CIS-01435; No of Pages 6 Advances in Colloid and Interface Science xxx (2014) xxx–xxx
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Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces Bingquan Li, Ponisseril Somasundaran, Partha Patra ⁎ Langmuir Center for Colloids and Interfaces, Columbia University, NY 10027, United States
a r t i c l e
i n f o
Available online xxxx Keywords: Oil spreading Surfactants Self-assembled structures Tanner's law Frictional forces
a b s t r a c t Uniform spreading of oil on solid surfaces is important in many processes where proper lubrication is required and this can be controlled using surfactants. The role of oil–solid interfacial self-assembled surfactant structure (SASS) in oil spreading is examined in this study for the case of hexadecane-surfactant droplet spreading on a flat horizontal copper surface, with triphenyl phosphorothionate surfactants having varying chain lengths (0 to 9). It is shown that the frictional forces (FSASS) as determined by the SASS regulate droplet spreading rate according to surfactant chain length; surfactants with longer chains led to higher reduction in the spreading rate. The extent of such forces, FSASS, depends on the surfactant density of the evolving SASS, and specific configuration the evolving SASS exhibit as per the orientations of the surfactant chains therein. Thus, FSASS = [k1 + k2(t)] Γδ(t), where Γδ(t) is the surfactant adsorption density of SASS at time ‘t’ during evolution, and, k1 and k2(t) are the force coefficients for Γδ(t) and orientations (as a function of spreading time) of the surfactant chains respectively. As a SASS evolves/grows along with adsorption of surfactants at the spreading induced fresh interface, the k1Γδ(t) component of FSASS increases and contributes to reduction in the net spreading force (S). With a decrease in the net spreading force, the existence of a cross-over period, during which the transition of the spatial dynamics of the chains from disordered to realignment/packing induced ordered orientation occurs, has been inferred from the FSASS vs. chain length relationships. Such relationships also suggested that the rate of realignment/packing is increased progressively particularly due the realignment/packing induced decrease in the net spreading force. Therefore, the realignment process is a self-induced process, which spans a measurable period of time (several minutes), the cross-over period, during which the net spreading force decreases essentially due to such self-induced process. © 2014 Elsevier B.V. All rights reserved.
Contents 1. 2.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Imaging and analysis of oil droplet spreading . . . . . . . . . . . . . . . . 2.3. Rheological measurements . . . . . . . . . . . . . . . . . . . . . . . . 3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Effect of surfactant chain length on spreading rate . . . . . . . . . . . . . 4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Macroscopic force balance accounting for frictional forces at SASS–oil interface 5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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0 0 0 0 0 0 0 0 0 0 0 0
1. Introduction ⁎ Corresponding author. Tel.: +1 212 854 2925. E-mail address: [email protected] (P. Patra).
An understanding of the mechanisms by which oil–solid interfacial self-assembled surfactant structures (SASS)—surfactant film—impart
http://dx.doi.org/10.1016/j.cis.2014.04.004 0001-8686/© 2014 Elsevier B.V. All rights reserved.
Please cite this article as: Li B, et al, Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces, Adv Colloid Interface Sci (2014), http://dx.doi.org/10.1016/j.cis.2014.04.004
2
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specific oil spreading behavior is fundamentally important to many applications including engine oil lubrication, coating, painting, oil recovery, micro-fluidics, and drug delivery [1–6]. Depending on the concentration of surfactants and their molecular architecture (polarity of the head group, and chain length and branching), interfacial surfactant films attain form such as uniform monolayer or irregular hemicelles [7,8]. SASS formation is not necessarily a spontaneous event but structurally evolves along with adsorption of surfactants at the fresh oil– solid interface generated during spreading and, alignment/packing of the surfactants in the SASS. In spite of interference from structural and configurational dynamics associated with evolution of SASS, possibly spanning the entire spreading duration, the spreading behavior has been seen to follow Tanner's power law [9]. 3
1
1
Rðt Þ ¼ Ω10 ðσ =ηÞ10 t 10
ð1Þ
where, ‘R’ is the radius of a droplet on a surface, ‘t’ is the spreading time, ‘σ’ represents surface tension, ‘η’ refers to the droplet viscosity, and ‘Ω’ is the droplet volume. Here, the spreading behavior of the hexadecane droplet (having triphenyl phosphorothionate (TPPT) type surfactants of varying chain lengths) on a flat horizontal copper surface was studied to determine the role of the surfactant structure on spreading behavior. Self-assembly of the surfactants upon their adsorption at the solid–oil (s/o) interface and along the solid/oil/air (s/o/a) contact line can be viewed microscopically as a flexible soft SASS “tray” electrochemically glued to the interface and having wedges at the s/o/a contact line (Fig. 1). The forces (FSASS)—frictional forces at the SASS–oil interface— which vary with structural evolution are governed by surfactant density and alignment/packing of surfactants. In order to determine the progressive effects of an evolving SASS on the spreading rate (determined as n = ln (normalized base area of a droplet)/ln t, area/time), particularly with emphasis on structural evolution being unique as per surfactant structures that constitute a SASS, this study focuses on the how variations in surfactant chain lengths from 0 to 9 regulate spreading rate. Typically, for surfactants having similar head groups, adsorption density and alignment of the chains in the SASS are dependent on the surfactant chain length [10].
chain lengths [triphenyl phosphorothionate (TPPT), butylated triphenyl phosphorothionate (butylated TPPT), nonylated triphenyl phosphorothionate (nonylated TPPT)] were obtained from Ciba (Fig. 2). Solutions of these surfactants were prepared in hexadecane at desired concentrations. 2.2. Imaging and analysis of oil droplet spreading The substrate was placed on the stage of a microscope (Nikon) and a 2 μL droplet of the surfactant solution was gently placed onto a stage using a syringe and taking care to avoid any effect due to the loading impact. The ambient temperature was controlled at 25 °C. The images of the droplet during the spreading process were captured by a Hitachi CCD camera from the top and recorded by a Labview program at preset intervals. The base contact area values of the droplets were analyzed from the images with software ImageJ (National Institutes of Health). The droplet area was measured as soon as a pure hexadecane droplet was placed on the Cu metal surface. This area was accounted for in the estimation of the normalized areas of the droplets during spreading. 2.3. Rheological measurements Kinematic viscosity values of hexadecane-surfactant solutions were measured using an Anton Paar DSR rheometer. 100 mL of solution was poured into a glass cylinder and measurements were taken using a vane type probe, and at 25 °C. Hexadecane density was considered to be 0.77 g/cm3. Kinematic viscosity values were determined within the shear rate range of 0.1–100 s−1, and using Cannon viscosity standards.
2. Experimental 2.1. Materials The non-aqueous solvent used was hexadecane (N99%, Sigma). The copper metal surface of 100 nm thickness was prepared by thermal evaporation (Edwards BOC Auto 306) of 99.99% pure copper (Kurt J. Lesker Co.) from a tungsten boat followed by deposition on a silicon wafer (University Silicon) at a rate of 2 Å/s and at 5 × 10−7 Torr pressure. The surface tension of solid copper is about 1300 mN/m [11]. Triphenylphosphorothionate type surfactants having different
Hexadecane + Surfactants
FVISC V C
SASS - A Flexible Tray
FSAASSS VIS SC
Fig. 1. Illustration of the forces contributing to spreading of a hexadecane-surfactant droplet on a flat horizontal copper substrate. SASS—resembling a flexible tray (blue in color)— can be seen at the ‘substrate Cu’–droplet interface; viscous forces (FVISC) are in the spreading direction and FSASS towards the droplet center, (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Molecular structures of triphenyl phosphorothionate (TPPT), butylated triphenyl phosphorothionate (butylated TPPT), and nonylated triphenyl phosphorothionate (nonylated TPPT) surfactants.
Please cite this article as: Li B, et al, Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces, Adv Colloid Interface Sci (2014), http://dx.doi.org/10.1016/j.cis.2014.04.004
B. Li et al. / Advances in Colloid and Interface Science xxx (2014) xxx–xxx
3. Results 3.1. Effect of surfactant chain length on spreading rate The effects of TPPT surfactants having 0, 4 and 9 alkyl groups on the spreading behavior of hexadecane droplets were studied in the concentration range of 0.01 to 2 wt.%. Particle size measurement was carried out to investigate surfactant aggregation in the oil phase and surfactant aggregation was not observed in the concentration range from 0.01 to
1st min
3
2 wt.%. Ideally, it can be inferred from numerous studies that a SASS exhibits a configuration where the head groups are contact with the substrate and the chains being buried in the oil phase (Fig. 1) [7]. Fig. 3 indicated that irrespective of the surfactant concentrations in the droplets the spreading rate decreased (smaller droplet areas) with an increase in the chain length: 0 b 4 b 9. Complete wetting of a pure hexadecane droplet on a flat copper surface (surface tension 1300 mN/m) [11] was observed with the droplet areas ‘A’ scaling with time, t, as A ~ t0.2. For a droplet having TPPT at 0.01 wt.%, the spreading
26th min
51st min n = 0.2
TPPT n = 0.019
n = 0.009
n = 0.2
Butylated TPPT
n = 0.015
n = 0.009
n = 0.04
Nonlylated TPPT
n = 0.008
n≈0
Fig. 3. Optical images of hexadecane-surfactant droplets at 1st, 26th and 51st min during spreading, with droplets having varying (0.01, 0.1 and 2 wt.%) concentrations of TPPT, butylated TPPT, and nonylated TPPT. The spreading rate, ‘n’, at 51 min is shown.
Please cite this article as: Li B, et al, Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces, Adv Colloid Interface Sci (2014), http://dx.doi.org/10.1016/j.cis.2014.04.004
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rate was ‘n’ ~ 0.2 (Fig. 4a). The spreading rate decreased further at higher TPPT concentration (0.1 wt.%) and exhibited two regimes, the first regimen being faster than the second; in comparison to ‘n’ ~ 0.2 at 0.01 wt.%, ‘n’ was 0.11 in the faster regime (0th to 8th min) and ‘n’ ~ 0.019 in the slower regime (from 8th min to droplet pinning) at 0.1 wt.% TPPT (Fig. 4b). At 2 wt.% of TPPT, droplet pinning was observed in less than 1 min (Figs. 3 and 4c). The spreading rate with ‘butylated TPPT’ (4 alkyl groups) at 0.01 wt.% was similar to that of TPPT, i.e., ‘n’ ~ 0.2. With an increase in the concentration of butylated TPPT from 0.01 to 0.1 wt.% the spreading rate decreased with ‘n’ values as 0.08 and 0.015 (n ~ 0.11/0.019 for TPPT) in faster and slower
(a)
4. Discussion TPPT, 0.01%
0.5
Butylated TPPT, 0.01%
4.1. Macroscopic force balance accounting for frictional forces at SASS–oil interface
Log(Normalized Base Area)
Nonylated TPPT, 0.01%
0.4
t
0.2
The interfacial tension of either s/o (solid/oil) or o/a (oil/air) interface decreases with an increase in surfactant chain length; in particular, the s/o interfacial tension ‘σs/o’ decreases significantly with an increase in chain length [12]. The spreading power which is a parameter for the measure of wetting is determined as [13]:
0.3
t
0.2
0.04
0.1
t
0.0
S ¼ σ s=a −σ o=a −σ s=o
0.13
-0.1 0.0
0.4
0.8
1.2
1.6
2.0
Log (Time), min.
(b) 0.5
Log(Normalized Base Area)
TPPT, 0.1% Butylated TPPT, 0.1%
0.4
Nonylated TPPT, 0.1%
0.3 0.2
t
0.1
t
0.019
0.11
0.015
t
0.0
t
-0.1 0.0
0.4
0.8
1.2
0.08 1.6
2.0
Log (Time), min.
0.5 TPPT 2%
0.4
Butylated TPPT 2% Nonylated TPPT 2%
0.3 0.2 0.1 0.0 -0.1 0.0
0.4
0.8
ð2Þ
where, ‘S’ indicates spreading power, and σs/a, σo/a and σs/o indicate solid–air, oil–air and solid–oil interfacial tensions respectively. If σσs/o and σσo/adecrease with an increase in chain length, it suggests in accordance with Eq. (1) that the spreading power ‘S’ is less negative with an increase in chain length, suggesting wetting, and an increase in the spreading rate. On the contrary, a reduction in the spreading rate with an increase in chain length indicated that there exist forces that contribute to the reduction in the spreading rate which are opposite in direction of the forces which promote spreading, namely the viscous and/or capillary forces [14]. As such forces led to reduction in the spreading rate with an increase in surfactant chain length, the extent of these forces owe to chain length dependent structural forms of the SASS, and variations in ‘η’ and ‘σ’ are assumed negligible. It has been reported that self-assembled surfactant structures impart frictional forces (FSASS), and thereof, modulate the oil spreading rate [13,15,16]. Generally, in assessment of the contributions of the forces that govern droplet spreading, the capillary forces balance with the viscous forces [18,19]. S∞ þ
γθ2d ¼ F VISC 2
ð3Þ
The left hand side of the equation includes capillary forces, where γ and θd indicate interfacial tension and oil droplet contact angle respectively. The right hand side of Eq. (2) indicated forces owing to viscous forces (FVISC). In corroborating this relationship with the chain length dependent reduction in the spreading rate, balancing of the contributions from the viscous and capillary forces theoretically predict faster spreading with an increase in chain length, and thus, these forces fail to account for the observed reduction in the spreading rate. Hence, it is further clear that the contributions of the frictional forces, FSASS, during structural evolution of SASS are measurable enough to cause reduction in spreading, where the frictional forces vary according to chain length dependent SASS types and their evolving forms in the course of spreading.
(c) Log(Normalized Base Area)
spreading regimes respectively. As similar to the effect of TPPT surfactants at 2 wt.%, with butylated TPPT type surfactant, droplet pinning was observed in less than 1 min (Fig. 4c) at 2 wt.%. With nonylated TPPT (9 alkyl groups), even at a lower (0.01 wt.%) concentration, the spreading rate reduced considerably in comparison to that with TPPT or butylated-TPPT, i.e., ‘n’ values were 0.13 and 0.04 (Fig. 4b) respectively in faster and slower spreading regimes (compared to ‘n’ ~ 0.2 for both TPPT and butylated TPPT). The marked contribution of the 9 alkyl groups to the reduction in spreading rate was evident when the droplet exhibited significantly slower spreading rate (n = 0.008)—almost pinning—at lower concentration (0.1 wt.%).
1.2
1.6
2.0
Log (Time), min. Fig. 4. Spreading behavior (droplet area as a function of spreading time) of hexadecane droplets having TPPT, butylated TPPT, and nonylated TPPT type surfactants at different concentrations: (a) 0.01 wt.%, (b) 0.1 wt.% and (c) 2 wt.%.
θ2 S∞ þ γ d ¼ F VISC 2
! þ F SASS ¼ F VISC
ð4Þ
Here, Table 1 shows that with an increase in the TPPT chain length the changes in the kinematic viscosity values of hexadecanesurfactant solutions are negligible. Thus, the contributions of the chain
Please cite this article as: Li B, et al, Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces, Adv Colloid Interface Sci (2014), http://dx.doi.org/10.1016/j.cis.2014.04.004
B. Li et al. / Advances in Colloid and Interface Science xxx (2014) xxx–xxx Faster Spreading Regimen
Table 1 Kinematic viscosity of hexadecane as a function of chain-length (0–9) and concentration (0.01–2 wt.%). Kinematic viscosity (centistokes, cs) vs. surfactant concentrations 0.01 wt.%
0.10 wt.%
2 wt.%
0 4 9
4.458 4.558 4.498
4.698 4.498 4.598
5.158 5.258 5.158
Slower Spreading Regimen
FSASS, measured as: [-noil-nsurf.]
Chain length
length dependent variations in the capillary forces to the reduction in spreading are negligible, and therefore, the FVISC predominantly regulates the droplet spreading behavior. Thus, the force balance for oil spreading can be written as: ð5Þ
where ‘S’ is the spreading power. The term FSASS is negative as the direction of these forces is opposite to that of the spreading direction— viscous forces. The FSASS depends on the SASS surfactant density at the solid–oil interface and is derived as: ΔG 0 Γ δ ¼ lC 0 e RT
ð6Þ
[12],where, ‘Γδ’ denotes adsorption density, ‘l’ represents surfactant chain length and C0 as the concentration of surfactants in an oil droplet. As the interfacial area A0 (spontaneous area as soon as a droplet is placed on the copper surface) increases during spreading, the adsorption density, Γδ(t), depends on normalized (‘interfacial area’ wise) bulk surfactant concentration at time ‘t’, Ct, where Ct changes with an increase in the interfacial area ΔA as [C0 A0] / [(A0 + (ΔA)]. If ΔA is derived from Tanner's law, then ΔG ΔG 0 0 A 0 1 e RT Γ δðtÞ ¼ lC t e RT ¼ lC 0 3 10 n σ A0 þ Δ Ω10 η t
ð7Þ
As ‘Ω’ and ‘η’ values can reasonably be considered as constant here for the hexadecane-surfactant system, the ‘Ω3/10(1/η) 1/10’ term equates to a constant value K. Thus, with initial surfactant concentration as C0 and droplet area A0 at time t = 0, the adsorption density, Γδ (t), at any time ‘t’ is a function of ‘n’, σ and l as: Γ δðt Þ
2 3 ΔG 0 A0 RT 4 5 h i ¼ l C0e 1 A0 þ Δ K ðσ Þ10 t n
ð8Þ
With increase in chain length Γδ(t) is higher and correspondingly the frictional forces FSASS. Due to significantly higher Γδ(t) at higher (2 wt.%) concentration of TPPT type surfactants in a droplet, higher FSASS resulted in droplet pinning at an early stage (Fig. 4c). A similar explanation applies for spreading of droplets having lower (0.01 wt.%) surfactant concentrations, where the droplet spreading rate changed moderately due to lower adsorption density. In the intermediate concentration (~0.1 wt.%) range, the spreading rate, as shown through Figs. 4, 5 and 6, demonstrated two spreading regimes. Two spreading regimes exhibited different spreading rates, faster followed by slower. Fig. 5 shows that in either of the two spreading regimens the FSASS (represented as −Δn = (noil − nsurfactant)) from the evolving SASS is higher with an increase in chain length. After a certain period of time, from the time spreading commenced, the faster spreading rate reduced markedly, and progressively thereafter and, until an equilibrium spreading rate value had been attained. Such marked reduction in the spreading rate at certain time during spreading is not due to the spontaneous increase in the surfactant density in SASS, but, we propose that the marked
0.20
≈ [(k2) Γδ (t)) ]
0.15
0.10
0
4
8
Chain (Alkyl) Length Fig. 5. Realignment/packing induced frictional forces as a function of surfactant chain length for hexadecane droplets having TPPT type surfactants in the intermediate concentration range (0.1 wt.%).
increase in the forces that led to such reduction in the spreading rate is predominantly due to changes in the structural configuration of SASS. Such configurational changes occur through the process of realignment/packing of surfactants in the SASS, where the outcome of this process was contributive to the reduction in the spreading rate only under conducive oil spreading dynamics at the end of the faster spreading regimen. While the realignment process features surfactants attaining uniformity in terms of their spatial orientations (relative to the horizontal substrate base), in packing, the intermolecular chains tend be at closer proximity [17,18]. A few research investigations reporting the effect of SASS on oil spreading behavior infer that realignment of chains could lead to changes in the spreading rate [17]. Here, accounting for the realignment/packing of surfactant in the SASS, the frictional forces increase as: ‘k2(t)Γδ(t)’, where k2(t) is the force coefficient owing to the realignment/packing of surfactants in the SASS. Thus, under scenarios where chain length induced variations in the interfacial tensions have a negligible effect on the spreading behavior, which is seen here, the net spreading power at time ‘t’ can be written as: h i St ¼ F VISC − k1 þ k2ðtÞ Γ δðt Þ
ð9Þ
Fig. 6 shows that there exists a measurable (several minutes) period of time in the entire spreading duration during which the spreading rate, represented as ‘n’, progressively reduces to an equilibrium value.
Spreading rate Coeffcient, n
S ¼ F VISCþ ð−F SASS Þ
5
0.2
0.1
0.0 0.4
0.8
1.2
1.6
2.0
Spreading time (min), Log scale Fig. 6. Spreading rate coefficient vs. spreading time relationship demonstrates time of initiation (vertical dotted lines) and time-span of the cross-over regimes (vertical bars). The horizontal bars indicate cross-over periods for nonylated-TPPT (blue) at 0.01 wt.%, and TPPT (green) and butylated TPPT (red) at 0.1 wt.%. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Please cite this article as: Li B, et al, Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces, Adv Colloid Interface Sci (2014), http://dx.doi.org/10.1016/j.cis.2014.04.004
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The forces contributive to such reduction in the spreading rate corroborate the differences (Figs. 5 and 6) of the forces in the faster and slower spreading regimes. These forces, k2(t)Γδ(t), measured as the differences (Fig. 5) of the forces in the faster and lower spreading regimens are significantly high enough and cannot be accounted to an increase in the surfactant adsorption density, as in such a short period of time it is unlikely that there will be a flux of surfactants adsorbing onto the surface to consequence a significant increase in the frictional forces. Thus, the transitional (faster-to-slower) period, during which the FSASS increases, attributes to realignment/packing of the surfactants in SASS. For aqueous surfactant solutions, similar spreading regimes have been demonstrated, where the transitional/‘cross-over period’ is described as a molecular kinetic regime followed by a hydrodynamic regime [19–22], and according to the power law shift from t1/7 to t1/10, with an asymptotic regime corresponding to a longer relaxation time to equilibrium. Furthermore, the characteristic time at which the cross-over between the regimes occurs is of the order of seconds [19–22], much shorter than the time in this study, where, it is ~6 min for 0.01 wt.% nonylated TPPT solution and, 5 and 7 min for 0.1 wt.% TPPT and butylated TPPT respectively. The exponent ‘n’ in the power law is much smaller than either 1/7 or 1/10, i.e., 1/50. The time period spans from the commencement of the realignment/packing process to until an equilibrium state (spreading rate, ‘n’, in the slower spreading regimen) is reached. During this period, the realignment/packing induces an increase in frictional forces, k2(t)Γδ(t), which contributes to the reduction in the spreading rate until a steady value is reached. Fig. 6 shows that the extent of the cross-over period has no particular relationship with the surfactant chain length, where the extent spans several minutes (~ 6 min) and the rate (slope of the line ‘n’ vs. spreading time in the cross-over period) at which k2(t)Γδ(t) increases is similar. Such regularity also suggests that the reduction of the spreading rate in the cross-over period is less dependent on the net spreading power and, there exist other self-induced forces that govern chain realignment/packing. By following the progression of the changes in the spreading rate, which progressively decreases in the cross-over period, it can be inferred that the realignment/packing event that occurred at time ‘t’ promotes the event that occurs at time ‘t + Δt’. It is notable that the spreading rate at time ‘t + Δt’ is less that that at ‘t’. Thus, the realignment/packing event at time ‘t’, which resulted an increase in the frictional forces, k2(t)Γδ(t), contributed towards an increase in the rate of realignment/ packing in the duration Δt. Thus, an increase in the rate of realignment/ packing is likely to increase during the cross-over period until an equilibrium spreading rate is attained. Thus, realignment/packing event is a self-induced process. 5. Conclusions For spreading of oil-surfactant droplets on flat surfaces, depending on surfactant adsorption density, Γδ(t), at the oil–‘flat surface’ interface, the frictional forces (FSASS) at the ‘interfacial self-assembled surfactant structure (SASS)’–oil interface can be measurable enough over viscous (FVISC) and capillary forces to regulate the spreading behavior. Such forces increase progressively as a SASS structurally evolves along with adsorption of surfactants at the spreading induced fresh interface. The frictional forces act in a direction that is opposite to the spreading direction, and the extent of such forces at time ‘t’ during spreading can be accounted as: FSASS = [k1Γδ(t)]. In addition, the extent of such forces at any particular time during spreading also depend on the surfactant adsorption kinetics, where, for surfactants which adsorb spontaneously, e.g., amino acid based surfactants, FSASS = [k1Γδ(t)] will be measurable enough early on in spreading. Thus, the extent of
frictional forces primarily depends on the adsorption density and adsorption kinetics; accordingly, it is seen here that as the substrate affinity of surfactants having longer chains is higher the frictional forces are higher. As spreading progresses, the frictional forces which restrict spreading increase, and the effect of FVISC which promotes spreading decreases. Thus, in the entire spreading regime, depending on the relative measure of both k1Γδ(t) and FVISC, the spreading behavior in term of the spreading rate can be categorized as: 1) faster spreading rate, where FVISC is significantly higher than k1Γδ(t), which is due to lower adsorption density, 2) significantly slower spreading rate from the beginning, almost pinning behavior, where k1Γδ(t) is significantly higher than FVISC due to faster adsorption kinetics and higher adsorption density, and, 3) mixed spreading behavior, where depending on the relative values of FVISC and k1Γδ(t) the spreading rate is higher at the beginning and slower in the later stage. Depending on the droplet volume the spreading rate is likely to be regulated by the FVISC in the first regime [23], and, in the second regime, dewetting in separate regions across the s/o interface could be a possibility due to formation of SASSs in patches. For droplets exhibiting mixed spreading behavior, there exist a cross-over period during which progressive transition in the spreading rate from faster to slower occurs. At the beginning of the transition period St (net spreading power) becomes significantly less to promote realignment/packing of the surfactants/chains in the SASS. As seen here, realignment of chains is not a spontaneous event and spans several minutes, particularly for spreading of oil-surfactant droplet, during which there is a measurable increase in the frictional forces, especially owing to the realignment/packing process. The process of realignment/ packing, which is favorable under quiescent spreading dynamics, would typically include uncoiling of the chains, chains attaining similar orientations, and packing—reduction in the distances between the surfactants. A better understanding of how realignment process occurs and the steps thereof, sought further investigation.
Acknowledgements The authors are thankful to NSF I/UCR Center for Particulate and Surfactant Systems (Grant #: IIP-0749461) for supporting the research program.
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Ananthapadmanabhan KP, Goddard ED, Chandar P. Colloids Surf 1990;44:281. Biebuyck HA, Whitesides GM. Langmuir 1994;10(12):4581–7. Wasan DT, Nikolov AD, Bierwagen GP. Nature 2003;423:156. Somasundaran P, Zhang L. J Pet Sci Eng 2006;52:198. De Coninck J, de Ruijter M, Voue M. Curr Opin Colloid Interface Sci 2001;6:49–53. Monica CB, Schneidera JP. Acta Biomater 2009;5(3):817. Kavehpour HP, Ovryn B, Gareth McKinley H. Phys Rev Lett 2003;91(19):4. Martin JI, Wang ZG, Schick M. Langmuir 1996;12(20):4950–9. Tanner LH. J Phys D Appl Phys 1979;12(9):1473. Zhang R, Somasundaran P. Adv Colloid Interface Sci 2006;123–126:213–29. Brillo J, Egry I. J Mater Sci 2005;40:2213. Somasundaran P, Healy TW, Fuerstenau DW. J Phys Chem 1964;68(12):3562. de Gennes P-G. Wetting: statics and dynamics. Rev Mod Phys 1985;52(827). Bonn D, Eggers J, Indekeu J, Meunier J. Rev Mod Phys 2009;81(2):739–805. Xiao X, Hu J, Charych DH, Salmeron M. Langmuir 1996;12:235. Brewer NJ, Beake BD, Leggett GJ. Langmuir 2001;17(6):1970. Liu Y, Evans DF. Langmuir 1996;12:1235. Small DM. The Physical Chemistry of Lipids. New York: Plenum Press; 1986 [Chapter 3]. Biance AL, Clanet C, Que´re D. Phys Rev E 2004;69:016301. Dussan EBV. Annu Rev Fluid Mech 1979;11:371. Lee S, Shon YS, Colorado Jr R, Guenard RL, Lee TR, Perry SS. Langmuir 2000;16:2220. Rojas OJ, Macakova L, Blomberg E, Emmer Å, Claesson PM. Langmuir 2002;18:8085. Heine David R, Grest Gary S, Webb III Edmund B. Phys Rev Lett 2005;95:107801.
Please cite this article as: Li B, et al, Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces, Adv Colloid Interface Sci (2014), http://dx.doi.org/10.1016/j.cis.2014.04.004
Contents lists available at ScienceDirect
Advances in Colloid and Interface Science journal homepage: www.elsevier.com/locate/cis
Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces Bingquan Li, Ponisseril Somasundaran, Partha Patra ⁎ Langmuir Center for Colloids and Interfaces, Columbia University, NY 10027, United States
a r t i c l e
i n f o
Available online xxxx Keywords: Oil spreading Surfactants Self-assembled structures Tanner's law Frictional forces
a b s t r a c t Uniform spreading of oil on solid surfaces is important in many processes where proper lubrication is required and this can be controlled using surfactants. The role of oil–solid interfacial self-assembled surfactant structure (SASS) in oil spreading is examined in this study for the case of hexadecane-surfactant droplet spreading on a flat horizontal copper surface, with triphenyl phosphorothionate surfactants having varying chain lengths (0 to 9). It is shown that the frictional forces (FSASS) as determined by the SASS regulate droplet spreading rate according to surfactant chain length; surfactants with longer chains led to higher reduction in the spreading rate. The extent of such forces, FSASS, depends on the surfactant density of the evolving SASS, and specific configuration the evolving SASS exhibit as per the orientations of the surfactant chains therein. Thus, FSASS = [k1 + k2(t)] Γδ(t), where Γδ(t) is the surfactant adsorption density of SASS at time ‘t’ during evolution, and, k1 and k2(t) are the force coefficients for Γδ(t) and orientations (as a function of spreading time) of the surfactant chains respectively. As a SASS evolves/grows along with adsorption of surfactants at the spreading induced fresh interface, the k1Γδ(t) component of FSASS increases and contributes to reduction in the net spreading force (S). With a decrease in the net spreading force, the existence of a cross-over period, during which the transition of the spatial dynamics of the chains from disordered to realignment/packing induced ordered orientation occurs, has been inferred from the FSASS vs. chain length relationships. Such relationships also suggested that the rate of realignment/packing is increased progressively particularly due the realignment/packing induced decrease in the net spreading force. Therefore, the realignment process is a self-induced process, which spans a measurable period of time (several minutes), the cross-over period, during which the net spreading force decreases essentially due to such self-induced process. © 2014 Elsevier B.V. All rights reserved.
Contents 1. 2.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Imaging and analysis of oil droplet spreading . . . . . . . . . . . . . . . . 2.3. Rheological measurements . . . . . . . . . . . . . . . . . . . . . . . . 3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Effect of surfactant chain length on spreading rate . . . . . . . . . . . . . 4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Macroscopic force balance accounting for frictional forces at SASS–oil interface 5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1. Introduction ⁎ Corresponding author. Tel.: +1 212 854 2925. E-mail address: [email protected] (P. Patra).
An understanding of the mechanisms by which oil–solid interfacial self-assembled surfactant structures (SASS)—surfactant film—impart
http://dx.doi.org/10.1016/j.cis.2014.04.004 0001-8686/© 2014 Elsevier B.V. All rights reserved.
Please cite this article as: Li B, et al, Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces, Adv Colloid Interface Sci (2014), http://dx.doi.org/10.1016/j.cis.2014.04.004
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specific oil spreading behavior is fundamentally important to many applications including engine oil lubrication, coating, painting, oil recovery, micro-fluidics, and drug delivery [1–6]. Depending on the concentration of surfactants and their molecular architecture (polarity of the head group, and chain length and branching), interfacial surfactant films attain form such as uniform monolayer or irregular hemicelles [7,8]. SASS formation is not necessarily a spontaneous event but structurally evolves along with adsorption of surfactants at the fresh oil– solid interface generated during spreading and, alignment/packing of the surfactants in the SASS. In spite of interference from structural and configurational dynamics associated with evolution of SASS, possibly spanning the entire spreading duration, the spreading behavior has been seen to follow Tanner's power law [9]. 3
1
1
Rðt Þ ¼ Ω10 ðσ =ηÞ10 t 10
ð1Þ
where, ‘R’ is the radius of a droplet on a surface, ‘t’ is the spreading time, ‘σ’ represents surface tension, ‘η’ refers to the droplet viscosity, and ‘Ω’ is the droplet volume. Here, the spreading behavior of the hexadecane droplet (having triphenyl phosphorothionate (TPPT) type surfactants of varying chain lengths) on a flat horizontal copper surface was studied to determine the role of the surfactant structure on spreading behavior. Self-assembly of the surfactants upon their adsorption at the solid–oil (s/o) interface and along the solid/oil/air (s/o/a) contact line can be viewed microscopically as a flexible soft SASS “tray” electrochemically glued to the interface and having wedges at the s/o/a contact line (Fig. 1). The forces (FSASS)—frictional forces at the SASS–oil interface— which vary with structural evolution are governed by surfactant density and alignment/packing of surfactants. In order to determine the progressive effects of an evolving SASS on the spreading rate (determined as n = ln (normalized base area of a droplet)/ln t, area/time), particularly with emphasis on structural evolution being unique as per surfactant structures that constitute a SASS, this study focuses on the how variations in surfactant chain lengths from 0 to 9 regulate spreading rate. Typically, for surfactants having similar head groups, adsorption density and alignment of the chains in the SASS are dependent on the surfactant chain length [10].
chain lengths [triphenyl phosphorothionate (TPPT), butylated triphenyl phosphorothionate (butylated TPPT), nonylated triphenyl phosphorothionate (nonylated TPPT)] were obtained from Ciba (Fig. 2). Solutions of these surfactants were prepared in hexadecane at desired concentrations. 2.2. Imaging and analysis of oil droplet spreading The substrate was placed on the stage of a microscope (Nikon) and a 2 μL droplet of the surfactant solution was gently placed onto a stage using a syringe and taking care to avoid any effect due to the loading impact. The ambient temperature was controlled at 25 °C. The images of the droplet during the spreading process were captured by a Hitachi CCD camera from the top and recorded by a Labview program at preset intervals. The base contact area values of the droplets were analyzed from the images with software ImageJ (National Institutes of Health). The droplet area was measured as soon as a pure hexadecane droplet was placed on the Cu metal surface. This area was accounted for in the estimation of the normalized areas of the droplets during spreading. 2.3. Rheological measurements Kinematic viscosity values of hexadecane-surfactant solutions were measured using an Anton Paar DSR rheometer. 100 mL of solution was poured into a glass cylinder and measurements were taken using a vane type probe, and at 25 °C. Hexadecane density was considered to be 0.77 g/cm3. Kinematic viscosity values were determined within the shear rate range of 0.1–100 s−1, and using Cannon viscosity standards.
2. Experimental 2.1. Materials The non-aqueous solvent used was hexadecane (N99%, Sigma). The copper metal surface of 100 nm thickness was prepared by thermal evaporation (Edwards BOC Auto 306) of 99.99% pure copper (Kurt J. Lesker Co.) from a tungsten boat followed by deposition on a silicon wafer (University Silicon) at a rate of 2 Å/s and at 5 × 10−7 Torr pressure. The surface tension of solid copper is about 1300 mN/m [11]. Triphenylphosphorothionate type surfactants having different
Hexadecane + Surfactants
FVISC V C
SASS - A Flexible Tray
FSAASSS VIS SC
Fig. 1. Illustration of the forces contributing to spreading of a hexadecane-surfactant droplet on a flat horizontal copper substrate. SASS—resembling a flexible tray (blue in color)— can be seen at the ‘substrate Cu’–droplet interface; viscous forces (FVISC) are in the spreading direction and FSASS towards the droplet center, (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Molecular structures of triphenyl phosphorothionate (TPPT), butylated triphenyl phosphorothionate (butylated TPPT), and nonylated triphenyl phosphorothionate (nonylated TPPT) surfactants.
Please cite this article as: Li B, et al, Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces, Adv Colloid Interface Sci (2014), http://dx.doi.org/10.1016/j.cis.2014.04.004
B. Li et al. / Advances in Colloid and Interface Science xxx (2014) xxx–xxx
3. Results 3.1. Effect of surfactant chain length on spreading rate The effects of TPPT surfactants having 0, 4 and 9 alkyl groups on the spreading behavior of hexadecane droplets were studied in the concentration range of 0.01 to 2 wt.%. Particle size measurement was carried out to investigate surfactant aggregation in the oil phase and surfactant aggregation was not observed in the concentration range from 0.01 to
1st min
3
2 wt.%. Ideally, it can be inferred from numerous studies that a SASS exhibits a configuration where the head groups are contact with the substrate and the chains being buried in the oil phase (Fig. 1) [7]. Fig. 3 indicated that irrespective of the surfactant concentrations in the droplets the spreading rate decreased (smaller droplet areas) with an increase in the chain length: 0 b 4 b 9. Complete wetting of a pure hexadecane droplet on a flat copper surface (surface tension 1300 mN/m) [11] was observed with the droplet areas ‘A’ scaling with time, t, as A ~ t0.2. For a droplet having TPPT at 0.01 wt.%, the spreading
26th min
51st min n = 0.2
TPPT n = 0.019
n = 0.009
n = 0.2
Butylated TPPT
n = 0.015
n = 0.009
n = 0.04
Nonlylated TPPT
n = 0.008
n≈0
Fig. 3. Optical images of hexadecane-surfactant droplets at 1st, 26th and 51st min during spreading, with droplets having varying (0.01, 0.1 and 2 wt.%) concentrations of TPPT, butylated TPPT, and nonylated TPPT. The spreading rate, ‘n’, at 51 min is shown.
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B. Li et al. / Advances in Colloid and Interface Science xxx (2014) xxx–xxx
rate was ‘n’ ~ 0.2 (Fig. 4a). The spreading rate decreased further at higher TPPT concentration (0.1 wt.%) and exhibited two regimes, the first regimen being faster than the second; in comparison to ‘n’ ~ 0.2 at 0.01 wt.%, ‘n’ was 0.11 in the faster regime (0th to 8th min) and ‘n’ ~ 0.019 in the slower regime (from 8th min to droplet pinning) at 0.1 wt.% TPPT (Fig. 4b). At 2 wt.% of TPPT, droplet pinning was observed in less than 1 min (Figs. 3 and 4c). The spreading rate with ‘butylated TPPT’ (4 alkyl groups) at 0.01 wt.% was similar to that of TPPT, i.e., ‘n’ ~ 0.2. With an increase in the concentration of butylated TPPT from 0.01 to 0.1 wt.% the spreading rate decreased with ‘n’ values as 0.08 and 0.015 (n ~ 0.11/0.019 for TPPT) in faster and slower
(a)
4. Discussion TPPT, 0.01%
0.5
Butylated TPPT, 0.01%
4.1. Macroscopic force balance accounting for frictional forces at SASS–oil interface
Log(Normalized Base Area)
Nonylated TPPT, 0.01%
0.4
t
0.2
The interfacial tension of either s/o (solid/oil) or o/a (oil/air) interface decreases with an increase in surfactant chain length; in particular, the s/o interfacial tension ‘σs/o’ decreases significantly with an increase in chain length [12]. The spreading power which is a parameter for the measure of wetting is determined as [13]:
0.3
t
0.2
0.04
0.1
t
0.0
S ¼ σ s=a −σ o=a −σ s=o
0.13
-0.1 0.0
0.4
0.8
1.2
1.6
2.0
Log (Time), min.
(b) 0.5
Log(Normalized Base Area)
TPPT, 0.1% Butylated TPPT, 0.1%
0.4
Nonylated TPPT, 0.1%
0.3 0.2
t
0.1
t
0.019
0.11
0.015
t
0.0
t
-0.1 0.0
0.4
0.8
1.2
0.08 1.6
2.0
Log (Time), min.
0.5 TPPT 2%
0.4
Butylated TPPT 2% Nonylated TPPT 2%
0.3 0.2 0.1 0.0 -0.1 0.0
0.4
0.8
ð2Þ
where, ‘S’ indicates spreading power, and σs/a, σo/a and σs/o indicate solid–air, oil–air and solid–oil interfacial tensions respectively. If σσs/o and σσo/adecrease with an increase in chain length, it suggests in accordance with Eq. (1) that the spreading power ‘S’ is less negative with an increase in chain length, suggesting wetting, and an increase in the spreading rate. On the contrary, a reduction in the spreading rate with an increase in chain length indicated that there exist forces that contribute to the reduction in the spreading rate which are opposite in direction of the forces which promote spreading, namely the viscous and/or capillary forces [14]. As such forces led to reduction in the spreading rate with an increase in surfactant chain length, the extent of these forces owe to chain length dependent structural forms of the SASS, and variations in ‘η’ and ‘σ’ are assumed negligible. It has been reported that self-assembled surfactant structures impart frictional forces (FSASS), and thereof, modulate the oil spreading rate [13,15,16]. Generally, in assessment of the contributions of the forces that govern droplet spreading, the capillary forces balance with the viscous forces [18,19]. S∞ þ
γθ2d ¼ F VISC 2
ð3Þ
The left hand side of the equation includes capillary forces, where γ and θd indicate interfacial tension and oil droplet contact angle respectively. The right hand side of Eq. (2) indicated forces owing to viscous forces (FVISC). In corroborating this relationship with the chain length dependent reduction in the spreading rate, balancing of the contributions from the viscous and capillary forces theoretically predict faster spreading with an increase in chain length, and thus, these forces fail to account for the observed reduction in the spreading rate. Hence, it is further clear that the contributions of the frictional forces, FSASS, during structural evolution of SASS are measurable enough to cause reduction in spreading, where the frictional forces vary according to chain length dependent SASS types and their evolving forms in the course of spreading.
(c) Log(Normalized Base Area)
spreading regimes respectively. As similar to the effect of TPPT surfactants at 2 wt.%, with butylated TPPT type surfactant, droplet pinning was observed in less than 1 min (Fig. 4c) at 2 wt.%. With nonylated TPPT (9 alkyl groups), even at a lower (0.01 wt.%) concentration, the spreading rate reduced considerably in comparison to that with TPPT or butylated-TPPT, i.e., ‘n’ values were 0.13 and 0.04 (Fig. 4b) respectively in faster and slower spreading regimes (compared to ‘n’ ~ 0.2 for both TPPT and butylated TPPT). The marked contribution of the 9 alkyl groups to the reduction in spreading rate was evident when the droplet exhibited significantly slower spreading rate (n = 0.008)—almost pinning—at lower concentration (0.1 wt.%).
1.2
1.6
2.0
Log (Time), min. Fig. 4. Spreading behavior (droplet area as a function of spreading time) of hexadecane droplets having TPPT, butylated TPPT, and nonylated TPPT type surfactants at different concentrations: (a) 0.01 wt.%, (b) 0.1 wt.% and (c) 2 wt.%.
θ2 S∞ þ γ d ¼ F VISC 2
! þ F SASS ¼ F VISC
ð4Þ
Here, Table 1 shows that with an increase in the TPPT chain length the changes in the kinematic viscosity values of hexadecanesurfactant solutions are negligible. Thus, the contributions of the chain
Please cite this article as: Li B, et al, Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces, Adv Colloid Interface Sci (2014), http://dx.doi.org/10.1016/j.cis.2014.04.004
B. Li et al. / Advances in Colloid and Interface Science xxx (2014) xxx–xxx Faster Spreading Regimen
Table 1 Kinematic viscosity of hexadecane as a function of chain-length (0–9) and concentration (0.01–2 wt.%). Kinematic viscosity (centistokes, cs) vs. surfactant concentrations 0.01 wt.%
0.10 wt.%
2 wt.%
0 4 9
4.458 4.558 4.498
4.698 4.498 4.598
5.158 5.258 5.158
Slower Spreading Regimen
FSASS, measured as: [-noil-nsurf.]
Chain length
length dependent variations in the capillary forces to the reduction in spreading are negligible, and therefore, the FVISC predominantly regulates the droplet spreading behavior. Thus, the force balance for oil spreading can be written as: ð5Þ
where ‘S’ is the spreading power. The term FSASS is negative as the direction of these forces is opposite to that of the spreading direction— viscous forces. The FSASS depends on the SASS surfactant density at the solid–oil interface and is derived as: ΔG 0 Γ δ ¼ lC 0 e RT
ð6Þ
[12],where, ‘Γδ’ denotes adsorption density, ‘l’ represents surfactant chain length and C0 as the concentration of surfactants in an oil droplet. As the interfacial area A0 (spontaneous area as soon as a droplet is placed on the copper surface) increases during spreading, the adsorption density, Γδ(t), depends on normalized (‘interfacial area’ wise) bulk surfactant concentration at time ‘t’, Ct, where Ct changes with an increase in the interfacial area ΔA as [C0 A0] / [(A0 + (ΔA)]. If ΔA is derived from Tanner's law, then ΔG ΔG 0 0 A 0 1 e RT Γ δðtÞ ¼ lC t e RT ¼ lC 0 3 10 n σ A0 þ Δ Ω10 η t
ð7Þ
As ‘Ω’ and ‘η’ values can reasonably be considered as constant here for the hexadecane-surfactant system, the ‘Ω3/10(1/η) 1/10’ term equates to a constant value K. Thus, with initial surfactant concentration as C0 and droplet area A0 at time t = 0, the adsorption density, Γδ (t), at any time ‘t’ is a function of ‘n’, σ and l as: Γ δðt Þ
2 3 ΔG 0 A0 RT 4 5 h i ¼ l C0e 1 A0 þ Δ K ðσ Þ10 t n
ð8Þ
With increase in chain length Γδ(t) is higher and correspondingly the frictional forces FSASS. Due to significantly higher Γδ(t) at higher (2 wt.%) concentration of TPPT type surfactants in a droplet, higher FSASS resulted in droplet pinning at an early stage (Fig. 4c). A similar explanation applies for spreading of droplets having lower (0.01 wt.%) surfactant concentrations, where the droplet spreading rate changed moderately due to lower adsorption density. In the intermediate concentration (~0.1 wt.%) range, the spreading rate, as shown through Figs. 4, 5 and 6, demonstrated two spreading regimes. Two spreading regimes exhibited different spreading rates, faster followed by slower. Fig. 5 shows that in either of the two spreading regimens the FSASS (represented as −Δn = (noil − nsurfactant)) from the evolving SASS is higher with an increase in chain length. After a certain period of time, from the time spreading commenced, the faster spreading rate reduced markedly, and progressively thereafter and, until an equilibrium spreading rate value had been attained. Such marked reduction in the spreading rate at certain time during spreading is not due to the spontaneous increase in the surfactant density in SASS, but, we propose that the marked
0.20
≈ [(k2) Γδ (t)) ]
0.15
0.10
0
4
8
Chain (Alkyl) Length Fig. 5. Realignment/packing induced frictional forces as a function of surfactant chain length for hexadecane droplets having TPPT type surfactants in the intermediate concentration range (0.1 wt.%).
increase in the forces that led to such reduction in the spreading rate is predominantly due to changes in the structural configuration of SASS. Such configurational changes occur through the process of realignment/packing of surfactants in the SASS, where the outcome of this process was contributive to the reduction in the spreading rate only under conducive oil spreading dynamics at the end of the faster spreading regimen. While the realignment process features surfactants attaining uniformity in terms of their spatial orientations (relative to the horizontal substrate base), in packing, the intermolecular chains tend be at closer proximity [17,18]. A few research investigations reporting the effect of SASS on oil spreading behavior infer that realignment of chains could lead to changes in the spreading rate [17]. Here, accounting for the realignment/packing of surfactant in the SASS, the frictional forces increase as: ‘k2(t)Γδ(t)’, where k2(t) is the force coefficient owing to the realignment/packing of surfactants in the SASS. Thus, under scenarios where chain length induced variations in the interfacial tensions have a negligible effect on the spreading behavior, which is seen here, the net spreading power at time ‘t’ can be written as: h i St ¼ F VISC − k1 þ k2ðtÞ Γ δðt Þ
ð9Þ
Fig. 6 shows that there exists a measurable (several minutes) period of time in the entire spreading duration during which the spreading rate, represented as ‘n’, progressively reduces to an equilibrium value.
Spreading rate Coeffcient, n
S ¼ F VISCþ ð−F SASS Þ
5
0.2
0.1
0.0 0.4
0.8
1.2
1.6
2.0
Spreading time (min), Log scale Fig. 6. Spreading rate coefficient vs. spreading time relationship demonstrates time of initiation (vertical dotted lines) and time-span of the cross-over regimes (vertical bars). The horizontal bars indicate cross-over periods for nonylated-TPPT (blue) at 0.01 wt.%, and TPPT (green) and butylated TPPT (red) at 0.1 wt.%. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Please cite this article as: Li B, et al, Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces, Adv Colloid Interface Sci (2014), http://dx.doi.org/10.1016/j.cis.2014.04.004
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The forces contributive to such reduction in the spreading rate corroborate the differences (Figs. 5 and 6) of the forces in the faster and slower spreading regimes. These forces, k2(t)Γδ(t), measured as the differences (Fig. 5) of the forces in the faster and lower spreading regimens are significantly high enough and cannot be accounted to an increase in the surfactant adsorption density, as in such a short period of time it is unlikely that there will be a flux of surfactants adsorbing onto the surface to consequence a significant increase in the frictional forces. Thus, the transitional (faster-to-slower) period, during which the FSASS increases, attributes to realignment/packing of the surfactants in SASS. For aqueous surfactant solutions, similar spreading regimes have been demonstrated, where the transitional/‘cross-over period’ is described as a molecular kinetic regime followed by a hydrodynamic regime [19–22], and according to the power law shift from t1/7 to t1/10, with an asymptotic regime corresponding to a longer relaxation time to equilibrium. Furthermore, the characteristic time at which the cross-over between the regimes occurs is of the order of seconds [19–22], much shorter than the time in this study, where, it is ~6 min for 0.01 wt.% nonylated TPPT solution and, 5 and 7 min for 0.1 wt.% TPPT and butylated TPPT respectively. The exponent ‘n’ in the power law is much smaller than either 1/7 or 1/10, i.e., 1/50. The time period spans from the commencement of the realignment/packing process to until an equilibrium state (spreading rate, ‘n’, in the slower spreading regimen) is reached. During this period, the realignment/packing induces an increase in frictional forces, k2(t)Γδ(t), which contributes to the reduction in the spreading rate until a steady value is reached. Fig. 6 shows that the extent of the cross-over period has no particular relationship with the surfactant chain length, where the extent spans several minutes (~ 6 min) and the rate (slope of the line ‘n’ vs. spreading time in the cross-over period) at which k2(t)Γδ(t) increases is similar. Such regularity also suggests that the reduction of the spreading rate in the cross-over period is less dependent on the net spreading power and, there exist other self-induced forces that govern chain realignment/packing. By following the progression of the changes in the spreading rate, which progressively decreases in the cross-over period, it can be inferred that the realignment/packing event that occurred at time ‘t’ promotes the event that occurs at time ‘t + Δt’. It is notable that the spreading rate at time ‘t + Δt’ is less that that at ‘t’. Thus, the realignment/packing event at time ‘t’, which resulted an increase in the frictional forces, k2(t)Γδ(t), contributed towards an increase in the rate of realignment/ packing in the duration Δt. Thus, an increase in the rate of realignment/ packing is likely to increase during the cross-over period until an equilibrium spreading rate is attained. Thus, realignment/packing event is a self-induced process. 5. Conclusions For spreading of oil-surfactant droplets on flat surfaces, depending on surfactant adsorption density, Γδ(t), at the oil–‘flat surface’ interface, the frictional forces (FSASS) at the ‘interfacial self-assembled surfactant structure (SASS)’–oil interface can be measurable enough over viscous (FVISC) and capillary forces to regulate the spreading behavior. Such forces increase progressively as a SASS structurally evolves along with adsorption of surfactants at the spreading induced fresh interface. The frictional forces act in a direction that is opposite to the spreading direction, and the extent of such forces at time ‘t’ during spreading can be accounted as: FSASS = [k1Γδ(t)]. In addition, the extent of such forces at any particular time during spreading also depend on the surfactant adsorption kinetics, where, for surfactants which adsorb spontaneously, e.g., amino acid based surfactants, FSASS = [k1Γδ(t)] will be measurable enough early on in spreading. Thus, the extent of
frictional forces primarily depends on the adsorption density and adsorption kinetics; accordingly, it is seen here that as the substrate affinity of surfactants having longer chains is higher the frictional forces are higher. As spreading progresses, the frictional forces which restrict spreading increase, and the effect of FVISC which promotes spreading decreases. Thus, in the entire spreading regime, depending on the relative measure of both k1Γδ(t) and FVISC, the spreading behavior in term of the spreading rate can be categorized as: 1) faster spreading rate, where FVISC is significantly higher than k1Γδ(t), which is due to lower adsorption density, 2) significantly slower spreading rate from the beginning, almost pinning behavior, where k1Γδ(t) is significantly higher than FVISC due to faster adsorption kinetics and higher adsorption density, and, 3) mixed spreading behavior, where depending on the relative values of FVISC and k1Γδ(t) the spreading rate is higher at the beginning and slower in the later stage. Depending on the droplet volume the spreading rate is likely to be regulated by the FVISC in the first regime [23], and, in the second regime, dewetting in separate regions across the s/o interface could be a possibility due to formation of SASSs in patches. For droplets exhibiting mixed spreading behavior, there exist a cross-over period during which progressive transition in the spreading rate from faster to slower occurs. At the beginning of the transition period St (net spreading power) becomes significantly less to promote realignment/packing of the surfactants/chains in the SASS. As seen here, realignment of chains is not a spontaneous event and spans several minutes, particularly for spreading of oil-surfactant droplet, during which there is a measurable increase in the frictional forces, especially owing to the realignment/packing process. The process of realignment/ packing, which is favorable under quiescent spreading dynamics, would typically include uncoiling of the chains, chains attaining similar orientations, and packing—reduction in the distances between the surfactants. A better understanding of how realignment process occurs and the steps thereof, sought further investigation.
Acknowledgements The authors are thankful to NSF I/UCR Center for Particulate and Surfactant Systems (Grant #: IIP-0749461) for supporting the research program.
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Please cite this article as: Li B, et al, Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces, Adv Colloid Interface Sci (2014), http://dx.doi.org/10.1016/j.cis.2014.04.004
