# Surface area and density relationship

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

Volume is a gateway to a lot of other concepts like density, which is a fancy word for the ratio between mass and volume. If something has a high density, then it. Correlation of the Specific Surface Area and Bulk Density of No conclusive relationship could be established between bulk density and the. I assume you imply the term "surface density". This apply on materials in sheets or plates, like iron plates or sheets, aluminum foils, laminated sheets, rubber.

Other authors have also used this result for controlled adhesion and migration of cells Ekaputra et al. Another feature of electrospun networks that can be controlled by the fibre diameter is the available surface area. Reducing fibre diameter increases the surface area to volume ratio, and vice versa. The available surface area of fibres will clearly have an effect on the ability of cells to attach and migrate.

Although the mechanisms for enhanced strength and stiffness in composite materials are well understood, those leading to enhanced toughness in nanocomposite materials are not. In the case of spherical silica nanoparticles in epoxy, it has been shown that debonding, voiding and subsequent plastic void growth is the dominant toughening mechanism Johnsen et al.

For carbon nanotubes, which have a significant aspect ratio cf. Both in the cases of particles and nanofibres, the toughness of the composite material scales proportionally to the surface area, i. Since this is intrinsically related to the fibre diameter, and given that electrospun fibres have been proposed as possible reinforcements of composites, a treatment of the relationship between fibre morphology and available surface fraction is timely.

The mechanical properties of composite materials are affected also by the distribution of resin within their structure. The occurrence of resin-rich regions can produce local anisotropy, and so a treatment of the interrelationship between fibre geometry, the available surface area and pore dimensions in a network of fibres is timely also.

Electrospun fibres can be formed with a variety of morphologies: It is now known that phase separation between moisture from changes in ambient humidity and the solvents typically used for electrospinning cause these effects Pai et al. These changes in morphology are also known to effect the mechanical properties of single fibres Pai et al.

It is known that mechanical properties do, however, play a significant role in terms of the ability of electrospun networks to support cell growth McManus et al.

Accordingly, knowledge of the influence of fibre geometry on the structure of electrospun networks will guide our understanding of the mechanical properties of composite materials and tissue-engineering substrates, and the ability of cells to migrate within electrospun networks. In the main body of this paper, we provide a theory relating the specific surface area and interfibre pore dimensions of electrospun networks to fibre and network variables.

## QbD Quantitative Measurements of CQA's

We do not consider networks of porous electrospun fibres Czado et al. We shall see that for networks of solid fibres, specific surface area and pore dimensions depend strongly on the extent of interfibre contact and our derivations will use expressions from the literature for this property. Accordingly, we begin with a discussion of these models for fibre contact. For materials such as paper, non-woven textiles and fibrous filters, fibres have finite length, so fibre centres are assumed to be distributed according to a point Poisson process in the plane.

For electrospun networks, fibres can be assumed to have infinite length. Such networks can be modelled as a random network of infinite lines that represent the longitudinal axes of fibres and pass through points distributed according to a point Poisson process in the plane with uniformly distributed orientation Miles For a process of nf fibres per unit area, the mean coverage is 2. Typically, real networks will exhibit much higher mean coverages than two-dimensional networks and will have a significant structural component perpendicular to their plane.

A consequence of this is that vertically adjacent fibres may or may not make contact with each other, depending on the influence of nearby fibres.

We will take account of such effects in our subsequent analysis. In the two-dimensional case, however, we may assume that every crossing generates an interfibre contact.

On this basis, Kallmes and Corte derived the expected number of crossings between fibres per unit area in a two-dimensional network as 2. The expected number of crossings per unit area for a Poisson fibre process is therefore 2.

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

This is convenient because it means that the statistics of interfibre crossings in stochastic fibrous materials are not influenced by the length of fibres, but are determined instead by the total fibre length per unit area.

An extension of this is that fibre curvature does not influence the expected number of crossings in the network.

The resultant change in surface area after compression becomes of greater importance to physiochemical and mechanical properties of drug product performance. Milling and compaction will cause a change to particle size, which directly affects surface area.

Surface area is a viable and important parameter to predict mechanical and processing behavior, especially in material handling, compaction, and fragmentation. These void spaces are present in crystalline materials and can also be present in amorphous regions.

During roller compaction the variability batch-to-batch of a change in the ratio of amorphous to crystalline content can produce erratic mechanical and physiochemical behavior.

Knowing the surface area can be helpful in optimizing powder flow characteristics. By reducing the specific surface area, you can prevent or control inter-particulate interaction and the resultant cohesion to improve flow.

- Density, viscosity and surface area relationship in grinding.

Surface area by gas adsorption is the preferred measurement technique. When coupled with mercury porosimetry, this provides two complimentary techniques for pore size, pore size distribution, and surface area. It is capable of increasing the speed and efficiency of routine quality control analyses, yet has the accuracy, resolution, and data reduction capability to meet most research requirements.

Each analysis station is upgradeable from mesopore to micropore. All analysis stations can be configured for krypton analysis of low surface area materials.

### Essential Physics

The 3Flex is capable of analyzing three samples in parallel so that three complete isotherms are collected in the time required for one analysis. Each of the analysis ports is capable of achieving very low absolute pressures as a direct result of our innovative design.

Since smaller pore sizes are measured at lower relative pressures, micropore data are more accurately measured. Several mechanisms are at work within this process that have material effect on the final dosage form, including content uniformity. These include material flow properties, compactibility, compressibility, roll pressure, roll speed, and hopper feeding dynamics.

**Surface area to volume ratio of cells**

One of the key elements in roller compaction is roll pressure.