Ink Diffusion Research Articles

A fractal approach to the diffusion process of red ink in a saline water

The diffusion of the red ink in saline water is completely stochastic and highly unpredictable, and no differential model can precisely describe the process. This paper elucidates that the diffusion takes place in a molecule scale, therefore, the continuum assumption in fluid mechanics becomes totally invalid, and the two-scale fractal calculus has to be adopted to take into account the effects of the particles? size in the red ink and the properties of the saline solution including its concentration, water molecule?s size and distribution on the diffusion process. On the molecule?s scale, the diffusion becomes completely deterministic and predictable. An experiment is carefully designed and some phenomena, including optical observation and highly selective diffusion routine, are theoretically explained. This paper sheds light on modeling various contamination diffusion in air and water.

Polydimethylsiloxane-Assisted Catalytic Printing for Highly Conductive, Adhesive, and Precise Metal Patterns Enabled on Paper and Textiles.

Paper and textile are two ideal carriers in wearable and printed electronics because of their flexibility and low price. However, the porous and fibrous structures restrain their use in printed electronics because the capillary effect results in ink diffusion. Especially, conventional metal ink needs to be post-treated at high temperatures (>150 °C), which is not compatible with paper and textile. To address problems involved in ink diffusion and avoid high-temperature treatment, herein, a new strategy is proposed: screen-printing of high-viscosity catalytic inks combined with electroless deposition of metal layers on paper and textile substrates. The ink consists of Ag nanoparticles, a polydimethylsiloxane (PDMS) prepolymer, and a curing agent. PDMS as a viscoelastic matrix of catalysts plays key roles in limiting ink diffusion, enhancing interfacial adhesion between the substrate and metal layer, keeping metal flexible. As a demonstration, metal Cu and Ni are printed, respectively. The printed precision (diffusion < 1% on filter paper) can be controlled by adjusting the Ag content in the PDMS matrix; interfacial adhesion can be enhanced by ink coating on substrate microfibers and metal embedding into the PDMS matrix. In addition, Cu on paper shows extremely low sheet resistance (0.29 mΩ/□), and Cu on nylon shows outstanding foldability with a resistance of less than five times of initial resistance during 5000 folding cycles.

Mathematical characterization of ink diffusion and imbibition processes in chromatography paper as a potential biosensing platform

Materials used for biosensor development normally include silicon, glass, and synthetic polymers, however, paper is a practical and cheap option for the reduction of manufacturing costs with a wide range of applications. Paper-based biosensors have been widely produced, yet poorly characterized on the interaction of different type of molecules with its intricate microstructure. In this work, five ink solutions were prepared as model samples to examine their diffusion and imbibition behavior on grade 3MM chromatography paper. Different mathematical models, previously reported for porous matrices, were fitted and results revealed that upward wicking (r2 ≥ 0.90) equations described the experimental data during the initial stage (< 5 s) and yielded similar permeability values to those calculated from the matrix structural properties. The diffusion coefficient was determined up to attaining equilibrium using the diffusion equation in a cylinder element (r2 ≥ 0.90). This study enabled the characterization of the performance from 3MM chromatography paper, by using ink as a surrogate model of small molecules (e.g. mycotoxins) or small colloidal particles.

Clean production of polyester fabric inkjet printing process without fabric pretreatment and soaping

We report an improved printing ink of polyester fabric employed in the production process of inkjet printing. In the design of printing ink, the solubility parameters of reagent and HLB value of surfactant are used to prepare the ink. This production process does not require the pretreatment of polyester fabric to directly carry out inkjet printing. By regulating the intermolecular force relationship between the components of ink and the compactness of ink microstructure, it can improve the diffusion of ink on the surface of polyester fabric. The low-field NMR (LF-NMR) revealed the correlation between the fluidity and transverse relaxation time of main reagent solutions and ink. The test results show that there are three types of water: hydrogen-bond water, bound water and free water in main reagent solutions and ink. The LF-NMR was also used to investigate the relationship between ink viscosity and transverse relaxation time. It was observed that the transverse relaxation time (1084.4–410.3 m s, peak maximum time of T22) of ink decreases with the increase of ink viscosity (2.3–11.1 mPa s). The viscosity and transverse relaxation time of ink is associated with the intermolecular force and the compactness of microstructure of ink. The formation of ink droplets was systematically observed by the ink droplet observation instrument. When the surface tension and viscosity of ink are 32.2–37.4 mN/m and 2.3–8.8 mPa s, respectively, the ink can be smoothly inkjet. With the increase of viscosity of the ink (2.3–8.8 mPa s), the sharpness of printing pattern is obviously improved, and the change rate of the line width (W) of the printing pattern is reduced from 52.6% to 4.4%. The microstructure of ink can bound the solvent of the ink, reduce the fluidity of the solvent, and improve the sharpness of the printing pattern. The test results of KES style and color fastness of the printed fabric show that the printed fabric fully meets the wearing requirements. Compared with other the soap liquid of printed fabric, the soap liquid of printed fabric RD-2B has strong UV absorption strength, the soap liquid RD-2B has a higher dye content. The characterization results of volatile organic compounds (VOC) in ink SDS R7 is 17.0 g/kg. The chemical oxygen demand (COD) values of printed fabrics RD-2B and SDS R7 are 150.0 and 102.0 mg/L, and the biochemical oxygen demand (BOD5) values of printed fabrics RD-2B and SDS R7 are 130.0 and 97.7 mg/L. Compared with the common polyester fabric printing ink (ink RD-2B), the prepared ink has the characteristics of environmental protection, high production efficiency and low energy consumption, which has the potential to achieve green printing.

Flame-retardant paper with robust hydrophobicity enabled by perfluorodecane doped SiO2 nanofibers

Paper plays an important role in various aspects of human life. However, most of the paper materials are vulnerable to both flame and water, which seriously restrict their performance in many applications. Here, we report a new kind of flame-retardant paper with high-temperature-resistant hydrophobicity. This kind of paper was fabricated by vacuum filtration of electrospun fluorinated SiO2 fibers and methyl silicon resin. It is mechanically flexible. Its Young’s modulus is 94 MPa, similar to normal printing paper. The optimized paper demonstrated a water contact angle (WCA) of 151°, which can be maintained as high as 126° even after 30 min of annealing at the temperature of 600 °C. Finally, writing with inorganic ink can be performed on this paper with inhibited ink diffusion. The written paper can maintain its integrity after 5 min of firing by alcohol flame. The flame-retardant and hydrophobic paper here may extend the applications of paper in wide range of fields.

Effective improvement of the Chinese ink diffusion properties of Xuan paper by cellulose microfibrils-precipitated calcium carbonate composite filler

The cellulose microfibril-precipitated calcium carbonate (CMF–PCC) composite filler has been studied in improving the printing and optical properties of ordinary paper. However, the effect of CMF–PCC composite filler on the properties of Xuan paper, especially the ink diffusion properties, has rarely been investigated. In this study, the CMF–PCC composite filler was prepared by double-exchange reaction. The effects of CMF–PCC composite filler on the physical properties and ink diffusion properties of Xuan paper were detailedly studied. The results showed that the PCC particles in the CMF–PCC composite filler were rhombohedral calcite, with a uniform particle size and high adhesion rate, under the optimum reaction conditions. The Xuan paper filled with the CMF–PCC composite filler had higher tensile strengths and opacity than the conventional PCC or GCC loading. Notably, the CMF–PCC composite filler can effectively improve and regulate the Chinese ink diffusion properties of Xuan paper.

Imbibition of Femtoliter-Scale DNA-Rich Aqueous Droplets into Porous Nylon Substrates by Molecular Printing.

This work presents the first reported imbibition mechanism of femtoliter (fL)-scale droplets produced by microchannel cantilever spotting (μCS) of DNA molecular inks into porous substrates (hydrophilic nylon). Differently from macroscopic or picoliter droplets, the downscaling to the fL-size leads to an imbibition process controlled by the subtle interplay of evaporation, spreading, viscosity, and capillarity, with gravitational forces being quasi-negligible. In particular, the minimization of droplet evaporation, surface tension, and viscosity allows for a reproducible droplet imbibition process. The dwell time on the nylon surface permits further tuning of the droplet lateral size, in accord with liquid ink diffusion mechanisms. The functionality of the printed DNA molecules is demonstrated at different imbibed oligonucleotide concentrations by hybridization with a fluorolabeled complementary sequence, resulting in a homogeneous coverage of DNA within the imbibed droplet. This study represents a first step toward the μCS-enabled fabrication of DNA-based biosensors and microarrays into porous substrates.

Effect of the basic surface properties of woven lining fabric on printing precision and electrical performance of screen-printed conductive lines

Conductive lines are essential for the integration of electronic devices into fabrics, and their direct screen printing on fabrics is a promising, simple and low-cost method for mass-manufactured textile-based conductive lines. However, the intrinsic porous structures and texture characteristic of textiles complicate the diffusion and penetration of conductive ink, and will deteriorate the printing precision and electrical performance of conductive lines. To establish the relationship between the surface characteristics (i.e. porosity, roughness, contact angle) and printing precision as well as electrical performance, the screen-printed conductive lines on six different nylon woven lining fabrics were examined and compared. Moreover, to study the printing precision and the minimum printable line width on woven lining fabric, conductive lines with different widths were screen printed. The results showed that the fabric substrate with the smallest pore size and roughness shows a higher printing precision and lower electrical resistance of screen-printed conductive lines. Relatively, the dynamic contact angle and wetting time of ink on the surface of the fabric have a significant effect on the printing precision. Therefore, the surface structure of the fabric substrate determines to some degree the printing precision of conductive lines, the printable minimum line width and its electrical properties. It is believed that these findings will provide some important support for screen printing flexible electronic devices on woven textiles.

The influence of ink viscosity, water and fabric construction on the quality of ink‐jet printed polyester

AbstractThis paper is concerned with the quality of lines and disperse ink in printing patterns on different untreated polyester fabric constructions. The lines running in the weft and warp directions were printed on polyester fabric constructions, and printing accuracy was assessed. Ink spreading is one of the important factors that influences the ink distribution. Thus, in order to acquire satisfactory ink‐jet printing products, it is essential to control the spreading of ink on the polyester fabric. To meet these conditions, a series of chemicals (disperse dye 5.01 wt%, PVP‐K30 0‐2 wt%, DEG 5‐20 wt%, water 64.17‐79.17 wt%, etc) with different mass fractions was used to prepare disperse ink. The jetting behaviour of ink was related to its surface tension and viscosity, which was characterised by an automatic surface tensiometer and rotational viscometer. Line profile was used to evaluate the printing effect. Low field nuclear magnetic resonance and three‐dimensional super depth digital microscopy were used to reveal the relationships between the state of water, ink diffusion behaviour and printing sharpness. The results showed that increasing ink viscosity or decreasing free water content is advantageous to improve the sharpness of the printing pattern. The effects of fabric structural parameters on line image quality are discussed. The printing quality was closely related to the weight and structure of fabric. The heavy weight fabrics had accurate print pattern sharpness. The fastness test results showed that the ink printing pattern had good colour fastness.

Color Degradation of Printed Images

Numerous color images are digitally reproduced today, mainly using the cyan, magenta, yellow and black ink set. The information in a printed image, however, may be distorted or lost due to the image's gradual color degradation as the result of ink fading and diffusion on the substrate. The degradation behavior of the inks can be difficult to predict when catalytic fading is introduced by a variety of ink mixtures produced in the printing process. In this article, we prove that the fading or diffusion rate has an equivalent interpretation as the hazard function in reliability modeling, and the degradation model of printed images with constant fading and diffusion rates can be reformulated as a Markov process model. Hence, the degradation of printed images with time-varying fading and diffusion rates can be modeled as a semi-Markov process. The semi-Markov process model provides a deterministic degradation prediction. We further propose a spatio-temporal Wiener process model for stochastic prediction of the ink fading and diffusion of printed images. Numerical examples and a real-life case study are provided to illustrate the proposed approach.

Controlling the micro-structure of disperse water-based inks for ink-jet printing

The study aims to investigate the effect of additives (poly (vinyl pyrrolidone) PVP, glycerol, ethylene glycol) on the performances of disperse water-based inks for ink-jet printing and how such additives interact with water. This should help into design suitable inks for textile printing by ink-jet printing, in particular for synthetic fibers such as polyester fabrics. Thirteen kinds of inks were prepared, and the glycerol content was replaced by water and PVP (K15, K30, K60), and the solubility parameter of the additive was calculated by the group contribution method. Low field nuclear magnetic resonance (LF-NMR) reveals the existence of bound water, intra-microstructure water, and extra-microstructure water in the ink, and the intra-microstructure water is entrapped inside the micro-structure formed by additives, mainly due to the presence of PVP. The optimal ink (Y5K30) has a low linewidth relative change (0.4%) and excellent sharpness. The reason is the existence of microstructure in ink, which reduces the mobility of solvent in ink and the diffusion of ink on fabric. PVP and disperse dyes have a strong affinity and help to improve the color depth and color fastness of the fabric.

Multiplexed Biomolecular Arrays Generated via Parallel Dip-Pen Nanolithography.

The capability of transferring target materials especially functionality-reliable biomolecules, into specific locations and with arbitrarily designed patterns are of critical importance for high-throughput disease diagnosis, multiplexing, and drug screening. Herein, we report the simultaneous patterning of two types of biomolecules using the parallel dip-pen nanolithography technology where an array of the atomic force microscope (AFM) tips can be selectively and alternately coated with target biomolecules via a specially designed inkwell array. Moreover, mixing target biomolecules at a proper volumetric ratio with polyethylene glycol dissolved in PBS buffer solution that works as an ink carrier can not only facilitate the smooth transfer of ink materials from the AFM tip to the substrate,it can also help to adjust the ink diffusion constant of different biomolecules to be highly similar so that the multiplexed biofunctional dot and/or line arrays at similar sizes can be reliably generated.

Degradation Modeling and Prediction of Ink Fading and Diffusion of Printed Images

A great number of images are produced by color printers. Many factors lead to the degradation of printed images and its accurate prediction modeling is of a great interest. Previous research that addresses image degradation usually measures ink density or color of the prints. In this paper, we predict image degradation by the area coverage of inks. We propose a multilayered degradation transition diagram based on the halftone printing technique used by modern color printers and develop an ink fading model based on differential equations that describe the transition diagram. In addition, a vector autoregression ink diffusion model is developed by discretizing two-dimensional diffusion equation using finite difference method. The two models are integrated into a mixture degradation model to predict the area coverage change of printed images over time. We provide the parameter estimation method of the mixture degradation model. Numerical examples and a real-world case study are given to illustrate the proposed approach.

Haptic Decorating on the Surface of Virtual Clay Model

A novel haptic decorating method on the surface of virtual clay model is proposed. The relationship between brush deformation and endured force is researched for the first time by applying the spring-mass model to construct the 3D brush model. Then, the collision detection between virtual hairy brush and virtual clay model is researched based on collision algorithm of weighted average distance. When the hairy brush initially collides with 3D exterior, the tactility is simulated and the interactive virtual painting on the 3D exterior is carried out practically. The 3D brush stroke is formed by superimposing 3D brush footprints along the painting direction and controlling the stress of the brush. The ink quantity in the brush footprint is determined according to the proposed positive correlation between the exerted pressure on brush and outflow ink quantity of the brush. A painting storage method is also presented for storing and displaying 3D stroke painting results. The proposed method has been successfully applied in the 3D virtual painting system based on real-time force feedback technology. With this system, the 3D brush strokes with 3D half-dry and ink diffusion results can be painted with a Phantom Desktop haptic device, which effectively enhance reality to users.

Improved Water-Resistance Test Methods Utilizing a Multispectral Imaging System to Quantify Black and Color Ink Bleeding for Plain Paper Office and Legal Documents Printed with Pigment- and Dye-Based Inkjet Inks

Current ISO standards that pertain to water-resistance testing with inkjet prints were developed for moisture-impermeable RC photo papers and do not take into account the kinds of ink diffusion behavior that can occur with inkjet printing on highly absorbent plain papers, especially with dye-based inks. Contact with water with plain paper documents can result in significant lateral ink bleeding, migration of inks through the paper to the backside of the sheet, transfer of ink from one sheet to adjacent sheets, and two-way transfer of inks with double-sided printed documents. Shipping labels and envelopes can become illegible should they become wet, and Barcodes and QR codes may be rendered completely unreadable. This study attempts to better understand the water-resistance behavior of plain paper documents printed with dye-based and pigment inkjet inks. The use of high-resolution multispectral imaging and colorimetric analysis systems to provide a quantitative assessment of ink bleeding, migration, and ink transfer to adjacent pages is explored as an alternative to the subjective, qualitative, water-resistance evaluation methods specified in current ISO standards.

In‐Plane Micro‐Supercapacitors for an Integrated Device on One Piece of Paper

AbstractPortable and wearable sensors have attracted considerable attention in the healthcare field because they can be worn or implanted into a human body to monitor environmental information. However, sensors cannot work independently and require power. Flexible in‐plane micro‐supercapacitor (MSC) is a suitable power device that can be integrated with sensors on a single chip. Meanwhile, paper is an ideal flexible substrate because it is cheap and disposable and has a porous and rough surface that enhances interface adhesion with electronic devices. In this study, a new strategy to integrate MSCs, which have excellent electrochemical and mechanical performances, with sensors on a single piece of paper is proposed. The integration is achieved by printing Ni circuit on paper without using a precoating underlay. Ink diffusion is also addressed to some degree. Meanwhile, a UV sensor is integrated on a single paper, and the as‐integrated device shows good sensing and self‐powering capabilities. MSCs can also be integrated with a gas sensor on one‐piece paper and can be charged by connecting it to a solar cell. Thus, it is potentially feasible that a flexible paper can be used for integrating MSCs with solar cell and various sensors to generate, store, and use energy.

Fabrication of Patterned Concave Microstructures by Inkjet Imprinting

Concave microstructures such as microwells and microgrooves are widely utilized in fields such as biochips, microfluidics, and functional devices. Previously, concave microstructure fabrication was mostly based on laser etching or lithography which is either costly or of multisteps. The inkjet etching method is a direct structuring technique, but limited by its inherent transverse ink diffusion that leads to low feature resolution. Nanoimprint lithography can reach submicro and even nano ranges, whereas an elaborate template is needed. Thus, it is still a challenge to realize controllable fabrication of concave microstructures in large areas with high efficiency and resolution. Here, a template‐free strategy to fabricate concave microstructures with high resolution by inkjet imprinting is provided. In this method, a sacrificial ink is inkjet‐printed onto a precured viscoelastic surface and imprints its shapes to construct concave microstructures. The morphology of the microstructures could be adjusted by controlling the interaction between the two immiscible phases. The microwells/microgrooves could be used to pattern single cells and functional materials such as optical, electronic, and magnetic nanoparticles. These results will open a new pathway to fabricate concave microstructures and broaden their applications in various functional devices.

Modeling ink diffusion within paper to achieve a raggedness ruler for print quality control

Raggedness is one of the most important print quality factors. It is defined as the appearance of geometric distortion of an edge from its ideal position that should be absolutely straight along the length of the line. Raggedness is caused by several phenomena. The non-uniformity absorption of ink, which may be because of the paper roughness or ink quality, may cause various degree of raggedness. Print quality assessments are usually based on comparing a test sample with a reference as a ruler of different quality samples. Therefore, it is important to prepare appropriate rulers for different quality metrics. The present study introduces a new method for modeling of raggedness by simulating ink diffusion within paper. It is assumed that different parts of a paper have different diffusion coefficients, so the ink can randomly diffuse through different paths. These paths can be changed via paper properties and drying time. Using this method and controlling the effective variables it is expected to generate different levels of raggedness. The experimental results show that with the proposed method it is possible to achieve different levels of raggedness, which can be used to generate test targets and raggedness rulers. Also, it can standardize objective and subjective test methods for measuring raggedness.

Simulation of ink diffusion on Xuan paper

Ink diffusion is a complex physical phenomenon. Concerning the problem of simulating ink diffusion on Xuan paper, this paper proposed a simulation method based on diffusion equation with variable coefficient, and its diffusion coefficient depended on Xuan paper structure and the residue of ink which reduced with time. There were two steps for simulation: simulating Xuan paper structure and simulating the dynamic procedure of diffusion. To simulate Xuan paper structure, a weighting fiber structure was proposed, which consisted of uniformly distributed line segments with different weights and random directions. The dynamic procedure of ink diffusion was described by the diffusion equation. To generate the diffusion image efficiently, Crank-Nicolson method was used to solve the diffusion equation, fiber structure was precomputed, and the diffusion image was updated dynamically. Compared with the previous similar simulation methods, this method rendered more natural diffusion boundary, and overcame the problem of excessively smooth boundary. The experimental results demonstrate that this approach is able to simulate the effects of ink diffusion on different Xuan paper realistically.

Molecular Flux Dependence of Chemical Patterning by Microcontact Printing

We address the importance of the dynamic molecular ink concentration at a polymer stamp/substrate interface during microcontact displacement or insertion printing. We demonstrate that by controlling molecular flux, we can influence both the molecular-scale order and the rate of molecular exchange of self-assembled monolayers (SAMs) on gold surfaces. Surface depletion of molecular ink at a polymer stamp/substrate interface is driven predominantly by diffusion into the stamp interior; depletion occurs briefly at the substrate by SAM formation, but diffusion of molecules into the bulk of the stamp dominates over practical experimental time scales. As contact time is increased, the interface concentration varies significantly due to diffusion, affecting the quality and coverage of printed films. Controlling interfacial concentration improves printed film reproducibility and the fractional coverage of multicomponent films can be controlled to within a few percent. We first briefly review the important aspects of molecular ink diffusion at a stamp interface and how it relates to experimental duration. We then describe two examples that illustrate control over ink transfer during experiments: the role of contact time on monolayer reproducibility and molecular order, and the fine control of fractional monolayer coverage for the displacement printing of 1-adamantanethiolate SAMs by 1-dodecanethiol.