W. W. Sampson

Statistical geometry of pores and statistics of porous nanofibrous assemblies

The application of theoretical models to describe the structure of the types of fibrous network produced by the electrospinning of polymers for use in tissue engineering and a number of other applications is presented. Emphasis is placed on formal analyses of the pore size distribution and porosities that one would encounter with such structures and the nature of their relationships with other structural characteristics likely to be important for the performance of nanofibrous materials. The theoretical structures considered result from interactions between randomly placed straight rods that represent fibres with nanoscale dimensions. The dominant role of fibre diameter in controlling the pore diameter of the networks is shown and we discuss the perhaps counter-intuitive finding that at a given network mass per unit area and porosity, increasing fibre diameter results in an increase in mean pore radius. Larger pores may be required for ingrowth of cells to nanofibrous networks, hence this study clarifies that simply making the diameters of the fibres smaller might not be the way to improve cell proliferation on such substrates. An extensive review of structural features of the network such as the distribution of mass, inter-fibre contacts and available surface for cell attachment, fibre contact distributions for integrity of the networks and the porosity and pore size distributions is given, with emphasis placed on nanofibre dimensions for the first time.

Comprehensive elucidation of the effect of residual lignin on the physical, barrier, mechanical and surface properties of nanocellulose films

We elucidate the effect of residual lignin on the interfacial, physical and mechanical properties of lignocellulose nanofibrils (LCNF) and respective nanopapers. Fibers containing ∼0, 2, 4, and 14 wt% residual lignin were microfluidized into LCNF aqueous suspensions and were processed into dry films (nanopapers). A systematic decrease in fibril diameter with increasing residual lignin was observed upon fibrillation, consistent with the radical scavenging ability of the lignin that results in better cell wall deconstruction. The stiff nature of the lignin-containing fibrils made them less able to conform during filtration and improved extensively dewatering, owing to a more open structure. However, the softening of the lignin during hot-pressing of the nanopapers and its amorphous nature enabled a binding effect, filling the voids between the nanofibers (thus reducing the number of micropores) and making the surface of the nanopapers smoother. The interfacial free energy of interaction changed drastically with the increased lignin content: the corresponding water contact angles were 35° and 78° for the lignin-free and for the (14%) lignin-containing nanopaper, respectively, revealing the increase in hydrophobicity. Together with the significantly less porous structure of LCNF nanopapers, lower water absorbency was observed with increased lignin content. Lignin in the nanopapers reduced the oxygen permeability by up to 200-fold. Water vapor permeability, in turn, did not correlate linearly with lignin content but depended most significantly on material density. The tensile strength, modulus, and strain for the LCNF nanopapers were found to be in the range 116–164 MPa, 10.5–14.3 GPa, and 1.7–3.5%, respectively. To a good degree of approximation, these mechanical properties were rather insensitive to lignin content and comparable to those of nanopapers derived from fully bleached CNF. Whilst it might be expected that lignin interferes in hydrogen bonding between fibrils, this was apparently counteracted by the uniform distribution of lignin seemingly aiding stress-transfer between fibrils and thus preserving mechanical properties. Overall, LCNF is demonstrated to be a suitable precursor of nanopaper, especially when reduced polarity and low hydrophilicity are desirable in related bio-products.

A multiplanar model for the pore radius distribution in isotropic near-planar stochastic fibre networks

A model is presented for the pore radius distribution in isotropic near-planar stochastic fibre networks. At a given areal density, the mean pore radius of two-dimensional random networks is shown to decrease with increasing fibre width and to increase with increasing fibre linear density.For structures with a structural component in the third dimension the standard deviation of pore radii is shown to be proportional to the mean for changes in areal density and porosity in agreement with data reported in the literature. At a given porosity, near-planar networks exhibit an increase in mean pore radius with increasing fibre width and linear density.

Relationships between specific surface area and pore size in electrospun polymer fibre networks.

From consideration of the extent of contact between fibres in electrospun polymer networks, we provide theory relating the specific surface area of the network to the characteristic dimensions of interfibre voids. We show that these properties are strongly influenced by the cross-sectional morphologies of fibres. Whereas porosity has a strong influence on pore dimensions, in the range of porosities typically obtained in real networks, its influence on specific surface area is weak. By considering reference geometries of collapsed ribbons and fibres with circular cross sections, we demonstrate that at a given network porosity, fibre parameters that increase the specific surface area reduce the characteristic dimensions of voids. The implications of the theory, mainly in the context of cell proliferation on electrospun polymer scaffolds, are discussed; the theory has relevance also to future applications of these materials in composites.

Modeling a class of stochastic porous media

This note extends E. H. Lloyds model of pore structure in random fibre networks to a large class of stochastic fibre networks containing the random model as a special case. The key to the generalization is the substitution of a family of gamma distributions for the negative exponential family used for intercrossing distances on fibres. This allows closed expressions to be obtained for the variance and mean of the equivalent pore size distributions in a planar array of line elements representing fibres. The analytical details have been made available in a Mathematica notebook, via the World Wide Web. The result has application in modeling the forming of nonwoven textiles and paper from fibre suspensions, and in modeling their void structures and transmission of fluids.

Spatial Statistics of Stochastic Fiber Networks

From the known statistics of fiber-fiber contacts in random fiber networks, an analytic estimate is obtained for the variance of local porosity in random fiber suspensions and evolving filtrate networks. The variance of local porosity, and hence the distribution of projected areal density, seem to depend on fiber geometry only through the cube of mean diameter. Also, the coefficient of variation of local flow rate perpendicular to the plane of the pad is, to a first approximation, independent of the mode of flow. Analytic estimates are obtained also for the effect of fiber clumping on the variance of local porosity of pads for small inspection zones.

Comments on the pore radius distribution in near-planar stochastic fibre networks

The pore radius distribution in near-planar stochastic fibre networks is known to be influenced by changes in the mean number of fibres per unit area and their distribution in the plane. Experimental data is presented that confirms the established result that the standard deviation of pore radii is proportional to the mean. The data shows also that this proportionality is the same for changes in the number of fibres per unit area and for changes in the uniformity of their in-plane distribution. Data from the literature suggests that processes that increase the mean pore radius, increase also the coefficient of variation of pore radii. Theoretical considerations and experimental data are presented that show that the coefficient of variation of pore radii is in fact constant for near-random and non-random stochastic fibre networks.

Bivariate Normal Thickness-Density Structure in Real Near-Planar Stochastic Fiber Networks

We present the analysis of experimental data that supports the recently presented hypothesis that the relationship between local areal density and local thickness in planar stochastic fiber networks may be described by the bivariate normal distribution. Measurements of the local averages of areal density and thickness have been made on experimental fiber networks with differing degrees of structural uniformity. The experimentally determined variance of local density at the 1 mm scale is in excellent agreement with that calculated from the theory. Also, the use of the bivariate normal distribution to describe the relationship between local areal density and local thickness measured in complete sampling schemes is appropriate for both near-random and clumped networks.

Flow Simulation in Stochastic Porous Media

A family of gamma distributions can be used to model the pore size distributions in a range of stochastic porous media. Our simu lator generates distributional and net flow data for different fluid flow regimes through such networks. The outputs from the simu lation show strong relationships between mean flow and the variance of pore radii for turbulent, laminar, molecular and capillary flow. We observe also affine relationships between the coefficient of variation of local flow rate and the variance of pore radii for each of the above flow modes.

Estimation of the profile of cross-machine shrinkage of paper

In common with many other materials, paper tends to shrink as it dries. Although every attempt is made to restrain paper, some shrinkage occurs on all paper machines in the direction perpendicular to that of manufacture and this shrinkage is always much higher at the edges of the machine than in the centre. Measurement of the profile of this cross-machine shrinkage is possible using the fast Fourier transform to locate and measure periodic elements imprinted by the filtration fabrics used during the formation of the paper web. This paper describes a new method which allows the geometrical relationships within the fabric to be used along with dimensional changes to estimate shrinkage. The method has the advantages over previous methods of more tolerant sampling protocols, operator independent analysis and improved accuracy.