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Mathematical Model of the Electrospinning ProcessII. Effect of the technological parameters on the electrospun fibers diameter

LILIANA ROZEMARIE MANEA1,2,*, ANDREI BERTEA1, ELENA NECHITA3, CARMEN VIOLETA POPESCU3, ION SANDU2,4*

1Gheorghe Asachi Technical University Iasi, Faculty of Textile and Leather Engineering and Industrial Management, 29 DimitrieMangeron Str., 700050, Iasi, Romania2Romanian Inventors Forum, 3 Sf.P.Movila Str., L11, III/3, 700089, Iasi, Romania3Department of Mathematics, Informatics and Educational Sciences, Faculty of Sciences, Vasile Alecsandri University of Bacau,Romania, 157 Calea Marasesti , 600115, Bacau, Romania4Alexandru Ioan Cuza University of Iasi, ARHEOINVEST Interdisciplinary Platform, 11 Carol I Blvd., G building, 700506, 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 theelectrospinning process are highly influenced by a series of constructive, technological and environmentalparameters involved, the study of the overall phenomena requires a multi-disciplinary approach. Our presentstudy 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 theanalysis of the experimental data. The obtained mathematical models revealed the 2D most favorable zoneof the two parameters under discussion.

Keywords: electrospinning, polymeric nanofibers, polyetherimide, flow rate, voltage, mathematical models

*email: manearozemarie@yahoo.com; Tel: (+40)721334034 ; sandu_i03@yahoo.com; Tel: (+40)744431709

Electrospinning is by far one of the most knowntechnology used to produce fibers of nanometer size, withquite diverse structures and functional applications [1-8].The main applications of the polymeric nanofibers obtainedthrough electrospinning are in areas such as biomedicine(regenerative medicine- implants, tents, bandages,structures with drug control release) [9-13], industrialbiotechnologies (filtering mediums for environmentalprotection [14-19], separator membrane [20-23],protection clothes [24-33] etc.

Nanostructures morphology, structure and composition,their architecture, orientation of their disposal, constructiveand technological processing parameters, play all a crucialrole in the engineering applications of electrospunnanofibers [34-36]. Based on the understanding of materialstructure and properties, the new nanomaterials producedthrough electrospinning can be created or structurallymodified, depending strictly on the implementation domainor sub-domain [37-40]. Each strict destination imposes theutilization of basic material with certain prioritycharacteristics [41-44]. The present work studies the effectof technological parameters on the diameter of electro-spun polymeric nanofibers obtained from polyetherimidesolution, for applications in industrial biotechnology [45-48].

The most relevant applications of the electrospunnanofibers in industrial biotechnologies are [49-51] inproducing: a. systems for air, chemical and biologicalfiltering; b. filters for aerosols, filtering membranes; c.photonic crystals, flexible photocells, polymers forphotovoltaic diodes; d. anorganic and organic materialsand semiconductor systems functionalized through ananometer structuring; e. catalyst-loaded fibers,nanostructures with morphologic core-mantle dispositionfor optical applications.

The implementation of polymeric nanofibers producedthrough electrospinning to obtain filtering mediums is well

known. As compared to the conventional fibers, the mainadvantages when using electrospun nanofibrous filteringmediums are [52-56]:

- high separation capacity, even in the range ofsubmicron particles;

- high absorption capacity and excellent filteringproperties, due to nanofibers small size, and a large area/surface ratio;

- high filtering efficacy (up to 98% for filtration of particlesunder 2 microns); long life of the filtering elements; smallinvestment costs due to a compact filtering system;reduced occupied surface; small energy consumption,reduced CO2 emissions.

The big surface area/weight makes the nanofibers anideal substrate for molecular separation [57-63]. Theseparation principle is similar to that of chromatographyaffinity. Acknowledging the efficacy of filters made ofelectrospun polymeric structures, their applications werealso extended for military clothes, for protection againstbiochemical attacks. The electrospun fibrous polymericmembranes are used to obtain sensors and actuators,supercondensers, solar cells, transistors, electronicdevices. Given the fact that the speed of theelectrochemical reactions changes in proportion with theelectrode surface area, the electrospun conductivenanofibrous membranes are used as porous electrodes toproduce highly performing batteries (for lap-tops, cellphones) [64-67].

The success of electrospun nanofibers implementationconsists in obtaining highly performing, durablenanostructures for environment protection, by means of arelatively simple technology, with an acknowledgedvacillation and with high capacity to filter the gaseous fluidswith dispersions, up to the nanometer scale.

The analysis of the correlations displayed in variouselectrospinning processes between nanofibers structureand quality characteristics on one side, and electrospinning

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parameters on the other, represents a priority in the studyof the advanced electrospinning technology [54, 60, 68-71]. The present study uses mathematical modelling andfocuses on the influence of flow rate and of the voltage onthe diameter of the electrospun fibers obtained frompolyetherimide solution 12%, and dimethylacetamide/tetrahydrofuran (1:1 ratio).

Experimental part Materials

A solution of polyetherimide polymer with the molecularmass 41.000 and concentration 12% and a mixed DMAC/THF (1:1 ratio) was used as solvent[60, 65,71]. Table 1presents the characteristics of each solvent.

71]. A Lucia image analysis software was used todetermine the diameter of the electrospun fibers. For eachtechnological variant, 100 determinations of theelectrospun fiber diameter were carried out [60, 65, 71].

Statistical instruments for the analysis of the experimentaldata

Empirical modeling is one of the most commonly usedanalytical methods in science, engineering, technology andmanagement. It raises design, model development anddata collection challenges, requiring appropriate tools forcalibrating and testing the model. Since our study intendsto determine a quantitative model for the dependency flowrate and voltage, we have chosen the Response SurfaceMethodology (RSM) [68-71] as a mathematical andstatistical technique. Within our study [71], RSM was usedto analyse the dependence between dmed - the mean fibersdiameter and D - the distance between needles andcollector, in conjunction with the flow rate Q and the voltageU. Throughout this paper, we have preserved the samenotations for the variable parameters: x1 for D, x2 for Q andx3 for U. These are the predictors of the model, variedtogether according to the experimental plan, with the aimof determining the most favourable combinations of Q andU which determine the desired fiber diameters resultedfrom the electrospinning process.

Results and discussionsAccording to the notations already established in our

previous studies [60, 65, 71], the dependent variable (orthe response) of the model is written as dmed = f(x1, x2, x3),where the function f expressing the dependency of dmed onthe three predictors is unknown. As expected, if we try toapproximate f with a second order polynomial in x1, x2, x3,we get a model which is not complex enough to allow thestudy of the real functional dependency with sufficientprecision. Consequently, we have approached the dataanalysis with RSM, in order to study the three partialdependencies: dmed = u(x1, x2), dmed = v(x2, x3) and dmed =w(x1, x3). The dependency u(x1, x2) and its behaviour havebeen extensively discussed in [48, 54, 71]. Our attentionwill now focus on the results provided by RSM for dmed =v(x2, x3), for three values of x1 = D which are the mostfavorable for the aim of obtaining very small fiber diameters,and for dmed = w(x1, x3), for two values of x2 = Q.

The model u(x1, x2) revealed that dmed decreases as x1decreases [71]. Therefore, in representing the responsesurfaces for the dependency dmed = v(x2, x3), we haveconsidered for x1 = D only the three smallest values: D =45mm, D = 70mm and D = 100mm. The surfaces arerepresented in figure 1 (a) to (c).

It appears that small values of the flow rate entail smallmean fiber diameters: dmed decreases as Q decreases.Therefore, the approximation models for the third partialdependency dmed = w(x1, x3) have been determined onlyfor the two smallest values of the flow rate: Q = 0.05mL/min and Q = 0.075mL/min. The corresponding responsesurfaces are presented in figure 2 (a), (b) and (c) and showthat dmed decreases as x3 = U increases. As already provedby the model dmed = u(x1, x2), [71]), dmed also increaseswith x1=D.

Our data were subject to an analysis performed onMatlab 7.5.0 (R2007b). In what follows, we shall integratethe three models u(x1, x2), v(x2, x3), w(x1, x3) and providethe technical interpretation of the results. This interpretationconsiders the behaviors and facts communicated on thistopic, derived by other researchers [39, 55, 66] from similarexperiments.

Table 1CHARACTERISTICS 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, 0.191Pas. The solubility of PEI was tested in DMA/THF solvent(1:1) ratio by computing the Hansen coefficients, andamong the tested solutions with concentrations rangingbetween 8 and 14% PEI, the PEI solution with theconcentration of 12% has an excellent solubility [49, 71].For the preparation of the polymer solution, the polymerwas dried for 2 hours at 100oC under vacuum conditions.The polymer dissolution in the solvent mix was made bymagnetic stirring for 24 h at 500oC.

Choice of parameters and rangeIn our experiments, we have used three syringes with

the volume of 3mL and 0.2mm inner needle diameter; theinter-nozzle distance was 2.5mm. The interval ofdisplacement along the Ox axis was 100mm, and alongthe Oz axis was 80mm. The equipment has as collectingmechanism type a rotating cylinder, with the cylinderrotation speed v = 1000rpm. The experiments wereperformed under the following environmental conditions:20oC, RH = 40%, normal atmospheric pressure. Under theseconditions, we have selected the values for spinningdistance, applied voltage and volume flow rate to establishthe influence of these parameters on PEI nanofiberelectrospinning.

The experiment that we have designed in order to studythe electrospinning process [71] comprised the realizationof 5x4x5=100 technological variants. These resulted fromall the possible combinations of values for the constructiveand technological parameters, as follows: D = 45mm, D= 70mm, D = 100mm, D = 120mm and D = 130mm forthe 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 theexperimental plan.

Investigation methodsMethods of fiber characterization

The scanning electron microscope (SEM) was used tocharacterize the obtained PEI fibers, which were previouslygold plated using a Phenom G2 equipment [38, 48, 54, 60,

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The response surfaces graphically represented in theprevious section allow us to visualize the relationshipbetween the predictors flow rate (Q) and voltage (U) andthe mean fibers diameter (both in correlation with the thirdconstructive parameter D, the distance between needlesand collector), as dependent variable. The influence of thespinning distance D (denoted x1) on the fibers diameterhas been discussed in [71]. The specialty literature reports

both increase in fiber diameter and decrease in fiberdiameter [39, 53, 55, 66] upon D, depending on the ratiobetween D and the electric field strength E (KV/cm),polymer solution concentration and solvent evaporationrate. For the polyetherimide solution that we have used inelectrospinning, the mathematical models showed thatlonger spinning distance induces an increase in the fiberdiameter.

Fig.1. Response surfaces for mean fiberdiameter in terms of voltage (U) and flow rate(Q) for three values of D: (a) D = 45mm, (b) D

= 70mm, (c) D = 100mm, (d) simultaneousrepresentation for the three response

surfaces

b

c

d

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Influence of the flow rate Q = x2 (mL/min) on the meanfibers diameter

In our experiment, dmed increased with the volume flowrate, as depicted in Figure 1 (a) to (f) in [71], and also infigure 1 (a) to (c). The equations (3) to (6) [71] support thisconclusion, as the coefficient of DQ is positive and thecorresponding terms are significant. Our findings areconsistent with previous research [39, 55, 66].

Influence of the voltage U = x3 (KV) on the mean fibersdiameter

In our experiment, the fibers diameter decrease whenthe 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 theminimum value for fibers diameter is recorded for U=35kV.

Figure 3 presents the projection of the response surfacein figure 2 (e) from [71], for the most favorable value of U,which leads to small diameter of fibers, namely 35kV. Thedark-grey lines are displayed in the favorable zone of theparameters (while the light-grey ones are higher).

ConclusionsThis paper presents the study of the influence of the

process variables U (the applied voltage) and Q (the feedrate) on the average values of the diameters of the fiberselectrospun from polyetherimide solution (PEI) with

a

b

c

Fig. 2. Response surfaces for mean fiberdiameter in terms of distance (D) and voltage(U) for two values of Q: (a) Q = 0.05mL/min,

(b) Q = 0.075mL/min, (c) simultaneousrepresentation for the four values of Q

Fig. 3. The projection of the response surface forU =35kV

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concentration of 12%, using as solvents a mixture ofdimethylacetamide/tetrahydrofuran (DMAC/THF) 1:1 ratio.The study and its interpretation are made in conjunctionwith the similar ones performed for the constructiveparameter D (spinning distance). Several significantresponse surfaces have been plotted for the partialdependencies: dmed as function of D(mm) and Q(mL/min)in our study, and for dmed as function of Q(mL/min) andU(kV), and D(mm) and U(kV) in the present paper. Theirjoint analysis show that the optimum technological domainis defined by small values of the spinning distance (D =45-70mm), small values of the flow rate (Q = 0.05 -0.075mL/min) and high values of the voltage (U = 30-35kV). The smallest values of D(mm) and Q(mL/min) leadto convenient values of the mean fiber diameters, whilethe desired characteristics for the fibers diameter isobtained for the highest value of U(kV).

An accurate choice of all environmental andtechnological parameters for each polymer solution (withoptimal values of concentration, viscosity, molecularweight, solution conductivity) and a proper correlation ofthese parameters lead to obtaining flawless fibers withpredetermined diameter.

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Manuscript received: 8.09.2015