**3. Surfactant free emulsion polymerization**

Used for manufacture of adhesives and water resistant polymers. By absence of surfactant, intensive coagulation of the particles greatly reduces the number of particles per unit volume of water so, particle nucleation and growth reduced [1]. Several literature had been reported about surfactant free emulsion polymerization, in this section a brief hint about these publications will be considered. Tauer et al. [45] studied the surfactant-free emulsion polymerization of styrene initiated by KPS. Wang and Pan [46] studied the surfactant-free emulsion polymerization of styrene with the water soluble co-monomer as 4-vinylpyridine. Ni et al. [47] studied mechanism of particle nucleation through adding 8% ethyl acetate at low speed agitation (100–200 rpm) through polymerization of 4-vinyl pyridine and styrene. Ou et al. [48] investigated the effect of the hydrophilic co monomer (vinyl acetate or methyl methacrylate) on particle nucleation in the surfactant-free emulsion polymerization of styrene. Yan et al. [49] investigated the surfactant-free emulsion copolymerization of styrene, methyl methacrylate and acrylic acid initiated by ammonium persulfate. Other literature reported by Mahdavian and Abdollahi, Zhang et al., Shaffei et al., and Sahoo and Mohapatra [50–53].

#### **3.1. Emulsion polymerization mechanism**

Emulsion polymerization is a free radical polymerization protocol occurs in three distinct steps; initiation, propagation, and termination.

#### *3.1.1. Initiation*

In which the initiator decomposed to free radicals either by (1) hemolytic fission (hemolysis) through thermal decomposition or radiation and by (2) chemical reaction through redox reactions. Rate of initiator dissociation (Rd) is the rate determining step and given by Eqs. (1)–(3);

$$I \xleftarrow{\textsc{Kd}} 2\mathtt{R} \bullet \tag{1}$$

$$\mathbf{R}\_d = \mathbf{\mathcal{Z}} \mathbf{\mathcal{K}}\_d \mathbf{I} \mathbf{I} \tag{2}$$

$$R\bullet + M \xrightarrow{K\_{\hookrightarrow}} RM\bullet \tag{3}$$

Rate of initiation (Ri ) is given by Eq. (4);

$$\mathbf{R}\_{i} = \mathbf{2}\_{i} \mathbf{f} \mathbf{K}\_{i} \mathbf{I} \mathbf{I} \tag{4}$$

*Kd* rate constant for initiator dissociation

*f* Initiator efficiency

*[I]* Initiator concentration

*Ki* rate constant for initiation

#### *3.1.2. Propagation*

Involve continuous addition of monomer particles to active centers (RM•) to form polymer chains.

Rate of polymerization (Rp) given by Eq. (5);

$$R\_p = -\frac{d[M]}{dt} = k\_\text{[} \mathbf{R} \bullet \mathbf{J}[M] + k\_p [M \bullet \mathbf{J}[M]] \tag{5}$$

Where [R•] is the free radicals concentration, [M] is the monomer concentration and [M•] is the total concentration of active monomers. Since consumed monomers in initiation stage is very small as compared to propagation, so the term "*ki* [*R*•][*M*]" can be neglected and rate of polymerization is determined by rate of propagation; Eq. (6).

$$R\_p = k\_p \text{[M} \bullet \text{]} \text{[M]} \tag{6}$$

#### *3.1.3. Termination*

**3.1. Emulsion polymerization mechanism**

*3.1.1. Initiation*

8 Recent Research in Polymerization

Rate of initiation (Ri

*f* Initiator efficiency

*3.1.2. Propagation*

*[I]* Initiator concentration

rate constant for initiation

*Kd*

*Ki*

chains.

steps; initiation, propagation, and termination.

*Rd* = 2*fKd*

*Ri* = 2*fKi*

rate constant for initiator dissociation

Rate of polymerization (Rp) given by Eq. (5);

*Rp* = *kp*

very small as compared to propagation, so the term "*ki*

polymerization is determined by rate of propagation; Eq. (6).

*Rp* <sup>=</sup> <sup>−</sup> *<sup>d</sup>*[*M*] \_\_\_\_

) is given by Eq. (4);

Emulsion polymerization is a free radical polymerization protocol occurs in three distinct

In which the initiator decomposed to free radicals either by (1) hemolytic fission (hemolysis) through thermal decomposition or radiation and by (2) chemical reaction through redox reactions. Rate of initiator dissociation (Rd) is the rate determining step and given by Eqs. (1)–(3);

*<sup>I</sup> Kd* ⎯→2*R*• (1)

*<sup>R</sup>*• <sup>+</sup> *<sup>M</sup>*⟶*Ki RM*• (3)

Involve continuous addition of monomer particles to active centers (RM•) to form polymer

Where [R•] is the free radicals concentration, [M] is the monomer concentration and [M•] is the total concentration of active monomers. Since consumed monomers in initiation stage is

[*R*•][*M*] + *kp*

*dt* <sup>=</sup> *ki*

[*I*] (2)

[*I*] (4)

[*M*•][*M*] (5)

[*R*•][*M*]" can be neglected and rate of

[*M*•][*M*] (6)

Termination leads to loss of two growing polymer chains [3]. It occurs by either recombination or disproportionation. Recombination involves reaction of one polymer chain with another growing one and reactive sites are blocked according to the following equation.

$$P\_u \bullet + P\_m \bullet \xrightarrow{K\_L} P\_u + m \tag{7}$$

Disproportionation where one chain abstract a hydrogen proton from another leaving it with unsaturated end group according to the following equation. This termination mechanism result in two polymer chain fractions one is saturated and the other is unsaturated [31].

$$P\_n \bullet + P\_m \bullet \xrightarrow{K\_l} P\_n + P\_m \tag{8}$$

Termination may occur by chain transfer reactions, which involves removal of atom and formation of new radical which may initiate the reaction forming other segments or cannot initiate the reaction so, the propagation progress ceased [31]. Other literature reported about termination occur by addition of retarders or inhibitors like phenols and catechol's to terminate active sites [31, 54].

#### **3.2. Kinetics of emulsion polymerization**

Since rate of polymerization expressed by Eq. (9);

$$R\_p = \, k\_p \mathbf{I} M \bullet \mathbf{I} \vert M \rangle \tag{9}$$

Where [*M*•] expressed by Eq. 10;

$$\{M\bullet\} = \frac{N}{NA} \tag{10}$$

N concentration of micelles plus particles

n the average number of radicals per micelle plus particle

NA is the Avogadro number

$$R\_p = \frac{N'nkp[M]}{NA} \tag{11}$$

The value of "n" determine rate of polymerization and depend on radical diffusion out of the polymer particles (desorption), the particle size, modes of termination, and the rates of initiation and termination relative to each other and to the other reaction parameters [5]. Depending on "n" value there are three cases that can be summarized as;

#### *3.2.1. Case 1: n = 0.5*

Means that at any given moment half of the polymer particles contain one radical and are growing while the other half are dormant, and known as zero–one systems to indicate that a polymer particle contains either zero or one radical at any given moment [5].

#### *3.2.2. Case 2: n < 0.5*

In which radical desorption from particles and termination in the aqueous phase are low especially for small particle sizes and low initiation rates.

#### *3.2.3. Case 3: n > 0.5*

In which particle size is large or the termination rate constant is low while termination in the aqueous phase and the initiation rate is fast, as some polymer particles contain two or more radicals.

• Degree of polymerization (Xn) is defined as the rate of growth of a polymer chain divided by the rate at which primary radicals enter the polymer particle and given by the following Eq. (12);

$$X\_u = \frac{r\_p}{r\_i} = \frac{\text{NKp} \text{[M]}}{R\_i} \tag{12}$$

This equation neglect any termination by chain transfer, if chain transfer occur the degree of polymerization given by Eq. (13).

$$X\_u = \frac{r\_p}{r\_i \Sigma r\_t} \tag{13}$$

where, ∑*rt* is the sum of termination reactions by chain transfer.

• Number of polymer particles is dependent on the total surface area of surfactant present in the system and given by Eq. (14);

$$N = K \left(\frac{Ri}{\mu}\right)^{2\beta} \langle a\_s S \rangle^{3\beta} \tag{14}$$

as is the interfacial surface area occupied by a surfactant molecule

S is the total concentration of surfactant in the system (micelles, solution, monomer droplets)

μ is the rate of volume increase of polymer particle

The number of polymer particles can be increased by increasing the emulsifier concentration while maintaining a constant rate of radical generation.
