Michael Thomas Flanagan's Java Scientific Library

Class GouyChapmanStern:      Models the Gouy-Chapman and Gouy-Chapman-Stern Equations

      

Last update: 7 July 2008
Main Page of Michael Thomas Flanagan's Java Scientific Library

Theory Java Class implementing above theory

Gouy-Chapman-Stern model used by this class

This class contains the methods needed to calculate the surface charge density or surface potential and the charge and ion profiles at a charged surface in contact with an electrolyte.

The model shown, in Figure 1, contains a charged interface of surface charge density, σ C m-1,and an electrolyte with n ionic species, Si, of which m are cationic, Si = Ci, and n-m are anionic, Si = Ai. There may be any number of anionic and catonic species as long as overall charge neutrality is maintained, i.e.


where [Si] is the concentration of the ith ionic species, [Ci] is the concentration of the ith cationic species, [Ai] is the concentration of the ith anionic species and zi is the charge on ionic species i in signed units of electronic charge (e.g. +2 for Ca++, -1 for Cl-), The unit of concentration used in the calculation, described on this page, is mol m-3. However, note that concentrations entered through the set methods of this class are entered as mol dm-3, i.e. as Molar concentrations.

The following potentials [units - volts] are indicated in Figure 1:
and δ is the thickness of the Stern layer.

Each ionic species may be specifically adsorbed to a surface site, I. Each of these adsorption processes is characterised by an association constant, Ki, where

where [SI,i] is the concentration of the surface adsorption site - ion complex for the ith ionic species (mol m-2), [Io] is the total concentration ((mol m-2) of the surface sites and [Sbulk,i] is the concentration of ionic species, Si, in the bulk of the electrolyte. In many uses of this class no or only one or two of the ionic species will form a complex with the ionophore, i.e. most Ki = 0.

This class uses the Gouy-Chapmann-Sterm model in calculating the values of these parameters. The relevant equations used in the methods in this class will simply be listed in the description below. Detailed descriptions of this model may be found in the books listed in the Bibliography below.

1 Calculation of the surface charge density, σ, and the Stern layer potential, ψδ, for a known surface potential, ψo

1.1 Stern layer ignored, i.e. Gouy-Chapman theory

 1.1.1 Asymmetric electrolyte
An asymmetric electrolyte is one in which the absolute values of the signed units of charge, zi, are the different for at least two of the ionic species present, e.g. a mixed Ca++/Na+/Cl- electrolyte.
The surface charge density for an asymmetrical electrolyte, neglecting the Stern layer, is obtained as:

where NA is Avagadro's Number (6.02205 x 1023 mol-1), εo is the electrical permittivity of free space (8.85419 x 10-12 C2 N-1 m-1), εr is the relative electrical permittivity (dielectric constant) of the electrolyte, k is the Boltzmann constant (1.38066 x 10-23 J/K), T is the absolute temperature, e is the absolute value of the quantity of charge on the electron (1.60219 X 10-19 C) and sign(ψo) is the sign of ψo, i.e. +1 or -1.

1.1.2 Symmetric electrolyte
A symmetric electrolyte is one in which the absolute values of the signed units of charge, zi, are the same for all ions present, e.g. a mixed Li+Br-/Na+Cl- electrolyte.
The surface charge density for a symmetrical electrolyte, neglecting the Stern layer, is obtained as:

where z is the absolute value of the ionic charge, i.e. z = zi for the cationic species and z = -zi for the anionic species, and NT is the concentration of the electrolyte, i.e.


1.2 Stern layer included, i.e. Gouy-Chapman-Stern theory

1.2.1 No specific adsorption
The thickness of the Stern layer is approximated to the number average radius of the ions in at the Stern layer-diffuse layer interface, i.e.

and the Stern layer capacitance, as F m-2, Cδ, is calculated as

where εStern is the relative electrical permittivity of the electrolyte in the Stern layer. Note that this may not be the same as the bulk value, e.g. water has been reported to have values of εδ in the range 5 to 10 at a silver iodide / aqueous electrolyte intetrface [Ref: Duncan J Shaw (2003) Colloid and Surface Chemistry, Butterworth-Heinemann, Fourth Edition, 'The inner part of the double layer', pp 181-185].


1.2.1.i Asymmetric electrolyte
The surface charge density for an asymmetrical electrolyte, including the Stern modification but in the absence of specific adsorption, is given by:

where ψδ is given by

The surface charge density, σ, is, thus, obtained as the root of

The relevant method in this class solves Equation 10 using a bisection procedure with with bounds, to σ, of zero and the value obtained by substituting ψo into Equation 3 (section 1.1.1 above). On each calculation of g(σ) the diffuse potential ψδ is calculated using Equation 27 (section 2.2.1.i below) and CStern is calculated using Equations 7 and 6 (section 1.2.1 above).

1.2.1.ii Symmetric electrolyte
The surface charge density for an symmetrical electrolyte, including the Stern modification but in the absence of specific adsorption, is given by:

See section 1.1.2 (above) for the meaning of the symbols. The surface charge density, σ, is, thus, obtained as the root of

The relevant method in this class solves Equation 11 using a bisection procedure with bounds, to σ, of zero and the value obtained by substituting ψo into Equation 4 (section 1.1.2 above). On each calculation of g(σ) the diffuse potential ψδ is calculated using Equation 28 (section 2.2.1.ii below) and CStern is calculated using Equations 7 and 6 (section 1.2.1 above).

1.2.2 Specific adsorption of one or more of ionic species
The thickness of the Stern layer is now approximated to the number average radius of the ions in at the Stern layer-diffuse layer interface, including the adsorbed ions, i.e.

i.e. as the root of the quadratic

and the Stern layer capacitance, as F m-2, CStern, is calculated as before

A single ionic species adsorbed
If only one ionic species is specifically adsorbed, the adsorbed surface concentration (moles per square metre), is given by rearranging Equation 2 to give

where

A is the surface area and V is the volume of the electrolyte solution.
The adsorbed ion concentrations, [SI,i], are thus obtained as the root of the quadratic


Several ionic species adsorbed
If more than one, i.e. k, ionic species is specifically adsorbed, the adsorbed surface concentrations, are obtained solving the k quadratics obtained on rearranging the k Equations 2

A Nelder-Mead simplex minimisation of

has been used to obtain the [SI,i]. Initial estimates for the minimisation were obtained by solving the set of linear equations

where A is a k by k matrix with elements

x is a vector of length k with elements

and the vector b contains the k required initial etimates of [SI,i], i.e. the values of [SI,i] if the adsorption process does not measurably deplete the bulk concentrations of the ion. The subscripts are calculated to point at the relevant subscripts for the non-zero Ki. In this class these k Equations 16c is solved using an LU decompostion method.

The total adsorbed charge, σads, is calculated as

The total surface charge, σ, is related to the adsorbed charge, σads, and the charge in the diffuse layer, σdiff, by


1.2.2.i Asymmetric electrolyte
The charge in the diffuse layer is given by


The surface charge density, σ, in the presence of specific adsorption, for an asymmetric electrolyte is, now also, obtained as the root of

The relevant method in this class solves Equation 10 using a bisection procedure with with the following bounds, to σ:
where σads, max = [Io]eNA and σdiff0,max is the value of σ obtained by substituting ψointo Equation 3.

On each calculation of f(σ) the Stern potential ψδ is obtained as the root of

i.e. from Equations 6, 7 and 9. using Equations 7, 9 and 14 through to 18.

1.2.2.ii Symmetric electrolyte
The charge in the diffuse layer is given by


The surface charge density, σ, in the presence of specific adsorption, for a symmetric electrolyte is, now also, obtained as the root of

by the same procedure as described in section 1.2.2.i but using Equation 4 instead of Equation 3 as well as Equations 7, 9 and 14 through to 18.



2 Calculation of the surface potential, ψo, and the Stern layer potential, ψδ, for a known surface charge density, σ

2.1 Stern layer ignored, i.e. Gouy-Chapman theory

2.1.1 Asymmetric electrolyte
In the absence of specific adsorption and on neglecting the Stern layer the surface potential, ψo, for an asymmetric electrolyte is related to the surface charge σ, by Equation 3 (section 1.1.1 above) and is obtained as the root of

A bisection method is used to obtain this root with bounds to ψo of zero and

where



2.1.2 Symmetric electrolyte
In the absence of specific adsorption and on neglecting the Stern layer the surface potential, ψo, for a symmetric electrolyte is given by

See section 1.1.2 for the explanation of the symbols z and NT.

2.2 Stern layer included, i.e. Gouy-Chapman-Stern theory

 2.2.1 No specific adsorption
2.2.1.i Asymmetric electrolyte
In the absence of specific adsorption but on including the Stern layer the surface potential, ψo, for an asymmetric electrolyte is related to the surface charge σ, by Equations 6, 7, 8 and 9 (above - sections 1.2 and 1.2.1.i) and is obtained from

after ψδ has been obtained as the root of

The capacitance CStern is calculated using Equations 6 and 7. The root of Equation 27 is obtained by an analogous procedure to that used in section 2.1.1 for Equation 23 with ψδ replacing ψo.

2.2.1.ii Symmetric electrolyte
In the absence of specific adsorption but on including the Stern layer the surface potential, ψo, for a symmetric electrolyte is obtained from

after ψδ has been obtained as

The capacitance CStern is calculated using Equations 6 and 7. See section 1.1.2 for the explanation of the symbols z and NT.

2.2.2 Specific adsorption of one or more ionic species
The adsorbed ion concentrations, Stern layer thickness and Stern capacitance are calculated as described in Equations 14, 15, 16, 17 and 18 (section 1.2.2 above).

2.2.2.i Asymmetric electrolyte
In the presence of specific adsorption and on including the Stern layer the surface potential, ψδ, for an asymmetric electrolyte is related to the surface charge σ, by Equation 19 (section 1.2.2.i) and after ψδ has been obtained as the root of

ψo is calculated using

The capacitance CStern is calculated using Equations 14 and 7 (section 1.2.2). The root of Equation 27 is obtained by an analogous procedure to that used in section 1.2.2.i for Equation 20 with ψδ replacing ψo.

2.2.2.ii Symmetric electrolyte
In the presence of specific adsorption and on including the Stern layer the surface potential, ψδ, for a symmetric electrolyte is related to the surface charge σ, by Equation 21 (section 1.2.2.ii) and after ψδ has been obtained as

ψo is calculated using

The capacitance CStern is calculated using Equations 14 and 7 (section 1.2.2).



3 Calculation of the potential profile, concentration profiles and Debye length

3.1 Potential profile

3.1.1 Asymmetric electrolyte
The potential at a distance x from the electrolyte-charged surface interface, ψx, for an asymmetic electrolyte is given by

in the Stern layer and by

in the diffuse layer, where
ψl = ψδ if the Gouy-Chapman-Stern theory has been used
ψl = ψo if the Gouy-Chapman theory has been used. The potential at x, ψx, is obtained as the root of

The integral in Equation 32a and 32b is integrated numerically, in this class, by a 2000 interval trapezoid procedure.

3.1.1 Symmetric electrolyte
The potential at a distance x from the electrolyte-charged surface interface, ψx, for a symmetric electrolyte is given by

in the Stern layer and by

in the diffuse layer. where


and
ψl = ψδ if the Gouy-Chapman-Stern theory has been used
ψl = ψo if the Gouy-Chapman theory has been used.
The reciprocal length, κ, is the reciprocal of the Debye length (see section 3.3 below).

3.2 Concentration profiles

The concentraion of an ion at a distance x from the electrolyte-charged surface interface, [Sx,i], is given by


3.3 Debye length

The Debye length, dD, a measure of the thickness of the diffuse layer, is given by

which simplifies to

in the case of a symmetric electrolyte.



Bibliography





Details of the Java class GouyChapmanStern

PARTS STILL IN PREPARATION
Related classes

SUMMARY OF CONSTRUCTORS AND METHODS
Constructor public GouyChapmanStern()
 
Stern modification options include Stern modification
(default option) 		public void includeStern()
ignore Stern modification public void ignoreStern()
Ionic radii options
 hydrated radii
(default option) 		public void setHydratedRadii()
bare radii public void setBareRadii()
 
Enter an ion public void setIon(String ion, double concn, double radius, int charge, double assocK)
public void setIon(String ion, double concn, double radius, int charge)
public void setIon(String ion, double concn, double assocK)
public void setIon(String ion, double concn)
Enter the adsorption site density public void setSurfaceSiteDensity(double density)
Enter the surface charge density, σ public void setSurfaceChargeDensity(double chargeDensity)
public void setSurfaceCharge(double charge, double area)
public void setSurfaceCharge(double charge)
Enter the surface area public void setSurfaceArea(double area)
Enter the electrolyte volume public void setVolume(double volume)
Enter the surface potential, ψo public void setSurfacePotential(double surfacePotential)
Enter relative electrical permittivities public void setRelPerm(double relPerm, double relPermStern)
public void setRelPerm(double relPerm)
Enter the temperature public void setTemp(double temp)
 
 
Get the calculated charge densities Surface charge density, σ public double getSurfaceChargeDensity()
Surface charge public double getSurfaceCharge()
Diffuse layer charge density public double getDiffuseChargeDensity()
Adsorbed ion charge density public double getAdsorbedChargeDensity()
Get the calculated potentials Surface Potential potential, ψo public double getSurfacePotential()
Stern layer - diffuse layer interface potential, ψδ public double getDiffuseLayerPotential()
Stern layer potential difference, ψo - ψδ public double getSternLayerPotential()
Potential at a distance, x, from the surface public double getPotentialAtX()
Get the concentrations Equilibrium bulk concentrations public double[] getBulkConcn()
Adsorbed ion surface concentrations public double[] getSiteConcns()
Initial concentrations public double[] getInitConcns()
Concentrations at a distance, x, from the surface public double[] getConcnsAtX()
Initial ionic strength public double getIonicStrength()
Get the calculated lengths Debye length public double getDebyeLength()
Stern layer thickness public double getSternThickness()
Get the calculated capacitances Total interface capacitance public double getTotalCapacitance()
public double getTotalCapPerSquareMetre()
Diffuse double layer capacitance public double getDiffuseLayerCapacitance()
public double getDiffuseLayerCapPerSquareMetre()
Stern layer capacitance public double getSternCapacitance()
public double getSternCapPerSquareMetre()




CONSTRUCTOR

 public GouyChapmanStern()
Usage:                      GouyChapmanStern gcs = new GouyChapmanStern();
This creates a new instance, in this example, don, of GouyChapmanStern().
On creation of this instance the following default option are automatically set:

METHODS

Set options

Stern modification of the Gouy-Chapman theory

 The surgace charge density, σ, surface potential, ψo, and related parameters may be calculated
 i.  by a method that includes Stern's modification of the Gouy-Chapman theory.
or
 ii. by a method that neglects Stern's modification of the Gouy-Chapman theory.
The former (option i) is the default option set on creating an instance of Donnan().

public void ignoreStern()
Usage:                      gcs.ignoreStern();
This method removes the Stern modification from all calculations (option ii above).

public void includeStern()
Usage:                      gcs.includeStern();
This method resets the option to include Stern modification from all calculations.(option i above).

Radii

 The radii, ri, are needed if the interface charge is to be included in the calculation of the Donnan potential. They may be entered by the user or taken from the class IonicRadii. If they are taken from the class IonicRadii either the hydrated ionic radii or the bare ionic radii may be selected. The default option, set on creating an instance of Donnan(), is the hydrated radius.

public void setBareRadii()
Usage:                      gcs.setBareRadii();
This method sets the option to select bare radii from the class IonicRadii.

public void setHydratedRadii()
Usage:                      gcs.setHydratedRadii();
This method resets the option to select hydrated radii from the class IonicRadii.





Entering an ion

Any number of ions may be entered. There must be overall charge neutrality when all the ions have been entered.

Entering an ion when the Born charging option has been chosen
public void setIon(String ion, double concn, double radius, int charge, double assocK)
public void setIon(String ion, double concn, double radius, int charge)
public void setIon(String ion, double concn, double assocK)
public void setIon(String ion, double concn)
Usage:                      gcs.setIon(ionName, concn, radius, charge, assocK);
The argument list is: Usage:                      gcs.setIon(ionName, concn, radius, charge);
The arguments as above with the exception that the association constant, assocK, of the ion with the surface adsorption sites is automatically set to zero.

Usage:                      gcs.setIon(ionName, concn, assocK);
The arguments as above with the exceptions that the charge is taken from the class IonicRadii and the ion name, ionName, must conform to one of the conventions used by IonicRadii, i.e. the ion should be entered as the atomic symbol [see list in IonicRadii], e.g. Ag, or symbols, e.g. NH4, followed by the signed units of charge. This combination of symbol and valency may be represented in any of the following ways, e.g. Ca(+2), Ca(2+), Ca(++), Ca+2, Ca2+ or Ca++.

Usage:                      gcs.setIon(ionName, concn);
The arguments as above with the exceptions that the association constant, assocK, of the ion with the surface adsorption sites is automatically set to zero, that the charge is taken from the class IonicRadii and that the ion name, ionName, must conform to one of the conventions used by IonicRadii, i.e. the ion should be entered as the atomic symbol [see list in IonicRadii], e.g. Ag, or symbols, e.g. NH4, followed by the signed units of charge. This combination of symbol and valency may be represented in any of the following ways, e.g. Ca(+2), Ca(2+), Ca(++), Ca+2, Ca2+ or Ca++.

Entering the surface adsorption site density

public void setSurfaceSiteDensity(double density)
Usage:                      gcs.setSurfaceSiteDensity(density);
This method allows the surface adsorption site density, in moles per square metre, to be entered.

Entering the surface charge density

The surface charge density may be entered directly, as a charge density, or indirectly as the total surface charge and the surface area. This density must be entered if the surface potential is to be calculated.

public void setSurfaceChargeDensity(double density)
public void setSurfaceCharge(double charge, double area)
public void setSurfaceCharge(double charge)
Usage:                      gcs.setSurfaceChargeDensity(density);
This method allows the surface charge density, in Coulombs per square metre, to be entered.

Usage:                      gcs.setSurfaceCharge(charge, area);
This method allows the total surface charge, in Coulombs, and the surface area, in square metres, to be entered. This method calculates the surface charge density.



Usage:                      gcs.setSurfaceCharge(charge);
This method allows the total surface charge, in Coulombs. This method requires that the the surface area is also entered through the method setSurfaceArea.

Entering the surface area

public void setSurfaceArea(double area)
Usage:                      gcs.setSurfaceArea(area);
This method allows the area of the surface to be entered, in square metres.

Entering the electrolyte volume

public void setVolume(double volume)
Usage:                      gcs.setVolume(volume);
This method allows the volume of the electrolyte to be entered, in cubic metres. The volume is needed if the Stern modification is included.

Entering the surface potential

The surface potential must be entered if the surface charge density is to be calculated.

public void setSurfacePotential(double potential)
Usage:                      gcs.setSurfacePotential(potential);
This method allows the surface potential, in volts, to be entered.

Entering the relative electrical permittivities

public void setRelPerm(double relPerm, double sternPerm)
Usage:                      gcs.setRelPerm(eps, epsStern);
This method allows the relative electrical permittivity (dielectric constant) of the bulk phase (eps) and of the Stern (epsStern) to be entered. See the comment and reference after Equations 7 (above) on the values of 'Stern permittivities'. The Stern layer permittivity is not required if the Stern modification is ignored (see immediately below for method that then is appropriate).

Usage:                      gcs.setRelPerm(eps);
This method allows the relative electrical permittivity (dielectric constant) of the bulk phase (eps) and equates the permittivity of the electrolyte in the Stern layer to that of the bulk phase if that permittivity is required. See the comment and reference after Equations 7 (above) on the values of 'Stern permittivities'. The Stern layer permittivity is not required if the Stern modification is ignored.

Entering the temperature

public void setTemp(double temp)
Usage:                      gcs.setTemp(temp);
This method allows the temperature (argument, e.g. temp, in degrees Celsius) to be entered. The default value, on not calling this method, is 25 degrees Celsius.

Getting the calculated values

Getting the charge densities

Getting the surface charge density
public double getSurfaceChargeDensity()
Usage:                      double sigma = gcs.getSurfaceChargeDensity();
This method calculates and returns the charge density, as Coulombs per square metre, if the relevant data, e.g. surface potential, have been entered. It returns the set value if the surface charge density has been set.

Getting the surface charge
public double getSurfaceCharge()
Usage:                      double tSigma = gcs.getSurfaceCharge();
This method calculates and returns the charge, as Coulombs, if the relevant data, e.g. surface potential and surface area, have been entered.

Getting the diffuse layer charge density
public double getDiffuseChargeDensity()
Usage:                      double diffSigma = gcs.getDiffuseChargeDensity();
This method calculates and returns the diffuse layer charge density, as Coulombs per square metre, if the relevant data, e.g. surface potential or surface charge density, have been entered.

Getting the adsorbed ion charge density
public double getAdsorbedChargeDensity()
Usage:                      double adsSigma = gcs.getAdsorbedChargeDensity();
This method calculates and returns the adsorbed charge density, as Coulombs per square metre, if the relevant data, e.g. surface potential or surface charge density, have been entered.

Getting the potentials

Getting the calculated surface potential, ψo
public double getSurfacePotential()
Usage:                      double psi0 = gcs.getSurfacePotential();
This method calculates and returns the surface potential, ψo, as volts, if the relevant data, e.g. surface charge density, have been entered. It returns the set value if the surface potential has been set.

Getting the calculated diffuse layer - Stern layer potential, ψδ
public double getDiffuseLayerPotential()
Usage:                      double psiDelta = gcs.getDiffuseLayerPotential();
This method calculates and returns the diffuse layer potential, ψδ, as volts, if the relevant data, e.g. surface charge density or surface potential, ψo, have been entered.

Getting the calculated Stern layer potential difference, ψo - ψδ
public double getSternLayerPotential()
Usage:                      double psiStern = gcs.getSternLayerPotential();
This method calculates and returns the Stern layer potential difference, ψo - ψδ, as volts, if the relevant data, e.g. surface charge density or surface potential, ψo, have been entered.

Getting the potential difference at a distance, x, from the surface
public double getPotentialAtX()
Usage:                      double psiAtX = gcs.getPotentialAtX();
This method calculates and returns the potential, ψx, as volts, at a distance, x, from the electrolyte - charged surface interface if the relevant data, e.g. surface charge density or surface potential, ψo, have been entered.



Getting the concentrations

Getting the equilibrium bulk concentrations
public double getBulkConcn()
Usage:                      double[] bulk = gcs.getBulkConcn();
This method returns an array containing the concentrations of the ions in the bulk phase at equilibrium in mol dm-3.

Getting the adsorbed ion concentrations
public double getSiteConcn()
Usage:                      double[] adsb = gcs.getSiteConcn();
This method returns an array containing the surface concentrations of the ions specifically adsorbed onto the surface in mol m-2.

Getting the initial ion concentrations
public double getInitConcn()
Usage:                      double[] init = gcs.getInitConcn();
This method returns an array containing the total concentrations of the ions initially provided in mol dm-3.

Getting the ion concentrations at a distance, x, from the surface
public double getConcnAtX(double xDistance)
Usage:                      double[] concAtX = gcs.getConcnAtX(xDistance);
This method returns an array containing the concentrations, in mol dm-3, of the ions at a distance, x [xDistance in above example], from the electrolyte - charged surface interface if the relevant data, e.g. surface charge density or surface potential, ψo, have been entered.

Getting the initial ionic strength
public double getIonicStrength()
Usage:                      double ionStr = gcs.getIonicStrength();
This method returns the ionic strength, in mole dm-3, of the electrolyte calculated using the initially provided concentrations.

Getting the calculated lengths

Getting the Debye lengths
public double getDebyeLength()
Usage:                      double dLen = gcs.getDebyeLength();
This method returns the Debye length, δDebye [Equation ??], in metres.

Getting the Stern thickness
public double getSternThichkness()
Usage:                      double sLen = gcs.getSternThichkness();
This method returns the Debye length, δStern,, in metres.

Getting the capacitances

Getting the total interface capacitance
public double getTotalCapPerSquareMetre()
Usage:                      double tCap = gcs.getTotalCapPerSquareMetre();
This method returns the total interface capacitance, CTotal, in Farads per square metre.

public double getTotalCapacitance()
Usage:                      double tCap = gcs.getTotalCapacitance();
This method returns the total interface capacitance, CTotalA, in Farads. If a surface area, A, has not been entered the capacitance per square metre is returned.

Getting the diffuse layer capacitance
public double getDiffuseLayerCapPerSquareMetre()
Usage:                      double dCap = gcs.getDiffuseLayerCapPerSquareMetre();
This method returns the diffuse layer capacitance, Cdiff, in Farads per Square metre.

public double getDiffuseLayerCapacitance()
Usage:                      double dCap = gcs.getDiffuseLayerCapacitance();
This method returns the diffuse layer capacitance, CdiffA, in Farads. If a surface area, A, has not been entered the capacitance per square metre is returned.

Getting the Stern layer capacitance
public double getSternCapPerSquareMetre()
Usage:                      double sCap = gcs.getSternCapPerSquareMetre();
This method returns the Stern layer capacitance, CStern, in Farads per square metre.

public double getSternCapacitance()
Usage:                      double sCap = gcs.getSternCapacitance();
This method returns the Stern layer capacitance, CSternA, in Farads. If a surface area, A, has not been entered the capacitance per square metre is returned.





OTHER CLASSES USED BY THIS CLASS

 This class uses the following classes in Michael Thomas Flanagan's library:





This page was prepared by Michael Thomas Flanagan