Retarded relaxation and breakup of deformed PA6 droplets filled with nanosilica in PS matrix during annealing

Polymer 52 (2011) 5231e5236

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Retarded relaxation and breakup of deformed PA6 droplets filled with nanosilica in PS matrix during annealing Miqiu Kong, Yajiang Huang*, Guangling Chen, Qi Yang, Guangxian Li* College of Polymer Science and Engineering, State Key Laboratory of Polymer Materials Engineering, Sichuan University, Chengdu 610065, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 May 2011 Received in revised form 22 August 2011 Accepted 28 August 2011 Available online 2 September 2011

The effect of hydrophilic silica nanoparticles (SiO2) on the relaxation and breakup dynamics of selectively filled polyamide (PA6) droplets with different degrees of deformation in polystyrene (PS) matrix during quiescent annealing were in situ investigated. It was found that, with the increase of silica content, the relaxation process of PA6 droplets was slowed down gradually and the relaxation mode was changed correspondingly. The critical break aspect ratios (ARcr) of PA6 droplets were also improved with the increase in SiO2 nanoparticle contents. Comparisons of the experimental values of ARcr, characteristic relaxation time (sd) and breakup time (tb) of the SiO2-filled PA6 droplets with corresponding theoretical values were made. The results of comparison were discussed in terms of viscoelasticity and interfacial tension. It was proposed that the alternation of the viscoelastic properties of PA6 droplets in stead of the interfacial tension change of the blends was responsible for the phenomena observed. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: Silica nanoparticles Interfacial tension Viscoelasticity

1. Introduction Majority of multicomponent polymers are thermodynamically immiscible, and blending of different polymers usually leads to the formation of heterogeneous morphologies such as droplets/fibers in a matrix or a co-continuous structure. The properties of the blends are to a large extent determined by the type of morphology formed together with their phase sizes [1]. However, morphologies of immiscible polymer blends are usually unstable due to the presence of interfacial tension between phases. Various processes of coarsening, relaxation and disintegration can be identified if the phase structure is not frozen in fast, and that will give rise to weak interfacial adhesion and poor mechanical properties after melt processing. One of the classical methods to ensure the stability of the phase structure and thus enhance the mechanical performances of immiscible blends is the use of a third component, a compatibilizer such as a block copolymer [2,3] or a graft copolymer [4] and the use of reactive compatibilizers [5]. Polymer blends filled with nanoparticles can offer significant enhancement in properties. This classical method has been utilized in various applications for many years. However, it is only recently that the role of nanoparticles in controlling the morphology and

* Corresponding authors. Tel.: þ86 28 85401841; fax: þ86 28 85405402. E-mail addresses: [email protected] (Y. Huang), [email protected] (G. Li). 0032-3861/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymer.2011.08.052

behavior of multiphase polymeric systems has become the subject of experimental and theoretical investigations. Available investigations so far are mainly focused on revealing the impact of nanoparticles on the final morphology (including compatibilization mechanisms), mechanical properties and rheological properties of blends after melting processing [6e16]. The effect of nanoparticles on the morphology formation in systems with dropletematrix structure or seaeisland structure was found to depend largely on the selective distribution of nanoparticles within the blends [17e21]. Usually, the reduced domain size and the significantly improved morphology stability were found in those blends with nanoparticle preferential filled at the interface or within the matrix phase [7,8,14]. One mechanism proposed for these morphological changes was the reduction of interfacial tension induced by interfacially active nanoparticles. Another suggested mechanism was the hindrance of coalescence between droplets due to the formation of the rigid particle layer or a slower film drainage process. For blends with a co-continuous morphology, the adding of nanoparticles was reported to retard the coarsening or disintegration process of blends during quiescent molten annealing, leading to the presence of so-called morphology refinement. The reduced coarsening rate of blends was ascribed to the increased viscoelastic properties of polymeric component which had more affinity with nanoparticles [12,16]. On the other hand, efforts to reveal the effect of nanoparticles on the structural evolution of deformed or fibrillar structures in

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immiscible polymer blends are relatively scarce [17e21]. It may be ascribed to the complexity of the relaxation behavior (such as retraction, end-pinching, Rayleigh-type instability, etc) involved during the shape relaxation of these slender structures which is controlled by both the interfacial and viscoelastic properties of components. Dharaiya and Jana [17] reported the expedited breakup of clay-filled PP threads in PA6 matrix due to the rapid growth of capillary waves on the surface of threads. Zhang et al. [18] reported the enhanced fibrillation of TLCP droplets due to the improvement of interfacial adhesion and the suppression of interfacial slip between TLCP and nylon phases by nanoclays which dispersed preferentially in the nylon matrix. Similar phenomena were also found in TLCP/polycarbonate (PC) [19] and LCP/PP [20] blends filled with nano-SiO2. The knowledge on the relaxation dynamics of deformed droplets upon the incorporation of nanoparticles is of great significance because it may facilitate a better understanding about the improved stability of the fibrillar or the co-continuous structure induced by nanoparticles [22,23]. However, till now, there are few systematic studies on the relaxation behavior of a deformed or slender structure upon the addition of nanoparticles. Also, the relative contribution of interfacial properties and viscoelastic properties to the morphology development of blends induced by nanoparticles has not yet been clarified clearly, possibly due to the difficulty in finding a direct and appropriate experimental means. In this work, a simple model system consisted of SiO2 nanoparticle-filled polyamide 6 (PA6) droplets sandwiched between two polystyrene (PS) disks, is presented for investigating the effect of nanoparticles on the shape stability of PA6 droplet during annealing. This kind of sandwiched structure is usually used to estimate interfacial tension of polymer blends during quiescent conditions [24,25] or to investigate the dynamics of unfilled droplets in the matrix [26e29]. This method not only can avoid the possible migration of nanoparticle between phases which usually occur during melt mixing but also can guarantee a predefined distribution of SiO2 nanoparticles in PA6 droplet. Moreover, the influence of nearby droplets on the relaxation dynamics of an individual droplet, as presented in practical polymer blends with multi-droplet morphology, can be excluded. By the combination of optical-shear technique and rheology technique, the relative contributions of interfacial properties and viscoelastic properties induced by the addition of nanoparticles on the relaxation and breakup dynamics of deformed droplets during quiescent annealing were discussed in this work. The experimental results and the theoretical values were discussed based on the viscoelasticity of components and interfacial tension of blend. 2. Experimental 2.1. Materials The PS (GP5250) was supplied by Taihua Plastic (Ningbo) co., Ltd. and has a MFI of 7.0 g/10 min. The PA6 (YH800) was provided by Yueyang petrochemical co., Ltd., and has a melting point of 215e220  C. Hydrophilic pyrogenic silica (Aerosil A200), with a specific surface area of 200  25 m2/g and density of 2.3 g/cm3, was purchased from Degussa Corp. The SiO2 nanoparticles were aggregates of primary spherical particles having an average diameter of 12 nm. In this study, SiO2 nanoparticles did not receive any surface treatment prior to use. Before melt mixing, all of the materials were dried under vacuum at 80  C for at least 48 h, in order to make the moisture level below 0.2%, thereby, minimize the possibility of oxidative degradation or hydrolysis

during sample experiments.

preparation

and

subsequent

morphology

2.2. Preparation and characterization 2.2.1. Compounding procedure PA6 was compounded with 0, 1, 3, and 5 vol.% of SiO2 nanoparticles by using a TSE minitype twin-screw extruder having counter-rotating screws. The screw diameter was 18 mm and the L/ D ratio was 20. The screw rotation rate was set to 100 rpm. The temperature of the extruder from hopper to die was maintained at 230  C, 245  C, 250  C, 245  C and 225  C, respectively. The extrudates were cooled by water and then pelletized. All of the materials were placed in a vacuum oven at 80  C for at least 24 h prior to testing. Then the obtained materials were used for rheological test and fiber preparations. 2.2.2. Sample preparation PA6 or PA6/SiO2 fibers with diameters varied from 50 mm to 200 mm were obtained by melt spinning of molten pellets on a hot plate. Before each test, the fibers were annealed in a vacuum oven at 80  C for 24 h to avoid the influence of the residual stresses and the moisture. PS disks which used as the matrix phase in the annealing experiments were obtained by compression molding. The disk samples with thickness about 1 mm and diameter of 25 mm were molded at 200  C and 10 MPa with a holding time of 3 min. The compression molded PS disks were dried in a vacuum oven at 80  C for about 24 h before each test, in order to minimize eventual problems with air bubble. 2.2.3. Rheology experiments All the samples for rheological test were prepared by using compression molding at 245  C and at pressure of 10 MPa. The thickness and diameter of samples were 2 mm and 25 mm, respectively. A strain-controlled rheometer (ARES from TA instruments, USA) was employed for rheological experiments. All tests were carried out by using 25 mm parallel plates with a gap of 1.7 mm at 230  C. Dynamic strain sweep has shown that the viscoelastic behavior of the blends to be linear up to strain amplitude of 10% for all the frequencies investigated. Dynamic frequency sweep measurements were performed at strain amplitude of 2% in order to investigate the rheological behavior within the linear viscoelastic region. The frequency range investigated was from u ¼ 100 rad s1 to 0.1 rad s1. The zero viscosities (h0) of PS, PA6 and PA6/SiO2 at 230  C were obtained in the stationary flow region via creep tests with a stress of 50 Pa. 2.2.4. In situ morphological analysis The visualization of microstructural evolutions of deformed PA6 droplets in PS matrix was accomplished on a shear-optical system, which combined a microscope (Olympus BX51, Japan) and a double-side heated Cambridge shearing stage (CSS450 from Linkam Scientific, UK). PA6 or PA6/SiO2 fibers with different aspect ratios (AR) were first placed between two PS disks, and then the sandwiched sample was put into the shearing stage. The temperature was elevated to 180  C and hold for 3 min, allowing the merging of two melt PS disks and the setting a gap of 1600 mm. Relaxation experiments were carried out at 230  C after a rapid heating process from 180  C with a rate of 30  C/min. The morphology of droplets during the relaxation and breakup process was recorded with a Linksys32 DV image acquisition system and was analyzed using a home-developed digital image analysis software package. The interfacial tension between PA6 and PS was also determined with the shear-optical system via a retraction of deformed drop method (DDRM) [30].

M. Kong et al. / Polymer 52 (2011) 5231e5236

3. Results and discussion 3.1. Retraction of slightly deformed droplets The shape of a slightly deformed droplet can be described by the deformation parameter or deformability defined as D ¼ (L  B)/ (L þ B) (0  D < 1), where L and B are the length and width of the droplet, respectively. The deformation (D) of PA6 droplets filled and unfilled with silica nanoparticles as a function of the retraction time (t) is shown in Fig. 1. The equilibrium radiuses of these droplets were all about 80 mm and possessed an initial deformability about 0.35. It was showed that the relaxation dynamics of PA6 droplets was slowed down in the presence of SiO2 nanoparticles. The higher the SiO2 nanoparticle content was, the slower the relaxation dynamics was. The dynamics of the relaxation was dramatically slowed down especially when the SiO2 nanoparticle content was beyond 3 vol.%. The retarded retraction dynamics of filled droplets indicated that the shape stability of deformed PA6 droplets was enhanced after the addition of SiO2 nanoparticles. 3.2. Relaxation of slender droplets The shape of a moderated or highly extended droplet can be described by the aspect ratio AR ¼ L/D, where L and D are the length and diameter of the droplet, respectively. There exists a critical aspect ratio (ARcr) above which the annealed slender droplet will break up into smaller fragments by Rayleigh instability, and below which the droplet will eventually retract back to a sphere, and for droplets with intermediate aspect ratio the breakup is dominated by ending-pinching [26e29]. Fig. 2 describes the relaxation and breakup process of a pure PA6 droplet (AR ¼ 10.8) and a PA6/SiO2 droplet filled with 1 vol.% SiO2 nanoparticles (AR ¼ 11.5) in PS matrix at 230  C. The ends of the pure PA6 droplet became rounded firstly and then pinched off from the middle of the filament eventually, whereas the PA6/SiO2 droplet with higher AR tended to undergo a slow end-pinching and finally retracted into a spherical droplet. This indicated that the relaxation mechanism of PA6 droplet was changed even if 1 vol.% SiO2 nanoparticles was added. The ARcr of pure PA6 droplet was about 9 at 230  C. However, the ARcr of PA6 droplets upon the addition of 1 vol.%, 3 vol.% and 5 vol.% nanoparticles increased to 12, 15 and 22, respectively. Moreover, the relaxation dynamics of PA6 droplet filled with 5 vol.% SiO2 nanoparticles was drastically slowed 1

D=(L-B)/(L+B)

0 vol.% 1 vol.% 3 vol.% 5 vol.% 0.1

0.01

100

200

300

400

500

Time (s) Fig. 1. Deformability (D ¼ (L  B)/(L þ B)) of deformed PA6 droplets with different SiO2 contents (0, 1, 3 and 5 vol.%) as a function of retraction time in PS matrix at 230  C. The equilibrium radius for these PA6 droplets is about 80 mm.

5233

down, as shown in Fig. 3. In the investigated time scale, the fragment of 5 vol.% SiO2-filled PA6 droplet after breakup was difficult to retract into a sphere completely. These experiments suggested that the critical aspect ratio and the shape stability of slender PA6 droplets could be effectively improved with the increase in SiO2 nanoparticle contents, especially when the concentration of the SiO2 nanoparticles is beyond 3 vol.%. 3.3. Discussion The relaxation and breakup mechanisms of a droplet in an immiscible matrix usually depend on the initial shape of droplets, viscoelastic properties of the components and interfacial tension s of the system [9]. The change in the relaxation dynamics and critical breakup aspect ratio of PA6 droplets in the presence of SiO2 nanoparticles may be related with the change of the viscoelastic properties and interfacial tension of system by SiO2 nanoparticles. The viscoelastic properties of PS and PA6 filled with 0, 1, 3, and 5 vol.% of SiO2 nanoparticles are shown in Fig. 4 as a function of 0 frequency (u). It can be found that both storage modulus (G ) and * complex viscosity (h ) of PA6/SiO2 increased with the increase of SiO2 nanoparticle volume fractions. The zero shear viscosity (h0) calculated from creep test [31,32] and corresponding viscosity ratio (p) are shown in Table 1. It was found that the h0 of PA6/SiO2 increased with the SiO2 nanoparticle contents. When the SiO2 nanoparticle contents increased to 5 vol.%, the viscosity ratio between PA6/SiO2 and PS raised dramatically to 17. This finding can be explained by the interactions between the fillers and PA6 molecules attached to their surfaces which reduce their molecular mobility [31]. Fig. 4 indicates that PA6 with 3 vol.% of SiO2 nanoparticles should be very close to the percolation threshold in rheology [33], which means a dramatic enhancement in the viscoelastic properties of PA6/SiO2 beyond this threshold volume fraction. As shown in Table 1, the interfacial tension for unfilled PA6/PS blends obtained from DDRM method is s ¼ 7.4 mN/m, which is in good agreement with values reported in the literature [30]. The introduction of 1 vol.% SiO2 nanoparticles in PA6 decreased the interfacial tension to 5.8 mN/m. However, the further increase in the silica nanoparticle concentration only decreased the interfacial tension slightly, which is in accord with the reports of Hong et al. in PBT/PE/Clay systems [13]. It was reported that the amplitude in the change of interfacial tension upon the addition of nanoparticles depended on the quantity of nanoparticles dispersed at the interface between the droplet and the matrix [14]. Our calculation revealed that the SiO2 loading required for a full interface coverage of the droplet in Fig. 2(b) is only 0.04 vol.%. Thus, the quantity of SiO2 nanoparticles that located at the interface may reach a relative high value at 1 vol.% SiO2 loading and did not increase significantly at higher SiO2 nanoparticle concentrations. It is understandable since hydrophilic SiO2 nanoparticles have specific affinity for PA6 than PS [34e36] and much of them should be encapsulated by PA6 melts. The relaxation dynamics of a droplet driving by the interfacial tension is relevant to its initial deformation of the droplets, namely whether the droplet begins with a nearly spherical shape (slightly deformed droplets) or a highly extended thread. The shape evolution of a slightly deformed droplet can be depicted as the following time-dependent relation proposed by Utracki et al. [37],


D ¼ D0 exp



s 40ðp þ 1Þ t ð2p þ 3Þð19p þ 16Þ hm R0




t ¼ D0 exp 

sd

(1) where D0 is the deformation parameter at t0, s is the interfacial tension, hm is the viscosity of the matrix, R0 is the radius of a droplet

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Fig. 2. Relaxation of (a) a pure PA6 droplet (AR ¼ 10.8) and (b) a PA6 droplet (AR ¼ 11.5) filled with 1 vol.% nano-SiO2 in PS matrix at 230  C. The scale bar denotes 200 mm.

at equilibrium, t and sd are the retraction time and characteristic relaxation time of droplet, respectively. The retraction dynamics of a slightly deformed droplet can be discussed with a characteristic relaxation time. According to Equation (1), the characteristic relaxation time sd of a deformed droplet can be calculated as [30],

sd ¼

ð2p þ 3Þð19p þ 16Þhm R0 s 40ðp þ 1Þ

(2)

The theoretical relaxation time sd for PA6 droplets in Fig. 1 filled with 0, 1, 3, and 5 vol.% of SiO2 nanoparticles was 49 s, 74 s, 121 s and 1000 s, respectively. The corresponding experimental relaxation times (sd) were determined to be 78 s, 108 s, 339 s and 1046 s, respectively. It is a little higher than the theoretical values. However, both the theoretical and experimental relaxation times showed that as the SiO2 nanoparticle contents increased the relaxation time was increased and the retraction dynamics of deformed droplets were slowed down, which are in good agreement with the results shown in Fig. 1. Based on Equation (2), it is known that the retraction dynamics of the slightly deformed droplets depended largely on the viscosity ratio, the interfacial tension of blends and the droplet radius at

equilibrium. The sd increases with the increasing viscosity ratio but with the decreasing interfacial tension for droplets with a given equilibrium radius. The rheological results in Fig. 4 indicate that the viscosity ratio (p) of the system was significantly improved in the presence of SiO2 nanoparticles. However, Table 1 reveals that the interfacial tension (s) between PA6/SiO2 droplet and PS matrix only decreased to a half of that between pure PA6 droplet and PS matrix. The contribution of the viscosity ratio to the relaxation time in terms of (2p þ 3)(19p þ 16)/40(p þ 1) in Equation (2) is only 1.30 for pure PA6 droplets, while it increased to 17.42 for PA6 droplets filled with 5 vol.% SiO2 nanoparticles. Thus, the significant change in the viscoelastic properties of PA6 droplet in the presence of SiO2 nanoparticles, in stead of the slight change in the interfacial tension between PA6 droplet and PS, should be responsible for the remarkable slowing down in the relaxation dynamics of PA6 droplets in PS melt. For a slender droplet, the critical aspect ratio can be predicted theoretically by using the theory for breakup of extended droplets developed by Tomotika [28]. The Tomotika’s theory is about the development of sinusoidal disturbances on their surface of the highly extended droplets. The interfacial area decreases when the amplitude of the disturbance increases. Willemse et al. [38] applied

Fig. 3. The relaxation process of a PA6 droplet (AR ¼ 23.2) filled with 5 vol.% SiO2 in PS matrix annealing at 230  C. The scale bar denotes 200 mm.

M. Kong et al. / Polymer 52 (2011) 5231e5236

a 10

b 10

5

5235

5

PS PA6 PA6+1 vol.% SiO 2 PA6+3 vol.% SiO 2 PA6+5 vol.% SiO 2

104

G' (Pa)

102

PS PA6 PA6 + 1 vol.% SiO2 PA6 + 3 vol.% SiO2 PA6 + 5 vol.% SiO2

101

η* (Pa.s)

104

103

0

10 -1 10

100

101

103

102 10-1

102

100

101

102

ω (rad/s)

ω (rad/s) 0

Fig. 4. (a) Storage modulus (G ) and (b) complex viscosity (h*) as a function of frequency (u) for PS and PA6 composites filled with different volume fractions of SiO2 nanoparticles at 230  C.

 ARcr ¼

L 2r



 ¼

lm

cr

2r

 ¼

p

(3)

Xm ðpÞ

where L and r is the length and radius of threads, respectively. The relation between a dominant wave number (Xm) and dominant wavelength (lm) is usually expressed as Xm ¼ 2pr/lm. When the wavelength of distortions (l) is larger than the initial circumference of thread (2pr), breakup of the thread occurs. Equation (3) shows that ARcr is inversely proportional to Xm(p). The theoretical Xm as a function of viscosity ratio (p) is shown in Fig. 5, which calculated by using the theory of Tomotika [28]. It should be noted that Equation (3) only considered the effect of viscosity ratio on ARcr, leaving out of the changes in the elasticity of the PA6 droplets and the interfacial tension of the system. The theoretical values of Xm for systems with different silica contents are listed in Table 2, and the theoretical values of ARcr calculated by Equation (3) and the experimental ARcr are also listed in Table 2. The effects of initial droplet shape and the concentration of SiO2 nanoparticles on the dynamics of the relaxation and/or breakup processes of PA6 droplets in PS matrix at 230  C are summarized in Table 2. The theoretical values of the ARcr as a function of p are plotted as a thick line in Fig. 6 and the experimental data was shown by the scatter points. Stone et al. [39,40] have investigated the relaxation process of droplets with different aspect ratios in systems with different viscosity ratios caused by changing the component molecular weights. Their results are also mapped out as two thin lines in Fig. 6 as done by Tucker and Moldenaers [9]. It is found that the dependence of the experimental critical aspect ratios obtained in this work (the scatter points) on the viscosity ratio is tend to consist qualitatively with that of theoretical predication, but noticeable differences exist in the exact values. However, it is clearly that the critical aspect ratios of SiO2-filled PA6 droplets obtained in this study are more in accordance with the experimental values reported by Stone et al. [39,40]. It is probably because Willemse’s method is an idealized model, whereas the

critical aspect ratio reported by Stone et al. was summarized from their experimental results. The data reported in Table 2 also indicates that even if two droplets have the same aspect ratio, the difference in their viscosity ratios will lead to different relaxation mechanisms. The above assertion can be verified by Fig. 3, in which the slight change in viscosity of PA6 droplet upon the addition of 1 vol.% SiO2 nanoparticles changed the relaxation behavior of PA6 droplet with an initial aspect ratio of 11 from breakup to retraction. The above discussion indicates that the significant change in the viscoelastic properties of PA6 droplets in the presence of SiO2 nanoparticles is responsible for the increased ARcr observed. The dynamics of highly extended droplets can be discussed by using the breakup time (tb) during the shape relaxation process. The tb of a molten droplet in an immiscible matrix under quiescent conditions derived by Elemans et al. [25] is

1:39sr02 h r tb ¼ m 0 ln Um s kT

! (4)

where r0 is the initial radius of the fibers (in m), s is the interfacial tension (in N/m), k is the Boltzmann constant and T is the absolute temperature (in K). The dimensionless growth rates, Um, which is a complex tabulated function of both the viscosity ratio (p) and the wavelength (l) and calculated by Tomotika [28], were dramatically decreased as a function of viscosity ratio p. For a given viscosity ratio (p), there will be one dominant wavelength, lm, at which the amplitude grows with the fast rate; the distortion having this wavelength consequently causes the thread to break up into droplets. The theoretical values of Um obtained from Fig. 5 are listed 1.0

0.8

Χm Ωm

this theory to interpret the stability of fibers and co-continuous structures. The critical aspect ratio is given by

Χm

0.6

p=0.61 p=0.63 p=1.87 p=17.0

0.4

Table 1 Zero shear viscosities and viscosity ratios of components at 230  C. SiO2 contents 0 vol.% 1 vol.% 3 vol.% 5 vol.%

2 hPA6=SiO 0

hPS 0

(Pa s)

(Pa s)

666.7 684.9 2046.2 18,638.2

1095.3 e e e

2 hPA6=SiO =hPS 0 0

0.61 0.63 1.87 17.0

Interfacial tension (mN/m) 7.4 5.8 5.6 5.4

0.2

Ωm 0.0

10-3

10-2

10-1

p

100

101

102

Fig. 5. Theoretical values of wave number (Xm) and dimensionless growth rate Um as a function of viscosity ratio (p) [38].

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M. Kong et al. / Polymer 52 (2011) 5231e5236

Table 2 The theoretical and experimental values of parameters involved during the breakup process of droplets. SiO2 contents

p

0 vol.% 1 vol.% 3 vol.% 5 vol.%

0.61 0.63 1.87 17.00

Um

Xm

0.5829 0.5825 0.5317 0.3472

0.096 0.092 0.053 0.022

ARcr

tb (s)

Theoretical

Experimental

Theoretical (r ¼ 50 mm)

5.38 5.39 5.91 9.04

9 12 15 22

1698 2236 4014 10,011

2

10

dynamics of deformed PA6 droplets during annealing within PS matrix. The characteristic relaxation time (sd) and breakup time (tb) of PA6 droplets were greatly increased upon the addition of SiO2 nanoparticles. The critical breakup aspect ratios ARcr of filled PA6 droplets were increased accordingly as a function of the SiO2 nanoparticle concentrations and could be predicted qualitatively by Willemse’s theory in the light of viscosity ratio. However, the experimental ARcr was closer to the experimental result obtained by Stone et al. The significant change in the viscoelastic properties of PA6 droplets after the addition of nanoparticles should be responsible for the enhanced shape stability of PA6 droplets, while the contribution from the reduction in interfacial tension may be less important.

ARcrit

Acknowledgment The authors are grateful to the financial support from the National Natural Science Foundation of China (51003062). This work was also supported in part by the State Key Laboratory of Polymer Materials Engineering of China, Sichuan University.

1

10

References

0

10

-3

10

-2

10

-1

10

0

p

10

1

10

2

10

Fig. 6. Experimental and theoretical values of critical aspect ratio (ARcr) as a function of the viscosity ratio (p). The thick line represents the prediction from Equation (3). The two thin lines correspond to the experimental results of Stone et al. [39], the bottom thin line denotes the largest ARcr for which a drop relaxed back to a sphere; the top thin line denotes the smallest ARcr for which a drop was observed to breakup, and the intermediate region denotes the uncertainty in the critical aspect ratio. Our experimental data were indicated by the scatter points: (-) p ¼ 0.61 (0 vol.% SiO2), (C) p ¼ 0.63 (1 vol.% SiO2), (:) p ¼ 1.87 (3 vol.% SiO2) and (A) p ¼ 17.0 (5 vol.% SiO2).

in Table 2. Therefore, the theoretical values of tb for PA6 droplets with the same initial radius of 50 mm but different SiO2 concentrations are calculated from Equation (4). The results are also summarized in Table 2. It is found that the theoretical values of tb are increased with the increase of SiO2 nanoparticle concentrations. In particular, increasing the SiO2 content in excess of the threshold value will prolong the tb of the droplets dramatically. The tendency of the experimental results is in good agreement with that deduced by Equation (4). The experimental and corresponding theoretical tb of pure PA6 is 505 s and 1474 s if the initial radius of the fiber is about 43.9 mm. For PA6 droplets filled with 1 vol.% SiO2, the experimental value of tb is 620 s when the initial radius of the fiber is about 44.5 mm, and corresponding theoretical value is 1969 s. In case of 3 vol.% SiO2 and 5 vol.% SiO2 nanoparticle-filled PA6 droplets, the tb is 885 s and 3000 s if the radius of the droplets is 36 mm, 38.6 mm, respectively. The difference between experimental and theoretical results may be ascribed to the increase in the elasticity of the droplets because an increase in the elasticity of the droplets can extend the time of droplet deformation and breakup [41]. The results also showed that the tb is markedly depended on the values of Um while it displays only a weak dependence on R0 and s. This indicates again that the slower dynamics of PA6 droplets in the presence of SiO2 nanoparticles was mainly due to the significant improvement in the viscoelastic properties of PA6. 4. Conclusions In the present work it has been demonstrated that hydrophilic SiO2 nanoparticles could slow down the relaxation and breakup

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