1. guest molecule dynamics and free volume
On the relationships
between
guest molecule dynamics and free volume in
a series of small molecular and polymer glass-formers
by means of E S R and P A L S techniques
H.Švajdlenková1, O.Šauša2, M.Iskrová2, V.Majerník2, J.Krištiak2 and J.Bartoš1
1 Polymer Institute of SAS, Dúbravská cesta 9, Bratislava 45, Slovakia
2 Institute of Physics of SAS, Dúbravská cesta 9, Bratislava 45, Slovakia
PPC 10 , Smolenice, Slovakia 2011

2. Introduction and motivation
The structural - dynamic state of condensed materials can be measured
directly, i.e. by i n t e r n a l structural and dynamic probe techniques
such as X-ray diffraction (XD) and scattering (NS , ... ), or relaxation (DS , ... ) and
nuclear resonance (NMR , ... ) techniques, respectively
indirectly, i.e., by e x t e r n a l structural - dynamic techniques such as
a) m o l e c u l a r probing the local structure and its fluctuation using
stable radical species , the so - called spin probes, e.g. , TEMPO
via the reorientation behavior by means of electron spin resonance E S R
b) a t o m i c probing the static or/and dynamic free volume using
ortho - positronium (o-Ps) probe
via the annihilation behavior by means of P A L S
The actual questions:
What are the relationships between the E S R and P A L S responses ?
What is the role of free volume detectable by P A L S in the spin probe dynamics ?

3. E S R - spin probe method B0 Nitroxide - type spin probes: TEMPO
VprobeW = Å3 =>
RprobeW,eq = Å
Energy MS 1 -1 MI ΔE
+1/2
-1/2
B=0
B0
Magnetic field
fine splitting
hyperfine
splitting
ESR follows the dynamics of magnetization
of spin system M in static magnetic field
B0 (0 = B0) making precession motion
with angle frequency ω (ω/2 ~ 9 GHz)
Resonance condition and selection rules:
  0 : ΔE = hν = ge e Bext
MS = ± 1/ and  MS = 1
MI = -1, 0, +1 and  MI = 0

4. E S R spectral evolution of TEMPO
s l o w regime
The spectral evolution
from
b r o a d triplet ( G)
from spin probes in s l o w motional regime to
n a r r o w triplet (40 – 30 G)
from spin probes in f a s t motional regime
f a s t regime

5. A. E S R spectral evolution and analysis methods:
The f i r s t quantitative measure of
the spin probe reorientation dynamics:
 spectral parameter of mobility: 2AZZ’(T)
directly from ESR spectra using WIN - EPR program
Features:
quasi - sigmoidal dependence with various effects from
- s l o w to f a s t regime transition at
the basic characteristic ESR temperature: T50G
- a c c e l e r a t i o n s within s l o w or/and
f a s t regime at further characteristic ESR
temperatures:
e.g. TX1s,Azz , TX2s,Azz and TX1f,Azz

6. I. Molecular vdW-bonded glass-formers
Propylene carbonate (Pc)
Dietyl phthalate (DEP)
meta-Tricresyl phosphate (m-TCP)
Diglycidyl-ether of bis-phenol A (DGEBA)

7. E S R : molecular vdW-bonded glass-formers
System Tg , K T50G , K T50G/Tg Pc
DEP
m-TCP
DGEBA
Empirical findings:
1) T50G > Tg and
2) T50G  (1.1 – 1.25) Tg
T50G

8. P A L S : molecular vdW-bonded glass-formers
τ3 (T50G) = 2.28 ± 0.17 ns
DGEBA:
G. Dlubek et al.: PRE (2006)

9. II. Molecular H - bonded glass-formers
Propylene glycols (PGs)
n = 1, 2 and 3
Glycerol (GL)
meta – Toluidine (m-TOL)

10. E S R : molecular H-bonded glass-formers
System Tg , K T50G ,K T50G/Tg PG
DPG
TPG
m-TOL GL
Empirical findings:
1) T50G > Tg and
2) T50G  (1.3– 1.5) Tg
T50G

11. P A L S : molecular H-bonded glass-formers
τ3 (T50G) = 2.20 ± 0.15 ns

12. III. Polymer glass-formers
H o m o polymers:
Diene type:
cis-trans-1,4-PBD
cis-1,4-PIP
Vinyl – and Vinylidene type:
PIB
PVME
H e t e r o polymer:
PPG

13. E S R : polymeric glass-formers
System Tg , K T50G ,K T50G/Tg
c-t-1,4 PBD
PPG
c-1,4-PIP
PIB
PVME
Empirical findings:
1) T50G > Tg and
2) T50G  (1.1– 1.3) Tg
T50G

14. P A L S : polymeric glass-formers
τ3(T50G) = 2.14 ± 0.19 ns
PIB :
D.Kilburn, G.Dlubek et al.:
Macrom.Chem.Phys. (2006)
c-1,4-PIP:
Y.Yu:
PhD Thesis (2011)

15. B. E S R spectral evolution and analysis methods:
The s e c o n d quantitative measure of
spin probe reorientation dynamics:
 rotational correlation time: c(T)
from
relaxation model of spin system magnetization
by simulation of the ESR spectra using
Non-linear Least Square Line (NLSL) program
(B u d i l et al. 1996)
Outputs:
correlation times : c  ( – s ) and
- fractions of s l o w and f a s t spin probes:
Fs  <1;0> and Ff =1 - Fs  <0;1>

16. ESR data: c vs. 1/T and Fs , Ff vs.T
Mutual relationships between the t w o measures of spin probe TEMPO mobility:
1) dynamic heterogeneity in cis-1,4-PIP over 80K fromTX1s = 170K up toT50G = 250K
2) Tcτ  TCFf  T50G
3) TX1f,  TX1s  TX1Ff ; TX1s,  TX2s  TX2Ff and TX2f,  TX1f but no F counterpart

17. ESR vs. PALS relationships
TX1s,Azz and TX1Fs  Tb1,G
TX2s,Azz and TX2Ff  Tg PALS
T50G and TCFf  Tb1L and  Tb1,L
TX1 f,Azz  Tb2L and Tb2,L
LT 9.0
and m o r e o v e r:
c (T50G)  3 (T50G)
Y.Yu: PhD Thesis (2011)

18. PALS and free volume (FV) data
Standard quantum - mechanical (SQM) model of o-Ps annihilation
in spherical hole:
[Tao (1972) – Eldrup (1981) – Nakanishi &Jean (1988) ]
3 = 3,0{ 1 – Rh/(Rh + R) + (1/2).sin[ 2Rh/(Rh + R) ] }-1
where
Rh – free volume hole radius => Vh = (4 /3) Rh3
3,0 and R - empirical parameters
Usually,
the SQM model used in the sense of equivalent m e a n free volume size:
=> the s l o w to f a s t transition of the smallest spin probe TEMPO at T50G
appears to be due to the relation Vh(T50G) = 122 ± 15 Å3 < VTEMPOW = 170 Å3
closely related to the local free volume fluctuation as observed by PALS

19. PALS and FV data: Rh and n(Rh) vs.T
RTEMPOW,eq vs. Rh relationships:
a c c e l e r a t i o n within the s l o w regime at T X1s,Azz:
RW,eqTEMPO -> the h i g h e s t (tail) value of hole volume distribution
a c c e l e r a t i o n within the f a s t regime at T X1f,AZZ:
RW,eqTEMPO -> the m a x i m a l (peak) value of hole volume distribution

20. Summary and Conclusions
The most pronounced effect in the ESR response in a series of small molecular
and polymer glass-formers / TEMPO systems, i.e., s l o w to f a s t transition
in the spin probe TEMPO mobility at T50G  ( )Tg is characterized by
the empirical finding:
3 (T50G) = ± ns
corresponding according to the SQM model (Tao – Eldrup - Nakanishi & Jean) to
the occurrence of the mean equivalent free volume hole size:
Vh (T50G) = ± 15 Å3
almost i n d e p e n d e n t of the intra-molecular structure (topology,rigidity)
as well as of the type of inter-molecular (vdW- or H-bonding) interactions between
the matrix constituents, being a characteristic of the given spin probe TEMPO
The changes in the smallest spin probe TEMPO dynamics at characteristic ESR temperatures are closely related to the local free volume fluctuation as observed by PALS

22. Outline
1. Introduction and motivation 2. Phenomenological and semi-empirical results E S R responses on a series of amorphous glass-forming systems of various intra-molecular chemical structure (topology, rigidity) and inter-molecular physical interactions a) two measures of spin probe (TEMPO) dynamics: spectral parameter of mobility: 2Azz’ (T) and correlation time, c (T) 2) characteristic E S R temperatures P A L S responses on the same glass-formers a) ortho-positronium (o-Ps) lifetime 3(T) and dispersion 3(T) ; mean free volume Vh and its distribution n(Rh) from the SQM model b) characteristic P A L S temperatures 3. General relationship between the E S R and P A L S parameters i.e. between molecular and atomic e x t e r n a l probing of the organic matter 4. Summary and Conclusion

23. Partial summary
The most pronounced effect in the ESR response of the spin system,
i.e., s l o w to f a s t transition in the smallest spin probe TEMPO mobility in
a series of small molecular and polymer glass-formers at T50G is
characterized by the empirical 3 (T50G) finding:
3 (T50G) = ± 0.4 ns
corresponding to the occurrence of the equivalent m e a n free volume hole,
Vh (T50G) = 122 ± 15 Å3
nearly i n d e p e n d e n t of the chemical structure, i.e. topology (molecular
vs. macromolecular) and rigidity (rigid vs. flexible) of the matrix constitutents
as well as of the type of inter-molecular (H - or vdW - bonding) interactions
between the matrix constituents
Since Vh (T50G) < VTEMPO it may be interpreted as a fluctuation free volume
needed for the spin probe transition from s l o w to f a s t motional regime