## Abstract

The characterization “thermal diode” (TD) has been used to portray systems that spread heat very efficiently in a specific direction but obstruct it from flowing in the opposite direction. In this study, a planar vapor chamber (VC) with a wickless, wettability-patterned side and an opposing wick-lined side is fabricated and tested as a thermal diode. When the chamber operates in the forward mode, heat is naturally driven away from the heat source; in the reverse mode, the system blocks heat flow, thus acting as a thermal diode. The low-profile assembly takes advantage of the phase-changing properties of water inside a sealed chamber. The wettability-patterned plate—when on the cooled side, e.g., forward operation mode—enables spatially controlled dropwise condensation (high heat transfer rate) and filmwise condensation (high drainage rate), thus facilitating an efficient transport mechanism of the condensed medium on superhydrophilic wedge tracks by way of Laplace pressure-driven capillary forces. The same chamber acts as a thermal blocker when the wick-covered plate is on the cooled side (reverse operating mode), trapping the condensate in the wick pores and blocking heat flow to the opposite side. The system's thermal behavior is similar to the theoretical electrical diode. This work explores the effect of the condenser's wettability pattern design and the chamber's fluid charging ratio (CR). With this system, thermal diodicities exceeding 20 have been achieved, and are tunable by altering the wettability pattern. The thermal rectification concept and its proper quantification in terms of possible definitions are discussed. The present vapor chamber—thermal diode design could be well-suited for an extensive range of thermal-management applications, ranging from aerospace, spacecraft, and smart-building construction materials, to electronics protection, electronics packaging, refrigeration, thermal control during energy harvesting, thermal isolation, etc.

## 1 Introduction

Effective thermal control of electrical and electronic components is a challenge, which in recent years has hindered technological advancement [13]. The search for effective thermal management solutions has become a bottleneck, especially in view of the ever-rising demands on electronics performance [46]. Ever-advancing designs are needed to dissipate excess heat and to protect fragile electronic parts from overheating damage. A valid solution to this problem is provided by closed systems known as vapor chambers (VCs), which due to their internal architecture, spread heat very efficiently from one side to the other. If the construction features of each side differ, these systems can block heat flow in the opposite direction (i.e., acting as thermal diodes (TDs)). The term thermal diode is used here to describe a system that allows heat to flow preferably in a specific direction. TDs can rectify heat currents and are similar to electrical diodes, the well-known electrical parts with asymmetric electrical-current transport characteristics, namely, low resistance in one direction, ideally zero, and high resistance in the other, ideally infinite [7]. Such direction-dependent heat transport is beneficial for thermal-management functions and is the theme of this work.

Electronic diodes are straightforward, with silicon being the most common material in the field; however, silicon does not offer a viable option for a thermal analog [8]. Phase-change heat transfer [9] is a key method used to achieve high thermal diodicity, which is defined as the heat flux ratio in the forward (FWD) and reverse (RVS) modes of operation. The diodicity or thermal rectification ratio of a thermal directional system is defined as
$γ= kFWD− kRVSkRVS$
(1)
where k denotes the effective thermal conductivity along x and across an area A, and is given by
$k= Q dxA ΔT$
(2)

where dx is the total thickness of the system and ΔΤ is the difference between the average temperatures of the hot and the cold sides.

As shown in previous studies [10,11], a TD filled with a phase-change fluid and relying on jumping dropwise condensation achieved very high diodicity ∼250, while solid-state thermal diodes show orders of magnitude lower thermal rectification. Another study [12] presented a small-footprint VC integrating the functions of a heat spreader, a thermal diode, and a thermal switch with a nanostructured superhydrophobic surface acting as a condenser. TDs vary in size, shape, diodicity value, material, working principle, etc., and can be custom made to meet the specific needs of each distinct use. A variety of systems and applications for TDs has been studied in the literature, as, for example, liquid-trap heat pipes for rockets [13], systems for thermal control of robotic spacecraft [14], TD panels for buildings [15], advanced thermal management systems (e.g., thermal transistors and thermal logic gates) [16], passive solar heating with liquid convective diodes [17], thermal vacuum sensors for micro-electronics [18], and heat pipe with assisted performance from passive radiative cooling [19]

This work describes the design and fabrication of a novel vapor chamber, which also performs well as a thermal diode. The chamber features both a wick-lined (Fig. 1(1)) and a wickless wettability-patterned side (Fig. 1(2)). When the heat flows from the wick-lined to the wickless side, the system acts as an efficient heat spreader, but when the heat flows in the opposite direction, the system acts as a heat blocker (Fig. 2). Thus, the chamber has two distinct modes of operation. In the FWD mode, the chamber demonstrates high effective thermal conductivity with a low temperature drop across it. In the RVS mode, the chamber exhibits low effective thermal conductivity with high temperature gradient between the two sides. The thermal rectification is enabled by the design of the wickless plate, which promotes heat flow in the FWD mode but obstructs it in the RVS mode.

Fig. 1
Fig. 1
Close modal
Fig. 2
Fig. 2
Close modal

## 2 Experimental Setup

### 2.1 Chamber Design.

This work extends the vapor-chamber prototype of Koukoravas et al. [20]. This system facilitates a phase-change closed chamber, with a wick evaporator opposing a wettability-patterned [21] condenser. This type of biphilic patterning [22] has been shown to improve the condensation heat transfer coefficient [23]. The wick-free condenser offers discrete areas for controlled dropwise (DwC) and filmwise (FwC) condensation. The patterning combines micro- and nano‐textured superhydrophilic surface domains shaped as wedge tracks connected with straight veins ending on round wells. Those features can enable pumpless and rapid transport of water on their surface and rely on the size, texture, and chemistry of the underlying solid. The assembly components are:

#### 2.1.1 Wick-Lined Plate.

A typical wick-lined copper plate can be seen in Fig. 1 (1) after undergoing continuous testing for a week. This part was fabricated from a mirror-finish copper plate with dimensions 63.5 × 63.5 × 3.175 mm3. On this plate, a pocket was milled with dimensions 50.8 × 50.8  × 2 mm3. The remaining surrounding mirror-finish area was meant to provide the seat for a sealing gasket. On one side of the plate, a 1.6-mm diameter hole was drilled, and a 25.4-mm long copper tube was press-fitted inside this hole. This pipe was later used to evacuate the VC before startup. The copper tube was sealed on the plate with epoxy to prevent leaking. A 0.7 mm-thick copper wick was laid in the milled pocket. To achieve that, the sample was filled with copper powder and sintered at 950 °C for 15 min in a single-zone tube furnace (Blue-M-HTF55322c; Lindberg, Waltham, MA) using a heating ramp rate of 20 °C/min, inside a reducing atmosphere consisting of 90% Ar and 10% H2.

#### 2.1.2 Wickless Plate.

The wickless plate is seen in Fig. 1(2). Even after continuous testing for one week, the plate's surface revealed minimal alterations/defects. The plate shown in this figure is equipped with the wettability pattern design demonstrated in Fig. 3(b). This part was produced from a mirror-finish copper plate with dimensions 63.5 × 63.5 × 1 mm3. The surface was functionalized by spin-coating Teflon AF (AF 2400, Amorphous Fluoroplastics Solution, Chemours Co., Wilmington, DE). The sample was then cured in the same furnace in three stages, namely, 80, 180, and 260 °C. Next, a laser marking system (EMS400; TYKMA Electrox®, Chillicothe, OH) with 80% power, 10 kHz intensity, and 200 mm/s traverse speed was used to etch the desired pattern. The laser selectively ablated the Teflon coating from the copper plate, rendering the treated domains superhydrophilic.

Fig. 3
Fig. 3
Close modal

The process continued by immersing the plate sample in an aqueous solution of 2.5 mol/L sodium hydroxide (415413-500ML; Sigma-Aldrich, St. Louis, MO) and 0.1 mol/L ammonium persulfate (≥98%, MKCF3704, Sigma-Aldrich) at room temperature for 5 min. The goal of this step was to cover the laser-etched regions with copper hydroxide nanoneedles [24], while at the same time, the Teflon-coated mirror-finish regions stayed hydrophobic. The final product was a wick-free copper plate with a superhydrophilic pattern laid in hydrophobic surroundings. Two distinct wettability patterns were used, as shown in Figs. 3(a) and 3(b). Moreover, in Fig. 3(c), the flow pattern of condensate spreading on a wedge-shaped track is presented. The white background denotes a less wettable surface, while the wettable track is denoted with black color. The spreading of fluid from the narrow to the wide end of the wedge is ascribed to the Laplace pressure difference, a mechanism analyzed in detail elsewhere [25].

The gasket, as seen in Fig. 1(3), was incorporated to facilitate disassembly and reassembly of the system, as required for repeated testing. This gasket allowed the chamber to remain sealed for the entire period of each experimental run, while also allowing easy disassembly at the end of each run.

### 2.2 Experimental Setup.

The components of the experimental setup, as shown in Fig. 4, are described below:

Fig. 4
Fig. 4
Close modal

Sealing mechanism: As presented in Fig. 4(1), two metal plates secured by four parallel cylindrical posts were used to provide the appropriate sealing and effective contact between the experimental components.

Thermal insulation: Three distinct insulators were used. As presented in Fig. 4(2), a Teflon block (Teflon® PTFE, 8735K67, McMaster-Carr, Atlanta, GA) with dimensions 73.2 × 73.2 × 12.7 mm3 covered the upper part of the cold plate. A second Teflon block, as presented in Fig. 4(7) (Teflon® PTFE, 8735K67, McMaster-Carr), with dimensions 76.2 × 76.2 × 25.4 mm3, insulated the lower part of the heater. Around the outer sides of the two lower Teflon blocks (Figs. 4(5) and 4(7)) a 25.4-mm thick ceramic fiber insulation (B015GD0QCW, Amazon, Seattle, WA) block was placed (Fig. 4(8)). Consequently, the Teflon parts insulated the heater, the chamber, the copper block on top of the heater, and the cold plate from their surroundings, thus facilitating one-dimensional heat transfer (along the vertical direction in this case).

Heat-transfer assembly: The most vital part of the experimental setup was comprised of a heater, the chamber, and a cold plate. On the upper side of the diode, a liquid-cooled plate was placed (LC-SSX1, TE Technology, Traverse City, MI), functioning as heat sink removing heat from the system in a controllable manner. This plate (Fig. 4(3)) was connected to a chiller (RTE-110, Neslab, Portsmouth, NH) circulating pure ethylene glycol (Ethylene glycol 99%, Alfa Aesar, Haverhill, MA) and maintaining the cold plate at 30 °C. The chamber in Fig. 4(4) is positioned underneath the cold plate, on top of a copper block surrounded by a Teflon rectangular frame (Figs. 4(5) and 5). The copper block had a shallow (1 mm-deep) 63.5 × 63.5 mm2 milled pocket to ensure proper seating of the diode inside the block (Multipurpose 110 Copper Bar, 89275K35, McMaster-Carr), which had dimensions 50.8 × 50.8 × 9.5 mm3. This copper block was implanted in a Teflon frame (Teflon® PTFE, 8735K67, McMaster-Carr) with dimensions 76.2 × 76.2 × 10.5 mm3 (Fig. 5). A flexible heater (KH-303/10-P, 90 W, Omegalux, Norwalk, CT) with dimensions 76.2 × 76.2 × 0.254 mm3 was the heat source (Fig. 4(6)). The heater output was controlled by regulating the voltage through an AC power supply (Type 3, 3PN1010, Staco Energy Products Co., Dayton, OH). The geometric centers of both blocks were aligned with the center of the chamber and the flexible heater's, and as demonstrated in Fig. 5, where the dashed line marks the seating area of the chamber. The objective of this placement was to enable heat flow to the chamber in the most unidirectional way from the heater through the copper block to the wick-lined area of the chamber. The heat transfer up to this point relied on conduction. To minimize contact resistance, a thin layer of thermal conductive paste (Omegatherm 201, Omega, Norwalk, CT) was spread over every external interface through which heat flowed.

Fig. 5
Fig. 5
Close modal

A vacuum pump (2008A, Alcatel, Annecy, France) was utilized to rid the closed system of air and noncondensable gases. The pump was attached to the chamber via the copper tube on the evaporator side through leak-proof tubing, an on/off valve (see Fig. 1(4)) and a flow-regulating valve connected in series. The on/off valve was nearest to the chamber and a vacuum gauge was attached in between the two valves to monitor the pressure during the evacuation procedure. Moreover, six thermocouples (TCs) were positioned in TC grooves on the outside of each copper plate. On the TC tip, conductive paste was placed to ensure accurate temperature reading and data collection. Temperature data were recorded using a data acquisition system (USB 2400 series, DAQ, Omega, Norwalk, CT) at a sampling frequency of 1 Hz. The voltage regulator was utilized to modulate the heat input provided to the chamber by adjusting the voltage.

### 2.3 Experimental Procedure

In the FWD mode, the copper wick-lined plate is on top of the copper block with three thermocouples (TC1, TC2, and TC3) attached in between (Fig. 4). Originally, the wick is filled with the desired water quantity. The gasket is positioned on top of the flange around the wick of the evaporator. Thermocouples TC4, TC5, and TC6 are placed between the wickless condenser and the cold-plate heat sink (Fig. 4).

After the chamber was sealed, the first pump down procedure evacuated the chamber. The initialization procedure was continued by heating up (from room temperature to 40 $°C$) the system for 30 min, followed by a second degassing stage until the system's internal pressure reached approximately 4 kPa. Subsequently, the system was left to thermally equilibrate down to 30 $°C$ and the initialization procedure ended. For all tests presented in this study, three experimental runs were completed under the same conditions to produce error estimates. Each experimental run for the FWD mode lasted 7 min, while each RVS-mode run lasted 10 min, with both time frames found adequate to reach steady-state. The data from the last 100 s of each run were used for the analysis. When an experimental run ended, the system was left to equilibrate again down to 30 $°C$, and the next cycle started. TC1, TC2, and TC3 recorded temperatures between the copper block and the evaporator, while TC4, TC5, and TC6 provided the temperatures between the condenser and the cold plate. Those temperatures were used to monitor the lateral temperature uniformity on both sides of the chamber.

#### 2.3.2 Reverse (Heat-Blocking) Operation.

In the RVS mode, the same experimental procedure was followed, but with a change in the VC placement, namely, the system was upturned, with the wick-free plate brought to contact with the heated copper block, while the wick-lined part came in contact with the cold plate.

#### 2.3.3 Vapor Loss During Chamber Evacuation.

Throughout the evacuation procedure, a loss of vapor mass took place, since the system was precharged with deionized (DI) water. The weight of the chamber was measured shortly after the experiment was finished to determine the vapor loss. The chamber was disassembled and left open to dry for 8 h on a weight scale. Following full dry out, the weight of the chamber parts was again measured. During each experiment, the weight difference before and after the dry-out process produced the weight of the working medium (DI water) within the sealed chamber.

### 2.4 Performance Metrics and Data Reduction

#### 2.4.1 Heat Input (Q).

The heat passing through the system was determined by the following procedure. One-dimensional heat was generated by the flexible heater, and we assumed no heat losses to the environment. This assumption is justified by the small heater thickness (0.254 mm) and the insulation placed all around the heater area (Fig. 4(8)). An order of magnitude analysis supported this assumption. The heat generated from the flexible thin heater (red in Fig. 6) can spread along three pathways (noted with white arrows in Fig. 6) inside the experimental setup. The spread through the copper block Qcu prevails, as it occurs through the high-conductivity metal (brown in Fig. 6). The insulating Teflon parts are denoted in gray. The total heat produced by the heater (Qtot) is distributed among the copper block (Qcu), the Teflon block around the copper (QT,u), and the Teflon block under the heater (QT,d), i.e.,
$Qtot= Qcu+QT,u+QT,d$
(3)
Fig. 6
Fig. 6
Close modal
From Fourier's law, Q can be expressed as
$Q=k AdTdx$
(4)
Combining Eqs. (1) and (2),
$Qtot=kcuAcudTcudxcu+ kT AT,u dTT,udxT,u+ kT AT,d dTT,ddxT,d$
(5)
Substituting values from Table 1 into Eq. (3), it was deduced that the most important term on the right-hand side of the equation is Qcu, which is three orders of magnitude larger than all other terms of this equation. Thus, the following formula has been used for Qtot
$Qtot≈ Qcu=kcu AcudTcudx$
(6)
Table 1

Property values and parameter magnitudes

Values and magnitudes
SymbolDescriptionValueMagnitude
$kcu$Conductivity of copper [26]385 W/m KO(102)
$kT$Conductivity of Teflon [27]0.32 W/m KO(10−1)
$Acu$Area of copper block0.0025 m2O(10−3)
$AT,u$Area of Teflon (top)0.0032 m2O(10−3)
$AT,d$Area of Teflon (bottom)0.0058 m2O(10−3)
dxcuThickness of copper block0.00925 mO(10−3)
dxT,uThickness of Teflon plate (top)0.01025 mO(10−2)
dxT,dThickness of Teflon plate (bottom)0.0127 mO(10−2)
$δTcu$Maximum lateral temperature difference, copper2 $°C$O(10)
$δTT,u$Maximum lateral temperature difference, Teflon (top)40 $°C$O(101)
$δTT,d$Maximum lateral temperature difference Teflon (bottom)20 $°C$O(101)
Values and magnitudes
SymbolDescriptionValueMagnitude
$kcu$Conductivity of copper [26]385 W/m KO(102)
$kT$Conductivity of Teflon [27]0.32 W/m KO(10−1)
$Acu$Area of copper block0.0025 m2O(10−3)
$AT,u$Area of Teflon (top)0.0032 m2O(10−3)
$AT,d$Area of Teflon (bottom)0.0058 m2O(10−3)
dxcuThickness of copper block0.00925 mO(10−3)
dxT,uThickness of Teflon plate (top)0.01025 mO(10−2)
dxT,dThickness of Teflon plate (bottom)0.0127 mO(10−2)
$δTcu$Maximum lateral temperature difference, copper2 $°C$O(10)
$δTT,u$Maximum lateral temperature difference, Teflon (top)40 $°C$O(101)
$δTT,d$Maximum lateral temperature difference Teflon (bottom)20 $°C$O(101)
The lateral temperature variations on the copper block $δTcu$ were minimal and close to the instrument error (∼0.5 $°C$). To minimize error propagation, another formula was utilized to determine the heater power with greater accuracy
$Q= V2Rheat$
(7)

where Q is measured in W, V is the voltage (in V) applied to the heater, and Rheat is the electrical heater's resistance in Ω (resistive load).

#### 2.4.2 Total Thermal Resistance (Rtot).

A vital performance metric of the chamber is the total thermal resistance (K/W)
$Rtot=ΔTQ$
(8)

where Q is the heat input and ΔΤ the difference between the average temperatures of the hot and the cold sides.

#### 2.4.3 Chamber Charging Ratio.

Another important parameter is the charging or filling ratio of the chamber
$CR=water volumevapor chamber empty space=mwρwVVC$
(9)

where mw is the mass of water inside the sealed chamber, ρw the density of water, and VVC the volume of the empty space inside the chamber before any charging with the working fluid. The optimum charging ratio (CR) is attained when the system reaches its maximum effective thermal conductivity (likewise, lowest thermal resistance).

#### 2.4.4 Wettability Area Ratio.

A new parameter was defined to identify each wettability pattern used herein. This parameter Φ is the ratio of the superhydrophilic area (laser-etched and chemically processed) divided by the total area of the wickless plate (see Fig. 3).
$Φ=superhydrophilic areatotal surface area$
(10)

Superhydrophilic areas facilitate the nucleation of condensate, leading to FwC, whereas hydrophobic areas promote DwC, thus hindering the transition to FwC [28]. This ratio offers a nondimensional measure of the FwC over the DwC area of the condenser. The two condensation modes are critical, and Φ is a primary parameter describing the system's wettability architecture.

#### 2.4.5 Diodicity.

There is a significant difference in the performance of the system at the two modes of operation. During FWD operation, the heat input is successfully removed from the heater via phase-change heat transfer. Throughout the RVS mode, no considerable latent heat transfer is expected. The diodicity of the system is presented at a standard and constant ΔT where disproportionate magnitudes of heat (Q) are allowed to pass through. This unequal heat transfer can be quantified by the rectification coefficient γ, defined by Eq. (1) [10].

### 2.5 Data and Errors.

Data were collected for a system with Φ = 0.40, CR=21% operating in the FWD mode (Fig. 7) and in the RVS mode (Fig. 8). The right sides of those figures depict the two layouts of the chamber orientation with respect to the heater, copper block and the cooling plate; the chamber is flipped by 180° in the RVS mode compared to the FWD mode. Two different heating loads were applied for each mode. The two graphs emphasize how the same heat load affected performance when the apparatus operated in the two modes. For both cases, the system starts in thermal equilibrium at ∼$30 °C$. In the FWD mode (Fig. 7), it is evident that the two applied heat loads create minor temperature differences between the evaporator and the condenser. More specifically, the 23 W heat load creates a ΔΤ = 0.8 ± 0.4 $°C$, while the 37 W heat load creates a ΔΤ = 2.2 ± 0.4 $°C$, where ΔT = average (TC1, TC2, TC3)—average (TC4, TC5, TC6).

Fig. 7
Fig. 7
Close modal
Fig. 8
Fig. 8
Close modal

This happens because in the FWD mode, the system works as a high-performance vapor chamber, in contrast to the RVS mode, where the system performs as a heat blocker (Fig. 8). In the RVS mode, the two applied heat loads create high temperature differences between the evaporator and the condenser in a shorter time. Specifically, the 23 W heat load generates a ΔΤ = 17.7 ± 0.5 °C, while the 37 W heat load generates a ΔΤ = 34.1 ± 0.8 °C, eventually pushing the system to thermal runaway.

#### 2.5.1 Error Calculation.

The experimental error for each performance metric α was determined using the following formula for the standard deviation
$σα=(∂α∂β)2σβ2+(∂α∂γ)2σγ2+⋯$
(11)
where the quantity α depends on parameters β, γ, etc. The standard deviation for each value of β, γ, etc., was
$σx=σ2xexp+σ2xinstr$
(12)

where x stands for each one of the parameters β, γ, etc., while $σxexp$ is the standard deviation of the experimental measurements, and $σxinstr$ is the instrument error associated with the respective measurement. For the voltage (V), heater resistance (Rheat), and all measured temperatures (T), the respective instrument errors were $σVinstr=0.05 V$, $σRheatinstr$ = 0.005 Ω, and $σTinstr$ = 0.6 °C. The results below are presented in terms of$X¯ ± σx¯$, where $X¯$ is the mean measured value calculated by the time-averaged values above, and $σx¯$ is the standard error of the mean, calculated by $σx¯=σx3$, for three experimental tests run with the same conditions.

#### Heat Input.

Since Q = Q (V, Rheat), then
$σQ=(∂Q∂V)2σV2+(∂Q∂Rheat)2σRheat2$
(13)

#### 2.5.2 Thermal Conductivity.

Since k = k (V, Rheat, Thot, Tcold), with Thot being the average value of the temperatures measured by thermocouples TC1, TC2, and TC3 on the hot side of the chamber, Tcold being the average value of the temperatures measured by thermocouples TC4, TC5, and TC6 on the cold side of the chamber, then
$σk=(∂k∂V)2σV2+(∂k∂Rheat)2σRheat2+(∂k∂Thot)2σThot 2+(∂k∂Tcold)2σTcold 2$
(14)

#### • Thermal Resistance.

The total thermal resistance of the system is R = R(V, Rheat, Thot, Tcold). Thus,
$σR=(∂R∂V)2σV2+(∂R∂Rheat)2σRheat2+(∂R∂Thot)2σThot 2+(∂R∂Tcold)2σTcold 2$
(15)

#### • Diodicity.

For the diodicity γ = γ (k) and the simple relative error method
$σγ=σkFWD2kRVS2+ kFWD2kRVS4σkRVS 2$
(16)

## 3 Results and Discussion

### 3.1 Working Principle.

The thermodynamic cycle of the diode comprises of evaporation, condensation, and transport of condensate back to the evaporation (heated) point. The first two stages are governed by the temperature difference between the vapor core and the high and low temperature of each side, respectively, while the fluid replenishment at the heated area is highly dependent on the physical design of the chamber. The distance between the two opposing plates (one acting as evaporator, the other as condenser), the amount of the sealed working fluid, the wick thickness, and the wettability pattern on the wickless plate are the main physical parameters affecting performance. In this study, only the fluid charging ratio and Φ (Eq. (10)) were changed.

In the FWD mode (Fig. 9, left), the wick-lined evaporator intrinsically tends to hold the water evenly, while its higher temperature causes thin-film evaporation. When the water vapor reaches the wickless condenser on the opposite side, droplets start forming on the hydrophobic domains, while a film develops on the superhydrophilic parts. The droplets on the hydrophobic part grow until they contact the superhydrophilic areas or coalesce with each other first and then get transported to the main drainage vein through the wedge-shaped tracks (Fig. 3). The circular reservoirs purposely designed along the superhydrophilic main tracks, due to their low curvature, form low Laplace-pressure points, thus attracting the condensate being pumped through the tracks. As condensation progresses and more water is collected in the superhydrophilic domains, more water is transported to the low-pressure reservoir sites and bulges grow until they reach the wick on the opposing plate. At this moment, a capillary bridge forms between the condenser and the wick on the evaporator and water starts permeating through the wick until the capillary bridge becomes unstable and snaps due to water volume loss to the wick. Figure 1(1) shows a discoloration on the surface of the evaporator wick after intermittent testing for a week. These dark round spots are the exact points were the capillary bridges formed and snapped demonstrating that all the condensate-return points remain across the low-pressure points on the wickless side of the system. These marks on the wick serve to confirm the system's design and show that the condensate is collected in predetermined points on the cold side and bridges across to the hot side only at the desired points. Thus, a full cycle of evaporation and condensation is completed. The stability of this cycle is affected by the working fluid charging ratio, the number and size of low-pressure sites on the condenser and the heat flux forced through the system. These capillary bridges are crucial for heat manipulation inside the chamber since they determine the mass exchange between the hot and the cold sides of the chamber, in turn affecting heat transfer.

Fig. 9
Fig. 9
Close modal

In the RVS mode (Fig. 9, right), the wickless plate acts as the evaporator. After evaporation, the water vapor condenses on the opposing wick, which is cooled in this case. The porous wick spreads the condensate laterally through capillary action. After the wick gets saturated with water, there is no direct mechanism to drive it back to the evaporator, since there is no physical connection between the opposing plates other than at their edges. The mass connection between the two plates in the FWD mode was made by the water bulges forming due to the wettability patterns. In the RVS mode, this connection cannot occur, thus obstructing heat transfer.

The distance from the patterned surface to the wick is 2.5 mm. Since the two working surfaces are close to one another and in the FWD mode the condensate accumulates in wells forming capillary bridges, the gravitational orientation does not play an important role for sustained operation. In the RVS mode, however, the gravitational orientation is more important, since the wick-lined condenser (top side), traps the condensate, which eventually drips down by gravity onto the wickless plate (bottom side) to complete the boiling-condensation cycle. This gravity-assisted operation of the RVS mode hinders the diodic performance of the system and was selected to quantify the system's diodicity as the worst-case scenario. In contrast, the best-case scenario to achieve even higher diodicity would be to place the cooling block at the bottom of the setup, underneath the wick-lined plate (operating as condenser) and the wickless plate (operating as evaporator) placed on top. This reverse placement would lead to sustained water accumulation at the bottom side of the system, where the gravity cannot assist the fluid to return to the evaporator (at top), thus blocking the condensate resupply mechanism, and in turn, causing even higher diodicity (not measured in this work).

### 3.2 Diodic Behavior.

To showcase the diodic behavior of the system, Fig. 10 (left) presents the theoretical graph of an electric diode. For this diode, the voltage differential is on the x-axis and the electric current on the y-axis. On the right-hand side of Fig. 10, the corresponding curve for the best-performing thermal diode of this study is presented. For both cases, the negative horizontal axis represents the reverse operation, when the electric diode allows very little electric current to pass through. Similarly, in RVS operation of the present chamber, the heat transfer is mostly blocked. The thermal analog of the current is the heat, while the analog of the voltage differential is the temperature difference between the evaporator and condenser plates. Among all cases studied herein, the greatest value of diodicity measured was γ = 23.5 ± 0.9. This case corresponded to an average effective thermal conductivity kFWD = 71.0 ± 0.1 W/m K in the FWD mode, and kRVS = 2.9 ± 0.1 W/m K in the RVS mode. These values were achieved with a wettability patterned plate having Φ = 0.65 and a fluid charging ratio CR21% (Fig. 10, right). It is noted that the above value of γ would have been higher if the system shown at right in Fig. 9 were placed upside down so that gravity did not assist any condensate transfer from the wick to the evaporator side.

Fig. 10
Fig. 10
Close modal

### 3.3 Thermal Resistance Comparison for the Best Performing Chamber.

The heat load applied to one chamber in FWD and RVS operations versus the total thermal resistance is presented in Fig. 11 (top), and with respect to the temperature difference between the cold and the hot side of the system in Fig. 11 (bottom). This apparatus had a wickless plate with Φ = 0.65 (see Figs. 1(2) and 3(b)) and was filled with DI water at CR = 21%. The black-square symbols denote the FWD mode, while the red-dot curves signify the RVS mode of operation. As seen for both plots, the two modes were tested over different heat-input ranges because only a minor amount of heat input (i.e., Qin = 7.9 W) was enough to drive the system to a potential thermal runaway in the RVS mode. The maximum heat load without reaching thermal runaway in the FWD mode was 77 W, almost ten times greater than the maximum value in RVS mode.

Fig. 11
Fig. 11
Close modal

While operating in the FWD mode, the system showed very low thermal resistance over the entire heat input range. The minimum value was Rtot = 0.02 ± 0.03 K/W at 27.1 W and the maximum value was Rtot = 0.04 ± 0.01 K/W at 77 W. This performance is almost flat for the entire range and proves that this hybrid system with wickless and wick-lined components is indeed a high-performing vapor chamber. The resistance values on the RVS mode of operation indicate the thermal rectification by the system. The system while operating in the RVS mode demonstrated high thermal resistance for low heat loads. The minimum value was Rtot = 0.44 ± 0.27 K/W at 1.85 W, and the maximum value was Rtot = 0.93 ± 0.06 K/W at 7.9 W. Furthermore, the performance difference in the two modes of operation is evident by comparing the temperature difference between the hot and cold sides of the system. At the highest heat input values, the temperature difference is ΔΤ = 7.3 ± 0.1 $°C$ at 7.9 W for the RVS mode, while on the FWD mode, ΔΤ = 2.9 ± 0.6 $°C$ at 77 W. At intermediate heat loads in both modes, ΔΤ = 2.5 ± 0.3 $°C$ at 3.5 W (RVS mode), and ΔΤ = 2.3 ± 0.6 $°C$ at an almost 20× heat input 67.8 W (FWD mode).

### 3.4 Effect of Condenser Wettability Pattern.

A vital factor for tuning the diodicity of the chamber is the value of Φ. Plates with three different Φ values were compared in this study. After the chamber reaches steady-state operation, the effective thermal conductivity depends only on the temperature difference for a fixed geometry. Of course, ΔT is the driving force of the heat current. Ideally for a constant ΔT, comparisons can be made of the amount of heat that the assembly lets pass through. However, it is not feasible to make precise local measurements of ΔT neither in the FWD nor the RVS mode. Instead, the average effective thermal conductivity was measured for each case and the diodicity was calculated from Eq. (1). Figure 12 and the embedded table present the experimental results for the FWD and RVS operation of three chambers, each featuring a plate with a different wettability pattern (characterized by a distinct Φ). All curves for the FWD mode are marked with a triangle pointing up, while the corresponding curves for the RVS mode are denoted with the same-colored triangle pointing downward. The slopes of all the FWD curves are steeper than the corresponding ones for the RVS mode. Since the slope of these curves is proportional to the thermal conductance, this is an expected outcome. When the system operates in the FWD mode, evaporation from the wick, condensation on the wettability patterns, and subsequent return of the condensate back to the wick allow for heat to flow efficiently through the assembly. However, in the reverse mode, this cycle is disrupted due to the lack of a condensate return mechanism, which reduces heat flow through the system. So, the effective thermal conductivity in the FWD mode is higher than its counterpart in the RVS condition.

Fig. 12
Fig. 12
Close modal

Comparing the FWD curves in Fig. 12, and since the RVS curves are not that different, the slope differences offer insight on how to optimize the wettability pattern for maximizing diodicity. The forward curve for Φ = 0.65 (green triangles) has an average effective thermal conductivity 71 ± 0.1 W/m K, while the corresponding values for Φ = 0.40 and Φ = 1 (no pattern, superhydrophilic surface) are 26.9 ± 0.1 W/m K and 17.4 ± 0.1 W/m K, respectively. High values of effective thermal conductivity mean that high loads of heat Q can pass through the system with low ΔT (e.g., Q = 77 W at ΔT =2.9 ± 1.1 $°C$ for the Φ = 0.65 curve). At Q =53 W, the ΔT values are 1.6 ± 1.1 $°C$ and 5.9 ± 1.1 $°C,$respectively for Φ = 0.65 and Φ = 1. At Q =77 W, the ΔT values are 6.5 ± 1.1 $°C$ and 2.9 ± 1.1 $°C,$respectively, for Φ = 0.40 and 0.65, meaning a 44% greater ΔΤ for the former compared to the latter. The curves for the RVS mode do not show significant differences, with their slopes all indicating low effective thermal conductivity.

The three different chambers of Fig. 12 also have different diodicity, as listed in the embedded table. Since the only parameter changing here is the value of Φ, the system diodicity is tunable by changing the wettability pattern of the wickless part of the chamber. As the diodicity is the ratio of the conductivities in the FWD and RVS modes, controlling one of them and keeping the other unchanged allows tuning of the diodicity. The best performing system in Fig. 12 is the one with Φ = 0.65 (pattern shown in Fig. 3(b)). This wettability pattern was expected to outperform the others, as also suggested from results from our previous work [20].

Figure 13 plots the effective thermal conductivity versus heat load for the FWD mode of the cases shown in Fig. 12. The same color scheme applies to both figures for easy comparison. The highest effective thermal conductivity was 95 ± 0.4 W/m K for Φ = 0.65 at 27 W. It is evident that for the whole test range, the green curve outperforms the other two, even at the worst performing point at 77 W where the effective thermal conductivity drops to 52 ± 0.2 W/m K, almost two times higher than the best performing point of the red curve (29 ± 0.1 W/m K at 53.1 W) and almost three times higher than the best performing point of the blue curve (25 ± 0.1 W/m K at 18.2 W). The red curve with the wickless condenser pattern shown in Fig. 3(a), and the blue curve with a superhydrophilic condenser performed in a similar manner in the range 11–27.5 W. For even higher heat fluxes, the wettability patterns on the condenser are responsible for the performance difference; eventually at 53.1 W, the system with the patterned condenser demonstrates effective thermal conductivity equal to 29 ± 0.1 W/m K, a value 45% higher than the system with the unpatterned condenser, which had effective thermal conductivity 20.1 ± 0.1 W/m K. The worst performance is seen for the system with the superhydrophilic condenser because there is no wettability pattern to enhance condensation heat transfer or to effectively facilitate the condensate return. The difference between the two systems with patterned condensers is attributed to the different pattern designs. The key distinctions between the two designs are: (i) the condenser with Φ = 0.65 has 63% more superhydrophilic area than the Φ = 0.40 case, (ii) the Φ = 0.65 condenser has 36 collecting/returning points instead of 16 of the Φ = 0.40 case, (iii) the Φ = 0.65 condenser has six straight stems, while the Φ = 0.40 one has only 4, and (iv) on the Φ = 0.65 design, the maximum allowed (as designated by the pattern interspacing) droplet diameter on DwC areas is 0.41 mm, while for the Φ = 0.40 design, the maximum droplet diameter is 0.69 mm, meaning that the surface replenishment rate is greater for the former case.

Fig. 13
Fig. 13
Close modal

### 3.5 Effect of Charging Ratio.

After determining the value of Φ for best diodic performance at a fixed charging ratio (CR=21%), one more experiment was performed at a different charging ratio to check how much CR affects the diodicity of the system. The differences in diodicity for the FWD and RVS mode for the two different charging ratios were analyzed. Figure 14 compares the heat loads applied to the two chambers versus the temperature difference ΔT between the hot and the cold sides. In both cases, Φ was kept fixed at 0.65. The respective diodicity values for two different charging ratios (21% and 14%) are listed in the embedded table in Fig. 14. For the FWD mode, there is a notable difference in the slopes of the two curves. To quantify this difference, a comparison is made when both systems are under the same Qin; on the last point of the CR = 14% curve (Q =67 W, ΔT =6.2 ± 0.5 °C), with the respective values for the CR = 21% curve (Q =67 W, ΔT =2.3 ± 1.1 °C) demonstrates a ΔT difference of 3.9 °C, a 63% decrease in the thermal gradient (the plate interspace distance is the same). For the RVS mode, both curves have very similar slopes. The CR = 21% case had the better performance in terms of diodicity.

Fig. 14
Fig. 14
Close modal

### 3.6 Quantifying the Thermal Rectification Value.

Various definitions of the diodicity of a system have been used in the literature. The thermal rectification ratio represents the diodicity of a system with a simple correlation; the higher the rectification value, the greater diodic performance is expected. Table 2 lists the formulas reported in the literature for calculating the diodicity.

Table 2

Equations used to calculate the highest diodicity attained with the present system

Ref.EquationDiodicity value
[29] [30]$γ= kFWDkRVS(17)$24.6
[10] [29] [31]$γ= kFWD− kRVSkRVS(1)$23.5
[29] [32]$γ= |kFWD− kRVS|max(kFWD, kRVS)(18)$0.96
[33] [34]$γ= |kFWD− kRVS|kFWD (19)$0.96
[29] [35]$γ= kFWD− kRVSkFWD+kRVS(20)$0.92
[36]$γ= QFWD− QRVSQRVS(21)$20.9
Ref.EquationDiodicity value
[29] [30]$γ= kFWDkRVS(17)$24.6
[10] [29] [31]$γ= kFWD− kRVSkRVS(1)$23.5
[29] [32]$γ= |kFWD− kRVS|max(kFWD, kRVS)(18)$0.96
[33] [34]$γ= |kFWD− kRVS|kFWD (19)$0.96
[29] [35]$γ= kFWD− kRVSkFWD+kRVS(20)$0.92
[36]$γ= QFWD− QRVSQRVS(21)$20.9

For all equations listed in Table 2, the effective thermal conductivity, or the heat input values of the FWD and RVS mode of operation are used to derive the value of γ. Equation (17) provides the simplest and most intuitive formula, by basically comparing how much greater is the average effective thermal conductivity in the FWD mode than in the RVS mode. The minimum value from this equation is γ = 1 when the two conductivities are equal (no diodicity); from all other equations for this case, γ = 0 (due to difference of conductivities in the numerator). Equation (1) is used in this work because it is very common and most suitable for the specific type of thermal diode studied herein (relying on phase-change phenomena and a conduction-convection combination, as in vapor chambers). Equation (18) is similar to (1), with the important difference in the denominator, where the maximum value of the two conductivities appears. As also reported in Ref. [29], many researchers define the FWD and RVS performance in different ways, each one specifically designed to suit each study, and thus the reason for Eq. (18). The maximum diodicity that can be derived from this equation will be 1. For the present study, Eqs. (18) and (19) provide the same result. Equations (18)(20) limit the diodicity values between 0 and 1, with Eq. (20) normalizing the value. For these equations, the average values of effective thermal conductivity for FWD and RVS operation are utilized. However, the average effective thermal conductivity is not an ideal metric to calculate the diodicity because its value can be manipulated by the number of temperature points utilized for the calculation and because it cannot be directly measured experimentally. To avoid ambiguity, other researchers [37] measured and presented the diodicity value for each experimental point, ending up with several rectification ratios for a single system. Equation (21) was derived in a similar way as Eq. (1) and produces a single diodicity value by utilizing the magnitude of the heat flow in the FWD and RVS directions but applies only for a set (fixed) temperature difference between the hot and cold side of the device. The diodicity values for the present system as determined using Eqs. (1), (17), and (21) were 23.5, 24.6, and 20.9, respectively, being in a relatively narrow range. The other three equations presented in Table 2 provide rectification-ratio values of 0.92 and 0.96 (for a possible maximum of 1). This analysis using criteria used in prior studies shows that all equations for γ produce comparable results, with all values indicating a high-performance diode.

## 4 Conclusions

This work demonstrated a vapor chamber that can act as a high-performance heat spreader in addition to acting as a directional thermal barrier. This system features a wickless wettability-patterned plate and an opposing wick-lined plate, and is able to transport heat with a strong directional preference (thermal diode, TD). The unique directional heat flow is ascribed to the differential characteristics of the chamber. The effective thermal conductivities for the forward and the reverse mode of operation were reported, and the diodicity was quantified and discussed. The working prototype was a thermal rectifier with high effective thermal conductivity in the forward mode. The low profile and light weight of the system are advantageous for scalability. The fabrication method is straightforward and scalable to larger dimensions, while the materials are durable and commonly used at industrial scale. The operating conditions of the present experiments emulated common micro-electronics working temperatures. Thus, the present chamber can be used for protection of sensitive electronics from reaching elevated temperatures and could be beneficial for a wide spectrum of other applications in thermal management, aerospace thermal systems, electronic packaging, or even exterior construction components in smart buildings.

## Acknowledgment

The authors thank David Mecha (Senior Laboratory Mechanic) at the UIC College of Engineering Machine Shop and the personnel of the UIC Department of Physics Machine Shop for machining the samples. An earlier and more limited version of this study appeared as a paper in the 19th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITHERM 2020).

## Funding Data

• The U. S. Office of Naval Research under Award No. N00014-20-1-2025.

• The University of Nebraska, Lincoln via a subcontract to UIC (Funder ID: 10.13039/100000006).

## Nomenclature

A =

heat transfer area (m2)

CR =

charging ratio

dx =

chamber thickness (m)

k =

thermal conductivity (W/m K)

mw =

water mass in chamber

Q =

heat input (W)

Rheat =

heater electrical resistance (Ω)

Rtot =

total thermal resistance (K/W)

V =

voltage applied to heater (V)

VVC =

empty space volume in chamber

ΔΤ =

temperature difference between cold and hot side (°C)

### Greek Symbols

Greek Symbols
γ =

diodicity

ρw =

water density

σ =

standard deviation

Φ =

superhydrophilic area ratio of wettability-patterned plate

### Subscripts/Superscripts

Subscripts/Superscripts
Cold =

cold side of chamber—in contact with heat sink

Cu =

copper block

exp =

experimental

hot =

hot side of chamber—in contact with heater

in =

input

Instr =

instrument

T,d =

Teflon block-down

T,u =

Teflon block-upper

tot =

total

w =

water

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