Sustainable Hydrochar Production from Biomass via Conventional Hydrothermal Carbonization: Optimization, Characterization, and Adsorption Capacity on Cu²⁺

Abstract

Sustainable valorization of biomass through hydrothermal carbonization (HTC) represents an environmentally benign method for producing carbon materials for water treatment applications. This research aims to optimize the production of hydrochar from waste food by focusing on parameter optimization, physicochemical characterization, and the capacity of hydrochar to act as an adsorbent for the removal of the copper (II) ion from polluted water. A design of experiments using the RSM approach was employed to evaluate and optimize the influence of carbonization temperature, ranging from 180 to 250 °C, with a residence time of 2–5 h. The predictive ability of the MINITAB-generated model was close to accurate, as demonstrated by the design application for process simulation. The maximum % hydrochar yield was 72.65% for the experimental yield and 71.53% for the predicted yield, both obtained from a sample carbonized at 166 °C for 3.5 h. Batch adsorption experiments were conducted to assess the hydrochar’s ability to remove Cu²⁺ from aqueous solutions, and the Langmuir and the Freundlich isotherms were fitted at different pH levels. A comprehensive characterization of the produced hydrochar was conducted using Fourier-transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), X-ray fluorescence (XRF), and scanning electron microscopy (SEM-EDS). The results revealed significant modifications in surface morphology, pore development, and the presence of oxygen-containing functional groups. Based on the findings in this report, it is safe to conclude that hydrochar derived from food waste could serve as a potential adsorbent. Overall, the study demonstrates that sustainable hydrochar production from biomass can simultaneously address waste management challenges and provide an efficient solution for heavy metal removal, thereby advancing circular bioeconomy and environmental protection.

1. Introduction

With the growth of industrial development and population, pressure on the environment has increased, particularly through the generation of organic waste and the contamination of water resources with toxic waste [1,2]. Of particular interest among these pollutants are the heavy metals, including lead (Pb), cadmium (Cd), copper (Cu), and nickel (Ni), due to their toxicity, non-biodegradability, and bioaccumulation in living organisms [3,4,5]. Excessive exposure to heavy metals in the long term may cause serious health problems, such as organ impairment, neurological problems, and cancer [3,6,7]. Conventional treatment methods, including ion exchange, chemical precipitation, electrochemical techniques, and membrane separation, often face limitations, such as high operational costs, limited removal at low concentrations, and the production of secondary waste streams [8,9]. These drawbacks highlight the need for cost-effective, efficient, and sustainable adsorbents for the remediation of heavy metals [1,10]. This has led to significant interest in biomass-based adsorbents, which are abundant, renewable, and have minimal environmental impact [11,12]. Hydrothermal carbonization (HTC) is a promising thermochemical route for as hydrochar [13]. In contrast to pyrolysis, which needs dry feedstocks and high temperatures, HTC is run in subcritical water and moderate temperatures (180–250 °C), which does not require energy-intensive drying [2,13,14,15]. The resulting hydrochar still possesses diverse oxygenated functional groups, versatile surface chemistry, and a porous structure, which is highly applicable to environmental applications, such as the adsorption of contaminants in aqueous systems [16,17,18].

Hydrothermal carbonization of hydrochar derived from agricultural waste has been used to remove heavy metals (including mixed metal ions) from water. The mechanism of metal ion adsorption, such as Cu (II), in hydrochar is due to surface functional groups, porosity, and ion-exchange capacity. In support of these efforts, hydrochar has recently been investigated as a potential adsorbent for the remediation of heavy metals, with prior research demonstrating its effectiveness in removing multi-metal ions and copper from water. This supports its application as a reliable and sustainable water treatment material, as demonstrated in this study. The adsorption results obtained in this study are consistent with previous studies on hydrochar produced from agro-waste, further supporting its application for Cu (II) remediation [19].

Moreover, converting agricultural residues, food waste, and other biomass streams into hydrochar is a viable way to manage waste sustainably and produce value-added products for water treatment [13], although the physicochemical characteristics are strongly influenced by the conditions of the process (carbonization temperature, residence time, and post-synthesis activation methods) [20,21,22].

Conventional optimization techniques, including the one-factor-at-a-time (OFAT) method, have limitations in modeling complex interactions among process parameters and, as a result, often yield suboptimal conditions [23,24]. The design of experiments (DOE) methodology, in contrast, offers a structured, statistically sound approach to simultaneously optimize multiple parameters, identify key factors, and reduce the number of experimental runs [25,26,27]. Not only does the use of DOE in hydrochar research improve process efficiency, but it also ensures the reproducibility and reliability of the optimized material properties.

Besides maximizing hydrochar production, this study conducted detailed characterization, which is necessary to understand its structural, chemical, and thermal characteristics and has a direct impact on its adsorption properties. Fourier-transform infrared spectroscopy (FTIR) was used to systematically characterize the optimized hydrochar to provide information on surface functional groups that dictate the interactions between metals [28,29,30]. Scanning electron microscopy (SEM) was used to provide information on surface morphology. X-ray diffraction (XRD) was used to assess the presence of crystalline and amorphous phases, while XRF was used to determine the elemental composition [31,32]. Thermogravimetric analysis (TGA), which determines the thermal stability and decomposition properties of hydrochar, is significant because this material is durable in practical applications [32,33,34], but it is not applied in this report. Integrating these characterization techniques allows for a holistic evaluation of hydrochar properties and facilitates correlation with adsorption performance.

In this study, hydrochar was synthesized from food waste and agricultural residues through 100 mL PTFE-lined hydrothermal synthesis manufactured by LabXSCI (Labxsci, online scientific equipment supplier), USA. Figure 1 illustrates the process of carbonizing hydrochar. The critical process parameters (carbonization temperature (180–250 °C) and residence time (2–6 h)) were optimized using a DOE-based approach. Lastly, their performance as adsorbents was evaluated in the removal of Cu²⁺ from aqueous solutions. The study is useful for the rational design and development of sustainable hydrochar-based adsorbents for environmental remediation. The research also assesses the impact of pH on the pattern of various samples using both the Langmuir and the Freundlich isotherm models. Adsorption data at pH 4, 5, and 6 were analyzed to establish optimal adsorption conditions that yield maximum adsorption efficiency and to identify a model that describes adsorption mechanisms under different pH conditions.

1.1. Experimental Design

Statistical Design of Experiments Using MINITAB 19

An experimental design is a detailed plan for conducting an experiment. DOE is the methodical way of establishing the connections between what influences a process and its result [27,35]. This investigates the concurrent effects of input variables (factors) on the output variable (response). It is primarily used to determine cause-and-effect relationships, which are critical for defining process inputs and maximizing the outcomes of an experiment.

In an experiment, a process factor or variable is intentionally manipulated to determine its effect on one or more response variables. DOE (design of experiments) is an effective process for designing experiments so that the collected data can be analyzed to yield valid, objective conclusions [36]. MINITAB is an effective statistical package commonly used to analyze data, improve processes, and control quality [37]. This paper used MINITAB 19 to perform statistical analysis, generate descriptive statistics, and visualize data trends. The software’s powerful computational capabilities enabled accurate data interpretation, supporting sound decision-making. To evaluate the impact of different process parameters on hydrochar yield, MINITAB 19 was used to conduct regression analysis and design of experiments (DOE). The software enabled the identification of the main influencing factors and ensured optimal process conditions [27,38].

2. Materials and Methods

2.1. Hydrochar Sample Preparation

Preparation of Biomass Feedstock: Food waste (FW) was obtained from the FAMU food pantry and the students’ cafeteria.

Hydrothermal Carbonization: Hydrochar was generated through hydrothermal carbonization in a batch stainless-steel autoclave reactor lined with PTFE (polytetrafluoroethylene) (LABXSCI 100mL PTFE-lined hydrothermal synthesis reactor) [39,40]. The raw biomass used was taken in a wet state to represent feedstock conditions. Before carbonization, the dry matter and moisture content were determined using the methods described by [41,42]. A fixed amount of feedstock was weighed out, combined with deionized water at a predetermined mass ratio of solid to liquid, and loaded into the reactor. The reactor was heated to the required temperature (180–250 °C) and held for 2–6 h, as indicated in the experimental design. Once it was completed, the reactor was left to cool down at room temperature. The solid product obtained was filtered, washed with deionized water until the pH was neutral, and then dried at 105 °C for 12 h. The produced hydrochar was ground and sieved to a particle size fraction less than 500 µm, and all experiments were performed under similar conditions, making them comparable [39,43].

2.2. Design of Experiments (DOE) and Optimization Procedure

The Response Surface Methodology (RSM) was used to optimize and determine the effect of two independent variables: carbonization temperature [180–250 °C] and residence time [2–6 h]. The CCD experiment was analyzed in MINITAB statistical software, and a second-order polynomial regression model was fitted to the data to describe the relationship between the process variables (temperature and time) and the response (dry hydrochar yield). The model accuracy, along with the coefficient of determination (R²), predicted R², adjusted R², and the standard error of regression were analyzed using analysis of variance (ANOVA). Statistical analysis was conducted to test the significance of the model, the interactions among the factors, and the optimal working conditions [36].

The experimental runs were generated using a central composite design (CCD) because it is effective for predicting second-order polynomial models and determining the optimal operating conditions.

• Central Composite Design [CCD]

Factors:	2	Replicates:	1
Base runs:	12	Total runs:	12
Base blocks:	1	Total blocks:	1
Two-level factorial: Full factorial
Cube points:	4
Center points in cube:	5
Axial points:	4
Center points in axial:	0
α: 1.41421

The experimental factors are presented in

Table 1. CCD for % yield composition.

Factors/Variables	Symbol	Minimum	Maximum
Time (hours)	X1	2	5
Temperature (°C)	X2	180	250

. This design was based on experimental results obtained and analyzed using CCD to fit quadratic polynomials, generating an equation correlating the DOE variables (X₁ and X₂).

The response variable (% yield) was fitted by a second-order polynomial to correlate the design variables (X₁, X₂), which are presented in the model below:

%Y = α₀ − α₁X₁ − α₂X₂ + α_1,1X₁X₁ + α_1,2X₁X₂ − α_2,2X₂X₂

(1)

The % hydrochar yield composition responses are represented by Y, which is associated with each factor level combination, while α₀, α₁, α₂, α_1,2, and α_2,2 are the regression coefficients. X₁ and X₂ are the factors, and X₁X₁, X₁X₂, and X₂X₂ are the interactions of the variables.

2.3. Batch Adsorption Experiments (Cu²⁺)

Chemical Preparation: A stock solution of Cu²⁺ was prepared from analytical-grade CuSO₄·5H₂O and diluted to the required concentration using the method described by [2,3]. All the chemicals were of analytical grade and used without further purification, and all experiments were performed in deionized water.

Batch adsorption experiments were conducted to assess the influence of pH on the uptake of Cu²⁺ by hydrochar [4,5]. In each run, 0.05 g of the food-waste-based adsorbent was placed in a centrifuge tube containing 10 mL of a solution. Then, 0.1 M HCl and 0.1 M NaOH were used to adjust the pH of the solutions to 4, 5, and 6, and a digital pH meter was used to measure the pH [6,7]. Equilibrium was achieved by agitation of the flasks in an end-over-end GLS-Col rotator at 70 rpm over 24 h at ambient temperature (25 ± 2 °C). The mixtures were filtered through a 0.2 µm filter, after which the supernatants/remaining Cu²⁺ concentration were analyzed using the Agilent 5800 inductively coupled plasma–optical emission spectroscopy, USA (ICP-OES) [2,8]. ICP-OES calibration standards were matrix-matched to the sample matrix to ensure accuracy. Experiments with blanks and controls were conducted to confirm adsorption.

2.4. Characterization Techniques

The identification of functional groups was performed using the JASCO FT/IR-6800 spectrometer (JASCO Corporation, Japan), which featured gold optical surfaces that enhanced FT-Raman analysis and fast scanning. Surface morphology was studied with the help of a JOEL JSM-IT800 SEM-EDS, (JEOL Ltd., Japan), at an acceleration voltage of 2–10 kV and an EDAX detector using a microscope with an energy dispersive analytical system. Characterization was performed using an X-ray fluorometer (Panalytical Epsilon 3 XL, rhodium light source, silicon drift detector) PANalytical/Malvern Panalytical (Netherlands/UK) to ascertain the elemental composition of the adsorbent produced. A powder X-ray diffractometer (Panalytical Xpert Pro MPD, copper or molybdenum light source, X’Celerator RTMS detectors) Malvern Panalytical/PANalytical (Netherlands/UK) was used to determine the amorphous and crystalline structure of the hydrochar samples. An ICP5000 Dual View Inductively Coupled Plasma (ICP-OES) manufactured by Agilent Technologies (USA) system was used to determine the concentration of metal in solution.

2.5. Adsorption Data Analysis

The adsorption capacity (q_e, mg g⁻¹) and percentage removal were calculated using standard mass balance equations. Adsorption equilibrium data were examined using isotherm models, such as the Langmuir and the Freundlich models, to explain adsorption behavior and surface heterogeneity [3,9,10].

Adsorption capacity per unit mass of adsorbent (equilibrium uptake) is calculated as follows:

$$\text{Adsorption} \text{capacity} q_e = {\displaystyle \frac{\left({\mathit{C}}_{\mathit{o}}-{\mathit{C}}_{\mathit{e}}\right)\mathit{V}}{\mathit{m}}} \text{(mg metal/g)}$$

(2)

$$\text{Removal (Efficiency)},\%\mathrm{R}={\displaystyle \frac{C_o-C_e}{C_o}}\ast 100$$

(3)

where:

$q_e$ = amount of adsorbed Cu²⁺ by hydrochar in mg/g;

m = adsorbent mass in mg;

V = volume of the solution in mL;

%R = removal efficiency of Cu²⁺ by the adsorbent;

$C_o$ = initial concentration of Cu²⁺ (ppm or mg/L);

$C_e$ = final concentration of Cu²⁺ (ppm or mg/L).

2.6. Calculating the Yield

Dry matter was determined by weighing the samples after heating them in an oven at 105 °C to a constant weight. The ratio of dried hydrochar to dried feedstock, based on dry mass, was used as the hydrochar yield. The initial mass of wet biomass was 40 g (30 percent dry matter, which is the same as 12 g dry feedstock). The recovered hydrochar was carbonized, washed, filtered, and dried at 105 °C to a constant weight.

The following equation was used to calculate dry hydrochar yield:

$$\text{Dry hydrochar yield} \text{(\%)} = {\displaystyle \frac{\text{Mass} \text{of} \text{dry} \text{biomas} (\text{after} \text{carbonization})}{\text{Mass} \text{of} \text{dry} \text{hydrochar} (\text{before} \text{carbonization})}}\ast 100$$

(4)

Since the starting mass of dry biomass was 12 g (calculated as 30 percent of 40 g wet biomass), this value was maintained for all the experimental runs.

3. Results & Discussion

3.1. Experimental Design Using CCD

Table 2. Experimental design for a two-level-factor response surface and predicted dry hydrochar yields using CCD.

Run	Time (Hours) (X1)	Temp (°C) (X2)	Dry Yield Experimental (%)	Predicted Yield %	Residual
1	5	250	9.30	9.280	0.0200
2	3.5	215	26.57	26.568	0.0019
3	1.38	215	36.16	35.849	0.3105
4	5.62	215	17.51	17.376	0.1335
5	3.5	215	26.57	26.568	0.0019
6	3.5	215	26.57	26.568	0.0019
7	2	250	23.05	23.000	0.0495
8	3.5	215	26.57	26.568	0.0019
9	5	180	49.00	48.884	0.1154
10	3.5	215	26.57	26.568	0.0019
11	3.5	166	72.65	71.529	1.1207
12	2	180	62.04	61.305	0.7348

shows the outcome of an RSM-based experiment to study the influence of time (X₁) and temperature (X₂) on the experimental yield. The low residual values and the close correlation between the experimental and predicted data indicate that the quadratic model provides a reasonable fit [11,12]. Most of the residuals are less than 1, indicating a small difference between the experimental and predicted values [13]. Temperatures 250 °C and above are found to have a negative influence on yield, as suggested in the literature [14,15]. The maximum experimental yield (72.65%) is at 3.5 h and 166 °C, implying that low temperatures and short reaction times favor yield [16].

The minimum yield (9.30%) occurs at 5 h and 250 °C, indicating that high temperature negatively affects yield. Runs at 3.5 h and 215 °C appear multiple times (runs 2,5, 6, 8, and 10) and consistently yield 26.57%, proving reproducibility [17,18]. The standard deviations of these replicated experiments are extremely low (0.0019), indicating the reliability of the experiments [19,20,21]. The low values of the residue across all experimental runs indicate a very good fit between the actual and expected yields. Overall, the model can be highly predictive and is applicable to the optimization and interpretation of the response surface [19,22,23].

3.1.1. Quadratic Regression Model

The experimental data were fitted to a second-order polynomial to explain the correlation between the variables (temperature and residence time) and hydrochar yield.

The uncoded regression equation is as follows:

Dry Yield (%) = 497.56 − 3.096(Time) − 3.7035(Temperature) + 0.0100(Time²) + 0.007369(Temperature²) − 0.00619(Time × Temperature)

(5)

While the coded version is:

Dry Yield (%) = 497.56 − 3.096[X₁] − 3.7035[X₂] + 0.0100[X₁²] + 0.007369[X₂²] − 0.00619[X₁X₂]

(6)

The negative linear coefficients for both temperature and time imply that as either factor increases, the yield of hydrochar decreases, while the positive quadratic coefficients affirm the curvilinear nature of the response surface [20,24,25]. This is typical of hydrothermal carbonization reactions: the harder the reaction, the greater the devolatilization and solubilization, and the lower the solid yield [26,27,28].

The temperature–time interaction term also indicates that the joint effect of a long residence time at high temperature accelerates biomass decomposition faster than the independent effects of the factors [29,30].

The difference between the experimental and predicted yields was small, indicating that the developed quadratic model was very successful in prediction. This close correspondence further confirms that the response surface model is sufficient to explain the relationship between temperature, residence time, and hydrochar yield.

3.1.2. Model Summary

The statistical parameters for assessing the adequacy of the developed quadratic model were analyzed using analysis of variance (ANOVA).

Table 3. Model summary statistics.

Statistic	Value
S	0.319
R2 (%)	99.98
Adjusted R2 (%)	99.97
Predicted R2 (%)	99.84

shows the model summary statistics.

This is demonstrated by the exceptionally large coefficient of determination (R² = 99.98), with virtually all variability in the dry hydrochar yield being accounted for by the model [20,31]. The fact that R², adjusted R², and predicted R² are almost identical indicates that there is no overfitting and that the model has high predictive reliability [32]. The extremely small standard error (S = 0.319) also shows the high accuracy of the model predictions [19,33].

3.1.3. Analysis of Variance (ANOVA)

Table 4. Analysis of variance (ANOVA).

Source	DF	Adj SS	Adj MS	F-Value	p-Value
Model	5	3707.34	741.47	7289.82	0.000
Linear	2	3372.90	1686.45	16,580.47	0.000
Time (h)	1	308.16	308.16	3029.66	0.000
Temp (°C)	1	3064.74	3064.74	30,131.29	0.000
Square	2	344.77	172.38	1694.81	0.000
Time (h) × Time (h)	1	0.00	0.00	0.03	0.864
Temp (°C) × Temp (°C)	1	343.13	343.13	3373.55	0.000
2-Way Interaction	1	0.42	0.42	4.15	0.088
Time (h) × Temp (°C)	1	0.42	0.42	4.15	0.088
Error	6	0.61	0.10	*	*
Lack-of-Fit	2	0.61	0.31	*	*
Pure Error	4	0.00	0.00	*	*
Total	11	3707.95		*	*

* Lack-of-fit test cannot be evaluated.

summarizes the ANOVA findings of the quadratic model. The total model was highly significant (p < 0.001), indicating that the regression equation involving the process variables and hydrochar yield is statistically meaningful [34,35]. Both temperature and residence time had statistically significant linear effects on the dry hydrochar yield (p < 0.001), with temperature accounting for the greatest proportion of the model’s sum of squares [36,37]. This means that temperature is the predominant parameter affecting hydrochar yield within the investigated design space [36,38].

The quadratic term for temperature was also highly significant (p < 0.001), indicating a high curvature in the response surface and justifying the application of a second-order model [39]. The quadratic term for time, on the other hand, was not significant (p = 0.864), indicating that time primarily influences yield through its linear effect [20,36].

3.1.4. Lack-of-Fit Analysis

The lack-of-fit test compares the variation of the model residuals with the pure experimental error estimated from replicated center points [20]. The lack of fit in this research was not significant relative to the pure error, indicating that the quadratic model is sufficient to explain the experimental data within the factor ranges under investigation [20,40]. The presence of insignificant error also indicates that the experiments were highly reproducible and that the fitted model was reliable [19,34].

Figure 2 shows the parity plot of the experimentally measured hydrochar yield under dry conditions versus the response surface model prediction. The slope of the regression equation (y = 0.9829x + 0.3681) is near unity, and the intercept is insignificant, indicating strong consistency and minimal bias in prediction [41]. The extremely high coefficient of determination (R² = 0.9999) indicates that the model captures the relationship between process variables and yield in the experimental domain. The close clustering of data points around the fitted line also indicates the strength and predictive appropriateness of the developed quadratic model, as indicated by the high R², adjusted R², and predicted R² values obtained in the model statistics.

Figure 3 presents a 3D response surface plot illustrating the combined effect of temperature and residence time on dry hydrochar yield. It is evident that yield decreases with increasing temperature and time, showing a clear downward trend; more severe hydrothermal conditions yield lower solid yields. This is in line with the gradual breakdown of biomass components during hydrothermal carbonization, in which higher temperature and residence time lead to greater hydrolysis, decarboxylation, and dehydration reactions, and, accordingly, greater transformation of solid biomass into soluble and gaseous products. The results of [28,42,43] support this report.

The moderate temperature effect illustrates the strong quadratic effect observed in the ANOVA results. The yield decline is more pronounced above 200 °C, indicating that temperature has a stronger effect on hydrochar yield than residence time in the examined temperature range [43,44].

Figure 4 shows a contour plot that visually represents the distribution of hydrochar yields across the design space and identifies areas with low and high yields. The smooth levels of contours improve the visualization of yield distribution in the design space. The yield of dry hydrochar is also affected by temperature and residence time, and it is observed that the severity of carbonization significantly impacts solid retention [42,43]. The diagonal orientation of the contour lines indicates that two variables interact, with temperature having a stronger impact, consistent with ANOVA findings. Optimal yield (>70%) is observed at temperatures below about 175 °C and residence times below 3 h, which closely match the numerically optimized conditions. Nevertheless, the highest yield is not a sure sign of optimal material performance, which underscores the need for further hydrochar characterization. The smooth and elliptical form of the contour lines indicates stable system behavior, further supporting the adequacy of the quadratic response surface model [45,46]. The lack of sharp ridges or discontinuities indicates that the experimental region was appropriately selected and that neither an abrupt phase change nor an uncontrolled reaction occurred under the conditions studied.

3.1.5. Optimization Solution

The desirability of 1 can be observed in

Table 5. Optimal HTC conditions for maximum dry hydrochar yield.

Time (h)	Temperature (°C)	Predicted Dry Yield (%)	Composite Desirability
2.80	165.5	71.53	1.000

, which shows the optimal score of the optimization, that is, MINITAB determined these conditions as optimal according to the model [47,48,49]. Increasing temperature and additional time of carbonization influence the yield of hydrochar, which depends on the conditions of the hydrothermal carbonization (HTC) process, although in general, the higher the temperature, the less hydrochar is yielded as biomass, and volatile components are more likely to be degraded, while oxygen-containing functional groups are degraded to produce gases (CO₂, CO, CH₄) and liquid-phase products, reducing the solid hydrochar yield [44,50]. Increased temperatures favor dehydration, decarboxylation, and demethanation, converting more of the original biomass into bio-oil and gases, thereby lowering hydrochar formation [51,52,53]. The degradation of lignin, hemicellulose, and cellulose occurs at various temperatures, with higher temperatures resulting in faster degradation and lower hydrochar yields. Higher temperature lowers the yield of hydrochar but raises carbon content and improves fuel properties (high fixed carbon, low oxygen content) [44,54,55].

The longer the carbonization time, the lower the hydrochar yield; however, this effect occurs more gradually than with temperature [14,55,56]. The longer the residence time, the more the organic matter is broken down, resulting in more gas and liquid formation and, thus, less solid hydrochar [14,57]. Long carbonization enhances repolymerization and secondary decomposition, forming more carbon-rich but lower-yielding hydrochar [58]. A longer reaction time enhances aromatization and graphitization, thereby improving the quality of hydrochar at the expense of the quantity [58].

3.1.6. Optimal Conditions for Maximum Yield of Dry Hydrochar

In the design space, the optimization process found one optimum. Table 5 summarizes the optimum operating conditions and the response predicted.

The composite desirability of 1.000 shows that the optimization goal was achieved perfectly and that the optimal solution is within the experimental space. The maximum yield of 71.53% is predicted under mild hydrothermal conditions, characterized by relatively low temperature and short residence time [36].

3.2. Adsorption Isotherm Models

Based on

Table 6. The samples are selected for the characterization and adsorption study.

Sample ID	Description	Reason for the Selection
A	Food waste was carbonized at 166 °C for 3.5 h	Lowest temperature and the highest dry hydrochar yield
B	Food waste was carbonized at 215 °C for 1.35 h	Lowest residence time
C	Food waste was carbonized at 215 °C for 3.5 h	Most occurring
D	Food waste was carbonized at 250 °C for 5 h	Highest temperature and lowest yield

, only 4 samples were selected from the 12 optimized runs for characterization and adsorption processes. These samples were analyzed before and after Cu²⁺ adsorption to monitor the effects of temperature, residence time, and pH. This methodology recognizes that hydrochar production optimization is directly linked to its functional application, thereby enhancing the study’s practical significance [14,59]. The pH values [4,5,6] were selected to achieve metal stability in solution and to limit the formation of metal hydroxide precipitates.

It was found that the critical factors that determined adsorption performance were the solution pH [60]. Competition between protons and metal ions for the active sites at low pH inhibited adsorption. The deprotonation of surface functional groups by increasing pH facilitated electrostatic attraction and complexation of metal ions, thereby increasing adsorption capacity [61,62]. The pH was kept within a moderately acidic range to make sure that the removal was due to adsorption rather than metal hydroxide precipitation. The optimal pH range (4–6) provided maximum adsorption and maintained the metal ions in a soluble state, supporting the reliability of the mechanism and the precise interpretation of the isotherm [63,64].

The equilibrium adsorption data for Cu²⁺ on food-waste-derived hydrochar at pH 4, 5, and 6 were fitted to both the Langmuir and the Freundlich isotherm models. The Langmuir model assumes that the adsorption process is a monolayer on a homogeneous surface, and this model is expressed as:

• Langmuir Model

$$\text{Linear} \text{form:} {\displaystyle \frac{C_e}{qe}}={\displaystyle \frac{1}{Q_{max}b}}+{\displaystyle \frac{C_e}{Q_{max}}}$$

(7)

The regression equation from Equation (7) provided the slope, intercept, and $R^2$ (Q_max and b (K_L), respectively).

• The Langmuir Separation Factor, $R_L$

$$R_L={\displaystyle \frac{1}{1+{bC}_o}}$$

(8)

where:

Ce is the equilibrium concentration (mg/L);

qe is the amount adsorbed per unit mass of adsorbent (mg/g);

Q_max is the maximum adsorption capacity (mg/g);

b or K_L is the Langmuir constant related to energy (L/mg).

• Freundlich Model

The Freundlich model describes adsorption on a heterogeneous surface and is given by Equation (9):

$$\text{Linear} \text{form:} {logq}_e = {logK}_F+{\displaystyle \frac{1}{n}}{logC}_e$$

(9)

where K_F is the Freundlich constant indicating adsorption capacity, and n is the heterogeneity factor.

The regression equation from Equation (9) provided the slope, intercept, and $R^2$ (n and K_F, respectively). Linear regression was used to determine the model parameters and correlation coefficients (R²), allowing for comparison of the model fit across different pH levels.

Model Fits for Samples A–D

R_L is a key parameter from the Langmuir isotherm that indicates whether adsorption is favorable under the given conditions. The R_L values at all pH levels and concentrations are presented in Figure 5, which confirms the favorable adsorption of Cu²⁺, with pH 4 showing the most favorable condition (R_L = 0.345), but with a reduced capacity and a strong binding affinity. These are consistent with the general trend of carbonaceous absorbents, with pH determining the surface charge and metal speciation [65]. As the R_L decreases and the initial concentration (Co) increases, adsorption becomes more favorable at higher concentration [66]. The high R_L at pH 6 exhibits a good capacity but a low binding affinity [67]. This is consistent with the trend observed in Q_max.

Table 7. Adsorption isotherm summary for sample A.

Sample A	Langmuir Model				Freundlich Model				Best Fit Model
pH	Qmax (mg/g)	${\mathit{K}}_{\mathit{L}}$ (L/mg)	R2	RSME	n	${\mathit{K}}_{\mathit{F}}$	R2	RSME
4	1.57	0.38	0.9427	0.236	2.35	0.41	0.7443	0.308	Langmuir
5	2.38	0.16	0.9858	0.122	2.21	0.47	0.8973	0.236	Langmuir
6	2.96	0.10	0.9848	0.112	1.87	0.40	0.9170	0.236	Langmuir

,

Table 8. Adsorption isotherm summary for sample B.

Sample B	Langmuir Model				Freundlich Model				Best Fit Model
pH	Qmax (mg/g)	${\mathit{K}}_{\mathit{L}}$ (L/mg)	R2	RMSE (mg/g)	n	${\mathit{K}}_{\mathit{F}}$	R2	RMSE
4	3.055	0.0171	0.6984	0.0693	2.39	0.363	0.9605	0.4802	Freundlich
5	3.77	0.0230	0.0451	0.9587	1.41	0.137	0.096	0.9771	Poor fit
6	5.46	1.50	0.9984	0.3744	2.77	2.61	0.7272	1.3581	Langmuir

,

Table 9. Adsorption isotherm summary for sample C.

Sample C	Langmuir Model				Freundlich Model				Best Fit Model
pH	Qmax (mg/g)	${\mathit{K}}_{\mathit{L}}$ (L/mg)	R2	RMSE	n	${\mathit{K}}_{\mathit{F}}$	R2	RMSE
4	1.854	0.5477	0.8532	0.7709	7.00	1.18	0.0705	0.6732	Langmuir
5	0.923	−17.50	0.9403	335.99	48.31	0.787	0.0062	0.2020	Langmuir
6	5.48	1.41	0.9938	0.5020	3.85	2.83	0.8656	0.5752	Langmuir

and

Table 10. Adsorption isotherm summary for sample D.

Sample D	Langmuir Model				Freundlich Model				Best Fit Model
pH	Qmax (mg/g)	${\mathit{K}}_{\mathit{L}}$ (L/mg)	R2	RMSE	n	${\mathit{K}}_{\mathit{F}}$	R2	RMSE
4	0.836	−0.228	0.9188	1.2249	14.49	1.30	0.0755	0.4829	Langmuir
5	1.973	0.655	0.9383	0.4025	8.15	1.28	0.5804	0.2821	Langmuir
6	2.17	−1.58	0.9934	3.5313	6.14	1.59	0.5628	0.4511	Langmuir

summarize the adsorption mechanism observed in the samples.

Langmuir Isotherm: In sample A, Figure 6, the adsorption capacity (Q_max) increases with pH, which means stronger adsorption at a higher pH of 6. This implies that Cu²⁺ binds better at higher pH, which can be attributed to less competition from H+ ions and greater availability of deprotonated functional groups such as -OH and -COOH. The Langmuir affinity constant (K_L) decreases with increasing pH, while capacity increases [68,69]. This implies that, at elevated pH, the adsorption of Cu²⁺ is high, but the binding affinity per site is weak [70].

The Freundlich isotherm (Figure 7) exhibitsmoderate to high correlation (R² = 0.74–0.92) and n values greater than 1, indicating good adsorption behavior across all pH conditions. Nevertheless, the higher correlation coefficients (R² > 0.94) observed for the Langmuir model imply that monolayer adsorption on a homogeneous surface prevailed throughout the adsorption process [71]. The adsorption intensity parameter, n > 1, at all pH levels also confirms favorable adsorption behavior. The n values were high at pH 4, indicating stronger interactions between the sites at acidic pH. This could be due to the increasing electrostatic attraction of Cu²⁺ ions and protonated surface groups [72,73]. With a high R² (>0.94), a homogeneous surface, and monolayer adsorption, with a finite number of active sites, the model provided a good fit to the adsorption data for sample A across pH levels [74,75]. The Freundlich adsorption intensity parameter, n, is greater than 1, indicating that adsorption is favorable; a decrease in pH shows that the surface is more heterogeneous [76].

The Freundlich constant K_F appears to be relatively pH-independent, which might indicate that the overall adsorption capacity of sample A was not very pH-sensitive in the Freundlich model. Nevertheless, the increasing R² values at higher pH indicate that surface heterogeneity increases as functional groups deprotonate, enabling multilayer or variable-energy site adsorption [77,78].

Mechanistically, sample A behaves as a largely homogeneous adsorbent with increasing capacity at high pH, consistent with monolayer adsorption and surface deprotonation.

Root-mean-square error (RMSE) was used to further test the goodness-of-fit of the adsorption models. The Langmuir model produced lower RMSE than the Freundlich model, indicating better agreement with the experimental and predicted adsorption capacities. The goodness-of-fit test based on the root mean square error (RMSE) also supported the superiority of the Langmuir model. The Langmuir isotherm had a lower RMSE (0.236 mg/g) than the Freundlich model (0.308 mg/g) at pH 4, indicating that the Langmuir model better predicts the experimental adsorption data.

Sample B (Figure 8) exhibited a very strong pH dependence, which was presumably due to a change in surface chemistry and speciation of Cu²⁺ [79]. In the case of the Langmuir isotherm, Q_max also increases with increasing pH, indicating that Cu²⁺ binds more favorably at higher pH. At pH 4, adsorption efficiency, R², Q_max, and a weak K_L were all very low; this could be due to surface protonation and competition between H+ ions and the adsorption process. Both models failed at pH 5, with R² very low (0.045) and poor linearity. This indicates that heterogeneous or multilayer adsorption could be controlling at the pH of 5 [80]. The model exhibited a strong fit (R² = 0.9984) at pH 6, a good Q_max of 5.46 mg/g, and a strong K_L of 1.5 L/mg. The R_L (0.118) indicates favorable adsorption and monolayer coverage on energetically favorable homogeneous sites.

The Freundlich model for Sample B (Figure 9) showed clear pH-dependent adsorption behavior, with a stronger fit at pH 4 (R² = 0.9605, favorable n = 2.39, and moderate K_F = 0.363). This indicates that adsorption occurs on a heterogeneous or multilayer surface with variable-energy sites. The Freundlich model failed, with R² = 0.096, K_F = 0.137, and n = 1.41 at pH 5, indicating unreliable, weak adsorption properties. This can be attributed to transitional surface chemistry, in which neither protonation nor deprotonation dominates, leading to inconsistent Cu²⁺ uptake, a poor model fit, and instability in the adsorption–desorption equilibrium [81].

An average fit was obtained at pH 6 (R² = 0.7272), strong K_F, and n values of 2.61 and 2.77, respectively. This likely indicates multilayer adsorption on a more activated surface, consistent with increased deprotonation and stronger Cu²⁺ complexation [81].

In general, sample B exhibits ideal Freundlich behavior at pH 4; the model fits well and shows a favorable adsorption intensity. These results complement the Langmuir findings, supporting the conclusion that, at low pH, adsorption mechanisms shift from heterogeneous multilayer behavior to more uniform monolayer adsorption at high pH [82,83].

A high pH-dependent adsorption is also exhibited in the Langmuir isotherm of sample C. The Langmuir fit at pH 4 was also good (R² = 0.8532), with a moderate Q_max = 1.855 mg/g and K_L = 0.5472 L/mg, indicating effective adsorption even in the presence of partial surface protonation [84].

At a pH of 5, the R² value was high (0.9403), but the negative intercept (−17.50) suggests that the Langmuir assumptions were violated (Figure 10), either due to experimental variability or non-ideal adsorption behavior. The estimated Q_max (0.923 mg/g) and negative K_L indicate that the model is not reliable for describing the adsorption mechanism at this pH.

The model exhibited an excellent fit (R² = 0.9938) at pH 6, resulting in a high maximum adsorption capacity (Q_max = 5.485 mg/g) and a high affinity constant (K_L 1.412 L/mg). The R_L value of 0.124 indicates very good adsorption, suggesting that the monolayer covers homogeneous high-energy sites [85].

The Freundlich model that fits sample C (Figure 11) indicates a highly variable adsorption behavior across pH values. This model failed to capture the data because R² is too low, implying that K_F (1.18) and n (7.00) do not reflect a strong adsorption intensity at pH 4. This discrepancy might have arisen due to site saturation effects or non-ideal behavior. At pH 5, the Freundlich model likewise failed, with R² = 0.0062, an excessively large n = 48.31, and a low K_F = 0.787, indicating that the model was unreliable in estimating the parameters and was likely to break down. This indicates that adsorption at pH 5 can be controlled by mechanisms beyond the Freundlich model, such as site-specific interactions or competition.

In general, sample C exhibits an ideal Freundlich isotherm at pH 6, consistent with enhanced surface activation and favorable adsorption conditions. The poor fits at pH 4 and 5 support caution when interpreting the Freundlich parameters with low R² values.

The model produced a strong fit (R² = 0.8656), a favorable n = 3.85, and a moderate K_F = 2.83. These values indicate multilayer adsorption on a heterogeneous surface, likely facilitated by surface deprotonation and increased Cu²⁺ complexation.

Altogether, sample C shows optimal Cu²⁺ adsorption at pH 6, consistent with increased surface deprotonation and stronger electrostatic interactions. The Langmuir model is a good model for describing monolayer adsorption in both acidic and alkaline solutions, but it has limitations at intermediate pH values.

For sample D (Figure 12), the Langmuir isotherm fit was linear with all the pH levels. Strong model fit was observed at pH 4, and the negative K_L (−0.228) confirms the affinity constant and the R_L values. Low Q_max indicates the degree of monolayer adsorption, though the model may not capture the underlying mechanism.

The Langmuir model performed well at pH 5 (R² = 0.9383), with a moderate Q_max (1.973 mg/g) and a positive affinity constant (b = 0.6547 L/mg), yielding an R_L value of 0.234, indicative of favorable adsorption. This indicates that sample D exhibits optimal Langmuir behavior at pH 5, with homogenous site coverage and strong Cu²⁺ binding. The model showed an excellent fit (R² = 0.9934) and high Q_max (2.169 mg/g) at pH 6, indicating efficient monolayer adsorption [74,86]. This sample showed weak to moderate adsorption behavior, as indicated by the Freundlich model across pH values. At pH 5, the model provided the best fit (R² = 0.5804), with n = 8.15 and K_F = 1.28 mg/g (L/mg¹/ⁿ). Such values imply good adsorption on a heterogeneous surface, where partial deprotonation of functional groups and active sites becomes more accessible [84]. At pH 6, the model was also comparable (R² = 0.5628), with K_F = 1.59 and n = 6.14, indicating good adsorption. This implies multilayer adsorption on variable-energy sites, which aligns with the increase in surface activation at higher pH. At pH 4, the Freundlich model (Figure 13) performed poorly (R² = 0.0755), despite a high n = 14.49 and K_F = 1.30. The highly inflated intensity value and low correlation coefficient indicate that parameter estimation is not feasible, likely due to the dominant protonation of surface sites and decreased uptake of Cu²⁺.

Generally, sample D exhibits positive Freundlich behavior at pH 5 and 6, although the low R² values across all conditions indicate that the Langmuir model is a better fit for this sample.

3.3. Study of the Physicochemical Properties of Hydrochar

As pH 6 yielded the best Cu²⁺ uptake and the most acceptable adsorption parameters, the hydrochar in its crude state and the post-adsorption sample at pH 6 were characterized to elucidate the predominant removal mechanisms under these optimal conditions. Although numerical optimization identified mild hydrothermal conditions (165.5 °C and 2.8 h) as optimal for maximizing hydrochar yield, maximum yield is not always the best indicator of material performance. Hydrochar formed under very mild conditions can have a high percentage of uncarbonized biomass components, leading to lower aromaticity, reduced structural stability, and fewer surface functional groups. Thus, based on the optimized operating conditions, the produced hydrochar was subjected to comprehensive physicochemical characterization to assess the impact of hydrothermal treatment on its material properties. Characterization methods included FTIR, XRD, XRF, and SEM. Such analyses provide a critical understanding of the structural and chemical characteristics of the optimized hydrochar and establish a direct link between processing conditions and material properties.

3.3.1. FTIR—Fourier-Transform Infrared Spectroscopy

The JASCO 6800 FT-IR Spectrometer was used for this analysis. The spectra were baseline-corrected in the instrument software, and the data were plotted in OriginPro. Spectral normalization was performed and displayed in the 4000–500 cm⁻¹ range. A comparative analysis of the hydrocar obtained was performed to identify changes in the functional groups.

Figure 14 shows that hydrothermal carbonization enhances the formation of oxygen-containing functional groups (such as hydroxyl, carbonyl, and carboxyl groups) on the hydrochar surface, which are essential for the adsorption and binding of metal ions [87,88]. The FTIR results showed that the hydrothermal carbonization temperature had a profound effect on the surface chemistry of the four hydrochar samples and, in turn, on their interaction with Cu²⁺ ions.

Broad peaks related to C-H stretching (around ~2920 cm⁻¹) show slight decreases in intensity after adsorption for all samples, indicating limited participation of aliphatic functional groups in adsorption. The band at ~2160 cm⁻¹ (C≡H/C≡C related vibrations) exhibits little change, suggesting minimal involvement of these groups in ion adsorption [89].

Significant changes are evident in the functional group region (1700–1000 cm⁻¹) that is important for adsorption processes. The C=O stretching vibration (~1700 cm⁻¹) exhibits a minor shift and to carbonyl groups, likely via complexation. Likewise, the C-C vibrations (~1480 cm⁻¹) show slight variations in intensity, implying potential structural modifications or indirect adsorption participation. The largest change occurs in the C–O stretching region (~1020 cm⁻¹), where a substantial decrease in intensity and a slight broadening of the peak are observed after adsorption in all samples. This suggests that the oxygen-containing functional groups, such as hydroxyl and ether groups, are involved in binding with metal ions, most likely through ion-exchange and coordination reactions [90].

A closer examination of the pre- and post-adsorption spectra of samples A–D shows subtle but systematic changes, indicating binding between Cu²⁺ ions and surface functional groups. While the FTIR spectra are quite similar, there are slight shifts, intensity changes, and peak broadening, especially in the O-H, C=O, and C-O regions, which indicates their participation in metal binding. For sample A, intense O–H and C-O bands and broad carbonyl peaks suggest a highly functionalized surface with hydroxyl, phenolic, and ether groups. The decrease in O–H intensity following Cu²⁺ adsorption indicates that surface hydroxyl functional groups are involved in binding via hydrogen bonding, deprotonation and/or surface complexation. The decrease in the C-O and carbonyl bands also indicates that oxygen-functional groups are major binding sites for Cu²⁺ [91]. Similar behavior was observed in sample B, but with lower O–H and C–O intensities, indicating that the sample has undergone gentle thermal condensation. Still, adsorption-induced changes were observed in these regions, showing that hydroxyl, phenolic, and carbonyl coordination were still observed. Sample C, produced at a higher hydrothermal temperature, showed a further decrease in O-H/C-O signals, with a more distinct carbonyl and aromatic (C=C) peak. Following adsorption, the most obvious changes were observed in the carbonyl region, indicative of a shift toward carbonyl-dominated Cu²⁺ binding as hydroxyl sites became saturated [92]. Sample D, derived from the highest hydrothermal temperature, had a more condensed carbon structure, with weak O–H and C–O peaks and strong carbonyl/aromatic peaks. Similarly, changes after adsorption were mostly confined to the C=O and aromatic C=C regions, suggesting that Cu²⁺ coordination was mainly through carbonyl and π-electron-rich aromatic groups, but not through hydroxyl groups. In summary, while FTIR changes after Cu²⁺ adsorption are minor, comparison of the FTIR spectra after adsorption reveals that the primary interaction between Cu²⁺ and the carbon samples is with oxygen-containing functional groups. The subtle shifts and intensity changes in the O-H, C=O, and C-O regions (highlighted in the spectra) suggest the formation of inner-sphere surface complexes. Similar trends in all samples suggest that the adsorption process is consistent and involves surface complexation and ion exchange. Crucially, the type of active adsorption sites changes with increasing hydrothermal temperature: the hydrochar obtained at lower temperatures (samples A and B) mainly uses hydroxyl and phenolic groups, whereas those at higher temperatures (samples C and D) mainly use carbonyl and aromatic groups. These shifts in surface chemistry with increasing hydrothermal temperature account for the differences in Cu²⁺ adsorption and offer a mechanistic basis for the correlation between hydrothermal conditions and Cu²⁺ adsorption [93,94].

In general, the FTIR results demonstrate that Cu²⁺ adsorption on all samples occurred through inner-sphere complexation with oxygen-containing functional groups; however, the dominant binding sites changed with increasing hydrothermal temperature [95]. Lower-temperature hydrochar (samples A and B) relied on hydroxyl and phenolic groups, while higher-temperature materials (samples C and D) relied more on carbonyl and aromatic structures. This temperature-dependent development of surface chemistry explains why Cu²⁺ uptake differs and provides a mechanistic rationale for associating the hydrothermal processing conditions with adsorption performance [92]. The changes in the fingerprint region also demonstrate the development of surface complexes between the metal ions and oxygen-containing functional groups on the hydrochar.

3.3.2. XRD Analysis

Figure 15 shows the diffraction pattern of samples A–D prior to and following adsorption. Copper K-alpha radiation (20 = 1.5406) was used for analysis, with a scanning range of 10–70 (2). All samples show a broad diffraction hump in the range of about 10° to 25° (2θ), typical of amorphous carbon structures. This broad band indicates that the hydrochar contains an extremely disordered carbon matrix with a low degree of graphitization, a characteristic of materials produced by hydrothermal carbonization of biomass [93,94]. The presence of amorphous carbon is beneficial for adsorption processes because it provides abundant surface defects and active sites that enhance adsorption performance [95,96].

In addition to the amorphous band, there were also clear diffraction peaks at around 29.4°, 39.4°, 43.1°, 47.5°, and 64.5° (2θ). The diffraction peaks are compared with standard reference patterns in the ICDD Powder Diffraction File, which shows that most of the peaks are primarily attributed to calcite (CaCO₃) and correspond to crystallographic planes (104), (113), (202), and (300) [97,98]. The presence of calcite indicates that calcium inorganic components in food waste feedstock were retained throughout the hydrothermal carbonization process and crystallized as calcium carbonate minerals [99]. This is consistent with XRF results showing high calcium content in the samples. Other mineral phases with minor contributions to the composition (e.g., quartz, SiO₂) and alkali salts (e.g., NaCl and KCl) can also exist, indicating the heterogeneous nature of the food waste precursor.

A comparison of patterns pre- and post-adsorption shows no significant changes in peak positions or the appearance of new peaks, indicating that the mineral‘s crystalline phases remained stable. This implies that the amorphous carbon matrix binds to the adsorbent mainly at the surface, rather than by forming new crystalline structures [93].

In general, the XRD findings indicate that the hydrochar materials consist predominantly of amorphous carbon with crystalline calcium minerals, and that the adsorption process does not significantly alter the structural framework of the hydrochar.

3.3.3. Elemental Composition and Mineral Oxides (XRF)

An X-ray fluorometer (Panalytical Epsilon 3 XL, rhodium light source, silicon drift detector) was used to characterize samples A–D pre- and post-adsorption; see

Table 11. Elemental composition of samples A–D before and after Cu²⁺ adsorption.

Sample	Ca (%)	K (ppm)	P (%)	S (%)	Si (ppm)	Al (ppm)	Mg (ppm)	Fe (ppm)	Cu (ppm)
A Before	1.396	386.1	0.173	1.036	962.6	109.3	9.1	824.3	Native
A After	0.504	219.4	0.168	1.275	1420	192.2	1.5	748.4	↑ Cu
B Before	9.070	156.2	0.847	0.494	532.4	126.9	37.9	376.5	Native
B After	4.811	123.0	0.350	0.540	779.8	96.8	15.1	373.6	↑ Cu
C Before	14.55	247.8	1.310	0.399	590.9	147.6	148.2	726.7	Native
C After	13.79	136.7	0.723	0.416	639.2	87.6	30.5	401.0	↑ Cu
D Before	2.35	304.0	0.305	0.470	879.5	69.1	9.6	377.1	Native
D After	2.345	132.2	0.315	0.400	742.3	73.9	17.1	265.2	↑ Cu

Notes: “Native” = pre-existing Cu in the hydrochar (not from adsorption). “↑ Cu” = Cu increased due to adsorption (solid-phase confirmation). Ca, K, P, S, Si, Al, Mg, and Fe are retained because they influence adsorption mechanisms.

and

Table 12. Oxide composition of samples A–D before and after Cu²⁺ adsorption.

Sample	SiO2 (ppm)	Al2O3 (ppm)	MgO (ppm)	P2O5 (%)	SO4 (%)	K2O (ppm)	CaCO3 (%)	Fe2O3 (ppm)
A Before	962.6	109.3	9.1	0.173	1.036	386.1	1.396	824.3
A After	1420	192.2	1.5	0.168	1.275	219.4	0.504	748.4
B Before	532.4	126.9	37.9	0.847	0.494	156.2	9.070	376.5
B After	779.8	96.8	15.1	0.350	0.540	123.0	4.811	373.6
C Before	590.9	147.6	148.2	1.310	0.399	247.8	14.55	726.7
C After	639.2	87.6	30.5	0.723	0.416	136.7	13.79	401.0
D Before	879.5	69.1	9.6	0.305	0.470	304.0	2.35	377.1
D After	742.3	73.9	17.1	0.315	0.400	132.2	2.345	265.2

.

XRF results revealed that the hydrochar contained high levels of mineral-related elements prior to adsorption, especially Ca, K, P, S, Si, Al, Mg, and Fe. These elements correspond to key mineral phases, like calcite (CaCO₃), sylvite (KCl), quartz (SiO₂), and aluminosilicates. Following the exposure to Cu (II), there were significant reductions in Ca and K in all the samples, particularly in the Ca-rich samples B and C, as well as the K-rich samples A and D. These reductions indicate strong Ca²⁺ → Cu²⁺ and K⁺ → Cu²⁺ ion-exchange reactions. Reduction in phosphorus was also reported in samples B and C, suggesting phosphate-mediated Cu binding, whereas Si and Al increased slightly due to the concentration effects of organic matter loss. All samples showed an increase in solid-phase Cu, confirming the retention of Cu on the hydrochar surface after adsorption.

Altogether, the XRF, XRD, and FTIR findings revealed a consistent adsorption mechanism: ion exchange (mineral-driven), in which Ca²⁺ and K⁺ are substituted by Cu²⁺. This is confirmed by the XRF results, which show reduced Ca and K levels. The XRD indicates that the peaks of calcite and sylvite are weakening, whereas FTIR shows a slight shift in the carbonate band. Surface complexation is the second mechanism revealed when Cu interacts with O–H, C=O, and C–O groups. The FTIR shifts and the lack of crystalline Cu phases in XRD support this. Lastly, there is the phosphate-mediated binding, where P decreases in XRF and the P-O bands shift in FTIR, notably in samples B and C. Si and Al increase due to organic matter loss, consistent with the stable quartz peaks in XRD. All these pathways indicate that hydrochar possesses a synergistic combination of mineral-exchange sites and reactive functional groups, enabling efficient Cu (II) removal.

3.3.4. SEM-EDS Analysis

Surface Morphology Before Adsorption (Pristine Samples)

SEM micrographs revealed distinct baseline morphologies across the samples (A–D) analyzed, showing differences in carbon structure and mineral inclusions.

Sample A [Figure 16(A1)] displayed a compact carbon structure with layered domains and scattered embedded particulates. Sample B [Figure 16(B1)] exhibited a porous, loosely aggregated carbon network with large, interconnected voids and scattered spherical particles, indicating high pore accessibility. Sample C [Figure 16(C1)] exhibited a fibrous and open network with long strands and globular inclusions scattered on the surface. Sample D [Figure 16(D1)] consisted of well-defined, smooth microspheres spread across the surface, indicating an ordered morphology with an open, accessible surface characteristic. These microspheres are also typical of hydrothermal carbonization products, and they increase the available surface area for adsorption. These morphological characteristics indicate that all samples have available surface areas and pore structures that can interact with Cu(II) through both surface complexation and ion-exchange mechanisms [100,101].

Surface Morphology Post-Adsorption

After Cu (II) adsorption, morphological changes became evident in all samples and were consistent with surface deposition and structural transformation. Sample A [Figure 16(A2)] formed a more heterogeneous surface, with fragmented carbon sheets, granular aggregates, and mineral-like clusters overlaying the matrix. Sample B [Figure 16(B2)] transitioned to a more consolidated, fibrous structure, roughened strands, and particulate deposits that bridged or narrowed pores, suggesting microscale deposition of adsorbed species. Sample C [Figure 16(C2)] showed widespread deposition of irregular aggregates along the fibrous network, giving it a roughened, coated appearance.

For sample D, [Figure 16(D2)] Cu (II) adsorption resulted in a significant change in surface morphology. Discrete micro-spherical structures were mostly obscured, and the surface was rough, irregular, and highly agglomerated. The implication of this change is that there was significant surface coverage and potential deposition of Cu-bearing species onto the hydrochar. Moreover, the increased compactness and disappearance of well-defined structures are indicators of pore blocking and structural rearrangement during the adsorption process. Such morphological changes demonstrate that adsorption of Cu (II) is not merely a surface-level interaction with functional groups but can also result in physical deposition and aggregation on the hydrochar surface. The changes observed are consistent with adsorption processes involving surface complexation and potential precipitation, leading to total removal efficiency [102,103].

EDS Analysis Pre-Adsorption

EDS analysis focused on the most significant functional elements relevant to adsorption: C and O from the hydrochar matrix; K, Na, Mg, Al, Si, and Fe, representing mineral-related and exchangeable cations; and Cu, the adsorbate of interest. The selection of these elements is based on their direct support of ion-exchange and surface-complexation processes. Pre-absorption EDS spectra identified the carbonaceous nature of all samples, with predominant C and O peaks indicative of the hydrochar matrix. These elements represent the remnants of salt and mineral phases identified by XRF (e.g., K-bearing salts, Fe-oxides, Mg-bearing minerals). Their presence indicates the potential for ion exchange and mineral-assisted adsorption during Cu (II) uptake.

Post-Adsorption EDS Analysis

Following exposure of the samples to Cu (II), all samples showed the appearance of Cu (II) peaks not observed in the pre-adsorption spectra, indicating successful Cu (II) uptake. The emergence of Cu signals, along with changes in mineral-related elements (e.g., depletion or replacement of Na, K, Mg, and Fe in some sample regions), suggests that ion exchange was also involved in the uptake of Cu (II), especially in mineral-rich samples (A and B).

The overall SEM–EDS findings indicate that adsorption of Cu (II) onto hydrochar occurs through three complementary processes: ion exchange, surface complexation, and deposition. Exchangeable cations (K⁺, Na⁺, Mg²⁺) identified in the pre-adsorption spectra were partially substituted by Cu²⁺ after adsorption. This is most evident in samples A and B, wherein the mineral phases were more abundant. Oxygenated functional groups (carboxyl, hydroxyl, carbonyl) and mineral surfaces provided binding sites for Cu (II), resulting in granular coatings, particulate aggregates, and narrowing pore structures as seen in the post-adsorption SEM images.

4. Conclusions

The results of the optimization process show that numerical optimization maximizes hydrochar yield under mild hydrothermal conditions, with the optimal solution of 165.5 °C and 2.8 h. Through a combination of response surface optimization, material-specific characterization, and adsorption evaluation, this paper provides a comprehensive framework for hydrochar development. The optimization approach will ensure that the conditions for producing hydrochar are not only statistically optimal but also practically applicable to environmental remediation processes.

The relative study across different pH conditions supports the hypothesis that hydrochar adsorption of Cu²⁺ is highly pH sensitive. At acidic conditions, the heterogeneous multilayer adsorption is favored, whereas at near neutral conditions, uniform monolayer adsorption with higher capacities is favored. Samples B and C are the most effective adsorbents with both high capacity and satisfactory model fit among the four samples. These results emphasize the importance of hydrochar type and solution pH in maximizing adsorption efficiency for environmental use. Solution pH significantly affected Cu²⁺ adsorption on hydrochar samples (A–D), with distinct mechanistic differences between acidic (pH 4) and near-neutral (pH 6) conditions. The equilibrium data were modeled using both the Langmuir and the Freundlich models, and the results showed that the adsorption capacity, affinity, and surface heterogeneity exhibit distinct trends.

The XRD, FTIR, SEM, and XRF analyses are combined to confirm that the hydrochar has a carbon-rich structure and mineral phases that are actively involved in Cu (II) uptake. XRD indicated poorly crystallized carbon frameworks with impurities of mineral components, whereas FTIR indicated oxygenated functional groups (–OH, –COOH, C=O), which present important binding sites. XRF showed the presence of exchangeable cations, including K, Na, Mg, and Fe, which confirms an ion-exchange contribution to adsorption. SEM images showed a porous morphology, which was coated and structurally modified in the presence of Cu (II), and EDS confirmed the presence of Cu on all surfaces. These methods collectively indicate that Cu (II) removal occurs via a two-phase process involving ion exchange between mineral-associated cations and surface complexation of oxygenated carbon sites.