The Cohesive Energy Ratio CER Concept

Beerbower and HiUs [21] considered the dispersing tendency on the oil and water interfaces of the surfactant or emulsifier in terms of the ratio of the cohesive energies of the mixtures of oil with the lipophilic portion of the surfactant and the water with the hydrophilic portion. For this, the Winsor concept was used, which is the ratio of the intermolecular attraction of oil molecules (O) and hpophihc portion of surfactant (L), Clq, to that of water (W) and hydrophihc portion (H), 

In the absence of an emulsifier, there will be only three interaction parameters, namely Cqq, Cq, but if Cq the emulsion will break. 

The above interaction parameters may be related to the Hildebrand solubility parameter [22] 8 (at the oil side of the interface) and the Hansen [23] nonpolar, hydrogen-bonding and polar contributions to 8 at the water side of the interface. The solubility parameter of any component is related to its heat of vapourisation AH by the expression. 

Hansen considered S (at the water side of the interface) to consist of three main contributions a dispersion contribution, 5 a polar contribution, 8, and a hydrogen-bonding contribution, These contributions have different weighting factors. 

Beerbower and Hills used the following expression for the HLB number. 

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Four different emulsifier selection methods can be applied to the formulation of microemulsions (i) the hydrophilic-lipophilic-balance (HLB) system (ii) the phase-inversion temperature (PIT) method (iii) the cohesive energy ratio (CER) concept and (iv) partitioning of the cosurfactant between the oil and water phases. The first three methods are essentially the same as those used for the selection of emulsifiers for macroemulsions. However, with microemulsions attempts should be made to match the chemical type of the emulsifier with that of the oil. A summary of these various methods is given below. 

I summarize briefly below the basic concepts of this approach, which is derived from that developed by Beerbower and Hill [31] for the stability of classical nonionic emulsions, which is referred to as the cohesive energy ratio (CER) concept. The treatment lies in a perfect chemical match between the partial solubility parameters of oil ( ) and surfactant lipophilic tail 6]) and of water and hydrophilic head. Under these conditions, one obtains for the optimum HLB (hydrophile-lipophile balance) of the surfactant the relation... 

The selection of different surfactants in the preparation of EWs emulsion is still made on an empirical basis. This is discussed in detail in Chapter 6, and only a summary is given here. One of the earliest semi-empirical scales for selecting an appropriate surfactant or blend of surfactants was proposed by Griffin [49, 50] and is usually referred to as the hydrophilic-lipophilic balance or HLB number. Another closely related concept, introduced by Shinoda and co-workers [51-53, 58], is the phase inversion temperature (PIT) volume. Both the HLB and PIT concepts are fairly empirical and one should be careful in applying them in emulsifier selection. A more quantitative index that has received little attention is that of the cohesive energy ratio (CER) concept introduced by Beerbower and Hill [54] (see Chapter 6). The HLB system that is commonly used in selecting surfactants in agrochemical emulsions is described briefly below. 

The property of interest to characterize a surfactant or a mixture of surfactants is its hydrophilic-lipophilic tendency, which has been expressed in many different ways through a variety of concepts such as the hydrophiUc-lipophilic balance (HLB), the phase inversion temperature (PIT), the cohesive energy ratio (CER), the surfactant affinity difference (SAD) or the hydrophilic-lipophilic deviation (HLD) [1], which were found to be more or less satisfactory depending on the case. In the next section, the quantification of the effects of the different compounds involved in the formulation of surfactant-oil-water systems will be discussed in details to extract the concept of characteristic parameter of the surfactant, as a way to quantify its hydrophilic-lipophilic property independently of the nature of the physicochemical environment. 

For nonionic surfactants, an optimization of the process was achieved by using a similar approach to the so-called Cohesive Energy Ratio (CER) concept developed by Beerbower and Hill for the stability of classical emulsions (H). Its basic assumption is that the partial solubility parameters of oil and emulsifier lipophilic tail and of water and hydrophilic head are perfectly matched. Thus, the Vinsor cohesive energy ratio Ro, which determines the nature and the stability of an emulsion, is directly related to the emulsifier HliB (hydrophile-lipophile balance) by... 

The choice of emulsifier is critical since it controls the stability of the emulsions prior to and after polymerization. Moreover, polymerization conditions typically represent destabilizing factors vigorous stirring, temperature rise and evolution of acrylamide content in the aqueous phase. In the case of inverse emulsions, the HLB values mostly used by the formulators range between 4 and 6. Some attempts were made to predict quantitatively the optimal HLB value corresponding to the most stable dispersions [18,19]. The treatment was based on the so-called cohesive energy ratio (CER) concept devekq)ed by Beer-bower and Hill for conventional emulsions [20]. Tins approach is based on a perfect chemical match between the partial solubility parameters of oil (ig)... 

In a tentative approach to attain a formulation concept with both the theoretical content of Winsor s R and the down-the-bench numerical data feature of the Hl-B. Beerbower and collaborators introduced the cohesive energy ratio (CER) approach in 1971 (53.. i4). From the conceptual point of view it was very similar to Winsor interaction energies ratio, but this time it was the ratio between the adhesion energy of the surfactant "layer" with the oil phase and the adhesion energy of the surfactant "layer" with the water phase, It must be recalled that the cohesion energy between molecules of a pure component system is calculated as ... 

Research into optimal formulations is based on the idea of cohesive energy ratio (CER). This was originally developed to stabilise classic non-ionic surfactant emulsions [6.13]. Despite its limitations, the CER concept unifies the ideas of solubility parameters and HUB. Recall that the HLB is a measure of the emulsifying power of surfactants and is based on their hydrophile-lipophile balance [6.3]. It can be calculated from a simple formula involving only relative weights of sequences HLB = 20 x Mh/Mt, where Mh is the molecular weight... 

Holtzseherer C, Candau F (1988) Applieation of the cohesive energy ratio concept (CER) to the formation of polymerizable mieroemulsions. Colloids Surf 29 411-423... 

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