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Investigation of surfactant surface tension and its correlation with temperature and concentration Cheng, Li Yaw (Michael); Wei, Su Min (Lisa) 2012-06-07

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INVESTIGATION OF SURFACTANT SURFACE TENSION AND ITS CORRELATION WITH TEMPERATURE AND CONCENTRATION Li Yaw (Michael) Cheng Su Min (Lisa) Wei Science One Program The University of British Columbia Vancouver, Canada June 20121 Abstract Surface tension is a property that def_ines the energy per unit area of a liquid-gas interface. T_he purpose of this study is to investigate the surface properties and the process of aggregation of surfactant micelles in detergents. By using a drop-weight method, the surface tension of detergent solutions was determined under standard pressure condition 1 bar. A 100% concentrated detergent solution was subject to heating. Data analysis showed that surface tension de- creased linearly with increasing temperature, as represented by the equation γ = – 0.1766 mN/(m⋅K)(x) + 94.654 mN/m, where x is temperature. When subjected to variations in concentration, surface tension of the detergent de- creased until reaching the critical micelle concentration, as modelled by the segmented linear regression γ = – 0.565 mN/(m⋅%)(x) + 61.7 mN/m when x < 50%, and γ = 33.45 mN/m when x ≥ 50%, where x is concentration. 2 Introduction Surface tension of a solvent or solution, denoted by the Greek letter gamma γ, represents a well-def_ined physico- chemical property. It is caused by cohesion of f_luid molecules and allows for its resistance of an external force [1]. T_he unit of measurement has dimensions of force per unit length, or equivalently, energy per unit area. Molecules at the surface experience a net inward force which results in internal pressure. Considering the isoperimetric inequality, liquid surfaces minimize its energy of conf_iguration by contracting to minimal area [2]. Surface tension is ubiquitous in the natural world. For instance, water striders are able to f_loat on top of water due to the surface tension of water providing the restoring force to the insect’s weight. In surface and colloidal chemistry, surface tension can be useful in characterizing the chemical activity, adsorption, and dissolution of materials [3]. A specif_ic branch of study in surface chemistry is the surface tension of surfactants, which are surface-active agents that adsorb to a f_luid surface. Besides the common usage of surfactants in food additives, detergents, and cosmetics, these molecules are of_ten used as surface active agents in the production of drugs within both medicinal and phar- maceutical sciences [4]. When dissolved in solvent, surfactants disrupt the intermolecular interactions of the liquid, thereby decreasing the solvent’s surface tension. Water-soluble polymers have amphipathic structures, with non-polar hydrophobic parts and hydrophilic parts that favour interaction with polar solvents such as water [3]. T_he formation of micelles can be understood through principles of thermodynamics; micelles can form spontaneously because of a balance between entropy and enthalpy. In water, hydrophobic ef_fects and London van der Waals forces between water and surfactant molecules drive the micellization process. In the present study, we have selected a particular detergent brand named “Palmolive Original.” T_he primary surfac- tant agent is lauramidopropylamine oxide, a non-ionic surfactant. As its name suggests, non-ionic surfactants do not possess electrical charges [9]. T_he substance’s surface properties were characterized by measuring the surface tension of the detergent at dif_ferent temperatures and concentrations. T_he du Nuöy ring method was adopted as a model for the conduction of surface tension measurement [5]. 3 Method 3.1 Equipment Calibration T_he main component of the apparatus is the dial-o-gram (Ohaus, #1650-WO). Figure 1 depicts the setup of our ex- periment. A stif_f copper wire of negligible mass was used to construct a ring and secured to the beam. To ensure the copper ring was circular and completely f_lat, the wire was tied around a cylindrical container and hammered into circular conformation. T_he ring was f_lattened using a hammer on a smooth table. T_he ring’s f_latness and circular shape were crucial to achieving even distribution of the pulling force upon the liquid surface. When securing the extended arm of the ring onto the beam, tweezers were used to minimize the wiggle room of the twisted wire. A 1 kg calibration weight was placed on the stainless steel plate and weight was adjusted on the beam to create an initial rough balance. A clean and lightweight Styrofoam cup was placed onto the plate. T_he f_ine-tuning knob was adjusted so the beam hit the zero-mark, which indicated the exact point of balance. T_his marked the initial position. Cheng and Wei (2012) 1 Figure 1: Experimental Setup. From lef_t to right, the Styro- foam cup for addition of water as mass applied, calibration bulk weight of 1 kg, minor control knob to obtain equilibrium posi- tion, three beams (two are used for balancing and the third for the attachment of ring), and the ring for contacting the periph- ery of the f_luid. Figure 2: Visual representation of torque calculation. M is the mass added to maintain and eventually disrupt the equilib- rium position. L is the mean perimeter of the ring. Fmass is the gravitational force exerted by the applied mass. Ftension is the force exerted by f_luid periphery against Fmass. rR is the arm length between the axis of rotation and the ring. rP is the arm length between the axis of rotation and the centre of the stain- less steel plate. 3.2 Measurement of Surface Tension A 250 mL beaker was used to hold the solution subjected to measurement. T_he beaker was f_illed to precisely the 200 mL mark. T_his mark was the level that allowed the ring to rest on top of the liquid surface without disrupting the equilibrium position of the beam. T_he cup was pre-weighed on an analytical balance to obtain the mass to 5 signif_i- cant digits. Since surface tension is considered a weak force compared to a gravitational pull by the applied force, a dropper bottle was used to add water drops to the Styrofoam cup in small increments until the beam at the delicately balanced position was tipped and the ring detached from the liquid surface. Clean water from the tap was used. T_he cup and added water were weighed on the analytical balance, and the mass of water added was calculated. Five repli- cates were carried out for each trial. Note the dial-o-gram was used because it has a high degree of sensitivity to min- uscule additions of mass. An addition of one hundredths of a drop of water can be suf_f_icient to tip the balance. 3.3 Mathematical Derivation of Surface Tension Formula Considering the du Noüy formula [5], the surface tension is given by γ = Mg/(2L) where γ is the surface tension, M is the mass used to applied force, g is the gravitational acceleration (9.807 m/s2 was used throughout the experiment), and L is the mean circumference of the ring. T_he unit of measurement is force per unit length with SI units N/m. T_he surface tension of the liquid was calculated using principles of torque and rotational dynamics [5]. Torque is the prod- uct of arm length r with the force component F that is perpendicular to the radial line. T_he formula is given by τ ≡ rFsinθ, where θ is the angle between the moment arm and the force applied. In the experiment, θ = 90°, since the surface tension and the weight of water drops were both tangent to the beam. Initially, the system was at rotational equilibrium. As shown in Figure 2, the addition of drops of water to the Styrofoam cup resulted in a gravitational torque greater than the torque exerted by surface tension. T_his caused the system to rotate counter-clockwise about the fulcrum (the pivot point). Given τR is depicted as the torque on the ring side where tension exerts force and τP as the torque on the plate side where mass exerts a downward force, then the formula for surface tension can be derived as follows: Ftension( ) rR( ) = Fmass( ) rP( ) γ 2LrR = MgrP γ = MgrP 2LrR . (1) Cheng and Wei (2012) 23.4 Statistical Analysis T_he uncertainty (σm) in each measurement of surface tension was derived from standard deviation. T_he formula is σm = σ/ N , where the standard deviation is calculated as follows: σ = 1 N −1 yi − µ( )2 i=1 N ∑ , (2) where the mean (µ) is µ = 1 N yi i=1 N ∑ . (3) For each linear regression model in the form of y = mx + b, the best-f_it line was generated on Excel 2010 by using the weighted best-f_it slope, its uncertainty δm and y-intercept b as displayed below: m = 1 Δ 1 δ yi( )2i=1 N ∑ xiyiδ yi( )2i=1 N ∑ − xiδ yi( )2i=1 N ∑ yiδ yi( )2i=1 N ∑ ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ , (4) δ m = 1 Δ 1 δ yi( )2i=1 N ∑ , (5) b = 1 Δ xi 2 δ yi( )2i=1 N ∑ yiδ yi( )2i=1 N ∑ − xiδ yi( )2i=1 N ∑ xiyiδ yi( )2i=1 N ∑ ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ , (6) where Δ = 1 δ yi( )2i=1 N ∑ xi 2 δ yi( )2i=1 N ∑ − xiδ yi( )2i=1 N ∑ ⎛ ⎝ ⎜ ⎞ ⎠⎟ 2 . (7) Each resultant linear regression model is then evaluated using weighted least square analysis derived as follows: χw2 = 1 N yi − f (xi ) δ yi ⎡ ⎣ ⎢ ⎤ ⎦⎥ 2 i=1 N ∑ . (8) 3.5 Varying Temperature T_he temperature of a 100% concentration surfactant solution and of clean tap water was varied. Identical procedures of temperature variations were carried out for both types of solutions. A 250mL beaker was f_illed with 200mL of solu- tion and put in a standard refrigerator to be cooled to 273K. A thermometer was used to monitor the temperature drop. T_hen the beaker was taken out and placed on an insulating mat to prevent heat to be transferred to or from the solution to the surroundings. Surface tension was measured using standard protocols as delineated in the above pro- cedural section. T_he solution was heated in 5K increments with the glass beaker placed in a pan. T_he pan is then placed on an electric stove to prevent the glass from cracking due to large pressure changes from cooling or heating. T_he temperature was monitored using a thermo-anemometer (Extech Instruments), which detects air velocity, rela- tive humidity and temperature of the system. T_his instrument was used to ensure the uniformity of environmental conditions other than experimental variable, which is temperature. Cheng and Wei (2012) 33.6 Varying Concentrations Surface tension was also correlated with surfactant concentration. “Palmolive Original” detergent was used as the surfactant. Multiple concentrations of detergent were employed to ensure accuracy of the direct relation between surfactant and change in magnitude of surface tension. Varying concentrations without af_fecting volume was achieved by the volume replacement method, where the volume was set to 200mL. T_he following equation was used for concentration and dilution, respectively: ΔV (xk , xk+1) = 200 xk+1 − xk( ) 1− xk ΔV (xk , ′xk+1) = 200 xk − ′xk+1( ) xk , (9) where ∆V is the volume replaced to achieve a certain concentrated or diluted concentration. T_his volume of solution was either discarded and replaced with pure detergent when increasing surfactant concentration or replaced with water when performing dilutions. T_he calculated amount should result in a mixture of desired concentration while returning its volume to 200mL as the control volume. xk is the initial concentration, xk+1 is the increased concentra- tion, and x'k+1 is the decreased concentration upon dilution. Concentrating from 0% detergent to 100% detergent and its reverse (i.e., diluting) were carried out to optimize the precision of each concentration data point. T_his resulted in the number of replicates doubling to ten. 4 Results and Analysis 4.1 Temperature Dependence of Surface Tension 45 50 55 60 65 70 75 80 270 285 300 315 330 345 360 375 y = -0.2866x + 152.86 Sur fa ce Te ns io n (mN/m ) Temperature (K)   Figure 3: Surface Tension of Water at Various Temperatures at Standard Pressure Condition 1 bar. Bars represent stan- dard errors. Each data point represents total number of f_ive replicates (n = 5). χw2 = 8.361, m = – 0.288 mN/m, b = 152.86 mN/m. Figure 4: Surface Tension of Detergent at Various Tempera- tures at Standard Pressure Condition 1 bar. Bars represent standard errors. Each data point represents a total number of f_ive replicates (n = 5). χw2=2.310, m = – 0.177 mN/m, b = 94.654 mN/m. Linear relation is observed and hypothesized for both Figure 3 and Figure 4 using y = mx + b, where m is the slope and b is the y-intercept of the model function. Using the weighted least square f_itting as the linear model, it was de- termined that for water, the linear model yields a minimum weighted chi-square value of 8.361, with m = – 0.288 mN/(m⋅K) and b = 152.86 mN/m, resulting in a critical temperature of 531.024K. T_he critical temperature marks the point at which surface tension is expected to drop to zero (equivalent to the x-intercept). However, the extrapolated value of the critical temperature for water has no physically relevant meaning because water would already be in gas phase at 373K. With the same method, it was determined that for detergent, the linear model yields a minimum weighted chi-square value of 2.310 with m = – 0.177 mN/(m⋅K) and b = 94.654 mN/m, resulting in a critical tem- perature of 535.896K. T_he linear model for water shows a steeper slope and a higher y-intercept than the parameters of the linear model for detergent. 25 30 35 40 45 50 270 285 300 315 330 345 360 375 y = -0.1766x + 94.654 Sur fa ce Te ns io n (mN/m ) Temperature (K) Cheng and Wei (2012) 4Distinct discretization of surface tension decrement can be observed in Figure 3 and Figure 4. Consecutive dif_fer- ences are not uniform. Signif_icant drops in value occur in a stepwise fashion. T_he cause was f_irst hypothesized to be the discrete mass added for each drop of water and the sensitivity of the equipment used. To test the hypothesis, the weight of several drops of water was determined and was divided by the number of drops to obtain mass per drop. Mean mass is applied to equation (2) to obtain the mean gravitational force per length per drop. T_his renders the value 0.212 mN/m per drop, which was compared to mean signif_icant changes in surface tension in Figure 3 and Figure 4. Mean signif_icant changes are quantif_ied as the mean of the greatest ten consecutive f_luctuations of data. In Figure 3, the mean signif_icant change in surface tension is 4.422 mN/m. In Figure 4, the mean signif_icant change in surface tension is 2.122 mN/m. Both results show low correlations to the mean gravitational force exerted per drop. T_he higher values in f_luctuation can be rationalized with the additional applied force when squirting the water into the Styrofoam cup. 4.2 Concentration Dependence of Surface Tension 20 30 40 50 60 70 80 270 285 300 315 330 345 360 375 y = -0.2866x + 152.86 y = -0.1766x + 94.654 Sur fa ce Te ns io n (mN/m ) Temperature (K)  Figure 5: Surface Tension of Water and Detergent at Various Temperatures at Standard Pressure Condition 1 bar. Bars represent standard error calculated according to the appendix. Each data point represents a total number of f_ive replicates (n = 5). Figure 6: Surface Tension of Water-Detergent Mixture Meas- ured with Di! erent Concentrations at Room Temperature 298K and Standard Conditions with Varying Concentra- tions. Bars represent standard errors. Each data point repre- sents a total number of ten replicates (n = 10). χw2 = 20.217, m = – 0.565 mN/m⋅K, b = 61.700 mN/m, C = 50%. Considering the formula for uncertainty shown in the procedural section, the surface tension of water at pressure 1 bar and room temperature (273K) was measured to be 70.000 ± 3.200 mN/m and the surface tension of detergent is 36.000 ± 1.700 mN/m. By comparing Figures 3 and Figure 4 in the composite graph Figure 5, the surface tension of water is consistently higher than the detergent, by nearly 50%. T_here is no ambiguity with this statement since the uncertainty ranges do not overlap. However, as shown by the small error bars, this absence of ambiguity may be due to underestimation of error propagation in measurements or instrumental error (Please refer to Qualitative Error Analysis for in-depth discussion). In Figure 6, the surface tension af_ter the critical point decreases steadily with increasing surfactant concentration. However, close inspection reveals that the decreasing nature halts at about 50% concentration. Surface tension af_ter this concentration lacks a particular trend; it could be oscillating, increasing, or constant. Most of the data points demonstrate signif_icance with no overlaps. Minimum uncertainty is observed at 50% concentration and maximum uncertainty is determined to be at 62.500%. Hence, linear regression termed the “hockey stick function” was used to f_it the data shown in Figure 6: y = m1x + b2 x < C m2x + b2 x ≥ C ⎧ ⎨ ⎪ ⎩⎪ , (10) where m1 and m2 are slopes, b1 and b2 are y-intercepts, and C is the critical breakpoint of the segmented linear regres- sion where behaviour changes dramatically. T_he parameters are generated by determining the least chi-square value. For this segmented linear regression model, since the best-f_it slope and y-intercept cannot be determined with the 25.00 36.25 47.50 58.75 70.00 0 25 50 75 100 Sur fa ce Te ns io n (mN/m ) Concentration of Detergent (%) Cheng and Wei (2012) 5aforementioned formula, manual minimization of f_it parameters was employed. T_he minimality of the slopes, y- intercepts and value of C were conf_irmed by plotting trial values to generate parabolic functions. T_he point at which the derivative is zero depicts the minimum value of the parameter. T_he set of graphs are shown in Figure 7 below. 20.20 20.25 20.30 20.35 20.40 20.45 -0.555 -0.56 -0.565 -0.57 y = 0.0019x2 - 0.0433x + 20.459 Optimal Slope (m) χ2 Va lu es Values of m    Figure 7. Manual Minimization of Chi-Square Values. T_he parameters were generated by determining the minimum points on the graphs, each corresponding to a specif_ic parameter. As shown in Figure 6, the values are χw2 = 20.217, m = – 0.565 mN/m⋅%, b = 61.7 mN/m, C = 50%. T_he uncertainty associated with each data value in Figure 6 is one sigma bar, which suggests two-thirds of the data values should cross the f_it line. However, only two-ninths of the error bars cross the line. T_his may be due to the aforementioned underestimation of error.  5 Discussion 5.1 Surface Activity of Surfactant T_he cause of the general decreasing trend in the surface tension of detergent-water mixture may be due to the pres- ence of the cleaning and foaming agent lauramidopropylamine oxide (C17H36N2O2). T_his molecule is a nitrogenated, non-ionic surfactant [9]. As shown in Figure 8, non-ionic surfactants contain tertiary amine oxides that are of_ten used as emulsif_iers since they have high solubility in water [9]. Lauramidopropylamine oxide contains a long hydrophobic alkyl chain and a highly polar N-O bond. T_he nitrogen atom involved in this bond readily donates its electrons, re- sulting in a negative oxygen atom which readily captures a proton in aqueous solution [7]. T_he highly polar N-O bond drives the hydrophilic interactions with water, subsequently modifying and disrupting the hydrogen bonding be- tween water molecules. T_he amphiphilic property of the surfactant molecule also allows this hydrophilic end to ad- sorb to the f_luid surface. T_he collective energy that generates water’s high surface tension decreases. Figure 8: Chemical structure of lauramidopropylamine ox- ide. T_he highly polar N-O bond in lauramidopropylamine ox- ide disrupts the hydrogen bonding between water molecules, causing surface tension of the aqueous solution to decrease linearly until reaching the critical micelle concentration. 5.2 Critical Micelle Concentration T_he position upon which the plateau is reached in Figure 6 can be attributed to the critical micelle concentration (CMC). In colloidal and surface chemistry, CMC is def_ined as the concentration of surfactant above which micelles spontaneously form in solution [1][7]. T_he value of CMC and surface tension itself are intensive thermodynamic pa- rameters [4]. T_hese quantities are therefore dependent upon temperature, pressure, and on the presence and concen- tration of other surface-active electrolytes [8]. T_he value of the critical micelle concentration quantif_ies the degree of packing and the orientation of the adsorbed surfactant molecules [1]. As surfactant concentration increases, surface coverage of surfactant molecules increase, and the maximum coverage are reached at CMC [1][9]. At that point, mole- cules begin to aggregate into micelles. Monomers and micelles thereaf_ter exist in dynamic equilibrium, and the spac- ing between adjacent molecules attains its most favourable distance to minimize the intermolecular potential energy. Any subsequent formation of micelles will have minor ef_fects on surface tension. T_he surface tension of the surfactant at which the experimental CMC value was reached was compared to those at- tained by Atta et al. [1] who worked with non-ionic surfactants under similar conditions. Shown in Figure 6, the criti- cal micelle concentration was determined to be 50% surfactant concentration. T_he average constant surface tension 20.0 20.5 21.0 21.5 22.0 22.5 60.5 60.9 61.3 61.7 62.1 62.5 y = 0.0132x2 - 0.3532x + 22.583 Optimal y-Intercept (b) χ2 Va lu es Values of b 20.0 20.5 21.0 21.5 22.0 49 49.3 49.6 49.9 50.2 50.5 50.8 Optimal Breakpoint (C) χ2 Va lu es Values of C Cheng and Wei (2012) 6was 33.45mN/m at 298K based on the segmented linear regression model. Atta et al. [1] showed that the non-ionic surfactant CMC was reached at surface tension 34.8 ± 0.5mN/m at 303K. When comparing Figure 3 and Figure 4, the detergent surface tension decreased much more slowly than did water. T_his is because in the 100% concentrated surfactant solution, the area per molecule at the surface decreased at the surface due to increased dehydration of the hydrophilic group at higher temperature [7] yet increased due to enhanced molecular motion and thermal agitation at higher temperatures. T_he two opposing forces result in lower decreasing rate for surfactant surface tension when compared to that of water. 5.3 Qualitative Error Analysis Some transparent soap bubbles formed around the copper ring and between the ring and the surface of the surfactant as the ring was tilted out of the solution. T_his made it more dif_f_icult to distinguish the exact point at which the ring loses contact with the liquid surface. T_his would result in a slightly greater amount of water being added to the cup than the volume suf_f_icient to break surface tension. As observed in Figure 3, there are large f_luctuations from 273K to 308K, and the values do not correspond to the slope of the general decreasing trend of the measurements above 308K. Bubble-formation was frequent in the range 273K to 308K. Large uncertainties were associated with measure- ments at lower temperature, as can be seen in Figure 3. T_he maximum error was detected at 288K temperature, with surface tension 43.460 ± 2.460mN/m. Due to the ring’s frequent contact with the detergent, the ring’s smooth wax layer was observed to dissolve. T_he strength of contact between the liquid surface and the wax layer of the ring would be signif_icantly dif_ferent from the tension between the surfactant surface and the rougher, grey metal layer underneath the wax. T_he rough layer of the wire would, in principle, have greater interaction with the water as the wax layer is smoother. T_his would result in the surfactant clinging more tightly to the ring and exert a larger resistant force to the upward pull. T_he wax layer has a more hydrophobic surface [4][8]. T_his results in hydrophobic repulsion that increases the f_luid’s energy per unit of sur- face area. T_he f_luid would have a greater tendency to minimize its contact with the waxy surface than to the rougher ring surface [6][7]. As can be observed in Figure 3 and Figure 4, the values remain at a generally constant value with smaller f_luctuations. T_he signif_icantly stronger pull exerted by the non-waxy layer of wire may have contributed to similar measurements. Tap water contains impurities such as electrolytes, sediments and minerals. T_his would cause the measured surface tension of water to deviate from literature values (see Appendix). T_he experimental surface tension values are lower than literature values, especially at temperatures above 298K. T_he greatest deviation from literature value can be seen at 368K: the measured tension was 50.610 ± 1.250mN/m, whereas the value listed in the CRC Handbook was 59.87mN/m. T_he 9.260 ± 1.250mN/m dif_ference marks a signif_icant deviation. T_he general decreasing trend in Fig- ure 3 and Figure 4 may be attributed to increased thermal motion and energy of the molecules with increasing tem- perature. However, the presence of electrolytes disrupts hydrogen bonding in water molecules. Since intermolecular forces were already weakened before heating, the molecules could attain greater degree of freedom, resulting in lower than predicted surface tension. 5.4 Future Directions Discrepancy in concentration of mixture may be due to measurement of insuf_f_icient accuracy. A graduated cylinder with smaller and more accurate increments of measurement should be used in further investigations. T_he material of the ring should be switched plastic to prevent degradation of the ring's surface layer. To increase conf_idence in the uniform sizes of water drops added as weight, a Pasteur pipet should be used. When detergent solution was heated to 353K, intense bubbling occurred and the detergent was observed to undergo drastic compositional change, resulting in a more opaque and deeper green solution. T_he cause of this phenomenon was not known. It may be useful to utilize spectroscopy, generating ref_lection imaging using lasers, to detect the de- composition mechanism of the surfactant surface layer or layers [1][5]. Further studies of this surface tension of the surfactant solution and of water-surfactant mixtures should be conducted via measurement of the f_luid’s contact an- gle in a capillary tube [1][3]. Cheng and Wei (2012) 76 Conclusion We have concluded that under standard pressure condition 1 bar and 298K, the surface tension of “Palmolive Origi- nal” surfactant solution decreases linearly as temperature increases, as indicated by the weighted least square f_it γ = – 0.177 mN/(m⋅K)(x) + 94.654 mN/m, where x is temperature. When concentration was varied at constant tempera- ture, surface tension decreased linearly until a particular concentration, which is C = 50% for the non-ionic surfac- tant. Beyond that threshold concentration, the surface tension was interpreted to remain constant. T_he “hockey stick function” was used to model the trend, with the initial linear γ = – 0.565 mN/(m⋅%)(x) + 61.7 mN/m when x < 50%, and γ = 33.45 mN/m when x ≥ 50%, where x is concentration. T_his model adsorption isotherm is extremely useful in characterizing the surface properties of the surfactant solution. T_he surface tension of water was observed to be con- sistently higher than the surface tension of surfactants. T_hese model parameters allow us to make reasonable predic- tions of the mechanisms of micelle-formation and the energy at the liquid-gas and liquid-solid interface. 7 Acknowledgement We would like to thank the UBC Chemistry labs for lending us the hotplate and the Physics department for lending us various measuring equipment. Our mentor James Charbonneau has been a tremendous help throughout this process. We would also like to acknowledge our peer reviewers, Samantha Tan, Liz Geum and Gurkaran Singh, for their numerous suggestions and invaluable advice. 8 Literature Cited [1] Atta, A. M., El-Kafrawy, A. F., Abdel-Rauf, M. E., Maysour, N. E., & Gafer, A. K. Surface and thermodynamic properties of nonionic surfactants based on rosin- maleic anhydride and acrylic acid adducts. J. Dispersion Sci. Technol. 31, 567-576 (2010). [2] Bhairi, S. M., & Mohan, C. (2007). Detergents - A guide to the properties and uses of detergents in biology and biochemistry. Retrieved February 28, 2012 from ! e Wolfson Centre for Applied Structural Biology: http://wolfson.huji.ac.il/puri" cation/PDF/detergents/CALBIOCHEM-DetergentsIV.pdf [3] Billings, B. H., & Gray, D. E. (1972). American Institute of Physics handbook (3rd ed.). New York: McGraw-Hill. [4] Carazzo, D., Wohlfeil, A., & Ziegler, F. Dynamic surface tension measurement of water surfactant solutions. J. Chem. Eng. Data 54, 3092-3095 (2009). [5] Du Noüy, P. L. An interfacial tensiometer for universal use. J. Gen. Physiol. 7, 625-631 (1925). [6] Lange, N. A., & Speight, J. G. (2005). Lange's handbook of chemistry (16th ed.). New York: McGraw-Hill. [7] Liao, X., Gautam, M., & Zhu, H. J. E#ect of position isomerism on the formation and physicochemical properties of pharmaceutical co-crystals. J. Pharm. Sci. 99, 264-254 (2010). [8] Lunkenheimer, K., Lind, A., & Jost, M. Surface tension of surfactant solutions. J. Phys. Chem. B, 107, 7527-7531 (2003). [9] Salager, J.-L. (2002, December 15). Surfactants - Types and Use. Retrieved February 28, 2012 from Nanoparticles.org: http://nanoparticles.org/pdf/Salager-E300A.pdf 9 Appendix 9.1 Literature Values for Water Surface Tension Temperature Experimental Result Literature Value Table 1: Literature Values for Water Sur- face Tension from CRC Handbook, AIP Handbook, and Lange’s Handbook. T_he values are derived from three published handbooks. Highlighted values demon- strate complete agreement with experimen- tal data range. Since CRC Handbook pro- vides temperatures with increments of 2K, odd number temperatures are estimated by averaging adjacent values with common dif_ference of 1K. 273.16K is estimated to be 273.15K and 371.05K is estimated as 371.15K. T_he f_irst surface tension for 298.15K is taken from initial measurement of water surface tension at room tempera- ture and standard condition. T_he bottom value is taken during heating the substance. ºC K CRC Handbook AIP Handbook Lange’s Handbook 0 273.15 76.17 ± 1.04 75.65 75.60 75.83 5 278.15 73.87 ± 0.48 74.94 74.90 75.09 10 283.15 67.48 ± 1.69 74.22 74.22 74.36 15 288.15 70.04 ± 2.60 73.49 73.49 73.62 20 293.15 68.51 ± 2.08 72.74 72.75 72.88 25 298.15 70.04 ± 3.22 71.97 71.97 72.1469.27 ± 2.26 30 303.15 62.88 ± 0.48 71.19 71.18 71.40 35 308.15 65.44 ± 1.53 70.40 - 70.66 40 313.15 67.23 ± 1.43 69.60 69.56 69.92 45 318.15 63.65 ± 1.30 68.78 - - 50 323.15 64.16 ± 2.23 67.94 67.91 68.45 55 328.15 62.88 ± 1.30 67.10 - - 60 333.15 61.12 ± 1.11 66.24 66.18 66.97 65 338.15 65.95 ± 1.43 65.37 - - 70 343.15 58.79 ± 2.29 64.48 64.40 65.49 75 348.15 53.17 ± 2.38 63.58 - - 80 353.15 51.64 ± 2.27 62.67 62.60 64.01 85 358.15 48.82 ± 1.10 61.75 - - 90 363.15 47.29 ± 0.40 60.82 - 62.54 95 368.15 50.61 ± 1.74 59.87 - - 97.9 371.05 50.36 ± 1.25 59.30 - - Cheng and Wei (2012) 8


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