Surfactants Effects on Coagulation of Latex During Polymerization: A Short Review

A general trend in emulsion polymerization is the search for ways to conduct the process less expensive and with less negative effects. Some of the problems come upon in emulsion polymerization and the application of its products relate to the use of surfactants, needed for stabilization during the production stage and storage. One of the most important problems which can cause coagulation, arise when the surfactant gradually desorbs from the surface of the latex particles during the preparation process or storage.

This work reviews the publications concerning the use of various kinds of surfactants in polymerization, especially emulsion polymerization, to find which kind of surfactants can cause less coagulation in the highest conversion. We wrote some facts about various kinds of surfactant, collect the surfactants which used in literatures about polymerization with their formula or structures and their probably effects on coagulation. This work is a new valuable short and quick reference for investigators who are studying in polymerization area.

Surfactants are a very important class of reagents which using in some different categories. There are many review articles about, for example their application in developing  effective fluorescent sensors[1], a surfactant flooding technique in oil recovery industries[2], surfactant adsorption on nanostructured surfaces[3], their effects on the dynamics and characteristics of plain and composite electroless nickel plating[4] and surfactant behavior of polymer-tethered nanoparticles[5].

There are also some other review articles  about  simulation methodologies to obtain the critical micelle concentration (CMC) and equilibrium distribution of aggregate sizes in dilute surfactant solutions[6], the bulk phase behavior multilayering of surfactant systems at the air–dilute aqueous solution interface, including surfactants with oligomers and polymers and the unusual system of ethanolamine and stearic acid etc.[7] and distinct character of surfactant gels comparing with crystalline fibrillar networks[8].

Although the later reviews are somehow being related to polymerization, none of them focused on surfactant kind effects on coagulation during polymerization. We published an article and discussed two separate procedures of AGET emulsion ATRP of methyl methacrylate, and mentioned that the major problem has been coagulation phenomenon during the polymerization especially at high monomer conversion[9]. Although this harmful phenomenon could have weakened by adding more surfactant, or by lowering the temperature, but leading to low monomer conversion which is not favorable.

Also, we found this problem during polymerization of butyl methacrylate, methyl acrylate and so on. One of the parameters which can be effeteness on this phenomenon is the kind of surfactant. In this review, we are attempting to find the effect of surfactant type on coagulation during the polymerization. A very new review is reported about particle coagulation of emulsion polymers by T. F. L. McKenna[10]. All variables, including the concentration and type of monomer, surfactant, buffer, initiator, the type of reactor, and the operating conditions (temperature, stirring rate, pressure, flow rates, …) etc. can influence coagulation phenomenon and hence the final particle size distribution (PSD) of emulsion polymerizations.

They emphasized that although there is a considerable amount of results about particle coagulation, an important problem in interpreting the results is that this phenomenon is coupled with particle growth and/or nucleation sub-processes almost in all the procces, so it is difficult to identify the exact contribution of particle coagulation. Therefore, works were carried out to examine the coagulation phenomenon independently. In another review reported by Krzysztof Matyjaszewski[11], he only discussed mechanisms and applications of ATRP, but emphasized also, the catalyst complexes should be sufficiently hydrophobic to be preferentially located in the organic phase in heterogeneous systems, so the choice of surfactant is important.

No any other discussion about surfactant effects reported in his article.  The particle number (Np) that some authors used in their reports define according to the following expression: where M₀ is the monomer/water ratio, is the fractional conversion, _p is the polymer density, and D_p is the v-average size of the particle[12]. Aspects of coagulation during emulsion polymerization of styrene and vinyl acetate is the title of an important article about coagulation, written by J. Meuldijk et al[13]. They reported recipe and process conditions’ effects on the coagulation behavior of polystyrene (PS) and polyvinyl acetate (PVAc) latexes, but there is no discussion about the effect of surfactant, SDS.

The dominating effect on coagulation behavior has been the electrolyte concentration and the coagulation of PVAc-latexes appeared to be more sensitive to electrolyte concentration than the coagulation of PS-lattices.Surfactants are a widely used contraction for surface active agents. The term surface active means that the surfactant reduces the free energy of surfaces and interfaces or reduces the surface and the interfacial tensions. Although the most water-soluble organic compounds have such an action when added to an aqueous solution, their effect is normally much less than for surfactants.

The unique behavior of a surfactant is that it self-assembles at interfaces and forms tightly packed structures: monolayers at the air-water and the oil-water interface, and monolayers and aggregates at the solid-water interface [14]. Surfactants have various chemical structures and contain both hydrophilic and hydrophobic parts. Their hydrophobic tail usually is a linear or branched hydrocarbon chain, which can be an unsaturated, or, less frequently, a halogenated or oxygenated hydrocarbon, or a siloxane chain, and, can be short, long, rigid, flexible, aromatic, aliphatic, etc. Their hydrophilic head group is ionic or another highly polar group, and, can be negative, positive, nonionic, amphoteric. Generally, surfactants are classified by their hydrophilic part.

The anionic surfactants are those carries a negatively charged group, (e.g., RCOO^– Na⁺ and RS0₃^– Na⁺).

The cationic surfactants are those bears a positively charged group (e.g., RNH₃⁺Cl^– and RN(CH₃) ₃⁺ Cl ^–).

The zwitterionic surfactants are those have both positively and negatively charged groups in the surface-active part (e.g., RNH₂⁺CH2COO ^– and RN(CH₃)₂ ⁺CH₂CH₂S0₃ ^–).

The nonionic surfactants have no ionic charge (e.g., RCOOCH₂CHOHCH₂OH and R(OC₂H₄) _xOH).

In most cases, the anionic and nonionic types of surfactants used in emulsion polymerization. When an anionic surfactant is applied, an anionic inisurf (surface active initiator) will be formed which its effect of on emulsion polymerization is probably similar to the results obtained by the emulsifier-free process[15]. Therefore, their chemical structure can play a very important role in emulsion polymerization.

The size of surfactant micelles, aggregation numbers, hydrophilic-lipophilic balance (HLB) is among the important factors affecting the polymerization. There are also polymerizable surfactants, which are those that have suitable conditions in their structures for auto-polymerization or polymerization assisted with other reagents[14]. Monoethanolamide ethoxylate of an unsaturated fatty acid capable of undergoing autoxidative polymerization, sulfated nonylphenol ethoxylate derivative capable of undergoing free-radical polymerization, and copolymer based on polyoxyethylene and polyoxybutylene segments with a methacrylate group at the hydrophobic end, also capable of undergoing free radical polymerization are some examples for polymerizable surfactants.

It is well known that one of the negative features of conventional surfactants is they physically adsorb on the surface of polymer particles and may migrate or desorb from the product. This is the reason that new surfactants, namely “the reactive surfactants”, found attracted increasing attention. A surface-active agent surfactant, not only emulsify the monomer but it also affects the mechanism of the emulsion polymerization reactions and the morphology of the resulting latex. The water-soluble hydrophobic heads of surfactant could be visualized as being bonded strongly with water molecules and the water-insoluble hydrophobic tails are adsorbed on the polymer surface by hydrophobic attractions[16]. It can also adsorb at the water-air interface, but at any instant, there is an equilibrium between the totally adsorbed surfactant molecules in media and the freely moving ones in the aqueous phase.

The useful role of surfactants in emulsion polymerization defined by J. R. Leiza et al.[17] are as follows:

Nucleation step. Emulsification of monomer droplets and/or seed particles. Stabilization of the polymer particles during the polymerization for the shelf life of the products.They also have mentioned that there is at least one negative effect. Any surfactant which has weak hydrophobic interaction with the polymer particles can be desorbed from the latex particle surface and reduce the latex stability, especially under high shear, freezing and high anionic strength conditions. So, quenching for stopping the polymerization process can be root the coagulation, itself. Another negative effect is the migration of surfactant from the surface of the resulting polymer during applying as a film. The reason for the bad effects of surfactants is their physical bonds, so one of the best resolvings of the problem is using the polymerizable surfactants which are chemically bonded to the particles of polymer.

The authors have presented the feasibility of Latemul®PD-104, Sipomer®Pam-200 and Sipomer®Cops-1as sole surfactant/stabilizer in the emulsion polymerization of model acrylic latexes with coating formulation and found the following results:

The polymerizable surfactant Latemul®PD-104 behaved as the conventional surfactant Dowfax®2A1 (as reference) above the CMC. The polymer particles were formed by micellar nucleation and homogeneous nucleation for both surfactants. Increasing the surfactant concentration caused higher molecular weights due to the generation of higher N_p. The Sipomer®Pam-200 has been more effective than Latemul®PD-104 and reference surfactant (Dowfax®2A1). Only gel found in the case of Sipomer®Pam-200 (coagulation). The phosphate head groups can form hydrogen bonds which made the polymer insoluble in THF (pH dependent); decreasing the pH of the reaction led to higher gel contents. SDS or sodium dodecyl sulfate, which also named (a solecism) sodium dodecyl sulfonate[18], has been used as the most popular anionic surfactant in literature related to polymerization[18-23]. The term “emulsifier” has been used instead of “surfactant” in some articles[24].

Nonionic surfactants have either a polyether or a polyhydroxy unit as the polar group. Polyether-based surfactants dominate, and the polyether consists of oxyethylene units (with a typical number of 5-10) made by polymerization of ethylene oxide (EO). Examples of polyhydroxy-based (polyol-based) surfactants are sucrose esters, alkyl glucosides, and polyglycerol esters, the latter type being a combination of polyol and polyether surfactant. The Sorbitan (a five-membered ring formed by dehydration of sorbitol) esters are another example, which, are edible and hence, useful for food and drug applications. Some common nonionic surfactants show in following[14]:

Important facts about nonionic surfactants are as following[14]:

They are the second largest class of surfactant.

They are normally compatible with all other types of surfactants.

They are not sensitive to hard water.

Contrary to ionic surfactants, their physicochemical properties are not markedly affected by electrolytes. The physicochemical properties of ethoxylates are very temperature dependent. Contrary to most organic compounds they become less water soluble and more hydrophobic at higher temperatures. Polyol-based nonionic surfactants exhibit the normal temperature dependence, that is, their solubility in water increases with temperature.

Some of the nonionic surfactants which reported in literature about polymerization are as following: Polyethylene glycol dodecyl ether (Brij-35) as a commercial polyether polyol[23], polyoxyethylene (2) stearyl ether (Brij-72), polyoxyethylene (10) stearyl ether (Brij-76) and polyoxyethylene (20) stearyl ether (Brij-78) which have no carbon-carbon double bond in their the stearyl moiety[25], polyoxyethylene (2) oleyl ether (Brij-92), polyoxyethylene (10) oleyl ether (Brij-97), and polyoxyethylene (20) oleyl ether (Brij-98) which have carbon-carbon double bond in their oleyl moiety[25], n-octyl tetra-ethylene glycol ether, n-dodecyl tetra ethylene glycol ether and n-dodecyl octa ethylene glycol ether[26], polyoxyethylene (9) nonylphenylether(Igepal CO-630)[27], polyethylene glycol sorbitan monostearate or polyoxyethylene sorbitan monostearate (TWEEN® 60)[28], octylphenol ethoxylate(Triton X-305)[20], polyoxyethylene nonyl phenyl ether with 23 units of ethylene oxide (PEO23)[29], a poly(ethylene oxide).hexadecyl ether with an EO block length of about 50 units (Lutensol AT-50)[30], and Triton-X 100[31].

Carboxylate, sulfate, sulfonate, and phosphate are the polar groups found in anionic surfactants which used in a larger volume than any other class of surfactant due to the ease and low cost of manufacturing. The most generally counter ions which used for manufacturing of anionic surfactants are sodium, potassium, ammonium, calcium, and various protonated alkyl amines. Sodium and potassium impart water solubility, calcium and magnesium promote oil solubility, and amine or alkanol amine salts give products with both oil and water solubility. Alkylbenzene sulfonates are the largest class of synthetic surfactants[14]. Some common anionic surfactants show in following: Important facts about anionic surfactants are as following[14]: They constitute the largest class of surfactant. They have limited compatibility with cationic surfactants (shorter surfactants have better compatibility). They are generally sensitive to hard water and the sensitivity decreases in the order carboxylate > phosphate > sulfate ≅ sulfonate. A short polyoxyethylene chain between the anionic group and the hydrophobic tail improves hard water tolerance. A short polyoxypropylene chain between the anionic group and the hydrophobic tail improves solubility in organic solvents (but may reduce the rate of biodegradation). Alkyl sulfates are rapidly hydrolyzed at low pH in an autocatalytic process.

The other types are hydrolytically stable unless extreme conditions are used The CMC values of anionic surfactants with linear carbon chains are more than of zwitterionic surfactants[32]. Some of the anionic surfactants, except SDS as a highly common surfactant, which reported in literature about polymerization are as following: sodium dodecyl benzyl sulfonate[22], sodium salt of n-undecyl carboxylate and n-dodecyl tetra ethoxy sulfate[26], Dowfax 2A (an alkyl diphenyl oxide disulfonate )[24, 33], Alipal EP-110 (ammonium nonoxynol-9 sulfate), EP-120 (ethoxylated nonylphenol sulfate, ammonium salt), A-102 (disodium,4-(2-dodecoxy ethoxy)-3-sulfonato butanoate) , SLS (sodium lauryl sulfate, a synonym of SDS)[27, 29, 34, 35], SDBS (Sodium dodecyl benzene sulfonate), SHS (sodium hexadecyl sulfate), and SOS (sodium octadecyl sulfate)[36].Although both amine and quaternary ammonium-based surfactants, in which, the nitrogen atom carrying the positive charge are common as cationic, but the phosphonium, sulfonium, and sulfoxonium surfactants also exist. The amines cannot be used at high pH, while the quaternary ammonium compounds (quats) are not pH sensitive.

The structures of typical cationic surfactants are as following[14]:

The important facts about cationic surfactants are:

They are the third largest class of surfactant, maybe due to most surfaces of metals, minerals, plastics, fibers, cell membranes and so on, are negatively charged, so they tend to adsorb at these surfaces. They have limited compatibility with anionic (shorter surfactants have better compatibility). Hydrolytically stable cationic show higher aquatic toxicity than most other classes of surfactants. They adsorb strongly to most surfaces and their main uses are related to this interaction. The CMC values of cationic surfactants with linear carbon chains are more than of zwitterionic surfactants[32]. Some of the cationic surfactants which reported in literature about polymerization are as following: N′-hexadecyl-N,N-dimethyl acetamidinium bicarbonate) and (N′-dodecyl-N,N-dimethyl acetamidinium bicarbonate)[37], n-hexadecyl trimethyl ammonium chloride (synonym of cetyltrimethylammonium chloride, CTMA-Cl) [26, 30], n-dodecyl trimethyl ammonium chloride, and n-octadecyl dimethyl benzyl ammonium chloride[26], didodecyl-dimethylammonium bromide (DDDAB)[31]. Zwitterionic surfactants contain two charged groups of different signs, positive and negative.

Sometimes they referred to as amphoteric[36], but these two terms are not identical. In fact, a zwitterionic surfactant has the amphoteric nature [26]. Amphoteric surfactants are those which can have (like an amino acid) anionic, cationic or zwitterionic properties. These three forms exist in an equilibrium, depending on the pH range (following scheme). At an acidic pH, the molecules will be protonated to form cations, while at an alkaline pH they will be deprotonated to form anionic species. Only in a mid-pH range can they exist as neutral molecules and demonstrate their zwitterionic character. This pH is called the isoelectric point. Amphoteric behavior requires the presence of a secondary or tertiary amine group, which can be protonated easily[38]. The positivecharge in a zwitterionic surfactant is almost invariably ammonium, whereas the source of negative charge can vary, althoughcarboxylate is by far the most common.

The behavior of zwitterionic surfactants is depend strongly on the pH of the solution. They have isoelectric point at which the physicochemical behavior often resembles that of nonionic surfactants. Below and above the isoelectric point, there is a gradual shift towards the cationic and anionic character, respectively[14]. The mono alkyl esters of sulfuric acid, alkyl sulfonic acid or alkyl aryl sulfonic acid have the very low pKa values, therefore, the related surfactants remain zwitterionic down to very low pH values. The structures of common zwitterionic surfactants are as follows. In the amine oxide case (N-oxides of tertiary amines) which are prepared by hydrogen peroxide oxidation of the corresponding tertiary amine, there are two ways for showing the bond between oxygen and nitrogen. Showing by the arrow means the electron donating from nitrogen to the oxygen (dative bond) without using positive and negative charge on any of them. and show. Sometimes the formula is written with a normal bond between the two heteroatoms, in which there is a positive sign on the nitrogen and a negative sign on the oxygen. This kind of surfactants (amine oxide) sometimes categorized as nonionic (normally at low pH), and, as cationic (in the presence of an anionic surfactant).

The important facts about zwitterionic surfactants are: They are expensive, so, are the smallest class of surfactant. They are normally compatible with all other types of surfactants. They are not sensitive to hard water. They are generally stable in acids and bases. The betaines retain their surface activity at high pH, which is unusual. Most types show very low eye and skin irritation. They are, therefore, well suited for use in shampoos and other personal care products. The CMC values of zwitterionic surfactants with linear carbon chains are between nonionic and anionic/cationic surfactants[32]. Some of the zwitterionic surfactants which reported in literature about polymerization are as follows: containing some n-alkyl dimethyl betaine (C_xDMB, X=12,14,16), n-dodecyl amido  propyl betaine, n-dodecyl dimethyl amine oxide[26], tetradecyl dimethyl amine oxide[39].

The problems with residual surfactant may be environmentally unwanted (slowly biodegradable surfactants). The problems may also be of a technical nature since the presence of surface-active agents in the final product may affect the product performance in a negative way. For example, in the dried polymerized film (paint), the residual surfactant acts as an external plasticizer, imparting softness and flexibility as a negative effect. A way to overcome the problems associated with the presence of surfactant in the final product is to make the surfactant polymerize during the setting or curing stage. In principle, the surfactant may either undergo homo-polymerization or copolymerization with some other component of the system[40].

In another word, this is possible if the surfactants include polymerizable functional groups capable of interacting with the radical polymerization process. Comparing to copolymerization, the homo-polymerization of the polymerizable surfactants, surfmers, will rarely occur in a bulk phase due to their very low concentration. Conversion of vinyl chloride to poly (vinyl chloride), and of acrylates and vinyl acetate to related latexes for coatings are some of the examples of using the polymerizable surfactants in emulsion polymerization. Using the polymerizable surfactants can bring about several advantages such as improved stability against shear, freezing, and dilution; reduced foaming; reduced problems with competitive adsorption; improved adhesion properties of the film; and improved water and chemical resistance of the film[14].

Some of the polymerizable surfactants which reported in literature about polymerization are as following:

LatemulPD-104 and SipomerPam-200 as anionic polymerizable surfactants[17, 24], sodium 11-crotonoyl undecane-1-yl sulfate (an ester of methacrylic acid, CRO), sodium 11-methacryloyl undecane-1-sulfate (an ester of methacrylic acid, MET), and sodium sulfopropyl tetradecyl maleate (a diester of maleic acid, M14) as three anionic surfmers [41]. The block copolymer surfactants are triblocks copolymers based on poly(ethylene oxide), PEO, as the water soluble block, and a hydrophobic part such as poly(propylene oxide), PPO; poly(butadiene oxide), PBO; polystyrene, PS; poly(iso butylene), PIB; polyalkanes (e.g. poly(ethyl ethylene), PEE; and poly(dimethyl siloxane), PDMS. All of these are known commercially as pluronics or superionics or through the generic name as poloxamers[42]. The stability of colloids has been controlled by polymeric surfactants to accommodate colloid applications.

The simplest type of a polymeric surfactant is a homopolymer that is formed from the same repeating units such as poly(ethylene oxide) (PEO); poly(vinylpyrrolidone) (PVP), which normally have little surface activity and are not the most suitable emulsifiers at the oil-water systems [43]. In this kind of surfactant, the polymer acts as a nucleation site and the surfactant forms micellar aggregates on the polymer backbone at concentrations well below the normal critical micelle concentration (CMC) of the surfactant. The polymer-surfactant complex formation needs to a minimum surfactant concentration which known as the critical aggregation concentration (CAC). A pearl-necklace structure form by interaction of polymer chain with several micelles, which can be saturated with micelles when the surfactant concentration is increased.

At this point, micelles also begin to form in the bulk solution[44]. Some of the block copolymer surfactants which reported in literature about polymerization are as following: Poly(ethylene-cobutylene)-b-poly(ethylene oxide) (P(E/B)-PEO1- 9800 g/mol, P(E/B)-PEO2- 6700 g/mol, P(E/B)-PEO3- 6200 g/mol)[45], four different block copolymer surfactant containing diethylenetriamine (DETA) as central nuclei of copolymer and 4, 6, and 9 polymer chains of polypropylene oxide (PPO)/polyethylene oxide (PEO) or a dendrimer form of them[46], amphiphilic tri-block copolymer P105 (E37P56E37) mixed by sodium dodecyl sulfate (SDS), dodecyl trimethylammonium bromide (DTAB) and polyoxyethylene (10) isooctyl phenyl ether (TX-100) as additives[47], polystyrene-co-maleic anhydride cumene terminated (SMA)[48], Pluronic P105 poly(ethylene oxide)–poly(propylene oxide)–poly(ethylene oxide), ((EO)₃₇(PO)₅₈(EO)₃₇)[49].This kind of surfactants which we call them “inisurf”, have three parts containing the radical generating group, a hydrophobic part, and a hydrophilic part.

There are three methods for subdividing of inisurfs:

Dividing to azo or peroxy compounds: Regarding to the chemical nature of the radical generating group.

Dividing to symmetrical or non-symmetrical groups attached to the radical generating group: Symmetrical inisurfs produce two surface active radicals with the same structure after decomposition, while non-symmetrical inisurfs produce one surface-active and one non-surface-active radical after decomposition. Dividing based on the chemical nature of the hydrophobic and hydrophilic groups: The hydrophilic groups may be anionic or cationic ones or an oxyethylene chain of an appropriate chain length. Hydrocarbon chains (alkyl chain, alkyl phenol chains) or a propylene oxide chain are used as hydrophobic molecule parts. Oxyethylene chains are also used as hydrophobic groups if they are about ionic groups[50]. Although inisurfs have low radical efficiencies, they form micelles and adsorb at surfaces, as like as other surfactants. They, besides other advantages, are also environmentally friendly and their use can reduce the costs of chemical processes. Their surface activity is the most important physical property, influencing strongly their polymerization behavior. So, for instance, the decomposition behavior of inisurfs strongly depends on whether their concentration is above or below the critical micelle concentration. 

Some of the surface-active initiators (in surfactant role in polymerization) which reported in the literature are as follows:

2,2’-azo bis (N-2’-methyl propanoyl-2-aminoalkyl-1)- sulfonate type[51], poly(ethylene) glycol-sulfonate-azo-compounds, (n = 4–5 for PEGAS200 and n = 12–15 for PEGAS600) and 2,2’-azobis(N-2-methylpropanoyl-2-amino-alkyl-1)sulfonate, (n=7 for DAS, n=13 for HDAS)[52], disodium 4-(10-(2-bromo-2-methylpropanoyloxy)decyloxy)-4-oxo-2-sulfonatobutanoate[53], 4-(10-(2-bromo-2-methyl propanoyloxy)decyloxy)- 4-oxo-2-sulfonatobutanoate[54]. Coagulation is caused by a loss of colloidal stability of the latex particles which is mainly governed by electrostatic repulsion when anionic surfactants are used. Coagulation will occur if the kinetic energy of the particles is sufficiently high to overcome the potential energy barrier[13].

This, which also called “destabilization”, can accelerate by reducing mentioned barrier height as intrinsic chemical influences. High surfactant concentration increases the surface charge, resulting in a high electrostatic repulsion, so the other particles feel a high energy barrier to coagulation. Any condition in process recipe which can decrease this barrier, such as low concentration of surfactant, may increase coagulation probability. Normally, the industrial recipes contain the initiator, pH buffer and a lot of other additives, which may increase the electrolyte concentration to preventing coagulation. The other way for accelerating of “destabilization/coagulation” is increasing the average kinetic energy of the particles as physical influences, for example by raising the process temperature.

Sometimes the coagulum formation is inherent in the nucleation process itself and somewhen is due to mechanical instability during the later stages of the reaction[20]. There are also reports about coagulative nucleation in surfactant-free emulsion polymerization[55, 56] which are useful for understanding the “coagulation” phenomena. There is limited stability in this approach and the droplet size of a stirred emulsion is typically large enough to rule out significant radical entry which is exist during the process. In another word, stabilization is purely electrostatic and depends on the surface charge density of the particles and on the anionic strength of the aqueous medium. Both parameters supply with the initiator (spontaneous stabilizing and destabilizing effects). Small precursor particles have a high surface-to-volume ratio; therefore their coagulation occurs rapidly until the resulting aggregates attain the minimum surface charge density and minimum stable radius for electrostatic stability.

The authors introduced a simple model for coagulation in surfactant-free emulsion polymerization. Based on opinion of M. J. J. Mayer et al. the particle coagulation occur by the loss of colloidal stabilization when the surface coverage of surfactant molecules on particle surface dropped below the critical value (_cr) [57].