Micellar Aggregation Number Calculator

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Colloidal Structures in Surfactant Solutions

BET Adsorption Isotherm

Capillarity and Surface Forces in Liquids (Curved Surfaces)

Freundlich adsorption isotherm

Important Formulas of Adsorption Isotherm

Important Formulas of Colloids

Important Formulas on Surface Tension

Langmuir Adsorption Isotherm

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Micellar Aggregation Number

Critical Packing Parameter

Electrophoresis and other Electrokinetics Phenomena

Specific Surface Area

Tanford Equation

✖Micelle Core Radius is defined as the distance from the center to the circumference of a micelle.ⓘ Micelle Core Radius [R_mic]			+10% -10%
✖The volume of Hydrophobic Tail is defined as the amount of space the hydrophobic tail occupies.ⓘ Volume of Hydrophobic Tail [V_hydrophobic]			+10% -10%

✖Micellar Aggregation Number is defined as the number of surfactant molecules required to form the micelles.ⓘ Micellar Aggregation Number [N_mic]

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Formula

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Micellar Aggregation Number

Formula

`"N"_{"mic"} = ((4/3)*pi*("R"_{"mic"}^3))/"V"_{"hydrophobic"}`

Example

`"6.7E^37"=((4/3)*pi*(("0.113E^-6m")^3))/"90E^-30m³"`

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Micellar Aggregation Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Micellar Aggregation Number = ((4/3)*pi*(Micelle Core Radius^3))/Volume of Hydrophobic Tail
N_mic = ((4/3)*pi*(R_mic^3))/V_hydrophobic
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Micellar Aggregation Number - Micellar Aggregation Number is defined as the number of surfactant molecules required to form the micelles.
Micelle Core Radius - (Measured in Angstrom) - Micelle Core Radius is defined as the distance from the center to the circumference of a micelle.
Volume of Hydrophobic Tail - (Measured in Cubic Meter) - The volume of Hydrophobic Tail is defined as the amount of space the hydrophobic tail occupies.

STEP 1: Convert Input(s) to Base Unit

Micelle Core Radius: 1.13E-07 Meter --> 1130 Angstrom (Check conversion here)
Volume of Hydrophobic Tail: 9E-29 Cubic Meter --> 9E-29 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_mic = ((4/3)*pi*(R_mic^3))/V_hydrophobic --> ((4/3)*pi*(1130^3))/9E-29

Evaluating ... ...

N_mic = 6.7155475779063E+37

STEP 3: Convert Result to Output's Unit

6.7155475779063E+37 --> No Conversion Required

FINAL ANSWER

6.7155475779063E+37 ≈ 6.7E+37 <-- Micellar Aggregation Number

(Calculation completed in 00.004 seconds)

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Created by Pratibha

Amity Institute Of Applied Sciences (AIAS, Amity University), Noida, India

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< 4 Micellar Aggregation Number Calculators

Micellar Core Radius given Micellar Aggregation Number

Go Micelle Core Radius = ((Micellar Aggregation Number*3*Volume of Hydrophobic Tail)/(4*pi))^(1/3)

Volume of Hydrophobic Tail given Micellar Aggregation Number

Go Volume of Hydrophobic Tail = ((4/3)*pi*(Micelle Core Radius^3))/Micellar Aggregation Number

Micellar Aggregation Number

Go Micellar Aggregation Number = ((4/3)*pi*(Micelle Core Radius^3))/Volume of Hydrophobic Tail

Mass of aggregate enclosed within distance r

Go Mass of Aggregate = (4/3)*(Density*pi*(Radius of Curvature)^3)

< 16 Important Formulas of Colloids Calculators

Surface Enthalpy given Critical Temperature

Go Surface Enthalpy = (Constant for each Liquid)*(1-(Temperature/Critical Temperature))^(Empirical Factor-1)*(1+((Empirical Factor-1)*(Temperature/Critical Temperature)))

Surface Entropy given Critical Temperature

Go Surface Entropy = Empirical Factor*Constant for each Liquid*(1-(Temperature/Critical Temperature))^(Empirical Factor)-(1/Critical Temperature)

Ionic Mobility given Zeta Potential using Smoluchowski Equation

Go Ionic Mobility = (Zeta Potential*Relative Permittivity of Solvent)/(4*pi*Dynamic Viscosity of Liquid)

Number of Moles of Surfactant given Critical Micelle Concentration

Go Number of Moles of Surfactant = (Total Concentration of Surfactant-Critical Micelle Concentration)/Degree of Aggregation of Micelle

Zeta Potential using Smoluchowski Equation

Go Zeta Potential = (4*pi*Dynamic Viscosity of Liquid*Ionic Mobility)/Relative Permittivity of Solvent

Micellar Core Radius given Micellar Aggregation Number

Go Micelle Core Radius = ((Micellar Aggregation Number*3*Volume of Hydrophobic Tail)/(4*pi))^(1/3)

Volume of Hydrophobic Tail given Micellar Aggregation Number

Go Volume of Hydrophobic Tail = ((4/3)*pi*(Micelle Core Radius^3))/Micellar Aggregation Number

Micellar Aggregation Number

Go Micellar Aggregation Number = ((4/3)*pi*(Micelle Core Radius^3))/Volume of Hydrophobic Tail

Critical Packing Parameter

Go Critical Packing Parameter = Surfactant Tail Volume/(Optimal Area*Tail Length)

Specific Surface Area for array of n Cylindrical Particles

Go Specific Surface Area = (2/Density)*((1/Cylinder Radius)+(1/Length))

Electrophoretic Mobility of Particle

Go Electrophoretic Mobility = Drift Velocity of Dispersed Particle/Electric Field Intensity

Surface Viscosity

Go Surface Viscosity = Dynamic Viscosity/Thickness of Surface Phase

Critical Chain Length of Hydrocarbon Tail using Tanford Equation

Go Critical Chain Length of Hydrocarbon Tail = (0.154+(0.1265*Number of Carbon Atoms))

Specific Surface Area

Go Specific Surface Area = 3/(Density*Radius of Sphere)

Number of Carbon Atoms given Critical Chain Length of Hydrocarbon

Go Number of Carbon Atoms = (Critical Chain Length of Hydrocarbon Tail-0.154)/0.1265

Volume of Hydrocarbon Chain using Tanford Equation

Go Micelle Core Volume = (27.4+(26.9*Number of Carbon Atoms))*(10^(-3))

Micellar Aggregation Number Formula

Micellar Aggregation Number = ((4/3)*pi*(Micelle Core Radius^3))/Volume of Hydrophobic Tail
N_mic = ((4/3)*pi*(R_mic^3))/V_hydrophobic

What is Micellar Aggregation Number?

Micellar Aggregation Number is a description of the number of molecules present in a micelle once the critical micelle concentration has been reached.
Traditionally, it is being determined by the small-angle neutron scattering experiments.

What is the range of Micellar Aggregation Number ?

Micellar Aggregation Number ranges from less than 100 for the ionic surfactants to several hundred for non-ionic surfactants.
The Micellar Aggregation Number increases with the increasing length of the hydrocarbon chains of the surfactant molecules.

How to Calculate Micellar Aggregation Number?

Micellar Aggregation Number calculator uses Micellar Aggregation Number = ((4/3)*pi*(Micelle Core Radius^3))/Volume of Hydrophobic Tail to calculate the Micellar Aggregation Number, The Micellar Aggregation Number is defined as the number of surfactant molecules required to form micelles. Micellar Aggregation Number is denoted by N_mic symbol.

How to calculate Micellar Aggregation Number using this online calculator? To use this online calculator for Micellar Aggregation Number, enter Micelle Core Radius (R_mic) & Volume of Hydrophobic Tail (V_hydrophobic) and hit the calculate button. Here is how the Micellar Aggregation Number calculation can be explained with given input values -> 6.7E+37 = ((4/3)*pi*(1.13E-07^3))/9E-29.

FAQ

What is Micellar Aggregation Number?

The Micellar Aggregation Number is defined as the number of surfactant molecules required to form micelles and is represented as N_mic = ((4/3)*pi*(R_mic^3))/V_hydrophobic or Micellar Aggregation Number = ((4/3)*pi*(Micelle Core Radius^3))/Volume of Hydrophobic Tail. Micelle Core Radius is defined as the distance from the center to the circumference of a micelle & The volume of Hydrophobic Tail is defined as the amount of space the hydrophobic tail occupies.

How to calculate Micellar Aggregation Number?

The Micellar Aggregation Number is defined as the number of surfactant molecules required to form micelles is calculated using Micellar Aggregation Number = ((4/3)*pi*(Micelle Core Radius^3))/Volume of Hydrophobic Tail. To calculate Micellar Aggregation Number, you need Micelle Core Radius (R_mic) & Volume of Hydrophobic Tail (V_hydrophobic). With our tool, you need to enter the respective value for Micelle Core Radius & Volume of Hydrophobic Tail and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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