{"uid":"cap_yLqy-14N288-IL4tX3hy-","slug":"ideal-donnan-multivalent-membrane-partition-electroneutrality-ec5661f9","name":"Ideal Donnan Multivalent Membrane Partition & Electroneutrality Calculator","description":"Compute ideal ionic partition and Donnan potential for an explicit membrane equilibrium.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B007/ideal-donnan-multivalent-membrane-partition-electroneutrality?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["donnan"],"properties":{"donnan":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["temperature_kelvin","fixed_charge_molar_density","ions"],"properties":{"ions":{"type":"array","items":{"type":"object","required":["charge","bulk_molar_density"],"properties":{"charge":{"type":"integer","maximum":2,"minimum":-2},"bulk_molar_density":{"type":"number","maximum":10000,"minimum":0.000001}},"additionalProperties":false},"maxItems":8,"minItems":2},"temperature_kelvin":{"type":"number","maximum":1000,"minimum":200},"fixed_charge_molar_density":{"type":"number","maximum":10000,"minimum":-10000}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_w_KcNYUF3_uGpJWsAE5Cs","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the ideal ionic partition coefficients and Donnan potential for a charged membrane in equilibrium with a multi-ion solution, enforcing electroneutrality.","exampleAgentPrompt":"Calculate the ideal Donnan equilibrium for a negatively charged membrane with a fixed charge density of -500 mM at 298 K, with Na+ (charge +1, bulk 100 mM) and Cl- (charge -1, bulk 100 mM) as the ion species.","exampleUseCases":[{"title":"Nanofiltration membrane ion rejection modeling","prompt":"I'm designing a nanofiltration membrane with a fixed charge density of -300 mM. At 298 K, with a feed of 50 mM NaCl and 10 mM CaCl2 (so Na+ charge +1 at 50 mM, Ca2+ charge +2 at 10 mM, Cl- charge -1 at 80 mM), what are the ideal Donnan partition coefficients and the membrane potential?"},{"title":"Ion exchange membrane selectivity for desalination","prompt":"For a positively charged ion exchange membrane with fixed charge density of +200 mM at 310 K, compute the Donnan equilibrium partitioning for SO4 2- (charge -2, bulk 20 mM) and Cl- (charge -1, bulk 100 mM) and Na+ (charge +1, bulk 140 mM). I need the partition coefficients and Donnan potential."},{"title":"Temperature effect on membrane equilibrium","prompt":"How does temperature affect Donnan equilibrium? Please compute the ideal ionic partition and Donnan potential at 350 K for a membrane with fixed charge density of -100 mM, with K+ (charge +1, 50 mM bulk) and Cl- (charge -1, 50 mM bulk) ions."}],"resultDescription":"Returns the computed Donnan potential (in volts or millivolts) and the ideal partition coefficients for each ion species between the bulk solution and the membrane phase, satisfying electroneutrality within the membrane, given the specified fixed charge density, temperature, and ion compositions.","failureModes":["Electroneutrality cannot be satisfied for the given ion set — solver fails to converge","Ion charge out of range (must be integer between -2 and +2)","Fewer than 2 ion species provided (minimum required)","More than 8 ion species provided (maximum exceeded)","Temperature out of valid range (200–1000 K)","Fixed charge density magnitude exceeds 10000 mM limit","Bulk molar density below minimum threshold (0.000001 mM)","Invalid or missing claim field in artifact payload"],"whenToPreferThis":"Choose this endpoint when you need a rigorous, physics-based ideal Donnan equilibrium calculation for charged membranes with multivalent ion mixtures (charges -2 to +2), particularly for ion exchange membranes, nanofiltration modeling, or electrochemical systems. Prefer this over simplified monovalent-only models when your solution contains divalent or asymmetric electrolytes. It enforces electroneutrality explicitly, making it suitable for precise membrane science workflows.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-01T06:51:45.342Z","isFirstParty":false,"canonicalSlug":"ideal-donnan-multivalent-membrane-partition-electroneutrality-ec5661f9"}