rus
Issue #1/2016
A.Aygubova, G.Kozlov, G.Magomedov
Interconnection of reinforcement degree of polymer nanocomposites and radius of ring-like structures of carbon nanotubes (nanofilaments)
Interconnection of reinforcement degree of polymer nanocomposites and radius of ring-like structures of carbon nanotubes (nanofilaments)
The influence of structure of carbon nanotubes (nanofilaments) in polymer matrix on real anisotropy degree of these nanofillers has been studied. It has been shown that formation of ring-like structures reduces the indicated anisotropy degree, that results in decreasing of reinforcement of nanocomposites.
Теги: carbon nanofilaments carbon nanotubes nanocomposite нанокомпозит углеродные нановолокна углеродные нанотрубки
It is known [1] that carbon nanotubes (nanofilaments) have very high longitudinal modulus of elasticity (1000–2000 GPa) and low transverse stiffness. These factors, together with a large length/diameter ratio (high degree of anisotropy) of these nanofilaments lead to the formation of the ring-like structures, which are similar in appearance to a macromolecular tangles [2, 3]. This fact has already been noted in the literature. Thus, in [2] it is assumed that the ring-like structures of carbon nanotubes can be considered as macromolecular tangles in semi-dilute solutions. The authors of [4] use the Flory formula for rod-like macromolecules for determining the percolation threshold of carbon nanotubes in polymer nanocomposites. However, studies of this problem are quite rare and not systematic.
As shown in [3], reducing the radius of ring-like structures of carbon nanotubes (nanofilaments) with the increasing of the content of nanofiller negatively affects the degree of strengthening of polymer nanocomposites. The aim of this project is to study the influence of the structure of a ring-like formations of carbon nanotubes (nanofilaments) on the degree of strengthening of polymer nanocomposites.
The industrial produced polypropylene (PP) "Kaplan" 01 030 was used as the matrix polymer. This PP has a melt flow rate of 2.3 to 3.6 g/10 min, the average molecular weight from 2∙105 to 3∙105 and the polydispersity index of 4.5.
The carbon nanotubes (CNT) "Taunit" were used as nanofiller, having the outer diameter of 20–70 nm, inner diameter of 5–10 nm and length of 2 μm or more. In the studied nanocomposites of PP/CNT the CNT content has been varied from 0.25 to 3.0 wt. %. In addition, the multilayer carbon nanofilaments (CNF) with the number of layers of 20–30, diameter of 20–30 nm and a length of about 2 μm were used. The content of the CNF in the nanocomposites PP/CNF has been varied from 0.15 to 3.0 of the mass. %.
Nanocomposites PP/CNT and PP/CNF were obtained by mixing the components in the melt using twin screw extruder Thermo Haake Reomex RTW 25/42 (Germany). The mixing is performed at a temperature of 463–503 K and at screw speed of 50 rpm within 5 min. Test specimens obtained by injection molding using an injection molding machine Test Sample Molding Apparate RR/TS MP of Ray-Ran (Taiwan) at temperature of 503 K and pressure of 43 MPa.
For mechanical uniaxial tensile test the samples in the form of double-sided blades with sizes according to GOST 112 62-80 were used. Tests were carried out using universal testing machine Gotech Testing Machine CT-TCS 2000 (Germany) at temperature of 293 K and strain rate of about 2∙10–3 s–1.
The authors of [2] proposed the following equation to estimate the degree of reinforcement of nanocomposites polymer/carbon nanotubes:
, (1)
where Ен and Ем are elastic modulus of nanocomposite and matrix polymer (the Ен/Ем ratio is the degree of reinforcement of the nanocomposite); са is the orientation factor, which is equal to 0.2 for carbon nanotubes [2]; α is aspect of the sides of the anisotropic nanofiller or the ratio of its length and diameter, which characterise the degree of anisotropy of carbon nanotubes; ϕн is volume content of nanofiller.
ϕн can be determined according to well known equation [5]:
, (2)
where Wн is mass content of nanofiller; ρн is density of nanofiller, kg/m3. The latter is calculated for nanoparticles as follows [5]:
, (3)
where DCNT is diameter of carbon nanotube (nanofilament), nm.
The radius of the ring-like structures of CNT RУНТ can be evaluated using the following percolation ratio [6]:
, (4)
where LУНТ и rУНТ are length and radius of carbon nanotube (nanofilament).
Fig.1 shows the dependence of the degree of anisotropy of carbon nanotubes (nanofilaments) characterized by the α on the radius of their circular structures for the considered nanocomposites.
The observed increase α with the increase of RУНТ according to equation (1) corresponds to the increase in the degree of reinforcement Ен/Ем of the nanocomposites. Thus, Fig.1 demonstrates that the negative effect of reducing of RУНТ with the increase of ϕн on the degree of reinforcement of nanocomposites is caused by the reduction of the real degree of anisotropy of carbon nanotubes (nanofilaments) α.
Analytically the correlation between α and RУНТ can be described by the following empirical equations:
(5)
for carbon nanotubes, and
(6)
for carbon nanofilaments, where RУНТ is measured in nm.
Equations (5) and (6) show that when RУНТ = 140 and 90 nm, respectively, the carbon nanotubes or nanofilaments become infinitely flexible (α = 0) and lose the ability to reinforce the nanocomposite. Equations (4) and (2) show that this effect is achieved by ϕн = 0.579 or Wн=39 mass.% for CNT and ϕн = 0.672 or Wн = 37 mass. % for CNF.
As is known [3], the structure of a ring-like formations of CNT (CNF) can be most precisely characterized by their fractal dimension Df, which is a true structural characteristic, because it describes a distribution of elements in space [5]. The methodology described in [3] was used to estimate Df. Calculation of the RУНТ according to equation (4) showed her decrease with increase of ϕн. At the higher values of ϕн corresponding to Wн = 3 mass. %, these dependencies tend to go on the asymptotic branch, which implies the achievement by ring-like structures of CNT or CNF of its minimum values of RУНТ. By analogy with macromolecular coils this means achieving the most dense ring-like structure with a maximum value of its fractal dimension Df (Dfnp), which is determined according to equation [7]:
, (7)
where d is the dimension of the Euclidean space, in which fractal is considered. Obviously that in our case d = 3 and Dfnp = 2.286.
Next, to estimate Df we can use the model of irreversible aggregation, which describes the polymerization (the formation of a macromolecular coil) and gives the following relation for determining the radius of the particle aggregation Rагр [8]:
, (8)
where с0 is the initial concentration of particles.
The coefficient in equation (8) can be determined by the following conditions: Rагр = RУНТ, C0 = ϕн and Df = Dfnp. RУНТ and ϕн values taken for Wн = 3.0 mass. %. According to the estimates according to the above formula, the value of Df increases with ϕн (reduce of RУНТ) from 1.91 to 2.29 for nanocomposites PP/CNT and from 1.76 to 2.21 for nanocomposites PP/CNF.
By the above-mentioned limit values RУНТ = 140 and 90 nm for CNT and CNF, respectively, Df = 2.86 for CNT and Df = 2.89 for CNF. The authors of [2] have experimentally obtained the value of Df = 2.85 for carbon nanotubes with α = 4.4. According to equations (5) and (6) this corresponds to RУНТ = 151 nm for CNT and RУНТ = 104 nm for CNF, which is quite close to the above-mentioned limit values of RУНТ.
Equations (1), (5) and (6) allow to obtain the direct dependence of reinforcement on the radius of the ring-like structures of CNT (CNF):
(9)
for carbon nanotubes, and
(10)
for carbon nanofilaments, where RУНТ is measured in nm.
Fig.2 shows the comparison of experimental and calculated according to the equations (9) and (10) dependencies Ен/Ем(ϕн) for the considered nanocomposites. As can be seen on Fig.2, a good coincidence of theory and experiment (the average difference is 3.5%) is obtained, which confirms the validity of proposed interpretations.
Thus, the results of this project showed that reducing of the radius of ring-like structures of carbon nanotubes (nanofilaments), or their compaction leads to a decrease of the degree of anisotropy of these nanofillers. The latter effect reduces the degree of reinforcement of nanocomposites "polymer/carbon nanotubes (nanofilaments)" compared to the maximum achievable. The proposed model shows good agreement with the experimental data.
As shown in [3], reducing the radius of ring-like structures of carbon nanotubes (nanofilaments) with the increasing of the content of nanofiller negatively affects the degree of strengthening of polymer nanocomposites. The aim of this project is to study the influence of the structure of a ring-like formations of carbon nanotubes (nanofilaments) on the degree of strengthening of polymer nanocomposites.
The industrial produced polypropylene (PP) "Kaplan" 01 030 was used as the matrix polymer. This PP has a melt flow rate of 2.3 to 3.6 g/10 min, the average molecular weight from 2∙105 to 3∙105 and the polydispersity index of 4.5.
The carbon nanotubes (CNT) "Taunit" were used as nanofiller, having the outer diameter of 20–70 nm, inner diameter of 5–10 nm and length of 2 μm or more. In the studied nanocomposites of PP/CNT the CNT content has been varied from 0.25 to 3.0 wt. %. In addition, the multilayer carbon nanofilaments (CNF) with the number of layers of 20–30, diameter of 20–30 nm and a length of about 2 μm were used. The content of the CNF in the nanocomposites PP/CNF has been varied from 0.15 to 3.0 of the mass. %.
Nanocomposites PP/CNT and PP/CNF were obtained by mixing the components in the melt using twin screw extruder Thermo Haake Reomex RTW 25/42 (Germany). The mixing is performed at a temperature of 463–503 K and at screw speed of 50 rpm within 5 min. Test specimens obtained by injection molding using an injection molding machine Test Sample Molding Apparate RR/TS MP of Ray-Ran (Taiwan) at temperature of 503 K and pressure of 43 MPa.
For mechanical uniaxial tensile test the samples in the form of double-sided blades with sizes according to GOST 112 62-80 were used. Tests were carried out using universal testing machine Gotech Testing Machine CT-TCS 2000 (Germany) at temperature of 293 K and strain rate of about 2∙10–3 s–1.
The authors of [2] proposed the following equation to estimate the degree of reinforcement of nanocomposites polymer/carbon nanotubes:
, (1)
where Ен and Ем are elastic modulus of nanocomposite and matrix polymer (the Ен/Ем ratio is the degree of reinforcement of the nanocomposite); са is the orientation factor, which is equal to 0.2 for carbon nanotubes [2]; α is aspect of the sides of the anisotropic nanofiller or the ratio of its length and diameter, which characterise the degree of anisotropy of carbon nanotubes; ϕн is volume content of nanofiller.
ϕн can be determined according to well known equation [5]:
, (2)
where Wн is mass content of nanofiller; ρн is density of nanofiller, kg/m3. The latter is calculated for nanoparticles as follows [5]:
, (3)
where DCNT is diameter of carbon nanotube (nanofilament), nm.
The radius of the ring-like structures of CNT RУНТ can be evaluated using the following percolation ratio [6]:
, (4)
where LУНТ и rУНТ are length and radius of carbon nanotube (nanofilament).
Fig.1 shows the dependence of the degree of anisotropy of carbon nanotubes (nanofilaments) characterized by the α on the radius of their circular structures for the considered nanocomposites.
The observed increase α with the increase of RУНТ according to equation (1) corresponds to the increase in the degree of reinforcement Ен/Ем of the nanocomposites. Thus, Fig.1 demonstrates that the negative effect of reducing of RУНТ with the increase of ϕн on the degree of reinforcement of nanocomposites is caused by the reduction of the real degree of anisotropy of carbon nanotubes (nanofilaments) α.
Analytically the correlation between α and RУНТ can be described by the following empirical equations:
(5)
for carbon nanotubes, and
(6)
for carbon nanofilaments, where RУНТ is measured in nm.
Equations (5) and (6) show that when RУНТ = 140 and 90 nm, respectively, the carbon nanotubes or nanofilaments become infinitely flexible (α = 0) and lose the ability to reinforce the nanocomposite. Equations (4) and (2) show that this effect is achieved by ϕн = 0.579 or Wн=39 mass.% for CNT and ϕн = 0.672 or Wн = 37 mass. % for CNF.
As is known [3], the structure of a ring-like formations of CNT (CNF) can be most precisely characterized by their fractal dimension Df, which is a true structural characteristic, because it describes a distribution of elements in space [5]. The methodology described in [3] was used to estimate Df. Calculation of the RУНТ according to equation (4) showed her decrease with increase of ϕн. At the higher values of ϕн corresponding to Wн = 3 mass. %, these dependencies tend to go on the asymptotic branch, which implies the achievement by ring-like structures of CNT or CNF of its minimum values of RУНТ. By analogy with macromolecular coils this means achieving the most dense ring-like structure with a maximum value of its fractal dimension Df (Dfnp), which is determined according to equation [7]:
, (7)
where d is the dimension of the Euclidean space, in which fractal is considered. Obviously that in our case d = 3 and Dfnp = 2.286.
Next, to estimate Df we can use the model of irreversible aggregation, which describes the polymerization (the formation of a macromolecular coil) and gives the following relation for determining the radius of the particle aggregation Rагр [8]:
, (8)
where с0 is the initial concentration of particles.
The coefficient in equation (8) can be determined by the following conditions: Rагр = RУНТ, C0 = ϕн and Df = Dfnp. RУНТ and ϕн values taken for Wн = 3.0 mass. %. According to the estimates according to the above formula, the value of Df increases with ϕн (reduce of RУНТ) from 1.91 to 2.29 for nanocomposites PP/CNT and from 1.76 to 2.21 for nanocomposites PP/CNF.
By the above-mentioned limit values RУНТ = 140 and 90 nm for CNT and CNF, respectively, Df = 2.86 for CNT and Df = 2.89 for CNF. The authors of [2] have experimentally obtained the value of Df = 2.85 for carbon nanotubes with α = 4.4. According to equations (5) and (6) this corresponds to RУНТ = 151 nm for CNT and RУНТ = 104 nm for CNF, which is quite close to the above-mentioned limit values of RУНТ.
Equations (1), (5) and (6) allow to obtain the direct dependence of reinforcement on the radius of the ring-like structures of CNT (CNF):
(9)
for carbon nanotubes, and
(10)
for carbon nanofilaments, where RУНТ is measured in nm.
Fig.2 shows the comparison of experimental and calculated according to the equations (9) and (10) dependencies Ен/Ем(ϕн) for the considered nanocomposites. As can be seen on Fig.2, a good coincidence of theory and experiment (the average difference is 3.5%) is obtained, which confirms the validity of proposed interpretations.
Thus, the results of this project showed that reducing of the radius of ring-like structures of carbon nanotubes (nanofilaments), or their compaction leads to a decrease of the degree of anisotropy of these nanofillers. The latter effect reduces the degree of reinforcement of nanocomposites "polymer/carbon nanotubes (nanofilaments)" compared to the maximum achievable. The proposed model shows good agreement with the experimental data.
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