Abstract:
Systems and methods are provided for digital transport of paramagnetic particles. The systems and methods may include providing a magnetic garnet film having a plurality of magnetic domain walls, disposing a liquid solution on a surface of the magnetic garnet film, wherein the liquid solution includes a plurality of paramagnetic particles, and applying an external field to transport at least a portion of the paramagnetic particles from a first magnetic domain wall to a second magnetic domain wall of the plurality of magnetic domain walls.

Description:
RELATED APPLICATION 
   The present application claims priority to U.S. Provisional Application Ser. No. 60/827,904, fled Oct. 3, 2006, and entitled “Digital Transport of Paramagnetic Beads On Magnetic Garnet Films,” which is hereby incorporated by reference in its entirety as if fully set forth herein. 

   FIELD OF THE INVENTION 
   Aspects of an embodiment of the invention relate generally to the programmable motion of an ensemble of paramagnetic particles on magnetic garnet films. 
   BACKGROUND OF THE INVENTION 
   Controlling the motion or transport of small particles and molecules on a film using external fields has been proven to be an extremely difficult task. Indeed, when external fields are applied to the particles and molecules, their resulting motions have tended to be random and unpredictable. Accordingly, random and unpredictable motions are not suitable for a variety of applications that require the ability to control the motion or transport of individualized particles and molecules in a deterministic manner. Accordingly, there is a need in the industry for systems and methods for the controlled motion or transport of small particles and/or molecules. 
   SUMMARY OF THE INVENTION 
   According to an example embodiment of the invention, there is a system for digital transport of paramagnetic particles. The system may include a magnetic garnet film having a plurality of magnetic domain walls, a liquid solution disposed on a surface of the magnetic garnet film, and a plurality of paramagnetic particles disposed within the liquid solution, where at least a portion of the paramagnetic particles are transported from a first magnetic domain wall to a second magnetic domain wall of the plurality of magnetic domains by applying an external field. 
   According to another example embodiment of the invention, there is a method for digital transport of paramagnetic particles. The method may include providing a magnetic garnet film having a plurality of magnetic domain walls, disposing a liquid solution on a surface of the magnetic garnet film, where the liquid solution includes a plurality of paramagnetic particles, and applying an external field to transport at least a portion of the paramagnetic particles from a first magnetic domain wall to a second magnetic domain wall of the plurality of magnetic domain walls. 
   According to yet another example embodiment of the invention, there is a system. The system may include a magnetic garnet film having a plurality of magnetic domain walls, a liquid solution disposed on a surface of the magnetic garnet film, a plurality of paramagnetic particles disposed within the liquid solution, and means for transporting at least a portion of the paramagnetic particles from a first magnetic domain wall to a second magnetic domain wall. 

   
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S) 
     Reference will be made to the accompanying drawings, which are not necessarily drawn to scale, and wherein: 
       FIG. 1  illustrates a paramagnetic particle transport system according to an example embodiment of the invention. 
       FIG. 2  illustrates example parallel stripe domains of a magnetic garnet film, according to an example embodiment of the invention. 
       FIG. 3A  illustrates the magnetic field at a magnetic domain wall prior to the application of oscillating magnetic field, according to an example embodiment of the invention. 
       FIG. 3B  illustrates the magnetic field at a magnetic domain wall during the application of a half cycle of a oscillating magnetic field pulse, according to an example embodiment of the invention. 
       FIG. 4  illustrates a periodic array of magnetic bubble domains of a magnetic garnet film, according to an example embodiment of the invention. 
       FIG. 5A  illustrates a paramagnetic particle trapped in a localized orbit around a single bubble domain, according to an example embodiment of the invention. 
       FIG. 5B  illustrates a paramagnetic particle moving in a superdiffusive manner, according to an example embodiment of the invention. 
       FIG. 5C  illustrates a paramagnetic particle moving in a ballistic manner, according to an example embodiment of the invention. 
       FIG. 5D  illustrates a trapped paramagnetic particle between neighboring bubble domains, according to an example embodiment of the invention. 
       FIG. 6  illustrates a top view of an example magnetic labyrinth pattern of a garnet film, according to an example embodiment of the invention. 
       FIG. 7A  illustrates a type of paramagnetic particle carrier where the paramagnetic particles may be adhered, at least temporarily, to a variety of cargo, according to an example embodiment of the invention. 
       FIG. 7B  illustrates a motion of the paramagnetic particles that may provide secondary flow to transport cargo, according to an example embodiment of the invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Embodiments of the invention will now be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the invention are shown. Indeed, these inventions may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. Like numbers refer to like elements throughout. 
   Embodiments of the invention may provide for paramagnetic particle transport systems that may allow for transporting or otherwise moving paramagnetic particles in a liquid solution in a deterministic manner. According to an embodiment of the invention, the paramagnetic particles may be utilized as carriers. More specifically, the paramagnetic particles may be used to transport cargo either directly or indirectly with the transported paramagnetic particles. 
   The transport or movement of the paramagnetic particles, with or without cargo, within a paramagnetic particle carrier system may be utilized for a variety of applications. Examples of such applications include memory devices, molecular shift registers, optical bar-coding, mixing of particles, particle separation, DNA sequencing, fluorescent markers (e.g., for use in microrheological experiments of the cytoskeleton), and microfluidics applications where cargo is to be transported on a lab-on-a-chip device. It will be appreciated that while some examples of applications have been listed above, other applications will be available without departing from embodiments of the invention. 
   I. Paramagnetic Particle Transport System Overview 
     FIG. 1  illustrates a paramagnetic particle transport system  100  according to an example embodiment of the invention. The paramagnetic particle transport system  100  of  FIG. 1  may include a substrate  101 , a garnet film  102  formed on the substrate  101 , a liquid solution  104  formed on a surface of the garnet film  102 , and one or more paramagnetic particles  105  disposed within the liquid solution  104  (e.g., an aqueous solution). Optionally, a barrier layer  103  may be provided as an electrostatic coating on the garnet film  102  to prevent one or more paramagnetic particles  105  from being absorbed by the garnet film  102 . In an embodiment of the invention, the barrier layer  103  may be a polyelectrolyte, polysodium-4-styrene sulfonate, or the like. 
   The garnet film  102  may be formed on a surface of the substrate  101 , according to an example embodiment of the invention. For example, the magnetized patterns of garnet films  102  may be grown by liquid-phase epitaxy on surfaces of a substrate  101  such as a gadolinium gallium garnet (GGG) substrate. Additionally, external magnetic fields, including high frequency magnetic fields, may be applied to the garnet film  102  to form metastable magnetization patterns as will be described in further detail below. 
   The paramagnetic particles  105  may be paramagnetic colloidal particles, paramagnetic nano particles, and the like, according to an example embodiment of the invention. According to an embodiment of the invention, the paramagnetic particles  105  may include a paramagnetic core made of superparamagnetic grains surrounded by a polymer shell. According to another embodiment of the invention, the paramagnetic particles  105  may be polystyrene particles doped with superparamagnetic iron oxide grains. These superparamagnetic iron oxide grains may range from 10 to 100 angstroms, according to an example embodiment of the invention. A type of paramagnetic particle  105  may be available from Dynal, Norway in sizes ranging from 0.5 to 5 microns in diameter. According to yet another embodiment of the invention, the paramagnetic particles  105  may include a polymer matrix that is doped with tiny superparamagnetic magnetite grains. 
   In the presence of a magnetic field, the paramagnetic particles  105  may become magnetized with their magnetostatic energy being proportional to the product of the magnetic field and the paramagnetic particle  105  magnetization. Accordingly, the paramagnetic particles  105  may be subject to a force pointing in the direction of the gradient of the square of the magnetic field, according to an example embodiment of the invention. Thus, the paramagnetic particles  105  may be capable of being manipulated by an external magnetic field. However, other paramagnetic particles  105  may be manipulated by other external fields, including electric and/or optical fields. 
   II. Magnetic Domains for Garnet Films 
   According to an example embodiment of the invention, the domain walls of the garnet film  102  (e.g., a ferrimagnetic garnet film) may generate magnetic fields heterogeneous on the colloidal scale. When a liquid solution  104  of the paramagnetic particles  105  is placed on the garnet film  102 , the paramagnetic particles  105  may be pinned or constrained to the domain walls by the stray magnetic field of the garnet film  102 . According to an example embodiment of the invention, an external field, perhaps an external magnetic field, may be applied to change the domain distribution in the garnet film  102  and thus move the paramagnetic particles  105  in a predetermined direction. 
   The paramagnetic particles  105  may be manipulated with the aid of non-invasive external fields, including magnetic fields, electric fields, and optical fields. According to an embodiment of the invention, the magnetic fields utilized for the paramagnetic particle transport system  100  may be generated and/or manipulated using magnetic tweezers, microcoil, micromagnetic systems, an array of permalloy elements, or electromagnetic traps. It will be appreciated however, that other embodiments of the invention, may instead utilize electric and optical external fields. For example, optical tweezers may be utilized for generating and/or manipulating optical fields. 
   According to an example embodiment of the invention, the garnet film  102  of the paramagnetic particle transport system  100  may include one of a variety of magnetic domain patterns. Generally, the magnetic domain patterns may determine the manner in which a paramagnetic particles  105 , with or without cargo, may be transported across the garnet film  102 . Some examples of magnetic domain patterns in accordance with example embodiments of the invention include (A) parallel stripe domains and (B) magnetic bubble domains. It will be appreciated, however, that other magnetic domain patterns may be available in accordance with other embodiments of the invention. 
   A. Parallel Stripe Domains 
     FIG. 2  illustrates example parallel stripe domains  202  of a magnetic garnet film  102 , according to an example embodiment of the invention. In  FIG. 2 , the magnetic stripe domain  202  walls are parallel to each other and alternate between opposing magnetic directions. It will be appreciated that application of an external magnetic field normal to the garnet film  102  may increase (decrease) the size the stripe domain  202  wall with parallel (anti-parallel) magnetization direction, according to an example embodiment of the invention. Accordingly, the application of an external, anti-parallel, normal magnetic field can be used to release and move paramagnetic particles  105  from one stripe domain  202  wall to another stripe domain  202  wall. It also be appreciated that the size of the paramagnetic particles  105  may determine the choice of wavelength λ of the particular stripe pattern of the garnet film  102  to be used. In particular, the wavelength λ of the particular stripe pattern of the garnet film  102  may be directly proportional to the size of the paramagnetic particles  105 . 
   According to an example embodiment of the invention, the parallel stripe domains  202  of  FIG. 2  may be created using a uniaxial magnetic garnet film of composition Y 2.5 Bi 0.5 Fe 5-q Ga q O 12  (q=0.5−1), thickness 5 μm, and saturation magnetization of M S =1.7×10 4  A/m. In this example embodiment, each stripe domain  202  wall may have a size of λ/2 where λ=10.9 μm is the wavelength of the stripe pattern. The paramagnetic particles  105  may have a mean diameter of 2.8±0.1 μm, density ρ=1.4 g/cm 3  and effective magnetic susceptibility χ=0.17 (e.g., Dynabeads M-270), according to an example embodiment of the invention. To move the paramagnetic particle  105  in a defined direction, oscillating magnetic field pulses in the (x,z) plane, H ext =Ĥ(sin ωt, 0, cos ωt) may be applied with frequency 6 s −1 &lt;ω&lt;125 s −1  (e.g., ω=18.8 s −1 ), amplitude Ĥ=1.3×10 4  A/m, and inclination θ=45° with respect to the z axis. The component of the field normal to the garnet film  102  may displace the domain wall by increasing the width of the stripe domains  202  having parallel magnetization direction. Colloidal particles  105  hopping across the stripe domains  202  walls may occur because the pinning sites alternate between weak and strong during the magnetic modulation of the planar component of the magnetic field, as illustrated in  FIGS. 3A and 3B . In particular,  FIG. 3A  illustrates the magnetic field at the domain  202  wall prior to the application of oscillating magnetic field pulse while  FIG. 3B  illustrates the magnetic field at the domain  202  wall during the application of a half cycle of a oscillating magnetic field pulse. Accordingly, as illustrated by  FIG. 3B , the paramagnetic particle  105  motion may be directed normal to the stripe domain  202  pattern and the paramagnetic particles  105  may move by one wavelength λ during one magnetic field pulse cycle. The hopping from one to the next domain  202  wall renders the longitudinal motion free of dispersion. Individual differences in speed due to different drag coefficients may be erased after each hop. This may ensure that the paramagnetic particles  105  do not separate along the direction of motion, and they all move with a defined speed, v p =λω/2π. 
   The magnetic garnet film  102  of  FIG. 2  having parallel stripe domains  202  may be utilized in a variety of applications, including memory and computing applications. In particular, in accordance with an embodiment of the invention, the paramagnetic particles  105  in the liquid solution  104  may be transported in digital steps on the surface of a garnet film from one stripe domain  202  wall to another stripe domain  202  wall. Additionally, these paramagnetic particles  105  may be loaded with single molecules to form, for example, shift registers, libraries, memory devices, and computing devices. 
   B. Magnetic Bubble Domains 
     FIG. 4  illustrates a periodic array of magnetic bubble domains  402  of a magnetic garnet film  102 , according to an example embodiment of the invention. These magnetic bubble domains  402  may be achieved by applying a high frequency magnetic field to the garnet film  102 . According to an embodiment of the invention, the magnetic bubble domains  402  may be metastable in that they may be maintained, at least temporarily, after the high frequency magnetic field is removed. Accordingly, the magnetic garnet films  102  may include circular spots that form a periodic array of magnetic bubble domains  402 . 
   Prior to the application of an external field, perhaps an external magnetic field, a paramagnetic particle  105  may be trapped by a stray magnetic field provided by a magnetic bubble domain  402 . Indeed, according to an example embodiment, the paramagnetic particle  105  may be trapped in a localized orbit  502  around a single bubble domain  402  wall, as illustrated by  FIG. 5A . As an increasing external static field is applied normal to the garnet film  102 , the paramagnetic particle  105  may break its localized orbit  502  around a single bubble domain  402  wall, and instead move in a superdiffusive manner  504 , as illustrated in  FIG. 5B , or further in a ballistic motion, as illustrated in  FIG. 5C . In particular, with the superdiffusive motion  506  of  FIG. 5B , the paramagnetic particle  105  may meander towards the desired direction. However, with the ballistic motion  506  of  FIG. 5C , the paramagnetic particle  105  may move along a substantially straight sequence of bubble domains  402  walls with a symmetry broken direction of motion that may be decided by the relative phase of the paramagnetic particle  105  with respect to the external field modulation. According to an embodiment of the invention, the application of an even higher external static field normal to the garnet film  102  may trap a paramagnetic particle  105  in an orbit  508  around a continuous domain area in between three neighboring bubble domain  402  walls. 
   According to an example embodiment of the invention, the magnetic bubble domains  402  of  FIG. 4  may be created using a garnet film  102 , perhaps a ferrite garnet film, with uniaxial anisotropy and composition Y 2.5 Bi 0.5 Fe 5-q Ga q O 12  (q=0.5−1), thickness ˜5 μm and saturation magnetization M s =1.7×10 4  A/m. High frequency (e.g., ˜12×10 3  s −1 ) magnetic field pulses of amplitude ˜10 5  A/m normal to the garnet film  102  may enforce the formation of the metastable magnetic bubble inside the garnet film  102 , according to an example embodiment of the invention. The bubbles may be cylindrical domains  402 , perhaps with diameter 2R=8.2±0.1 μm, of reverse magnetization separated by a continuous magnetized film  102 . Application of an external magnetic field Hz parallel (antiparallel) to the bubble magnetization direction may increase (decrease) the size of the cylindrical domain  402  walls. The colloidal suspension may consist of paramagnetic particles  105  (e.g., polystyrene paramagnetic particles) with a diameter D=2.8 μm and magnetic susceptibility χ=0.17 (e.g., Dynabeads M-270). 
   According to an example embodiment of the invention, with a magnetic field H, a paramagnetic particle  105  of volume V may acquire a magnetic moment m=V χ H along the field. The magnetic energy of the paramagnetic particle  105  may be E=−μm·H∝H 2 , where μ is the magnetic susceptibility of the liquid solution  104  (e.g., water). Without an external field, the paramagnetic particles  105  may be attracted toward the bubble domain  402  walls, where the magnetic stray field of the film  102  may be maximal. If ignoring the field of the neighboring magnetic bubble domains  402 , the magnetic stray field may have cylindrical symmetry and each paramagnetic particle  105  position on the bubble domain  402  boundary may have the same energy. This symmetry may be broken with an external field by using a precessing magnetic field of frequency Ω and θ: 
   H=Ĥ[cos θe z +sin θ(cos(Ωt)e x +sin(Ωt)e y )]. This external field, when averaged over one period of the modulation, may have no preferred direction and motion into a particular direction can only be achieved via symmetry breaking for the individual paramagnetic particles  105 , thereby releasing the paramagnetic particles  105 . Accordingly, the paramagnetic particles  105  when released may then move in a superdiffusive motion  504  or in a ballistic motion  506 , according to an example embodiment of the invention. 
   C. Other Magnetic Domains 
   The magnetic garnet films  102  may alternatively be provided with magnetic domain patterns other than the stripe domain patterns or bubble domain patterns described above. For example, the stripe domain pattern of  FIG. 2  may be altered using strong magnetic fields to form a magnetic labyrinth pattern.  FIG. 6  illustrates a top view of an example magnetic labyrinth pattern of a garnet film  102 , according to an example embodiment of the invention. As illustrated by  FIG. 6 , the magnetic labyrinth pattern forms channels  602  that define flow directions for paramagnetic particles  105 . 
   III. Applications 
   A. Transport of Cargo 
   The paramagnetic particles  105  in accordance with an embodiment of the invention may serve as carriers.  FIG. 7A  illustrates a type of carrier where the paramagnetic particles  105  may be adhered, at least temporarily, to a variety of cargo  702 . Indeed, the paramagnetic particles  105  may include adhesives or surface reactive groups  704  to adhere the paramagnetic particles  105  to a variety of cargo  702 . Thus, both the paramagnetic particles  105  and the attached cargo  702  may be transported at the same speed Vp. 
   According to another embodiment of the invention,  FIG. 73  illustrates a motion of the paramagnetic particles  105  that may provide secondary flow  706  to transport the cargo  702 . The secondary flow  706  may drag the cargo  702  in the same direction as the transported paramagnetic particles  105 . In this embodiment of the invention, a sufficient number of paramagnetic particles  105  may be needed to create sufficient secondary flow  706 . The paramagnetic particles  105  may be transported at particle speed Vp while the cargo  702  may be transported at cargo speed Vd. In an example embodiment of the invention, the cargo speed Vd may be less than or equal to the particle speed Vp. For example, the cargo speed Vd may be only half of the particle speed Vp. 
   In either embodiment, the cargo  702  may include one or more molecules or particles, including, but not limited to, nucleic acids (e.g., DNA), cells such as biological cells, chemicals, and polymer molecules. It will be appreciated that the transport of cargo may be achieved using any of the magnetic domain patterns described in  FIGS. 2 ,  4 , and  6 , as well as a yet other magnetic domain patterns. 
   B. Mixing 
   According to an embodiment of the invention, the garnet film  102  of  FIG. 4  having an array of bubble domains  402  may be utilized in a paramagnetic particle transport system  100  that operates as a mixer. Generally, external magnetic field gradients may be used to move paramagnetic particles  105  in a liquid solution  104 , and thus drag or mix small volumes of reactants. According to an embodiment of the invention, the orbit of paramagnetic particles  105  around a bubble domain  402  in either direction (e.g., clockwise, counterclockwise) may be operative to mix these reactants. 
   C. Digital Particle Separation 
   According to an embodiment of the invention, the paramagnetic particle transport system  100  using the garnet films  102  of  FIG. 2  or  4  may be operative to digitally separate paramagnetic particles  105 , including those that may include cargo  702 . Generally, the trapping force may depend on the distance of the paramagnetic particle  105  from the domain wall. Thus, smaller paramagnetic particles  105  with their center close to a domain wall may be trapped stronger than larger particles  105  that are on average farther away from the wall. According to an embodiment of the invention, paramagnetic particles  105  of different sizes may be separated by applying an external field too weak to move the smaller particles but large enough for the large particles. According to another embodiment of the invention, an external field modulation may be applied to carry the smaller paramagnetic particles  105  in one direction and the larger particles  105  in an opposite direction. For example a modulation of the form (Hx, Hz)=Ĥ (sin 3ωt, sin ωt) may create a motion where the large particles hop two steps (e.g., domain walls) to the right while the smaller particles remain at their domain current wall. When the magnetic field amplitude reaches its maximum value the in-plane field changes sign and both large and small paramagnetic particles  105  may hop left. The net motion may be that the large paramagnetic particles  105  may move to the right while the small paramagnetic particles  105  may move to the left. Accordingly, the larger paramagnetic particles  105  may be separated from the smaller paramagnetic particles  105 . 
   D. Shift Registers 
   According to an example embodiment of the invention, the garnet film  102  of  FIG. 2  may be used to implement a molecular shift register that may include paramagnetic particles  105  disposed on top of the magnetic domain walls in the magnetic garnet film  102  having the magnetic stripe pattern of  FIG. 2  or another magnetic pattern. In the absence of external magnetic fields, this configuration provides a non-volatile form of data storage at a definite position. In accordance with an embodiment of the present invention, simple time dependent magnetic pulses may shift the entire assembly of paramagnetic particles  105  by one period of the magnetic domain pattern. Single molecules attached to the particles may be address in this way and may be moved sequentially into a desired region where they may be analyzed. Since the motion is digital—that is, one magnetic period per pulse, there is no dispersion of the particles as they move along the path such that the order of the paramagnetic particles  105  may be conserved. Accordingly, there is no loss of data. 
   Many modifications and other embodiments of the inventions set forth herein will come to mind to one skilled in the art to which these inventions pertain having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is to be understood that the inventions are not to be limited to the specific embodiments disclosed and that modifications and other embodiments are intended to be included within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.