Calculator
Choose a model, select a solvent preset or enter er, then compute screening or solvation impacts with consistent units.
Plotly graph
Example data table
Sample values showing screening and solvation factors for common solvents.
| Solvent | er | Screening (1/er) | Born factor (1 - 1/er) |
|---|---|---|---|
| Water | 78.50 | 0.012739 | 0.987261 |
| DMSO | 46.70 | 0.021413 | 0.978587 |
| Ethanol | 24.30 | 0.041152 | 0.958848 |
| Acetone | 20.70 | 0.048309 | 0.951691 |
| Hexane | 1.89 | 0.529101 | 0.470899 |
Formula used
Electrostatic screening (Coulomb): Force and potential energy scale by 1/er in a uniform dielectric.
- F = (1 / (4*pi*e0*er)) * (q1*q2 / r^2)
- U = (1 / (4*pi*e0*er)) * (q1*q2 / r)
Born solvation energy (single ion): Approximates stabilization when moving an ion into a dielectric medium.
- dG = -(NA*z^2*e^2)/(8*pi*e0*rion) * (1 - 1/er)
How to use this calculator
- Select a model: screening for two charges, or Born solvation for one ion.
- Pick a solvent preset or type a custom er value.
- Enter the required inputs with units.
- Press Calculate to show results above the form.
- Use CSV or PDF export buttons for reporting.
Why dielectric constant matters in solutions
Relative permittivity, er, controls how strongly charges interact in a solvent. In the screening model, force and potential energy drop in direct proportion to 1/er. Moving from hexane (er about 1.89) to water (er about 78.5) reduces electrostatic interactions by roughly forty times for the same geometry.
What the screening factor tells you
The calculator reports 1/er as the screening factor. For er = 20.7 (acetone), 1/er is 0.0483, meaning only 4.83% of the vacuum interaction remains. This helps estimate whether ion pairs persist, whether salts dissociate, and how strongly charged catalysts pre-organize reactants.
Born solvation as an energy benchmark
Born theory approximates the free energy change when an ion is transferred into a dielectric medium. The solvation factor (1 - 1/er) approaches 1 as er increases, so high-er solvents give larger magnitude stabilization. For a monovalent ion with 2.0 A radius, the predicted stabilization rises quickly up to er around 30, then levels off.
Interpreting the Plotly curve
The graph recalculates outputs across er from 1.6 to 90 using your current inputs. In screening mode, both force and energy curves share the same 1/er shape, so doubling er halves both values. In Born mode, dG becomes more negative with increasing er, but changes slow at high er.
Practical solvent comparisons
Typical er values are approximately: water 78.5, DMSO 46.7, acetonitrile 35.9, methanol 32.6, ethanol 24.3, acetone 20.7, and hexane 1.89. Use these numbers to sanity-check outputs and to rank media for charge separation, conductivity, and ionic reaction pathways.
Quality checks for reliable inputs
Keep units consistent: separation distance strongly affects magnitude because F scales with 1/r^2 and U scales with 1/r. When using elementary charges, enter q values as integers or fractions of e. For Born results, choose an ion radius consistent with your model, because smaller radii yield larger magnitude solvation energies.
FAQs
Does a higher er always mean weaker interactions?
For uniform dielectric screening, yes: electrostatic force and energy scale as 1/er. Real solutions can deviate due to specific solvation, ion pairing, and structure, but the trend is a reliable first estimate.
Why does the Born curve level off at high er?
Born energy depends on (1 - 1/er). Once er is large, 1/er becomes small, so increases in er change the factor only slightly, producing diminishing returns in predicted stabilization.
Which inputs affect the screening results most?
Distance has the largest impact: force varies with 1/r^2 and energy with 1/r. Charges matter linearly through q1*q2. The dielectric constant then scales both values by 1/er.
Can I use this for dipoles or multipoles?
This version focuses on point charges and a single-ion Born model. You can approximate dipoles by converting to equivalent charge separations, but accurate dipole interactions need dedicated formulas and geometry.
Why are some Born energies negative?
The sign indicates stabilization when moving a charge from vacuum to a polar medium. Higher er solvents lower the electrostatic self-energy of the ion, giving a negative free energy change.
What er range should I plot for lab solvents?
Most common solvents fall between about 1.8 and 80. The default plot spans 1.6 to 90 to cover hydrocarbons through water and to show the diminishing changes at very high er.