Nanobursa

Twin-screw extrusion / electrospinning (TSEE) hybrid process

Conventional electrospinning operates by applying a high electric field (typically 10–30 kV over a 10–20 cm gap) across a polymer solution or melt delivered through a capillary needle, drawing a charged jet that attenuates into fibers collected on a grounded substrate. It lacks inherent capacity for solids conveying, compounding, melting of high-viscosity resins, or controlled dispersion of nanoparticulate fillers.

The TSEE process,^[2] pioneered at Stevens Institute, integrates a co-rotating twin-screw extruder as the front end of an electrospinning system. The extruder provides:

• Solids conveying and metered feeding of CNT-loaded polymer granules;
• Dispersive and distributive mixing via kneading disc elements to de-agglomerate CNT clusters;
• Precise temperature profiling and devolatilization;
• Controlled pressurization to deliver the melt/solution uniformly to a multi-nozzle spinneret.

The multi-nozzle spinneret is necessary to achieve throughputs at industrially relevant rates, since the volumetric flow rate per nozzle in electrospinning is severely limited by hydrodynamic and electrostatic stability constraints (see §Electrospinning jet stability below).

Graded nanobursa meshes are formed by sequentially collecting layers produced from different CNT-suspension feedstocks, each bearing a distinct metallic nanoparticle type, on the same rotating drum collector. This yields a stratified, functionally graded architecture.

Metal nanoparticle functionalization of CNTs

Before incorporation into the polymer melt, multi-walled CNTs (MWCNTs) are surface-functionalized. A representative sequence is:

1. Acid treatment (H₂SO₄/HNO₃ mixture, typical volume ratio 3:1, 60–80 °C, 1–4 h) to introduce carboxyl (–COOH) and hydroxyl (–OH) surface groups;
2. Chelation of metal precursor salts (e.g., PdCl₂, CoCl₂, AgNO₃, H₂PtCl₆) to the oxidized surface;
3. Chemical reduction (NaBH₄, hydrazine, or thermal) to generate metallic nanoparticles anchored to the CNT wall.

The resulting nanoparticle-on-tube structures are then dispersed in a polymeric carrier (e.g., polycaprolactone, PCL) prior to TSEE processing.

Electrospinning jet instability and fiber diameter

The transition from a steady cone-jet (Taylor cone) to an electrically driven bending instability determines the final fiber diameter. The electric field strength E at the capillary tip of radius R charged to potential V relative to a collector at distance d is approximated by

${\displaystyle E_{\mathrm {tip} }\approx {\frac {V}{2R\ln(4d/R)}}}$

The critical condition for jet ejection (Taylor cone formation) requires that the Maxwell stress exceed the surface tension restoring force:

${\displaystyle {\frac {\varepsilon _{0}E^{2}}{2}}\geq {\frac {2\gamma }{R_{\mathrm {jet} }}}}$

where ${\displaystyle \varepsilon _{0}}$ is the permittivity of free space, ${\displaystyle \gamma }$ is the polymer solution surface tension, and ${\displaystyle R_{\mathrm {jet} }}$ is the jet radius at the onset of instability. Solving for the jet radius:

${\displaystyle R_{\mathrm {jet} }={\frac {4\gamma }{\varepsilon _{0}E^{2}}}}$

The final fiber diameter ${\displaystyle d_{f}}$, accounting for viscoelastic stretching and solvent evaporation, scales as^[3]

${\displaystyle d_{f}\sim \left({\frac {Q\eta }{\pi \varepsilon _{0}E^{2}}}\right)^{1/3}}$

where ${\displaystyle Q}$ is the volumetric flow rate per nozzle, ${\displaystyle \eta }$ is the apparent viscosity of the spinning solution, and ${\displaystyle E}$ is the applied electric field. This relationship predicts that increasing the applied voltage (raising E) or reducing the flow rate reduces the fiber diameter, consistent with experimental observations on PCL–CNT nanobursa precursor suspensions.

Rheology of CNT-loaded polymer suspensions

The precursor suspension of CNTs dispersed in a polymer carrier is a non-Newtonian fluid. For concentrated suspensions exhibiting a yield stress ${\displaystyle \tau _{y}}$, the Herschel–Bulkley model is appropriate:

${\displaystyle {\dot {\gamma }}=0,\quad |{\boldsymbol {\tau }}|\leq \tau _{y}}$

${\displaystyle {\boldsymbol {\tau }}=\left({\frac {\tau _{y}}{\dot {\gamma }}}+K{\dot {\gamma }}^{n-1}\right){\dot {\boldsymbol {\gamma }}},\quad |{\boldsymbol {\tau }}|>\tau _{y}}$

where ${\displaystyle K}$ is the flow consistency index, ${\displaystyle n}$ is the flow behavior index (${\displaystyle n<1}$ for shear-thinning behavior typical of CNT suspensions), and ${\displaystyle {\dot {\gamma }}=|{\dot {\boldsymbol {\gamma }}}|}$ is the magnitude of the rate-of-strain tensor ${\displaystyle {\dot {\boldsymbol {\gamma }}}=\nabla \mathbf {v} +(\nabla \mathbf {v} )^{T}}$.

For the twin-screw extrusion stage, the relevant dimensionless number is the Deborah number

${\displaystyle \mathrm {De} ={\frac {\lambda _{r}{\dot {\gamma }}_{\mathrm {screw} }}{{\mathcal {L}}/{\mathcal {U}}}}}$

where ${\displaystyle \lambda _{r}}$ is the terminal relaxation time of the melt, ${\displaystyle {\dot {\gamma }}_{\mathrm {screw} }}$ is the characteristic shear rate imposed by the screw, ${\displaystyle {\mathcal {L}}}$ is a characteristic length of the die/nozzle, and ${\displaystyle {\mathcal {U}}}$ is the mean velocity. Optimal dispersion of CNT agglomerates requires ${\displaystyle \mathrm {De} \gg 1}$ in the kneading zones.

The Mooney–Kalyon plot

By analogy with the linearization introduced by Melvin Mooney (1940) for rubber elasticity, wherein a normalized stress ${\displaystyle T^{*}}$ plotted against ${\displaystyle \beta =1/\alpha }$ (reciprocal stretch) yields the material constants ${\displaystyle C_{1}}$ and ${\displaystyle C_{2}}$ from intercept and slope respectively, an analogous linearization termed the Mooney–Kalyon plot, is introduced for the rheological characterization of nanobursa precursor suspensions undergoing steady simple shear.

Define the reduced apparent viscosity

${\displaystyle \eta _{\mathrm {MK} }^{*}:={\frac {\tau -\tau _{y}}{\dot {\gamma }}}}$

and the reciprocal shear rate variable

${\displaystyle \beta _{\mathrm {MK} }:={\frac {1}{\dot {\gamma }}}}$

Then, for a Herschel–Bulkley fluid,

${\displaystyle \eta _{\mathrm {MK} }^{*}=K{\dot {\gamma }}^{n-1}=K\beta _{\mathrm {MK} }^{1-n}}$

Taking logarithms:

${\displaystyle \ln \eta _{\mathrm {MK} }^{*}=\ln K+(1-n)\ln \beta _{\mathrm {MK} }}$

A plot of ${\displaystyle \ln \eta _{\mathrm {MK} }^{*}}$ versus ${\displaystyle \ln \beta _{\mathrm {MK} }}$ yields a straight line whose slope gives ${\displaystyle (1-n)}$ and whose intercept gives ${\displaystyle \ln K}$. This is the Mooney–Kalyon plot for nanobursa precursor suspensions.

Formally, the analogy with the Mooney–Rivlin framework for hyperelastic solids^[4][5] is structural: just as the Mooney–Rivlin plot

${\displaystyle T_{11}^{*}=2C_{1}+2C_{2}\beta ,\quad \beta ={\frac {1}{\alpha }}}$

extracts the constants ${\displaystyle C_{1}}$ (intercept) and ${\displaystyle C_{2}}$ (slope) governing the strain energy density function

${\displaystyle W=C_{1}({\bar {I}}_{1}-3)+C_{2}({\bar {I}}_{2}-3)}$

the Mooney–Kalyon plot extracts the rheological parameters ${\displaystyle K}$ and ${\displaystyle n}$ governing the viscoplastic constitutive equation of the CNT-laden nanobursa precursor. In both cases the key insight is a linearization that reduces a nonlinear constitutive relationship to a straight-line fit on suitably chosen axes, with slope and intercept directly yielding the material constants.

Catalytic reaction model: hydrocarbon oxidation

The primary demonstrated application of the nanobursa mesh in catalysis is the oxidation of hydrocarbons. A generic complete oxidation reaction is

${\displaystyle \mathrm {C} _{x}\mathrm {H} _{y}+\left(x+{\frac {y}{4}}\right)\mathrm {O} _{2}\xrightarrow {\mathrm {Pd/Pt} } x\,\mathrm {CO} _{2}+{\frac {y}{2}}\,\mathrm {H} _{2}\mathrm {O} }$

The catalytic rate per unit geometric area of the nanobursa mesh is modeled using a Langmuir–Hinshelwood mechanism. Denoting the hydrocarbon partial pressure as ${\displaystyle p_{\mathrm {HC} }}$ and oxygen partial pressure as ${\displaystyle p_{\mathrm {O} _{2}}}$, the surface reaction rate ${\displaystyle r_{s}}$ (mol m⁻² s⁻¹) is

${\displaystyle r_{s}={\frac {k_{s}(T)\,K_{\mathrm {HC} }\,p_{\mathrm {HC} }\,K_{\mathrm {O} _{2}}\,p_{\mathrm {O} _{2}}}{(1+K_{\mathrm {HC} }\,p_{\mathrm {HC} }+K_{\mathrm {O} _{2}}\,p_{\mathrm {O} _{2}})^{2}}}}$

where ${\displaystyle k_{s}(T)}$ is the surface rate constant following an Arrhenius temperature dependence

${\displaystyle k_{s}(T)=A\,\exp \!\left(-{\frac {E_{a}}{RT}}\right)}$

with ${\displaystyle A}$ the pre-exponential factor, ${\displaystyle E_{a}}$ the activation energy, ${\displaystyle R}$ the universal gas constant, and ${\displaystyle T}$ absolute temperature. ${\displaystyle K_{\mathrm {HC} }}$ and ${\displaystyle K_{\mathrm {O} _{2}}}$ are adsorption equilibrium constants for the hydrocarbon and oxygen, respectively.

The effectiveness factor ${\displaystyle \eta _{\mathrm {eff} }}$ of the nanobursa mesh accounts for intrafiber mass-transfer limitations. For a flat slab geometry of half-thickness ${\displaystyle L}$,

${\displaystyle \eta _{\mathrm {eff} }={\frac {\tanh(\phi )}{\phi }}}$

where ${\displaystyle \phi }$ is the Thiele modulus

${\displaystyle \phi =L{\sqrt {\frac {k_{s}a_{s}}{D_{\mathrm {eff} }}}}}$

Here ${\displaystyle a_{s}}$ is the specific surface area of the metallic nanoparticles per unit volume of the fiber (m² m⁻³), and ${\displaystyle D_{\mathrm {eff} }}$ is the effective diffusivity of the reactant within the porous fiber, estimated using

${\displaystyle {\frac {1}{D_{\mathrm {eff} }}}={\frac {1}{D_{\mathrm {mol} }}}+{\frac {1}{D_{K}}}}$

where ${\displaystyle D_{\mathrm {mol} }}$ is the bulk molecular diffusivity and ${\displaystyle D_{K}={\frac {d_{p}}{3}}{\sqrt {\frac {8RT}{\pi M}}}}$ is the Knudsen diffusivity with ${\displaystyle d_{p}}$ the mean pore diameter and ${\displaystyle M}$ the molar mass of the diffusing species.

The overall volumetric conversion rate in a differential reactor element of mesh volume ${\displaystyle dV}$ is

${\displaystyle r_{\mathrm {vol} }=\eta _{\mathrm {eff} }\,r_{s}\,a_{s}\,\rho _{\mathrm {fiber} }\,(1-\varepsilon )\,dV}$

where ${\displaystyle \varepsilon }$ is the mesh void fraction and ${\displaystyle \rho _{\mathrm {fiber} }}$ is the skeletal density of the fiber material.

Graded layer architecture and optimization

The performance of a multi-layer nanobursa mesh (with ${\displaystyle N}$ layers, each bearing a different metal ${\displaystyle {\mathcal {M}}_{i}}$ at concentration ${\displaystyle c_{i}}$) can be described by a transfer-matrix formalism. Let ${\displaystyle \mathbf {x} ^{(i)}}$ denote the state vector (reactant concentration, temperature) at the inlet of layer ${\displaystyle i}$. Then

${\displaystyle \mathbf {x} ^{(i+1)}=\mathbf {T} _{i}(\mathbf {x} ^{(i)};\,c_{i},\,d_{f}^{(i)},\,\varepsilon _{i})}$

where ${\displaystyle \mathbf {T} _{i}}$ is the layer transfer operator encoding the species and energy balances for that layer. The overall performance objective (e.g., total conversion ${\displaystyle X}$) is

${\displaystyle X=1-{\frac {[\mathrm {HC} ]_{\mathrm {out} }}{[\mathrm {HC} ]_{\mathrm {in} }}}={\mathcal {F}}\!\left(\{\mathbf {T} _{i}\}_{i=1}^{N}\right)}$

Optimization of the layer sequence—including the choice of metal identity, nanoparticle loading, fiber diameter, and void fraction for each layer—is a combinatorial problem that can be cast as

${\displaystyle \max _{\{c_{i},\,d_{f}^{(i)},\,\varepsilon _{i},\,{\mathcal {M}}_{i}\}}\;X\quad {\text{subject to}}\quad \sum _{i=1}^{N}m_{i}\leq m_{\mathrm {total} },\quad \Delta P\leq \Delta P_{\max }}$

where ${\displaystyle m_{i}}$ is the mass of layer ${\displaystyle i}$ and ${\displaystyle \Delta P}$ is the total pressure drop across the mesh, approximated for the fibrous medium by the Kozeny–Carman equation:

${\displaystyle \Delta P={\frac {180\,\mu \,u_{0}\,L_{\mathrm {total} }}{d_{f}^{2}}}\,{\frac {(1-\varepsilon )^{2}}{\varepsilon ^{3}}}}$

where ${\displaystyle \mu }$ is the fluid dynamic viscosity, ${\displaystyle u_{0}}$ is the superficial velocity, and ${\displaystyle L_{\mathrm {total} }}$ is the total mesh thickness.

Heterogeneous catalysis

The primary application demonstrated in the original nanobursa publication^[1] is catalytic hydrocarbon oxidation. The graded architecture allows sequential or cooperative catalytic action: for example, a Pd-rich upstream layer initiates partial oxidation, while a downstream Pt-rich layer drives complete combustion to CO₂ and H₂O. The mathematical framework for this is the layer transfer operator formalism described above.

Filtration and respiratory protection

^[6] By incorporating antiviral nanoparticles (Ag, Au, Pt, Pd) into electrospun PCL nanofibers produced by TSEE, nanobursa type meshes have been proposed as high-performance membrane layers for N95-class respirators. The sub-200-nm fiber diameters accessible via TSEE yield higher single-fiber efficiencies in the most penetrating particle size range (MPPS, approximately 100–300 nm) compared with conventional melt-blown polypropylene webs (fiber diameter typically 1–10 μm).

Tissue engineering and biomedical scaffolds

The TSEE platform that underlies nanobursa fabrication has been applied to the production of graded tissue engineering scaffolds, including:

• Functionally graded PCL / β-tricalcium phosphate (β-TCP) scaffolds for osteochondral interface Tissue engineering;^[2]
• Shell-core bi-layered scaffolds for engineering of vascularized osteon-like bone structures.^[7]

In biomedical contexts the encapsulation of CNTs within the polymeric shell of the nanobursa fiber serves the dual purpose of exploiting CNT mechanical reinforcement while limiting direct biological exposure to bare CNT surfaces, which carry cytotoxicity concerns.