Micellization, spontaneous association of surfactant molecules in solution. As a result, micelles-associates of a characteristic structure appear in the surfactant-solvent system, consisting of dozens of amphiphilic molecules with long-chain hydrophobic radicals and polar hydrophilic groups. In the so-called straight micelles, the core is formed by hydrophobic radicals, while the hydrophilic groups are oriented outward. The number of surfactant molecules forming a micelle is called the aggregation number; By analogy with the molar mass, micelles are also characterized by the so-called micellar mass. Typically, the aggregation numbers are 50-100, micellar masses are 10 3 -10 5 . The micelles formed during micelle formation are polydisperse and are characterized by size distribution (or aggregation numbers).
Micellization is characteristic of various kinds Surfactants are ionic (anion- and cation-active), ampholytic and non-ionic and have a number of general patterns, however, it is also associated with the structural features of surfactant molecules (the size of the non-polar radical, the nature of the polar group), so it is more correct to talk about micellization of this class of surfactants.
Micellization occurs in a temperature range defined for each surfactant, the most important characteristics of which are the Kraft point and cloud point. The Kraft point is the lower temperature limit of micellization of ionic surfactants, usually it is 283-293 K; at temperatures below the Kraft point, the surfactant solubility is insufficient for the formation of micelles. The cloud point is the upper temperature limit of micelle formation of non-ionic surfactants, its usual values are 323-333 K; at higher temperatures, the surfactant-solvent system loses its stability and separates into two macrophases. Micelles of ionic surfactants at high temperatures (388-503 K) decompose into smaller associates-dimers and trimers (the so-called demicellization).
Determination of CMC can be carried out when studying almost any property of solutions, depending on the change in their concentration. Most often in research practice, dependences of the turbidity of solutions are used, surface tension, electrical conductivity, refractive index of light and viscosity from the total concentration of solutions.
The critical concentration of micelle formation is determined by the point that corresponds to the break in the curves of dependences of the properties of solutions on concentration. It is believed that at concentrations lower than CMC in surfactant solutions, only molecules are present, and the dependence of any property is determined precisely by the concentration of molecules. When micelles are formed in solutions, the property will undergo a sharp change due to an abrupt increase in the size of dissolved particles. For example, molecular solutions of ionic surfactants exhibit electrical properties characteristic of strong electrolytes, while micellar solutions are characteristic of weak electrolytes. This is manifested in the fact that the equivalent electrical conductivity in solutions of ionic surfactants at concentrations below CMC, depending on the square root of the solution concentration, turns out to be linear, which is typical for strong electrolytes, and after CMC, its dependence turns out to be typical for weak electrolytes.
Rice. 2
- 1. stalagmometric method, or the method of counting drops, although inaccurate, but due to its exceptional simplicity, is still used in laboratory practice. The determination is made by counting the drops that come off when a certain volume of liquid flows out and from the capillary opening of a special Traube stalagmometer.
- 2. Conductometric method- this is an analysis method based on studies of the electrical conductivity of the studied solutions. Direct conductometry is understood as a method by which the study of electrolyte concentrations is carried out directly. The determinations are made by measuring the electrical conductivity of solutions whose qualitative composition is known.
- 3. Refractometric method of analysis(refractometry) is based on the dependence of the refractive index of light on the composition of the system. This dependence is established by determining the refractive index for a number of standard mixtures of solutions. The refractometry method is used for the quantitative analysis of binary, ternary and various complex systems of solutions.
Rice. 3 Refractometer
Objective : Determination of the critical concentration of micelle formation from the concentration dependence of the surface tension of surfactant solutions.
Brief theoretical introduction
The most effective surface-active substances (surfactants) have an amphiphilic molecular structure. This term means that part of the molecule has a high affinity for water and other polar solvents, i.e. is hydrophilic, while another part of the same molecule has a high affinity for non-polar solvents and is lipophilic. With respect to water, lipophilicity is equivalent to hydrophobicity. The hydrophobic part is the hydrocarbon radical, which must include from 8 to 20 carbon atoms for the molecule to have really high surface activity. The hydrophilic part is the polar group capable of dissociating into ions in the case of ionic surfactants or unable to dissociate in the case of nonionic surfactants. Often, the term surfactant refers to substances with just such a structure, although more general definition Surfactants are substances that reduce the surface tension of a solution, regardless of what structure they have and how many carbon atoms they contain in the chain.
The amphiphilic structure of molecules is the cause of a number of unique properties. Surfactants are easily adsorbed on any interfaces between phases. In this case, the hydrophilic parts of the molecules are oriented towards the more polar phase, while the hydrophobic chains are located in the nonpolar phase. Adsorption is usually reversible and therefore can be characterized by chemical equilibrium. Denoting the surfactant molecule as A and the solvent molecule as W, the adsorption equilibrium can be written as:
A + W(adsorb.) A(adsorb.) + W (5.1)
where (adsorb.) means the location of the molecule in the adsorption layer.
In the volume of the solution, regardless of the presence or absence of phase interfaces, surfactant molecules are in the form of separate molecules (that is, in a molecularly dispersed state), but they can also combine with each other to form colloidal particles that are in equilibrium with a molecularly dispersed surfactant. Such particles are called micelles. At a low ionic strength of an aqueous solution, micelles are spherical in shape and consist of surfactant molecules, the hydrophilic groups of which are located on the surface of the micelle and are in contact with the solvent, and the hydrophobic chains are oriented inside the micelle and form its core, isolated from water by the hydrophilic surface (see Fig. 7.2 and 7.3). In the absence of other lipophilic components, the size of micelles is determined by the length of the hydrocarbon radical, and for a given surfactant it can fluctuate within relatively small limits. For most surfactants, the average radius of spherical micelles ranges from 1 to 10 nm. The number of surfactant molecules forming a micelle is commonly referred to as the aggregation number of a micelle. This number is determined by the need to form a closed sphere, the surface of which consists only of hydrophilic groups. In most cases, it is 50 - 100.
The driving force of micelle formation is the so-called hydrophobic interactions, which appear when surfactants are dissolved in polar solvents. In particular, in water, solvent molecules interact with each other using hydrogen bonds. The appearance of extended hydrocarbon radicals in water leads to disruption of cooperative hydrogen bonding between solvent molecules, which is energetically unfavorable, since it is not compensated by the solvation of hydrocarbon radicals. Thus, in terms of energy, hydrophobic interactions are explained not so much by interactions between hydrocarbon chains in the core of a micelle, but rather by the energetic advantage of interactions of polar solvent molecules with each other outside the micelle. Similarly, when a surfactant is dissolved in a nonpolar solvent, one can speak of hydrophilic interactions, the essence of which is the energy unfavorability of contacts between the hydrophilic groups of the surfactant and the molecules of the nonpolar solvent. This results in the formation of so-called reverse micelles, the core of which is formed by hydrophilic groups of surfactant molecules and other polar molecules (if present), and the outer surface is formed by lipophilic hydrocarbon chains.
Micellization depends on the concentration of surfactants in the solution. For a given surfactant, at a given temperature, there is a certain concentration, below which the entire surfactant is in a molecularly dispersed state, and above which micelles are formed that are in equilibrium with the molecularly dispersed surfactant. This concentration is called the critical micelle concentration (CMC). Since the size of micelles exceeds 1 nm, surfactant solutions with concentrations above CMC are colloidal. They are usually referred to the class of lyophilic colloids, that is, those that are formed spontaneously and are thermodynamically equilibrium.
There are two theories of micellization. In one of them, called the pseudophase theory, micelles are considered as particles of a separate phase, which, despite the very high dispersity, are thermodynamically stable due to the very low interfacial tension at the micelle/solution interface. Micellization is considered as the formation of a new phase, while CMC is considered as the solubility of this phase. At concentrations below CMC, the solutions are unsaturated; at a concentration equal to CMC, they are saturated, and at a concentration above CMC, they are a heterogeneous system consisting of a saturated solution with a concentration of molecularly dispersed surfactant equal to CMC and colloidal particles of another phase, including all surfactant in excess of CMC.
In an alternative theory, which is sometimes called quasi-chemical, surfactant solutions are considered as homogeneous, and micellization is explained by an equilibrium of the form
nA An(5.2)
where An- micelle with aggregation number n.
Equilibria of this type are known in chemistry as association reactions. (For this reason, colloidal surfactants are also called "associative colloids"). A well-known example is the association of acetic acid
2CH 3 COOH (CH 3 COOH)2 (5.3)
which occurs due to the formation of strong hydrogen bonds between the C–OH hydroxyl group of one molecule and the C=O hydroxy group of another. However, most of these reactions are characterized by an aggregation number of 2, in contrast to micellization, in which n = 50-100.
To understand how this theory explains the existence of CMC, it is necessary to consider the mathematical aspect of equilibrium (5.2). Neglecting the activity coefficients, this equilibrium can be described by a constant:
where parentheses denote the equilibrium concentration on the molar scale. If the entire surfactant is in the form of either molecules BUT, or micelles An, total analytical concentration of surfactants in solution, FROM, is equal to the sum
FROM = [A] + n[An] (5.5)
It is convenient to consider the fraction of the total surfactant concentration per micelles:
x = n[An]/FROM(5.6)
Then the equilibrium concentrations can be written as
[An] = xC/n, and [ A] = (1–x) C
whence it follows
(5.7)
This equation cannot be solved analytically with respect to x due to the high degree n, but it can be solved with respect to C:
(5.8)
and calculate FROM for any value x. Rice. 5.1 a) shows the results of calculations for n= 2 and 100 for some arbitrary equilibrium constants. Rice. 5.1 b) shows the same results at low concentrations. It can be seen that at n= 2, the proportion of A molecules in the composition of A 2 dimers increases gradually with an increase in the total concentration, without visible features on the curve. At n = 100, aggregated A 100 particles are practically absent at concentrations less than ~0.09 mmol/L (9 × 10–5 mol/L), but appear and rapidly increase in their content in a narrow concentration range adjacent to 0.09 mmol/L. Accordingly, the share of 1– x molecularly dispersed substance A is almost 1 at low concentrations, but decreases at FROM> ~ 0.09 mmol / l, so that its absolute concentration remains almost constant (Fig. 5.1 c). This critical concentration, 0.09 mmol/L, represents this case"point" KKM.
The position of the CMC point depends on the degree of aggregation n and on the equilibrium constant To, while the very fact of the existence of CMC, that is, a narrow range of concentrations within which there is a rapid increase in the proportion x aggregated matter, is solely a consequence of the large value of n. At small n, for example n= 2 (Fig. 5.1 a and b), there is no critical concentration. From a comparison of curves for n= 2 and 100 in fig. 5.1 it is also clear that for a well-defined CMC value to exist, micelles must be more or less monodisperse, because a wide distribution of aggregation numbers will lead to a gradual increase in x in a wide range of concentrations.
It should be noted that the micelle formation equilibrium (5.2) is usually characterized by the CMC value, and not by the equilibrium constant (5.4). There are two reasons for this. Firstly, CMC can be determined experimentally without much difficulty and with comparatively high precision, while for the equilibrium constant To and aggregation numbers n only rough estimates are possible. Second, using the constant To inconvenient due to mathematical difficulties in calculating the equilibrium concentrations associated with high powers of n in equations (5.4, 5.7 and 5.8).
For various amphiphilic surfactants, the CMC values are in the concentration range from approximately 10 to 0.1 mmol/L (from 10–2 to 10–4 mol/L). The exact value depends on the nature of the surfactant and the external conditions. In particular, with a given type of hydrophilic group, the CMC changes as follows:
Decreases with increasing length of the hydrocarbon radical;
Decreases with decreasing counterion radius in the case of cationic surfactants (for example, the CMC of cetyltrimethylammonium bromide is much smaller than the CMC of cetyltrimethylammonium fluoride);
It weakly depends on the radius of the counterion in the case of anionic surfactants, but decreases markedly with an increase in its charge (for example, calcium dodecyl sulfate has a lower CMC than the same sodium salt);
Decreases with an increase in the ionic strength of the solution in the case of ionic surfactants (for example, when adding NaCl or a similar salt to a surfactant solution).
The CMC decreases with decreasing temperature; however, for each surfactant, micelle formation is limited by a certain temperature range, below which (in the case of ionic surfactants) or above which (in the case of nonionic surfactants) the solution separates into two macroscopic phases. One of them is a molecularly dispersed solution that does not contain micelles, and the other is a solid or liquid phase of a surfactant.
Instruments and measurement methods
Experimental methods for determining the CMC are based on the change in the dependence of the properties of the solution on the concentration near the CMC. For example, if some property J is described by the dependency ¦( FROM) in the area of FROM < ККМ, то в области FROM> KKM it should be described by another dependence, say J = j( FROM). The concentration at which the most obvious transition from ¦( FROM) to j( FROM), is considered as CMC. Some examples of such dependences are collected in Fig. 5.2.
A direct method for determining CMC is to measure the turbidity of a solution as a function of concentration (turbidimetric or nephelometric measurements). In the region of low concentrations ( FROM < ККМ) раствор является истинным, поэтому его мутность низкая и едва увеличивается с ростом концентрации. В области FROM> CMC solution is colloidal, so its turbidity increases rapidly with increasing concentration in this area. If we plot the dependence of turbidity on concentration FROM in the interval FROM covering the CMC, then near the CMC there will be a change in the course of this dependence.
Osmotic pressure can also be used to find the CMC. If we choose a semipermeable membrane through which surfactant molecules pass, but micelles do not pass, then the pressure on both sides of the membrane will be the same, because the molecularly dispersed surfactant will be in equilibrium (5.2) with micelles in both chambers of the osmometer. If you choose the right membrane - that is, one that does not allow micelles or molecularly dispersed surfactants to pass through, then the osmotic pressure in the chamber with the surfactant solution will increase with increasing concentration : quickly up to CMC, but slowly at more high concentrations(See Figure 5.2). This is explained by the fact that micelles have a much higher molecular weight than a molecularly dispersed surfactant, and therefore they have little effect on the osmotic pressure. The application of this method is limited by the need to work with very dense membranes capable of retaining relatively small surfactant molecules.
A more common method, in the case of ionic surfactants, is conductometric measurements (measurements of electrical conductivity). An ionic molecularly dispersed surfactant is usually a strong electrolyte. Therefore, with the growth FROM in the area of FROM< ККМ удельная проводимость растёт, а эквивалентная проводимость уменьшается, последняя в соответствии с законом квадратного корня l = l¥– AOS. In the area of FROM> CMC, with increasing concentration, the specific conductivity grows much more slowly, and the equivalent conductivity decreases much faster than in the region FROM < ККМ. Для этого есть две причины. Во-первых, подвижность мицелл значительно меньше подвижности молекулярно дисперсных ионов. Во-вторых, ПАВ в составе мицелл является слабым электролитом, потому что значительная часть противоионов связана электростатическими силами в слое Штерна мицелл и при наложении внешнего электрического поля эти противоионы не могут перемещаться самостоятельно (см. рис. 7.2 в работе 7). Упрощенно можно сказать, что весь электрический ток переносится молекулярно-дисперсным ПАВ, тогда как мицеллярный ПАВ почти не участвует в переносе электричества. В результате, при FROM> CMC conductivity per unit volume of the solution (specific conductivity) is almost independent of the surfactant concentration, since in this region the concentration [ A] is constant (Fig. 5.1 c), while the conductivity per mole of dissolved surfactant (equivalent conductivity) decreases, because the fraction 1– x molecularly dispersed surfactant decreases.
Another method is the potentiometric measurement of counterion activity using ion-selective electrodes. For example, the activity of Na + counterions can be easily measured using a Na + selective glass electrode, complete with a conventional pH meter. The activity of counterions always increases with increasing surfactant concentration, however, in the region FROM> CMC, the slope of the curve turns out to be less, due to the fact that part of the counterions remains in the Stern layer of the micelles. This method has become widespread in recent years (along with the spread of ion-selective electrodes) due to the fact that it is less sensitive to the presence of foreign impurities than turbidimetric or conductometric methods.
In this work, the CMC is determined from the data on the dependence of the surface tension of a solution on its concentration. Surface tension is related to adsorption G according to the well-known Gibbs equation. In its simple notation (3.6a), it is valid for solutions containing only one dissolved component, while diphilic surfactant solutions generally contain two dissolved components - a molecularly dispersed surfactant and micelles. For this reason, for the surface tension s, it is necessary to use the more general equation 3.5a, which, in the notation of this paper, can be written as follows:
In the area of concentrations FROM < ККМ, концентрация мицелл равна нулю и [A] = FROM. Taking this into account, from (5.9) we obtain the following dependence of s on the concentration
, (5.10)
where s 0 is the surface tension of a pure solvent. The Gibbs and Langmuir equations in this concentration range have the form
where b is the ratio of the equilibrium constant (5.1) to the concentration of the solvent (water).
In the area of concentrations FROM³ CMC, the concentration of molecularly dispersed surfactant is approximately constant and equal to CMC, and the concentration of micelles is = FROM- KKM. Therefore, the term d ln[A] in equation (5.9) is approximately equal to zero. Then from equation (5.9) it follows:
(5.10a)
So the dependency s on concentration is described by different equations in the concentration ranges FROM < ККМ и FROM³ KKM. These equations (5.10 and 5.10a) differ in adsorption values G A and . Molecularly dispersed amphiphilic surfactant has an asymmetric chemical structure - a hydrophilic group of atoms at one end of the molecule and an extended hydrocarbon radical on the other side. Because of this, its adsorption G A great and positive. Therefore, in the area FROM < ККМ следует ожидать сильное уменьшениеs with increasing concentration. Micelles have a symmetrical chemical structure. The hydrocarbon chains in them are turned inside the nuclei, and the spherical surface is hydrophilic. Because of this, little negative or near-zero adsorption can be expected for them. Therefore, according to equation (5.10a), s can be expected to be approximately constant or slightly increase as the concentration increases above the CMC point.
In fact, in most amphiphilic surfactants, s greatly decreases in the region FROM < ККМ и продолжает уменьшаться в областиFROM> CMC, but to a much lesser extent than with C< ККМ (см. рис. 5.2). Вероятно, это объясняется тем, что концентрация молекулярно-дисперсного ПАВ не совсем постоянна в области FROM> KKM. However, the CMC can be easily found from the dependency plot s from FROM as the concentration at which a transition from one dependence is observed s from FROM to another.
In this work, the stalagmometric method is used to measure the surface tension. A stalagmometer is a vertical capillary tube used for slow controlled flow of liquid in the form of individual drops. According to the Tait equation (1863), the drop weight ( mg) coming off the tip of the tube is proportional to the length of the outer circumference of the tube 2p R and surface tension s:
mg= 2p Rs(5.11)
where R is the outer radius of the tube. This equation is based on the assumption that after reaching a critical weight sufficient to overcome the forces of surface tension, the entire protruding drop breaks off completely, leaving the tip of the tube "dry". In fact, as shown in Fig. 5.3, when the critical weight is reached, the drop is elongated with the formation of a cylindrical neck, along which it breaks. As a result, only a part of the protruding drop breaks off, and a part remains hanging on the tip of the tube. To take into account the remaining part of the drop, it is necessary to introduce a correction factor Y
mg= 2p Rs×Y, (5.11a)
which depends on the radius R and the cube root of the volume of the drop v:
Y= ¦ (5.12)
This function is empirical and is set in the form of a table or graph (Fig. 5.4).
In the stalagmometric method, the weight of drops is determined indirectly, by counting the number of drops n, for which a certain volume of the test liquid flows out of the capillary. For this purpose, the capillary tube has an extension that serves as a reservoir for liquid (not shown in Figure 5.3). The liquid is lifted into the tube to the upper mark located above the dilation and allowed to drain until the meniscus drops to the lower mark located below the dilation. The number of drops is counted. n. If the total volume of the leaked liquid is V, then the average volume v and average weight mg drops can be calculated using the formulas
v = V/n(5.13)
mg = v×r×g(5.14)
where r is the density of the liquid. Combining (5.14) and (5.11a) one can find the working expression for the surface tension
Volume V, required for calculations according to equation (5.13), is in separate calibration measurements and is constant for a given stalagmometer. However, the radius of the end of the stalagmometer has to be determined periodically ·. This can be done by experimenting with a liquid whose surface tension and density are known with good accuracy. Radius R calculated according to the equation:
in which index zero indicates the ratio of this parameter to the calibration liquid (in this work, to water). Since the coefficient Y in this equation is a function of the desired radius R, calculations have to be carried out by successive approximations in accordance with the cyclic algorithm described in Table. 5.1. The loop is terminated when the difference between two successive approximations R becomes equal to or less than some acceptable error. Last approximation (eg. R""") is taken as the desired radius R and are further used to calculate the surface tension of the studied surfactant solutions.
For the applicability of equation (5.11a), it is necessary that a drop of liquid detached from the tip of the capillary tube at the moment of detachment be in equilibrium with its vapor in environment. For this, two features of the experimental setup are important. First, the end of the stalagmometer must be in an atmosphere of saturated or near-saturated vapors of the liquid being tested. This is achieved by lowering it as low as possible above the surface of the corresponding liquid in the receiver. In the most accurate measurements, the liquid receiver is isolated from the surrounding atmosphere by a cover with a narrow hole for a stalagmometer, as shown in Fig. 5.3, and thermostated at a certain temperature until the saturation vapor pressure is established above the liquid surface. However, this is not sufficient to ensure drop/vapour equilibrium, because the surface of the liquid in the receiver is flat, while the drop coming out of the tube has a curved surface. As is known from the Kelvin equation, the vapor pressure R over a curved liquid surface is somewhat different from the vapor pressure over a flat surface R¥: R =
where v m is the molar volume of the liquid, r is the radius of curvature of the surface, which is equal to the radius of the ball in the case of a spherical drop. Therefore, the vapor pressure that is in equilibrium with respect to the drop is somewhat different from the pressure that is in equilibrium with respect to the flat surface of the liquid in the receiver. In order for the drop/vapour equilibrium to be established more accurately, the rate of drop formation at the end of the tube should be as low as possible. To do this, the inner diameter of the capillary must be very small. In the most accurate measurements, the rate of formation of each drop is additionally regulated by putting a rubber or other elastic tube on the upper end of the stalagmometer with a device that regulates air access (metal clamp, glass tap, etc.). With this device, the drop is allowed to form approximately 80% by volume, then the air access is blocked and it is forced to hang at the end of the stalagmometer for several minutes, after which the air access is opened and the drop is allowed to completely form and flow out.
Work sequence
1. At least six dilutions are prepared from the initial aqueous solution of sodium oleate C 17 H 33 COONa with a concentration of 1.00 g/l and distilled water to the lowest concentration ~ 0.1 mmol/l. For example, the following schema could be used:
First you need to make sure that the temperature of the solutions is the same to within 1 °C. The temperature of the solutions T, as well as the volume of the stalagmometer V are recorded in the laboratory journal. (Unless otherwise specified by the teacher or laboratory assistant, the volume V 1.103 cm should be taken 3)
2. About 10 ml of the next solution is poured into a vessel (glass or flask), which serves as a receiver of the liquid flowing from the stalagmometer, and the stalagmometer is lowered into it so that its lower tip is only slightly above the liquid level and much below the edges of the vessel. Leave the installation in this form for 5-10 minutes to establish an approximate liquid / vapor equilibrium above the surface of the solution.
3. Raising the receiver so that the tip of the stalagmometer is immersed in the test solution, fill the stalagmometer with a solution above the upper mark using a bulb or a vacuum pump. Disconnect the pear (or pump) and lower the receiver. When the liquid meniscus reaches the upper mark, counting of the number of drops begins and stops when the liquid meniscus reaches the lower mark. Number of drops n write down.
The flow rate of the liquid should be no more than 1 drop per minute. If the speed is greater, it is regulated by periodically closing and manually opening the air access to the upper end of the capillary tube.
4. Measurements start with distilled water and continue in order of increasing surfactant concentration, repeating them according to paragraphs. 2 and 3 at least three times for each solution.
Processing and presentation of results
1. Results of measuring the number of drops n for each solution, enter in the table (see table. 5.2) and calculate the average number of drops.
2. Calculate the average volume v 0 drops of water ( With= 0) according to equation 5.13, using the average number of drops . Next calculate the radius R stalagmometer according to the algorithm given in Table. 5.1. Values s 0 and r 0 required to calculate the coefficient AT, should be found by interpolating the data in Table. P4.2 in appendix 4 for the actual measurement temperature. Intermediate calculations of successive approximations Y and R it is convenient to keep in a separate table (Table 5.3). Values Y find for given on fig. 5.4. Calculations continue until successive approximations R ii R i-1 will not differ by the amount of discrepancy e= , less than 0.5%. After reaching this accuracy, the calculations are stopped and the last approximation R is taken as the final value.
3. Calculate the average drop volume according to equation 5.13 for each surfactant solution and the corresponding ratios. These values should be recorded in a separate table (see Table 5.4). Found in Fig. 5.4 odds Y for computed values. With the help of the obtained values v and Y calculate surface tension s according to equation 5.15. Regarding density r solutions of surfactants included in Equation 5.15, it should be taken into account that at concentrations less than 0.1 g/l, it is practically equal to the density of water at a given temperature (Appendix 4, Table A4.3)
4. Build a dependency graph s from concentration. The molar concentration should be used, since it is on this scale that it is customary to compare the CMC values of different surfactants. Typically, the graph has a break or bend point at CMC (Fig. 5.5), which is more clearly visible when the logarithm of concentration is plotted as a variable along the abscissa. If, however, the break in the resulting curve is not clear enough, the graphical method shown in fig. 5.5: find two approximately linear sections on the curve and build tangents to them, the abscissa of the intersection of which represents the desired value of the CMC (the logarithm of the CMC, if a logarithmic scale is used).
5. As a conclusion from the work, indicate the value of CMC in molar and weight (g/l) scales of concentration.
test questions
1. What is called diphilicity of molecules? How are amphiphilic surfactants classified?
2. What special properties do amphiphilic surfactant solutions have in comparison with solutions of other substances?
3. What is called the critical micelle concentration?
4. What is the driving force behind micellization?
5. What are the theoretical explanations of CMC?
6. What is the CMC value of most colloidal surfactants? What factors influence it?
7. What experimental methods are used to determine the CMC?
8. How does the electrical conductivity of amphiphilic surfactant solutions depend on concentration? Does this dependence differ from what is known for ordinary electrolytes?
9. How does the surface tension of amphiphilic surfactant solutions depend on concentration? How does this dependence differ from that known for ordinary surfactants, for example, for aqueous solutions of butyl alcohol?
10. What is called a stalagmometer? Describe the principle of stalagmometric determination of surface tension.
11. What determines the weight of a drop coming off the tip of a stalagmometer?
12. What determines the accuracy of determining s by the stalagmometric method? What is important in this method to get the right results?
13. Why does the surface tension not change with increasing surfactant concentration above CMC?
14. What role does the inner diameter of the capillary play in the method of stalagmometric measurement of s? Does it affect the weight of the drop coming off the tip of the stalagmometer tube?
15. What is the form of the Langmuir equation for the adsorption of surfactants in the concentration ranges below CMC and above CMC?
Literature
Zimon A.D., Balakirev A.A., Dekhtyarenko N.G., Babak V.G., Aksenov V.N. colloidal chemistry. Laboratory practice. Part 1. M: VZIPP 1986, Lab. work 5.
Berthod A. Structures physico-chimiques des milieux disperses, micelles, emulsions et microemulsions. Journal de chimie physique 1983, vol. 80, p. 407-424 (about KKM).
Adamson A. Physical chemistry of surfaces. (translated from English) M: Mir 1979, Chapter 1 (about the definition of s), Chapter 11 (about KKM).
Dickinson E., Stainsby G. Colloids in food. L: Applied Science 1982, Chapter 4 (on CMC).
Melvin-Hughes E.A. Physical chemistry. Volume 2. (translated from English) M: Izdatinlit 1962, Chapter 19 (on the definition of s).
Micelles, membranes, microemulsions, and monolayers. (Ed. W.M. Gelbart, A. Ben-Shaul, D. Roux) N.Y.: Springer-Verlag, 1994, Chapter 1 (Figure 5.2)
Harkins W.D., Brown F.E. The determination of surface tension (free surface energy), and the weight of falling drop. Journal of the American Chemical Society 1919, vol. 41, 499-524 (experimental points for Fig. 5.4)
Bovkun O.P., Markina Z.N., Grakova T.S. Determination of the critical micelle concentration of aqueous solutions of soaps with the addition of dioxane, methyl alcohol and ethylene glycol. colloid magazine 1970, volume 32, 327-332 (experimental points for Fig. 5.5)
Rice. 5.1 (a, b) Distribution of a solute between associated molecules (x, in fractions of a unit) and non-associated molecules (1–x) for some arbitrary values of the equilibrium constants. (mM - mmol/l) (c) dependence of the absolute concentrations of associated and non-associated surfactant molecules on the total concentration of C at n = 100.
Rice. 5.2 Dependence of some properties of J on the concentration of a typical surfactant (sodium dodecyl sulfate) near the CMC
Rice. 5.3 Schematic representation of a drop flowing from the tip of a capillary tube. The tip is in a glass receiver above the surface of the liquid, which is poured some time before dripping from the tube.
Rice. 5.4 Correction factor Y as a function of the ratio . At > 0.3, Fig (a) should be used, at< 0.3 – рис. (б)
Rice. 5.5 (sample) Change in surface tension over a concentration range encompassing CMC. The elements of graphic constructions are shown, which can be useful for more reliable determination of this point.
· The outer circumference of the end of the stalagmometer must be very smooth. Therefore, it is subjected to periodic grinding.
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The special amphiphilic structure of surfactant molecules was successfully characterized by Gartley, who was one of the first to study micellar solutions, as a “split personality”. It is the amphiphilic nature of surfactant molecules that causes their tendency to accumulate at the phase boundary, immersing the hydrophilic part in water and isolating the hydrophobic part from water. This tendency determines their surface activity, i.e. the ability to be adsorbed at the water–air or water–oil interface, to wet the surface of hydrophobic bodies, to form structures such as soap films or lipid membranes.
With an increase in the asymmetry of molecules (elongation of the hydrophobic part), their surface activity increases - Traube's rule. This enhances their special behavior in solution.
Long-chain surfactants (the number of carbon atoms in the chain n c = 10 - 20), which are characterized by an optimal balance of hydrophobic and hydrophilic properties, which in solutions special properties are of great interest. These surfactants at low concentrations form true solutions, being dispersed to individual molecules (ions). With an increase in the concentration of surfactants in solution, due to the duality of the properties of molecules, their self-association in solution occurs, resulting in the formation of micelles. The term micelle was introduced by McBain in 1913.
Micelles are aggregates formed during the cooperative binding of monomers to each other at surfactant concentrations in solution, the values of which exceed a narrow range called the critical micelle concentration (CMC).
When CMC is reached in surfactant solutions in a polar solvent (water), the hydrocarbon chains of surfactant molecules combine into a hydrocarbon core due to hydrophobic interactions, and hydrated polar groups facing the aqueous phase form a hydrophilic shell. Micelles are in thermodynamic equilibrium with molecules (ions).
The methods for determining the CMC are based on the analysis of the experimentally obtained dependence physical property solution on the surfactant concentration, since in the area of CMC there is a sharp change in a number of properties of micellar surfactant solutions. Most often in practice, the dependences of the turbidity of solutions (t) or optical density, surface tension (s), electrical conductivity (χ), light refractive index (n), diffusion (D), viscosity (h), osmotic pressure (p) on surfactant concentrations. CMC is determined by the point corresponding to the break in the curves of the dependence of the properties of solutions on the concentration of surfactants. Typical examples of logged dependencies are shown in Figure 1.
Figure 11 - Dependence of the properties of the system on the concentration of surfactants
Currently, more than a hundred different methods for determining CMC are known, some of which also provide information on the structure of solutions, the size and shape of micelles, and other properties. Consider the most commonly used methods.
The conductometric method for determining CMC consists in changing the specific electrical conductivity of the solution depending on the concentration of the ionic surfactant.
The method of determining the CMC according to the measurement of surface tension has become widespread.
The viscometric method for determining CMC uses the dependences of the reduced viscosity on the concentration of surfactant solutions. This method is convenient for nonionic surfactants.
Finding CMC by light scattering is based on a sharp increase in light scattering by particles and the turbidity of the system during the formation of micelles in surfactant solutions. Also, this method allows you to determine the micellar mass (the sum of the molecular masses of the molecules that form the micelle) and the aggregation number (the number of molecules in the micelle) and their forms.
Determination of CMC by diffusion is carried out by measuring the diffusion coefficients (D), which are associated both with the size of micelles in solutions, and with their shape and hydration. Usually, the CMC value is found at the intersection of two linear sections of the dependence of D on the dilution of solutions. Diffusion monitoring is usually carried out when an additional component is introduced into solutions - a micelle label, which is recent times use radioactive isotopes that do not shift micellar equilibrium.
The determination of CMC by the refractometric method is based on the change in the refractive index of surfactant solutions during micelle formation. This method is convenient because it does not require the introduction of additional components.
The determination of CMC by the ultraacoustic method is based on the change in the nature of the passage of ultrasound through the solution during the formation of micelles. When studying ionic surfactants, this method is convenient even for very dilute solutions (with low CMC values); systems with nonionic substances are more difficult to characterize by this method.
All dispersed systems, depending on the mechanism of their formation, according to the classification of P. A. Rebinder, are divided into lyophilic, which are obtained by spontaneous dispersion of one of the phases (spontaneous formation of a heterogeneous free-dispersed system), and lyophobic, resulting from dispersion and condensation with supersaturation (forced formation of a heterogeneous free-range system).
The presence of hydrophilic and oleophilic parts in surfactant molecules is a characteristic distinguishing feature of their structure. According to the ability to dissociate in aqueous solutions, surfactants are divided into ionic and nonionic. In turn, ionic surfactants are divided into anionic, cationic and ampholytic (amphoteric).
1) Anionic surfactants dissociate in water to form a surface-active anion.
2) Cationic surfactants dissociate in water to form a surface-active cation.
3) Ampholytic surfactants contain two functional groups, one of which is acidic and the other basic, such as carboxyl and amine groups. Depending on the pH of the medium, ampholytic surfactants exhibit anionic or cationic properties.
All surfactants with respect to their behavior in water are divided into truly soluble and colloidal.
Truly soluble surfactants in solution are in a molecularly dispersed state up to concentrations corresponding to their saturated solutions and the separation of the system into two continuous phases.
The main distinguishing feature of colloidal surfactants is the ability to form thermodynamically stable (lyophilic) heterogeneous disperse systems (associative, or micellar, colloids). The main properties of colloidal surfactants, which determine their valuable qualities and wide application, include high surface activity; the ability to spontaneous micelle formation - the formation of lyophilic colloidal solutions at a surfactant concentration above a certain specific value, called the critical micelle concentration (KKM); the ability to solubilize - a sharp increase in the solubility of substances in solutions of colloidal surfactants due to their "introduction" into the micelles; high ability to stabilize various disperse systems.
At concentrations above KKM, surfactant molecules are collected into micelles (associate) and the solution transforms into a micellar (associative) colloidal system.
A surfactant micelle is understood as an associate of amphiphilic molecules, the lyophilic groups of which are facing the corresponding solvent, and the lyophobic groups are connected to each other, forming the core of the micelle. The number of molecules that make up a micelle is called the association number, and the total sum of the molecular weights of the molecules in the micelle, or the product of the mass of the micelle and the Avogadro number, is called the micellar mass. A certain orientation of amphiphilic surfactant molecules in a micelle provides a minimum interfacial tension at the micelle-environment boundary.
At concentrations of surfactants in an aqueous solution slightly exceeding KKM, according to Hartley's ideas, spherical micelles (Hartley micelles) are formed. The inner part of Gartley micelles consists of intertwining hydrocarbon radicals, the polar groups of surfactant molecules are turned into the aqueous phase. The diameter of such micelles is equal to twice the length of surfactant molecules. The number of molecules in a micelle grows rapidly within a narrow concentration range, and with a further increase in concentration, it practically does not change, but the number of micelles increases. Spherical micelles can contain from 20 to 100 molecules or more.
As the surfactant concentration increases, the micellar system passes through a series of equilibrium states that differ in association numbers, sizes, and shapes of micelles. When a certain concentration is reached, spherical micelles begin to interact with each other, which contributes to their deformation. Micelles tend to take a cylindrical, disc-shaped, rod-shaped, lamellar shape.
Micellization in non-aqueous media, as a rule, is the result of the action of attractive forces between the polar groups of surfactants and the interaction of hydrocarbon radicals with solvent molecules. The inverted micelles formed contain non-hydrated or hydrated polar groups inside, surrounded by a layer of hydrocarbon radicals. The association number (from 3 to 40) is much less than for aqueous solutions of surfactants. As a rule, it grows with an increase in the hydrocarbon radical up to a certain limit.
The critical micelle concentration is the most important characteristic of surfactant solutions. It depends primarily on the structure of the hydrocarbon radical in the surfactant molecule and the nature of the polar group, the presence of electrolytes and nonelectrolytes in the solution, temperature, and other factors.
Factors affecting KKM:
1) With an increase in the length of the hydrocarbon radical, the surfactant solubility increases and the KKM increases. Branching, unsaturation, and cyclization of the hydrocarbon radical reduce the tendency to micelle formation and increase the KKM. The nature of the polar group plays a significant role in micellization in aqueous and non-aqueous media.
2) The introduction of electrolytes into aqueous solutions of nonionic surfactants has little effect on the CMC and micelle size. For ionogenic surfactants, this effect is significant.
3) The introduction of non-electrolytes (organic solvents) into aqueous solutions of surfactants also leads to a change in the KKM.
4) Temperature
Methods for determining KKM are based on recording a sharp change in the physicochemical properties of surfactant solutions depending on the concentration (for example, surface tension σ, turbidity τ, equivalent electrical conductivity λ, osmotic pressure π, refractive index n). A kink usually appears on the property-composition curve in the KKM region.
1
) The conductometric method is used to determine the KKM of ionic surfactants.
2) Another method for determining KKM is based on measuring the surface tension of aqueous surfactant solutions, which sharply decreases with increasing concentration up to KKM, and then remains constant.
3) Solubilization of dyes and hydrocarbons in micelles makes it possible to determine the KKM of ionic and nonionic surfactants both in aqueous and non-aqueous solutions. When a concentration corresponding to KKM is reached in a surfactant solution, the solubility of hydrocarbons and dyes increases sharply.
4) Measuring the intensity of light scattering during micelle formation makes it possible not only to find KKM from a sharp increase in the slope of the concentration curve, but also to determine the micellar mass and association numbers.