Intrinsic Viscosity of Polyvinyl

Alcohol: Part B

1

Nuwan Bandara

nbandara@chm.uri.edu

Office Hour: Monday @ 10

Beaupre 390

(or by appointment)

➢ Viscosity – frictional drag between layers of a liquid as itflows down a tube; “thickness”. (more viscous the liquid,longer to pass through tube)

➢ Specific Viscosity (ηsp):η, solution viscosity (units?)η0, viscosity of solvent (units?)When will ηsp be zero?

Concepts

𝛈𝐬𝐩 =𝛈

𝛈𝟎− 𝟏

➢ Intrinsic viscosity [η]:

▪ [η] is the value of ηsp/c extrapolated to zero concentration

▪ [η] is used to measure molecular weight of a soluble polymer in a given solvent

▪ By convention, the unit of c is g/(100mL)

▪ The unit of [η] is (100 mL)/g

Coiled

polymer

3

[h] = limc®0

hsp

c

Concepts

➢Recall last week’s viscosity of water and polyvinyl alcohol (PVA)

➢Head-to-tail bond:

➢Head-to-head bond:

head tail

4

1

2

1

2

1

2

12

12

Concepts

Start Time End Time

See page 320 of text book

Setup – Ostwald Viscometer

➢ Purpose:

▪ Use viscosity data to determine the average molecular weight of PVA

▪ Determine the percentage of head-to-head linkage

➢Method:

▪ Obtain viscosity data for 4 different concentrations of PVA

▪ Use potassium periodate (KIO4) to cleave head-to-head linkage and determine the viscosity of 4 different concentrations of cleaved PVA

▪ Calculate the percentage of head-to-head coupling6

Purpose and Method

➢ Experimentally:

▪ compare the viscosity of PVA with and without head-to-head linkage.

▪ Head-to-head linkage is cleaved by periodate

▪ Head-to-tail linkage remains intact

▪ What happens to the number of molecules after cleavage? 7

head

tail

head

head

Experimental Design

1. Record the concentration of the stock PVA and error

2. Record error of all volumetric glassware

3. Obtain 50mL of PVA in a beaker and place it on a hot plate

with stir bar

4. Add 0.25g KIO4 to the beaker and heat until clear (30 minutes,

turn the heat knob to 5). Do not heat above 75°C, cool to

room temp.

5. After each run, Show me the results!

6. Rinse viscosimeter 2x with water, determine viscosity of water

3x

7. Rinse 2x with stock PVA, determine viscosity of stock PVA 3x8

Procedure

7. Pipet 40 mL of stock PVA into 50 mL volumetric flask and

dilute – label. Preform 2 more serial dilutions in this manner.

8. Rinse 2x with PVA-DS1, determine viscosity 3x

9. Repeat (8) for PVA-DS2 (30 mL of stock PVA to 50 mL) and

PVA-DS3 (20 mL of stock PVA to 50 mL)

10. Rinse viscosimeter 3x with water, determine viscosity of

water 3x – if is not close to previous results rinse until it is

11. Rinse viscosimeter 3x with cleaved PVA, determine viscosity

3x

12. Pipet 40 mL of cleaved PVA into 50 mL volumetric flask and

dilute – label. Preform 2 more serial dilutions in this manner.9

Procedure

13. Rinse 2x with cleaved PVA-DC1, determine viscosity 3x

7. Repeat (15) with PVA-DC2 (30 mL of cleaved PVA to 50

mL) and PVA-DC3 (20 mL of cleaved PVA to 50 mL)

13. Rinse 3x with water, determine viscosity 3x. Show meresults.

14. Clean all glassware and properly dispose of chemicalwaste

10

Procedure

▪ Start cleaving right away - do not boil

▪ Record the temperature of each trail

▪ Record the error of any solutions, glassware or equipment

▪ Clean equipment carefully

▪ Not create bubbles

▪ Not use too much solution to rinse

11

Remember To:

▪ Handle the viscometer with great care as they are fragile and expensive.

▪ Dispose the waste in properly labeled waste bottle.

▪ Make sure you wash your hands after the lab.

Precautions and Protocols

▪ t = average time for species (seconds)

▪ ρ = density ( g cm-3), (assume r PVA = r water)

▪ B = apparatus constant

▪ h = viscosity (1 mP = 10-3 g·cm-1 ·s−1)

Calculations

(1)

➢ Make table of flow times for distilled water and polyvinyl alcohol solution

➢ Calculate average flow time for each

➢ From distilled water data, find B—the apparatus constant

➢ both η and ρ can be determined from tables in the

syllabus packet

Calculations

➢ Determine ηPVA and ηsp for each polymer

solution

𝛈𝐏𝐕𝐀 = 𝐁𝛒𝐭

➢ B is from above; ρ is from table for water at

measured temperature

𝛈𝐬𝐩 =𝛈𝐏𝐕𝐀𝛈𝟎

− 𝟏

Calculations

16

• Extrapolate to c = 0 to obtain the value of intercept.

• This cannot be done on Excel! Must be done by hand! (On graph paper)Reasons: Prepare for the in-class report writing for final. It is an essential life skill.

Calculations

➢ Use 𝑪𝟏𝑽𝟏 = 𝑪𝟐𝑽𝟐to determine concentration of all dilutionsUnit of concentration is g/100 mL, volume is in mL

➢ Graph ηsp Vs C

Extrapolate to get y-intercept—intrinsic viscosity [η]

Systematic Errors Random Errors

Have a definite algebraic sign

We have some control

No definite algebraic sign

± is used to denote the size

Magnitude Precision

300 K

300K 310Kt/s

T/K

Error Analysis

➢ Say, f is a function of two measured quantities x and y, then total

differential of f would be,

df = (𝜕𝑓

𝜕𝑥)𝑦𝑑𝑥 + (

𝜕𝑓

𝜕𝑦)𝑥𝑑𝑦

ϵ(f) = (𝜕𝑓

𝜕𝑥)𝑦ϵ(𝑥) + (

𝜕𝑓

𝜕𝑦)𝑥ϵ(𝑦)

Square it, and take the average

Note -> Tell me why, by averaging, the cross term

containing terms become zero!

ϵ(f)2 = (𝜕𝑓

𝜕𝑥)𝑦ϵ(𝑥)2 + (

𝜕𝑓

𝜕𝑦)𝑥ϵ(𝑦)2

Random Errors and Total Differentials

➢ Derive (“show”) the equation for ε(B) and calculate the value (for water).

➢ From ε(B), you can obtain,

➢ Evaluate the partial derivatives in (2). You should be able to obtain:

(2)

Random Errors

➢ Use𝛜 𝐁

𝐁and

𝛜 𝐭

𝐭from this week

➢ Derive the equation for the propagation of errors for:

F =𝜂𝑠𝑝𝑐

=

𝜂𝑃𝑉𝐴𝜂0

− 1

𝑐

▪ Hint: find the partial derivatives

ϵ(𝐹)2=𝜕𝐹

𝜕𝜂𝑃𝑉𝐴

2

ϵ 𝜂𝑃𝑉𝐴2 +

𝜕𝐹

𝜕𝜂0

2

ϵ 𝜂02+

𝜕𝐹

𝜕𝑐

2

ϵ c 2

𝜕F

𝜕𝜂𝑃𝑉𝐴=

1

𝜂0𝑐

𝜕F

𝜕𝜂0= …

𝜕F

𝜕𝑐= ⋯

20

Calculations: Error Analysis

➢ Determine ϵ ηPVA − see last week lab

➢ ϵ(t) is found by using yourϵ t

tfrom last week and the flow time

for each solution

➢ ϵ(B) Is calculated in the same manner as ϵ(t) . Be sure to use

this week’s B value with last week’sϵ B

B.

➢ ϵ 𝜌 is the same as last week:

▪ 𝜖 𝜌𝑤𝑎𝑡𝑒𝑟 = 𝜌𝑤𝑎𝑡𝑒𝑟 𝑇ℎ𝑖𝑔ℎ − 𝜌𝑤𝑎𝑡𝑒𝑟 𝑇𝑙𝑜𝑤

▪ If you did not observe a temperature change above 0.5°C add

0.5°C to your lowest recorded temperature

21

Calculations: Error Analysis

➢ ϵ(ηo) is found using the table in the lab manual

▪ ϵ η0 = ηHigh− ηLow

▪ If you did not observe a temperature change above 0.5°C add 0.5°C to

your lowest recorded temperature

➢ ϵ c is obtained from cstockVstock = cdilVdil

▪ ϵ c1st dil = c1st dilϵ cstock

cstock

2

+ϵ V25mL pipet

25mL

2

+ϵ V50mL flask

50mL

2

▪ Errors are obtained from the stock solution flask and respective

volumetric glassware – be sure to record these

▪ Show equations for other dilutions with the appropriate propagation

➢ On graph (next slide): add error bars from the value of ϵ F . They will differ

from point-to-point22

Calculations: Error Analysis

▪ Get the intercept [η] and the range of error (R).

▪ R, max and min slopes MUST be done by hand.

▪ See Page 31 of CHM335 syllabus.

23Note: Graphical error analysis could be done either on original graph or separately.

R

Max

Min

𝜂 = 𝜂 ±𝑅

2

𝜖 𝜂 =𝑅

2

Calculations: Error Analysis

➢After obtaining [η] ± R/2, the viscosity average MW for cleaved and uncleaved PVA can be found through,

➢Use Mv and M’v to determine Δ.

Calculations: Δ

➢ Summary Calculations:▪ Use η0 from the trial with the shortest time

▪ Show sample calculations for ηPVA, ηsp, ϵ t , ϵ ρ , ϵ c , ϵηsp

cand calculations for B, M, M’, and Δ.

▪ Show equations for each ϵ c

▪ Show all partials of ϵ F

➢ Final Table:▪ Make a table with flow times of water and all solutions (label

cleaved and uncleaved)▪ Report values with errors and correct SF – remember errors are

always 1 SF

▪ Include values for ηPVA, ηsp, c,ηsp

c, [η] as well as everything

from calculations (errors) and graphs▪ Be sure to follow all instructions from page 9-15 in your lab

report

25

Results

• This is your first full lab report. Please refer to pages 38-39 prior to writing

• It must include:

– Title Page

• My name is

• My partner’s name

• Date/Section

– Abstract: This is the last thing you write even though it is the first thing that will appear in your report!

• 1 paragraph summary of what is to follow (including results)

• Write last

– Introduction

• Discussion of purpose

– Theory

• Derive any key formulas used in experiment/data analysis (refer to text)

• Define all symbols used in words

– Ex. ρ is density in g/cm3

– Procedure

• Attach the procedure you brought to class

• Must be signed by me

– Original Data Sheet

• Attach data sheet

• Must be signed by me

– Results

• Tabulate the data collected during the experiment26

Lab Report

• Questions in the presentation

• Calculations

– Provide sample calculations taking one from the original data to the final result

• Error Analysis

– Preform analysis as described previously (pgs 15-17)

• Graphical Analysis

– Preform analysis as described (pg 18)

• Final Table (with associated errors)

• Summary of Data

– Summarize final results. Include: Average intrinsic viscosity, average molecular weight and Δ

– Report errors and use proper SFs

• Conclusion

– Discuss:

• The significance of results

• Frequency of head-to-head connections

• Sources of error

• How experiment could be improved

• References

– Cite all sources referenced (this includes the textbook) 27

Lab Report

• Make sure all PVA solutions go into the

appropriate waste container

• Examine the data as you collect it – are your

results in agreement with the physical

principles at work?

• If you are confused or have questions please

come to my office hour or send an e-mail

28

Reminders

• Show me the results of the water runs after

the cleaning the viscometer

• Lab report: both electronic and physical copies

29

DO NOT FORGET TO TURN IN YOUR LAB

REPORTS

Reminders