Ultra-soft 100 nm Thick Zero Poisson’s Ratio Film with 60% Reversible Compressibility

Abstract

About a 100 nm thick multilayer film of nanoparticle monolayers and polymer layers is shown to behave like cellular-foam with a modulus below 100 KPa. The 1.25 cm radius film adhered to a rigid surface can be compressed reversibly to 60% strain. The more than four orders of magnitude lower modulus compared to its constituents is explained by considering local bending in the (nano)cellular structure, similar to cork and wings of beetles. As the rigidity of the polymer backbone is increased in just four monolayers the modulus of the composite increases by over 70%. Electro-optical map of the strain distribution over the area of compression and increase in modulus with thickness indicates the films have zero Poisson’s ratio.

Graphical Abstract

Squeezing films of most solids, liquids and granular materials causes dilation in the lateral dimension which is characterized by a positive Poisson’s ratio. Auxetic materials,¹ such as, special foams,² crumpled graphite,³ zeolites,⁴ spectrin/actin membrane,^5,6 and carbon nanotube laminates⁷ shrink, i.e., their Poisson’s ratio is negative. As a result of Poisson’s effect, the force to squeeze an amorphous material, for example, a viscous thin film coating adhered to rigid surface increases by over million fold as the thickness decreases from 10 μm to 100 nm due to constrain on lateral deformations and off-plane relaxation.⁸ In contrast, for zero-Poisson’s ratio material, the absence of lateral deformation on bending, compressing, or extending, they can be tightly rolled or designed to make soft ultra thin film without any thickness enhancement. Due to a special cellular structure,⁹ cork is a near- zero- Poisson’s- ratio- material that does not dilate or contract on compression,¹⁰ therefore it can be pressed in a wine bottle with ease to form a seal.² Wings of beetles also have near zero Poisson’s ratio.¹¹ No lateral strain during flight allows the wings to morph without (energy expensive) bulging and buckling in other directions.¹² Biomimicked special cellular urethane foams are designed with zero Poisson’s ratio to make morphing wings for (future) fuel efficient aircraft.¹³ Gas, is an ideal zero Poisson’s ratio material that, easily compresses while constrained in the lateral direction.¹ Thus, a soft, gas-like, solid thin film that can be conformally deposited on surfaces of any shape will be an effective coating for improving damping, cushioning, and traction for gripping. Especially, the soft modulus comparable to tissue (i.e., less than 100 KPa)¹⁴ will have potential applications, for example, as coating on surgical tools to improve traction to grip delicate tissue samples with high precision for robotics and minimally invasive surgery, ^15–18 as a surface coating on a complex 3D scaffold to regulate differentiation of stem cells by regulating the modulus in the 10 to 100 KPa range,¹⁹ as a highly compressible pressure-sensitive dielectric or conductive film for tactile sensing on par with a human finger for surgical and robotic applications, ^17,20–23 and as soft-cellular-structured porous coating on to 3D scaffold surface for cell proliferation²⁴.

We demonstrate, ultra-soft, 100 nm films of polymer/nanoparticle composite made by conventional dip coating on solid surface that can be reversibly compressed over 60% strain between rigid plates requiring (very low) stresses below 100 KPa. Using a strategy similar to cellular foams where compressive strain is distributed in the off-plane direction by local bending,²⁵ we demonstrate a general approach to fabricate nano-structured composite films of modulus in 30 to 100 KPa range. The modulii of individual components of the film, Au and CdS nanoparticles in a polymer matrix, are well above 1 GPa, including the polymer matrix.²⁶ The 10⁴-fold reduction in modulus and gas-like compressibility is explained as local (reversible) bending of the polymer layer as the nanoparticles in adjacent layers interdigitate on compression.

The composite film is made by dip coating alternate layers of poly(allylamine hydrochloride) (PAH) and poly(styrene sulfonate) (PSS) followed by absorbing a monolayer of 10 nm Au or 3 nm CdS particles²⁷ (Fig. 1(a) and (b)). The molecular weights are 15,000 and 70,000 Daltons; and solution concentrations are 0.1% and 0.2% by weight, for PAH and PSS, respectively. The films are deposited on an Indium-Tin-Oxide (ITO) electrode on glass. The final structure is composed of three layers of Au nanoparticles and two layers of CdS nanoparticles spaced by N layers of PSS and PAH that alternate such that PAH is in contact with the nanoparticle layer or the electrode. Over 60 samples with N ranging from 3 to 21 layers are studied. The average thickness of the PSS/PAH layer, measured by ellipsometry for N = 3 to 21 layer films on Si is 1.12 nm/layer. The estimated thickness of the composite film ranges from 65 to 180 nm. The load is applied by pressing a flat Al platen onto a 12.5 mm radius optically smooth quartz disk coated with 500 nm thick Cr/Au electrode placed on the device. The Al platen is attached to a ball-and-socket joint to ensure uniform force distribution. A bias, V, is applied across the thickness of the film and the current, I, and electroluminescence intensity, I_el, from CdS is recorded concomitantly as a function of applied stress, σ, to quantitatively measure the strain, ε, in the film. The “tactile image” is recorded by focusing the electroluminescent light distribution on CCD camera (instead of PMT tube) (Fig. 1(c)). The tactile image is sensitive to local modulation in electron tunneling due to local strain.²³ The uniform light in tactile image, especially closer to the edge compared to the center indicates that the stress distribution is uniform. A uniform stress distribution under no slip condition from center to the edge indicates no Poisson’s effect.⁸

Figure 1:

(a) Schematic of electrical characterization of the device showing the load application and optical signal collection on a photomultiplier tube (PMT). Films are made with three and two monolayer of Au and CdS particles, respectively. (b) The 140 nm wide scanning electron microscope (SEM) image (with no metal deposition) shows the three 10 nm Au particle layers. The CdS particles are too small to visualize. (c) The tactile image of the quartz disk formed on the CCD camera at 40 KPa. Reproduced with permission from Reference 21. Copyright 2008 WILEY-VCH.

As the film is squeezed, the particles come closer; and both I and I_EL increase. The sensitivity on I-V characteristics of the device to stresses <100 KPa indicates that the modulus of the film is expected to be low (Fig. 2(a)). In contrast, the current, through a pure polymer film made of 84 layers of PSS/PAH incorporating no nanoparticles, does not exhibit any dependence on σ for the same range (Fig. 2(b)). The (expected) high toughness of pure polymer film on squeezing is typical for a solid thin film due to confinement of in-plane strain. The linear I-V behavior of the film made from just PSS and PAH is due to (ohmic) ionic current, I_N, due to the hygroscopic nature of polyelectrolytes. The ohmic current, I_N = V/R, where R is the (ionic) resistance. An order of magnitude higher current and nonlinear I-V behavior in the composite film, compared to pure polymer, is due to electron tunneling between the adjacent nanoparticles along the thickness direction superimposed on I_N. The nonlinear tunneling current, I_T, given by the Fowler- Nordheim equation is I_T = Pexp(−aK/V), where P is proportional to the number of percolating channels, a is the tunneling distance between the particles, and K is a proportionality constant. ^23,28 As a result, the total current for the composite film is given by I = V/R + Pexp(−aK/V). By differentiating the I-V at fixed σ, the differential conductance, dI/dV, as a function of V is obtained (Fig. 2(c)). On extrapolating to V→0, [dI/dV]_V=0 = 1/R at various σ is estimated (Fig. 2(c) inset). As expected, R deceases monotonically as σ increases. Subsequently, by subtracting the ionic current and fitting a single exponential to V versus I – V/R (= I_t), P and aK are determined. Interestingly, from the IT characteristics, as the film deforms, the tunneling current increases largely due to P (Fig. 2(d)) while the inter-particle distance remains nominally constant (Fig. 2(d) inset). Thus, on deformation, the rise in tunneling current occurs primarily due to a liner increase in the number of percolation channels as the particles come closer, i.e., I_T ~ P. Furthermore, the tunneling current is exclusively through the CdS nanoparticles; and electroluminescence only occurs due to transport through CdS, i.e., I_EL ~ I_T. Thus, a linear correspondence between I_EL ~ P at all the σ is expected (Fig. 2(e)).

Figure 2:

Electrical response of the film on uniaxial compression. (a) A typical change in I-V response at different applied stress (N = 13). The line is a fit to the tunneling and ionic current model. Inset: Corresponding I_EL measured concomitantly with the I-V characterization. (b) The I-V curve does not change for PSS/PAH film (N =84 with no nanoparticles). (c) Typical effect of stress on dI/dV versus V behavior (N =5). (d) Typical behavior of tunneling parameters, P and aK, as a function of stress for three films. Each data point is based on an I-V curve at fixed. σ. (e) Typical correspondence between P and I_EL (N = 5).

The compressive strain in the film is estimated from R. The ionic resistance is given by R = ρL/A, where ρ is the resistivity, L is the film thickness, and A is the “effective” cross-sectional area for ion transport along the thickness of the film. The resistivity, ρ ~ 1/c, where c is a concentration of mobile ions, i.e., charge density. Assuming the number of ions does not change on compression (i.e., the lateral strain is negligible), c ~ 1/AL. Thus, R ~ (1/AL)⁻¹(L/A), or R ~ L². Important to note is that even though A may change on deformation due to a more constricted path for ion conduction as particles come closer, the scaling R ~ L² is still valid. Considering affine deformation, the strain in the film is given by ε_aff = (Ro^0.5 – R^0.5)/R_O^0.5, where R_O is obtained by extrapolating the ionic resistance to σ = 0 (Fig. 2(c) inset). A typical stress-strain curve shows two distinct regimes: at low stress, the deformation is linear with low modulus; and subsequently, the strain tends to flatten leading to a higher modulus similar to the densification observed in foams²⁵ (Fig. 3 and Fig. S1 in the Supporting Information Online (SIO)). Typical stress-strain curves for the other values of N studied among the more than 60 films tested are shown in the SIO (Fig. S1). The data at low stress-strain is difficult due to the small forces involved. Although a low friction universal joint is used to ensure flat contact, a small force is needed to “settle” the parallelism between the film and the Al platen before deformation of the film commences. Based on the data obtained for the low stress linear regime, the strains are 35% to 60% for all of the samples tested. Similar to conventional foams, at high strains, the actual strain may be smaller than ε_aff in the densification region.²⁵

Figure 3:

Typical mechanical behavior of two films calculated from ionic resistance exhibiting the reversible deformation to high compressive strains. Typical behavior of other values of N studied is in SOM, Fig. S1.

The large reversible strain with low modulus of the composite films is qualitatively explained in terms of a simple model (Fig. 4(a)). Owing to large particle density,²³ highly stratified, parallel layers of Au nanoparticles are formed (Fig. 1, SEM image). The non-conformal coating of the polymer on high density Au particle coverage leads to inter-particle voids (Fig. 4(a)). Voids in the interstitial regions have been inferred from x-reflectivity measurements on similar multilayer structure incorporating nanoparticle.²⁹ As the film is compressed, the larger Au nanoparticle will bend or squeeze the polymer layer containing the smaller CdS particles. The schematic, nominally to scale for N = 7 that will have a nominal thickness of ~7 nm for the PSS/PAH layers, shows ε of ~40% by local bending and squeezing of the polymer layer. As the tunneling current is exponentially sensitive to inter-particle distance, which does not change significantly (Fig. 2(d) inset), the primary mode of deformation is by bending and not squeezing. The reversibility also suggests that the film does not rupture during buckling. The deformation of the cellular structure in Fig. 4(a) is similar to cork¹⁰ where the schematically marked nodes of the cell correspond to the location of the Au nanoparticles (Fig 4(b). Consistent with the bending, as the interposer layer gets thicker, the film becomes stiffer leading to higher modulus (Fig. 4(c), even though the amount of polymer relative to the nanoparticles increases. Conventionally, due to Poisson’s effect, the lateral strain on compression is relived more effectively as thickness increases leading to lower stiffness. A reverse effect is observed in films studied: The stiffness increases monotonically with thickness in the range studied (Fig. 4(c), inset). This implies that the strain in the lateral direction is insignificant or zero, in other words, the Poisson’s ratio is close to zero.

Figure 4:

(a) The two local deformation modes on compression are bending and squeezing of the dielectric layer. The relative dimensions of the schematic are nominally to scale depicting a strain of about 40% in N =7 film. (b) The electron microscope image of the cellular structure of cork. Reproduced with permission from Reference 9. Copyright 2005 Maney Publishing. Idealized model with an overlay of the nanoparticle/polymer layered structure. The width of the image is 350 μm. Reproduced with permission from Reference 10. Copyright 2010 John Wiley and Sons. (c) Effect of N on the modulus of the film based on initial linear region (Fig. 3) averaged over 60 samples. (d) The effect of stiffness of the polymer layer on the modulus of the film made from three layers of 10 nm Au particle monolayer with no CdS particles.

To further evaluate the validity of the bending model, the stiffness of the interposer layer is significantly reduced by eliminating CdS particles. As expected, the modulus is lowered compared to CdS-containing film (Fig. 4(d)). Furthermore, the plateau occurs at a lower stress level indicating that the pure polymer interposer layer is easier to bend at lower stress levels (Fig. 4(d) and Fig S1 in SIO). Conversely, consistent with the bending model, replacing the flexible PSS polymer with a more rigid electrolyte, heparin, the modulus is enhanced twofold. Furthermore, the modulus can be reduced by increasing the Au particle size to incorporate larger voids. For example, for N = 9, the modulus is reduced from ~55 to ~30 KPa as Au particle size increases from 10 to 15 nm (Fig. S2, SIO).

In summary, a ~100 nm thick layered film of polymer and nanoparticle monolayers is self-assembled to impart gas-like compressibility with a modulus of 50 to 100 KPa that is comparable to tissue. The compression modulus of the film is four orders of magnitude lower than its individual constituents. The low modulus and large reversible compressibility up to 60% strain is explained by local bending of the polymer layer. The modulus of the composite film increases with film thickness. The measurements on the mechanics of the film indicate that the Poisson’s ratio is zero. The films can be self-assembled by sequential dip coating process to form a soft, foam-like coating for applications, such as, improving traction to grip delicate tissues by surgical tools, sensitive tactile devices, and coatings on scaffolds for stem cell differentiation. To our knowledge, this is the first demonstration of thin films of thickness in nanometer scale that exhibit zero Poisson’s ratio. The approach can be generalized to micron to centimeter scale by using larger particles and inter particle layering material.