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weights Oli omers Telomers
Pleistomers Telechelic polymers Macromers
Measurement of MW are usually ondissolved polymers
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Wetting of surface Then diffusion of solvent into polymer (case I Fickian
diffusion, or case II swelling)
Finally, polymer diffuses and dissolves
Solubility parameter determines which solventwill dissolve which polymer, from:
21/ 2 1/ 2
M M MG H T S
E E
1 2
1 2
anM M
V V
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Solubility parameter is the cohesive energy
density, EV
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experiments: For cross-linked polymers, from swelling coefficient,
0 1m m
Q m
For non-cross-linked polymers, from intrinsic
viscosity of the polymer in different solutions
Or theoretically, from group molar attraction constant
G
M
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. , . ,104g/mol3 1/21.05 .
104
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,
Ideal solutions is when the heat of mixing is zero, andRaoults law is obeyed
For incompressible mixtures,
1 1 2 2 1 1 2 2( ln ln )MG N G N G kT N n N n
1 1 2 2( ln ln )MS k N n N n
,relationlnMS k
0 1 2where !/ ! !N N N
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For ol mer ofx-mers then
1 1 2 2( ln ln )MS k N v N v
ori iiM
i
i
kV V
1
1
1 2
where vN xN
2
1 2
and v N xN
solutions also exist
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For dilute solutions we use Flor -Hu ins theor with
1 to represent heat of mixingMH
1 2
1 1 2 2 1 1 2
so ( ln ln )M
v
G kT N v N v N v
2
1 2 2 1 2
1ln(1 ) 1G RT v v v
and the osmotic pressure is:
2 2 1 2
1 1
n(1 ) 1v v vv V x
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By separating out the second virial coefficient, we can
n e ory - empera ure:2
22 1
1vA
1
1 2
1
At T when , 02
A
A To relate 1 to solubility parameter,
21V 1 1 2
and is related to the -temperature by
RT
5 3 1/ 2
12 1mC M
T
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Example:
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-
divided by total number of molecules
End-group analysis Specific functionalities at the ends ofmolecules measured from titration etc,
Usually for low MW because of poorsensitivity at high MW.
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2 1T RT
Properties thatdepends on number of
0
2
mc v nc H M
molecules and nottheir chemistry
0lim
f
c
f n
c H M
,
depression, vaporpressure lowering,
1 12
1
o
o
P PX
P
osmo c pressure0
limc
n
RT
c M
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Osmotic ressure exists because of the difference
between chemical potentials of the pure solvent andthe solvent in a solutionc
2
rom ,
1
nM
At Flor -tem erature, = 0, so osmotic ressure is
2 3 ...n
c M
independent of concentration, one concentration cangiveMn
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-
light-scattering (or X-ray and small-angle neutronscattering) Scattering occurs when radiation hits a particle with
size close to the radiation wavelength ue o uc ua ons n re rac ve n ex, g sscattered, and measurements of the intensities atdifferent angles give the size
2 2 2 2
1 0
4
2 ( / )1where ( ) and
I w n dn dcHcR H
R RT c I V N
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The basic equation is
For very small particles, P() = 1, is the scattering form2
2( ) ( ) ( )w
A cR R solvent M P
factor
0
3
( ) where turbidity fromx
R I I e
For particles > 0.05 times wavelength, P() 1, is thesingle chain form factor. At very small angles,
2 2 2 24 42( ) 1 exp( ) 1 ...3g
g g
g
R KP R K R K R K
14where sin2
K
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Limiting to zero angle and zero concentration
2
0
1
2 ...( ) w
c
H A cR M
2 21
0
41 11 sin ...
( ) 3 ' 2g
wc
cH R
R M
Summing both equations gives the Zimm plot
PlottingH[c/R()] vs sin2 (/2), we get
22
2
1
3( ') (initial slope)
16 (intercept)g
R
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The radius of gyration must be determined when
So the range of angles are limited
1gK R
g ,usually between 45 to 135
The radius of gyration is related to the end-to-enddistance, r, by
22
g
rR
For random coils, rdepends on MW, r2 = CM, and
r n l
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D namic li ht scatterin measures fluctuation of
scattering intensity with time at very small volumes forvery short times
g ves mo ecu ar mo on an us on coe c en
Used to study aggregation, adsorption, structural
chan es chain d namics
2 2
0( , ) (1 )(1 )app z g DcD K c D CR K k
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expensive Fast and chea methods measures relative MW
such as by intrinsic viscosity, and using Gel
Permeation Chromatography Intrinsic viscosity
Calculates the viscosity-average MW
1/1
, where a between 0.5 and 0.8aa
i iiv
i i
N MM
N M
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Dissolvin ol mers in solution increases solution
viscosity Define:
0solvent viscosity =
relative viscosity,
0
specific viscosity, 1sp rel
0 0
nintrinsic viscosity, sp rel
c cc c
ninherent viscosity =
rel
c
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For a dilute dis ersion of uniform ri id non-interactin
spheres, 0 2(1 2.5 )v
Assuming the polymer molecule is an equivalentsphere of radiusRe, then
0 2
0
2.5sp en
VV
2 1/ 2 301
0
42.53
sp eA
c
RN Mc M
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An em irical correlation for MW and intrinsic viscosit
the Mark-Houwink-Sakurada equation:K a
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Theoreticall the constant a can be used to determine
the shape of the molecule (Table 3.11) The MHS equation can also be expressed as
3/ 2
21/ 2 3 1/ 2 30K
rM M
In a Flory -solvent or a good solvent,
3/
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Ex erimentall a series of dilute ol mer solutions is
prepared and their viscosity measured (usingUbbelhode viscometer usually),
en ca cu a e rom nown an a
2
'sp
k cc
2ln''rel k c
c
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Chromatography(GPC) Separation based on
size-exclusion
so ca e zeExclusionChromatography
(SEC) Related to HPLC
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Stationary phase usually made of cross-linkedpolymers with pores
Mobile phase usually solvent that can dissolve thepolymers of interest
,time is the length of time a particular fraction remainsin the column
Distribution of analyte between mobile and stationaryphase
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The distribution coefficient is related to Gibbs freeenergy:R i
d
V VK
V
exp
d
d
S HK
GPC HPLCbut usually dK K K
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Smaller particles pass through the column slower Larger particles pass through the column faster
Detection usually by concentration (refractive index or
UV absorption) or by molar mass (light-scattering,
Calibration is required, usually with polymer standardsof PS, PMMA, PEO etc
But there is error when using non-similar polymers(Rg2/Mnot similar)
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So use a universal calibration From MHS equation, a polymer hydrodynamic volume
is proportional to MW:
3/ 22 3
0M r o ns ea o p o ng vs e u on vo ume, we p oVHvs elution volume
,
but what will it not work for?
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