Molecular weight and dimensions of polymers and their ... weight and dimensions of polymers and...
Transcript of Molecular weight and dimensions of polymers and their ... weight and dimensions of polymers and...
UNESCO/IUPAC Postgraduate Course in
Polymer Science
Molecular weight and dimensions of polymers and their assemblies
Jiří Horský
Institute of Macromolecular Chemistry ASCR, Heyrovsky sq. 2, Prague -162 06
http://www.imc.cas.cz/unesco/index.html
Lecture:
Polymers
M gives independent information
M affects
properties such as density, degree of crystallization, Young modulus, melt viscosity, glass transition temperature etc
Consequently, M affects application use and processing methods
M
cRTc =Π → 0
[ ] aKM=η
+
+=
→
...2
sin3
161
1 2222
0
θλ
πθ
g
c
Rn
MR
Kc
Osmotic pressure (absolute, 5 103-106)
Static Light scattering (absolute, 104-107)
Intrinsic viscosity (relative, >103)
And many more - analytical ultracentrifugation, ebullioscopy, end-group analysis, vapor pressure osmometry, ….
Classical methods for determination of molecular weight of polymers(see Polymer solutions in a nutshell )
(Mark-Houwink Eq.)
Zimm plot (2 D plot for 2 independent variables) => M, A2, Rg
Polymer sample (usually) contains molecules of various polymerization degree
Experimental methods give us only some average of the molecular weight
a
c
KMc
Y =
→0
∑=i
iYY ∑=i
aii
a KMcMcK a
i
aiiMwM
1
= ∑
rigid 0.8 flexible8.05.011ηLS >−==−=Π aaa
∑
∑∑ −
−− =
=
iii
iii
iii
Mw
MwMwM 1
01
1n ∑
∑∑ ==
iii
iii
iii
Mw
MwMwM 0
1
w
∑
∑=
iii
iii
Mw
MwM 1
2
z
number-average weight-average z-average mol. weight
∑
∑∑ =
=−
iii
iii
iii
Mx
MxMxM 0
11
n∑
∑=
iii
iii
Mx
MxM 1
2
w∑
∑=
iii
iii
Mx
MxM 2
3
z
Averages with integer a can be defined as the ratio of moments around the origin
w weight fraction, x molar fraction
Combined averages give only partial information on the sample molecular weight non-uniformity : polydispersity index Mw/MnFull information:relative amount of each polymerization degree – a distribution function
number DF - xi, weight (mass) DF – wi
cumulative discrete vs continous DF
cumulative vs differential DF
∑∑==
i
ji
i
jj wx
11
dM
dcumDFdifDF =
Mathematically defined DF
Discrete DF Poisson most-probable)!1)(1(
1
−+=
−−
Pa
aPew
Pa
P12 )1( −−= P
P aPaw
0 25 50 75 1000.00
0.02
0.04
0.06
0.08
0.10
x
DP
Poisson PI=1.01Most probable PI=1.95
0 25 50 75 1000.00
0.02
0.04
0.06
0.08
0.10
w
DP
Poisson PI=1.01Most probable PI=1.95
Continuous DF
Schulz-Zimm
MaMMb
aw b
b
d)exp()1(
d1
−+Γ
=+
Mb
M
aMaw d)ln
1exp(
1d 2
2−=π
0 50000 100000 1500000.00000
0.00002
0.00004
dx/d
M
M
Mn=40000
PI = 1.1,1.3, 1.75, 2.0
0 50000 100000 1500000.00000
0.00002
0.00004
dw/d
M
M
Mn=40000
PI = 1.1,1.3, 1.75, 2.0
logarithmic normal
0 50000 100000 1500000.0
0.2
0.4
0.6
0.8
1.0
cummulative DFs
x, w
M
Mn=40000 M
w=60000
number DF, weight DF
0 50000 100000 1500000.00000
0.00001
0.00002
dw/d
M
M
Mn=40000 M
w=60000
log-normal, Schulz-Zimm
Principle of Size Exclusion Chromatography
solvent flow
Partition between the flowing solvent and the solvent in the pores
Elution time (volume) is a function of the particle (hydrodynamic) size
Above certain size all particles are equal, flow only through the interstitial volume
log M
V0 V0+ Vi
log M=a +b V +….
Detectors: (i) mass sensitive (refractometer, evaporative light scattering detection)(ii) molecularly sensitive (end group UV absorption)(iii) molecular-mass sensitive (light scattering, viscometric)
Standard configuration (i); up-to-date = multidetector (i)&(iii)
Me
5 6 7 8 9
V [mL]
I [a
rbitr
ary
units
] Baseline substraction
Normalization
∫=
R
L
d)(
)()( V
V
VVI
VIVw
5 6 7 8 90.0
0.5
1.0
1.5
2.0
2.5
V [mL]
d w
/d V
[1/
mL
]
Point to point correspondence of cumulative V and M or log M distributions
∫ ∫∫ ==L
LL
log
log
log
log
dlogdlog
d)(d)(dlog)(log
V
V
M
M
M
M
MM
VVwVVwMMw
V
MVw
Mw
dlogd
)()(log
−=M
MwMw
303.2)(log
)( =
5 6 7 8 90.0
0.5
1.0
1.5
2.0
2.5
V [mL]
d w
/d V
[1/
mL
]
3 40
1
2
3
M
d w
/d lo
gM
log M
∫ ∫∞ ∞
==0 0
1ddd
dloglogdd
MM
wM
M
w Mn = 3100 Mw = 3780 PI = 1.22
0 5000 10000 150000.0
0.1
0.2
0.3
0.4
M
104 d
w/d
M
M(V) – valid for the column, polymer, solvent etc
SEC with a mass detector only
• calibration by polymer standards
• universal calibration – hydrodynamic volume [η]M (V) Mark-Houwink Eq. log [η]M =log K+(1+a)log M
• polystyrene calibration
SEC with mass & molecular-mass detectors
viscosity detector – gives M through the universal calibration without Mark-Houwink parameters
static light-scattering detector
Averages of M: directly according discreet definitions
Distribution: in two steps (i) LS data are used for the calibration equation (ii) RI data are treated in standard way
Sedimentation Analysis – Analytical Ultracentrifuge(macromolecular archelogy? – Swedberg 1923, Nobel prize 1926)
Declared clinically dead in 1980’s but then resurrected (natural macromolecules)
centrifugal force=friction resistance (f u) => sedimentation velocity u
sedimentation coefficient sω
sedimentation velocity
T
vMD
f
vM
r
us
R
)1(
N
)1(
A2
ρρω
−=−==
ω
sedimentation equilibriumsmall ω sedimentation creates temporal concentration gradient
which is opposed by diffusion, equilibrium gradient is achieved
c
Mr
c
r~
d
d1
Principle of Field –Flow Fractionation(J. C. Giddings)
solvent flow
Elution time (volume) is a function of the particle (hydrodynamic) sizebigger particles (up to 0.1 mm vs. SEC <100 nm) smaller adsorption
change of mechanism (bigger particles first), absolute detection LS
Force perpendicular to the flow
fieldthermal, electrical..assymetrical flow
Why MS if we have SEC? ResolutionMS: M/w1/2=10000 SEC: Ntp=5.54(V/w1/2)2=10000 V/w1/2=42
The Nobel Prize in Chemistry 2002
“ for the development of soft desorptionionisation methods for mass spectrometricanalyses of biological macromolecules”
MALDI-TOF mass spectrometry
Mass Spectrometry
Mass spectrometry
zeUmv =2
21
Principle: a charge particle is accelerated in electromagnetic field
For measurement of molecular weight, M,
(i) the sample must be vaporized and charged (ion source)(ii) particles must be separated according to M/z (mass analyzer)(iii) particles with the same M/z must be counted (detector)
In electric field
Low-molecular-weight compounds:
M is used for identification
vaporization puts an upper limit on measured M
the most widely used electron impact ionizations fragments the sample molecules
Fragmentation gives information on the structure of the compound
For a long time, polymer researches used MS only for analyzing
At the same time, they were fascinated by the MS precision
polymer additives pyrolysis products
etc…
M atrixA ssitedL aserD esorptionI onization
T imeO fF light
M assS pectrometry
Matrix:2,5-dihydroxybenzoic acid1,8,9-trihydroxyantracene
Laser:337 nm, pulse <4 ns, 40 kW/4mW
Sample preparation
1- 2 µµµµL per spot (2-10x)
0.2% sample
1-2% matrix
& ionizitation agent (NaCl, AgTFA)
+
++
PST Mw/Mn(kDa)
MALDI 62.3/61.9
SEC 71.3/71.1
For samples with M>20 000 multidetector SEC is the first choice
3000 4000 50000
2000
4000
a.i.
m/z
40000
2000
4000
a.i.
m/z
3940 3960 39800
2000
4000
a.i.
m/z
MALDI-TOF MS can distinguish individual oligomers
and even isotopic resolution(in reflector mode)
Monoisotopic peak (C12 only)
The strength of MALDI-TOF is with samples M<20000 (For samples with M>20 000, the first choice is the multi-detector SEC)
M = Meg1 + n Mm + Meg2+Mia
HO [CH2CH2O] [CH2CH2O].....[CH2CH2O] H Na+
1200 1400 1600 1800 2000 2200 2400 2600 28000
1000
2000a.
i.
M/z
17+ 39 * 44 + 1 + 23= 1758
PEG:MPEGPEG:MPEG1 : 1
18000
1000
a.i.
M/z
1714
1758
17721816
1200 1400 1600 1800 2000 2200 2400 2600 28000
1000
2000
3000
4000
5000
6000
7000
a.i.
M/z
Mixture of two homopolymers
PEG:PPG
1700 1720 1740 1760 1780 1800 1820 1840 18600
1000
2000
3000
4000
5000
6000
7000
a.i.
M/z
PEG : PPG2 : 1
1758
1782
18021724
1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 35000
1000
2000
a.i.
M/z
Binary copolymers (PEG/PPG -Pluronic)
M = Meg1+ n Ma + m Mb + Meg2 + Mia
17500
1000
2000
a.i.
M/z
1750 1760 1770 1780 1790 18000
1000
2000
a.i.
M/z
1782
1782=17+30*58+1+23 1782=17+29*44+8*58+1+2322*58 = 29*44
d e n d r i m e r
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
10 00 1 500 2 000 25 000
2 00
4 00
6 00
8 00
10 00
12 00a.
i.
M /z
∆ 126
1812
Si
SiSi Si
Si
Si
Si
Si
Si
SiSi
Si
Si
Ag
MALDI-TOF mass spektrumof 2nd generatiom carbosilane dendrimer
(defect detection)
Montaudo G et al. Prog. Polym. Sci 31, 277-357 (2006 )
www.iupac.org/publications/books/pbook/PurpleBook-C3.pdf
Kostanski LK et al. J. Biochem. Biophys. Methods 58, 159–186 (2004)
Literature:
UNESCO/IUPAC Postgraduate Course in
Polymer Science
Molecular weight and dimensions of polymers and their assemblies
Jiří Horský
Institute of Macromolecular Chemistry ASCR, Heyrovsky sq. 2, Prague -162 06
http://www.imc.cas.cz/unesco/index.html
Lecture: