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Anomalous Decoupling of Translational and Rotational Motion Under 1D Confinement, Evidences from Crystallization and Diffusion Experiments

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Dynamics in Geometrical Confinement

Part of the book series: Advances in Dielectrics ((ADVDIELECT))

Abstract

The molecular diffusion is intrinsically bound to the viscosity of the environment via the Stokes–Einstein (SE) relation, fixing an equality between the energetic barrier for translational motion and that for rotational motion. This relation, valid for melts at equilibrium, usually breaks down upon supercooling in proximity of the glass transition. As a common feature of the glassy dynamics, diffusion is enhanced compared to the viscosity and the segmental relaxation. In this chapter, we revise recent experimental evidence on the anomalous decoupling between rotational and translation motion in thin polymer films. While the segmental relaxation is almost unperturbed down to few tens of nanometers, diffusion of small molecules and cold crystallization kinetics tremendously slow down already at thicknesses exceeding by several folds the macromolecular size. After reviewing experimental methods permitting to assess the dynamics in confinement, we propose a unifying picture on the anomaly in the SE relation based on the different impact of irreversible chain adsorption on the rotational and translation motion. In particular, we experimentally verified the validity of a relation to predict the crystallization time of thin polymer films based on finite size effects and the slowing down in the dynamics scaling according to the SE relation. Remarkably, such expression fails in correspondence of a critical size comparable to the thickness of the layer irreversibly adsorbed within the timeframe of the experiment. Similarly, we observe a severe drop in tracer diffusivity of dielectric probes into apolar matrices, not explainable in terms of perturbations in the segmental dynamics, but ascribable to the presence of adsorbed layers, limiting the Brownian movements, precursors of molecular diffusion.

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Abbreviations

\(\alpha \)–:

Structural (segmental) process

\(\alpha ^{\prime }\)–:

Constraint structural (segmental) process

\(\beta \) :

Avrami exponent

\(\Gamma \) :

Drop in \(\Delta \varepsilon \) due to crystallization

\(\delta \) :

Drop in \(\Delta \varepsilon \) due to adsorption

\(\Delta \varepsilon \) :

Dielectric strength

\(\Delta \)E:

Transport energy barrier to the growth front

\(\Delta \)F*:

Barrier for nucleation

\(\varepsilon _{\infty }\) :

Instantaneous dielectric constant

\(\eta \) :

Viscosity

\(\mu \) :

Dipole moment

\(\Lambda \) :

Nucleation term of the crystallization rate

\(\xi \) :

Fractional coefficient

\(\tau \) :

Segmental relaxation time

\(\tau _{D}\) :

Diffusion time

1D:

1-dimensional

a :

Radius

AFM:

Atomic force microscopy

Al:

Aluminum

BDS:

Broadband dielectric spectroscopy

C:

Crystallization rate

D:

Diffusion term of the crystallization rate

DSC:

Differential scanning calorimetry

\(\mathrm{D}_\mathrm{tr}\) :

Tracer diffusion coefficient

g:

Kirkwood factor

G:

Crystal growth rate

\(\mathrm{G}_{1}\) :

Linear crystal growth rate

h:

Film thickness

\(\mathrm{h}_\mathrm{ads}\) :

Thickness of the irreversibly adsorbed layer

\(\mathrm{k}_\mathrm{B}\) :

Boltzmann constant

L:

Diffusive length

l-PS:

Polystyrene labeled with 4-[(4-cyanophenyl) diazenyl] phenyl}(methyl) amino

\(\mathrm{M}_\mathrm{w}\) :

Weight average molecular weight

Ñ:

Density of dipole moments

p:

Pressure

PDI:

Polydispersity index

PHB:

Poly(hydroxy butyrate)

PET:

Poly(ethylene terephthalate)

PS:

Polystyrene

SE:

Stokes–Einstein

t:

Time

T:

Temperature

\(\mathrm{T}_{0}\) :

Temperature where molecular motion would cease

\({ t}_\mathrm{{tads}}\) :

Characteristic adsorption time

\({ t}_\mathrm{{CRY}}\) :

Crystallization time

\(\mathrm{t}_\mathrm{{N}}\) :

Induction time

\(\mathrm{t}_\mathrm{{P}}\) :

Characteristic time

\(\mathrm{T}_\mathrm{{g}}\) :

Glass transition temperature

\(\mathrm{T}_\mathrm{{M}}\) :

Melting point

\(\mathrm{X}_\mathrm{{C}}\) :

Crystallinity

\(\mathrm{T}_\mathrm{{CC}}\) :

Cold crystallization temperature

\(< {\ldots } >\) :

Statistical average

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Acknowledgments

S.N. acknowledges financial support from the funds FER of the Université Libre de Bruxelles. M.W. acknowledge financial support from the Research Council of the KU Leuven, Project No. OT/11/065, and financial support from FWO (Fonds Wetenschappelijk Onderzoeks-Vlaanderen), Project G.0642.08.

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Authors and Affiliations

  1. Laboratory of Polymer and Soft Matter Dynamics, Faculté des Sciences, Université Libre de Bruxelles, Boulevard du Triomphe, Bâtiment NO, 1050, Bruxelles, Belgium

    Simone Napolitano

  2. Laboratory of Acoustics and Thermal Physics, Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200D, 3001, Leuven, Belgium

    Michael Wübbenhorst

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  1. Simone Napolitano
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Correspondence to Simone Napolitano .

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  1. Group of Molecular Physics, University of Leipzig, Leipzig, Germany

    Friedrich Kremer

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Napolitano, S., Wübbenhorst, M. (2014). Anomalous Decoupling of Translational and Rotational Motion Under 1D Confinement, Evidences from Crystallization and Diffusion Experiments. In: Kremer, F. (eds) Dynamics in Geometrical Confinement. Advances in Dielectrics. Springer, Cham. https://doi.org/10.1007/978-3-319-06100-9_11

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