Spreading Dynamics of Molten Polymer Drops on Glass Substrates

Subscriber access provided by Warwick University Library

Article

Spreading Dynamics of Molten Polymer Drops on Glass Substrates Yichuan Zhang, Carlos A. Fuentes, Robin Koekoekx, Christian Clasen, Aart Willem van Vuure, Joel De Coninck, and David Seveno Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b01500 • Publication Date (Web): 02 Aug 2017 Downloaded from http://pubs.acs.org on August 3, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Spreading Dynamics of Molten Polymer Drops on Glass Substrates Yichuan Zhang,*,†,‡ Carlos A. Fuentes,† Robin Koekoekx,§ Christian Clasen,§ Aart W. Van Vuure,† Joël De Coninck,‡ and David Seveno† †

Department of Materials Engineering, KU Leuven, 3001 Leuven, Belgium

‡

Laboratory of Surface and Interfacial Physics, Université de Mons, 7000 Mons,

Belgium §

Department of Chemical Engineering, KU Leuven, 3001 Leuven, Belgium

ABSTRACT: Wetting dynamics drive numerous processes involving liquids in contact with solid substrates with a wide range of geometries. The spreading dynamics of organic liquids and liquid metals at, respectively, room temperature and above 1000 °C have been studied extensively, both experimentally and numerically. However, almost no attention has been paid to the wetting behavior of molten drops of thermoplastic polymers, despite its importance, for example, in the processing of fiber-reinforced polymer composites. Indeed, the ability of classical theories of dynamic wetting, i.e. the hydrodynamic and the molecular-kinetic theories, to model these complex liquids is unknown. We have therefore investigated the spreading dynamics on glass, over temperatures between 200 and 260°C, of two thermoplastics: polypropylene (PP) and poly(vinylidene fluoride) (PVDF). PP and PVDF showed, respectively, the highest and lowest slip lengths due to their different interactions with the glass substrate. The jump lengths of PP and PVDF are comparable with their 1

ACS Paragon Plus Environment

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Kuhn segment lengths, suggesting that the wetting process of these polymers is mediated by segmental displacements. The present work not only provides evidence of the suitability of the classical models to model dynamic wetting of molten polymers, but also advances our understanding of the wetting dynamics of molten thermoplastics at the liquid/solid interface.

INTRODUCTION Numerous modern technologies are dependent on the precise control of liquid spreading, such as the application of adhesives, painting and oil recovery as the movement of a liquid front often controls their efficiency and stability.1-4 As a consequence, spreading phenomena have been studied extensively, both from theoretical and experimental aspects.5-8 To date, the spreading dynamics of both classical liquids (water and organic liquids) and liquid metals at respectively room temperature and temperature above 1000°C are well documented.9-11 However, compared to classical liquids and liquid metals, little attention has been paid to the wetting behaviors of molten thermoplastic polymers despites its importance, for example, in the processing of fiber-reinforced polymer composites.12 The root of this issue might be due to the experimental difficulties associated with the manipulation of high viscous molten polymer liquids, to their sensitivity to temperature, and to the precise control of the environment.

2


Page 2 of 28

Page 3 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

To describe the dynamics of wetting, two main different theoretical approaches have been proposed: the hydrodynamic approach (HD) and the molecular-kinetic theory (MKT), which differ from each other mostly in the consideration of the dominant channel of dissipation.2,3,5,6 The first approach emphasizes the dissipation due to viscous flows generated in the core of the spreading drop, and has been scrutinized by many researchers during the last several decades.13-16 In contrast to the HD approach, the MKT proposed by Blake and Hayes17 concentrates on the dissipative processes occurring in the vicinity of the advancing contact line. This prediction has also been successfully tested against numerous experimental and numerical liquid/solid systems.3,5,10,18 Yet, to our knowledge, there is no knowledge about the relevancy of the HD approach and the MKT to model the behavior of molten thermoplastic polymers. Actually, the slip length at the microscale and the contact line friction at the molecular scale, obtained from the HD approach and MKT respectively, can provide a comprehensive basis for understanding and elucidating the flow behaviors of polymer melts during processing. This is important for controlling the structural evolution and suppressing unstable surface defects (such as sharkskin commonly observed in polymer extrudates) of polymer products.19-21 This work therefore investigates the spreading dynamics of two typical thermoplastics, polypropylene (PP) and polyvinylidene fluoride (PVDF) on clean glass substrates. These polymers were chosen based on the fact that they should have different physical interactions with this substrate, and are commonly used to process glass fiber-reinforced polymers. The PP/glass substrate interaction should be 3


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

dominated by relatively weak van der Waals interaction. In the case of PVDF, additionally to the van der Waals forces, many hydrogen bonds can be created with the OH groups on the substrate, owing to the electronegativity of the fluorine groups.22

The present study checks the reliability of the classical HD approach and

MKT to model the spreading dynamics of highly viscous molten polymer liquids, sheds light on the physical properties of the liquid/solid interface with the overall objective to clarify our understanding of the wetting dynamics of molten thermoplastics, and will finally identify ways to better engineer the glass/polymer interface.

MATERIALS AND METHODOLOGY Materials. The materials used in this work are glass slide, PP and PVDF polymers. The glass slides were obtained from Marienfeld, Germany. PP is a commercial isotactic PP (515A) with a number average molecular weight of 43×103 g/mol (Sabic, Germany). PVDF is also a commercial grade (Solef 1008) with a number average molecular weight of 114 ×103 g/mol, and was provided by Solvay, Belgium. The melt flow rates for PP and PVDF are respectively 24 g/10min and 8 g/10 min at 230 °C and 2.16 kg. All polymers were obtained in the form of pellets and used without any additional purification. Cleaning of Glass Substrates. Prior to the spreading experiments, the glass slides were first submerged in sulfuric acid at 100 °C for 40 minutes, then washed with demineralized water. Afterwards, glass slides were submerged in a Piranha solution (a 4


Page 4 of 28

Page 5 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

mixture of sulfuric acid and hydrogen peroxide with a volume ratio of 3:1) at 60 °C for 40 minutes.23 Finally, these glass slides were rinsed abundantly with purified water and stored in ultrapure water for avoiding environmental organic contamination.24 After this cleaning procedure, the glass surface becomes highly hydrophilic due to the exposed hydroxyl groups. Rheological Measurements. The rheological measurements were performed using an Advanced Rheological Extension System (ARES, TA Instruments, USA). A parallel-plate fixture with a diameter of 25 mm and fixed space of 1.5 mm was used to perform small amplitude oscillatory shear (SAOS) tests at angular frequencies from 0.01 to 10 rad/s with experimental temperatures in the range 200~260°C. The strain amplitude was maintained at 1% and verified to be within the linear viscoelastic response regime of all samples. No obvious sign of wall slip was detected during these measurements. There was no obvious difference during dynamic time and strain sweeps when changing the thickness of the molten sample (the gap in parallel-plate fixture) by normal stress. Surface Tension Measurements. A thermalized syringe and chamber (Ramé-Hart instrument co., USA) were employed to melt solid polymers to form pendant drops at a controlled temperature. After filling the syringe with the polymer in solid state, we heated up independently the syringe and the chamber to the same target temperature (200, 220, 240 and 260°C). We then gave an additional half an hour to the system to acclimatize to the set temperature. Besides, we calibrated the temperature of the cell by videotaping the melting of Sn (melting point: 231.9°C) at different positions away 5


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

from the bottom substrate (the distance between the needle tip and the substrate is around 15 mm). The melting of Sn was observed at 231.8°C, 232.6 °C, 234.2°C, 233.6°C and 232.2°C at respectively positions of 0, 4, 8, 12, 15 mm away from the substrate. Therefore, the temperature deviation is less than 3°C in the considered chamber. Figure 1 illustrates the whole experimental process including pendant drop and spreading dynamics measurements. First, a stable pendant drop was formed (Figure 1a), from which the liquid/vapor interfacial tension (γ) could be calculated by the pendant drop method25 (based on images obtained from a Motic camera, Motic Images version Plus 2.0, Motic co., Germany). Then, the drop elongated by slightly screwing the piston of the syringe, until it contacted the substrate (Figure 1b). A sessile drop finally formed and spread spontaneously (Figure 1c).

Figure 1. Schematic illustration of the testing procedure. (a) pendant drop for surface tension measurements, (b) and (c) spreading dynamics.

Spreading Dynamics Measurements. The spreading dynamics were monitored when drops touched the glass substrate (Figure 1b) in the thermalized chamber. The 6


Page 6 of 28

Page 7 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

time when the drops contacted the glass substrate was set as the initial moment of the spreading dynamics. The entire spreading process was videotaped and then analyzed using a homemade software26 to extract the relaxation of the contact angles and the dynamic of the drop base radius, both key parameters to characterize the dynamics. During the dynamic wetting, the contact angles were obtained by fitting the drop surface in the vicinity of contact line with part of a circle based on the Canny edge-detection algorithm.26 In such a way one can obtain the local contact angle even though the drop shape is not a perfect spherical cap due to gravity effect in the late stage of wetting. In this stage, gravity can cause a little flat surface at the drop top, but it cannot affect the local contact angle.27 In other words, gravity does not play a dominant role in the analysis of the spreading dynamics. Argon gas was continuously flowed in the thermalized chamber to prevent degradation of the polymer drops during the entire experiment. Differential scanning calorimetry (DSC) analysis confirmed that the thermal properties of these polymers were indeed not altered after the experiments (Figure S1 in the supporting information). Moreover, we checked whether the glass substrate was contaminated or not after the spreading experiment. An equilibrium contact angle of 11.82°±1.22° was obtained for water drops on a clean glass substrate prior to the spreading experiments. Then, after each experiment, a drop of ultrapure water was deposited next to the cooled down polymer drop to check the potential contamination of the substrate. An average water contact angle of 24.95°±1.22° was obtained, indicating a low level of contamination,24 probably because of the argon gas-borne and adsorption of volatile components in the polymers. 7


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 28

The spreading experiments with each polymer drops were repeated at least three times to check repeatability.

THEORETICAL CONSIDERATIONS Brochard-Wyart and De Gennes28 suggested that three channels of dissipation, i.e., viscous dissipation, dissipation in the close vicinity of the solid near the contact line and dissipation in the precursor film associated with the complete wetting case, can compensate the out-of-balance interfacial tension forces. In partial wetting, the viscous dissipation described by the HD approach and the dissipation near the contact line described by the MKT are the dominant channels.29 HD Approach. The HD approach13,15 predicts the evolution of the dynamic contact angle θd as a function of the contact-line velocity V, 3   L  γ  3 V = θ d − (θ 0 )  ln        Ls   9η 

−1

(1)

0

where η, θ , Ls and L are respectively, the liquid viscosity (Pa.s), the static contact

angle (°), the slip length (m) and a characteristic length scale of the droplet (m) (θ0 and ln(L/Ls) are the free parameters). Molecular-kinetic Theory. The MKT proposed by Blake and Haynes17 describes the contact line motion within the three-phase zone in terms of molecular displacements, i.e., jump length λ (m) and jump frequency

κ 0 (Hz) between

adsorption sites of the solid surface. The relationship between θd and the contact line velocity V is given by

8


Page 9 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

V = 2κ 0λ sinh(

γ (cos θ 0 − cos θ d ) 2nk BT

(2)

)

where T is the absolute temperature, kB is the Boltzmann constant, and n is the number of adsorption sites per unit area of the substrate, usually set to λ-2

(θ0, λ and

κ 0 are

here the free parameters). When the argument of the sinh function is small, Eq. 2 can be simplified to

V=

γ (cosθ 0 − cosθd ) ζ

(3)

with ζ (Pa.s) the contact line friction per unit length of the contact line given by ζ = k B T / (κ 0 λ 3 ) . ζ provides an index of the energy dissipation stemming from the

movement of the three-phase contact line across the surface of the solid. Blake30 proposed that κ can be written in terms of the activation free energy of wetting per 0

unit area due to solid/liquid interactions ( ∆ g s* )

κ0 =

k BT −∆g s* exp( ) η vL nk BT

(4)

where v L is the volume of the unit of flow. Later, Blake and De Coninck4 argued that 0 0 ∆ g s* could be approximated by the reversible work of adhesion Wa = γ (1 + cos θ ) ,

leading to  λ 2Wa 0  vL  exp   3  λ   k BT 

ζ = η 

(5)

or equivalently

( η)

ln ζ

=

λ 2Wa 0 k BT

+ ln

(v λ ) L

3

(6)

This indicates that ζ is proportional to η and exponentially dependent on the work of adhesion. Recently, systematic underestimation of n due to the roughness and 9


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 28

heterogeneity of real solid surfaces was taken into account, and a semi-empirical approach31 was proposed

( η)

ln ζ

~α⋅

λ 2Wa 0 k BT

+ ln

(v λ ) L

3

(7)

with α = 0.51 ± 0.082 matching for numerous experimental dynamic wetting data.31 This relation seems more universal since Eq.7 considers both the effects of roughness and heterogeneity of the real solid surfaces.

RESULTS AND DISCUSSION Effect of Temperature on Surface Tensions and Viscosities. Figure 2a shows the surface tension values as a function of temperature for PP and PVDF. As expected, the surface tension decreases with temperature for all the polymers.25 The surface tensions of PP are close to the results obtained by Kwok et al.25 and Funke et al.32, validating the current measurements. PVDF has the highest surface tension due its high polarity. Figure 2b shows the zero-shear viscosity versus temperature for the two polymers. The zero-shear viscosity is obtained from the angular frequency dependence of the complex viscosity (inset of Figure 2b for PP). The relationships for PVDF are provided in Figure S2a in the supporting information. It is observed that the viscosities exhibit a constant value at low frequencies and eventually decrease with increasing frequency. During the spreading process, the maximum velocities are respectively about 5.68×10-6 m/s and 3.07×10-6 m/s for PVDF and PP from Figure 4a, and their heights are estimated to be respectively about 2.81 mm and 2.65 mm based on the base radius. Thus, the maximum shear rates encountered are estimated to be 10


Page 11 of 28

2.02×10-3 s-1 and 1.16×10-3 s-1 for PVDF and PP if we assume there is no spreading velocity at the apex of drop in the horizontal direction.33 This ensures that the viscosities encountered are for rates below the critical value of 0.01 s-1 ( applying the Cox-Merz rule,34 thus for frequencies below 0.01 rad/s), thus PP and PVDF indicate a constant zero-shear viscosity. An increasing temperature accelerates the relaxation process of the polymer chains, resulting in a decrease in the viscosity with temperature. Besides, the activation energies of viscous flow35 are respectively about 53.2 and 49.9 kJ/mol for PP and PVDF (Figure S2b), indicating that these two polymers have a similar sensitivity to temperature variations. (b)

25

Zero-shear viscosity (Pa.S)

PP PVDF PP of Kwok et al. PP of Funke et al.

20

15

PP PVDF

4000

200 °C 220 °C 240 °C 260 °C

PP 10

3

Viscosity (Pa.S)

(a) Surface tension (mN/m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

0.01

0.1

ω (rad/s)

1

10

2000

0

200

220

240

260

200

o

Temperature ( C)

220

240

Temperature (oC)

260

Figure 2. Temperature dependence of surface tension (a) and zero-shear viscosity (b) for PP and PVDF . The inset in (a) shows a typical image of a pendant PP drop at 240 °C. Surface tensions for PP obtained by Kwok et al.25 and Funke et al.32 are also shown. The viscosity in (b) is estimated to contain 5% error in the following analysis, even though there is a weak flow velocity gradient. The inset in (b) shows angular frequency dependence of viscosity for PP at different temperatures.

Spreading Dynamics. The spreading dynamics for a typical polymer drop, in this 11


Langmuir

case for a PP drop at 240°C, is illustrated in Figure S3 in the supporting information. The contact angle and base radius are analyzed simultaneously when the drop contacts the glass surface. Figure 3a and b displays, respectively, the contact angle relaxations for PP and PVDF drops at different temperatures. It is expected that high temperature promotes the spreading process due to the rapid reduction of viscosity with temperature. It should be noted that the drops have different volumes as they detach from the filament at different time. They vary from 20 to 40 mm3. As Figure S4 and Table S1 confirm, contact angle relaxations and spreading velocities are nearly unaffected by the volumes. Biance et al.36 have shown that when a liquid drop is deposited on a solid surface, the initial evolutions of the dynamic contact angles and drop radii are dominated by inertia. The effect of inertia can be distinguished by a change of slope26 in the evolution of the contact angle relaxation (inset of Figure 3a), and it indicates that inertia affects the spreading dynamics of the polymer drops until the contact angles reach around 140°. The HD and MKT models do not model inertial spreading in the present work; thus, the spreading dynamics are analyzed below 140° in the following discussion. (b)

180

200°C 220°C 240°C 260°C

Contact angle (°)

140

120

90

120

80

60

40 10

100

1000

Time (s)

60

200°C 220°C 240°C 260°C

160

100

1

180

150

Contact angle (°)

160

150

Contact angle (°)

(a)

Contact angle (°)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 28

120

140 120 100

80

60

90

1

10

100

Time (s)

1000

10000

60 30 0

1000

0

2000

2000

4000

6000

8000

10000

Time (s)

Time (s)

Figure 3. Contact angle relaxation versus time for PP (a) and PVDF (b) drops at 12


Page 13 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

different temperatures. The inset shows this relationship in logarithmic scale, in which the arrows indicate the end of the inertial regime.26

Spreading Dynamics: HD Approach. Figure 4a shows a typical relationship between the dynamic contact angle and contact line velocity for the two polymer drops at 240°C. The contact angle relaxations are smooth indicating that the rupture of the filament did not significantly influence the displacement of the contact-line. Figure 4a show an excellent fitting agreement between the experimental data and the model over several decades of velocities, indicating the HD approach is relevant here. The distributions for ln(L/Ls) are narrow and obey Gaussian distribution for the two polymers (Figure 4b and S5 in the supporting information). The calculation of simple averages and their associated standard deviation are then meaningful. Their temperature dependences are presented in Figure 5. No clear trend can be identified except that the two polymers show different characteristic slip lengths (its definition is shown in Figure 6a) with values between 236.2 and 386.2 µm, 10.6 and 20.7 µm, for respectively PP and PVDF (L was fixed to 1 mm). We compared these values with the ones reported by Denn,20 and found a good agreement between them. Besides, Mhetar and Archer19 used a tracer particle velocimetry method to study slip of polybutadiene melts on clean silica surfaces and the slip length ranged from tens to few hundreds of micrometers. They also studied the effect of surface treatment on slip of polymer melts and found the slip length can be increased to 358.7± 33.1 µm on perfluorosilane-treated silica surface from 12.5± 3.3 µm on clean silica surfaces.21 In 13


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

the present work, it is indeed expected that different chemical structures of the polymer chains at the liquid/solid interface generate distinct interactions leading thus to disparity in slip lengths. The underlying mechanism controlling the influence of the interfacial interactions on the slip length are schematically shown in Figure 6. Actually, the explicit slip mechanism of an adsorbed macromolecular chain still remains an open question. For examples, Migler et al.37 and Inn et al.38 suggested different mechanisms for the hydrodynamic slip even if both works involved the same type of interface. Generally, two distinct situations may arise under the effect of flow:39-41 (i) interfacial polymer chains debond from a weakly adsorbing surface. This type of slip originating from chain detachment/desorption is termed true slip (or adhesive slip); (ii) partial chain disentanglement occurs between the adsorbed chains and the surrounding bulk chains at strong melt/wall interfaces. Since this type of slip does not occur strictly at the polymer/solid interface, it is termed apparent slip (or cohesive slip). Figure 6b illustrates the physical interactions between PP chains and the glass substrate by virtue of Van der Waals forces, giving rise to a weak adsorption of polymer chains on the glass substrate. During the spreading of PP drops, slip can occur relatively easily when the drag force exerted on the adsorbed PP segments due to entanglements is larger than the weak adsorption force on the glass surface. This slip is governed by Van der Waals forces and the friction between the polymer segments and the bare surface. For PVDF (Figure 6c), the electronegativity of the fluorine groups triggers the formation of numerous hydrogen bonds between the PVDF chains and OH groups on the glass substrate.22 The glass surface behaves like a 14


Page 14 of 28

Page 15 of 28

fluffy carpet,42 and thus dampens the slip of PVDF chains by entanglements with the chains adsorbed via hydrogen bonds. Another factor leading to low slip lengths is that its spreading velocity is much lower than for PP drops (Figure 4a), causing a lower stress exerted on the adsorbed PVDF segments. During spreading, the magnitude of such slip is dominated by the friction between the adsorbed PVDF chains and the ones in the bulk of the drop. (b) 25

(a) 120

PP PVDF

100

80

60

40 -8 10

PVDF 240 °C

HD approach

Frequency Count (%)

140

Dynamic contact angle (°)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

20

xc=3.909 15

ω=0.004 2

R =0.995 10

5

0 -7

10

-6

3.900

-5

10

10

3.905

Contact line velocity (m/s)

3.910

3.915

3.920

Ln(L/Ls)

Figure 4. Dynamic contact angle versus contact line velocity fitted by the HD approach for the two polymer drops at 240 °C. (a) Black symbols show the experimental results and the full lines show the best HD fits obtained using the G-Dyna software.29 Distribution of ln(L/Ls) for PVDF (b), their mean values (xc) and standard deviations (ω) in histograms are obtained by fitting a Gaussian distribution.

15


Langmuir

6 PP PVDF

Ln(L/Ls)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 28

4 PVDF: Ls~10.6-20.7 µm

2

PP: Ls~ 236.2-386.2 µm

0 200

220

240

260

Temperature (°C)

Figure 5. Temperature dependence of ln(L/Ls) for the two polymers.

Figure 6. Schematic definition of the slip length Ls according to De Gennes et al.1,42 (a). Schematic illustrations of the molten polymer/glass interfaces for PP (b) and PVDF drops (c).

Spreading Dynamics: MKT. It is generally accepted that the viscous dissipation is the main channel of dissipation for highly viscous systems.43 It is unexpected that the MKT can work well for these molten polymers. Surprisingly, the fitting procedures 16


Page 17 of 28

lead to excellent agreements between the model and the experimental data (Figure 7a), suggesting that they can be analyzed in the context of this approach. The distributions for jump frequency κ 0 and jump length λ are narrow for all polymers. For clarity, the distributions of these parameters are shown for PVDF (Figure 7b-d) and parameters for PP are provided in Figure S6 in the supporting information. Histograms of the κ 0 and λ values show both unimodal distributions with small standard deviations and can be described by Gaussian distribution. The λ values fall in the range of some other liquids as reported in previous work.26,29 However, κ 0 values are much lower than the ones obtained in some other liquids, which is attributed to the high viscosity of the polymers. An interesting point lies in the inverse correlation between λ and κ 0 : smaller values of κ 0 yield larger values of λ, and vice versa (Figure 7c). Such correlations were also obtained in previous studies26,29 and are consistent with the theoretical prediction of Blake and De Coninck.4 (a)

120

(b) xc=0.199

PP PVDF

100

80

60

40 -8 10

PVDF 240 °C

25

MKT

Frequency Count (%)

140

Dynamic contact angle (°)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

ω=0.002 2 R =0.987

20

15

10

5

0 -7

10

-6

10

-5

10

-4

10

0.194

0.196

Contact line velocity (m/s)

17


0.198 0

0.200

κ (kHz)

0.202

0.204

Langmuir

(c)

(d)

PVDF 240 °C 1.320

PVDF 240 °C

1.320

λ (nm)

λ (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 28

1.316

1.315

xc=1.315

ω=0.002 2 R =0.995

1.312 1.310

0.192

0.194

0.196

0.198

0.200

0.202

0.204

0

0

5

κ (kHz)

10

15

20

Frequency Count (%)

Figure 7. Dynamic contact angle versus contact line velocity fitted by MKT for the two polymer drops at 240 °C. (a) Black symbols show the experimental results and the full line show the best MKT fits. (b) Distribution of jump frequency κ 0 for PVDF. (c) Correlation between jump length λ and κ 0 for PVDF. (d) Distribution of

λ for PVDF. The mean values (xc) and standard deviations (ω) in histograms of κ 0 and λ are obtained by fitting a Gaussian distribution.

Figure 8 depicts the temperature dependence of λ for the two polymer drops. The values of λ show a slight increasing trend, from 1.1 to 1.4 nm for PP and PVDF, with temperature. These values can be compared with the Kuhn segment length of their freely-jointed chains.44-46 Taking PP as an example, the reported Kuhn segment length (1.1~1.2 nm)44,45 is in good agreement with λ values (1.1~1.4 nm), suggesting that the wetting process is mediated by the molecular displacements of the polymer chain segments. This may also imply that the segment of a polymer chain moves as a single unit during spreading.35,47

18


Page 19 of 28

2.5

PP PVDF

2.0

λ (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

1.5

1.0

0.5

0.0 200

220

240

260

Temperature (°C) Figure 8. The temperature dependence of jump length λ obtained in best MKT fits for the polymer drops.

Figure 9 compares the relationship between contact line friction ζ and viscosity η for the two different polymers. ζ increases with η linearly for PP and PVDF drops. This linear relationship was also found in previous experimental work.26,31,48 The slopes of the straight lines are equal to 2.2 and 13.6 for PP and PVDF, respectively. The average v L is then estimated to be respectively 0.448 nm3 and 0.557 nm3 for PP and PVDF (Eq.7 with α=0.45). The former value is close to the reported volumes (0.423 nm3,49 and 0.354 nm3,50) of PP chain segments (To our knowledge, the volume of PVDF chain segment is not known). It suggests that analyzing dynamic wetting data of molten polymer drops by the MKT might provide some partial conformational information about polymer chains, usually measured by small-angle neutron scattering.45 Besides, contact line frictions (Figure 9), interfacial morphologies (Figure S7) and Wa0 values (Figure S8) for PVDF imply that the glass/PVDF 19


Langmuir

interfacial strength is superior to the one of glass/PP system, as already confirmed by Fuentes et al.24 for glass fiber/polymer composites.

PP PVDF

60000

Contact-line friction (Pa.s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 28

R2=0.99

40000

20000

R2=0.89 0 0

2000

4000

6000

Viscosity (Pa.s) Figure 9. Contact line friction ζ versus viscosity η.

CONCLUSIONS We have investigated the spreading dynamics of PP and PVDF drops on glass over temperatures between 200 and 260°C. The HD approach and MKT showed both excellent agreement with the experimental data. PP and PVDF drops have the high and low slip lengths respectively due to the weak interaction with the substrate for PP and strong hydrogen bonds with the substrate for PVDF. The jump lengths are in good agreement with the characteristic length of the polymer chains. Besides, a linear relationship between ζ and η for PP and PVDF was obtained. According to the present work, it is still difficult to make reliable claims as to which channel of dissipation is dominant for molten polymer systems. The question about the channels of dissipation is still open and is the subject of vivid discussions in the wetting community. 20


Page 21 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

ASSOCIATED CONTENT Supporting Information DSC analysis, Angular frequency dependence of the complex viscosity, Activation energies of viscous flow, Snapshots for spreading dynamics, Spreading Dynamics with different volumes, Parameters for PP in HD and MKT analysis, Morphological images and work of adhesion.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS The authors gratefully acknowledge Dr. T.D. Blake for fruitful discussions and invaluable comments. Thanks are also given to Mr. T. Shahid, Dr. Y. Mei and Prof. P. Moldenaers from Department of Chemical Engineering, KU Leuven, for their kind assistance in viscosity measurements and discussion, and Mr. J. Wang from Department of Materials Engineering, KU Leuven, for his help in the SEM observation. This research has been partially funded by the Interuniversity Attraction Poles Programme (IAP 7/38 MicroMAST) initiated by the Belgian Science Policy Office. R.K. and C.C. would like to acknowledge financial support from the research foundation Flanders (FWO, project G0A3916N). 21


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

REFERENCES (1) De Gennes, P. G. Wetting: statics and dynamics. Rev. Mod. Phys. 1985, 57, 827-863. (2) Cazabat, A. M.; Gerdes, S.; Valignat, M. P.; Villette, S. Dynamics of wetting: from theory to experiment. Interface Sci. 1997, 5, 129-139. (3) De Coninck, J.; De Ruijter, M. J.; Voué, M. Dynamics of wetting. Curr. Opin.

Colloid Interface Sci. 2001, 6, 49-53. (4) Blake, T. D.; De Coninck, J. The influence of solid–liquid interactions on dynamic wetting. Adv. Colloid Interface Sci. 2002, 96, 21-36. (5) Blake, T. D. The physics of moving wetting lines. J. Colloid Interface Sci. 2006,

299, 1-13. (6) Bonn, D.; Eggers, J.; Indekeu, J.; Meunier, J.; Rolley, E. Wetting and spreading.

Rev. Mod. Phys. 2009, 81, 739-805. (7) De Coninck, J.; Blake, T. D. Wetting and molecular dynamics simulations of simple liquids. Annu. Rev. Mater. Res. 2008, 38, 1-22. (8) Extrand, C. W. Origins of wetting. Langmuir 2016, 32, 7697-7706. (9) Chen, L.; Auernhammer, G. K.; Bonaccurso, E. Short time wetting dynamics on soft surfaces. Soft Matter 2011, 7, 9084-9089. (10) Saiz, E.; Tomsia, A.; Rauch, N.; Scheu, C.; Ruehle, M.; Benhassine, M.; Seveno, D.; De Coninck, J.; Lopez-Esteban, S. Nonreactive spreading at high temperature: molten metals and oxides on molybdenum. Phys. Rev. E 2007, 76, 041602. 22


Page 22 of 28

Page 23 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(11) Wang, X.; Venzmer, J.; Bonaccurso, E. Surfactant-Enhanced Spreading of Sessile Water Drops on Polypropylene Surfaces. Langmuir 2016, 32, 8322-8328. (12) Mäder, E.; Jacobasch, H. J.; Grundke, K.; Gietzelt, T. Influence of an optimized interphase on the properties of polypropylene/glass fibre composites. Composites Part

A 1996, 27, 907-912. (13) Voinov, O. Hydrodynamics of wetting. Fluid Dynamics 1976, 11, 714-721. (14) Tanner, L. The spreading of silicone oil drops on horizontal surfaces. J. Phys. D:

Appl. Phys. 1979, 12, 1473. (15) Cox, R. The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 1986, 168, 169-194. (16) Mitra, S.; Mitra, S. K. Understanding the early regime of drop spreading.

Langmuir 2016, 32, 8843-8848. (17) Blake, T. D.; Haynes, J. M. Kinetics of liquid/liquid displacement. J. Colloid

Interface Sci. 1969, 30, 421-423. (18) Sedev, R. The molecular-kinetic approach to wetting dynamics: Achievements and limitations. Adv. Colloid Interface Sci. 2015, 222, 661-669. (19) Mhetar, V.; Archer, L. Slip in entangled polymer melts. 1. General features.

Macromolecules 1998, 31, 8607-8616. (20) Denn, M. M. Extrusion instabilities and wall slip. Annu. Rev. Fluid Mech. 2001,

33, 265-287. (21) Mhetar, V.; Archer, L. Slip in entangled polymer melts. 2. Effect of surface treatment. Macromolecules 1998, 31, 8617-8622. 23


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(22) Martín, J.; Mijangos, C.; Sanz, A.; Ezquerra, T. A.; Nogales, A. Segmental dynamics of semicrystalline poly(vinylidene fluoride) nanorods. Macromolecules

2009, 42, 5395-5401. (23) Zhang, G.; Wang, D.; Gu, Z. Z.; Möhwald, H. Fabrication of superhydrophobic surfaces from binary colloidal assembly. Langmuir 2005, 21, 9143-9148. (24) Fuentes, C. A.; Brughmans, G.; Tran, L.; Dupont-Gillain, C.; Verpoest, I.; Van Vuure, A. W. Mechanical behaviour and practical adhesion at a bamboo composite interface: Physical adhesion and mechanical interlocking. Compos. Sci. Technol. 2015,

109, 40-47. (25) Kwok, D.; Cheung, L.; Park, C.; Neumann, A. Study on the surface tensions of polymer melts using axisymmetric drop shape analysis. Polym. Eng. Sci. 1998, 38, 757-764. (26) Duvivier, D.; Seveno, D.; Rioboo, R.; Blake, T. D.; De Coninck, J. Experimental evidence of the role of viscosity in the molecular kinetic theory of dynamic wetting.

Langmuir 2011, 27, 13015-13021. (27) De Gennes, P. G.; Brochard-Wyart, F.; Quere, D. Capillarity and wetting

phenomena: drops, bubbles, pearls, waves. Springer-Verlag: New York, 2004. (28) Brochard-Wyart, F.; De Gennes, P. Dynamics of partial wetting. Adv. Colloid

Interface Sci. 1992, 39, 1-11. (29) Seveno, D.; Vaillant, A.; Rioboo, R.; Adao, H.; Conti, J.; De Coninck, J. Dynamics of wetting revisited. Langmuir 2009, 25, 13034-13044. (30) Blake, T. D. Dynamic contact angles and wetting kinetics. In Wettability, Berg, J. 24


Page 24 of 28

Page 25 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

C., Ed. Marcel Dekker: New York, 1993; Vol. 49, pp 251-309. (31) Duvivier, D.; Blake, T. D.; De Coninck, J. Toward a predictive theory of wetting dynamics. Langmuir 2013, 29, 10132-10140. (32) Funke, Z.; Schwinger, C.; Adhikari, R.; Kressler, J. Surface tension in polymer blends of isotactic poly (propylene) and atactic polystyrene. Macromol. Mater. Eng.

2001, 286, 744-751. (33) Blake, T. D.; Fernandez-Toledano, J. C.; Doyen, G.; De Coninck, J. Forced wetting and hydrodynamic assist. Phys. Fluids 2015, 27, 112101. (34) Clasen, C.; Kulicke, W. M. Determination of viscoelastic and rheo-optical material functions of water-soluble cellulose derivatives. Prog. Polym. Sci. 2001, 26, 1839-1919. (35)

Schott, H. Dependence

of

activation energy for

viscous flow of

polyhydrocarbons on bulk of substituents. J. Appl. Polym. Sci. 1962, 6, S29-S30. (36) Biance, A. L.; Clanet, C.; Quéré, D. First steps in the spreading of a liquid droplet. Phys. Rev. E 2004, 69, 016301. (37) Migler, K.; Hervet, H.; Leger, L. Slip transition of a polymer melt under shear stress. Phys. Rev. Lett. 1993, 70, 287. (38) Inn, Y. W.; Wang, S. Q. Molecular interfacial slip between solid and liquid in polymer suspensions of hard spheres. Langmuir 1995, 11, 1589-1594. (39) Inn, Y. W.; Wang, S. Q. Hydrodynamic slip: Polymer adsorption and desorption at melt/solid interfaces. Phys. Rev. Lett. 1996, 76, 467. (40) Hatzikiriakos, S. G. Slip mechanisms in complex fluid flows. Soft Matter 2015, 25


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 28

11, 7851-7856. (41) Jalaal, M.; Balmforth, N. J.; Stoeber, B. Slip of Spreading Viscoplastic Droplets.

Langmuir 2015, 31, 12071-12075. (42) Brochard, F.; De Gennes, P. Shear-dependent slippage at a polymer/solid interface. Langmuir 1992, 8, 3033-3037. (43) Vega, M. J.; Seveno, D.; Lemaur, G.; Adão, M. H.; De Coninck, J. Dynamics of the rise around a fiber: experimental evidence of the existence of several time scales.

Langmuir 2005, 21, 9584-9590. (44) Krygier, E.; Lin, G.; Mendes, J.; Mukandela, G.; Azar, D.; Jones, A. A.; Pathak, J. A.; Colby, R. H.; Kumar, S. K.; Floudas, G. Segmental dynamics of head-to-head polypropylene and polyisobutylene

in their blend and pure components.

Macromolecules 2005, 38, 7721-7729. (45) Rubinstein, M.; Colby, R. H. Polymer Physics. Oxford University Press: Oxford, U.K., 2003. (46) Shao, H.; Fang, J.; Wang, H.; Lin, T. Effect of electrospinning parameters and polymer

concentrations

on

mechanical-to-electrical

energy

conversion

of

randomly-oriented electrospun poly (vinylidene fluoride) nanofiber mats. RSC Adv.

2015, 5, 14345-14350. (47) Kauzmann, W.; Eyring, H. The viscous flow of large molecules. J. Am. Chem.

Soc. 1940, 62, 3113-3125. (48) Li, H.; Sedev, R.; Ralston, J. Dynamic wetting of a fluoropolymer surface by ionic liquids. Phys. Chem. Chem. Phys. 2011, 13, 3952-3959. 26


Page 27 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(49) Sylvester, M. F.; Yip, S.; Argon, A. S. In Molecular Dynamics Simulation of

Atactic Poly(Propylene) Structural Differences between the Liquid and Glassy State, Abstr. Pap. Am. Chem. Soc., 1989; 1989; pp 89-90. (50) Tiño, J.; Hloušková, Z. Study of the molecular mobility in isotactic polypropylene by the spin-probe method. Chem. Papers 1986, 40, 419-426.

27


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table of Contents Graphic

28


Page 28 of 28

Spreading Dynamics of Molten Polymer Drops on Glass Substrates

Recommend Documents