rus
TS_pub
technospheramag
technospheramag
ТЕХНОСФЕРА_РИЦ
Issue #1/2024
L.B.Atlukhanova, I.V.Dolbin
THE INTERCONNECTION OF PROPERTIES AND DISPERSION DEGREE OF NANOFILLER FOR NANOCOMPOSITES POLYMER/CARBON NANOTUBE
THE INTERCONNECTION OF PROPERTIES AND DISPERSION DEGREE OF NANOFILLER FOR NANOCOMPOSITES POLYMER/CARBON NANOTUBE
DOI: 10.22184/1993-8578.2024.17.1.74.79
In present work, the parameter of the dispersion degree of nanofiller is introduced, which characterizes quantitatively the dispersion level of the latter in nanocomposites polymer/carbon nanotube. This parameter is a function of size of the nanofiller aggregate and content. The relationship between the dispersion level of the nanofiller and the reinforcement degree is shown, which makes it possible to predict the properties of the nanocomposites under consideration.
In present work, the parameter of the dispersion degree of nanofiller is introduced, which characterizes quantitatively the dispersion level of the latter in nanocomposites polymer/carbon nanotube. This parameter is a function of size of the nanofiller aggregate and content. The relationship between the dispersion level of the nanofiller and the reinforcement degree is shown, which makes it possible to predict the properties of the nanocomposites under consideration.
Теги: carbon nanotubes dispersion nanocomposite reinforcement degree ring-like structures дисперсия кольцеобразные структуры нанокомпозит степень усиления углеродные нанотрубки
INTRODUCTION
The importance of the aggregation process (and the opposite physical meaning of the dispersion process) of nanofiller for formation of properties of polymer nanocomposites is now well known [1, 2]. However, the study of the two mentioned complementary processes uses mainly electron microscopy methods, studying them on a purely qualitative level [2]. The authors [3] described dependence of the properties of polymer nanocomposites filled with carbon nanotubes on the degree of nanofiller aggregation χ analytically, using the following percolation relation:
, (1)
where Ен and Ем are the elastic moduli of nanocomposite and matrix polymer, respectively (the ratio Ен/Ем is called the degree of nanocomposite reinforcement), and ϕн is the nanofiller volume content.
The degree of aggregation of nanofiller χ was determined in [3] as follows:
, (2)
where ϕмф is the relative content of interfacial regions in the nanocomposite.
The aim of the present work is to analytically determine the dispersion degree of nanofiller and its relationship with the carbon nanotubes structure and macroscopic properties of nanocomposite on the example of epoxy polymer/carbon nanotubes nanocomposites [4].
RESEARCH METHODS
Multilayer carbon nanotubes (MCNTs) obtained by chemical vapour deposition (CVD) at the Petroleum Industry Research Institute (Iran) were used as nanofillers. They had an outer diameter of 10–50 nm, length of 1–3 μm and their mass content in the nanocomposites under consideration varied in the range of 0.25–10.0 wt% [4].
Low viscosity industrial epoxy resin (ER) grade LY-5052 and hardener grade HY-5052 were used to form the polymer matrix of EP/MСNT nanocomposites. Firstly, the MCNTs were dispersed in the hardener by ultrasonic treatment for 30 min. The ultrasonic treatment process was performed by pulse method at 60% of amplitude value to avoid overheating of the material. The epoxy resin and hardener were mixed with a ratio by weight of 100 : 30 and then the mixture was stirred at 900 rpm for 15 min. The mixture was then poured into metal moulds and cured at 333 K for 15 h [4].
Mechanical uniaxial tensile tests were performed using a Zwick/Roel apparatus at a temperature of 293 K and a slider speed of 1 mm/min. The specimens used were 168 mm long, 13 mm wide and 5 mm thick. The average value for five specimens was taken as the test result [4].
RESULTS AND DISCUSSION
As mentioned above, the nanofiller aggregation and dispersion processes are opposite in their physical meaning, which allows us to determine the degrees of nanofiller dispersion ηd as follows:
. (3)
The authors [5] showed that the value of χ is related to the interfacial adhesion level indicator bα in polymer nanocomposites according to a simple relationship:
, (4)
where ϕс is the percolation threshold of nanofiller in polymer matrix, further taken as 0.34±0.02 [5].
The combination of equations (3) and (4) yields the following equation to quantify the degree of dispersion of the nanofiller ηd:
. (5)
As is well known [6], carbon nanotubes in the polymer matrix of nanocomposites form ring-like formations structurally similar to macromolecular coils of branched polymer chains. Such ring-shaped formations are a specific way of aggregation of any strongly anisotropic one-dimensional fillers [7, 8]. The radius RУНТ of these ring-shaped formations can be estimated using the following equation [7]:
, (6)
where LУНТ and rУНТ are the length and outer radius of carbon nanotube, respectively, ϕн is the volume content of nanofiller.
Calculation of the parameters ϕн and bα necessary for further description of the degree of dispersion can be performed using the following equations – for ϕн [9]:
, (7)
where Wн and ρн are mass content and density of carbon nanotubes, the value of ρн for which is taken as 1500 kg/m3 [4].
The following percolation relationship was used to calculate the interfacial adhesion level bα [5]:
. (8)
Based on the above postulates, it should be assumed that the degree of dispersion ηd of carbon nanotubes in the polymer matrix of the nanocomposite will increase as the radius RУНТ of their ring-shaped formations increases and decrease as the content of nanofiller ϕн increases. Fig.1 shows the dependence of the dispersion degree ηd of carbon nanotubes, determined according to equation (5), on the complex index (RУНТ/ϕн)1/2 for EP/MСNT nanocomposites. Note that this form of the complex index implies an equal influence of the parameters RУНТ and ϕн on the degree of dispersion of the nanofiller. As follows from the graph in Fig.1, a linear correlation is observed between the parameters ηd and (RУНТ/ϕн)1/2, which can be expressed analytically by the following equation:
, (9)
where RУНТ is given in µm.
As shown earlier [5], the dispersion degree of ηd nanofiller is a function of the structure of its aggregates characterised by their fractal dimension Df:
. (10)
From the comparison of equations (9) and (10), a very simple correlation between the dimension Df and radius RУНТ of the ring-shaped formations of carbon nanotubes in the polymer matrix of the nanocomposite can be obtained:
, (11)
where RУНТ is given in µm.
An alternative way to determine dimension of Df is the following equation [10]:
. (12)
Fig.2 shows a comparison of the dimensions of ring-shaped MCNT formations calculated according to equation (12) Df1 and (11) Df2 for the considered nanocomposites. As follows from this comparison, the mentioned methods give close values of Df (the average disperancy between Df1 and Df2 is 8.3%).
The combination of equations (1) and (3) allows us to obtain the following version of the percolation relation for evaluating the degree of reinforcement of polymer/carbon nanotube nanocomposites:
. (13)
Further, the combination of equations (6), (9) and (13) makes it possible to predict the enhancement degree of Ен/Ем of polymer/carbon nanotube nanocomposites as a function of the geometry of carbon nanotubes, i.e., their length and outer diameter. Fig.3 shows a comparison of the calculated by the above method and experimentally obtained dependences of Ен/Ем(ϕн) for nanocomposites EP/MСNT, which showed a good agreement between theory and experiment (their average discrepancy is 4%, which is approximately equal to the experimental error in determining this parameter). This correspondence serves to confirm the correctness of the theoretical treatment proposed in this work.
CONCLUSIONS
Thus, in the present work a parameter (degree of dispersion of nanofiller) quantitatively characterising the process of its dispersion is proposed. It is shown, that dispersion degree is a function of the size (radius) of ring-like formations of carbon nanotubes in the polymer matrix of nanocomposite or alternatively their fractal dimension, as well as the content of nanofiller. An analytical relation determining dependence of the properties (in the considered case – the reinforcement degree) of the nanocomposite on the dispersion level of the nanofiller is proposed. The obtained theoretical treatment allows predicting the polymer/carbon nanotube nanocomposites properties.
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
The importance of the aggregation process (and the opposite physical meaning of the dispersion process) of nanofiller for formation of properties of polymer nanocomposites is now well known [1, 2]. However, the study of the two mentioned complementary processes uses mainly electron microscopy methods, studying them on a purely qualitative level [2]. The authors [3] described dependence of the properties of polymer nanocomposites filled with carbon nanotubes on the degree of nanofiller aggregation χ analytically, using the following percolation relation:
, (1)
where Ен and Ем are the elastic moduli of nanocomposite and matrix polymer, respectively (the ratio Ен/Ем is called the degree of nanocomposite reinforcement), and ϕн is the nanofiller volume content.
The degree of aggregation of nanofiller χ was determined in [3] as follows:
, (2)
where ϕмф is the relative content of interfacial regions in the nanocomposite.
The aim of the present work is to analytically determine the dispersion degree of nanofiller and its relationship with the carbon nanotubes structure and macroscopic properties of nanocomposite on the example of epoxy polymer/carbon nanotubes nanocomposites [4].
RESEARCH METHODS
Multilayer carbon nanotubes (MCNTs) obtained by chemical vapour deposition (CVD) at the Petroleum Industry Research Institute (Iran) were used as nanofillers. They had an outer diameter of 10–50 nm, length of 1–3 μm and their mass content in the nanocomposites under consideration varied in the range of 0.25–10.0 wt% [4].
Low viscosity industrial epoxy resin (ER) grade LY-5052 and hardener grade HY-5052 were used to form the polymer matrix of EP/MСNT nanocomposites. Firstly, the MCNTs were dispersed in the hardener by ultrasonic treatment for 30 min. The ultrasonic treatment process was performed by pulse method at 60% of amplitude value to avoid overheating of the material. The epoxy resin and hardener were mixed with a ratio by weight of 100 : 30 and then the mixture was stirred at 900 rpm for 15 min. The mixture was then poured into metal moulds and cured at 333 K for 15 h [4].
Mechanical uniaxial tensile tests were performed using a Zwick/Roel apparatus at a temperature of 293 K and a slider speed of 1 mm/min. The specimens used were 168 mm long, 13 mm wide and 5 mm thick. The average value for five specimens was taken as the test result [4].
RESULTS AND DISCUSSION
As mentioned above, the nanofiller aggregation and dispersion processes are opposite in their physical meaning, which allows us to determine the degrees of nanofiller dispersion ηd as follows:
. (3)
The authors [5] showed that the value of χ is related to the interfacial adhesion level indicator bα in polymer nanocomposites according to a simple relationship:
, (4)
where ϕс is the percolation threshold of nanofiller in polymer matrix, further taken as 0.34±0.02 [5].
The combination of equations (3) and (4) yields the following equation to quantify the degree of dispersion of the nanofiller ηd:
. (5)
As is well known [6], carbon nanotubes in the polymer matrix of nanocomposites form ring-like formations structurally similar to macromolecular coils of branched polymer chains. Such ring-shaped formations are a specific way of aggregation of any strongly anisotropic one-dimensional fillers [7, 8]. The radius RУНТ of these ring-shaped formations can be estimated using the following equation [7]:
, (6)
where LУНТ and rУНТ are the length and outer radius of carbon nanotube, respectively, ϕн is the volume content of nanofiller.
Calculation of the parameters ϕн and bα necessary for further description of the degree of dispersion can be performed using the following equations – for ϕн [9]:
, (7)
where Wн and ρн are mass content and density of carbon nanotubes, the value of ρн for which is taken as 1500 kg/m3 [4].
The following percolation relationship was used to calculate the interfacial adhesion level bα [5]:
. (8)
Based on the above postulates, it should be assumed that the degree of dispersion ηd of carbon nanotubes in the polymer matrix of the nanocomposite will increase as the radius RУНТ of their ring-shaped formations increases and decrease as the content of nanofiller ϕн increases. Fig.1 shows the dependence of the dispersion degree ηd of carbon nanotubes, determined according to equation (5), on the complex index (RУНТ/ϕн)1/2 for EP/MСNT nanocomposites. Note that this form of the complex index implies an equal influence of the parameters RУНТ and ϕн on the degree of dispersion of the nanofiller. As follows from the graph in Fig.1, a linear correlation is observed between the parameters ηd and (RУНТ/ϕн)1/2, which can be expressed analytically by the following equation:
, (9)
where RУНТ is given in µm.
As shown earlier [5], the dispersion degree of ηd nanofiller is a function of the structure of its aggregates characterised by their fractal dimension Df:
. (10)
From the comparison of equations (9) and (10), a very simple correlation between the dimension Df and radius RУНТ of the ring-shaped formations of carbon nanotubes in the polymer matrix of the nanocomposite can be obtained:
, (11)
where RУНТ is given in µm.
An alternative way to determine dimension of Df is the following equation [10]:
. (12)
Fig.2 shows a comparison of the dimensions of ring-shaped MCNT formations calculated according to equation (12) Df1 and (11) Df2 for the considered nanocomposites. As follows from this comparison, the mentioned methods give close values of Df (the average disperancy between Df1 and Df2 is 8.3%).
The combination of equations (1) and (3) allows us to obtain the following version of the percolation relation for evaluating the degree of reinforcement of polymer/carbon nanotube nanocomposites:
. (13)
Further, the combination of equations (6), (9) and (13) makes it possible to predict the enhancement degree of Ен/Ем of polymer/carbon nanotube nanocomposites as a function of the geometry of carbon nanotubes, i.e., their length and outer diameter. Fig.3 shows a comparison of the calculated by the above method and experimentally obtained dependences of Ен/Ем(ϕн) for nanocomposites EP/MСNT, which showed a good agreement between theory and experiment (their average discrepancy is 4%, which is approximately equal to the experimental error in determining this parameter). This correspondence serves to confirm the correctness of the theoretical treatment proposed in this work.
CONCLUSIONS
Thus, in the present work a parameter (degree of dispersion of nanofiller) quantitatively characterising the process of its dispersion is proposed. It is shown, that dispersion degree is a function of the size (radius) of ring-like formations of carbon nanotubes in the polymer matrix of nanocomposite or alternatively their fractal dimension, as well as the content of nanofiller. An analytical relation determining dependence of the properties (in the considered case – the reinforcement degree) of the nanocomposite on the dispersion level of the nanofiller is proposed. The obtained theoretical treatment allows predicting the polymer/carbon nanotube nanocomposites properties.
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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