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, 845 41 Bratislava 45, Slovakia 2 Institute of Physics of SAS, Dúbravská cesta 9, 845 11 Bratislava 45, Slovakia PPC 10 , Smolenice, Slovakia 2011

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 ?

E S R - spin probe method B0 Nitroxide - type spin probes: TEMPO VprobeW = 170 Å3 => RprobeW,eq = 3.43 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 = ± 1/2 and  MS = 1 MI = -1, 0, +1 and  MI = 0

E S R spectral evolution of TEMPO s l o w regime The spectral evolution from b r o a d triplet (70 - 60 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

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

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

E S R : molecular vdW-bonded glass-formers ---------------------------------------------- System Tg , K T50G , K T50G/Tg ---------------------------------------------------------------------- Pc 158 194 1.23 DEP 184 230 1.25 m-TCP 205 249 1.22 DGEBA 257 283 1.10 Empirical findings: 1) T50G > Tg and 2) T50G  (1.1 – 1.25) Tg T50G

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

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

E S R : molecular H-bonded glass-formers ---------------------------------------------- System Tg , K T50G ,K T50G/Tg ---------------------------------------------------------------------- PG 172 248 1.44 DPG 189 250 1.32 TPG 186 247 1.33 m-TOL 187 239 1.28 GL 190 283 1.49 Empirical findings: 1) T50G > Tg and 2) T50G  (1.3– 1.5) Tg T50G

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

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

E S R : polymeric glass-formers --------------------------------------------------- System Tg , K T50G ,K T50G/Tg ------------------------------------------------------------------------------ c-t-1,4 PBD 174 224 1.29 PPG 197 242 1.23 c-1,4-PIP 205 251 1.22 PIB 205 263 1.28 PVME 250 276 1.11 ---------------------------------------------------- Empirical findings: 1) T50G > Tg and 2) T50G  (1.1– 1.3) Tg T50G

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)

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  ( 10 -6 – 10 -11 s ) and - fractions of s l o w and f a s t spin probes: Fs  <1;0> and Ff =1 - Fs  <0;1>

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

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)

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

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

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  (1.1 -1.5)Tg is characterized by the empirical finding: 3 (T50G) = 2.25 ± 0.15 ns corresponding according to the SQM model (Tao – Eldrup - Nakanishi & Jean) to the occurrence of the mean equivalent free volume hole size: Vh (T50G) = 122 ± 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

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

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) = 2.2 ± 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