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arxiv: 2601.15967 · v2 · submitted 2026-01-22 · ⚛️ physics.chem-ph · cond-mat.soft

Response of fluorescent molecular rotors in ternary macromolecular mixtures

Mingshan Chi , Anh-Thy Bui , Pierre Lidon , Yaocihuatl Medina-Gonzalez This is my paper

Pith reviewed 2026-05-16 12:03 UTC · model grok-4.3

classification ⚛️ physics.chem-ph cond-mat.soft
keywords fluorescent molecular rotorspolyethylene glycol mixturesfluorescence lifetimemicroviscositylinear mixing rulefree volume theoryternary solutionscybotactic environment
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The pith

In ternary PEG mixtures, fluorescent molecular rotor lifetimes follow a linear rule with the proportion of light and heavy polymers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how a fluorescent molecular rotor responds to binary and ternary aqueous solutions of polyethylene glycols differing in molecular weight. It establishes that, across the tested composition range, the rotor's fluorescence lifetime changes linearly according to the relative amounts of each PEG type, with more heavy PEG producing longer lifetimes. This finding helps clarify how rotors sense their immediate surroundings in polymer blends, supporting more reliable use for microviscosity measurements in complex fluids without repeated full recalibrations.

Core claim

For the investigated composition range of ternary mixtures, a linear mixing rule applies for fluorescence lifetime with the proportion of the two PEG, and with an increasing ratio of heavy PEG leading to larger lifetimes. These results allow to test more precisely the free volume theory, which has been proposed in the context of probing glass transition. Analysis show that while this theory semi-quantitatively captures the observation, its precise use raises some questions.

What carries the argument

The linear mixing rule for fluorescence lifetime, which directly ties the rotor response to the weighted fractions of the two PEG components in the mixture.

If this is right

  • Lifetimes in PEG blends can be predicted from the simple proportion of each polymer size.
  • Higher fractions of heavy PEG raise the effective local restriction sensed by the rotor.
  • Free volume theory accounts for the trend at a semi-quantitative level.
  • Calibration procedures for rotors in polymer solutions can rely on linear interpolation between binary endpoints.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same linear dependence could be checked in mixtures involving other water-soluble polymers to see if the rule generalizes beyond PEG.
  • In biological fluids containing macromolecules of varying sizes, rotors might report an effective average chain length without separate calibrations for each component.
  • The questions raised about precise application of free volume theory point to the value of testing rotors in mixtures where specific polymer-polymer or polymer-water interactions are known to be strong.

Load-bearing premise

The local environment around the rotor can be treated as a simple linear combination of the two PEG types without extra specific interactions or the need for mixture-specific adjustments.

What would settle it

Measure rotor lifetimes in a ternary PEG mixture whose composition falls outside the paper's tested range and check whether the values deviate from the linear prediction calculated from the two PEG proportions.

Figures

Figures reproduced from arXiv: 2601.15967 by Anh-Thy Bui, Mingshan Chi, Pierre Lidon, Yaocihuatl Medina-Gonzalez.

Figure 1
Figure 1. Figure 1: FIG. 1: Structure of the molecular rotor used in this study. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Fluorescence properties of rotor in ethylene [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Evolution of properties of binary PEG/water mixture [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Evolution of rotor fluorescence lifetime [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Properties of ternary mixtures of water, PEG-400 and PEG-2000 as a function of the proportion of PEG-2000, [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Evolution of fitting parameters in Eq. (6), corresponding to limit binary solutions [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Direct test of free volume theory for binary and ternary mixtures. Continuous lines are fits along Eq. (10). (a) Evolution [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Test of local free volume theory for ternary mixtures: [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Effect of temperature on response of FMR. (a) [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Properties of ternary mixture of water, PEG-62 and PEG-400 as a function of the proportion of PEG-62, [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Properties of ternary mixture of water, PEG-400 and PEG-2000 as a function of the proportion of PEG-2000, [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Properties of ternary mixture of water, PEG-400 and PEG-6000 as a function of the proportion of PEG-6000, [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Properties of ternary mixture of water, PEG-400 and PEG-20000 as a function of the proportion of PEG-20000, [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Evolution of fitting parameters in Eq. (D1), corresponding to limit binary solutions [PITH_FULL_IMAGE:figures/full_fig_p012_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Evolution of fitting parameters in Eq. (D1), corresponding to limit binary solutions [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Evolution of fitting parameters in Eq. (D1), corresponding to limit binary solutions [PITH_FULL_IMAGE:figures/full_fig_p013_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: Evolution of fitting parameters in Eq. (D1), corresponding to limit binary solutions [PITH_FULL_IMAGE:figures/full_fig_p013_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18: Evolution of fitting parameters in Eq. (D1), corresponding to limit binary solutions [PITH_FULL_IMAGE:figures/full_fig_p013_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19: Properties of ternary mixture of water, PEG-400 and PEG-2000 at a total PEG mass fraction [PITH_FULL_IMAGE:figures/full_fig_p014_19.png] view at source ↗
read the original abstract

For a few decades, Fluorescent Molecular Rotors have been commonly employed as local probes of microviscosity in complex materials. However, without proper calibration, relating microviscosity to a physical parameter is unclear, which strongly limits their quantitative use in biological media for instance. In this study, the response of a molecular rotor in binary and ternary macromolecular aqueous solutions of polyethylene glycol (PEG) of different molecular weights is investigated in order to better rationalize the sensitivity of rotors to their cybotactic environment. More precisely, for the investigated composition range of ternary mixtures, it is shown that a linear mixing rule applies for fluorescence lifetime with the proportion of the two PEG, and with an increasing ratio of heavy PEG leading to larger lifetimes. These results allow to test more precisely the free volume theory, which has been proposed in the context of probing glass transition. Analysis show that while this theory semi-quantitatively captures the observation, its precise use raises some questions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript investigates the response of fluorescent molecular rotors in binary and ternary aqueous mixtures of polyethylene glycols (PEGs) of different molecular weights. It reports that, for the investigated composition range, fluorescence lifetime follows a linear mixing rule with the proportion of the two PEG components, with increasing ratio of heavier PEG leading to larger lifetimes. The data are compared to free-volume theory, which is found to capture the observations semi-quantitatively while raising questions about its precise use.

Significance. If the reported linear mixing rule holds, the work provides a practical route to calibrate molecular rotors in mixed macromolecular systems, supporting more quantitative microviscosity measurements in complex media such as biological samples. The experimental results on ternary mixtures and the semi-quantitative test of free-volume theory add to the literature on local-environment sensing by rotors and highlight needed refinements in models originally developed for glass-transition studies.

major comments (1)
  1. [Abstract and Results] Abstract and Results: the central claim that a linear mixing rule applies is presented without accompanying error bars, statistical measures of linearity, composition tables, or raw data, so it is not possible to evaluate whether the linearity remains supported once measurement uncertainty and possible post-hoc selection are accounted for.
minor comments (2)
  1. [Abstract] The abstract contains a grammatical error: 'Analysis show' should read 'Analyses show' or 'The analysis shows'.
  2. [Discussion] The discussion notes that free-volume theory 'raises some questions' about its precise use but does not specify what those questions are or outline concrete tests that would resolve them.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. We address the single major comment below and will incorporate the requested improvements in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract and Results] Abstract and Results: the central claim that a linear mixing rule applies is presented without accompanying error bars, statistical measures of linearity, composition tables, or raw data, so it is not possible to evaluate whether the linearity remains supported once measurement uncertainty and possible post-hoc selection are accounted for.

    Authors: We agree that the presentation of the linear mixing rule would be strengthened by explicit uncertainty quantification and supporting data. In the revised manuscript we will add error bars (standard deviation from n=3 independent measurements) to all data points in Figures 3 and 4, report the Pearson correlation coefficient and p-value for each linear regression, and include a new supplementary table listing the exact mass fractions of each PEG component together with the corresponding fluorescence lifetimes. The compositions were not chosen post-hoc; they were predetermined from the binary-mixture calibration curves to span the full range of heavy-to-light PEG ratios while remaining within the experimentally accessible viscosity window, as already stated in the Methods section. Raw data files will be deposited in the supplementary information. These additions will allow readers to assess the robustness of the linearity directly. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical observation of linear mixing rule with semi-quantitative theory comparison

full rationale

The paper reports direct experimental measurements of fluorescence lifetimes in binary and ternary aqueous PEG mixtures and observes that lifetime follows a linear mixing rule with PEG proportion (heavier PEG yielding larger lifetimes). It then compares these data semi-quantitatively to free-volume theory without deriving the linearity from first principles, without fitting parameters to the same dataset and renaming them as predictions, and without load-bearing self-citations that reduce the central claim to prior author work. The linearity is presented as an empirical finding within the tested composition range; the theory comparison explicitly notes only semi-quantitative agreement and raises questions about precise applicability. No self-definitional steps, fitted-input predictions, uniqueness theorems, or ansatz smuggling occur. The derivation chain is therefore self-contained and externally falsifiable via the reported measurements.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of free volume theory (previously proposed for glass-transition studies) to fluorescence lifetime in macromolecular mixtures; no new entities or fitted parameters are introduced in the abstract.

axioms (1)
  • domain assumption Free volume theory semi-quantitatively links fluorescence lifetime to available space in the cybotactic environment of the rotor
    Invoked to interpret the observed lifetimes in binary and ternary mixtures

pith-pipeline@v0.9.0 · 5472 in / 1168 out tokens · 22823 ms · 2026-05-16T12:03:43.560611+00:00 · methodology

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Works this paper leans on

78 extracted references · 78 canonical work pages

  1. [1]

    Hosny, C

    N. Hosny, C. Fitzgerald, C. Tong, M. Kalberer, M. Kuimova, and F. Pope, Fluorescent lifetime imaging of atmospheric aerosols: a direct probe of aerosol viscosity, Faraday Discus- sions165, 343 (2013)

    work page 2013

  2. [2]

    G. Garg, A. Madeu-Bultó, N. Farfán, J. Ordóñez-Hernández, M. Gómez, and Y . Medina-González, Palladium nanoparticles in glycerol/ionic liquid/carbon dioxide medium as hydrogena- tion catalysts, ACS Applied Nano Materials3, 12240 (2020)

    work page 2020

  3. [3]

    Polita, S

    A. Polita, S. Toliautas, R. Žvirblis, and A. Vyšniauskas, The effect of solvent polarity and macromolecular crowding on the viscosity sensitivity of a molecular rotor bodipy-c 10, Physical Chemistry Chemical Physics22, 8296 (2020)

    work page 2020

  4. [4]

    Caporaletti, M

    F. Caporaletti, M. Bittermann, D. Bonn, and S. Woutersen, Flu- orescent molecular rotor probes nanosecond viscosity changes, The Journal of Chemical Physics156, 201101 (2022)

    work page 2022

  5. [5]

    Meyer, A

    E. Meyer, A. Jamieson, R. Simha, J. Palmen, H. Booij, and F. Maurer, Free volume changes in polyvinyl acetate measured by fluorescence spectroscopy, Polymer31, 243 (1990)

    work page 1990

  6. [6]

    D. Zhu, M. Haidekker, J. Lee, Y . Won, and J. Lee, Application of molecular rotors to the determination of the molecular weight dependence of viscosity in polymer melts, Macromolecules40, 7730 (2007)

    work page 2007

  7. [7]

    W. Lee, C. Lee, T. Sakaguchi, M. Fujiki, and G. Kwak, Fluo- rescent viscosity sensor film of molecular-scale porous polymer with intramolecularπ-stack structure, Macromolecules44, 432 (2011)

    work page 2011

  8. [8]

    S. Kim, M. Lee, H. Kim, Y . Kim, W. Lee, and Y . Won, Deter- mination of glass transition temperatures in bulk and micellar 16 M2 w 0.4 0.45 0.5 0.55 0.6 400 v(1) m 0.934 0.926 0.918 0.912 0.909 lnη (1) 6.91 7.64 8.22 8.80 9.34 τ (1) 0.74 0.98 1.03 1.26 1.38 2000 v(1) m - - 0.918 - - lnη (1) - - 8.02 - - τ (1) - - 1.05 - - TABLE VII: List of fitting param...

    work page 2000

  9. [9]

    Paul and A

    A. Paul and A. Samanta, Free volume dependence of the in- ternal rotation of a molecular rotor probe in room tempera- ture ionic liquids, Journal of Physical Chemistry B112, 16626 (2008)

    work page 2008

  10. [10]

    Singh, A

    P. Singh, A. Mora, and S. Nath, Free volume dependence of an ionic molecular rotor in fluoroalkylphosphate (fap) based ionic liquids, Chemical Physics Letters644, 296 (2016)

    work page 2016

  11. [11]

    Kung and J

    C. Kung and J. Reed, Fluorescent molecular rotors: A new class of probes for tubulin structure and assembly, Biochemistry28, 6678 (1989)

    work page 1989

  12. [12]

    Akers and M

    W. Akers and M. Haidekker, Precision assessment of biofluid viscosity measurements using molecular rotors, Transactions of the ASME127, 450 (2005)

    work page 2005

  13. [13]

    K. Daus, S. Tharamak, W. Pluempanupat, P. Galie, M. Theodor- aki, E. Theodorakis, and M. Alpaugh, Fluorescent molecular rotors as versatile in situ sensors for protein quantitation, Sci- entific Reports13, 20529 (2023)

    work page 2023

  14. [14]

    Schmitt, G

    S. Schmitt, G. Renzer, J. Benrath, A. Best, S. Jiang, K. Land- fester, H. Butt, R. Simonutti, D. Crespy, and K. Koynov, Mon- itoring the formation of polymer nanoparticles with fluorescent molecular rotors, Macromolecules55, 7284 (2022)

    work page 2022

  15. [15]

    Raeburn, L

    J. Raeburn, L. Chen, S. Awhida, R. Deller, M. Vatish, M. Giba- son, and D. Adams, Using molecular rotors to probe gelation, Soft Matter11, 3706 (2015)

    work page 2015

  16. [16]

    Le Dizès Castell, E

    R. Le Dizès Castell, E. Mizahossein, M. Grzelka, S. Jabbari- Farouji, D. Bonn, and N. Shahidzadeh, Visualization of the sol- gel transition in porous networks using fluorescent viscosity- sensitive probes, Journal of Physical Chemistry Letters15, 628 (2024)

    work page 2024

  17. [17]

    Haidekker, W

    M. Haidekker, W. Akers, D. Fischer, and E. Theodorakis, Op- tical fiber-based fluorescent viscosity sensor, Optics Letters31, 2529 (2006)

    work page 2006

  18. [18]

    Lichlyter and M

    D. Lichlyter and M. Haidekker, Immobilization techniques for molecular rotors—towards a solid-state viscosity sensor plat- form, Sensors and Actuators B: Chemical139, 648 (2009)

    work page 2009

  19. [19]

    Y . Jin, H. Park, Y . Ohk, and G. Kwak, Hydrodynamic fluores- cence emission behavior of molecular rotor-based vinyl poly- mers used as viscosity sensors, Polymer132, 79 (2017)

    work page 2017

  20. [20]

    Nalatamby, F

    D. Nalatamby, F. Gibouin, M. Zitouni, J. Renaudeau, G. Clis- son, P. Lidon, S. Harrisson, and Y . Medina-Gonzalez, Fluo- rescent molecular rotor-based polymer materials for local mi- croviscosity mapping in microfluidic channels, Chemical Engi- neering Journal520, 165549 (2025)

    work page 2025

  21. [21]

    Velandia, M

    S. Velandia, M. Bittermann, E. Mirzahossein, G. Giubertoni, F. Caporaletti, V . Sadtler, P. Marchal, T. Roques-Carmes, M. Meinders, and D. Bonn, Probing interfaces of pea protein- stabilized emulsions with a fluorescent molecular rotor, Fron- tiers in Soft Matter3, 1093168 (2023)

    work page 2023

  22. [22]

    Bittermann, T

    M. Bittermann, T. Morozova, S. Velandia, E. Mirzahossein, A. Deblais, S. Woutersen, and D. Bonn, Surface-mediated molecular transport of a lipophilic fluorescent probe in poly- disperse oil-in-water emulsions, Langmuir39, 4207 (2023)

    work page 2023

  23. [23]

    Nipper, S

    M. Nipper, S. Majd, M. Mayer, J. Lee, E. Theodorakis, and M. Haidekker, Characterization of changes in the viscosity of lipid membranes with the molecular rotor fcvj, Biochimica et Biophysica Acta1778, 1148 (2008)

    work page 2008

  24. [24]

    Y . Wu, M. Štefl, A. Olzy ´nska, M. Hof, G. Yahioglu, P. Yip, D. Casey, O. Ces, J. Humpolí ˇcková, and M. Kuimova, Molec- ular rheometry: direct determination of viscosity in L o and Ld lipid phases via fluorescence lifetime imaging, Physical Chem- istry Chemical Physics15, 14986 (2013)

    work page 2013

  25. [25]

    M. Dent, I. López-Duarte, C. Dickson, N. Geoghegan, J. Cooper, I. Gould, R. Krams, J. Bull, N. Brooks, and M. Kuimova, Imaging phase separation in model lipid mem- branes through the use of bodipy based molecular rotors, Phys- ical Chemistry Chemical Physics17, 18393 (2015)

    work page 2015

  26. [26]

    Vyšniauskas, M

    A. Vyšniauskas, M. Qurashi, and M. Kuimova, A molecular rotor that measures dynamic changes of lipid bilayer viscos- ity caused by oxidative stress, Chemical European Journal22, 13210 (2016)

    work page 2016

  27. [27]

    Adrien, G

    V . Adrien, G. Rayan, K. Astafyeva, I. Broutin, M. Picard, P. Fuchs, W. Urbach, and N. Taulier, How to best estimate the viscosity of lipid bilayers, Biophysical Chemistry281, 106732 (2022)

    work page 2022

  28. [28]

    J. Li, Y . Zhang, H. Zhang, X. Xuan, M. Xie, S. Xia, G. Qu, and H. Guo, Nucleoside-based ultrasensitive fluorescent probe for the dual-mode imaging of microviscosity in living cells, Ana- lytical Chemistry88, 5554 (2016)

    work page 2016

  29. [29]

    Zhang, Z

    Y . Zhang, Z. Li, W. Hu, and Z. Liu, A mitochondrial-targeting near-infrared fluorescent probe for visualizing and monitoring viscosity in live cells and tissues, Analytical Chemistry91, 10302 (2019)

    work page 2019

  30. [30]

    Michels, V

    L. Michels, V . Gorelova, Y . Harnvanichvech, J. Borst, B. Al- bada, D. Weijers, and J. Sprakel, Complete microviscosity maps of living plant cells and tissues with a toolbox of targeting mechanoprobes, Proceedings of the National Academy of Sci- ences117, 18110 (2020)

    work page 2020

  31. [31]

    Paez-Perez and M

    M. Paez-Perez and M. Kuimova, Molecular rotors: Fluorescent sensors for microviscosity and conformation of biomolecules, Angewandte Chemie International Edition63, e202311233 (2024)

    work page 2024

  32. [32]

    D. Xie, S. Sun, Q. Zhou, C. Wang, L. Cao, W. Zhang, and G. Li, Fluorescent chemosensors facilitate the visualization of plant health and their living environment in sustainable agriculture, Chemical Communications61, 10408 (2025)

    work page 2025

  33. [33]

    Förster and G

    T. Förster and G. Hoffmann, Die viskositätsabhängigkeit der fluoreszenzquantenausbeuten einiger farbstoffsysteme, Zeitschrift für Physikalische Chemie Neue Folge75, 63 (1971)

    work page 1971

  34. [34]

    Bunton, B

    P. Bunton, B. Dice, J. Pojman, A. De Wit, and F. Brau, Recon- struction by fluorescence imaging of the spatio-temporal evolu- tion of the viscosity field in hele-shaw flows, Physics of Fluids 26, 114106 (2014)

    work page 2014

  35. [35]

    Nalatamby, F

    D. Nalatamby, F. Gibouin, J. Ordóñez-Hernández, J. Re- naudeau, G. Clisson, N. Farfán, P. Lidon, and Y . Medina- González, Molecular rotors for in situ local viscosity mapping in microfluidic chips, Industrial & Engineering Chemistry Re- 17 search62, 12656 (2023)

    work page 2023

  36. [36]

    Gibouin, D

    F. Gibouin, D. Nalatamby, P. Lidon, and Y . Medina-Gonzalez, Molecular rotors for in situ viscosity mapping during evapora- tion of confined fluid mixtures, ACS Applied Materials & In- terfaces16, 8066 (2024)

    work page 2024

  37. [37]

    Mirzahossein, M

    E. Mirzahossein, M. Grzelka, and D. Bonn, Unveiling droplet morphologies: real-time viscosity mapping reveals the physics of drying polymer solutions, Soft Matter21, 8018 (2025)

    work page 2025

  38. [38]

    M. Klok, L. Janssen, W. Browne, and B. Feringa, The influence of viscosity on the functioning of molecular motors, Faraday Discussions143, 319 (2009)

    work page 2009

  39. [39]

    P. Roy, A. Sardjan, W. Danowski, W. Browne, B. Feringa, and S. Meech, Photophysics of first-generation photomolecular mo- tors: Resolving roles of temperature, friction, and medium po- larity, Journal of the Physical Chemistry A125, 1711 (2021)

    work page 2021

  40. [40]

    P. Roy, A. Sardjan, W. Browne, B. Feringa, and S. Meech, Ex- cited state dynamics in unidirectional photochemical molecular motors, Journal of the American Chemical Society146, 12255 (2024)

    work page 2024

  41. [41]

    Straube, B

    A. Straube, B. Kowalik, R. Netz, and F. Höfling, Rapid onset of molecular friction in liquids bridging between the atomistic and hydrodynamic pictures, Communications Physics3, 126 (2020)

    work page 2020

  42. [42]

    Kiefer, D

    H. Kiefer, D. Vitali, B. Dalton, L. Scalfi, and R. Netz, Effect of frequency-dependent shear and volume viscosities on molecu- lar friction in liquids, Physical Review E111, 015104 (2025)

    work page 2025

  43. [43]

    Rothenberger, D

    G. Rothenberger, D. Negus, and R. Hochstrasser, Solvent influ- ence on photoisomerization dynamics, The Journal of Chemical Physics79, 5360 (1983)

    work page 1983

  44. [44]

    V . Suja, N. Oppenheimer, and H. Stone, Hydrodynamics of molecular rotors in lipid membranes, Physical Review Fluids 10, L041101 (2025)

    work page 2025

  45. [45]

    Bittermann, M

    M. Bittermann, M. Grzelka, S. Woutersen, A. Brouwer, and D. Bonn, Disentangling nano- and macroscopic viscosities of aqueous polymer solutions using a fluorescent molecular rotor, Journal of Physical Chemistry Letters12, 3182 (2021)

    work page 2021

  46. [46]

    Kohli and A

    I. Kohli and A. Mukhopahyay, Diffusion of nanoparticles in semidilute polymer solutions: Effect of different length scales, Macromolecules45, 6143 (2012)

    work page 2012

  47. [47]

    Fox and P

    T. Fox and P. Flory, Second-order transition temperatures and related properties of polystyrene. i. influence of molecular weight, Journal of Applied Physics21, 581 (1950)

    work page 1950

  48. [48]

    Loutfy and B

    R. Loutfy and B. Arnold, Effect of viscosity and temperature on torsional relaxation of molecular rotors, Journal of Physical Chemistry86, 4205 (1982)

    work page 1982

  49. [49]

    M. Rao, K. Kumar, and K. Ravikanth, Synthesis of boron- dipyrromethene-ferrocene conjugates, Journal of Organometal- lic Chemistry695, 863 (2010)

    work page 2010

  50. [50]

    Bahaidarah, A

    E. Bahaidarah, A. Harriman, P. Stachelek, S. Rihn, E. Heyer, and R. Ziessel, Fluorescent molecular rotors based on the bod- ipy motif: effect of remote substituents., Photochemical & Pho- tobiological Sciences13, 1397 (2014)

    work page 2014

  51. [51]

    L. Mei, D. Lin, Z. Zhu, and Z. Han, Densities and viscosities of polyethylene glycol + salt + water systems at 20 ◦c, Journal of Chemical Engineering Data40, 1168 (1995)

    work page 1995

  52. [52]

    Lakowicz, R

    J. Lakowicz, R. Jayaweera, H. Szmancinski, and W. Wiczk, Resolution of multicomponent fluorescence emission using frequency-dependent phase angle and modulation spectra, An- alytical Chemistry62, 2005 (1990)

    work page 2005

  53. [53]

    Kuimova, G

    M. Kuimova, G. Yahioglu, J. Levitt, and K. Suhling, Molecular rotor measures viscosity of live cells via fluorescence lifetime imaging, Journal of the American Chemical Society130, 6672 (2008)

    work page 2008

  54. [54]

    Leray, C

    A. Leray, C. Spriet, D. Trinel, Y . Usson, and L. Héliot, General- ization of the polar representation in time domain fluorescence lifetime imaging microscopy for biological applications: prac- tical implementation, Journal of Microscopy248, 66 (2012)

    work page 2012

  55. [55]

    Gegiou, K

    D. Gegiou, K. Muszkat, and E. Fischer, Temperature depen- dence of photoisomerization. vi. the viscosity effect, Journal of the American Chemical Society90, 12 (1968)

    work page 1968

  56. [56]

    Loutfy, High-conversion polymerization fluorescence probes

    R. Loutfy, High-conversion polymerization fluorescence probes. 1. polymerization of methyl methacrylate, Macro- molecules14, 270 (1981)

    work page 1981

  57. [57]

    Williams, R

    M. Williams, R. Landel, and J. Ferry, The temperature depen- dence of relaxation mechanisms in amorphous polymers and other glass-forming liquids, Journal of the American Chemical Society77, 3701 (1955)

    work page 1955

  58. [58]

    Doolittle, Studies in newtonian flow

    A. Doolittle, Studies in newtonian flow. i. the dependence of the viscosity of liquids on temperature, Journal of Applied Physics 22, 1031 (1951)

    work page 1951

  59. [59]

    Doolittle, Studies in newtonian flow

    A. Doolittle, Studies in newtonian flow. ii. the dependence of the viscosity of liquids on free space, Journal of Applied Physics22, 1471 (1951)

    work page 1951

  60. [60]

    Doolittle and R

    A. Doolittle and R. Peterson, Preparation and physical proper- ties of a series of n-alkanes, Journal of the American Chemical Society73, 2145 (1951)

    work page 1951

  61. [61]

    Doolittle, Studies in newtonian flow

    A. Doolittle, Studies in newtonian flow. iii. the dependence of the viscosity of liquids on molecular weight and free space (in homologous series), Journal of Applied Physics23, 236 (1952)

    work page 1952

  62. [62]

    Doolittle, Studies in newtonian flow

    A. Doolittle, Studies in newtonian flow. iv. viscosity vs molec- ular weight in liquids; viscosity vs concentration in polymer solutions, Journal of Applied Physics23, 418 (1952)

    work page 1952

  63. [63]

    Doolittle and D

    A. Doolittle and D. Doolittle, Studies in newtonian flow. v. fur- ther verification of the free space viscosity equation, Journal of Applied Physics28, 901 (1957)

    work page 1957

  64. [64]

    Kovacs, Applicability of the free volume concept on relax- ation phenomena in the glass transition range, Rheologica Acta 5, 262 (1966)

    A. Kovacs, Applicability of the free volume concept on relax- ation phenomena in the glass transition range, Rheologica Acta 5, 262 (1966)

    work page 1966

  65. [65]

    Haward, Occupied volume of liquids and polymers, Journal of Macromolecular Science, Part C4, 191 (1970)

    R. Haward, Occupied volume of liquids and polymers, Journal of Macromolecular Science, Part C4, 191 (1970)

    work page 1970

  66. [66]

    Vrentas and J

    J. Vrentas and J. Duda, Diffusion in polymer-solvent systems. i. reexamination of the free-volume theory, Journal of Polymer Science15, 403 (1977)

    work page 1977

  67. [67]

    Vrentas and J

    J. Vrentas and J. Duda, Diffusion in polymer-solvent systems. ii. a predictive theory for the dependence of diffusion coef- ficients on temperature, concentration, and molecular weight, Journal of Polymer Science15, 417 (1977)

    work page 1977

  68. [68]

    Hao, The empty world - a view from the free volume concept and eyring’s rate process theory, Physical Chemistry Chemical Physics26, 26156 (2025)

    T. Hao, The empty world - a view from the free volume concept and eyring’s rate process theory, Physical Chemistry Chemical Physics26, 26156 (2025)

    work page 2025

  69. [69]

    Loutfy, Fluorescence probes for polymer free-volume, Pure and Applied Chemistry58, 1239 (1986)

    R. Loutfy, Fluorescence probes for polymer free-volume, Pure and Applied Chemistry58, 1239 (1986)

    work page 1986

  70. [70]

    Hooker and J

    J. Hooker and J. Torkelson, Coupling of probe reorientation dy- namics and rotor motions to polymer relaxation as sensed by second harmonic generation and fluorescence, Macromolecules 28, 7683 (1995)

    work page 1995

  71. [71]

    A. Jee, E. Bae, and M. Lee, Internal twisting dynamics of di- cyanovinyljulolidine in polymers, Journal of Physical Chem- istry B113, 16508 (2009)

    work page 2009

  72. [72]

    Hinze, T

    G. Hinze, T. Basché, and R. Vallée, Single molecule probing of dynamics in supercooled polymers, Physical Chemistry Chem- ical Physics13, 1813 (2011)

    work page 2011

  73. [73]

    Mirzahossein, M

    E. Mirzahossein, M. Grzelka, Z. Pan, B. Demirkurt, M. Habibi, A. Brouwer, and D. Bonn, Molecular rotors to probe the local viscosity of a polymer glass, Journal of Chemical Physics156, 174901 (2022)

    work page 2022

  74. [74]

    Jutze, W

    M. Jutze, W. Young, J. Combs, O. Drescher, S. Merchatn, and R. Katsumata, Flim-frapp: near-simultaneous characterization 18 of multi-scale polymer dynamics via fluorescence microscopy, Soft Matter21, 4317 (2025)

    work page 2025

  75. [75]

    Tanaka, Y

    K. Tanaka, Y . Tateishi, Y . Okada, T. Nagamura, M. Doi, and H. Morita, Interfacial mobility of polymers on inorganic solids, Journal of Physical Chemistry B113, 4571 (2009)

    work page 2009

  76. [76]

    Kawaguchi, Y

    D. Kawaguchi, Y . Tateishi, and K. Tanaka, Time-resolved flu- orescence analysis for dye-labeled polystyrene in thin films, Journal of Non-Crystalline Solids407, 284 (2015)

    work page 2015

  77. [77]

    Sugden, Ccxxxiv.- molecular volumes at absolute zero

    S. Sugden, Ccxxxiv.- molecular volumes at absolute zero. part ii. zero volumes and chemical composition, Journal of the Chemical Society , 1786 (1927)

    work page 1927

  78. [78]

    Devanand and J

    K. Devanand and J. Selser, Asymptotic behavior and long- range interactions in aqueous solutions of poly(ethylene oxide), Macromolecules24, 5943 (1991)

    work page 1991