Andrew Alderson

Do Zeolites Have Negative Poisson's Ratios?

Consequently, the size of the resulting nanoparticles matches the dimension of the nanometer-sized cavities inside these swollen domains. The possibility of controlling the growth of the metal nanoclusters by changing the morphological features of the support represents a unique feature of resin supports, in which the metal nanoparticles are generated inside the swollen polymer network and not simply at its surface. It can be inferred that functional resins characterized by a narrower distribution of nanoporous domains will make it possible to control even more precisely the size and size distribution of the metal nanoclusters generated inside them, a task that we are going to turn to in the near future.

Auxetic two-dimensional polymer networks. An example of tailoring geometry for specific mechanical properties

The Poissons ratios and Youngs moduli of 2D molecular networks having conventional and re-entrant honeycomb forms have been modelled using molecular modelling. Three principle deformation mechanisms were observed : bond hinging, flexure and stretching. Analytical models have also been developed that can be used to describe each of these modes of deformation acting either independently or concurrently. A parametric fit of the force constants in the concurrent analytical model calculations to the molecular model calculations yields good agreement in the mechanical properties for all the structures studied. Specific trends in the force constants required to fit the data are observed. Consequently, a force constants library can be compiled and has been used to predict accurately the properties of more complex variants of the networks. This semi-analytical sub-unit approach enables a more efficient use of computer-intensive molecular modelling programs.

On the potential of connected stars as auxetic systems

Auxetic materials and structures exhibit the unexpected behaviour of getting wider when stretched and thinner when compressed. This behaviour requires the structures (the internal structure in the case of materials) to have geometric features, which must deform in a way that results in the structure expanding when stretched. This paper assesses the potential for auxetic behaviour of a novel class of two-dimensional periodic structures which can be described as “connected stars” as they contain star-shaped units of different rotational symmetry which are connected together to form two-dimensional periodic structures. These structures will be studied through a technique based on force-field based methods (the EMUDA technique) and it will be shown that some, but not all, of these structures can exhibit auxetic behaviour. An attempt is made to explain the reasons for the presence or absence of a negative Poissons ratio in these systems.

The interpretation of the strain-dependent Poisson's ratio in auxetic polyethylene

Abstract The strain-dependent behaviour characteristic of auxetic (i.e. having a negative Poissons ratio) polymers has been modelled using a simple geometric model which consists of rectangular nodules intecronnected by fibrils. Careful consideration of the correct form of the model to use depending on the experimental method employed to test samples of auxetic ultra high molecular weight polyethylene (UHMWPE) has resulted in very good agreement between the experimental and theoretical Poissons ratios and total engineering strain ratios when the deformation is predominantly due to hinging of the fibrils. Auxetic UHMWPE has been processed to yield a very wide range of Poissons ratios depending on its microstructural parameters (i.e. nodule shape and size, fibril length and the angle between the fibril and nodule). These can be predicted using the model, allowing the possibility of tailoring Poissons ratio of the material.

Natrolite: A zeolite with negative Poisson’s ratios

The recently published experimental elastic constants [C. Sanchez-Valle, S. V. Sinogeikin, Z. A. Lethbridge, R. I. Walton, C. W. Smith, K. E. Evans, and J. D. Bass, J. Appl. Phys. 98, 053508 (2005)] for single crystals of the orthorhombic aluminosilicate zeolite NAT (natrolite, Na2(Al2Si3O10)2H2O, Fdd2) throw valuable light on the potential of NAT as a material which exhibits single crystalline negative Poisson’s ratios (auxetic). On performing an off-axis analysis of these elastic constants we confirm that the zeolite natrolite exhibits auxetic behavior in the (001) plane. This supports our preliminary report that NAT-type zeolites exhibit auxetic behavior through a mechanism involving microscopic rotation of semi-rigid structural units.

An Alternative Explanation for the Negative Poisson's Ratios in Auxetic Foams

Auxetic materials exhibit the unusual property of becoming fatter when stretched and thinner when compressed, in other words they exhibit a negative Poisson’s ratio. A class of such materials which have attracted a lot of attention are auxetic foams which exhibit various enhanced physical characteristics. Foams with negative Poisson’s ratios (see Fig. 1) were first manufactured by Lakes and can be produced from commercially available conventional foams through a process involving volumetric compression, heating beyond the polymer’s softening temperature and then cooling whilst remaining under compression. Various two-dimensional models which represent a crosssection of foams have been proposed in an attempt to relate the experimentally measured values of the Poisson’s ratios to the microstructure of the foams. For example it has been proposed that conventional foams can be modelled using hexagonal and diamond-shaped honeycombs whilst the auxetic foams can be modelled through modified versions of these honeycombs. In the case of the 2D hexagonal honeycomb model, the required structural modification for auxetic behaviour requires the junctions connecting the honeycomb cell walls (‘ribs’) to be transformed during processing from ‘Y’-shaped joints to ‘arrow head’-shaped joints. For the diamond honeycomb model, auxetic behaviour requires selective removal in a regular manner of ribs during the transformation process. One should note that these two modifications need not be simultaneously applied for a foam or honeycomb to become auxetic. For example, the creation of acute angles in the hexagonal honeycombs through the conversion of the ‘Y’-shaped joints to ‘arrow head’-shaped joints is enough to make the honeycombs auxetic without the need of altering the topology of the cells by the removal of ribs. Although the above models probably play some role in modelling the auxetic behaviour in foams, and these models can reproduce the experimentally measured values of the Poisson’s ratios, one may argue that there is not enough experimental evidence to justify the assumption that either of these are the main structural modifications which result in the observed auxetic effect. For example, whilst there is experimental evidence that there are ‘broken ribs’ on the surface of the auxetic foams [see Fig. 1(b)], it is still not clear whether ‘broken ribs’ are also present in the bulk of the foam material. Also, the requirement in the diamond honeycomb model for the removal of ribs in a regular fashion is not likely to occur in the existing foam conversion process. In the case of the hexagonal models there is no clear experimental evidence that a majority of the ‘Y’ shaped joints in the conventional foam are converted to the required ‘arrow shaped’ joints during the compression/heat treatment process. In fact, one may argue that it is unlikely that the majority of the changes in the foam manufacture process are concentrated at the joints of the foam as one usually observes that the ribs of open cell foams are slightly thicker in the proximity of the joints than at the centre of the ribs. In view of this we propose a new model to explain the presence of negative Poisson’s ratios in foams. This new model is based on the hypothesis that it is more likely that changes in the microstructure during the compression/heat treatment process will conserve the geometry at the joints (i.e., they do not become re-entrant) and the topology of the system (i.e., there are no rib breakages, as was the case in the re-entrant systems) and instead, the major deformations will occur along the length of the ribs which buckle (the foam is typically subjected to ca. 30% compressive strain along each axis). Figure 1(b) provides clear evidence of the presence of buckled ribs in the transformed auxetic foam microstructure. We also assume that the additional thickness in the proximity of the joints will make it possible for the joints to behave, to a first approximation, as ‘rigid joints’. It is proposed that the rigid joints rotate relative to each other during the foam conversion process. The foam microstructure then ‘freezes’ in this much more compact form when the foam is cooled to below its softening temperature. An illustration of this is given in Fig. 2 which shows how a conventional two-dimensional hexagonal honeycomb in Fig. 2(a) (which can be treated as a two-dimensional model for conventional foams) can be converted through the compression/heat treatment process into an auxetic form shown in Fig. 2(b). We propose that the ‘rigid joints’ behave like ‘rigid triangles’ [Fig. 2(a)] which, during the heating/ compression process, rotate relative to each other to produce the more compact microstructure shown in Fig. 2(b). (This occurs though the formation of ‘kinks’ at the centre of the ribs which are the result of extensive buckling of the ribs in the compression/heat treatment process.) Uniaxial tensile loading of the idealised microstructure in Fig. 2(b) will cause a re-rotation of the triangles to generate the auxetic effect as illustrated in Fig. 2(c). (This corresponds to reFig. 1. SEM images of (a) conventional (non auxetic) open-cell polyurethane foams, and (b) auxetic open-cell polyurethane foam.

On the origin of auxetic behaviour in the silicate α-cristobalite

The experimentally observed negative Poissons ratios in the silicate α-cristobalite are explained through a two-dimensional ‘rotation of rigid units’ model involving ‘rotating rectangles’ hence providing a new insight into the way nature can achieve this unusual property.

Negative Poisson’s Ratio Polyester Fibers

Auxetic materials are referred to as those having negative Poisson’s ratio (ν). Initial work at Bolton successfully fabricated auxetic polypropylene fiber using a novel thermal melt-spinning technique. This paper reports in detail both the methods and principles involved in screening polyester powder and also the manufacturing method for successful production of auxetic polyester fibers. Videoextensometry along with micro-tensile testing were used to measure the Poisson’s ratio of the fiber. The Poisson’s ratio of the polyester fiber was found to vary between -0.65 and -0.75.

On the Auxetic Properties of 'Rotating Rectangles' with Different Connectivity

Auxetic materials and structures exhibit the unusual property of becoming wider when stretched and thinner when compressed, i.e., they have negative Poisson’s ratios. In recent years, this unusual behaviour has been predicted or experimentally measured in a number of naturally-occurring and man-made materials ranging from foams where the auxetic effect arises from the particular microstructure of the foams to silicates and zeolites where the auxetic behaviour occurs at themolecular level. In these auxetic systems, the negative Poisson’s ratios can be explained in terms of models based on the geometry of the system (i.e., the geometry of the material’s internal structure) and the way this geometry changes as a result of applied loads (deformationmechanism). In recent years various two and three dimensional theoretical models and structures which can lead to negative Poisson’s ratio have been proposed including, two and threedimensional ‘re-entrant’ systems, models based on rigid ‘free’ molecules, chiral structures and systems made from ‘rotating rigid units’ such as squares, triangles, rectangles or tetrahdera. In all of these systems, the Poisson’s ratio does not depend on scale although it can depend on the relative dimensions of certain features in the geometry. In particular we have recently shown that whilst a two-dimensional system constructed from perfectly rigid squares connected together through simple hinges at the vertices of the squares will always maintain its aspect ratio when stretched or compressed [see Fig. 1(a)], i.e., it will exhibit constant Poisson’s ratios equal to 1 irrespective of the size of the square or direction of loading, the equivalent structure built from hinged rigid rectangles as illustrated in Fig. 1(b) will exhibit in-plane Poisson’s ratios which depend on the shape of the rectangles (the ratio of the lengths of the two sides) and the relative orientation of the rectangles (i.e., the angles that two adjacent rectangles make with respect to each other). This means that for such a system, the Poisson’s ratios will be strain dependent and dependent on the direction of loading. This note is aimed at highlighting the fact that there exist two types of ‘rotating rectangles’ structures, and that two systems based on the same ‘building block’ (rigid rectangle) and same deformation mechanism (rectangle rotation), but different connectivity, exhibit very different mechanical properties. More specifically, for rectangles of the same size (a b), tessellating corner-sharing rectangular networks in which each corner is shared between two rectangles can only be formed from two connectivity schemes, which we shall refer to as Type I and Type II. The Type I network refers to the system where four rectangles are connected in such a way that the empty spaces between the rectangles form rhombi of size (a a) and (b b) as illustrated in Fig. 1(b). The Type II network refers to the system with a connectivity where the empty spaces between the rectangles form parallelograms of size (a b) as illustrated in Fig. 1(c). If the four rectangles are connected in any other way (for example, with the empty spaces between the rectangles forming a ‘kite’ of side lengths ‘a, a, b, b’) the resulting unit cannot form a tessellating structure. The Type I ‘rotating rectangles’ structure has been extensively studied and it has been shown that this structure exhibits properties which are dependent on the shape and size of the rectangles and are strain dependent and anisotropic. In particular it has been shown that such Type I ‘rotating rectangles’ structures are capable of exhibiting both positive and negative Poisson’s ratio where, for example, the on-axis Poisson’s ratios are dependent on the ratio of the lengths (a=b) and on the angle between the rectangles since: v21 1⁄4 ðv12Þ 1 1⁄4 a sin 2 ð Þ b cos 2 ð Þ a2 cos2 2 ð Þ b2 sin 2 ð Þ Here we study, for the first time, the behaviour of the Type II ‘rotating rectangles’ which as we will show exhibits very different properties. As illustrated in Fig. 1(c), a rectangular unit cell with cell sides are parallel to the Ox1 and Ox2 axis may be used to describe the Type II network. This unit cell contains two (a b) rectangles with projections in the Oxi directions given by:

Auxetic polymeric filters display enhanced de-fouling and pressure compensation properties

Abstract This article briefly shows how auxetic materials offer improved filter performance from the macro-scale to the nano-scale because of their unique pore-opening properties and characteristics.