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Ma Y, Hudson SD, Salipante PF, Douglas JF, Prabhu VM. Applicability of the Generalized Stokes-Einstein Equation of Mode-Coupling Theory to Near-Critical Polyelectrolyte Complex Solutions. ACS Macro Lett 2023; 12:288-294. [PMID: 36762915 PMCID: PMC10015504 DOI: 10.1021/acsmacrolett.2c00647] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
Abstract
We examine whether the mode-coupling theory of Kawasaki and Ferrell (KF) [Kawasaki, K. Kinetic Equations and Time Correlation Functions of Critical Fluctuations. Ann. Phys. 1970, 61 (1), 1-56; Ferrell, R. A. Decoupled-Mode Dynamical Scaling Theory of the Binary-Liquid Phase Transition. Phys. Rev. Lett. 1970, 24 (21), 1169-1172] can describe dynamic light scattering (DLS) measurements of the dynamic structure factor of near-critical polyelectrolyte complex (PC) solutions that have been previously shown to exhibit a theoretically unanticipated lower critical solution temperature type phase behavior, i.e., phase separation upon heating, and a conventional pattern of static critical properties (low angle scattering intensity and static correlation, ξs) as a function of reduced temperature. Good qualitative accord is observed between our DLS measurements and the KF theory. In particular, we observe that the collective diffusion coefficient Dc of the PC solutions obeys the generalized Stokes-Einstein equation (GSE), Dc = kBT/6πηξs, where ξs is specified from our previous measurements and where η is measured by capillary rheometry under the same thermodynamic conditions as in our previous study of these solutions, allowing for a no-free-parameter test of the GSE. We also find that even the wavevector (q)-dependent collective diffusion coefficient Dc(q), measured by varying the scattering angle in the DLS measurements over a large range, is also well-described by the mean-field version of the KF theory. We find it remarkable that the KF theory provides such a robust description of collective diffusion in these complex charged polyelectrolyte blends under near-critical conditions given that charge fluctuations and association of the polymers might be expected to lead to physical complications that would invalidate the standard model of uncharged fluid mixtures.
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Affiliation(s)
- Yuanchi Ma
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Steven D Hudson
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Paul F Salipante
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Jack F Douglas
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Vivek M Prabhu
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
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Sheyfer D, Servis MJ, Zhang Q, Lal J, Loeffler T, Dufresne EM, Sandy AR, Narayanan S, Sankaranarayanan SKRS, Szczygiel R, Maj P, Soderholm L, Antonio MR, Stephenson GB. Advancing Chemical Separations: Unraveling the Structure and Dynamics of Phase Splitting in Liquid-Liquid Extraction. J Phys Chem B 2022; 126:2420-2429. [PMID: 35315675 DOI: 10.1021/acs.jpcb.1c09996] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Liquid-liquid extraction (LLE), the go-to process for a variety of chemical separations, is limited by spontaneous organic phase splitting upon sufficient solute loading, called third phase formation. In this study we explore the applicability of critical phenomena theory to gain insight into this deleterious phase behavior with the goal of improving separations efficiency and minimizing waste. A series of samples representative of rare earth purification were constructed to include each of one light and one heavy lanthanide (cerium and lutetium) paired with one of two common malonamide extractants (DMDOHEMA and DMDBTDMA). The resulting postextraction organic phases are chemically complex and often form rich hierarchical structures whose statics and dynamics near the critical point were probed herein with small-angle X-ray scattering and high-speed X-ray photon correlation spectroscopy. Despite their different extraction behaviors, all samples show remarkably similar critical behavior with exponents well described by classical critical point theory consistent with the 3D Ising model, where the critical behavior is characterized by fluctuations with a single diverging length scale. This unexpected result indicates a significant reduction in relevant chemical parameters at the critical point, indicating that the underlying behavior of phase transitions in LLE rely on far fewer variables than are generally assumed. The obtained scalar order parameter is attributed to the extractant fraction of the extractant/diluent mixture, revealing that other solution components and their respective concentrations simply shift the critical temperature but do not affect the nature of the critical fluctuations. These findings point to an opportunity to drastically simplify studies of liquid-liquid phase separation and phase diagram development in general while providing insights into LLE process improvement.
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Affiliation(s)
- D Sheyfer
- X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Michael J Servis
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Qingteng Zhang
- X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - J Lal
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, United States
| | - T Loeffler
- Nanoscale Science and Technology Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - E M Dufresne
- X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - A R Sandy
- X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - S Narayanan
- X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Subramanian K R S Sankaranarayanan
- Nanoscale Science and Technology Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
- Department of Mechanical and Industrial Engineering, University of Illinois, Chicago, Illinois 60607,United States
| | - R Szczygiel
- AGH University of Science and Technology, Krakow 30-059, Poland
| | - P Maj
- AGH University of Science and Technology, Krakow 30-059, Poland
| | - L Soderholm
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Mark R Antonio
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - G B Stephenson
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
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Sheyfer D, Zhang Q, Lal J, Loeffler T, Dufresne EM, Sandy AR, Narayanan S, Sankaranarayanan SKRS, Szczygiel R, Maj P, Soderholm L, Antonio MR, Stephenson GB. Nanoscale Critical Phenomena in a Complex Fluid Studied by X-Ray Photon Correlation Spectroscopy. PHYSICAL REVIEW LETTERS 2020; 125:125504. [PMID: 33016761 DOI: 10.1103/physrevlett.125.125504] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2020] [Revised: 05/27/2020] [Accepted: 07/14/2020] [Indexed: 06/11/2023]
Abstract
The advent of high-speed x-ray photon correlation spectroscopy now allows the study of critical phenomena in fluids to much smaller length scales and over a wider range of temperatures than is possible with dynamic light scattering. We present an x-ray photon correlation spectroscopy study of critical fluctuation dynamics in a complex fluid typical of those used in liquid-liquid extraction (LLE) of ions, dodecane-DMDBTDMA with extracted aqueous Ce(NO_{3})_{3}. We observe good agreement with both static and dynamic scaling without the need for significant noncritical background corrections. Critical exponents agree with 3D Ising values, and the fluctuation dynamics are described by simple exponential relaxation. The form of the dynamic master curve deviates somewhat from the Kawasaki result, with a more abrupt transition between the critical and noncritical asymptotic behavior. The concepts of critical phenomena thus provide a quantitative framework for understanding the structure and dynamics of LLE systems and a path forward to new LLE processes.
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Affiliation(s)
- D Sheyfer
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Qingteng Zhang
- X-Ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - J Lal
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - T Loeffler
- Nanoscale Science and Technology Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - E M Dufresne
- X-Ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - A R Sandy
- X-Ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - S Narayanan
- X-Ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - S K R S Sankaranarayanan
- Nanoscale Science and Technology Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Department of Mechanical and Industrial Engineering, University of Illinois, Chicago, Illinois 60607, USA
| | - R Szczygiel
- AGH University of Science and Technology, Krakow 30-059, Poland
| | - P Maj
- AGH University of Science and Technology, Krakow 30-059, Poland
| | - L Soderholm
- Chemical Science and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - M R Antonio
- Chemical Science and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - G B Stephenson
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
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