Nanofibers with diameter below one nanometer from electrospinning

Sub-nanometer materials have received wide attention due to their unique properties in recent years. Most studies focus on the preparation and properties investigation of the inorganic sub-nanometer materials, while there are few reports on organic especially polymeric sub-nanometer materials such as sub-nanometer fiber due to the obstacles with respect to fabricating such small nanofibers. In this work we prepare PAA nanofibers with diameters ranging from hundreds of nanometers down to sub-nanometer via electrospinning from a polyamic acid (PAA) with ultrahigh molecular weight. The morphologies and size of the electrospun ultrathin nanofibers are characterized using scanning electron microscopy (SEM), transmission electron microscopy (TEM), and atomic force microscopy (AFM). AFM images combined with theoretic calculations show that sub-nanometer fiber of approximate 0.17–0.63 nm only containing one molecular chain was generated via electrospinning from ultra-dilute PAA solutions for the first time. These quite small sub-nanometer fibers would open a new area of electrospinning and provide further explorations on the production and application of electrospun sub-nanometer fibers with single molecular chains.


Introduction
In the past several decades, huge progress has been made in nanomaterials, and sub-nanometer materials (SNMs) is a burgeoning multi-disciplinary topic in nanoscience.The term, subnanometer, is used to delimit the size below one nanometer. 1NMs feature molecular level size, as well as exhibit distinct properties which are different from their nano-counterparts with larger sizes such as molecule-like properties, exibility induced behaviors and unique electronic structure.3][4][5][6][7] SNWs were usually synthesized by template assisted growth, 8 oriented attached growth, 9 ligand controlled growth, 10 catalyst-guided growth. 11Most of the SNMs are made from carbon materials, metal or inorganic materials.However, there are few reports regarding the one dimensional sub-nanometer polymeric bers.Generally, sub-nanometer polymeric bers refer to the one dimensional structure with ultrahigh aspect ratio with the diameter ranging from several angstroms to dozens of angstroms.From the theoretic point of view, such sub-nanometer polymeric bers can only contain several polymer chains or even single macromolecular chain.These sub-nanometer bers consisting of only one polymer chain have potential applications for size standards or molecular mass.The behavior of sub-nanometer bers is expected to be different from bulk polymer materials or even conventional nanomaterials.Direct behavioral information of sub-nanometer bers will inspire the appearance of new theories in polymer physics and also be very useful for the development of molecular devices based on high performance polymer materials.However, it was difficult to obtain its single molecular level information, e.g.mechanical, electrical and magnetic properties due to the obstacle toward fabricating such small nanober.Ultrathin nanobers with the diameter of less than 100 nm can be produced by phase separation, 12 selfassembling, 13 sea-island method, 14 template synthesis, 15 electrospinning, 16 and bubble-electrospinning. 17 For example, crystalline nanobers of linear polyethylene with the diameter of ranging from 30 to 50 nm was obtain by freeze-drying the polymeric mass with ultra-high molecular weight polyethylene. 18Fu Renchun et al. fabricated pure PANI nanobers with high electrical conductivity and a diameter of 40-50 nm using ethyl cellulose as the template. 19Kazuhiro Nakata et al. prepared continuous PET nanobers with the diameter of 39 nm by sea-island-type conjugated meltspinning and laser-heated ow drawing method. 20Yang et al. successfully produced ultrane PVA nanobers with diameter of 20 nm or less through bubble-electrospinning method. 21In our previous work, continuous nylon-4,6 nanober with diameter of 1.6 nm had been successfully yielded by electrospinning, which only contains tens of polymer chains in theory. 22To the best of our knowledge, it is the smallest nanober which has been reported until now.4][25] Electrospinning occurs when the electrical forces form the electrostatic repulsion at the surface of a polymer solution or melt overcome the surface tension and creates an electrically charged jet out of the pipette. 268][29] Although electrospinning is a facile technology to produce ultrathin nanobers, till now, to the best of our knowledge, it is still a great challenge to prepare sub-nanometer bers by electrospinning.
In this work, we break through the constraint of the formation mechanism of traditional electrospun bers and proposed the concept to produce sub-nanometer bers by electrospinning ultra-dilute polymer solution with weak macromolecular entanglement.Via electrospinning an ultra-dilute solution (0.03-0.01 wt%) from a polyamic acid (PAA) with ultra-high molecular weight (M n > 10 6 g mol À1 ), the sub-nanometer bers with diameter approximate 0.17-0.63nm were achieved.Further molecular simulation suggests that such small nano-ber contains even only one molecular chain.This is the rst time to produce single molecular chain-based sub-nanometer bers from electrospinning, and this discovery is expected to open a new insight to the preparation of single molecular chainbased sub-nanometer bers and future investigations on their properties and applications.

Preparation of polymer solution for electrospinning
The PAA solution (8.74 wt%) for electrospinning, was synthesized from equimolar ratio of dianhydride BPDA and BPA by a polycondensation in DMAc at À5 C with intense mechanical stirring for 24 h. 30,31The macromolecular structure of PAA was shown in Fig. S1.† The intrinsic viscosity ([h]) and the average molecular weight (M w ) were 5.4 dL g À1 and 1.09 Â 10 6 g mol À1 , respectively.

Electrospinning
The solutions for electrospinning were prepared by diluting the as-prepared PAA solution (8.74 wt%) with different concentrations from 6 wt% to 0.01 wt%.0.1 wt% of DTAC with respect to DMAc was added to increase the electrical conductivity of the solutions when the PAA solution concentration was below 2 wt%.Polymer solution in DMAc was held in a syringe with an internal diameter of about 12.5 mm with a needle (internal diameter of 0.45 mm).The electric elds were 200 kV m À1 , by applying a positive 30 kV and a negative 10 kV electrical potential between a spinneret and a collector.The electrospun nanobers were collected with 20 cm collecting distance by copper grids with holy carbon lms for SEM and highresolution TEM measurement and freshly cleaved mica for AFM characterization respectively.All the samples were dried at 80 C for 8 h in vacuum to remove the residual solvent.

Measurements and characterization
The intrinsic viscosity measurements were measured at 25 C using an ubbelohde capillary viscometer.The morphologies of polymer nanobers were examined by scanning electron microscopy (SEM), transmission electron microscopy (TEM), and atomic force microscopy (AFM).SEM measurements were performed with a JSM-6701F microscope (JEOL Ltd, Japan) at an acceleration voltage of 5 kV.TEM images were obtained using a JEM 2100 microscope (JEOL Ltd, Japan) and a Technai-12 microscope (FEI, USA) with an operation voltage of 200 kV and 120 kV, respectively.AFM measurement was carried out with a Multimode V8 instrument equipped with a NanoScope V controller (Bruker Corporation, Germany) and a standard silicon cantilever (OTESPA model) with a length ranging from 140 to 180 mm and typically resonance frequency of about 300 kHz.The tip radius is about 7 nm.All AFM images (512 Â 512 pixels) were obtained with a scan rate of 1.0 Hz and scan angle of 0 in tapping mode at room temperature under ambient conditions.Offline images were only simply attened by Nanoscope III 5.12r2 soware without any further process.

Effect of concentration and conductivity on the ber morphology
3][34] The formation of macromolecular chain entanglements has been acknowledged as the primary effect for the ber formation.According to the concentration dependence of viscosity of linear polymers in good solvents, Colby et al. identied four different concentration regimes including dilute, semidilute unentangled, semidilute entangled, and concentrated regimes. 35The critical chain overlap concentration (c*), is the boundary between the dilute and the semidilute concentration regimes.The entanglement concentration (c e ) is the crossover concentration between the semidilute unentangled and semidilute entangled regimes.Electrospinning of dilute, semidilute unentangled, semidilute entangled and concentrated polymer solutions resulted in the formation of only polymer droplets or beads, a mixture of polymer droplets and beaded bers, beaded bers, uniform and beaded free bers, respectively.In general, the critical chain overlap concentration (c*) is frequently dened by the reciprocal of the intrinsic viscosity, 36,37 1/[h].Hence, according to Guopta's study, c* of the PAA solution is about 0.19 wt%, and the concentrations used to electrospinning in this study can be divided into four categories: dilute regime (0.01-0.1 wt%), semidilute unentangled regime (0.3 wt% and 0.5 wt%), semidilute entangled (1 wt%), and concentrated regime (2-6 wt%).The absolute viscosity and electrical conductivity of the above polymer solutions with different concentrations were summarized in Table S1 † and plotted in Fig. 1.It can be seen that the absolute viscosity of polymer solutions increases with the concentration increased.In concentrated regime (2-6 wt%), polymer chains entangled with each other, therefore the interactions between polymer chains increase, resulting in signicant increasing in viscosity as the solution concentrations increase.While polymer chains are isolated by solvent and act as separate coil in other three regimes (<2 wt%), so increasing solution concentrations do not affect the viscosity obviously.The electrical conductivity of polymer solution is dependent on both the concentration and the additional organic salt in the solution because the charge density of the polymer solution increases from the ions ionized mainly from DTAC.The electrical conductivity of polymer solution decreases with the increasing of concentration when the solution concentrations below 2 wt% because the amounts of DTAC (0.1 wt% of the solvent) increase with the decreased solution concentrations.
In this work, electrospun nanobers with different diameters can be obtained by adjusting the concentrations of PAA solution.Fig. 2 shows SEM images of nanobers with corresponding diameter distributions from PAA solutions with various concentrations.For the 6-2 wt% solutions in concentrated regime, the polymer chains in solutions entangle with each other, leading to the smooth and uniform electrospun PAA nanobers without any beads on the bers (Fig. 2a-e).As expected, the average diameters of nanobers decreased dramatically from 490 AE 60 to 100 AE 21 nm when the concentrations decreased from 6 wt% to 2 wt%.When the concentration decreased to semidilute entangled regime (1.0 wt%), some beaded bers but with very thinner diameters of 21 AE 4 nm were generated (Fig. 2f).These beaded bers could be because of the insufficient intermolecular entanglements between polymer chains to overcome the capillary instability.Further investigation by TEM images (see Fig. S2 †) on the ber morphology and ber diameter was well agreement with the results obtained by SEM analysis (Fig. 2).
Further decreasing the concentration of PAA solution in semidilute unentangled regime led to a mixture of ultra-thin nanobers, beaded bers and few polymer droplets (Fig. 3a  and b), and the average ber diameter further decreased.The sub-nanometer bers with diameter less than 1 nm (indicated by white arrows, Fig. 3c and e) could be achieved when the concentration of PAA solutions was in the dilute regime of 0.1, 0.06 and 0.03 wt%.The smallest measured diameter of the subnanometer ber by TEM was 0.98 nm (Fig. 3d).In this regime, a few large polymer droplets simultaneously (indicated by red arrows, Fig. 3c-e) were observed due to the insufficient chain overlap between the chains.Unfortunately, the morphology and size of the sub-nanometer ber with thinner diameter could not be precisely measured even by electron microscopy because the spatial resolution of SEM and TEM can hardly reach that regime (several faint ber images indicated by white arrows in Fig. 3ce).In addition, when the concentration further decreased to 0.02 wt%, it is difficult to observe sub-nanometer bers, which could be because of the resolution limitations of TEM caused by holy carbon lms covered on the copper grid (Fig. 3f).Therefore, it is highly required that a technique can be used for precise determination on the morphology and ber diameters for the samples, which were prepared from ultra-dilute PAA solutions by electrospinning.

Sub-nanometer PAA bers by AFM
AFM with tapping mode can greatly reduce the irreversible destruction of sample surfaces, and has been widely utilized to study the structure and morphology of samples at molecular or even atomic resolutions in three dimensions. 38,39For AFM characterization, electrospun bers obtained from PAA solutions with various concentrations were collected by using newly exfoliated mica.The morphologies of the bers were shown in Fig. S3 † and 4. The corresponding ber diameters measured by AFM height images were shown in Table S1.† The ber diameter was well consistent with the results obtained by TEM and SEM analysis when the PAA concentration in the range of 0.3-5 wt%.When the PAA concentration came to 0.1-0.01wt%, continuous sub-nanometer bers with diameter of  less than 1 nm could be achieved by electrospinning.It is well known that phase images in AFM were generated as a consequence of variations in material properties, such as viscoelasticity, friction, and adhesion. 40,41In this experiment, phase images together with height images were used to discriminate the topography of the single-molecule chains on the surface of sub-nanometer bers.It is evident that phase images can produce very high material contrast of ne structures unveiling more details of the morphology that barely can be seen in height images as shown in Fig. 4. From the cross-section analysis (Fig. 4c, f and i), it can be seen that the diameter of nanobers electrospun from 0.03 wt% PAA solution can be small to 0.3-0.7 nm; the diameters of nanobers electrospun from 0.02 wt% and 0.01 wt% solutions can be thin to 0.17-0.4nm.The different diameters at different position of the same sub-nanometer ber could be attributed to the different macromolecular conformation along the bers.The width of sub-nanometer ber is approximate 50 nm due to the convolution effect. 42,433 Effect of c/c* on ber diameter By correlation the ber diameters to the solution concentrations, the c/c* dependent ber diameters was plotted in Fig. 5.
The relationship between ber diameter (Y) and c/c* (X) in this study can be tted by cubic model (dashed blue line in Fig. 5) with the eqn (1): where a, b, c, and d have values of 0.61948, 0.08154, 0.92149 and À0.01383 (Table S2 †), respectively.When the c/c* > 6, the solution concentration was in the concentrated regime (IV) and the ber diameter Y increased dramatically.In the semidilute entangled regime (III) and semidilute unentangled regime (II), the effect of solution concentration on the ber diameter became smaller and smaller.When the solution concentration shied into dilute regime (I), it had a tiny effect on the ber diameters.In this regime (I), the ber diameter decreased in the range of sub-nanometer, where bers composed of single molecular chain or several molecular chains could be obtained.

Model of repeat unit of PAA molecules
To investigate the molecular conformation in such sub-nanometer bers, theoretical calculations were performed.The structural optimizations for macromolecules of PAA were performed using the projector-augmented wave (PAW) formalism of density functional theory (DFT), as implemented in the Vienna ab initio simulation package (VASP), [44][45][46] and the Perdew-Burke-Ernzerhof (PBE) type exchange-correlation. 47 The kinetic energy cutoff for the plane-wave expansion was set to 500 eV, and the effects of spin polarization were considered.The repeat unit of single PAA chain contains 28 C atoms, 2 N atoms, 6 O atoms and 18 H atoms in the systems with the dimension of 30 Â 30 Â 21.86 Å.The minimum distance between the sidewall of the individual macromolecules of PAA and its periodic images is greater than 24.0 Å, which is large enough to avoid the interaction between the neighboring single PAA chains.And a (1 Â 1 Â 3) Monkhorst-Pack was used for the k-point sampling.The role of the van der Waals (vdW) interaction was investigated using DFT-D2 method including the pairwise force eld implemented by Grimme. 485 Simulation of PAA molecules in sub-nanometer bers Theoretical simulation was performed to investigate the stack of PAA macromolecules in the sub-nanometer bers.Fig. 6 and S4 † present the molecular structure models for individual, two and three molecules of PAA molecular chain (cross-section, side view, and molecular chain).The smallest sub-nanometer bers composed of only one PAA molecular chain.According to the simulation, the single PAA molecule should possess a diameter ranging from 0.17 to 0.65 nm.As shown in Fig. 6a, when the individual PAA molecule is parallelly anchored onto the substrate, the smallest diameters of around 0.17-0.33nm could be obtained.If the individual PAA molecule is vertically anchored onto the substrate, the calculated diameters are ranging from 0.43 nm to 0.65 nm.This simulation on the diameter is well agreed with the measurement by AFM in Fig. 4d-i (0.17-0.37 nm).Therefore, we can speculate that the PAA nanober observed at AFM images as shown in Fig. 4d-i should contain only one individual PAA molecular chain.The PAA bers with two molecular chains were also studied by the simulation.The model in Fig. 6b showed the best thermodynamical stability of the two PAA molecules while Fig. S4a and  b † presented the models with energy 0.37 eV and 0.74 eV higher than the most stable model in Fig. 6b, respectively.For the stable structures in Fig. 6b and S4a, † the diameter of the two stacked PAA molecules was in the range of 0.5-0.7 nm, either for parallel or vertical model.This size is consistent with the diameters results of sub-nanometer by AFM measurement in Fig. 4a-c (0.33-0.63 nm).The simulated diameter around 0.7 nm was also detected when the individual PAA molecule is vertically anchored onto the substrate (Fig. 6a), but this vertical mode should be not stable.Thus, the simulation and analysis on two PAA molecules proved that the sub-nanometer bers with diameter in the range of 0.5-0.7 nm by AFM should contain only two PAA molecules.Further simulation of stack of three PAA molecules was presented in Fig. 6c and S4c, † which shows the most stable conguration and the model with energy 0.79 eV higher, respectively.In these two cases, the observed sizes of the three PAA chains were in the range of 0.61-1.51nm, which agreed with the diameter results from electrospinning of 0.1 wt% and 0.06 wt% PAA solutions (Table S1, † 0.93 AE 0.20 nm, and 0.88 AE 0.20 nm).The simulated diameter more than 1 nm was also observed for the two stacked PAA molecules chains in Fig. S4b † with vertical mode, but this vertical mode was usually not stable and could not obtained in the bers.Therefore, these bers from 0.1 wt% and 0.06 wt% PAA solutions with diameter around 1 nm should compose of three PAA molecules.

Formation of sub-nanometer PAA bers
It is well known that nanober properties can be effect by numerous parameters such as applied voltage, needle to collector distance, initial jet radius, relaxation time, and solution properties like viscosity, polymer concentration, conductivity and solvent. 26,33,49,50Polymer chain entanglements are one of many parameters that can signicantly affect nanober formation during the electrospinning process.At high concentration, chain entanglement behaves in a similar manner as chemical cross links, signicant overlap of neighboring chains occurs, so uniform nanobers can be produced via electrospinning.In ultra-dilute polymer solutions, the randomly distributed chains are separated and there is no topological constraint or polymer chains entanglement in initial electrospun solution.From the perspective of the ber formation by traditional electrospinning, in dilute regime, application of voltage results in electrospraying or bead formation primarily due to Rayleigh instability. 28However, in this paper, we successfully fabricated sub-nanometer PAA bers via electrospinning of ultra-dilute PAA solutions (concentrations below 0.1 wt%).The formation mechanism of traditional electrospinning had been investigated in detail by Reneker group 51,52 and other researchers. 53,54Reneker et al. found that the detail motion path of the continuous jet is complex and the draw ratio of the jet under the applied electrical forces can reach up to 10 5 accounting for evaporation of the solvent. 51When longitudinal strain rate multiplied by the conformational relaxation time of the molecule is greater than 0.5, the random coil begins to transform to a stretched macromolecule and the macromolecular coils are likely to be stretched along the axis of the jet, which led to the decrease of cross-sectional area of the jet as much as 10 5 .Presumably, in the process of electrospinning of ultra-dilute solution, when the ejected jet ows far away from the tip, the solvent evaporates rapidly and the concentration of jet increases considerable.Subsequently, weak topological constraint between polymer chains and gradient viscosity occurs.It gives the macromolecular chains a chance to entangle with each other.When the chain entanglements can sufficiently stabilize the electrospinning jet, sub-nanometer bers can be yielded, otherwise the jet break up into little droplets.

Conclusions
In this work, sub-nanometer bers containing only one or two polymer molecular chains were successfully prepared for the rst time by electrospinning from ultra-dilute PAA solution.The ber diameters are greatly inuenced by the solution concentration and conductivity.The PAA solutions in dilute regime (0.01-0.1 wt%) with electrical conductivity $120 mS cm À1 can lead to the electrospun bers in sub-nanometer.SEM and TEM are difficult to observe such small bers due to the sensitivity of polymer molecules to electron beam and the spatial resolution of electron microscopy.AFM with tapping mode are useful to observe the morphology and measure the ber diameter of such sub-nanometer PAA bers.From AFM measurements, the smallest sub-nanometer PAA bers possessed diameters in the range of 0.17-0.63nm.Further theoretic simulations suggest that such sub-nanometer bers contain only one or two PAA molecular chains.Future developments on such electrospun sub-nanometer bers could be their physical properties and applications.

Fig. 1
Fig. 1 Absolute viscosity (a) and electrical conductivity (b) of polymer solutions with different concentrations (0.1 wt% of DTAC with respect to the DMAc solvent was added in to the solutions when the concentrations were <2 wt%).

Fig. 6
Fig. 6 Optimized ground state structures for individual (a), two (b) and three (c) molecules of PAA molecular chain (cross-section, side view, and molecular chain).The labelled diameter are given in nm.