. Above procedure is followed for 8 different values of time lag, ∆t.

9. Room temperature is noted down.

Observations and calculations

Measured variables data

• Temperature:

• Dynamic viscosity of water:

• Radius of polystyrene particles:

4

Data collection

Table 1: Standard format of table for data collection and calculation

Sl. x y x(tn+1)− x(tn) y(tn+1)− y(tn) (x(tn+1)− x(tn))2 (y(tn+1)− y(tn))2

no. (µm) (µm) (µm) (µm) (µm2) (µm2)

1234567891011121314151617181920

Average

Sources of error

1. There may be manual errors while locating the center of the particle at different instantsof time.

2. There should not be any air bubble left between the cover glass and glass slide as it mayadd some error.

3. The time between the images should not be less than 100ms as the motion will be verysmall to locate and should not be greater than 1100ms as the particles can move in the

5

z-direction and thus, exact displacement can not be recognized.

4. Care should be taken on tracing only one single particle. If for one set of data 2 particlesare being traced then error will be huge.

5. Particle with minimal diffusion in z direction during the time of reference should betaken.

6


Experiment No. 9: Vapour Pressure Osmometer

Room No.: 227 (Organic Processing lab)

Lab Manual



Vapour Pressure Osmometry Objective

Determination of molecular weight of a given polymer using vapour pressure osmotry.

Introduction

Determination of the molar mass of polymers is of considerable importance because the chain

length is a controlling factor in the evolution of solubility, elasticity, fiber formation, and

mechanical strength properties. Methods used to determine the molar mass are either relative

or absolute. Relative methods require calibration with samples of known molecular weight

and absolute methods require no such calibration. This report will focus on the use of vapor

pressure osmometry to determine the number average molecular weight. These techniques are

useful in different molecular weight ranges and depend on the change in osmotic pressure and

the lowering of vapor pressure (respectively) by polymers in solution.

THEORY

Determination of number average molecular weight depends on basic equations of dilute solution chemistry and physical chemistry. In a dilute solution, the vapour pressure of a solvent is given by basic Raoult’s Law:

P1=P10 *X1 P1 = partial pressure of solvent in solution P10 = vapor pressure of pure solvent X1 = mole fraction of solvent So, vapour pressure of any solution is lower than vapour pressure of its pure solvent. If one places the drop of solution along with that of pure solvent in the vapour environment of pure solvent, then condensation will occur on the solution drop because its vapour pressure will be less than that of the solvent. Condensation will lead to relative increase in temperature of the solution drop with respect to the pure solvent drop. Increased temperature in turn changes resistance and hence, generates a potential difference. This potential difference is recorded until equilibrium is reached.

The basic relation for molecular mass determination equals:

nsample

msolvent

=

msample

M sample

msolvent

n = Number of sample molecules

m = Mass of sample and solvent respectively

M = Molecular mass of the sample

For a molecular mass less than 500 g/mol the measurement value is proportional to the number of moles. The change in vapour pressure is proportional to the number of species present in the solution, which is measured in terms of osmol units. Hence the this is very similar to the osmolality determination. A sample is measured where concentration and molecular mass are known (c in mol/kg). The slope of the graph of measurement value v/s concentration is 𝐾𝑐𝑎𝑙𝑖𝑏 with kg/mol.

Kcalibration=MVc

Unknown molecular mass of the sample can be determined by a known concentration. The slope of the curve of measured value gives Kmeasurement

The molecular weight of unknown sample is determined with:

M( gmol)= Kcalibration /Kmeasurement

Methodology

Vapour pressure osmometer K-7000 is designed to exactly measure the number average molecular weight of polymers. This measurement is based on the principle that chemical potential of a solvent is altered in presence of a non-volatile substance. In dilute solution this phenomenon depends only on the number of particles dissolved. Therefore change in chemical potential is measured in terms of change of osmotic pressure and number average molecular weight is determined. Figure 1 gives the internal view of the instrument.

Apparatus

Vapour pressure osmometer, volumetric flasks, pipette

Chemicals

NaCl (AR Grade), Millipore water, Sucrose

PROCEDURE

1. Prepare samples of different concentration for which molecular weight is to be determined

2. Check whether thermistors are working or not Press TEST, if it displays OK then carry on, otherwise stop.

3. Fill 25% of beaker with pure solvent along with the wick. 4. Insert the thermistor assembly inside the beaker and place it in an equipment chamber

and tighten to avoid leakage which will disturb the stabilization. 5. Place all the syringes inside the syringe ports. Fill two syringes with pure solvent and

place them back to the syringe holders to attain the temperature of head.

6. Set the temperature according to your requirement but within a limit given in an equipment manual for different solvents. Selectable cell temperature 20OC -130OC.

7. After temperature setting, place GAIN value to maximum (256).Then let it stabilize. Selectable gain settings are 1,2,4,8,16,32,64,128,256

8. Before starting the experiment adjust the Wheatstone bridge signal value to zero with the help of AUTOZERO function. After that add a drop of one of the solution prepared on one thermistor. If the signal value is showing OVERLOAD then adjust the gain accordingly to get signal value. In this way note down the signal and gain value for every solution.

RESULTS

Table1: Format of generating the Calibration data for standard solute (NaCl)

Concentration of NaCl (mole/kg)

Gain Signal (mv) Signal/Gain Average Signal

(mv)

0.2 16

8

0.4 8

4

0.6 8

4

0.8

4

2

From the Table, a calibration graph and calibration factor may be generated.

Fig.1: Calibration graph for NaCl

Fig. 1: Concentration vs Signal (mV) for NaCl.

For NaCl sample, the relationship between the mol concentration and the osmol concentration may

be obtained by referring to the standard manuals (Table-2).

Table2: Osmolality data of NaCl (From Manual)

Conentration (Na+, Cl-) (mmol/kg)

Conentration (mol/kg) Osmolality (mOsmol/kg) Osmolality (Osmol/kg)

105.6 100

213.3 200

323.1 300

433.8 400

545 500

655.7 600

767.5 700

823.9 750

1325.1 1200

1983.2 1800

Fig.2: Concentration vs Osmolality (NaCl)

Table3: Data for unknown sample (Sucrose)

Concentration Polymer (g/kg)

Gain Signal (mv) Signal/Gain Average Signal

(mv)

2 256

128

4 64

32

6 256

128

8 256

128

Fig.3: Measurement graph of sucrose

Method of calculating the molecular weight of sample

From Figure 3,

Kmeasurement = .............. mv.Kg/g of sucrose

Molecular weight of sucrose = Kcalibration/ Kmeasurement = ..............g/Osmol.

Discussions and Conclusion

The implication of the results, comparison with the actual Molecular weight of

the sample may be made. The reasons for the difference, if any, may be

presented (Moisture content in sucrose, Varying droplet size of solution on the thermistors,

Unstable temperature which is noted manually etc.)

CL610-Experimental Methods

Experiment No.10

Nanoparticle aerosol size distribution measurement using a Scanning Mobility Particle Sizer (SMPS)

TAs:

Rakhi Dhuriya ([email protected])

Sagar Sant ([email protected])

Lab Location:

Particle and Aerosol Research Laboratory (PeARL), Room 321, 2nd Floor

Department of Chemical Engineering

Indian Institute of Technology-Bombay

Spring, 2015

1. Objectives - Understand the principle of aerosol measurement using a Scanning Mobility Particle

Sizer (SMPS). - Carry out aerosol synthesis of stearic acid nanoparticles with controlled median

diameter. - Derive the power law exponent relating median nanoparticle size to precursor

concentration. - Fit log-normal size distributions and derive size distribution parameters.

2. Introduction An aerosol is a metastable, gaseous suspension of multiphase particles. Aerosol measurement is a complex and elegant field of research, wherein instruments have been developed based, both on laser light scattering or particle charging followed by mobility measurements along with optical detection, to size particles of 2.5 nm to 20 µm diameter and count number concentrations (ranging from 102-105 particles/cm3) quantitatively.

Aerosol routes to process materials into nanoparticles rely on high temperature nucleation-coagulation processes or controlled temperature droplet drying of solution aerosols (gas-phase suspensions of liquid or solid particles) in aerosol flow reactors. Unlike colloidal methods of nanoparticles synthesis, which utilize several post-processing separation steps, aerosol methods offer a single-step continuous method for producing nanoparticles which can be collected as dry powders or directly into liquid media to form a suspension. The aerosol route has been used to prepare nanoparticles for catalyst, photoelectric, drug delivery.

In this experiment, the aerosol route will be used to make stearic acid nanoparticles of controlled median diameter. The principle of aerosol measurement using mobility sizing will be demonstrated, to measure and analyse nanoparticle size distribution.

3. Theory When a charged nanoparticle is exposed to an electric field, it migrates at a velocity that is determined by a balance between the resulting electrostatic force and aerodynamic drag that resists its motion. This characteristic migration velocity is described as electrical mobility of the particle, , the migration velocity per unit of applied electrical field strength.

3.1. Non-continuum effects

The force resisting the motion of a sphere passing through a fluid is the drag force. The Stokes’ law form, , hold for a rigid sphere that moves through a fluid at constant velocity, with particle Reynolds number much less than unity. The particle can be many diameters away from surface and much larger than mean free path of the gas molecules, , which is about at .

For small particles whose size approaches the mean free path of gas where ), the drag for a given velocity becomes less than predicted from Stokes law and continues to decrease with particle size. These particles experience a slip at the surface, termed non-continuum effect. The ‘slip effect’ is corrected by introducing Cunningham correction factor (or slip correction factor) for particles less than 0.1 µm diameter (Allen and Raabe 1985), which follow either “free molecular” or “intermediate” regime behaviour. An interpolation formula below calculates the slip factor over both regimes of particle behaviour.

Eqn. 1

Eqn. 2

Kn is Knudsen number = 2λ /dp

3.2. Bipolar diffusion charging

An effective method of charging nanoparticles to obtain unit charge (with a high probability) bipolar diffusion charging. It has been hypothesized that, after long exposure to such bipolar ion mixtures, frequent ion-particle collisions will bring the particles to a state of charge equilibrium with the ionic atmosphere. In this equilibrium state, the fraction of particles of diameter that carry charges is described by the Boltzmann charge distribution, that is,

Eqn. 3

Eqn. 4

3.3. Particle mobility in an electric field

A particle with charge in an electric field of strength experiences a force of strength . Because of the low ion densities and slow charge transfer kinetics in ambient temperature gases, aerosol particles usually carry only a small number of elementary charges. The charge is, therefore, conveniently represented as , where is the magnitude of the elementary unit of ( for negatively charged particles, and for positively charged particles). For times that are long compared with the aerodynamic relaxation time, , ( is the particle mass and is electrical mobility of the particle), a charged particle will migrate at a steady-state migration velocity relative to the gas motion of

Eqn. 5

For motion of spherical particles with diameter in Stokes regime, this mobility is

Eqn. 6

= slip correction factor, = Knudsen No. = , = mean free path of gas molecules, = gas viscosity.

4. Experimental Set-up The experimental set-up includes an atomizer, an aerosol flow reactor and a scanning mobility particle sizer.

Figure 1: Experimental setup for aerosol synthesis of nanoparticles

4.1. Atomizer

Atomizer produces small liquid droplets at the rate of 2 × 106 particles/cm3 (108 particles/sec) with mean droplet diameter of 300-350nm and a geometric standard deviation of 1.6-2.0. The atomizer is operated at an air flow rate of 3.0–3.5 dm3/min at 35 psig

4.2. Scanning Mobility Particle Sizer (SMPS)

An SMPS system consists of a neutralizer and particle charger, a differential mobility analyser (DMA) and a condensation parsticle counter (CPC). A Kr-85 radioactive bipolar charger neutralizes pre-existing charges on particles, establishing a bipolar equilibrium charge level on the particles. Particles receive either positive, negative, or zero charge(s) negative (like +1 or -1, following a Boltzmann charge distribution). The DMA classifies particles by size which are counted in single particle mode in the CPC. The CPC can detect airborne particles down to 4 nm in diameter. It provides highly accurate measurements over a wide concentration range from 0-107 particles/cm3.

5. Materials and methods

5.1. Materials

Stearic acid (>95% pure; Sigma Aldrich, Saint Louis, USA, Chloroform (>99% pure; Sigma Aldrich, Saint Louis, USA).

Solution Chloroform (mL) Stearic Acid (mg) Concentration(mg/ml) 1 25 12.5 0.5 2 25 25 1 3 25 75 3 4 25 125 5

6. Experimental procedure 1) Dismantle all the components of atomizer, aerosol reactor gently and carefully. Clean all

these components with acetone and allow it to dry. 2) Assemble all the components of the aerosol reactor, and atomizer according to the flow

diagram. 3) Start the nitrogen supply at 35 psig and check for leaks at all joints using soap solution

(10% v/v in distilled water). 4) Start SMPS scanning for the blank at 120 sec/scan scan rate. Take 3 consecutive scans. 5) Prepare the solution with required concentration and load in a 20ml syringe. The syringe

pump is operated at 1.2ml/min to feed the precursor solution. 6) Start SMPS scanning for aerosol, at 120 sec/scan scan rate. Take 3 consecutive scans. 7) After the scanning is over, note down the readings.

8) Repeat the procedure for all four concentrations. 9) Clean the components and keep everything in place.

7. Observations and results

7.1. Stearic acid with four different precursor concentrations

Record size distribution parameters:

Number

Median (nm)

Geo. St. Dev.

Total Conc.

7.2. Data analysis

1) Record in EXCEL and hardcopy the size distribution data. Plot all four size distributions as log-normal size distribution. Plot them on probability-log axis. What are parameters of a log-normal distribution? Determine them for each case. Compare the median mobility diameter and geometric standard deviation in each case.

2) Establish the power law relation between initial solute concentration and the number median diameter of the synthesized nanoparticles. Derive the power law exponent through a mass balance on an evaporated drop. Plot median particle mobility diameter versus and find the power-law

exponent relating them. Compare the theoretical and experimental values and explain reasons if they differ.

8. Questions 1) How does median particle diameter vary with initial solute concentration in the

precursor? Why does it not follow the 1/3 power law? 2) If you would like to use this method to make nanoparticles with median diameter 10 nm,

what concentration of precursors is needed? Is this feasible? How else can you modify this method to make much smaller nanoparticles?

3) If particles entering the SMPS carried large charges, and the neutralizer was not working well, what shift in mobility size would you expect and why?

4) If particles were non-spherical what shift in mobility size would you expect and why? 5) If particles had a fluffy morphology, with highly irregular surfaces, what shift in mobility

size would you expect and why? 6) If GSD is similar, explain why? How can you reduce the GSD of this size distribution to

make it more monodisperse (or single sized)?

9. References Kulkarni, Pramod, Paul A. Baron, and Klaus Willeke, eds. 2011. Aerosol Measurement: Principles, Techniques, and

Applications. Chapter 18, Hoboken, NJ, USA: John Wiley & Sons, Inc. http://doi.wiley.com/10.1002/9781118001684.

Seinfeld, John H., and Spyros N. Pandis. Atmospheric chemistry and physics: from air pollution to climate change. Chapter 7, John Wiley & Sons, 2012.

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