WordNet

of or involving or characteristic of critics or criticism; "critical acclaim"
forming or having the nature of a turning point or crisis; "a critical point in the campaign"; "the critical test" (同)decisive
urgently needed; absolutely necessary; "a critical element of the plan"; "critical medical supplies"; "vital for a healthy society"; "of vital interest" (同)vital
at or of a point at which a property or phenomenon suffers an abrupt change especially having enough mass to sustain a chain reaction; "a critical temperature of water is 100 degrees C--its boiling point at standard atmospheric pressure"; "critical mass"; "go critical"
being in or verging on a state of crisis or emergency; "a critical shortage of food"; "a critical illness"; "an illness at the critical stage"
characterized by careful evaluation and judgment; "a critical reading"; "a critical dissertation"; "a critical analysis of Melvilles writings"
marked by a tendency to find and call attention to errors and flaws; "a critical attitude"
the spatial property of being crowded together (同)density, denseness, tightness, compactness
bringing together military forces
strengthening the concentration (as of a solute in a mixture) by removing diluting material
the strength of a solution; number of molecules of a substance in a given volume
complete attention; intense mental effort (同)engrossment, absorption, immersion
increase in density
a person who is professionally engaged in the analysis and interpretation of works of art
anyone who expresses a reasoned judgment of something
someone who frequently finds fault or makes harsh and unfair judgments
an electrically charged particle built up from polymeric molecules or ions and occurring in certain colloidal electrolytic solutions like soaps and detergents

PrepTutorEJDIC

『評論の』,批評の / 批判的な,物を見る眼のある / 『酷評的な』,あら捜しの,手きびしい / 『危機の』,危急の;(病気が)危篤の / 臨界の(温度・圧力などにより物質が急速にその状態を変える境),臨界点における
〈U〉(…への)(光線・注意などの)集中;(仕事などへの)専念,専心《+『on』+『名』》 / 〈C〉(人口などの)集中 / 〈U〉濃縮;〈液体の〉濃度
(特に文学・美術・音楽の)『評論家』,『批評家』 / あら捜しをする人,酷評する人

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/06/10 02:12:33」(JST)

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In colloidal and surface chemistry, the critical micelle concentration (CMC) is defined as the concentration of surfactants above which micelles form and all additional surfactants added to the system go to micelles.^[1]

The CMC is an important characteristic of a surfactant. Before reaching the CMC, the surface tension changes strongly with the concentration of the surfactant. After reaching the CMC, the surface tension remains relatively constant or changes with a lower slope. The value of the CMC for a given dispersant in a given medium depends on temperature, pressure, and (sometimes strongly) on the presence and concentration of other surface active substances and electrolytes. Micelles only form above critical micelle temperature.

For example, the value of CMC for sodium dodecyl sulfate in water (no other additives or salts) at 25 °C, atmospheric pressure, is 8x10^-3 mol/L.^[2]

The study of the aggregation of lipids (amphiphiles) is known as lipid polymorphism.

Description [edit]

Upon introduction of surfactants (or any surface active materials) into the system, they will initially partition into the interface, reducing the system free energy by:

lowering the energy of the interface (calculated as area times surface tension), and
removing the hydrophobic parts of the surfactant from contact with water.

Subsequently, when the surface coverage by the surfactants increases, the surface free energy (surface tension) decreases and the surfactants start aggregating into micelles, thus again decreasing the system's free energy by decreasing the contact area of hydrophobic parts of the surfactant with water. Upon reaching CMC, any further addition of surfactants will just increase the number of micelles (in the ideal case).

There are several theoretical definitions of CMC. One well-known definition is that CMC is the total concentration of surfactants under the conditions:^{[citation needed]}

if C = CMC, (d³F/dC_t³) = 0

F = a[micelle] + b[monomer]: function of surfactant solution

C_t: total concentration

a, b: proportional constants

The CMC generally depends on the method of measuring the samples, since a and b depend on the properties of the solution such as conductance and photochemical characteristics. When the degree of aggregation is monodisperse, then the CMC is not related to the method of measurement. On the other hand, when the degree of aggregation is polydisperse, then CMC is related to both the method of measurement and the dispersion.

The CMC is the concentration of surfactants in the bulk at which micelles start forming. The word bulk is important because surfactants partition between the bulk and interface and CMC is independent of interface and is therefore a characteristic of the surfactant molecule. In most situations, such as surface tension measurements or conductivity measurements, the amount of surfactant at the interface is negligible compared to that in the bulk and CMC can be approximated by the total concentration.

Top to Bottom: Increasing concentration of surfactant in water slowly forming a layer on the surface and eventually forming micelles at or above the CMC. Notice that the existence of micelles does not preclude the existence of individual surfactant molecules in solution.

There are important situations where interfacial areas are large and the amount of surfactant at the interface cannot be neglected. For example if we take a solution of a surfactant above CMC and start introducing air bubbles at the bottom of the solution, these bubbles, as they rise to the surface, pull out the surfactants from the bulk to the top of the solution creating a foam column thus bringing down the concentration in bulk to below CMC. This is one of the easiest methods to remove surfactants from effluents (foam flotation). Thus in foams with sufficient interfacial area there will not be any micelles. Similar reasoning holds for emulsions.

The other situation arises in detergency. One initially starts off with concentrations greater than CMC in water and on adding fabric with large interfacial area and waiting for equilibrium, the surfactant concentration goes below CMC and no micelles are left. Therefore the solubilization plays a minor role in detergency. Removal of oily soil occurs by modification of the contact angles and release of oil in the form of emulsion.

References [edit]

^ IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook. Entry " critical micelle concentration, cmc".
^ Ana Domínguez, Aurora Fernández, Noemí González, Emilia Iglesias, and Luis Montenegro "Determination of Critical Micelle Concentration of Some Surfactants by Three Techniques", Journal of Chemical Education, Vol. 74 No. 10 October 1997, p. 1227-1231 (pdf)

External links [edit]

Theory of CMC and surface tension measurements
CMCs and molecular weights of several detergents on OpenWetWare

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