intrinsic vis c

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Paul Russo 2/17/2014

Intrinsic Viscosity

Introduction

One of the most precise measurements in polymer science is also the simplest and

cheapest. Intrinsic viscosity !hich is measured from the flo! time of a solution throu"h asimple "lass capillary has considera#le historical importance for esta#lishin" the very

e$istence of polymer molecules. It also provides considera#le physical insi"ht. In this la#

each "roup !ill study the intrinsic viscosity of hydro$ypropylcellulose a common polymerderived from cellulose%%hopefully at a different temperature.

Viscosity in general

&or a discussion of viscosity refer to the '(o!)o' document on usin" the *ells%

+roo,field cone and plate viscometer. )he viscosity measured in a capillary viscometer is

not o#tained at a defined shear rate. Of several fi$es to this pro#lem the simplest is simply

to i"nore it. )his amounts to assumin" that the fluid is -e!tonian over the entire ran"e ofshear rates encountered #y the fluid as it passes do!n the capillary.

The Ubbelohde capillary viscometer

)he most useful ,ind of viscometer for determinin" intrinsic viscosity is the'suspended level' or ##elohde viscometer s,etched #elo!

)he viscometer is called 'suspended level' #ecause the liuid initially dra!n into the small

upper #ul# is not connected to the reservoir as it flo!s do!n the capillary durin"

measurement. )he capillary is suspended a#ove the reservoir. In conunction !ith the pressure%eualiation tu#e this ensures that the only pressure difference #et!een the top of

the #ul# and the #ottom of the capillary is that due to the hydrostatic pressure%%i.e. the

!ei"ht of the liuid. Other desi"ns e.". the 3annon%&ens,e viscometer do not provide forthis and !ill "ive erroneous results in an intrinsic viscosity determination. uch

Intrinsic Viscosity 1

3opyri"ht P.. Russo 2005

+

6 Plu" !hile dra!in" fluid

into capillary

)imin" lines

3 Pressure euili#rationarm

+i" +ul#/Reservoir

8ittle #ul# !hosevolume 9 V.

: 9 V/tflo!

3apillary


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viscometers are useful in other e$periments%%e.". chec,in" the sta#ility of some polymer

solution !here one is only interested in measurin" a chan"e in the flo! time.

Use of the Ubbelohde viscometer

)he theory of the viscometer is rele"ated to 6ppendi$ I. &or no! it is sufficient toaccept that a capillary viscometer measures a viscosity as defined in the *ells%+roo,field

handout althou"h no parallel plates or force determinations are involved. 3apillary

viscometry is conceptually simple the time it ta,es a volume of polymer solution to flo!throu"h a thin capillary is compared to the time for a solvent flo!. It turns out that the flo!

time for either is proportional to the viscosity and inversely proportional to the density.

solvent

solvent solvent t

ρ

η =

n sol

n sol

n sol t ;

;

; ρ

η

=

*e define the relative viscosity to #e the ratio solvent n sol η η /; . &or most polymer solutions at

the concentrations of interest 1/; ≈ solvent n sol ρ ρ . )hus to a very "ood appro$imation therelative viscosity is a simple time ratio

solvent n sol rel t t /;=η

*e also define a 'specific viscosity' to #e the fractional chan"e in viscosity upon addition

of polymer

solvent

solvent n sol sp

η

η η η

−= ; easurin" at ero

concentration .

B. aunders and &. C. Daras Macromolecules 1@ 25EF%25E@


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-ote that #oth plots have the same intercept !hich is called Gη ] the intrinsic viscosity.

[ ] rel c

sp

cc

cη

η η lnlimlim

1

00

−→→

≡=

C$ercise prove the second relation in the a#ove euation%%i.e. that Gη ] o#tained

from rel c η ln1− vs. c plots is identical to Gη ] o#tained from

c

spη vs. c plots.

)he units of Gη H are inverse concentration. Intrinsic viscosity has '"ro!n up' around

some fairly unconventional units re"ardin" concentration. )he most commonly used

concentration is "/d8 ore importantly for our purposes is the scalin" relationship #et!een Gη H and

molecular !ei"ht

[ ] a KM =η ar,%(ou!in, Relationship=

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)hus lo"%lo" plots of Gη H a"ainst molecular !ei"ht have the intercept lo"


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6 more modern !ay to "enerate >ar,%(ou!in, plots is to couple a ?P3 apparatus to an

on%line intrinsic viscometer. Ideally one uses three detectors ar,%(ou!in, parameters from triple detectors are not

al!ays very ro#ust.

Guidelines for use of the Ubbelohde viscometer

One must first select the viscometer and then the initial concentration. )here are nohard and fast rules #ut these "uidelines are helpful

• )he flo! time of the pure solvent should e$ceed 100 s

• )he flo! time of the most concentrated polymer solution should #e 2% times lon"er

than that of the pure solvent. &or hydro$ypropylcellulose 9F0000= a#out 0. "/d8should #e OD. &or de$tran 9150000= a#out 1.E "/d8 should #e OD.

• Lou must ,no! the minimum amount of fluid reuired to operate the viscometer.

• 6dd that much of the most concentrated solution


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• Plot as you "o.

• Deep dilutin" the solution until

a= Lour plots strai"hten out and "ive nearly identical intercepts


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,tep 5. Put a non volume of your most concentated solution into the viscometer. )his

should #e the minimum reuired to operate the viscometer rounded up!ard to some even

num#er of m8. easure the flo! time as an avera"e. If it e$ceeds

the flo! time of the pure solvent #y a factor of 2%E then "ood. If not empty the viscometerand adust your initial concentration accordin"ly.

,tep 3. Repeat flo! time measurements on your solution until the standard deviation is solvent if usin" plastic!are=. &ailin" that use a syrin"e and insolu#le tu#in" then !ei"h

the amount removed and convert to m8 usin" density of the solution • Remove 2.0 m8 and replace !ith 2.0 m8 solvent


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• Remove 4.0 m8 and replace !ith 4.0 solvent a,e #oth the necessary plots in C$cel. Lou can save an Intrinsic Viscosity templateM

• In Ori"in it;s easy to "ive the plots proper error #ars usin" those standard deviation datayou "ot from C$cel.

• Report GηH as the avera"e of the intercepts of the t!o plots.

• Report ± the uncertainty in GηH as half the difference.

• Report !hether or not your plots follo! the slope relationship "iven in &lory 1@E4. )he

t!o slopes are mathematically relatedM

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