Critical micelle concentration method

ISO Standard 4311. Determination of the critical micelle concentration method by measuring surface tension with a plate, stirrup or ring. 

Critical Micelle Concentration. The rate at which the properties of surfactant solutions vary with concentration changes at the concentration where micelle formation starts. Surface and interfacial tension, equivalent conductance (50), dye solubilization (51), iodine solubilization (52), and refractive index (53) are properties commonly used as the basis for methods of CMC determination. 

K is K, just below the collectors critical micelle concentration, C,. Ko is Ki at some higher cohector concentration, C,. E is the relative effectiveness, in adsorbing cohigend, of surface cohector versus micehar collector. Generally, E > 1. F, is the surface excess of collector. More about each K is avahable [Lemhch, Adsubble Methods, in Li (ed.). Recent Developments in Separation Science, vol. 1, CRC Press, Cleveland, 1972, pp. 113-127 Jashnani and Lemlich, Ind. Eng. Chem. Process Des. Dev., 12, 312 (1973)]. 

FIG. 1 Critical micelle concentration as a function of the number of carbon atoms in the hydrophobic rest of sodium a-sulfo fatty acid methyl esters. Methods O, surface tension +, conductivity A, solubilization of a dye x, solubility (all without electrolyte) , surface tension with a constant electrolyte concentration of 5 x 10"2 mol/L. (From Ref. 57.)... 

Saunders, R. A., Platts, J. A. Correlation and prediction of critical micelle concentration using polar surface area and LFER methods. /. Phys. Org. Chem. 2004, 17,431 38. 

Recently, the newly developed time-resolved quasielastic laser scattering (QELS) has been applied to follow the changes in the surface tension of the nonpolarized water nitrobenzene interface upon the injection of cetyltrimethylammonium bromide [34] and sodium dodecyl sulfate [35] around or beyond their critical micelle concentrations. As a matter of fact, the method is based on the determination of the frequency of the thermally excited capillary waves at liquid-liquid interfaces. Since the capillary wave frequency is a function of the surface tension, and the change in the surface tension reflects the ion surface concentration, the QELS method allows us to observe the dynamic changes of the ITIES, such as the formation of monolayers of various surfactants [34]. 

The critical concentration at which the first micelle forms is called the critical micelle concentration, or CMC. As the concentration of block copolymer chains increases in the solution, more micelles are formed while the concentration of nonassociated chains, called unimers, remains constant and is equal to the value of the CMC. This ideal situation corresponds to a system at thermodynamic equilibrium. However, experimental investigations on the CMC have revealed that its value depends on the method used for its determination. Therefore, it seems more reasonable to define phenomenologically the CMC as the concentration at which a sufficient number of micelles is formed to be detected by a given method [16]. In practical terms, the CMC is often determined from plots of the surface tension as a function of the logarithm of the concentration. The CMC is then defined as the concentration at which the surface tension stops decreasing and reaches a plateau value. 

Estimation is easier and less time-consuming because use is made of empirical relationships between the BCF and physicochemical properties of the compound, such as water solubility (S) [42-48], Km, (solid organic carbon/water partition coefficient) [48], Kmw (membrane water partition coefficient), iipw (liposome water partition coefficient) [49], critical micelle concentration (CMC) [45], steric factors, molecular weight [47,48], and others. The most common regression method is the estimation of BCF from the octanol-water partition coefficient (Kovl) [18,42,44-48,50,51],... 

Part—IV has been entirely devoted to various Optical Methods that find their legitimate recognition in the arsenal of pharmaceutical analytical techniques and have been spread over nine chapters. Refractometry (Chapter 18) deals with refractive index, refractivity, critical micelle concentration (CMC) of various important substances. Polarimetry (Chapter 19) describes optical rotation and specific optical rotation of important pharmaceutical substances. Nephelometry and turbidimetry (Chapter 20) have been treated with sufficient detail with typical examples of chloroetracyclin, sulphate and phosphate ions. Ultraviolet and absorption spectrophotometry (Chapter 21) have been discussed with adequate depth and with regard to various vital theoretical considerations, single-beam and double-beam spectrophotometers besides typical examples amoxycillin trihydrate, folic acid, glyceryl trinitrate tablets and stilbosterol. Infrared spectrophotometry (IR) (Chapter 22) essentially deals with a brief introduction of group-frequency... 

It turned out that for all the polymeric amphiphiles of the (EO) -(PO)m-(EO) type there was an increase in enantioselectivity compared with the reaction without amphiphile. Moreover, the ratio of the length of the (PO) block compared with the (EO) block seemed to determine enantioselectivity and activity and not the cmc (critical micelle concentration). A (PO) block length of 56 units works best with different length of the (EO)n block in this type of hydrogenation [30]. for the work-up of the experiments, G. Oehme et al. used the extraction method, but initial experiments failed and the catalyst could not be recycled that way. To solve this problem the authors applied a membrane reactor in combination with the amphiphile (EO)37-(PO)5g-(EO)37 (Tab. 6.1, entry 9) [31]. By doing so, the poly-mer/Rh-catalyst was retained and could be reused several times without loss of activity and enantioselectivity by more than 99%. 

Test Methods. Surface tension (y) measurements were taken by Wil-helmy method (25+0.1°C). Critical micelle concentrations (cmc) were obtained from Y logC curves. Contact angle. Type GI, Japan. Wetting test. Canvas disk method, CIS,HG-2-380-66. Foam test, Ross-Miles lather method. Emulslbillty was determined by mixing 20 ml of 2.5%... 

The electrophoretic mobility of sodium dodecyl sulfate micelles was determined by the moving-boundary method after the micelles were made visible by solubilizing dye in them. This quantity was measured at the critical micelle concentration (CMC) in the presence of various concentrations of NaCl. The radius of the micelles was determined by light scatteringj... 

Adsorption was performed using the batch method by placing a constant mass (200 mg) of the powdered adsorbent in Erlenmeyer flasks. The solid was sonicated with an appropriate amount of water (30 cm3) in order to homogenise and decrease the particle size. Surfactant solution (20 cm3) was then added to produce a final concentration ranging from one order of magnitude below the respective critical micelle concentration (CMC) to a concentration about three times higher than the CMC. 

The critical micelle concentration (cmc) in block copolymer solutions can be determined by measurement of the surface tension (y) as a function of concentration. The method detects completion of the Gibbs monolayer at the air/water interface, and is a secondary indicator of the onset of micellization. The cmc for solutions of monodisperse polymers is indicated by a fairly sharp decrease in y versus log(c). 

This chapter is organized as follows. The thermodynamics of the critical micelle concentration are considered in Section 3.2. Section 3.3 is concerned with a summary of experiments characterizing micellization in block copolymers, and tables are used to provide a summary of some of the studies from the vast literature. Theories for dilute block copolymer solutions are described in Section 3.4, including both scaling models and mean field theories. Computer simulations of block copolymer micelles are discussed in Section 3.5. Micellization of ionic block copolymers is described in Section 3.6. Several methods for the study of dynamics in block copolymer solutions are sketched in Section 3.7. Finally, Section 3.8 is concerned with adsorption of block copolymers at the liquid interface. 

Micelles are formed by association of molecules in a selective solvent above a critical micelle concentration (one). Since micelles are a thermodynamically stable system at equilibrium, it has been suggested (Chu and Zhou 1996) that association is a more appropriate term than aggregation, which usually refers to the non-equilibrium growth of colloidal particles into clusters. There are two possible models for the association of molecules into micelles (Elias 1972,1973 Tuzar and Kratochvil 1976). In the first, termed open association, there is a continuous distribution of micelles containing 1,2,3,..., n molecules, with an associated continuous series of equilibrium constants. However, the model of open association does not lead to a cmc. Since a cmc is observed for block copolymer micelles, the model of closed association is applicable. However, as pointed out by Elias (1973), the cmc does not correspond to a thermodynamic property of the system, it can simply be defined phenomenologically as the concentration at which a sufficient number of micelles is formed to be detected by a given method. Thermodynamically, closed association corresponds to an equilibrium between molecules (unimers), A, and micelles, Ap, containingp molecules ... 

A particular problem encountered with nonpolar detergent solutions is the lack of suitable methods to determine critical micelle concentrations. This is due mainly to two reasons ... 

The up to now most frequently used techniques as, for example, vapour pressure osmometry (VPO) or freezing point depression (with its limitation regarding the solvent dependent measuring temperature) are based upon the colligative properties of the system the classical absolute light-scattering and ultracentrifugation techniques are only occasionally and approximately applicable with respect to the determination of CMC values. Evaluation of critical micelle concentrations which are based on these latter methods suffer considerably from the insensitivity of these techniques if measurements below the CMC, i.e., below about 10-3 mol dm-3, are carried out. More sensitive methods will be discussed below. 

In spite of many favorable examples of coincidence between the conventionally defined CMC-values obtained by this method and, for example, spectroscopic or other techniques, it appears a priori not advisable to assign these breaks directly to critical micelle concentrations without further analyses of these systems. 

Methods. All experiments were performed at 25°C. Critical micelle concentrations were determined using the maximum bubble pressure method on a SensaDyne 6000 surface tensiometer. Dry nitrogen was used as the gas source for the process and was bubbled through the solution at a rate of 1 bubble/sec. Cmc s measured using the Wilhemy plate method were in agreement with those obtained from the bubble tensiometer however, the bubble pressure method was used since it is less susceptible to error due to impurities and the nitrogen environment makes pH control easier. 

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