Methods

Eight disciplines, one decision.

Choosing which ionic liquid to make draws on quantum chemistry, thermodynamics, statistics, optimization, transport, toxicology, life-cycle assessment and quality engineering. Each panel below works through one of them using published data, a calculation run for this page, or the standard method, and says which.

  • Published researchReplotted from peer-reviewed papers. The source is under each figure.
  • Computed for this pageCalculations run for this site from stated inputs. Not Avestiq experimental data.
  • MethodologyStandard methods and equations. No result is claimed.
  • PlannedTo be built with pre-seed funding.

Methods library

Eight chapters, from first principles to the design problem.

Each chapter sets out the equations, shows how the founder’s published work used them, and includes labs that compute in your browser from published data and parameters. Chapter 5 states the integrated problem LILM is designed to solve; it is a formulation, not a built system.

01 Quantum chemistry Computed for this page

Electrostatics decide how ions meet.

Density-functional calculations for the 1-butyl-3-methylimidazolium cation and the tetrafluoroborate anion. Color shows the electrostatic potential on each ion’s surface. Drag to rotate.

Electrostatic potential on the 0.001 e bohr−3 density surface

[C4mim]+

[BF4]−

Method: B3LYP/6-31G* (PySCF). Potential evaluated at the vertices of the 0.001 e bohr−3 electron-density isosurface (marching cubes, 0.8 bohr grid; on a 0.62 bohr grid, surface areas and extremes change by less than 2%). [C4mim]+ geometry: RDKit conformer minimized with MMFF94, not DFT-optimized. [BF4]−: Td symmetry with r(B–F) = 1.412 Å, optimized at B3LYP/6-31G*. These are isolated ions in vacuum; in the liquid, ion pairing and polarization change the potential.

Surface area by potential

Å2 of surface per 5 kcal mol−1 bin, both ions

View data
Surface statistics of the electrostatic potential for each ion

What it shows. The cation’s potential is positive everywhere but uneven. It peaks at the ring C2–H hydrogen and is lowest on the terminal methyl of the butyl chain. The anion’s surface is uniformly negative.

Why it matters. Such surface-charge distributions underlie COSMO-RS, the quantum-chemistry-based thermodynamic model used in the screening study in section 02. COSMO-RS uses charge densities from a conductor-embedded calculation, not gas-phase potentials like these.

02 Thermodynamic screening Published research Historical founder research

13,356 combinations to ten candidates, every step recorded.

A screening of ionic liquids for physical CO2 absorption (Farahipour, Mehrkesh & Karunanithi, Chemical Engineering Science 2016, 145, 126–132). COSMO-RS gave the Henry’s constants, corrected against experiment; group-contribution models gave viscosity and melting point.

Screening sequence

Index minimized in the screen

ADI = H152H45

H15, H45: Henry’s constants of CO2 at the absorption (15 °C) and desorption (45 °C) temperatures, from COSMO-RS activity coefficients (H = PsatCO₂ γCO₂), corrected with the equation below and converted to a molality basis (paper, Eqns. 4–6). ADI combines solubility at absorption with the change in H between the two temperatures, which the paper relates to the enthalpy of dissolution through the van ’t Hoff equation.

Correction applied to COSMO-RS

Hmod = 0.7403 Hpred + 7.9697

Fitted on 50 literature measurements (parameterization BP_TZVP_C21_0108). Section 03 tests it.

Absorption–desorption index, 21 anions × 10 cations

ADI in bar; lower is better

View data
Source: Tables 2–4 of the paper. Outlined cells are the ten candidates the paper selected. With the screen on, cells removed by the paper’s group-contribution melting-point constraint (Lazzús) are hatched, exactly as published in Table 3.

The ten selected candidates: predicted properties

Cell color scales within each column (darker = lower). Sensible heat in GJ per tonne of CO2 captured.

Predicted properties of the ten ionic liquids selected for CO2 capture
Source: Tables 4 and 6 of the paper. Henry’s constants from corrected COSMO-RS; heat capacity (30 °C), viscosity (298 K) and melting point from group-contribution methods. All values are predictions; none were measured in that study.

ADI: selected candidates vs seven conventional ionic liquids

Conventional set: optimal candidates from Zhang et al. (Applied Energy, 2016), recomputed with the same index

Source: Table 5 of the paper. The paper reports conventional values about 65% higher on average. A lower index is a screening signal, not a measured process advantage.

03 Statistics and data analysis Published research Computed for this page

Correct the physics, then measure what is left.

COSMO-RS overpredicted the Henry’s constant of CO2 systematically. The paper fitted a linear correction on 50 measurements and tested it on 18 more. Those 18 test points are replotted here, then re-analyzed with Bayesian inference that runs in your browser.

Held-out test set, before and after correction

18 ionic liquid + CO2 systems; Henry’s constant in bar (H = Psatγ, paper Eqn. 4)

    View data
    Source: Table 1 of the paper. Average absolute percentage error: 36.6% before correction and 12.7% after (paper’s values). After correction every test point still reads high, by 1% to 35%.

    Posterior of the correction coefficients

    Hexp = a·Hpred + b + ε, ε ~ N(0, σ2); fitted to the 18 test points

    Random-walk Metropolis sampler, flat priors on a, b and log σ, 2,000 burn-in and 20,000 kept iterations, seeded. Cross-check: ordinary least squares on the same points gives a = 0.553 ± 0.035 and b = 17.0 ± 3.9 (±1 standard error), which the chain should reproduce.

    What the re-analysis shows. The 18 held-out points prefer a shallower slope than the 50-point training fit. The published coefficients sit far outside the 95% credible region of the test-set posterior; the distance is reported under the chart. The correction still cut the test error by two-thirds. A single corrected number hides this shift; a posterior shows it. LILM is designed to report intervals and to check them on held-out data.

    Did the sampler converge? Four chains from scattered starting points

    Same model and 18 points as above; each chain starts far from the others, and the diagnostics test whether they end up sampling the same distribution

    Computed for this page

    Trace plots

    Joint posterior of a and b, kept draws

      Marginal distributions by chain (dashed: pooled 95% interval)

      Autocorrelation of a, kept draws

      Posterior summaries and convergence diagnostics

      Random-walk Metropolis, flat priors on a, b and log σ; the first half of each chain is discarded as warm-up. Split-R̂ compares eight half-chains (Gelman et al., Bayesian Data Analysis, 3rd ed., ch. 11); ESS uses the variogram autocorrelation estimate with Geyer’s initial-positive-sequence truncation. PASS: every R̂ < 1.01 and every ESS > 400, the thresholds recommended by Vehtari et al. (Bayesian Anal. 2021, 16, 667–718, doi:10.1214/20-BA1221) for four chains. CAUTION: R̂ < 1.05 and ESS ≥ 100, a band this page uses between that recommendation and clear failure. FAIL: anything worse. This R̂ is the classic split version, not the rank-normalized one Vehtari et al. propose. Try step × 0.05 or × 8 to see a sampler that has not mixed.

      How stable is the ranking? Monte Carlo over Henry’s-constant error

      Probability that each candidate lands at each rank; 4,000 draws, recomputed live

      Computed from published data · assumed error model

      Each draw multiplies H15 and H45 by lognormal factors with standard deviation σ and correlation ρ, recomputes ADI = H152/H45 and re-ranks the ten. σ and ρ are assumptions, not measurements. A bias shared by every candidate would not change the ranking, so only scatter matters here. The default σ = 0.08 equals the scatter of the corrected test-set errors (log scale; their mean bias is +0.12). ρ is unknown, which is why it is a slider. Errors are independent between candidates.

      Rank summary for each candidate under the Monte Carlo error model
      E[rank] = Σ r·P(rank r). The 90% rank interval runs from the 5th to the 95th percentile of each candidate’s rank distribution. 4,000 draws with a fixed seed, so the table changes only when σ or ρ changes. With 4,000 draws the 95% Monte Carlo margin on a probability is about ±1.5 percentage points at 50% and ±0.3 points at 1%.

      04 Optimization Published research Historical founder research

      Molecular design is a mixed-integer nonlinear program.

      A 2013 formulation co-authored by the founder (Karunanithi & Mehrkesh, AIChE J. 59, 4627–4640) writes ionic-liquid design as optimization over discrete structure choices and continuous process variables.

      maxf(c, a, y, ng, x)objective, e.g. selectivity or conductivity
      s.t.h1(c, a, y, ng) = 0structural feasibility and complexity (equalities), incl. a modified octet rule
      h2(c, a, y, ng) ≤ 0structural feasibility and complexity (inequalities)
      g2(c, a, y, ng) ≤ 0pure-component property limits
      d1(c, a, y, ng, x) = 0design equalities
      d2(c, a, y, ng, x) ≤ 0mixture-property limits
      c ∈ {0,1}m cation coresa ∈ {0,1}n anionsy ∈ {0,1}u alkyl side chainsng integer group countsx ∈ ℝr compositions, flows

      Mixture model (UNIFAC)

      ln γi = ln γiC + ln γiR

      Combinatorial (size and shape) plus residual (energetic) terms, built from group parameters.

      Liquid–liquid equilibrium

      γiI xiI = γiII xiII

      The binary structure variables enter these nonlinear terms, so the problem is nonconvex.

      Viscosity (Orrick–Erbar type, group contribution)

      ln ηρM = A + BT

      Solution methods

        The 2013 paper solved its case studies by decomposition and by a genetic algorithm (MATLAB; population 20; crossover fraction 0.8) and cited deterministic branch-and-bound methods as alternatives. The decomposition result is replotted on the Science page (185 → 27 → 1). The 2016 thermal-storage study optimized a single objective; the Pareto chart there is Avestiq’s multi-objective replot of its published data.

        05 Transport and process simulation Computed for this page Methodology

        Properties become process consequences.

        Viscosity, density, heat capacity and solubility enter process design through conservation equations. Below: a fluid-flow solver running live in this page, the equilibrium-stage equations used to design absorbers, and published regeneration-energy estimates.

        Flow past a heated cylinder, Re = 100, solved live

        Lattice-Boltzmann solver · starting

        Plane Poiseuille flow, 20,000 steps, compared with the analytical profile.

        D2Q9 lattice-Boltzmann method (BGK collision, halfway bounce-back on the cylinder) with a D2Q5 passive scalar for temperature (Prandtl number 1; cylinder at T = 1, inflow at T = 0). Side boundaries are periodic; the cylinder diameter is about 20% of the domain height. Checks with this code: plane Poiseuille flow matches the analytical velocity profile to a relative L2 error of 3.1 × 10−4; the shedding Strouhal number changes by less than 2% across three grids (diameter 14, 18 and 24 lattice units: 0.195, 0.198, 0.198). A demonstration of method, not a model of an ionic-liquid process.

        Temperature-swing absorption loop Methodology

        Schematic only. The 15 °C and 45 °C temperatures are the screening assumptions of the published screen; no Avestiq process model exists yet.

        MESH equations, stage j, component i

        MLj−1xi,j−1 + Vj+1yi,j+1 + Fjzi,j − Ljxi,j − Vjyi,j = 0
        Eyi,j = Ki,j xi,j,  with KCO₂ = H/P for physical absorption (H on a mole-fraction basis)
        SΣi xi,j = 1,  Σi yi,j = 1
        HLj−1hj−1 + Vj+1Hj+1 + FjhF,j − Ljhj − VjHj + Qj = 0

        Material balance, equilibrium, summation and enthalpy balance for each stage, solved simultaneously. LILM is designed to supply the property inputs (K, h, ρ, η, cp) with intervals. Planned

        Sensible heat in regeneration (paper, Eqn. 7)

        Qsens = mILcp,ILΔT + mCO₂cp,CO₂ΔT

        Sensible heat to regenerate the solvent

        GJ per tonne of CO2 captured. Selected candidates: from predicted heat capacities. Conventional ILs: values from Zhang et al., based on experimental data. The two sets are not on an identical basis.

        Source: Table 6 of the paper, following the procedure of Zhang et al. On average the selected candidates are 20% lower (paper). Estimates, not measurements.

        06 Toxicology Methodology Published research

        A prediction is the first tier of evidence, not the last.

        Hazard evidence comes in tiers: computational models, then in vitro assays including human cell lines, then standardized tests on algae and invertebrates, and vertebrate studies where regulation requires them. Avestiq has no test results of its own yet. This section shows the framework and published data.

          Test numbers refer to the OECD Guidelines for the Testing of Chemicals. Planned Avestiq intends to commission these tests from accredited partner laboratories as candidates advance; it does not run them in-house.

          Chronic EC50 by species, five ionic liquids

          mg L−1, log color scale; brighter = more toxic

          Historical founder research

          Most sensitive species. Daphnia magna, for all five ionic liquids (5.4–16.9 mg L−1).

          Lowest HC50. [BPy][Cl], 40.5 mg L−1. It also has the highest freshwater characterization factor of the five (1,768 CTUe kg−1, same paper).

          Gaps. Seven of the thirty species–liquid cells have no data. Sparse, uneven coverage like this is the setting LILM is designed for.

          View data
          Source: Mehrkesh & Karunanithi, Environ. Sci. Technol. 2016, 50, 6814–6821, Table 1 (literature data compiled for USEtox). Acute values converted to chronic with an acute-to-chronic ratio of 2. Cells marked ≥ derive from LC50 ≥ 100 mg L−1 and are lower bounds; the fish value for [Bmim][Cl] combines one such bound with a measured EC50. HC50: geometric mean across species. Daphnia magna is the most sensitive species for all five.

          Human cell lines in published ionic-liquid studies

          Published research

          Cytotoxicity assay layout

          Schematic layout of a cytotoxicity assay (serial dilution across columns, replicates down rows). No data. A cytotoxicity result in one cell line does not establish human safety.

          IARC classifications of four common industrial solvents

          Published research
          Hazardous-solvent substitution is one of Avestiq’s candidate applications. Benzene also appears upstream of ionic liquids: it is one of the emissions itemized in the production-phase ecotoxicity breakdown for [Bmim][Br], [Bmim][Cl] and [BPy][Cl] (ES&T 2016, Table 5). A substitute is an improvement only if its own hazard and production burden are measured and found lower.

          Physiologically based pharmacokinetic (PBPK) model

          MethodologyPlanned

          Each tissue t

          Vt dCtdt = Qt (Ca − CtPt)

          Liver adds metabolic clearance

          − CLint fu CLPL

          Perfusion-limited, well-stirred tissues: blood flow Q, volume V, tissue:plasma partition coefficient P, unbound fraction fu, intrinsic clearance CLint scaled from in vitro data (IVIVE). The founder directs PBPK and IVIVE modeling for human clinical PK/PD programs in his current role, outside Avestiq (founder CV). For ionic liquids this is planned; no Avestiq PBPK model exists.

          07 Life-cycle assessment Published research Historical founder research

          Ionic is not automatically green.

          Negligible vapor pressure removes one emission route. It says nothing about the burden of making the chemical. Two of the founder’s life-cycle studies quantified that burden.

            System boundary: freshwater ecotoxicity of 1 kg of ionic liquid

            Production phase and use-phase release, as modeled in ES&T 2016

            Source: Mehrkesh & Karunanithi, ES&T 2016. The 2% loss is the paper’s conservative upper bound; recovery assumes salting out with aluminum salts. For all five ionic liquids, mean production-phase impact was nearly an order of magnitude above use-phase release.

            An energetic ionic salt vs TNT, per MJ of energy content

            Ratio of cradle-to-gate impacts, 1,2,3-triazolium nitrate ÷ TNT (TRACI midpoints)

            View data
            Source: Mehrkesh & Karunanithi, ACS Sustainable Chem. Eng. 2013, 1, 448–455, Table 1. Ratios computed from the tabulated totals. Seven of the eight categories are shown. Ecotoxicity is omitted because the paper’s tabulated values and its text give different ratios.

            08 Quality engineering Methodology Planned

            Scale-up is a variation problem.

            A candidate that meets specification at the bench has to keep meeting it, batch after batch. Lean and Six Sigma tools make that measurable. The founder holds a Six Sigma Green Belt (founder CV).

            Process capability

            Interactive calculator; any property with lower and upper specification limits

            Specification limits at ±1 (arbitrary units). Out-of-specification fraction assumes a normal distribution.

            Potential capability

            Cp = USL − LSL6σ

            Actual capability

            Cpk = min(USL − μ, μ − LSL)3σ

            Expected out of specification

            Φ((LSL − μ)/σ) + 1 − Φ((USL − μ)/σ)

            DMAIC, mapped to the Avestiq loop

            Value-stream map: specification to qualified supply

            Data boxes are empty on purpose: cycle times, waits and yields will be measured in the first programs, not estimated here.

            Each discipline here is mature on its own. LILM is designed to connect them, so that one decision carries all of their evidence.

            See the LILM architecture

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