Surfactant$-$based self$-$assemblies serve as liquid$-$phase templates for synthesizing

nanoparticles with desired shape and size. Water$-$insoluble nanoparticles are prepared using

water$-$in$-$oil microemulsions, comprising nanosized water droplets in a continuous oil phase, with

droplet size tuned by adjusting the water$-$to$-$surfactant molar ratio. Two types of w$/$o

microemulsion methods for nanoparticle synthesis exist: A$)$ one involves pre$-$dissolving or

dispersing one reactant in the drops, B$)$ while the other introduces both reactants directly into the

microemulsion solution, allowing for diffusion and reaction within the drops through the oil

medium. So$,$ nanoparticles form via reactant mass transport or mixing pre$-$dissolved reactants.

Coalescence of drops leads to dimers where reaction occurs, forming insoluble product

molecules. Nucleation and growth inside drops result in nanoparticle formation, with size tunable

by adjusting drop size through water$-$to$-$surfactant ratio. Coalescence exchange redistributes

molecules, crucial for correct distribution which follows binomial distribution. $8$

Consider the first case $($A only$)$ and write a monte carlo code for formation and growth of

nanoparticles provided the condition written in the text and shown diagrammatically:

a$)$ Reactant mass transport $($km$)$: Reactant molecules transport into drops through the oil

medium at a rate km$.$

b$)$ Coalescence$-$Exchange $($kc$)$: Two drops collide to form dimers, which then split and

redistributed into two daughter drops. Coalescence rate is kc$.$

c$)$ Solubilization $($kcp$)$: Solubilization occurs when an empty drop collides with a drop

containing reactant, with rate kcp$.$

d$)$ Reaction $($kr$)$: Drops with opposite reactants coalesce, undergo reaction, and form insoluble

products with rate kr$.$

e$)$ Nucleation $($kn$)$: After reaction, dimers disperse into daughter drops. Drops with a threshold

of product molecules undergo nucleation, forming solid nanoparticles. Nucleation rate is kn$.$

f$)$ Growth $($kg$)$: Drops with solute particles coalesce with drops containing product molecules,

consuming the product to grow in size. Coalescence rate remains the same.a$)$

A

transport of reactant $A$

A

$($A$)$

$($b$)$

$$cdots

B

B $\frac{\text{s}\text{o}\text{l}\text{u}\text{b}\text{i}\text{l}\text{i}\text{z}\text{a}\text{t}\text{i}\text{o}\text{n}}{ofreactantB}$

B

B$)$

B

$($c$)($A$,$B$)$

$($d$)$

$($C$)-$ A

$($C$,$A$)$

C$,$A

$()\frac{\text{c}\text{o}\text{l}\text{l}\text{i}\text{s}\text{i}\text{o}\text{n}\text{,}}{\text{c}\text{o}\text{a}\text{l}\text{e}\text{s}\text{c}\text{e}\text{n}\text{c}\text{e}}$

redispersion of

$A,B$ and $C(I)$

B$)$

$($e$)$

$($

$($f$)$

$($C$)$growthofparticleC$(s)()$