The dilational modulus (E) is a vital parameter in industrial applications involving protein films as it quantifies the rigidity of an adsorbed film and provides insights into their mechanical characteristics and functionality. However, the influence of surface area (SA) fluctuation and the effect of rapid-forced perturbation (substantial and rapid SA change) on the E of a protein film is not well-understood. Moreover, there is limited information about the effect of bulk concentration on E. Such gaps in the literature can negatively impact industrial operations.
This study examined how E of an adsorbed protein film, from a clean air-water interface to a saturated film, is affected by periodic fluctuations in the SA, rapid-forced perturbations and the bulk concentration of the solution. The model proteins used were bovine serum albumin (BSA) and human serum albumin (HSA). The E was evaluated by analyzing relaxations of surface tension (ST) and SA, acquired using a pendant bubble tensiometer.
The data revealed that a large fluctuation in SA affected the E: a distinct peak and minima in E detected at the onset and end, respectively (at ΔA/A > ~3%, oscillation frequency, f = 0.3 – 1.1 mHz for adsorbed BSA/HSA films). In contrast, a comparatively smaller SA fluctuation caused only a slight variation in E.
At the latter stages of adsorption, the pendant bubble was subjected to large, forced perturbations (rapid compression-expansion). The data revealed that such perturbation led to a rise in E, exhibiting a distinctly high value after a rapid compression, followed by a subsequent decrease to a distinctly low E.
The variation in E of a saturated BSA/HSA film (Esat) was also examined at a wide concentration range. An increase in CHSA [0.052 – 1 (10-10 mol/cm3)] led to an initial increase on Esat (~20 – 50 mN/m). At further increase in CHSA (>1X10-10 mol/cm3), Esat remained relatively constant at ~50 mN/m albeit minor fluctuations. A similar tendency was observed for the Esat¬ of a BSA film, showing an initial increase (~20 – 45 mN/m) as CBSA increased [0.052 – 6 (10-10 mol/cm3)], and later oscillating between 40 – 50 mN/m (at CBSA >6X10-10 mol/cm3). A preliminary study on LYS films indicated that their Esat is higher than those of BSA and HSA, oscillating between ~60 – 85 mN/m at CLYS = 0.3 – 500 (10-10 mol/cm3), although showing a large variation and no clear tendency in Esat upon increasing CLYS. Further study is needed to confirm these observations.
Additionally, a preliminary study on polyacrylic acid (PAA) films was conducted, wherein the data revealed that it takes a long time to reach the Esat of the adsorbed polymer film. Besides, both Esat and equilibrium- ST increase with PAA MW.

References
[1] M.J. Rosen. Surfactants and interfacial phenomena, John Wiley & Sons, New York, 1978.
[2] D. Myer s, Surfaces, interfaces, and colloids, John Wiley & Sons, Inc., New York, USA, 1999.
[3] C. I. Branden, J. Tooze, Introduction to protein structure, CRC Press, United States, 2012.
[4] D. Whitford. Proteins: structure and function, John Wiley & Sons, West Sussex. 2005.
[5] G. Walsh. Proteins biochemistry and biotechnology. 2nd ed., Wiley Blackwell, West Sussex, 2014.
[6] LabXchange. Protein. Retrieved May 14, 2023, from https://www.labxchange.org/library/items/lb:LabXchange:06368646:lx_image:1
[7] O. Becconi, E. Ahlstrand, A. Salis, R. Friedman, Protein-ion interactions: simulations of bovine serum albumin in physiological solutions of NaCl, KCl and LiCl. Israel Journal of Chemistry, 57 (2017) 403 – 412.
[8] D. Charbonneau, M. Beauregard, H.-A. Tajmir-Riahi,. Structural analysis of human serum albumin complexes with cationic lipids. The Journal of Physical Chemistry B, 113 (6) (2009) 1777 – 1784.
[9] F. Yang, Y. Zhang, H. Liang, Interactive association of drugs binding to human serum albumin. International Journal of Molecular Sciences, 15 (3) (2014) 3580 – 3595.
[10] M. S. Weiss, G.J. Palm, R. Hilgenfeld, Crystallization, structure solution and refinement of hen egg-white lysozyme at pH 8.0 in the presence of MPD. Acta Crystallographica Section D Biological Crystallography, 56 (8) (2000) 952 – 958.
[11] J.R. Hunter, P.K. Kilpatrick, R.G. Carbonell, Lysozyme adsorption at the air/water interface. J. Colloid Interface Sci., 137 (1990) 462 – 482.
[12] P.A. Kralchevsky, K. Nagayama, Surface bending moment and curvature elastic moduli, in: K. Nagayama, Particles at fluids interfaces and membranes attachment of colloid particles and proteins to interfaces and formation of two-dimensional arrays. Elsevier BV, 2001: pp. 105 – 136.
[13] J.T. Carl Ivar Brande. Introduction to protein structure. 2nd ed., Garland Science, New York, 1998.
[14] LabXchange. The 20 Amino Acids Have Diverse Properties. Retrieved May 13, 2023, from https://www.labxchange.org/library/pathway/lx-pathway:573b19de-1dda-48de-b82c-7cf4c3524f3c/items/lx-pb:573b19de-1dda-48de-b82c-7cf4c3524f3c:html:4f257f77
[15] A.R .Nesarikar, Rheology of polymer blend liquid-liquid phase separation. Macromolecules, 28 (1995) 7202 – 7207.
[16] T.D. Gurkov, P.A. Kralchevsky. Surface tension and surface energy of curved interfaces and membranes. Colloid Surface, 47 (1990) 45 – 68.
[17] J.W. Gibbs, The scientific papers. Vol. 1, Thermodynamics, Dover Publications Inc., New York, 1961.
[18] L. Pauling, R.B. Corey, H.R. Branson. The structure of proteins; two hydrogen-bonded helical configurations of the polypeptide chain. P. Natl. Acad. Sci. U. S. A., 37 (4) (1951) 205 – 211.
[19] R. Miller, L. Liggieri, Interfacial rheology. 2nd ed. CRC Press, London, 2009.
[20] L. de Souza Soares, J.T. de Faria, M.L. Amorim, J.M. de Araujo, L.A. Minim, J.S. dos Reis Coimbra, A.V.N. de Carvalho, E.B. de Oliveria, Rheological and physicochemical studies on emulsions formulated with chitosan previously dispersed in aqueous solutions of lactic acid. Food biophys., 12 (2017) 109 – 118.
[21] C. Gallegos, J. Franco, P. Partal. Rheology of food dispersions, Bristish Society of Rheology Place, United Kingdom, 2004.
[22] A.O. Gbadamosi, R. Junin, M.A. Manan, A. Agi, J.O. Oseh, J. Usman, Effect of aluminium oxide nanoparticles on oilfield polyacrylamide: Rheology, interfacial tension, wettability and oil displacement studies. J. Mol. Liq., 296 (2019) 111863.
[23] D. Weaire, The rheology of foam. Curr. Opin. Colloid Interface Sci., 13 (3) (2008) 171 – 176.
[24] H.A Barnes, Rheology of emulsions - a review. Colloid Surface A: Physicochem. Eng. Asp., 91 (1994) 89 – 95.
[25] X. Zhang, Z. Wang, K. Wang, J.A. Reyes-Labarta, J. Gao, D. Xu, Y. Wang, Liquid-liquid phase equilibrium and interaction exploration for separation of azeotrope (2,2,3,3-tetrafluoro-1-propanol + water) with two imidazolium-based ionic liquids. J. Mol. Liq., 300 (2020) 112266.
[26] J. Benjamins, A Cagna, E.H. Lucassen-Reynders, Viscoelastic properties of triacylglycerol/water interfaces covered by proteins. Colloid Surface A: Physicochem. Eng. Asp., 114 (1996) 245 – 254.
[27] B.A. Noskov, A.A. Mikhailovskaya, S.Y. Lin, G. Loglio, R. Miller. Bovine serum albumin unfolding at the air/water interface as studied by dilational surface rheology. Langmuir, 26 (2010) 17225 – 17231.
[28] J.W. Gibbs, Collected works, Vol. 1, Longmans, New York, 1928.
[29] J. Benjamins, A. Cagna, E.H. Lucassen-Reynders, Viscoelastic properties of triacylglycerol/water interfaces covered by proteins. Colloid Surface A: Physicochem. Eng. Asp., 114 (1996) 245 – 254.
[30] V.I. Kovalchuk, E.V. Aksenenko, D.V. Trukhin, A.V. Makievski, V.B. Fainerman, R. Miller, Effect of amplitude on the surface dilational visco-elasticity of protein solutions. Colloid Interface, 2 (2018) 57.
[31] E.H. Lucassen-Reynders, Interfacial viscoelasticity in emulsions and foams. J. Food Struct., 12 (1993) 1 – 12.
[32] N.A. Alexandrov, K.G. Marinova, T.D. Gurkov, K.D. Danov, .PA. Kralchevsky, S.D. Stoyanov, T.B.J. Blijdenstein, L.N. Arnaudov, E.G. Palan, A. Lips, Interfacial layers from the protein HFBII hydrophobin: dynamic surface tension, dilatational elasticity and relaxation times. J. Colloid Interface Sci., 375 (2012) 296 – 306.
[33] J.T. Petkov, T.D. Gurkov, B.E. Campbell, R.P. Borwankar, Dilatational and shear elasticity of gel-like protein layers on air/water interface. Langmuir, 16 (2000) 3703 – 3711.
[34] J. Lucassen, M. van Den Tempel, Longitudinal waves on visco-elastic surfaces. J. Colloid Interface Sci., 41 (1972) 491 – 498.
[35] C. Lemaire, D. Langevin, Longitudinal surface waves at liquid interfaces: measurement of monolayer viscoelasticity. Colloid Surface, 65 (1992) 101 – 112.
[36] F. Ravera, G. Loglio, V.I. Kovalchuk, Interfacial dilational rheology by oscillating bubble/drop methods. Curr. Opin. Colloid Interface Sci., 15 (2010) 217 – 228.
[37] N. Mucic, A. Javadi, N.M. Kovalchuk, E.V. Aksenenko, R. Miller, Dynamics of interfacial layers—experimental feasibilities of adsorption kinetics and dilational rheology. Adv. Colloid Interface Sci., 168 (2011) 167 – 178.
[38] M. Karbaschi, M. Lotfi, J. Krägel, A. Javadi, D. Bastani, R. Miller, Rheology of interfacial layers. Curr. Opin. Colloid Interface Sci., 19 (2014) 514 – 519.
[39] B.A. Noskov, A.V. Akentiev, A.Y. Bilibin, I.M. Zorin, R. Miller, Dilational surface viscoelasticity of polymer solutions. Adv. Colloid Interface Sci., 104 (2003) 245 – 271.
[40] P. Cicuta, I. Hopkinson, Recent developments of surface light scattering as a tool for optical-rheology of polymer monolayers. Colloids Surf A Physicochem Eng Asp., 233 (2004) 97 – 107.
[41] W.C. Tseng, R.Y. Tsay, T.T.Y. Le, S. Hussain, B.A. Noskov, A. Akentiev, H.H. Yeh, S.Y. Lin, Evaluation of the dilational modulus of protein films by pendant bubble tensiometry. J. Mol Liq., 349 (2022) 118113.
[42] E.H. Lucassen-Reynders, Interfacial viscoelasticity in emulsions and foams. J. Food Struct., 12 (1993) 1 – 12.
[43] B.A. Noskov, A.A. Mikhailovskaya, S.Y. Lin, G. Loglio, R. Miller, Bovine serum albumin unfolding at the air/water interface as studied by dilational surface rheology. Langmuir, 26 (2010) 17225 – 17231.
[44] G. Walsh, Proteins biochemistry and biotechnology, Wiley Blackwell, West Sussex, 2014.
[45] Le Thi Yen Thu, A study on the dilatational modulus and adsorption kinetics of bovine serum albumin. Digital, National Taiwan University of Science and Technology, 2022.
[46] S.Y. Lin, H.-F. Hwang, Measurement of low interfacial tension by pendant drop digitization. Langmuir, 10 (1194) 4703 – 4709.
[47] M.E. Leser, S. Acquistapace, A. Cagna, A.V. Makievski, R. Miller, Ideal and nonideal mixing effects of amino acid based-surfactant on interfacial rheology and foam properties. Colloids Surfaces A Physicochem. Eng. Asp., 261 (2005) 25 – 28.
[48] A.I. Rusanov, V.A. Prokhorov, Interfacial tensiometry, vol. 3, 1st ed., Elsevier, 1996.
[49] T. Thi-Yen Le, S. Hussain, R.Y. Tsay, S.Y. Lin, On the adsorption kinetics of bovine serum albumin at the air–water interface. J. Mol Liq., 353 (2022) 118813.
[50] H.Y. Wang, Influence of oleic acid and electrolyte on the interfacial dilational properties of surfactant/polymer systems at the decane-water interface. J. Dispers. Sci. Technol., 31 (2010) 1658 – 1666.
[51] J. Lucassen, Dynamic dilational properties of composite surfaces. Colloids and Surfaces, 65 (1992) 139 – 149.
[52] P. Walstra, Physical Chemistry of Foods, CRC Press, Boca Raton, 2002.
[53] C. Gicquaud, J.P. Chauvet, G. Grenier, P. Tancrède, G. Coulombe, Adsorption of actin at the air-water interface: A monolayer study. Biopolymers, 70 (2003) 289 – 296.
[54] M. Deleu, G. Vaca-Medina, J.F. Fabre, J. Roïz, R.Valentin, Z. Mouloungui, Interfacial properties of oleosins and phospholipids from rapeseed for the stability of oil bodies in aqueous medium. Colloids Surf. B Biointerfaces, 80 (2010) 125 – 132.
[55] S. A. Roberts, I. W. Kellaway, K.M.G. Taylor, B. Warburton, K. Peters, Combined surface pressure−interfacial shear rheology study of the effect of pH on the adsorption of proteins at the air−water interface. Langmuir, 21 (2005) 7342 – 7348.
[56] F. Ravera, K. Dziza, E. Santini, L. Cristofolini, L. Liggieri, Emulsification and emulsion stability: the role of the interfacial properties. Adv. Colloid Interface Sci., 288 (2021) 102344.
[57] H.Q. Sun, L. Zhang, Z.Q. Li, L. Zhang, L. Luo, S. Zhao, Interfacial dilational rheology related to enhance oil recovery. Soft Matter., 7 (2011) 7601.
[58] A. Kessel, N, Ben-Tal, Introduction to proteins: structure, function, and motion. Second Edition, Chapman and Hall/CRC, 2018.
[59] A.G. Bykov, S.Y. Lin, G. Loglio, R. Miller, B.A. Noskov, Kinetics of Adsorption Layer Formation in Solutions of Polyacid/Surfactant Complexes. J. of Phys. Chem. C., 113 (2009) 5664 – 5671.
[60] A.G. Bykov, S.Y. Lin, G. Loglio, V.V. Lyadinskaya, R. Miller, B.A. Noskov, Impact of surfactant chain length on dynamic surface properties of alkyltrimethylammonium bromide/polyacrylic acid solutions. Colloids and Surfaces A: Physicochem. Eng. Aspects, 354 (2010) 382 – 389.
[61] L. Aricov, H. Petkova, D. Arabadzhieva, A. Iovescu, E. Mileva, K. Khristov, G. Stinga, C.F. Mihailescu, D.F. Anghel, R. Todorov, Aqueous solutions of associative poly(acrylates): Bulk and interfacial properties. Colloids and Surfaces A: Physicochem. Eng. Aspects, 505 (2016) 138 – 149.
[62] A.Y. Gyurova, S. Halacheva, E. Mileva, Aqueous solutions of random poly(methyl methacrylate-co-acrylic acid): effect of the acrylic acid content. RSC Advances, 7 (2017) 13372 – 13382.
[63] A. Diez-Pascual, F. Monroy, F. Ortega, R. Rubio, R. Miller, B. Noskov, Adsorption of Water-Soluble Polymers with Surfactant Character. Dilational Viscoelasticity. Langmuir, 23 (2007) 3802 – 3808.
[64] S. Hussain, J.E.M. Rivas, W.C. Tseng, R.Y. Tsay, B. Noskov, G. Loglio, S.Y. Lin, Measurement of Dilational Modulus of an Adsorbed BSA Film Using Pendant Bubble Tensiometry: From a Clean Interface to Saturation. Coll. Interf., 8 (2024) 4.
[65] T.T.Y. Le, S. Hussain, R.Y. Tsay, B. Noskov, A. Akentiev, S.Y. Lin, On the equilibrium surface tension of aqueous protein solutions – Bovine serum albumin. J. Mol. Liq. 347 (2022) 118305.
[66] V.N. Tran, J.E.M. Rivas, S. Hussain, W.C. Tseng, A. Akentiev, B. Noskov, G. Loglio, S.Y. Lin, A comparison of surface properties for bovine serum albumin and human serum albumin – Dynamic/equilibrium surface tension and dilational modulus. J. Mol. Liq. 391(2023) 123285.
[67] J.E.M. Rivas, S. Hussain, W.C. Tseng, B. Noskov, S.Y. Lin, A study on the dilational modulus of adsorbed globular protein films – Under a near periodic area fluctuation and rapid surface perturbation. J. Taiwan Inst. Chem. Eng., 155 (2024) 105288.
[68] V.G. Babak, J. Desbrieres, V.E. Tikhonov, Dynamic surface tension and dilational viscoelasticity of adsorption layers of a hydrophobically modified chitosan. Colloids Surf A: Physicochem Eng Asp. 255 (1-3) (2005) 119-130.
[69] J. Kokelaar, A. Prins, M. De Gee, A new method for measuring the surface dilational modulus of a liquid. J Colloid Interf Sci. 146(2) (1991) 507-511.
[70] Sheng-Hsiang Hung, "牛血清蛋白之表面活性和界面擴張模量-磷酸鹽緩衝溶液濃度效應 The effect of phosphate buffer concentration on the surface activity and dilatational rheology of bovine serum albumin," Hardcover, National Taiwan University of Science and Technology, 2022.
[71] Tran Van Nho, "Measurement of surface tension and dilational modulus of aqueous human serum albumin solution," Hardcover, National Taiwan University of Science and Technology, 2022.