Manel Ben-Romdhane

Chiheb Rebai
email: chiheb.rebai@supcom.rnu.tn

Adel Ghazel

Patricia Desgreys

Patrick Loumeau

PSEUDORANDOMLY CONTROLLED ADC CHARACTERIZATION TOWARDS MULTISTANDARD RECEIVER

Keywords: Radio communication, Signal sampling, Signal reconstruction, Analog-digital conversion, Clocks

The radio communication tendency is to reach Software Radio applied to multistandard receiver. Non uniform sampling controlling Analog-to-Digital Converter in Homodyne multistandard receiver was previously proposed in our works. Non uniform sampling offers the advantage of alias-free sampling. This can lead to many advantages in the multistandard based non uniform sampling receiver such as, essentially, relaxing antialiasing filter and reducing power consumption of the analog-to-digital converter. In this paper, we present a pseudo-random signal sampler to control the analog-todigital converter. This circuit consumes less than the difference between the non uniform sampling and the uniform over-sampling. A complete test setup with instrumentation and spectral analysis will be presented to illustrate alias-free processing measurement.

INTRODUCTION

With the continuous increase of the number of standards, the challenge is to realize a multistandard software defined radio receiver. Such a receiver ought to be low cost, low power and use highly integrated devices. Our previous works propose to control non uniformly the Analog-to-Digital Converter (ADC) in homodyne receiver [START_REF] Ben-Romdhane | Non-Uniform Sampled Signal Reconstruction for Multistandard WiMax/WiFi Receiver[END_REF]. The problem is to generate a non uniform clock with a low power consumption, low area and high frequencies to adapt our work to SDR multistandard receiver.

We proposed in previous work an initial solution to generate a non uniform clock [START_REF] Ben-Romdhane | Pseudo Random Clock Signal Generation for Data Conversion in a Multistandard Receiver[END_REF]. In this paper, an enhanced solution is proposed, Pseudorandom Signal Sampler (PSS). Implementation and synthesis were done on FPGA and 65 nm CMOS digital technology. A test setup platform is prepared to compare reconstruction and analysis in uniform and non uniform sampling cases. This paper is organized as following. The second section presents suitable cases for using Non Uniform Sampling (NUS) to verify anti-aliasing sampling. In the third section, we present the multistandard NUS-based homodyne receiver and its advantages. A state-of-the-art of commercial available ADCs is also presented to choose the suitable ADC to the proposed receiver architecture and to identify its power consumption. In section IV, we propose pseudorandom signal sampler circuit design. In section V, we focus on the PSS circuit implementations on FPGA and ASIC targets. We evaluate maximum frequency, dynamic power consumption and area of the PSS circuit. Then, we realize a test platform to compare spectrum analysis in non uniform sampling and uniform sampling cases. Finally, conclusions and perspectives of this work are outlined.

ANTI-ALIASING SAMPLING

Non uniform sampling has a particular advantage which is the anti-aliasing characteristic under some conditions. Instead of the uniform sampling instants , ≤ ≤ , assume the non uniform sampling instants , ≤ ≤ with = . The instants defined by a probability density function , have to satisfy stationary condition introduced by Bilinskis [START_REF] Bilinskis | Randomized Signal Processing[END_REF] and given by (1).

= = 1 (1)
with considered as the mean sampling period.

Some non uniform sampling schemes such Jittered Random Sampling (JRS) and Additive Random Sampling (ARS) satisfy this condition. In case of implementation, it is advised to use Time-Quantized Random Sampling applied to the ARS or JRS scheme. A summary of suitable sequences is drawn in Table 1. We define as the probability density function of independent and identically distributed variables with a variance . The mean of is zero for JRS scheme and for ARS scheme. In JRS scheme, only uniform distribution is valid with a statistical parameter / equal to 0.2887.

One more adapted scheme to implementation is the pseudorandom version of the TQ-RS scheme. Figure 1 illustrates the Time Quantized PseudoRandom Sampling (TQ-PRS) scheme. In fact, each random instant is replaced by the nearest quantized instant ," . Each instant ," is a multiple of a step Δ with Δ equal to /$ % and $ % is the quantization time factor. The rank &, in the ' th interval, is a pseudorandom number with a cycle length $ % . The TQ-PRS scheme is a kind of implicit over-sampling technique with some restrictions. In uniform sampling, in the spectrum band 0, $ % C , aliases are located at frequencies $ % C -C D and 'C ± C D for ' between 1 and $ % -1 where C D is the carrier frequency of the sampled signal and C the mean sampling frequency equal to 1/ . When we non uniformly sample with TQ-PRS scheme, we obtain only one alias at a frequency equal to $ % C -C D . However, some wideband noise replaces the other aliases. This wideband noise could be suppressed with a reconstruction algorithm [START_REF] Ben-Romdhane | Non-Uniform Sampled Signal Reconstruction for Multistandard WiMax/WiFi Receiver[END_REF][START_REF] Shapiro | Alias-Free Sampling of Random Noise[END_REF].

MULTISTANDARD NUS-BASED HOMODYNE

RECEIVER

Homodyne architecture is the most adapted for multistandard receiver. In fact, this architecture offers to use a number of discrete components lower than in the other conventional receiver architectures. Homodyne receiver suffers from some drawbacks as DC-offset and I/Q mismatch. All of these are corrected digitally in DSP as explained in [START_REF] Sohn | Data-aided approach to I/Q mismatch and DC offset compensation in communication receivers[END_REF]. We propose in previous work to non uniformly control the Analog-to-Digital Converter [START_REF] Ben-Romdhane | Non-Uniform Sampled Signal Reconstruction for Multistandard WiMax/WiFi Receiver[END_REF]. As presented in Figure 2, the homodyne architecture is composed of an RF switch to select the suitable RF filter for the standard received and a multiband LNA to amplify the received signal with a low added noise [START_REF] Brandolini | Toward multistandard mobile terminals-fully integrated receivers requirements and architectures[END_REF]. In previous work [START_REF] Ben-Romdhane | Non-Uniform Sampled Signal Reconstruction for Multistandard WiMax/WiFi Receiver[END_REF], we explain how to benefit from the anti-aliasing advantage of the non uniform sampling. In Figure 2, comparing the parts (a) for conventional baseband receiver and (b) for NUS based baseband receiver, we use a relaxed Anti-Aliasing Filter (AAF), we move out, or at least relax, the Automatic gain control (AGC), we replace the clock controlling the ADC by a non uniform clock and we add a digital Reconstruction Algorithm in the DSP.

Relaxing AAF is obtained thanks to the TQ-PRS scheme and its implicit over-sampling characteristic as explained in previous section. Consequently, for instance, we use a 3 rd order AAF as in the uniform over-sampling case instead of a large order AAF in sampling case at Nyquist frequency. The IEEE802.11a characterizes the choice of the sampling frequency. When using a 40 dB dynamic AGC, a 10-bit ADC in case of uniform over-sampling at 265.6 MHz is required. This required ADC would be power-hungry, as mentioned in Figure 3 showing ADC power consumption, as stated by the manufacturer, versus resolution and sampling frequency. Therefore, we propose non uniform sampling technique to also benefit from decreasing ADC dynamic power consumption versus sampling frequency. We ought to use a 10-bit ADC with mean sampling frequency C at 16.6 MHz. These results are taken in case of quantization time factor $ % equal to 16. In spite of these advantages, we need to replace the uniform clock CLK controlling the ADC by a non uniform clock CLK_NUS.

PSEUDORANDOM SIGNAL SAMPLER CIRCUIT DESIGN

According to TQ-RS scheme, non uniform sampling instants occur at quantized values equal to a multiple of ∆. This quantization can be obtained if we first use a ∆ delay block to generate $ % phases FΦ , Φ : , … , Φ " I 9: J where ∆ is the minimum spacing defined by /$ % . Then, the Linear Feedback Shift Register (LFSR) returns pseudorandom numbers K L -1: 0 taken in the set of 1, … , $ % at the Φ rate (1/ ). The obtained numbers perform a uniform probability density in accordance to the JRS scheme because each generated number is taken independently from the previous one as JRS scheme is defined in Table 1.

The drawback of this solution is the overlap between phases in FΦ : , … , Φ " I / 9: J and phases in FΦ " I / , … , Φ " I 9: J. We propose a new design, first introduced in [START_REF] Ben-Romdhane | Pseudo Random Clock Signal Generation for Data Conversion in a Multistandard Receiver[END_REF], called Pseudorandom Signal Sampler (PSS) to overcome overlap problem. Figure 4 The selective combiner stage, a multiplexer MUX $ % : 1, selects the phase Φ P addressed by the generated pseudorandom number i each period of Φ . The multiplexer. However, the multiplexer introduces some delay and its output presents some glitches which are shorter than the specified minimum spacing ∆. For that reason, the multiplexer output is fed through a D-latch controlled by the main clock C QRS to suppress glitches and deliver pseudorandom clock PSS out . The main clock C QRS has a period equal ∆ needed for the TQ-PRS scheme as described in Table 1 and Figure 1. The obtained statistical parameter σ/T V is given in (2).

= 1 $ % W $ % -1 -1 12 (2)
The "mean" sampling frequency is C = C QRS /$ % .

According to the proposed PSS design, we define the instantaneous pulsewidth, number of ∆ occurrences, given in (3).

P = + ∆XK ' + 1 -K ' Y, 1 ≤ ' ≤ $ % -1 (3)
where K ' is the current LFSR output value. In the case of $ % = 16, instantaneous sampling frequency C P , equal to 1/ P , takes values between C [P\ = C QRS /24 and C []^= C QRS /9. ADC should be able to convert at all these rates to deliver data at f s which decreases its dynamic power consumption. In fact, generated frequencies should satisfy [START_REF] Shapiro | Alias-Free Sampling of Random Noise[END_REF].

C [P\ ≥ C ab"cP d and C []^≤ 20efg (4)
with C ab"cP d is minimum frequency defined by Shannon theorem to avoid overlap between signal and aliases. Consequently, instead of mean sampling frequency equal to 16.6 MHz, we need to choose C at 24.9 MHz to make the minimum sampling frequency, C QRS /24, satisfy the Shannon theorem and be at least equal to the IEEE802.11a channel bandwidth.

The signal hii jcd is applied to the ADC at 0klmn0 input to convert the analog signal o P\ to n-bit resolution digital signal n. ADC timing diagram, in Figure 5, presents timing parameters [7]. An accurate analog-todigital conversion is only achieved if the hii jcd pulsewidth high is higher than the 0klmn0 pulsewidth high pq and the hii jcd pulsewidth low is higher than the 0klmn0 pulsewidth low pR . Therefore, we propose (5) to verify these conditions.

nl P . P > pq and 1 -nl P . P > pR [START_REF] Sohn | Data-aided approach to I/Q mismatch and DC offset compensation in communication receivers[END_REF] where nl P , as we define in ( 6), is the duty cycle of the signal hii jcd relative to the current LFSR output value K ' .

nl P = -∆ L3s tK ' , $ % 2 u P , 1 ≤ ' ≤ $ % -1 (6)
Moreover, aperture delay v , clock jitter, output valid time w and output propagation delay xy have to be lower than the minimum spacing ∆ as defined by (7).

L3s v , zK {4, w , xy < ∆ (7) MHz. These frequencies are obtained when using a main clock frequency between 16 MHz and 3.2 GHz.

TEST SETUP AND MEASUREMENT

PSS Validation

Acquisition Methods

Before analyzing ADC output, we need to adapt available acquisition methods to the non uniform sampling. The viable methods are the acquisition based on data storage in a FIFO [START_REF] Camarero | Mixed-signal clock-skew calibration technique for Time-Interleaved ADCs[END_REF] and the acquisition based on logic analyzer. Both of these methods are driven the main clock of the PSS. Then, we follow the processing with a cubic spline reconstruction algorithm on DSP (Digital Signal Processing).

The received data is composed of binary PSS output and 10-bit ADC output. In both acquisition methods, we extract sampling instants and convert ADC output to decimal data. The obtained results are presented in Figure 6.

The test setup is presented in Figure 7 and is described as follows:

• A clock generator delivers the main clock to the PSS implementation on the FPGA device. External clock generator could be avoided by the FPGA internal clocks and PLL (Phase-Locked Loop). • A sine wave generator delivers analog signal to A in ADC pin. The PSS output is also fed to the 0klmn0 ADC pin.

• The FIFO based acquisition method is implemented on FPGA. Acquisition control is performed by the main clock.

• ADC digital outputs D n-1 ...D 0 are taken into a multibit FIFO however PSS output is taken into a single bit FIFO.

• Acquisition data is sent through UART (RS232) to DSP board. The signal reconstruction is performed with interpolation algorithm.

• Spectral analysis is performed by Matlab software on data coming from ADC and DSP.

• FPGA configuration is done by Quartus through USB blaster. We have used digital analyser from Agilent 16700-Series to verify and calibrate the proposed acquisition method.

ADC Results after reconstruction

For the current results, we achieve our tests with the AD9214 analog-to-digital converter from Analog Devices [7]. Equations ( 4), ( 5) and ( 7) are generally verified by the most commercialized ADCs. The chosen PSS configuration is for $ % equal to 16 because the error compared to σ/T V = 0.2887 is only 6.5%. A 100 kHz sine wave is sampled non uniformly at a mean frequency 3.125 MHz. The PSS and acquisition main clock is a 50 MHz square wave. The required FIFO sizes are respectively 16384 bits for the PSS FIFO and 163840 bits for ADC FIFO to reconstruct 1024 uniform samples.

The second step consists on applying PSS output signal on the AD9214 pipeline ADC, PSS and output ADC acquisition, reconstruction and spectrum analysis presented in Figure 8. We notice odd signal harmonics compared to uniform case. The drawback of the AD9214 to offer the required signal is the fact that the Analog Devices design contains a Timing block as shown in Figure 9. The Timing block is essential in uniform sampling ADC to correct signal clock. It is designed to correct the modified duty cycle due to any noise, distortion or timing jitter on the clock controlling the ADC and fed to the ENCODE ADC input [7]. Applying the PSS output sequence to a S/H Simulink model, then performing spectrum analysis after reconstruction return the spectrum presented in Figure 10. We verify that we recover exactly the same results as in uniform sampling case. The test described above is also done with $ % equal to 32 and results are similar to those in Figures 8 and10.

CONCLUSION

In this paper, we summarize some interesting theory formulation results on non uniform sampling. In fact, under some conditions, non uniform sampling offers the advantages of anti-aliasing spectrum. This advantage motivates our work to be oriented on the non uniform sampling based baseband stage in multistandard receiver. We are especially interested on the strategy of reducing mean sampling frequency to reduce ADC dynamic power consumption. We propose a pseudorandom signal sampler circuit to control the ADC. From FPGA implementation and synthesis and from implementation on CMOS 65 nm digital technology, we evaluate the attainable maximum frequency and the low power consumption of the PSS circuit. A test platform is realized and we compare the ADC spectrum analysis and performances in the non uniform sampling case using PSS circuit compared to uniform sampling case at frequency equal to the main clock frequency of the pseudorandom signal sampler circuit. We obtain some odd harmonics due to timing block required to correct duty cycle. The solution is to replace the pipeline ADC by a full-flash converter. These results for a main clock frequency equal to 50 MHz and results from previous works [START_REF] Ben-Romdhane | Non-Uniform Sampled Signal Reconstruction for Multistandard WiMax/WiFi Receiver[END_REF][START_REF] Ben-Romdhane | Pseudo Random Clock Signal Generation for Data Conversion in a Multistandard Receiver[END_REF] are optimistic to realize a closer test platform to the multistandard NUS-based homodyne receiver.

  Figure 1. TQ-PRS scheme description for $ % = 4.

Figure 2 .

 2 Figure 2. Multistandard Homodyne Receiver (a) Conventional baseband processing (b) NUS-based baseband processing.

Figure 3 .

 3 Figure 3. State-of-the-art of commercially available ADC.

  illustrates the digital architecture and building blocks of PSS. To produce convenient FΦ , Φ : , … , Φ " I 9: J for pseudorandom clock generation without overlap, we combine signals N L -1: 0 delivered by the Gray counter at the main clock rate (C DO = 1/∆). Indeed, the Gray counter stage reduces the number of jumps between delivered signals, and therefore glitches are reduced in the following stages. The FΦ , Φ : , … , Φ " I 9: J duty cycles are now different from each other and avoid the overlap.

Figure 4 .

 4 Figure 4. Description of the PSS.

Figure 5 .

 5 Figure 5. Timing Diagram.

Figure 6 .

 6 Figure 6. Timing sampling and output ADC

Figure 8 .

 8 Figure 8. PSS based ADC spectrum analysis after cubic spline reconstruction (y_PSS_FPGA_ADC) versus uniform sampling spectrum analysis (yus).

Figure 9 .

 9 Figure 9. AD9214 Functional Block Diagram.

Figure 10 .

 10 Figure 10. PSS based S/H Simulink Model spectrum analysis after cubic spline reconstruction (y_PSS_FPGA_Simulink) versus uniform sampling spectrum analysis (yus).

Table 1 .

 1 Suitable sequences for anti-aliasing sampling.

	Scheme	()*	,	+	,/-.

  The target FPGA device is EP2C35F672C6 from Altera. The maximum value for mean sampling frequency for q T equal to 8, 16 and 32 are respectively 13.125 MHz, 26.25 MHz and 52.5 MHz. The obtained statistical parameter σ/T s is near to the theoretical values, computed from (2), as presented in Table2. Errors comparing those values with σ/T V = 0.2887 required value are 13.4 %, 6.5 % and 3.2 % respectively for $ % equal to 8, 16 and 32.

Functional verification of the proposed PSS architecture is synthesized in VHDL to generate a non uniform sampling clock from a main clock at C QRS = 420 |}~.

Table 2 .

 2 Theoretical and synthesis results for statistical parameter σ/T V .

				200
		Theoretical	Simulation	Errors vs
	$ % = 8 $ % = 16 $ % = 32	results 0.25 0.27 0.2795	results 0.2503 0.2703 0.2796	/T V = 0.2887 13.4 % 6.5 % 3.2 %
	According to the results in Table 2 and to validate
	proposed idea for circuit design, we choose to implement
	the PSS architecture, described in the previous section for
	$ % equal to 16, in CADENCE for a 65 nm digital CMOS technology. The signal generation as described above has
	been verified through electrical post-layout simulation.
	PSS occupies a 470 (µm)² die area. It allows a mean
	sampling frequency up to 200 MHz. PSS circuit
	consumes between 1.21 µA and 242 µA from 1.2V
	supply for obtained frequency test between 1 MHz and

ACKNOWLEDGMENT

The authors would like to thank the CMCU organization (Comité Mixte de Coopération Universitaire) to financially support this project. The authors would like also to express gratitude to their colleagues for helpful discussions and experimental work to realize the ADC tests and measurements.


Xuemei Li

Wengang Huang

Andraž Krajnc

Yuwei Yang

Atul Shukla

Jaeho Lee

Merhi Ghasemi

Isaac Martens

Bun Chan

Dominique Appadoo

Peng Chen

Xiaoming Weng

Julian A Steele

Qiang Sun

Gregor Mali

Rijia Lin

Nicholas Bedford

Vicki Chen

Anthony K Cheetham

H G Luiz

Tizei

Sean M Collins

Lianzhou Wang

Jingwei Hou

Interfacial alloying between lead halide perovskite crystals and hybrid glasses

The stellar optoelectronic properties of metal halide perovskites provide enormous promise for next-generation optical devices with excellent conversion efficiencies and lower manufacturing costs. However, there is a long-standing ambiguity as to whether the perovskite surface/interface (e.g. structure, charge transfer or source of off-target recombination) or bulk properties are the more determining factor in device performance. We fabricated an array of CsPbI3 crystal and hybrid glass composites by sintering and globally visualised the property-performance landscape. Our findings reveal that the interface is the primary determinant of the crystal phases, optoelectronic quality, and stability of CsPbI3. In particular, the presence of a diffusion "alloying" layer is discovered to be critical for passivating surface traps, and beneficially altering the energy landscape of crystal phases. However, high-temperature sintering results in the promotion of a non-stoichiometric perovskite and excess traps at the interface, despite the short-range structure of halide is retained within the alloying layer. By shedding light on functional hetero-interfaces, our research offers the key factors for engineering high-performance perovskite devices.

Introduction

Lead halide perovskites feature exceptional optoelectronic properties such as high light-toenergy conversion, emission colour purity, and photoluminescence quantum yield. These characteristics make them a popular candidate for next-generation semiconducting materials to be used within solar panels, sensors, and light-emitting diodes (LEDs) [START_REF] Das | Perovskites for Laser and Detector Applications[END_REF][START_REF] Kumawat | Blue perovskite light-emitting diodes: progress, challenges and future directions[END_REF][START_REF] Yoo | Efficient perovskite solar cells via improved carrier management[END_REF] . Great effort has been spent in uncovering the mechanistic aspects that contribute to their exceptional performance and finding the origin of their large absorption coefficients, low exciton binding energies, and long carrier diffusion lengths and lifetimes [START_REF] Zhang | Metastable Dion-Jacobson 2D structure enables efficient and stable perovskite solar cells[END_REF][START_REF] Zhang | Ion-modulated radical doping of spiro-OMeTAD for more efficient and stable perovskite solar cells[END_REF][START_REF] Steele | Thermal unequilibrium of strained black CsPbI3 thin films[END_REF] . Although immense effort has been devoted to device development, a practical application of perovskites is still hampered by their low stability in multiple aspects 7,[START_REF] Li | Constructing heterojunctions by surface sulfidation for efficient inverted perovskite solar cells[END_REF] . For instance, in addition to being susceptible to light, polar solvents and oxygen, the hybrid perovskite formamidinium lead iodide (FAPbI3), which is popular in solar energy conversion, is susceptible to cation sublimation [START_REF] Conings | Intrinsic Thermal Instability of Methylammonium Lead Trihalide Perovskite[END_REF][START_REF] Chen | Dual Passivation of Perovskite and SnO(2) for High-Efficiency MAPbI(3) Perovskite Solar Cells[END_REF] . Although inorganic perovskites like CsPbI3 overcome thermal stability issues, polymorphism remains a key challenge, where the optoelectronically active α-, β-and γ-phases exist exclusively at elevated temperatures (>250 °C), with the inactive δ-phase being thermodynamically favoured at ambient temperatures [START_REF] Steele | Thermal unequilibrium of strained black CsPbI3 thin films[END_REF][START_REF] Tan | Temperature-Reliable Low-Dimensional Perovskites Passivated Black-Phase CsPbI(3) toward Stable and Efficient Photovoltaics[END_REF] .

One common strategy for addressing these challenges associated with pure perovskite compounds is to composite them with secondary components [START_REF] Hou | Intermarriage of Halide Perovskites and Metal-Organic Framework Crystals[END_REF][START_REF] Shin | Self-assembled dynamic perovskite composite cathodes for intermediate temperature solid oxide fuel cells[END_REF] . Within this context, organic ligands, polymers, inorganic zeolites and glasses, and recently metal-organic frameworks (MOFs) have all been studied, with each type having its own advantages, and simultaneously disadvantages [START_REF] Luo | Halide perovskite composites for photocatalysis: A mini review[END_REF][START_REF] Xu | High-Performance Perovskite Composite Electrocatalysts Enabled by Controllable Interface Engineering[END_REF][START_REF] Han | Perovskite-polymer composite cross-linker approach for highly-stable and efficient perovskite solar cells[END_REF][START_REF] Wang | Ultrastable Perovskite-Zeolite Composite Enabled by Encapsulation and In Situ Passivation[END_REF][START_REF] Sun | Three-dimensional direct lithography of stable perovskite nanocrystals in glass[END_REF] . Understanding the behaviour and function of the interface inside the composites is critical. Such knowledge will further aid in the development of more efficient composite materials and devices: perovskites are typically sandwiched between electron and hole transport layers in LEDs and solar panel systems, and the properties of these interfaces can be critical to device performance [START_REF] Kim | Conformal quantum dot-SnO2 layers as electron transporters for efficient perovskite solar cells[END_REF] . However, studying both positive and negative effects from the interface remains a difficult task since most high-performing composites are not sufficiently stable to keep their original properties/functions against prolonged exposure to handling and inspection [START_REF] Tan | Stability-limiting heterointerfaces of perovskite photovoltaics[END_REF][START_REF] Zhao | Accelerated aging of all-inorganic, interface-stabilized perovskite solar cells[END_REF] . Other composites may lack a distinct chemical and/or physical contrast between two phases, reducing the capacity to extract important interfacial information [START_REF] Hu | Tracking the evolution of materials and interfaces in perovskite solar cells under an electric field[END_REF] .

MOF hybrid glass perovskite composites offer a unique opportunity to pinpoint the interface. The rich structural, chemical, and physical features, as well as the contrasts across phases, allow for the controlled isolation and investigation of the interfaces in composites and the establishment of property-performance correlation. In particular, these high performing composites are stable for characterisation by electron, synchrotron X-ray, and Terahertz beams and storage under ambient conditions [START_REF] Hou | Liquid-phase sintering of lead halide perovskites and metal-organic framework glasses[END_REF] . Herein, we fabricated a series of hybrid glassy perovskite composites via sintering, and uncovered the origin of their exceptional performance. The atomic-level chemical and structural profile of the CsPbI3 and hybrid glass composite are mapped using a combination of advanced characterisations, revealing the controllable formation of interdiffusion alloying layer during sintering. The layer stabilises CsPbI3 optoelectronic phases and passivates its trap states. On the other hand, alloying can create nonstoichiometric perovskite regions and quenches photoluminescence after high-temperature sintering, despite the preservation of short-range rigid halide structures in the nanometer-thick alloying layer (Figure 1a).

Results and Discussion

Fabrication of composites

The crystal-glass composites were fabricated with pre-formed agZIF-62 (ag refers to amorphous glass) [Zn(Im)1.95(bIm)0.05] (Im: imidazolate and bIm: benzimidazolate) and mechanochemically produced CsPbI3 powders, with detailed procedures in Supplementary Information. Given the polymorphism nature of CsPbI3, computational chemistry (at the xTB level) was applied to investigate its energy profiles. First, we calculated the energies of pure α (cubic) and δ (orthorhombic) CsPbI3 with periodic boundary conditions, finding that the δphase was more stable by 18 kJ mol -1 per CsPbI3 unit. This is qualitatively consistent with experimental observations and provides a degree of confidence for the use of xTB for further investigations. We then used several molecular cluster models to evaluate the energetics of surface formation to reveal the energy landscape of the CsPbI3 within composites. Figure 1b shows two of the representative products between a fragment of the CsPbI3 surface and an agZIF-62 fragment. They were two of the most stable structures that we identified, with ligand exchange at the interface. The generation of the interfacial α-phase product was more exothermic than that of the δ-phase product. At the xTB level, the reaction energies were -1224 (α) and -1033 (δ) kJ mol -1 . The difference was sufficient to overcome the inherent stability of the δ-phase over the α-phase (18 kJ mol -1 per CsPbI3 unit, and thus by ~150 kJ mol -1 for the surface models with 8 or 9 units). The calculation results indicate the interfacial bond favours the formation of optoelectronically active phases of CsPbI3 within composite.

An array of composites was then fabricated with different agZIF-62 and CsPbI3 ratios and sintering temperatures. ZIF-62 glass, instead of ZIF-62 crystal, was implemented to promote the formation of adaptive interfaces within the composites, given its higher enthalpy and lower temperature required to access the viscous flowing state [START_REF] Zheng | Understanding Glass through Differential Scanning Calorimetry[END_REF] . The composite samples were hereby referred to as (CsPbI3)(agZIF-62) (X/Y) (prior to sintering) and (CsPbI3)X(agZIF-62)Y (after sintering), where X and Y are the percentage mass of each component, with X values ranging from 1 to 85. Sintering pure CsPbI3 at temperatures greater than 320 ℃ transformed the nonperovskite δ-phase into an optoelectronically active cubic perovskite α-phase, which returned to an inactive δ-phase during returning to ambient (Figure S1) [START_REF] Steele | Thermal unequilibrium of strained black CsPbI3 thin films[END_REF][START_REF] Marronnier | Anharmonicity and Disorder in the Black Phases of Cesium Lead Iodide Used for Stable Inorganic Perovskite Solar Cells[END_REF] . Ex-situ X-ray diffraction (XRD) revealed that the CsPbI3 structures within the composites were highly dependent on its fraction and the sintering temperature (Figure 1c and Figure S2). Prior to sintering, the powder mixtures exhibited poor crystallinity as expected for the mechanochemically synthesised CsPbI3. Following the sintering process, CsPbI3 crystallinity enhanced with several phases emerged on top of two agZIF-62 broad peaks (centred near 15 and 35°). Higher sintering temperatures and lower CsPbI3 loading, in general, can better preserve the CsPbI3 perovskite phase. Figure 1d and Figure S3 shows a summary of the relative proportion of active γ-CsPbI3 phase within the composites. After sintering at 350 ℃, (CsPbI3)0.4(agZIF-62)0.6 can achieve nearly complete preservation of the γ-phase, and further increase of the CsPbI3 loading resulted in a mixed active γ-and inactive δ-phases. In-situ XRD was used to track the sintering-induced phase changes in (CsPbI3)(agZIF-62)(40/60) (Figure S4), showing the emergence of active phase CsPbI3 from 150 ℃, which was substantially lower than the intrinsic phase transition temperature of pure CsPbI3 near equilibrium (320 ℃). Further heating improved the crystallinity and the proportion of perovskite crystal formed. After sintering, the composite showed a smooth and continuous surface morphology, with clear phase contrast under scanning electron microscope (SEM, Figure S5).

Stable optical performance

The composites exhibited characteristic red-emitting PL under UV excitation, originated from the stable formations of active γ-CsPbI3 phase (Figure S6), with their relative intensity of emissions charted in Figure 2a. The overall PL maximum was realised by (CsPbI3)0.25(agZIF-62)0.75 at 275 °C sintering. The corresponding maximum intensity of the PL emission from composites with different CsPbI3 loadings occurred at different sintering temperatures: generally, samples with greater CsPbI3 loadings achieved their PL maxima at a lower temperature: e.g. (CsPbI3)0.01(agZIF-62)0.99 showed a PL maximum for sintering at 300 ℃ whereas (CsPbI3)0.85(agZIF-62)0.15 showed a PL maximum for sintering at 225 ℃. Similar behaviour was also identified for the PL quantum yield (PLQY), with the highest PLQY of 81.3% for (CsPbI3)0.05(agZIF-62)0.95 at 275 ℃ sintering (Figure S7). This value is greater than the majority of previously reported CsPbI3 [START_REF] Abhishek Swarnkar | Quantum dot-induced phase stabilization of α-CsPbI3 perovskite for high-efficiency photovoltaics[END_REF][START_REF] Shamsi | Metal Halide Perovskite Nanocrystals: Synthesis, Post-Synthesis Modifications, and Their Optical Properties[END_REF][START_REF] Guo | Large-scale continuous preparation of highly stable α-CsPbI3/m-SiO2 nanocomposites by a microfluidics reactor for solid state lighting application[END_REF][START_REF] Wei | Constructing All-Inorganic Perovskite/Fluoride Nanocomposites for Efficient and Ultra-Stable Perovskite Solar Cells[END_REF][30] . With increased CsPbI3 loading, the PL peak red-shifted first and then blue-shifted (Figure S8), which was paralleled by similar changes in the γ-phase absorption edge shown in the UV-Vis absorption spectra (Figure S9). The composites demonstrated photostability under continuous excitation, showing negligible shifts in the peak position and variation in intensity during the test (Figure 2b).

Scanning transmission electron microscopy (STEM) based cathodoluminescence (CL) further demonstrated that the CsPbI3 nanometer-scale particles were indeed the source of the light emitted, and the luminescence properties of the composite exhibited different characteristics at the bulk nanocrystals and the interface regions (Figure 2c-f). The emission spectra from these particles peaked at around 710 nm (Figure 2e), and the inter-particle emission peak wavelength varied in the +/-5 nm range based on a Gaussian model fitting of the dataset (Figure S10-11). In the field of view, the variation of the emission intensity was not directly related to the size of the particles, indicating the quantum confinement was not the main contributor to the strong light emission. The width parameter σ of the Gaussian fitted to the emission spectra had a tendency for larger value at the edge of the particles (Figure 2f). Histograms of the fitted coefficients for the data acquired across a relatively large (6.9 µm 2 ) projected surface showed that the sample was quite homogeneous (Figure S11). In addition, correlations between emission peak center wavelength with its width and intensity were observed (2D histograms in Figure S11). It is worth mentioning that to achieve single particle emission profile STEM lamellae samples were prepared by focused ion beam (FIB), which is known to be prone to damaging perovskites and to quenching CL emission. However, the FIB lamellae emitted light at the same wavelength and with the same emission spectral shape as those powder samples prepared by crushing the composite using a mortar and a pestle, confirming the strong stabilisation effects within the composites.

The PL emission properties from pure perovskites are closely related to their underlying crystal structures and trap states. Enhanced crystallinity should reduce bulk and surface defects, suppressing non-radiative exciton recombination and enhancing PL emission [START_REF] Wang | Chemically Stable Black Phase CsPbI3 Inorganic Perovskites for High-Efficiency Photovoltaics[END_REF][START_REF] Chu | Soft Lattice and Defect Covalency Rationalize Tolerance of beta-CsPbI3 Perovskite Solar Cells to Native Defects[END_REF] . The data presented here, on the other hand, clearly illustrates the presence of additional prominent effects within the composites, such as the fact that a higher sintering temperature (e.g., >300 ℃) enhances crystallinity of the active CsPbI3 but dramatically reduces the PL for all composites. The PL spectra of (CsPbI3)0.40(agZIF-62)0.60 is plotted on a log scale against photon energy to elucidate the nature of the trap states for the composites (Figure 2g and Figure S12). PL emissions consist of a primary Gaussian-type peak and can contain tails on the low-energy shoulders usually being associated with the formation of near-edge traps [START_REF] Falsini | Analysis of the Urbach tail in cesium lead halide perovskites[END_REF] . For the case of CsPbI3 perovskite, the lower-energy Urbach tail is typically associated with disorder at the crystal surface [START_REF] Chen | Cu(2+)-Doped CsPbI(3) Nanocrystals with Enhanced Stability for Light-Emitting Diodes[END_REF][START_REF] Zhang | Unraveling Urbach Tail Effects in High-Performance Organic Photovoltaics: Dynamic vs Static Disorder[END_REF] .The Urbach tail slopes for composites remained generally unchanged as sintering temperature increased, demonstrating that the defects at the crystal surface can be well passivated even at the early stages of sintering. This is consistent with the fitting of PL spectra with a two-Gaussian function (Figure S13-S14) [START_REF] Wen | Intrinsic and Extrinsic Fluorescence in Carbon Nanodots: Ultrafast Time-Resolved Fluorescence and Carrier Dynamics[END_REF] , in which the low energy peaks contributed only a minor to modest part of the overall intensity.

Composite property evolution during sintering

Differential scanning calorimetry (DSC) can reveal overall information on the thermodynamic and kinetic phase transitions, interfacial interactions and particle aggregations during sintering. DSC curves of pure CsPbI3 and agZIF-62 were relatively featureless except for their phase transition (δ-to α-CsPbI3, ca. 320 ℃) and Tg (agZIF-62, ca. 290 ℃) (Figure S1 andS15). In contrast, a broad endothermal peak for the composites began to develop at temperatures as low as 110 ℃ (Figure 3a) during the first heating ramp, and the cooling and 2 nd heating ramp were featureless, except for the Tg. The endothermal enthalpy of the composite (ca. from 110 to 190 ℃) was much greater and wider than the phase transition enthalpy of the corresponding CsPbI3. Furthermore, the Tg of the composite decreased with higher CsPbI3 loading, implying that the compositing increased entropy and changed the chemical composition of the agZIF-62 phase (Figure 3b and Figure S16).

Particle coarsening and the evolution of a diffusion layer at the interface were identified via the synchrotron X-ray small angle scattering (SAXS) on (CsPbI3)0.1(agZIF-62)0.9 composites (Figure 3c and Figure S17). Within the measured scattering vector (q) range, higher temperature sintering coarsened small CsPbI3 particles particularly when temperature approached the Tg (275 ℃), where the viscous flow rates of MOF liquid facilitated the diffusion of the perovskite particles. This also suggested the DSC endothermic feature at ca. 110 -190 ℃ was predominately attributed to phase transition and interfacial interaction, instead of particle coarsening. Further analysis of the SAXS with the Porod's plot (Figure 3d) showed higher sintering temperature led to more significant positive deviation from the Porod's law [START_REF] Koberstein | The determination of diffuse-boundary thicknesses of polymers by small-angle X-ray scattering[END_REF] , i.e. limq 4 I(q)=K when q → ∞, where q is the scattering vector, I(q) is the scattering intensity and K is the Porod constant. The Porod's law describes a system with sharp phase boundary with clear contrast of electron density. The positive deviation may originate in the microfluctuations of electron density within the sample, indicating the evolution of a diffusion layer along with sintering.

The development of interfacial bonding within the composites was studied with in situ temperature-resolved synchrotron terahertz (THz) FarIR vibrational spectroscopy (Figure S18). The primary characteristics of (CsPbI3)(agZIF-62)(10/90) can be attributed to Zn-N stretching (ca. 300 cm -1 ) and the aromatic ring deformation (ca. 670 cm -1 ) (Figure S19) [START_REF] Hou | Halogenated Metal-Organic Framework Glasses and Liquids[END_REF] . Additional features (ca. 135 and 275 cm -1 ) associated with Zn-I formation emerged from ca. 110 ℃ (concurrent with the endothermal feature in DSC), visible in the 2 nd derivative of the in-situ spectra (Figure 3e). With further increase of the sintering temperature, the Zn-I features gradually intensified and remained substantially invariant after cooling. Similar behaviour was found in other composite samples (Figure S20

Element specific atomic-scale structures at the interface

Solid state nuclear magnetic resonance (SS-NMR) spectroscopy can shed a clear picture on the Cs chemical environment evolution. It identified a nice interplay between different perovskite phases and the greatest proportional contribution of interfacial Cs occurred at 250 ℃ sintering, correlating with the fluctuation in PL intensity against different sintering temperature. The disordered nature of the glassy matrix was confirmed by the broad 1 H and 13 C NMR spectra (Figure S26) [START_REF] Baxter | Combined experimental and computational NMR study of crystalline and amorphous zeolitic imidazolate frameworks[END_REF] . In the 133 Cs NMR spectra (Figure 4a), for the sample without sintering, the narrow peaks at ca. 260 ppm and 280 ppm were attributed to δ-CsPbI3 and CsI, respectively. The broad, low-amplitude signals extending between 0 and ca. 350 ppm were attributed to poorly crystalline, highly defective CsPbI3, as expected for mechanochemically synthesised perovskites [START_REF] Hou | Liquid-phase sintering of lead halide perovskites and metal-organic framework glasses[END_REF] . After sintering, the broad contributions and CsI peaks diminished, and the major signals stemmed from γ-CsPbI3. Notably, the asymmetric 'shoulder' of the γ-CsPbI3 peaks (below ca. 160 ppm, Figure 4a) was related to the γ-CsPbI3 impacted by the chemical environment at the interface, directly in contact with glassy matrix, forming gradient interdiffusion and modified bonding at the interface. Additionally, 1 H-133 Cs cross-polarization magic angle spinning (CPMAS) NMR showed a non-negligible cross-polarization transfer between the protons of agZIF-62 and the "shoulder-peak" of γ-CsPbI3 at the interface (Figure 4b), pointing to close proximity between the imidazole ligands and Cs atoms. This interfacial Cs contribution was the most substantial for the composite sintered at 250 ℃, and gradually decreased along with higher sintering temperature and particle coarsening, showing similar tendency to the variation of PL intensity against different sintering temperatures. Extended X-ray absorption fine structure (EXAFS) and wavelet transforms (WTs) were performed on to explore the change of Zn and Pb coordination environments through sintering (Figure S27-28), and to identify the change of the first layer structure for these atoms. Wavelet transformation (WT) provides complementary information to FT-EXAFS, which can help differentiate different coordinating pairs at similar atomic distances. EXAFS spectra and wavelet transform contours of the Zn K edge (Figure 4c-e and Figure S28) revealed both samples exhibited main peaks at the R space distance of ca. 1.5 Å, corresponding to the distance of Zn-N pairs. The local environment of the Zn prior to sintering was identical in the crystalline ZIF-62 [START_REF] Bennett | Melt-Quenched Glasses of Metal-Organic Frameworks[END_REF] , indicating Zn atom maintains the tetrahedral configuration within the composites. After sintering, the emerging peak at ca. 2.7 Å can be assigned to Zn-I, in good agreement with the THz results. Change to the Pb local environment were more pronounced, particularly considering the evolution of disparate crystal structures (Figure 4f-h and Figure S29). The peaks prior to sintering located at ca. 1.7 Å and 2.8 Å can be assigned to Pb-O and Pb-I, respectively [START_REF] Ye | Below 200° C fabrication strategy of black-phase CsPbI3 film for ambient-airstable solar cells[END_REF] . The presence of Pb-O is attributed to the surface oxidation through high energy ball milling synthesis. Crystallisation of CsPbI3 during sintering eliminate the Pb-O bonding and, therefore, Pb-I became more dominating after sintering. In addition, the emerging peak at ca. 1.4 Å and 2.5 Å can be attributed to Pb-N and Pb-Zn pairs formed at the interfaces. The formation of new atom pairs was supported by the X-ray adsorption near-edge structure (XANES) of the Pb L3-edge spectra (Figure S27-28), which exhibit a shift toward lower energy after sintering, due to the higher electronegativity of N and Pb over Zn.

Annular dark-field scanning transmission electron microscopy (ADF-STEM) identified the emergence of interdiffusion alloying layers after high temperature sintering. FIB milling was first used to extract a ca. 10 nm thick lamella from a piece of (CsPbI3)0.1(agZIF-62)0.9 sintered at 350 °C to expose individual LHP grains (Figure S30). The sample showed pronounced atomic number contrast between two phases. In STEM, electron energy loss spectroscopy (EELS) provides a sensitive method for analysing the chemical environment using transmitted sub-nanometer electron probes [START_REF] Collins | Functional Group Mapping by Electron Beam Vibrational Spectroscopy from Nanoscale Volumes[END_REF] . Although we cannot rule out entirely contributions from FIB milling-induced modifications to the sample, after 350 ℃ sintering, an EELS line scan across the interface quantifies an excess quantity of I outside the CsPbI3 (Figure 5a-b and Figure S31), while such a behaviour was not observed at 275 ℃ sintering (Figure S32). The gradual diffusion of heavier I atoms towards the glassy phase at high temperature aligns with the microfluctuation in electron density as demonstrated in SAXS, and the gradual intensified Zn-I THz features up on sintering. The diffusion of Cs, in comparison, has not reached beyond nanometer range from the perovskite grain.

Atomic pair distribution functions (PDFs) identified the interfacial diffusion layers mainly contained Pb-I, Cs-I and Pb-N atomic pairs with only short-range orders. Ex-situ synchrotron X-ray total scattering measurements were performed on a series of composites sintered at 350 °C. The PDF, obtained by Fourier transform, showed the short-to-long range fine structure of the composites (Figure 5c). Rietveld analysis of the composite (CsPbI3)0.50(agZIF-62)0.50 was performed with desolvated ZIF-62, γ-and δ-CsPbI3 reference structures. We found that ZIF structure was only maintained in the short-range order. Good fitting was achieved in the medium and long-range (Rwp of 11 % in the range of 15-50 Å), with 13.7 wt% of γ-CsPbI3 and 30.1 wt% of δ-CsPbI3 being identified. The difference pattern in the short-range suggested the structural distortion originated from the surface of the crystalline phases, with the main feature being assigned to Pb-I (ca. 3.2 Å). This is an indication of presence of discrete, rigid and slightly distorted Pb-I octahedra within the diffusion alloying layer. These difference features are highly composition-and sintering temperature dependent, showing more contribution from these amorphous perovskite components at higher sintering temperatures, or from composites with larger expected interfaces (Figure S33-34). These observations further confirm the amorphous structures are originated from the interface, instead of the amorphous regions within the bulk perovskites.

Conclusions and discussions

This study identified the presence of interfacial alloying layers between perovskite and hybrid glass phases, which were mainly consisted of amorphous Pb-I structures. Different behaviours were observed for different atoms during the alloying: high temperature sintering promoted the crystallisation for Cs to form bulk perovskites, possible through a fluxing mechanism. In comparison, the diffusion of the I into the glassy phases was significant (can reach up to 10 nm away from the CsPbI3 grain), together with the preservation of Pb-I octahedron structure within the diffused alloying layer. This work also unveiled the complex performance -property relationship within the perovskite glass composites. We identified that the optoelectronic performance of composite perovskite was predominately determined by the interface, instead of the bulk particle crystallinity. The interfacial alloying favoured the formation of active perovskite phases, stabilised the optoelectronic performance and, more importantly, effectively passivated the trap states. Nevertheless, it can also be detrimental to light emission: for all composites with varying CsPbI3 loadings, the maximum PL intensity was obtained by sintering at a temperature at the corresponding Tg. Above the Tg, glass enters a viscous flowing state, leading to faster diffusion and generate non-stochiometric perovskite near the interface. Though the coarsening can promote the overall crystallinity, the diffusion of Pb-I away from perovskite can lead to nonradiative recombination and quenching of PL. This study has notable implications for the fundamental understanding of defect formation and control in perovskite materials and the design of halide perovskite devices through interfacial engineering. It exemplified that how the interface can passivate and then generate defects. The investigation of this multimodal system has provided significant progress in comprehending the fundamental processes and interfacial atomic level structures, shedding light onto governing the performance of perovskite materials in practical applications such as solar panels, LEDs and sensing devices. Our findings indicate that prioritising the attainment of bulk crystal perfection may not necessarily lead to the most advantageous outcomes for improving the performance of this particular class of semiconductors. Rather, further research efforts should be focused on interfacial engineering, with consideration of different diffusion behaviour for different perovskite components.

Figure 1 .

 1 Figure 1. Fabrication of (CsPbI3)X(agZIF-62)Y composites. (a) Schmatic diagram of the CsPbI3 phase transition and evolution of the interfacial atomic structures during sintering. (b) Schematic diagram of the DFT calculation for composites with different CsPbI3 crystal phases. (c) Ex-situ XRD pattern of (CsPbI3)X(agZIF-62)Y composites sintered at 350 ℃. X-ray λ: 1.5406 Å. (d) γ-phase CsPbI3 proportion within of different (CsPbI3)X(agZIF-62)Y composites, as retrieved from Rietveld refinement of the XRD profiles.

Figure 2 .

 2 Figure 2. Light emission profile of the composites. (a) Relative PL intensity of different (CsPbI3)X(agZIF-62)Y composites. (b) Evolution of PL spectra under constant laser excitation (440 nm with 82 mW/cm 2 ) for (CsPbI3)0.05(agZIF-62)0.95. (c) High angle annular dark field (HAADF) image, (d) integrated CL intensity map around the main emission peak at 710 nm and (e) selected CL spectra in the regions of interest marked in E and F. Panel (f) represents the Gaussian fitted σ (nm) values. Scale bar, 200 nm. (g) PL spectra for (CsPbI3)0.40(agZIF-62)0.60 composite shown in log scale.

  -23), and the variation of bonding environment was confirmed by X-ray photoelectron spectroscopy (XPS) (FigureS24-25).

Figure 3 .

 3 Figure 3. Evolution of interfacial interaction during the sintering. (a) DSC results for (CsPbI3)(agZIF-62)(10/90). Data was collected under constant flowing nitrogen protection (20 mL/min). The temperature ramping rate for the first up-scan was 20 ℃/min, and the ramping rate was 10 ℃/min during the DSC cooling and second up-scan. (b) Glass transition temperature, Tg, of the composites as a function of CsPbI3 loading. (c) Particle size evolution for (CsPbI3)0.1(agZIF-62)0.9 composites sintered at different temperature. (d) Change of the Porod's plot of the corresponding SAXS patterns. (e) Second derivative of temperature-resolved in-situ THz FarIR spectra for (CsPbI3)(agZIF-62)(10/90) composites.

Figure 4 .

 4 Figure 4. Structure of the interface. (a) 133 Cs MAS NMR spectra of (CsPbI3)0.25(agZIF-62)0.75 composites sintered at 200, 250, 300, and 350 ℃. (b) 1 H-133 Cs CPMAS NMR spectra of (CsPbI3)0.25(agZIF-62)0.75 sintered at 250 and 350 ℃. (c-e) Extended X-ray absorption fine structure (EXAFS) signal and the full-range wavelet transform (WT) representation for the Zn K edge of (CsPbI3)0.40(agZIF-62)0.60 composites. (f-h) Extended X-ray absorption fine structure (EXAFS) signal and the full-range wavelet transform (WT) representation for the Pb L3 edge of (CsPbI3)0.40(agZIF-62)0.60 composites. Composites were sintered at 350 °C.

Figure 5 .

 5 Figure 5. Chemistry and structure of the alloying layer at the interface. (a) ADF-STEM image of (CsPbI3)0.1(agZIF-62)0.9 composites sintered at 350 ℃. (b) EELS core loss spectra acquired from the marked points shown in TEM image with background subtracted. (c-d) Atomic pair distribution functions for (CsPbI3)0.50(agZIF-62)0.50 composites sintered at 350 ℃. Pair distribution function D(r) calculated via Fourier transform of the X-ray total scattering function. Panel (d) is the enlarged fitted data in the r range of 1.5-12 Å.

Associated content

Supporting information

Acknowledgments

The authors acknowledge the funding support from the Australian Research Council (ARC) (FT210100589; DP230101901 and FL190100139). We gratefully acknowledge research funding from the Hyogo Science and Technology Association, Japan (Project 4019), and FOCUS Establishing Supercomputing Center of Excellence, Japan. Computational resources were provided by the RIKEN Information Systems Division, Japan (Q22266). This research was supported by an AINSE Ltd. Postgraduate Research Award (PGRA) and Early Career Researcher Grant (ECRG). XL acknowledge the support by an Australian Government Research Training Program (RTP) Scholarship. The authors acknowledge the facilities, and the scientific and technical assistance, of the Australian Microscopy & Microanalysis Research Facility at the Centre for Microscopy and Microanalysis, The University of Queensland. This work used the Queensland node of the NCRIS-enabled Australian National Fabrication Facility (ANFF). This research was undertaken on the THz and SAXS beamline at the Australian Synchrotron, part of ANSTO. SMC acknowledges support from the UK Engineering and Physical Sciences Research Council (EPSRC, EP/V044907/1). This project has been funded in part by the European Union's Horizon 2020 research and innovation programme under Grant Agreements 823717 (ESTEEM3). A.K. and G.M. acknowledge the financial support from the Slovenian Research Agency (research core funding no. P1-0021).

Author Information

Corresponding Author

Jingwei.hou@uq.edu.au


Clément Comminges

Stefano Frasca

Martin Suetterlin

Erik Wischerhoff

Andre Laschewsky

Ulla Wollenberger

Martin Sütterlin

André Laschewsky

Surface modification with thermoresponsive polymer brushes for a switchable electrochemical sensor

come

Surface modification with thermoresponsive polymer

brushes for a switchable electrochemical sensor

Introduction

Stimuli responsive polymers are macromolecules that can undergo structural changes as a response to external stimuli. The most common triggers for this transition are changes in temperature, pH or ionic strength 1 . When such polymers are grafted on a substrate as dense brush, interfacial properties such as surface adhesion, wettability or interfacial viscoelastic properties can be reversibly modified as result of transition induced structural changes [2][3][4] . This makes such responsive brushes attractive candidates as switchable elements in electrochemical systems 5,6 .

In the case of thermoresponsive polymers in aqueous media, the coil-to-globule transition is mostly characterized by a lower critical solution temperature (LCST). Below the transition temperature, the grafted polymer chains are strongly swollen and stretch away from the surface, whereas above the transition, such brushes expel most of the solvent, deswell and finally collapse on the substrate. The transition temperature is characteristic for the polymer studied and the specific aqueous solvent used. It can be conveniently tuned by co-polymerization of different monomers.

Macromolecules constructed with short oligo(ethylene glycol) methacrylates (OEGMA) constitute an interesting class of thermoresponsive polymers for preparing biorelevant and biocompatible switchable surfaces 7 . While the phase transition of these copolymers is reversible, the precise transition temperature of a given copolymer depends to some extent on system parameters such as molar mass and polydispersity, polymer concentration, and the ionic strength of the medium [7][8][9][10][11] . Random copolymers of 2-(2-methoxyethoxy)ethyl methacrylate (MEO2MA) and OEGMA typically exhibit a LCST in water, which can be precisely adjusted by varying the co-monomer ratio 7,10,[12][13][14][15] . Interestingly, this LCST-type transition can be 50 detected by electrochemical methods 16 . We herein report a molecular architecture of a LCST polymer modified gold surface, and its interfacial properties in terms of charge transfer towards an electrochemical probe. The modular character of the straightforward coating process enables a priori 55 the simple and versatile functionalization of such polymer modified electrodes. We also introduce differential E-QCM-D measurement to characterize the ability of the system to actively respond upon temperature variations in order to develop a switchable readout system exploiting the structural changes of the 60 surface.

Experimental methods

Chemicals

Poly(4-styrenesulfonic acid) (PSS, Mw = 70,000 g•mol -1 ), Ferrocene carboxylic acid (FcCOOH), Tris(hydroxymethyl)aminomethane (Tris), hydroxyethyl methacrylate (HEMA), Dithiobis(succinimidyl propionate) (DTSP), branched polyethyleneimine (PEI, Mw = 25,000 g•mol -1 ), and azo-bisisobutyronitrile (V-601) were purchased from Sigma (Steinheim, Germany) and used as received, when not specified otherwise. Poly(diallyldimethylammonium chloride) (PDADMAC , Mn = 230,000 g•mol -1 , Mw = 570,000 g•mol -1 ) was prepared according to a published procedure 17 .

Surface modification: DTSP self assembled monolayer (SAM), coupling with PEI and layer by layer assembly

All surface modifications were monitored with an Electrochemical Quartz Crystal Microbalance with Dissipation (E-QCM-D), as it is a well suited method for monitoring the consecutive surface modification steps 18 , using a Q-Sense E4instrument (Q-Sense, AB, Göteborg, Sweden) incorporating a Q-Sense Electrochemistry Module, QEM 401 and polished AT-cut piezoelectric quartz crystals with gold electrodes with a fundamental frequency of 5 MHz as substrates. The gold 25 substrates (disk for E-QCM-D and wires for electrochemical measurements) were cleaned according to a previously published procedure 19 . Briefly, crystals were immersed in a mixture of ammonia (25%), hydrogen peroxide (30%), and Milli-Q water (1:1:5), held at 70 °C for 10 min, rinsed extensively with Milli-Q 30 water, and dried under a stream of nitrogen.

A first modifying layer consisting of a SAM of the functional disulfide DTSP was prepared by incubating the clean gold electrode in a 10 mmol•l -1 DTSP solution in CHCl3 at 4 °C overnight. DTSP modified electrodes were rinsed with CHCl3 35 and water and assembled in the E-QCM-D module. PEI aqueous solution (1 g•l -1 ) was flown (10 µl•min -1 ) over the SAM to covalently couple the primary amine moieties of PEI to DTSP. Then, layer-by-layer assembly (LBL) 20,[START_REF] Decher | Multilayer Thin Films[END_REF] of 4 alternate layer pairs of PSS and PDADMAC (0.2 g•l -1 solution in 5 mmol•l -1 40 Tris buffer pH 7.2) was applied in order to build a polyelectrolyte multilayer. Each deposition step was followed by rinsing with 5 mmol•l -1 Tris buffer pH 7.2 to remove the loosely adhering molecules. The flow rate was always 50 µl•min -1 , if not otherwise mentioned, and the injected solution was changed only after a stable frequency signal was reached. Finally, the sulfonated polyanion macroinitiator MI (scheme 1) (0.2 mg•ml -1 in water), synthesized according to a published procedure [START_REF] Wischerhoff | [END_REF] , was adsorbed onto the terminal PDADMAC layer.

Surface initiated polymerization

The MI on top of the polyelectrolyte multilayer was used as starting point for the surface-initiated atom transfer radical random copolymerization (ATRP) of MEO2MA and OEGMA monomers (ratio 95:5), [23][24][25] which was catalysed with a copper 2,2'-bipyridine bromide complex (CuBr2bpy2). A stock solution of co-monomers and copper complex is bubbled with nitrogen and pumped into the E-QCM-D chamber. The polymerization was monitored by following both frequency shift and dissipation with time. The resulting modified surface will be referred to as the Polymer Modified Electrode (PME) in the following. The phase transition temperatures of the grafted polymer brushes PME were determined by E-QCM-D measurements using a temperature ramp of 0.2 °•min -1 from 15 °C to 38 °C in a 25 mmol•l -1 TRIS buffer pH 8.

Electrochemical measurements

Cyclic voltammetry and electrochemical impedance spectroscopy (EIS) were performed on a CH Instrument Model 750 A (Austin, USA) to characterize the electronic transfer for FcCOOH oxidation (5 mmol•l -1 solution in citrate-phosphate buffer 0.

Results and discussion

Surface modification

The E-QCM-D measurements show that PEI covalent grafting Where Δm is the mass uptake (ng•cm -2 ), c is a constant related to the quartz crystal (17.7 ng•Hz -1 •cm -2 for a 5 MHz crystal) and n is the overtone number. Most of the time, the fundamental resonance frequency f1 is noisy because of energy trapping or piezoelectric stiffening 26 . We therefore used the 3 rd overtone in all measurements.

The LBL assembly was monitored by E-QCM-D (fig. 1a). A negative frequency shift is observed after each layer deposition.

A final frequency shift of 350 Hz is measured for a chip covered by 4 bilayers of PSS/PDADMAC and one layer of macroinitiator. The corresponding dissipation is rather high (84×10 -6 ) (supporting figure 2) due to the flexibility of the polyelectrolyte chains, so the Sauerbrey equation was not applicable 27 . Fig. 1b shows the on-line monitoring of the polymerization with E-QCM-D, which leads to 2700 Hz frequency decrease after 4.5 h of polymerization, indicating a large mass increase over the surface and 700.10 -6 dissipation increase which is typical for the formation of a viscoelastic film 28 . The proposed final PME architecture is represented on Fig. 1c. According to previous studies on similar structures 23 , thicknesses of LBL underlayer (~ 40 nm), MI layer (~ 20 nm) and polymer layer (~ 70 nm) were obtained.

Phase transition of the responsive polymer

Fig. 2a and2b show the resonance frequency and dissipation variation upon temperature changes. A bare gold chip and an assembled system without polymer layer show linear evolution of frequency and dissipation change with temperature, which are expected for solvent density and viscosity variation. However, frequency and dissipation change displays a totally different behavior for the PME. Upon temperature increase, a large negative frequency shift is observed. This is related to the collapsing of the polymer, passing from a stretched and viscoelastic form to a more rigid structure. According to Laloyaux et al. 29 , this can be described as a two-step collapsing. Zone 1 corresponds to the fully swollen state, where frequency and dissipation data are close to the underlayer behavior. In zone 2, dissipation is increasing whereas frequency decreases. This difference with the under layer response shows the beginning of the bulk brushes collapsing. The increase of dissipation in that zone indicates a metastable behavior of the brushes which appear to be more flexible. In zone 3, the surface brushes are fully collapsed, indicated by a large dissipation and frequency decrease. The frequency shows a minimum, indicating a maximal synergy between surface and bulk collapse. After this minimum, the frequency change is increasing again, indicating that surface collapse is progressively completed and the polymer chains are confined and almost no more flexible. In zone 4 and 4', the film 50 is behaving like the under layer as a rigid coating on the surface. Zones 3' and 2' are the reversible processes of surface and bulk re-swelling upon cooling.

As the Au/under layer assembly behaves as a thick rigid film, Δf and ΔD follow the linear density and viscosity dependency on 55 temperature. Therefore, plotting the change in frequency over the change in time (i.e. the first derivative) versus the temperature, the under layer dependency on temperature for frequency data will be removed. This enables the observation of the thermoresponsive behavior independently from solvent density 60 and viscosity changes. Such a plot is presented in fig. 2c, where three cooling / heating cycles applied to the system are shown. Clearly, the switching is fully reversible, showing mean peak frequencies at 20.5°C for cooling ramps and 24.6 °C for heating ramps. Taking the hysteresis (coming from the time constant of 65 the system) into account, the average of these two mean values is representative of a steady state measurement, what gives a frequency peak at 22.6 °C, in good agreement with a reported transition temperature of 24.6°C for brushes with a similar composition grown on SiO2 surfaces 29 . Fig. 2d schematically 70 shows the two steps collapse. These structural changes create new interfaces that modulate the interfacial viscosity.

Electrochemistry of FcCOOH and barrier effect of the polymer film

We performed the electrochemical oxidation of ferrocene 75 carboxylic acid (FcCOOH) as a function of temperature in order to investigate the barrier effect of the polymer film towards electron transfer and diffusion. Since the transition temperature determined by E-QCM-D measurements is close to 22.6 °C, the temperature was varied between 10 and 47°C. Fig. 3a shows the 80 peak separation (ΔEp) and the ratio of anodic peak current over the reference peak current in a fully swollen state at 10 °C (r = ip a /ip a °) as a function of temperature for both a bare gold electrode and PME. Comparison of the reference temperature dependency on bare gold with PME demonstrates that ΔEp and r differ 85 strongly for the two electrodes. For both parameters, values shift continuously in the temperature range of 10 to about 40°C, where a plateau value is reached, in the case of PME, indicating that both the kinetics for electron transfer and diffusion issues are greatly affected by the polymer phase transition. ΔEp and r are 90 linearly evolving till reaching a plateau, corresponding to the fully collapsed state, indicating a gradual thermal collapse. This finding is in agreement with temperature dependent thickness studies of similar surface brushes of poly(OEGMA-co-MEO2MA) copolymers 30 . EIS was performed at several temperatures (fig. 3b) ranging from 10 °C (fully swollen polymer) to 47 °C (fully collapsed polymer). Fig. 3c shows the RCT dependency on temperature. The temperature of 22.6°C, where the collapsing was observed to be the most intense from E-QCM-D measurements, corresponds to the largest changes in RCT. RCT is no more strongly affected at temperatures above 30-10 33°C. This corresponds to the beginning of zone 4 in figs. 2a and b, where the polymer is considered to approach the maximum collapsed state. Finally, an 86 % decrease of RCT is observed between fully swollen state (10 °C) and collapsed state (47 °C). This spectacular evolution of RCT points out the strong barrier 15 effect of the swollen polymer.

Conclusions

We demonstrate that thermoresponsive brushes made of poly(OEGMA-co-MEO2MA) can be grown by surface initiated ATRP from gold substrates stepwise modified by a covalently 20 attached polyamine layer and subsequent layer-by-layer (LBL) deposition of PSS, PDADMAC and of a polyelectrolyte macroinitiator as top layer. The modular character of the nevertheless rather simple built-up procedure allows for versatile and modular functionalizations of such polymer modified electrodes. As determined by electrochemical quartz crystal microbalance with dissipation (E-QCM-D), the film shows reversible switching between the swollen and the collapsed states by changing the temperature around the lower critical solution temperature (LCST). The dissipation profile with temperature suggests a two steps mechanism of the transition. This is confirmed by electrochemical oxidation of ferrocene carboxylic acid (FcCOOH) using the PME at different temperatures. The charge transfer resistance is gradually decreased with ongoing dehydration of the polymer brush while temperature is raised, till 35 reaching a constant value when the polymer is fully collapsed. We believe that this large change of charge transfer resistance associated to the polymer state can be further implemented into switchable electrochemical systems.

Notes

Scheme 1 Fig. 1

 11 Scheme 1 Structure of the macroinitiator (MI)

Fig. 2 (

 2 Fig.2 (a) Resonance frequency shift and (b) dissipation shift and temperature change for Au, Au/PEI/[PSS-PDADMAC]4/MI and PME. vs. time. (c) Derivative of the frequency over the temperature of PME for 3 thermal cycles. (d) Scheme of the three states of the polymer layer involving sequential collapse of polymer layers, and their proposed interfacial viscosity (η) evolution vs. distance from the surface (x).

Fig. 3 (

 3 Fig.3 (a) ΔEp (filled symbols) and r (open symbols) vs. temperature (50 mV.s -1 ) on bare Au (squares) and on PME (circles) electrodes, (b) EIS: full circle corresponds to 14 Hz. From largest to smallest semi-circle: 10; 19; 24; 26; 30; 35 and 47 °C and (c) RCT vs. temperature for the PME.

  Institut für Biochemie und Biologie, Universität Potsdam, Karl-Liebknecht-Str.24-25, Haus 25, 14476 Potsdam-Golm, Germany. Fax:

	105
		+49 331 977 5128; Tel: +49 331 977 5122; E-mail: uwollen@uni-
		potsdam.de
		b Institut für Chemie, , Universität Potsdam , Karl-Liebknechtstraße 24-
		25, 14476 Potsdam-Golm, Germany.
	110	c Fraunhofer-Institut für Angewandte Polymerforschung (IAP),
		Geiselbergstraße 69, 14476 Potsdam-Golm, Germany.
		† Permanent address, Université de Poitiers, UFR SFA -Bâtiment B27, 4
		rue Michel Brunet,TSA 51106, 86073 Poitiers cedex 9, France. Fax: +33
		5 49453580; Tel: (+33)5 49453628; E-mail: clement.comminges@univ-
		poitiers.fr

a

Acknowledgements 40

We gratefully acknowledge financial support from the Bundesministerium für Bildung und Forschung BMBF (German Federal Ministry of Education and Research), Initiative "Spitzenforschung & Innovation in den neuen Ländern" ("Das Taschentuchlabor", FKZ 03IS2201B).

Supporting informations


Frédéric André

Pierre Bernardi

Nikita M Ryskin

Fabrice Doveil

Yves Elskens

Hamiltonian Description of Electron Dynamics and its Radiated Field in a Periodic Structure

Keywords: Classical electrodynamics, Hamiltonian theory, beam-wave interaction, Traveling Wave Tube

We present an Hamiltonian formulation of the classical electron dynamics and the electro-magnetic field it radiates. The relativistic electron dynamics is governed by the Lorentz force and the fields by Maxwell equations. It is shown that this set of equations can be derived from an Hamiltonian that will be detailed in this presentation.

Introduction

Except with restrictions (e.g. in a cavity, see W. Heitler [1, chapter 1]) the electron dynamics and its radiated field are modeled by a set of equations whose Hamiltonian nature is not apparent. Starting from the well known Lorentz force and Maxwell equations Poynting has shown that the electro-magnetic field is carrying energy and impulse. A first difficulty appears even in the case of the static electron because the energy of the 1/r² electrostatic field of the electron is diverging. This is the problem of the infinite rest mass of the electron. Other difficulties appear in non-static situations. Starting from Maxwell equations, Liénard-Wiechert derivation shows that an accelerated electron radiates an electromagnetic field whose energy and impulse is not zero. When we consider for example an electron in a constant magnetic field following a circular trajectory at constant velocity, one end up with the contradiction that in this situation an electron with constant kinetic energy radiates power. This is of course in contradiction with energy conservation, or, said differently, the theory can not be derived from an Hamiltonian. In order to solve this problem it has been proposed to complement the Lorentz force with a correction that accounts for the radiated momentum. This is the Abraham-Lorentz force. By doing so however we introduce non-physical trajectories where the electron can experience self-acceleration (so called "run aways" [START_REF] Jackson | Classical Electrodynamics[END_REF]) and the physics is acausal [START_REF] Hartemann | High-field electrodynamics[END_REF]. Therefore this classical theory is not satisfactory and the only consistent theory has been found within a quantum description (quantum electrodynamics theory). But the question remains why it is not possible to find a consistent Hamiltonian classical limit of this quantum theory while a classical limit is normally found in other fields of quantum physics? To progress on this point and to clarify the question of energy and momentum balance in electrodynamics we have continued the search of an Hamiltonian description of the classical theory which can help to simulate beam-wave interaction in TWTs [START_REF] Bernardi | Utilisation et amélioration du modèle discret d'excitation d'un guide d'onde périodique pour la simulation pratique du tube à onde progressive en régime temporel[END_REF] [START_REF] Ryskin | Nonstationary nonlinear discrete model of a coupledcavity traveling wave tube amplifier[END_REF].

Method

First we improve a method originally developed by S. Kuznetsov [START_REF] Kuznetsov | On one form of excitation equations of a periodic waveguide[END_REF] and later by N. Ryskin [START_REF] Ryskin | Nonstationary nonlinear discrete model of a coupled-cavity traveling wave tube amplifier[END_REF] where the fields are first decomposed onto functions which satisfy the Floquet condition thanks to a transform proposed by I. Gel'fand [START_REF]Gel'fand, Expansion in characteristic functions of an equation with periodic coefficients (in Russian)[END_REF]. Then we perform the well known modal decomposition of these functions. Thanks to this double decomposition we find an Hamiltonian for the fields alone and we find an expression for the excitation by the electrons. By adding it to the well known Hamiltonian of an electron in a given electromagnetic field we find the complete Hamiltonian. From this Hamiltonian we derive the time derivative of the electron momentum, i.e. the force acting on the electron. Finally we adjust the amplitudes of the base functions used in the previous modal decomposition so that this expression is the expected Lorentz force. At this point the derivation is complete, we have found an Hamiltonian from which both the Maxwell equations and the Lorentz force can be derived, and where these two sets of equations are coupled self consistently.

Acknowledgements

Pierre Bernardi was supported by a CIFRE stipend from the French Ministère de l'industrie.