Critical Micellization Concentration Determination using Phenomenon 1. Introduction Surface-active agents (surfactants) were already known in ancient times, when their properties were used in everyday life (soaps, oils, detergents, etc.). Later, when the mechanism of their behavior became known, theoretical studies were initiated and the range of industrial applications was introduced. Presently, surface-active compounds are studied in most physicochemical, physical and biological laboratories of the universities worldwide, and are widely applied in industry by food, pharmaceutical, cosmetic, computer and textile companies. Such versatile applications of such surface active compounds originate from their amphiphilic structure. Typically, they are built of two parts: A hydrophobic tail, which may be built by one or more aliphatic chains, either saturated or unsaturated, aromatic system of condensed or uncondensed rings, or an aliphatic-aromatic system. The other part is a hydrophilic head-group, e.g., amine, hydroxyl, carboxyl, ester, sulfate, etc. Due to such a structure, the surfactants gather at the free water surface in a particular way, namely, their hydrophilic part is anchored in the aqueous phase, whereas the hydrophobic part is directed towards the air. 1.1 In the bulk of a solution, adhesion forces are present, which balance as each molecule, surrounded by the statistically equal number of neighboring molecules, experiences symmetrical intermolecular interactions. On the other hand, molecules present at the surface, experience imbalanced forces from the air and aqueous phases, as illustrated in figure 1. The surface tension (γ) is defined as the force (F) between the molecules in the liquid per unit length (L) [5]: γ = F L (1) Figure 1: Schematic representation of intermolecular interactions for a molecule in the water bulk phase and at the phase boundary. A molecule in the bulk liquid phase experiences a potential field of spherical symmetry, whereas a molecule in the phase boundary region experiences asymmetric interactions Due to such dissymmetric interactions, molecules present in the phase boundary region move towards the interior of aqueous phase and are immediately replaced by other molecules, heading to the interfacial region from inside the bulk phase. Transferring a molecule from the bulk phase to the phase boundary demands certain work against adhesion forces, which is equal to the change of the system free energy in isothermal-isobaric conditions at constant liquid volume. In the formula 2 below dw is the work needed to increase the free surface of the liquid by the area da: γ = dw da 1 Rev2-30.12.2015 (2)
Surface tension is one of the most important physicochemical properties characterizing surfactant solutions. The existence of non-balanced surface forces is responsible for a change in the number of molecules present in the surface layer as compared to the interior of any surrounding phase. In aqueous surfactant solution, this can be macroscopically observed as decrease of surface tension of water (72.80 mn/m at 20 0 C). The phenomenon of transferring the molecules from the bulk solution to the boundary surface is called adsorption. If the surfactant concentration is higher in the phase boundary region than in the bulk phase, adsorption is called positive. Negative adsorption occurs when the surfactant concentration in the phase boundary is lower than in the bulk. Quantitatively, adsorption is described by the isotherm: surface tension is plotted against the activity of surfactant solution (for diluted solutions it is assumed that activity is approximately equal to concentration). Three types of adsorption isotherms are described in literature [1], and are schematically presented in figure 2. Figure 2: Surface tension is plotted against surfactant concentration and shows three typical kinds of adsorption isotherms. Curves 1 and 3 represent positive adsorption, characteristic of most non-ionic surfactants (curve 1) and ionic amphiphilic compounds (curve 3), whereas curve 2 represents negative adsorption, which is often the case in solutions of simple inorganic electrolytes. The detailed, thermodynamic description of the adsorption process at the air-water interface was presented by Gibbs. He introduced the concept of surface excess (Γ), characterizing the excess of surfactant molecules at the interface as compared to the equivalent volume of a neighboring phase with following formula 3 [6], where R represents the gas constant, T the absolute temperature and c the molar concentration of surfactants in the solution: Γ = c RT (dγ dc ) T = 1 RT ( dγ dlnc ) T (3) According to the Gibbs law, surface excess is interpreted as the tangent of the slope of the surface tension, γ, plotted against the natural logarithm of surfactant solution concentration, c. Thus, it is possible to quantitatively determine a molecular property (surface excess) from the macroscopic measurements of surface tension. It is assumed, that the solvent surface excess is zero. Consequently, from equation (3) the relative surface excess of the dissolved substance is obtained. The graphic representation of the surface excess plotted against the surfactant concentration is called a Gibbs isotherm. Since surface excess increases as the surfactant solution concentration in the aqueous phase increases, for a certain concentration one can expect that the surface will be saturated by most densely packed surfactant molecules. Surface tension will no longer change and the surface excess will achieve the maximum value, Γ max, as illustrated in figure 3. The surface excess, Γ, is given in mol/m 2, whereas its inverse, given in m 2 /mol, is the area occupied by one mole of molecules on the free surface of a solution. Dividing this area by the Avogadro number leads to the area available to one molecule in the adsorption film (area per molecule). 2 Rev2-30.12.2015
Figure 3: A Gibbs adsorption isotherm. Surface excess Γ is plotted against the surfactant concentration c. 1.2 Self-assembly into micelles Another possibility of stagnation in surface tension with increasing surfactant concentration is the consumption of the surfactant by another process. Such a process would need to remove or absorb the freely available surfactant molecules from the bulk solution, leading to a constant concentration on the water-air interface. Such a free molecule absorbing processes can occur with tensides. In solution amphiphilic molecules are able to form supramolecular aggregates in order to shield their hydrophobic parts from the aqueous environment and overcoming thereby solubility problems. Most often, spherical micelles are formed, as presented in Figure 4, with aggregation numbers of about. 50-100 (average number of amphiphilic molecules per micelle) [7]. Bulk surfactant concentration, at which micelle formation occurs, is called Critical Micelle Concentration (CMC). It strongly depends on the solubility of the surfactant and is therefore also linked to temperature. The CMC can be measured by many physicochemical methods, since the properties of a solution, such as turbidity, conductivity, or surface tension, change abruptly once micelles appear in solution. Figure 4: Schematic representation of surfactants as monomers and self-assembled into spherical micelles as soon as the CMC is reached. 3 Rev2-30.12.2015
1.3 Surface tension measurement In this experiment we will measure surface tension of a detergent solution to determine the CMC. The measurement will be done by the Wilhelmy Plate method [2], Figure 5 [8]. Figure 5: A scheme of the surface tension measurement by Wilhelmy plate method with σ as surface tension and ϴ as contact angle. Shortly, a thin plate made of a very wettable material (rough platinum, aluminum, filter paper) is placed at the air-water interface. If a surfactant monolayer is present, the height of the meniscus between the plate and the liquid will change (with regard to pure water). The force related to that process by pulling the plate out of the solution will be measured by a very sensitive balance. This force corresponds to the surface tension multiplied by the Wilhelmy plate perimeter, if the contact angle remains zero (this needs to be assured by very careful cleaning of the plate!). Other experimental methods to measure surface tension include the ring (Du Noüy) method, pendant drop or bubble pressure method [3]. 2. Experimental a) Materials and Methods Hexadecyltrimethylammonium bromide (CTAB): Sodium dodecyl sulfate (SDS): b) Preparation 1) Calculate the molecular mass for each material 2) Estimate which material will have the higher CMC 3) Prepare the stock solutions of SDS at 0.1 M (20 ml) 4) Dilute the stock solutions (do not take the other solutions, since this will increase the error due to multiple dilution!) to obtain the following concentrations [M] (10 ml each) of SDS: 3x10-2, 2x10-2, 1x10-2, 5x10-3, 2x10-3, 1x10-3, 5x10-4, 2x10-4, 1x10-4 4 Rev2-30.12.2015
c) Procedure PC Praktikum 1) Familiarize yourself with the KSV Sigma tensiometer, make sure to always lock the screw when you aren t measuring (introduction by assistant). 2) Carefully clean and flame the Wilhelmy Plate (the platinum plate you are going to use costs ca. 600 Euro, so please try not to break the connecting wire). Cleaning has to be repeated before changing to a new concentration of SDS. 3) Measure surface tension of water and the surfactant solutions at room temperature. Repeat each measurement three times. Start with water as a reference and then continue with the most diluted solution. 3. Exercises Write a report containing introduction, materials & methods, results, and conclusion/discussion. Also include the following exercises: 1) Describe in detail one method that can be used for surface tension measurement. 2) Calculate the mean value for surface tension for each concentration. 3) Plot «surface tension γ» versus «ln (c)», including the errors for each point in x and y. 4) Determine the CMC: Fit two linear functions trough the two linear parts of the plot. 5) Where would you expect the CMC of CTAB compared to SDS? Why? 6) Calculate the Gibbs surface excess for each surfactant concentration and plot it versus the concentration, including the errors for each point in x and y. 7) Try to estimate Γ max. What is the mean molecular area (area per molecule) for a dense monolayer (at Γ max)? Is the measurement precise enough? Why is it so sensitive? 8) How does the CMC of SDS change when we use water/ethanol mixture, instead of pure water? 9) How does the CMC change with temperature and why? 10) Which detergent concentration (below or above CMC) should be best used to reach the highest efficiency for dishwashing/laundry? Why? 11) Small objects like paper clips can swim on water surface, even though they are heavier than water. Some insects can walk on water. These phenomena are related to surface tension of water. What happens to a paper clip / insect, if we add some soap to water? Why? 12) The maximum size of water droplets is always bigger than for an aqueous solution of a detergent. Why? 4. Literature [1] P.C. Hiemenz, Principles of colloid and surface chemistry, Marcel Dekker Inc., New York and Basel, 1986 [2] N.R. Pallas, Colloids and Surfaces, 6 (1983), 221-227 [3] http://www.kibron.com/company/science-technology/surface-tension-measurement-techniques [4] http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html [5] http://physics.tutorvista.com/fluid-dynamics/surface-tension.html [6] http://www.kruss.de/de/service/schulung-theorie/glossar/ueberschusskonzentration/ [7] C. Thévenot, B. Grassi, G. Bastiat, W. Binana, Colloids and Surfaces A: Physicochem. Eng. Aspects 252 (2005) 105-111 [8] http://www.kruss.de/en/theory/measurements/surface-tension/plate-method.html 5 Rev2-30.12.2015