Method for producing elongated structures such as fibers from polymer solutions by straining flow spinning

Abstract

A method of molecular self-assembly is disclosed using two interacting streams that are allowed to interact and are subsequently forced through an orifice. A first stream of a dope solution of polymer molecules is extruded out of a capillary. The dope stream is surrounded by a focusing fluid which is miscible with the dope solution. The interaction between the jet of dope solution and surrounding focusing fluid creates hydrodynamic stretching and allows for extracting solvent from the dope solution. Concentrated polymers within the solution at stretched regions of the jet interact, and finally self-assembly takes place after the fluids are forced through the outlet of a converging nozzle. The formation of the structure can be optionally completed in a coagulating space. The structures thus obtained such as fibers or threads can be wound onto a mandrel.

Claims

1. A method of molecular self-assembly, comprising: extruding a stream of a dope solution of polymer molecules out of a capillary into a surrounding environment of a coaxially flowing focusing fluid miscible with the dope solution in a space limited by a convergent nozzle with an outlet that the dope and focusing fluid are forced to traverse; hydrodynamically stretching the extruded stream of polymer dope solution inside the convergent nozzle due to its interaction with the focusing fluid while simultaneously and selectively extracting solvent into the focusing fluid from the dope solution by molecular diffusion; wherein polymer concentration in the dope solution at a stretched region of the stream reaches a level such that contact among polymer molecules results in molecular self-assembly of the polymer molecules and subsequently, a stretching is imposed when the dope solution and the focusing fluid are forced through the convergent nozzle outlet; and continuously extracting an elongated structure of self-assembled polymer molecules such as a fiber or a thread; wherein the capillary-nozzle system presents the following parameters: distance between the end of the capillary and the outlet of the convergent nozzle (d.sub.6) between 400 and 15000 pm, diameter of convergent nozzle outlet (d.sub.6) between 250 and 800 pm, dope capillary tapering angle (α) of 100 to 900, and the rate of flow of the dope solution and focusing fluid flow is at least 10−.sup.20 m.sup.3/s.

2. The method according to claim 1, wherein the length of the convergent region of the convergent nozzle (d.sub.7) is between 2000 to 4000 μm.

3. The method according to claim 1, wherein the convergent nozzle outlet is circular.

4. The method according to claim 1, wherein the convergent nozzle outlet is a slit in a plate.

5. The method according to claim 1, wherein the dope solution and the focusing fluid go through the outlet of the convergent nozzle and enter a coagulating space.

6. The method according to claim 5, wherein the coagulating space is a coagulating tube.

7. The method according to claim 5, wherein the coagulating space is a coagulating bath.

8. The method according to claim 7, wherein the focusing fluid and/or the coagulating bath comprise an alcohol, acetone, an aqueous salt solution or mixtures thereof.

9. The method according to claim 7, wherein the pH of the focusing fluid and/or the pH of the coagulating bath differs from the pH of the dope solution by more than 0.1.

10. The method according to claim 1, wherein the dope solution and the focusing fluid go through the outlet of the convergent nozzle and enter a coagulating space, wherein the convergent nozzle outlet is a slit in a plate and wherein the coagulating space is a space created by two parallel plates.

11. The method according to claim 1, wherein the polymer comprises amino acids.

12. The method according to claim 11, wherein the polymer is a peptide of at least 5 amino acids.

13. The method according to claim 11, wherein the polymer includes at least one amino acid motif selected from the group consisting of: -GA-, -A.sub.n-, -GPG- and -GGX-, wherein n is the number of amino acids A and ranges from 2 to 20 and where X is an amino acid other than Glycine.

14. The method according to claim 1, wherein the ratio of dope flow rate Q.sub.d to the focusing fluid flow rate Q.sub.f is less than 0.7%.

15. The method according to claim 14, wherein Q.sub.f is less than 0.2%.

16. The method according to claim 1, wherein the spun fiber or thread is retrieved on a take up device such as a rotating mandrel or a suction instrument.

17. The method according to claim 16, wherein the ratio of the speed of the fiber or thread at the take up device to the speed of the focusing fluid ranges between 20% and 500%.

18. The method according to claim 16, wherein the ratio of the speed of the fiber or thread at the take up device to the speed of the focusing fluid ranges between 50% and 200%.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention is best understood from the following detailed description when read in conjunction with the accompanying drawings. It is emphasized that, according to common practice, the various features of the drawings are not to-scale. On the contrary, the dimensions of the various features are arbitrarily expanded or reduced for clarity. Included in the drawings are the following figures:

(2) FIG. 1 is a schematic cross sectional view of components used in one embodiment of the method of the invention showing the end portion of the capillary-nozzle system. The figure is schematically labeled with respect to different speeds, flow rates and some important geometric parameters useful in understanding aspects of the invention. Ud, Qd, Uf and Qf stand for the dope speed, dope flow rate, focusing fluid speed and focusing fluid flow rate, respectively. The geometrical parameters correspond to the diameter of the nozzle outlet, d.sub.6, and the diameter of the dope stream, d.sub.d.

(3) FIG. 2 is a cross sectional schematic view of components used in one embodiment of the method of the invention showing different geometric parameters with different speeds and flow rates at large distances from the capillary-nozzle system outlet.

(4) FIG. 3 is a schematic cross sectional view of a system suitable for carrying out the method of the invention showing a spinning process using the capillary-nozzle system and a coagulating bath. Reference signs are as follows: syringe connected to a pump (1), focusing fluid (1′), syringe connected to a pump (2), dope (2′), capillary (3), nozzle (4), coagulating bath (5), and take up device such as a mandrel (6)

(5) FIG. 4 is a cross sectional schematic view of components of the invention showing details of the capillary-nozzle system geometry of an embodiment with the coagulating bath (for instance, FIG. 3) while including relevant dimension information. Reference signs are as follows: inner diameter of the capillary (d.sub.1), outer diameter of the capillary (d.sub.2), inner diameter of the nozzle (d.sub.3), outer diameter of the nozzle (d.sub.4), distance between the end of the capillary and the outlet of the nozzle (d.sub.5), diameter of the outlet in the nozzle (d.sub.6), length of the convergent region of the nozzle (d.sub.7), and tapering at the end of the capillary (α).

(6) FIG. 5 is a schematic cross sectional view of an extrusion device used in a spinning process using the capillary-nozzle system with a coagulating tube or capillary. Reference signs are as follows: syringe connected to a pump (1), focusing fluid (1′), syringe connected to a pump (2), dope (2′), dope capillary (3), nozzle (4), coagulating tube (capillary) (5), and take up device such as a mandrel (6).

(7) FIG. 6 shows specific aspects of components used in connection with one embodiment of the method of the invention showing details and relevant dimensions of the capillary-nozzle system coupled to a coagulating tube (or capillary). Reference signs are as follows: inner diameter of the capillary (d.sub.1), outer diameter of the capillary (d.sub.2), inner diameter of the nozzle (d.sub.3), outer diameter of the nozzle (d.sub.4), diameter of the outlet in the nozzle (d.sub.6), and outer diameter of the coagulating capillary (d.sub.8), distance between the dope capillary and the nozzle outlet (d.sub.5), length of the coagulating capillary (L), and tapering at the end of the dope capillary (α),

(8) FIG. 7 consists of a graph showing data relating to spinnable conditions in terms of focusing fluid velocity (U.sub.f) and dope initial velocity (U.sub.d) for the geometrical parameters: d.sub.6=400 μm, α=90° and d.sub.5=1000 μm; in composition of dope: Low Molecular Weight (LMW, protein obtained after a degumming process in Na.sub.2CO.sub.3) 20% fibroin concentration in acetate buffer 0.5 M with a pH=5.5; focusing fluid and coagulating fluid: absolute ethanol; described in connection with the present invention. Filled circles: continuous spinning, Open circles: no spinning, Squares: insoluble fibers are retrieved from spinning, Dashed lines: limits of the spinnable regions for the corresponding speed of the take-up mandrel (V.sub.m).

(9) FIG. 8 provides a graph showing data providing a comparison of the experimental value of the ratio D/d.sub.6, where D is the diameter of the fiber and d.sub.6 the diameter of the outlet of the nozzle, the theoretical values of d.sub.d/d.sub.6 where d.sub.d is the calculated value of the diameter of the dope using equation (4) (squares) or equation (9) (circles).

(10) FIG. 9 consists of two graphs showing a comparison of the measured values of the diameter of the fiber and the theoretical value as a function of (the upper graph) the ratio between U.sub.f (focusing flow velocity) and V.sub.m (take-up mandrel velocity) and (the lower graph) the ratio between U.sub.d (dope flow velocity) and V.sub.m.

(11) FIG. 10 consists of two graphs showing data demonstrating the quality of the fibers measured as standard deviation of the mean diameter along the fibers length with respect to the mean diameter as a function of the ratio U.sub.f/Vm (the upper graph) and U.sub.d/V.sub.m (the lower graph).

(12) FIG. 11 shows a comparison of the FTIR spectra of regenerated fibers spun under different spinning conditions and silkworm silk fibers. The region of the amide I corresponding to the C═O vibration of the protein back bone is shown as it contains information on the secondary structure of the proteins. Continuous dark line: degummed silkworm silk; dashed line: regenerated fiber from large molecular weight dope; dotted line: regenerated fiber from small molecular weight dope; Continuous light line: fibroin with no β-sheet. The vertical lines indicate the position of the peak.

(13) FIG. 12 consists of two graphs showing a comparison of the stress-strain curves of regenerated silk fibers spun under different spinning conditions (upper graph) and a zoom on the initial elastic behavior to facilitate the comparison (lower graph). All the fibers were spun using a nozzle with an orifice diameter of d.sub.6=400 μm, a distance between the end of the capillary and the outlet of the nozzle of d.sub.5>2000 μm, a flow rate of the dope of Q.sub.d=5 μl/min and a roller speed of V.sub.R=3 m/min, the flow rate of the focusing fluid was adapted to obtain a continuous spinning Black line: regenerated fiber spun from 30% fibroin concentration, low molecular weight dope and coagulated with ethanol 80% and acetic acid 0.2M; Dashed line: regenerated fiber spun from 16% fibroin concentration and CaCl.sub.2 1 M high molecular weight dope and coagulated with ethanol 80% and acetic acid 0.2M (the fiber was subjected to post-spinning stretching in water, i.e. to wet-stretching); Dotted line: regenerated fiber spun from 8% fibroin concentration and CaCl.sub.2 1 M high molecular weight dope and coagulated with PEG 30%.

DETAILED DESCRIPTION OF THE INVENTION

(14) A method of producing elongated structures such as fibers or threads from polymer solutions, in particular silk protein solutions is disclosed. The method uses at least two miscible fluids which are brought into contact by injecting a dope solution of polymer molecules into a surrounding flow of a focusing fluid and, after an interaction time, are forced through an orifice. Both fluids undergo molecular exchange mainly by either or both of diffusion, and reactions while the two fluid streams are in contact. The straining flow between the inner dope solution and outer focusing fluid, to which the name of the process refers, is believed to result from the reduction in the cross sectional area of the dope solution stream at the outlet of the nozzle. After going through the nozzle outlet the fibers enter a coagulating space, which can be for instance a coagulating bath or a coagulating tube (or coagulating capillary). Spun fibers or threads may be recovered in a take up device, such as a rotating mandrel.

(15) Without being bound to any theory, the applicants consider that the process results in elongated structures including fibers and threads produced by the combined effect of (a) polymer molecules capable of physical organization at micrometer scale based on appropriate matching of given regions along their sequence, such as that obtained with silk and silk-related proteins, (b) the diffusion of the chemical species between the dope, the focusing fluid and, possibly, an external coagulating bath, (c) the relative displacement induced in the dope proteins by the interaction of the dope solution and the focusing stream as a result of traversing an orifice, and (d) in some embodiments, the relative speed between the fluid streams and the rotating mandrel or the like used as take up device. Thus, the method makes it possible to carry out the spinning of fibers having a wide range of microstructures and properties.

(16) The invention includes, in essence, four primary components and four secondary components, each of which are described below in further detail. The primary components are referred to below as the dope feeding capillary, dope, focusing fluid and nozzle. These components are referred to, at times, by somewhat different names as will be understood by the context. For example the dope feeding capillary is also referred to as the feeding source, the “dope” is also referred to as the dope solution or polymer solution. The “focusing fluid” is also referred to as a surrounding environment which is comprised of a fluid used to focus and stretch the dope solution. The “nozzle” is also referred to as nozzle outlet or simply outlet. As will be understood from the further description and examples below, the invention can be carried out with the basic primary components. However, by including certain secondary components, it is possible to supplement the results obtained and provide more commercially useful fibers.

(17) Description of the Elements and Procedure

(18) Dope Feeding Capillary.

(19) The capillary creates a stream of polymer solution (dope) such as a protein solution. The material of the dope feeding capillary is not restricted in principle, except for its compatibility with the dope and focusing fluid composition. A possible choice is silica for the capillary. The capillary is tapered at the end to obtain a smooth flow of focusing fluid, in particular the dope capillary tapering angle (α) ranges from 10° to 90°.

(20) Dope.

(21) The main parameters that define the composition of the dope are (a) the chemical nature of the polymers (i.e. natural (regenerated) silk fibroin, recombinant silk proteins, etc.), (b) the concentration of the polymers, (c) the pH of the solution, and (d) the addition of other chemical species (e.g. salts).

(22) According to one embodiment, the dopes used for the spinning are aqueous solutions of silk fibroin with a concentration that range from about 3 to about 40% (w/v). In a more particular embodiment, the fibroin concentration of the dope is from about 3 to about 20% (w/v) for high molecular weight fibroin, and a preferred range is from 15 to 20% (w/v). Whereas when the dope is a solution of low molecular weight fibroin the concentration range usually ranges from about 15 to about 40% (w/v), being a preferred range from about 30 to about 40% (w/v).

(23) Additionally the solution can be pH adjusted using different buffers like acetic acid 0.5 M for acid pHs or sodium carbonate 0.5 M for alkaline pHs. On the other hand, salts like CaCl.sub.2, MgCl.sub.2 or NaCl can be added to the dope to stabilize the fibroin chains in solution. The salt concentration can be preferably fixed in a range from 0 M to 1 M.

(24) In preferred polymer used in the dope solution is high molecular weight silk fibroin, preferably obtained from degumming silkworm silk cocoons in water (with a weight ratio of 1/50) at 121° C. in an autoclave for 1 hour.

(25) Focusing Fluid.

(26) The focusing fluid surrounds the dope solution and creates a stable stream of the dope under the conditions imposed by the geometry of the system, and by the flow rates of the dope and the focusing fluid itself. As described below, the focusing fluid is believed to initiate the coagulation process of the dope by (a) varying the composition of the dope or (b) by leading to a first stress-induced reorganization of the dope polymer or both (a) and (b).

(27) Nozzle.

(28) The combination feeding capillary-nozzle determines the geometry of the system and allows establishing three critical parameters of the process, the distance between the end of the capillary and the outlet of the nozzle ((d.sub.5), between 400 and 15000 μm), the diameter of the outlet in the nozzle ((d.sub.6), between 250 and 800 μm) and the distance and shape of the convergent region of the nozzle. Formation of a stable straining stream demands that the region geometry should not lead to instabilities, which requires a convergent geometry. In a particular embodiment, the length of the convergent region of the nozzle (d.sub.7) is between 2000 to 4000 μm. The material of the nozzle is not restricted in principle, except for its compatibility with the dope and focusing fluid composition. A possible choice is glass for the nozzle.

(29) The secondary components of the invention are:

(30) Coagulating Bath.

(31) The coagulating bath completes the solidification process of the elongated structure (fiber, thread, etc.) by inducing chemical changes, and consists of a container, which may have one side open to the atmosphere, that allows maintaining the streams of dope and focusing fluid for a sufficient distance after going through the nozzle outlet.

(32) Confined Coagulating Region.

(33) The confined coagulating region consists of a limited space in which the dope and focusing streams remain stable for a sufficient distance to allow coagulation after going through the nozzle outlet. It can be implemented, for instance, with a coagulating tube or capillary whose cross sectional area is reduced downstream.

(34) Coagulating Fluid.

(35) The use of a coagulating bath allows using a coagulating fluid that can be the same or different from the focusing fluid.

(36) The coagulation fluids can be grouped according to the nature of the main components. In an embodiment of the present invention, the coagulant used is selected from an alcoholic coagulant, a polyethylene glycol coagulant, glycol, glycerol and a salt-based coagulant.

(37) Alcoholic coagulants are mixtures of alcohol (e.g. ethanol or isopropanol) and water. The ratio of alcohol:water usually ranges from 100:0 to 60:40. Additionally, acetic acid can be added to the coagulation fluid to a final concentration that may range from 0 to 0.5 M.

(38) Polyethylene glycol coagulants are made of PEG aqueous solutions, typically in a range from about 10 to about 50% (w/v). The PEG molecular weight can generally range from about 2 to about 8 kDa. Additionally, acetic acid can be added to the coagulation fluid to a final concentration that may range from 0 to 0.5 M.

(39) Glycol and glycerol may also be used as coagulants.

(40) Salt-based coagulants are for instance ammonium sulphate or potassium phosphate solutions.

(41) Take Up Device.

(42) The spun fiber or thread is retrieved on a take up device from where it can be collected. Take up devices are, for instance, a rotating mandrel or a suction instrument. A post-spinning drawing step, either in air or in a different environment can be added. Retrieval of the fiber is characterized by the take up drawing ratio, DR1, defined as the ratio between the speed of the dope at the nozzle outlet and the linear speed of the take up mandrel. The post-spinning drawing step is characterized by the post-spinning draw ratio, DR2, defined as the ratio between the linear speed of the take up mandrel and the linear speed of the post-spinning drawing mandrel.

(43) Without being bond to any theory it is believed that production of fibers with the straining flow spinning procedure implies the following fundamental processes: Formation of nanocrystals by the dope polymers, interaction of the dope and the focusing streams, shear stresses exerted on the fibers leading to their relative displacement in the dope stream when traversing the nozzle outlet, and creation of a stable focusing stream in the coagulating space.

(44) Formation of Nanocrystals by the Dope Polymers.

(45) Straining flow spinning requires that the polymer molecules of the dope form nanocrytalline regions upon solidification. Exemplary representative of this type of molecules are silk fibroins. Natural silk fibroins of either silkworm or spiders, and related silk-bioinspired proteins are characterized by a small number of sequence motifs that allow the formation of solid elongated structures, for instance fibers. These motifs are basically -GAGAGS- (silkworm silk) and -An- (spider silk, with n ranging from 5 to 10). Solidification is the result of the assembly of these motifs in structures known as β-nanocrystals. The study of the natural silk spinning systems has revealed that the process of formation of the nanocrystals from the soluble protein dope consists of two steps. Initially, variations of the pH and removal of water molecules from the dope solution induce conformational changes in the proteins that lead to their reorganization. Subsequent relative displacement of the contacting proteins leads to further conformational changes and the creation of nanocrystals.

(46) Interaction of the Dope and the Focusing Streams.

(47) The solidification process is at least initiated, and could even be completed to some extent, through the interaction between the dope and the focusing streams. In parallel with the natural system, the first effect of this interaction is the modification of the chemical composition of the dope. This modification, in turn, depends on the diffusion of the different species from or to the dope and the focusing streams. In principle, the solvent molecules of the dope should diffuse to the focusing stream, increasing the effective concentration of protein in the dope stream. Additionally, some chemical species, such as protons, might diffuse from the focusing to the dope stream. In the particular case of protons, this type of diffusion would induce a change in the pH of the dope, which is relevant for the solidification in a natural system.

(48) To achieve an efficient diffusion process, a number of conditions on the focusing stream is preferably met: (1) Dope and focusing fluid should be miscible, (2) the length of the focusing stream should be long enough so as to allow sufficient diffusion of the dope solvent, (3) flow rates of the dope and focusing streams should be such that all along the process the dope stream is always confronted with non-saturated focusing fluid, so that the interchange of chemical species between the dope and the focusing fluid is effective. These conditions represent significant deviations from the flow focusing technology as described specifically in U.S. Pat. No. 6,116,516 “Stabilized capillary microjet and devices and methods for producing same”. The '516 patent indicates that the fluids used in the flow focusing processes should be immiscible and devote a detailed discussion to the influence of the surface tension between both fluids on the process. The '516 patent also teaches that the maximum length of the microjet obtained is 50 mm, which is below the values for the production of fibers with the present procedure, which typically exceed a length of 100 mm.

(49) According to one embodiment of the present invention, the flow rate of the dope is fixed between about 1 and about 50 μl/min. In particular, great results were obtained with low flow rates, in the range from about 3 to about 9 μl/min. The spinning can be performed in a wide range of flow rates of the focusing fluid, for instance from about 0.1 to about 20 ml/min.

(50) Shear Stresses in the Dope Stream and Relative Displacement of the Proteins.

(51) The fiber formation supposedly requires the relative displacement of the contacting polymer molecules, so that the regions susceptible to forming a crystalline phase are aligned. Simultaneously, the reorganization of the molecules favors interactions that eventually lead to fiber formation. In this regard, it is critical to reach a final polymer concentration in the dope that allows contact among proteins (or other polymers) in an environment that fosters relative displacements. The proposed technology allows the relative displacement of the proteins in the dope at two different steps. Initially, the difference between the flow rates of the dope and focusing streams induces a first mechanical effect on the dope which is simultaneous in time with the chemical interaction between both fluids. It is a singular feature of SFS that it allows exerting a further mechanical stress on the dope when the dope and the focusing fluid move along the converging geometry of the nozzle and eventually traverse the nozzle outlet. In this regard, the interaction between the dope and the focusing fluid extends along the d.sub.5 length within the nozzle, and the molecules in the dope are subjected to mechanical stresses when traversing the nozzle outlet. This way the effects of chemical interaction and mechanical forces on the molecules of the dope are largely uncoupled.

(52) The characteristic axial length of the focusing region is summarized as d.sub.7, which reflects the rate at which the focusing fluid accelerates from its passage around the feeding capillary of diameter d.sub.2 towards the discharge orifice of diameter d.sub.6. Specifically, for a given shape of the focusing nozzle given by a function g(z;d.sub.3,d.sub.6,d.sub.7), where z is the axial coordinate from the exit of the feeding capillary, the acceleration undergone by the focusing fluid at any point along the axis can be very approximately expressed as:

(53) $a=\frac{-2Q_f^2}{g^5}\frac{\mathrm{dg}}{\mathrm{dz}},$ For example, for a shape of the focusing nozzle given by the function:
g(z;d.sub.3,d.sub.6,d.sub.7)=(d.sub.3+d.sub.6+(d.sub.3−d.sub.6)Tan h(2(1−2z/d.sub.7)))/2, the acceleration approximately takes the form:

(54) $a=\frac{2^7\left(d_3-d_6\right)\mathrm{Sech}\left(2\left(1-2z/d_7\right)\right)Q_f^2}{{\left(d_3+d_6+\left(d_3-d_6\right)\mathrm{Tanh}\left(2\left(1-2z/d_7\right)\right)\right)}^5{d}_7},$
as long as d.sub.7 is sufficiently larger than d.sub.3. This acceleration imposes the local rate of axial stretching undergone by the focusing stream at any point along the axial length. Anyone skilled in the art may observe that this acceleration is maximum very close to the exit of the nozzle, and that most of the initial region after the exit of the feeding capillary is dominated by a slow motion compared to that of the high straining rate region around the exit of the focusing nozzle. This clearly separates the focusing region into two ones: (i) a first region where the dope is dominated by molecular diffusion processes that for example may lead to a change in pH, and (ii) a second region (downstream of the first one) dominated by a high straining and stress rate.

(55) The possibility of exerting mechanical stresses on the dope proteins after a given interaction time between the dope and the focusing fluid is characteristic of this technology and represents a major difference with respect to other technologies such as those presented in WO03060099A2, WO2005017237A2, WO2007141131A1 and WO2015048433A1.

(56) Creation of a Stable Focusing Stream in the Coagulating Bath or Confined Coagulating Region.

(57) The final solidification of the fiber can be favoured by extending the interaction between the dope and the focusing fluid within the coagulating bath or confined coagulating region, which implies the creation of a stable stream. The creation of a stable stream mainly depends on (1) the combined geometry of the dope feeding capillary and the nozzle, (2) the viscosity of the focusing fluid and, (3) if different from the latter, on the viscosity of the coagulating fluid. To a lesser extent it might also be influenced by (4) the viscosity of the dope. In certain embodiments, formation of a stable stream is favoured by a convergent geometry for the profile of the inner side of the nozzle (i.e. smaller inner diameter close to the nozzle outlet). The geometry of the nozzle represents a major difference compared with U.S. Pat. No. 6,116,516 and WO 01/69289 A2 “Methods for producing optical fiber by focusing high viscosity liquid”, since both patent documents require either divergent (U.S. Pat. No. 6,116,516) or convergent-divergent (WO 01/69289 A2) geometries. The formation of a stable stream of the focusing fluid is not indicated in any of the aforementioned patents, since the flow focusing effect is produced by a variation of pressure from the pressure chamber to the outer environment. In this regard, the stable microjet from the solution or melt in the former patent documents is formed due to pressure difference in the focusing fluid which prompts a smooth emission of material from a stable capillary cusp.

(58) Simplified Model of Some Basic Parameters of the Straining Flow Spinning Process

(59) A basic model of the straining flow system can be formulated as follows:

(60) The relationship between the flow rate and speed of the dope can be established from the continuity equation as:

(61) $\begin{array}{cc}{U}_d~\frac{Q_d}{d_d^2}& \left(1\right)\end{array}$
and that of the focusing fluid as:

(62) $\begin{array}{cc}{U}_f~\frac{Q_f}{d_6^2-d_d^2}~\frac{Q_f}{d_6^2}& \left(2\right)\end{array}$
where Ud, Qd, Uf and Qf stand for the dope speed, dope flow rate, focusing fluid speed and focusing fluid flow rate, respectively. The geometrical parameters correspond to the diameter of the nozzle outlet, d.sub.6, and the diameter of the dope stream, d.sub.d. The latter varies with increasing distance from the capillary outlet. The parameters are indicated in FIG. 1.

(63) The diameter of the dope stream, d.sub.d, can be calculated from the boundary layer theory, which assumes that the shear stresses at the boundary layer of the dope and focusing streams are equal. Application of this theory leads to the equation:
μ.sub.ƒρ.sub.ƒU.sub.ƒ.sup.3˜μ.sub.dρ.sub.dU.sub.d.sup.3  (3)

(64) Where μf (μd) and ρf (ρd) correspond to the viscosity of the focusing fluid (dope) and density of the focusing fluid (dope), respectively.

(65) Combination of equations (1)-(3) leads to the equation:

(66) $\begin{array}{cc}{d}_6~{d_6\left(\frac{{\mu }_d{\rho }_d{Q}_d^3}{{\mu }_f{\rho }_f{Q}_f^3}\right)}^{1/6}& \left(4\right)\end{array}$

(67) That establishes a relationship between d.sub.d and the geometrical and hydrodynamic parameters of the system. Equation (4) can be expressed in terms of the Reynolds number of the dope and focusing fluids as:

(68) $\begin{array}{cc}{\mathrm{Re}}_d=\frac{{\rho }_d{Q}_d}{{\mu }_d{d}_d};{\mathrm{Re}}_f=\frac{{\rho }_f{Q}_f}{{\mu }_f{d}_f}{d}_d~d_6\left(\frac{{\mathrm{Re}}_d}{{\mathrm{Re}}_f}\right){\left(\frac{{\rho }_f}{{\rho }_d}\right)}^{2/3}{\left(\frac{{\mu }_d}{{\mu }_f}\right)}^{4/3}& \left(5\right)\end{array}$

(69) For sufficiently large distances to the nozzle outlet, the previous analysis can be simplified using the continuity equation and assuming equality of the speeds of the dope and focusing fluid at the boundary.
U.sub.d.sup.∞≈U.sub.ƒ.sup.∞  (6)

(70) Assuming that the lateral size of the dope stream is much smaller than that of the focusing fluid:
d.sub.ƒ.sup.∞>>d.sub.d.sup.∞

(71) The following relationship can be established:
Q.sub.ƒ≈π/4(d.sub.ƒ.sup.∞).sup.2U.sub.ƒ.sup.∞  (7)

(72) Since by the equation of continuity:
Q.sub.d≈π/4(d.sub.d.sup.∞).sup.2U.sub.d.sup.∞  (8)

(73) And applying equation (6), it is finally found that:

(74) $\begin{array}{cc}\frac{Q_d}{Q_f}={\left(\frac{d_d^{\infty }}{d_f^{\infty }}\right)}^2.Math.d_d^{\infty }={d_f^{\infty }\left(\frac{Q_d}{Q_f}\right)}^{1/2}& \left(9\right)\end{array}$

(75) The hypotheses of the simplified model at large distances from the nozzle outlet are strictly true for the coagulating capillary embodiment and can be considered as an approximate value for the coagulating bath embodiment. The assumption of mass conservation was experimentally validated as shown below.

(76) At this point, the description of the process has proceeded by taking advantage of the prevalent role of the relative displacement of the molecules in the formation of the fiber. In this context, the stresses required to induce these relative displacements are assigned a secondary role, since it is implicitly assumed that the same lateral displacements of the contacting molecules in different dopes are assumed to lead to similar microstructures of the fibers. Following this rationale dopes with different viscosities and, consequently, subjected to different stresses might lead to the same final microstructure as long as the lateral displacements of the macromolecules are comparable. However, it is worth giving at least an estimation of the stresses involved in the process. Such an estimation can be provided by applying Bernouilli's equation to the flow near the nozzle to calculate the pressure drop, and by assuming that all stresses are of the same order of magnitude. The pressure drop is:

(77) $\begin{array}{cc}\Delta p\approx \frac{1}{2}{\rho }_f\frac{4^2{Q}_f^2}{{\pi }^2{d}_6^4}& \left(10\right)\end{array}$

(78) Using typical values of a straining flow process: ρf˜1000 kg/m.sup.3, Qf˜8.Math.10.sup.−8 m.sup.3/s (4.8 ml/min) and d.sub.6=400 μm, a value of Δp˜0.2 kPa is obtained. Equation (10) also shows that stresses increase with increasing values of the focusing fluid flow rate which, assuming a constant value of the dope flow rate, implies smaller values of the ratio Q.sub.d/Q.sub.f. As shown below, the improvement of the properties of the fibers for smaller values of the ratio Q.sub.d/Q.sub.f was validated experimentally, in agreement with the theory used to describe the straining flow process.

(79) It is worth indicating that the basic equations of this simplified model including equations (2), (4) and (10) depend critically on the nozzle outlet (d.sub.6), which is parameter characteristic of the SFS technology. Under the assumption that the value of the lateral size of the focusing fluid at a long distance from the nozzle outlet, d.sub.ƒ.sup.∞, is comparable to the value of the nozzle outlet, d.sub.6, equation (9) holds. Equation (9) predicts a dependence of the lateral size of the dope stream at large distances from the nozzle outlet (and, consequently, of the fiber) with the diameter of the nozzle outlet and the ratio between the flow rates of the dope and of the focusing fluid.

(80) As used herein, the term “about” means a slight variation of the value specified, preferably within 10 percent of the value specified. Nevertheless, the term “about” can mean a higher tolerance of variation depending on for instance the experimental technique used. Said variations of a specified value are understood by the skilled person and are within the context of the present invention. Further, to provide a more concise description, some of the quantitative expressions given herein are not qualified with the term “about”. It is understood that, whether the term “about” is used explicitly or not, every quantity given herein is meant to refer to the actual given value, and it is also meant to refer to the approximation to such given value that would reasonably be inferred based on the ordinary skill in the art, including equivalents and approximations due to the experimental and/or measurement conditions for such given value.

EXAMPLES

(81) The following examples are put forth so as to provide those of ordinary skill in the art with a complete disclosure and description of how to make and use the present invention, and are not intended to limit the scope of what the inventors regard as their invention nor are they intended to represent that the experiments below are all or the only experiments performed. Efforts have been made to ensure accuracy with respect to numbers used (e.g. amounts, temperature, etc.) but some experimental errors and deviations should be accounted for. Unless indicated otherwise, parts are parts by weight, molecular weight is average molecular weight, temperature is in degrees Centigrade, and pressure is at or near atmospheric.

(82) The following Table shows the explored range of spinning parameters with which fibers were obtained using a coagulating bath. It does not imply that spinning is not possible outside the values indicated in the Table.

(83) TABLE-US-00001 Minimum Maximum Parameter value value Diameter of Nozzle Outlet (μm), d.sub.6 250 800 Nozzle tube internal diameter 1100 (μm), d.sub.3 Capillary internal diameter (μm), 150 d.sub.1 Capillary external diameter (μm), 360 d.sub.2 Dope capillary-nozzle outlet 400 15000 distance (μm), d.sub.5 Dope capillary angle, α 10° 90° Length of the convergent region of 2000 4000 the nozzle, d.sub.7 (μm) Focusing fluid flow rate (ml/min), 0.3 16.5 Q.sub.f Dope flow rate (μl/min), Q.sub.d 1 50 Take-up mandrel speed (m/min), 1.3 12 V.sub.m Dope composition Silkworm silk fibroin (two different molecular weight distributions). Acetate buffer 500 mM, pH = 5.5 Distilled water CaCl.sub.2 1M Focusing fluid composition Ethanol/Water: (100/0)-(60/40) Isopropanol/Water: (100/0)-(60/40) Ammonium sulphate PEG (10-30%) Coagulating bath composition Ethanol/Water: (100/0)-(60/40) Isopropanol/Water: (100/0)-(60/40) Ammonium sulphate PEG (10-30%)

(84) In particular, the following embodiment has led to the production of fibers. Spinnable conditions are shown in FIG. 7 as a function of the take-up mandrel velocity (dashed lines), focusing fluid velocity (U.sub.f) and dope velocity (U.sub.d).

(85) Geometrical parameters of the embodiment: tapering angle of the capillary, α, 23°, diameter of the nozzle outlet, d.sub.6, 400 μm, distance between the end of the capillary and nozzle, d.sub.5, 1000 μm, and length of the convergent region of the nozzle, d.sub.7, 3500 μm.

(86) Dope composition: Silkworm Bombyx mori silk fibroin solution 20% w/v in a buffered aqueous solution with 500 mM acetate and pH=5.5. Fibroin was obtained from silkworm cocoons after a degumming step in boiling water with 0.5% Na.sub.2CO.sub.3. This degumming treatment leads to a significant decrease in the molecular weight of silk proteins.

(87) Focusing fluid composition: Absolute ethanol

(88) Coagulating bath composition: Absolute ethanol

(89) Some Properties of the Spun Fibers

(90) The basic features established in the theoretical analysis of the straining flow process as described above were validated from experimental data. Thus, if the diameter of the fiber, D, is assumed to be equal or at least proportional to the diameter of the dope stream, d.sub.d, equations (4) and (9) establish a linear relationship between the ratio D/d.sub.6 and the ratio of the flow rates, Q.sub.d and Q.sub.f. The exact relationship between both parameters depends on whether the conditions of infinite distance of the stream for the nozzle are admitted (equation 9) or not (equation 4). FIG. 8 represents the experimental values of the functions defined in eqs. (4) and (9) vs. the ratio D/d.sub.6, and it shows that a linear relationship is found in both cases.

(91) The hypotheses of the mass conservation as supposed from the use of the continuity equation and of the increased quality of the fibers for lower values of the ratio Q.sub.d/Q.sub.f are shown in FIGS. 9 and 10. The graphs (a) upper and (b) lower of FIG. 9 compare the diameter of the spun fibers with the theoretical diameter obtained by applying the conservation of mass equation as a function of [graph (a) of FIG. 9] the ratio between the focusing flow velocity, U.sub.f(=4Q.sub.f/πd.sub.6.sup.2) and take-up mandrel velocity (V.sub.m) and [graph (b) of FIG. 9] of the ratio between the dope initial velocity, U.sub.d(=4Qd/πd.sub.1), and take-up mandrel velocity. An excellent agreement is found between both values independently from the ratio between U.sub.f, U.sub.d and V.sub.m.

(92) Graphs (a) and (b) of FIG. 10 compare the quality of the fibers in terms of the variations observed in the diameter along the fiber measured as standard deviation from the mean diameter as a function of the ratio between U.sub.f and V.sub.m, and U.sub.d and V.sub.m, respectively. It is observed that lower values of any of the ratios (i.e. V.sub.m larger compared with either flow rate) leads to a significant improvement of the quality of the fiber, in agreement with the increased straining speed and induced protein reorganization associated with lower values of the ratio U.sub.d/V.sub.m.

(93) The possibility of modifying the microstructure of the fibers by varying the spinning conditions is shown in FIG. 11, where the Fourier Transformed Infrared Spectra (FTIR) of different samples are compared. The regions studied correspond to the range between wavelengths 1590 cm.sup.−1 and 1680 cm.sup.−1, since these peaks contain information on the amide I bond of the peptide chains. The amide I is produced by the vibration of the C═O group of the protein backbone, and its detailed position yields information on the secondary structure of the protein. The spectrum of natural silkworm silk is also shown, since the peak appearing as approximately 1620 cm.sup.−1 corresponds to the presence of β-nanocrystals. As indicated above, the presence of the β-nanocrystals is essential for the mechanical performance of natural silk fibers.

(94) The tensile properties of fibers spun under different conditions are shown in FIG. 12 as stress-strain curves. One of the fibers (dotted line), spun under the geometrical conditions: d.sub.6=400 μm, α=90°, d.sub.5=3500 μm and d.sub.7=4000 μm; with hydrodynamic conditions; Q.sub.d=5 μl/min, Q.sub.f=0.5 ml/min and V.sub.m=3 m/min; from a HMW dope with 8% fibroin concentration and CaCl.sub.2 1 M and using PEG 30% as coagulating fluid, shows a strain at breaking of 2.5 and a tensile strength of 28 MPa, which yield a work to fracture of approximately 50 MJ/m.sup.3. This value is comparable to the work to fracture of conventional polymeric fibers and, to the authors' best knowledge, is the largest work to fracture reported in regenerated silkworm silk fibers without a post-spinning step. With a post-spinning treatment that consists in stretching the fiber in water, higher tensile strength (110 MPa) and work to fracture (75 MJ/m.sup.3), although lower strain at breaking (0.8), can be obtained (FIG. 12, dashed line). These results were obtained using the same geometrical parameters explained above, with hydrodynamic conditions; Q.sub.d=5 μl/min, Q.sub.f=2.5 ml/min and V.sub.m=3 m/min; from a HMW dope with 16% fibroin concentration and CaCl.sub.2 1 M and using ethanol 80% with acetic acid 0.2 M as coagulating fluid.

(95) The preceding merely illustrates the principles of the invention. It will be appreciated that those skilled in the art will be able to devise various arrangements which, although not explicitly described or shown herein, embody the principles of the invention and are included within its spirit and scope. Furthermore, all examples and conditional language recited herein are principally intended to aid the reader in understanding the principles of the invention and the concepts contributed by the inventors to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and embodiments of the invention as well as specific examples thereof, are intended to encompass both structural and functional equivalents thereof. Additionally, it is intended that such equivalents include both currently known equivalents and equivalents developed in the future, i.e., any elements developed that perform the same function, regardless of structure. The scope of the present invention, therefore, is not intended to be limited to the exemplary embodiments shown and described herein. Rather, the scope and spirit of present invention is embodied by the appended claims.