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arxiv: 2605.28329 · v1 · pith:O3DZZHWSnew · submitted 2026-05-27 · ❄️ cond-mat.soft · cond-mat.mtrl-sci

Dry Glass Reference Perturbation Theory: Development, Applications and Extensions

Bennett D. Marshall This is my paper

Pith reviewed 2026-06-29 09:53 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.mtrl-sci
keywords glassy polymerssorptionperturbation theorymembrane separationnon-equilibrium thermodynamicsdiffusioncrude oil fractionationalcohol hydrocarbon mixtures
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The pith

Dry glass reference perturbation theory enables self-consistent sorption predictions from complex liquid mixtures into glassy polymers.

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

The paper reviews the dry glass reference perturbation theory (DGRPT) as a closure for non-equilibrium thermodynamics of glassy polymers. DGRPT was developed specifically to deliver accurate and self-consistent predictions of how complex liquid mixtures sorb into glassy polymers. The theory is then used with diffusion models to forecast membrane separations, including crude oil fractionation and alcohol-hydrocarbon mixtures. Extensions to higher-order expansions are also examined. These capabilities matter because they support the design of polymer membranes for industrial liquid separations without relying on inconsistent approximations.

Core claim

DGRPT was developed to allow for the self-consistent and accurate predictions of sorption from complex liquid mixtures into glassy polymers. DGRPT is applied in the context of diffusion theory to predict the membrane based separations of complex liquid mixtures with glassy polymer membranes. Several examples are given, including the membrane based fractionation of crude oil as well as the membrane based separation of highly non-ideal alcohol / hydrocarbon liquid mixtures. Extensions of the theory to higher order expansions are reviewed and evaluated.

What carries the argument

The DGRPT closure to the non-equilibrium thermodynamics of glassy polymers (NETGP), which supplies the sorption and diffusion relations needed for mixture predictions.

If this is right

  • Membrane-based crude oil fractionation can be modeled directly from DGRPT sorption inputs and diffusion theory.
  • Separation performance for highly non-ideal alcohol/hydrocarbon mixtures follows from the same DGRPT framework.
  • Higher-order expansions of DGRPT can be evaluated for cases where the base closure is insufficient.
  • Self-consistent calculations replace earlier inconsistent approximations for glassy-polymer sorption.

Where Pith is reading between the lines

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

  • If DGRPT holds, membrane design for additional complex mixtures could proceed with fewer trial-and-error experiments.
  • The reviewed extensions suggest a route to refine predictions for polymers or conditions outside the crude-oil and alcohol examples.
  • Coupling DGRPT outputs to process-scale simulations could quantify energy savings in industrial separations.

Load-bearing premise

The DGRPT closure provides accurate and self-consistent sorption predictions when applied to the membrane separation examples described, such as crude oil fractionation and alcohol/hydrocarbon mixtures.

What would settle it

Direct comparison of DGRPT-predicted sorption isotherms for an alcohol/hydrocarbon mixture against laboratory measurements on a glassy polymer membrane; large systematic deviations would falsify the accuracy claim.

Figures

Figures reproduced from arXiv: 2605.28329 by Bennett D. Marshall.

Figure 1
Figure 1. Figure 1: Diagram of separation of binary liquid mixture with a polymer membrane The system is assumed to be isothermal at fixed temperature T. The fluid upstream of the membrane is called the retentate and is characterized by the pressure Pret, fluid mole fractions ൛𝑥௝ ௥௘௧ൟ and chemical potentials µ௜ ௥௘௧൫𝑇, 𝑃௥௘௧,൛𝑥௝ ௥௘௧ൟ ൯. The fluid downstream of the membrane is called the permeate and is characterized by the pres… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of PC-SAFT predictions of liquid density, heat of vaporization, and vapor pressure at saturation for pure octacosane using parameters Set 1 and Set 2. Symbols represent DIPPR25 correlation values Parameter sets which give nearly identical density predictions can give vastly different predictions of other properties which depend on the cohesive energy of the liquid. This exercise demonstrates tha… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of DGRPT model predictions (curves)8 to data (symbols) for sorption27 and swelling11 of a binary DMC / methanol vapor on PTMSP at 40 ∘C. Different curves represent different methanol mole fractions in the vapor phase Further, the DGRPT model8 was applied to predict polymer swelling in ethanol / water binary liquid mixtures in [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Top: Comparison of data (squares-water28, circles-ethanol29) to DGRPT predcitions8 for pure vapor sorption in PTMSP. Bottom: Comparison of data (circles28, square30) to DGRPT predictions for the swelling of PTMSP in contact with an ethanol / water liquid mixture [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of DGRPT predictions33 (solid curve), NETGP-RS34 predictions (dashed curve) to experimental data35, 36 for the sorption of heptane, toluene, methanol and DMC vapors in PIM-1 [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Top: Comparison of DGRPT predictions33 to data36 for the mixed vapor sorption of DMC / methanol at 40 ∘C and total pressure fixed to 48% of the dew point pressure. Bottom: Comparison of Maxwell-Stefan diffusion + DGRPT model prediction33 to data36 for the membrane pervaporation of methanol / DMC liquid mixtures at 40 ∘C [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of DGRPT predictions8 (curves) to data41 (symbols) for sorption of hydrocarbons on SBAD-1 at T = 25 ⸰C. MCYC6 = methylcyclohexane, TBB = tert-butyl benzene, TIPB = 1,3,5-triisopropylbenzene, 1MN = 1-methylnaphthalene The membrane model is applied by employing DGRPT to calculate the fluid species solubilities at the permeate and retentate boundaries, and then regressing Ɖip in Eq. (15) to reprodu… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of model40 and data (points)8 for the flux of pure hydrocarbon liquids through SBAD-1 at 22 ℃. The variations in pressure dependence can be explained by DGRPT predictions of solubilities as illustrated in [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: DGRPT predictions40 of sorption and membrane thickness for several pure liquids permeating through an SBAD-1 membrane. ℓoo is the dry membrane thickness at atmospheric pressure. It was demonstrated by Marshall et al.40 that a diffusivity averaging approach could be used to predict the OSRO separation of hydrocarbon mixtures in several glassy polymer membranes. 𝑁௜ = − ఘ೔ ௞ಳ் Đೌೡ೒ ௫೛ ௗఓ೔ ௗ௭ (16) where Ɖavg i… view at source ↗
Figure 10
Figure 10. Figure 10: Model predictions39 and experimental results4 for the OSRO separation of light Permian crude oil at 130 ∘C and 55 bar using a SBAD-1 membrane. Top: Comparison of model and date for the simulated distillation of the permeate. Middle: Model predicts of selectivity for several homologous series. Bottom: 2D-GC measurement4 of alkane selectivity [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Top: Comparison of DGRPT predictions46 to hydrocarbon sorption data46 at 25 °C. Data for triisopropylbenzene (TIPB), isooctane (IC8) and propylbenzene are unpublished.48 Binary interaction parameters for these three species were fit in the current work: TIPB(0.16), IC8(0.16), propylbenzene(0.082). Center: DGRPT predictions of polymer swelling. Bottom: Comparison of DGRPT predictions to Ethanol and pentano… view at source ↗
Figure 12
Figure 12. Figure 12: illustrates the model predictions for the OSRO separation of n-pentanol / toluene and ethanol / heptane liquid mixtures [PITH_FULL_IMAGE:figures/full_fig_p030_12.png] view at source ↗
Figure 12
Figure 12. Figure 12: As can be seen, the second order DGRPT gives a better description of the 25 [PITH_FULL_IMAGE:figures/full_fig_p035_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of modified DGRPT52 using closure Eq. (24) to data10 for the sorption of CO2 in PMMA at 33 ∘C. Polymer PC-SAFT parameters and binary interaction parameter (ki,p = 0.0284) same as ref[52] Unlike the closure Eq. (21), the closure Eq. (26), does not introduce any additional parameters. Marshall proposed the following generalization of Eq. (26), 𝜇𝑝 ቀ𝜌𝑝 , 𝜌𝑖 , 𝑇ቁ ≈ 𝜇𝑝 ቀ𝜌𝑝 𝑜 , 𝑇ቁ + 𝜕𝜇𝑝 ቀ𝜌𝑝 𝑜 , 𝜌𝑖 , 𝑇… view at source ↗
read the original abstract

This manuscript reviews the development, application and extensions of the dry glass reference perturbation theory (DGRPT) closure to the non-equilibrium thermodynamics of glassy polymers (NETGP). DGRPT was developed to allow for the self-consistent and accurate predictions of sorption from complex liquid mixtures into glassy polymers. DGRPT is applied in the context of diffusion theory to predict the membrane based separations of complex liquid mixtures with glassy polymer membranes. Several examples are given, including the membrane based fractionation of crude oil as well as the membrane based separation of highly non-ideal alcohol / hydrocarbon liquid mixtures. Extensions of the theory to higher order expansions are reviewed and evaluated.

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

0 major / 0 minor

Summary. This manuscript is a review of the development, applications, and extensions of the dry glass reference perturbation theory (DGRPT) closure to the non-equilibrium thermodynamics of glassy polymers (NETGP). It claims that DGRPT was developed to enable self-consistent and accurate predictions of sorption from complex liquid mixtures into glassy polymers, applies this in diffusion theory to predict membrane-based separations (e.g., crude oil fractionation and alcohol/hydrocarbon mixtures), and reviews higher-order expansions.

Significance. If the central claims hold, the review consolidates the construction of DGRPT within NETGP and its cited applications to membrane separations, providing a reference resource for researchers working on glassy polymer sorption and complex mixture separations. The presentation of the theory's development and example applications is a strength for the field.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of the manuscript and for recommending acceptance. The review consolidates the DGRPT framework and its applications as intended.

Circularity Check

0 steps flagged

No significant circularity; review presents theory construction without self-referential reduction

full rationale

The manuscript is explicitly a review of DGRPT development within NETGP, its applications to sorption and membrane separations, and extensions. No derivation chain, equations, or load-bearing steps are exhibited in the provided abstract or summary. The central claim rests on the theory's construction and cited application examples rather than any internal prediction that reduces to a fitted input or self-citation by construction. No self-definitional, fitted-input, or uniqueness-imported patterns are identifiable from the given text. This is the expected outcome for a review-style paper whose internal logic is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms or invented entities can be identified from the abstract alone.

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Reference graph

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