Mathematical Model of the Electrospinning Process

Transcription

1 Mathematical Model of the Electrospinning Process II. Effect of the technological parameters on the electrospun fibers diameter LILIANA ROZEMARIE MANEA 1,2, *, ANDREI BERTEA1, ELENA NECHITA 3, CARMEN VIOLETA POPESCU 3, ION SANDU 2,4 * 1 Gheorghe Asachi Technical University Iasi, Faculty of Textile and Leather Engineering and Industrial Management, 29 Dimitrie Mangeron Str., , Iasi, Romania 2 Romanian Inventors Forum, 3 Sf.P.Movila Str., L11, III/3, , Iasi, Romania 3 Department of Mathematics, Informatics and Educational Sciences, Faculty of Sciences, Vasile Alecsandri University of Bacau, Romania, 157 Calea Marasesti, , Bacau, Romania 4 Alexandru Ioan Cuza University of Iasi, ARHEOINVEST Interdisciplinary Platform, 11 Carol I Blvd., G building, , Iasi, Romania The electrospinning technology is a complex one, whose research has been boosted, during the last decade, by the impressive potential of its applications. Since the characteristics of the nanofibers resulted from the electrospinning process are highly influenced by a series of constructive, technological and environmental parameters involved, the study of the overall phenomena requires a multi-disciplinary approach. Our present study further focuses on the influence of the flow rate and of the voltage, as variable technological parameters. The Response Surface Methodology and the MATLAB simulation software have been used to perform the analysis of the experimental data. The obtained mathematical models revealed the 2D most favorable zone of the two parameters under discussion. Keywords: electrospinning, polymeric nanofibers, polyetherimide, flow rate, voltage, mathematical models Electrospinning is by far one of the most known technology used to produce fibers of nanometer size, with quite diverse structures and functional applications [1-8]. The main applications of the polymeric nanofibers obtained through electrospinning are in areas such as biomedicine (regenerative medicine- implants, tents, bandages, structures with drug control release) [9-13], industrial biotechnologies (filtering mediums for environmental protection [14-19], separator membrane [20-23], protection clothes [24-33] etc. Nanostructures morphology, structure and composition, their architecture, orientation of their disposal, constructive and technological processing parameters, play all a crucial role in the engineering applications of electrospun nanofibers [34-36]. Based on the understanding of material structure and properties, the new nanomaterials produced through electrospinning can be created or structurally modified, depending strictly on the implementation domain or sub-domain [37-40]. Each strict destination imposes the utilization of basic material with certain priority characteristics [41-44]. The present work studies the effect of technological parameters on the diameter of electrospun polymeric nanofibers obtained from polyetherimide solution, for applications in industrial biotechnology [45-48]. The most relevant applications of the electrospun nanofibers in industrial biotechnologies are [49-51] in producing: a. systems for air, chemical and biological filtering; b. filters for aerosols, filtering membranes; c. photonic crystals, flexible photocells, polymers for photovoltaic diodes; d. anorganic and organic materials and semiconductor systems functionalized through a nanometer structuring; e. catalyst-loaded fibers, nanostructures with morphologic core-mantle disposition for optical applications. The implementation of polymeric nanofibers produced through electrospinning to obtain filtering mediums is well known. As compared to the conventional fibers, the main advantages when using electrospun nanofibrous filtering mediums are [52-56]: - high separation capacity, even in the range of submicron particles; - high absorption capacity and excellent filtering properties, due to nanofibers small size, and a large area/ surface ratio; - high filtering efficacy (up to 98% for filtration of particles under 2 microns); long life of the filtering elements; small investment costs due to a compact filtering system; reduced occupied surface; small energy consumption, reduced CO 2 emissions. The big surface area/weight makes the nanofibers an ideal substrate for molecular separation [57-63]. The separation principle is similar to that of chromatography affinity. Acknowledging the efficacy of filters made of electrospun polymeric structures, their applications were also extended for military clothes, for protection against biochemical attacks. The electrospun fibrous polymeric membranes are used to obtain sensors and actuators, supercondensers, solar cells, transistors, electronic devices. Given the fact that the speed of the electrochemical reactions changes in proportion with the electrode surface area, the electrospun conductive nanofibrous membranes are used as porous electrodes to produce highly performing batteries (for lap-tops, cell phones) [64-67]. The success of electrospun nanofibers implementation consists in obtaining highly performing, durable nanostructures for environment protection, by means of a relatively simple technology, with an acknowledged vacillation and with high capacity to filter the gaseous fluids with dispersions, up to the nanometer scale. The analysis of the correlations displayed in various electrospinning processes between nanofibers structure and quality characteristics on one side, and electrospinning * manearozemarie@yahoo.com; Tel: (+40) ; sandu_i03@yahoo.com; Tel: (+40) REV.CHIM.(Bucharest) 67 No

2 parameters on the other, represents a priority in the study of the advanced electrospinning technology [54, 60, 68-71]. The present study uses mathematical modelling and focuses on the influence of flow rate and of the voltage on the diameter of the electrospun fibers obtained from polyetherimide solution 12%, and dimethylacetamide/ tetrahydrofuran (1:1 ratio). Experimental part Materials A solution of polyetherimide polymer with the molecular mass and concentration 12% and a mixed DMAC/ THF (1:1 ratio) was used as solvent[60, 65,71]. Table 1 presents the characteristics of each solvent Table 1 CHARACTERISTICS OF THE SOLVENTS USED IN EXPERIMENTS The characteristics of the 12% PEI solution in the DMAC/ THF mix. [48-54, 71] are: conductivity 1.18mS/cm, surface tension 30.3 mn/m, zero shear viscosity, Pas. The solubility of PEI was tested in DMA/THF solvent (1:1) ratio by computing the Hansen coefficients, and among the tested solutions with concentrations ranging between 8 and 14% PEI, the PEI solution with the concentration of 12% has an excellent solubility [49, 71]. For the preparation of the polymer solution, the polymer was dried for 2 hours at 100 o C under vacuum conditions. The polymer dissolution in the solvent mix was made by magnetic stirring for 24 h at 500 o C. Choice of parameters and range In our experiments, we have used three syringes with the volume of 3mL and 0.2mm inner needle diameter; the inter-nozzle distance was 2.5mm. The interval of displacement along the Ox axis was 100mm, and along the Oz axis was 80mm. The equipment has as collecting mechanism type a rotating cylinder, with the cylinder rotation speed v = 1000rpm. The experiments were performed under the following environmental conditions: 20 o C, RH = 40%, normal atmospheric pressure. Under these conditions, we have selected the values for spinning distance, applied voltage and volume flow rate to establish the influence of these parameters on PEI nanofiber electrospinning. The experiment that we have designed in order to study the electrospinning process [71] comprised the realization of 5x4x5=100 technological variants. These resulted from all the possible combinations of values for the constructive and technological parameters, as follows: D = 45mm, D = 70mm, D = 100mm, D = 120mm and D = 130mm for the distance between needle and collector, U = 15kV, U = 20kV, U = 25kV, U = 30kV, U = 35kV for the applied voltage, and Q = 0.05mL/min, Q = 0.075mL/min, Q = 0.1mL/min, Q = 0.15mL/min as consecutive flow rates adopted in the experimental plan. Investigation methods Methods of fiber characterization The scanning electron microscope (SEM) was used to characterize the obtained PEI fibers, which were previously gold plated using a Phenom G2 equipment [38, 48, 54, 60, 71]. A Lucia image analysis software was used to determine the diameter of the electrospun fibers. For each technological variant, 100 determinations of the electrospun fiber diameter were carried out [60, 65, 71]. Statistical instruments for the analysis of the experimental data Empirical modeling is one of the most commonly used analytical methods in science, engineering, technology and management. It raises design, model development and data collection challenges, requiring appropriate tools for calibrating and testing the model. Since our study intends to determine a quantitative model for the dependency flow rate and voltage, we have chosen the Response Surface Methodology (RSM) [68-71] as a mathematical and statistical technique. Within our study [71], RSM was used to analyse the dependence between d med - the mean fibers diameter and D - the distance between needles and collector, in conjunction with the flow rate Q and the voltage U. Throughout this paper, we have preserved the same notations for the variable parameters: x 1 for D for Q and x 3 for U. These are the predictors of the model, varied together according to the experimental plan, with the aim of determining the most favourable combinations of Q and U which determine the desired fiber diameters resulted from the electrospinning process. Results and discussions According to the notations already established in our previous studies [60, 65, 71], the dependent variable (or the response) of the model is written as d med = f(x 1 ), where the function f expressing the dependency of d med on the three predictors is unknown. As expected, if we try to approximate f with a second order polynomial in x 1, we get a model which is not complex enough to allow the study of the real functional dependency with sufficient precision. Consequently, we have approached the data analysis with RSM, in order to study the three partial dependencies: d med = u(x 1 ), d med = v(x 2 ) and d med = w(x 1 ). The dependency u(x 1 ) and its behaviour have been extensively discussed in [48, 54, 71]. Our attention will now focus on the results provided by RSM for d med = v(x 2 ), for three values of x 1 = D which are the most favorable for the aim of obtaining very small fiber diameters, and for d med = w(x 1 ), for two values of x 2 = Q. The model u(x 1 ) revealed that d med decreases as x 1 decreases [71]. Therefore, in representing the response surfaces for the dependency d med = v(x 2 ), we have considered for x 1 = D only the three smallest values: D = 45mm, D = 70mm and D = 100mm. The surfaces are represented in figure 1 (a) to (c). It appears that small values of the flow rate entail small mean fiber diameters: d med decreases as Q decreases. Therefore, the approximation models for the third partial dependency d med = w(x 1 ) have been determined only for the two smallest values of the flow rate: Q = 0.05mL/ min and Q = 0.075mL/min. The corresponding response surfaces are presented in figure 2 (a), (b) and (c) and show that d med decreases as x 3 = U increases. As already proved by the model d med = u(x 1 ), [71]), d med also increases with x 1 =D. Our data were subject to an analysis performed on Matlab (R2007b). In what follows, we shall integrate the three models u(x 1 ), v(x 2 ), w(x 1 ) and provide the technical interpretation of the results. This interpretation considers the behaviors and facts communicated on this topic, derived by other researchers [39, 55, 66] from similar experiments. REV.CHIM.(Bucharest) 67 No

3 b Fig.1. Response surfaces for mean fiber diameter in terms of voltage (U) and flow rate (Q) for three values of D: (a) D = 45mm, (b) D = 70mm, (c) D = 100mm, (d) simultaneous representation for the three response surfaces c The response surfaces graphically represented in the previous section allow us to visualize the relationship between the predictors flow rate (Q) and voltage (U) and the mean fibers diameter (both in correlation with the third constructive parameter D, the distance between needles and collector), as dependent variable. The influence of the spinning distance D (denoted x 1 ) on the fibers diameter has been discussed in [71]. The specialty literature reports d both increase in fiber diameter and decrease in fiber diameter [39, 53, 55, 66] upon D, depending on the ratio between D and the electric field strength E (KV/cm), polymer solution concentration and solvent evaporation rate. For the polyetherimide solution that we have used in electrospinning, the mathematical models showed that longer spinning distance induces an increase in the fiber diameter. REV.CHIM.(Bucharest) 67 No

4 a Fig. 2. Response surfaces for mean fiber diameter in terms of distance (D) and voltage (U) for two values of Q: (a) Q = 0.05mL/min, (b) Q = 0.075mL/min, (c) simultaneous representation for the four values of Q b c Fig. 3. The projection of the response surface for U =35kV Influence of the flow rate Q = x 2 (ml/min) on the mean fibers diameter In our experiment, d med increased with the volume flow rate, as depicted in Figure 1 (a) to (f) in [71], and also in figure 1 (a) to (c). The equations (3) to (6) [71] support this conclusion, as the coefficient of DQ is positive and the corresponding terms are significant. Our findings are consistent with previous research [39, 55, 66]. Influence of the voltage U = x 3 (KV) on the mean fibers diameter In our experiment, the fibers diameter decrease when the voltage increases. The chart (a) to (c) in figure 1 and (a) to (b) in figure 2 also display this behavior. The experimental data comply with this conclusion, as the minimum value for fibers diameter is recorded for U=35kV. Figure 3 presents the projection of the response surface in figure 2 (e) from [71], for the most favorable value of U, which leads to small diameter of fibers, namely 35kV. The dark-grey lines are displayed in the favorable zone of the parameters (while the light-grey ones are higher). Conclusions This paper presents the study of the influence of the process variables U (the applied voltage) and Q (the feed rate) on the average values of the diameters of the fibers electrospun from polyetherimide solution (PEI) with REV.CHIM.(Bucharest) 67 No

5 concentration of 12%, using as solvents a mixture of dimethylacetamide/tetrahydrofuran (DMAC/THF) 1:1 ratio. The study and its interpretation are made in conjunction with the similar ones performed for the constructive parameter D (spinning distance). Several significant response surfaces have been plotted for the partial dependencies: d med as function of D(mm) and Q(mL/min) in our study, and for d med as function of Q(mL/min) and U(kV), and D(mm) and U(kV) in the present paper. Their joint analysis show that the optimum technological domain is defined by small values of the spinning distance (D = 45-70mm), small values of the flow rate (Q = mL/min) and high values of the voltage (U = 30-35kV). The smallest values of D(mm) and Q(mL/min) lead to convenient values of the mean fiber diameters, while the desired characteristics for the fibers diameter is obtained for the highest value of U(kV). 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